%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWV116+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 : n023.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 67.96s 9.52s % Output : Proof 169.34s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.11 % Problem : SWV116+1 : TPTP v8.1.2. Bugfixed v3.3.0. % 0.12/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.33 % Computer : n023.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 300 % 0.12/0.33 % DateTime : Tue Aug 29 04:07:40 EDT 2023 % 0.12/0.33 % CPUTime : % 0.63/0.59 ________ _____ % 0.63/0.59 ___ __ \_________(_)________________________________ % 0.63/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.63/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.63/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.63/0.59 % 0.63/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.63/0.59 (2023-06-19) % 0.63/0.59 % 0.63/0.59 (c) Philipp Rümmer, 2009-2023 % 0.63/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.63/0.59 Amanda Stjerna. % 0.63/0.59 Free software under BSD-3-Clause. % 0.63/0.59 % 0.63/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.63/0.59 % 0.63/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.63/0.61 Running up to 7 provers in parallel. % 0.63/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.63/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.63/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.63/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.63/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.63/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.63/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 5.68/1.48 Prover 4: Preprocessing ... % 5.68/1.49 Prover 1: Preprocessing ... % 5.68/1.49 Prover 0: Preprocessing ... % 5.68/1.49 Prover 2: Preprocessing ... % 5.68/1.49 Prover 5: Preprocessing ... % 5.68/1.49 Prover 3: Preprocessing ... % 5.68/1.49 Prover 6: Preprocessing ... % 11.97/2.32 Prover 1: Warning: ignoring some quantifiers % 12.56/2.39 Prover 3: Warning: ignoring some quantifiers % 12.56/2.40 Prover 6: Proving ... % 12.56/2.41 Prover 1: Constructing countermodel ... % 12.56/2.42 Prover 3: Constructing countermodel ... % 13.28/2.49 Prover 4: Warning: ignoring some quantifiers % 14.24/2.61 Prover 4: Constructing countermodel ... % 14.24/2.66 Prover 2: Proving ... % 14.87/2.69 Prover 5: Proving ... % 14.87/2.70 Prover 0: Proving ... % 67.96/9.52 Prover 3: proved (8901ms) % 67.96/9.52 % 67.96/9.52 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 67.96/9.52 % 67.96/9.52 Prover 2: stopped % 67.96/9.52 Prover 6: stopped % 67.96/9.53 Prover 0: stopped % 67.96/9.56 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 67.96/9.56 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 67.96/9.56 Prover 5: stopped % 67.96/9.56 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 67.96/9.56 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 67.96/9.56 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 69.30/9.71 Prover 8: Preprocessing ... % 69.30/9.74 Prover 7: Preprocessing ... % 69.30/9.74 Prover 10: Preprocessing ... % 69.30/9.75 Prover 13: Preprocessing ... % 69.30/9.76 Prover 11: Preprocessing ... % 71.06/9.93 Prover 8: Warning: ignoring some quantifiers % 71.06/9.95 Prover 8: Constructing countermodel ... % 71.06/9.95 Prover 7: Warning: ignoring some quantifiers % 71.06/9.97 Prover 10: Warning: ignoring some quantifiers % 71.06/9.98 Prover 7: Constructing countermodel ... % 71.57/10.00 Prover 13: Warning: ignoring some quantifiers % 71.57/10.01 Prover 10: Constructing countermodel ... % 71.57/10.01 Prover 13: Constructing countermodel ... % 71.57/10.03 Prover 11: Warning: ignoring some quantifiers % 71.57/10.04 Prover 11: Constructing countermodel ... % 101.41/13.86 Prover 13: stopped % 101.77/13.90 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 102.80/14.02 Prover 16: Preprocessing ... % 103.77/14.17 Prover 16: Warning: ignoring some quantifiers % 104.12/14.19 Prover 16: Constructing countermodel ... % 117.75/15.98 Prover 1: stopped % 118.28/16.00 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 118.82/16.08 Prover 19: Preprocessing ... % 121.10/16.40 Prover 19: Warning: ignoring some quantifiers % 121.10/16.42 Prover 19: Constructing countermodel ... % 140.88/19.03 Prover 16: stopped % 145.94/19.75 Prover 19: stopped % 167.27/23.65 Prover 10: Found proof (size 5143) % 167.27/23.65 Prover 10: proved (14105ms) % 167.27/23.66 Prover 7: stopped % 167.27/23.66 Prover 4: stopped % 167.27/23.66 Prover 8: stopped % 167.27/23.67 Prover 11: stopped % 167.27/23.67 % 167.27/23.67 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 167.27/23.67 % 167.27/23.73 % SZS output start Proof for theBenchmark % 167.27/23.74 Assumptions after simplification: % 167.27/23.74 --------------------------------- % 167.27/23.74 % 167.27/23.74 (finite_domain_1) % 167.27/23.74 $i(n1) & $i(n0) & ! [v0: $i] : (v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0, % 167.27/23.74 n1) | ~ leq(n0, v0)) % 167.27/23.74 % 167.27/23.74 (finite_domain_2) % 167.27/23.75 $i(n2) & $i(n1) & $i(n0) & ! [v0: $i] : (v0 = n2 | v0 = n1 | v0 = n0 | ~ % 167.27/23.75 $i(v0) | ~ leq(v0, n2) | ~ leq(n0, v0)) % 167.27/23.75 % 167.27/23.75 (finite_domain_5) % 167.27/23.75 $i(n5) & $i(n4) & $i(n3) & $i(n2) & $i(n1) & $i(n0) & ! [v0: $i] : (v0 = n5 | % 167.27/23.75 v0 = n4 | v0 = n3 | v0 = n2 | v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0, n5) % 167.27/23.75 | ~ leq(n0, v0)) % 167.27/23.75 % 167.27/23.75 (irreflexivity_gt) % 167.27/23.75 ! [v0: $i] : ( ~ $i(v0) | ~ gt(v0, v0)) % 167.27/23.75 % 167.27/23.75 (leq_gt2) % 167.27/23.75 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ leq(v0, v1) % 167.27/23.75 | gt(v1, v0)) % 167.27/23.75 % 167.27/23.75 (leq_gt_pred) % 167.70/23.78 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (pred(v1) = v2) | ~ $i(v1) | ~ % 167.70/23.78 $i(v0) | ~ leq(v0, v2) | gt(v1, v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 167.70/23.78 $i] : ( ~ (pred(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ gt(v1, v0) | leq(v0, % 167.70/23.78 v2)) % 167.70/23.78 % 167.70/23.78 (pred_minus_1) % 167.70/23.78 $i(n1) & ! [v0: $i] : ! [v1: $i] : ( ~ (minus(v0, n1) = v1) | ~ $i(v0) | % 167.70/23.78 (pred(v0) = v1 & $i(v1))) % 167.70/23.78 % 167.70/23.78 (pred_succ) % 167.70/23.78 ! [v0: $i] : ! [v1: $i] : ( ~ (succ(v0) = v1) | ~ $i(v0) | pred(v1) = v0) % 167.70/23.78 % 167.70/23.78 (quaternion_ds1_symm_0009) % 167.70/23.79 $i(id_ds1_filter) & $i(pminus_ds1_filter) & $i(r_ds1_filter) & % 167.70/23.79 $i(q_ds1_filter) & $i(n6) & $i(n999) & $i(pv5) & $i(n3) & $i(n1) & $i(n0) & ? % 167.70/23.79 [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] % 167.70/23.79 : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? % 167.70/23.79 [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : (minus(n6, n1) = v1 & % 167.70/23.79 minus(n999, n1) = v0 & minus(n3, n1) = v2 & $i(v12) & $i(v11) & $i(v8) & % 167.70/23.79 $i(v7) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & leq(pv5, v0) & leq(n0, % 167.70/23.79 pv5) & ! [v15: $i] : ! [v16: $i] : ! [v17: $i] : ( ~ % 167.70/23.79 (a_select3(id_ds1_filter, v15, v16) = v17) | ~ $i(v16) | ~ $i(v15) | ~ % 167.70/23.79 leq(v16, v1) | ~ leq(v15, v1) | ~ leq(n0, v16) | ~ leq(n0, v15) | % 167.70/23.79 (a_select3(id_ds1_filter, v16, v15) = v17 & $i(v17))) & ! [v15: $i] : ! % 167.70/23.79 [v16: $i] : ! [v17: $i] : ( ~ (a_select3(pminus_ds1_filter, v15, v16) = % 167.70/23.79 v17) | ~ $i(v16) | ~ $i(v15) | ~ leq(v16, v1) | ~ leq(v15, v1) | ~ % 167.70/23.79 leq(n0, v16) | ~ leq(n0, v15) | (a_select3(pminus_ds1_filter, v16, v15) = % 167.70/23.79 v17 & $i(v17))) & ! [v15: $i] : ! [v16: $i] : ! [v17: $i] : ( ~ % 167.70/23.79 (a_select3(r_ds1_filter, v15, v16) = v17) | ~ $i(v16) | ~ $i(v15) | ~ % 167.70/23.79 leq(v16, v2) | ~ leq(v15, v2) | ~ leq(n0, v16) | ~ leq(n0, v15) | % 167.70/23.79 (a_select3(r_ds1_filter, v16, v15) = v17 & $i(v17))) & ! [v15: $i] : ! % 167.70/23.79 [v16: $i] : ! [v17: $i] : ( ~ (a_select3(q_ds1_filter, v15, v16) = v17) | % 167.70/23.79 ~ $i(v16) | ~ $i(v15) | ~ leq(v16, v1) | ~ leq(v15, v1) | ~ leq(n0, % 167.70/23.79 v16) | ~ leq(n0, v15) | (a_select3(q_ds1_filter, v16, v15) = v17 & % 167.70/23.79 $i(v17))) & (( ~ (v14 = v13) & a_select3(q_ds1_filter, v12, v11) = v14 & % 167.70/23.79 a_select3(q_ds1_filter, v11, v12) = v13 & $i(v14) & $i(v13) & leq(v12, % 167.70/23.79 v1) & leq(v11, v1) & leq(n0, v12) & leq(n0, v11)) | ( ~ (v10 = v9) & % 167.70/23.79 a_select3(r_ds1_filter, v8, v7) = v10 & a_select3(r_ds1_filter, v7, v8) % 167.70/23.79 = v9 & $i(v10) & $i(v9) & leq(v8, v2) & leq(v7, v2) & leq(n0, v8) & % 167.70/23.79 leq(n0, v7)) | ( ~ (v6 = v5) & a_select3(pminus_ds1_filter, v4, v3) = v6 % 167.70/23.79 & a_select3(pminus_ds1_filter, v3, v4) = v5 & $i(v6) & $i(v5) & leq(v4, % 167.70/23.79 v1) & leq(v3, v1) & leq(n0, v4) & leq(n0, v3)))) % 167.70/23.79 % 167.70/23.79 (successor_1) % 167.70/23.79 succ(n0) = n1 & $i(n1) & $i(n0) % 167.70/23.79 % 167.70/23.79 (successor_2) % 167.70/23.79 $i(n2) & $i(n0) & ? [v0: $i] : (succ(v0) = n2 & succ(n0) = v0 & $i(v0)) % 167.70/23.79 % 167.70/23.79 (successor_3) % 167.70/23.79 $i(n3) & $i(n0) & ? [v0: $i] : ? [v1: $i] : (succ(v1) = n3 & succ(v0) = v1 & % 167.70/23.79 succ(n0) = v0 & $i(v1) & $i(v0)) % 167.70/23.79 % 167.70/23.79 (successor_4) % 167.70/23.79 $i(n4) & $i(n0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (succ(v2) = n4 & % 167.70/23.79 succ(v1) = v2 & succ(v0) = v1 & succ(n0) = v0 & $i(v2) & $i(v1) & $i(v0)) % 167.70/23.79 % 167.70/23.79 (successor_5) % 167.70/23.79 $i(n5) & $i(n0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 167.70/23.79 (succ(v3) = n5 & succ(v2) = v3 & succ(v1) = v2 & succ(v0) = v1 & succ(n0) = v0 % 167.70/23.79 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 167.70/23.79 % 167.70/23.79 (successor_6) % 167.70/23.80 $i(n6) & $i(n0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? % 167.70/23.80 [v4: $i] : (succ(v4) = n6 & succ(v3) = v4 & succ(v2) = v3 & succ(v1) = v2 & % 167.70/23.80 succ(v0) = v1 & succ(n0) = v0 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 167.70/23.80 % 167.70/23.80 (function-axioms) % 167.70/23.80 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 167.70/23.80 $i] : (v1 = v0 | ~ (tptp_update3(v5, v4, v3, v2) = v1) | ~ % 167.70/23.80 (tptp_update3(v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 167.70/23.80 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_update2(v4, v3, v2) = % 167.70/23.80 v1) | ~ (tptp_update2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 167.70/23.80 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (sum(v4, v3, v2) = v1) | % 167.70/23.80 ~ (sum(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 167.70/23.80 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_const_array2(v4, v3, v2) = v1) | % 167.70/23.80 ~ (tptp_const_array2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 167.70/23.80 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (a_select3(v4, v3, v2) = % 167.70/23.80 v1) | ~ (a_select3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 167.70/23.80 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (minus(v3, v2) = v1) | ~ (minus(v3, % 167.70/23.80 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 167.70/23.80 = v0 | ~ (plus(v3, v2) = v1) | ~ (plus(v3, v2) = v0)) & ! [v0: $i] : ! % 167.70/23.80 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (tptp_mmul(v3, v2) = v1) % 167.70/23.80 | ~ (tptp_mmul(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 167.70/23.80 ! [v3: $i] : (v1 = v0 | ~ (tptp_msub(v3, v2) = v1) | ~ (tptp_msub(v3, v2) = % 167.70/23.80 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 167.70/23.80 ~ (tptp_madd(v3, v2) = v1) | ~ (tptp_madd(v3, v2) = v0)) & ! [v0: $i] : ! % 167.70/23.80 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (dim(v3, v2) = v1) | ~ % 167.70/23.80 (dim(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 167.70/23.80 : (v1 = v0 | ~ (tptp_const_array1(v3, v2) = v1) | ~ (tptp_const_array1(v3, % 167.70/23.80 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 167.70/23.80 = v0 | ~ (a_select2(v3, v2) = v1) | ~ (a_select2(v3, v2) = v0)) & ! [v0: % 167.70/23.80 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 167.70/23.80 (uniform_int_rnd(v3, v2) = v1) | ~ (uniform_int_rnd(v3, v2) = v0)) & ! % 167.70/23.80 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (inv(v2) = v1) | ~ % 167.70/23.80 (inv(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 167.70/23.80 (trans(v2) = v1) | ~ (trans(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 167.70/23.80 [v2: $i] : (v1 = v0 | ~ (succ(v2) = v1) | ~ (succ(v2) = v0)) & ! [v0: $i] : % 167.70/23.80 ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (pred(v2) = v1) | ~ (pred(v2) = % 167.70/23.80 v0)) % 167.70/23.80 % 167.70/23.80 Further assumptions not needed in the proof: % 167.70/23.80 -------------------------------------------- % 167.70/23.81 const_array1_select, const_array2_select, defuse, finite_domain_0, % 167.70/23.81 finite_domain_3, finite_domain_4, finite_domain_6, gt_0_tptp_minus_1, gt_1_0, % 167.70/23.81 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, % 167.70/23.81 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, % 167.70/23.81 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, % 167.70/23.81 gt_6_3, gt_6_4, gt_6_5, gt_6_tptp_minus_1, gt_999_0, gt_999_1, gt_999_2, % 167.70/23.81 gt_999_3, gt_999_4, gt_999_5, gt_999_6, gt_999_tptp_minus_1, gt_succ, leq_geq, % 167.70/23.81 leq_gt1, leq_minus, leq_succ, leq_succ_gt, leq_succ_gt_equiv, leq_succ_succ, % 167.70/23.81 lt_gt, matrix_symm_aba1, matrix_symm_aba2, matrix_symm_add, matrix_symm_inv, % 167.70/23.81 matrix_symm_joseph_update, matrix_symm_sub, matrix_symm_trans, % 167.70/23.81 matrix_symm_update_diagonal, reflexivity_leq, sel2_update_1, sel2_update_2, % 167.70/23.81 sel2_update_3, sel3_update_1, sel3_update_2, sel3_update_3, succ_plus_1_l, % 167.70/23.81 succ_plus_1_r, succ_plus_2_l, succ_plus_2_r, succ_plus_3_l, succ_plus_3_r, % 167.70/23.81 succ_plus_4_l, succ_plus_4_r, succ_plus_5_l, succ_plus_5_r, succ_pred, % 167.70/23.81 succ_tptp_minus_1, sum_plus_base, sum_plus_base_float, totality, % 167.70/23.81 transitivity_gt, transitivity_leq, ttrue, uniform_int_rand_ranges_hi, % 167.70/23.81 uniform_int_rand_ranges_lo % 167.70/23.81 % 167.70/23.81 Those formulas are unsatisfiable: % 167.70/23.81 --------------------------------- % 167.70/23.81 % 167.70/23.81 Begin of proof % 167.98/23.81 | % 167.98/23.81 | ALPHA: (leq_gt_pred) implies: % 167.98/23.81 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (pred(v1) = v2) | ~ % 167.98/23.81 | $i(v1) | ~ $i(v0) | ~ gt(v1, v0) | leq(v0, v2)) % 167.98/23.81 | % 167.98/23.81 | ALPHA: (pred_minus_1) implies: % 167.98/23.81 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (minus(v0, n1) = v1) | ~ $i(v0) | % 167.98/23.81 | (pred(v0) = v1 & $i(v1))) % 167.98/23.81 | % 167.98/23.81 | ALPHA: (finite_domain_5) implies: % 167.98/23.81 | (3) ! [v0: $i] : (v0 = n5 | v0 = n4 | v0 = n3 | v0 = n2 | v0 = n1 | v0 = % 167.98/23.81 | n0 | ~ $i(v0) | ~ leq(v0, n5) | ~ leq(n0, v0)) % 167.98/23.81 | % 167.98/23.81 | ALPHA: (finite_domain_1) implies: % 167.98/23.81 | (4) ! [v0: $i] : (v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0, n1) | ~ % 167.98/23.81 | leq(n0, v0)) % 167.98/23.81 | % 167.98/23.81 | ALPHA: (finite_domain_2) implies: % 167.98/23.81 | (5) ! [v0: $i] : (v0 = n2 | v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0, n2) % 167.98/23.81 | | ~ leq(n0, v0)) % 167.98/23.81 | % 167.98/23.81 | ALPHA: (successor_4) implies: % 167.98/23.81 | (6) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (succ(v2) = n4 & succ(v1) = % 167.98/23.81 | v2 & succ(v0) = v1 & succ(n0) = v0 & $i(v2) & $i(v1) & $i(v0)) % 167.98/23.81 | % 167.98/23.81 | ALPHA: (successor_5) implies: % 167.98/23.81 | (7) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (succ(v3) = n5 % 167.98/23.81 | & succ(v2) = v3 & succ(v1) = v2 & succ(v0) = v1 & succ(n0) = v0 & % 167.98/23.81 | $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 167.98/23.81 | % 167.98/23.81 | ALPHA: (successor_6) implies: % 167.98/23.81 | (8) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 167.98/23.81 | (succ(v4) = n6 & succ(v3) = v4 & succ(v2) = v3 & succ(v1) = v2 & % 167.98/23.81 | succ(v0) = v1 & succ(n0) = v0 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & % 167.98/23.81 | $i(v0)) % 167.98/23.81 | % 167.98/23.81 | ALPHA: (successor_1) implies: % 167.98/23.82 | (9) succ(n0) = n1 % 167.98/23.82 | % 167.98/23.82 | ALPHA: (successor_2) implies: % 167.98/23.82 | (10) ? [v0: $i] : (succ(v0) = n2 & succ(n0) = v0 & $i(v0)) % 167.98/23.82 | % 167.98/23.82 | ALPHA: (successor_3) implies: % 167.98/23.82 | (11) ? [v0: $i] : ? [v1: $i] : (succ(v1) = n3 & succ(v0) = v1 & succ(n0) % 167.98/23.82 | = v0 & $i(v1) & $i(v0)) % 167.98/23.82 | % 167.98/23.82 | ALPHA: (quaternion_ds1_symm_0009) implies: % 167.98/23.82 | (12) $i(n0) % 167.98/23.82 | (13) $i(n6) % 167.98/23.82 | (14) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 167.98/23.82 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : % 167.98/23.82 | ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: % 167.98/23.82 | $i] : (minus(n6, n1) = v1 & minus(n999, n1) = v0 & minus(n3, n1) = % 167.98/23.82 | v2 & $i(v12) & $i(v11) & $i(v8) & $i(v7) & $i(v4) & $i(v3) & $i(v2) % 167.98/23.82 | & $i(v1) & $i(v0) & leq(pv5, v0) & leq(n0, pv5) & ! [v15: $i] : ! % 167.98/23.82 | [v16: $i] : ! [v17: $i] : ( ~ (a_select3(id_ds1_filter, v15, v16) = % 167.98/23.82 | v17) | ~ $i(v16) | ~ $i(v15) | ~ leq(v16, v1) | ~ leq(v15, % 167.98/23.82 | v1) | ~ leq(n0, v16) | ~ leq(n0, v15) | % 167.98/23.82 | (a_select3(id_ds1_filter, v16, v15) = v17 & $i(v17))) & ! [v15: % 167.98/23.82 | $i] : ! [v16: $i] : ! [v17: $i] : ( ~ % 167.98/23.82 | (a_select3(pminus_ds1_filter, v15, v16) = v17) | ~ $i(v16) | ~ % 167.98/23.82 | $i(v15) | ~ leq(v16, v1) | ~ leq(v15, v1) | ~ leq(n0, v16) | ~ % 167.98/23.82 | leq(n0, v15) | (a_select3(pminus_ds1_filter, v16, v15) = v17 & % 167.98/23.82 | $i(v17))) & ! [v15: $i] : ! [v16: $i] : ! [v17: $i] : ( ~ % 167.98/23.82 | (a_select3(r_ds1_filter, v15, v16) = v17) | ~ $i(v16) | ~ % 167.98/23.82 | $i(v15) | ~ leq(v16, v2) | ~ leq(v15, v2) | ~ leq(n0, v16) | ~ % 167.98/23.82 | leq(n0, v15) | (a_select3(r_ds1_filter, v16, v15) = v17 & % 167.98/23.82 | $i(v17))) & ! [v15: $i] : ! [v16: $i] : ! [v17: $i] : ( ~ % 167.98/23.82 | (a_select3(q_ds1_filter, v15, v16) = v17) | ~ $i(v16) | ~ % 167.98/23.82 | $i(v15) | ~ leq(v16, v1) | ~ leq(v15, v1) | ~ leq(n0, v16) | ~ % 167.98/23.82 | leq(n0, v15) | (a_select3(q_ds1_filter, v16, v15) = v17 & % 167.98/23.82 | $i(v17))) & (( ~ (v14 = v13) & a_select3(q_ds1_filter, v12, v11) % 167.98/23.82 | = v14 & a_select3(q_ds1_filter, v11, v12) = v13 & $i(v14) & % 167.98/23.82 | $i(v13) & leq(v12, v1) & leq(v11, v1) & leq(n0, v12) & leq(n0, % 167.98/23.82 | v11)) | ( ~ (v10 = v9) & a_select3(r_ds1_filter, v8, v7) = v10 % 167.98/23.82 | & a_select3(r_ds1_filter, v7, v8) = v9 & $i(v10) & $i(v9) & % 167.98/23.82 | leq(v8, v2) & leq(v7, v2) & leq(n0, v8) & leq(n0, v7)) | ( ~ (v6 % 167.98/23.82 | = v5) & a_select3(pminus_ds1_filter, v4, v3) = v6 & % 167.98/23.82 | a_select3(pminus_ds1_filter, v3, v4) = v5 & $i(v6) & $i(v5) & % 167.98/23.82 | leq(v4, v1) & leq(v3, v1) & leq(n0, v4) & leq(n0, v3)))) % 167.98/23.82 | % 167.98/23.82 | ALPHA: (function-axioms) implies: % 167.98/23.83 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (pred(v2) = % 167.98/23.83 | v1) | ~ (pred(v2) = v0)) % 167.98/23.83 | (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (succ(v2) = % 167.98/23.83 | v1) | ~ (succ(v2) = v0)) % 167.98/23.83 | (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 167.98/23.83 | (v1 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) % 167.98/23.83 | = v0)) % 167.98/23.83 | % 167.98/23.83 | DELTA: instantiating (10) with fresh symbol all_55_0 gives: % 167.98/23.83 | (18) succ(all_55_0) = n2 & succ(n0) = all_55_0 & $i(all_55_0) % 167.98/23.83 | % 167.98/23.83 | ALPHA: (18) implies: % 167.98/23.83 | (19) $i(all_55_0) % 167.98/23.83 | (20) succ(n0) = all_55_0 % 167.98/23.83 | (21) succ(all_55_0) = n2 % 167.98/23.83 | % 167.98/23.83 | DELTA: instantiating (11) with fresh symbols all_57_0, all_57_1 gives: % 167.98/23.83 | (22) succ(all_57_0) = n3 & succ(all_57_1) = all_57_0 & succ(n0) = all_57_1 % 167.98/23.83 | & $i(all_57_0) & $i(all_57_1) % 167.98/23.83 | % 167.98/23.83 | ALPHA: (22) implies: % 167.98/23.83 | (23) $i(all_57_0) % 167.98/23.83 | (24) succ(n0) = all_57_1 % 167.98/23.83 | (25) succ(all_57_1) = all_57_0 % 167.98/23.83 | (26) succ(all_57_0) = n3 % 167.98/23.83 | % 167.98/23.83 | DELTA: instantiating (6) with fresh symbols all_60_0, all_60_1, all_60_2 % 167.98/23.83 | gives: % 167.98/23.83 | (27) succ(all_60_0) = n4 & succ(all_60_1) = all_60_0 & succ(all_60_2) = % 167.98/23.83 | all_60_1 & succ(n0) = all_60_2 & $i(all_60_0) & $i(all_60_1) & % 167.98/23.83 | $i(all_60_2) % 167.98/23.83 | % 167.98/23.83 | ALPHA: (27) implies: % 167.98/23.83 | (28) $i(all_60_0) % 167.98/23.83 | (29) succ(n0) = all_60_2 % 167.98/23.83 | (30) succ(all_60_2) = all_60_1 % 167.98/23.83 | (31) succ(all_60_1) = all_60_0 % 167.98/23.83 | (32) succ(all_60_0) = n4 % 167.98/23.83 | % 167.98/23.83 | DELTA: instantiating (7) with fresh symbols all_62_0, all_62_1, all_62_2, % 167.98/23.83 | all_62_3 gives: % 167.98/23.83 | (33) succ(all_62_0) = n5 & succ(all_62_1) = all_62_0 & succ(all_62_2) = % 167.98/23.83 | all_62_1 & succ(all_62_3) = all_62_2 & succ(n0) = all_62_3 & % 167.98/23.83 | $i(all_62_0) & $i(all_62_1) & $i(all_62_2) & $i(all_62_3) % 167.98/23.83 | % 167.98/23.83 | ALPHA: (33) implies: % 167.98/23.83 | (34) $i(all_62_0) % 167.98/23.83 | (35) succ(n0) = all_62_3 % 167.98/23.83 | (36) succ(all_62_3) = all_62_2 % 167.98/23.83 | (37) succ(all_62_2) = all_62_1 % 167.98/23.83 | (38) succ(all_62_1) = all_62_0 % 167.98/23.83 | (39) succ(all_62_0) = n5 % 167.98/23.83 | % 167.98/23.83 | DELTA: instantiating (8) with fresh symbols all_64_0, all_64_1, all_64_2, % 167.98/23.83 | all_64_3, all_64_4 gives: % 167.98/23.83 | (40) succ(all_64_0) = n6 & succ(all_64_1) = all_64_0 & succ(all_64_2) = % 167.98/23.83 | all_64_1 & succ(all_64_3) = all_64_2 & succ(all_64_4) = all_64_3 & % 167.98/23.83 | succ(n0) = all_64_4 & $i(all_64_0) & $i(all_64_1) & $i(all_64_2) & % 167.98/23.83 | $i(all_64_3) & $i(all_64_4) % 167.98/23.83 | % 167.98/23.83 | ALPHA: (40) implies: % 167.98/23.83 | (41) $i(all_64_0) % 167.98/23.83 | (42) succ(n0) = all_64_4 % 167.98/23.83 | (43) succ(all_64_4) = all_64_3 % 167.98/23.83 | (44) succ(all_64_3) = all_64_2 % 167.98/23.83 | (45) succ(all_64_2) = all_64_1 % 167.98/23.83 | (46) succ(all_64_1) = all_64_0 % 167.98/23.83 | (47) succ(all_64_0) = n6 % 167.98/23.83 | % 167.98/23.83 | DELTA: instantiating (14) with fresh symbols all_74_0, all_74_1, all_74_2, % 167.98/23.83 | all_74_3, all_74_4, all_74_5, all_74_6, all_74_7, all_74_8, all_74_9, % 167.98/23.83 | all_74_10, all_74_11, all_74_12, all_74_13, all_74_14 gives: % 167.98/23.84 | (48) minus(n6, n1) = all_74_13 & minus(n999, n1) = all_74_14 & minus(n3, % 167.98/23.84 | n1) = all_74_12 & $i(all_74_2) & $i(all_74_3) & $i(all_74_6) & % 167.98/23.84 | $i(all_74_7) & $i(all_74_10) & $i(all_74_11) & $i(all_74_12) & % 167.98/23.84 | $i(all_74_13) & $i(all_74_14) & leq(pv5, all_74_14) & leq(n0, pv5) & % 167.98/23.84 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (a_select3(id_ds1_filter, % 167.98/23.84 | v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ leq(v1, all_74_13) | % 167.98/23.84 | ~ leq(v0, all_74_13) | ~ leq(n0, v1) | ~ leq(n0, v0) | % 167.98/23.84 | (a_select3(id_ds1_filter, v1, v0) = v2 & $i(v2))) & ! [v0: $i] : ! % 167.98/23.84 | [v1: $i] : ! [v2: $i] : ( ~ (a_select3(pminus_ds1_filter, v0, v1) = % 167.98/23.84 | v2) | ~ $i(v1) | ~ $i(v0) | ~ leq(v1, all_74_13) | ~ leq(v0, % 167.98/23.84 | all_74_13) | ~ leq(n0, v1) | ~ leq(n0, v0) | % 167.98/23.84 | (a_select3(pminus_ds1_filter, v1, v0) = v2 & $i(v2))) & ! [v0: $i] % 167.98/23.84 | : ! [v1: $i] : ! [v2: $i] : ( ~ (a_select3(r_ds1_filter, v0, v1) = % 167.98/23.84 | v2) | ~ $i(v1) | ~ $i(v0) | ~ leq(v1, all_74_12) | ~ leq(v0, % 167.98/23.84 | all_74_12) | ~ leq(n0, v1) | ~ leq(n0, v0) | % 167.98/23.84 | (a_select3(r_ds1_filter, v1, v0) = v2 & $i(v2))) & ! [v0: $i] : ! % 167.98/23.84 | [v1: $i] : ! [v2: $i] : ( ~ (a_select3(q_ds1_filter, v0, v1) = v2) | % 167.98/23.84 | ~ $i(v1) | ~ $i(v0) | ~ leq(v1, all_74_13) | ~ leq(v0, all_74_13) % 167.98/23.84 | | ~ leq(n0, v1) | ~ leq(n0, v0) | (a_select3(q_ds1_filter, v1, v0) % 167.98/23.84 | = v2 & $i(v2))) & (( ~ (all_74_0 = all_74_1) & % 167.98/23.84 | a_select3(q_ds1_filter, all_74_2, all_74_3) = all_74_0 & % 167.98/23.84 | a_select3(q_ds1_filter, all_74_3, all_74_2) = all_74_1 & % 167.98/23.84 | $i(all_74_0) & $i(all_74_1) & leq(all_74_2, all_74_13) & % 167.98/23.84 | leq(all_74_3, all_74_13) & leq(n0, all_74_2) & leq(n0, all_74_3)) % 167.98/23.84 | | ( ~ (all_74_4 = all_74_5) & a_select3(r_ds1_filter, all_74_6, % 167.98/23.84 | all_74_7) = all_74_4 & a_select3(r_ds1_filter, all_74_7, % 167.98/23.84 | all_74_6) = all_74_5 & $i(all_74_4) & $i(all_74_5) & % 167.98/23.84 | leq(all_74_6, all_74_12) & leq(all_74_7, all_74_12) & leq(n0, % 167.98/23.84 | all_74_6) & leq(n0, all_74_7)) | ( ~ (all_74_8 = all_74_9) & % 167.98/23.84 | a_select3(pminus_ds1_filter, all_74_10, all_74_11) = all_74_8 & % 167.98/23.84 | a_select3(pminus_ds1_filter, all_74_11, all_74_10) = all_74_9 & % 167.98/23.84 | $i(all_74_8) & $i(all_74_9) & leq(all_74_10, all_74_13) & % 167.98/23.84 | leq(all_74_11, all_74_13) & leq(n0, all_74_10) & leq(n0, % 167.98/23.84 | all_74_11))) % 167.98/23.84 | % 167.98/23.84 | ALPHA: (48) implies: % 167.98/23.84 | (49) $i(all_74_11) % 167.98/23.84 | (50) $i(all_74_10) % 167.98/23.84 | (51) $i(all_74_7) % 167.98/23.84 | (52) $i(all_74_6) % 167.98/23.84 | (53) $i(all_74_3) % 167.98/23.84 | (54) $i(all_74_2) % 167.98/23.84 | (55) minus(n3, n1) = all_74_12 % 167.98/23.84 | (56) minus(n6, n1) = all_74_13 % 167.98/23.84 | (57) ( ~ (all_74_0 = all_74_1) & a_select3(q_ds1_filter, all_74_2, % 167.98/23.84 | all_74_3) = all_74_0 & a_select3(q_ds1_filter, all_74_3, all_74_2) % 167.98/23.84 | = all_74_1 & $i(all_74_0) & $i(all_74_1) & leq(all_74_2, all_74_13) % 167.98/23.84 | & leq(all_74_3, all_74_13) & leq(n0, all_74_2) & leq(n0, all_74_3)) % 167.98/23.84 | | ( ~ (all_74_4 = all_74_5) & a_select3(r_ds1_filter, all_74_6, % 167.98/23.84 | all_74_7) = all_74_4 & a_select3(r_ds1_filter, all_74_7, all_74_6) % 167.98/23.84 | = all_74_5 & $i(all_74_4) & $i(all_74_5) & leq(all_74_6, all_74_12) % 167.98/23.84 | & leq(all_74_7, all_74_12) & leq(n0, all_74_6) & leq(n0, all_74_7)) % 167.98/23.84 | | ( ~ (all_74_8 = all_74_9) & a_select3(pminus_ds1_filter, all_74_10, % 167.98/23.85 | all_74_11) = all_74_8 & a_select3(pminus_ds1_filter, all_74_11, % 167.98/23.85 | all_74_10) = all_74_9 & $i(all_74_8) & $i(all_74_9) & % 167.98/23.85 | leq(all_74_10, all_74_13) & leq(all_74_11, all_74_13) & leq(n0, % 167.98/23.85 | all_74_10) & leq(n0, all_74_11)) % 167.98/23.85 | (58) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (a_select3(q_ds1_filter, % 167.98/23.85 | v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ leq(v1, all_74_13) | % 167.98/23.85 | ~ leq(v0, all_74_13) | ~ leq(n0, v1) | ~ leq(n0, v0) | % 167.98/23.85 | (a_select3(q_ds1_filter, v1, v0) = v2 & $i(v2))) % 167.98/23.85 | (59) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (a_select3(r_ds1_filter, % 167.98/23.85 | v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ leq(v1, all_74_12) | % 167.98/23.85 | ~ leq(v0, all_74_12) | ~ leq(n0, v1) | ~ leq(n0, v0) | % 167.98/23.85 | (a_select3(r_ds1_filter, v1, v0) = v2 & $i(v2))) % 167.98/23.85 | (60) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 167.98/23.85 | (a_select3(pminus_ds1_filter, v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) % 167.98/23.85 | | ~ leq(v1, all_74_13) | ~ leq(v0, all_74_13) | ~ leq(n0, v1) | % 167.98/23.85 | ~ leq(n0, v0) | (a_select3(pminus_ds1_filter, v1, v0) = v2 & % 167.98/23.85 | $i(v2))) % 167.98/23.85 | % 167.98/23.85 | GROUND_INST: instantiating (16) with all_60_2, all_62_3, n0, simplifying with % 167.98/23.85 | (29), (35) gives: % 167.98/23.85 | (61) all_62_3 = all_60_2 % 167.98/23.85 | % 167.98/23.85 | GROUND_INST: instantiating (16) with all_57_1, all_62_3, n0, simplifying with % 167.98/23.85 | (24), (35) gives: % 167.98/23.85 | (62) all_62_3 = all_57_1 % 167.98/23.85 | % 167.98/23.85 | GROUND_INST: instantiating (16) with all_55_0, all_62_3, n0, simplifying with % 167.98/23.85 | (20), (35) gives: % 167.98/23.85 | (63) all_62_3 = all_55_0 % 167.98/23.85 | % 167.98/23.85 | GROUND_INST: instantiating (16) with all_57_1, all_64_4, n0, simplifying with % 167.98/23.85 | (24), (42) gives: % 167.98/23.85 | (64) all_64_4 = all_57_1 % 167.98/23.85 | % 167.98/23.85 | GROUND_INST: instantiating (16) with n1, all_64_4, n0, simplifying with (9), % 167.98/23.85 | (42) gives: % 167.98/23.85 | (65) all_64_4 = n1 % 167.98/23.85 | % 167.98/23.85 | COMBINE_EQS: (64), (65) imply: % 167.98/23.85 | (66) all_57_1 = n1 % 167.98/23.85 | % 167.98/23.85 | SIMP: (66) implies: % 167.98/23.85 | (67) all_57_1 = n1 % 167.98/23.85 | % 167.98/23.85 | COMBINE_EQS: (61), (63) imply: % 167.98/23.85 | (68) all_60_2 = all_55_0 % 167.98/23.85 | % 167.98/23.85 | COMBINE_EQS: (61), (62) imply: % 167.98/23.85 | (69) all_60_2 = all_57_1 % 167.98/23.85 | % 167.98/23.85 | COMBINE_EQS: (68), (69) imply: % 167.98/23.85 | (70) all_57_1 = all_55_0 % 167.98/23.85 | % 167.98/23.85 | SIMP: (70) implies: % 167.98/23.85 | (71) all_57_1 = all_55_0 % 167.98/23.85 | % 167.98/23.85 | COMBINE_EQS: (67), (71) imply: % 167.98/23.85 | (72) all_55_0 = n1 % 167.98/23.85 | % 167.98/23.85 | COMBINE_EQS: (68), (72) imply: % 167.98/23.85 | (73) all_60_2 = n1 % 167.98/23.85 | % 167.98/23.85 | COMBINE_EQS: (61), (73) imply: % 167.98/23.85 | (74) all_62_3 = n1 % 167.98/23.85 | % 167.98/23.85 | REDUCE: (43), (65) imply: % 167.98/23.85 | (75) succ(n1) = all_64_3 % 167.98/23.85 | % 167.98/23.85 | REDUCE: (36), (74) imply: % 167.98/23.85 | (76) succ(n1) = all_62_2 % 167.98/23.85 | % 167.98/23.85 | REDUCE: (30), (73) imply: % 167.98/23.85 | (77) succ(n1) = all_60_1 % 167.98/23.85 | % 167.98/23.85 | REDUCE: (25), (67) imply: % 167.98/23.85 | (78) succ(n1) = all_57_0 % 167.98/23.85 | % 167.98/23.85 | REDUCE: (21), (72) imply: % 167.98/23.85 | (79) succ(n1) = n2 % 167.98/23.85 | % 167.98/23.85 | REDUCE: (19), (72) imply: % 167.98/23.85 | (80) $i(n1) % 167.98/23.85 | % 167.98/23.85 | GROUND_INST: instantiating (16) with all_60_1, all_62_2, n1, simplifying with % 167.98/23.85 | (76), (77) gives: % 167.98/23.85 | (81) all_62_2 = all_60_1 % 167.98/23.85 | % 167.98/23.85 | GROUND_INST: instantiating (16) with all_57_0, all_62_2, n1, simplifying with % 167.98/23.85 | (76), (78) gives: % 167.98/23.85 | (82) all_62_2 = all_57_0 % 167.98/23.85 | % 167.98/23.85 | GROUND_INST: instantiating (16) with all_60_1, all_64_3, n1, simplifying with % 167.98/23.85 | (75), (77) gives: % 167.98/23.85 | (83) all_64_3 = all_60_1 % 167.98/23.85 | % 167.98/23.85 | GROUND_INST: instantiating (16) with n2, all_64_3, n1, simplifying with (75), % 167.98/23.85 | (79) gives: % 167.98/23.85 | (84) all_64_3 = n2 % 167.98/23.85 | % 167.98/23.85 | COMBINE_EQS: (83), (84) imply: % 167.98/23.86 | (85) all_60_1 = n2 % 167.98/23.86 | % 167.98/23.86 | SIMP: (85) implies: % 167.98/23.86 | (86) all_60_1 = n2 % 167.98/23.86 | % 167.98/23.86 | COMBINE_EQS: (81), (82) imply: % 167.98/23.86 | (87) all_60_1 = all_57_0 % 167.98/23.86 | % 167.98/23.86 | SIMP: (87) implies: % 167.98/23.86 | (88) all_60_1 = all_57_0 % 167.98/23.86 | % 167.98/23.86 | COMBINE_EQS: (86), (88) imply: % 167.98/23.86 | (89) all_57_0 = n2 % 167.98/23.86 | % 167.98/23.86 | SIMP: (89) implies: % 167.98/23.86 | (90) all_57_0 = n2 % 167.98/23.86 | % 167.98/23.86 | COMBINE_EQS: (82), (90) imply: % 167.98/23.86 | (91) all_62_2 = n2 % 167.98/23.86 | % 167.98/23.86 | REDUCE: (44), (84) imply: % 167.98/23.86 | (92) succ(n2) = all_64_2 % 167.98/23.86 | % 167.98/23.86 | REDUCE: (37), (91) imply: % 167.98/23.86 | (93) succ(n2) = all_62_1 % 167.98/23.86 | % 167.98/23.86 | REDUCE: (31), (86) imply: % 167.98/23.86 | (94) succ(n2) = all_60_0 % 167.98/23.86 | % 167.98/23.86 | REDUCE: (26), (90) imply: % 167.98/23.86 | (95) succ(n2) = n3 % 167.98/23.86 | % 167.98/23.86 | REDUCE: (23), (90) imply: % 167.98/23.86 | (96) $i(n2) % 167.98/23.86 | % 167.98/23.86 | GROUND_INST: instantiating (16) with all_60_0, all_62_1, n2, simplifying with % 167.98/23.86 | (93), (94) gives: % 167.98/23.86 | (97) all_62_1 = all_60_0 % 167.98/23.86 | % 167.98/23.86 | GROUND_INST: instantiating (16) with all_62_1, all_64_2, n2, simplifying with % 167.98/23.86 | (92), (93) gives: % 167.98/23.86 | (98) all_64_2 = all_62_1 % 167.98/23.86 | % 167.98/23.86 | GROUND_INST: instantiating (16) with n3, all_64_2, n2, simplifying with (92), % 167.98/23.86 | (95) gives: % 167.98/23.86 | (99) all_64_2 = n3 % 167.98/23.86 | % 167.98/23.86 | COMBINE_EQS: (98), (99) imply: % 167.98/23.86 | (100) all_62_1 = n3 % 167.98/23.86 | % 167.98/23.86 | SIMP: (100) implies: % 167.98/23.86 | (101) all_62_1 = n3 % 167.98/23.86 | % 167.98/23.86 | COMBINE_EQS: (97), (101) imply: % 167.98/23.86 | (102) all_60_0 = n3 % 167.98/23.86 | % 167.98/23.86 | SIMP: (102) implies: % 167.98/23.86 | (103) all_60_0 = n3 % 167.98/23.86 | % 167.98/23.86 | REDUCE: (45), (99) imply: % 167.98/23.86 | (104) succ(n3) = all_64_1 % 167.98/23.86 | % 167.98/23.86 | REDUCE: (38), (101) imply: % 167.98/23.86 | (105) succ(n3) = all_62_0 % 167.98/23.86 | % 167.98/23.86 | REDUCE: (32), (103) imply: % 167.98/23.86 | (106) succ(n3) = n4 % 167.98/23.86 | % 167.98/23.86 | REDUCE: (28), (103) imply: % 167.98/23.86 | (107) $i(n3) % 167.98/23.86 | % 167.98/23.86 | GROUND_INST: instantiating (16) with all_62_0, all_64_1, n3, simplifying with % 167.98/23.86 | (104), (105) gives: % 167.98/23.86 | (108) all_64_1 = all_62_0 % 167.98/23.86 | % 167.98/23.86 | GROUND_INST: instantiating (16) with n4, all_64_1, n3, simplifying with (104), % 167.98/23.86 | (106) gives: % 167.98/23.86 | (109) all_64_1 = n4 % 167.98/23.86 | % 167.98/23.86 | COMBINE_EQS: (108), (109) imply: % 167.98/23.86 | (110) all_62_0 = n4 % 167.98/23.86 | % 167.98/23.86 | SIMP: (110) implies: % 167.98/23.86 | (111) all_62_0 = n4 % 167.98/23.86 | % 167.98/23.86 | REDUCE: (46), (109) imply: % 167.98/23.86 | (112) succ(n4) = all_64_0 % 167.98/23.86 | % 167.98/23.86 | REDUCE: (39), (111) imply: % 167.98/23.86 | (113) succ(n4) = n5 % 167.98/23.86 | % 167.98/23.86 | REDUCE: (34), (111) imply: % 167.98/23.86 | (114) $i(n4) % 167.98/23.86 | % 167.98/23.86 | GROUND_INST: instantiating (16) with n5, all_64_0, n4, simplifying with (112), % 167.98/23.86 | (113) gives: % 167.98/23.86 | (115) all_64_0 = n5 % 167.98/23.86 | % 167.98/23.86 | REDUCE: (47), (115) imply: % 167.98/23.86 | (116) succ(n5) = n6 % 167.98/23.86 | % 167.98/23.86 | REDUCE: (41), (115) imply: % 167.98/23.86 | (117) $i(n5) % 167.98/23.86 | % 167.98/23.86 | GROUND_INST: instantiating (pred_succ) with n1, n2, simplifying with (79), % 167.98/23.86 | (80) gives: % 167.98/23.86 | (118) pred(n2) = n1 % 167.98/23.86 | % 167.98/23.86 | GROUND_INST: instantiating (pred_succ) with n2, n3, simplifying with (95), % 167.98/23.86 | (96) gives: % 167.98/23.86 | (119) pred(n3) = n2 % 167.98/23.86 | % 167.98/23.86 | GROUND_INST: instantiating (pred_succ) with n3, n4, simplifying with (106), % 167.98/23.86 | (107) gives: % 167.98/23.86 | (120) pred(n4) = n3 % 167.98/23.86 | % 167.98/23.86 | GROUND_INST: instantiating (pred_succ) with n4, n5, simplifying with (113), % 167.98/23.86 | (114) gives: % 167.98/23.86 | (121) pred(n5) = n4 % 167.98/23.86 | % 167.98/23.86 | GROUND_INST: instantiating (pred_succ) with n5, n6, simplifying with (116), % 167.98/23.86 | (117) gives: % 167.98/23.86 | (122) pred(n6) = n5 % 167.98/23.86 | % 167.98/23.86 | GROUND_INST: instantiating (2) with n3, all_74_12, simplifying with (55), % 167.98/23.86 | (107) gives: % 167.98/23.86 | (123) pred(n3) = all_74_12 & $i(all_74_12) % 167.98/23.86 | % 167.98/23.86 | ALPHA: (123) implies: % 167.98/23.86 | (124) $i(all_74_12) % 167.98/23.86 | (125) pred(n3) = all_74_12 % 167.98/23.86 | % 167.98/23.86 | GROUND_INST: instantiating (2) with n6, all_74_13, simplifying with (13), (56) % 167.98/23.86 | gives: % 167.98/23.86 | (126) pred(n6) = all_74_13 & $i(all_74_13) % 167.98/23.86 | % 167.98/23.86 | ALPHA: (126) implies: % 167.98/23.86 | (127) $i(all_74_13) % 167.98/23.86 | (128) pred(n6) = all_74_13 % 167.98/23.86 | % 167.98/23.86 | GROUND_INST: instantiating (15) with n2, all_74_12, n3, simplifying with % 167.98/23.86 | (119), (125) gives: % 167.98/23.86 | (129) all_74_12 = n2 % 167.98/23.86 | % 167.98/23.86 | GROUND_INST: instantiating (15) with n5, all_74_13, n6, simplifying with % 167.98/23.86 | (122), (128) gives: % 167.98/23.86 | (130) all_74_13 = n5 % 167.98/23.86 | % 167.98/23.86 | BETA: splitting (57) gives: % 167.98/23.86 | % 167.98/23.87 | Case 1: % 167.98/23.87 | | % 167.98/23.87 | | (131) ~ (all_74_0 = all_74_1) & a_select3(q_ds1_filter, all_74_2, % 167.98/23.87 | | all_74_3) = all_74_0 & a_select3(q_ds1_filter, all_74_3, % 167.98/23.87 | | all_74_2) = all_74_1 & $i(all_74_0) & $i(all_74_1) & % 167.98/23.87 | | leq(all_74_2, all_74_13) & leq(all_74_3, all_74_13) & leq(n0, % 167.98/23.87 | | all_74_2) & leq(n0, all_74_3) % 167.98/23.87 | | % 167.98/23.87 | | ALPHA: (131) implies: % 168.27/23.87 | | (132) ~ (all_74_0 = all_74_1) % 168.27/23.87 | | (133) leq(n0, all_74_3) % 168.27/23.87 | | (134) leq(n0, all_74_2) % 168.27/23.87 | | (135) leq(all_74_3, all_74_13) % 168.27/23.87 | | (136) leq(all_74_2, all_74_13) % 168.27/23.87 | | (137) a_select3(q_ds1_filter, all_74_3, all_74_2) = all_74_1 % 168.27/23.87 | | (138) a_select3(q_ds1_filter, all_74_2, all_74_3) = all_74_0 % 168.27/23.87 | | % 168.27/23.87 | | REDUCE: (130), (136) imply: % 168.27/23.87 | | (139) leq(all_74_2, n5) % 168.27/23.87 | | % 168.27/23.87 | | REDUCE: (130), (135) imply: % 168.27/23.87 | | (140) leq(all_74_3, n5) % 168.27/23.87 | | % 168.27/23.87 | | GROUND_INST: instantiating (leq_gt2) with n0, all_74_3, simplifying with % 168.27/23.87 | | (12), (53), (133) gives: % 168.27/23.87 | | (141) all_74_3 = n0 | gt(all_74_3, n0) % 168.27/23.87 | | % 168.27/23.87 | | GROUND_INST: instantiating (leq_gt2) with n0, all_74_2, simplifying with % 168.27/23.87 | | (12), (54), (134) gives: % 168.27/23.87 | | (142) all_74_2 = n0 | gt(all_74_2, n0) % 168.27/23.87 | | % 168.27/23.87 | | GROUND_INST: instantiating (3) with all_74_3, simplifying with (53), (133), % 168.27/23.87 | | (140) gives: % 168.27/23.87 | | (143) all_74_3 = n5 | all_74_3 = n4 | all_74_3 = n3 | all_74_3 = n2 | % 168.27/23.87 | | all_74_3 = n1 | all_74_3 = n0 % 168.27/23.87 | | % 168.27/23.87 | | GROUND_INST: instantiating (leq_gt2) with all_74_3, n5, simplifying with % 168.27/23.87 | | (53), (117), (140) gives: % 168.27/23.87 | | (144) all_74_3 = n5 | gt(n5, all_74_3) % 168.27/23.87 | | % 168.27/23.87 | | GROUND_INST: instantiating (3) with all_74_2, simplifying with (54), (134), % 168.27/23.87 | | (139) gives: % 168.27/23.87 | | (145) all_74_2 = n5 | all_74_2 = n4 | all_74_2 = n3 | all_74_2 = n2 | % 168.27/23.87 | | all_74_2 = n1 | all_74_2 = n0 % 168.27/23.87 | | % 168.27/23.87 | | GROUND_INST: instantiating (leq_gt2) with all_74_2, n5, simplifying with % 168.27/23.87 | | (54), (117), (139) gives: % 168.27/23.87 | | (146) all_74_2 = n5 | gt(n5, all_74_2) % 168.27/23.87 | | % 168.27/23.87 | | BETA: splitting (142) gives: % 168.27/23.87 | | % 168.27/23.87 | | Case 1: % 168.27/23.87 | | | % 168.27/23.87 | | | (147) gt(all_74_2, n0) % 168.27/23.87 | | | % 168.27/23.87 | | | BETA: splitting (141) gives: % 168.27/23.87 | | | % 168.27/23.87 | | | Case 1: % 168.27/23.87 | | | | % 168.27/23.87 | | | | (148) gt(all_74_3, n0) % 168.27/23.87 | | | | % 168.27/23.87 | | | | BETA: splitting (144) gives: % 168.27/23.87 | | | | % 168.27/23.87 | | | | Case 1: % 168.27/23.87 | | | | | % 168.27/23.87 | | | | | (149) gt(n5, all_74_3) % 168.27/23.87 | | | | | % 168.27/23.87 | | | | | GROUND_INST: instantiating (1) with all_74_3, n5, n4, simplifying with % 168.27/23.87 | | | | | (53), (117), (121), (149) gives: % 168.27/23.87 | | | | | (150) leq(all_74_3, n4) % 168.27/23.87 | | | | | % 168.27/23.87 | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_3, n4, simplifying % 168.27/23.87 | | | | | with (53), (114), (150) gives: % 168.27/23.87 | | | | | (151) all_74_3 = n4 | gt(n4, all_74_3) % 168.27/23.87 | | | | | % 168.27/23.87 | | | | | BETA: splitting (146) gives: % 168.27/23.87 | | | | | % 168.27/23.87 | | | | | Case 1: % 168.27/23.87 | | | | | | % 168.27/23.87 | | | | | | (152) gt(n5, all_74_2) % 168.27/23.87 | | | | | | % 168.27/23.87 | | | | | | GROUND_INST: instantiating (1) with all_74_2, n5, n4, simplifying % 168.27/23.87 | | | | | | with (54), (117), (121), (152) gives: % 168.27/23.87 | | | | | | (153) leq(all_74_2, n4) % 168.27/23.87 | | | | | | % 168.27/23.87 | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_2, n4, simplifying % 168.27/23.87 | | | | | | with (54), (114), (153) gives: % 168.27/23.87 | | | | | | (154) all_74_2 = n4 | gt(n4, all_74_2) % 168.27/23.87 | | | | | | % 168.27/23.87 | | | | | | BETA: splitting (145) gives: % 168.27/23.87 | | | | | | % 168.27/23.87 | | | | | | Case 1: % 168.27/23.87 | | | | | | | % 168.27/23.87 | | | | | | | (155) all_74_2 = n0 % 168.27/23.87 | | | | | | | % 168.27/23.87 | | | | | | | REF_CLOSE: (54), (147), (155), (irreflexivity_gt) are inconsistent % 168.27/23.87 | | | | | | | by sub-proof #34. % 168.27/23.87 | | | | | | | % 168.27/23.87 | | | | | | Case 2: % 168.27/23.87 | | | | | | | % 168.27/23.87 | | | | | | | (156) ~ (all_74_2 = n0) % 168.27/23.87 | | | | | | | % 168.27/23.87 | | | | | | | BETA: splitting (143) gives: % 168.27/23.87 | | | | | | | % 168.27/23.87 | | | | | | | Case 1: % 168.27/23.87 | | | | | | | | % 168.27/23.87 | | | | | | | | (157) all_74_3 = n0 % 168.27/23.87 | | | | | | | | % 168.27/23.87 | | | | | | | | REF_CLOSE: (53), (148), (157), (irreflexivity_gt) are % 168.27/23.87 | | | | | | | | inconsistent by sub-proof #33. % 168.27/23.87 | | | | | | | | % 168.27/23.87 | | | | | | | Case 2: % 168.27/23.87 | | | | | | | | % 168.27/23.87 | | | | | | | | (158) ~ (all_74_3 = n0) % 168.27/23.87 | | | | | | | | % 168.27/23.87 | | | | | | | | REF_CLOSE: (1), (4), (17), (53), (54), (58), (96), (107), (114), % 168.27/23.87 | | | | | | | | (118), (119), (120), (130), (132), (133), (134), % 168.27/23.87 | | | | | | | | (137), (138), (139), (140), (151), (154), (156), % 168.27/23.87 | | | | | | | | (158), (leq_gt2) are inconsistent by sub-proof #28. % 168.27/23.87 | | | | | | | | % 168.27/23.87 | | | | | | | End of split % 168.27/23.87 | | | | | | | % 168.27/23.87 | | | | | | End of split % 168.27/23.87 | | | | | | % 168.27/23.87 | | | | | Case 2: % 168.27/23.87 | | | | | | % 168.27/23.87 | | | | | | (159) all_74_2 = n5 % 168.27/23.87 | | | | | | % 168.27/23.87 | | | | | | REDUCE: (138), (159) imply: % 168.27/23.88 | | | | | | (160) a_select3(q_ds1_filter, n5, all_74_3) = all_74_0 % 168.27/23.88 | | | | | | % 168.27/23.88 | | | | | | REDUCE: (137), (159) imply: % 168.27/23.88 | | | | | | (161) a_select3(q_ds1_filter, all_74_3, n5) = all_74_1 % 168.27/23.88 | | | | | | % 168.27/23.88 | | | | | | REDUCE: (139), (159) imply: % 168.27/23.88 | | | | | | (162) leq(n5, n5) % 168.27/23.88 | | | | | | % 168.27/23.88 | | | | | | REDUCE: (134), (159) imply: % 168.27/23.88 | | | | | | (163) leq(n0, n5) % 168.27/23.88 | | | | | | % 168.27/23.88 | | | | | | BETA: splitting (143) gives: % 168.27/23.88 | | | | | | % 168.27/23.88 | | | | | | Case 1: % 168.27/23.88 | | | | | | | % 168.27/23.88 | | | | | | | (164) all_74_3 = n0 % 168.27/23.88 | | | | | | | % 168.27/23.88 | | | | | | | REF_CLOSE: (53), (148), (164), (irreflexivity_gt) are inconsistent % 168.27/23.88 | | | | | | | by sub-proof #33. % 168.27/23.88 | | | | | | | % 168.27/23.88 | | | | | | Case 2: % 168.27/23.88 | | | | | | | % 168.27/23.88 | | | | | | | (165) ~ (all_74_3 = n0) % 168.27/23.88 | | | | | | | % 168.27/23.88 | | | | | | | REF_CLOSE: (1), (4), (17), (53), (58), (96), (107), (114), (117), % 168.27/23.88 | | | | | | | (118), (119), (120), (130), (132), (133), (140), (151), % 168.27/23.88 | | | | | | | (160), (161), (162), (163), (165), (leq_gt2) are % 168.27/23.88 | | | | | | | inconsistent by sub-proof #26. % 168.27/23.88 | | | | | | | % 168.27/23.88 | | | | | | End of split % 168.27/23.88 | | | | | | % 168.27/23.88 | | | | | End of split % 168.27/23.88 | | | | | % 168.27/23.88 | | | | Case 2: % 168.27/23.88 | | | | | % 168.27/23.88 | | | | | (166) all_74_3 = n5 % 168.27/23.88 | | | | | % 168.27/23.88 | | | | | REDUCE: (138), (166) imply: % 168.27/23.88 | | | | | (167) a_select3(q_ds1_filter, all_74_2, n5) = all_74_0 % 168.27/23.88 | | | | | % 168.27/23.88 | | | | | REDUCE: (137), (166) imply: % 168.27/23.88 | | | | | (168) a_select3(q_ds1_filter, n5, all_74_2) = all_74_1 % 168.27/23.88 | | | | | % 168.27/23.88 | | | | | REDUCE: (140), (166) imply: % 168.27/23.88 | | | | | (169) leq(n5, n5) % 168.27/23.88 | | | | | % 168.27/23.88 | | | | | REDUCE: (133), (166) imply: % 168.27/23.88 | | | | | (170) leq(n0, n5) % 168.27/23.88 | | | | | % 168.27/23.88 | | | | | BETA: splitting (146) gives: % 168.27/23.88 | | | | | % 168.27/23.88 | | | | | Case 1: % 168.27/23.88 | | | | | | % 168.27/23.88 | | | | | | (171) gt(n5, all_74_2) % 168.27/23.88 | | | | | | % 168.27/23.88 | | | | | | GROUND_INST: instantiating (1) with all_74_2, n5, n4, simplifying % 168.27/23.88 | | | | | | with (54), (117), (121), (171) gives: % 168.27/23.88 | | | | | | (172) leq(all_74_2, n4) % 168.27/23.88 | | | | | | % 168.27/23.88 | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_2, n4, simplifying % 168.27/23.88 | | | | | | with (54), (114), (172) gives: % 168.27/23.88 | | | | | | (173) all_74_2 = n4 | gt(n4, all_74_2) % 168.27/23.88 | | | | | | % 168.27/23.88 | | | | | | BETA: splitting (145) gives: % 168.27/23.88 | | | | | | % 168.27/23.88 | | | | | | Case 1: % 168.27/23.88 | | | | | | | % 168.27/23.88 | | | | | | | (174) all_74_2 = n0 % 168.27/23.88 | | | | | | | % 168.27/23.88 | | | | | | | REF_CLOSE: (54), (147), (174), (irreflexivity_gt) are inconsistent % 168.27/23.88 | | | | | | | by sub-proof #34. % 168.27/23.88 | | | | | | | % 168.27/23.88 | | | | | | Case 2: % 168.27/23.88 | | | | | | | % 168.27/23.88 | | | | | | | (175) ~ (all_74_2 = n0) % 168.27/23.88 | | | | | | | % 168.27/23.88 | | | | | | | REF_CLOSE: (1), (4), (17), (54), (58), (96), (107), (114), (117), % 168.27/23.88 | | | | | | | (118), (119), (120), (130), (132), (134), (139), (167), % 168.27/23.88 | | | | | | | (168), (169), (170), (173), (175), (leq_gt2) are % 168.27/23.88 | | | | | | | inconsistent by sub-proof #25. % 168.27/23.88 | | | | | | | % 168.27/23.88 | | | | | | End of split % 168.27/23.88 | | | | | | % 168.27/23.88 | | | | | Case 2: % 168.27/23.88 | | | | | | % 168.27/23.88 | | | | | | (176) all_74_2 = n5 % 168.27/23.88 | | | | | | % 168.27/23.88 | | | | | | REDUCE: (167), (176) imply: % 168.27/23.88 | | | | | | (177) a_select3(q_ds1_filter, n5, n5) = all_74_0 % 168.27/23.88 | | | | | | % 168.27/23.88 | | | | | | REDUCE: (168), (176) imply: % 168.27/23.88 | | | | | | (178) a_select3(q_ds1_filter, n5, n5) = all_74_1 % 168.27/23.88 | | | | | | % 168.27/23.88 | | | | | | GROUND_INST: instantiating (17) with all_74_1, all_74_0, n5, n5, % 168.27/23.88 | | | | | | q_ds1_filter, simplifying with (177), (178) gives: % 168.27/23.88 | | | | | | (179) all_74_0 = all_74_1 % 168.27/23.88 | | | | | | % 168.27/23.88 | | | | | | REDUCE: (132), (179) imply: % 168.27/23.88 | | | | | | (180) $false % 168.27/23.88 | | | | | | % 168.27/23.88 | | | | | | CLOSE: (180) is inconsistent. % 168.27/23.88 | | | | | | % 168.27/23.88 | | | | | End of split % 168.27/23.88 | | | | | % 168.27/23.88 | | | | End of split % 168.27/23.88 | | | | % 168.27/23.88 | | | Case 2: % 168.27/23.88 | | | | % 168.27/23.88 | | | | (181) all_74_3 = n0 % 168.27/23.88 | | | | (182) ~ gt(all_74_3, n0) % 168.27/23.88 | | | | % 168.27/23.88 | | | | REDUCE: (181), (182) imply: % 168.27/23.88 | | | | (183) ~ gt(n0, n0) % 168.27/23.88 | | | | % 168.27/23.88 | | | | REF_CLOSE: (1), (4), (17), (53), (54), (58), (96), (107), (114), (117), % 168.27/23.88 | | | | (118), (119), (120), (121), (130), (132), (133), (134), % 168.27/23.88 | | | | (137), (138), (139), (140), (141), (143), (144), (145), % 168.27/23.88 | | | | (146), (147), (183), (leq_gt2) are inconsistent by sub-proof % 168.27/23.88 | | | | #21. % 168.27/23.88 | | | | % 168.27/23.88 | | | End of split % 168.27/23.88 | | | % 168.27/23.88 | | Case 2: % 168.27/23.88 | | | % 168.27/23.88 | | | (184) all_74_2 = n0 % 168.27/23.88 | | | (185) ~ gt(all_74_2, n0) % 168.27/23.88 | | | % 168.27/23.88 | | | REDUCE: (184), (185) imply: % 168.27/23.88 | | | (186) ~ gt(n0, n0) % 168.27/23.88 | | | % 168.27/23.88 | | | BETA: splitting (142) gives: % 168.27/23.88 | | | % 168.27/23.88 | | | Case 1: % 168.27/23.88 | | | | % 168.27/23.88 | | | | (187) gt(all_74_2, n0) % 168.27/23.88 | | | | % 168.27/23.88 | | | | REF_CLOSE: (1), (4), (17), (53), (54), (58), (96), (107), (114), (117), % 168.27/23.88 | | | | (118), (119), (120), (121), (130), (132), (133), (134), % 168.27/23.88 | | | | (137), (138), (139), (140), (141), (143), (144), (145), % 168.27/23.88 | | | | (146), (186), (187), (leq_gt2) are inconsistent by sub-proof % 168.27/23.88 | | | | #21. % 168.27/23.88 | | | | % 168.27/23.88 | | | Case 2: % 168.27/23.88 | | | | % 168.27/23.88 | | | | % 168.27/23.88 | | | | REDUCE: (138), (184) imply: % 168.27/23.88 | | | | (188) a_select3(q_ds1_filter, n0, all_74_3) = all_74_0 % 168.27/23.88 | | | | % 168.27/23.88 | | | | REDUCE: (137), (184) imply: % 168.27/23.88 | | | | (189) a_select3(q_ds1_filter, all_74_3, n0) = all_74_1 % 168.27/23.88 | | | | % 168.27/23.88 | | | | REDUCE: (139), (184) imply: % 168.27/23.88 | | | | (190) leq(n0, n5) % 168.27/23.88 | | | | % 168.27/23.88 | | | | REDUCE: (134), (184) imply: % 168.27/23.88 | | | | (191) leq(n0, n0) % 168.27/23.88 | | | | % 168.27/23.88 | | | | BETA: splitting (141) gives: % 168.27/23.88 | | | | % 168.27/23.88 | | | | Case 1: % 168.27/23.88 | | | | | % 168.27/23.88 | | | | | (192) gt(all_74_3, n0) % 168.27/23.88 | | | | | % 168.27/23.88 | | | | | BETA: splitting (144) gives: % 168.27/23.88 | | | | | % 168.27/23.88 | | | | | Case 1: % 168.27/23.88 | | | | | | % 168.27/23.88 | | | | | | (193) gt(n5, all_74_3) % 168.27/23.88 | | | | | | % 168.27/23.88 | | | | | | GROUND_INST: instantiating (1) with all_74_3, n5, n4, simplifying % 168.27/23.88 | | | | | | with (53), (117), (121), (193) gives: % 168.27/23.88 | | | | | | (194) leq(all_74_3, n4) % 168.27/23.88 | | | | | | % 168.27/23.88 | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_3, n4, simplifying % 168.27/23.88 | | | | | | with (53), (114), (194) gives: % 168.27/23.88 | | | | | | (195) all_74_3 = n4 | gt(n4, all_74_3) % 168.27/23.88 | | | | | | % 168.27/23.88 | | | | | | BETA: splitting (143) gives: % 168.27/23.88 | | | | | | % 168.27/23.88 | | | | | | Case 1: % 168.27/23.88 | | | | | | | % 168.27/23.88 | | | | | | | (196) all_74_3 = n0 % 168.27/23.88 | | | | | | | % 168.27/23.88 | | | | | | | REDUCE: (192), (196) imply: % 168.27/23.88 | | | | | | | (197) gt(n0, n0) % 168.27/23.88 | | | | | | | % 168.27/23.88 | | | | | | | PRED_UNIFY: (186), (197) imply: % 168.27/23.88 | | | | | | | (198) $false % 168.27/23.88 | | | | | | | % 168.27/23.88 | | | | | | | CLOSE: (198) is inconsistent. % 168.27/23.88 | | | | | | | % 168.27/23.88 | | | | | | Case 2: % 168.27/23.88 | | | | | | | % 168.27/23.88 | | | | | | | (199) ~ (all_74_3 = n0) % 168.27/23.88 | | | | | | | % 168.27/23.88 | | | | | | | BETA: splitting (195) gives: % 168.27/23.88 | | | | | | | % 168.27/23.88 | | | | | | | Case 1: % 168.27/23.88 | | | | | | | | % 168.27/23.89 | | | | | | | | (200) gt(n4, all_74_3) % 168.27/23.89 | | | | | | | | % 168.27/23.89 | | | | | | | | GROUND_INST: instantiating (1) with all_74_3, n4, n3, % 168.27/23.89 | | | | | | | | simplifying with (53), (114), (120), (200) gives: % 168.27/23.89 | | | | | | | | (201) leq(all_74_3, n3) % 168.27/23.89 | | | | | | | | % 168.27/23.89 | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_3, n3, % 168.27/23.89 | | | | | | | | simplifying with (53), (107), (201) gives: % 168.27/23.89 | | | | | | | | (202) all_74_3 = n3 | gt(n3, all_74_3) % 168.27/23.89 | | | | | | | | % 168.27/23.89 | | | | | | | | BETA: splitting (202) gives: % 168.27/23.89 | | | | | | | | % 168.27/23.89 | | | | | | | | Case 1: % 168.27/23.89 | | | | | | | | | % 168.27/23.89 | | | | | | | | | (203) gt(n3, all_74_3) % 168.27/23.89 | | | | | | | | | % 168.27/23.89 | | | | | | | | | GROUND_INST: instantiating (1) with all_74_3, n3, n2, % 168.27/23.89 | | | | | | | | | simplifying with (53), (107), (119), (203) gives: % 168.27/23.89 | | | | | | | | | (204) leq(all_74_3, n2) % 168.27/23.89 | | | | | | | | | % 168.27/23.89 | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_3, n2, % 168.27/23.89 | | | | | | | | | simplifying with (53), (96), (204) gives: % 168.27/23.89 | | | | | | | | | (205) all_74_3 = n2 | gt(n2, all_74_3) % 168.27/23.89 | | | | | | | | | % 168.27/23.89 | | | | | | | | | BETA: splitting (205) gives: % 168.27/23.89 | | | | | | | | | % 168.27/23.89 | | | | | | | | | Case 1: % 168.27/23.89 | | | | | | | | | | % 168.27/23.89 | | | | | | | | | | (206) gt(n2, all_74_3) % 168.27/23.89 | | | | | | | | | | % 168.27/23.89 | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_3, n2, n1, % 168.27/23.89 | | | | | | | | | | simplifying with (53), (96), (118), (206) gives: % 168.27/23.89 | | | | | | | | | | (207) leq(all_74_3, n1) % 168.27/23.89 | | | | | | | | | | % 168.27/23.89 | | | | | | | | | | GROUND_INST: instantiating (4) with all_74_3, simplifying with % 168.27/23.89 | | | | | | | | | | (53), (133), (207) gives: % 168.27/23.89 | | | | | | | | | | (208) all_74_3 = n1 | all_74_3 = n0 % 168.27/23.89 | | | | | | | | | | % 168.27/23.89 | | | | | | | | | | BETA: splitting (208) gives: % 168.27/23.89 | | | | | | | | | | % 168.27/23.89 | | | | | | | | | | Case 1: % 168.27/23.89 | | | | | | | | | | | % 168.27/23.89 | | | | | | | | | | | (209) all_74_3 = n0 % 168.27/23.89 | | | | | | | | | | | % 168.27/23.89 | | | | | | | | | | | REDUCE: (199), (209) imply: % 168.27/23.89 | | | | | | | | | | | (210) $false % 168.27/23.89 | | | | | | | | | | | % 168.27/23.89 | | | | | | | | | | | CLOSE: (210) is inconsistent. % 168.27/23.89 | | | | | | | | | | | % 168.27/23.89 | | | | | | | | | | Case 2: % 168.27/23.89 | | | | | | | | | | | % 168.27/23.89 | | | | | | | | | | | (211) all_74_3 = n1 % 168.27/23.89 | | | | | | | | | | | % 168.27/23.89 | | | | | | | | | | | REDUCE: (189), (211) imply: % 168.27/23.89 | | | | | | | | | | | (212) a_select3(q_ds1_filter, n1, n0) = all_74_1 % 168.27/23.89 | | | | | | | | | | | % 168.27/23.89 | | | | | | | | | | | REDUCE: (188), (211) imply: % 168.27/23.89 | | | | | | | | | | | (213) a_select3(q_ds1_filter, n0, n1) = all_74_0 % 168.27/23.89 | | | | | | | | | | | % 168.27/23.89 | | | | | | | | | | | REDUCE: (140), (211) imply: % 168.27/23.89 | | | | | | | | | | | (214) leq(n1, n5) % 168.27/23.89 | | | | | | | | | | | % 168.27/23.89 | | | | | | | | | | | REDUCE: (133), (211) imply: % 168.27/23.89 | | | | | | | | | | | (215) leq(n0, n1) % 168.27/23.89 | | | | | | | | | | | % 168.27/23.89 | | | | | | | | | | | GROUND_INST: instantiating (58) with n0, n1, all_74_0, % 168.27/23.89 | | | | | | | | | | | simplifying with (12), (80), (191), (213), (215) % 168.27/23.89 | | | | | | | | | | | gives: % 168.27/23.89 | | | | | | | | | | | (216) ~ leq(n1, all_74_13) | ~ leq(n0, all_74_13) | % 168.27/23.89 | | | | | | | | | | | (a_select3(q_ds1_filter, n1, n0) = all_74_0 & % 168.27/23.89 | | | | | | | | | | | $i(all_74_0)) % 168.27/23.89 | | | | | | | | | | | % 168.27/23.89 | | | | | | | | | | | BETA: splitting (216) gives: % 168.27/23.89 | | | | | | | | | | | % 168.27/23.89 | | | | | | | | | | | Case 1: % 168.27/23.89 | | | | | | | | | | | | % 168.27/23.89 | | | | | | | | | | | | (217) ~ leq(n0, all_74_13) % 168.27/23.89 | | | | | | | | | | | | % 168.27/23.89 | | | | | | | | | | | | REDUCE: (130), (217) imply: % 168.27/23.89 | | | | | | | | | | | | (218) ~ leq(n0, n5) % 168.27/23.89 | | | | | | | | | | | | % 168.27/23.89 | | | | | | | | | | | | PRED_UNIFY: (190), (218) imply: % 168.27/23.89 | | | | | | | | | | | | (219) $false % 168.27/23.89 | | | | | | | | | | | | % 168.27/23.89 | | | | | | | | | | | | CLOSE: (219) is inconsistent. % 168.27/23.89 | | | | | | | | | | | | % 168.27/23.89 | | | | | | | | | | | Case 2: % 168.27/23.89 | | | | | | | | | | | | % 168.27/23.89 | | | | | | | | | | | | (220) ~ leq(n1, all_74_13) | (a_select3(q_ds1_filter, % 168.27/23.89 | | | | | | | | | | | | n1, n0) = all_74_0 & $i(all_74_0)) % 168.27/23.89 | | | | | | | | | | | | % 168.27/23.89 | | | | | | | | | | | | BETA: splitting (220) gives: % 168.27/23.89 | | | | | | | | | | | | % 168.27/23.89 | | | | | | | | | | | | Case 1: % 168.27/23.89 | | | | | | | | | | | | | % 168.27/23.89 | | | | | | | | | | | | | (221) ~ leq(n1, all_74_13) % 168.27/23.89 | | | | | | | | | | | | | % 168.27/23.89 | | | | | | | | | | | | | REDUCE: (130), (221) imply: % 168.27/23.89 | | | | | | | | | | | | | (222) ~ leq(n1, n5) % 168.27/23.89 | | | | | | | | | | | | | % 168.27/23.89 | | | | | | | | | | | | | PRED_UNIFY: (214), (222) imply: % 168.27/23.89 | | | | | | | | | | | | | (223) $false % 168.27/23.89 | | | | | | | | | | | | | % 168.27/23.89 | | | | | | | | | | | | | CLOSE: (223) is inconsistent. % 168.27/23.89 | | | | | | | | | | | | | % 168.27/23.89 | | | | | | | | | | | | Case 2: % 168.27/23.89 | | | | | | | | | | | | | % 168.27/23.89 | | | | | | | | | | | | | (224) a_select3(q_ds1_filter, n1, n0) = all_74_0 & % 168.27/23.89 | | | | | | | | | | | | | $i(all_74_0) % 168.27/23.89 | | | | | | | | | | | | | % 168.27/23.89 | | | | | | | | | | | | | ALPHA: (224) implies: % 168.27/23.89 | | | | | | | | | | | | | (225) a_select3(q_ds1_filter, n1, n0) = all_74_0 % 168.27/23.89 | | | | | | | | | | | | | % 168.27/23.89 | | | | | | | | | | | | | REF_CLOSE: (17), (132), (212), (225) are inconsistent by % 168.27/23.89 | | | | | | | | | | | | | sub-proof #24. % 168.27/23.89 | | | | | | | | | | | | | % 168.27/23.89 | | | | | | | | | | | | End of split % 168.27/23.89 | | | | | | | | | | | | % 168.27/23.89 | | | | | | | | | | | End of split % 168.27/23.89 | | | | | | | | | | | % 168.27/23.89 | | | | | | | | | | End of split % 168.27/23.89 | | | | | | | | | | % 168.27/23.89 | | | | | | | | | Case 2: % 168.27/23.89 | | | | | | | | | | % 168.27/23.89 | | | | | | | | | | (226) all_74_3 = n2 % 168.27/23.89 | | | | | | | | | | % 168.27/23.89 | | | | | | | | | | REDUCE: (189), (226) imply: % 168.27/23.89 | | | | | | | | | | (227) a_select3(q_ds1_filter, n2, n0) = all_74_1 % 168.27/23.89 | | | | | | | | | | % 168.27/23.89 | | | | | | | | | | REDUCE: (188), (226) imply: % 168.27/23.89 | | | | | | | | | | (228) a_select3(q_ds1_filter, n0, n2) = all_74_0 % 168.27/23.89 | | | | | | | | | | % 168.27/23.89 | | | | | | | | | | REDUCE: (140), (226) imply: % 168.27/23.89 | | | | | | | | | | (229) leq(n2, n5) % 168.27/23.89 | | | | | | | | | | % 168.27/23.89 | | | | | | | | | | REDUCE: (133), (226) imply: % 168.27/23.89 | | | | | | | | | | (230) leq(n0, n2) % 168.27/23.89 | | | | | | | | | | % 168.27/23.89 | | | | | | | | | | GROUND_INST: instantiating (58) with n0, n2, all_74_0, % 168.27/23.89 | | | | | | | | | | simplifying with (12), (96), (191), (228), (230) % 168.27/23.89 | | | | | | | | | | gives: % 168.27/23.89 | | | | | | | | | | (231) ~ leq(n2, all_74_13) | ~ leq(n0, all_74_13) | % 168.27/23.89 | | | | | | | | | | (a_select3(q_ds1_filter, n2, n0) = all_74_0 & % 168.27/23.89 | | | | | | | | | | $i(all_74_0)) % 168.27/23.89 | | | | | | | | | | % 168.27/23.89 | | | | | | | | | | BETA: splitting (231) gives: % 168.27/23.89 | | | | | | | | | | % 168.27/23.89 | | | | | | | | | | Case 1: % 168.27/23.89 | | | | | | | | | | | % 168.27/23.89 | | | | | | | | | | | (232) ~ leq(n0, all_74_13) % 168.27/23.89 | | | | | | | | | | | % 168.27/23.89 | | | | | | | | | | | REDUCE: (130), (232) imply: % 168.27/23.89 | | | | | | | | | | | (233) ~ leq(n0, n5) % 168.27/23.89 | | | | | | | | | | | % 168.27/23.89 | | | | | | | | | | | PRED_UNIFY: (190), (233) imply: % 168.27/23.89 | | | | | | | | | | | (234) $false % 168.27/23.89 | | | | | | | | | | | % 168.27/23.89 | | | | | | | | | | | CLOSE: (234) is inconsistent. % 168.27/23.89 | | | | | | | | | | | % 168.27/23.89 | | | | | | | | | | Case 2: % 168.27/23.89 | | | | | | | | | | | % 168.27/23.89 | | | | | | | | | | | (235) ~ leq(n2, all_74_13) | (a_select3(q_ds1_filter, % 168.27/23.89 | | | | | | | | | | | n2, n0) = all_74_0 & $i(all_74_0)) % 168.27/23.89 | | | | | | | | | | | % 168.27/23.89 | | | | | | | | | | | BETA: splitting (235) gives: % 168.27/23.89 | | | | | | | | | | | % 168.27/23.89 | | | | | | | | | | | Case 1: % 168.27/23.89 | | | | | | | | | | | | % 168.27/23.89 | | | | | | | | | | | | (236) ~ leq(n2, all_74_13) % 168.27/23.89 | | | | | | | | | | | | % 168.27/23.89 | | | | | | | | | | | | REDUCE: (130), (236) imply: % 168.27/23.89 | | | | | | | | | | | | (237) ~ leq(n2, n5) % 168.27/23.89 | | | | | | | | | | | | % 168.27/23.89 | | | | | | | | | | | | PRED_UNIFY: (229), (237) imply: % 168.27/23.89 | | | | | | | | | | | | (238) $false % 168.27/23.89 | | | | | | | | | | | | % 168.27/23.89 | | | | | | | | | | | | CLOSE: (238) is inconsistent. % 168.27/23.89 | | | | | | | | | | | | % 168.27/23.89 | | | | | | | | | | | Case 2: % 168.27/23.89 | | | | | | | | | | | | % 168.27/23.89 | | | | | | | | | | | | (239) a_select3(q_ds1_filter, n2, n0) = all_74_0 & % 168.27/23.89 | | | | | | | | | | | | $i(all_74_0) % 168.27/23.89 | | | | | | | | | | | | % 168.27/23.89 | | | | | | | | | | | | ALPHA: (239) implies: % 168.27/23.89 | | | | | | | | | | | | (240) a_select3(q_ds1_filter, n2, n0) = all_74_0 % 168.27/23.89 | | | | | | | | | | | | % 168.27/23.89 | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_74_0, all_74_1, n0, % 168.27/23.89 | | | | | | | | | | | | n2, q_ds1_filter, simplifying with (227), (240) % 168.27/23.89 | | | | | | | | | | | | gives: % 168.27/23.89 | | | | | | | | | | | | (241) all_74_0 = all_74_1 % 168.27/23.89 | | | | | | | | | | | | % 168.27/23.89 | | | | | | | | | | | | REDUCE: (132), (241) imply: % 168.27/23.89 | | | | | | | | | | | | (242) $false % 168.27/23.89 | | | | | | | | | | | | % 168.27/23.89 | | | | | | | | | | | | CLOSE: (242) is inconsistent. % 168.27/23.89 | | | | | | | | | | | | % 168.27/23.89 | | | | | | | | | | | End of split % 168.27/23.89 | | | | | | | | | | | % 168.27/23.89 | | | | | | | | | | End of split % 168.27/23.89 | | | | | | | | | | % 168.27/23.89 | | | | | | | | | End of split % 168.27/23.89 | | | | | | | | | % 168.27/23.89 | | | | | | | | Case 2: % 168.27/23.89 | | | | | | | | | % 168.27/23.89 | | | | | | | | | (243) all_74_3 = n3 % 168.27/23.89 | | | | | | | | | % 168.27/23.89 | | | | | | | | | REDUCE: (189), (243) imply: % 168.27/23.89 | | | | | | | | | (244) a_select3(q_ds1_filter, n3, n0) = all_74_1 % 168.27/23.89 | | | | | | | | | % 168.27/23.89 | | | | | | | | | REDUCE: (188), (243) imply: % 168.27/23.89 | | | | | | | | | (245) a_select3(q_ds1_filter, n0, n3) = all_74_0 % 168.27/23.89 | | | | | | | | | % 168.27/23.89 | | | | | | | | | REDUCE: (140), (243) imply: % 168.27/23.89 | | | | | | | | | (246) leq(n3, n5) % 168.27/23.89 | | | | | | | | | % 168.27/23.89 | | | | | | | | | REDUCE: (133), (243) imply: % 168.27/23.89 | | | | | | | | | (247) leq(n0, n3) % 168.27/23.89 | | | | | | | | | % 168.27/23.89 | | | | | | | | | GROUND_INST: instantiating (58) with n0, n3, all_74_0, % 168.27/23.89 | | | | | | | | | simplifying with (12), (107), (191), (245), (247) % 168.27/23.89 | | | | | | | | | gives: % 168.27/23.90 | | | | | | | | | (248) ~ leq(n3, all_74_13) | ~ leq(n0, all_74_13) | % 168.27/23.90 | | | | | | | | | (a_select3(q_ds1_filter, n3, n0) = all_74_0 & % 168.27/23.90 | | | | | | | | | $i(all_74_0)) % 168.27/23.90 | | | | | | | | | % 168.27/23.90 | | | | | | | | | BETA: splitting (248) gives: % 168.27/23.90 | | | | | | | | | % 168.27/23.90 | | | | | | | | | Case 1: % 168.27/23.90 | | | | | | | | | | % 168.27/23.90 | | | | | | | | | | (249) ~ leq(n0, all_74_13) % 168.27/23.90 | | | | | | | | | | % 168.27/23.90 | | | | | | | | | | REDUCE: (130), (249) imply: % 168.27/23.90 | | | | | | | | | | (250) ~ leq(n0, n5) % 168.27/23.90 | | | | | | | | | | % 168.27/23.90 | | | | | | | | | | PRED_UNIFY: (190), (250) imply: % 168.27/23.90 | | | | | | | | | | (251) $false % 168.27/23.90 | | | | | | | | | | % 168.27/23.90 | | | | | | | | | | CLOSE: (251) is inconsistent. % 168.27/23.90 | | | | | | | | | | % 168.27/23.90 | | | | | | | | | Case 2: % 168.27/23.90 | | | | | | | | | | % 168.27/23.90 | | | | | | | | | | (252) ~ leq(n3, all_74_13) | (a_select3(q_ds1_filter, % 168.27/23.90 | | | | | | | | | | n3, n0) = all_74_0 & $i(all_74_0)) % 168.27/23.90 | | | | | | | | | | % 168.27/23.90 | | | | | | | | | | BETA: splitting (252) gives: % 168.27/23.90 | | | | | | | | | | % 168.27/23.90 | | | | | | | | | | Case 1: % 168.27/23.90 | | | | | | | | | | | % 168.27/23.90 | | | | | | | | | | | (253) ~ leq(n3, all_74_13) % 168.27/23.90 | | | | | | | | | | | % 168.27/23.90 | | | | | | | | | | | REDUCE: (130), (253) imply: % 168.27/23.90 | | | | | | | | | | | (254) ~ leq(n3, n5) % 168.27/23.90 | | | | | | | | | | | % 168.27/23.90 | | | | | | | | | | | PRED_UNIFY: (246), (254) imply: % 168.27/23.90 | | | | | | | | | | | (255) $false % 168.27/23.90 | | | | | | | | | | | % 168.27/23.90 | | | | | | | | | | | CLOSE: (255) is inconsistent. % 168.27/23.90 | | | | | | | | | | | % 168.27/23.90 | | | | | | | | | | Case 2: % 168.27/23.90 | | | | | | | | | | | % 168.27/23.90 | | | | | | | | | | | (256) a_select3(q_ds1_filter, n3, n0) = all_74_0 & % 168.27/23.90 | | | | | | | | | | | $i(all_74_0) % 168.27/23.90 | | | | | | | | | | | % 168.27/23.90 | | | | | | | | | | | ALPHA: (256) implies: % 168.27/23.90 | | | | | | | | | | | (257) a_select3(q_ds1_filter, n3, n0) = all_74_0 % 168.27/23.90 | | | | | | | | | | | % 168.27/23.90 | | | | | | | | | | | GROUND_INST: instantiating (17) with all_74_0, all_74_1, n0, % 168.27/23.90 | | | | | | | | | | | n3, q_ds1_filter, simplifying with (244), (257) % 168.27/23.90 | | | | | | | | | | | gives: % 168.27/23.90 | | | | | | | | | | | (258) all_74_0 = all_74_1 % 168.27/23.90 | | | | | | | | | | | % 168.27/23.90 | | | | | | | | | | | REDUCE: (132), (258) imply: % 168.27/23.90 | | | | | | | | | | | (259) $false % 168.27/23.90 | | | | | | | | | | | % 168.27/23.90 | | | | | | | | | | | CLOSE: (259) is inconsistent. % 168.27/23.90 | | | | | | | | | | | % 168.27/23.90 | | | | | | | | | | End of split % 168.27/23.90 | | | | | | | | | | % 168.27/23.90 | | | | | | | | | End of split % 168.27/23.90 | | | | | | | | | % 168.27/23.90 | | | | | | | | End of split % 168.27/23.90 | | | | | | | | % 168.27/23.90 | | | | | | | Case 2: % 168.27/23.90 | | | | | | | | % 168.27/23.90 | | | | | | | | (260) all_74_3 = n4 % 168.27/23.90 | | | | | | | | % 168.27/23.90 | | | | | | | | REDUCE: (189), (260) imply: % 168.27/23.90 | | | | | | | | (261) a_select3(q_ds1_filter, n4, n0) = all_74_1 % 168.27/23.90 | | | | | | | | % 168.27/23.90 | | | | | | | | REDUCE: (188), (260) imply: % 168.27/23.90 | | | | | | | | (262) a_select3(q_ds1_filter, n0, n4) = all_74_0 % 168.27/23.90 | | | | | | | | % 168.27/23.90 | | | | | | | | REDUCE: (140), (260) imply: % 168.27/23.90 | | | | | | | | (263) leq(n4, n5) % 168.27/23.90 | | | | | | | | % 168.27/23.90 | | | | | | | | REDUCE: (133), (260) imply: % 168.27/23.90 | | | | | | | | (264) leq(n0, n4) % 168.27/23.90 | | | | | | | | % 168.27/23.90 | | | | | | | | GROUND_INST: instantiating (58) with n0, n4, all_74_0, % 168.27/23.90 | | | | | | | | simplifying with (12), (114), (191), (262), (264) % 168.27/23.90 | | | | | | | | gives: % 168.27/23.90 | | | | | | | | (265) ~ leq(n4, all_74_13) | ~ leq(n0, all_74_13) | % 168.27/23.90 | | | | | | | | (a_select3(q_ds1_filter, n4, n0) = all_74_0 & % 168.27/23.90 | | | | | | | | $i(all_74_0)) % 168.27/23.90 | | | | | | | | % 168.27/23.90 | | | | | | | | BETA: splitting (265) gives: % 168.27/23.90 | | | | | | | | % 168.27/23.90 | | | | | | | | Case 1: % 168.27/23.90 | | | | | | | | | % 168.27/23.90 | | | | | | | | | (266) ~ leq(n0, all_74_13) % 168.27/23.90 | | | | | | | | | % 168.27/23.90 | | | | | | | | | REDUCE: (130), (266) imply: % 168.27/23.90 | | | | | | | | | (267) ~ leq(n0, n5) % 168.27/23.90 | | | | | | | | | % 168.27/23.90 | | | | | | | | | PRED_UNIFY: (190), (267) imply: % 168.27/23.90 | | | | | | | | | (268) $false % 168.27/23.90 | | | | | | | | | % 168.27/23.90 | | | | | | | | | CLOSE: (268) is inconsistent. % 168.27/23.90 | | | | | | | | | % 168.27/23.90 | | | | | | | | Case 2: % 168.27/23.90 | | | | | | | | | % 168.27/23.90 | | | | | | | | | (269) ~ leq(n4, all_74_13) | (a_select3(q_ds1_filter, n4, % 168.27/23.90 | | | | | | | | | n0) = all_74_0 & $i(all_74_0)) % 168.27/23.90 | | | | | | | | | % 168.27/23.90 | | | | | | | | | BETA: splitting (269) gives: % 168.27/23.90 | | | | | | | | | % 168.27/23.90 | | | | | | | | | Case 1: % 168.27/23.90 | | | | | | | | | | % 168.27/23.90 | | | | | | | | | | (270) ~ leq(n4, all_74_13) % 168.27/23.90 | | | | | | | | | | % 168.27/23.90 | | | | | | | | | | REDUCE: (130), (270) imply: % 168.27/23.90 | | | | | | | | | | (271) ~ leq(n4, n5) % 168.27/23.90 | | | | | | | | | | % 168.27/23.90 | | | | | | | | | | PRED_UNIFY: (263), (271) imply: % 168.27/23.90 | | | | | | | | | | (272) $false % 168.27/23.90 | | | | | | | | | | % 168.27/23.90 | | | | | | | | | | CLOSE: (272) is inconsistent. % 168.27/23.90 | | | | | | | | | | % 168.27/23.90 | | | | | | | | | Case 2: % 168.27/23.90 | | | | | | | | | | % 168.27/23.90 | | | | | | | | | | (273) a_select3(q_ds1_filter, n4, n0) = all_74_0 & % 168.27/23.90 | | | | | | | | | | $i(all_74_0) % 168.27/23.90 | | | | | | | | | | % 168.27/23.90 | | | | | | | | | | ALPHA: (273) implies: % 168.27/23.90 | | | | | | | | | | (274) a_select3(q_ds1_filter, n4, n0) = all_74_0 % 168.27/23.90 | | | | | | | | | | % 168.27/23.90 | | | | | | | | | | REF_CLOSE: (17), (132), (261), (274) are inconsistent by % 168.27/23.90 | | | | | | | | | | sub-proof #23. % 168.27/23.90 | | | | | | | | | | % 168.27/23.90 | | | | | | | | | End of split % 168.27/23.90 | | | | | | | | | % 168.27/23.90 | | | | | | | | End of split % 168.27/23.90 | | | | | | | | % 168.27/23.90 | | | | | | | End of split % 168.27/23.90 | | | | | | | % 168.27/23.90 | | | | | | End of split % 168.27/23.90 | | | | | | % 168.27/23.90 | | | | | Case 2: % 168.27/23.90 | | | | | | % 168.27/23.90 | | | | | | (275) all_74_3 = n5 % 168.27/23.90 | | | | | | % 168.27/23.90 | | | | | | REDUCE: (189), (275) imply: % 168.27/23.90 | | | | | | (276) a_select3(q_ds1_filter, n5, n0) = all_74_1 % 168.27/23.90 | | | | | | % 168.27/23.90 | | | | | | REDUCE: (188), (275) imply: % 168.27/23.90 | | | | | | (277) a_select3(q_ds1_filter, n0, n5) = all_74_0 % 168.27/23.90 | | | | | | % 168.27/23.90 | | | | | | REDUCE: (140), (275) imply: % 168.27/23.90 | | | | | | (278) leq(n5, n5) % 168.27/23.90 | | | | | | % 168.27/23.90 | | | | | | GROUND_INST: instantiating (58) with n0, n5, all_74_0, simplifying % 168.27/23.90 | | | | | | with (12), (117), (190), (191), (277) gives: % 168.27/23.90 | | | | | | (279) ~ leq(n5, all_74_13) | ~ leq(n0, all_74_13) | % 168.27/23.90 | | | | | | (a_select3(q_ds1_filter, n5, n0) = all_74_0 & $i(all_74_0)) % 168.27/23.90 | | | | | | % 168.27/23.90 | | | | | | BETA: splitting (279) gives: % 168.27/23.90 | | | | | | % 168.27/23.90 | | | | | | Case 1: % 168.27/23.90 | | | | | | | % 168.27/23.90 | | | | | | | (280) ~ leq(n0, all_74_13) % 168.27/23.90 | | | | | | | % 168.27/23.90 | | | | | | | REDUCE: (130), (280) imply: % 168.27/23.90 | | | | | | | (281) ~ leq(n0, n5) % 168.27/23.90 | | | | | | | % 168.27/23.90 | | | | | | | PRED_UNIFY: (190), (281) imply: % 168.27/23.90 | | | | | | | (282) $false % 168.27/23.90 | | | | | | | % 168.27/23.90 | | | | | | | CLOSE: (282) is inconsistent. % 168.27/23.90 | | | | | | | % 168.27/23.90 | | | | | | Case 2: % 168.27/23.90 | | | | | | | % 168.27/23.90 | | | | | | | (283) ~ leq(n5, all_74_13) | (a_select3(q_ds1_filter, n5, n0) % 168.27/23.90 | | | | | | | = all_74_0 & $i(all_74_0)) % 168.27/23.90 | | | | | | | % 168.27/23.90 | | | | | | | BETA: splitting (283) gives: % 168.27/23.90 | | | | | | | % 168.27/23.90 | | | | | | | Case 1: % 168.27/23.90 | | | | | | | | % 168.27/23.90 | | | | | | | | (284) ~ leq(n5, all_74_13) % 168.27/23.90 | | | | | | | | % 168.27/23.90 | | | | | | | | REDUCE: (130), (284) imply: % 168.27/23.90 | | | | | | | | (285) ~ leq(n5, n5) % 168.27/23.90 | | | | | | | | % 168.27/23.90 | | | | | | | | PRED_UNIFY: (278), (285) imply: % 168.27/23.90 | | | | | | | | (286) $false % 168.27/23.90 | | | | | | | | % 168.27/23.90 | | | | | | | | CLOSE: (286) is inconsistent. % 168.27/23.90 | | | | | | | | % 168.27/23.90 | | | | | | | Case 2: % 168.27/23.90 | | | | | | | | % 168.27/23.90 | | | | | | | | (287) a_select3(q_ds1_filter, n5, n0) = all_74_0 & % 168.27/23.90 | | | | | | | | $i(all_74_0) % 168.27/23.90 | | | | | | | | % 168.27/23.90 | | | | | | | | ALPHA: (287) implies: % 168.27/23.90 | | | | | | | | (288) a_select3(q_ds1_filter, n5, n0) = all_74_0 % 168.27/23.90 | | | | | | | | % 168.27/23.90 | | | | | | | | REF_CLOSE: (17), (132), (276), (288) are inconsistent by % 168.27/23.90 | | | | | | | | sub-proof #22. % 168.27/23.90 | | | | | | | | % 168.27/23.90 | | | | | | | End of split % 168.27/23.90 | | | | | | | % 168.27/23.90 | | | | | | End of split % 168.27/23.90 | | | | | | % 168.27/23.90 | | | | | End of split % 168.27/23.90 | | | | | % 168.27/23.90 | | | | Case 2: % 168.27/23.90 | | | | | % 168.27/23.90 | | | | | (289) all_74_3 = n0 % 168.27/23.90 | | | | | % 168.27/23.90 | | | | | REDUCE: (189), (289) imply: % 168.27/23.90 | | | | | (290) a_select3(q_ds1_filter, n0, n0) = all_74_1 % 168.27/23.90 | | | | | % 168.27/23.90 | | | | | REDUCE: (188), (289) imply: % 168.27/23.90 | | | | | (291) a_select3(q_ds1_filter, n0, n0) = all_74_0 % 168.27/23.90 | | | | | % 168.27/23.90 | | | | | GROUND_INST: instantiating (17) with all_74_1, all_74_0, n0, n0, % 168.27/23.90 | | | | | q_ds1_filter, simplifying with (290), (291) gives: % 168.27/23.90 | | | | | (292) all_74_0 = all_74_1 % 168.27/23.90 | | | | | % 168.27/23.90 | | | | | REDUCE: (132), (292) imply: % 168.27/23.90 | | | | | (293) $false % 168.27/23.90 | | | | | % 168.27/23.90 | | | | | CLOSE: (293) is inconsistent. % 168.27/23.90 | | | | | % 168.27/23.90 | | | | End of split % 168.27/23.90 | | | | % 168.27/23.90 | | | End of split % 168.27/23.90 | | | % 168.27/23.90 | | End of split % 168.27/23.90 | | % 168.27/23.90 | Case 2: % 168.27/23.90 | | % 168.27/23.90 | | (294) ( ~ (all_74_4 = all_74_5) & a_select3(r_ds1_filter, all_74_6, % 168.27/23.90 | | all_74_7) = all_74_4 & a_select3(r_ds1_filter, all_74_7, % 168.27/23.90 | | all_74_6) = all_74_5 & $i(all_74_4) & $i(all_74_5) & % 168.27/23.90 | | leq(all_74_6, all_74_12) & leq(all_74_7, all_74_12) & leq(n0, % 168.27/23.90 | | all_74_6) & leq(n0, all_74_7)) | ( ~ (all_74_8 = all_74_9) & % 168.27/23.90 | | a_select3(pminus_ds1_filter, all_74_10, all_74_11) = all_74_8 & % 168.27/23.90 | | a_select3(pminus_ds1_filter, all_74_11, all_74_10) = all_74_9 & % 168.27/23.90 | | $i(all_74_8) & $i(all_74_9) & leq(all_74_10, all_74_13) & % 168.27/23.90 | | leq(all_74_11, all_74_13) & leq(n0, all_74_10) & leq(n0, % 168.27/23.90 | | all_74_11)) % 168.27/23.91 | | % 168.27/23.91 | | BETA: splitting (294) gives: % 168.27/23.91 | | % 168.27/23.91 | | Case 1: % 168.27/23.91 | | | % 168.27/23.91 | | | (295) ~ (all_74_4 = all_74_5) & a_select3(r_ds1_filter, all_74_6, % 168.27/23.91 | | | all_74_7) = all_74_4 & a_select3(r_ds1_filter, all_74_7, % 168.27/23.91 | | | all_74_6) = all_74_5 & $i(all_74_4) & $i(all_74_5) & % 168.27/23.91 | | | leq(all_74_6, all_74_12) & leq(all_74_7, all_74_12) & leq(n0, % 168.27/23.91 | | | all_74_6) & leq(n0, all_74_7) % 168.27/23.91 | | | % 168.27/23.91 | | | ALPHA: (295) implies: % 168.27/23.91 | | | (296) ~ (all_74_4 = all_74_5) % 168.27/23.91 | | | (297) leq(n0, all_74_7) % 168.27/23.91 | | | (298) leq(n0, all_74_6) % 168.27/23.91 | | | (299) leq(all_74_7, all_74_12) % 168.27/23.91 | | | (300) leq(all_74_6, all_74_12) % 168.27/23.91 | | | (301) a_select3(r_ds1_filter, all_74_7, all_74_6) = all_74_5 % 168.27/23.91 | | | (302) a_select3(r_ds1_filter, all_74_6, all_74_7) = all_74_4 % 168.27/23.91 | | | % 168.27/23.91 | | | REDUCE: (129), (300) imply: % 168.27/23.91 | | | (303) leq(all_74_6, n2) % 168.27/23.91 | | | % 168.27/23.91 | | | REDUCE: (129), (299) imply: % 168.27/23.91 | | | (304) leq(all_74_7, n2) % 168.27/23.91 | | | % 168.27/23.91 | | | GROUND_INST: instantiating (leq_gt2) with n0, all_74_7, simplifying with % 168.27/23.91 | | | (12), (51), (297) gives: % 168.27/23.91 | | | (305) all_74_7 = n0 | gt(all_74_7, n0) % 168.27/23.91 | | | % 168.27/23.91 | | | GROUND_INST: instantiating (leq_gt2) with n0, all_74_6, simplifying with % 168.27/23.91 | | | (12), (52), (298) gives: % 168.27/23.91 | | | (306) all_74_6 = n0 | gt(all_74_6, n0) % 168.27/23.91 | | | % 168.27/23.91 | | | GROUND_INST: instantiating (5) with all_74_7, simplifying with (51), % 168.27/23.91 | | | (297), (304) gives: % 168.27/23.91 | | | (307) all_74_7 = n2 | all_74_7 = n1 | all_74_7 = n0 % 168.27/23.91 | | | % 168.27/23.91 | | | GROUND_INST: instantiating (leq_gt2) with all_74_7, n2, simplifying with % 168.27/23.91 | | | (51), (96), (304) gives: % 168.27/23.91 | | | (308) all_74_7 = n2 | gt(n2, all_74_7) % 168.27/23.91 | | | % 168.27/23.91 | | | GROUND_INST: instantiating (5) with all_74_6, simplifying with (52), % 168.27/23.91 | | | (298), (303) gives: % 168.27/23.91 | | | (309) all_74_6 = n2 | all_74_6 = n1 | all_74_6 = n0 % 168.27/23.91 | | | % 168.27/23.91 | | | GROUND_INST: instantiating (leq_gt2) with all_74_6, n2, simplifying with % 168.27/23.91 | | | (52), (96), (303) gives: % 168.27/23.91 | | | (310) all_74_6 = n2 | gt(n2, all_74_6) % 168.27/23.91 | | | % 168.27/23.91 | | | BETA: splitting (305) gives: % 168.27/23.91 | | | % 168.27/23.91 | | | Case 1: % 168.27/23.91 | | | | % 168.27/23.91 | | | | (311) gt(all_74_7, n0) % 168.27/23.91 | | | | % 168.27/23.91 | | | | BETA: splitting (306) gives: % 168.27/23.91 | | | | % 168.27/23.91 | | | | Case 1: % 168.27/23.91 | | | | | % 168.27/23.91 | | | | | (312) gt(all_74_6, n0) % 168.27/23.91 | | | | | % 168.27/23.91 | | | | | BETA: splitting (310) gives: % 168.27/23.91 | | | | | % 168.27/23.91 | | | | | Case 1: % 168.27/23.91 | | | | | | % 168.27/23.91 | | | | | | (313) gt(n2, all_74_6) % 168.27/23.91 | | | | | | % 168.27/23.91 | | | | | | GROUND_INST: instantiating (1) with all_74_6, n2, n1, simplifying % 168.27/23.91 | | | | | | with (52), (96), (118), (313) gives: % 168.27/23.91 | | | | | | (314) leq(all_74_6, n1) % 168.27/23.91 | | | | | | % 168.27/23.91 | | | | | | GROUND_INST: instantiating (4) with all_74_6, simplifying with (52), % 168.27/23.91 | | | | | | (298), (314) gives: % 168.27/23.91 | | | | | | (315) all_74_6 = n1 | all_74_6 = n0 % 168.27/23.91 | | | | | | % 168.27/23.91 | | | | | | BETA: splitting (308) gives: % 168.27/23.91 | | | | | | % 168.27/23.91 | | | | | | Case 1: % 168.27/23.91 | | | | | | | % 168.27/23.91 | | | | | | | (316) gt(n2, all_74_7) % 168.27/23.91 | | | | | | | % 168.27/23.91 | | | | | | | GROUND_INST: instantiating (1) with all_74_7, n2, n1, simplifying % 168.27/23.91 | | | | | | | with (51), (96), (118), (316) gives: % 168.27/23.91 | | | | | | | (317) leq(all_74_7, n1) % 168.27/23.91 | | | | | | | % 168.27/23.91 | | | | | | | BETA: splitting (307) gives: % 168.27/23.91 | | | | | | | % 168.27/23.91 | | | | | | | Case 1: % 168.27/23.91 | | | | | | | | % 168.27/23.91 | | | | | | | | (318) all_74_7 = n0 % 168.27/23.91 | | | | | | | | % 168.27/23.91 | | | | | | | | REF_CLOSE: (51), (311), (318), (irreflexivity_gt) are % 168.27/23.91 | | | | | | | | inconsistent by sub-proof #20. % 168.27/23.91 | | | | | | | | % 168.27/23.91 | | | | | | | Case 2: % 168.27/23.91 | | | | | | | | % 168.27/23.91 | | | | | | | | (319) ~ (all_74_7 = n0) % 168.27/23.91 | | | | | | | | % 168.27/23.91 | | | | | | | | BETA: splitting (309) gives: % 168.27/23.91 | | | | | | | | % 168.27/23.91 | | | | | | | | Case 1: % 168.27/23.91 | | | | | | | | | % 168.27/23.91 | | | | | | | | | (320) all_74_6 = n0 % 168.27/23.91 | | | | | | | | | % 168.27/23.91 | | | | | | | | | REF_CLOSE: (52), (312), (320), (irreflexivity_gt) are % 168.27/23.91 | | | | | | | | | inconsistent by sub-proof #19. % 168.27/23.91 | | | | | | | | | % 168.27/23.91 | | | | | | | | Case 2: % 168.27/23.91 | | | | | | | | | % 168.27/23.91 | | | | | | | | | (321) ~ (all_74_6 = n0) % 168.27/23.91 | | | | | | | | | % 168.27/23.91 | | | | | | | | | BETA: splitting (315) gives: % 168.27/23.91 | | | | | | | | | % 168.27/23.91 | | | | | | | | | Case 1: % 168.27/23.91 | | | | | | | | | | % 168.27/23.91 | | | | | | | | | | (322) all_74_6 = n0 % 168.27/23.91 | | | | | | | | | | % 168.27/23.91 | | | | | | | | | | REDUCE: (321), (322) imply: % 168.27/23.91 | | | | | | | | | | (323) $false % 168.27/23.91 | | | | | | | | | | % 168.27/23.91 | | | | | | | | | | CLOSE: (323) is inconsistent. % 168.27/23.91 | | | | | | | | | | % 168.27/23.91 | | | | | | | | | Case 2: % 168.27/23.91 | | | | | | | | | | % 168.27/23.91 | | | | | | | | | | (324) all_74_6 = n1 % 168.27/23.91 | | | | | | | | | | % 168.27/23.91 | | | | | | | | | | REDUCE: (302), (324) imply: % 168.27/23.91 | | | | | | | | | | (325) a_select3(r_ds1_filter, n1, all_74_7) = all_74_4 % 168.27/23.91 | | | | | | | | | | % 168.27/23.91 | | | | | | | | | | REDUCE: (301), (324) imply: % 168.27/23.91 | | | | | | | | | | (326) a_select3(r_ds1_filter, all_74_7, n1) = all_74_5 % 168.27/23.91 | | | | | | | | | | % 168.27/23.91 | | | | | | | | | | GROUND_INST: instantiating (4) with all_74_7, simplifying with % 168.27/23.91 | | | | | | | | | | (51), (297), (317) gives: % 168.27/23.91 | | | | | | | | | | (327) all_74_7 = n1 | all_74_7 = n0 % 168.27/23.91 | | | | | | | | | | % 168.27/23.91 | | | | | | | | | | BETA: splitting (327) gives: % 168.27/23.91 | | | | | | | | | | % 168.27/23.91 | | | | | | | | | | Case 1: % 168.27/23.91 | | | | | | | | | | | % 168.27/23.91 | | | | | | | | | | | (328) all_74_7 = n0 % 168.27/23.91 | | | | | | | | | | | % 168.27/23.91 | | | | | | | | | | | REDUCE: (319), (328) imply: % 168.27/23.91 | | | | | | | | | | | (329) $false % 168.27/23.91 | | | | | | | | | | | % 168.27/23.91 | | | | | | | | | | | CLOSE: (329) is inconsistent. % 168.27/23.91 | | | | | | | | | | | % 168.27/23.91 | | | | | | | | | | Case 2: % 168.27/23.91 | | | | | | | | | | | % 168.27/23.91 | | | | | | | | | | | (330) all_74_7 = n1 % 168.27/23.91 | | | | | | | | | | | % 168.27/23.91 | | | | | | | | | | | REDUCE: (326), (330) imply: % 168.27/23.91 | | | | | | | | | | | (331) a_select3(r_ds1_filter, n1, n1) = all_74_5 % 168.27/23.91 | | | | | | | | | | | % 168.27/23.91 | | | | | | | | | | | REDUCE: (325), (330) imply: % 168.27/23.91 | | | | | | | | | | | (332) a_select3(r_ds1_filter, n1, n1) = all_74_4 % 168.27/23.91 | | | | | | | | | | | % 168.27/23.91 | | | | | | | | | | | GROUND_INST: instantiating (17) with all_74_5, all_74_4, n1, % 168.27/23.91 | | | | | | | | | | | n1, r_ds1_filter, simplifying with (331), (332) % 168.27/23.91 | | | | | | | | | | | gives: % 168.27/23.91 | | | | | | | | | | | (333) all_74_4 = all_74_5 % 168.27/23.91 | | | | | | | | | | | % 168.27/23.91 | | | | | | | | | | | REDUCE: (296), (333) imply: % 168.27/23.91 | | | | | | | | | | | (334) $false % 168.27/23.91 | | | | | | | | | | | % 168.27/23.91 | | | | | | | | | | | CLOSE: (334) is inconsistent. % 168.27/23.91 | | | | | | | | | | | % 168.27/23.91 | | | | | | | | | | End of split % 168.27/23.91 | | | | | | | | | | % 168.27/23.91 | | | | | | | | | End of split % 168.27/23.91 | | | | | | | | | % 168.27/23.91 | | | | | | | | End of split % 168.27/23.91 | | | | | | | | % 168.27/23.91 | | | | | | | End of split % 168.27/23.91 | | | | | | | % 168.27/23.91 | | | | | | Case 2: % 168.27/23.91 | | | | | | | % 168.27/23.91 | | | | | | | (335) all_74_7 = n2 % 168.27/23.91 | | | | | | | % 168.27/23.91 | | | | | | | REDUCE: (302), (335) imply: % 168.27/23.91 | | | | | | | (336) a_select3(r_ds1_filter, all_74_6, n2) = all_74_4 % 168.27/23.91 | | | | | | | % 168.27/23.91 | | | | | | | REDUCE: (301), (335) imply: % 168.27/23.91 | | | | | | | (337) a_select3(r_ds1_filter, n2, all_74_6) = all_74_5 % 168.27/23.91 | | | | | | | % 168.27/23.91 | | | | | | | REDUCE: (304), (335) imply: % 168.27/23.91 | | | | | | | (338) leq(n2, n2) % 168.27/23.91 | | | | | | | % 168.27/23.91 | | | | | | | REDUCE: (297), (335) imply: % 168.27/23.91 | | | | | | | (339) leq(n0, n2) % 168.27/23.91 | | | | | | | % 168.27/23.91 | | | | | | | BETA: splitting (309) gives: % 168.27/23.91 | | | | | | | % 168.27/23.91 | | | | | | | Case 1: % 168.27/23.91 | | | | | | | | % 168.27/23.91 | | | | | | | | (340) all_74_6 = n0 % 168.27/23.91 | | | | | | | | % 168.27/23.91 | | | | | | | | REF_CLOSE: (52), (312), (340), (irreflexivity_gt) are % 168.27/23.91 | | | | | | | | inconsistent by sub-proof #19. % 168.27/23.91 | | | | | | | | % 168.27/23.91 | | | | | | | Case 2: % 168.27/23.91 | | | | | | | | % 168.27/23.91 | | | | | | | | (341) ~ (all_74_6 = n0) % 168.27/23.91 | | | | | | | | % 168.27/23.91 | | | | | | | | REF_CLOSE: (17), (52), (59), (96), (129), (296), (298), (303), % 168.27/23.91 | | | | | | | | (315), (336), (337), (338), (339), (341) are % 168.27/23.91 | | | | | | | | inconsistent by sub-proof #18. % 168.27/23.91 | | | | | | | | % 168.27/23.91 | | | | | | | End of split % 168.27/23.91 | | | | | | | % 168.27/23.91 | | | | | | End of split % 168.27/23.91 | | | | | | % 168.27/23.91 | | | | | Case 2: % 168.27/23.91 | | | | | | % 168.27/23.91 | | | | | | (342) all_74_6 = n2 % 168.27/23.91 | | | | | | % 168.27/23.91 | | | | | | REDUCE: (302), (342) imply: % 168.27/23.91 | | | | | | (343) a_select3(r_ds1_filter, n2, all_74_7) = all_74_4 % 168.27/23.91 | | | | | | % 168.27/23.91 | | | | | | REDUCE: (301), (342) imply: % 168.27/23.91 | | | | | | (344) a_select3(r_ds1_filter, all_74_7, n2) = all_74_5 % 168.27/23.91 | | | | | | % 168.27/23.91 | | | | | | REDUCE: (303), (342) imply: % 168.27/23.91 | | | | | | (345) leq(n2, n2) % 168.27/23.91 | | | | | | % 168.27/23.91 | | | | | | REDUCE: (298), (342) imply: % 168.27/23.91 | | | | | | (346) leq(n0, n2) % 168.27/23.91 | | | | | | % 168.27/23.91 | | | | | | BETA: splitting (308) gives: % 168.27/23.91 | | | | | | % 168.27/23.91 | | | | | | Case 1: % 168.27/23.91 | | | | | | | % 168.27/23.91 | | | | | | | (347) gt(n2, all_74_7) % 168.27/23.91 | | | | | | | % 168.27/23.91 | | | | | | | GROUND_INST: instantiating (1) with all_74_7, n2, n1, simplifying % 168.27/23.91 | | | | | | | with (51), (96), (118), (347) gives: % 168.27/23.91 | | | | | | | (348) leq(all_74_7, n1) % 168.27/23.92 | | | | | | | % 168.27/23.92 | | | | | | | GROUND_INST: instantiating (4) with all_74_7, simplifying with % 168.27/23.92 | | | | | | | (51), (297), (348) gives: % 168.27/23.92 | | | | | | | (349) all_74_7 = n1 | all_74_7 = n0 % 168.27/23.92 | | | | | | | % 168.27/23.92 | | | | | | | BETA: splitting (307) gives: % 168.27/23.92 | | | | | | | % 168.27/23.92 | | | | | | | Case 1: % 168.27/23.92 | | | | | | | | % 168.27/23.92 | | | | | | | | (350) all_74_7 = n0 % 168.27/23.92 | | | | | | | | % 168.27/23.92 | | | | | | | | REF_CLOSE: (51), (311), (350), (irreflexivity_gt) are % 168.27/23.92 | | | | | | | | inconsistent by sub-proof #20. % 168.27/23.92 | | | | | | | | % 168.27/23.92 | | | | | | | Case 2: % 168.27/23.92 | | | | | | | | % 168.27/23.92 | | | | | | | | (351) ~ (all_74_7 = n0) % 168.27/23.92 | | | | | | | | % 168.27/23.92 | | | | | | | | REF_CLOSE: (17), (51), (59), (96), (129), (296), (297), (304), % 168.27/23.92 | | | | | | | | (343), (344), (345), (346), (349), (351) are % 168.27/23.92 | | | | | | | | inconsistent by sub-proof #17. % 168.27/23.92 | | | | | | | | % 168.27/23.92 | | | | | | | End of split % 168.27/23.92 | | | | | | | % 168.27/23.92 | | | | | | Case 2: % 168.27/23.92 | | | | | | | % 168.27/23.92 | | | | | | | (352) all_74_7 = n2 % 168.27/23.92 | | | | | | | % 168.27/23.92 | | | | | | | REDUCE: (344), (352) imply: % 168.27/23.92 | | | | | | | (353) a_select3(r_ds1_filter, n2, n2) = all_74_5 % 168.27/23.92 | | | | | | | % 168.27/23.92 | | | | | | | REDUCE: (343), (352) imply: % 168.27/23.92 | | | | | | | (354) a_select3(r_ds1_filter, n2, n2) = all_74_4 % 168.27/23.92 | | | | | | | % 168.27/23.92 | | | | | | | GROUND_INST: instantiating (17) with all_74_5, all_74_4, n2, n2, % 168.27/23.92 | | | | | | | r_ds1_filter, simplifying with (353), (354) gives: % 168.27/23.92 | | | | | | | (355) all_74_4 = all_74_5 % 168.27/23.92 | | | | | | | % 168.27/23.92 | | | | | | | REDUCE: (296), (355) imply: % 168.27/23.92 | | | | | | | (356) $false % 168.27/23.92 | | | | | | | % 168.27/23.92 | | | | | | | CLOSE: (356) is inconsistent. % 168.27/23.92 | | | | | | | % 168.27/23.92 | | | | | | End of split % 168.27/23.92 | | | | | | % 168.27/23.92 | | | | | End of split % 168.27/23.92 | | | | | % 168.27/23.92 | | | | Case 2: % 168.27/23.92 | | | | | % 168.27/23.92 | | | | | (357) all_74_6 = n0 % 168.27/23.92 | | | | | (358) ~ gt(all_74_6, n0) % 168.27/23.92 | | | | | % 168.27/23.92 | | | | | REDUCE: (357), (358) imply: % 168.27/23.92 | | | | | (359) ~ gt(n0, n0) % 168.27/23.92 | | | | | % 168.27/23.92 | | | | | REF_CLOSE: (1), (4), (17), (51), (52), (59), (96), (118), (129), % 168.27/23.92 | | | | | (296), (297), (298), (301), (302), (303), (304), (306), % 168.27/23.92 | | | | | (307), (308), (309), (310), (311), (359) are inconsistent % 168.27/23.92 | | | | | by sub-proof #14. % 168.27/23.92 | | | | | % 168.27/23.92 | | | | End of split % 168.27/23.92 | | | | % 168.27/23.92 | | | Case 2: % 168.27/23.92 | | | | % 168.27/23.92 | | | | (360) all_74_7 = n0 % 168.27/23.92 | | | | (361) ~ gt(all_74_7, n0) % 168.27/23.92 | | | | % 168.27/23.92 | | | | REDUCE: (360), (361) imply: % 168.27/23.92 | | | | (362) ~ gt(n0, n0) % 168.27/23.92 | | | | % 168.27/23.92 | | | | BETA: splitting (305) gives: % 168.27/23.92 | | | | % 168.27/23.92 | | | | Case 1: % 168.27/23.92 | | | | | % 168.27/23.92 | | | | | (363) gt(all_74_7, n0) % 168.27/23.92 | | | | | % 168.27/23.92 | | | | | REF_CLOSE: (1), (4), (17), (51), (52), (59), (96), (118), (129), % 168.27/23.92 | | | | | (296), (297), (298), (301), (302), (303), (304), (306), % 168.27/23.92 | | | | | (307), (308), (309), (310), (362), (363) are inconsistent % 168.27/23.92 | | | | | by sub-proof #14. % 168.27/23.92 | | | | | % 168.27/23.92 | | | | Case 2: % 168.27/23.92 | | | | | % 168.27/23.92 | | | | | % 168.27/23.92 | | | | | REDUCE: (302), (360) imply: % 168.27/23.92 | | | | | (364) a_select3(r_ds1_filter, all_74_6, n0) = all_74_4 % 168.27/23.92 | | | | | % 168.27/23.92 | | | | | REDUCE: (301), (360) imply: % 168.27/23.92 | | | | | (365) a_select3(r_ds1_filter, n0, all_74_6) = all_74_5 % 168.27/23.92 | | | | | % 168.27/23.92 | | | | | REDUCE: (304), (360) imply: % 168.27/23.92 | | | | | (366) leq(n0, n2) % 168.27/23.92 | | | | | % 168.27/23.92 | | | | | REDUCE: (297), (360) imply: % 168.27/23.92 | | | | | (367) leq(n0, n0) % 168.27/23.92 | | | | | % 168.27/23.92 | | | | | BETA: splitting (306) gives: % 168.27/23.92 | | | | | % 168.27/23.92 | | | | | Case 1: % 168.27/23.92 | | | | | | % 168.27/23.92 | | | | | | (368) gt(all_74_6, n0) % 168.27/23.92 | | | | | | % 168.27/23.92 | | | | | | BETA: splitting (310) gives: % 168.27/23.92 | | | | | | % 168.27/23.92 | | | | | | Case 1: % 168.27/23.92 | | | | | | | % 168.27/23.92 | | | | | | | (369) gt(n2, all_74_6) % 168.27/23.92 | | | | | | | % 168.27/23.92 | | | | | | | GROUND_INST: instantiating (1) with all_74_6, n2, n1, simplifying % 168.27/23.92 | | | | | | | with (52), (96), (118), (369) gives: % 168.27/23.92 | | | | | | | (370) leq(all_74_6, n1) % 168.27/23.92 | | | | | | | % 168.27/23.92 | | | | | | | GROUND_INST: instantiating (4) with all_74_6, simplifying with % 168.27/23.92 | | | | | | | (52), (298), (370) gives: % 168.27/23.92 | | | | | | | (371) all_74_6 = n1 | all_74_6 = n0 % 168.27/23.92 | | | | | | | % 168.27/23.92 | | | | | | | BETA: splitting (309) gives: % 168.27/23.92 | | | | | | | % 168.27/23.92 | | | | | | | Case 1: % 168.27/23.92 | | | | | | | | % 168.27/23.92 | | | | | | | | (372) all_74_6 = n0 % 168.27/23.92 | | | | | | | | % 168.27/23.92 | | | | | | | | REDUCE: (368), (372) imply: % 168.27/23.92 | | | | | | | | (373) gt(n0, n0) % 168.27/23.92 | | | | | | | | % 168.27/23.92 | | | | | | | | PRED_UNIFY: (362), (373) imply: % 168.27/23.92 | | | | | | | | (374) $false % 168.27/23.92 | | | | | | | | % 168.27/23.92 | | | | | | | | CLOSE: (374) is inconsistent. % 168.27/23.92 | | | | | | | | % 168.27/23.92 | | | | | | | Case 2: % 168.27/23.92 | | | | | | | | % 168.27/23.92 | | | | | | | | (375) ~ (all_74_6 = n0) % 168.27/23.92 | | | | | | | | % 168.27/23.92 | | | | | | | | BETA: splitting (371) gives: % 168.27/23.92 | | | | | | | | % 168.27/23.92 | | | | | | | | Case 1: % 168.27/23.92 | | | | | | | | | % 168.27/23.92 | | | | | | | | | (376) all_74_6 = n0 % 168.27/23.92 | | | | | | | | | % 168.27/23.92 | | | | | | | | | REDUCE: (375), (376) imply: % 168.27/23.92 | | | | | | | | | (377) $false % 168.27/23.92 | | | | | | | | | % 168.27/23.92 | | | | | | | | | CLOSE: (377) is inconsistent. % 168.27/23.92 | | | | | | | | | % 168.27/23.92 | | | | | | | | Case 2: % 168.27/23.92 | | | | | | | | | % 168.27/23.92 | | | | | | | | | (378) all_74_6 = n1 % 168.27/23.92 | | | | | | | | | % 168.27/23.92 | | | | | | | | | REDUCE: (364), (378) imply: % 168.27/23.92 | | | | | | | | | (379) a_select3(r_ds1_filter, n1, n0) = all_74_4 % 168.27/23.92 | | | | | | | | | % 168.27/23.92 | | | | | | | | | REDUCE: (365), (378) imply: % 168.27/23.92 | | | | | | | | | (380) a_select3(r_ds1_filter, n0, n1) = all_74_5 % 168.27/23.92 | | | | | | | | | % 168.27/23.92 | | | | | | | | | REDUCE: (303), (378) imply: % 168.27/23.92 | | | | | | | | | (381) leq(n1, n2) % 168.27/23.92 | | | | | | | | | % 168.27/23.92 | | | | | | | | | REDUCE: (298), (378) imply: % 168.27/23.92 | | | | | | | | | (382) leq(n0, n1) % 168.27/23.92 | | | | | | | | | % 168.27/23.92 | | | | | | | | | GROUND_INST: instantiating (59) with n0, n1, all_74_5, % 168.27/23.92 | | | | | | | | | simplifying with (12), (80), (367), (380), (382) % 168.27/23.92 | | | | | | | | | gives: % 168.27/23.92 | | | | | | | | | (383) ~ leq(n1, all_74_12) | ~ leq(n0, all_74_12) | % 168.27/23.92 | | | | | | | | | (a_select3(r_ds1_filter, n1, n0) = all_74_5 & % 168.27/23.92 | | | | | | | | | $i(all_74_5)) % 168.27/23.92 | | | | | | | | | % 168.27/23.92 | | | | | | | | | BETA: splitting (383) gives: % 168.27/23.92 | | | | | | | | | % 168.27/23.92 | | | | | | | | | Case 1: % 168.27/23.92 | | | | | | | | | | % 168.27/23.92 | | | | | | | | | | (384) ~ leq(n0, all_74_12) % 168.27/23.92 | | | | | | | | | | % 168.27/23.92 | | | | | | | | | | REDUCE: (129), (384) imply: % 168.27/23.92 | | | | | | | | | | (385) ~ leq(n0, n2) % 168.27/23.92 | | | | | | | | | | % 168.27/23.92 | | | | | | | | | | PRED_UNIFY: (366), (385) imply: % 168.27/23.92 | | | | | | | | | | (386) $false % 168.27/23.92 | | | | | | | | | | % 168.27/23.92 | | | | | | | | | | CLOSE: (386) is inconsistent. % 168.27/23.92 | | | | | | | | | | % 168.27/23.92 | | | | | | | | | Case 2: % 168.27/23.92 | | | | | | | | | | % 168.27/23.92 | | | | | | | | | | (387) ~ leq(n1, all_74_12) | (a_select3(r_ds1_filter, % 168.27/23.92 | | | | | | | | | | n1, n0) = all_74_5 & $i(all_74_5)) % 168.27/23.92 | | | | | | | | | | % 168.27/23.92 | | | | | | | | | | BETA: splitting (387) gives: % 168.27/23.92 | | | | | | | | | | % 168.27/23.92 | | | | | | | | | | Case 1: % 168.27/23.92 | | | | | | | | | | | % 168.27/23.92 | | | | | | | | | | | (388) ~ leq(n1, all_74_12) % 168.27/23.92 | | | | | | | | | | | % 168.27/23.92 | | | | | | | | | | | REDUCE: (129), (388) imply: % 168.27/23.92 | | | | | | | | | | | (389) ~ leq(n1, n2) % 168.27/23.92 | | | | | | | | | | | % 168.27/23.92 | | | | | | | | | | | PRED_UNIFY: (381), (389) imply: % 168.27/23.92 | | | | | | | | | | | (390) $false % 168.27/23.92 | | | | | | | | | | | % 168.27/23.92 | | | | | | | | | | | CLOSE: (390) is inconsistent. % 168.27/23.92 | | | | | | | | | | | % 168.27/23.92 | | | | | | | | | | Case 2: % 168.27/23.92 | | | | | | | | | | | % 168.27/23.92 | | | | | | | | | | | (391) a_select3(r_ds1_filter, n1, n0) = all_74_5 & % 168.27/23.92 | | | | | | | | | | | $i(all_74_5) % 168.27/23.92 | | | | | | | | | | | % 168.27/23.92 | | | | | | | | | | | ALPHA: (391) implies: % 168.27/23.92 | | | | | | | | | | | (392) a_select3(r_ds1_filter, n1, n0) = all_74_5 % 168.27/23.92 | | | | | | | | | | | % 168.27/23.92 | | | | | | | | | | | REF_CLOSE: (17), (296), (379), (392) are inconsistent by % 168.27/23.92 | | | | | | | | | | | sub-proof #16. % 168.27/23.92 | | | | | | | | | | | % 168.27/23.92 | | | | | | | | | | End of split % 168.27/23.92 | | | | | | | | | | % 168.27/23.92 | | | | | | | | | End of split % 168.27/23.92 | | | | | | | | | % 168.27/23.92 | | | | | | | | End of split % 168.27/23.92 | | | | | | | | % 168.27/23.92 | | | | | | | End of split % 168.27/23.92 | | | | | | | % 168.27/23.92 | | | | | | Case 2: % 168.27/23.92 | | | | | | | % 168.27/23.92 | | | | | | | (393) all_74_6 = n2 % 168.27/23.92 | | | | | | | % 168.27/23.92 | | | | | | | REDUCE: (364), (393) imply: % 168.27/23.92 | | | | | | | (394) a_select3(r_ds1_filter, n2, n0) = all_74_4 % 168.27/23.92 | | | | | | | % 168.27/23.92 | | | | | | | REDUCE: (365), (393) imply: % 168.27/23.92 | | | | | | | (395) a_select3(r_ds1_filter, n0, n2) = all_74_5 % 168.27/23.92 | | | | | | | % 168.27/23.92 | | | | | | | REDUCE: (303), (393) imply: % 168.27/23.92 | | | | | | | (396) leq(n2, n2) % 168.27/23.92 | | | | | | | % 168.27/23.92 | | | | | | | GROUND_INST: instantiating (59) with n0, n2, all_74_5, simplifying % 168.27/23.92 | | | | | | | with (12), (96), (366), (367), (395) gives: % 168.27/23.92 | | | | | | | (397) ~ leq(n2, all_74_12) | ~ leq(n0, all_74_12) | % 168.27/23.92 | | | | | | | (a_select3(r_ds1_filter, n2, n0) = all_74_5 & % 168.27/23.92 | | | | | | | $i(all_74_5)) % 168.27/23.92 | | | | | | | % 168.27/23.92 | | | | | | | BETA: splitting (397) gives: % 168.27/23.92 | | | | | | | % 168.27/23.92 | | | | | | | Case 1: % 168.27/23.92 | | | | | | | | % 168.27/23.92 | | | | | | | | (398) ~ leq(n0, all_74_12) % 168.27/23.92 | | | | | | | | % 168.27/23.92 | | | | | | | | REDUCE: (129), (398) imply: % 168.27/23.92 | | | | | | | | (399) ~ leq(n0, n2) % 168.27/23.92 | | | | | | | | % 168.27/23.92 | | | | | | | | PRED_UNIFY: (366), (399) imply: % 168.27/23.92 | | | | | | | | (400) $false % 168.27/23.92 | | | | | | | | % 168.27/23.92 | | | | | | | | CLOSE: (400) is inconsistent. % 168.27/23.92 | | | | | | | | % 168.27/23.92 | | | | | | | Case 2: % 168.27/23.92 | | | | | | | | % 168.27/23.92 | | | | | | | | (401) ~ leq(n2, all_74_12) | (a_select3(r_ds1_filter, n2, % 168.27/23.92 | | | | | | | | n0) = all_74_5 & $i(all_74_5)) % 168.27/23.92 | | | | | | | | % 168.27/23.92 | | | | | | | | BETA: splitting (401) gives: % 168.27/23.92 | | | | | | | | % 168.27/23.92 | | | | | | | | Case 1: % 168.27/23.92 | | | | | | | | | % 168.27/23.92 | | | | | | | | | (402) ~ leq(n2, all_74_12) % 168.27/23.92 | | | | | | | | | % 168.27/23.92 | | | | | | | | | REDUCE: (129), (402) imply: % 168.27/23.92 | | | | | | | | | (403) ~ leq(n2, n2) % 168.27/23.92 | | | | | | | | | % 168.27/23.92 | | | | | | | | | PRED_UNIFY: (396), (403) imply: % 168.27/23.92 | | | | | | | | | (404) $false % 168.27/23.92 | | | | | | | | | % 168.27/23.92 | | | | | | | | | CLOSE: (404) is inconsistent. % 168.27/23.92 | | | | | | | | | % 168.27/23.92 | | | | | | | | Case 2: % 168.27/23.92 | | | | | | | | | % 168.27/23.92 | | | | | | | | | (405) a_select3(r_ds1_filter, n2, n0) = all_74_5 & % 168.27/23.92 | | | | | | | | | $i(all_74_5) % 168.27/23.92 | | | | | | | | | % 168.27/23.92 | | | | | | | | | ALPHA: (405) implies: % 168.27/23.92 | | | | | | | | | (406) a_select3(r_ds1_filter, n2, n0) = all_74_5 % 168.27/23.92 | | | | | | | | | % 168.27/23.92 | | | | | | | | | REF_CLOSE: (17), (296), (394), (406) are inconsistent by % 168.27/23.92 | | | | | | | | | sub-proof #15. % 168.27/23.92 | | | | | | | | | % 168.27/23.92 | | | | | | | | End of split % 168.27/23.92 | | | | | | | | % 168.27/23.93 | | | | | | | End of split % 168.27/23.93 | | | | | | | % 168.27/23.93 | | | | | | End of split % 168.27/23.93 | | | | | | % 168.27/23.93 | | | | | Case 2: % 168.27/23.93 | | | | | | % 168.27/23.93 | | | | | | (407) all_74_6 = n0 % 168.27/23.93 | | | | | | % 168.27/23.93 | | | | | | REDUCE: (364), (407) imply: % 168.27/23.93 | | | | | | (408) a_select3(r_ds1_filter, n0, n0) = all_74_4 % 168.27/23.93 | | | | | | % 168.27/23.93 | | | | | | REDUCE: (365), (407) imply: % 168.27/23.93 | | | | | | (409) a_select3(r_ds1_filter, n0, n0) = all_74_5 % 168.27/23.93 | | | | | | % 168.27/23.93 | | | | | | GROUND_INST: instantiating (17) with all_74_5, all_74_4, n0, n0, % 168.27/23.93 | | | | | | r_ds1_filter, simplifying with (408), (409) gives: % 168.27/23.93 | | | | | | (410) all_74_4 = all_74_5 % 168.27/23.93 | | | | | | % 168.27/23.93 | | | | | | REDUCE: (296), (410) imply: % 168.27/23.93 | | | | | | (411) $false % 168.27/23.93 | | | | | | % 168.27/23.93 | | | | | | CLOSE: (411) is inconsistent. % 168.27/23.93 | | | | | | % 168.27/23.93 | | | | | End of split % 168.27/23.93 | | | | | % 168.27/23.93 | | | | End of split % 168.27/23.93 | | | | % 168.27/23.93 | | | End of split % 168.27/23.93 | | | % 168.27/23.93 | | Case 2: % 168.27/23.93 | | | % 168.27/23.93 | | | (412) ~ (all_74_8 = all_74_9) & a_select3(pminus_ds1_filter, % 168.27/23.93 | | | all_74_10, all_74_11) = all_74_8 & a_select3(pminus_ds1_filter, % 168.27/23.93 | | | all_74_11, all_74_10) = all_74_9 & $i(all_74_8) & $i(all_74_9) % 168.27/23.93 | | | & leq(all_74_10, all_74_13) & leq(all_74_11, all_74_13) & leq(n0, % 168.27/23.93 | | | all_74_10) & leq(n0, all_74_11) % 168.27/23.93 | | | % 168.27/23.93 | | | ALPHA: (412) implies: % 168.27/23.93 | | | (413) ~ (all_74_8 = all_74_9) % 168.27/23.93 | | | (414) leq(n0, all_74_11) % 168.27/23.93 | | | (415) leq(n0, all_74_10) % 168.27/23.93 | | | (416) leq(all_74_11, all_74_13) % 168.27/23.93 | | | (417) leq(all_74_10, all_74_13) % 168.27/23.93 | | | (418) a_select3(pminus_ds1_filter, all_74_11, all_74_10) = all_74_9 % 168.27/23.93 | | | (419) a_select3(pminus_ds1_filter, all_74_10, all_74_11) = all_74_8 % 168.27/23.93 | | | % 168.27/23.93 | | | REDUCE: (130), (417) imply: % 168.27/23.93 | | | (420) leq(all_74_10, n5) % 168.27/23.93 | | | % 168.27/23.93 | | | REDUCE: (130), (416) imply: % 168.27/23.93 | | | (421) leq(all_74_11, n5) % 168.27/23.93 | | | % 168.27/23.93 | | | GROUND_INST: instantiating (leq_gt2) with n0, all_74_11, simplifying with % 168.27/23.93 | | | (12), (49), (414) gives: % 168.27/23.93 | | | (422) all_74_11 = n0 | gt(all_74_11, n0) % 168.27/23.93 | | | % 168.27/23.93 | | | GROUND_INST: instantiating (leq_gt2) with n0, all_74_10, simplifying with % 168.27/23.93 | | | (12), (50), (415) gives: % 168.27/23.93 | | | (423) all_74_10 = n0 | gt(all_74_10, n0) % 168.27/23.93 | | | % 168.27/23.93 | | | GROUND_INST: instantiating (3) with all_74_11, simplifying with (49), % 168.27/23.93 | | | (414), (421) gives: % 168.27/23.93 | | | (424) all_74_11 = n5 | all_74_11 = n4 | all_74_11 = n3 | all_74_11 = n2 % 168.27/23.93 | | | | all_74_11 = n1 | all_74_11 = n0 % 168.27/23.93 | | | % 168.27/23.93 | | | GROUND_INST: instantiating (leq_gt2) with all_74_11, n5, simplifying with % 168.27/23.93 | | | (49), (117), (421) gives: % 168.27/23.93 | | | (425) all_74_11 = n5 | gt(n5, all_74_11) % 168.27/23.93 | | | % 168.27/23.93 | | | GROUND_INST: instantiating (3) with all_74_10, simplifying with (50), % 168.27/23.93 | | | (415), (420) gives: % 168.27/23.93 | | | (426) all_74_10 = n5 | all_74_10 = n4 | all_74_10 = n3 | all_74_10 = n2 % 168.27/23.93 | | | | all_74_10 = n1 | all_74_10 = n0 % 168.27/23.93 | | | % 168.27/23.93 | | | GROUND_INST: instantiating (leq_gt2) with all_74_10, n5, simplifying with % 168.27/23.93 | | | (50), (117), (420) gives: % 168.27/23.93 | | | (427) all_74_10 = n5 | gt(n5, all_74_10) % 168.27/23.93 | | | % 168.27/23.93 | | | BETA: splitting (423) gives: % 168.27/23.93 | | | % 168.27/23.93 | | | Case 1: % 168.27/23.93 | | | | % 168.27/23.93 | | | | (428) gt(all_74_10, n0) % 168.27/23.93 | | | | % 168.27/23.93 | | | | BETA: splitting (422) gives: % 168.27/23.93 | | | | % 168.27/23.93 | | | | Case 1: % 168.27/23.93 | | | | | % 168.27/23.93 | | | | | (429) gt(all_74_11, n0) % 168.27/23.93 | | | | | % 168.27/23.93 | | | | | BETA: splitting (425) gives: % 168.27/23.93 | | | | | % 168.27/23.93 | | | | | Case 1: % 168.27/23.93 | | | | | | % 168.27/23.93 | | | | | | (430) gt(n5, all_74_11) % 168.27/23.93 | | | | | | % 168.27/23.93 | | | | | | GROUND_INST: instantiating (1) with all_74_11, n5, n4, simplifying % 168.27/23.93 | | | | | | with (49), (117), (121), (430) gives: % 168.27/23.93 | | | | | | (431) leq(all_74_11, n4) % 168.27/23.93 | | | | | | % 168.27/23.93 | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_11, n4, simplifying % 168.27/23.93 | | | | | | with (49), (114), (431) gives: % 168.27/23.93 | | | | | | (432) all_74_11 = n4 | gt(n4, all_74_11) % 168.27/23.93 | | | | | | % 168.27/23.93 | | | | | | BETA: splitting (427) gives: % 168.27/23.93 | | | | | | % 168.27/23.93 | | | | | | Case 1: % 168.27/23.93 | | | | | | | % 168.27/23.93 | | | | | | | (433) gt(n5, all_74_10) % 168.27/23.93 | | | | | | | % 168.27/23.93 | | | | | | | GROUND_INST: instantiating (1) with all_74_10, n5, n4, simplifying % 168.27/23.93 | | | | | | | with (50), (117), (121), (433) gives: % 168.27/23.93 | | | | | | | (434) leq(all_74_10, n4) % 168.27/23.93 | | | | | | | % 168.27/23.93 | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_10, n4, % 168.27/23.93 | | | | | | | simplifying with (50), (114), (434) gives: % 168.27/23.93 | | | | | | | (435) all_74_10 = n4 | gt(n4, all_74_10) % 168.27/23.93 | | | | | | | % 168.27/23.93 | | | | | | | BETA: splitting (426) gives: % 168.27/23.93 | | | | | | | % 168.27/23.93 | | | | | | | Case 1: % 168.27/23.93 | | | | | | | | % 168.27/23.93 | | | | | | | | (436) all_74_10 = n0 % 168.27/23.93 | | | | | | | | % 168.27/23.93 | | | | | | | | REDUCE: (428), (436) imply: % 168.27/23.93 | | | | | | | | (437) gt(n0, n0) % 168.27/23.93 | | | | | | | | % 168.27/23.93 | | | | | | | | GROUND_INST: instantiating (irreflexivity_gt) with n0, % 168.27/23.93 | | | | | | | | simplifying with (12), (437) gives: % 168.27/23.93 | | | | | | | | (438) $false % 168.27/23.93 | | | | | | | | % 168.27/23.93 | | | | | | | | CLOSE: (438) is inconsistent. % 168.27/23.93 | | | | | | | | % 168.27/23.93 | | | | | | | Case 2: % 168.27/23.93 | | | | | | | | % 168.27/23.93 | | | | | | | | (439) ~ (all_74_10 = n0) % 168.27/23.93 | | | | | | | | % 168.27/23.93 | | | | | | | | BETA: splitting (424) gives: % 168.27/23.93 | | | | | | | | % 168.27/23.93 | | | | | | | | Case 1: % 168.27/23.93 | | | | | | | | | % 168.27/23.93 | | | | | | | | | (440) all_74_11 = n0 % 168.27/23.93 | | | | | | | | | % 168.27/23.93 | | | | | | | | | REDUCE: (419), (440) imply: % 168.27/23.93 | | | | | | | | | (441) a_select3(pminus_ds1_filter, all_74_10, n0) = % 168.27/23.93 | | | | | | | | | all_74_8 % 168.27/23.93 | | | | | | | | | % 168.27/23.93 | | | | | | | | | REDUCE: (418), (440) imply: % 168.27/23.93 | | | | | | | | | (442) a_select3(pminus_ds1_filter, n0, all_74_10) = % 168.27/23.93 | | | | | | | | | all_74_9 % 168.27/23.93 | | | | | | | | | % 168.27/23.93 | | | | | | | | | REDUCE: (421), (440) imply: % 168.27/23.93 | | | | | | | | | (443) leq(n0, n5) % 168.27/23.93 | | | | | | | | | % 168.27/23.93 | | | | | | | | | REDUCE: (414), (440) imply: % 168.27/23.93 | | | | | | | | | (444) leq(n0, n0) % 168.27/23.93 | | | | | | | | | % 168.27/23.93 | | | | | | | | | REF_CLOSE: (1), (4), (12), (17), (50), (60), (96), (107), % 168.27/23.93 | | | | | | | | | (114), (118), (119), (120), (130), (413), (415), % 168.27/23.93 | | | | | | | | | (420), (435), (439), (441), (442), (443), (444), % 168.27/23.93 | | | | | | | | | (leq_gt2) are inconsistent by sub-proof #10. % 168.27/23.93 | | | | | | | | | % 168.27/23.93 | | | | | | | | Case 2: % 168.27/23.93 | | | | | | | | | % 168.27/23.93 | | | | | | | | | (445) ~ (all_74_11 = n0) % 168.27/23.93 | | | | | | | | | % 168.27/23.93 | | | | | | | | | REF_CLOSE: (1), (4), (17), (49), (50), (60), (96), (107), % 168.27/23.93 | | | | | | | | | (114), (118), (119), (120), (130), (413), (414), % 168.27/23.93 | | | | | | | | | (415), (418), (419), (420), (421), (432), (435), % 168.27/23.93 | | | | | | | | | (439), (445), (leq_gt2) are inconsistent by % 168.27/23.93 | | | | | | | | | sub-proof #6. % 168.27/23.93 | | | | | | | | | % 168.27/23.93 | | | | | | | | End of split % 168.27/23.93 | | | | | | | | % 168.27/23.93 | | | | | | | End of split % 168.27/23.93 | | | | | | | % 168.27/23.93 | | | | | | Case 2: % 168.27/23.93 | | | | | | | % 168.27/23.93 | | | | | | | (446) all_74_10 = n5 % 168.27/23.93 | | | | | | | % 168.27/23.93 | | | | | | | REDUCE: (419), (446) imply: % 168.27/23.93 | | | | | | | (447) a_select3(pminus_ds1_filter, n5, all_74_11) = all_74_8 % 168.27/23.93 | | | | | | | % 168.27/23.93 | | | | | | | REDUCE: (418), (446) imply: % 168.27/23.93 | | | | | | | (448) a_select3(pminus_ds1_filter, all_74_11, n5) = all_74_9 % 168.27/23.93 | | | | | | | % 168.27/23.93 | | | | | | | REDUCE: (420), (446) imply: % 168.27/23.93 | | | | | | | (449) leq(n5, n5) % 168.27/23.93 | | | | | | | % 168.27/23.93 | | | | | | | REDUCE: (415), (446) imply: % 168.27/23.93 | | | | | | | (450) leq(n0, n5) % 168.27/23.93 | | | | | | | % 168.27/23.93 | | | | | | | BETA: splitting (424) gives: % 168.27/23.93 | | | | | | | % 168.27/23.93 | | | | | | | Case 1: % 168.27/23.93 | | | | | | | | % 168.27/23.93 | | | | | | | | (451) all_74_11 = n0 % 168.27/23.93 | | | | | | | | % 168.27/23.93 | | | | | | | | REDUCE: (429), (451) imply: % 168.27/23.93 | | | | | | | | (452) gt(n0, n0) % 168.27/23.93 | | | | | | | | % 168.27/23.93 | | | | | | | | GROUND_INST: instantiating (irreflexivity_gt) with n0, % 168.27/23.93 | | | | | | | | simplifying with (12), (452) gives: % 168.27/23.93 | | | | | | | | (453) $false % 168.27/23.93 | | | | | | | | % 168.27/23.93 | | | | | | | | CLOSE: (453) is inconsistent. % 168.27/23.93 | | | | | | | | % 168.27/23.93 | | | | | | | Case 2: % 168.27/23.93 | | | | | | | | % 168.27/23.93 | | | | | | | | (454) ~ (all_74_11 = n0) % 168.27/23.93 | | | | | | | | % 168.27/23.93 | | | | | | | | REF_CLOSE: (1), (4), (17), (49), (60), (96), (107), (114), % 168.27/23.93 | | | | | | | | (117), (118), (119), (120), (130), (413), (414), % 168.27/23.93 | | | | | | | | (421), (432), (447), (448), (449), (450), (454), % 168.27/23.93 | | | | | | | | (leq_gt2) are inconsistent by sub-proof #4. % 168.27/23.93 | | | | | | | | % 168.27/23.93 | | | | | | | End of split % 168.27/23.93 | | | | | | | % 168.27/23.93 | | | | | | End of split % 168.27/23.93 | | | | | | % 168.27/23.93 | | | | | Case 2: % 168.27/23.93 | | | | | | % 168.27/23.93 | | | | | | (455) all_74_11 = n5 % 168.27/23.93 | | | | | | % 168.27/23.93 | | | | | | REDUCE: (419), (455) imply: % 168.27/23.93 | | | | | | (456) a_select3(pminus_ds1_filter, all_74_10, n5) = all_74_8 % 168.27/23.93 | | | | | | % 168.27/23.93 | | | | | | REDUCE: (418), (455) imply: % 168.27/23.93 | | | | | | (457) a_select3(pminus_ds1_filter, n5, all_74_10) = all_74_9 % 168.27/23.93 | | | | | | % 168.27/23.93 | | | | | | REDUCE: (421), (455) imply: % 168.27/23.93 | | | | | | (458) leq(n5, n5) % 168.27/23.93 | | | | | | % 168.27/23.93 | | | | | | REDUCE: (414), (455) imply: % 168.27/23.93 | | | | | | (459) leq(n0, n5) % 168.27/23.93 | | | | | | % 168.27/23.93 | | | | | | BETA: splitting (427) gives: % 168.27/23.93 | | | | | | % 168.27/23.93 | | | | | | Case 1: % 168.27/23.93 | | | | | | | % 168.27/23.93 | | | | | | | (460) gt(n5, all_74_10) % 168.27/23.93 | | | | | | | % 168.27/23.93 | | | | | | | GROUND_INST: instantiating (1) with all_74_10, n5, n4, simplifying % 168.27/23.93 | | | | | | | with (50), (117), (121), (460) gives: % 168.27/23.93 | | | | | | | (461) leq(all_74_10, n4) % 168.27/23.93 | | | | | | | % 168.27/23.93 | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_10, n4, % 168.27/23.93 | | | | | | | simplifying