%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWV115+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 : n007.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 22:54:58 EDT 2023 % Result : Theorem 77.52s 10.69s % Output : Proof 234.14s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.11 % Problem : SWV115+1 : TPTP v8.1.2. Bugfixed v3.3.0. % 0.11/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.33 % Computer : n007.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 06:30:28 EDT 2023 % 0.12/0.33 % CPUTime : % 0.18/0.58 ________ _____ % 0.18/0.58 ___ __ \_________(_)________________________________ % 0.18/0.58 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.18/0.58 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.18/0.58 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.18/0.58 % 0.18/0.58 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.18/0.58 (2023-06-19) % 0.18/0.58 % 0.18/0.58 (c) Philipp Rümmer, 2009-2023 % 0.18/0.58 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.18/0.58 Amanda Stjerna. % 0.18/0.58 Free software under BSD-3-Clause. % 0.18/0.58 % 0.18/0.58 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.18/0.58 % 0.18/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.63/0.59 Running up to 7 provers in parallel. % 0.63/0.61 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.63/0.61 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.63/0.61 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.63/0.61 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.63/0.61 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.63/0.61 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.63/0.61 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 5.00/1.39 Prover 4: Preprocessing ... % 5.00/1.39 Prover 1: Preprocessing ... % 5.00/1.41 Prover 0: Preprocessing ... % 5.00/1.41 Prover 3: Preprocessing ... % 5.00/1.41 Prover 6: Preprocessing ... % 5.00/1.41 Prover 2: Preprocessing ... % 5.00/1.41 Prover 5: Preprocessing ... % 11.65/2.26 Prover 1: Warning: ignoring some quantifiers % 11.65/2.28 Prover 3: Warning: ignoring some quantifiers % 12.10/2.34 Prover 3: Constructing countermodel ... % 12.10/2.35 Prover 1: Constructing countermodel ... % 12.55/2.36 Prover 6: Proving ... % 12.74/2.41 Prover 4: Warning: ignoring some quantifiers % 12.99/2.47 Prover 0: Proving ... % 12.99/2.48 Prover 5: Proving ... % 12.99/2.50 Prover 4: Constructing countermodel ... % 12.99/2.53 Prover 2: Proving ... % 74.23/10.29 Prover 2: stopped % 74.23/10.29 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 75.16/10.45 Prover 7: Preprocessing ... % 77.11/10.62 Prover 7: Warning: ignoring some quantifiers % 77.11/10.65 Prover 7: Constructing countermodel ... % 77.52/10.69 Prover 3: proved (10088ms) % 77.52/10.69 % 77.52/10.69 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 77.52/10.69 % 77.52/10.69 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 77.52/10.69 Prover 5: stopped % 77.52/10.70 Prover 6: stopped % 77.52/10.71 Prover 0: stopped % 77.52/10.71 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 77.52/10.71 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 77.52/10.71 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 78.96/10.85 Prover 8: Preprocessing ... % 78.96/10.86 Prover 10: Preprocessing ... % 78.96/10.88 Prover 13: Preprocessing ... % 78.96/10.88 Prover 11: Preprocessing ... % 79.74/10.98 Prover 10: Warning: ignoring some quantifiers % 79.