with (50), (114), (461) gives: % 168.27/23.93 | | | | | | | (462) all_74_10 = n4 | gt(n4, all_74_10) % 168.27/23.93 | | | | | | | % 168.27/23.93 | | | | | | | BETA: splitting (426) gives: % 168.27/23.93 | | | | | | | % 168.27/23.93 | | | | | | | Case 1: % 168.27/23.93 | | | | | | | | % 168.27/23.94 | | | | | | | | (463) all_74_10 = n0 % 168.27/23.94 | | | | | | | | % 168.27/23.94 | | | | | | | | REDUCE: (428), (463) imply: % 168.27/23.94 | | | | | | | | (464) gt(n0, n0) % 168.27/23.94 | | | | | | | | % 168.27/23.94 | | | | | | | | GROUND_INST: instantiating (irreflexivity_gt) with n0, % 168.27/23.94 | | | | | | | | simplifying with (12), (464) gives: % 168.27/23.94 | | | | | | | | (465) $false % 168.27/23.94 | | | | | | | | % 168.27/23.94 | | | | | | | | CLOSE: (465) is inconsistent. % 168.27/23.94 | | | | | | | | % 168.27/23.94 | | | | | | | Case 2: % 168.27/23.94 | | | | | | | | % 168.27/23.94 | | | | | | | | (466) ~ (all_74_10 = n0) % 168.27/23.94 | | | | | | | | % 168.27/23.94 | | | | | | | | REF_CLOSE: (1), (4), (17), (50), (60), (96), (107), (114), % 168.27/23.94 | | | | | | | | (117), (118), (119), (120), (130), (413), (415), % 168.27/23.94 | | | | | | | | (420), (456), (457), (458), (459), (462), (466), % 168.27/23.94 | | | | | | | | (leq_gt2) are inconsistent by sub-proof #3. % 168.27/23.94 | | | | | | | | % 168.27/23.94 | | | | | | | End of split % 168.27/23.94 | | | | | | | % 168.27/23.94 | | | | | | Case 2: % 168.27/23.94 | | | | | | | % 168.27/23.94 | | | | | | | (467) all_74_10 = n5 % 168.27/23.94 | | | | | | | % 168.27/23.94 | | | | | | | REDUCE: (456), (467) imply: % 168.27/23.94 | | | | | | | (468) a_select3(pminus_ds1_filter, n5, n5) = all_74_8 % 168.27/23.94 | | | | | | | % 168.27/23.94 | | | | | | | REDUCE: (457), (467) imply: % 168.27/23.94 | | | | | | | (469) a_select3(pminus_ds1_filter, n5, n5) = all_74_9 % 168.27/23.94 | | | | | | | % 168.27/23.94 | | | | | | | GROUND_INST: instantiating (17) with all_74_9, all_74_8, n5, n5, % 168.27/23.94 | | | | | | | pminus_ds1_filter, simplifying with (468), (469) % 168.27/23.94 | | | | | | | gives: % 168.27/23.94 | | | | | | | (470) all_74_8 = all_74_9 % 168.27/23.94 | | | | | | | % 168.27/23.94 | | | | | | | REDUCE: (413), (470) imply: % 168.27/23.94 | | | | | | | (471) $false % 168.27/23.94 | | | | | | | % 168.27/23.94 | | | | | | | CLOSE: (471) is inconsistent. % 168.27/23.94 | | | | | | | % 168.27/23.94 | | | | | | End of split % 168.27/23.94 | | | | | | % 168.27/23.94 | | | | | End of split % 168.27/23.94 | | | | | % 168.27/23.94 | | | | Case 2: % 168.27/23.94 | | | | | % 168.27/23.94 | | | | | (472) all_74_11 = n0 % 168.27/23.94 | | | | | (473) ~ gt(all_74_11, n0) % 168.27/23.94 | | | | | % 168.27/23.94 | | | | | REDUCE: (472), (473) imply: % 168.27/23.94 | | | | | (474) ~ gt(n0, n0) % 168.27/23.94 | | | | | % 168.27/23.94 | | | | | REF_CLOSE: (1), (4), (17), (49), (50), (60), (96), (107), (114), % 168.27/23.94 | | | | | (117), (118), (119), (120), (121), (130), (413), (414), % 168.27/23.94 | | | | | (415), (418), (419), (420), (421), (422), (424), (425), % 168.27/23.94 | | | | | (426), (427), (428), (474), (leq_gt2) are inconsistent by % 168.27/23.94 | | | | | sub-proof #1. % 168.27/23.94 | | | | | % 168.27/23.94 | | | | End of split % 168.27/23.94 | | | | % 168.27/23.94 | | | Case 2: % 168.27/23.94 | | | | % 168.27/23.94 | | | | (475) all_74_10 = n0 % 168.27/23.94 | | | | (476) ~ gt(all_74_10, n0) % 168.27/23.94 | | | | % 168.27/23.94 | | | | REDUCE: (475), (476) imply: % 168.27/23.94 | | | | (477) ~ gt(n0, n0) % 168.27/23.94 | | | | % 168.27/23.94 | | | | BETA: splitting (423) gives: % 168.27/23.94 | | | | % 168.27/23.94 | | | | Case 1: % 168.27/23.94 | | | | | % 168.27/23.94 | | | | | (478) gt(all_74_10, n0) % 168.27/23.94 | | | | | % 168.27/23.94 | | | | | REF_CLOSE: (1), (4), (17), (49), (50), (60), (96), (107), (114), % 168.27/23.94 | | | | | (117), (118), (119), (120), (121), (130), (413), (414), % 168.27/23.94 | | | | | (415), (418), (419), (420), (421), (422), (424), (425), % 168.27/23.94 | | | | | (426), (427), (477), (478), (leq_gt2) are inconsistent by % 168.27/23.94 | | | | | sub-proof #1. % 168.27/23.94 | | | | | % 168.27/23.94 | | | | Case 2: % 168.27/23.94 | | | | | % 168.27/23.94 | | | | | % 168.27/23.94 | | | | | REDUCE: (419), (475) imply: % 168.27/23.94 | | | | | (479) a_select3(pminus_ds1_filter, n0, all_74_11) = all_74_8 % 168.27/23.94 | | | | | % 168.27/23.94 | | | | | REDUCE: (418), (475) imply: % 168.27/23.94 | | | | | (480) a_select3(pminus_ds1_filter, all_74_11, n0) = all_74_9 % 168.27/23.94 | | | | | % 168.27/23.94 | | | | | REDUCE: (420), (475) imply: % 168.27/23.94 | | | | | (481) leq(n0, n5) % 168.27/23.94 | | | | | % 168.27/23.94 | | | | | REDUCE: (415), (475) imply: % 168.27/23.94 | | | | | (482) leq(n0, n0) % 168.27/23.94 | | | | | % 168.27/23.94 | | | | | BETA: splitting (422) gives: % 168.27/23.94 | | | | | % 168.27/23.94 | | | | | Case 1: % 168.27/23.94 | | | | | | % 168.27/23.94 | | | | | | (483) gt(all_74_11, n0) % 168.27/23.94 | | | | | | % 168.27/23.94 | | | | | | BETA: splitting (425) gives: % 168.27/23.94 | | | | | | % 168.27/23.94 | | | | | | Case 1: % 168.27/23.94 | | | | | | | % 168.27/23.94 | | | | | | | (484) gt(n5, all_74_11) % 168.27/23.94 | | | | | | | % 168.27/23.94 | | | | | | | GROUND_INST: instantiating (1) with all_74_11, n5, n4, simplifying % 168.27/23.94 | | | | | | | with (49), (117), (121), (484) gives: % 168.27/23.94 | | | | | | | (485) leq(all_74_11, n4) % 168.27/23.94 | | | | | | | % 168.27/23.94 | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_11, n4, % 168.27/23.94 | | | | | | | simplifying with (49), (114), (485) gives: % 168.27/23.94 | | | | | | | (486) all_74_11 = n4 | gt(n4, all_74_11) % 168.27/23.94 | | | | | | | % 168.27/23.94 | | | | | | | BETA: splitting (424) gives: % 168.27/23.94 | | | | | | | % 168.27/23.94 | | | | | | | Case 1: % 168.27/23.94 | | | | | | | | % 168.27/23.94 | | | | | | | | (487) all_74_11 = n0 % 168.27/23.94 | | | | | | | | % 168.27/23.94 | | | | | | | | REDUCE: (483), (487) imply: % 168.27/23.94 | | | | | | | | (488) gt(n0, n0) % 168.27/23.94 | | | | | | | | % 168.27/23.94 | | | | | | | | PRED_UNIFY: (477), (488) imply: % 168.27/23.94 | | | | | | | | (489) $false % 168.27/23.94 | | | | | | | | % 168.27/23.94 | | | | | | | | CLOSE: (489) is inconsistent. % 168.27/23.94 | | | | | | | | % 168.27/23.94 | | | | | | | Case 2: % 168.27/23.94 | | | | | | | | % 168.27/23.94 | | | | | | | | (490) ~ (all_74_11 = n0) % 168.27/23.94 | | | | | | | | % 168.27/23.94 | | | | | | | | BETA: splitting (486) gives: % 168.27/23.94 | | | | | | | | % 168.27/23.94 | | | | | | | | Case 1: % 168.27/23.94 | | | | | | | | | % 168.27/23.94 | | | | | | | | | (491) gt(n4, all_74_11) % 168.27/23.94 | | | | | | | | | % 168.27/23.94 | | | | | | | | | GROUND_INST: instantiating (1) with all_74_11, n4, n3, % 168.27/23.94 | | | | | | | | | simplifying with (49), (114), (120), (491) gives: % 168.27/23.94 | | | | | | | | | (492) leq(all_74_11, n3) % 168.27/23.94 | | | | | | | | | % 168.27/23.94 | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_11, n3, % 168.27/23.94 | | | | | | | | | simplifying with (49), (107), (492) gives: % 168.27/23.94 | | | | | | | | | (493) all_74_11 = n3 | gt(n3, all_74_11) % 168.27/23.94 | | | | | | | | | % 168.27/23.94 | | | | | | | | | BETA: splitting (493) gives: % 168.27/23.94 | | | | | | | | | % 168.27/23.94 | | | | | | | | | Case 1: % 168.27/23.94 | | | | | | | | | | % 168.27/23.94 | | | | | | | | | | (494) gt(n3, all_74_11) % 168.27/23.94 | | | | | | | | | | % 168.27/23.94 | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_11, n3, n2, % 168.27/23.94 | | | | | | | | | | simplifying with (49), (107), (119), (494) gives: % 168.27/23.94 | | | | | | | | | | (495) leq(all_74_11, n2) % 168.27/23.94 | | | | | | | | | | % 168.27/23.94 | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_11, n2, % 168.27/23.94 | | | | | | | | | | simplifying with (49), (96), (495) gives: % 168.27/23.94 | | | | | | | | | | (496) all_74_11 = n2 | gt(n2, all_74_11) % 168.27/23.94 | | | | | | | | | | % 168.27/23.94 | | | | | | | | | | BETA: splitting (496) gives: % 168.27/23.94 | | | | | | | | | | % 168.27/23.94 | | | | | | | | | | Case 1: % 168.27/23.94 | | | | | | | | | | | % 168.27/23.94 | | | | | | | | | | | (497) gt(n2, all_74_11) % 168.27/23.94 | | | | | | | | | | | % 168.27/23.94 | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_11, n2, n1, % 168.27/23.94 | | | | | | | | | | | simplifying with (49), (96), (118), (497) gives: % 168.27/23.94 | | | | | | | | | | | (498) leq(all_74_11, n1) % 168.27/23.94 | | | | | | | | | | | % 168.27/23.94 | | | | | | | | | | | GROUND_INST: instantiating (4) with all_74_11, simplifying with % 168.27/23.94 | | | | | | | | | | | (49), (414), (498) gives: % 168.27/23.94 | | | | | | | | | | | (499) all_74_11 = n1 | all_74_11 = n0 % 168.27/23.94 | | | | | | | | | | | % 168.27/23.94 | | | | | | | | | | | BETA: splitting (499) gives: % 168.27/23.94 | | | | | | | | | | | % 168.27/23.94 | | | | | | | | | | | Case 1: % 168.27/23.94 | | | | | | | | | | | | % 168.27/23.94 | | | | | | | | | | | | (500) all_74_11 = n0 % 168.27/23.94 | | | | | | | | | | | | % 168.27/23.94 | | | | | | | | | | | | REDUCE: (490), (500) imply: % 168.27/23.94 | | | | | | | | | | | | (501) $false % 168.27/23.94 | | | | | | | | | | | | % 168.27/23.94 | | | | | | | | | | | | CLOSE: (501) is inconsistent. % 168.27/23.94 | | | | | | | | | | | | % 168.27/23.94 | | | | | | | | | | | Case 2: % 168.27/23.94 | | | | | | | | | | | | % 168.27/23.94 | | | | | | | | | | | | (502) all_74_11 = n1 % 168.27/23.94 | | | | | | | | | | | | % 168.27/23.94 | | | | | | | | | | | | REDUCE: (480), (502) imply: % 168.27/23.94 | | | | | | | | | | | | (503) a_select3(pminus_ds1_filter, n1, n0) = all_74_9 % 168.27/23.94 | | | | | | | | | | | | % 168.27/23.94 | | | | | | | | | | | | REDUCE: (479), (502) imply: % 168.27/23.94 | | | | | | | | | | | | (504) a_select3(pminus_ds1_filter, n0, n1) = all_74_8 % 168.27/23.94 | | | | | | | | | | | | % 168.27/23.94 | | | | | | | | | | | | REDUCE: (421), (502) imply: % 168.27/23.94 | | | | | | | | | | | | (505) leq(n1, n5) % 168.27/23.94 | | | | | | | | | | | | % 168.27/23.94 | | | | | | | | | | | | REDUCE: (414), (502) imply: % 168.27/23.94 | | | | | | | | | | | | (506) leq(n0, n1) % 168.27/23.94 | | | | | | | | | | | | % 168.27/23.94 | | | | | | | | | | | | GROUND_INST: instantiating (60) with n0, n1, all_74_8, % 168.27/23.94 | | | | | | | | | | | | simplifying with (12), (80), (482), (504), (506) % 168.27/23.94 | | | | | | | | | | | | gives: % 168.27/23.94 | | | | | | | | | | | | (507) ~ leq(n1, all_74_13) | ~ leq(n0, all_74_13) | % 168.27/23.94 | | | | | | | | | | | | (a_select3(pminus_ds1_filter, n1, n0) = all_74_8 & % 168.27/23.94 | | | | | | | | | | | | $i(all_74_8)) % 168.27/23.94 | | | | | | | | | | | | % 168.27/23.94 | | | | | | | | | | | | BETA: splitting (507) gives: % 168.27/23.94 | | | | | | | | | | | | % 168.27/23.94 | | | | | | | | | | | | Case 1: % 168.27/23.94 | | | | | | | | | | | | | % 168.27/23.94 | | | | | | | | | | | | | (508) ~ leq(n0, all_74_13) % 168.27/23.94 | | | | | | | | | | | | | % 168.27/23.94 | | | | | | | | | | | | | REDUCE: (130), (508) imply: % 168.27/23.94 | | | | | | | | | | | | | (509) ~ leq(n0, n5) % 168.27/23.94 | | | | | | | | | | | | | % 168.27/23.94 | | | | | | | | | | | | | PRED_UNIFY: (481), (509) imply: % 168.27/23.94 | | | | | | | | | | | | | (510) $false % 168.27/23.94 | | | | | | | | | | | | | % 168.27/23.94 | | | | | | | | | | | | | CLOSE: (510) is inconsistent. % 168.27/23.94 | | | | | | | | | | | | | % 168.27/23.94 | | | | | | | | | | | | Case 2: % 168.27/23.94 | | | | | | | | | | | | | % 168.27/23.94 | | | | | | | | | | | | | (511) ~ leq(n1, all_74_13) | % 168.27/23.94 | | | | | | | | | | | | | (a_select3(pminus_ds1_filter, n1, n0) = all_74_8 & % 168.27/23.94 | | | | | | | | | | | | | $i(all_74_8)) % 168.27/23.94 | | | | | | | | | | | | | % 168.27/23.94 | | | | | | | | | | | | | BETA: splitting (511) gives: % 168.27/23.94 | | | | | | | | | | | | | % 168.27/23.94 | | | | | | | | | | | | | Case 1: % 168.27/23.94 | | | | | | | | | | | | | | % 168.27/23.94 | | | | | | | | | | | | | | (512) ~ leq(n1, all_74_13) % 168.27/23.94 | | | | | | | | | | | | | | % 168.27/23.94 | | | | | | | | | | | | | | REDUCE: (130), (512) imply: % 168.27/23.94 | | | | | | | | | | | | | | (513) ~ leq(n1, n5) % 168.27/23.94 | | | | | | | | | | | | | | % 168.27/23.94 | | | | | | | | | | | | | | PRED_UNIFY: (505), (513) imply: % 168.27/23.94 | | | | | | | | | | | | | | (514) $false % 168.27/23.94 | | | | | | | | | | | | | | % 168.27/23.94 | | | | | | | | | | | | | | CLOSE: (514) is inconsistent. % 168.27/23.94 | | | | | | | | | | | | | | % 168.27/23.94 | | | | | | | | | | | | | Case 2: % 168.27/23.94 | | | | | | | | | | | | | | % 168.27/23.94 | | | | | | | | | | | | | | (515) a_select3(pminus_ds1_filter, n1, n0) = all_74_8 & % 168.27/23.94 | | | | | | | | | | | | | | $i(all_74_8) % 168.27/23.94 | | | | | | | | | | | | | | % 168.27/23.94 | | | | | | | | | | | | | | ALPHA: (515) implies: % 168.27/23.94 | | | | | | | | | | | | | | (516) a_select3(pminus_ds1_filter, n1, n0) = all_74_8 % 168.27/23.94 | | | | | | | | | | | | | | % 168.27/23.94 | | | | | | | | | | | | | | REF_CLOSE: (17), (413), (503), (516) are inconsistent by % 168.27/23.94 | | | | | | | | | | | | | | sub-proof #13. % 168.27/23.94 | | | | | | | | | | | | | | % 168.27/23.94 | | | | | | | | | | | | | End of split % 168.27/23.94 | | | | | | | | | | | | | % 168.27/23.94 | | | | | | | | | | | | End of split % 168.27/23.94 | | | | | | | | | | | | % 168.27/23.94 | | | | | | | | | | | End of split % 168.27/23.94 | | | | | | | | | | | % 168.27/23.94 | | | | | | | | | | Case 2: % 168.27/23.94 | | | | | | | | | | | % 168.27/23.94 | | | | | | | | | | | (517) all_74_11 = n2 % 168.27/23.94 | | | | | | | | | | | % 168.27/23.94 | | | | | | | | | | | REDUCE: (480), (517) imply: % 168.27/23.94 | | | | | | | | | | | (518) a_select3(pminus_ds1_filter, n2, n0) = all_74_9 % 168.27/23.94 | | | | | | | | | | | % 168.27/23.94 | | | | | | | | | | | REDUCE: (479), (517) imply: % 168.27/23.94 | | | | | | | | | | | (519) a_select3(pminus_ds1_filter, n0, n2) = all_74_8 % 168.27/23.94 | | | | | | | | | | | % 168.27/23.94 | | | | | | | | | | | REDUCE: (421), (517) imply: % 168.27/23.94 | | | | | | | | | | | (520) leq(n2, n5) % 168.27/23.94 | | | | | | | | | | | % 168.27/23.94 | | | | | | | | | | | REDUCE: (414), (517) imply: % 168.27/23.94 | | | | | | | | | | | (521) leq(n0, n2) % 168.27/23.94 | | | | | | | | | | | % 168.27/23.94 | | | | | | | | | | | GROUND_INST: instantiating (60) with n0, n2, all_74_8, % 168.27/23.94 | | | | | | | | | | | simplifying with (12), (96), (482), (519), (521) % 168.27/23.94 | | | | | | | | | | | gives: % 168.27/23.95 | | | | | | | | | | | (522) ~ leq(n2, all_74_13) | ~ leq(n0, all_74_13) | % 168.27/23.95 | | | | | | | | | | | (a_select3(pminus_ds1_filter, n2, n0) = all_74_8 & % 168.27/23.95 | | | | | | | | | | | $i(all_74_8)) % 168.27/23.95 | | | | | | | | | | | % 168.27/23.95 | | | | | | | | | | | BETA: splitting (522) gives: % 168.27/23.95 | | | | | | | | | | | % 168.27/23.95 | | | | | | | | | | | Case 1: % 168.27/23.95 | | | | | | | | | | | | % 168.27/23.95 | | | | | | | | | | | | (523) ~ leq(n0, all_74_13) % 168.27/23.95 | | | | | | | | | | | | % 168.27/23.95 | | | | | | | | | | | | REDUCE: (130), (523) imply: % 168.27/23.95 | | | | | | | | | | | | (524) ~ leq(n0, n5) % 168.27/23.95 | | | | | | | | | | | | % 168.27/23.95 | | | | | | | | | | | | PRED_UNIFY: (481), (524) imply: % 168.27/23.95 | | | | | | | | | | | | (525) $false % 168.27/23.95 | | | | | | | | | | | | % 168.27/23.95 | | | | | | | | | | | | CLOSE: (525) is inconsistent. % 168.27/23.95 | | | | | | | | | | | | % 168.27/23.95 | | | | | | | | | | | Case 2: % 168.27/23.95 | | | | | | | | | | | | % 168.27/23.95 | | | | | | | | | | | | (526) ~ leq(n2, all_74_13) | % 168.27/23.95 | | | | | | | | | | | | (a_select3(pminus_ds1_filter, n2, n0) = all_74_8 & % 168.27/23.95 | | | | | | | | | | | | $i(all_74_8)) % 168.27/23.95 | | | | | | | | | | | | % 168.27/23.95 | | | | | | | | | | | | BETA: splitting (526) gives: % 168.27/23.95 | | | | | | | | | | | | % 168.27/23.95 | | | | | | | | | | | | Case 1: % 168.27/23.95 | | | | | | | | | | | | | % 168.27/23.95 | | | | | | | | | | | | | (527) ~ leq(n2, all_74_13) % 168.27/23.95 | | | | | | | | | | | | | % 168.27/23.95 | | | | | | | | | | | | | REDUCE: (130), (527) imply: % 168.27/23.95 | | | | | | | | | | | | | (528) ~ leq(n2, n5) % 168.27/23.95 | | | | | | | | | | | | | % 168.27/23.95 | | | | | | | | | | | | | PRED_UNIFY: (520), (528) imply: % 168.27/23.95 | | | | | | | | | | | | | (529) $false % 168.27/23.95 | | | | | | | | | | | | | % 168.27/23.95 | | | | | | | | | | | | | CLOSE: (529) is inconsistent. % 168.27/23.95 | | | | | | | | | | | | | % 168.27/23.95 | | | | | | | | | | | | Case 2: % 168.27/23.95 | | | | | | | | | | | | | % 168.27/23.95 | | | | | | | | | | | | | (530) a_select3(pminus_ds1_filter, n2, n0) = all_74_8 & % 168.27/23.95 | | | | | | | | | | | | | $i(all_74_8) % 168.27/23.95 | | | | | | | | | | | | | % 168.27/23.95 | | | | | | | | | | | | | ALPHA: (530) implies: % 168.27/23.95 | | | | | | | | | | | | | (531) a_select3(pminus_ds1_filter, n2, n0) = all_74_8 % 168.27/23.95 | | | | | | | | | | | | | % 168.27/23.95 | | | | | | | | | | | | | REF_CLOSE: (17), (413), (518), (531) are inconsistent by % 168.27/23.95 | | | | | | | | | | | | | sub-proof #12. % 168.27/23.95 | | | | | | | | | | | | | % 168.27/23.95 | | | | | | | | | | | | End of split % 168.27/23.95 | | | | | | | | | | | | % 168.27/23.95 | | | | | | | | | | | End of split % 168.27/23.95 | | | | | | | | | | | % 168.27/23.95 | | | | | | | | | | End of split % 168.27/23.95 | | | | | | | | | | % 168.27/23.95 | | | | | | | | | Case 2: % 168.27/23.95 | | | | | | | | | | % 168.27/23.95 | | | | | | | | | | (532) all_74_11 = n3 % 168.27/23.95 | | | | | | | | | | % 168.27/23.95 | | | | | | | | | | REDUCE: (480), (532) imply: % 168.27/23.95 | | | | | | | | | | (533) a_select3(pminus_ds1_filter, n3, n0) = all_74_9 % 168.27/23.95 | | | | | | | | | | % 168.27/23.95 | | | | | | | | | | REDUCE: (479), (532) imply: % 168.27/23.95 | | | | | | | | | | (534) a_select3(pminus_ds1_filter, n0, n3) = all_74_8 % 168.27/23.95 | | | | | | | | | | % 168.27/23.95 | | | | | | | | | | REDUCE: (421), (532) imply: % 168.27/23.95 | | | | | | | | | | (535) leq(n3, n5) % 168.27/23.95 | | | | | | | | | | % 168.27/23.95 | | | | | | | | | | REDUCE: (414), (532) imply: % 168.27/23.95 | | | | | | | | | | (536) leq(n0, n3) % 168.27/23.95 | | | | | | | | | | % 168.27/23.95 | | | | | | | | | | GROUND_INST: instantiating (60) with n0, n3, all_74_8, % 168.27/23.95 | | | | | | | | | | simplifying with (12), (107), (482), (534), (536) % 168.27/23.95 | | | | | | | | | | gives: % 168.27/23.95 | | | | | | | | | | (537) ~ leq(n3, all_74_13) | ~ leq(n0, all_74_13) | % 168.27/23.95 | | | | | | | | | | (a_select3(pminus_ds1_filter, n3, n0) = all_74_8 & % 168.27/23.95 | | | | | | | | | | $i(all_74_8)) % 168.27/23.95 | | | | | | | | | | % 168.27/23.95 | | | | | | | | | | BETA: splitting (537) gives: % 168.27/23.95 | | | | | | | | | | % 168.27/23.95 | | | | | | | | | | Case 1: % 168.27/23.95 | | | | | | | | | | | % 168.27/23.95 | | | | | | | | | | | (538) ~ leq(n0, all_74_13) % 168.27/23.95 | | | | | | | | | | | % 168.27/23.95 | | | | | | | | | | | REDUCE: (130), (538) imply: % 168.27/23.95 | | | | | | | | | | | (539) ~ leq(n0, n5) % 168.27/23.95 | | | | | | | | | | | % 168.27/23.95 | | | | | | | | | | | PRED_UNIFY: (481), (539) imply: % 168.27/23.95 | | | | | | | | | | | (540) $false % 168.27/23.95 | | | | | | | | | | | % 168.27/23.95 | | | | | | | | | | | CLOSE: (540) is inconsistent. % 168.27/23.95 | | | | | | | | | | | % 168.27/23.95 | | | | | | | | | | Case 2: % 168.27/23.95 | | | | | | | | | | | % 168.27/23.95 | | | | | | | | | | | (541) ~ leq(n3, all_74_13) | % 168.27/23.95 | | | | | | | | | | | (a_select3(pminus_ds1_filter, n3, n0) = all_74_8 & % 168.27/23.95 | | | | | | | | | | | $i(all_74_8)) % 168.27/23.95 | | | | | | | | | | | % 168.27/23.95 | | | | | | | | | | | BETA: splitting (541) gives: % 168.27/23.95 | | | | | | | | | | | % 168.27/23.95 | | | | | | | | | | | Case 1: % 168.27/23.95 | | | | | | | | | | | | % 168.27/23.95 | | | | | | | | | | | | (542) ~ leq(n3, all_74_13) % 168.27/23.95 | | | | | | | | | | | | % 168.27/23.95 | | | | | | | | | | | | REDUCE: (130), (542) imply: % 168.27/23.95 | | | | | | | | | | | | (543) ~ leq(n3, n5) % 168.27/23.95 | | | | | | | | | | | | % 168.27/23.95 | | | | | | | | | | | | PRED_UNIFY: (535), (543) imply: % 168.27/23.95 | | | | | | | | | | | | (544) $false % 168.27/23.95 | | | | | | | | | | | | % 168.27/23.95 | | | | | | | | | | | | CLOSE: (544) is inconsistent. % 168.27/23.95 | | | | | | | | | | | | % 168.27/23.95 | | | | | | | | | | | Case 2: % 168.27/23.95 | | | | | | | | | | | | % 168.27/23.95 | | | | | | | | | | | | (545) a_select3(pminus_ds1_filter, n3, n0) = all_74_8 & % 168.27/23.95 | | | | | | | | | | | | $i(all_74_8) % 168.27/23.95 | | | | | | | | | | | | % 168.27/23.95 | | | | | | | | | | | | ALPHA: (545) implies: % 168.27/23.95 | | | | | | | | | | | | (546) a_select3(pminus_ds1_filter, n3, n0) = all_74_8 % 168.27/23.95 | | | | | | | | | | | | % 168.27/23.95 | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_74_9, all_74_8, n0, % 168.27/23.95 | | | | | | | | | | | | n3, pminus_ds1_filter, simplifying with (533), % 168.27/23.95 | | | | | | | | | | | | (546) gives: % 168.27/23.95 | | | | | | | | | | | | (547) all_74_8 = all_74_9 % 168.27/23.95 | | | | | | | | | | | | % 168.27/23.95 | | | | | | | | | | | | REDUCE: (413), (547) imply: % 168.27/23.95 | | | | | | | | | | | | (548) $false % 168.27/23.95 | | | | | | | | | | | | % 168.27/23.95 | | | | | | | | | | | | CLOSE: (548) is inconsistent. % 168.27/23.95 | | | | | | | | | | | | % 168.27/23.95 | | | | | | | | | | | End of split % 168.27/23.95 | | | | | | | | | | | % 168.27/23.95 | | | | | | | | | | End of split % 168.27/23.95 | | | | | | | | | | % 168.27/23.95 | | | | | | | | | End of split % 168.27/23.95 | | | | | | | | | % 168.27/23.95 | | | | | | | | Case 2: % 168.27/23.95 | | | | | | | | | % 168.27/23.95 | | | | | | | | | (549) all_74_11 = n4 % 168.27/23.95 | | | | | | | | | % 168.27/23.95 | | | | | | | | | REDUCE: (480), (549) imply: % 168.27/23.95 | | | | | | | | | (550) a_select3(pminus_ds1_filter, n4, n0) = all_74_9 % 168.27/23.95 | | | | | | | | | % 168.27/23.95 | | | | | | | | | REDUCE: (479), (549) imply: % 168.27/23.95 | | | | | | | | | (551) a_select3(pminus_ds1_filter, n0, n4) = all_74_8 % 168.27/23.95 | | | | | | | | | % 168.27/23.95 | | | | | | | | | REDUCE: (421), (549) imply: % 168.27/23.95 | | | | | | | | | (552) leq(n4, n5) % 168.27/23.95 | | | | | | | | | % 168.27/23.95 | | | | | | | | | REDUCE: (414), (549) imply: % 168.27/23.95 | | | | | | | | | (553) leq(n0, n4) % 168.27/23.95 | | | | | | | | | % 168.27/23.95 | | | | | | | | | GROUND_INST: instantiating (60) with n0, n4, all_74_8, % 168.27/23.95 | | | | | | | | | simplifying with (12), (114), (482), (551), (553) % 168.27/23.95 | | | | | | | | | gives: % 168.27/23.95 | | | | | | | | | (554) ~ leq(n4, all_74_13) | ~ leq(n0, all_74_13) | % 168.27/23.95 | | | | | | | | | (a_select3(pminus_ds1_filter, n4, n0) = all_74_8 & % 168.27/23.95 | | | | | | | | | $i(all_74_8)) % 168.27/23.95 | | | | | | | | | % 168.27/23.95 | | | | | | | | | BETA: splitting (554) gives: % 168.27/23.95 | | | | | | | | | % 168.27/23.95 | | | | | | | | | Case 1: % 168.27/23.95 | | | | | | | | | | % 168.27/23.95 | | | | | | | | | | (555) ~ leq(n0, all_74_13) % 168.27/23.95 | | | | | | | | | | % 168.27/23.95 | | | | | | | | | | REDUCE: (130), (555) imply: % 168.27/23.95 | | | | | | | | | | (556) ~ leq(n0, n5) % 168.27/23.95 | | | | | | | | | | % 168.27/23.95 | | | | | | | | | | PRED_UNIFY: (481), (556) imply: % 168.27/23.95 | | | | | | | | | | (557) $false % 168.27/23.95 | | | | | | | | | | % 168.27/23.95 | | | | | | | | | | CLOSE: (557) is inconsistent. % 168.27/23.95 | | | | | | | | | | % 168.27/23.95 | | | | | | | | | Case 2: % 168.27/23.95 | | | | | | | | | | % 168.27/23.95 | | | | | | | | | | (558) ~ leq(n4, all_74_13) | % 168.27/23.95 | | | | | | | | | | (a_select3(pminus_ds1_filter, n4, n0) = all_74_8 & % 168.27/23.95 | | | | | | | | | | $i(all_74_8)) % 168.27/23.95 | | | | | | | | | | % 168.27/23.95 | | | | | | | | | | BETA: splitting (558) gives: % 168.27/23.95 | | | | | | | | | | % 168.27/23.95 | | | | | | | | | | Case 1: % 168.27/23.95 | | | | | | | | | | | % 168.27/23.95 | | | | | | | | | | | (559) ~ leq(n4, all_74_13) % 168.27/23.95 | | | | | | | | | | | % 168.27/23.95 | | | | | | | | | | | REDUCE: (130), (559) imply: % 168.27/23.95 | | | | | | | | | | | (560) ~ leq(n4, n5) % 168.27/23.95 | | | | | | | | | | | % 168.27/23.95 | | | | | | | | | | | PRED_UNIFY: (552), (560) imply: % 168.27/23.95 | | | | | | | | | | | (561) $false % 168.27/23.95 | | | | | | | | | | | % 168.27/23.95 | | | | | | | | | | | CLOSE: (561) is inconsistent. % 168.27/23.95 | | | | | | | | | | | % 168.27/23.95 | | | | | | | | | | Case 2: % 168.27/23.95 | | | | | | | | | | | % 168.27/23.95 | | | | | | | | | | | (562) a_select3(pminus_ds1_filter, n4, n0) = all_74_8 & % 168.27/23.95 | | | | | | | | | | | $i(all_74_8) % 168.27/23.95 | | | | | | | | | | | % 168.27/23.95 | | | | | | | | | | | ALPHA: (562) implies: % 168.27/23.95 | | | | | | | | | | | (563) a_select3(pminus_ds1_filter, n4, n0) = all_74_8 % 168.27/23.95 | | | | | | | | | | | % 168.27/23.95 | | | | | | | | | | | REF_CLOSE: (17), (413), (550), (563) are inconsistent by % 168.27/23.95 | | | | | | | | | | | sub-proof #11. % 168.27/23.95 | | | | | | | | | | | % 168.27/23.95 | | | | | | | | | | End of split % 168.27/23.95 | | | | | | | | | | % 168.27/23.95 | | | | | | | | | End of split % 168.27/23.95 | | | | | | | | | % 168.27/23.95 | | | | | | | | End of split % 168.27/23.95 | | | | | | | | % 168.27/23.95 | | | | | | | End of split % 168.27/23.95 | | | | | | | % 168.27/23.95 | | | | | | Case 2: % 168.27/23.95 | | | | | | | % 168.27/23.95 | | | | | | | (564) all_74_11 = n5 % 168.27/23.95 | | | | | | | % 168.27/23.95 | | | | | | | REDUCE: (480), (564) imply: % 168.27/23.95 | | | | | | | (565) a_select3(pminus_ds1_filter, n5, n0) = all_74_9 % 168.27/23.95 | | | | | | | % 168.27/23.95 | | | | | | | REDUCE: (479), (564) imply: % 168.27/23.95 | | | | | | | (566) a_select3(pminus_ds1_filter, n0, n5) = all_74_8 % 168.27/23.95 | | | | | | | % 168.27/23.95 | | | | | | | REDUCE: (421), (564) imply: % 168.27/23.95 | | | | | | | (567) leq(n5, n5) % 168.27/23.95 | | | | | | | % 168.27/23.95 | | | | | | | GROUND_INST: instantiating (60) with n0, n5, all_74_8, simplifying % 168.27/23.95 | | | | | | | with (12), (117), (481), (482), (566) gives: % 168.27/23.95 | | | | | | | (568) ~ leq(n5, all_74_13) | ~ leq(n0, all_74_13) | % 168.27/23.95 | | | | | | | (a_select3(pminus_ds1_filter, n5, n0) = all_74_8 & % 168.27/23.95 | | | | | | | $i(all_74_8)) % 168.27/23.95 | | | | | | | % 168.27/23.95 | | | | | | | BETA: splitting (568) gives: % 168.27/23.95 | | | | | | | % 168.27/23.95 | | | | | | | Case 1: % 168.27/23.95 | | | | | | | | % 168.27/23.95 | | | | | | | | (569) ~ leq(n0, all_74_13) % 168.27/23.95 | | | | | | | | % 168.27/23.95 | | | | | | | | REDUCE: (130), (569) imply: % 168.27/23.95 | | | | | | | | (570) ~ leq(n0, n5) % 168.27/23.95 | | | | | | | | % 168.27/23.95 | | | | | | | | PRED_UNIFY: (481), (570) imply: % 168.27/23.95 | | | | | | | | (571) $false % 168.27/23.95 | | | | | | | | % 168.27/23.95 | | | | | | | | CLOSE: (571) is inconsistent. % 168.27/23.95 | | | | | | | | % 168.27/23.95 | | | | | | | Case 2: % 168.27/23.95 | | | | | | | | % 168.27/23.95 | | | | | | | | (572) ~ leq(n5, all_74_13) | (a_select3(pminus_ds1_filter, % 168.27/23.95 | | | | | | | | n5, n0) = all_74_8 & $i(all_74_8)) % 168.27/23.95 | | | | | | | | % 168.27/23.95 | | | | | | | | BETA: splitting (572) gives: % 168.27/23.95 | | | | | | | | % 168.27/23.95 | | | | | | | | Case 1: % 168.27/23.95 | | | | | | | | | % 168.27/23.95 | | | | | | | | | (573) ~ leq(n5, all_74_13) % 168.27/23.95 | | | | | | | | | % 168.27/23.95 | | | | | | | | | REDUCE: (130), (573) imply: % 168.27/23.95 | | | | | | | | | (574) ~ leq(n5, n5) % 168.27/23.95 | | | | | | | | | % 168.27/23.95 | | | | | | | | | PRED_UNIFY: (567), (574) imply: % 168.27/23.95 | | | | | | | | | (575) $false % 168.27/23.95 | | | | | | | | | % 168.27/23.95 | | | | | | | | | CLOSE: (575) is inconsistent. % 168.27/23.95 | | | | | | | | | % 168.27/23.95 | | | | | | | | Case 2: % 168.27/23.95 | | | | | | | | | % 168.27/23.95 | | | | | | | | | (576) a_select3(pminus_ds1_filter, n5, n0) = all_74_8 & % 168.27/23.95 | | | | | | | | | $i(all_74_8) % 168.27/23.95 | | | | | | | | | % 168.27/23.95 | | | | | | | | | ALPHA: (576) implies: % 168.27/23.95 | | | | | | | | | (577) a_select3(pminus_ds1_filter, n5, n0) = all_74_8 % 168.27/23.95 | | | | | | | | | % 168.27/23.95 | | | | | | | | | REF_CLOSE: (17), (413), (565), (577) are inconsistent by % 168.27/23.95 | | | | | | | | | sub-proof #2. % 168.27/23.95 | | | | | | | | | % 168.27/23.95 | | | | | | | | End of split % 168.27/23.95 | | | | | | | | % 168.27/23.95 | | | | | | | End of split % 168.27/23.95 | | | | | | | % 168.27/23.95 | | | | | | End of split % 168.27/23.95 | | | | | | % 168.27/23.95 | | | | | Case 2: % 168.27/23.95 | | | | | | % 168.27/23.95 | | | | | | (578) all_74_11 = n0 % 168.27/23.95 | | | | | | % 168.27/23.95 | | | | | | REDUCE: (480), (578) imply: % 168.27/23.95 | | | | | | (579) a_select3(pminus_ds1_filter, n0, n0) = all_74_9 % 168.27/23.95 | | | | | | % 168.27/23.95 | | | | | | REDUCE: (479), (578) imply: % 168.27/23.95 | | | | | | (580) a_select3(pminus_ds1_filter, n0, n0) = all_74_8 % 168.27/23.95 | | | | | | % 168.27/23.95 | | | | | | GROUND_INST: instantiating (17) with all_74_9, all_74_8, n0, n0, % 168.27/23.95 | | | | | | pminus_ds1_filter, simplifying with (579), (580) gives: % 168.27/23.96 | | | | | | (581) all_74_8 = all_74_9 % 168.27/23.96 | | | | | | % 168.27/23.96 | | | | | | REDUCE: (413), (581) imply: % 168.27/23.96 | | | | | | (582) $false % 168.27/23.96 | | | | | | % 168.27/23.96 | | | | | | CLOSE: (582) is inconsistent. % 168.27/23.96 | | | | | | % 168.27/23.96 | | | | | End of split % 168.27/23.96 | | | | | % 168.27/23.96 | | | | End of split % 168.27/23.96 | | | | % 168.27/23.96 | | | End of split % 168.27/23.96 | | | % 168.27/23.96 | | End of split % 168.27/23.96 | | % 168.27/23.96 | End of split % 168.27/23.96 | % 168.27/23.96 End of proof % 168.27/23.96 % 168.27/23.96 Sub-proof #1 shows that the following formulas are inconsistent: % 168.27/23.96 ---------------------------------------------------------------- % 168.68/23.96 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (pred(v1) = v2) | ~ $i(v1) % 168.68/23.96 | ~ $i(v0) | ~ gt(v1, v0) | leq(v0, v2)) % 168.68/23.96 (2) all_74_13 = n5 % 168.68/23.96 (3) pred(n5) = n4 % 168.68/23.96 (4) all_74_11 = n5 | gt(n5, all_74_11) % 168.68/23.96 (5) all_74_10 = n5 | gt(n5, all_74_10) % 168.68/23.96 (6) $i(n2) % 168.68/23.96 (7) ~ gt(n0, n0) % 168.68/23.96 (8) pred(n4) = n3 % 168.68/23.96 (9) a_select3(pminus_ds1_filter, all_74_11, all_74_10) = all_74_9 % 168.68/23.96 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 168.68/23.96 (a_select3(pminus_ds1_filter, v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 168.68/23.96 ~ leq(v1, all_74_13) | ~ leq(v0, all_74_13) | ~ leq(n0, v1) | ~ % 168.68/23.96 leq(n0, v0) | (a_select3(pminus_ds1_filter, v1, v0) = v2 & $i(v2))) % 168.68/23.96 (11) leq(all_74_10, n5) % 168.68/23.96 (12) all_74_11 = n5 | all_74_11 = n4 | all_74_11 = n3 | all_74_11 = n2 | % 168.68/23.96 all_74_11 = n1 | all_74_11 = n0 % 168.68/23.96 (13) ! [v0: $i] : (v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0, n1) | ~ % 168.68/23.96 leq(n0, v0)) % 168.68/23.96 (14) $i(all_74_10) % 168.68/23.96 (15) pred(n3) = n2 % 168.68/23.96 (16) ~ (all_74_8 = all_74_9) % 168.68/23.96 (17) a_select3(pminus_ds1_filter, all_74_10, all_74_11) = all_74_8 % 168.68/23.96 (18) $i(n4) % 168.68/23.96 (19) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 168.68/23.96 (v1 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 168.68/23.96 v0)) % 168.68/23.96 (20) leq(all_74_11, n5) % 168.68/23.96 (21) $i(all_74_11) % 168.68/23.96 (22) all_74_10 = n5 | all_74_10 = n4 | all_74_10 = n3 | all_74_10 = n2 | % 168.68/23.96 all_74_10 = n1 | all_74_10 = n0 % 168.68/23.96 (23) leq(n0, all_74_11) % 168.68/23.96 (24) pred(n2) = n1 % 168.68/23.96 (25) gt(all_74_10, n0) % 168.68/23.96 (26) $i(n3) % 168.68/23.96 (27) all_74_11 = n0 | gt(all_74_11, n0) % 168.68/23.96 (28) $i(n5) % 168.68/23.96 (29) leq(n0, all_74_10) % 168.68/23.96 (30) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ % 168.68/23.96 leq(v0, v1) | gt(v1, v0)) % 168.68/23.96 % 168.68/23.96 Begin of proof % 168.68/23.96 | % 168.68/23.96 | BETA: splitting (27) gives: % 168.68/23.96 | % 168.68/23.96 | Case 1: % 168.68/23.96 | | % 168.68/23.96 | | (31) gt(all_74_11, n0) % 168.68/23.96 | | % 168.68/23.96 | | BETA: splitting (4) gives: % 168.68/23.96 | | % 168.68/23.96 | | Case 1: % 168.68/23.96 | | | % 168.68/23.96 | | | (32) gt(n5, all_74_11) % 168.68/23.96 | | | % 168.68/23.96 | | | GROUND_INST: instantiating (1) with all_74_11, n5, n4, simplifying with % 168.68/23.96 | | | (3), (21), (28), (32) gives: % 168.68/23.96 | | | (33) leq(all_74_11, n4) % 168.68/23.96 | | | % 168.68/23.96 | | | GROUND_INST: instantiating (30) with all_74_11, n4, simplifying with (18), % 168.68/23.96 | | | (21), (33) gives: % 168.68/23.96 | | | (34) all_74_11 = n4 | gt(n4, all_74_11) % 168.68/23.96 | | | % 168.68/23.96 | | | BETA: splitting (5) gives: % 168.68/23.96 | | | % 168.68/23.96 | | | Case 1: % 168.68/23.96 | | | | % 168.68/23.96 | | | | (35) gt(n5, all_74_10) % 168.68/23.96 | | | | % 168.68/23.96 | | | | GROUND_INST: instantiating (1) with all_74_10, n5, n4, simplifying with % 168.68/23.96 | | | | (3), (14), (28), (35) gives: % 168.68/23.96 | | | | (36) leq(all_74_10, n4) % 168.68/23.96 | | | | % 168.68/23.96 | | | | GROUND_INST: instantiating (30) with all_74_10, n4, simplifying with % 168.68/23.96 | | | | (14), (18), (36) gives: % 168.68/23.96 | | | | (37) all_74_10 = n4 | gt(n4, all_74_10) % 168.68/23.96 | | | | % 168.68/23.96 | | | | BETA: splitting (22) gives: % 168.68/23.96 | | | | % 168.68/23.96 | | | | Case 1: % 168.68/23.96 | | | | | % 168.68/23.96 | | | | | (38) all_74_10 = n0 % 168.68/23.96 | | | | | % 168.68/23.96 | | | | | REDUCE: (25), (38) imply: % 168.68/23.96 | | | | | (39) gt(n0, n0) % 168.68/23.96 | | | | | % 168.68/23.96 | | | | | PRED_UNIFY: (7), (39) imply: % 168.68/23.96 | | | | | (40) $false % 168.68/23.96 | | | | | % 168.68/23.96 | | | | | CLOSE: (40) is inconsistent. % 168.68/23.96 | | | | | % 168.68/23.96 | | | | Case 2: % 168.68/23.96 | | | | | % 168.68/23.96 | | | | | (41) ~ (all_74_10 = n0) % 168.68/23.96 | | | | | % 168.68/23.96 | | | | | BETA: splitting (12) gives: % 168.68/23.96 | | | | | % 168.68/23.96 | | | | | Case 1: % 168.68/23.96 | | | | | | % 168.68/23.96 | | | | | | (42) all_74_11 = n0 % 168.68/23.96 | | | | | | % 168.68/23.96 | | | | | | REDUCE: (31), (42) imply: % 168.68/23.96 | | | | | | (43) gt(n0, n0) % 168.68/23.96 | | | | | | % 168.68/23.96 | | | | | | PRED_UNIFY: (7), (43) imply: % 168.68/23.96 | | | | | | (44) $false % 168.68/23.96 | | | | | | % 168.68/23.96 | | | | | | CLOSE: (44) is inconsistent. % 168.68/23.96 | | | | | | % 168.68/23.96 | | | | | Case 2: % 168.68/23.96 | | | | | | % 168.68/23.96 | | | | | | (45) ~ (all_74_11 = n0) % 168.68/23.96 | | | | | | % 168.68/23.96 | | | | | | REF_CLOSE: (1), (2), (6), (8), (9), (10), (11), (13), (14), (15), % 168.68/23.96 | | | | | | (16), (17), (18), (19), (20), (21), (23), (24), (26), % 168.68/23.96 | | | | | | (29), (30), (34), (37), (41), (45) are inconsistent by % 168.68/23.96 | | | | | | sub-proof #6. % 168.68/23.96 | | | | | | % 168.68/23.96 | | | | | End of split % 168.68/23.96 | | | | | % 168.68/23.96 | | | | End of split % 168.68/23.96 | | | | % 168.68/23.96 | | | Case 2: % 168.68/23.96 | | | | % 168.68/23.96 | | | | (46) all_74_10 = n5 % 168.68/23.96 | | | | % 168.68/23.96 | | | | REDUCE: (17), (46) imply: % 168.68/23.96 | | | | (47) a_select3(pminus_ds1_filter, n5, all_74_11) = all_74_8 % 168.68/23.96 | | | | % 168.68/23.96 | | | | REDUCE: (9), (46) imply: % 168.68/23.96 | | | | (48) a_select3(pminus_ds1_filter, all_74_11, n5) = all_74_9 % 168.68/23.96 | | | | % 168.68/23.96 | | | | REDUCE: (11), (46) imply: % 168.68/23.96 | | | | (49) leq(n5, n5) % 168.68/23.96 | | | | % 168.68/23.96 | | | | REDUCE: (29), (46) imply: % 168.68/23.96 | | | | (50) leq(n0, n5) % 168.68/23.96 | | | | % 168.68/23.96 | | | | BETA: splitting (12) gives: % 168.68/23.96 | | | | % 168.68/23.96 | | | | Case 1: % 168.68/23.96 | | | | | % 168.68/23.96 | | | | | (51) all_74_11 = n0 % 168.68/23.96 | | | | | % 168.68/23.96 | | | | | REDUCE: (31), (51) imply: % 168.68/23.96 | | | | | (52) gt(n0, n0) % 168.68/23.96 | | | | | % 168.68/23.96 | | | | | PRED_UNIFY: (7), (52) imply: % 168.68/23.96 | | | | | (53) $false % 168.68/23.96 | | | | | % 168.68/23.96 | | | | | CLOSE: (53) is inconsistent. % 168.68/23.96 | | | | | % 168.68/23.96 | | | | Case 2: % 168.68/23.96 | | | | | % 168.68/23.96 | | | | | (54) ~ (all_74_11 = n0) % 168.68/23.96 | | | | | % 168.68/23.96 | | | | | REF_CLOSE: (1), (2), (6), (8), (10), (13), (15), (16), (18), (19), % 168.68/23.96 | | | | | (20), (21), (23), (24), (26), (28), (30), (34), (47), (48), % 168.68/23.96 | | | | | (49), (50), (54) are inconsistent by sub-proof #4. % 168.68/23.96 | | | | | % 168.68/23.96 | | | | End of split % 168.68/23.96 | | | | % 168.68/23.96 | | | End of split % 168.68/23.96 | | | % 168.68/23.96 | | Case 2: % 168.68/23.96 | | | % 168.68/23.96 | | | (55) all_74_11 = n5 % 168.68/23.96 | | | % 168.68/23.96 | | | REDUCE: (17), (55) imply: % 168.68/23.96 | | | (56) a_select3(pminus_ds1_filter, all_74_10, n5) = all_74_8 % 168.68/23.96 | | | % 168.68/23.96 | | | REDUCE: (9), (55) imply: % 168.68/23.96 | | | (57) a_select3(pminus_ds1_filter, n5, all_74_10) = all_74_9 % 168.68/23.96 | | | % 168.68/23.96 | | | REDUCE: (20), (55) imply: % 168.68/23.96 | | | (58) leq(n5, n5) % 168.68/23.96 | | | % 168.68/23.96 | | | REDUCE: (23), (55) imply: % 168.68/23.97 | | | (59) leq(n0, n5) % 168.68/23.97 | | | % 168.68/23.97 | | | BETA: splitting (5) gives: % 168.68/23.97 | | | % 168.68/23.97 | | | Case 1: % 168.68/23.97 | | | | % 168.68/23.97 | | | | (60) gt(n5, all_74_10) % 168.68/23.97 | | | | % 168.68/23.97 | | | | GROUND_INST: instantiating (1) with all_74_10, n5, n4, simplifying with % 168.68/23.97 | | | | (3), (14), (28), (60) gives: % 168.68/23.97 | | | | (61) leq(all_74_10, n4) % 168.68/23.97 | | | | % 168.68/23.97 | | | | GROUND_INST: instantiating (30) with all_74_10, n4, simplifying with % 168.68/23.97 | | | | (14), (18), (61) gives: % 168.68/23.97 | | | | (62) all_74_10 = n4 | gt(n4, all_74_10) % 168.68/23.97 | | | | % 168.68/23.97 | | | | BETA: splitting (22) gives: % 168.68/23.97 | | | | % 168.68/23.97 | | | | Case 1: % 168.68/23.97 | | | | | % 168.68/23.97 | | | | | (63) all_74_10 = n0 % 168.68/23.97 | | | | | % 168.68/23.97 | | | | | REDUCE: (25), (63) imply: % 168.68/23.97 | | | | | (64) gt(n0, n0) % 168.68/23.97 | | | | | % 168.68/23.97 | | | | | PRED_UNIFY: (7), (64) imply: % 168.68/23.97 | | | | | (65) $false % 168.68/23.97 | | | | | % 168.68/23.97 | | | | | CLOSE: (65) is inconsistent. % 168.68/23.97 | | | | | % 168.68/23.97 | | | | Case 2: % 168.68/23.97 | | | | | % 168.68/23.97 | | | | | (66) ~ (all_74_10 = n0) % 168.68/23.97 | | | | | % 168.68/23.97 | | | | | REF_CLOSE: (1), (2), (6), (8), (10), (11), (13), (14), (15), (16), % 168.68/23.97 | | | | | (18), (19), (24), (26), (28), (29), (30), (56), (57), (58), % 168.68/23.97 | | | | | (59), (62), (66) are inconsistent by sub-proof #3. % 168.68/23.97 | | | | | % 168.68/23.97 | | | | End of split % 168.68/23.97 | | | | % 168.68/23.97 | | | Case 2: % 168.68/23.97 | | | | % 168.68/23.97 | | | | (67) all_74_10 = n5 % 168.68/23.97 | | | | % 168.68/23.97 | | | | REDUCE: (56), (67) imply: % 168.68/23.97 | | | | (68) a_select3(pminus_ds1_filter, n5, n5) = all_74_8 % 168.68/23.97 | | | | % 168.68/23.97 | | | | REDUCE: (57), (67) imply: % 168.68/23.97 | | | | (69) a_select3(pminus_ds1_filter, n5, n5) = all_74_9 % 168.68/23.97 | | | | % 168.68/23.97 | | | | GROUND_INST: instantiating (19) with all_74_9, all_74_8, n5, n5, % 168.68/23.97 | | | | pminus_ds1_filter, simplifying with (68), (69) gives: % 168.68/23.97 | | | | (70) all_74_8 = all_74_9 % 168.68/23.97 | | | | % 168.68/23.97 | | | | REDUCE: (16), (70) imply: % 168.68/23.97 | | | | (71) $false % 168.68/23.97 | | | | % 168.68/23.97 | | | | CLOSE: (71) is inconsistent. % 168.68/23.97 | | | | % 168.68/23.97 | | | End of split % 168.68/23.97 | | | % 168.68/23.97 | | End of split % 168.68/23.97 | | % 168.68/23.97 | Case 2: % 168.68/23.97 | | % 168.68/23.97 | | (72) all_74_11 = n0 % 168.68/23.97 | | (73) ~ gt(all_74_11, n0) % 168.68/23.97 | | % 168.68/23.97 | | REDUCE: (17), (72) imply: % 168.68/23.97 | | (74) a_select3(pminus_ds1_filter, all_74_10, n0) = all_74_8 % 168.68/23.97 | | % 168.68/23.97 | | REDUCE: (9), (72) imply: % 168.68/23.97 | | (75) a_select3(pminus_ds1_filter, n0, all_74_10) = all_74_9 % 168.68/23.97 | | % 168.68/23.97 | | REDUCE: (21), (72) imply: % 168.68/23.97 | | (76) $i(n0) % 168.68/23.97 | | % 168.68/23.97 | | REDUCE: (20), (72) imply: % 168.68/23.97 | | (77) leq(n0, n5) % 168.68/23.97 | | % 168.68/23.97 | | REDUCE: (23), (72) imply: % 168.68/23.97 | | (78) leq(n0, n0) % 168.68/23.97 | | % 168.68/23.97 | | BETA: splitting (5) gives: % 168.68/23.97 | | % 168.68/23.97 | | Case 1: % 168.68/23.97 | | | % 168.68/23.97 | | | (79) gt(n5, all_74_10) % 168.68/23.97 | | | % 168.68/23.97 | | | GROUND_INST: instantiating (1) with all_74_10, n5, n4, simplifying with % 168.68/23.97 | | | (3), (14), (28), (79) gives: % 168.68/23.97 | | | (80) leq(all_74_10, n4) % 168.68/23.97 | | | % 168.68/23.97 | | | GROUND_INST: instantiating (30) with all_74_10, n4, simplifying with (14), % 168.68/23.97 | | | (18), (80) gives: % 168.68/23.97 | | | (81) all_74_10 = n4 | gt(n4, all_74_10) % 168.68/23.97 | | | % 168.68/23.97 | | | BETA: splitting (22) gives: % 168.68/23.97 | | | % 168.68/23.97 | | | Case 1: % 168.68/23.97 | | | | % 168.68/23.97 | | | | (82) all_74_10 = n0 % 168.68/23.97 | | | | % 168.68/23.97 | | | | REDUCE: (25), (82) imply: % 168.68/23.97 | | | | (83) gt(n0, n0) % 168.68/23.97 | | | | % 168.68/23.97 | | | | PRED_UNIFY: (7), (83) imply: % 168.68/23.97 | | | | (84) $false % 168.68/23.97 | | | | % 168.68/23.97 | | | | CLOSE: (84) is inconsistent. % 168.68/23.97 | | | | % 168.68/23.97 | | | Case 2: % 168.68/23.97 | | | | % 168.68/23.97 | | | | (85) ~ (all_74_10 = n0) % 168.68/23.97 | | | | % 168.68/23.97 | | | | REF_CLOSE: (1), (2), (6), (8), (10), (11), (13), (14), (15), (16), (18), % 168.68/23.97 | | | | (19), (24), (26), (29), (30), (74), (75), (76), (77), (78), % 168.68/23.97 | | | | (81), (85) are inconsistent by sub-proof #10. % 168.68/23.97 | | | | % 168.68/23.97 | | | End of split % 168.68/23.97 | | | % 168.68/23.97 | | Case 2: % 168.68/23.97 | | | % 168.68/23.97 | | | (86) all_74_10 = n5 % 168.68/23.97 | | | % 168.68/23.97 | | | REDUCE: (74), (86) imply: % 168.68/23.97 | | | (87) a_select3(pminus_ds1_filter, n5, n0) = all_74_8 % 168.68/23.97 | | | % 168.68/23.97 | | | REDUCE: (75), (86) imply: % 168.68/23.97 | | | (88) a_select3(pminus_ds1_filter, n0, n5) = all_74_9 % 168.68/23.97 | | | % 168.68/23.97 | | | REDUCE: (11), (86) imply: % 168.68/23.97 | | | (89) leq(n5, n5) % 168.68/23.97 | | | % 168.68/23.97 | | | GROUND_INST: instantiating (10) with n0, n5, all_74_9, simplifying with % 168.68/23.97 | | | (28), (76), (77), (78), (88) gives: % 168.68/23.97 | | | (90) ~ leq(n5, all_74_13) | ~ leq(n0, all_74_13) | % 168.68/23.97 | | | (a_select3(pminus_ds1_filter, n5, n0) = all_74_9 & $i(all_74_9)) % 168.68/23.97 | | | % 168.68/23.97 | | | BETA: splitting (90) gives: % 168.68/23.97 | | | % 168.68/23.97 | | | Case 1: % 168.68/23.97 | | | | % 168.68/23.97 | | | | (91) ~ leq(n0, all_74_13) % 168.68/23.97 | | | | % 168.68/23.97 | | | | REDUCE: (2), (91) imply: % 168.68/23.97 | | | | (92) ~ leq(n0, n5) % 168.68/23.97 | | | | % 168.68/23.97 | | | | PRED_UNIFY: (77), (92) imply: % 168.68/23.97 | | | | (93) $false % 168.68/23.97 | | | | % 168.68/23.97 | | | | CLOSE: (93) is inconsistent. % 168.68/23.97 | | | | % 168.68/23.97 | | | Case 2: % 168.68/23.97 | | | | % 168.68/23.97 | | | | (94) ~ leq(n5, all_74_13) | (a_select3(pminus_ds1_filter, n5, n0) = % 168.68/23.97 | | | | all_74_9 & $i(all_74_9)) % 168.68/23.97 | | | | % 168.68/23.97 | | | | BETA: splitting (94) gives: % 168.68/23.97 | | | | % 168.68/23.97 | | | | Case 1: % 168.68/23.97 | | | | | % 168.68/23.97 | | | | | (95) ~ leq(n5, all_74_13) % 168.68/23.97 | | | | | % 168.68/23.97 | | | | | REDUCE: (2), (95) imply: % 168.68/23.97 | | | | | (96) ~ leq(n5, n5) % 168.68/23.97 | | | | | % 168.68/23.97 | | | | | PRED_UNIFY: (89), (96) imply: % 168.68/23.97 | | | | | (97) $false % 168.68/23.97 | | | | | % 168.68/23.97 | | | | | CLOSE: (97) is inconsistent. % 168.68/23.97 | | | | | % 168.68/23.97 | | | | Case 2: % 168.68/23.97 | | | | | % 168.68/23.97 | | | | | (98) a_select3(pminus_ds1_filter, n5, n0) = all_74_9 & $i(all_74_9) % 168.68/23.97 | | | | | % 168.68/23.97 | | | | | ALPHA: (98) implies: % 168.68/23.97 | | | | | (99) a_select3(pminus_ds1_filter, n5, n0) = all_74_9 % 168.68/23.97 | | | | | % 168.68/23.97 | | | | | REF_CLOSE: (16), (19), (87), (99) are inconsistent by sub-proof #2. % 168.68/23.97 | | | | | % 168.68/23.97 | | | | End of split % 168.68/23.97 | | | | % 168.68/23.97 | | | End of split % 168.68/23.97 | | | % 168.68/23.97 | | End of split % 168.68/23.97 | | % 168.68/23.97 | End of split % 168.68/23.97 | % 168.68/23.97 End of proof % 168.68/23.97 % 168.68/23.97 Sub-proof #2 shows that the following formulas are inconsistent: % 168.68/23.97 ---------------------------------------------------------------- % 168.68/23.97 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 168.68/23.97 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 168.68/23.97 v0)) % 168.68/23.97 (2) a_select3(pminus_ds1_filter, n5, n0) = all_74_8 % 168.68/23.97 (3) a_select3(pminus_ds1_filter, n5, n0) = all_74_9 % 168.68/23.97 (4) ~ (all_74_8 = all_74_9) % 168.68/23.97 % 168.68/23.97 Begin of proof % 168.68/23.97 | % 168.68/23.97 | GROUND_INST: instantiating (1) with all_74_9, all_74_8, n0, n5, % 168.68/23.97 | pminus_ds1_filter, simplifying with (2), (3) gives: % 168.68/23.97 | (5) all_74_8 = all_74_9 % 168.68/23.97 | % 168.68/23.97 | REDUCE: (4), (5) imply: % 168.68/23.97 | (6) $false % 168.68/23.97 | % 168.68/23.97 | CLOSE: (6) is inconsistent. % 168.68/23.97 | % 168.68/23.97 End of proof % 168.68/23.97 % 168.68/23.97 Sub-proof #3 shows that the following formulas are inconsistent: % 168.68/23.97 ---------------------------------------------------------------- % 168.68/23.97 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (pred(v1) = v2) | ~ $i(v1) % 168.68/23.97 | ~ $i(v0) | ~ gt(v1, v0) | leq(v0, v2)) % 168.68/23.97 (2) all_74_10 = n4 | gt(n4, all_74_10) % 168.68/23.97 (3) all_74_13 = n5 % 168.68/23.97 (4) $i(n2) % 168.68/23.97 (5) pred(n4) = n3 % 168.68/23.97 (6) a_select3(pminus_ds1_filter, all_74_10, n5) = all_74_8 % 168.68/23.97 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 168.68/23.97 (a_select3(pminus_ds1_filter, v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 168.68/23.97 ~ leq(v1, all_74_13) | ~ leq(v0, all_74_13) | ~ leq(n0, v1) | ~ % 168.68/23.97 leq(n0, v0) | (a_select3(pminus_ds1_filter, v1, v0) = v2 & $i(v2))) % 168.68/23.97 (8) leq(all_74_10, n5) % 168.68/23.97 (9) ! [v0: $i] : (v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0, n1) | ~ % 168.68/23.97 leq(n0, v0)) % 168.68/23.97 (10) $i(all_74_10) % 168.68/23.97 (11) leq(n5, n5) % 168.68/23.97 (12) pred(n3) = n2 % 168.68/23.97 (13) ~ (all_74_10 = n0) % 168.68/23.97 (14) ~ (all_74_8 = all_74_9) % 168.68/23.97 (15) $i(n4) % 168.68/23.97 (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 168.68/23.97 (v1 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 168.68/23.98 v0)) % 168.68/23.98 (17) leq(n0, n5) % 168.68/23.98 (18) a_select3(pminus_ds1_filter, n5, all_74_10) = all_74_9 % 168.68/23.98 (19) pred(n2) = n1 % 168.68/23.98 (20) $i(n3) % 168.68/23.98 (21) $i(n5) % 168.68/23.98 (22) leq(n0, all_74_10) % 168.68/23.98 (23) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ % 168.68/23.98 leq(v0, v1) | gt(v1, v0)) % 168.68/23.98 % 168.68/23.98 Begin of proof % 168.68/23.98 | % 168.68/23.98 | BETA: splitting (2) gives: % 168.68/23.98 | % 168.68/23.98 | Case 1: % 168.68/23.98 | | % 168.68/23.98 | | (24) gt(n4, all_74_10) % 168.68/23.98 | | % 168.68/23.98 | | GROUND_INST: instantiating (1) with all_74_10, n4, n3, simplifying with (5), % 168.68/23.98 | | (10), (15), (24) gives: % 168.68/23.98 | | (25) leq(all_74_10, n3) % 168.68/23.98 | | % 168.68/23.98 | | GROUND_INST: instantiating (23) with all_74_10, n3, simplifying with (10), % 168.68/23.98 | | (20), (25) gives: % 168.68/23.98 | | (26) all_74_10 = n3 | gt(n3, all_74_10) % 168.68/23.98 | | % 168.68/23.98 | | BETA: splitting (26) gives: % 168.68/23.98 | | % 168.68/23.98 | | Case 1: % 168.68/23.98 | | | % 168.68/23.98 | | | (27) gt(n3, all_74_10) % 168.68/23.98 | | | % 168.68/23.98 | | | GROUND_INST: instantiating (1) with all_74_10, n3, n2, simplifying with % 168.68/23.98 | | | (10), (12), (20), (27) gives: % 168.68/23.98 | | | (28) leq(all_74_10, n2) % 168.68/23.98 | | | % 168.68/23.98 | | | GROUND_INST: instantiating (23) with all_74_10, n2, simplifying with (4), % 168.68/23.98 | | | (10), (28) gives: % 168.68/23.98 | | | (29) all_74_10 = n2 | gt(n2, all_74_10) % 168.68/23.98 | | | % 168.68/23.98 | | | BETA: splitting (29) gives: % 168.68/23.98 | | | % 168.68/23.98 | | | Case 1: % 168.68/23.98 | | | | % 168.68/23.98 | | | | (30) gt(n2, all_74_10) % 168.68/23.98 | | | | % 168.68/23.98 | | | | GROUND_INST: instantiating (1) with all_74_10, n2, n1, simplifying with % 168.68/23.98 | | | | (4), (10), (19), (30) gives: % 168.68/23.98 | | | | (31) leq(all_74_10, n1) % 168.68/23.98 | | | | % 168.68/23.98 | | | | GROUND_INST: instantiating (9) with all_74_10, simplifying with (10), % 168.68/23.98 | | | | (22), (31) gives: % 168.68/23.98 | | | | (32) all_74_10 = n1 | all_74_10 = n0 % 168.68/23.98 | | | | % 168.68/23.98 | | | | BETA: splitting (32) gives: % 168.68/23.98 | | | | % 168.68/23.98 | | | | Case 1: % 168.68/23.98 | | | | | % 168.68/23.98 | | | | | (33) all_74_10 = n0 % 168.68/23.98 | | | | | % 168.68/23.98 | | | | | REDUCE: (13), (33) imply: % 168.68/23.98 | | | | | (34) $false % 168.68/23.98 | | | | | % 168.68/23.98 | | | | | CLOSE: (34) is inconsistent. % 168.68/23.98 | | | | | % 168.68/23.98 | | | | Case 2: % 168.68/23.98 | | | | | % 168.68/23.98 | | | | | (35) all_74_10 = n1 % 168.68/23.98 | | | | | % 168.68/23.98 | | | | | REDUCE: (6), (35) imply: % 168.68/23.98 | | | | | (36) a_select3(pminus_ds1_filter, n1, n5) = all_74_8 % 168.68/23.98 | | | | | % 168.68/23.98 | | | | | REDUCE: (18), (35) imply: % 168.68/23.98 | | | | | (37) a_select3(pminus_ds1_filter, n5, n1) = all_74_9 % 168.68/23.98 | | | | | % 168.68/23.98 | | | | | REDUCE: (10), (35) imply: % 168.68/23.98 | | | | | (38) $i(n1) % 168.68/23.98 | | | | | % 168.68/23.98 | | | | | REDUCE: (8), (35) imply: % 168.68/23.98 | | | | | (39) leq(n1, n5) % 168.68/23.98 | | | | | % 168.68/23.98 | | | | | REDUCE: (22), (35) imply: % 168.68/23.98 | | | | | (40) leq(n0, n1) % 168.68/23.98 | | | | | % 168.68/23.98 | | | | | GROUND_INST: instantiating (7) with n1, n5, all_74_8, simplifying with % 168.68/23.98 | | | | | (17), (21), (36), (38), (40) gives: % 168.68/23.98 | | | | | (41) ~ leq(n5, all_74_13) | ~ leq(n1, all_74_13) | % 168.68/23.98 | | | | | (a_select3(pminus_ds1_filter, n5, n1) = all_74_8 & % 168.68/23.98 | | | | | $i(all_74_8)) % 168.68/23.98 | | | | | % 168.68/23.98 | | | | | BETA: splitting (41) gives: % 168.68/23.98 | | | | | % 168.68/23.98 | | | | | Case 1: % 168.68/23.98 | | | | | | % 168.68/23.98 | | | | | | (42) ~ leq(n5, all_74_13) % 168.68/23.98 | | | | | | % 168.68/23.98 | | | | | | REDUCE: (3), (42) imply: % 168.68/23.98 | | | | | | (43) ~ leq(n5, n5) % 168.68/23.98 | | | | | | % 168.68/23.98 | | | | | | PRED_UNIFY: (11), (43) imply: % 168.68/23.98 | | | | | | (44) $false % 168.68/23.98 | | | | | | % 168.68/23.98 | | | | | | CLOSE: (44) is inconsistent. % 168.68/23.98 | | | | | | % 168.68/23.98 | | | | | Case 2: % 168.68/23.98 | | | | | | % 168.68/23.98 | | | | | | (45) ~ leq(n1, all_74_13) | (a_select3(pminus_ds1_filter, n5, % 168.68/23.98 | | | | | | n1) = all_74_8 & $i(all_74_8)) % 168.68/23.98 | | | | | | % 168.68/23.98 | | | | | | BETA: splitting (45) gives: % 168.68/23.98 | | | | | | % 168.68/23.98 | | | | | | Case 1: % 168.68/23.98 | | | | | | | % 168.68/23.98 | | | | | | | (46) ~ leq(n1, all_74_13) % 168.68/23.98 | | | | | | | % 168.68/23.98 | | | | | | | REDUCE: (3), (46) imply: % 168.68/23.98 | | | | | | | (47) ~ leq(n1, n5) % 168.68/23.98 | | | | | | | % 168.68/23.98 | | | | | | | PRED_UNIFY: (39), (47) imply: % 168.68/23.98 | | | | | | | (48) $false % 168.68/23.98 | | | | | | | % 168.68/23.98 | | | | | | | CLOSE: (48) is inconsistent. % 168.68/23.98 | | | | | | | % 168.68/23.98 | | | | | | Case 2: % 168.68/23.98 | | | | | | | % 168.68/23.98 | | | | | | | (49) a_select3(pminus_ds1_filter, n5, n1) = all_74_8 & % 168.68/23.98 | | | | | | | $i(all_74_8) % 168.68/23.98 | | | | | | | % 168.68/23.98 | | | | | | | ALPHA: (49) implies: % 168.68/23.98 | | | | | | | (50) a_select3(pminus_ds1_filter, n5, n1) = all_74_8 % 168.68/23.98 | | | | | | | % 168.68/23.98 | | | | | | | GROUND_INST: instantiating (16) with all_74_9, all_74_8, n1, n5, % 168.68/23.98 | | | | | | | pminus_ds1_filter, simplifying with (37), (50) gives: % 168.68/23.98 | | | | | | | (51) all_74_8 = all_74_9 % 168.68/23.98 | | | | | | | % 168.68/23.98 | | | | | | | REDUCE: (14), (51) imply: % 168.68/23.98 | | | | | | | (52) $false % 168.68/23.98 | | | | | | | % 168.68/23.98 | | | | | | | CLOSE: (52) is inconsistent. % 168.68/23.98 | | | | | | | % 168.68/23.98 | | | | | | End of split % 168.68/23.98 | | | | | | % 168.68/23.98 | | | | | End of split % 168.68/23.98 | | | | | % 168.68/23.98 | | | | End of split % 168.68/23.98 | | | | % 168.68/23.98 | | | Case 2: % 168.68/23.98 | | | | % 168.68/23.98 | | | | (53) all_74_10 = n2 % 168.68/23.98 | | | | % 168.68/23.98 | | | | REDUCE: (6), (53) imply: % 168.68/23.98 | | | | (54) a_select3(pminus_ds1_filter, n2, n5) = all_74_8 % 168.68/23.98 | | | | % 168.68/23.98 | | | | REDUCE: (18), (53) imply: % 168.68/23.98 | | | | (55) a_select3(pminus_ds1_filter, n5, n2) = all_74_9 % 168.68/23.98 | | | | % 168.68/23.98 | | | | REDUCE: (8), (53) imply: % 168.68/23.98 | | | | (56) leq(n2, n5) % 168.68/23.98 | | | | % 168.68/23.98 | | | | REDUCE: (22), (53) imply: % 168.68/23.98 | | | | (57) leq(n0, n2) % 168.68/23.98 | | | | % 168.68/23.98 | | | | GROUND_INST: instantiating (7) with n2, n5, all_74_8, simplifying with % 168.68/23.98 | | | | (4), (17), (21), (54), (57) gives: % 168.68/23.98 | | | | (58) ~ leq(n5, all_74_13) | ~ leq(n2, all_74_13) | % 168.68/23.98 | | | | (a_select3(pminus_ds1_filter, n5, n2) = all_74_8 & $i(all_74_8)) % 168.68/23.98 | | | | % 168.68/23.98 | | | | BETA: splitting (58) gives: % 168.68/23.98 | | | | % 168.68/23.98 | | | | Case 1: % 168.68/23.98 | | | | | % 168.68/23.98 | | | | | (59) ~ leq(n5, all_74_13) % 168.68/23.98 | | | | | % 168.68/23.98 | | | | | REDUCE: (3), (59) imply: % 168.68/23.98 | | | | | (60) ~ leq(n5, n5) % 168.68/23.98 | | | | | % 168.68/23.98 | | | | | PRED_UNIFY: (11), (60) imply: % 168.68/23.98 | | | | | (61) $false % 168.68/23.98 | | | | | % 168.68/23.98 | | | | | CLOSE: (61) is inconsistent. % 168.68/23.98 | | | | | % 168.68/23.98 | | | | Case 2: % 168.68/23.98 | | | | | % 168.68/23.98 | | | | | (62) ~ leq(n2, all_74_13) | (a_select3(pminus_ds1_filter, n5, n2) % 168.68/23.98 | | | | | = all_74_8 & $i(all_74_8)) % 168.68/23.98 | | | | | % 168.68/23.98 | | | | | BETA: splitting (62) gives: % 168.68/23.98 | | | | | % 168.68/23.98 | | | | | Case 1: % 168.68/23.98 | | | | | | % 168.68/23.98 | | | | | | (63) ~ leq(n2, all_74_13) % 168.68/23.98 | | | | | | % 168.68/23.98 | | | | | | REDUCE: (3), (63) imply: % 168.68/23.98 | | | | | | (64) ~ leq(n2, n5) % 168.68/23.98 | | | | | | % 168.68/23.98 | | | | | | PRED_UNIFY: (56), (64) imply: % 168.68/23.98 | | | | | | (65) $false % 168.68/23.98 | | | | | | % 168.68/23.98 | | | | | | CLOSE: (65) is inconsistent. % 168.68/23.98 | | | | | | % 168.68/23.98 | | | | | Case 2: % 168.68/23.98 | | | | | | % 168.68/23.98 | | | | | | (66) a_select3(pminus_ds1_filter, n5, n2) = all_74_8 & % 168.68/23.98 | | | | | | $i(all_74_8) % 168.68/23.98 | | | | | | % 168.68/23.98 | | | | | | ALPHA: (66) implies: % 168.68/23.98 | | | | | | (67) a_select3(pminus_ds1_filter, n5, n2) = all_74_8 % 168.68/23.98 | | | | | | % 168.68/23.98 | | | | | | GROUND_INST: instantiating (16) with all_74_9, all_74_8, n2, n5, % 168.68/23.98 | | | | | | pminus_ds1_filter, simplifying with (55), (67) gives: % 168.68/23.98 | | | | | | (68) all_74_8 = all_74_9 % 168.68/23.98 | | | | | | % 168.68/23.98 | | | | | | REDUCE: (14), (68) imply: % 168.68/23.98 | | | | | | (69) $false % 168.68/23.98 | | | | | | % 168.68/23.98 | | | | | | CLOSE: (69) is inconsistent. % 168.68/23.98 | | | | | | % 168.68/23.98 | | | | | End of split % 168.68/23.98 | | | | | % 168.68/23.98 | | | | End of split % 168.68/23.98 | | | | % 168.68/23.98 | | | End of split % 168.68/23.98 | | | % 168.68/23.98 | | Case 2: % 168.68/23.98 | | | % 168.68/23.98 | | | (70) all_74_10 = n3 % 168.68/23.98 | | | % 168.68/23.98 | | | REDUCE: (6), (70) imply: % 168.68/23.98 | | | (71) a_select3(pminus_ds1_filter, n3, n5) = all_74_8 % 168.68/23.98 | | | % 168.68/23.98 | | | REDUCE: (18), (70) imply: % 168.68/23.98 | | | (72) a_select3(pminus_ds1_filter, n5, n3) = all_74_9 % 168.68/23.98 | | | % 168.68/23.98 | | | REDUCE: (8), (70) imply: % 168.68/23.98 | | | (73) leq(n3, n5) % 168.68/23.98 | | | % 168.68/23.98 | | | REDUCE: (22), (70) imply: % 168.68/23.98 | | | (74) leq(n0, n3) % 168.68/23.98 | | | % 168.68/23.98 | | | GROUND_INST: instantiating (7) with n3, n5, all_74_8, simplifying with % 168.68/23.98 | | | (17), (20), (21), (71), (74) gives: % 168.68/23.98 | | | (75) ~ leq(n5, all_74_13) | ~ leq(n3, all_74_13) | % 168.68/23.98 | | | (a_select3(pminus_ds1_filter, n5, n3) = all_74_8 & $i(all_74_8)) % 168.68/23.98 | | | % 168.68/23.98 | | | BETA: splitting (75) gives: % 168.68/23.98 | | | % 168.68/23.98 | | | Case 1: % 168.68/23.98 | | | | % 168.68/23.98 | | | | (76) ~ leq(n5, all_74_13) % 168.68/23.98 | | | | % 168.68/23.98 | | | | REDUCE: (3), (76) imply: % 168.68/23.98 | | | | (77) ~ leq(n5, n5) % 168.68/23.98 | | | | % 168.68/23.98 | | | | PRED_UNIFY: (11), (77) imply: % 168.68/23.98 | | | | (78) $false % 168.68/23.98 | | | | % 168.68/23.98 | | | | CLOSE: (78) is inconsistent. % 168.68/23.98 | | | | % 168.68/23.98 | | | Case 2: % 168.68/23.98 | | | | % 168.68/23.98 | | | | (79) ~ leq(n3, all_74_13) | (a_select3(pminus_ds1_filter, n5, n3) = % 168.68/23.98 | | | | all_74_8 & $i(all_74_8)) % 168.68/23.98 | | | | % 168.68/23.98 | | | | BETA: splitting (79) gives: % 168.68/23.98 | | | | % 168.68/23.98 | | | | Case 1: % 168.68/23.98 | | | | | % 168.68/23.98 | | | | | (80) ~ leq(n3, all_74_13) % 168.68/23.98 | | | | | % 168.68/23.98 | | | | | REDUCE: (3), (80) imply: % 168.68/23.98 | | | | | (81) ~ leq(n3, n5) % 168.68/23.98 | | | | | % 168.68/23.98 | | | | | PRED_UNIFY: (73), (81) imply: % 168.68/23.98 | | | | | (82) $false % 168.68/23.98 | | | | | % 168.68/23.98 | | | | | CLOSE: (82) is inconsistent. % 168.68/23.98 | | | | | % 168.68/23.98 | | | | Case 2: % 168.68/23.98 | | | | | % 168.68/23.98 | | | | | (83) a_select3(pminus_ds1_filter, n5, n3) = all_74_8 & $i(all_74_8) % 168.68/23.98 | | | | | % 168.68/23.98 | | | | | ALPHA: (83) implies: % 168.68/23.98 | | | | | (84) a_select3(pminus_ds1_filter, n5, n3) = all_74_8 % 168.68/23.98 | | | | | % 168.68/23.98 | | | | | GROUND_INST: instantiating (16) with all_74_9, all_74_8, n3, n5, % 168.68/23.98 | | | | | pminus_ds1_filter, simplifying with (72), (84) gives: % 168.68/23.98 | | | | | (85) all_74_8 = all_74_9 % 168.68/23.98 | | | | | % 168.68/23.98 | | | | | REDUCE: (14), (85) imply: % 168.68/23.98 | | | | | (86) $false % 168.68/23.98 | | | | | % 168.68/23.98 | | | | | CLOSE: (86) is inconsistent. % 168.68/23.98 | | | | | % 168.68/23.98 | | | | End of split % 168.68/23.98 | | | | % 168.68/23.98 | | | End of split % 168.68/23.98 | | | % 168.68/23.98 | | End of split % 168.68/23.98 | | % 168.68/23.98 | Case 2: % 168.68/23.98 | | % 168.68/23.98 | | (87) all_74_10 = n4 % 168.68/23.98 | | % 168.68/23.98 | | REDUCE: (6), (87) imply: % 168.68/23.98 | | (88) a_select3(pminus_ds1_filter, n4, n5) = all_74_8 % 168.68/23.98 | | % 168.68/23.98 | | REDUCE: (18), (87) imply: % 168.68/23.98 | | (89) a_select3(pminus_ds1_filter, n5, n4) = all_74_9 % 168.68/23.98 | | % 168.68/23.98 | | REDUCE: (8), (87) imply: % 168.68/23.98 | | (90) leq(n4, n5) % 168.68/23.98 | | % 168.68/23.98 | | REDUCE: (22), (87) imply: % 168.68/23.98 | | (91) leq(n0, n4) % 168.68/23.98 | | % 168.68/23.99 | | GROUND_INST: instantiating (7) with n4, n5, all_74_8, simplifying with (15), % 168.68/23.99 | | (17), (21), (88), (91) gives: % 168.68/23.99 | | (92) ~ leq(n5, all_74_13) | ~ leq(n4, all_74_13) | % 168.68/23.99 | | (a_select3(pminus_ds1_filter, n5, n4) = all_74_8 & $i(all_74_8)) % 168.68/23.99 | | % 168.68/23.99 | | BETA: splitting (92) gives: % 168.68/23.99 | | % 168.68/23.99 | | Case 1: % 168.68/23.99 | | | % 168.68/23.99 | | | (93) ~ leq(n5, all_74_13) % 168.68/23.99 | | | % 168.68/23.99 | | | REDUCE: (3), (93) imply: % 168.68/23.99 | | | (94) ~ leq(n5, n5) % 168.68/23.99 | | | % 168.68/23.99 | | | PRED_UNIFY: (11), (94) imply: % 168.68/23.99 | | | (95) $false % 168.68/23.99 | | | % 168.68/23.99 | | | CLOSE: (95) is inconsistent. % 168.68/23.99 | | | % 168.68/23.99 | | Case 2: % 168.68/23.99 | | | % 168.68/23.99 | | | (96) ~ leq(n4, all_74_13) | (a_select3(pminus_ds1_filter, n5, n4) = % 168.68/23.99 | | | all_74_8 & $i(all_74_8)) % 168.68/23.99 | | | % 168.68/23.99 | | | BETA: splitting (96) gives: % 168.68/23.99 | | | % 168.68/23.99 | | | Case 1: % 168.68/23.99 | | | | % 168.68/23.99 | | | | (97) ~ leq(n4, all_74_13) % 168.68/23.99 | | | | % 168.68/23.99 | | | | REDUCE: (3), (97) imply: % 168.68/23.99 | | | | (98) ~ leq(n4, n5) % 168.68/23.99 | | | | % 168.68/23.99 | | | | PRED_UNIFY: (90), (98) imply: % 168.68/23.99 | | | | (99) $false % 168.68/23.99 | | | | % 168.68/23.99 | | | | CLOSE: (99) is inconsistent. % 168.68/23.99 | | | | % 168.68/23.99 | | | Case 2: % 168.68/23.99 | | | | % 168.68/23.99 | | | | (100) a_select3(pminus_ds1_filter, n5, n4) = all_74_8 & $i(all_74_8) % 168.68/23.99 | | | | % 168.68/23.99 | | | | ALPHA: (100) implies: % 168.68/23.99 | | | | (101) a_select3(pminus_ds1_filter, n5, n4) = all_74_8 % 168.68/23.99 | | | | % 168.68/23.99 | | | | REF_CLOSE: (14), (16), (89), (101) are inconsistent by sub-proof #5. % 168.68/23.99 | | | | % 168.68/23.99 | | | End of split % 168.68/23.99 | | | % 168.68/23.99 | | End of split % 168.68/23.99 | | % 168.68/23.99 | End of split % 168.68/23.99 | % 168.68/23.99 End of proof % 168.68/23.99 % 168.68/23.99 Sub-proof #4 shows that the following formulas are inconsistent: % 168.68/23.99 ---------------------------------------------------------------- % 168.68/23.99 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (pred(v1) = v2) | ~ $i(v1) % 168.68/23.99 | ~ $i(v0) | ~ gt(v1, v0) | leq(v0, v2)) % 168.68/23.99 (2) all_74_13 = n5 % 168.81/23.99 (3) a_select3(pminus_ds1_filter, all_74_11, n5) = all_74_9 % 168.81/23.99 (4) all_74_11 = n4 | gt(n4, all_74_11) % 168.81/23.99 (5) ~ (all_74_11 = n0) % 168.81/23.99 (6) $i(n2) % 168.81/23.99 (7) pred(n4) = n3 % 168.81/23.99 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 168.81/23.99 (a_select3(pminus_ds1_filter, v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 168.81/23.99 ~ leq(v1, all_74_13) | ~ leq(v0, all_74_13) | ~ leq(n0, v1) | ~ % 168.81/23.99 leq(n0, v0) | (a_select3(pminus_ds1_filter, v1, v0) = v2 & $i(v2))) % 168.81/23.99 (9) ! [v0: $i] : (v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0, n1) | ~ % 168.81/23.99 leq(n0, v0)) % 168.81/23.99 (10) leq(n5, n5) % 168.81/23.99 (11) pred(n3) = n2 % 168.81/23.99 (12) ~ (all_74_8 = all_74_9) % 168.81/23.99 (13) $i(n4) % 168.81/23.99 (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 168.81/23.99 (v1 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 168.81/23.99 v0)) % 168.81/23.99 (15) leq(all_74_11, n5) % 168.81/23.99 (16) $i(all_74_11) % 168.81/23.99 (17) leq(n0, n5) % 168.81/23.99 (18) a_select3(pminus_ds1_filter, n5, all_74_11) = all_74_8 % 168.81/23.99 (19) leq(n0, all_74_11) % 168.81/23.99 (20) pred(n2) = n1 % 168.81/23.99 (21) $i(n3) % 168.81/23.99 (22) $i(n5) % 168.81/23.99 (23) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ % 168.81/23.99 leq(v0, v1) | gt(v1, v0)) % 168.81/23.99 % 168.81/23.99 Begin of proof % 168.81/23.99 | % 168.81/23.99 | BETA: splitting (4) gives: % 168.81/23.99 | % 168.81/23.99 | Case 1: % 168.81/23.99 | | % 168.81/23.99 | | (24) gt(n4, all_74_11) % 168.81/23.99 | | % 168.81/23.99 | | GROUND_INST: instantiating (1) with all_74_11, n4, n3, simplifying with (7), % 168.81/23.99 | | (13), (16), (24) gives: % 168.81/23.99 | | (25) leq(all_74_11, n3) % 168.81/23.99 | | % 168.81/23.99 | | GROUND_INST: instantiating (23) with all_74_11, n3, simplifying with (16), % 168.81/23.99 | | (21), (25) gives: % 168.81/23.99 | | (26) all_74_11 = n3 | gt(n3, all_74_11) % 168.81/23.99 | | % 168.81/23.99 | | BETA: splitting (26) gives: % 168.81/23.99 | | % 168.81/23.99 | | Case 1: % 168.81/23.99 | | | % 168.81/23.99 | | | (27) gt(n3, all_74_11) % 168.81/23.99 | | | % 168.81/23.99 | | | GROUND_INST: instantiating (1) with all_74_11, n3, n2, simplifying with % 168.81/23.99 | | | (11), (16), (21), (27) gives: % 168.81/23.99 | | | (28) leq(all_74_11, n2) % 168.81/23.99 | | | % 168.81/23.99 | | | GROUND_INST: instantiating (23) with all_74_11, n2, simplifying with (6), % 168.81/23.99 | | | (16), (28) gives: % 168.81/23.99 | | | (29) all_74_11 = n2 | gt(n2, all_74_11) % 168.81/23.99 | | | % 168.81/23.99 | | | BETA: splitting (29) gives: % 168.81/23.99 | | | % 168.81/23.99 | | | Case 1: % 168.81/23.99 | | | | % 168.81/23.99 | | | | (30) gt(n2, all_74_11) % 168.81/23.99 | | | | % 168.81/23.99 | | | | GROUND_INST: instantiating (1) with all_74_11, n2, n1, simplifying with % 168.81/23.99 | | | | (6), (16), (20), (30) gives: % 168.81/23.99 | | | | (31) leq(all_74_11, n1) % 168.81/23.99 | | | | % 168.81/23.99 | | | | GROUND_INST: instantiating (9) with all_74_11, simplifying with (16), % 168.81/23.99 | | | | (19), (31) gives: % 168.81/23.99 | | | | (32) all_74_11 = n1 | all_74_11 = n0 % 168.81/23.99 | | | | % 168.81/23.99 | | | | BETA: splitting (32) gives: % 168.81/23.99 | | | | % 168.81/23.99 | | | | Case 1: % 168.81/23.99 | | | | | % 168.81/23.99 | | | | | (33) all_74_11 = n0 % 168.81/23.99 | | | | | % 168.81/23.99 | | | | | REDUCE: (5), (33) imply: % 168.81/23.99 | | | | | (34) $false % 168.81/23.99 | | | | | % 168.81/23.99 | | | | | CLOSE: (34) is inconsistent. % 168.81/23.99 | | | | | % 168.81/23.99 | | | | Case 2: % 168.81/23.99 | | | | | % 168.81/23.99 | | | | | (35) all_74_11 = n1 % 168.81/23.99 | | | | | % 168.81/23.99 | | | | | REDUCE: (3), (35) imply: % 168.81/23.99 | | | | | (36) a_select3(pminus_ds1_filter, n1, n5) = all_74_9 % 168.81/23.99 | | | | | % 168.81/23.99 | | | | | REDUCE: (18), (35) imply: % 168.81/23.99 | | | | | (37) a_select3(pminus_ds1_filter, n5, n1) = all_74_8 % 168.81/23.99 | | | | | % 168.81/23.99 | | | | | REDUCE: (16), (35) imply: % 168.81/23.99 | | | | | (38) $i(n1) % 168.81/23.99 | | | | | % 168.81/23.99 | | | | | REDUCE: (15), (35) imply: % 168.81/23.99 | | | | | (39) leq(n1, n5) % 168.81/23.99 | | | | | % 168.81/23.99 | | | | | REDUCE: (19), (35) imply: % 168.81/23.99 | | | | | (40) leq(n0, n1) % 168.81/23.99 | | | | | % 168.81/23.99 | | | | | GROUND_INST: instantiating (8) with n1, n5, all_74_9, simplifying with % 168.81/23.99 | | | | | (17), (22), (36), (38), (40) gives: % 168.81/23.99 | | | | | (41) ~ leq(n5, all_74_13) | ~ leq(n1, all_74_13) | % 168.81/23.99 | | | | | (a_select3(pminus_ds1_filter, n5, n1) = all_74_9 & % 168.81/23.99 | | | | | $i(all_74_9)) % 168.81/23.99 | | | | | % 168.81/23.99 | | | | | BETA: splitting (41) gives: % 168.81/23.99 | | | | | % 168.81/23.99 | | | | | Case 1: % 168.81/23.99 | | | | | | % 168.81/23.99 | | | | | | (42) ~ leq(n5, all_74_13) % 168.81/23.99 | | | | | | % 168.81/23.99 | | | | | | REDUCE: (2), (42) imply: % 168.81/23.99 | | | | | | (43) ~ leq(n5, n5) % 168.81/23.99 | | | | | | % 168.81/23.99 | | | | | | PRED_UNIFY: (10), (43) imply: % 168.81/23.99 | | | | | | (44) $false % 168.81/23.99 | | | | | | % 168.81/23.99 | | | | | | CLOSE: (44) is inconsistent. % 168.81/23.99 | | | | | | % 168.81/23.99 | | | | | Case 2: % 168.81/23.99 | | | | | | % 168.81/23.99 | | | | | | (45) ~ leq(n1, all_74_13) | (a_select3(pminus_ds1_filter, n5, % 168.81/23.99 | | | | | | n1) = all_74_9 & $i(all_74_9)) % 168.81/23.99 | | | | | | % 168.81/23.99 | | | | | | BETA: splitting (45) gives: % 168.81/23.99 | | | | | | % 168.81/23.99 | | | | | | Case 1: % 168.81/23.99 | | | | | | | % 168.81/23.99 | | | | | | | (46) ~ leq(n1, all_74_13) % 168.81/23.99 | | | | | | | % 168.81/23.99 | | | | | | | REDUCE: (2), (46) imply: % 168.81/23.99 | | | | | | | (47) ~ leq(n1, n5) % 168.81/23.99 | | | | | | | % 168.81/23.99 | | | | | | | PRED_UNIFY: (39), (47) imply: % 168.81/23.99 | | | | | | | (48) $false % 168.81/23.99 | | | | | | | % 168.81/23.99 | | | | | | | CLOSE: (48) is inconsistent. % 168.81/23.99 | | | | | | | % 168.81/23.99 | | | | | | Case 2: % 168.81/23.99 | | | | | | | % 168.81/23.99 | | | | | | | (49) a_select3(pminus_ds1_filter, n5, n1) = all_74_9 & % 168.81/23.99 | | | | | | | $i(all_74_9) % 168.81/23.99 | | | | | | | % 168.81/23.99 | | | | | | | ALPHA: (49) implies: % 168.81/23.99 | | | | | | | (50) a_select3(pminus_ds1_filter, n5, n1) = all_74_9 % 168.81/23.99 | | | | | | | % 168.81/23.99 | | | | | | | GROUND_INST: instantiating (14) with all_74_9, all_74_8, n1, n5, % 168.81/23.99 | | | | | | | pminus_ds1_filter, simplifying with (37), (50) gives: % 168.81/23.99 | | | | | | | (51) all_74_8 = all_74_9 % 168.81/24.00 | | | | | | | % 168.81/24.00 | | | | | | | REDUCE: (12), (51) imply: % 168.81/24.00 | | | | | | | (52) $false % 168.81/24.00 | | | | | | | % 168.81/24.00 | | | | | | | CLOSE: (52) is inconsistent. % 168.81/24.00 | | | | | | | % 168.81/24.00 | | | | | | End of split % 168.81/24.00 | | | | | | % 168.81/24.00 | | | | | End of split % 168.81/24.00 | | | | | % 168.81/24.00 | | | | End of split % 168.81/24.00 | | | | % 168.81/24.00 | | | Case 2: % 168.81/24.00 | | | | % 168.81/24.00 | | | | (53) all_74_11 = n2 % 168.81/24.00 | | | | % 168.81/24.00 | | | | REDUCE: (3), (53) imply: % 168.81/24.00 | | | | (54) a_select3(pminus_ds1_filter, n2, n5) = all_74_9 % 168.81/24.00 | | | | % 168.81/24.00 | | | | REDUCE: (18), (53) imply: % 168.81/24.00 | | | | (55) a_select3(pminus_ds1_filter, n5, n2) = all_74_8 % 168.81/24.00 | | | | % 168.81/24.00 | | | | REDUCE: (15), (53) imply: % 168.81/24.00 | | | | (56) leq(n2, n5) % 168.81/24.00 | | | | % 168.81/24.00 | | | | REDUCE: (19), (53) imply: % 168.81/24.00 | | | | (57) leq(n0, n2) % 168.81/24.00 | | | | % 168.81/24.00 | | | | GROUND_INST: instantiating (8) with n2, n5, all_74_9, simplifying with % 168.81/24.00 | | | | (6), (17), (22), (54), (57) gives: % 168.81/24.00 | | | | (58) ~ leq(n5, all_74_13) | ~ leq(n2, all_74_13) | % 168.81/24.00 | | | | (a_select3(pminus_ds1_filter, n5, n2) = all_74_9 & $i(all_74_9)) % 168.81/24.00 | | | | % 168.81/24.00 | | | | BETA: splitting (58) gives: % 168.81/24.00 | | | | % 168.81/24.00 | | | | Case 1: % 168.81/24.00 | | | | | % 168.81/24.00 | | | | | (59) ~ leq(n5, all_74_13) % 168.81/24.00 | | | | | % 168.81/24.00 | | | | | REDUCE: (2), (59) imply: % 168.81/24.00 | | | | | (60) ~ leq(n5, n5) % 168.81/24.00 | | | | | % 168.81/24.00 | | | | | PRED_UNIFY: (10), (60) imply: % 168.81/24.00 | | | | | (61) $false % 168.81/24.00 | | | | | % 168.81/24.00 | | | | | CLOSE: (61) is inconsistent. % 168.81/24.00 | | | | | % 168.81/24.00 | | | | Case 2: % 168.81/24.00 | | | | | % 168.81/24.00 | | | | | (62) ~ leq(n2, all_74_13) | (a_select3(pminus_ds1_filter, n5, n2) % 168.81/24.00 | | | | | = all_74_9 & $i(all_74_9)) % 168.81/24.00 | | | | | % 168.81/24.00 | | | | | BETA: splitting (62) gives: % 168.81/24.00 | | | | | % 168.81/24.00 | | | | | Case 1: % 168.81/24.00 | | | | | | % 168.81/24.00 | | | | | | (63) ~ leq(n2, all_74_13) % 168.81/24.00 | | | | | | % 168.81/24.00 | | | | | | REDUCE: (2), (63) imply: % 168.81/24.00 | | | | | | (64) ~ leq(n2, n5) % 168.81/24.00 | | | | | | % 168.81/24.00 | | | | | | PRED_UNIFY: (56), (64) imply: % 168.81/24.00 | | | | | | (65) $false % 168.81/24.00 | | | | | | % 168.81/24.00 | | | | | | CLOSE: (65) is inconsistent. % 168.81/24.00 | | | | | | % 168.81/24.00 | | | | | Case 2: % 168.81/24.00 | | | | | | % 168.81/24.00 | | | | | | (66) a_select3(pminus_ds1_filter, n5, n2) = all_74_9 & % 168.81/24.00 | | | | | | $i(all_74_9) % 168.81/24.00 | | | | | | % 168.81/24.00 | | | | | | ALPHA: (66) implies: % 168.81/24.00 | | | | | | (67) a_select3(pminus_ds1_filter, n5, n2) = all_74_9 % 168.81/24.00 | | | | | | % 168.81/24.00 | | | | | | GROUND_INST: instantiating (14) with all_74_9, all_74_8, n2, n5, % 168.81/24.00 | | | | | | pminus_ds1_filter, simplifying with (55), (67) gives: % 168.81/24.00 | | | | | | (68) all_74_8 = all_74_9 % 168.81/24.00 | | | | | | % 168.81/24.00 | | | | | | REDUCE: (12), (68) imply: % 168.81/24.00 | | | | | | (69) $false % 168.81/24.00 | | | | | | % 168.81/24.00 | | | | | | CLOSE: (69) is inconsistent. % 168.81/24.00 | | | | | | % 168.81/24.00 | | | | | End of split % 168.81/24.00 | | | | | % 168.81/24.00 | | | | End of split % 168.81/24.00 | | | | % 168.81/24.00 | | | End of split % 168.81/24.00 | | | % 168.81/24.00 | | Case 2: % 168.81/24.00 | | | % 168.81/24.00 | | | (70) all_74_11 = n3 % 168.81/24.00 | | | % 168.81/24.00 | | | REDUCE: (3), (70) imply: % 168.81/24.00 | | | (71) a_select3(pminus_ds1_filter, n3, n5) = all_74_9 % 168.81/24.00 | | | % 168.81/24.00 | | | REDUCE: (18), (70) imply: % 168.81/24.00 | | | (72) a_select3(pminus_ds1_filter, n5, n3) = all_74_8 % 168.81/24.00 | | | % 168.81/24.00 | | | REDUCE: (15), (70) imply: % 168.81/24.00 | | | (73) leq(n3, n5) % 168.81/24.00 | | | % 168.81/24.00 | | | REDUCE: (19), (70) imply: % 168.81/24.00 | | | (74) leq(n0, n3) % 168.81/24.00 | | | % 168.81/24.00 | | | GROUND_INST: instantiating (8) with n3, n5, all_74_9, simplifying with % 168.81/24.00 | | | (17), (21), (22), (71), (74) gives: % 168.81/24.00 | | | (75) ~ leq(n5, all_74_13) | ~ leq(n3, all_74_13) | % 168.81/24.00 | | | (a_select3(pminus_ds1_filter, n5, n3) = all_74_9 & $i(all_74_9)) % 168.81/24.00 | | | % 168.81/24.00 | | | BETA: splitting (75) gives: % 168.81/24.00 | | | % 168.81/24.00 | | | Case 1: % 168.81/24.00 | | | | % 168.81/24.00 | | | | (76) ~ leq(n5, all_74_13) % 168.81/24.00 | | | | % 168.81/24.00 | | | | REDUCE: (2), (76) imply: % 168.81/24.00 | | | | (77) ~ leq(n5, n5) % 168.81/24.00 | | | | % 168.81/24.00 | | | | PRED_UNIFY: (10), (77) imply: % 168.81/24.00 | | | | (78) $false % 168.81/24.00 | | | | % 168.81/24.00 | | | | CLOSE: (78) is inconsistent. % 168.81/24.00 | | | | % 168.81/24.00 | | | Case 2: % 168.81/24.00 | | | | % 168.81/24.00 | | | | (79) ~ leq(n3, all_74_13) | (a_select3(pminus_ds1_filter, n5, n3) = % 168.81/24.00 | | | | all_74_9 & $i(all_74_9)) % 168.81/24.00 | | | | % 168.81/24.00 | | | | BETA: splitting (79) gives: % 168.81/24.00 | | | | % 168.81/24.00 | | | | Case 1: % 168.81/24.00 | | | | | % 168.81/24.00 | | | | | (80) ~ leq(n3, all_74_13) % 168.81/24.00 | | | | | % 168.81/24.00 | | | | | REDUCE: (2), (80) imply: % 168.81/24.00 | | | | | (81) ~ leq(n3, n5) % 168.81/24.00 | | | | | % 168.81/24.00 | | | | | PRED_UNIFY: (73), (81) imply: % 168.81/24.00 | | | | | (82) $false % 168.81/24.00 | | | | | % 168.81/24.00 | | | | | CLOSE: (82) is inconsistent. % 168.81/24.00 | | | | | % 168.81/24.00 | | | | Case 2: % 168.81/24.00 | | | | | % 168.81/24.00 | | | | | (83) a_select3(pminus_ds1_filter, n5, n3) = all_74_9 & $i(all_74_9) % 168.81/24.00 | | | | | % 168.81/24.00 | | | | | ALPHA: (83) implies: % 168.81/24.00 | | | | | (84) a_select3(pminus_ds1_filter, n5, n3) = all_74_9 % 168.81/24.00 | | | | | % 168.81/24.00 | | | | | GROUND_INST: instantiating (14) with all_74_9, all_74_8, n3, n5, % 168.81/24.00 | | | | | pminus_ds1_filter, simplifying with (72), (84) gives: % 168.81/24.00 | | | | | (85) all_74_8 = all_74_9 % 168.81/24.00 | | | | | % 168.81/24.00 | | | | | REDUCE: (12), (85) imply: % 168.81/24.00 | | | | | (86) $false % 168.81/24.00 | | | | | % 168.81/24.00 | | | | | CLOSE: (86) is inconsistent. % 168.81/24.00 | | | | | % 168.81/24.00 | | | | End of split % 168.81/24.00 | | | | % 168.81/24.00 | | | End of split % 168.81/24.00 | | | % 168.81/24.00 | | End of split % 168.81/24.00 | | % 168.81/24.00 | Case 2: % 168.81/24.00 | | % 168.81/24.00 | | (87) all_74_11 = n4 % 168.81/24.00 | | % 168.81/24.00 | | REDUCE: (3), (87) imply: % 168.81/24.00 | | (88) a_select3(pminus_ds1_filter, n4, n5) = all_74_9 % 168.81/24.00 | | % 168.81/24.00 | | REDUCE: (18), (87) imply: % 168.81/24.00 | | (89) a_select3(pminus_ds1_filter, n5, n4) = all_74_8 % 168.81/24.00 | | % 168.81/24.00 | | REDUCE: (15), (87) imply: % 168.81/24.00 | | (90) leq(n4, n5) % 168.81/24.00 | | % 168.81/24.00 | | REDUCE: (19), (87) imply: % 168.81/24.00 | | (91) leq(n0, n4) % 168.81/24.00 | | % 168.81/24.00 | | GROUND_INST: instantiating (8) with n4, n5, all_74_9, simplifying with (13), % 168.81/24.00 | | (17), (22), (88), (91) gives: % 168.81/24.00 | | (92) ~ leq(n5, all_74_13) | ~ leq(n4, all_74_13) | % 168.81/24.00 | | (a_select3(pminus_ds1_filter, n5, n4) = all_74_9 & $i(all_74_9)) % 168.81/24.00 | | % 168.81/24.00 | | BETA: splitting (92) gives: % 168.81/24.00 | | % 168.81/24.00 | | Case 1: % 168.81/24.00 | | | % 168.81/24.00 | | | (93) ~ leq(n5, all_74_13) % 168.81/24.00 | | | % 168.81/24.00 | | | REDUCE: (2), (93) imply: % 168.81/24.00 | | | (94) ~ leq(n5, n5) % 168.81/24.00 | | | % 168.81/24.00 | | | PRED_UNIFY: (10), (94) imply: % 168.81/24.00 | | | (95) $false % 168.81/24.00 | | | % 168.81/24.00 | | | CLOSE: (95) is inconsistent. % 168.81/24.00 | | | % 168.81/24.00 | | Case 2: % 168.81/24.00 | | | % 168.81/24.00 | | | (96) ~ leq(n4, all_74_13) | (a_select3(pminus_ds1_filter, n5, n4) = % 168.81/24.00 | | | all_74_9 & $i(all_74_9)) % 168.81/24.00 | | | % 168.81/24.00 | | | BETA: splitting (96) gives: % 168.81/24.00 | | | % 168.81/24.00 | | | Case 1: % 168.81/24.00 | | | | % 168.81/24.00 | | | | (97) ~ leq(n4, all_74_13) % 168.81/24.00 | | | | % 168.81/24.00 | | | | REDUCE: (2), (97) imply: % 168.81/24.00 | | | | (98) ~ leq(n4, n5) % 168.81/24.00 | | | | % 168.81/24.00 | | | | PRED_UNIFY: (90), (98) imply: % 168.81/24.00 | | | | (99) $false % 168.81/24.00 | | | | % 168.81/24.00 | | | | CLOSE: (99) is inconsistent. % 168.81/24.00 | | | | % 168.81/24.00 | | | Case 2: % 168.81/24.00 | | | | % 168.81/24.00 | | | | (100) a_select3(pminus_ds1_filter, n5, n4) = all_74_9 & $i(all_74_9) % 168.81/24.00 | | | | % 168.81/24.00 | | | | ALPHA: (100) implies: % 168.81/24.00 | | | | (101) a_select3(pminus_ds1_filter, n5, n4) = all_74_9 % 168.81/24.00 | | | | % 168.81/24.00 | | | | REF_CLOSE: (12), (14), (89), (101) are inconsistent by sub-proof #5. % 168.81/24.00 | | | | % 168.81/24.00 | | | End of split % 168.81/24.00 | | | % 168.81/24.00 | | End of split % 168.81/24.00 | | % 168.81/24.00 | End of split % 168.81/24.00 | % 168.81/24.00 End of proof % 168.81/24.00 % 168.81/24.00 Sub-proof #5 shows that the following formulas are inconsistent: % 168.81/24.00 ---------------------------------------------------------------- % 168.81/24.00 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 168.81/24.00 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 168.81/24.00 v0)) % 168.81/24.00 (2) a_select3(pminus_ds1_filter, n5, n4) = all_74_8 % 168.81/24.00 (3) a_select3(pminus_ds1_filter, n5, n4) = all_74_9 % 168.81/24.00 (4) ~ (all_74_8 = all_74_9) % 168.81/24.00 % 168.81/24.00 Begin of proof % 168.81/24.00 | % 168.81/24.00 | GROUND_INST: instantiating (1) with all_74_9, all_74_8, n4, n5, % 168.81/24.00 | pminus_ds1_filter, simplifying with (2), (3) gives: % 168.81/24.00 | (5) all_74_8 = all_74_9 % 168.81/24.00 | % 168.81/24.00 | REDUCE: (4), (5) imply: % 168.81/24.00 | (6) $false % 168.81/24.00 | % 168.81/24.00 | CLOSE: (6) is inconsistent. % 168.81/24.00 | % 168.81/24.00 End of proof % 168.81/24.00 % 168.81/24.00 Sub-proof #6 shows that the following formulas are inconsistent: % 168.81/24.00 ---------------------------------------------------------------- % 168.81/24.00 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (pred(v1) = v2) | ~ $i(v1) % 168.81/24.00 | ~ $i(v0) | ~ gt(v1, v0) | leq(v0, v2)) % 168.81/24.00 (2) all_74_10 = n4 | gt(n4, all_74_10) % 168.81/24.00 (3) all_74_13 = n5 % 168.81/24.00 (4) all_74_11 = n4 | gt(n4, all_74_11) % 168.81/24.00 (5) ~ (all_74_11 = n0) % 168.81/24.00 (6) $i(n2) % 168.81/24.00 (7) pred(n4) = n3 % 168.81/24.00 (8) a_select3(pminus_ds1_filter, all_74_11, all_74_10) = all_74_9 % 168.81/24.00 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 168.81/24.00 (a_select3(pminus_ds1_filter, v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 168.81/24.00 ~ leq(v1, all_74_13) | ~ leq(v0, all_74_13) | ~ leq(n0, v1) | ~ % 168.81/24.00 leq(n0, v0) | (a_select3(pminus_ds1_filter, v1, v0) = v2 & $i(v2))) % 168.81/24.00 (10) leq(all_74_10, n5) % 168.81/24.00 (11) ! [v0: $i] : (v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0, n1) | ~ % 168.81/24.00 leq(n0, v0)) % 168.81/24.00 (12) $i(all_74_10) % 168.81/24.00 (13) pred(n3) = n2 % 168.81/24.00 (14) ~ (all_74_10 = n0) % 168.81/24.00 (15) ~ (all_74_8 = all_74_9) % 168.81/24.00 (16) a_select3(pminus_ds1_filter, all_74_10, all_74_11) = all_74_8 % 168.81/24.00 (17) $i(n4) % 168.81/24.00 (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 168.81/24.00 (v1 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 168.81/24.00 v0)) % 168.81/24.00 (19) leq(all_74_11, n5) % 168.81/24.00 (20) $i(all_74_11) % 168.81/24.00 (21) leq(n0, all_74_11) % 168.81/24.00 (22) pred(n2) = n1 % 168.81/24.00 (23) $i(n3) % 168.81/24.00 (24) leq(n0, all_74_10) % 168.81/24.00 (25) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ % 168.81/24.00 leq(v0, v1) | gt(v1, v0)) % 168.81/24.00 % 168.81/24.00 Begin of proof % 168.81/24.00 | % 168.81/24.00 | BETA: splitting (4) gives: % 168.81/24.00 | % 168.81/24.00 | Case 1: % 168.81/24.00 | | % 168.81/24.00 | | (26) gt(n4, all_74_11) % 168.81/24.00 | | % 168.81/24.00 | | GROUND_INST: instantiating (1) with all_74_11, n4, n3, simplifying with (7), % 168.81/24.00 | | (17), (20), (26) gives: % 168.81/24.00 | | (27) leq(all_74_11, n3) % 168.81/24.00 | | % 168.81/24.01 | | GROUND_INST: instantiating (25) with all_74_11, n3, simplifying with (20), % 168.81/24.01 | | (23), (27) gives: % 168.81/24.01 | | (28) all_74_11 = n3 | gt(n3, all_74_11) % 168.81/24.01 | | % 168.81/24.01 | | BETA: splitting (2) gives: % 168.81/24.01 | | % 168.81/24.01 | | Case 1: % 168.81/24.01 | | | % 168.81/24.01 | | | (29) gt(n4, all_74_10) % 168.81/24.01 | | | % 168.81/24.01 | | | GROUND_INST: instantiating (1) with all_74_10, n4, n3, simplifying with % 168.81/24.01 | | | (7), (12), (17), (29) gives: % 168.81/24.01 | | | (30) leq(all_74_10, n3) % 168.81/24.01 | | | % 168.81/24.01 | | | GROUND_INST: instantiating (25) with all_74_10, n3, simplifying with (12), % 168.81/24.01 | | | (23), (30) gives: % 168.81/24.01 | | | (31) all_74_10 = n3 | gt(n3, all_74_10) % 168.81/24.01 | | | % 168.81/24.01 | | | BETA: splitting (28) gives: % 168.81/24.01 | | | % 168.81/24.01 | | | Case 1: % 168.81/24.01 | | | | % 168.81/24.01 | | | | (32) gt(n3, all_74_11) % 168.81/24.01 | | | | % 168.81/24.01 | | | | GROUND_INST: instantiating (1) with all_74_11, n3, n2, simplifying with % 168.81/24.01 | | | | (13), (20), (23), (32) gives: % 168.81/24.01 | | | | (33) leq(all_74_11, n2) % 168.81/24.01 | | | | % 168.81/24.01 | | | | GROUND_INST: instantiating (25) with all_74_11, n2, simplifying with % 168.81/24.01 | | | | (6), (20), (33) gives: % 168.81/24.01 | | | | (34) all_74_11 = n2 | gt(n2, all_74_11) % 168.81/24.01 | | | | % 168.81/24.01 | | | | BETA: splitting (31) gives: % 168.81/24.01 | | | | % 168.81/24.01 | | | | Case 1: % 168.81/24.01 | | | | | % 168.81/24.01 | | | | | (35) gt(n3, all_74_10) % 168.81/24.01 | | | | | % 168.81/24.01 | | | | | GROUND_INST: instantiating (1) with all_74_10, n3, n2, simplifying % 168.81/24.01 | | | | | with (12), (13), (23), (35) gives: % 168.81/24.01 | | | | | (36) leq(all_74_10, n2) % 168.81/24.01 | | | | | % 168.81/24.01 | | | | | GROUND_INST: instantiating (25) with all_74_10, n2, simplifying with % 168.81/24.01 | | | | | (6), (12), (36) gives: % 168.81/24.01 | | | | | (37) all_74_10 = n2 | gt(n2, all_74_10) % 168.81/24.01 | | | | | % 168.81/24.01 | | | | | BETA: splitting (34) gives: % 168.81/24.01 | | | | | % 168.81/24.01 | | | | | Case 1: % 168.81/24.01 | | | | | | % 168.81/24.01 | | | | | | (38) gt(n2, all_74_11) % 168.81/24.01 | | | | | | % 168.81/24.01 | | | | | | GROUND_INST: instantiating (1) with all_74_11, n2, n1, simplifying % 168.81/24.01 | | | | | | with (6), (20), (22), (38) gives: % 168.81/24.01 | | | | | | (39) leq(all_74_11, n1) % 168.81/24.01 | | | | | | % 168.81/24.01 | | | | | | GROUND_INST: instantiating (11) with all_74_11, simplifying with % 168.81/24.01 | | | | | | (20), (21), (39) gives: % 168.81/24.01 | | | | | | (40) all_74_11 = n1 | all_74_11 = n0 % 168.81/24.01 | | | | | | % 168.81/24.01 | | | | | | BETA: splitting (40) gives: % 168.81/24.01 | | | | | | % 168.81/24.01 | | | | | | Case 1: % 168.81/24.01 | | | | | | | % 168.81/24.01 | | | | | | | (41) all_74_11 = n0 % 168.81/24.01 | | | | | | | % 168.81/24.01 | | | | | | | REDUCE: (5), (41) imply: % 168.81/24.01 | | | | | | | (42) $false % 168.81/24.01 | | | | | | | % 168.81/24.01 | | | | | | | CLOSE: (42) is inconsistent. % 168.81/24.01 | | | | | | | % 168.81/24.01 | | | | | | Case 2: % 168.81/24.01 | | | | | | | % 168.81/24.01 | | | | | | | (43) all_74_11 = n1 % 168.81/24.01 | | | | | | | % 168.81/24.01 | | | | | | | REDUCE: (16), (43) imply: % 168.81/24.01 | | | | | | | (44) a_select3(pminus_ds1_filter, all_74_10, n1) = all_74_8 % 168.81/24.01 | | | | | | | % 168.81/24.01 | | | | | | | REDUCE: (8), (43) imply: % 168.81/24.01 | | | | | | | (45) a_select3(pminus_ds1_filter, n1, all_74_10) = all_74_9 % 168.81/24.01 | | | | | | | % 168.81/24.01 | | | | | | | REDUCE: (20), (43) imply: % 168.81/24.01 | | | | | | | (46) $i(n1) % 168.81/24.01 | | | | | | | % 168.81/24.01 | | | | | | | REDUCE: (19), (43) imply: % 168.81/24.01 | | | | | | | (47) leq(n1, n5) % 168.81/24.01 | | | | | | | % 168.81/24.01 | | | | | | | REDUCE: (21), (43) imply: % 168.81/24.01 | | | | | | | (48) leq(n0, n1) % 168.81/24.01 | | | | | | | % 168.81/24.01 | | | | | | | BETA: splitting (37) gives: % 168.81/24.01 | | | | | | | % 168.81/24.01 | | | | | | | Case 1: % 168.81/24.01 | | | | | | | | % 168.81/24.01 | | | | | | | | (49) gt(n2, all_74_10) % 168.81/24.01 | | | | | | | | % 168.81/24.01 | | | | | | | | GROUND_INST: instantiating (1) with all_74_10, n2, n1, % 168.81/24.01 | | | | | | | | simplifying with (6), (12), (22), (49) gives: % 168.81/24.01 | | | | | | | | (50) leq(all_74_10, n1) % 168.81/24.01 | | | | | | | | % 168.81/24.01 | | | | | | | | GROUND_INST: instantiating (11) with all_74_10, simplifying with % 168.81/24.01 | | | | | | | | (12), (24), (50) gives: % 168.81/24.01 | | | | | | | | (51) all_74_10 = n1 | all_74_10 = n0 % 168.81/24.01 | | | | | | | | % 168.81/24.01 | | | | | | | | BETA: splitting (51) gives: % 168.81/24.01 | | | | | | | | % 168.81/24.01 | | | | | | | | Case 1: % 168.81/24.01 | | | | | | | | | % 168.81/24.01 | | | | | | | | | (52) all_74_10 = n0 % 168.81/24.01 | | | | | | | | | % 168.81/24.01 | | | | | | | | | REDUCE: (14), (52) imply: % 168.81/24.01 | | | | | | | | | (53) $false % 168.81/24.01 | | | | | | | | | % 168.81/24.01 | | | | | | | | | CLOSE: (53) is inconsistent. % 168.81/24.01 | | | | | | | | | % 168.81/24.01 | | | | | | | | Case 2: % 168.81/24.01 | | | | | | | | | % 168.81/24.01 | | | | | | | | | (54) all_74_10 = n1 % 168.81/24.01 | | | | | | | | | % 168.81/24.01 | | | | | | | | | REDUCE: (44), (54) imply: % 168.81/24.01 | | | | | | | | | (55) a_select3(pminus_ds1_filter, n1, n1) = all_74_8 % 168.81/24.01 | | | | | | | | | % 168.81/24.01 | | | | | | | | | REDUCE: (45), (54) imply: % 168.81/24.01 | | | | | | | | | (56) a_select3(pminus_ds1_filter, n1, n1) = all_74_9 % 168.81/24.01 | | | | | | | | | % 168.81/24.01 | | | | | | | | | GROUND_INST: instantiating (18) with all_74_9, all_74_8, n1, % 168.81/24.01 | | | | | | | | | n1, pminus_ds1_filter, simplifying with (55), (56) % 168.81/24.01 | | | | | | | | | gives: % 168.81/24.01 | | | | | | | | | (57) all_74_8 = all_74_9 % 168.81/24.01 | | | | | | | | | % 168.81/24.01 | | | | | | | | | REDUCE: (15), (57) imply: % 168.81/24.01 | | | | | | | | | (58) $false % 168.81/24.01 | | | | | | | | | % 168.81/24.01 | | | | | | | | | CLOSE: (58) is inconsistent. % 168.81/24.01 | | | | | | | | | % 168.81/24.01 | | | | | | | | End of split % 168.81/24.01 | | | | | | | | % 168.81/24.01 | | | | | | | Case 2: % 168.81/24.01 | | | | | | | | % 168.81/24.01 | | | | | | | | (59) all_74_10 = n2 % 168.81/24.01 | | | | | | | | % 168.81/24.01 | | | | | | | | REDUCE: (44), (59) imply: % 168.81/24.01 | | | | | | | | (60) a_select3(pminus_ds1_filter, n2, n1) = all_74_8 % 168.81/24.01 | | | | | | | | % 168.81/24.01 | | | | | | | | REDUCE: (45), (59) imply: % 168.81/24.01 | | | | | | | | (61) a_select3(pminus_ds1_filter, n1, n2) = all_74_9 % 168.81/24.01 | | | | | | | | % 168.81/24.01 | | | | | | | | REDUCE: (10), (59) imply: % 168.81/24.01 | | | | | | | | (62) leq(n2, n5) % 168.81/24.01 | | | | | | | | % 168.81/24.01 | | | | | | | | REDUCE: (24), (59) imply: % 168.81/24.01 | | | | | | | | (63) leq(n0, n2) % 168.81/24.01 | | | | | | | | % 168.81/24.01 | | | | | | | | GROUND_INST: instantiating (9) with n1, n2, all_74_9, % 168.81/24.01 | | | | | | | | simplifying with (6), (46), (48), (61), (63) gives: % 168.81/24.01 | | | | | | | | (64) ~ leq(n2, all_74_13) | ~ leq(n1, all_74_13) | % 168.81/24.01 | | | | | | | | (a_select3(pminus_ds1_filter, n2, n1) = all_74_9 & % 168.81/24.01 | | | | | | | | $i(all_74_9)) % 168.81/24.01 | | | | | | | | % 168.81/24.01 | | | | | | | | BETA: splitting (64) gives: % 168.81/24.01 | | | | | | | | % 168.81/24.01 | | | | | | | | Case 1: % 168.81/24.01 | | | | | | | | | % 168.81/24.01 | | | | | | | | | (65) ~ leq(n2, all_74_13) % 168.81/24.01 | | | | | | | | | % 168.81/24.01 | | | | | | | | | REDUCE: (3), (65) imply: % 168.81/24.01 | | | | | | | | | (66) ~ leq(n2, n5) % 168.81/24.01 | | | | | | | | | % 168.81/24.01 | | | | | | | | | PRED_UNIFY: (62), (66) imply: % 168.81/24.01 | | | | | | | | | (67) $false % 168.81/24.01 | | | | | | | | | % 168.81/24.01 | | | | | | | | | CLOSE: (67) is inconsistent. % 168.81/24.01 | | | | | | | | | % 168.81/24.01 | | | | | | | | Case 2: % 168.81/24.01 | | | | | | | | | % 168.81/24.01 | | | | | | | | | (68) ~ leq(n1, all_74_13) | (a_select3(pminus_ds1_filter, % 168.81/24.01 | | | | | | | | | n2, n1) = all_74_9 & $i(all_74_9)) % 168.81/24.01 | | | | | | | | | % 168.81/24.01 | | | | | | | | | BETA: splitting (68) gives: % 168.81/24.01 | | | | | | | | | % 168.81/24.01 | | | | | | | | | Case 1: % 168.81/24.01 | | | | | | | | | | % 168.81/24.01 | | | | | | | | | | (69) ~ leq(n1, all_74_13) % 168.81/24.01 | | | | | | | | | | % 168.81/24.01 | | | | | | | | | | REDUCE: (3), (69) imply: % 168.81/24.01 | | | | | | | | | | (70) ~ leq(n1, n5) % 168.81/24.01 | | | | | | | | | | % 168.81/24.01 | | | | | | | | | | PRED_UNIFY: (47), (70) imply: % 168.81/24.01 | | | | | | | | | | (71) $false % 168.81/24.01 | | | | | | | | | | % 168.81/24.01 | | | | | | | | | | CLOSE: (71) is inconsistent. % 168.81/24.01 | | | | | | | | | | % 168.81/24.01 | | | | | | | | | Case 2: % 168.81/24.01 | | | | | | | | | | % 168.81/24.01 | | | | | | | | | | (72) a_select3(pminus_ds1_filter, n2, n1) = all_74_9 & % 168.81/24.01 | | | | | | | | | | $i(all_74_9) % 168.81/24.01 | | | | | | | | | | % 168.81/24.01 | | | | | | | | | | ALPHA: (72) implies: % 168.81/24.01 | | | | | | | | | | (73) a_select3(pminus_ds1_filter, n2, n1) = all_74_9 % 168.81/24.01 | | | | | | | | | | % 168.81/24.01 | | | | | | | | | | REF_CLOSE: (15), (18), (60), (73) are inconsistent by % 168.81/24.01 | | | | | | | | | | sub-proof #9. % 168.81/24.01 | | | | | | | | | | % 168.81/24.01 | | | | | | | | | End of split % 168.81/24.01 | | | | | | | | | % 168.81/24.01 | | | | | | | | End of split % 168.81/24.01 | | | | | | | | % 168.81/24.01 | | | | | | | End of split % 168.81/24.01 | | | | | | | % 168.81/24.01 | | | | | | End of split % 168.81/24.01 | | | | | | % 168.81/24.01 | | | | | Case 2: % 168.81/24.01 | | | | | | % 168.81/24.01 | | | | | | (74) all_74_11 = n2 % 168.81/24.01 | | | | | | % 168.81/24.01 | | | | | | REDUCE: (16), (74) imply: % 168.81/24.01 | | | | | | (75) a_select3(pminus_ds1_filter, all_74_10, n2) = all_74_8 % 168.81/24.01 | | | | | | % 168.81/24.01 | | | | | | REDUCE: (8), (74) imply: % 168.81/24.01 | | | | | | (76) a_select3(pminus_ds1_filter, n2, all_74_10) = all_74_9 % 168.81/24.01 | | | | | | % 168.81/24.01 | | | | | | REDUCE: (19), (74) imply: % 168.81/24.01 | | | | | | (77) leq(n2, n5) % 168.81/24.01 | | | | | | % 168.81/24.01 | | | | | | REDUCE: (21), (74) imply: % 168.81/24.01 | | | | | | (78) leq(n0, n2) % 168.81/24.01 | | | | | | % 168.81/24.01 | | | | | | BETA: splitting (37) gives: % 168.81/24.01 | | | | | | % 168.81/24.01 | | | | | | Case 1: % 168.81/24.01 | | | | | | | % 168.81/24.01 | | | | | | | (79) gt(n2, all_74_10) % 168.81/24.01 | | | | | | | % 168.81/24.01 | | | | | | | GROUND_INST: instantiating (1) with all_74_10, n2, n1, simplifying % 168.81/24.01 | | | | | | | with (6), (12), (22), (79) gives: % 168.81/24.01 | | | | | | | (80) leq(all_74_10, n1) % 168.81/24.01 | | | | | | | % 168.81/24.01 | | | | | | | GROUND_INST: instantiating (11) with all_74_10, simplifying with % 168.81/24.01 | | | | | | | (12), (24), (80) gives: % 168.81/24.01 | | | | | | | (81) all_74_10 = n1 | all_74_10 = n0 % 168.81/24.01 | | | | | | | % 168.81/24.01 | | | | | | | BETA: splitting (81) gives: % 168.81/24.01 | | | | | | | % 168.81/24.01 | | | | | | | Case 1: % 168.81/24.01 | | | | | | | | % 168.81/24.01 | | | | | | | | (82) all_74_10 = n0 % 168.81/24.01 | | | | | | | | % 168.81/24.01 | | | | | | | | REDUCE: (14), (82) imply: % 168.81/24.01 | | | | | | | | (83) $false % 168.81/24.01 | | | | | | | | % 168.81/24.01 | | | | | | | | CLOSE: (83) is inconsistent. % 168.81/24.01 | | | | | | | | % 168.81/24.01 | | | | | | | Case 2: % 168.81/24.01 | | | | | | | | % 168.81/24.01 | | | | | | | | (84) all_74_10 = n1 % 168.81/24.01 | | | | | | | | % 168.81/24.01 | | | | | | | | REDUCE: (75), (84) imply: % 168.81/24.01 | | | | | | | | (85) a_select3(pminus_ds1_filter, n1, n2) = all_74_8 % 168.81/24.01 | | | | | | | | % 168.81/24.01 | | | | | | | | REDUCE: (76), (84) imply: % 168.81/24.01 | | | | | | | | (86) a_select3(pminus_ds1_filter, n2, n1) = all_74_9 % 168.81/24.01 | | | | | | | | % 168.81/24.01 | | | | | | | | REDUCE: (12), (84) imply: % 168.81/24.01 | | | | | | | | (87) $i(n1) % 168.81/24.01 | | | | | | | | % 168.81/24.01 | | | | | | | | REDUCE: (10), (84) imply: % 168.81/24.01 | | | | | | | | (88) leq(n1, n5) % 168.81/24.01 | | | | | | | | % 168.81/24.01 | | | | | | | | REDUCE: (24), (84) imply: % 168.81/24.01 | | | | | | | | (89) leq(n0, n1) % 168.81/24.01 | | | | | | | | % 168.81/24.01 | | | | | | | | GROUND_INST: instantiating (9) with n1, n2, all_74_8, % 168.81/24.01 | | | | | | | | simplifying with (6), (78), (85), (87), (89) gives: % 168.81/24.01 | | | | | | | | (90) ~ leq(n2, all_74_13) | ~ leq(n1, all_74_13) | % 168.81/24.01 | | | | | | | | (a_select3(pminus_ds1_filter, n2, n1) = all_74_8 & % 168.81/24.01 | | | | | | | | $i(all_74_8)) % 168.81/24.01 | | | | | | | | % 168.81/24.01 | | | | | | | | BETA: splitting (90) gives: % 168.81/24.01 | | | | | | | | % 168.81/24.01 | | | | | | | | Case 1: % 168.81/24.01 | | | | | | | | | % 168.81/24.01 | | | | | | | | | (91) ~ leq(n2, all_74_13) % 168.81/24.01 | | | | | | | | | % 168.81/24.01 | | | | | | | | | REDUCE: (3), (91) imply: % 168.81/24.01 | | | | | | | | | (92) ~ leq(n2, n5) % 168.81/24.01 | | | | | | | | | % 168.81/24.01 | | | | | | | | | PRED_UNIFY: (77), (92) imply: % 168.81/24.01 | | | | | | | | | (93) $false % 168.81/24.01 | | | | | | | | | % 168.81/24.01 | | | | | | | | | CLOSE: (93) is inconsistent. % 168.81/24.01 | | | | | | | | | % 168.81/24.01 | | | | | | | | Case 2: % 168.81/24.01 | | | | | | | | | % 168.81/24.01 | | | | | | | | | (94) ~ leq(n1, all_74_13) | (a_select3(pminus_ds1_filter, % 168.81/24.01 | | | | | | | | | n2, n1) = all_74_8 & $i(all_74_8)) % 168.81/24.01 | | | | | | | | | % 168.81/24.01 | | | | | | | | | BETA: splitting (94) gives: % 168.81/24.01 | | | | | | | | | % 168.81/24.01 | | | | | | | | | Case 1: % 168.81/24.01 | | | | | | | | | | % 168.81/24.01 | | | | | | | | | | (95) ~ leq(n1, all_74_13) % 168.81/24.01 | | | | | | | | | | % 168.81/24.01 | | | | | | | | | | REDUCE: (3), (95) imply: % 168.81/24.01 | | | | | | | | | | (96) ~ leq(n1, n5) % 168.81/24.01 | | | | | | | | | | % 168.81/24.01 | | | | | | | | | | PRED_UNIFY: (88), (96) imply: % 168.81/24.01 | | | | | | | | | | (97) $false % 168.81/24.01 | | | | | | | | | | % 168.81/24.01 | | | | | | | | | | CLOSE: (97) is inconsistent. % 168.81/24.01 | | | | | | | | | | % 168.81/24.01 | | | | | | | | | Case 2: % 168.81/24.01 | | | | | | | | | | % 168.81/24.01 | | | | | | | | | | (98) a_select3(pminus_ds1_filter, n2, n1) = all_74_8 & % 168.81/24.01 | | | | | | | | | | $i(all_74_8) % 168.81/24.01 | | | | | | | | | | % 168.81/24.01 | | | | | | | | | | ALPHA: (98) implies: % 168.81/24.01 | | | | | | | | | | (99) a_select3(pminus_ds1_filter, n2, n1) = all_74_8 % 168.81/24.01 | | | | | | | | | | % 168.81/24.01 | | | | | | | | | | REF_CLOSE: (15), (18), (86), (99) are inconsistent by % 168.81/24.01 | | | | | | | | | | sub-proof #9. % 168.81/24.01 | | | | | | | | | | % 168.81/24.01 | | | | | | | | | End of split % 168.81/24.01 | | | | | | | | | % 168.81/24.01 | | | | | | | | End of split % 168.81/24.01 | | | | | | | | % 168.81/24.01 | | | | | | | End of split % 168.81/24.01 | | | | | | | % 168.81/24.01 | | | | | | Case 2: % 168.81/24.01 | | | | | | | % 168.81/24.01 | | | | | | | (100) all_74_10 = n2 % 168.81/24.01 | | | | | | | % 168.81/24.01 | | | | | | | REDUCE: (75), (100) imply: % 168.81/24.01 | | | | | | | (101) a_select3(pminus_ds1_filter, n2, n2) = all_74_8 % 168.81/24.01 | | | | | | | % 168.81/24.01 | | | | | | | REDUCE: (76), (100) imply: % 168.81/24.01 | | | | | | | (102) a_select3(pminus_ds1_filter, n2, n2) = all_74_9 % 168.81/24.01 | | | | | | | % 168.81/24.01 | | | | | | | GROUND_INST: instantiating (18) with all_74_9, all_74_8, n2, n2, % 168.81/24.01 | | | | | | | pminus_ds1_filter, simplifying with (101), (102) % 168.81/24.01 | | | | | | | gives: % 168.81/24.01 | | | | | | | (103) all_74_8 = all_74_9 % 168.81/24.01 | | | | | | | % 168.81/24.01 | | | | | | | REDUCE: (15), (103) imply: % 168.81/24.01 | | | | | | | (104) $false % 168.81/24.01 | | | | | | | % 168.81/24.01 | | | | | | | CLOSE: (104) is inconsistent. % 168.81/24.01 | | | | | | | % 168.81/24.01 | | | | | | End of split % 168.81/24.01 | | | | | | % 168.81/24.01 | | | | | End of split % 168.81/24.01 | | | | | % 168.81/24.01 | | | | Case 2: % 168.81/24.01 | | | | | % 168.81/24.01 | | | | | (105) all_74_10 = n3 % 168.81/24.01 | | | | | % 168.81/24.01 | | | | | REDUCE: (16), (105) imply: % 168.81/24.01 | | | | | (106) a_select3(pminus_ds1_filter, n3, all_74_11) = all_74_8 % 168.81/24.01 | | | | | % 168.81/24.01 | | | | | REDUCE: (8), (105) imply: % 168.81/24.01 | | | | | (107) a_select3(pminus_ds1_filter, all_74_11, n3) = all_74_9 % 168.81/24.01 | | | | | % 168.81/24.01 | | | | | REDUCE: (10), (105) imply: % 168.81/24.01 | | | | | (108) leq(n3, n5) % 168.81/24.01 | | | | | % 168.81/24.01 | | | | | REDUCE: (24), (105) imply: % 168.81/24.01 | | | | | (109) leq(n0, n3) % 168.81/24.01 | | | | | % 168.81/24.01 | | | | | BETA: splitting (34) gives: % 168.81/24.01 | | | | | % 168.81/24.01 | | | | | Case 1: % 168.81/24.01 | | | | | | % 168.81/24.01 | | | | | | (110) gt(n2, all_74_11) % 168.81/24.01 | | | | | | % 168.81/24.01 | | | | | | GROUND_INST: instantiating (1) with all_74_11, n2, n1, simplifying % 168.81/24.01 | | | | | | with (6), (20), (22), (110) gives: % 168.81/24.01 | | | | | | (111) leq(all_74_11, n1) % 168.81/24.01 | | | | | | % 168.81/24.01 | | | | | | GROUND_INST: instantiating (11) with all_74_11, simplifying with % 168.81/24.01 | | | | | | (20), (21), (111) gives: % 168.81/24.01 | | | | | | (112) all_74_11 = n1 | all_74_11 = n0 % 168.81/24.01 | | | | | | % 168.81/24.01 | | | | | | BETA: splitting (112) gives: % 168.81/24.01 | | | | | | % 168.81/24.01 | | | | | | Case 1: % 168.81/24.01 | | | | | | | % 168.81/24.01 | | | | | | | (113) all_74_11 = n0 % 168.81/24.01 | | | | | | | % 168.81/24.01 | | | | | | | REDUCE: (5), (113) imply: % 168.81/24.01 | | | | | | | (114) $false % 168.81/24.01 | | | | | | | % 168.81/24.01 | | | | | | | CLOSE: (114) is inconsistent. % 168.81/24.01 | | | | | | | % 168.81/24.01 | | | | | | Case 2: % 168.81/24.01 | | | | | | | % 168.81/24.01 | | | | | | | (115) all_74_11 = n1 % 168.81/24.01 | | | | | | | % 168.81/24.01 | | | | | | | REDUCE: (107), (115) imply: % 168.81/24.01 | | | | | | | (116) a_select3(pminus_ds1_filter, n1, n3) = all_74_9 % 168.81/24.01 | | | | | | | % 168.81/24.01 | | | | | | | REDUCE: (106), (115) imply: % 168.81/24.01 | | | | | | | (117) a_select3(pminus_ds1_filter, n3, n1) = all_74_8 % 168.81/24.01 | | | | | | | % 168.81/24.01 | | | | | | | REDUCE: (20), (115) imply: % 168.81/24.01 | | | | | | | (118) $i(n1) % 168.81/24.01 | | | | | | | % 168.81/24.01 | | | | | | | REDUCE: (19), (115) imply: % 168.81/24.01 | | | | | | | (119) leq(n1, n5) % 168.81/24.01 | | | | | | | % 168.81/24.01 | | | | | | | REDUCE: (21), (115) imply: % 168.81/24.01 | | | | | | | (120) leq(n0, n1) % 168.81/24.01 | | | | | | | % 168.81/24.01 | | | | | | | GROUND_INST: instantiating (9) with n1, n3, all_74_9, simplifying % 168.81/24.01 | | | | | | | with (23), (109), (116), (118), (120) gives: % 168.81/24.01 | | | | | | | (121) ~ leq(n3, all_74_13) | ~ leq(n1, all_74_13) | % 168.81/24.01 | | | | | | | (a_select3(pminus_ds1_filter, n3, n1) = all_74_9 & % 168.81/24.01 | | | | | | | $i(all_74_9)) % 168.81/24.01 | | | | | | | % 168.81/24.01 | | | | | | | BETA: splitting (121) gives: % 168.81/24.01 | | | | | | | % 168.81/24.01 | | | | | | | Case 1: % 168.81/24.01 | | | | | | | | % 168.81/24.01 | | | | | | | | (122) ~ leq(n3, all_74_13) % 168.81/24.01 | | | | | | | | % 168.81/24.01 | | | | | | | | REDUCE: (3), (122) imply: % 168.81/24.01 | | | | | | | | (123) ~ leq(n3, n5) % 168.81/24.01 | | | | | | | | % 168.81/24.01 | | | | | | | | PRED_UNIFY: (108), (123) imply: % 168.81/24.01 | | | | | | | | (124) $false % 168.81/24.01 | | | | | | | | % 168.81/24.01 | | | | | | | | CLOSE: (124) is inconsistent. % 168.81/24.01 | | | | | | | | % 168.81/24.01 | | | | | | | Case 2: % 168.81/24.01 | | | | | | | | % 168.81/24.01 | | | | | | | | (125) ~ leq(n1, all_74_13) | (a_select3(pminus_ds1_filter, % 168.81/24.01 | | | | | | | | n3, n1) = all_74_9 & $i(all_74_9)) % 168.81/24.01 | | | | | | | | % 168.81/24.01 | | | | | | | | BETA: splitting (125) gives: % 168.81/24.01 | | | | | | | | % 168.81/24.01 | | | | | | | | Case 1: % 168.81/24.01 | | | | | | | | | % 168.81/24.01 | | | | | | | | | (126) ~ leq(n1, all_74_13) % 168.81/24.01 | | | | | | | | | % 168.81/24.01 | | | | | | | | | REDUCE: (3), (126) imply: % 168.81/24.01 | | | | | | | | | (127) ~ leq(n1, n5) % 168.81/24.01 | | | | | | | | | % 168.81/24.01 | | | | | | | | | PRED_UNIFY: (119), (127) imply: % 168.81/24.01 | | | | | | | | | (128) $false % 168.81/24.01 | | | | | | | | | % 168.81/24.01 | | | | | | | | | CLOSE: (128) is inconsistent. % 168.81/24.01 | | | | | | | | | % 168.81/24.01 | | | | | | | | Case 2: % 168.81/24.01 | | | | | | | | | % 168.81/24.01 | | | | | | | | | (129) a_select3(pminus_ds1_filter, n3, n1) = all_74_9 & % 168.81/24.01 | | | | | | | | | $i(all_74_9) % 168.81/24.01 | | | | | | | | | % 168.81/24.01 | | | | | | | | | ALPHA: (129) implies: % 168.81/24.01 | | | | | | | | | (130) a_select3(pminus_ds1_filter, n3, n1) = all_74_9 % 168.81/24.01 | | | | | | | | | % 168.81/24.01 | | | | | | | | | GROUND_INST: instantiating (18) with all_74_8, all_74_9, n1, % 168.81/24.01 | | | | | | | | | n3, pminus_ds1_filter, simplifying with (117), % 168.81/24.01 | | | | | | | | | (130) gives: % 168.81/24.01 | | | | | | | | | (131) all_74_8 = all_74_9 % 168.81/24.01 | | | | | | | | | % 168.81/24.01 | | | | | | | | | REDUCE: (15), (131) imply: % 168.81/24.02 | | | | | | | | | (132) $false % 168.81/24.02 | | | | | | | | | % 168.81/24.02 | | | | | | | | | CLOSE: (132) is inconsistent. % 168.81/24.02 | | | | | | | | | % 168.81/24.02 | | | | | | | | End of split % 168.81/24.02 | | | | | | | | % 168.81/24.02 | | | | | | | End of split % 168.81/24.02 | | | | | | | % 168.81/24.02 | | | | | | End of split % 168.81/24.02 | | | | | | % 168.81/24.02 | | | | | Case 2: % 168.81/24.02 | | | | | | % 168.81/24.02 | | | | | | (133) all_74_11 = n2 % 168.81/24.02 | | | | | | % 168.81/24.02 | | | | | | REDUCE: (107), (133) imply: % 168.81/24.02 | | | | | | (134) a_select3(pminus_ds1_filter, n2, n3) = all_74_9 % 168.81/24.02 | | | | | | % 168.81/24.02 | | | | | | REDUCE: (106), (133) imply: % 168.81/24.02 | | | | | | (135) a_select3(pminus_ds1_filter, n3, n2) = all_74_8 % 168.81/24.02 | | | | | | % 168.81/24.02 | | | | | | REDUCE: (19), (133) imply: % 168.81/24.02 | | | | | | (136) leq(n2, n5) % 168.81/24.02 | | | | | | % 168.81/24.02 | | | | | | REDUCE: (21), (133) imply: % 168.81/24.02 | | | | | | (137) leq(n0, n2) % 168.81/24.02 | | | | | | % 168.81/24.02 | | | | | | GROUND_INST: instantiating (9) with n2, n3, all_74_9, simplifying % 168.81/24.02 | | | | | | with (6), (23), (109), (134), (137) gives: % 168.81/24.02 | | | | | | (138) ~ leq(n3, all_74_13) | ~ leq(n2, all_74_13) | % 168.81/24.02 | | | | | | (a_select3(pminus_ds1_filter, n3, n2) = all_74_9 & % 168.81/24.02 | | | | | | $i(all_74_9)) % 168.81/24.02 | | | | | | % 168.81/24.02 | | | | | | BETA: splitting (138) gives: % 168.81/24.02 | | | | | | % 168.81/24.02 | | | | | | Case 1: % 168.81/24.02 | | | | | | | % 168.81/24.02 | | | | | | | (139) ~ leq(n3, all_74_13) % 168.81/24.02 | | | | | | | % 168.81/24.02 | | | | | | | REDUCE: (3), (139) imply: % 168.81/24.02 | | | | | | | (140) ~ leq(n3, n5) % 168.81/24.02 | | | | | | | % 168.81/24.02 | | | | | | | PRED_UNIFY: (108), (140) imply: % 168.81/24.02 | | | | | | | (141) $false % 168.81/24.02 | | | | | | | % 168.81/24.02 | | | | | | | CLOSE: (141) is inconsistent. % 168.81/24.02 | | | | | | | % 168.81/24.02 | | | | | | Case 2: % 168.81/24.02 | | | | | | | % 168.81/24.02 | | | | | | | (142) ~ leq(n2, all_74_13) | (a_select3(pminus_ds1_filter, n3, % 168.81/24.02 | | | | | | | n2) = all_74_9 & $i(all_74_9)) % 168.81/24.02 | | | | | | | % 168.81/24.02 | | | | | | | BETA: splitting (142) gives: % 168.81/24.02 | | | | | | | % 168.81/24.02 | | | | | | | Case 1: % 168.81/24.02 | | | | | | | | % 168.81/24.02 | | | | | | | | (143) ~ leq(n2, all_74_13) % 168.81/24.02 | | | | | | | | % 168.81/24.02 | | | | | | | | REDUCE: (3), (143) imply: % 168.81/24.02 | | | | | | | | (144) ~ leq(n2, n5) % 168.81/24.02 | | | | | | | | % 168.81/24.02 | | | | | | | | PRED_UNIFY: (136), (144) imply: % 168.81/24.02 | | | | | | | | (145) $false % 168.81/24.02 | | | | | | | | % 168.81/24.02 | | | | | | | | CLOSE: (145) is inconsistent. % 168.81/24.02 | | | | | | | | % 168.81/24.02 | | | | | | | Case 2: % 168.81/24.02 | | | | | | | | % 168.81/24.02 | | | | | | | | (146) a_select3(pminus_ds1_filter, n3, n2) = all_74_9 & % 168.81/24.02 | | | | | | | | $i(all_74_9) % 168.81/24.02 | | | | | | | | % 168.81/24.02 | | | | | | | | ALPHA: (146) implies: % 168.81/24.02 | | | | | | | | (147) a_select3(pminus_ds1_filter, n3, n2) = all_74_9 % 168.81/24.02 | | | | | | | | % 168.81/24.02 | | | | | | | | REF_CLOSE: (15), (18), (135), (147) are inconsistent by % 168.81/24.02 | | | | | | | | sub-proof #8. % 168.81/24.02 | | | | | | | | % 168.81/24.02 | | | | | | | End of split % 168.81/24.02 | | | | | | | % 168.81/24.02 | | | | | | End of split % 168.81/24.02 | | | | | | % 168.81/24.02 | | | | | End of split % 168.81/24.02 | | | | | % 168.81/24.02 | | | | End of split % 168.81/24.02 | | | | % 168.81/24.02 | | | Case 2: % 168.81/24.02 | | | | % 168.81/24.02 | | | | (148) all_74_11 = n3 % 168.81/24.02 | | | | % 168.81/24.02 | | | | REDUCE: (16), (148) imply: % 168.81/24.02 | | | | (149) a_select3(pminus_ds1_filter, all_74_10, n3) = all_74_8 % 168.81/24.02 | | | | % 168.81/24.02 | | | | REDUCE: (8), (148) imply: % 168.81/24.02 | | | | (150) a_select3(pminus_ds1_filter, n3, all_74_10) = all_74_9 % 168.81/24.02 | | | | % 168.81/24.02 | | | | REDUCE: (19), (148) imply: % 168.81/24.02 | | | | (151) leq(n3, n5) % 168.81/24.02 | | | | % 168.81/24.02 | | | | REDUCE: (21), (148) imply: % 168.81/24.02 | | | | (152) leq(n0, n3) % 168.81/24.02 | | | | % 168.81/24.02 | | | | BETA: splitting (31) gives: % 168.81/24.02 | | | | % 168.81/24.02 | | | | Case 1: % 168.81/24.02 | | | | | % 168.81/24.02 | | | | | (153) gt(n3, all_74_10) % 168.81/24.02 | | | | | % 168.81/24.02 | | | | | GROUND_INST: instantiating (1) with all_74_10, n3, n2, simplifying % 168.81/24.02 | | | | | with (12), (13), (23), (153) gives: % 168.81/24.02 | | | | | (154) leq(all_74_10, n2) % 168.81/24.02 | | | | | % 168.81/24.02 | | | | | GROUND_INST: instantiating (25) with all_74_10, n2, simplifying with % 168.81/24.02 | | | | | (6), (12), (154) gives: % 168.81/24.02 | | | | | (155) all_74_10 = n2 | gt(n2, all_74_10) % 168.81/24.02 | | | | | % 168.81/24.02 | | | | | BETA: splitting (155) gives: % 168.81/24.02 | | | | | % 168.81/24.02 | | | | | Case 1: % 168.81/24.02 | | | | | | % 168.81/24.02 | | | | | | (156) gt(n2, all_74_10) % 168.81/24.02 | | | | | | % 168.81/24.02 | | | | | | GROUND_INST: instantiating (1) with all_74_10, n2, n1, simplifying % 168.81/24.02 | | | | | | with (6), (12), (22), (156) gives: % 168.81/24.02 | | | | | | (157) leq(all_74_10, n1) % 168.81/24.02 | | | | | | % 168.81/24.02 | | | | | | GROUND_INST: instantiating (11) with all_74_10, simplifying with % 168.81/24.02 | | | | | | (12), (24), (157) gives: % 168.81/24.02 | | | | | | (158) all_74_10 = n1 | all_74_10 = n0 % 168.81/24.02 | | | | | | % 168.81/24.02 | | | | | | BETA: splitting (158) gives: % 168.81/24.02 | | | | | | % 168.81/24.02 | | | | | | Case 1: % 168.81/24.02 | | | | | | | % 168.81/24.02 | | | | | | | (159) all_74_10 = n0 % 168.81/24.02 | | | | | | | % 168.81/24.02 | | | | | | | REDUCE: (14), (159) imply: % 168.81/24.02 | | | | | | | (160) $false % 168.81/24.02 | | | | | | | % 168.81/24.02 | | | | | | | CLOSE: (160) is inconsistent. % 168.81/24.02 | | | | | | | % 168.81/24.02 | | | | | | Case 2: % 168.81/24.02 | | | | | | | % 168.81/24.02 | | | | | | | (161) all_74_10 = n1 % 168.81/24.02 | | | | | | | % 168.81/24.02 | | | | | | | REDUCE: (149), (161) imply: % 168.81/24.02 | | | | | | | (162) a_select3(pminus_ds1_filter, n1, n3) = all_74_8 % 168.81/24.02 | | | | | | | % 168.81/24.02 | | | | | | | REDUCE: (150), (161) imply: % 168.81/24.02 | | | | | | | (163) a_select3(pminus_ds1_filter, n3, n1) = all_74_9 % 168.81/24.02 | | | | | | | % 168.81/24.02 | | | | | | | REDUCE: (12), (161) imply: % 168.81/24.02 | | | | | | | (164) $i(n1) % 168.81/24.02 | | | | | | | % 168.81/24.02 | | | | | | | REDUCE: (10), (161) imply: % 168.81/24.02 | | | | | | | (165) leq(n1, n5) % 168.81/24.02 | | | | | | | % 168.81/24.02 | | | | | | | REDUCE: (24), (161) imply: % 168.81/24.02 | | | | | | | (166) leq(n0, n1) % 168.81/24.02 | | | | | | | % 168.81/24.02 | | | | | | | GROUND_INST: instantiating (9) with n1, n3, all_74_8, simplifying % 168.81/24.02 | | | | | | | with (23), (152), (162), (164), (166) gives: % 168.81/24.02 | | | | | | | (167) ~ leq(n3, all_74_13) | ~ leq(n1, all_74_13) | % 168.81/24.02 | | | | | | | (a_select3(pminus_ds1_filter, n3, n1) = all_74_8 & % 168.81/24.02 | | | | | | | $i(all_74_8)) % 168.81/24.02 | | | | | | | % 168.81/24.02 | | | | | | | BETA: splitting (167) gives: % 168.81/24.02 | | | | | | | % 168.81/24.02 | | | | | | | Case 1: % 168.81/24.02 | | | | | | | | % 168.81/24.02 | | | | | | | | (168) ~ leq(n3, all_74_13) % 168.81/24.02 | | | | | | | | % 168.81/24.02 | | | | | | | | REDUCE: (3), (168) imply: % 168.81/24.02 | | | | | | | | (169) ~ leq(n3, n5) % 168.81/24.02 | | | | | | | | % 168.81/24.02 | | | | | | | | PRED_UNIFY: (151), (169) imply: % 168.81/24.02 | | | | | | | | (170) $false % 168.81/24.02 | | | | | | | | % 168.81/24.02 | | | | | | | | CLOSE: (170) is inconsistent. % 168.81/24.02 | | | | | | | | % 168.81/24.02 | | | | | | | Case 2: % 168.81/24.02 | | | | | | | | % 168.81/24.02 | | | | | | | | (171) ~ leq(n1, all_74_13) | (a_select3(pminus_ds1_filter, % 168.81/24.02 | | | | | | | | n3, n1) = all_74_8 & $i(all_74_8)) % 168.81/24.02 | | | | | | | | % 168.81/24.02 | | | | | | | | BETA: splitting (171) gives: % 168.81/24.02 | | | | | | | | % 168.81/24.02 | | | | | | | | Case 1: % 168.81/24.02 | | | | | | | | | % 168.81/24.02 | | | | | | | | | (172) ~ leq(n1, all_74_13) % 168.81/24.02 | | | | | | | | | % 168.81/24.02 | | | | | | | | | REDUCE: (3), (172) imply: % 168.81/24.02 | | | | | | | | | (173) ~ leq(n1, n5) % 168.81/24.02 | | | | | | | | | % 168.81/24.02 | | | | | | | | | PRED_UNIFY: (165), (173) imply: % 168.81/24.02 | | | | | | | | | (174) $false % 168.81/24.02 | | | | | | | | | % 168.81/24.02 | | | | | | | | | CLOSE: (174) is inconsistent. % 168.81/24.02 | | | | | | | | | % 168.81/24.02 | | | | | | | | Case 2: % 168.81/24.02 | | | | | | | | | % 168.81/24.02 | | | | | | | | | (175) a_select3(pminus_ds1_filter, n3, n1) = all_74_8 & % 168.81/24.02 | | | | | | | | | $i(all_74_8) % 168.81/24.02 | | | | | | | | | % 168.81/24.02 | | | | | | | | | ALPHA: (175) implies: % 168.81/24.02 | | | | | | | | | (176) a_select3(pminus_ds1_filter, n3, n1) = all_74_8 % 168.81/24.02 | | | | | | | | | % 168.81/24.02 | | | | | | | | | GROUND_INST: instantiating (18) with all_74_8, all_74_9, n1, % 168.81/24.02 | | | | | | | | | n3, pminus_ds1_filter, simplifying with (163), % 168.81/24.02 | | | | | | | | | (176) gives: % 168.81/24.02 | | | | | | | | | (177) all_74_8 = all_74_9 % 168.81/24.02 | | | | | | | | | % 168.81/24.02 | | | | | | | | | REDUCE: (15), (177) imply: % 168.81/24.02 | | | | | | | | | (178) $false % 168.81/24.02 | | | | | | | | | % 168.81/24.02 | | | | | | | | | CLOSE: (178) is inconsistent. % 168.81/24.02 | | | | | | | | | % 168.81/24.02 | | | | | | | | End of split % 168.81/24.02 | | | | | | | | % 168.81/24.02 | | | | | | | End of split % 168.81/24.02 | | | | | | | % 168.81/24.02 | | | | | | End of split % 168.81/24.02 | | | | | | % 168.81/24.02 | | | | | Case 2: % 168.81/24.02 | | | | | | % 168.81/24.02 | | | | | | (179) all_74_10 = n2 % 168.81/24.02 | | | | | | % 168.81/24.02 | | | | | | REDUCE: (149), (179) imply: % 168.81/24.02 | | | | | | (180) a_select3(pminus_ds1_filter, n2, n3) = all_74_8 % 168.81/24.02 | | | | | | % 168.81/24.02 | | | | | | REDUCE: (150), (179) imply: % 168.81/24.02 | | | | | | (181) a_select3(pminus_ds1_filter, n3, n2) = all_74_9 % 168.81/24.02 | | | | | | % 168.81/24.02 | | | | | | REDUCE: (10), (179) imply: % 168.81/24.02 | | | | | | (182) leq(n2, n5) % 168.81/24.02 | | | | | | % 168.81/24.02 | | | | | | REDUCE: (24), (179) imply: % 168.81/24.02 | | | | | | (183) leq(n0, n2) % 168.81/24.02 | | | | | | % 168.81/24.02 | | | | | | GROUND_INST: instantiating (9) with n2, n3, all_74_8, simplifying % 168.81/24.02 | | | | | | with (6), (23), (152), (180), (183) gives: % 168.81/24.02 | | | | | | (184) ~ leq(n3, all_74_13) | ~ leq(n2, all_74_13) | % 168.81/24.02 | | | | | | (a_select3(pminus_ds1_filter, n3, n2) = all_74_8 & % 168.81/24.02 | | | | | | $i(all_74_8)) % 168.81/24.02 | | | | | | % 168.81/24.02 | | | | | | BETA: splitting (184) gives: % 168.81/24.02 | | | | | | % 168.81/24.02 | | | | | | Case 1: % 168.81/24.02 | | | | | | | % 168.81/24.02 | | | | | | | (185) ~ leq(n3, all_74_13) % 168.81/24.02 | | | | | | | % 168.81/24.02 | | | | | | | REDUCE: (3), (185) imply: % 168.81/24.02 | | | | | | | (186) ~ leq(n3, n5) % 168.81/24.02 | | | | | | | % 168.81/24.02 | | | | | | | PRED_UNIFY: (151), (186) imply: % 168.81/24.02 | | | | | | | (187) $false % 168.81/24.02 | | | | | | | % 168.81/24.02 | | | | | | | CLOSE: (187) is inconsistent. % 168.81/24.02 | | | | | | | % 168.81/24.02 | | | | | | Case 2: % 168.81/24.02 | | | | | | | % 168.81/24.02 | | | | | | | (188) ~ leq(n2, all_74_13) | (a_select3(pminus_ds1_filter, n3, % 168.81/24.02 | | | | | | | n2) = all_74_8 & $i(all_74_8)) % 168.81/24.02 | | | | | | | % 168.81/24.02 | | | | | | | BETA: splitting (188) gives: % 168.81/24.02 | | | | | | | % 168.81/24.02 | | | | | | | Case 1: % 168.81/24.02 | | | | | | | | % 168.81/24.02 | | | | | | | | (189) ~ leq(n2, all_74_13) % 168.81/24.02 | | | | | | | | % 168.81/24.02 | | | | | | | | REDUCE: (3), (189) imply: % 168.81/24.02 | | | | | | | | (190) ~ leq(n2, n5) % 168.81/24.02 | | | | | | | | % 168.81/24.02 | | | | | | | | PRED_UNIFY: (182), (190) imply: % 168.81/24.02 | | | | | | | | (191) $false % 168.81/24.02 | | | | | | | | % 168.81/24.02 | | | | | | | | CLOSE: (191) is inconsistent. % 168.81/24.02 | | | | | | | | % 168.81/24.02 | | | | | | | Case 2: % 168.81/24.02 | | | | | | | | % 168.81/24.02 | | | | | | | | (192) a_select3(pminus_ds1_filter, n3, n2) = all_74_8 & % 168.81/24.02 | | | | | | | | $i(all_74_8) % 168.81/24.02 | | | | | | | | % 168.81/24.02 | | | | | | | | ALPHA: (192) implies: % 168.81/24.02 | | | | | | | | (193) a_select3(pminus_ds1_filter, n3, n2) = all_74_8 % 168.81/24.02 | | | | | | | | % 168.81/24.02 | | | | | | | | REF_CLOSE: (15), (18), (181), (193) are inconsistent by % 168.81/24.02 | | | | | | | | sub-proof #8. % 168.81/24.02 | | | | | | | | % 168.81/24.02 | | | | | | | End of split % 168.81/24.02 | | | | | | | % 168.81/24.02 | | | | | | End of split % 168.81/24.02 | | | | | | % 168.81/24.02 | | | | | End of split % 168.81/24.02 | | | | | % 168.81/24.02 | | | | Case 2: % 168.81/24.02 | | | | | % 168.81/24.02 | | | | | (194) all_74_10 = n3 % 168.81/24.02 | | | | | % 168.81/24.02 | | | | | REDUCE: (149), (194) imply: % 168.81/24.02 | | | | | (195) a_select3(pminus_ds1_filter, n3, n3) = all_74_8 % 168.81/24.02 | | | | | % 168.81/24.02 | | | | | REDUCE: (150), (194) imply: % 168.81/24.02 | | | | | (196) a_select3(pminus_ds1_filter, n3, n3) = all_74_9 % 168.81/24.02 | | | | | % 168.81/24.02 | | | | | GROUND_INST: instantiating (18) with all_74_9, all_74_8, n3, n3, % 168.81/24.02 | | | | | pminus_ds1_filter, simplifying with (195), (196) gives: % 168.81/24.02 | | | | | (197) all_74_8 = all_74_9 % 168.81/24.02 | | | | | % 168.81/24.02 | | | | | REDUCE: (15), (197) imply: % 168.81/24.02 | | | | | (198) $false % 168.81/24.02 | | | | | % 168.81/24.02 | | | | | CLOSE: (198) is inconsistent. % 168.81/24.02 | | | | | % 168.81/24.02 | | | | End of split % 168.81/24.02 | | | | % 168.81/24.02 | | | End of split % 168.81/24.02 | | | % 168.81/24.02 | | Case 2: % 168.81/24.02 | | | % 168.81/24.02 | | | (199) all_74_10 = n4 % 168.81/24.02 | | | % 168.81/24.02 | | | REDUCE: (16), (199) imply: % 168.81/24.02 | | | (200) a_select3(pminus_ds1_filter, n4, all_74_11) = all_74_8 % 168.81/24.02 | | | % 168.81/24.02 | | | REDUCE: (8), (199) imply: % 168.81/24.02 | | | (201) a_select3(pminus_ds1_filter, all_74_11, n4) = all_74_9 % 168.81/24.02 | | | % 168.81/24.02 | | | REDUCE: (10), (199) imply: % 168.81/24.02 | | | (202) leq(n4, n5) % 168.81/24.02 | | | % 168.81/24.02 | | | REDUCE: (24), (199) imply: % 168.81/24.02 | | | (203) leq(n0, n4) % 168.81/24.02 | | | % 168.81/24.02 | | | BETA: splitting (28) gives: % 168.81/24.02 | | | % 168.81/24.02 | | | Case 1: % 168.81/24.02 | | | | % 168.81/24.02 | | | | (204) gt(n3, all_74_11) % 168.81/24.02 | | | | % 168.81/24.02 | | | | GROUND_INST: instantiating (1) with all_74_11, n3, n2, simplifying with % 168.81/24.02 | | | | (13), (20), (23), (204) gives: % 168.81/24.02 | | | | (205) leq(all_74_11, n2) % 168.81/24.02 | | | | % 168.81/24.02 | | | | GROUND_INST: instantiating (25) with all_74_11, n2, simplifying with % 168.81/24.02 | | | | (6), (20), (205) gives: % 168.81/24.02 | | | | (206) all_74_11 = n2 | gt(n2, all_74_11) % 168.81/24.02 | | | | % 168.81/24.02 | | | | BETA: splitting (206) gives: % 168.81/24.02 | | | | % 168.81/24.02 | | | | Case 1: % 168.81/24.02 | | | | | % 168.81/24.02 | | | | | (207) gt(n2, all_74_11) % 168.81/24.02 | | | | | % 168.81/24.02 | | | | | GROUND_INST: instantiating (1) with all_74_11, n2, n1, simplifying % 168.81/24.02 | | | | | with (6), (20), (22), (207) gives: % 168.81/24.02 | | | | | (208) leq(all_74_11, n1) % 168.81/24.02 | | | | | % 168.81/24.02 | | | | | GROUND_INST: instantiating (11) with all_74_11, simplifying with (20), % 168.81/24.02 | | | | | (21), (208) gives: % 168.81/24.02 | | | | | (209) all_74_11 = n1 | all_74_11 = n0 % 168.81/24.02 | | | | | % 168.81/24.02 | | | | | BETA: splitting (209) gives: % 168.81/24.02 | | | | | % 168.81/24.02 | | | | | Case 1: % 168.81/24.02 | | | | | | % 168.81/24.02 | | | | | | (210) all_74_11 = n0 % 168.81/24.02 | | | | | | % 168.81/24.02 | | | | | | REDUCE: (5), (210) imply: % 168.81/24.02 | | | | | | (211) $false % 168.81/24.02 | | | | | | % 168.81/24.02 | | | | | | CLOSE: (211) is inconsistent. % 168.81/24.02 | | | | | | % 168.81/24.02 | | | | | Case 2: % 168.81/24.02 | | | | | | % 168.81/24.02 | | | | | | (212) all_74_11 = n1 % 168.81/24.02 | | | | | | % 168.81/24.02 | | | | | | REDUCE: (201), (212) imply: % 168.81/24.02 | | | | | | (213) a_select3(pminus_ds1_filter, n1, n4) = all_74_9 % 168.81/24.02 | | | | | | % 168.81/24.02 | | | | | | REDUCE: (200), (212) imply: % 168.81/24.02 | | | | | | (214) a_select3(pminus_ds1_filter, n4, n1) = all_74_8 % 168.81/24.02 | | | | | | % 168.81/24.02 | | | | | | REDUCE: (20), (212) imply: % 168.81/24.02 | | | | | | (215) $i(n1) % 168.81/24.02 | | | | | | % 168.81/24.02 | | | | | | REDUCE: (19), (212) imply: % 168.81/24.02 | | | | | | (216) leq(n1, n5) % 168.81/24.02 | | | | | | % 168.81/24.02 | | | | | | REDUCE: (21), (212) imply: % 168.81/24.02 | | | | | | (217) leq(n0, n1) % 168.81/24.02 | | | | | | % 168.81/24.02 | | | | | | GROUND_INST: instantiating (9) with n1, n4, all_74_9, simplifying % 168.81/24.02 | | | | | | with (17), (203), (213), (215), (217) gives: % 168.81/24.02 | | | | | | (218) ~ leq(n4, all_74_13) | ~ leq(n1, all_74_13) | % 168.81/24.02 | | | | | | (a_select3(pminus_ds1_filter, n4, n1) = all_74_9 & % 168.81/24.02 | | | | | | $i(all_74_9)) % 168.81/24.02 | | | | | | % 168.81/24.02 | | | | | | BETA: splitting (218) gives: % 168.81/24.02 | | | | | | % 168.81/24.02 | | | | | | Case 1: % 168.81/24.02 | | | | | | | % 168.81/24.02 | | | | | | | (219) ~ leq(n4, all_74_13) % 168.81/24.02 | | | | | | | % 168.81/24.02 | | | | | | | REDUCE: (3), (219) imply: % 168.81/24.02 | | | | | | | (220) ~ leq(n4, n5) % 168.81/24.02 | | | | | | | % 168.81/24.02 | | | | | | | PRED_UNIFY: (202), (220) imply: % 168.81/24.02 | | | | | | | (221) $false % 168.81/24.02 | | | | | | | % 168.81/24.02 | | | | | | | CLOSE: (221) is inconsistent. % 168.81/24.02 | | | | | | | % 168.81/24.02 | | | | | | Case 2: % 168.81/24.02 | | | | | | | % 168.81/24.02 | | | | | | | (222) ~ leq(n1, all_74_13) | (a_select3(pminus_ds1_filter, n4, % 168.81/24.02 | | | | | | | n1) = all_74_9 & $i(all_74_9)) % 168.81/24.02 | | | | | | | % 168.81/24.02 | | | | | | | BETA: splitting (222) gives: % 168.81/24.02 | | | | | | | % 168.81/24.02 | | | | | | | Case 1: % 168.81/24.02 | | | | | | | | % 168.81/24.02 | | | | | | | | (223) ~ leq(n1, all_74_13) % 168.81/24.02 | | | | | | | | % 168.81/24.02 | | | | | | | | REDUCE: (3), (223) imply: % 168.81/24.02 | | | | | | | | (224) ~ leq(n1, n5) % 168.81/24.02 | | | | | | | | % 168.81/24.02 | | | | | | | | PRED_UNIFY: (216), (224) imply: % 168.81/24.02 | | | | | | | | (225) $false % 168.81/24.02 | | | | | | | | % 168.81/24.02 | | | | | | | | CLOSE: (225) is inconsistent. % 168.81/24.02 | | | | | | | | % 168.81/24.02 | | | | | | | Case 2: % 168.81/24.02 | | | | | | | | % 168.81/24.02 | | | | | | | | (226) a_select3(pminus_ds1_filter, n4, n1) = all_74_9 & % 168.81/24.02 | | | | | | | | $i(all_74_9) % 168.81/24.02 | | | | | | | | % 168.81/24.02 | | | | | | | | ALPHA: (226) implies: % 168.81/24.02 | | | | | | | | (227) a_select3(pminus_ds1_filter, n4, n1) = all_74_9 % 168.81/24.02 | | | | | | | | % 168.81/24.02 | | | | | | | | GROUND_INST: instantiating (18) with all_74_9, all_74_8, n1, n4, % 168.81/24.02 | | | | | | | | pminus_ds1_filter, simplifying with (214), (227) % 168.81/24.02 | | | | | | | | gives: % 168.81/24.02 | | | | | | | | (228) all_74_8 = all_74_9 % 168.81/24.02 | | | | | | | | % 168.81/24.02 | | | | | | | | REDUCE: (15), (228) imply: % 168.81/24.02 | | | | | | | | (229) $false % 168.81/24.02 | | | | | | | | % 168.81/24.02 | | | | | | | | CLOSE: (229) is inconsistent. % 168.81/24.02 | | | | | | | | % 168.81/24.02 | | | | | | | End of split % 168.81/24.02 | | | | | | | % 168.81/24.02 | | | | | | End of split % 168.81/24.02 | | | | | | % 168.81/24.02 | | | | | End of split % 168.81/24.02 | | | | | % 168.81/24.02 | | | | Case 2: % 168.81/24.02 | | | | | % 168.81/24.02 | | | | | (230) all_74_11 = n2 % 168.81/24.02 | | | | | % 168.81/24.02 | | | | | REDUCE: (201), (230) imply: % 168.81/24.02 | | | | | (231) a_select3(pminus_ds1_filter, n2, n4) = all_74_9 % 168.81/24.02 | | | | | % 168.81/24.02 | | | | | REDUCE: (200), (230) imply: % 168.81/24.02 | | | | | (232) a_select3(pminus_ds1_filter, n4, n2) = all_74_8 % 168.81/24.02 | | | | | % 168.81/24.02 | | | | | REDUCE: (19), (230) imply: % 168.81/24.02 | | | | | (233) leq(n2, n5) % 168.81/24.02 | | | | | % 168.81/24.02 | | | | | REDUCE: (21), (230) imply: % 168.81/24.02 | | | | | (234) leq(n0, n2) % 168.81/24.02 | | | | | % 168.81/24.02 | | | | | GROUND_INST: instantiating (9) with n2, n4, all_74_9, simplifying with % 168.81/24.02 | | | | | (6), (17), (203), (231), (234) gives: % 168.81/24.02 | | | | | (235) ~ leq(n4, all_74_13) | ~ leq(n2, all_74_13) | % 168.81/24.02 | | | | | (a_select3(pminus_ds1_filter, n4, n2) = all_74_9 & % 168.81/24.02 | | | | | $i(all_74_9)) % 168.81/24.03 | | | | | % 168.81/24.03 | | | | | BETA: splitting (235) gives: % 168.81/24.03 | | | | | % 168.81/24.03 | | | | | Case 1: % 168.81/24.03 | | | | | | % 168.81/24.03 | | | | | | (236) ~ leq(n4, all_74_13) % 168.81/24.03 | | | | | | % 168.81/24.03 | | | | | | REDUCE: (3), (236) imply: % 168.81/24.03 | | | | | | (237) ~ leq(n4, n5) % 168.81/24.03 | | | | | | % 168.81/24.03 | | | | | | PRED_UNIFY: (202), (237) imply: % 168.81/24.03 | | | | | | (238) $false % 168.81/24.03 | | | | | | % 168.81/24.03 | | | | | | CLOSE: (238) is inconsistent. % 168.81/24.03 | | | | | | % 168.81/24.03 | | | | | Case 2: % 168.81/24.03 | | | | | | % 168.81/24.03 | | | | | | (239) ~ leq(n2, all_74_13) | (a_select3(pminus_ds1_filter, n4, % 168.81/24.03 | | | | | | n2) = all_74_9 & $i(all_74_9)) % 168.81/24.03 | | | | | | % 168.81/24.03 | | | | | | BETA: splitting (239) gives: % 168.81/24.03 | | | | | | % 168.81/24.03 | | | | | | Case 1: % 168.81/24.03 | | | | | | | % 168.81/24.03 | | | | | | | (240) ~ leq(n2, all_74_13) % 168.81/24.03 | | | | | | | % 168.81/24.03 | | | | | | | REDUCE: (3), (240) imply: % 168.81/24.03 | | | | | | | (241) ~ leq(n2, n5) % 168.81/24.03 | | | | | | | % 168.81/24.03 | | | | | | | PRED_UNIFY: (233), (241) imply: % 168.81/24.03 | | | | | | | (242) $false % 168.81/24.03 | | | | | | | % 168.81/24.03 | | | | | | | CLOSE: (242) is inconsistent. % 168.81/24.03 | | | | | | | % 168.81/24.03 | | | | | | Case 2: % 168.81/24.03 | | | | | | | % 168.81/24.03 | | | | | | | (243) a_select3(pminus_ds1_filter, n4, n2) = all_74_9 & % 168.81/24.03 | | | | | | | $i(all_74_9) % 168.81/24.03 | | | | | | | % 168.81/24.03 | | | | | | | ALPHA: (243) implies: % 168.81/24.03 | | | | | | | (244) a_select3(pminus_ds1_filter, n4, n2) = all_74_9 % 168.81/24.03 | | | | | | | % 168.81/24.03 | | | | | | | REF_CLOSE: (15), (18), (232), (244) are inconsistent by sub-proof % 168.81/24.03 | | | | | | | #7. % 168.81/24.03 | | | | | | | % 168.81/24.03 | | | | | | End of split % 168.81/24.03 | | | | | | % 168.81/24.03 | | | | | End of split % 168.81/24.03 | | | | | % 168.81/24.03 | | | | End of split % 168.81/24.03 | | | | % 168.81/24.03 | | | Case 2: % 168.81/24.03 | | | | % 168.81/24.03 | | | | (245) all_74_11 = n3 % 168.81/24.03 | | | | % 168.81/24.03 | | | | REDUCE: (201), (245) imply: % 168.81/24.03 | | | | (246) a_select3(pminus_ds1_filter, n3, n4) = all_74_9 % 168.81/24.03 | | | | % 168.81/24.03 | | | | REDUCE: (200), (245) imply: % 168.81/24.03 | | | | (247) a_select3(pminus_ds1_filter, n4, n3) = all_74_8 % 168.81/24.03 | | | | % 168.81/24.03 | | | | REDUCE: (19), (245) imply: % 168.81/24.03 | | | | (248) leq(n3, n5) % 168.81/24.03 | | | | % 168.81/24.03 | | | | REDUCE: (21), (245) imply: % 168.81/24.03 | | | | (249) leq(n0, n3) % 168.81/24.03 | | | | % 168.81/24.03 | | | | GROUND_INST: instantiating (9) with n3, n4, all_74_9, simplifying with % 168.81/24.03 | | | | (17), (23), (203), (246), (249) gives: % 168.81/24.03 | | | | (250) ~ leq(n4, all_74_13) | ~ leq(n3, all_74_13) | % 168.81/24.03 | | | | (a_select3(pminus_ds1_filter, n4, n3) = all_74_9 & % 168.81/24.03 | | | | $i(all_74_9)) % 168.81/24.03 | | | | % 168.81/24.03 | | | | BETA: splitting (250) gives: % 168.81/24.03 | | | | % 168.81/24.03 | | | | Case 1: % 168.81/24.03 | | | | | % 168.81/24.03 | | | | | (251) ~ leq(n4, all_74_13) % 168.81/24.03 | | | | | % 168.81/24.03 | | | | | REDUCE: (3), (251) imply: % 168.81/24.03 | | | | | (252) ~ leq(n4, n5) % 168.81/24.03 | | | | | % 168.81/24.03 | | | | | PRED_UNIFY: (202), (252) imply: % 168.81/24.03 | | | | | (253) $false % 168.81/24.03 | | | | | % 168.81/24.03 | | | | | CLOSE: (253) is inconsistent. % 168.81/24.03 | | | | | % 168.81/24.03 | | | | Case 2: % 168.81/24.03 | | | | | % 168.81/24.03 | | | | | (254) ~ leq(n3, all_74_13) | (a_select3(pminus_ds1_filter, n4, n3) % 168.81/24.03 | | | | | = all_74_9 & $i(all_74_9)) % 168.81/24.03 | | | | | % 168.81/24.03 | | | | | BETA: splitting (254) gives: % 168.81/24.03 | | | | | % 168.81/24.03 | | | | | Case 1: % 168.81/24.03 | | | | | | % 168.81/24.03 | | | | | | (255) ~ leq(n3, all_74_13) % 168.81/24.03 | | | | | | % 168.81/24.03 | | | | | | REDUCE: (3), (255) imply: % 168.81/24.03 | | | | | | (256) ~ leq(n3, n5) % 168.81/24.03 | | | | | | % 168.81/24.03 | | | | | | PRED_UNIFY: (248), (256) imply: % 168.81/24.03 | | | | | | (257) $false % 168.81/24.03 | | | | | | % 168.81/24.03 | | | | | | CLOSE: (257) is inconsistent. % 168.81/24.03 | | | | | | % 168.81/24.03 | | | | | Case 2: % 168.81/24.03 | | | | | | % 168.81/24.03 | | | | | | (258) a_select3(pminus_ds1_filter, n4, n3) = all_74_9 & % 168.81/24.03 | | | | | | $i(all_74_9) % 168.81/24.03 | | | | | | % 168.81/24.03 | | | | | | ALPHA: (258) implies: % 168.81/24.03 | | | | | | (259) a_select3(pminus_ds1_filter, n4, n3) = all_74_9 % 168.81/24.03 | | | | | | % 168.81/24.03 | | | | | | GROUND_INST: instantiating (18) with all_74_9, all_74_8, n3, n4, % 168.81/24.03 | | | | | | pminus_ds1_filter, simplifying with (247), (259) gives: % 168.81/24.03 | | | | | | (260) all_74_8 = all_74_9 % 168.81/24.03 | | | | | | % 168.81/24.03 | | | | | | REDUCE: (15), (260) imply: % 168.81/24.03 | | | | | | (261) $false % 168.81/24.03 | | | | | | % 168.81/24.03 | | | | | | CLOSE: (261) is inconsistent. % 168.81/24.03 | | | | | | % 168.81/24.03 | | | | | End of split % 168.81/24.03 | | | | | % 168.81/24.03 | | | | End of split % 168.81/24.03 | | | | % 168.81/24.03 | | | End of split % 168.81/24.03 | | | % 168.81/24.03 | | End of split % 168.81/24.03 | | % 168.81/24.03 | Case 2: % 168.81/24.03 | | % 168.81/24.03 | | (262) all_74_11 = n4 % 168.81/24.03 | | % 168.81/24.03 | | REDUCE: (16), (262) imply: % 168.81/24.03 | | (263) a_select3(pminus_ds1_filter, all_74_10, n4) = all_74_8 % 168.81/24.03 | | % 168.81/24.03 | | REDUCE: (8), (262) imply: % 168.81/24.03 | | (264) a_select3(pminus_ds1_filter, n4, all_74_10) = all_74_9 % 168.81/24.03 | | % 168.81/24.03 | | REDUCE: (19), (262) imply: % 168.81/24.03 | | (265) leq(n4, n5) % 168.81/24.03 | | % 168.81/24.03 | | REDUCE: (21), (262) imply: % 168.81/24.03 | | (266) leq(n0, n4) % 168.81/24.03 | | % 168.81/24.03 | | BETA: splitting (2) gives: % 168.81/24.03 | | % 168.81/24.03 | | Case 1: % 168.81/24.03 | | | % 168.81/24.03 | | | (267) gt(n4, all_74_10) % 168.81/24.03 | | | % 168.81/24.03 | | | GROUND_INST: instantiating (1) with all_74_10, n4, n3, simplifying with % 168.81/24.03 | | | (7), (12), (17), (267) gives: % 168.81/24.03 | | | (268) leq(all_74_10, n3) % 168.81/24.03 | | | % 168.99/24.03 | | | GROUND_INST: instantiating (25) with all_74_10, n3, simplifying with (12), % 168.99/24.03 | | | (23), (268) gives: % 168.99/24.03 | | | (269) all_74_10 = n3 | gt(n3, all_74_10) % 168.99/24.03 | | | % 168.99/24.03 | | | BETA: splitting (269) gives: % 168.99/24.03 | | | % 168.99/24.03 | | | Case 1: % 168.99/24.03 | | | | % 168.99/24.03 | | | | (270) gt(n3, all_74_10) % 168.99/24.03 | | | | % 168.99/24.03 | | | | GROUND_INST: instantiating (1) with all_74_10, n3, n2, simplifying with % 168.99/24.03 | | | | (12), (13), (23), (270) gives: % 168.99/24.03 | | | | (271) leq(all_74_10, n2) % 168.99/24.03 | | | | % 168.99/24.03 | | | | GROUND_INST: instantiating (25) with all_74_10, n2, simplifying with % 168.99/24.03 | | | | (6), (12), (271) gives: % 168.99/24.03 | | | | (272) all_74_10 = n2 | gt(n2, all_74_10) % 168.99/24.03 | | | | % 168.99/24.03 | | | | BETA: splitting (272) gives: % 168.99/24.03 | | | | % 168.99/24.03 | | | | Case 1: % 168.99/24.03 | | | | | % 168.99/24.03 | | | | | (273) gt(n2, all_74_10) % 168.99/24.03 | | | | | % 168.99/24.03 | | | | | GROUND_INST: instantiating (1) with all_74_10, n2, n1, simplifying % 168.99/24.03 | | | | | with (6), (12), (22), (273) gives: % 168.99/24.03 | | | | | (274) leq(all_74_10, n1) % 168.99/24.03 | | | | | % 168.99/24.03 | | | | | GROUND_INST: instantiating (11) with all_74_10, simplifying with (12), % 168.99/24.03 | | | | | (24), (274) gives: % 168.99/24.03 | | | | | (275) all_74_10 = n1 | all_74_10 = n0 % 168.99/24.03 | | | | | % 168.99/24.03 | | | | | BETA: splitting (275) gives: % 168.99/24.03 | | | | | % 168.99/24.03 | | | | | Case 1: % 168.99/24.03 | | | | | | % 168.99/24.03 | | | | | | (276) all_74_10 = n0 % 168.99/24.03 | | | | | | % 168.99/24.03 | | | | | | REDUCE: (14), (276) imply: % 168.99/24.03 | | | | | | (277) $false % 168.99/24.03 | | | | | | % 168.99/24.03 | | | | | | CLOSE: (277) is inconsistent. % 168.99/24.03 | | | | | | % 168.99/24.03 | | | | | Case 2: % 168.99/24.03 | | | | | | % 168.99/24.03 | | | | | | (278) all_74_10 = n1 % 168.99/24.03 | | | | | | % 168.99/24.03 | | | | | | REDUCE: (263), (278) imply: % 168.99/24.03 | | | | | | (279) a_select3(pminus_ds1_filter, n1, n4) = all_74_8 % 168.99/24.03 | | | | | | % 168.99/24.03 | | | | | | REDUCE: (264), (278) imply: % 168.99/24.03 | | | | | | (280) a_select3(pminus_ds1_filter, n4, n1) = all_74_9 % 168.99/24.03 | | | | | | % 168.99/24.03 | | | | | | REDUCE: (12), (278) imply: % 168.99/24.03 | | | | | | (281) $i(n1) % 168.99/24.03 | | | | | | % 168.99/24.03 | | | | | | REDUCE: (10), (278) imply: % 168.99/24.03 | | | | | | (282) leq(n1, n5) % 168.99/24.03 | | | | | | % 168.99/24.03 | | | | | | REDUCE: (24), (278) imply: % 168.99/24.03 | | | | | | (283) leq(n0, n1) % 168.99/24.03 | | | | | | % 168.99/24.03 | | | | | | GROUND_INST: instantiating (9) with n1, n4, all_74_8, simplifying % 168.99/24.03 | | | | | | with (17), (266), (279), (281), (283) gives: % 168.99/24.03 | | | | | | (284) ~ leq(n4, all_74_13) | ~ leq(n1, all_74_13) | % 168.99/24.03 | | | | | | (a_select3(pminus_ds1_filter, n4, n1) = all_74_8 & % 168.99/24.03 | | | | | | $i(all_74_8)) % 168.99/24.03 | | | | | | % 168.99/24.03 | | | | | | BETA: splitting (284) gives: % 168.99/24.03 | | | | | | % 168.99/24.03 | | | | | | Case 1: % 168.99/24.03 | | | | | | | % 168.99/24.03 | | | | | | | (285) ~ leq(n4, all_74_13) % 168.99/24.03 | | | | | | | % 168.99/24.03 | | | | | | | REDUCE: (3), (285) imply: % 168.99/24.03 | | | | | | | (286) ~ leq(n4, n5) % 168.99/24.03 | | | | | | | % 168.99/24.03 | | | | | | | PRED_UNIFY: (265), (286) imply: % 168.99/24.03 | | | | | | | (287) $false % 168.99/24.03 | | | | | | | % 168.99/24.03 | | | | | | | CLOSE: (287) is inconsistent. % 168.99/24.03 | | | | | | | % 168.99/24.03 | | | | | | Case 2: % 168.99/24.03 | | | | | | | % 168.99/24.03 | | | | | | | (288) ~ leq(n1, all_74_13) | (a_select3(pminus_ds1_filter, n4, % 168.99/24.03 | | | | | | | n1) = all_74_8 & $i(all_74_8)) % 168.99/24.03 | | | | | | | % 168.99/24.03 | | | | | | | BETA: splitting (288) gives: % 168.99/24.03 | | | | | | | % 168.99/24.03 | | | | | | | Case 1: % 168.99/24.03 | | | | | | | | % 168.99/24.03 | | | | | | | | (289) ~ leq(n1, all_74_13) % 168.99/24.03 | | | | | | | | % 168.99/24.03 | | | | | | | | REDUCE: (3), (289) imply: % 168.99/24.03 | | | | | | | | (290) ~ leq(n1, n5) % 168.99/24.03 | | | | | | | | % 168.99/24.03 | | | | | | | | PRED_UNIFY: (282), (290) imply: % 168.99/24.03 | | | | | | | | (291) $false % 168.99/24.03 | | | | | | | | % 168.99/24.03 | | | | | | | | CLOSE: (291) is inconsistent. % 168.99/24.03 | | | | | | | | % 168.99/24.03 | | | | | | | Case 2: % 168.99/24.03 | | | | | | | | % 168.99/24.03 | | | | | | | | (292) a_select3(pminus_ds1_filter, n4, n1) = all_74_8 & % 168.99/24.03 | | | | | | | | $i(all_74_8) % 168.99/24.03 | | | | | | | | % 168.99/24.03 | | | | | | | | ALPHA: (292) implies: % 168.99/24.03 | | | | | | | | (293) a_select3(pminus_ds1_filter, n4, n1) = all_74_8 % 168.99/24.03 | | | | | | | | % 168.99/24.03 | | | | | | | | GROUND_INST: instantiating (18) with all_74_9, all_74_8, n1, n4, % 168.99/24.03 | | | | | | | | pminus_ds1_filter, simplifying with (280), (293) % 168.99/24.03 | | | | | | | | gives: % 168.99/24.03 | | | | | | | | (294) all_74_8 = all_74_9 % 168.99/24.03 | | | | | | | | % 168.99/24.03 | | | | | | | | REDUCE: (15), (294) imply: % 168.99/24.03 | | | | | | | | (295) $false % 168.99/24.03 | | | | | | | | % 168.99/24.03 | | | | | | | | CLOSE: (295) is inconsistent. % 168.99/24.03 | | | | | | | | % 168.99/24.03 | | | | | | | End of split % 168.99/24.03 | | | | | | | % 168.99/24.03 | | | | | | End of split % 168.99/24.03 | | | | | | % 168.99/24.03 | | | | | End of split % 168.99/24.03 | | | | | % 168.99/24.03 | | | | Case 2: % 168.99/24.03 | | | | | % 168.99/24.03 | | | | | (296) all_74_10 = n2 % 168.99/24.03 | | | | | % 168.99/24.03 | | | | | REDUCE: (263), (296) imply: % 168.99/24.03 | | | | | (297) a_select3(pminus_ds1_filter, n2, n4) = all_74_8 % 168.99/24.03 | | | | | % 168.99/24.03 | | | | | REDUCE: (264), (296) imply: % 168.99/24.03 | | | | | (298) a_select3(pminus_ds1_filter, n4, n2) = all_74_9 % 168.99/24.03 | | | | | % 168.99/24.03 | | | | | REDUCE: (10), (296) imply: % 168.99/24.03 | | | | | (299) leq(n2, n5) % 168.99/24.03 | | | | | % 168.99/24.03 | | | | | REDUCE: (24), (296) imply: % 168.99/24.03 | | | | | (300) leq(n0, n2) % 168.99/24.03 | | | | | % 168.99/24.03 | | | | | GROUND_INST: instantiating (9) with n2, n4, all_74_8, simplifying with % 168.99/24.03 | | | | | (6), (17), (266), (297), (300) gives: % 168.99/24.03 | | | | | (301) ~ leq(n4, all_74_13) | ~ leq(n2, all_74_13) | % 168.99/24.03 | | | | | (a_select3(pminus_ds1_filter, n4, n2) = all_74_8 & % 168.99/24.03 | | | | | $i(all_74_8)) % 168.99/24.03 | | | | | % 168.99/24.03 | | | | | BETA: splitting (301) gives: % 168.99/24.03 | | | | | % 168.99/24.03 | | | | | Case 1: % 168.99/24.03 | | | | | | % 168.99/24.03 | | | | | | (302) ~ leq(n4, all_74_13) % 168.99/24.03 | | | | | | % 168.99/24.03 | | | | | | REDUCE: (3), (302) imply: % 168.99/24.03 | | | | | | (303) ~ leq(n4, n5) % 168.99/24.03 | | | | | | % 168.99/24.03 | | | | | | PRED_UNIFY: (265), (303) imply: % 168.99/24.03 | | | | | | (304) $false % 168.99/24.03 | | | | | | % 168.99/24.03 | | | | | | CLOSE: (304) is inconsistent. % 168.99/24.03 | | | | | | % 168.99/24.03 | | | | | Case 2: % 168.99/24.03 | | | | | | % 168.99/24.03 | | | | | | (305) ~ leq(n2, all_74_13) | (a_select3(pminus_ds1_filter, n4, % 168.99/24.03 | | | | | | n2) = all_74_8 & $i(all_74_8)) % 168.99/24.03 | | | | | | % 168.99/24.03 | | | | | | BETA: splitting (305) gives: % 168.99/24.03 | | | | | | % 168.99/24.03 | | | | | | Case 1: % 168.99/24.03 | | | | | | | % 168.99/24.03 | | | | | | | (306) ~ leq(n2, all_74_13) % 168.99/24.03 | | | | | | | % 168.99/24.03 | | | | | | | REDUCE: (3), (306) imply: % 168.99/24.03 | | | | | | | (307) ~ leq(n2, n5) % 168.99/24.03 | | | | | | | % 168.99/24.03 | | | | | | | PRED_UNIFY: (299), (307) imply: % 168.99/24.03 | | | | | | | (308) $false % 168.99/24.03 | | | | | | | % 168.99/24.03 | | | | | | | CLOSE: (308) is inconsistent. % 168.99/24.03 | | | | | | | % 168.99/24.03 | | | | | | Case 2: % 168.99/24.03 | | | | | | | % 168.99/24.03 | | | | | | | (309) a_select3(pminus_ds1_filter, n4, n2) = all_74_8 & % 168.99/24.03 | | | | | | | $i(all_74_8) % 168.99/24.03 | | | | | | | % 168.99/24.03 | | | | | | | ALPHA: (309) implies: % 168.99/24.03 | | | | | | | (310) a_select3(pminus_ds1_filter, n4, n2) = all_74_8 % 168.99/24.03 | | | | | | | % 168.99/24.03 | | | | | | | REF_CLOSE: (15), (18), (298), (310) are inconsistent by sub-proof % 168.99/24.03 | | | | | | | #7. % 168.99/24.03 | | | | | | | % 168.99/24.03 | | | | | | End of split % 168.99/24.03 | | | | | | % 168.99/24.03 | | | | | End of split % 168.99/24.03 | | | | | % 168.99/24.03 | | | | End of split % 168.99/24.03 | | | | % 168.99/24.03 | | | Case 2: % 168.99/24.03 | | | | % 168.99/24.03 | | | | (311) all_74_10 = n3 % 168.99/24.03 | | | | % 168.99/24.03 | | | | REDUCE: (263), (311) imply: % 168.99/24.03 | | | | (312) a_select3(pminus_ds1_filter, n3, n4) = all_74_8 % 168.99/24.03 | | | | % 168.99/24.03 | | | | REDUCE: (264), (311) imply: % 168.99/24.03 | | | | (313) a_select3(pminus_ds1_filter, n4, n3) = all_74_9 % 168.99/24.03 | | | | % 168.99/24.03 | | | | REDUCE: (10), (311) imply: % 168.99/24.03 | | | | (314) leq(n3, n5) % 168.99/24.03 | | | | % 168.99/24.03 | | | | REDUCE: (24), (311) imply: % 168.99/24.03 | | | | (315) leq(n0, n3) % 168.99/24.03 | | | | % 168.99/24.03 | | | | GROUND_INST: instantiating (9) with n3, n4, all_74_8, simplifying with % 168.99/24.03 | | | | (17), (23), (266), (312), (315) gives: % 168.99/24.03 | | | | (316) ~ leq(n4, all_74_13) | ~ leq(n3, all_74_13) | % 168.99/24.03 | | | | (a_select3(pminus_ds1_filter, n4, n3) = all_74_8 & % 168.99/24.03 | | | | $i(all_74_8)) % 168.99/24.03 | | | | % 168.99/24.03 | | | | BETA: splitting (316) gives: % 168.99/24.03 | | | | % 168.99/24.03 | | | | Case 1: % 168.99/24.03 | | | | | % 168.99/24.03 | | | | | (317) ~ leq(n4, all_74_13) % 168.99/24.03 | | | | | % 168.99/24.03 | | | | | REDUCE: (3), (317) imply: % 168.99/24.03 | | | | | (318) ~ leq(n4, n5) % 168.99/24.03 | | | | | % 168.99/24.03 | | | | | PRED_UNIFY: (265), (318) imply: % 168.99/24.03 | | | | | (319) $false % 168.99/24.03 | | | | | % 168.99/24.03 | | | | | CLOSE: (319) is inconsistent. % 168.99/24.03 | | | | | % 168.99/24.03 | | | | Case 2: % 168.99/24.03 | | | | | % 168.99/24.03 | | | | | (320) ~ leq(n3, all_74_13) | (a_select3(pminus_ds1_filter, n4, n3) % 168.99/24.03 | | | | | = all_74_8 & $i(all_74_8)) % 168.99/24.03 | | | | | % 168.99/24.03 | | | | | BETA: splitting (320) gives: % 168.99/24.03 | | | | | % 168.99/24.03 | | | | | Case 1: % 168.99/24.03 | | | | | | % 168.99/24.03 | | | | | | (321) ~ leq(n3, all_74_13) % 168.99/24.03 | | | | | | % 168.99/24.03 | | | | | | REDUCE: (3), (321) imply: % 168.99/24.03 | | | | | | (322) ~ leq(n3, n5) % 168.99/24.03 | | | | | | % 168.99/24.03 | | | | | | PRED_UNIFY: (314), (322) imply: % 168.99/24.03 | | | | | | (323) $false % 168.99/24.03 | | | | | | % 168.99/24.03 | | | | | | CLOSE: (323) is inconsistent. % 168.99/24.03 | | | | | | % 168.99/24.03 | | | | | Case 2: % 168.99/24.03 | | | | | | % 168.99/24.03 | | | | | | (324) a_select3(pminus_ds1_filter, n4, n3) = all_74_8 & % 168.99/24.03 | | | | | | $i(all_74_8) % 168.99/24.03 | | | | | | % 168.99/24.03 | | | | | | ALPHA: (324) implies: % 168.99/24.03 | | | | | | (325) a_select3(pminus_ds1_filter, n4, n3) = all_74_8 % 168.99/24.03 | | | | | | % 168.99/24.03 | | | | | | GROUND_INST: instantiating (18) with all_74_9, all_74_8, n3, n4, % 168.99/24.03 | | | | | | pminus_ds1_filter, simplifying with (313), (325) gives: % 168.99/24.03 | | | | | | (326) all_74_8 = all_74_9 % 168.99/24.03 | | | | | | % 168.99/24.03 | | | | | | REDUCE: (15), (326) imply: % 168.99/24.03 | | | | | | (327) $false % 168.99/24.03 | | | | | | % 168.99/24.03 | | | | | | CLOSE: (327) is inconsistent. % 168.99/24.03 | | | | | | % 168.99/24.03 | | | | | End of split % 168.99/24.03 | | | | | % 168.99/24.03 | | | | End of split % 168.99/24.03 | | | | % 168.99/24.03 | | | End of split % 168.99/24.03 | | | % 168.99/24.03 | | Case 2: % 168.99/24.03 | | | % 168.99/24.03 | | | (328) all_74_10 = n4 % 168.99/24.03 | | | % 168.99/24.03 | | | REDUCE: (263), (328) imply: % 168.99/24.03 | | | (329) a_select3(pminus_ds1_filter, n4, n4) = all_74_8 % 168.99/24.03 | | | % 168.99/24.03 | | | REDUCE: (264), (328) imply: % 168.99/24.03 | | | (330) a_select3(pminus_ds1_filter, n4, n4) = all_74_9 % 168.99/24.03 | | | % 168.99/24.03 | | | GROUND_INST: instantiating (18) with all_74_9, all_74_8, n4, n4, % 168.99/24.03 | | | pminus_ds1_filter, simplifying with (329), (330) gives: % 168.99/24.03 | | | (331) all_74_8 = all_74_9 % 168.99/24.03 | | | % 168.99/24.03 | | | REDUCE: (15), (331) imply: % 168.99/24.03 | | | (332) $false % 168.99/24.03 | | | % 168.99/24.03 | | | CLOSE: (332) is inconsistent. % 168.99/24.03 | | | % 168.99/24.03 | | End of split % 168.99/24.03 | | % 168.99/24.03 | End of split % 168.99/24.03 | % 168.99/24.03 End of proof % 168.99/24.03 % 168.99/24.03 Sub-proof #7 shows that the following formulas are inconsistent: % 168.99/24.03 ---------------------------------------------------------------- % 168.99/24.03 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 168.99/24.03 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 168.99/24.03 v0)) % 168.99/24.03 (2) a_select3(pminus_ds1_filter, n4, n2) = all_74_8 % 168.99/24.03 (3) a_select3(pminus_ds1_filter, n4, n2) = all_74_9 % 168.99/24.03 (4) ~ (all_74_8 = all_74_9) % 168.99/24.03 % 168.99/24.03 Begin of proof % 168.99/24.03 | % 168.99/24.03 | GROUND_INST: instantiating (1) with all_74_9, all_74_8, n2, n4, % 168.99/24.03 | pminus_ds1_filter, simplifying with (2), (3) gives: % 168.99/24.03 | (5) all_74_8 = all_74_9 % 168.99/24.03 | % 168.99/24.03 | REDUCE: (4), (5) imply: % 168.99/24.03 | (6) $false % 168.99/24.03 | % 168.99/24.03 | CLOSE: (6) is inconsistent. % 168.99/24.03 | % 168.99/24.03 End of proof % 168.99/24.03 % 168.99/24.03 Sub-proof #8 shows that the following formulas are inconsistent: % 168.99/24.03 ---------------------------------------------------------------- % 168.99/24.03 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 168.99/24.03 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 168.99/24.03 v0)) % 168.99/24.03 (2) a_select3(pminus_ds1_filter, n3, n2) = all_74_8 % 168.99/24.03 (3) a_select3(pminus_ds1_filter, n3, n2) = all_74_9 % 168.99/24.03 (4) ~ (all_74_8 = all_74_9) % 168.99/24.03 % 168.99/24.03 Begin of proof % 168.99/24.03 | % 168.99/24.03 | GROUND_INST: instantiating (1) with all_74_8, all_74_9, n2, n3, % 168.99/24.03 | pminus_ds1_filter, simplifying with (2), (3) gives: % 168.99/24.03 | (5) all_74_8 = all_74_9 % 168.99/24.03 | % 168.99/24.03 | REDUCE: (4), (5) imply: % 168.99/24.04 | (6) $false % 168.99/24.04 | % 168.99/24.04 | CLOSE: (6) is inconsistent. % 168.99/24.04 | % 168.99/24.04 End of proof % 168.99/24.04 % 168.99/24.04 Sub-proof #9 shows that the following formulas are inconsistent: % 168.99/24.04 ---------------------------------------------------------------- % 168.99/24.04 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 168.99/24.04 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 168.99/24.04 v0)) % 168.99/24.04 (2) a_select3(pminus_ds1_filter, n2, n1) = all_74_8 % 168.99/24.04 (3) a_select3(pminus_ds1_filter, n2, n1) = all_74_9 % 168.99/24.04 (4) ~ (all_74_8 = all_74_9) % 168.99/24.04 % 168.99/24.04 Begin of proof % 168.99/24.04 | % 168.99/24.04 | GROUND_INST: instantiating (1) with all_74_9, all_74_8, n1, n2, % 168.99/24.04 | pminus_ds1_filter, simplifying with (2), (3) gives: % 168.99/24.04 | (5) all_74_8 = all_74_9 % 168.99/24.04 | % 168.99/24.04 | REDUCE: (4), (5) imply: % 168.99/24.04 | (6) $false % 168.99/24.04 | % 168.99/24.04 | CLOSE: (6) is inconsistent. % 168.99/24.04 | % 168.99/24.04 End of proof % 168.99/24.04 % 168.99/24.04 Sub-proof #10 shows that the following formulas are inconsistent: % 168.99/24.04 ---------------------------------------------------------------- % 168.99/24.04 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (pred(v1) = v2) | ~ $i(v1) % 168.99/24.04 | ~ $i(v0) | ~ gt(v1, v0) | leq(v0, v2)) % 168.99/24.04 (2) all_74_10 = n4 | gt(n4, all_74_10) % 168.99/24.04 (3) all_74_13 = n5 % 168.99/24.04 (4) a_select3(pminus_ds1_filter, n0, all_74_10) = all_74_9 % 168.99/24.04 (5) leq(n0, n0) % 168.99/24.04 (6) $i(n2) % 168.99/24.04 (7) pred(n4) = n3 % 168.99/24.04 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 168.99/24.04 (a_select3(pminus_ds1_filter, v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 168.99/24.04 ~ leq(v1, all_74_13) | ~ leq(v0, all_74_13) | ~ leq(n0, v1) | ~ % 168.99/24.04 leq(n0, v0) | (a_select3(pminus_ds1_filter, v1, v0) = v2 & $i(v2))) % 168.99/24.04 (9) leq(all_74_10, n5) % 168.99/24.04 (10) ! [v0: $i] : (v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0, n1) | ~ % 168.99/24.04 leq(n0, v0)) % 168.99/24.04 (11) $i(all_74_10) % 168.99/24.04 (12) pred(n3) = n2 % 168.99/24.04 (13) ~ (all_74_10 = n0) % 168.99/24.04 (14) ~ (all_74_8 = all_74_9) % 168.99/24.04 (15) $i(n4) % 168.99/24.04 (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 168.99/24.04 (v1 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 168.99/24.04 v0)) % 168.99/24.04 (17) leq(n0, n5) % 168.99/24.04 (18) $i(n0) % 168.99/24.04 (19) a_select3(pminus_ds1_filter, all_74_10, n0) = all_74_8 % 168.99/24.04 (20) pred(n2) = n1 % 168.99/24.04 (21) $i(n3) % 168.99/24.04 (22) leq(n0, all_74_10) % 168.99/24.04 (23) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ % 168.99/24.04 leq(v0, v1) | gt(v1, v0)) % 168.99/24.04 % 168.99/24.04 Begin of proof % 168.99/24.04 | % 168.99/24.04 | BETA: splitting (2) gives: % 168.99/24.04 | % 168.99/24.04 | Case 1: % 168.99/24.04 | | % 168.99/24.04 | | (24) gt(n4, all_74_10) % 168.99/24.04 | | % 168.99/24.04 | | GROUND_INST: instantiating (1) with all_74_10, n4, n3, simplifying with (7), % 168.99/24.04 | | (11), (15), (24) gives: % 168.99/24.04 | | (25) leq(all_74_10, n3) % 168.99/24.04 | | % 168.99/24.04 | | GROUND_INST: instantiating (23) with all_74_10, n3, simplifying with (11), % 168.99/24.04 | | (21), (25) gives: % 168.99/24.04 | | (26) all_74_10 = n3 | gt(n3, all_74_10) % 168.99/24.04 | | % 168.99/24.04 | | BETA: splitting (26) gives: % 168.99/24.04 | | % 168.99/24.04 | | Case 1: % 168.99/24.04 | | | % 168.99/24.04 | | | (27) gt(n3, all_74_10) % 168.99/24.04 | | | % 169.03/24.04 | | | GROUND_INST: instantiating (1) with all_74_10, n3, n2, simplifying with % 169.03/24.04 | | | (11), (12), (21), (27) gives: % 169.03/24.04 | | | (28) leq(all_74_10, n2) % 169.03/24.04 | | | % 169.03/24.04 | | | GROUND_INST: instantiating (23) with all_74_10, n2, simplifying with (6), % 169.03/24.04 | | | (11), (28) gives: % 169.03/24.04 | | | (29) all_74_10 = n2 | gt(n2, all_74_10) % 169.03/24.04 | | | % 169.03/24.04 | | | BETA: splitting (29) gives: % 169.03/24.04 | | | % 169.03/24.04 | | | Case 1: % 169.03/24.04 | | | | % 169.03/24.04 | | | | (30) gt(n2, all_74_10) % 169.03/24.04 | | | | % 169.03/24.04 | | | | GROUND_INST: instantiating (1) with all_74_10, n2, n1, simplifying with % 169.03/24.04 | | | | (6), (11), (20), (30) gives: % 169.03/24.04 | | | | (31) leq(all_74_10, n1) % 169.03/24.04 | | | | % 169.03/24.04 | | | | GROUND_INST: instantiating (10) with all_74_10, simplifying with (11), % 169.03/24.04 | | | | (22), (31) gives: % 169.03/24.04 | | | | (32) all_74_10 = n1 | all_74_10 = n0 % 169.03/24.04 | | | | % 169.03/24.04 | | | | BETA: splitting (32) gives: % 169.03/24.04 | | | | % 169.03/24.04 | | | | Case 1: % 169.03/24.04 | | | | | % 169.03/24.04 | | | | | (33) all_74_10 = n0 % 169.03/24.04 | | | | | % 169.03/24.04 | | | | | REDUCE: (13), (33) imply: % 169.03/24.04 | | | | | (34) $false % 169.03/24.04 | | | | | % 169.03/24.04 | | | | | CLOSE: (34) is inconsistent. % 169.03/24.04 | | | | | % 169.03/24.04 | | | | Case 2: % 169.03/24.04 | | | | | % 169.03/24.04 | | | | | (35) all_74_10 = n1 % 169.03/24.04 | | | | | % 169.03/24.04 | | | | | REDUCE: (19), (35) imply: % 169.03/24.04 | | | | | (36) a_select3(pminus_ds1_filter, n1, n0) = all_74_8 % 169.03/24.04 | | | | | % 169.03/24.04 | | | | | REDUCE: (4), (35) imply: % 169.03/24.04 | | | | | (37) a_select3(pminus_ds1_filter, n0, n1) = all_74_9 % 169.03/24.04 | | | | | % 169.03/24.04 | | | | | REDUCE: (11), (35) imply: % 169.03/24.04 | | | | | (38) $i(n1) % 169.03/24.04 | | | | | % 169.03/24.04 | | | | | REDUCE: (9), (35) imply: % 169.03/24.04 | | | | | (39) leq(n1, n5) % 169.03/24.04 | | | | | % 169.03/24.04 | | | | | REDUCE: (22), (35) imply: % 169.03/24.04 | | | | | (40) leq(n0, n1) % 169.03/24.04 | | | | | % 169.03/24.04 | | | | | GROUND_INST: instantiating (8) with n0, n1, all_74_9, simplifying with % 169.03/24.04 | | | | | (5), (18), (37), (38), (40) gives: % 169.03/24.04 | | | | | (41) ~ leq(n1, all_74_13) | ~ leq(n0, all_74_13) | % 169.03/24.04 | | | | | (a_select3(pminus_ds1_filter, n1, n0) = all_74_9 & % 169.03/24.04 | | | | | $i(all_74_9)) % 169.03/24.04 | | | | | % 169.03/24.04 | | | | | BETA: splitting (41) gives: % 169.03/24.04 | | | | | % 169.03/24.04 | | | | | Case 1: % 169.03/24.04 | | | | | | % 169.03/24.04 | | | | | | (42) ~ leq(n0, all_74_13) % 169.03/24.04 | | | | | | % 169.03/24.04 | | | | | | REDUCE: (3), (42) imply: % 169.03/24.04 | | | | | | (43) ~ leq(n0, n5) % 169.03/24.04 | | | | | | % 169.03/24.04 | | | | | | PRED_UNIFY: (17), (43) imply: % 169.03/24.04 | | | | | | (44) $false % 169.03/24.04 | | | | | | % 169.03/24.04 | | | | | | CLOSE: (44) is inconsistent. % 169.03/24.04 | | | | | | % 169.03/24.04 | | | | | Case 2: % 169.03/24.04 | | | | | | % 169.03/24.04 | | | | | | (45) ~ leq(n1, all_74_13) | (a_select3(pminus_ds1_filter, n1, % 169.03/24.04 | | | | | | n0) = all_74_9 & $i(all_74_9)) % 169.03/24.04 | | | | | | % 169.03/24.04 | | | | | | BETA: splitting (45) gives: % 169.03/24.04 | | | | | | % 169.03/24.04 | | | | | | Case 1: % 169.03/24.04 | | | | | | | % 169.03/24.04 | | | | | | | (46) ~ leq(n1, all_74_13) % 169.03/24.04 | | | | | | | % 169.03/24.04 | | | | | | | REDUCE: (3), (46) imply: % 169.03/24.04 | | | | | | | (47) ~ leq(n1, n5) % 169.03/24.04 | | | | | | | % 169.03/24.04 | | | | | | | PRED_UNIFY: (39), (47) imply: % 169.03/24.04 | | | | | | | (48) $false % 169.03/24.04 | | | | | | | % 169.03/24.04 | | | | | | | CLOSE: (48) is inconsistent. % 169.03/24.04 | | | | | | | % 169.03/24.04 | | | | | | Case 2: % 169.03/24.04 | | | | | | | % 169.03/24.04 | | | | | | | (49) a_select3(pminus_ds1_filter, n1, n0) = all_74_9 & % 169.03/24.04 | | | | | | | $i(all_74_9) % 169.03/24.04 | | | | | | | % 169.03/24.04 | | | | | | | ALPHA: (49) implies: % 169.03/24.04 | | | | | | | (50) a_select3(pminus_ds1_filter, n1, n0) = all_74_9 % 169.03/24.04 | | | | | | | % 169.03/24.04 | | | | | | | REF_CLOSE: (14), (16), (36), (50) are inconsistent by sub-proof % 169.03/24.04 | | | | | | | #13. % 169.03/24.04 | | | | | | | % 169.03/24.04 | | | | | | End of split % 169.03/24.04 | | | | | | % 169.03/24.04 | | | | | End of split % 169.03/24.04 | | | | | % 169.03/24.04 | | | | End of split % 169.03/24.04 | | | | % 169.03/24.04 | | | Case 2: % 169.03/24.04 | | | | % 169.03/24.04 | | | | (51) all_74_10 = n2 % 169.03/24.04 | | | | % 169.03/24.04 | | | | REDUCE: (19), (51) imply: % 169.03/24.04 | | | | (52) a_select3(pminus_ds1_filter, n2, n0) = all_74_8 % 169.03/24.04 | | | | % 169.03/24.04 | | | | REDUCE: (4), (51) imply: % 169.03/24.04 | | | | (53) a_select3(pminus_ds1_filter, n0, n2) = all_74_9 % 169.03/24.04 | | | | % 169.03/24.04 | | | | REDUCE: (9), (51) imply: % 169.03/24.04 | | | | (54) leq(n2, n5) % 169.03/24.04 | | | | % 169.03/24.04 | | | | REDUCE: (22), (51) imply: % 169.03/24.04 | | | | (55) leq(n0, n2) % 169.03/24.04 | | | | % 169.03/24.04 | | | | GROUND_INST: instantiating (8) with n0, n2, all_74_9, simplifying with % 169.03/24.04 | | | | (5), (6), (18), (53), (55) gives: % 169.03/24.04 | | | | (56) ~ leq(n2, all_74_13) | ~ leq(n0, all_74_13) | % 169.03/24.04 | | | | (a_select3(pminus_ds1_filter, n2, n0) = all_74_9 & $i(all_74_9)) % 169.03/24.04 | | | | % 169.03/24.04 | | | | BETA: splitting (56) gives: % 169.03/24.04 | | | | % 169.03/24.04 | | | | Case 1: % 169.03/24.04 | | | | | % 169.03/24.04 | | | | | (57) ~ leq(n0, all_74_13) % 169.03/24.04 | | | | | % 169.03/24.04 | | | | | REDUCE: (3), (57) imply: % 169.03/24.04 | | | | | (58) ~ leq(n0, n5) % 169.03/24.04 | | | | | % 169.03/24.04 | | | | | PRED_UNIFY: (17), (58) imply: % 169.03/24.04 | | | | | (59) $false % 169.03/24.04 | | | | | % 169.03/24.04 | | | | | CLOSE: (59) is inconsistent. % 169.03/24.04 | | | | | % 169.03/24.04 | | | | Case 2: % 169.03/24.04 | | | | | % 169.03/24.04 | | | | | (60) ~ leq(n2, all_74_13) | (a_select3(pminus_ds1_filter, n2, n0) % 169.03/24.04 | | | | | = all_74_9 & $i(all_74_9)) % 169.03/24.04 | | | | | % 169.03/24.04 | | | | | BETA: splitting (60) gives: % 169.03/24.04 | | | | | % 169.03/24.04 | | | | | Case 1: % 169.03/24.04 | | | | | | % 169.03/24.04 | | | | | | (61) ~ leq(n2, all_74_13) % 169.03/24.04 | | | | | | % 169.03/24.04 | | | | | | REDUCE: (3), (61) imply: % 169.03/24.04 | | | | | | (62) ~ leq(n2, n5) % 169.03/24.04 | | | | | | % 169.03/24.04 | | | | | | PRED_UNIFY: (54), (62) imply: % 169.03/24.04 | | | | | | (63) $false % 169.03/24.04 | | | | | | % 169.03/24.04 | | | | | | CLOSE: (63) is inconsistent. % 169.03/24.04 | | | | | | % 169.03/24.04 | | | | | Case 2: % 169.03/24.04 | | | | | | % 169.03/24.04 | | | | | | (64) a_select3(pminus_ds1_filter, n2, n0) = all_74_9 & % 169.03/24.04 | | | | | | $i(all_74_9) % 169.03/24.04 | | | | | | % 169.03/24.04 | | | | | | ALPHA: (64) implies: % 169.03/24.04 | | | | | | (65) a_select3(pminus_ds1_filter, n2, n0) = all_74_9 % 169.03/24.04 | | | | | | % 169.03/24.04 | | | | | | REF_CLOSE: (14), (16), (52), (65) are inconsistent by sub-proof #12. % 169.03/24.04 | | | | | | % 169.03/24.04 | | | | | End of split % 169.03/24.04 | | | | | % 169.03/24.04 | | | | End of split % 169.03/24.04 | | | | % 169.03/24.04 | | | End of split % 169.03/24.04 | | | % 169.03/24.04 | | Case 2: % 169.03/24.04 | | | % 169.03/24.04 | | | (66) all_74_10 = n3 % 169.03/24.04 | | | % 169.03/24.04 | | | REDUCE: (19), (66) imply: % 169.03/24.04 | | | (67) a_select3(pminus_ds1_filter, n3, n0) = all_74_8 % 169.03/24.04 | | | % 169.03/24.04 | | | REDUCE: (4), (66) imply: % 169.03/24.04 | | | (68) a_select3(pminus_ds1_filter, n0, n3) = all_74_9 % 169.03/24.04 | | | % 169.03/24.04 | | | REDUCE: (9), (66) imply: % 169.03/24.04 | | | (69) leq(n3, n5) % 169.03/24.04 | | | % 169.03/24.04 | | | REDUCE: (22), (66) imply: % 169.03/24.04 | | | (70) leq(n0, n3) % 169.03/24.04 | | | % 169.03/24.04 | | | GROUND_INST: instantiating (8) with n0, n3, all_74_9, simplifying with % 169.03/24.04 | | | (5), (18), (21), (68), (70) gives: % 169.03/24.04 | | | (71) ~ leq(n3, all_74_13) | ~ leq(n0, all_74_13) | % 169.03/24.04 | | | (a_select3(pminus_ds1_filter, n3, n0) = all_74_9 & $i(all_74_9)) % 169.03/24.04 | | | % 169.03/24.04 | | | BETA: splitting (71) gives: % 169.03/24.04 | | | % 169.03/24.04 | | | Case 1: % 169.03/24.04 | | | | % 169.03/24.04 | | | | (72) ~ leq(n0, all_74_13) % 169.03/24.04 | | | | % 169.03/24.04 | | | | REDUCE: (3), (72) imply: % 169.03/24.04 | | | | (73) ~ leq(n0, n5) % 169.03/24.04 | | | | % 169.03/24.04 | | | | PRED_UNIFY: (17), (73) imply: % 169.03/24.04 | | | | (74) $false % 169.03/24.04 | | | | % 169.03/24.04 | | | | CLOSE: (74) is inconsistent. % 169.03/24.04 | | | | % 169.03/24.04 | | | Case 2: % 169.03/24.04 | | | | % 169.03/24.04 | | | | (75) ~ leq(n3, all_74_13) | (a_select3(pminus_ds1_filter, n3, n0) = % 169.03/24.04 | | | | all_74_9 & $i(all_74_9)) % 169.03/24.04 | | | | % 169.03/24.04 | | | | BETA: splitting (75) gives: % 169.03/24.04 | | | | % 169.03/24.04 | | | | Case 1: % 169.03/24.04 | | | | | % 169.03/24.04 | | | | | (76) ~ leq(n3, all_74_13) % 169.03/24.04 | | | | | % 169.03/24.04 | | | | | REDUCE: (3), (76) imply: % 169.03/24.04 | | | | | (77) ~ leq(n3, n5) % 169.03/24.04 | | | | | % 169.03/24.04 | | | | | PRED_UNIFY: (69), (77) imply: % 169.03/24.04 | | | | | (78) $false % 169.03/24.04 | | | | | % 169.03/24.04 | | | | | CLOSE: (78) is inconsistent. % 169.03/24.04 | | | | | % 169.03/24.04 | | | | Case 2: % 169.03/24.04 | | | | | % 169.03/24.04 | | | | | (79) a_select3(pminus_ds1_filter, n3, n0) = all_74_9 & $i(all_74_9) % 169.03/24.04 | | | | | % 169.03/24.04 | | | | | ALPHA: (79) implies: % 169.03/24.04 | | | | | (80) a_select3(pminus_ds1_filter, n3, n0) = all_74_9 % 169.03/24.04 | | | | | % 169.03/24.04 | | | | | GROUND_INST: instantiating (16) with all_74_9, all_74_8, n0, n3, % 169.03/24.04 | | | | | pminus_ds1_filter, simplifying with (67), (80) gives: % 169.03/24.04 | | | | | (81) all_74_8 = all_74_9 % 169.03/24.04 | | | | | % 169.03/24.04 | | | | | REDUCE: (14), (81) imply: % 169.03/24.04 | | | | | (82) $false % 169.03/24.04 | | | | | % 169.03/24.04 | | | | | CLOSE: (82) is inconsistent. % 169.03/24.04 | | | | | % 169.03/24.04 | | | | End of split % 169.03/24.04 | | | | % 169.03/24.04 | | | End of split % 169.03/24.04 | | | % 169.03/24.04 | | End of split % 169.03/24.04 | | % 169.03/24.04 | Case 2: % 169.03/24.04 | | % 169.03/24.04 | | (83) all_74_10 = n4 % 169.03/24.04 | | % 169.03/24.04 | | REDUCE: (19), (83) imply: % 169.03/24.04 | | (84) a_select3(pminus_ds1_filter, n4, n0) = all_74_8 % 169.03/24.04 | | % 169.03/24.04 | | REDUCE: (4), (83) imply: % 169.03/24.04 | | (85) a_select3(pminus_ds1_filter, n0, n4) = all_74_9 % 169.03/24.04 | | % 169.03/24.04 | | REDUCE: (9), (83) imply: % 169.03/24.04 | | (86) leq(n4, n5) % 169.03/24.04 | | % 169.03/24.04 | | REDUCE: (22), (83) imply: % 169.03/24.04 | | (87) leq(n0, n4) % 169.03/24.04 | | % 169.03/24.04 | | GROUND_INST: instantiating (8) with n0, n4, all_74_9, simplifying with (5), % 169.03/24.04 | | (15), (18), (85), (87) gives: % 169.03/24.04 | | (88) ~ leq(n4, all_74_13) | ~ leq(n0, all_74_13) | % 169.03/24.04 | | (a_select3(pminus_ds1_filter, n4, n0) = all_74_9 & $i(all_74_9)) % 169.03/24.04 | | % 169.03/24.04 | | BETA: splitting (88) gives: % 169.03/24.04 | | % 169.03/24.04 | | Case 1: % 169.03/24.04 | | | % 169.03/24.04 | | | (89) ~ leq(n0, all_74_13) % 169.03/24.04 | | | % 169.03/24.04 | | | REDUCE: (3), (89) imply: % 169.03/24.04 | | | (90) ~ leq(n0, n5) % 169.03/24.04 | | | % 169.03/24.04 | | | PRED_UNIFY: (17), (90) imply: % 169.03/24.04 | | | (91) $false % 169.03/24.04 | | | % 169.03/24.04 | | | CLOSE: (91) is inconsistent. % 169.03/24.04 | | | % 169.03/24.04 | | Case 2: % 169.03/24.04 | | | % 169.03/24.04 | | | (92) ~ leq(n4, all_74_13) | (a_select3(pminus_ds1_filter, n4, n0) = % 169.03/24.04 | | | all_74_9 & $i(all_74_9)) % 169.03/24.04 | | | % 169.03/24.04 | | | BETA: splitting (92) gives: % 169.03/24.04 | | | % 169.03/24.04 | | | Case 1: % 169.03/24.04 | | | | % 169.03/24.04 | | | | (93) ~ leq(n4, all_74_13) % 169.03/24.04 | | | | % 169.03/24.04 | | | | REDUCE: (3), (93) imply: % 169.03/24.04 | | | | (94) ~ leq(n4, n5) % 169.03/24.04 | | | | % 169.03/24.04 | | | | PRED_UNIFY: (86), (94) imply: % 169.03/24.04 | | | | (95) $false % 169.03/24.04 | | | | % 169.03/24.04 | | | | CLOSE: (95) is inconsistent. % 169.03/24.04 | | | | % 169.03/24.04 | | | Case 2: % 169.03/24.04 | | | | % 169.03/24.04 | | | | (96) a_select3(pminus_ds1_filter, n4, n0) = all_74_9 & $i(all_74_9) % 169.03/24.04 | | | | % 169.03/24.04 | | | | ALPHA: (96) implies: % 169.03/24.04 | | | | (97) a_select3(pminus_ds1_filter, n4, n0) = all_74_9 % 169.03/24.04 | | | | % 169.03/24.04 | | | | REF_CLOSE: (14), (16), (84), (97) are inconsistent by sub-proof #11. % 169.03/24.04 | | | | % 169.03/24.04 | | | End of split % 169.03/24.04 | | | % 169.03/24.04 | | End of split % 169.03/24.04 | | % 169.03/24.04 | End of split % 169.03/24.04 | % 169.03/24.04 End of proof % 169.03/24.04 % 169.03/24.04 Sub-proof #11 shows that the following formulas are inconsistent: % 169.03/24.04 ---------------------------------------------------------------- % 169.03/24.04 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 169.03/24.04 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 169.03/24.04 v0)) % 169.03/24.04 (2) a_select3(pminus_ds1_filter, n4, n0) = all_74_8 % 169.03/24.05 (3) a_select3(pminus_ds1_filter, n4, n0) = all_74_9 % 169.03/24.05 (4) ~ (all_74_8 = all_74_9) % 169.03/24.05 % 169.03/24.05 Begin of proof % 169.03/24.05 | % 169.03/24.05 | GROUND_INST: instantiating (1) with all_74_9, all_74_8, n0, n4, % 169.03/24.05 | pminus_ds1_filter, simplifying with (2), (3) gives: % 169.03/24.05 | (5) all_74_8 = all_74_9 % 169.03/24.05 | % 169.03/24.05 | REDUCE: (4), (5) imply: % 169.03/24.05 | (6) $false % 169.03/24.05 | % 169.03/24.05 | CLOSE: (6) is inconsistent. % 169.03/24.05 | % 169.03/24.05 End of proof % 169.03/24.05 % 169.03/24.05 Sub-proof #12 shows that the following formulas are inconsistent: % 169.03/24.05 ---------------------------------------------------------------- % 169.03/24.05 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 169.03/24.05 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 169.03/24.05 v0)) % 169.03/24.05 (2) a_select3(pminus_ds1_filter, n2, n0) = all_74_8 % 169.03/24.05 (3) a_select3(pminus_ds1_filter, n2, n0) = all_74_9 % 169.03/24.05 (4) ~ (all_74_8 = all_74_9) % 169.03/24.05 % 169.03/24.05 Begin of proof % 169.03/24.05 | % 169.03/24.05 | GROUND_INST: instantiating (1) with all_74_9, all_74_8, n0, n2, % 169.03/24.05 | pminus_ds1_filter, simplifying with (2), (3) gives: % 169.03/24.05 | (5) all_74_8 = all_74_9 % 169.03/24.05 | % 169.03/24.05 | REDUCE: (4), (5) imply: % 169.03/24.05 | (6) $false % 169.03/24.05 | % 169.03/24.05 | CLOSE: (6) is inconsistent. % 169.03/24.05 | % 169.03/24.05 End of proof % 169.03/24.05 % 169.03/24.05 Sub-proof #13 shows that the following formulas are inconsistent: % 169.03/24.05 ---------------------------------------------------------------- % 169.03/24.05 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 169.03/24.05 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 169.03/24.05 v0)) % 169.03/24.05 (2) a_select3(pminus_ds1_filter, n1, n0) = all_74_8 % 169.03/24.05 (3) a_select3(pminus_ds1_filter, n1, n0) = all_74_9 % 169.03/24.05 (4) ~ (all_74_8 = all_74_9) % 169.03/24.05 % 169.03/24.05 Begin of proof % 169.03/24.05 | % 169.03/24.05 | GROUND_INST: instantiating (1) with all_74_9, all_74_8, n0, n1, % 169.03/24.05 | pminus_ds1_filter, simplifying with (2), (3) gives: % 169.03/24.05 | (5) all_74_8 = all_74_9 % 169.03/24.05 | % 169.03/24.05 | REDUCE: (4), (5) imply: % 169.03/24.05 | (6) $false % 169.03/24.05 | % 169.03/24.05 | CLOSE: (6) is inconsistent. % 169.03/24.05 | % 169.03/24.05 End of proof % 169.03/24.05 % 169.03/24.05 Sub-proof #14 shows that the following formulas are inconsistent: % 169.03/24.05 ---------------------------------------------------------------- % 169.03/24.05 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (pred(v1) = v2) | ~ $i(v1) % 169.03/24.05 | ~ $i(v0) | ~ gt(v1, v0) | leq(v0, v2)) % 169.03/24.05 (2) all_74_7 = n2 | all_74_7 = n1 | all_74_7 = n0 % 169.03/24.05 (3) $i(all_74_7) % 169.03/24.05 (4) $i(n2) % 169.03/24.05 (5) ~ gt(n0, n0) % 169.03/24.05 (6) leq(n0, all_74_6) % 169.03/24.05 (7) all_74_7 = n2 | gt(n2, all_74_7) % 169.03/24.05 (8) all_74_6 = n0 | gt(all_74_6, n0) % 169.03/24.05 (9) leq(n0, all_74_7) % 169.03/24.05 (10) $i(all_74_6) % 169.03/24.05 (11) gt(all_74_7, n0) % 169.03/24.05 (12) ! [v0: $i] : (v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0, n1) | ~ % 169.03/24.05 leq(n0, v0)) % 169.03/24.05 (13) a_select3(r_ds1_filter, all_74_7, all_74_6) = all_74_5 % 169.03/24.05 (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (a_select3(r_ds1_filter, % 169.03/24.05 v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ leq(v1, all_74_12) | ~ % 169.03/24.05 leq(v0, all_74_12) | ~ leq(n0, v1) | ~ leq(n0, v0) | % 169.03/24.05 (a_select3(r_ds1_filter, v1, v0) = v2 & $i(v2))) % 169.03/24.05 (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 169.03/24.05 (v1 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 169.03/24.05 v0)) % 169.03/24.05 (16) all_74_6 = n2 | all_74_6 = n1 | all_74_6 = n0 % 169.03/24.05 (17) ~ (all_74_4 = all_74_5) % 169.03/24.05 (18) leq(all_74_6, n2) % 169.03/24.05 (19) leq(all_74_7, n2) % 169.03/24.05 (20) pred(n2) = n1 % 169.03/24.05 (21) a_select3(r_ds1_filter, all_74_6, all_74_7) = all_74_4 % 169.03/24.05 (22) all_74_12 = n2 % 169.03/24.05 (23) all_74_6 = n2 | gt(n2, all_74_6) % 169.03/24.05 % 169.03/24.05 Begin of proof % 169.03/24.05 | % 169.03/24.05 | BETA: splitting (8) gives: % 169.03/24.05 | % 169.03/24.05 | Case 1: % 169.03/24.05 | | % 169.03/24.05 | | (24) gt(all_74_6, n0) % 169.03/24.05 | | % 169.03/24.05 | | BETA: splitting (23) gives: % 169.03/24.05 | | % 169.03/24.05 | | Case 1: % 169.03/24.05 | | | % 169.03/24.05 | | | (25) gt(n2, all_74_6) % 169.03/24.05 | | | % 169.03/24.05 | | | GROUND_INST: instantiating (1) with all_74_6, n2, n1, simplifying with % 169.03/24.05 | | | (4), (10), (20), (25) gives: % 169.03/24.05 | | | (26) leq(all_74_6, n1) % 169.03/24.05 | | | % 169.03/24.05 | | | GROUND_INST: instantiating (12) with all_74_6, simplifying with (6), (10), % 169.03/24.05 | | | (26) gives: % 169.03/24.05 | | | (27) all_74_6 = n1 | all_74_6 = n0 % 169.03/24.05 | | | % 169.03/24.05 | | | BETA: splitting (7) gives: % 169.03/24.05 | | | % 169.03/24.05 | | | Case 1: % 169.03/24.05 | | | | % 169.03/24.05 | | | | (28) gt(n2, all_74_7) % 169.03/24.05 | | | | % 169.03/24.05 | | | | GROUND_INST: instantiating (1) with all_74_7, n2, n1, simplifying with % 169.03/24.05 | | | | (3), (4), (20), (28) gives: % 169.03/24.05 | | | | (29) leq(all_74_7, n1) % 169.03/24.05 | | | | % 169.03/24.05 | | | | GROUND_INST: instantiating (12) with all_74_7, simplifying with (3), % 169.03/24.05 | | | | (9), (29) gives: % 169.03/24.05 | | | | (30) all_74_7 = n1 | all_74_7 = n0 % 169.03/24.05 | | | | % 169.03/24.05 | | | | BETA: splitting (2) gives: % 169.03/24.05 | | | | % 169.03/24.05 | | | | Case 1: % 169.03/24.05 | | | | | % 169.03/24.05 | | | | | (31) all_74_7 = n0 % 169.03/24.05 | | | | | % 169.03/24.05 | | | | | REDUCE: (11), (31) imply: % 169.03/24.05 | | | | | (32) gt(n0, n0) % 169.03/24.05 | | | | | % 169.03/24.05 | | | | | PRED_UNIFY: (5), (32) imply: % 169.03/24.05 | | | | | (33) $false % 169.03/24.05 | | | | | % 169.03/24.05 | | | | | CLOSE: (33) is inconsistent. % 169.03/24.05 | | | | | % 169.03/24.05 | | | | Case 2: % 169.03/24.05 | | | | | % 169.03/24.05 | | | | | (34) ~ (all_74_7 = n0) % 169.03/24.05 | | | | | % 169.03/24.05 | | | | | BETA: splitting (30) gives: % 169.03/24.05 | | | | | % 169.03/24.05 | | | | | Case 1: % 169.03/24.05 | | | | | | % 169.03/24.05 | | | | | | (35) all_74_7 = n0 % 169.03/24.05 | | | | | | % 169.03/24.05 | | | | | | REDUCE: (34), (35) imply: % 169.03/24.05 | | | | | | (36) $false % 169.03/24.05 | | | | | | % 169.03/24.05 | | | | | | CLOSE: (36) is inconsistent. % 169.03/24.05 | | | | | | % 169.03/24.05 | | | | | Case 2: % 169.03/24.05 | | | | | | % 169.03/24.05 | | | | | | (37) all_74_7 = n1 % 169.03/24.05 | | | | | | % 169.03/24.05 | | | | | | REDUCE: (21), (37) imply: % 169.03/24.05 | | | | | | (38) a_select3(r_ds1_filter, all_74_6, n1) = all_74_4 % 169.03/24.05 | | | | | | % 169.03/24.05 | | | | | | REDUCE: (13), (37) imply: % 169.03/24.05 | | | | | | (39) a_select3(r_ds1_filter, n1, all_74_6) = all_74_5 % 169.03/24.05 | | | | | | % 169.03/24.05 | | | | | | BETA: splitting (16) gives: % 169.03/24.05 | | | | | | % 169.03/24.05 | | | | | | Case 1: % 169.03/24.05 | | | | | | | % 169.03/24.05 | | | | | | | (40) all_74_6 = n0 % 169.03/24.05 | | | | | | | % 169.03/24.05 | | | | | | | REDUCE: (24), (40) imply: % 169.03/24.05 | | | | | | | (41) gt(n0, n0) % 169.03/24.05 | | | | | | | % 169.03/24.05 | | | | | | | PRED_UNIFY: (5), (41) imply: % 169.03/24.05 | | | | | | | (42) $false % 169.03/24.05 | | | | | | | % 169.03/24.05 | | | | | | | CLOSE: (42) is inconsistent. % 169.03/24.05 | | | | | | | % 169.03/24.05 | | | | | | Case 2: % 169.03/24.05 | | | | | | | % 169.03/24.05 | | | | | | | (43) ~ (all_74_6 = n0) % 169.03/24.05 | | | | | | | % 169.03/24.05 | | | | | | | BETA: splitting (27) gives: % 169.03/24.05 | | | | | | | % 169.03/24.05 | | | | | | | Case 1: % 169.03/24.05 | | | | | | | | % 169.03/24.05 | | | | | | | | (44) all_74_6 = n0 % 169.03/24.05 | | | | | | | | % 169.03/24.05 | | | | | | | | REDUCE: (43), (44) imply: % 169.03/24.05 | | | | | | | | (45) $false % 169.03/24.05 | | | | | | | | % 169.03/24.05 | | | | | | | | CLOSE: (45) is inconsistent. % 169.03/24.05 | | | | | | | | % 169.03/24.05 | | | | | | | Case 2: % 169.03/24.05 | | | | | | | | % 169.03/24.05 | | | | | | | | (46) all_74_6 = n1 % 169.03/24.05 | | | | | | | | % 169.03/24.05 | | | | | | | | REDUCE: (38), (46) imply: % 169.03/24.05 | | | | | | | | (47) a_select3(r_ds1_filter, n1, n1) = all_74_4 % 169.03/24.05 | | | | | | | | % 169.03/24.05 | | | | | | | | REDUCE: (39), (46) imply: % 169.03/24.05 | | | | | | | | (48) a_select3(r_ds1_filter, n1, n1) = all_74_5 % 169.03/24.05 | | | | | | | | % 169.03/24.05 | | | | | | | | GROUND_INST: instantiating (15) with all_74_5, all_74_4, n1, n1, % 169.03/24.05 | | | | | | | | r_ds1_filter, simplifying with (47), (48) gives: % 169.03/24.05 | | | | | | | | (49) all_74_4 = all_74_5 % 169.03/24.05 | | | | | | | | % 169.03/24.05 | | | | | | | | REDUCE: (17), (49) imply: % 169.03/24.05 | | | | | | | | (50) $false % 169.03/24.05 | | | | | | | | % 169.03/24.05 | | | | | | | | CLOSE: (50) is inconsistent. % 169.03/24.05 | | | | | | | | % 169.03/24.05 | | | | | | | End of split % 169.03/24.05 | | | | | | | % 169.03/24.05 | | | | | | End of split % 169.03/24.05 | | | | | | % 169.03/24.05 | | | | | End of split % 169.03/24.05 | | | | | % 169.03/24.05 | | | | End of split % 169.03/24.05 | | | | % 169.03/24.05 | | | Case 2: % 169.03/24.05 | | | | % 169.03/24.05 | | | | (51) all_74_7 = n2 % 169.03/24.05 | | | | % 169.03/24.05 | | | | REDUCE: (21), (51) imply: % 169.03/24.05 | | | | (52) a_select3(r_ds1_filter, all_74_6, n2) = all_74_4 % 169.03/24.05 | | | | % 169.03/24.05 | | | | REDUCE: (13), (51) imply: % 169.03/24.05 | | | | (53) a_select3(r_ds1_filter, n2, all_74_6) = all_74_5 % 169.03/24.05 | | | | % 169.03/24.05 | | | | REDUCE: (19), (51) imply: % 169.03/24.05 | | | | (54) leq(n2, n2) % 169.03/24.05 | | | | % 169.03/24.05 | | | | REDUCE: (9), (51) imply: % 169.03/24.05 | | | | (55) leq(n0, n2) % 169.03/24.05 | | | | % 169.03/24.05 | | | | BETA: splitting (16) gives: % 169.03/24.05 | | | | % 169.03/24.05 | | | | Case 1: % 169.03/24.05 | | | | | % 169.03/24.05 | | | | | (56) all_74_6 = n0 % 169.03/24.05 | | | | | % 169.03/24.05 | | | | | REDUCE: (24), (56) imply: % 169.03/24.05 | | | | | (57) gt(n0, n0) % 169.03/24.05 | | | | | % 169.03/24.05 | | | | | PRED_UNIFY: (5), (57) imply: % 169.03/24.05 | | | | | (58) $false % 169.03/24.05 | | | | | % 169.03/24.05 | | | | | CLOSE: (58) is inconsistent. % 169.03/24.05 | | | | | % 169.03/24.05 | | | | Case 2: % 169.03/24.05 | | | | | % 169.03/24.05 | | | | | (59) ~ (all_74_6 = n0) % 169.03/24.05 | | | | | % 169.03/24.05 | | | | | REF_CLOSE: (4), (6), (10), (14), (15), (17), (18), (22), (27), (52), % 169.03/24.05 | | | | | (53), (54), (55), (59) are inconsistent by sub-proof #18. % 169.03/24.05 | | | | | % 169.03/24.05 | | | | End of split % 169.03/24.05 | | | | % 169.03/24.05 | | | End of split % 169.03/24.05 | | | % 169.03/24.05 | | Case 2: % 169.03/24.05 | | | % 169.03/24.05 | | | (60) all_74_6 = n2 % 169.03/24.05 | | | % 169.03/24.05 | | | REDUCE: (21), (60) imply: % 169.03/24.05 | | | (61) a_select3(r_ds1_filter, n2, all_74_7) = all_74_4 % 169.03/24.05 | | | % 169.03/24.05 | | | REDUCE: (13), (60) imply: % 169.03/24.05 | | | (62) a_select3(r_ds1_filter, all_74_7, n2) = all_74_5 % 169.03/24.05 | | | % 169.03/24.05 | | | REDUCE: (18), (60) imply: % 169.03/24.05 | | | (63) leq(n2, n2) % 169.03/24.05 | | | % 169.03/24.05 | | | REDUCE: (6), (60) imply: % 169.03/24.05 | | | (64) leq(n0, n2) % 169.03/24.05 | | | % 169.03/24.05 | | | BETA: splitting (7) gives: % 169.03/24.05 | | | % 169.03/24.05 | | | Case 1: % 169.03/24.05 | | | | % 169.03/24.05 | | | | (65) gt(n2, all_74_7) % 169.03/24.05 | | | | % 169.03/24.05 | | | | GROUND_INST: instantiating (1) with all_74_7, n2, n1, simplifying with % 169.03/24.05 | | | | (3), (4), (20), (65) gives: % 169.03/24.05 | | | | (66) leq(all_74_7, n1) % 169.03/24.05 | | | | % 169.03/24.05 | | | | GROUND_INST: instantiating (12) with all_74_7, simplifying with (3), % 169.03/24.05 | | | | (9), (66) gives: % 169.03/24.05 | | | | (67) all_74_7 = n1 | all_74_7 = n0 % 169.03/24.05 | | | | % 169.03/24.05 | | | | BETA: splitting (2) gives: % 169.03/24.05 | | | | % 169.03/24.05 | | | | Case 1: % 169.03/24.05 | | | | | % 169.03/24.05 | | | | | (68) all_74_7 = n0 % 169.03/24.05 | | | | | % 169.03/24.05 | | | | | REDUCE: (11), (68) imply: % 169.03/24.05 | | | | | (69) gt(n0, n0) % 169.03/24.05 | | | | | % 169.03/24.05 | | | | | PRED_UNIFY: (5), (69) imply: % 169.03/24.05 | | | | | (70) $false % 169.03/24.05 | | | | | % 169.03/24.05 | | | | | CLOSE: (70) is inconsistent. % 169.03/24.05 | | | | | % 169.03/24.05 | | | | Case 2: % 169.03/24.05 | | | | | % 169.03/24.05 | | | | | (71) ~ (all_74_7 = n0) % 169.03/24.05 | | | | | % 169.03/24.05 | | | | | REF_CLOSE: (3), (4), (9), (14), (15), (17), (19), (22), (61), (62), % 169.03/24.05 | | | | | (63), (64), (67), (71) are inconsistent by sub-proof #17. % 169.03/24.05 | | | | | % 169.03/24.05 | | | | End of split % 169.03/24.05 | | | | % 169.03/24.05 | | | Case 2: % 169.03/24.05 | | | | % 169.03/24.05 | | | | (72) all_74_7 = n2 % 169.03/24.05 | | | | % 169.03/24.05 | | | | REDUCE: (62), (72) imply: % 169.03/24.05 | | | | (73) a_select3(r_ds1_filter, n2, n2) = all_74_5 % 169.03/24.05 | | | | % 169.03/24.05 | | | | REDUCE: (61), (72) imply: % 169.03/24.05 | | | | (74) a_select3(r_ds1_filter, n2, n2) = all_74_4 % 169.03/24.05 | | | | % 169.03/24.05 | | | | GROUND_INST: instantiating (15) with all_74_5, all_74_4, n2, n2, % 169.03/24.05 | | | | r_ds1_filter, simplifying with (73), (74) gives: % 169.03/24.05 | | | | (75) all_74_4 = all_74_5 % 169.03/24.05 | | | | % 169.03/24.05 | | | | REDUCE: (17), (75) imply: % 169.03/24.05 | | | | (76) $false % 169.03/24.05 | | | | % 169.03/24.05 | | | | CLOSE: (76) is inconsistent. % 169.03/24.05 | | | | % 169.03/24.05 | | | End of split % 169.03/24.05 | | | % 169.03/24.05 | | End of split % 169.03/24.05 | | % 169.03/24.05 | Case 2: % 169.03/24.05 | | % 169.03/24.05 | | (77) all_74_6 = n0 % 169.03/24.05 | | (78) ~ gt(all_74_6, n0) % 169.03/24.05 | | % 169.03/24.05 | | REDUCE: (21), (77) imply: % 169.03/24.05 | | (79) a_select3(r_ds1_filter, n0, all_74_7) = all_74_4 % 169.03/24.05 | | % 169.03/24.05 | | REDUCE: (13), (77) imply: % 169.03/24.05 | | (80) a_select3(r_ds1_filter, all_74_7, n0) = all_74_5 % 169.03/24.05 | | % 169.03/24.05 | | REDUCE: (10), (77) imply: % 169.03/24.05 | | (81) $i(n0) % 169.03/24.05 | | % 169.03/24.05 | | REDUCE: (18), (77) imply: % 169.03/24.05 | | (82) leq(n0, n2) % 169.03/24.05 | | % 169.03/24.05 | | REDUCE: (6), (77) imply: % 169.03/24.05 | | (83) leq(n0, n0) % 169.03/24.05 | | % 169.03/24.05 | | BETA: splitting (7) gives: % 169.03/24.05 | | % 169.03/24.05 | | Case 1: % 169.03/24.05 | | | % 169.03/24.05 | | | (84) gt(n2, all_74_7) % 169.03/24.05 | | | % 169.03/24.05 | | | GROUND_INST: instantiating (1) with all_74_7, n2, n1, simplifying with % 169.03/24.05 | | | (3), (4), (20), (84) gives: % 169.03/24.05 | | | (85) leq(all_74_7, n1) % 169.03/24.05 | | | % 169.03/24.05 | | | GROUND_INST: instantiating (12) with all_74_7, simplifying with (3), (9), % 169.03/24.05 | | | (85) gives: % 169.03/24.05 | | | (86) all_74_7 = n1 | all_74_7 = n0 % 169.03/24.05 | | | % 169.03/24.05 | | | BETA: splitting (2) gives: % 169.03/24.05 | | | % 169.03/24.05 | | | Case 1: % 169.03/24.05 | | | | % 169.03/24.05 | | | | (87) all_74_7 = n0 % 169.03/24.05 | | | | % 169.03/24.05 | | | | REDUCE: (11), (87) imply: % 169.03/24.05 | | | | (88) gt(n0, n0) % 169.03/24.05 | | | | % 169.03/24.05 | | | | PRED_UNIFY: (5), (88) imply: % 169.03/24.05 | | | | (89) $false % 169.03/24.05 | | | | % 169.03/24.05 | | | | CLOSE: (89) is inconsistent. % 169.03/24.05 | | | | % 169.03/24.05 | | | Case 2: % 169.03/24.05 | | | | % 169.03/24.05 | | | | (90) ~ (all_74_7 = n0) % 169.03/24.05 | | | | % 169.03/24.05 | | | | BETA: splitting (86) gives: % 169.03/24.05 | | | | % 169.03/24.05 | | | | Case 1: % 169.03/24.05 | | | | | % 169.03/24.05 | | | | | (91) all_74_7 = n0 % 169.03/24.05 | | | | | % 169.03/24.05 | | | | | REDUCE: (90), (91) imply: % 169.03/24.05 | | | | | (92) $false % 169.03/24.05 | | | | | % 169.03/24.05 | | | | | CLOSE: (92) is inconsistent. % 169.03/24.05 | | | | | % 169.03/24.05 | | | | Case 2: % 169.03/24.05 | | | | | % 169.03/24.05 | | | | | (93) all_74_7 = n1 % 169.03/24.05 | | | | | % 169.03/24.05 | | | | | REDUCE: (80), (93) imply: % 169.03/24.05 | | | | | (94) a_select3(r_ds1_filter, n1, n0) = all_74_5 % 169.03/24.05 | | | | | % 169.03/24.05 | | | | | REDUCE: (79), (93) imply: % 169.03/24.05 | | | | | (95) a_select3(r_ds1_filter, n0, n1) = all_74_4 % 169.03/24.05 | | | | | % 169.03/24.05 | | | | | REDUCE: (3), (93) imply: % 169.03/24.05 | | | | | (96) $i(n1) % 169.03/24.05 | | | | | % 169.03/24.05 | | | | | REDUCE: (19), (93) imply: % 169.03/24.05 | | | | | (97) leq(n1, n2) % 169.03/24.05 | | | | | % 169.03/24.05 | | | | | REDUCE: (9), (93) imply: % 169.03/24.05 | | | | | (98) leq(n0, n1) % 169.03/24.05 | | | | | % 169.03/24.05 | | | | | GROUND_INST: instantiating (14) with n0, n1, all_74_4, simplifying % 169.03/24.05 | | | | | with (81), (83), (95), (96), (98) gives: % 169.03/24.05 | | | | | (99) ~ leq(n1, all_74_12) | ~ leq(n0, all_74_12) | % 169.03/24.05 | | | | | (a_select3(r_ds1_filter, n1, n0) = all_74_4 & $i(all_74_4)) % 169.03/24.05 | | | | | % 169.03/24.05 | | | | | BETA: splitting (99) gives: % 169.03/24.05 | | | | | % 169.03/24.05 | | | | | Case 1: % 169.03/24.05 | | | | | | % 169.03/24.05 | | | | | | (100) ~ leq(n0, all_74_12) % 169.03/24.05 | | | | | | % 169.03/24.05 | | | | | | REDUCE: (22), (100) imply: % 169.03/24.05 | | | | | | (101) ~ leq(n0, n2) % 169.03/24.05 | | | | | | % 169.03/24.05 | | | | | | PRED_UNIFY: (82), (101) imply: % 169.03/24.05 | | | | | | (102) $false % 169.03/24.05 | | | | | | % 169.03/24.05 | | | | | | CLOSE: (102) is inconsistent. % 169.03/24.05 | | | | | | % 169.03/24.05 | | | | | Case 2: % 169.03/24.05 | | | | | | % 169.03/24.05 | | | | | | (103) ~ leq(n1, all_74_12) | (a_select3(r_ds1_filter, n1, n0) = % 169.03/24.05 | | | | | | all_74_4 & $i(all_74_4)) % 169.03/24.05 | | | | | | % 169.03/24.05 | | | | | | BETA: splitting (103) gives: % 169.03/24.05 | | | | | | % 169.03/24.05 | | | | | | Case 1: % 169.03/24.05 | | | | | | | % 169.03/24.05 | | | | | | | (104) ~ leq(n1, all_74_12) % 169.03/24.05 | | | | | | | % 169.03/24.05 | | | | | | | REDUCE: (22), (104) imply: % 169.03/24.05 | | | | | | | (105) ~ leq(n1, n2) % 169.03/24.05 | | | | | | | % 169.03/24.05 | | | | | | | PRED_UNIFY: (97), (105) imply: % 169.03/24.05 | | | | | | | (106) $false % 169.03/24.05 | | | | | | | % 169.03/24.05 | | | | | | | CLOSE: (106) is inconsistent. % 169.03/24.05 | | | | | | | % 169.03/24.05 | | | | | | Case 2: % 169.03/24.05 | | | | | | | % 169.03/24.05 | | | | | | | (107) a_select3(r_ds1_filter, n1, n0) = all_74_4 & $i(all_74_4) % 169.03/24.05 | | | | | | | % 169.03/24.05 | | | | | | | ALPHA: (107) implies: % 169.03/24.05 | | | | | | | (108) a_select3(r_ds1_filter, n1, n0) = all_74_4 % 169.03/24.05 | | | | | | | % 169.03/24.05 | | | | | | | REF_CLOSE: (15), (17), (94), (108) are inconsistent by sub-proof % 169.03/24.05 | | | | | | | #16. % 169.03/24.05 | | | | | | | % 169.03/24.05 | | | | | | End of split % 169.03/24.05 | | | | | | % 169.03/24.05 | | | | | End of split % 169.03/24.05 | | | | | % 169.03/24.05 | | | | End of split % 169.03/24.05 | | | | % 169.03/24.05 | | | End of split % 169.03/24.05 | | | % 169.03/24.05 | | Case 2: % 169.03/24.05 | | | % 169.03/24.05 | | | (109) all_74_7 = n2 % 169.03/24.05 | | | % 169.03/24.05 | | | REDUCE: (80), (109) imply: % 169.03/24.05 | | | (110) a_select3(r_ds1_filter, n2, n0) = all_74_5 % 169.03/24.05 | | | % 169.03/24.05 | | | REDUCE: (79), (109) imply: % 169.03/24.06 | | | (111) a_select3(r_ds1_filter, n0, n2) = all_74_4 % 169.03/24.06 | | | % 169.03/24.06 | | | REDUCE: (19), (109) imply: % 169.03/24.06 | | | (112) leq(n2, n2) % 169.03/24.06 | | | % 169.03/24.06 | | | GROUND_INST: instantiating (14) with n0, n2, all_74_4, simplifying with % 169.03/24.06 | | | (4), (81), (82), (83), (111) gives: % 169.03/24.06 | | | (113) ~ leq(n2, all_74_12) | ~ leq(n0, all_74_12) | % 169.03/24.06 | | | (a_select3(r_ds1_filter, n2, n0) = all_74_4 & $i(all_74_4)) % 169.03/24.06 | | | % 169.03/24.06 | | | BETA: splitting (113) gives: % 169.03/24.06 | | | % 169.03/24.06 | | | Case 1: % 169.03/24.06 | | | | % 169.03/24.06 | | | | (114) ~ leq(n0, all_74_12) % 169.03/24.06 | | | | % 169.03/24.06 | | | | REDUCE: (22), (114) imply: % 169.03/24.06 | | | | (115) ~ leq(n0, n2) % 169.03/24.06 | | | | % 169.03/24.06 | | | | PRED_UNIFY: (82), (115) imply: % 169.03/24.06 | | | | (116) $false % 169.03/24.06 | | | | % 169.03/24.06 | | | | CLOSE: (116) is inconsistent. % 169.03/24.06 | | | | % 169.03/24.06 | | | Case 2: % 169.03/24.06 | | | | % 169.03/24.06 | | | | (117) ~ leq(n2, all_74_12) | (a_select3(r_ds1_filter, n2, n0) = % 169.03/24.06 | | | | all_74_4 & $i(all_74_4)) % 169.03/24.06 | | | | % 169.03/24.06 | | | | BETA: splitting (117) gives: % 169.03/24.06 | | | | % 169.03/24.06 | | | | Case 1: % 169.03/24.06 | | | | | % 169.03/24.06 | | | | | (118) ~ leq(n2, all_74_12) % 169.03/24.06 | | | | | % 169.03/24.06 | | | | | REDUCE: (22), (118) imply: % 169.03/24.06 | | | | | (119) ~ leq(n2, n2) % 169.03/24.06 | | | | | % 169.03/24.06 | | | | | PRED_UNIFY: (112), (119) imply: % 169.03/24.06 | | | | | (120) $false % 169.03/24.06 | | | | | % 169.03/24.06 | | | | | CLOSE: (120) is inconsistent. % 169.03/24.06 | | | | | % 169.03/24.06 | | | | Case 2: % 169.03/24.06 | | | | | % 169.03/24.06 | | | | | (121) a_select3(r_ds1_filter, n2, n0) = all_74_4 & $i(all_74_4) % 169.03/24.06 | | | | | % 169.03/24.06 | | | | | ALPHA: (121) implies: % 169.03/24.06 | | | | | (122) a_select3(r_ds1_filter, n2, n0) = all_74_4 % 169.03/24.06 | | | | | % 169.03/24.06 | | | | | REF_CLOSE: (15), (17), (110), (122) are inconsistent by sub-proof #15. % 169.03/24.06 | | | | | % 169.03/24.06 | | | | End of split % 169.03/24.06 | | | | % 169.03/24.06 | | | End of split % 169.03/24.06 | | | % 169.03/24.06 | | End of split % 169.03/24.06 | | % 169.03/24.06 | End of split % 169.03/24.06 | % 169.03/24.06 End of proof % 169.03/24.06 % 169.03/24.06 Sub-proof #15 shows that the following formulas are inconsistent: % 169.03/24.06 ---------------------------------------------------------------- % 169.03/24.06 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 169.03/24.06 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 169.03/24.06 v0)) % 169.03/24.06 (2) a_select3(r_ds1_filter, n2, n0) = all_74_4 % 169.03/24.06 (3) a_select3(r_ds1_filter, n2, n0) = all_74_5 % 169.03/24.06 (4) ~ (all_74_4 = all_74_5) % 169.03/24.06 % 169.03/24.06 Begin of proof % 169.03/24.06 | % 169.03/24.06 | GROUND_INST: instantiating (1) with all_74_4, all_74_5, n0, n2, r_ds1_filter, % 169.03/24.06 | simplifying with (2), (3) gives: % 169.03/24.06 | (5) all_74_4 = all_74_5 % 169.03/24.06 | % 169.03/24.06 | REDUCE: (4), (5) imply: % 169.03/24.06 | (6) $false % 169.03/24.06 | % 169.03/24.06 | CLOSE: (6) is inconsistent. % 169.03/24.06 | % 169.03/24.06 End of proof % 169.03/24.06 % 169.03/24.06 Sub-proof #16 shows that the following formulas are inconsistent: % 169.03/24.06 ---------------------------------------------------------------- % 169.03/24.06 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 169.03/24.06 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 169.03/24.06 v0)) % 169.03/24.06 (2) a_select3(r_ds1_filter, n1, n0) = all_74_4 % 169.03/24.06 (3) a_select3(r_ds1_filter, n1, n0) = all_74_5 % 169.03/24.06 (4) ~ (all_74_4 = all_74_5) % 169.03/24.06 % 169.03/24.06 Begin of proof % 169.03/24.06 | % 169.03/24.06 | GROUND_INST: instantiating (1) with all_74_4, all_74_5, n0, n1, r_ds1_filter, % 169.03/24.06 | simplifying with (2), (3) gives: % 169.03/24.06 | (5) all_74_4 = all_74_5 % 169.03/24.06 | % 169.03/24.06 | REDUCE: (4), (5) imply: % 169.03/24.06 | (6) $false % 169.03/24.06 | % 169.03/24.06 | CLOSE: (6) is inconsistent. % 169.03/24.06 | % 169.03/24.06 End of proof % 169.03/24.06 % 169.03/24.06 Sub-proof #17 shows that the following formulas are inconsistent: % 169.03/24.06 ---------------------------------------------------------------- % 169.03/24.06 (1) a_select3(r_ds1_filter, n2, all_74_7) = all_74_4 % 169.03/24.06 (2) leq(n0, n2) % 169.03/24.06 (3) $i(all_74_7) % 169.03/24.06 (4) $i(n2) % 169.03/24.06 (5) leq(n0, all_74_7) % 169.03/24.06 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (a_select3(r_ds1_filter, % 169.03/24.06 v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ leq(v1, all_74_12) | ~ % 169.03/24.06 leq(v0, all_74_12) | ~ leq(n0, v1) | ~ leq(n0, v0) | % 169.03/24.06 (a_select3(r_ds1_filter, v1, v0) = v2 & $i(v2))) % 169.03/24.06 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 169.03/24.06 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 169.03/24.06 v0)) % 169.03/24.06 (8) leq(n2, n2) % 169.03/24.06 (9) ~ (all_74_4 = all_74_5) % 169.03/24.06 (10) leq(all_74_7, n2) % 169.03/24.06 (11) ~ (all_74_7 = n0) % 169.03/24.06 (12) all_74_12 = n2 % 169.03/24.06 (13) all_74_7 = n1 | all_74_7 = n0 % 169.03/24.06 (14) a_select3(r_ds1_filter, all_74_7, n2) = all_74_5 % 169.03/24.06 % 169.03/24.06 Begin of proof % 169.03/24.06 | % 169.03/24.06 | BETA: splitting (13) gives: % 169.03/24.06 | % 169.03/24.06 | Case 1: % 169.03/24.06 | | % 169.03/24.06 | | (15) all_74_7 = n0 % 169.03/24.06 | | % 169.03/24.06 | | REDUCE: (11), (15) imply: % 169.03/24.06 | | (16) $false % 169.03/24.06 | | % 169.03/24.06 | | CLOSE: (16) is inconsistent. % 169.03/24.06 | | % 169.03/24.06 | Case 2: % 169.03/24.06 | | % 169.03/24.06 | | (17) all_74_7 = n1 % 169.03/24.06 | | % 169.03/24.06 | | REDUCE: (14), (17) imply: % 169.03/24.06 | | (18) a_select3(r_ds1_filter, n1, n2) = all_74_5 % 169.03/24.06 | | % 169.03/24.06 | | REDUCE: (1), (17) imply: % 169.03/24.06 | | (19) a_select3(r_ds1_filter, n2, n1) = all_74_4 % 169.03/24.06 | | % 169.03/24.06 | | REDUCE: (3), (17) imply: % 169.03/24.06 | | (20) $i(n1) % 169.03/24.06 | | % 169.03/24.06 | | REDUCE: (10), (17) imply: % 169.03/24.06 | | (21) leq(n1, n2) % 169.03/24.06 | | % 169.03/24.06 | | REDUCE: (5), (17) imply: % 169.03/24.06 | | (22) leq(n0, n1) % 169.03/24.06 | | % 169.03/24.06 | | GROUND_INST: instantiating (6) with n1, n2, all_74_5, simplifying with (2), % 169.03/24.06 | | (4), (18), (20), (22) gives: % 169.03/24.06 | | (23) ~ leq(n2, all_74_12) | ~ leq(n1, all_74_12) | % 169.03/24.06 | | (a_select3(r_ds1_filter, n2, n1) = all_74_5 & $i(all_74_5)) % 169.03/24.06 | | % 169.03/24.06 | | BETA: splitting (23) gives: % 169.03/24.06 | | % 169.03/24.06 | | Case 1: % 169.03/24.06 | | | % 169.03/24.06 | | | (24) ~ leq(n2, all_74_12) % 169.03/24.06 | | | % 169.03/24.06 | | | REDUCE: (12), (24) imply: % 169.03/24.06 | | | (25) ~ leq(n2, n2) % 169.03/24.06 | | | % 169.03/24.06 | | | PRED_UNIFY: (8), (25) imply: % 169.03/24.06 | | | (26) $false % 169.03/24.06 | | | % 169.03/24.06 | | | CLOSE: (26) is inconsistent. % 169.03/24.06 | | | % 169.03/24.06 | | Case 2: % 169.03/24.06 | | | % 169.03/24.06 | | | (27) ~ leq(n1, all_74_12) | (a_select3(r_ds1_filter, n2, n1) = % 169.03/24.06 | | | all_74_5 & $i(all_74_5)) % 169.03/24.06 | | | % 169.03/24.06 | | | BETA: splitting (27) gives: % 169.03/24.06 | | | % 169.03/24.06 | | | Case 1: % 169.03/24.06 | | | | % 169.03/24.06 | | | | (28) ~ leq(n1, all_74_12) % 169.03/24.06 | | | | % 169.03/24.06 | | | | REDUCE: (12), (28) imply: % 169.03/24.06 | | | | (29) ~ leq(n1, n2) % 169.03/24.06 | | | | % 169.03/24.06 | | | | PRED_UNIFY: (21), (29) imply: % 169.03/24.06 | | | | (30) $false % 169.03/24.06 | | | | % 169.03/24.06 | | | | CLOSE: (30) is inconsistent. % 169.03/24.06 | | | | % 169.03/24.06 | | | Case 2: % 169.03/24.06 | | | | % 169.03/24.06 | | | | (31) a_select3(r_ds1_filter, n2, n1) = all_74_5 & $i(all_74_5) % 169.03/24.06 | | | | % 169.03/24.06 | | | | ALPHA: (31) implies: % 169.03/24.06 | | | | (32) a_select3(r_ds1_filter, n2, n1) = all_74_5 % 169.03/24.06 | | | | % 169.03/24.06 | | | | GROUND_INST: instantiating (7) with all_74_5, all_74_4, n1, n2, % 169.03/24.06 | | | | r_ds1_filter, simplifying with (19), (32) gives: % 169.03/24.06 | | | | (33) all_74_4 = all_74_5 % 169.03/24.06 | | | | % 169.03/24.06 | | | | REDUCE: (9), (33) imply: % 169.03/24.06 | | | | (34) $false % 169.03/24.06 | | | | % 169.03/24.06 | | | | CLOSE: (34) is inconsistent. % 169.03/24.06 | | | | % 169.03/24.06 | | | End of split % 169.03/24.06 | | | % 169.03/24.06 | | End of split % 169.03/24.06 | | % 169.03/24.06 | End of split % 169.03/24.06 | % 169.03/24.06 End of proof % 169.03/24.06 % 169.03/24.06 Sub-proof #18 shows that the following formulas are inconsistent: % 169.03/24.06 ---------------------------------------------------------------- % 169.03/24.06 (1) leq(n0, n2) % 169.03/24.06 (2) $i(n2) % 169.03/24.06 (3) ~ (all_74_6 = n0) % 169.03/24.06 (4) leq(n0, all_74_6) % 169.03/24.06 (5) $i(all_74_6) % 169.03/24.06 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (a_select3(r_ds1_filter, % 169.03/24.06 v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ leq(v1, all_74_12) | ~ % 169.03/24.06 leq(v0, all_74_12) | ~ leq(n0, v1) | ~ leq(n0, v0) | % 169.03/24.06 (a_select3(r_ds1_filter, v1, v0) = v2 & $i(v2))) % 169.03/24.06 (7) a_select3(r_ds1_filter, n2, all_74_6) = all_74_5 % 169.03/24.06 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 169.03/24.06 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 169.03/24.06 v0)) % 169.03/24.06 (9) a_select3(r_ds1_filter, all_74_6, n2) = all_74_4 % 169.03/24.06 (10) leq(n2, n2) % 169.03/24.06 (11) ~ (all_74_4 = all_74_5) % 169.03/24.06 (12) leq(all_74_6, n2) % 169.03/24.06 (13) all_74_6 = n1 | all_74_6 = n0 % 169.03/24.06 (14) all_74_12 = n2 % 169.03/24.06 % 169.03/24.06 Begin of proof % 169.03/24.06 | % 169.03/24.06 | BETA: splitting (13) gives: % 169.03/24.06 | % 169.03/24.06 | Case 1: % 169.03/24.06 | | % 169.03/24.06 | | (15) all_74_6 = n0 % 169.03/24.06 | | % 169.03/24.06 | | REDUCE: (3), (15) imply: % 169.03/24.06 | | (16) $false % 169.03/24.06 | | % 169.03/24.06 | | CLOSE: (16) is inconsistent. % 169.03/24.06 | | % 169.03/24.06 | Case 2: % 169.03/24.06 | | % 169.03/24.06 | | (17) all_74_6 = n1 % 169.03/24.06 | | % 169.03/24.06 | | REDUCE: (9), (17) imply: % 169.03/24.06 | | (18) a_select3(r_ds1_filter, n1, n2) = all_74_4 % 169.03/24.06 | | % 169.03/24.06 | | REDUCE: (7), (17) imply: % 169.03/24.06 | | (19) a_select3(r_ds1_filter, n2, n1) = all_74_5 % 169.03/24.06 | | % 169.03/24.06 | | REDUCE: (5), (17) imply: % 169.03/24.06 | | (20) $i(n1) % 169.03/24.06 | | % 169.03/24.06 | | REDUCE: (12), (17) imply: % 169.03/24.06 | | (21) leq(n1, n2) % 169.03/24.06 | | % 169.03/24.06 | | REDUCE: (4), (17) imply: % 169.03/24.06 | | (22) leq(n0, n1) % 169.03/24.06 | | % 169.03/24.06 | | GROUND_INST: instantiating (6) with n1, n2, all_74_4, simplifying with (1), % 169.03/24.06 | | (2), (18), (20), (22) gives: % 169.03/24.06 | | (23) ~ leq(n2, all_74_12) | ~ leq(n1, all_74_12) | % 169.03/24.06 | | (a_select3(r_ds1_filter, n2, n1) = all_74_4 & $i(all_74_4)) % 169.03/24.06 | | % 169.03/24.06 | | BETA: splitting (23) gives: % 169.03/24.06 | | % 169.03/24.06 | | Case 1: % 169.03/24.06 | | | % 169.03/24.06 | | | (24) ~ leq(n2, all_74_12) % 169.03/24.06 | | | % 169.03/24.06 | | | REDUCE: (14), (24) imply: % 169.03/24.06 | | | (25) ~ leq(n2, n2) % 169.03/24.06 | | | % 169.03/24.06 | | | PRED_UNIFY: (10), (25) imply: % 169.03/24.06 | | | (26) $false % 169.03/24.06 | | | % 169.03/24.06 | | | CLOSE: (26) is inconsistent. % 169.03/24.06 | | | % 169.03/24.06 | | Case 2: % 169.03/24.06 | | | % 169.03/24.06 | | | (27) ~ leq(n1, all_74_12) | (a_select3(r_ds1_filter, n2, n1) = % 169.03/24.06 | | | all_74_4 & $i(all_74_4)) % 169.03/24.06 | | | % 169.03/24.06 | | | BETA: splitting (27) gives: % 169.03/24.06 | | | % 169.03/24.06 | | | Case 1: % 169.03/24.06 | | | | % 169.03/24.06 | | | | (28) ~ leq(n1, all_74_12) % 169.03/24.06 | | | | % 169.03/24.06 | | | | REDUCE: (14), (28) imply: % 169.03/24.06 | | | | (29) ~ leq(n1, n2) % 169.03/24.06 | | | | % 169.03/24.06 | | | | PRED_UNIFY: (21), (29) imply: % 169.03/24.06 | | | | (30) $false % 169.03/24.06 | | | | % 169.03/24.06 | | | | CLOSE: (30) is inconsistent. % 169.03/24.06 | | | | % 169.03/24.06 | | | Case 2: % 169.03/24.06 | | | | % 169.03/24.06 | | | | (31) a_select3(r_ds1_filter, n2, n1) = all_74_4 & $i(all_74_4) % 169.03/24.06 | | | | % 169.03/24.06 | | | | ALPHA: (31) implies: % 169.03/24.06 | | | | (32) a_select3(r_ds1_filter, n2, n1) = all_74_4 % 169.03/24.06 | | | | % 169.03/24.06 | | | | GROUND_INST: instantiating (8) with all_74_5, all_74_4, n1, n2, % 169.03/24.06 | | | | r_ds1_filter, simplifying with (19), (32) gives: % 169.03/24.06 | | | | (33) all_74_4 = all_74_5 % 169.03/24.06 | | | | % 169.03/24.06 | | | | REDUCE: (11), (33) imply: % 169.03/24.06 | | | | (34) $false % 169.03/24.06 | | | | % 169.03/24.06 | | | | CLOSE: (34) is inconsistent. % 169.03/24.06 | | | | % 169.03/24.06 | | | End of split % 169.03/24.06 | | | % 169.03/24.06 | | End of split % 169.03/24.06 | | % 169.03/24.06 | End of split % 169.03/24.06 | % 169.03/24.06 End of proof % 169.03/24.06 % 169.03/24.06 Sub-proof #19 shows that the following formulas are inconsistent: % 169.03/24.06 ---------------------------------------------------------------- % 169.03/24.06 (1) $i(all_74_6) % 169.03/24.06 (2) all_74_6 = n0 % 169.03/24.06 (3) gt(all_74_6, n0) % 169.03/24.06 (4) ! [v0: $i] : ( ~ $i(v0) | ~ gt(v0, v0)) % 169.03/24.06 % 169.03/24.06 Begin of proof % 169.03/24.06 | % 169.03/24.06 | REDUCE: (1), (2) imply: % 169.03/24.06 | (5) $i(n0) % 169.03/24.06 | % 169.03/24.06 | REDUCE: (2), (3) imply: % 169.03/24.06 | (6) gt(n0, n0) % 169.03/24.06 | % 169.03/24.06 | GROUND_INST: instantiating (4) with n0, simplifying with (5), (6) gives: % 169.03/24.06 | (7) $false % 169.03/24.06 | % 169.03/24.06 | CLOSE: (7) is inconsistent. % 169.03/24.06 | % 169.03/24.06 End of proof % 169.03/24.06 % 169.03/24.06 Sub-proof #20 shows that the following formulas are inconsistent: % 169.03/24.06 ---------------------------------------------------------------- % 169.03/24.06 (1) $i(all_74_7) % 169.03/24.06 (2) all_74_7 = n0 % 169.03/24.06 (3) gt(all_74_7, n0) % 169.03/24.06 (4) ! [v0: $i] : ( ~ $i(v0) | ~ gt(v0, v0)) % 169.03/24.06 % 169.03/24.06 Begin of proof % 169.03/24.06 | % 169.03/24.06 | REDUCE: (1), (2) imply: % 169.03/24.06 | (5) $i(n0) % 169.03/24.06 | % 169.03/24.06 | REDUCE: (2), (3) imply: % 169.03/24.06 | (6) gt(n0, n0) % 169.03/24.06 | % 169.03/24.06 | GROUND_INST: instantiating (4) with n0, simplifying with (5), (6) gives: % 169.03/24.06 | (7) $false % 169.03/24.06 | % 169.03/24.06 | CLOSE: (7) is inconsistent. % 169.03/24.06 | % 169.03/24.06 End of proof % 169.03/24.06 % 169.03/24.06 Sub-proof #21 shows that the following formulas are inconsistent: % 169.03/24.06 ---------------------------------------------------------------- % 169.03/24.06 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (pred(v1) = v2) | ~ $i(v1) % 169.03/24.06 | ~ $i(v0) | ~ gt(v1, v0) | leq(v0, v2)) % 169.03/24.06 (2) leq(all_74_3, n5) % 169.03/24.06 (3) all_74_13 = n5 % 169.03/24.06 (4) $i(all_74_3) % 169.03/24.06 (5) pred(n5) = n4 % 169.03/24.06 (6) a_select3(q_ds1_filter, all_74_2, all_74_3) = all_74_0 % 169.03/24.06 (7) leq(n0, all_74_2) % 169.03/24.06 (8) $i(n2) % 169.03/24.06 (9) ~ (all_74_0 = all_74_1) % 169.03/24.06 (10) ~ gt(n0, n0) % 169.03/24.06 (11) pred(n4) = n3 % 169.03/24.06 (12) all_74_3 = n5 | all_74_3 = n4 | all_74_3 = n3 | all_74_3 = n2 | all_74_3 % 169.03/24.06 = n1 | all_74_3 = n0 % 169.03/24.06 (13) ! [v0: $i] : (v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0, n1) | ~ % 169.03/24.06 leq(n0, v0)) % 169.03/24.06 (14) $i(all_74_2) % 169.03/24.06 (15) leq(n0, all_74_3) % 169.03/24.06 (16) pred(n3) = n2 % 169.03/24.06 (17) $i(n4) % 169.03/24.06 (18) all_74_3 = n0 | gt(all_74_3, n0) % 169.03/24.06 (19) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (a_select3(q_ds1_filter, % 169.03/24.06 v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ leq(v1, all_74_13) | ~ % 169.03/24.06 leq(v0, all_74_13) | ~ leq(n0, v1) | ~ leq(n0, v0) | % 169.03/24.06 (a_select3(q_ds1_filter, v1, v0) = v2 & $i(v2))) % 169.03/24.06 (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 169.03/24.06 (v1 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 169.03/24.06 v0)) % 169.03/24.06 (21) all_74_2 = n5 | all_74_2 = n4 | all_74_2 = n3 | all_74_2 = n2 | all_74_2 % 169.03/24.06 = n1 | all_74_2 = n0 % 169.03/24.06 (22) all_74_2 = n5 | gt(n5, all_74_2) % 169.03/24.06 (23) leq(all_74_2, n5) % 169.03/24.06 (24) pred(n2) = n1 % 169.03/24.06 (25) $i(n3) % 169.03/24.06 (26) all_74_3 = n5 | gt(n5, all_74_3) % 169.03/24.06 (27) a_select3(q_ds1_filter, all_74_3, all_74_2) = all_74_1 % 169.03/24.06 (28) $i(n5) % 169.03/24.06 (29) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ % 169.03/24.06 leq(v0, v1) | gt(v1, v0)) % 169.03/24.06 (30) gt(all_74_2, n0) % 169.03/24.06 % 169.03/24.06 Begin of proof % 169.03/24.06 | % 169.03/24.06 | BETA: splitting (18) gives: % 169.03/24.06 | % 169.03/24.06 | Case 1: % 169.03/24.06 | | % 169.03/24.06 | | (31) gt(all_74_3, n0) % 169.03/24.07 | | % 169.03/24.07 | | BETA: splitting (26) gives: % 169.03/24.07 | | % 169.03/24.07 | | Case 1: % 169.03/24.07 | | | % 169.03/24.07 | | | (32) gt(n5, all_74_3) % 169.03/24.07 | | | % 169.03/24.07 | | | GROUND_INST: instantiating (1) with all_74_3, n5, n4, simplifying with % 169.03/24.07 | | | (4), (5), (28), (32) gives: % 169.03/24.07 | | | (33) leq(all_74_3, n4) % 169.03/24.07 | | | % 169.03/24.07 | | | GROUND_INST: instantiating (29) with all_74_3, n4, simplifying with (4), % 169.03/24.07 | | | (17), (33) gives: % 169.03/24.07 | | | (34) all_74_3 = n4 | gt(n4, all_74_3) % 169.03/24.07 | | | % 169.03/24.07 | | | BETA: splitting (22) gives: % 169.03/24.07 | | | % 169.03/24.07 | | | Case 1: % 169.03/24.07 | | | | % 169.03/24.07 | | | | (35) gt(n5, all_74_2) % 169.03/24.07 | | | | % 169.03/24.07 | | | | GROUND_INST: instantiating (1) with all_74_2, n5, n4, simplifying with % 169.03/24.07 | | | | (5), (14), (28), (35) gives: % 169.03/24.07 | | | | (36) leq(all_74_2, n4) % 169.03/24.07 | | | | % 169.03/24.07 | | | | GROUND_INST: instantiating (29) with all_74_2, n4, simplifying with % 169.03/24.07 | | | | (14), (17), (36) gives: % 169.03/24.07 | | | | (37) all_74_2 = n4 | gt(n4, all_74_2) % 169.03/24.07 | | | | % 169.03/24.07 | | | | BETA: splitting (21) gives: % 169.03/24.07 | | | | % 169.03/24.07 | | | | Case 1: % 169.03/24.07 | | | | | % 169.03/24.07 | | | | | (38) all_74_2 = n0 % 169.03/24.07 | | | | | % 169.03/24.07 | | | | | REDUCE: (30), (38) imply: % 169.03/24.07 | | | | | (39) gt(n0, n0) % 169.03/24.07 | | | | | % 169.03/24.07 | | | | | PRED_UNIFY: (10), (39) imply: % 169.03/24.07 | | | | | (40) $false % 169.03/24.07 | | | | | % 169.03/24.07 | | | | | CLOSE: (40) is inconsistent. % 169.03/24.07 | | | | | % 169.03/24.07 | | | | Case 2: % 169.03/24.07 | | | | | % 169.03/24.07 | | | | | (41) ~ (all_74_2 = n0) % 169.03/24.07 | | | | | % 169.03/24.07 | | | | | BETA: splitting (12) gives: % 169.03/24.07 | | | | | % 169.03/24.07 | | | | | Case 1: % 169.03/24.07 | | | | | | % 169.03/24.07 | | | | | | (42) all_74_3 = n0 % 169.03/24.07 | | | | | | % 169.03/24.07 | | | | | | REDUCE: (31), (42) imply: % 169.03/24.07 | | | | | | (43) gt(n0, n0) % 169.03/24.07 | | | | | | % 169.03/24.07 | | | | | | PRED_UNIFY: (10), (43) imply: % 169.03/24.07 | | | | | | (44) $false % 169.03/24.07 | | | | | | % 169.03/24.07 | | | | | | CLOSE: (44) is inconsistent. % 169.03/24.07 | | | | | | % 169.03/24.07 | | | | | Case 2: % 169.03/24.07 | | | | | | % 169.03/24.07 | | | | | | (45) ~ (all_74_3 = n0) % 169.03/24.07 | | | | | | % 169.03/24.07 | | | | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (11), (13), (14), % 169.03/24.07 | | | | | | (15), (16), (17), (19), (20), (23), (24), (25), (27), % 169.03/24.07 | | | | | | (29), (34), (37), (41), (45) are inconsistent by % 169.03/24.07 | | | | | | sub-proof #28. % 169.03/24.07 | | | | | | % 169.03/24.07 | | | | | End of split % 169.03/24.07 | | | | | % 169.03/24.07 | | | | End of split % 169.03/24.07 | | | | % 169.03/24.07 | | | Case 2: % 169.03/24.07 | | | | % 169.03/24.07 | | | | (46) all_74_2 = n5 % 169.03/24.07 | | | | % 169.03/24.07 | | | | REDUCE: (6), (46) imply: % 169.03/24.07 | | | | (47) a_select3(q_ds1_filter, n5, all_74_3) = all_74_0 % 169.03/24.07 | | | | % 169.03/24.07 | | | | REDUCE: (27), (46) imply: % 169.03/24.07 | | | | (48) a_select3(q_ds1_filter, all_74_3, n5) = all_74_1 % 169.03/24.07 | | | | % 169.03/24.07 | | | | REDUCE: (23), (46) imply: % 169.03/24.07 | | | | (49) leq(n5, n5) % 169.03/24.07 | | | | % 169.03/24.07 | | | | REDUCE: (7), (46) imply: % 169.03/24.07 | | | | (50) leq(n0, n5) % 169.03/24.07 | | | | % 169.03/24.07 | | | | BETA: splitting (12) gives: % 169.03/24.07 | | | | % 169.03/24.07 | | | | Case 1: % 169.03/24.07 | | | | | % 169.03/24.07 | | | | | (51) all_74_3 = n0 % 169.03/24.07 | | | | | % 169.03/24.07 | | | | | REDUCE: (31), (51) imply: % 169.03/24.07 | | | | | (52) gt(n0, n0) % 169.03/24.07 | | | | | % 169.03/24.07 | | | | | PRED_UNIFY: (10), (52) imply: % 169.03/24.07 | | | | | (53) $false % 169.03/24.07 | | | | | % 169.03/24.07 | | | | | CLOSE: (53) is inconsistent. % 169.03/24.07 | | | | | % 169.03/24.07 | | | | Case 2: % 169.03/24.07 | | | | | % 169.03/24.07 | | | | | (54) ~ (all_74_3 = n0) % 169.03/24.07 | | | | | % 169.03/24.07 | | | | | REF_CLOSE: (1), (2), (3), (4), (8), (9), (11), (13), (15), (16), (17), % 169.03/24.07 | | | | | (19), (20), (24), (25), (28), (29), (34), (47), (48), (49), % 169.03/24.07 | | | | | (50), (54) are inconsistent by sub-proof #26. % 169.03/24.07 | | | | | % 169.03/24.07 | | | | End of split % 169.03/24.07 | | | | % 169.03/24.07 | | | End of split % 169.03/24.07 | | | % 169.03/24.07 | | Case 2: % 169.03/24.07 | | | % 169.03/24.07 | | | (55) all_74_3 = n5 % 169.03/24.07 | | | % 169.03/24.07 | | | REDUCE: (6), (55) imply: % 169.03/24.07 | | | (56) a_select3(q_ds1_filter, all_74_2, n5) = all_74_0 % 169.03/24.07 | | | % 169.03/24.07 | | | REDUCE: (27), (55) imply: % 169.03/24.07 | | | (57) a_select3(q_ds1_filter, n5, all_74_2) = all_74_1 % 169.03/24.07 | | | % 169.03/24.07 | | | REDUCE: (2), (55) imply: % 169.03/24.07 | | | (58) leq(n5, n5) % 169.03/24.07 | | | % 169.03/24.07 | | | REDUCE: (15), (55) imply: % 169.03/24.07 | | | (59) leq(n0, n5) % 169.03/24.07 | | | % 169.03/24.07 | | | BETA: splitting (22) gives: % 169.03/24.07 | | | % 169.03/24.07 | | | Case 1: % 169.03/24.07 | | | | % 169.03/24.07 | | | | (60) gt(n5, all_74_2) % 169.03/24.07 | | | | % 169.03/24.07 | | | | GROUND_INST: instantiating (1) with all_74_2, n5, n4, simplifying with % 169.03/24.07 | | | | (5), (14), (28), (60) gives: % 169.03/24.07 | | | | (61) leq(all_74_2, n4) % 169.03/24.07 | | | | % 169.03/24.07 | | | | GROUND_INST: instantiating (29) with all_74_2, n4, simplifying with % 169.03/24.07 | | | | (14), (17), (61) gives: % 169.03/24.07 | | | | (62) all_74_2 = n4 | gt(n4, all_74_2) % 169.03/24.07 | | | | % 169.03/24.07 | | | | BETA: splitting (21) gives: % 169.03/24.07 | | | | % 169.03/24.07 | | | | Case 1: % 169.03/24.07 | | | | | % 169.03/24.07 | | | | | (63) all_74_2 = n0 % 169.03/24.07 | | | | | % 169.03/24.07 | | | | | REDUCE: (30), (63) imply: % 169.03/24.07 | | | | | (64) gt(n0, n0) % 169.03/24.07 | | | | | % 169.03/24.07 | | | | | PRED_UNIFY: (10), (64) imply: % 169.03/24.07 | | | | | (65) $false % 169.03/24.07 | | | | | % 169.03/24.07 | | | | | CLOSE: (65) is inconsistent. % 169.03/24.07 | | | | | % 169.03/24.07 | | | | Case 2: % 169.03/24.07 | | | | | % 169.03/24.07 | | | | | (66) ~ (all_74_2 = n0) % 169.03/24.07 | | | | | % 169.03/24.07 | | | | | REF_CLOSE: (1), (3), (7), (8), (9), (11), (13), (14), (16), (17), % 169.03/24.07 | | | | | (19), (20), (23), (24), (25), (28), (29), (56), (57), (58), % 169.03/24.07 | | | | | (59), (62), (66) are inconsistent by sub-proof #25. % 169.03/24.07 | | | | | % 169.03/24.07 | | | | End of split % 169.03/24.07 | | | | % 169.03/24.07 | | | Case 2: % 169.03/24.07 | | | | % 169.03/24.07 | | | | (67) all_74_2 = n5 % 169.03/24.07 | | | | % 169.03/24.07 | | | | REDUCE: (56), (67) imply: % 169.03/24.07 | | | | (68) a_select3(q_ds1_filter, n5, n5) = all_74_0 % 169.03/24.07 | | | | % 169.03/24.07 | | | | REDUCE: (57), (67) imply: % 169.03/24.07 | | | | (69) a_select3(q_ds1_filter, n5, n5) = all_74_1 % 169.03/24.07 | | | | % 169.03/24.07 | | | | GROUND_INST: instantiating (20) with all_74_1, all_74_0, n5, n5, % 169.03/24.07 | | | | q_ds1_filter, simplifying with (68), (69) gives: % 169.03/24.07 | | | | (70) all_74_0 = all_74_1 % 169.03/24.07 | | | | % 169.03/24.07 | | | | REDUCE: (9), (70) imply: % 169.03/24.07 | | | | (71) $false % 169.03/24.07 | | | | % 169.03/24.07 | | | | CLOSE: (71) is inconsistent. % 169.03/24.07 | | | | % 169.03/24.07 | | | End of split % 169.03/24.07 | | | % 169.03/24.07 | | End of split % 169.03/24.07 | | % 169.03/24.07 | Case 2: % 169.03/24.07 | | % 169.03/24.07 | | (72) all_74_3 = n0 % 169.03/24.07 | | (73) ~ gt(all_74_3, n0) % 169.03/24.07 | | % 169.03/24.07 | | REDUCE: (6), (72) imply: % 169.03/24.07 | | (74) a_select3(q_ds1_filter, all_74_2, n0) = all_74_0 % 169.03/24.07 | | % 169.03/24.07 | | REDUCE: (27), (72) imply: % 169.03/24.07 | | (75) a_select3(q_ds1_filter, n0, all_74_2) = all_74_1 % 169.03/24.07 | | % 169.03/24.07 | | REDUCE: (4), (72) imply: % 169.03/24.07 | | (76) $i(n0) % 169.03/24.07 | | % 169.03/24.07 | | REDUCE: (2), (72) imply: % 169.03/24.07 | | (77) leq(n0, n5) % 169.03/24.07 | | % 169.03/24.07 | | REDUCE: (15), (72) imply: % 169.03/24.07 | | (78) leq(n0, n0) % 169.03/24.07 | | % 169.03/24.07 | | BETA: splitting (22) gives: % 169.03/24.07 | | % 169.03/24.07 | | Case 1: % 169.03/24.07 | | | % 169.03/24.07 | | | (79) gt(n5, all_74_2) % 169.03/24.07 | | | % 169.03/24.07 | | | GROUND_INST: instantiating (1) with all_74_2, n5, n4, simplifying with % 169.03/24.07 | | | (5), (14), (28), (79) gives: % 169.03/24.07 | | | (80) leq(all_74_2, n4) % 169.03/24.07 | | | % 169.03/24.07 | | | GROUND_INST: instantiating (29) with all_74_2, n4, simplifying with (14), % 169.03/24.07 | | | (17), (80) gives: % 169.03/24.07 | | | (81) all_74_2 = n4 | gt(n4, all_74_2) % 169.03/24.07 | | | % 169.03/24.07 | | | BETA: splitting (21) gives: % 169.03/24.07 | | | % 169.03/24.07 | | | Case 1: % 169.03/24.07 | | | | % 169.03/24.07 | | | | (82) all_74_2 = n0 % 169.03/24.07 | | | | % 169.03/24.07 | | | | REDUCE: (30), (82) imply: % 169.03/24.07 | | | | (83) gt(n0, n0) % 169.03/24.07 | | | | % 169.03/24.07 | | | | PRED_UNIFY: (10), (83) imply: % 169.03/24.07 | | | | (84) $false % 169.03/24.07 | | | | % 169.03/24.07 | | | | CLOSE: (84) is inconsistent. % 169.03/24.07 | | | | % 169.03/24.07 | | | Case 2: % 169.03/24.07 | | | | % 169.03/24.07 | | | | (85) ~ (all_74_2 = n0) % 169.03/24.07 | | | | % 169.03/24.07 | | | | BETA: splitting (81) gives: % 169.03/24.07 | | | | % 169.03/24.07 | | | | Case 1: % 169.03/24.07 | | | | | % 169.03/24.07 | | | | | (86) gt(n4, all_74_2) % 169.03/24.07 | | | | | % 169.03/24.07 | | | | | GROUND_INST: instantiating (1) with all_74_2, n4, n3, simplifying with % 169.03/24.07 | | | | | (11), (14), (17), (86) gives: % 169.03/24.07 | | | | | (87) leq(all_74_2, n3) % 169.03/24.07 | | | | | % 169.03/24.07 | | | | | GROUND_INST: instantiating (29) with all_74_2, n3, simplifying with % 169.03/24.07 | | | | | (14), (25), (87) gives: % 169.03/24.07 | | | | | (88) all_74_2 = n3 | gt(n3, all_74_2) % 169.03/24.07 | | | | | % 169.03/24.07 | | | | | BETA: splitting (88) gives: % 169.03/24.07 | | | | | % 169.03/24.07 | | | | | Case 1: % 169.03/24.07 | | | | | | % 169.03/24.07 | | | | | | (89) gt(n3, all_74_2) % 169.03/24.07 | | | | | | % 169.03/24.07 | | | | | | GROUND_INST: instantiating (1) with all_74_2, n3, n2, simplifying % 169.03/24.07 | | | | | | with (14), (16), (25), (89) gives: % 169.03/24.07 | | | | | | (90) leq(all_74_2, n2) % 169.03/24.07 | | | | | | % 169.03/24.07 | | | | | | GROUND_INST: instantiating (29) with all_74_2, n2, simplifying with % 169.03/24.07 | | | | | | (8), (14), (90) gives: % 169.03/24.07 | | | | | | (91) all_74_2 = n2 | gt(n2, all_74_2) % 169.03/24.07 | | | | | | % 169.03/24.07 | | | | | | BETA: splitting (91) gives: % 169.03/24.07 | | | | | | % 169.03/24.07 | | | | | | Case 1: % 169.03/24.07 | | | | | | | % 169.03/24.07 | | | | | | | (92) gt(n2, all_74_2) % 169.03/24.07 | | | | | | | % 169.03/24.07 | | | | | | | GROUND_INST: instantiating (1) with all_74_2, n2, n1, simplifying % 169.03/24.07 | | | | | | | with (8), (14), (24), (92) gives: % 169.03/24.07 | | | | | | | (93) leq(all_74_2, n1) % 169.03/24.07 | | | | | | | % 169.03/24.07 | | | | | | | GROUND_INST: instantiating (13) with all_74_2, simplifying with % 169.03/24.07 | | | | | | | (7), (14), (93) gives: % 169.03/24.07 | | | | | | | (94) all_74_2 = n1 | all_74_2 = n0 % 169.03/24.07 | | | | | | | % 169.03/24.07 | | | | | | | BETA: splitting (94) gives: % 169.03/24.07 | | | | | | | % 169.03/24.07 | | | | | | | Case 1: % 169.03/24.07 | | | | | | | | % 169.03/24.07 | | | | | | | | (95) all_74_2 = n0 % 169.03/24.07 | | | | | | | | % 169.03/24.07 | | | | | | | | REDUCE: (85), (95) imply: % 169.03/24.07 | | | | | | | | (96) $false % 169.03/24.07 | | | | | | | | % 169.03/24.07 | | | | | | | | CLOSE: (96) is inconsistent. % 169.03/24.07 | | | | | | | | % 169.03/24.07 | | | | | | | Case 2: % 169.03/24.07 | | | | | | | | % 169.03/24.07 | | | | | | | | (97) all_74_2 = n1 % 169.03/24.07 | | | | | | | | % 169.03/24.07 | | | | | | | | REDUCE: (74), (97) imply: % 169.03/24.07 | | | | | | | | (98) a_select3(q_ds1_filter, n1, n0) = all_74_0 % 169.03/24.07 | | | | | | | | % 169.03/24.07 | | | | | | | | REDUCE: (75), (97) imply: % 169.03/24.07 | | | | | | | | (99) a_select3(q_ds1_filter, n0, n1) = all_74_1 % 169.03/24.07 | | | | | | | | % 169.03/24.07 | | | | | | | | REDUCE: (14), (97) imply: % 169.03/24.07 | | | | | | | | (100) $i(n1) % 169.03/24.07 | | | | | | | | % 169.03/24.07 | | | | | | | | REDUCE: (23), (97) imply: % 169.03/24.07 | | | | | | | | (101) leq(n1, n5) % 169.03/24.07 | | | | | | | | % 169.03/24.07 | | | | | | | | REDUCE: (7), (97) imply: % 169.03/24.07 | | | | | | | | (102) leq(n0, n1) % 169.03/24.07 | | | | | | | | % 169.03/24.07 | | | | | | | | GROUND_INST: instantiating (19) with n0, n1, all_74_1, % 169.03/24.07 | | | | | | | | simplifying with (76), (78), (99), (100), (102) % 169.03/24.07 | | | | | | | | gives: % 169.03/24.07 | | | | | | | | (103) ~ leq(n1, all_74_13) | ~ leq(n0, all_74_13) | % 169.03/24.07 | | | | | | | | (a_select3(q_ds1_filter, n1, n0) = all_74_1 & % 169.03/24.07 | | | | | | | | $i(all_74_1)) % 169.03/24.07 | | | | | | | | % 169.03/24.07 | | | | | | | | BETA: splitting (103) gives: % 169.03/24.07 | | | | | | | | % 169.03/24.07 | | | | | | | | Case 1: % 169.03/24.07 | | | | | | | | | % 169.03/24.07 | | | | | | | | | (104) ~ leq(n0, all_74_13) % 169.03/24.07 | | | | | | | | | % 169.03/24.07 | | | | | | | | | REDUCE: (3), (104) imply: % 169.03/24.07 | | | | | | | | | (105) ~ leq(n0, n5) % 169.03/24.07 | | | | | | | | | % 169.03/24.07 | | | | | | | | | PRED_UNIFY: (77), (105) imply: % 169.03/24.07 | | | | | | | | | (106) $false % 169.03/24.07 | | | | | | | | | % 169.03/24.07 | | | | | | | | | CLOSE: (106) is inconsistent. % 169.03/24.07 | | | | | | | | | % 169.03/24.07 | | | | | | | | Case 2: % 169.03/24.07 | | | | | | | | | % 169.03/24.07 | | | | | | | | | (107) ~ leq(n1, all_74_13) | (a_select3(q_ds1_filter, n1, % 169.03/24.07 | | | | | | | | | n0) = all_74_1 & $i(all_74_1)) % 169.03/24.07 | | | | | | | | | % 169.03/24.07 | | | | | | | | | BETA: splitting (107) gives: % 169.03/24.07 | | | | | | | | | % 169.03/24.07 | | | | | | | | | Case 1: % 169.03/24.07 | | | | | | | | | | % 169.03/24.07 | | | | | | | | | | (108) ~ leq(n1, all_74_13) % 169.03/24.07 | | | | | | | | | | % 169.03/24.07 | | | | | | | | | | REDUCE: (3), (108) imply: % 169.03/24.07 | | | | | | | | | | (109) ~ leq(n1, n5) % 169.03/24.07 | | | | | | | | | | % 169.03/24.07 | | | | | | | | | | PRED_UNIFY: (101), (109) imply: % 169.03/24.07 | | | | | | | | | | (110) $false % 169.03/24.07 | | | | | | | | | | % 169.03/24.07 | | | | | | | | | | CLOSE: (110) is inconsistent. % 169.03/24.07 | | | | | | | | | | % 169.03/24.07 | | | | | | | | | Case 2: % 169.03/24.07 | | | | | | | | | | % 169.03/24.07 | | | | | | | | | | (111) a_select3(q_ds1_filter, n1, n0) = all_74_1 & % 169.03/24.07 | | | | | | | | | | $i(all_74_1) % 169.03/24.07 | | | | | | | | | | % 169.03/24.07 | | | | | | | | | | ALPHA: (111) implies: % 169.03/24.07 | | | | | | | | | | (112) a_select3(q_ds1_filter, n1, n0) = all_74_1 % 169.03/24.07 | | | | | | | | | | % 169.03/24.07 | | | | | | | | | | REF_CLOSE: (9), (20), (98), (112) are inconsistent by % 169.03/24.07 | | | | | | | | | | sub-proof #24. % 169.03/24.07 | | | | | | | | | | % 169.03/24.07 | | | | | | | | | End of split % 169.03/24.07 | | | | | | | | | % 169.03/24.07 | | | | | | | | End of split % 169.03/24.07 | | | | | | | | % 169.03/24.07 | | | | | | | End of split % 169.03/24.07 | | | | | | | % 169.03/24.07 | | | | | | Case 2: % 169.03/24.07 | | | | | | | % 169.03/24.07 | | | | | | | (113) all_74_2 = n2 % 169.03/24.07 | | | | | | | % 169.03/24.07 | | | | | | | REDUCE: (74), (113) imply: % 169.03/24.07 | | | | | | | (114) a_select3(q_ds1_filter, n2, n0) = all_74_0 % 169.03/24.07 | | | | | | | % 169.03/24.07 | | | | | | | REDUCE: (75), (113) imply: % 169.03/24.07 | | | | | | | (115) a_select3(q_ds1_filter, n0, n2) = all_74_1 % 169.03/24.07 | | | | | | | % 169.03/24.07 | | | | | | | REDUCE: (23), (113) imply: % 169.03/24.07 | | | | | | | (116) leq(n2, n5) % 169.03/24.07 | | | | | | | % 169.03/24.07 | | | | | | | REDUCE: (7), (113) imply: % 169.03/24.07 | | | | | | | (117) leq(n0, n2) % 169.03/24.07 | | | | | | | % 169.03/24.07 | | | | | | | GROUND_INST: instantiating (19) with n0, n2, all_74_1, simplifying % 169.03/24.07 | | | | | | | with (8), (76), (78), (115), (117) gives: % 169.03/24.07 | | | | | | | (118) ~ leq(n2, all_74_13) | ~ leq(n0, all_74_13) | % 169.03/24.07 | | | | | | | (a_select3(q_ds1_filter, n2, n0) = all_74_1 & % 169.03/24.07 | | | | | | | $i(all_74_1)) % 169.03/24.07 | | | | | | | % 169.03/24.07 | | | | | | | BETA: splitting (118) gives: % 169.03/24.07 | | | | | | | % 169.03/24.07 | | | | | | | Case 1: % 169.03/24.07 | | | | | | | | % 169.03/24.07 | | | | | | | | (119) ~ leq(n0, all_74_13) % 169.03/24.07 | | | | | | | | % 169.03/24.07 | | | | | | | | REDUCE: (3), (119) imply: % 169.03/24.07 | | | | | | | | (120) ~ leq(n0, n5) % 169.03/24.07 | | | | | | | | % 169.03/24.07 | | | | | | | | PRED_UNIFY: (77), (120) imply: % 169.03/24.07 | | | | | | | | (121) $false % 169.03/24.07 | | | | | | | | % 169.03/24.07 | | | | | | | | CLOSE: (121) is inconsistent. % 169.03/24.07 | | | | | | | | % 169.03/24.07 | | | | | | | Case 2: % 169.03/24.07 | | | | | | | | % 169.03/24.07 | | | | | | | | (122) ~ leq(n2, all_74_13) | (a_select3(q_ds1_filter, n2, % 169.03/24.07 | | | | | | | | n0) = all_74_1 & $i(all_74_1)) % 169.03/24.07 | | | | | | | | % 169.03/24.07 | | | | | | | | BETA: splitting (122) gives: % 169.03/24.07 | | | | | | | | % 169.03/24.07 | | | | | | | | Case 1: % 169.03/24.07 | | | | | | | | | % 169.03/24.07 | | | | | | | | | (123) ~ leq(n2, all_74_13) % 169.03/24.07 | | | | | | | | | % 169.03/24.07 | | | | | | | | | REDUCE: (3), (123) imply: % 169.03/24.07 | | | | | | | | | (124) ~ leq(n2, n5) % 169.03/24.07 | | | | | | | | | % 169.03/24.07 | | | | | | | | | PRED_UNIFY: (116), (124) imply: % 169.03/24.07 | | | | | | | | | (125) $false % 169.03/24.07 | | | | | | | | | % 169.03/24.07 | | | | | | | | | CLOSE: (125) is inconsistent. % 169.03/24.07 | | | | | | | | | % 169.03/24.07 | | | | | | | | Case 2: % 169.03/24.07 | | | | | | | | | % 169.03/24.07 | | | | | | | | | (126) a_select3(q_ds1_filter, n2, n0) = all_74_1 & % 169.03/24.07 | | | | | | | | | $i(all_74_1) % 169.03/24.07 | | | | | | | | | % 169.03/24.07 | | | | | | | | | ALPHA: (126) implies: % 169.03/24.07 | | | | | | | | | (127) a_select3(q_ds1_filter, n2, n0) = all_74_1 % 169.03/24.07 | | | | | | | | | % 169.03/24.07 | | | | | | | | | GROUND_INST: instantiating (20) with all_74_0, all_74_1, n0, % 169.03/24.07 | | | | | | | | | n2, q_ds1_filter, simplifying with (114), (127) % 169.03/24.07 | | | | | | | | | gives: % 169.03/24.07 | | | | | | | | | (128) all_74_0 = all_74_1 % 169.03/24.07 | | | | | | | | | % 169.03/24.07 | | | | | | | | | REDUCE: (9), (128) imply: % 169.03/24.07 | | | | | | | | | (129) $false % 169.03/24.07 | | | | | | | | | % 169.03/24.07 | | | | | | | | | CLOSE: (129) is inconsistent. % 169.03/24.07 | | | | | | | | | % 169.03/24.07 | | | | | | | | End of split % 169.03/24.07 | | | | | | | | % 169.03/24.07 | | | | | | | End of split % 169.03/24.07 | | | | | | | % 169.03/24.07 | | | | | | End of split % 169.03/24.07 | | | | | | % 169.03/24.07 | | | | | Case 2: % 169.03/24.07 | | | | | | % 169.03/24.07 | | | | | | (130) all_74_2 = n3 % 169.03/24.07 | | | | | | % 169.03/24.07 | | | | | | REDUCE: (74), (130) imply: % 169.03/24.07 | | | | | | (131) a_select3(q_ds1_filter, n3, n0) = all_74_0 % 169.03/24.07 | | | | | | % 169.03/24.07 | | | | | | REDUCE: (75), (130) imply: % 169.03/24.07 | | | | | | (132) a_select3(q_ds1_filter, n0, n3) = all_74_1 % 169.03/24.07 | | | | | | % 169.03/24.07 | | | | | | REDUCE: (23), (130) imply: % 169.03/24.07 | | | | | | (133) leq(n3, n5) % 169.03/24.07 | | | | | | % 169.03/24.07 | | | | | | REDUCE: (7), (130) imply: % 169.03/24.07 | | | | | | (134) leq(n0, n3) % 169.03/24.07 | | | | | | % 169.03/24.07 | | | | | | GROUND_INST: instantiating (19) with n0, n3, all_74_1, simplifying % 169.03/24.07 | | | | | | with (25), (76), (78), (132), (134) gives: % 169.03/24.07 | | | | | | (135) ~ leq(n3, all_74_13) | ~ leq(n0, all_74_13) | % 169.03/24.07 | | | | | | (a_select3(q_ds1_filter, n3, n0) = all_74_1 & $i(all_74_1)) % 169.03/24.07 | | | | | | % 169.03/24.07 | | | | | | BETA: splitting (135) gives: % 169.03/24.07 | | | | | | % 169.03/24.07 | | | | | | Case 1: % 169.03/24.07 | | | | | | | % 169.03/24.07 | | | | | | | (136) ~ leq(n0, all_74_13) % 169.03/24.07 | | | | | | | % 169.03/24.07 | | | | | | | REDUCE: (3), (136) imply: % 169.03/24.07 | | | | | | | (137) ~ leq(n0, n5) % 169.03/24.07 | | | | | | | % 169.03/24.07 | | | | | | | PRED_UNIFY: (77), (137) imply: % 169.03/24.07 | | | | | | | (138) $false % 169.03/24.07 | | | | | | | % 169.03/24.07 | | | | | | | CLOSE: (138) is inconsistent. % 169.03/24.07 | | | | | | | % 169.03/24.07 | | | | | | Case 2: % 169.03/24.07 | | | | | | | % 169.03/24.07 | | | | | | | (139) ~ leq(n3, all_74_13) | (a_select3(q_ds1_filter, n3, n0) % 169.03/24.07 | | | | | | | = all_74_1 & $i(all_74_1)) % 169.03/24.07 | | | | | | | % 169.03/24.07 | | | | | | | BETA: splitting (139) gives: % 169.03/24.07 | | | | | | | % 169.03/24.07 | | | | | | | Case 1: % 169.03/24.07 | | | | | | | | % 169.03/24.07 | | | | | | | | (140) ~ leq(n3, all_74_13) % 169.03/24.07 | | | | | | | | % 169.03/24.07 | | | | | | | | REDUCE: (3), (140) imply: % 169.03/24.07 | | | | | | | | (141) ~ leq(n3, n5) % 169.03/24.07 | | | | | | | | % 169.03/24.07 | | | | | | | | PRED_UNIFY: (133), (141) imply: % 169.03/24.07 | | | | | | | | (142) $false % 169.03/24.07 | | | | | | | | % 169.03/24.07 | | | | | | | | CLOSE: (142) is inconsistent. % 169.03/24.07 | | | | | | | | % 169.03/24.07 | | | | | | | Case 2: % 169.03/24.07 | | | | | | | | % 169.03/24.08 | | | | | | | | (143) a_select3(q_ds1_filter, n3, n0) = all_74_1 & % 169.03/24.08 | | | | | | | | $i(all_74_1) % 169.03/24.08 | | | | | | | | % 169.03/24.08 | | | | | | | | ALPHA: (143) implies: % 169.03/24.08 | | | | | | | | (144) a_select3(q_ds1_filter, n3, n0) = all_74_1 % 169.03/24.08 | | | | | | | | % 169.03/24.08 | | | | | | | | GROUND_INST: instantiating (20) with all_74_0, all_74_1, n0, n3, % 169.03/24.08 | | | | | | | | q_ds1_filter, simplifying with (131), (144) gives: % 169.03/24.08 | | | | | | | | (145) all_74_0 = all_74_1 % 169.03/24.08 | | | | | | | | % 169.03/24.08 | | | | | | | | REDUCE: (9), (145) imply: % 169.03/24.08 | | | | | | | | (146) $false % 169.03/24.08 | | | | | | | | % 169.03/24.08 | | | | | | | | CLOSE: (146) is inconsistent. % 169.03/24.08 | | | | | | | | % 169.03/24.08 | | | | | | | End of split % 169.03/24.08 | | | | | | | % 169.03/24.08 | | | | | | End of split % 169.03/24.08 | | | | | | % 169.03/24.08 | | | | | End of split % 169.03/24.08 | | | | | % 169.03/24.08 | | | | Case 2: % 169.03/24.08 | | | | | % 169.03/24.08 | | | | | (147) all_74_2 = n4 % 169.03/24.08 | | | | | % 169.03/24.08 | | | | | REDUCE: (74), (147) imply: % 169.03/24.08 | | | | | (148) a_select3(q_ds1_filter, n4, n0) = all_74_0 % 169.03/24.08 | | | | | % 169.03/24.08 | | | | | REDUCE: (75), (147) imply: % 169.03/24.08 | | | | | (149) a_select3(q_ds1_filter, n0, n4) = all_74_1 % 169.03/24.08 | | | | | % 169.03/24.08 | | | | | REDUCE: (23), (147) imply: % 169.03/24.08 | | | | | (150) leq(n4, n5) % 169.03/24.08 | | | | | % 169.03/24.08 | | | | | REDUCE: (7), (147) imply: % 169.03/24.08 | | | | | (151) leq(n0, n4) % 169.03/24.08 | | | | | % 169.03/24.08 | | | | | GROUND_INST: instantiating (19) with n0, n4, all_74_1, simplifying % 169.03/24.08 | | | | | with (17), (76), (78), (149), (151) gives: % 169.03/24.08 | | | | | (152) ~ leq(n4, all_74_13) | ~ leq(n0, all_74_13) | % 169.03/24.08 | | | | | (a_select3(q_ds1_filter, n4, n0) = all_74_1 & $i(all_74_1)) % 169.03/24.08 | | | | | % 169.03/24.08 | | | | | BETA: splitting (152) gives: % 169.03/24.08 | | | | | % 169.03/24.08 | | | | | Case 1: % 169.03/24.08 | | | | | | % 169.03/24.08 | | | | | | (153) ~ leq(n0, all_74_13) % 169.03/24.08 | | | | | | % 169.03/24.08 | | | | | | REDUCE: (3), (153) imply: % 169.03/24.08 | | | | | | (154) ~ leq(n0, n5) % 169.03/24.08 | | | | | | % 169.03/24.08 | | | | | | PRED_UNIFY: (77), (154) imply: % 169.03/24.08 | | | | | | (155) $false % 169.03/24.08 | | | | | | % 169.03/24.08 | | | | | | CLOSE: (155) is inconsistent. % 169.03/24.08 | | | | | | % 169.03/24.08 | | | | | Case 2: % 169.03/24.08 | | | | | | % 169.03/24.08 | | | | | | (156) ~ leq(n4, all_74_13) | (a_select3(q_ds1_filter, n4, n0) = % 169.03/24.08 | | | | | | all_74_1 & $i(all_74_1)) % 169.03/24.08 | | | | | | % 169.03/24.08 | | | | | | BETA: splitting (156) gives: % 169.03/24.08 | | | | | | % 169.03/24.08 | | | | | | Case 1: % 169.03/24.08 | | | | | | | % 169.03/24.08 | | | | | | | (157) ~ leq(n4, all_74_13) % 169.03/24.08 | | | | | | | % 169.03/24.08 | | | | | | | REDUCE: (3), (157) imply: % 169.03/24.08 | | | | | | | (158) ~ leq(n4, n5) % 169.03/24.08 | | | | | | | % 169.03/24.08 | | | | | | | PRED_UNIFY: (150), (158) imply: % 169.03/24.08 | | | | | | | (159) $false % 169.03/24.08 | | | | | | | % 169.03/24.08 | | | | | | | CLOSE: (159) is inconsistent. % 169.03/24.08 | | | | | | | % 169.03/24.08 | | | | | | Case 2: % 169.03/24.08 | | | | | | | % 169.03/24.08 | | | | | | | (160) a_select3(q_ds1_filter, n4, n0) = all_74_1 & $i(all_74_1) % 169.03/24.08 | | | | | | | % 169.03/24.08 | | | | | | | ALPHA: (160) implies: % 169.03/24.08 | | | | | | | (161) a_select3(q_ds1_filter, n4, n0) = all_74_1 % 169.03/24.08 | | | | | | | % 169.03/24.08 | | | | | | | REF_CLOSE: (9), (20), (148), (161) are inconsistent by sub-proof % 169.03/24.08 | | | | | | | #23. % 169.03/24.08 | | | | | | | % 169.03/24.08 | | | | | | End of split % 169.03/24.08 | | | | | | % 169.03/24.08 | | | | | End of split % 169.03/24.08 | | | | | % 169.03/24.08 | | | | End of split % 169.03/24.08 | | | | % 169.03/24.08 | | | End of split % 169.03/24.08 | | | % 169.03/24.08 | | Case 2: % 169.03/24.08 | | | % 169.03/24.08 | | | (162) all_74_2 = n5 % 169.03/24.08 | | | % 169.03/24.08 | | | REDUCE: (74), (162) imply: % 169.03/24.08 | | | (163) a_select3(q_ds1_filter, n5, n0) = all_74_0 % 169.03/24.08 | | | % 169.03/24.08 | | | REDUCE: (75), (162) imply: % 169.03/24.08 | | | (164) a_select3(q_ds1_filter, n0, n5) = all_74_1 % 169.03/24.08 | | | % 169.03/24.08 | | | REDUCE: (23), (162) imply: % 169.03/24.08 | | | (165) leq(n5, n5) % 169.03/24.08 | | | % 169.03/24.08 | | | GROUND_INST: instantiating (19) with n0, n5, all_74_1, simplifying with % 169.03/24.08 | | | (28), (76), (77), (78), (164) gives: % 169.03/24.08 | | | (166) ~ leq(n5, all_74_13) | ~ leq(n0, all_74_13) | % 169.03/24.08 | | | (a_select3(q_ds1_filter, n5, n0) = all_74_1 & $i(all_74_1)) % 169.03/24.08 | | | % 169.03/24.08 | | | BETA: splitting (166) gives: % 169.03/24.08 | | | % 169.03/24.08 | | | Case 1: % 169.03/24.08 | | | | % 169.03/24.08 | | | | (167) ~ leq(n0, all_74_13) % 169.03/24.08 | | | | % 169.03/24.08 | | | | REDUCE: (3), (167) imply: % 169.03/24.08 | | | | (168) ~ leq(n0, n5) % 169.03/24.08 | | | | % 169.03/24.08 | | | | PRED_UNIFY: (77), (168) imply: % 169.03/24.08 | | | | (169) $false % 169.03/24.08 | | | | % 169.03/24.08 | | | | CLOSE: (169) is inconsistent. % 169.03/24.08 | | | | % 169.03/24.08 | | | Case 2: % 169.03/24.08 | | | | % 169.03/24.08 | | | | (170) ~ leq(n5, all_74_13) | (a_select3(q_ds1_filter, n5, n0) = % 169.03/24.08 | | | | all_74_1 & $i(all_74_1)) % 169.03/24.08 | | | | % 169.03/24.08 | | | | BETA: splitting (170) gives: % 169.03/24.08 | | | | % 169.03/24.08 | | | | Case 1: % 169.03/24.08 | | | | | % 169.03/24.08 | | | | | (171) ~ leq(n5, all_74_13) % 169.03/24.08 | | | | | % 169.03/24.08 | | | | | REDUCE: (3), (171) imply: % 169.03/24.08 | | | | | (172) ~ leq(n5, n5) % 169.03/24.08 | | | | | % 169.03/24.08 | | | | | PRED_UNIFY: (165), (172) imply: % 169.03/24.08 | | | | | (173) $false % 169.03/24.08 | | | | | % 169.03/24.08 | | | | | CLOSE: (173) is inconsistent. % 169.03/24.08 | | | | | % 169.03/24.08 | | | | Case 2: % 169.03/24.08 | | | | | % 169.03/24.08 | | | | | (174) a_select3(q_ds1_filter, n5, n0) = all_74_1 & $i(all_74_1) % 169.03/24.08 | | | | | % 169.03/24.08 | | | | | ALPHA: (174) implies: % 169.03/24.08 | | | | | (175) a_select3(q_ds1_filter, n5, n0) = all_74_1 % 169.03/24.08 | | | | | % 169.03/24.08 | | | | | REF_CLOSE: (9), (20), (163), (175) are inconsistent by sub-proof #22. % 169.03/24.08 | | | | | % 169.03/24.08 | | | | End of split % 169.03/24.08 | | | | % 169.03/24.08 | | | End of split % 169.03/24.08 | | | % 169.03/24.08 | | End of split % 169.03/24.08 | | % 169.03/24.08 | End of split % 169.03/24.08 | % 169.03/24.08 End of proof % 169.03/24.08 % 169.03/24.08 Sub-proof #22 shows that the following formulas are inconsistent: % 169.03/24.08 ---------------------------------------------------------------- % 169.03/24.08 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 169.03/24.08 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 169.03/24.08 v0)) % 169.03/24.08 (2) a_select3(q_ds1_filter, n5, n0) = all_74_0 % 169.03/24.08 (3) a_select3(q_ds1_filter, n5, n0) = all_74_1 % 169.03/24.08 (4) ~ (all_74_0 = all_74_1) % 169.03/24.08 % 169.03/24.08 Begin of proof % 169.03/24.08 | % 169.03/24.08 | GROUND_INST: instantiating (1) with all_74_0, all_74_1, n0, n5, q_ds1_filter, % 169.03/24.08 | simplifying with (2), (3) gives: % 169.03/24.08 | (5) all_74_0 = all_74_1 % 169.03/24.08 | % 169.03/24.08 | REDUCE: (4), (5) imply: % 169.03/24.08 | (6) $false % 169.03/24.08 | % 169.03/24.08 | CLOSE: (6) is inconsistent. % 169.03/24.08 | % 169.03/24.08 End of proof % 169.03/24.08 % 169.03/24.08 Sub-proof #23 shows that the following formulas are inconsistent: % 169.03/24.08 ---------------------------------------------------------------- % 169.03/24.08 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 169.03/24.08 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 169.03/24.08 v0)) % 169.03/24.08 (2) a_select3(q_ds1_filter, n4, n0) = all_74_0 % 169.03/24.08 (3) a_select3(q_ds1_filter, n4, n0) = all_74_1 % 169.03/24.08 (4) ~ (all_74_0 = all_74_1) % 169.03/24.08 % 169.03/24.08 Begin of proof % 169.03/24.08 | % 169.03/24.08 | GROUND_INST: instantiating (1) with all_74_0, all_74_1, n0, n4, q_ds1_filter, % 169.03/24.08 | simplifying with (2), (3) gives: % 169.03/24.08 | (5) all_74_0 = all_74_1 % 169.03/24.08 | % 169.03/24.08 | REDUCE: (4), (5) imply: % 169.03/24.08 | (6) $false % 169.03/24.08 | % 169.03/24.08 | CLOSE: (6) is inconsistent. % 169.03/24.08 | % 169.03/24.08 End of proof % 169.03/24.08 % 169.03/24.08 Sub-proof #24 shows that the following formulas are inconsistent: % 169.03/24.08 ---------------------------------------------------------------- % 169.03/24.08 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 169.03/24.08 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 169.03/24.08 v0)) % 169.03/24.08 (2) a_select3(q_ds1_filter, n1, n0) = all_74_0 % 169.03/24.08 (3) a_select3(q_ds1_filter, n1, n0) = all_74_1 % 169.03/24.08 (4) ~ (all_74_0 = all_74_1) % 169.03/24.08 % 169.03/24.08 Begin of proof % 169.03/24.08 | % 169.03/24.08 | GROUND_INST: instantiating (1) with all_74_0, all_74_1, n0, n1, q_ds1_filter, % 169.03/24.08 | simplifying with (2), (3) gives: % 169.03/24.08 | (5) all_74_0 = all_74_1 % 169.03/24.08 | % 169.03/24.08 | REDUCE: (4), (5) imply: % 169.03/24.08 | (6) $false % 169.03/24.08 | % 169.03/24.08 | CLOSE: (6) is inconsistent. % 169.03/24.08 | % 169.03/24.08 End of proof % 169.03/24.08 % 169.03/24.08 Sub-proof #25 shows that the following formulas are inconsistent: % 169.03/24.08 ---------------------------------------------------------------- % 169.03/24.08 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (pred(v1) = v2) | ~ $i(v1) % 169.03/24.08 | ~ $i(v0) | ~ gt(v1, v0) | leq(v0, v2)) % 169.03/24.08 (2) all_74_13 = n5 % 169.03/24.08 (3) ~ (all_74_2 = n0) % 169.03/24.08 (4) leq(n0, all_74_2) % 169.03/24.08 (5) $i(n2) % 169.03/24.08 (6) ~ (all_74_0 = all_74_1) % 169.03/24.08 (7) all_74_2 = n4 | gt(n4, all_74_2) % 169.03/24.08 (8) pred(n4) = n3 % 169.03/24.08 (9) a_select3(q_ds1_filter, n5, all_74_2) = all_74_1 % 169.03/24.08 (10) ! [v0: $i] : (v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0, n1) | ~ % 169.03/24.08 leq(n0, v0)) % 169.03/24.08 (11) $i(all_74_2) % 169.03/24.08 (12) leq(n5, n5) % 169.03/24.08 (13) pred(n3) = n2 % 169.03/24.08 (14) $i(n4) % 169.03/24.08 (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (a_select3(q_ds1_filter, % 169.03/24.08 v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ leq(v1, all_74_13) | ~ % 169.03/24.08 leq(v0, all_74_13) | ~ leq(n0, v1) | ~ leq(n0, v0) | % 169.03/24.08 (a_select3(q_ds1_filter, v1, v0) = v2 & $i(v2))) % 169.03/24.08 (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 169.03/24.08 (v1 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 169.03/24.08 v0)) % 169.03/24.08 (17) a_select3(q_ds1_filter, all_74_2, n5) = all_74_0 % 169.03/24.08 (18) leq(n0, n5) % 169.03/24.08 (19) leq(all_74_2, n5) % 169.03/24.08 (20) pred(n2) = n1 % 169.03/24.08 (21) $i(n3) % 169.03/24.08 (22) $i(n5) % 169.03/24.08 (23) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ % 169.03/24.08 leq(v0, v1) | gt(v1, v0)) % 169.03/24.08 % 169.03/24.08 Begin of proof % 169.03/24.08 | % 169.03/24.08 | BETA: splitting (7) gives: % 169.03/24.08 | % 169.03/24.08 | Case 1: % 169.03/24.08 | | % 169.03/24.08 | | (24) gt(n4, all_74_2) % 169.03/24.08 | | % 169.03/24.08 | | GROUND_INST: instantiating (1) with all_74_2, n4, n3, simplifying with (8), % 169.03/24.08 | | (11), (14), (24) gives: % 169.03/24.08 | | (25) leq(all_74_2, n3) % 169.03/24.08 | | % 169.03/24.08 | | GROUND_INST: instantiating (23) with all_74_2, n3, simplifying with (11), % 169.03/24.08 | | (21), (25) gives: % 169.03/24.08 | | (26) all_74_2 = n3 | gt(n3, all_74_2) % 169.03/24.08 | | % 169.03/24.08 | | BETA: splitting (26) gives: % 169.03/24.08 | | % 169.03/24.08 | | Case 1: % 169.03/24.08 | | | % 169.03/24.08 | | | (27) gt(n3, all_74_2) % 169.03/24.08 | | | % 169.03/24.08 | | | GROUND_INST: instantiating (1) with all_74_2, n3, n2, simplifying with % 169.03/24.08 | | | (11), (13), (21), (27) gives: % 169.03/24.08 | | | (28) leq(all_74_2, n2) % 169.03/24.08 | | | % 169.03/24.08 | | | GROUND_INST: instantiating (23) with all_74_2, n2, simplifying with (5), % 169.03/24.08 | | | (11), (28) gives: % 169.03/24.08 | | | (29) all_74_2 = n2 | gt(n2, all_74_2) % 169.03/24.08 | | | % 169.03/24.08 | | | BETA: splitting (29) gives: % 169.03/24.08 | | | % 169.03/24.08 | | | Case 1: % 169.03/24.08 | | | | % 169.03/24.08 | | | | (30) gt(n2, all_74_2) % 169.03/24.08 | | | | % 169.03/24.08 | | | | GROUND_INST: instantiating (1) with all_74_2, n2, n1, simplifying with % 169.03/24.08 | | | | (5), (11), (20), (30) gives: % 169.03/24.08 | | | | (31) leq(all_74_2, n1) % 169.03/24.08 | | | | % 169.03/24.08 | | | | GROUND_INST: instantiating (10) with all_74_2, simplifying with (4), % 169.03/24.08 | | | | (11), (31) gives: % 169.03/24.08 | | | | (32) all_74_2 = n1 | all_74_2 = n0 % 169.03/24.08 | | | | % 169.03/24.08 | | | | BETA: splitting (32) gives: % 169.03/24.08 | | | | % 169.03/24.08 | | | | Case 1: % 169.03/24.08 | | | | | % 169.03/24.08 | | | | | (33) all_74_2 = n0 % 169.03/24.08 | | | | | % 169.03/24.08 | | | | | REDUCE: (3), (33) imply: % 169.03/24.08 | | | | | (34) $false % 169.03/24.08 | | | | | % 169.03/24.08 | | | | | CLOSE: (34) is inconsistent. % 169.03/24.08 | | | | | % 169.03/24.08 | | | | Case 2: % 169.03/24.08 | | | | | % 169.03/24.08 | | | | | (35) all_74_2 = n1 % 169.03/24.08 | | | | | % 169.03/24.08 | | | | | REDUCE: (17), (35) imply: % 169.03/24.08 | | | | | (36) a_select3(q_ds1_filter, n1, n5) = all_74_0 % 169.03/24.08 | | | | | % 169.03/24.08 | | | | | REDUCE: (9), (35) imply: % 169.03/24.08 | | | | | (37) a_select3(q_ds1_filter, n5, n1) = all_74_1 % 169.03/24.08 | | | | | % 169.03/24.08 | | | | | REDUCE: (11), (35) imply: % 169.03/24.08 | | | | | (38) $i(n1) % 169.03/24.08 | | | | | % 169.03/24.08 | | | | | REDUCE: (19), (35) imply: % 169.03/24.08 | | | | | (39) leq(n1, n5) % 169.03/24.08 | | | | | % 169.03/24.08 | | | | | REDUCE: (4), (35) imply: % 169.03/24.08 | | | | | (40) leq(n0, n1) % 169.03/24.08 | | | | | % 169.03/24.08 | | | | | GROUND_INST: instantiating (15) with n1, n5, all_74_0, simplifying % 169.03/24.08 | | | | | with (18), (22), (36), (38), (40) gives: % 169.03/24.08 | | | | | (41) ~ leq(n5, all_74_13) | ~ leq(n1, all_74_13) | % 169.03/24.08 | | | | | (a_select3(q_ds1_filter, n5, n1) = all_74_0 & $i(all_74_0)) % 169.03/24.08 | | | | | % 169.03/24.08 | | | | | BETA: splitting (41) gives: % 169.03/24.08 | | | | | % 169.03/24.08 | | | | | Case 1: % 169.03/24.08 | | | | | | % 169.03/24.08 | | | | | | (42) ~ leq(n5, all_74_13) % 169.03/24.08 | | | | | | % 169.03/24.08 | | | | | | REDUCE: (2), (42) imply: % 169.03/24.08 | | | | | | (43) ~ leq(n5, n5) % 169.03/24.08 | | | | | | % 169.03/24.08 | | | | | | PRED_UNIFY: (12), (43) imply: % 169.03/24.08 | | | | | | (44) $false % 169.03/24.08 | | | | | | % 169.03/24.08 | | | | | | CLOSE: (44) is inconsistent. % 169.03/24.08 | | | | | | % 169.03/24.08 | | | | | Case 2: % 169.03/24.08 | | | | | | % 169.03/24.08 | | | | | | (45) ~ leq(n1, all_74_13) | (a_select3(q_ds1_filter, n5, n1) = % 169.03/24.08 | | | | | | all_74_0 & $i(all_74_0)) % 169.03/24.08 | | | | | | % 169.03/24.08 | | | | | | BETA: splitting (45) gives: % 169.03/24.08 | | | | | | % 169.03/24.08 | | | | | | Case 1: % 169.03/24.08 | | | | | | | % 169.03/24.08 | | | | | | | (46) ~ leq(n1, all_74_13) % 169.03/24.08 | | | | | | | % 169.03/24.08 | | | | | | | REDUCE: (2), (46) imply: % 169.03/24.08 | | | | | | | (47) ~ leq(n1, n5) % 169.03/24.08 | | | | | | | % 169.03/24.08 | | | | | | | PRED_UNIFY: (39), (47) imply: % 169.03/24.08 | | | | | | | (48) $false % 169.03/24.08 | | | | | | | % 169.03/24.08 | | | | | | | CLOSE: (48) is inconsistent. % 169.03/24.08 | | | | | | | % 169.03/24.08 | | | | | | Case 2: % 169.03/24.08 | | | | | | | % 169.03/24.08 | | | | | | | (49) a_select3(q_ds1_filter, n5, n1) = all_74_0 & $i(all_74_0) % 169.03/24.08 | | | | | | | % 169.03/24.08 | | | | | | | ALPHA: (49) implies: % 169.03/24.08 | | | | | | | (50) a_select3(q_ds1_filter, n5, n1) = all_74_0 % 169.03/24.08 | | | | | | | % 169.03/24.08 | | | | | | | GROUND_INST: instantiating (16) with all_74_1, all_74_0, n1, n5, % 169.03/24.08 | | | | | | | q_ds1_filter, simplifying with (37), (50) gives: % 169.03/24.08 | | | | | | | (51) all_74_0 = all_74_1 % 169.03/24.08 | | | | | | | % 169.03/24.08 | | | | | | | REDUCE: (6), (51) imply: % 169.03/24.08 | | | | | | | (52) $false % 169.03/24.08 | | | | | | | % 169.03/24.08 | | | | | | | CLOSE: (52) is inconsistent. % 169.03/24.08 | | | | | | | % 169.03/24.08 | | | | | | End of split % 169.03/24.08 | | | | | | % 169.03/24.08 | | | | | End of split % 169.03/24.08 | | | | | % 169.03/24.08 | | | | End of split % 169.03/24.08 | | | | % 169.03/24.08 | | | Case 2: % 169.03/24.08 | | | | % 169.03/24.08 | | | | (53) all_74_2 = n2 % 169.03/24.08 | | | | % 169.03/24.08 | | | | REDUCE: (17), (53) imply: % 169.03/24.08 | | | | (54) a_select3(q_ds1_filter, n2, n5) = all_74_0 % 169.03/24.08 | | | | % 169.03/24.08 | | | | REDUCE: (9), (53) imply: % 169.03/24.08 | | | | (55) a_select3(q_ds1_filter, n5, n2) = all_74_1 % 169.03/24.08 | | | | % 169.03/24.08 | | | | REDUCE: (19), (53) imply: % 169.03/24.08 | | | | (56) leq(n2, n5) % 169.03/24.08 | | | | % 169.03/24.08 | | | | REDUCE: (4), (53) imply: % 169.03/24.08 | | | | (57) leq(n0, n2) % 169.03/24.08 | | | | % 169.03/24.08 | | | | GROUND_INST: instantiating (15) with n2, n5, all_74_0, simplifying with % 169.03/24.08 | | | | (5), (18), (22), (54), (57) gives: % 169.03/24.08 | | | | (58) ~ leq(n5, all_74_13) | ~ leq(n2, all_74_13) | % 169.03/24.08 | | | | (a_select3(q_ds1_filter, n5, n2) = all_74_0 & $i(all_74_0)) % 169.03/24.08 | | | | % 169.03/24.08 | | | | BETA: splitting (58) gives: % 169.03/24.08 | | | | % 169.03/24.08 | | | | Case 1: % 169.03/24.08 | | | | | % 169.03/24.08 | | | | | (59) ~ leq(n5, all_74_13) % 169.03/24.08 | | | | | % 169.03/24.08 | | | | | REDUCE: (2), (59) imply: % 169.03/24.08 | | | | | (60) ~ leq(n5, n5) % 169.03/24.08 | | | | | % 169.03/24.08 | | | | | PRED_UNIFY: (12), (60) imply: % 169.03/24.08 | | | | | (61) $false % 169.03/24.08 | | | | | % 169.03/24.08 | | | | | CLOSE: (61) is inconsistent. % 169.03/24.08 | | | | | % 169.03/24.08 | | | | Case 2: % 169.03/24.08 | | | | | % 169.03/24.09 | | | | | (62) ~ leq(n2, all_74_13) | (a_select3(q_ds1_filter, n5, n2) = % 169.03/24.09 | | | | | all_74_0 & $i(all_74_0)) % 169.03/24.09 | | | | | % 169.03/24.09 | | | | | BETA: splitting (62) gives: % 169.03/24.09 | | | | | % 169.03/24.09 | | | | | Case 1: % 169.03/24.09 | | | | | | % 169.03/24.09 | | | | | | (63) ~ leq(n2, all_74_13) % 169.03/24.09 | | | | | | % 169.03/24.09 | | | | | | REDUCE: (2), (63) imply: % 169.03/24.09 | | | | | | (64) ~ leq(n2, n5) % 169.03/24.09 | | | | | | % 169.03/24.09 | | | | | | PRED_UNIFY: (56), (64) imply: % 169.03/24.09 | | | | | | (65) $false % 169.03/24.09 | | | | | | % 169.03/24.09 | | | | | | CLOSE: (65) is inconsistent. % 169.03/24.09 | | | | | | % 169.03/24.09 | | | | | Case 2: % 169.03/24.09 | | | | | | % 169.03/24.09 | | | | | | (66) a_select3(q_ds1_filter, n5, n2) = all_74_0 & $i(all_74_0) % 169.03/24.09 | | | | | | % 169.03/24.09 | | | | | | ALPHA: (66) implies: % 169.03/24.09 | | | | | | (67) a_select3(q_ds1_filter, n5, n2) = all_74_0 % 169.03/24.09 | | | | | | % 169.03/24.09 | | | | | | GROUND_INST: instantiating (16) with all_74_1, all_74_0, n2, n5, % 169.03/24.09 | | | | | | q_ds1_filter, simplifying with (55), (67) gives: % 169.03/24.09 | | | | | | (68) all_74_0 = all_74_1 % 169.03/24.09 | | | | | | % 169.03/24.09 | | | | | | REDUCE: (6), (68) imply: % 169.03/24.09 | | | | | | (69) $false % 169.03/24.09 | | | | | | % 169.03/24.09 | | | | | | CLOSE: (69) is inconsistent. % 169.03/24.09 | | | | | | % 169.03/24.09 | | | | | End of split % 169.03/24.09 | | | | | % 169.03/24.09 | | | | End of split % 169.03/24.09 | | | | % 169.03/24.09 | | | End of split % 169.03/24.09 | | | % 169.03/24.09 | | Case 2: % 169.03/24.09 | | | % 169.03/24.09 | | | (70) all_74_2 = n3 % 169.03/24.09 | | | % 169.03/24.09 | | | REDUCE: (17), (70) imply: % 169.03/24.09 | | | (71) a_select3(q_ds1_filter, n3, n5) = all_74_0 % 169.03/24.09 | | | % 169.03/24.09 | | | REDUCE: (9), (70) imply: % 169.03/24.09 | | | (72) a_select3(q_ds1_filter, n5, n3) = all_74_1 % 169.03/24.09 | | | % 169.03/24.09 | | | REDUCE: (19), (70) imply: % 169.03/24.09 | | | (73) leq(n3, n5) % 169.03/24.09 | | | % 169.03/24.09 | | | REDUCE: (4), (70) imply: % 169.03/24.09 | | | (74) leq(n0, n3) % 169.03/24.09 | | | % 169.03/24.09 | | | GROUND_INST: instantiating (15) with n3, n5, all_74_0, simplifying with % 169.03/24.09 | | | (18), (21), (22), (71), (74) gives: % 169.03/24.09 | | | (75) ~ leq(n5, all_74_13) | ~ leq(n3, all_74_13) | % 169.03/24.09 | | | (a_select3(q_ds1_filter, n5, n3) = all_74_0 & $i(all_74_0)) % 169.03/24.09 | | | % 169.03/24.09 | | | BETA: splitting (75) gives: % 169.03/24.09 | | | % 169.03/24.09 | | | Case 1: % 169.03/24.09 | | | | % 169.03/24.09 | | | | (76) ~ leq(n5, all_74_13) % 169.03/24.09 | | | | % 169.03/24.09 | | | | REDUCE: (2), (76) imply: % 169.03/24.09 | | | | (77) ~ leq(n5, n5) % 169.03/24.09 | | | | % 169.03/24.09 | | | | PRED_UNIFY: (12), (77) imply: % 169.03/24.09 | | | | (78) $false % 169.03/24.09 | | | | % 169.03/24.09 | | | | CLOSE: (78) is inconsistent. % 169.03/24.09 | | | | % 169.03/24.09 | | | Case 2: % 169.03/24.09 | | | | % 169.03/24.09 | | | | (79) ~ leq(n3, all_74_13) | (a_select3(q_ds1_filter, n5, n3) = % 169.03/24.09 | | | | all_74_0 & $i(all_74_0)) % 169.03/24.09 | | | | % 169.03/24.09 | | | | BETA: splitting (79) gives: % 169.03/24.09 | | | | % 169.03/24.09 | | | | Case 1: % 169.03/24.09 | | | | | % 169.03/24.09 | | | | | (80) ~ leq(n3, all_74_13) % 169.03/24.09 | | | | | % 169.03/24.09 | | | | | REDUCE: (2), (80) imply: % 169.03/24.09 | | | | | (81) ~ leq(n3, n5) % 169.03/24.09 | | | | | % 169.03/24.09 | | | | | PRED_UNIFY: (73), (81) imply: % 169.03/24.09 | | | | | (82) $false % 169.03/24.09 | | | | | % 169.03/24.09 | | | | | CLOSE: (82) is inconsistent. % 169.03/24.09 | | | | | % 169.03/24.09 | | | | Case 2: % 169.03/24.09 | | | | | % 169.03/24.09 | | | | | (83) a_select3(q_ds1_filter, n5, n3) = all_74_0 & $i(all_74_0) % 169.03/24.09 | | | | | % 169.03/24.09 | | | | | ALPHA: (83) implies: % 169.03/24.09 | | | | | (84) a_select3(q_ds1_filter, n5, n3) = all_74_0 % 169.03/24.09 | | | | | % 169.03/24.09 | | | | | GROUND_INST: instantiating (16) with all_74_1, all_74_0, n3, n5, % 169.03/24.09 | | | | | q_ds1_filter, simplifying with (72), (84) gives: % 169.03/24.09 | | | | | (85) all_74_0 = all_74_1 % 169.03/24.09 | | | | | % 169.03/24.09 | | | | | REDUCE: (6), (85) imply: % 169.03/24.09 | | | | | (86) $false % 169.03/24.09 | | | | | % 169.03/24.09 | | | | | CLOSE: (86) is inconsistent. % 169.03/24.09 | | | | | % 169.03/24.09 | | | | End of split % 169.03/24.09 | | | | % 169.03/24.09 | | | End of split % 169.03/24.09 | | | % 169.03/24.09 | | End of split % 169.03/24.09 | | % 169.03/24.09 | Case 2: % 169.03/24.09 | | % 169.03/24.09 | | (87) all_74_2 = n4 % 169.03/24.09 | | % 169.03/24.09 | | REDUCE: (17), (87) imply: % 169.03/24.09 | | (88) a_select3(q_ds1_filter, n4, n5) = all_74_0 % 169.03/24.09 | | % 169.03/24.09 | | REDUCE: (9), (87) imply: % 169.03/24.09 | | (89) a_select3(q_ds1_filter, n5, n4) = all_74_1 % 169.03/24.09 | | % 169.03/24.09 | | REDUCE: (19), (87) imply: % 169.03/24.09 | | (90) leq(n4, n5) % 169.03/24.09 | | % 169.03/24.09 | | REDUCE: (4), (87) imply: % 169.03/24.09 | | (91) leq(n0, n4) % 169.03/24.09 | | % 169.03/24.09 | | GROUND_INST: instantiating (15) with n4, n5, all_74_0, simplifying with % 169.03/24.09 | | (14), (18), (22), (88), (91) gives: % 169.03/24.09 | | (92) ~ leq(n5, all_74_13) | ~ leq(n4, all_74_13) | % 169.03/24.09 | | (a_select3(q_ds1_filter, n5, n4) = all_74_0 & $i(all_74_0)) % 169.03/24.09 | | % 169.03/24.09 | | BETA: splitting (92) gives: % 169.03/24.09 | | % 169.03/24.09 | | Case 1: % 169.03/24.09 | | | % 169.03/24.09 | | | (93) ~ leq(n5, all_74_13) % 169.03/24.09 | | | % 169.03/24.09 | | | REDUCE: (2), (93) imply: % 169.03/24.09 | | | (94) ~ leq(n5, n5) % 169.03/24.09 | | | % 169.03/24.09 | | | PRED_UNIFY: (12), (94) imply: % 169.03/24.09 | | | (95) $false % 169.03/24.09 | | | % 169.03/24.09 | | | CLOSE: (95) is inconsistent. % 169.03/24.09 | | | % 169.03/24.09 | | Case 2: % 169.03/24.09 | | | % 169.03/24.09 | | | (96) ~ leq(n4, all_74_13) | (a_select3(q_ds1_filter, n5, n4) = % 169.03/24.09 | | | all_74_0 & $i(all_74_0)) % 169.03/24.09 | | | % 169.03/24.09 | | | BETA: splitting (96) gives: % 169.03/24.09 | | | % 169.03/24.09 | | | Case 1: % 169.03/24.09 | | | | % 169.03/24.09 | | | | (97) ~ leq(n4, all_74_13) % 169.03/24.09 | | | | % 169.03/24.09 | | | | REDUCE: (2), (97) imply: % 169.03/24.09 | | | | (98) ~ leq(n4, n5) % 169.03/24.09 | | | | % 169.03/24.09 | | | | PRED_UNIFY: (90), (98) imply: % 169.03/24.09 | | | | (99) $false % 169.03/24.09 | | | | % 169.03/24.09 | | | | CLOSE: (99) is inconsistent. % 169.03/24.09 | | | | % 169.03/24.09 | | | Case 2: % 169.03/24.09 | | | | % 169.03/24.09 | | | | (100) a_select3(q_ds1_filter, n5, n4) = all_74_0 & $i(all_74_0) % 169.03/24.09 | | | | % 169.03/24.09 | | | | ALPHA: (100) implies: % 169.03/24.09 | | | | (101) a_select3(q_ds1_filter, n5, n4) = all_74_0 % 169.03/24.09 | | | | % 169.03/24.09 | | | | REF_CLOSE: (6), (16), (89), (101) are inconsistent by sub-proof #27. % 169.03/24.09 | | | | % 169.03/24.09 | | | End of split % 169.03/24.09 | | | % 169.03/24.09 | | End of split % 169.03/24.09 | | % 169.03/24.09 | End of split % 169.03/24.09 | % 169.03/24.09 End of proof % 169.03/24.09 % 169.03/24.09 Sub-proof #26 shows that the following formulas are inconsistent: % 169.03/24.09 ---------------------------------------------------------------- % 169.03/24.09 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (pred(v1) = v2) | ~ $i(v1) % 169.03/24.09 | ~ $i(v0) | ~ gt(v1, v0) | leq(v0, v2)) % 169.03/24.09 (2) leq(all_74_3, n5) % 169.03/24.09 (3) all_74_3 = n4 | gt(n4, all_74_3) % 169.03/24.09 (4) all_74_13 = n5 % 169.03/24.09 (5) $i(all_74_3) % 169.03/24.09 (6) ~ (all_74_3 = n0) % 169.03/24.09 (7) $i(n2) % 169.03/24.09 (8) ~ (all_74_0 = all_74_1) % 169.03/24.09 (9) pred(n4) = n3 % 169.03/24.09 (10) ! [v0: $i] : (v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0, n1) | ~ % 169.03/24.09 leq(n0, v0)) % 169.03/24.09 (11) leq(n0, all_74_3) % 169.03/24.09 (12) leq(n5, n5) % 169.03/24.09 (13) pred(n3) = n2 % 169.03/24.09 (14) $i(n4) % 169.03/24.09 (15) a_select3(q_ds1_filter, n5, all_74_3) = all_74_0 % 169.03/24.09 (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (a_select3(q_ds1_filter, % 169.03/24.09 v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ leq(v1, all_74_13) | ~ % 169.03/24.09 leq(v0, all_74_13) | ~ leq(n0, v1) | ~ leq(n0, v0) | % 169.03/24.09 (a_select3(q_ds1_filter, v1, v0) = v2 & $i(v2))) % 169.03/24.09 (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 169.03/24.09 (v1 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 169.03/24.09 v0)) % 169.03/24.09 (18) leq(n0, n5) % 169.03/24.09 (19) pred(n2) = n1 % 169.03/24.09 (20) $i(n3) % 169.03/24.09 (21) $i(n5) % 169.03/24.09 (22) a_select3(q_ds1_filter, all_74_3, n5) = all_74_1 % 169.03/24.09 (23) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ % 169.03/24.09 leq(v0, v1) | gt(v1, v0)) % 169.03/24.09 % 169.03/24.09 Begin of proof % 169.03/24.09 | % 169.03/24.09 | BETA: splitting (3) gives: % 169.03/24.09 | % 169.03/24.09 | Case 1: % 169.03/24.09 | | % 169.03/24.09 | | (24) gt(n4, all_74_3) % 169.03/24.09 | | % 169.03/24.09 | | GROUND_INST: instantiating (1) with all_74_3, n4, n3, simplifying with (5), % 169.03/24.09 | | (9), (14), (24) gives: % 169.03/24.09 | | (25) leq(all_74_3, n3) % 169.03/24.09 | | % 169.03/24.09 | | GROUND_INST: instantiating (23) with all_74_3, n3, simplifying with (5), % 169.03/24.09 | | (20), (25) gives: % 169.03/24.09 | | (26) all_74_3 = n3 | gt(n3, all_74_3) % 169.03/24.09 | | % 169.03/24.09 | | BETA: splitting (26) gives: % 169.03/24.09 | | % 169.03/24.09 | | Case 1: % 169.03/24.09 | | | % 169.03/24.09 | | | (27) gt(n3, all_74_3) % 169.03/24.09 | | | % 169.03/24.09 | | | GROUND_INST: instantiating (1) with all_74_3, n3, n2, simplifying with % 169.03/24.09 | | | (5), (13), (20), (27) gives: % 169.03/24.09 | | | (28) leq(all_74_3, n2) % 169.03/24.09 | | | % 169.03/24.09 | | | GROUND_INST: instantiating (23) with all_74_3, n2, simplifying with (5), % 169.03/24.09 | | | (7), (28) gives: % 169.03/24.09 | | | (29) all_74_3 = n2 | gt(n2, all_74_3) % 169.03/24.09 | | | % 169.03/24.09 | | | BETA: splitting (29) gives: % 169.03/24.09 | | | % 169.03/24.09 | | | Case 1: % 169.03/24.09 | | | | % 169.03/24.09 | | | | (30) gt(n2, all_74_3) % 169.03/24.09 | | | | % 169.03/24.09 | | | | GROUND_INST: instantiating (1) with all_74_3, n2, n1, simplifying with % 169.03/24.09 | | | | (5), (7), (19), (30) gives: % 169.03/24.09 | | | | (31) leq(all_74_3, n1) % 169.03/24.09 | | | | % 169.03/24.09 | | | | GROUND_INST: instantiating (10) with all_74_3, simplifying with (5), % 169.03/24.09 | | | | (11), (31) gives: % 169.03/24.09 | | | | (32) all_74_3 = n1 | all_74_3 = n0 % 169.03/24.09 | | | | % 169.03/24.09 | | | | BETA: splitting (32) gives: % 169.03/24.09 | | | | % 169.03/24.09 | | | | Case 1: % 169.03/24.09 | | | | | % 169.03/24.09 | | | | | (33) all_74_3 = n0 % 169.03/24.09 | | | | | % 169.03/24.09 | | | | | REDUCE: (6), (33) imply: % 169.03/24.09 | | | | | (34) $false % 169.03/24.09 | | | | | % 169.03/24.09 | | | | | CLOSE: (34) is inconsistent. % 169.03/24.09 | | | | | % 169.03/24.09 | | | | Case 2: % 169.03/24.09 | | | | | % 169.03/24.09 | | | | | (35) all_74_3 = n1 % 169.03/24.09 | | | | | % 169.03/24.09 | | | | | REDUCE: (22), (35) imply: % 169.03/24.09 | | | | | (36) a_select3(q_ds1_filter, n1, n5) = all_74_1 % 169.03/24.09 | | | | | % 169.03/24.09 | | | | | REDUCE: (15), (35) imply: % 169.03/24.09 | | | | | (37) a_select3(q_ds1_filter, n5, n1) = all_74_0 % 169.03/24.09 | | | | | % 169.03/24.09 | | | | | REDUCE: (5), (35) imply: % 169.03/24.09 | | | | | (38) $i(n1) % 169.03/24.09 | | | | | % 169.03/24.09 | | | | | REDUCE: (2), (35) imply: % 169.03/24.09 | | | | | (39) leq(n1, n5) % 169.03/24.09 | | | | | % 169.03/24.09 | | | | | REDUCE: (11), (35) imply: % 169.03/24.09 | | | | | (40) leq(n0, n1) % 169.03/24.09 | | | | | % 169.03/24.09 | | | | | GROUND_INST: instantiating (16) with n1, n5, all_74_1, simplifying % 169.03/24.09 | | | | | with (18), (21), (36), (38), (40) gives: % 169.03/24.09 | | | | | (41) ~ leq(n5, all_74_13) | ~ leq(n1, all_74_13) | % 169.03/24.09 | | | | | (a_select3(q_ds1_filter, n5, n1) = all_74_1 & $i(all_74_1)) % 169.03/24.09 | | | | | % 169.03/24.09 | | | | | BETA: splitting (41) gives: % 169.03/24.09 | | | | | % 169.03/24.09 | | | | | Case 1: % 169.03/24.09 | | | | | | % 169.03/24.09 | | | | | | (42) ~ leq(n5, all_74_13) % 169.03/24.09 | | | | | | % 169.03/24.09 | | | | | | REDUCE: (4), (42) imply: % 169.03/24.09 | | | | | | (43) ~ leq(n5, n5) % 169.03/24.09 | | | | | | % 169.03/24.09 | | | | | | PRED_UNIFY: (12), (43) imply: % 169.03/24.09 | | | | | | (44) $false % 169.03/24.09 | | | | | | % 169.03/24.09 | | | | | | CLOSE: (44) is inconsistent. % 169.03/24.09 | | | | | | % 169.03/24.09 | | | | | Case 2: % 169.03/24.09 | | | | | | % 169.03/24.09 | | | | | | (45) ~ leq(n1, all_74_13) | (a_select3(q_ds1_filter, n5, n1) = % 169.03/24.09 | | | | | | all_74_1 & $i(all_74_1)) % 169.03/24.09 | | | | | | % 169.03/24.09 | | | | | | BETA: splitting (45) gives: % 169.03/24.09 | | | | | | % 169.03/24.09 | | | | | | Case 1: % 169.03/24.09 | | | | | | | % 169.03/24.09 | | | | | | | (46) ~ leq(n1, all_74_13) % 169.03/24.09 | | | | | | | % 169.03/24.09 | | | | | | | REDUCE: (4), (46) imply: % 169.03/24.09 | | | | | | | (47) ~ leq(n1, n5) % 169.03/24.09 | | | | | | | % 169.03/24.09 | | | | | | | PRED_UNIFY: (39), (47) imply: % 169.03/24.09 | | | | | | | (48) $false % 169.03/24.09 | | | | | | | % 169.03/24.09 | | | | | | | CLOSE: (48) is inconsistent. % 169.03/24.09 | | | | | | | % 169.03/24.09 | | | | | | Case 2: % 169.03/24.09 | | | | | | | % 169.03/24.09 | | | | | | | (49) a_select3(q_ds1_filter, n5, n1) = all_74_1 & $i(all_74_1) % 169.03/24.09 | | | | | | | % 169.03/24.09 | | | | | | | ALPHA: (49) implies: % 169.03/24.09 | | | | | | | (50) a_select3(q_ds1_filter, n5, n1) = all_74_1 % 169.03/24.09 | | | | | | | % 169.03/24.09 | | | | | | | GROUND_INST: instantiating (17) with all_74_1, all_74_0, n1, n5, % 169.03/24.09 | | | | | | | q_ds1_filter, simplifying with (37), (50) gives: % 169.03/24.09 | | | | | | | (51) all_74_0 = all_74_1 % 169.03/24.09 | | | | | | | % 169.03/24.09 | | | | | | | REDUCE: (8), (51) imply: % 169.03/24.09 | | | | | | | (52) $false % 169.03/24.09 | | | | | | | % 169.03/24.09 | | | | | | | CLOSE: (52) is inconsistent. % 169.03/24.09 | | | | | | | % 169.03/24.09 | | | | | | End of split % 169.03/24.09 | | | | | | % 169.03/24.09 | | | | | End of split % 169.03/24.09 | | | | | % 169.03/24.09 | | | | End of split % 169.03/24.09 | | | | % 169.03/24.09 | | | Case 2: % 169.03/24.09 | | | | % 169.03/24.09 | | | | (53) all_74_3 = n2 % 169.03/24.09 | | | | % 169.03/24.09 | | | | REDUCE: (22), (53) imply: % 169.03/24.09 | | | | (54) a_select3(q_ds1_filter, n2, n5) = all_74_1 % 169.03/24.09 | | | | % 169.03/24.09 | | | | REDUCE: (15), (53) imply: % 169.03/24.09 | | | | (55) a_select3(q_ds1_filter, n5, n2) = all_74_0 % 169.03/24.09 | | | | % 169.03/24.09 | | | | REDUCE: (2), (53) imply: % 169.03/24.09 | | | | (56) leq(n2, n5) % 169.03/24.09 | | | | % 169.03/24.09 | | | | REDUCE: (11), (53) imply: % 169.03/24.09 | | | | (57) leq(n0, n2) % 169.03/24.09 | | | | % 169.03/24.09 | | | | GROUND_INST: instantiating (16) with n2, n5, all_74_1, simplifying with % 169.03/24.09 | | | | (7), (18), (21), (54), (57) gives: % 169.03/24.09 | | | | (58) ~ leq(n5, all_74_13) | ~ leq(n2, all_74_13) | % 169.03/24.09 | | | | (a_select3(q_ds1_filter, n5, n2) = all_74_1 & $i(all_74_1)) % 169.03/24.09 | | | | % 169.03/24.09 | | | | BETA: splitting (58) gives: % 169.03/24.09 | | | | % 169.03/24.09 | | | | Case 1: % 169.03/24.09 | | | | | % 169.03/24.09 | | | | | (59) ~ leq(n5, all_74_13) % 169.03/24.09 | | | | | % 169.03/24.09 | | | | | REDUCE: (4), (59) imply: % 169.03/24.09 | | | | | (60) ~ leq(n5, n5) % 169.03/24.09 | | | | | % 169.03/24.09 | | | | | PRED_UNIFY: (12), (60) imply: % 169.03/24.09 | | | | | (61) $false % 169.03/24.09 | | | | | % 169.03/24.09 | | | | | CLOSE: (61) is inconsistent. % 169.03/24.09 | | | | | % 169.03/24.09 | | | | Case 2: % 169.03/24.09 | | | | | % 169.03/24.09 | | | | | (62) ~ leq(n2, all_74_13) | (a_select3(q_ds1_filter, n5, n2) = % 169.03/24.09 | | | | | all_74_1 & $i(all_74_1)) % 169.03/24.09 | | | | | % 169.03/24.09 | | | | | BETA: splitting (62) gives: % 169.03/24.09 | | | | | % 169.03/24.09 | | | | | Case 1: % 169.03/24.09 | | | | | | % 169.03/24.09 | | | | | | (63) ~ leq(n2, all_74_13) % 169.03/24.09 | | | | | | % 169.03/24.09 | | | | | | REDUCE: (4), (63) imply: % 169.03/24.09 | | | | | | (64) ~ leq(n2, n5) % 169.03/24.09 | | | | | | % 169.03/24.09 | | | | | | PRED_UNIFY: (56), (64) imply: % 169.03/24.09 | | | | | | (65) $false % 169.03/24.09 | | | | | | % 169.03/24.09 | | | | | | CLOSE: (65) is inconsistent. % 169.03/24.09 | | | | | | % 169.03/24.09 | | | | | Case 2: % 169.03/24.09 | | | | | | % 169.03/24.09 | | | | | | (66) a_select3(q_ds1_filter, n5, n2) = all_74_1 & $i(all_74_1) % 169.03/24.09 | | | | | | % 169.03/24.09 | | | | | | ALPHA: (66) implies: % 169.03/24.09 | | | | | | (67) a_select3(q_ds1_filter, n5, n2) = all_74_1 % 169.03/24.09 | | | | | | % 169.03/24.09 | | | | | | GROUND_INST: instantiating (17) with all_74_1, all_74_0, n2, n5, % 169.03/24.09 | | | | | | q_ds1_filter, simplifying with (55), (67) gives: % 169.03/24.09 | | | | | | (68) all_74_0 = all_74_1 % 169.03/24.09 | | | | | | % 169.03/24.09 | | | | | | REDUCE: (8), (68) imply: % 169.03/24.09 | | | | | | (69) $false % 169.03/24.09 | | | | | | % 169.03/24.09 | | | | | | CLOSE: (69) is inconsistent. % 169.03/24.09 | | | | | | % 169.03/24.09 | | | | | End of split % 169.03/24.09 | | | | | % 169.03/24.09 | | | | End of split % 169.03/24.09 | | | | % 169.03/24.09 | | | End of split % 169.03/24.09 | | | % 169.03/24.09 | | Case 2: % 169.03/24.09 | | | % 169.03/24.09 | | | (70) all_74_3 = n3 % 169.03/24.09 | | | % 169.03/24.09 | | | REDUCE: (22), (70) imply: % 169.03/24.09 | | | (71) a_select3(q_ds1_filter, n3, n5) = all_74_1 % 169.03/24.09 | | | % 169.03/24.09 | | | REDUCE: (15), (70) imply: % 169.03/24.09 | | | (72) a_select3(q_ds1_filter, n5, n3) = all_74_0 % 169.03/24.09 | | | % 169.03/24.09 | | | REDUCE: (2), (70) imply: % 169.03/24.09 | | | (73) leq(n3, n5) % 169.03/24.09 | | | % 169.03/24.09 | | | REDUCE: (11), (70) imply: % 169.03/24.09 | | | (74) leq(n0, n3) % 169.03/24.09 | | | % 169.03/24.09 | | | GROUND_INST: instantiating (16) with n3, n5, all_74_1, simplifying with % 169.03/24.09 | | | (18), (20), (21), (71), (74) gives: % 169.03/24.09 | | | (75) ~ leq(n5, all_74_13) | ~ leq(n3, all_74_13) | % 169.03/24.09 | | | (a_select3(q_ds1_filter, n5, n3) = all_74_1 & $i(all_74_1)) % 169.03/24.09 | | | % 169.03/24.09 | | | BETA: splitting (75) gives: % 169.03/24.09 | | | % 169.03/24.09 | | | Case 1: % 169.03/24.09 | | | | % 169.03/24.09 | | | | (76) ~ leq(n5, all_74_13) % 169.03/24.09 | | | | % 169.03/24.09 | | | | REDUCE: (4), (76) imply: % 169.03/24.09 | | | | (77) ~ leq(n5, n5) % 169.03/24.09 | | | | % 169.03/24.09 | | | | PRED_UNIFY: (12), (77) imply: % 169.03/24.09 | | | | (78) $false % 169.03/24.09 | | | | % 169.03/24.09 | | | | CLOSE: (78) is inconsistent. % 169.03/24.09 | | | | % 169.03/24.09 | | | Case 2: % 169.03/24.09 | | | | % 169.03/24.09 | | | | (79) ~ leq(n3, all_74_13) | (a_select3(q_ds1_filter, n5, n3) = % 169.03/24.09 | | | | all_74_1 & $i(all_74_1)) % 169.03/24.09 | | | | % 169.03/24.09 | | | | BETA: splitting (79) gives: % 169.03/24.09 | | | | % 169.03/24.09 | | | | Case 1: % 169.03/24.10 | | | | | % 169.03/24.10 | | | | | (80) ~ leq(n3, all_74_13) % 169.03/24.10 | | | | | % 169.03/24.10 | | | | | REDUCE: (4), (80) imply: % 169.03/24.10 | | | | | (81) ~ leq(n3, n5) % 169.03/24.10 | | | | | % 169.03/24.10 | | | | | PRED_UNIFY: (73), (81) imply: % 169.03/24.10 | | | | | (82) $false % 169.03/24.10 | | | | | % 169.03/24.10 | | | | | CLOSE: (82) is inconsistent. % 169.03/24.10 | | | | | % 169.03/24.10 | | | | Case 2: % 169.03/24.10 | | | | | % 169.03/24.10 | | | | | (83) a_select3(q_ds1_filter, n5, n3) = all_74_1 & $i(all_74_1) % 169.03/24.10 | | | | | % 169.03/24.10 | | | | | ALPHA: (83) implies: % 169.03/24.10 | | | | | (84) a_select3(q_ds1_filter, n5, n3) = all_74_1 % 169.03/24.10 | | | | | % 169.03/24.10 | | | | | GROUND_INST: instantiating (17) with all_74_1, all_74_0, n3, n5, % 169.03/24.10 | | | | | q_ds1_filter, simplifying with (72), (84) gives: % 169.03/24.10 | | | | | (85) all_74_0 = all_74_1 % 169.03/24.10 | | | | | % 169.03/24.10 | | | | | REDUCE: (8), (85) imply: % 169.03/24.10 | | | | | (86) $false % 169.03/24.10 | | | | | % 169.03/24.10 | | | | | CLOSE: (86) is inconsistent. % 169.03/24.10 | | | | | % 169.03/24.10 | | | | End of split % 169.03/24.10 | | | | % 169.03/24.10 | | | End of split % 169.03/24.10 | | | % 169.03/24.10 | | End of split % 169.03/24.10 | | % 169.03/24.10 | Case 2: % 169.03/24.10 | | % 169.03/24.10 | | (87) all_74_3 = n4 % 169.03/24.10 | | % 169.03/24.10 | | REDUCE: (22), (87) imply: % 169.03/24.10 | | (88) a_select3(q_ds1_filter, n4, n5) = all_74_1 % 169.03/24.10 | | % 169.03/24.10 | | REDUCE: (15), (87) imply: % 169.03/24.10 | | (89) a_select3(q_ds1_filter, n5, n4) = all_74_0 % 169.03/24.10 | | % 169.03/24.10 | | REDUCE: (2), (87) imply: % 169.03/24.10 | | (90) leq(n4, n5) % 169.03/24.10 | | % 169.03/24.10 | | REDUCE: (11), (87) imply: % 169.03/24.10 | | (91) leq(n0, n4) % 169.03/24.10 | | % 169.03/24.10 | | GROUND_INST: instantiating (16) with n4, n5, all_74_1, simplifying with % 169.03/24.10 | | (14), (18), (21), (88), (91) gives: % 169.03/24.10 | | (92) ~ leq(n5, all_74_13) | ~ leq(n4, all_74_13) | % 169.03/24.10 | | (a_select3(q_ds1_filter, n5, n4) = all_74_1 & $i(all_74_1)) % 169.03/24.10 | | % 169.03/24.10 | | BETA: splitting (92) gives: % 169.03/24.10 | | % 169.03/24.10 | | Case 1: % 169.03/24.10 | | | % 169.03/24.10 | | | (93) ~ leq(n5, all_74_13) % 169.03/24.10 | | | % 169.03/24.10 | | | REDUCE: (4), (93) imply: % 169.03/24.10 | | | (94) ~ leq(n5, n5) % 169.03/24.10 | | | % 169.03/24.10 | | | PRED_UNIFY: (12), (94) imply: % 169.03/24.10 | | | (95) $false % 169.03/24.10 | | | % 169.03/24.10 | | | CLOSE: (95) is inconsistent. % 169.03/24.10 | | | % 169.03/24.10 | | Case 2: % 169.03/24.10 | | | % 169.03/24.10 | | | (96) ~ leq(n4, all_74_13) | (a_select3(q_ds1_filter, n5, n4) = % 169.03/24.10 | | | all_74_1 & $i(all_74_1)) % 169.03/24.10 | | | % 169.03/24.10 | | | BETA: splitting (96) gives: % 169.03/24.10 | | | % 169.03/24.10 | | | Case 1: % 169.03/24.10 | | | | % 169.03/24.10 | | | | (97) ~ leq(n4, all_74_13) % 169.03/24.10 | | | | % 169.03/24.10 | | | | REDUCE: (4), (97) imply: % 169.03/24.10 | | | | (98) ~ leq(n4, n5) % 169.03/24.10 | | | | % 169.03/24.10 | | | | PRED_UNIFY: (90), (98) imply: % 169.03/24.10 | | | | (99) $false % 169.03/24.10 | | | | % 169.03/24.10 | | | | CLOSE: (99) is inconsistent. % 169.03/24.10 | | | | % 169.03/24.10 | | | Case 2: % 169.03/24.10 | | | | % 169.03/24.10 | | | | (100) a_select3(q_ds1_filter, n5, n4) = all_74_1 & $i(all_74_1) % 169.03/24.10 | | | | % 169.03/24.10 | | | | ALPHA: (100) implies: % 169.03/24.10 | | | | (101) a_select3(q_ds1_filter, n5, n4) = all_74_1 % 169.03/24.10 | | | | % 169.03/24.10 | | | | REF_CLOSE: (8), (17), (89), (101) are inconsistent by sub-proof #27. % 169.03/24.10 | | | | % 169.03/24.10 | | | End of split % 169.03/24.10 | | | % 169.03/24.10 | | End of split % 169.03/24.10 | | % 169.03/24.10 | End of split % 169.03/24.10 | % 169.03/24.10 End of proof % 169.03/24.10 % 169.03/24.10 Sub-proof #27 shows that the following formulas are inconsistent: % 169.03/24.10 ---------------------------------------------------------------- % 169.03/24.10 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 169.03/24.10 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 169.03/24.10 v0)) % 169.03/24.10 (2) a_select3(q_ds1_filter, n5, n4) = all_74_0 % 169.03/24.10 (3) a_select3(q_ds1_filter, n5, n4) = all_74_1 % 169.03/24.10 (4) ~ (all_74_0 = all_74_1) % 169.03/24.10 % 169.03/24.10 Begin of proof % 169.03/24.10 | % 169.03/24.10 | GROUND_INST: instantiating (1) with all_74_1, all_74_0, n4, n5, q_ds1_filter, % 169.03/24.10 | simplifying with (2), (3) gives: % 169.03/24.10 | (5) all_74_0 = all_74_1 % 169.03/24.10 | % 169.03/24.10 | REDUCE: (4), (5) imply: % 169.03/24.10 | (6) $false % 169.03/24.10 | % 169.03/24.10 | CLOSE: (6) is inconsistent. % 169.03/24.10 | % 169.03/24.10 End of proof % 169.03/24.10 % 169.03/24.10 Sub-proof #28 shows that the following formulas are inconsistent: % 169.03/24.10 ---------------------------------------------------------------- % 169.03/24.10 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (pred(v1) = v2) | ~ $i(v1) % 169.03/24.10 | ~ $i(v0) | ~ gt(v1, v0) | leq(v0, v2)) % 169.03/24.10 (2) leq(all_74_3, n5) % 169.03/24.10 (3) all_74_3 = n4 | gt(n4, all_74_3) % 169.03/24.10 (4) all_74_13 = n5 % 169.03/24.10 (5) $i(all_74_3) % 169.03/24.10 (6) ~ (all_74_3 = n0) % 169.03/24.10 (7) ~ (all_74_2 = n0) % 169.03/24.10 (8) a_select3(q_ds1_filter, all_74_2, all_74_3) = all_74_0 % 169.03/24.10 (9) leq(n0, all_74_2) % 169.03/24.10 (10) $i(n2) % 169.03/24.10 (11) ~ (all_74_0 = all_74_1) % 169.03/24.10 (12) all_74_2 = n4 | gt(n4, all_74_2) % 169.03/24.10 (13) pred(n4) = n3 % 169.03/24.10 (14) ! [v0: $i] : (v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0, n1) | ~ % 169.03/24.10 leq(n0, v0)) % 169.03/24.10 (15) $i(all_74_2) % 169.03/24.10 (16) leq(n0, all_74_3) % 169.03/24.10 (17) pred(n3) = n2 % 169.03/24.10 (18) $i(n4) % 169.03/24.10 (19) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (a_select3(q_ds1_filter, % 169.03/24.10 v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ leq(v1, all_74_13) | ~ % 169.03/24.10 leq(v0, all_74_13) | ~ leq(n0, v1) | ~ leq(n0, v0) | % 169.03/24.10 (a_select3(q_ds1_filter, v1, v0) = v2 & $i(v2))) % 169.03/24.10 (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 169.03/24.10 (v1 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 169.03/24.10 v0)) % 169.03/24.10 (21) leq(all_74_2, n5) % 169.03/24.10 (22) pred(n2) = n1 % 169.03/24.10 (23) $i(n3) % 169.03/24.10 (24) a_select3(q_ds1_filter, all_74_3, all_74_2) = all_74_1 % 169.03/24.10 (25) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ % 169.03/24.10 leq(v0, v1) | gt(v1, v0)) % 169.03/24.10 % 169.03/24.10 Begin of proof % 169.03/24.10 | % 169.03/24.10 | BETA: splitting (3) gives: % 169.03/24.10 | % 169.03/24.10 | Case 1: % 169.03/24.10 | | % 169.03/24.10 | | (26) gt(n4, all_74_3) % 169.03/24.10 | | % 169.03/24.10 | | GROUND_INST: instantiating (1) with all_74_3, n4, n3, simplifying with (5), % 169.03/24.10 | | (13), (18), (26) gives: % 169.03/24.10 | | (27) leq(all_74_3, n3) % 169.03/24.10 | | % 169.03/24.10 | | GROUND_INST: instantiating (25) with all_74_3, n3, simplifying with (5), % 169.03/24.10 | | (23), (27) gives: % 169.03/24.10 | | (28) all_74_3 = n3 | gt(n3, all_74_3) % 169.03/24.10 | | % 169.03/24.10 | | BETA: splitting (12) gives: % 169.03/24.10 | | % 169.03/24.10 | | Case 1: % 169.03/24.10 | | | % 169.03/24.10 | | | (29) gt(n4, all_74_2) % 169.03/24.10 | | | % 169.03/24.10 | | | GROUND_INST: instantiating (1) with all_74_2, n4, n3, simplifying with % 169.03/24.10 | | | (13), (15), (18), (29) gives: % 169.03/24.10 | | | (30) leq(all_74_2, n3) % 169.03/24.10 | | | % 169.03/24.10 | | | GROUND_INST: instantiating (25) with all_74_2, n3, simplifying with (15), % 169.03/24.10 | | | (23), (30) gives: % 169.03/24.10 | | | (31) all_74_2 = n3 | gt(n3, all_74_2) % 169.03/24.10 | | | % 169.03/24.10 | | | BETA: splitting (28) gives: % 169.03/24.10 | | | % 169.03/24.10 | | | Case 1: % 169.03/24.10 | | | | % 169.03/24.10 | | | | (32) gt(n3, all_74_3) % 169.03/24.10 | | | | % 169.03/24.10 | | | | GROUND_INST: instantiating (1) with all_74_3, n3, n2, simplifying with % 169.03/24.10 | | | | (5), (17), (23), (32) gives: % 169.03/24.10 | | | | (33) leq(all_74_3, n2) % 169.03/24.10 | | | | % 169.03/24.10 | | | | GROUND_INST: instantiating (25) with all_74_3, n2, simplifying with (5), % 169.03/24.10 | | | | (10), (33) gives: % 169.03/24.10 | | | | (34) all_74_3 = n2 | gt(n2, all_74_3) % 169.03/24.10 | | | | % 169.03/24.10 | | | | BETA: splitting (31) gives: % 169.03/24.10 | | | | % 169.03/24.10 | | | | Case 1: % 169.03/24.10 | | | | | % 169.03/24.10 | | | | | (35) gt(n3, all_74_2) % 169.03/24.10 | | | | | % 169.03/24.10 | | | | | GROUND_INST: instantiating (1) with all_74_2, n3, n2, simplifying with % 169.03/24.10 | | | | | (15), (17), (23), (35) gives: % 169.03/24.10 | | | | | (36) leq(all_74_2, n2) % 169.03/24.10 | | | | | % 169.03/24.10 | | | | | GROUND_INST: instantiating (25) with all_74_2, n2, simplifying with % 169.03/24.10 | | | | | (10), (15), (36) gives: % 169.03/24.10 | | | | | (37) all_74_2 = n2 | gt(n2, all_74_2) % 169.03/24.10 | | | | | % 169.03/24.10 | | | | | BETA: splitting (34) gives: % 169.03/24.10 | | | | | % 169.03/24.10 | | | | | Case 1: % 169.03/24.10 | | | | | | % 169.03/24.10 | | | | | | (38) gt(n2, all_74_3) % 169.03/24.10 | | | | | | % 169.03/24.10 | | | | | | GROUND_INST: instantiating (1) with all_74_3, n2, n1, simplifying % 169.03/24.10 | | | | | | with (5), (10), (22), (38) gives: % 169.03/24.10 | | | | | | (39) leq(all_74_3, n1) % 169.03/24.10 | | | | | | % 169.03/24.10 | | | | | | GROUND_INST: instantiating (14) with all_74_3, simplifying with (5), % 169.03/24.10 | | | | | | (16), (39) gives: % 169.03/24.10 | | | | | | (40) all_74_3 = n1 | all_74_3 = n0 % 169.03/24.10 | | | | | | % 169.03/24.10 | | | | | | BETA: splitting (40) gives: % 169.03/24.10 | | | | | | % 169.03/24.10 | | | | | | Case 1: % 169.03/24.10 | | | | | | | % 169.03/24.10 | | | | | | | (41) all_74_3 = n0 % 169.03/24.10 | | | | | | | % 169.03/24.10 | | | | | | | REDUCE: (6), (41) imply: % 169.03/24.10 | | | | | | | (42) $false % 169.03/24.10 | | | | | | | % 169.03/24.10 | | | | | | | CLOSE: (42) is inconsistent. % 169.03/24.10 | | | | | | | % 169.03/24.10 | | | | | | Case 2: % 169.03/24.10 | | | | | | | % 169.03/24.10 | | | | | | | (43) all_74_3 = n1 % 169.03/24.10 | | | | | | | % 169.03/24.10 | | | | | | | REDUCE: (8), (43) imply: % 169.03/24.10 | | | | | | | (44) a_select3(q_ds1_filter, all_74_2, n1) = all_74_0 % 169.03/24.10 | | | | | | | % 169.03/24.10 | | | | | | | REDUCE: (24), (43) imply: % 169.03/24.10 | | | | | | | (45) a_select3(q_ds1_filter, n1, all_74_2) = all_74_1 % 169.03/24.10 | | | | | | | % 169.03/24.10 | | | | | | | REDUCE: (5), (43) imply: % 169.03/24.10 | | | | | | | (46) $i(n1) % 169.03/24.10 | | | | | | | % 169.03/24.10 | | | | | | | REDUCE: (2), (43) imply: % 169.03/24.10 | | | | | | | (47) leq(n1, n5) % 169.03/24.10 | | | | | | | % 169.03/24.10 | | | | | | | REDUCE: (16), (43) imply: % 169.03/24.10 | | | | | | | (48) leq(n0, n1) % 169.03/24.10 | | | | | | | % 169.03/24.10 | | | | | | | BETA: splitting (37) gives: % 169.03/24.10 | | | | | | | % 169.03/24.10 | | | | | | | Case 1: % 169.03/24.10 | | | | | | | | % 169.03/24.10 | | | | | | | | (49) gt(n2, all_74_2) % 169.03/24.10 | | | | | | | | % 169.03/24.10 | | | | | | | | GROUND_INST: instantiating (1) with all_74_2, n2, n1, % 169.03/24.10 | | | | | | | | simplifying with (10), (15), (22), (49) gives: % 169.03/24.10 | | | | | | | | (50) leq(all_74_2, n1) % 169.03/24.10 | | | | | | | | % 169.03/24.10 | | | | | | | | GROUND_INST: instantiating (14) with all_74_2, simplifying with % 169.03/24.10 | | | | | | | | (9), (15), (50) gives: % 169.03/24.10 | | | | | | | | (51) all_74_2 = n1 | all_74_2 = n0 % 169.03/24.10 | | | | | | | | % 169.03/24.10 | | | | | | | | BETA: splitting (51) gives: % 169.03/24.10 | | | | | | | | % 169.03/24.10 | | | | | | | | Case 1: % 169.03/24.10 | | | | | | | | | % 169.03/24.10 | | | | | | | | | (52) all_74_2 = n0 % 169.03/24.10 | | | | | | | | | % 169.03/24.10 | | | | | | | | | REDUCE: (7), (52) imply: % 169.03/24.10 | | | | | | | | | (53) $false % 169.03/24.10 | | | | | | | | | % 169.03/24.10 | | | | | | | | | CLOSE: (53) is inconsistent. % 169.03/24.10 | | | | | | | | | % 169.03/24.10 | | | | | | | | Case 2: % 169.03/24.10 | | | | | | | | | % 169.03/24.10 | | | | | | | | | (54) all_74_2 = n1 % 169.03/24.10 | | | | | | | | | % 169.03/24.10 | | | | | | | | | REDUCE: (44), (54) imply: % 169.03/24.10 | | | | | | | | | (55) a_select3(q_ds1_filter, n1, n1) = all_74_0 % 169.03/24.10 | | | | | | | | | % 169.03/24.10 | | | | | | | | | REDUCE: (45), (54) imply: % 169.03/24.10 | | | | | | | | | (56) a_select3(q_ds1_filter, n1, n1) = all_74_1 % 169.03/24.10 | | | | | | | | | % 169.03/24.10 | | | | | | | | | GROUND_INST: instantiating (20) with all_74_1, all_74_0, n1, % 169.03/24.10 | | | | | | | | | n1, q_ds1_filter, simplifying with (55), (56) % 169.03/24.10 | | | | | | | | | gives: % 169.03/24.10 | | | | | | | | | (57) all_74_0 = all_74_1 % 169.03/24.10 | | | | | | | | | % 169.03/24.10 | | | | | | | | | REDUCE: (11), (57) imply: % 169.03/24.10 | | | | | | | | | (58) $false % 169.03/24.10 | | | | | | | | | % 169.03/24.10 | | | | | | | | | CLOSE: (58) is inconsistent. % 169.03/24.10 | | | | | | | | | % 169.03/24.10 | | | | | | | | End of split % 169.03/24.10 | | | | | | | | % 169.03/24.10 | | | | | | | Case 2: % 169.03/24.10 | | | | | | | | % 169.03/24.10 | | | | | | | | (59) all_74_2 = n2 % 169.03/24.10 | | | | | | | | % 169.03/24.10 | | | | | | | | REDUCE: (44), (59) imply: % 169.03/24.10 | | | | | | | | (60) a_select3(q_ds1_filter, n2, n1) = all_74_0 % 169.03/24.10 | | | | | | | | % 169.03/24.10 | | | | | | | | REDUCE: (45), (59) imply: % 169.03/24.10 | | | | | | | | (61) a_select3(q_ds1_filter, n1, n2) = all_74_1 % 169.03/24.10 | | | | | | | | % 169.03/24.10 | | | | | | | | REDUCE: (21), (59) imply: % 169.03/24.10 | | | | | | | | (62) leq(n2, n5) % 169.03/24.10 | | | | | | | | % 169.03/24.10 | | | | | | | | REDUCE: (9), (59) imply: % 169.03/24.10 | | | | | | | | (63) leq(n0, n2) % 169.03/24.10 | | | | | | | | % 169.03/24.10 | | | | | | | | GROUND_INST: instantiating (19) with n1, n2, all_74_1, % 169.03/24.10 | | | | | | | | simplifying with (10), (46), (48), (61), (63) % 169.03/24.10 | | | | | | | | gives: % 169.03/24.10 | | | | | | | | (64) ~ leq(n2, all_74_13) | ~ leq(n1, all_74_13) | % 169.03/24.10 | | | | | | | | (a_select3(q_ds1_filter, n2, n1) = all_74_1 & % 169.03/24.10 | | | | | | | | $i(all_74_1)) % 169.03/24.10 | | | | | | | | % 169.03/24.10 | | | | | | | | BETA: splitting (64) gives: % 169.03/24.10 | | | | | | | | % 169.03/24.10 | | | | | | | | Case 1: % 169.03/24.10 | | | | | | | | | % 169.03/24.10 | | | | | | | | | (65) ~ leq(n2, all_74_13) % 169.03/24.10 | | | | | | | | | % 169.03/24.10 | | | | | | | | | REDUCE: (4), (65) imply: % 169.03/24.10 | | | | | | | | | (66) ~ leq(n2, n5) % 169.03/24.10 | | | | | | | | | % 169.03/24.10 | | | | | | | | | PRED_UNIFY: (62), (66) imply: % 169.03/24.10 | | | | | | | | | (67) $false % 169.03/24.10 | | | | | | | | | % 169.03/24.10 | | | | | | | | | CLOSE: (67) is inconsistent. % 169.03/24.10 | | | | | | | | | % 169.03/24.10 | | | | | | | | Case 2: % 169.03/24.10 | | | | | | | | | % 169.03/24.10 | | | | | | | | | (68) ~ leq(n1, all_74_13) | (a_select3(q_ds1_filter, n2, % 169.03/24.10 | | | | | | | | | n1) = all_74_1 & $i(all_74_1)) % 169.03/24.10 | | | | | | | | | % 169.03/24.10 | | | | | | | | | BETA: splitting (68) gives: % 169.03/24.10 | | | | | | | | | % 169.03/24.10 | | | | | | | | | Case 1: % 169.03/24.10 | | | | | | | | | | % 169.03/24.10 | | | | | | | | | | (69) ~ leq(n1, all_74_13) % 169.03/24.10 | | | | | | | | | | % 169.03/24.10 | | | | | | | | | | REDUCE: (4), (69) imply: % 169.03/24.10 | | | | | | | | | | (70) ~ leq(n1, n5) % 169.03/24.10 | | | | | | | | | | % 169.03/24.10 | | | | | | | | | | PRED_UNIFY: (47), (70) imply: % 169.03/24.10 | | | | | | | | | | (71) $false % 169.03/24.10 | | | | | | | | | | % 169.03/24.10 | | | | | | | | | | CLOSE: (71) is inconsistent. % 169.03/24.10 | | | | | | | | | | % 169.03/24.10 | | | | | | | | | Case 2: % 169.03/24.10 | | | | | | | | | | % 169.03/24.10 | | | | | | | | | | (72) a_select3(q_ds1_filter, n2, n1) = all_74_1 & % 169.03/24.10 | | | | | | | | | | $i(all_74_1) % 169.03/24.10 | | | | | | | | | | % 169.03/24.10 | | | | | | | | | | ALPHA: (72) implies: % 169.03/24.10 | | | | | | | | | | (73) a_select3(q_ds1_filter, n2, n1) = all_74_1 % 169.03/24.10 | | | | | | | | | | % 169.03/24.10 | | | | | | | | | | REF_CLOSE: (11), (20), (60), (73) are inconsistent by % 169.03/24.10 | | | | | | | | | | sub-proof #32. % 169.03/24.10 | | | | | | | | | | % 169.03/24.10 | | | | | | | | | End of split % 169.03/24.10 | | | | | | | | | % 169.03/24.10 | | | | | | | | End of split % 169.03/24.10 | | | | | | | | % 169.03/24.10 | | | | | | | End of split % 169.03/24.10 | | | | | | | % 169.03/24.10 | | | | | | End of split % 169.03/24.10 | | | | | | % 169.03/24.10 | | | | | Case 2: % 169.03/24.10 | | | | | | % 169.03/24.10 | | | | | | (74) all_74_3 = n2 % 169.03/24.10 | | | | | | % 169.03/24.10 | | | | | | REDUCE: (8), (74) imply: % 169.03/24.10 | | | | | | (75) a_select3(q_ds1_filter, all_74_2, n2) = all_74_0 % 169.03/24.10 | | | | | | % 169.03/24.10 | | | | | | REDUCE: (24), (74) imply: % 169.03/24.10 | | | | | | (76) a_select3(q_ds1_filter, n2, all_74_2) = all_74_1 % 169.03/24.10 | | | | | | % 169.03/24.10 | | | | | | REDUCE: (2), (74) imply: % 169.03/24.10 | | | | | | (77) leq(n2, n5) % 169.03/24.10 | | | | | | % 169.03/24.10 | | | | | | REDUCE: (16), (74) imply: % 169.03/24.10 | | | | | | (78) leq(n0, n2) % 169.03/24.10 | | | | | | % 169.03/24.10 | | | | | | BETA: splitting (37) gives: % 169.03/24.10 | | | | | | % 169.03/24.10 | | | | | | Case 1: % 169.03/24.10 | | | | | | | % 169.03/24.10 | | | | | | | (79) gt(n2, all_74_2) % 169.03/24.10 | | | | | | | % 169.03/24.10 | | | | | | | GROUND_INST: instantiating (1) with all_74_2, n2, n1, simplifying % 169.03/24.10 | | | | | | | with (10), (15), (22), (79) gives: % 169.03/24.10 | | | | | | | (80) leq(all_74_2, n1) % 169.03/24.10 | | | | | | | % 169.03/24.10 | | | | | | | GROUND_INST: instantiating (14) with all_74_2, simplifying with % 169.03/24.10 | | | | | | | (9), (15), (80) gives: % 169.03/24.10 | | | | | | | (81) all_74_2 = n1 | all_74_2 = n0 % 169.03/24.10 | | | | | | | % 169.03/24.10 | | | | | | | BETA: splitting (81) gives: % 169.03/24.10 | | | | | | | % 169.03/24.10 | | | | | | | Case 1: % 169.03/24.10 | | | | | | | | % 169.03/24.10 | | | | | | | | (82) all_74_2 = n0 % 169.03/24.10 | | | | | | | | % 169.03/24.10 | | | | | | | | REDUCE: (7), (82) imply: % 169.03/24.10 | | | | | | | | (83) $false % 169.03/24.10 | | | | | | | | % 169.03/24.10 | | | | | | | | CLOSE: (83) is inconsistent. % 169.03/24.10 | | | | | | | | % 169.03/24.10 | | | | | | | Case 2: % 169.03/24.10 | | | | | | | | % 169.03/24.10 | | | | | | | | (84) all_74_2 = n1 % 169.03/24.10 | | | | | | | | % 169.03/24.10 | | | | | | | | REDUCE: (75), (84) imply: % 169.03/24.10 | | | | | | | | (85) a_select3(q_ds1_filter, n1, n2) = all_74_0 % 169.03/24.10 | | | | | | | | % 169.03/24.10 | | | | | | | | REDUCE: (76), (84) imply: % 169.03/24.10 | | | | | | | | (86) a_select3(q_ds1_filter, n2, n1) = all_74_1 % 169.03/24.10 | | | | | | | | % 169.03/24.10 | | | | | | | | REDUCE: (15), (84) imply: % 169.03/24.10 | | | | | | | | (87) $i(n1) % 169.03/24.10 | | | | | | | | % 169.03/24.10 | | | | | | | | REDUCE: (21), (84) imply: % 169.03/24.10 | | | | | | | | (88) leq(n1, n5) % 169.03/24.10 | | | | | | | | % 169.03/24.10 | | | | | | | | REDUCE: (9), (84) imply: % 169.03/24.10 | | | | | | | | (89) leq(n0, n1) % 169.03/24.10 | | | | | | | | % 169.03/24.10 | | | | | | | | GROUND_INST: instantiating (19) with n1, n2, all_74_0, % 169.03/24.10 | | | | | | | | simplifying with (10), (78), (85), (87), (89) % 169.03/24.10 | | | | | | | | gives: % 169.03/24.10 | | | | | | | | (90) ~ leq(n2, all_74_13) | ~ leq(n1, all_74_13) | % 169.03/24.10 | | | | | | | | (a_select3(q_ds1_filter, n2, n1) = all_74_0 & % 169.03/24.10 | | | | | | | | $i(all_74_0)) % 169.03/24.10 | | | | | | | | % 169.03/24.10 | | | | | | | | BETA: splitting (90) gives: % 169.03/24.10 | | | | | | | | % 169.03/24.10 | | | | | | | | Case 1: % 169.03/24.10 | | | | | | | | | % 169.03/24.10 | | | | | | | | | (91) ~ leq(n2, all_74_13) % 169.03/24.10 | | | | | | | | | % 169.03/24.10 | | | | | | | | | REDUCE: (4), (91) imply: % 169.03/24.10 | | | | | | | | | (92) ~ leq(n2, n5) % 169.03/24.10 | | | | | | | | | % 169.03/24.10 | | | | | | | | | PRED_UNIFY: (77), (92) imply: % 169.03/24.10 | | | | | | | | | (93) $false % 169.03/24.10 | | | | | | | | | % 169.03/24.10 | | | | | | | | | CLOSE: (93) is inconsistent. % 169.03/24.10 | | | | | | | | | % 169.03/24.10 | | | | | | | | Case 2: % 169.03/24.10 | | | | | | | | | % 169.03/24.10 | | | | | | | | | (94) ~ leq(n1, all_74_13) | (a_select3(q_ds1_filter, n2, % 169.03/24.10 | | | | | | | | | n1) = all_74_0 & $i(all_74_0)) % 169.03/24.10 | | | | | | | | | % 169.03/24.10 | | | | | | | | | BETA: splitting (94) gives: % 169.03/24.10 | | | | | | | | | % 169.03/24.10 | | | | | | | | | Case 1: % 169.03/24.10 | | | | | | | | | | % 169.03/24.10 | | | | | | | | | | (95) ~ leq(n1, all_74_13) % 169.03/24.10 | | | | | | | | | | % 169.03/24.10 | | | | | | | | | | REDUCE: (4), (95) imply: % 169.03/24.10 | | | | | | | | | | (96) ~ leq(n1, n5) % 169.03/24.10 | | | | | | | | | | % 169.03/24.10 | | | | | | | | | | PRED_UNIFY: (88), (96) imply: % 169.03/24.10 | | | | | | | | | | (97) $false % 169.03/24.10 | | | | | | | | | | % 169.03/24.10 | | | | | | | | | | CLOSE: (97) is inconsistent. % 169.03/24.10 | | | | | | | | | | % 169.03/24.10 | | | | | | | | | Case 2: % 169.03/24.10 | | | | | | | | | | % 169.03/24.10 | | | | | | | | | | (98) a_select3(q_ds1_filter, n2, n1) = all_74_0 & % 169.03/24.10 | | | | | | | | | | $i(all_74_0) % 169.03/24.10 | | | | | | | | | | % 169.03/24.10 | | | | | | | | | | ALPHA: (98) implies: % 169.03/24.10 | | | | | | | | | | (99) a_select3(q_ds1_filter, n2, n1) = all_74_0 % 169.03/24.10 | | | | | | | | | | % 169.03/24.10 | | | | | | | | | | REF_CLOSE: (11), (20), (86), (99) are inconsistent by % 169.03/24.10 | | | | | | | | | | sub-proof #32. % 169.03/24.10 | | | | | | | | | | % 169.03/24.10 | | | | | | | | | End of split % 169.03/24.10 | | | | | | | | | % 169.03/24.10 | | | | | | | | End of split % 169.03/24.10 | | | | | | | | % 169.03/24.10 | | | | | | | End of split % 169.03/24.10 | | | | | | | % 169.03/24.10 | | | | | | Case 2: % 169.03/24.10 | | | | | | | % 169.03/24.10 | | | | | | | (100) all_74_2 = n2 % 169.03/24.10 | | | | | | | % 169.03/24.10 | | | | | | | REDUCE: (75), (100) imply: % 169.03/24.10 | | | | | | | (101) a_select3(q_ds1_filter, n2, n2) = all_74_0 % 169.03/24.10 | | | | | | | % 169.03/24.11 | | | | | | | REDUCE: (76), (100) imply: % 169.03/24.11 | | | | | | | (102) a_select3(q_ds1_filter, n2, n2) = all_74_1 % 169.03/24.11 | | | | | | | % 169.03/24.11 | | | | | | | GROUND_INST: instantiating (20) with all_74_1, all_74_0, n2, n2, % 169.03/24.11 | | | | | | | q_ds1_filter, simplifying with (101), (102) gives: % 169.03/24.11 | | | | | | | (103) all_74_0 = all_74_1 % 169.03/24.11 | | | | | | | % 169.03/24.11 | | | | | | | REDUCE: (11), (103) imply: % 169.03/24.11 | | | | | | | (104) $false % 169.03/24.11 | | | | | | | % 169.03/24.11 | | | | | | | CLOSE: (104) is inconsistent. % 169.03/24.11 | | | | | | | % 169.03/24.11 | | | | | | End of split % 169.03/24.11 | | | | | | % 169.03/24.11 | | | | | End of split % 169.03/24.11 | | | | | % 169.03/24.11 | | | | Case 2: % 169.03/24.11 | | | | | % 169.03/24.11 | | | | | (105) all_74_2 = n3 % 169.03/24.11 | | | | | % 169.03/24.11 | | | | | REDUCE: (8), (105) imply: % 169.03/24.11 | | | | | (106) a_select3(q_ds1_filter, n3, all_74_3) = all_74_0 % 169.03/24.11 | | | | | % 169.03/24.11 | | | | | REDUCE: (24), (105) imply: % 169.03/24.11 | | | | | (107) a_select3(q_ds1_filter, all_74_3, n3) = all_74_1 % 169.03/24.11 | | | | | % 169.03/24.11 | | | | | REDUCE: (21), (105) imply: % 169.03/24.11 | | | | | (108) leq(n3, n5) % 169.03/24.11 | | | | | % 169.03/24.11 | | | | | REDUCE: (9), (105) imply: % 169.03/24.11 | | | | | (109) leq(n0, n3) % 169.03/24.11 | | | | | % 169.03/24.11 | | | | | BETA: splitting (34) gives: % 169.03/24.11 | | | | | % 169.03/24.11 | | | | | Case 1: % 169.03/24.11 | | | | | | % 169.03/24.11 | | | | | | (110) gt(n2, all_74_3) % 169.03/24.11 | | | | | | % 169.03/24.11 | | | | | | GROUND_INST: instantiating (1) with all_74_3, n2, n1, simplifying % 169.03/24.11 | | | | | | with (5), (10), (22), (110) gives: % 169.03/24.11 | | | | | | (111) leq(all_74_3, n1) % 169.03/24.11 | | | | | | % 169.03/24.11 | | | | | | GROUND_INST: instantiating (14) with all_74_3, simplifying with (5), % 169.03/24.11 | | | | | | (16), (111) gives: % 169.03/24.11 | | | | | | (112) all_74_3 = n1 | all_74_3 = n0 % 169.03/24.11 | | | | | | % 169.03/24.11 | | | | | | BETA: splitting (112) gives: % 169.03/24.11 | | | | | | % 169.03/24.11 | | | | | | Case 1: % 169.03/24.11 | | | | | | | % 169.03/24.11 | | | | | | | (113) all_74_3 = n0 % 169.03/24.11 | | | | | | | % 169.03/24.11 | | | | | | | REDUCE: (6), (113) imply: % 169.03/24.11 | | | | | | | (114) $false % 169.03/24.11 | | | | | | | % 169.03/24.11 | | | | | | | CLOSE: (114) is inconsistent. % 169.03/24.11 | | | | | | | % 169.03/24.11 | | | | | | Case 2: % 169.03/24.11 | | | | | | | % 169.03/24.11 | | | | | | | (115) all_74_3 = n1 % 169.03/24.11 | | | | | | | % 169.03/24.11 | | | | | | | REDUCE: (107), (115) imply: % 169.03/24.11 | | | | | | | (116) a_select3(q_ds1_filter, n1, n3) = all_74_1 % 169.03/24.11 | | | | | | | % 169.03/24.11 | | | | | | | REDUCE: (106), (115) imply: % 169.03/24.11 | | | | | | | (117) a_select3(q_ds1_filter, n3, n1) = all_74_0 % 169.03/24.11 | | | | | | | % 169.03/24.11 | | | | | | | REDUCE: (5), (115) imply: % 169.03/24.11 | | | | | | | (118) $i(n1) % 169.03/24.11 | | | | | | | % 169.03/24.11 | | | | | | | REDUCE: (2), (115) imply: % 169.03/24.11 | | | | | | | (119) leq(n1, n5) % 169.03/24.11 | | | | | | | % 169.03/24.11 | | | | | | | REDUCE: (16), (115) imply: % 169.03/24.11 | | | | | | | (120) leq(n0, n1) % 169.03/24.11 | | | | | | | % 169.03/24.11 | | | | | | | GROUND_INST: instantiating (19) with n1, n3, all_74_1, simplifying % 169.03/24.11 | | | | | | | with (23), (109), (116), (118), (120) gives: % 169.34/24.11 | | | | | | | (121) ~ leq(n3, all_74_13) | ~ leq(n1, all_74_13) | % 169.34/24.11 | | | | | | | (a_select3(q_ds1_filter, n3, n1) = all_74_1 & % 169.34/24.11 | | | | | | | $i(all_74_1)) % 169.34/24.11 | | | | | | | % 169.34/24.11 | | | | | | | BETA: splitting (121) gives: % 169.34/24.11 | | | | | | | % 169.34/24.11 | | | | | | | Case 1: % 169.34/24.11 | | | | | | | | % 169.34/24.11 | | | | | | | | (122) ~ leq(n3, all_74_13) % 169.34/24.11 | | | | | | | | % 169.34/24.11 | | | | | | | | REDUCE: (4), (122) imply: % 169.34/24.11 | | | | | | | | (123) ~ leq(n3, n5) % 169.34/24.11 | | | | | | | | % 169.34/24.11 | | | | | | | | PRED_UNIFY: (108), (123) imply: % 169.34/24.11 | | | | | | | | (124) $false % 169.34/24.11 | | | | | | | | % 169.34/24.11 | | | | | | | | CLOSE: (124) is inconsistent. % 169.34/24.11 | | | | | | | | % 169.34/24.11 | | | | | | | Case 2: % 169.34/24.11 | | | | | | | | % 169.34/24.11 | | | | | | | | (125) ~ leq(n1, all_74_13) | (a_select3(q_ds1_filter, n3, % 169.34/24.11 | | | | | | | | n1) = all_74_1 & $i(all_74_1)) % 169.34/24.11 | | | | | | | | % 169.34/24.11 | | | | | | | | BETA: splitting (125) gives: % 169.34/24.11 | | | | | | | | % 169.34/24.11 | | | | | | | | Case 1: % 169.34/24.11 | | | | | | | | | % 169.34/24.11 | | | | | | | | | (126) ~ leq(n1, all_74_13) % 169.34/24.11 | | | | | | | | | % 169.34/24.11 | | | | | | | | | REDUCE: (4), (126) imply: % 169.34/24.11 | | | | | | | | | (127) ~ leq(n1, n5) % 169.34/24.11 | | | | | | | | | % 169.34/24.11 | | | | | | | | | PRED_UNIFY: (119), (127) imply: % 169.34/24.11 | | | | | | | | | (128) $false % 169.34/24.11 | | | | | | | | | % 169.34/24.11 | | | | | | | | | CLOSE: (128) is inconsistent. % 169.34/24.11 | | | | | | | | | % 169.34/24.11 | | | | | | | | Case 2: % 169.34/24.11 | | | | | | | | | % 169.34/24.11 | | | | | | | | | (129) a_select3(q_ds1_filter, n3, n1) = all_74_1 & % 169.34/24.11 | | | | | | | | | $i(all_74_1) % 169.34/24.11 | | | | | | | | | % 169.34/24.11 | | | | | | | | | ALPHA: (129) implies: % 169.34/24.11 | | | | | | | | | (130) a_select3(q_ds1_filter, n3, n1) = all_74_1 % 169.34/24.11 | | | | | | | | | % 169.34/24.11 | | | | | | | | | REF_CLOSE: (11), (20), (117), (130) are inconsistent by % 169.34/24.11 | | | | | | | | | sub-proof #31. % 169.34/24.11 | | | | | | | | | % 169.34/24.11 | | | | | | | | End of split % 169.34/24.11 | | | | | | | | % 169.34/24.11 | | | | | | | End of split % 169.34/24.11 | | | | | | | % 169.34/24.11 | | | | | | End of split % 169.34/24.11 | | | | | | % 169.34/24.11 | | | | | Case 2: % 169.34/24.11 | | | | | | % 169.34/24.11 | | | | | | (131) all_74_3 = n2 % 169.34/24.11 | | | | | | % 169.34/24.11 | | | | | | REDUCE: (107), (131) imply: % 169.34/24.11 | | | | | | (132) a_select3(q_ds1_filter, n2, n3) = all_74_1 % 169.34/24.11 | | | | | | % 169.34/24.11 | | | | | | REDUCE: (106), (131) imply: % 169.34/24.11 | | | | | | (133) a_select3(q_ds1_filter, n3, n2) = all_74_0 % 169.34/24.11 | | | | | | % 169.34/24.11 | | | | | | REDUCE: (2), (131) imply: % 169.34/24.11 | | | | | | (134) leq(n2, n5) % 169.34/24.11 | | | | | | % 169.34/24.11 | | | | | | REDUCE: (16), (131) imply: % 169.34/24.11 | | | | | | (135) leq(n0, n2) % 169.34/24.11 | | | | | | % 169.34/24.11 | | | | | | GROUND_INST: instantiating (19) with n2, n3, all_74_1, simplifying % 169.34/24.11 | | | | | | with (10), (23), (109), (132), (135) gives: % 169.34/24.11 | | | | | | (136) ~ leq(n3, all_74_13) | ~ leq(n2, all_74_13) | % 169.34/24.11 | | | | | | (a_select3(q_ds1_filter, n3, n2) = all_74_1 & $i(all_74_1)) % 169.34/24.11 | | | | | | % 169.34/24.11 | | | | | | BETA: splitting (136) gives: % 169.34/24.11 | | | | | | % 169.34/24.11 | | | | | | Case 1: % 169.34/24.11 | | | | | | | % 169.34/24.11 | | | | | | | (137) ~ leq(n3, all_74_13) % 169.34/24.11 | | | | | | | % 169.34/24.11 | | | | | | | REDUCE: (4), (137) imply: % 169.34/24.11 | | | | | | | (138) ~ leq(n3, n5) % 169.34/24.11 | | | | | | | % 169.34/24.11 | | | | | | | PRED_UNIFY: (108), (138) imply: % 169.34/24.11 | | | | | | | (139) $false % 169.34/24.11 | | | | | | | % 169.34/24.11 | | | | | | | CLOSE: (139) is inconsistent. % 169.34/24.11 | | | | | | | % 169.34/24.11 | | | | | | Case 2: % 169.34/24.11 | | | | | | | % 169.34/24.11 | | | | | | | (140) ~ leq(n2, all_74_13) | (a_select3(q_ds1_filter, n3, n2) % 169.34/24.11 | | | | | | | = all_74_1 & $i(all_74_1)) % 169.34/24.11 | | | | | | | % 169.34/24.11 | | | | | | | BETA: splitting (140) gives: % 169.34/24.11 | | | | | | | % 169.34/24.11 | | | | | | | Case 1: % 169.34/24.11 | | | | | | | | % 169.34/24.11 | | | | | | | | (141) ~ leq(n2, all_74_13) % 169.34/24.11 | | | | | | | | % 169.34/24.11 | | | | | | | | REDUCE: (4), (141) imply: % 169.34/24.11 | | | | | | | | (142) ~ leq(n2, n5) % 169.34/24.11 | | | | | | | | % 169.34/24.11 | | | | | | | | PRED_UNIFY: (134), (142) imply: % 169.34/24.11 | | | | | | | | (143) $false % 169.34/24.11 | | | | | | | | % 169.34/24.11 | | | | | | | | CLOSE: (143) is inconsistent. % 169.34/24.11 | | | | | | | | % 169.34/24.11 | | | | | | | Case 2: % 169.34/24.11 | | | | | | | | % 169.34/24.11 | | | | | | | | (144) a_select3(q_ds1_filter, n3, n2) = all_74_1 & % 169.34/24.11 | | | | | | | | $i(all_74_1) % 169.34/24.11 | | | | | | | | % 169.34/24.11 | | | | | | | | ALPHA: (144) implies: % 169.34/24.11 | | | | | | | | (145) a_select3(q_ds1_filter, n3, n2) = all_74_1 % 169.34/24.11 | | | | | | | | % 169.34/24.11 | | | | | | | | GROUND_INST: instantiating (20) with all_74_0, all_74_1, n2, n3, % 169.34/24.11 | | | | | | | | q_ds1_filter, simplifying with (133), (145) gives: % 169.34/24.11 | | | | | | | | (146) all_74_0 = all_74_1 % 169.34/24.11 | | | | | | | | % 169.34/24.11 | | | | | | | | REDUCE: (11), (146) imply: % 169.34/24.11 | | | | | | | | (147) $false % 169.34/24.11 | | | | | | | | % 169.34/24.11 | | | | | | | | CLOSE: (147) is inconsistent. % 169.34/24.11 | | | | | | | | % 169.34/24.11 | | | | | | | End of split % 169.34/24.11 | | | | | | | % 169.34/24.11 | | | | | | End of split % 169.34/24.11 | | | | | | % 169.34/24.11 | | | | | End of split % 169.34/24.11 | | | | | % 169.34/24.11 | | | | End of split % 169.34/24.11 | | | | % 169.34/24.11 | | | Case 2: % 169.34/24.11 | | | | % 169.34/24.11 | | | | (148) all_74_3 = n3 % 169.34/24.11 | | | | % 169.34/24.11 | | | | REDUCE: (8), (148) imply: % 169.34/24.11 | | | | (149) a_select3(q_ds1_filter, all_74_2, n3) = all_74_0 % 169.34/24.11 | | | | % 169.34/24.11 | | | | REDUCE: (24), (148) imply: % 169.34/24.11 | | | | (150) a_select3(q_ds1_filter, n3, all_74_2) = all_74_1 % 169.34/24.11 | | | | % 169.34/24.11 | | | | REDUCE: (2), (148) imply: % 169.34/24.11 | | | | (151) leq(n3, n5) % 169.34/24.11 | | | | % 169.34/24.11 | | | | REDUCE: (16), (148) imply: % 169.34/24.11 | | | | (152) leq(n0, n3) % 169.34/24.11 | | | | % 169.34/24.11 | | | | BETA: splitting (31) gives: % 169.34/24.11 | | | | % 169.34/24.11 | | | | Case 1: % 169.34/24.11 | | | | | % 169.34/24.11 | | | | | (153) gt(n3, all_74_2) % 169.34/24.11 | | | | | % 169.34/24.11 | | | | | GROUND_INST: instantiating (1) with all_74_2, n3, n2, simplifying with % 169.34/24.11 | | | | | (15), (17), (23), (153) gives: % 169.34/24.11 | | | | | (154) leq(all_74_2, n2) % 169.34/24.11 | | | | | % 169.34/24.11 | | | | | GROUND_INST: instantiating (25) with all_74_2, n2, simplifying with % 169.34/24.11 | | | | | (10), (15), (154) gives: % 169.34/24.11 | | | | | (155) all_74_2 = n2 | gt(n2, all_74_2) % 169.34/24.11 | | | | | % 169.34/24.11 | | | | | BETA: splitting (155) gives: % 169.34/24.11 | | | | | % 169.34/24.11 | | | | | Case 1: % 169.34/24.11 | | | | | | % 169.34/24.11 | | | | | | (156) gt(n2, all_74_2) % 169.34/24.11 | | | | | | % 169.34/24.11 | | | | | | GROUND_INST: instantiating (1) with all_74_2, n2, n1, simplifying % 169.34/24.11 | | | | | | with (10), (15), (22), (156) gives: % 169.34/24.11 | | | | | | (157) leq(all_74_2, n1) % 169.34/24.11 | | | | | | % 169.34/24.11 | | | | | | GROUND_INST: instantiating (14) with all_74_2, simplifying with (9), % 169.34/24.11 | | | | | | (15), (157) gives: % 169.34/24.11 | | | | | | (158) all_74_2 = n1 | all_74_2 = n0 % 169.34/24.11 | | | | | | % 169.34/24.11 | | | | | | BETA: splitting (158) gives: % 169.34/24.11 | | | | | | % 169.34/24.11 | | | | | | Case 1: % 169.34/24.11 | | | | | | | % 169.34/24.11 | | | | | | | (159) all_74_2 = n0 % 169.34/24.11 | | | | | | | % 169.34/24.11 | | | | | | | REDUCE: (7), (159) imply: % 169.34/24.11 | | | | | | | (160) $false % 169.34/24.11 | | | | | | | % 169.34/24.11 | | | | | | | CLOSE: (160) is inconsistent. % 169.34/24.11 | | | | | | | % 169.34/24.11 | | | | | | Case 2: % 169.34/24.11 | | | | | | | % 169.34/24.11 | | | | | | | (161) all_74_2 = n1 % 169.34/24.11 | | | | | | | % 169.34/24.11 | | | | | | | REDUCE: (149), (161) imply: % 169.34/24.11 | | | | | | | (162) a_select3(q_ds1_filter, n1, n3) = all_74_0 % 169.34/24.11 | | | | | | | % 169.34/24.11 | | | | | | | REDUCE: (150), (161) imply: % 169.34/24.11 | | | | | | | (163) a_select3(q_ds1_filter, n3, n1) = all_74_1 % 169.34/24.11 | | | | | | | % 169.34/24.11 | | | | | | | REDUCE: (15), (161) imply: % 169.34/24.11 | | | | | | | (164) $i(n1) % 169.34/24.11 | | | | | | | % 169.34/24.11 | | | | | | | REDUCE: (21), (161) imply: % 169.34/24.11 | | | | | | | (165) leq(n1, n5) % 169.34/24.11 | | | | | | | % 169.34/24.11 | | | | | | | REDUCE: (9), (161) imply: % 169.34/24.11 | | | | | | | (166) leq(n0, n1) % 169.34/24.11 | | | | | | | % 169.34/24.11 | | | | | | | GROUND_INST: instantiating (19) with n1, n3, all_74_0, simplifying % 169.34/24.11 | | | | | | | with (23), (152), (162), (164), (166) gives: % 169.34/24.11 | | | | | | | (167) ~ leq(n3, all_74_13) | ~ leq(n1, all_74_13) | % 169.34/24.11 | | | | | | | (a_select3(q_ds1_filter, n3, n1) = all_74_0 & % 169.34/24.11 | | | | | | | $i(all_74_0)) % 169.34/24.11 | | | | | | | % 169.34/24.11 | | | | | | | BETA: splitting (167) gives: % 169.34/24.11 | | | | | | | % 169.34/24.11 | | | | | | | Case 1: % 169.34/24.11 | | | | | | | | % 169.34/24.11 | | | | | | | | (168) ~ leq(n3, all_74_13) % 169.34/24.11 | | | | | | | | % 169.34/24.11 | | | | | | | | REDUCE: (4), (168) imply: % 169.34/24.11 | | | | | | | | (169) ~ leq(n3, n5) % 169.34/24.11 | | | | | | | | % 169.34/24.11 | | | | | | | | PRED_UNIFY: (151), (169) imply: % 169.34/24.11 | | | | | | | | (170) $false % 169.34/24.11 | | | | | | | | % 169.34/24.11 | | | | | | | | CLOSE: (170) is inconsistent. % 169.34/24.11 | | | | | | | | % 169.34/24.11 | | | | | | | Case 2: % 169.34/24.11 | | | | | | | | % 169.34/24.11 | | | | | | | | (171) ~ leq(n1, all_74_13) | (a_select3(q_ds1_filter, n3, % 169.34/24.11 | | | | | | | | n1) = all_74_0 & $i(all_74_0)) % 169.34/24.11 | | | | | | | | % 169.34/24.11 | | | | | | | | BETA: splitting (171) gives: % 169.34/24.11 | | | | | | | | % 169.34/24.11 | | | | | | | | Case 1: % 169.34/24.11 | | | | | | | | | % 169.34/24.11 | | | | | | | | | (172) ~ leq(n1, all_74_13) % 169.34/24.11 | | | | | | | | | % 169.34/24.11 | | | | | | | | | REDUCE: (4), (172) imply: % 169.34/24.11 | | | | | | | | | (173) ~ leq(n1, n5) % 169.34/24.11 | | | | | | | | | % 169.34/24.11 | | | | | | | | | PRED_UNIFY: (165), (173) imply: % 169.34/24.11 | | | | | | | | | (174) $false % 169.34/24.11 | | | | | | | | | % 169.34/24.11 | | | | | | | | | CLOSE: (174) is inconsistent. % 169.34/24.11 | | | | | | | | | % 169.34/24.11 | | | | | | | | Case 2: % 169.34/24.11 | | | | | | | | | % 169.34/24.11 | | | | | | | | | (175) a_select3(q_ds1_filter, n3, n1) = all_74_0 & % 169.34/24.11 | | | | | | | | | $i(all_74_0) % 169.34/24.11 | | | | | | | | | % 169.34/24.11 | | | | | | | | | ALPHA: (175) implies: % 169.34/24.11 | | | | | | | | | (176) a_select3(q_ds1_filter, n3, n1) = all_74_0 % 169.34/24.11 | | | | | | | | | % 169.34/24.11 | | | | | | | | | REF_CLOSE: (11), (20), (163), (176) are inconsistent by % 169.34/24.11 | | | | | | | | | sub-proof #31. % 169.34/24.11 | | | | | | | | | % 169.34/24.11 | | | | | | | | End of split % 169.34/24.11 | | | | | | | | % 169.34/24.11 | | | | | | | End of split % 169.34/24.11 | | | | | | | % 169.34/24.11 | | | | | | End of split % 169.34/24.11 | | | | | | % 169.34/24.11 | | | | | Case 2: % 169.34/24.11 | | | | | | % 169.34/24.11 | | | | | | (177) all_74_2 = n2 % 169.34/24.11 | | | | | | % 169.34/24.11 | | | | | | REDUCE: (149), (177) imply: % 169.34/24.11 | | | | | | (178) a_select3(q_ds1_filter, n2, n3) = all_74_0 % 169.34/24.11 | | | | | | % 169.34/24.11 | | | | | | REDUCE: (150), (177) imply: % 169.34/24.11 | | | | | | (179) a_select3(q_ds1_filter, n3, n2) = all_74_1 % 169.34/24.11 | | | | | | % 169.34/24.11 | | | | | | REDUCE: (21), (177) imply: % 169.34/24.11 | | | | | | (180) leq(n2, n5) % 169.34/24.11 | | | | | | % 169.34/24.11 | | | | | | REDUCE: (9), (177) imply: % 169.34/24.11 | | | | | | (181) leq(n0, n2) % 169.34/24.11 | | | | | | % 169.34/24.11 | | | | | | GROUND_INST: instantiating (19) with n2, n3, all_74_0, simplifying % 169.34/24.11 | | | | | | with (10), (23), (152), (178), (181) gives: % 169.34/24.11 | | | | | | (182) ~ leq(n3, all_74_13) | ~ leq(n2, all_74_13) | % 169.34/24.11 | | | | | | (a_select3(q_ds1_filter, n3, n2) = all_74_0 & $i(all_74_0)) % 169.34/24.11 | | | | | | % 169.34/24.11 | | | | | | BETA: splitting (182) gives: % 169.34/24.11 | | | | | | % 169.34/24.11 | | | | | | Case 1: % 169.34/24.11 | | | | | | | % 169.34/24.11 | | | | | | | (183) ~ leq(n3, all_74_13) % 169.34/24.11 | | | | | | | % 169.34/24.11 | | | | | | | REDUCE: (4), (183) imply: % 169.34/24.11 | | | | | | | (184) ~ leq(n3, n5) % 169.34/24.11 | | | | | | | % 169.34/24.11 | | | | | | | PRED_UNIFY: (151), (184) imply: % 169.34/24.11 | | | | | | | (185) $false % 169.34/24.11 | | | | | | | % 169.34/24.11 | | | | | | | CLOSE: (185) is inconsistent. % 169.34/24.11 | | | | | | | % 169.34/24.11 | | | | | | Case 2: % 169.34/24.11 | | | | | | | % 169.34/24.11 | | | | | | | (186) ~ leq(n2, all_74_13) | (a_select3(q_ds1_filter, n3, n2) % 169.34/24.11 | | | | | | | = all_74_0 & $i(all_74_0)) % 169.34/24.11 | | | | | | | % 169.34/24.11 | | | | | | | BETA: splitting (186) gives: % 169.34/24.11 | | | | | | | % 169.34/24.11 | | | | | | | Case 1: % 169.34/24.11 | | | | | | | | % 169.34/24.11 | | | | | | | | (187) ~ leq(n2, all_74_13) % 169.34/24.11 | | | | | | | | % 169.34/24.11 | | | | | | | | REDUCE: (4), (187) imply: % 169.34/24.11 | | | | | | | | (188) ~ leq(n2, n5) % 169.34/24.11 | | | | | | | | % 169.34/24.11 | | | | | | | | PRED_UNIFY: (180), (188) imply: % 169.34/24.11 | | | | | | | | (189) $false % 169.34/24.11 | | | | | | | | % 169.34/24.11 | | | | | | | | CLOSE: (189) is inconsistent. % 169.34/24.11 | | | | | | | | % 169.34/24.11 | | | | | | | Case 2: % 169.34/24.11 | | | | | | | | % 169.34/24.11 | | | | | | | | (190) a_select3(q_ds1_filter, n3, n2) = all_74_0 & % 169.34/24.11 | | | | | | | | $i(all_74_0) % 169.34/24.11 | | | | | | | | % 169.34/24.11 | | | | | | | | ALPHA: (190) implies: % 169.34/24.11 | | | | | | | | (191) a_select3(q_ds1_filter, n3, n2) = all_74_0 % 169.34/24.11 | | | | | | | | % 169.34/24.11 | | | | | | | | GROUND_INST: instantiating (20) with all_74_0, all_74_1, n2, n3, % 169.34/24.11 | | | | | | | | q_ds1_filter, simplifying with (179), (191) gives: % 169.34/24.11 | | | | | | | | (192) all_74_0 = all_74_1 % 169.34/24.11 | | | | | | | | % 169.34/24.11 | | | | | | | | REDUCE: (11), (192) imply: % 169.34/24.11 | | | | | | | | (193) $false % 169.34/24.11 | | | | | | | | % 169.34/24.11 | | | | | | | | CLOSE: (193) is inconsistent. % 169.34/24.11 | | | | | | | | % 169.34/24.11 | | | | | | | End of split % 169.34/24.11 | | | | | | | % 169.34/24.11 | | | | | | End of split % 169.34/24.11 | | | | | | % 169.34/24.11 | | | | | End of split % 169.34/24.11 | | | | | % 169.34/24.11 | | | | Case 2: % 169.34/24.11 | | | | | % 169.34/24.11 | | | | | (194) all_74_2 = n3 % 169.34/24.11 | | | | | % 169.34/24.11 | | | | | REDUCE: (149), (194) imply: % 169.34/24.11 | | | | | (195) a_select3(q_ds1_filter, n3, n3) = all_74_0 % 169.34/24.11 | | | | | % 169.34/24.11 | | | | | REDUCE: (150), (194) imply: % 169.34/24.11 | | | | | (196) a_select3(q_ds1_filter, n3, n3) = all_74_1 % 169.34/24.11 | | | | | % 169.34/24.11 | | | | | GROUND_INST: instantiating (20) with all_74_1, all_74_0, n3, n3, % 169.34/24.11 | | | | | q_ds1_filter, simplifying with (195), (196) gives: % 169.34/24.11 | | | | | (197) all_74_0 = all_74_1 % 169.34/24.11 | | | | | % 169.34/24.11 | | | | | REDUCE: (11), (197) imply: % 169.34/24.11 | | | | | (198) $false % 169.34/24.11 | | | | | % 169.34/24.11 | | | | | CLOSE: (198) is inconsistent. % 169.34/24.11 | | | | | % 169.34/24.11 | | | | End of split % 169.34/24.11 | | | | % 169.34/24.11 | | | End of split % 169.34/24.11 | | | % 169.34/24.11 | | Case 2: % 169.34/24.11 | | | % 169.34/24.11 | | | (199) all_74_2 = n4 % 169.34/24.11 | | | % 169.34/24.11 | | | REDUCE: (8), (199) imply: % 169.34/24.11 | | | (200) a_select3(q_ds1_filter, n4, all_74_3) = all_74_0 % 169.34/24.11 | | | % 169.34/24.11 | | | REDUCE: (24), (199) imply: % 169.34/24.11 | | | (201) a_select3(q_ds1_filter, all_74_3, n4) = all_74_1 % 169.34/24.11 | | | % 169.34/24.11 | | | REDUCE: (21), (199) imply: % 169.34/24.11 | | | (202) leq(n4, n5) % 169.34/24.11 | | | % 169.34/24.11 | | | REDUCE: (9), (199) imply: % 169.34/24.11 | | | (203) leq(n0, n4) % 169.34/24.11 | | | % 169.34/24.11 | | | BETA: splitting (28) gives: % 169.34/24.11 | | | % 169.34/24.11 | | | Case 1: % 169.34/24.11 | | | | % 169.34/24.11 | | | | (204) gt(n3, all_74_3) % 169.34/24.11 | | | | % 169.34/24.11 | | | | GROUND_INST: instantiating (1) with all_74_3, n3, n2, simplifying with % 169.34/24.11 | | | | (5), (17), (23), (204) gives: % 169.34/24.11 | | | | (205) leq(all_74_3, n2) % 169.34/24.11 | | | | % 169.34/24.11 | | | | GROUND_INST: instantiating (25) with all_74_3, n2, simplifying with (5), % 169.34/24.11 | | | | (10), (205) gives: % 169.34/24.11 | | | | (206) all_74_3 = n2 | gt(n2, all_74_3) % 169.34/24.11 | | | | % 169.34/24.11 | | | | BETA: splitting (206) gives: % 169.34/24.11 | | | | % 169.34/24.11 | | | | Case 1: % 169.34/24.11 | | | | | % 169.34/24.11 | | | | | (207) gt(n2, all_74_3) % 169.34/24.11 | | | | | % 169.34/24.11 | | | | | GROUND_INST: instantiating (1) with all_74_3, n2, n1, simplifying with % 169.34/24.11 | | | | | (5), (10), (22), (207) gives: % 169.34/24.11 | | | | | (208) leq(all_74_3, n1) % 169.34/24.11 | | | | | % 169.34/24.11 | | | | | GROUND_INST: instantiating (14) with all_74_3, simplifying with (5), % 169.34/24.11 | | | | | (16), (208) gives: % 169.34/24.11 | | | | | (209) all_74_3 = n1 | all_74_3 = n0 % 169.34/24.11 | | | | | % 169.34/24.11 | | | | | BETA: splitting (209) gives: % 169.34/24.11 | | | | | % 169.34/24.11 | | | | | Case 1: % 169.34/24.11 | | | | | | % 169.34/24.11 | | | | | | (210) all_74_3 = n0 % 169.34/24.11 | | | | | | % 169.34/24.11 | | | | | | REDUCE: (6), (210) imply: % 169.34/24.11 | | | | | | (211) $false % 169.34/24.11 | | | | | | % 169.34/24.11 | | | | | | CLOSE: (211) is inconsistent. % 169.34/24.11 | | | | | | % 169.34/24.11 | | | | | Case 2: % 169.34/24.11 | | | | | | % 169.34/24.11 | | | | | | (212) all_74_3 = n1 % 169.34/24.11 | | | | | | % 169.34/24.11 | | | | | | REDUCE: (201), (212) imply: % 169.34/24.11 | | | | | | (213) a_select3(q_ds1_filter, n1, n4) = all_74_1 % 169.34/24.11 | | | | | | % 169.34/24.11 | | | | | | REDUCE: (200), (212) imply: % 169.34/24.11 | | | | | | (214) a_select3(q_ds1_filter, n4, n1) = all_74_0 % 169.34/24.11 | | | | | | % 169.34/24.11 | | | | | | REDUCE: (5), (212) imply: % 169.34/24.11 | | | | | | (215) $i(n1) % 169.34/24.11 | | | | | | % 169.34/24.11 | | | | | | REDUCE: (2), (212) imply: % 169.34/24.11 | | | | | | (216) leq(n1, n5) % 169.34/24.11 | | | | | | % 169.34/24.11 | | | | | | REDUCE: (16), (212) imply: % 169.34/24.11 | | | | | | (217) leq(n0, n1) % 169.34/24.11 | | | | | | % 169.34/24.11 | | | | | | GROUND_INST: instantiating (19) with n1, n4, all_74_1, simplifying % 169.34/24.11 | | | | | | with (18), (203), (213), (215), (217) gives: % 169.34/24.11 | | | | | | (218) ~ leq(n4, all_74_13) | ~ leq(n1, all_74_13) | % 169.34/24.11 | | | | | | (a_select3(q_ds1_filter, n4, n1) = all_74_1 & $i(all_74_1)) % 169.34/24.11 | | | | | | % 169.34/24.11 | | | | | | BETA: splitting (218) gives: % 169.34/24.11 | | | | | | % 169.34/24.11 | | | | | | Case 1: % 169.34/24.11 | | | | | | | % 169.34/24.11 | | | | | | | (219) ~ leq(n4, all_74_13) % 169.34/24.11 | | | | | | | % 169.34/24.11 | | | | | | | REDUCE: (4), (219) imply: % 169.34/24.11 | | | | | | | (220) ~ leq(n4, n5) % 169.34/24.11 | | | | | | | % 169.34/24.11 | | | | | | | PRED_UNIFY: (202), (220) imply: % 169.34/24.11 | | | | | | | (221) $false % 169.34/24.11 | | | | | | | % 169.34/24.11 | | | | | | | CLOSE: (221) is inconsistent. % 169.34/24.11 | | | | | | | % 169.34/24.11 | | | | | | Case 2: % 169.34/24.11 | | | | | | | % 169.34/24.12 | | | | | | | (222) ~ leq(n1, all_74_13) | (a_select3(q_ds1_filter, n4, n1) % 169.34/24.12 | | | | | | | = all_74_1 & $i(all_74_1)) % 169.34/24.12 | | | | | | | % 169.34/24.12 | | | | | | | BETA: splitting (222) gives: % 169.34/24.12 | | | | | | | % 169.34/24.12 | | | | | | | Case 1: % 169.34/24.12 | | | | | | | | % 169.34/24.12 | | | | | | | | (223) ~ leq(n1, all_74_13) % 169.34/24.12 | | | | | | | | % 169.34/24.12 | | | | | | | | REDUCE: (4), (223) imply: % 169.34/24.12 | | | | | | | | (224) ~ leq(n1, n5) % 169.34/24.12 | | | | | | | | % 169.34/24.12 | | | | | | | | PRED_UNIFY: (216), (224) imply: % 169.34/24.12 | | | | | | | | (225) $false % 169.34/24.12 | | | | | | | | % 169.34/24.12 | | | | | | | | CLOSE: (225) is inconsistent. % 169.34/24.12 | | | | | | | | % 169.34/24.12 | | | | | | | Case 2: % 169.34/24.12 | | | | | | | | % 169.34/24.12 | | | | | | | | (226) a_select3(q_ds1_filter, n4, n1) = all_74_1 & % 169.34/24.12 | | | | | | | | $i(all_74_1) % 169.34/24.12 | | | | | | | | % 169.34/24.12 | | | | | | | | ALPHA: (226) implies: % 169.34/24.12 | | | | | | | | (227) a_select3(q_ds1_filter, n4, n1) = all_74_1 % 169.34/24.12 | | | | | | | | % 169.34/24.12 | | | | | | | | REF_CLOSE: (11), (20), (214), (227) are inconsistent by % 169.34/24.12 | | | | | | | | sub-proof #30. % 169.34/24.12 | | | | | | | | % 169.34/24.12 | | | | | | | End of split % 169.34/24.12 | | | | | | | % 169.34/24.12 | | | | | | End of split % 169.34/24.12 | | | | | | % 169.34/24.12 | | | | | End of split % 169.34/24.12 | | | | | % 169.34/24.12 | | | | Case 2: % 169.34/24.12 | | | | | % 169.34/24.12 | | | | | (228) all_74_3 = n2 % 169.34/24.12 | | | | | % 169.34/24.12 | | | | | REDUCE: (201), (228) imply: % 169.34/24.12 | | | | | (229) a_select3(q_ds1_filter, n2, n4) = all_74_1 % 169.34/24.12 | | | | | % 169.34/24.12 | | | | | REDUCE: (200), (228) imply: % 169.34/24.12 | | | | | (230) a_select3(q_ds1_filter, n4, n2) = all_74_0 % 169.34/24.12 | | | | | % 169.34/24.12 | | | | | REDUCE: (2), (228) imply: % 169.34/24.12 | | | | | (231) leq(n2, n5) % 169.34/24.12 | | | | | % 169.34/24.12 | | | | | REDUCE: (16), (228) imply: % 169.34/24.12 | | | | | (232) leq(n0, n2) % 169.34/24.12 | | | | | % 169.34/24.12 | | | | | GROUND_INST: instantiating (19) with n2, n4, all_74_1, simplifying % 169.34/24.12 | | | | | with (10), (18), (203), (229), (232) gives: % 169.34/24.12 | | | | | (233) ~ leq(n4, all_74_13) | ~ leq(n2, all_74_13) | % 169.34/24.12 | | | | | (a_select3(q_ds1_filter, n4, n2) = all_74_1 & $i(all_74_1)) % 169.34/24.12 | | | | | % 169.34/24.12 | | | | | BETA: splitting (233) gives: % 169.34/24.12 | | | | | % 169.34/24.12 | | | | | Case 1: % 169.34/24.12 | | | | | | % 169.34/24.12 | | | | | | (234) ~ leq(n4, all_74_13) % 169.34/24.12 | | | | | | % 169.34/24.12 | | | | | | REDUCE: (4), (234) imply: % 169.34/24.12 | | | | | | (235) ~ leq(n4, n5) % 169.34/24.12 | | | | | | % 169.34/24.12 | | | | | | PRED_UNIFY: (202), (235) imply: % 169.34/24.12 | | | | | | (236) $false % 169.34/24.12 | | | | | | % 169.34/24.12 | | | | | | CLOSE: (236) is inconsistent. % 169.34/24.12 | | | | | | % 169.34/24.12 | | | | | Case 2: % 169.34/24.12 | | | | | | % 169.34/24.12 | | | | | | (237) ~ leq(n2, all_74_13) | (a_select3(q_ds1_filter, n4, n2) = % 169.34/24.12 | | | | | | all_74_1 & $i(all_74_1)) % 169.34/24.12 | | | | | | % 169.34/24.12 | | | | | | BETA: splitting (237) gives: % 169.34/24.12 | | | | | | % 169.34/24.12 | | | | | | Case 1: % 169.34/24.12 | | | | | | | % 169.34/24.12 | | | | | | | (238) ~ leq(n2, all_74_13) % 169.34/24.12 | | | | | | | % 169.34/24.12 | | | | | | | REDUCE: (4), (238) imply: % 169.34/24.12 | | | | | | | (239) ~ leq(n2, n5) % 169.34/24.12 | | | | | | | % 169.34/24.12 | | | | | | | PRED_UNIFY: (231), (239) imply: % 169.34/24.12 | | | | | | | (240) $false % 169.34/24.12 | | | | | | | % 169.34/24.12 | | | | | | | CLOSE: (240) is inconsistent. % 169.34/24.12 | | | | | | | % 169.34/24.12 | | | | | | Case 2: % 169.34/24.12 | | | | | | | % 169.34/24.12 | | | | | | | (241) a_select3(q_ds1_filter, n4, n2) = all_74_1 & $i(all_74_1) % 169.34/24.12 | | | | | | | % 169.34/24.12 | | | | | | | ALPHA: (241) implies: % 169.34/24.12 | | | | | | | (242) a_select3(q_ds1_filter, n4, n2) = all_74_1 % 169.34/24.12 | | | | | | | % 169.34/24.12 | | | | | | | GROUND_INST: instantiating (20) with all_74_1, all_74_0, n2, n4, % 169.34/24.12 | | | | | | | q_ds1_filter, simplifying with (230), (242) gives: % 169.34/24.12 | | | | | | | (243) all_74_0 = all_74_1 % 169.34/24.12 | | | | | | | % 169.34/24.12 | | | | | | | REDUCE: (11), (243) imply: % 169.34/24.12 | | | | | | | (244) $false % 169.34/24.12 | | | | | | | % 169.34/24.12 | | | | | | | CLOSE: (244) is inconsistent. % 169.34/24.12 | | | | | | | % 169.34/24.12 | | | | | | End of split % 169.34/24.12 | | | | | | % 169.34/24.12 | | | | | End of split % 169.34/24.12 | | | | | % 169.34/24.12 | | | | End of split % 169.34/24.12 | | | | % 169.34/24.12 | | | Case 2: % 169.34/24.12 | | | | % 169.34/24.12 | | | | (245) all_74_3 = n3 % 169.34/24.12 | | | | % 169.34/24.12 | | | | REDUCE: (201), (245) imply: % 169.34/24.12 | | | | (246) a_select3(q_ds1_filter, n3, n4) = all_74_1 % 169.34/24.12 | | | | % 169.34/24.12 | | | | REDUCE: (200), (245) imply: % 169.34/24.12 | | | | (247) a_select3(q_ds1_filter, n4, n3) = all_74_0 % 169.34/24.12 | | | | % 169.34/24.12 | | | | REDUCE: (2), (245) imply: % 169.34/24.12 | | | | (248) leq(n3, n5) % 169.34/24.12 | | | | % 169.34/24.12 | | | | REDUCE: (16), (245) imply: % 169.34/24.12 | | | | (249) leq(n0, n3) % 169.34/24.12 | | | | % 169.34/24.12 | | | | GROUND_INST: instantiating (19) with n3, n4, all_74_1, simplifying with % 169.34/24.12 | | | | (18), (23), (203), (246), (249) gives: % 169.34/24.12 | | | | (250) ~ leq(n4, all_74_13) | ~ leq(n3, all_74_13) | % 169.34/24.12 | | | | (a_select3(q_ds1_filter, n4, n3) = all_74_1 & $i(all_74_1)) % 169.34/24.12 | | | | % 169.34/24.12 | | | | BETA: splitting (250) gives: % 169.34/24.12 | | | | % 169.34/24.12 | | | | Case 1: % 169.34/24.12 | | | | | % 169.34/24.12 | | | | | (251) ~ leq(n4, all_74_13) % 169.34/24.12 | | | | | % 169.34/24.12 | | | | | REDUCE: (4), (251) imply: % 169.34/24.12 | | | | | (252) ~ leq(n4, n5) % 169.34/24.12 | | | | | % 169.34/24.12 | | | | | PRED_UNIFY: (202), (252) imply: % 169.34/24.12 | | | | | (253) $false % 169.34/24.12 | | | | | % 169.34/24.12 | | | | | CLOSE: (253) is inconsistent. % 169.34/24.12 | | | | | % 169.34/24.12 | | | | Case 2: % 169.34/24.12 | | | | | % 169.34/24.12 | | | | | (254) ~ leq(n3, all_74_13) | (a_select3(q_ds1_filter, n4, n3) = % 169.34/24.12 | | | | | all_74_1 & $i(all_74_1)) % 169.34/24.12 | | | | | % 169.34/24.12 | | | | | BETA: splitting (254) gives: % 169.34/24.12 | | | | | % 169.34/24.12 | | | | | Case 1: % 169.34/24.12 | | | | | | % 169.34/24.12 | | | | | | (255) ~ leq(n3, all_74_13) % 169.34/24.12 | | | | | | % 169.34/24.12 | | | | | | REDUCE: (4), (255) imply: % 169.34/24.12 | | | | | | (256) ~ leq(n3, n5) % 169.34/24.12 | | | | | | % 169.34/24.12 | | | | | | PRED_UNIFY: (248), (256) imply: % 169.34/24.12 | | | | | | (257) $false % 169.34/24.12 | | | | | | % 169.34/24.12 | | | | | | CLOSE: (257) is inconsistent. % 169.34/24.12 | | | | | | % 169.34/24.12 | | | | | Case 2: % 169.34/24.12 | | | | | | % 169.34/24.12 | | | | | | (258) a_select3(q_ds1_filter, n4, n3) = all_74_1 & $i(all_74_1) % 169.34/24.12 | | | | | | % 169.34/24.12 | | | | | | ALPHA: (258) implies: % 169.34/24.12 | | | | | | (259) a_select3(q_ds1_filter, n4, n3) = all_74_1 % 169.34/24.12 | | | | | | % 169.34/24.12 | | | | | | REF_CLOSE: (11), (20), (247), (259) are inconsistent by sub-proof % 169.34/24.12 | | | | | | #29. % 169.34/24.12 | | | | | | % 169.34/24.12 | | | | | End of split % 169.34/24.12 | | | | | % 169.34/24.12 | | | | End of split % 169.34/24.12 | | | | % 169.34/24.12 | | | End of split % 169.34/24.12 | | | % 169.34/24.12 | | End of split % 169.34/24.12 | | % 169.34/24.12 | Case 2: % 169.34/24.12 | | % 169.34/24.12 | | (260) all_74_3 = n4 % 169.34/24.12 | | % 169.34/24.12 | | REDUCE: (8), (260) imply: % 169.34/24.12 | | (261) a_select3(q_ds1_filter, all_74_2, n4) = all_74_0 % 169.34/24.12 | | % 169.34/24.12 | | REDUCE: (24), (260) imply: % 169.34/24.12 | | (262) a_select3(q_ds1_filter, n4, all_74_2) = all_74_1 % 169.34/24.12 | | % 169.34/24.12 | | REDUCE: (2), (260) imply: % 169.34/24.12 | | (263) leq(n4, n5) % 169.34/24.12 | | % 169.34/24.12 | | REDUCE: (16), (260) imply: % 169.34/24.12 | | (264) leq(n0, n4) % 169.34/24.12 | | % 169.34/24.12 | | BETA: splitting (12) gives: % 169.34/24.12 | | % 169.34/24.12 | | Case 1: % 169.34/24.12 | | | % 169.34/24.12 | | | (265) gt(n4, all_74_2) % 169.34/24.12 | | | % 169.34/24.12 | | | GROUND_INST: instantiating (1) with all_74_2, n4, n3, simplifying with % 169.34/24.12 | | | (13), (15), (18), (265) gives: % 169.34/24.12 | | | (266) leq(all_74_2, n3) % 169.34/24.12 | | | % 169.34/24.12 | | | GROUND_INST: instantiating (25) with all_74_2, n3, simplifying with (15), % 169.34/24.12 | | | (23), (266) gives: % 169.34/24.12 | | | (267) all_74_2 = n3 | gt(n3, all_74_2) % 169.34/24.12 | | | % 169.34/24.12 | | | BETA: splitting (267) gives: % 169.34/24.12 | | | % 169.34/24.12 | | | Case 1: % 169.34/24.12 | | | | % 169.34/24.12 | | | | (268) gt(n3, all_74_2) % 169.34/24.12 | | | | % 169.34/24.12 | | | | GROUND_INST: instantiating (1) with all_74_2, n3, n2, simplifying with % 169.34/24.12 | | | | (15), (17), (23), (268) gives: % 169.34/24.12 | | | | (269) leq(all_74_2, n2) % 169.34/24.12 | | | | % 169.34/24.12 | | | | GROUND_INST: instantiating (25) with all_74_2, n2, simplifying with % 169.34/24.12 | | | | (10), (15), (269) gives: % 169.34/24.12 | | | | (270) all_74_2 = n2 | gt(n2, all_74_2) % 169.34/24.12 | | | | % 169.34/24.12 | | | | BETA: splitting (270) gives: % 169.34/24.12 | | | | % 169.34/24.12 | | | | Case 1: % 169.34/24.12 | | | | | % 169.34/24.12 | | | | | (271) gt(n2, all_74_2) % 169.34/24.12 | | | | | % 169.34/24.12 | | | | | GROUND_INST: instantiating (1) with all_74_2, n2, n1, simplifying with % 169.34/24.12 | | | | | (10), (15), (22), (271) gives: % 169.34/24.12 | | | | | (272) leq(all_74_2, n1) % 169.34/24.12 | | | | | % 169.34/24.12 | | | | | GROUND_INST: instantiating (14) with all_74_2, simplifying with (9), % 169.34/24.12 | | | | | (15), (272) gives: % 169.34/24.12 | | | | | (273) all_74_2 = n1 | all_74_2 = n0 % 169.34/24.12 | | | | | % 169.34/24.12 | | | | | BETA: splitting (273) gives: % 169.34/24.12 | | | | | % 169.34/24.12 | | | | | Case 1: % 169.34/24.12 | | | | | | % 169.34/24.12 | | | | | | (274) all_74_2 = n0 % 169.34/24.12 | | | | | | % 169.34/24.12 | | | | | | REDUCE: (7), (274) imply: % 169.34/24.12 | | | | | | (275) $false % 169.34/24.12 | | | | | | % 169.34/24.12 | | | | | | CLOSE: (275) is inconsistent. % 169.34/24.12 | | | | | | % 169.34/24.12 | | | | | Case 2: % 169.34/24.12 | | | | | | % 169.34/24.12 | | | | | | (276) all_74_2 = n1 % 169.34/24.12 | | | | | | % 169.34/24.12 | | | | | | REDUCE: (261), (276) imply: % 169.34/24.12 | | | | | | (277) a_select3(q_ds1_filter, n1, n4) = all_74_0 % 169.34/24.12 | | | | | | % 169.34/24.12 | | | | | | REDUCE: (262), (276) imply: % 169.34/24.12 | | | | | | (278) a_select3(q_ds1_filter, n4, n1) = all_74_1 % 169.34/24.12 | | | | | | % 169.34/24.12 | | | | | | REDUCE: (15), (276) imply: % 169.34/24.12 | | | | | | (279) $i(n1) % 169.34/24.12 | | | | | | % 169.34/24.12 | | | | | | REDUCE: (21), (276) imply: % 169.34/24.12 | | | | | | (280) leq(n1, n5) % 169.34/24.12 | | | | | | % 169.34/24.12 | | | | | | REDUCE: (9), (276) imply: % 169.34/24.12 | | | | | | (281) leq(n0, n1) % 169.34/24.12 | | | | | | % 169.34/24.12 | | | | | | GROUND_INST: instantiating (19) with n1, n4, all_74_0, simplifying % 169.34/24.12 | | | | | | with (18), (264), (277), (279), (281) gives: % 169.34/24.12 | | | | | | (282) ~ leq(n4, all_74_13) | ~ leq(n1, all_74_13) | % 169.34/24.12 | | | | | | (a_select3(q_ds1_filter, n4, n1) = all_74_0 & $i(all_74_0)) % 169.34/24.12 | | | | | | % 169.34/24.12 | | | | | | BETA: splitting (282) gives: % 169.34/24.12 | | | | | | % 169.34/24.12 | | | | | | Case 1: % 169.34/24.12 | | | | | | | % 169.34/24.12 | | | | | | | (283) ~ leq(n4, all_74_13) % 169.34/24.12 | | | | | | | % 169.34/24.12 | | | | | | | REDUCE: (4), (283) imply: % 169.34/24.12 | | | | | | | (284) ~ leq(n4, n5) % 169.34/24.12 | | | | | | | % 169.34/24.12 | | | | | | | PRED_UNIFY: (263), (284) imply: % 169.34/24.12 | | | | | | | (285) $false % 169.34/24.12 | | | | | | | % 169.34/24.12 | | | | | | | CLOSE: (285) is inconsistent. % 169.34/24.12 | | | | | | | % 169.34/24.12 | | | | | | Case 2: % 169.34/24.12 | | | | | | | % 169.34/24.12 | | | | | | | (286) ~ leq(n1, all_74_13) | (a_select3(q_ds1_filter, n4, n1) % 169.34/24.12 | | | | | | | = all_74_0 & $i(all_74_0)) % 169.34/24.12 | | | | | | | % 169.34/24.12 | | | | | | | BETA: splitting (286) gives: % 169.34/24.12 | | | | | | | % 169.34/24.12 | | | | | | | Case 1: % 169.34/24.12 | | | | | | | | % 169.34/24.12 | | | | | | | | (287) ~ leq(n1, all_74_13) % 169.34/24.12 | | | | | | | | % 169.34/24.12 | | | | | | | | REDUCE: (4), (287) imply: % 169.34/24.12 | | | | | | | | (288) ~ leq(n1, n5) % 169.34/24.12 | | | | | | | | % 169.34/24.12 | | | | | | | | PRED_UNIFY: (280), (288) imply: % 169.34/24.12 | | | | | | | | (289) $false % 169.34/24.12 | | | | | | | | % 169.34/24.12 | | | | | | | | CLOSE: (289) is inconsistent. % 169.34/24.12 | | | | | | | | % 169.34/24.12 | | | | | | | Case 2: % 169.34/24.12 | | | | | | | | % 169.34/24.12 | | | | | | | | (290) a_select3(q_ds1_filter, n4, n1) = all_74_0 & % 169.34/24.12 | | | | | | | | $i(all_74_0) % 169.34/24.12 | | | | | | | | % 169.34/24.12 | | | | | | | | ALPHA: (290) implies: % 169.34/24.12 | | | | | | | | (291) a_select3(q_ds1_filter, n4, n1) = all_74_0 % 169.34/24.12 | | | | | | | | % 169.34/24.12 | | | | | | | | REF_CLOSE: (11), (20), (278), (291) are inconsistent by % 169.34/24.12 | | | | | | | | sub-proof #30. % 169.34/24.12 | | | | | | | | % 169.34/24.12 | | | | | | | End of split % 169.34/24.12 | | | | | | | % 169.34/24.12 | | | | | | End of split % 169.34/24.12 | | | | | | % 169.34/24.12 | | | | | End of split % 169.34/24.12 | | | | | % 169.34/24.12 | | | | Case 2: % 169.34/24.12 | | | | | % 169.34/24.12 | | | | | (292) all_74_2 = n2 % 169.34/24.12 | | | | | % 169.34/24.12 | | | | | REDUCE: (261), (292) imply: % 169.34/24.12 | | | | | (293) a_select3(q_ds1_filter, n2, n4) = all_74_0 % 169.34/24.12 | | | | | % 169.34/24.12 | | | | | REDUCE: (262), (292) imply: % 169.34/24.12 | | | | | (294) a_select3(q_ds1_filter, n4, n2) = all_74_1 % 169.34/24.12 | | | | | % 169.34/24.12 | | | | | REDUCE: (21), (292) imply: % 169.34/24.12 | | | | | (295) leq(n2, n5) % 169.34/24.12 | | | | | % 169.34/24.12 | | | | | REDUCE: (9), (292) imply: % 169.34/24.12 | | | | | (296) leq(n0, n2) % 169.34/24.12 | | | | | % 169.34/24.12 | | | | | GROUND_INST: instantiating (19) with n2, n4, all_74_0, simplifying % 169.34/24.12 | | | | | with (10), (18), (264), (293), (296) gives: % 169.34/24.12 | | | | | (297) ~ leq(n4, all_74_13) | ~ leq(n2, all_74_13) | % 169.34/24.12 | | | | | (a_select3(q_ds1_filter, n4, n2) = all_74_0 & $i(all_74_0)) % 169.34/24.12 | | | | | % 169.34/24.12 | | | | | BETA: splitting (297) gives: % 169.34/24.12 | | | | | % 169.34/24.12 | | | | | Case 1: % 169.34/24.12 | | | | | | % 169.34/24.12 | | | | | | (298) ~ leq(n4, all_74_13) % 169.34/24.12 | | | | | | % 169.34/24.12 | | | | | | REDUCE: (4), (298) imply: % 169.34/24.12 | | | | | | (299) ~ leq(n4, n5) % 169.34/24.12 | | | | | | % 169.34/24.12 | | | | | | PRED_UNIFY: (263), (299) imply: % 169.34/24.12 | | | | | | (300) $false % 169.34/24.12 | | | | | | % 169.34/24.12 | | | | | | CLOSE: (300) is inconsistent. % 169.34/24.12 | | | | | | % 169.34/24.12 | | | | | Case 2: % 169.34/24.12 | | | | | | % 169.34/24.12 | | | | | | (301) ~ leq(n2, all_74_13) | (a_select3(q_ds1_filter, n4, n2) = % 169.34/24.12 | | | | | | all_74_0 & $i(all_74_0)) % 169.34/24.12 | | | | | | % 169.34/24.12 | | | | | | BETA: splitting (301) gives: % 169.34/24.12 | | | | | | % 169.34/24.12 | | | | | | Case 1: % 169.34/24.12 | | | | | | | % 169.34/24.12 | | | | | | | (302) ~ leq(n2, all_74_13) % 169.34/24.12 | | | | | | | % 169.34/24.12 | | | | | | | REDUCE: (4), (302) imply: % 169.34/24.12 | | | | | | | (303) ~ leq(n2, n5) % 169.34/24.12 | | | | | | | % 169.34/24.12 | | | | | | | PRED_UNIFY: (295), (303) imply: % 169.34/24.12 | | | | | | | (304) $false % 169.34/24.12 | | | | | | | % 169.34/24.12 | | | | | | | CLOSE: (304) is inconsistent. % 169.34/24.12 | | | | | | | % 169.34/24.12 | | | | | | Case 2: % 169.34/24.12 | | | | | | | % 169.34/24.12 | | | | | | | (305) a_select3(q_ds1_filter, n4, n2) = all_74_0 & $i(all_74_0) % 169.34/24.12 | | | | | | | % 169.34/24.12 | | | | | | | ALPHA: (305) implies: % 169.34/24.12 | | | | | | | (306) a_select3(q_ds1_filter, n4, n2) = all_74_0 % 169.34/24.12 | | | | | | | % 169.34/24.12 | | | | | | | GROUND_INST: instantiating (20) with all_74_1, all_74_0, n2, n4, % 169.34/24.12 | | | | | | | q_ds1_filter, simplifying with (294), (306) gives: % 169.34/24.12 | | | | | | | (307) all_74_0 = all_74_1 % 169.34/24.12 | | | | | | | % 169.34/24.12 | | | | | | | REDUCE: (11), (307) imply: % 169.34/24.12 | | | | | | | (308) $false % 169.34/24.12 | | | | | | | % 169.34/24.12 | | | | | | | CLOSE: (308) is inconsistent. % 169.34/24.12 | | | | | | | % 169.34/24.12 | | | | | | End of split % 169.34/24.12 | | | | | | % 169.34/24.12 | | | | | End of split % 169.34/24.12 | | | | | % 169.34/24.12 | | | | End of split % 169.34/24.12 | | | | % 169.34/24.12 | | | Case 2: % 169.34/24.12 | | | | % 169.34/24.12 | | | | (309) all_74_2 = n3 % 169.34/24.12 | | | | % 169.34/24.12 | | | | REDUCE: (261), (309) imply: % 169.34/24.12 | | | | (310) a_select3(q_ds1_filter, n3, n4) = all_74_0 % 169.34/24.12 | | | | % 169.34/24.12 | | | | REDUCE: (262), (309) imply: % 169.34/24.12 | | | | (311) a_select3(q_ds1_filter, n4, n3) = all_74_1 % 169.34/24.12 | | | | % 169.34/24.12 | | | | REDUCE: (21), (309) imply: % 169.34/24.12 | | | | (312) leq(n3, n5) % 169.34/24.12 | | | | % 169.34/24.12 | | | | REDUCE: (9), (309) imply: % 169.34/24.12 | | | | (313) leq(n0, n3) % 169.34/24.12 | | | | % 169.34/24.12 | | | | GROUND_INST: instantiating (19) with n3, n4, all_74_0, simplifying with % 169.34/24.12 | | | | (18), (23), (264), (310), (313) gives: % 169.34/24.12 | | | | (314) ~ leq(n4, all_74_13) | ~ leq(n3, all_74_13) | % 169.34/24.12 | | | | (a_select3(q_ds1_filter, n4, n3) = all_74_0 & $i(all_74_0)) % 169.34/24.12 | | | | % 169.34/24.12 | | | | BETA: splitting (314) gives: % 169.34/24.12 | | | | % 169.34/24.12 | | | | Case 1: % 169.34/24.12 | | | | | % 169.34/24.12 | | | | | (315) ~ leq(n4, all_74_13) % 169.34/24.12 | | | | | % 169.34/24.12 | | | | | REDUCE: (4), (315) imply: % 169.34/24.12 | | | | | (316) ~ leq(n4, n5) % 169.34/24.12 | | | | | % 169.34/24.12 | | | | | PRED_UNIFY: (263), (316) imply: % 169.34/24.12 | | | | | (317) $false % 169.34/24.12 | | | | | % 169.34/24.12 | | | | | CLOSE: (317) is inconsistent. % 169.34/24.12 | | | | | % 169.34/24.12 | | | | Case 2: % 169.34/24.12 | | | | | % 169.34/24.12 | | | | | (318) ~ leq(n3, all_74_13) | (a_select3(q_ds1_filter, n4, n3) = % 169.34/24.12 | | | | | all_74_0 & $i(all_74_0)) % 169.34/24.12 | | | | | % 169.34/24.12 | | | | | BETA: splitting (318) gives: % 169.34/24.12 | | | | | % 169.34/24.12 | | | | | Case 1: % 169.34/24.12 | | | | | | % 169.34/24.12 | | | | | | (319) ~ leq(n3, all_74_13) % 169.34/24.12 | | | | | | % 169.34/24.12 | | | | | | REDUCE: (4), (319) imply: % 169.34/24.12 | | | | | | (320) ~ leq(n3, n5) % 169.34/24.12 | | | | | | % 169.34/24.12 | | | | | | PRED_UNIFY: (312), (320) imply: % 169.34/24.12 | | | | | | (321) $false % 169.34/24.12 | | | | | | % 169.34/24.12 | | | | | | CLOSE: (321) is inconsistent. % 169.34/24.12 | | | | | | % 169.34/24.12 | | | | | Case 2: % 169.34/24.12 | | | | | | % 169.34/24.12 | | | | | | (322) a_select3(q_ds1_filter, n4, n3) = all_74_0 & $i(all_74_0) % 169.34/24.12 | | | | | | % 169.34/24.12 | | | | | | ALPHA: (322) implies: % 169.34/24.12 | | | | | | (323) a_select3(q_ds1_filter, n4, n3) = all_74_0 % 169.34/24.12 | | | | | | % 169.34/24.12 | | | | | | REF_CLOSE: (11), (20), (311), (323) are inconsistent by sub-proof % 169.34/24.12 | | | | | | #29. % 169.34/24.12 | | | | | | % 169.34/24.12 | | | | | End of split % 169.34/24.12 | | | | | % 169.34/24.12 | | | | End of split % 169.34/24.12 | | | | % 169.34/24.12 | | | End of split % 169.34/24.12 | | | % 169.34/24.12 | | Case 2: % 169.34/24.12 | | | % 169.34/24.12 | | | (324) all_74_2 = n4 % 169.34/24.12 | | | % 169.34/24.12 | | | REDUCE: (261), (324) imply: % 169.34/24.12 | | | (325) a_select3(q_ds1_filter, n4, n4) = all_74_0 % 169.34/24.12 | | | % 169.34/24.12 | | | REDUCE: (262), (324) imply: % 169.34/24.12 | | | (326) a_select3(q_ds1_filter, n4, n4) = all_74_1 % 169.34/24.12 | | | % 169.34/24.12 | | | GROUND_INST: instantiating (20) with all_74_1, all_74_0, n4, n4, % 169.34/24.12 | | | q_ds1_filter, simplifying with (325), (326) gives: % 169.34/24.12 | | | (327) all_74_0 = all_74_1 % 169.34/24.12 | | | % 169.34/24.12 | | | REDUCE: (11), (327) imply: % 169.34/24.12 | | | (328) $false % 169.34/24.12 | | | % 169.34/24.12 | | | CLOSE: (328) is inconsistent. % 169.34/24.12 | | | % 169.34/24.12 | | End of split % 169.34/24.12 | | % 169.34/24.12 | End of split % 169.34/24.12 | % 169.34/24.12 End of proof % 169.34/24.12 % 169.34/24.12 Sub-proof #29 shows that the following formulas are inconsistent: % 169.34/24.12 ---------------------------------------------------------------- % 169.34/24.12 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 169.34/24.12 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 169.34/24.12 v0)) % 169.34/24.12 (2) a_select3(q_ds1_filter, n4, n3) = all_74_0 % 169.34/24.12 (3) a_select3(q_ds1_filter, n4, n3) = all_74_1 % 169.34/24.12 (4) ~ (all_74_0 = all_74_1) % 169.34/24.12 % 169.34/24.12 Begin of proof % 169.34/24.12 | % 169.34/24.12 | GROUND_INST: instantiating (1) with all_74_1, all_74_0, n3, n4, q_ds1_filter, % 169.34/24.12 | simplifying with (2), (3) gives: % 169.34/24.12 | (5) all_74_0 = all_74_1 % 169.34/24.12 | % 169.34/24.12 | REDUCE: (4), (5) imply: % 169.34/24.12 | (6) $false % 169.34/24.12 | % 169.34/24.12 | CLOSE: (6) is inconsistent. % 169.34/24.12 | % 169.34/24.12 End of proof % 169.34/24.12 % 169.34/24.12 Sub-proof #30 shows that the following formulas are inconsistent: % 169.34/24.12 ---------------------------------------------------------------- % 169.34/24.12 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 169.34/24.12 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 169.34/24.12 v0)) % 169.34/24.12 (2) a_select3(q_ds1_filter, n4, n1) = all_74_0 % 169.34/24.12 (3) a_select3(q_ds1_filter, n4, n1) = all_74_1 % 169.34/24.12 (4) ~ (all_74_0 = all_74_1) % 169.34/24.12 % 169.34/24.12 Begin of proof % 169.34/24.12 | % 169.34/24.12 | GROUND_INST: instantiating (1) with all_74_1, all_74_0, n1, n4, q_ds1_filter, % 169.34/24.12 | simplifying with (2), (3) gives: % 169.34/24.12 | (5) all_74_0 = all_74_1 % 169.34/24.12 | % 169.34/24.12 | REDUCE: (4), (5) imply: % 169.34/24.12 | (6) $false % 169.34/24.12 | % 169.34/24.12 | CLOSE: (6) is inconsistent. % 169.34/24.12 | % 169.34/24.12 End of proof % 169.34/24.12 % 169.34/24.12 Sub-proof #31 shows that the following formulas are inconsistent: % 169.34/24.12 ---------------------------------------------------------------- % 169.34/24.12 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 169.34/24.12 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 169.34/24.12 v0)) % 169.34/24.12 (2) a_select3(q_ds1_filter, n3, n1) = all_74_0 % 169.34/24.12 (3) a_select3(q_ds1_filter, n3, n1) = all_74_1 % 169.34/24.13 (4) ~ (all_74_0 = all_74_1) % 169.34/24.13 % 169.34/24.13 Begin of proof % 169.34/24.13 | % 169.34/24.13 | GROUND_INST: instantiating (1) with all_74_0, all_74_1, n1, n3, q_ds1_filter, % 169.34/24.13 | simplifying with (2), (3) gives: % 169.34/24.13 | (5) all_74_0 = all_74_1 % 169.34/24.13 | % 169.34/24.13 | REDUCE: (4), (5) imply: % 169.34/24.13 | (6) $false % 169.34/24.13 | % 169.34/24.13 | CLOSE: (6) is inconsistent. % 169.34/24.13 | % 169.34/24.13 End of proof % 169.34/24.13 % 169.34/24.13 Sub-proof #32 shows that the following formulas are inconsistent: % 169.34/24.13 ---------------------------------------------------------------- % 169.34/24.13 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 169.34/24.13 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 169.34/24.13 v0)) % 169.34/24.13 (2) a_select3(q_ds1_filter, n2, n1) = all_74_0 % 169.34/24.13 (3) a_select3(q_ds1_filter, n2, n1) = all_74_1 % 169.34/24.13 (4) ~ (all_74_0 = all_74_1) % 169.34/24.13 % 169.34/24.13 Begin of proof % 169.34/24.13 | % 169.34/24.13 | GROUND_INST: instantiating (1) with all_74_1, all_74_0, n1, n2, q_ds1_filter, % 169.34/24.13 | simplifying with (2), (3) gives: % 169.34/24.13 | (5) all_74_0 = all_74_1 % 169.34/24.13 | % 169.34/24.13 | REDUCE: (4), (5) imply: % 169.34/24.13 | (6) $false % 169.34/24.13 | % 169.34/24.13 | CLOSE: (6) is inconsistent. % 169.34/24.13 | % 169.34/24.13 End of proof % 169.34/24.13 % 169.34/24.13 Sub-proof #33 shows that the following formulas are inconsistent: % 169.34/24.13 ---------------------------------------------------------------- % 169.34/24.13 (1) $i(all_74_3) % 169.34/24.13 (2) all_74_3 = n0 % 169.34/24.13 (3) gt(all_74_3, n0) % 169.34/24.13 (4) ! [v0: $i] : ( ~ $i(v0) | ~ gt(v0, v0)) % 169.34/24.13 % 169.34/24.13 Begin of proof % 169.34/24.13 | % 169.34/24.13 | REDUCE: (1), (2) imply: % 169.34/24.13 | (5) $i(n0) % 169.34/24.13 | % 169.34/24.13 | REDUCE: (2), (3) imply: % 169.34/24.13 | (6) gt(n0, n0) % 169.34/24.13 | % 169.34/24.13 | GROUND_INST: instantiating (4) with n0, simplifying with (5), (6) gives: % 169.34/24.13 | (7) $false % 169.34/24.13 | % 169.34/24.13 | CLOSE: (7) is inconsistent. % 169.34/24.13 | % 169.34/24.13 End of proof % 169.34/24.13 % 169.34/24.13 Sub-proof #34 shows that the following formulas are inconsistent: % 169.34/24.13 ---------------------------------------------------------------- % 169.34/24.13 (1) $i(all_74_2) % 169.34/24.13 (2) all_74_2 = n0 % 169.34/24.13 (3) gt(all_74_2, n0) % 169.34/24.13 (4) ! [v0: $i] : ( ~ $i(v0) | ~ gt(v0, v0)) % 169.34/24.13 % 169.34/24.13 Begin of proof % 169.34/24.13 | % 169.34/24.13 | REDUCE: (1), (2) imply: % 169.34/24.13 | (5) $i(n0) % 169.34/24.13 | % 169.34/24.13 | REDUCE: (2), (3) imply: % 169.34/24.13 | (6) gt(n0, n0) % 169.34/24.13 | % 169.34/24.13 | GROUND_INST: instantiating (4) with n0, simplifying with (5), (6) gives: % 169.34/24.13 | (7) $false % 169.34/24.13 | % 169.34/24.13 | CLOSE: (7) is inconsistent. % 169.34/24.13 | % 169.34/24.13 End of proof % 169.34/24.13 % SZS output end Proof for theBenchmark % 169.34/24.13 % 169.34/24.13 23531ms %------------------------------------------------------------------------------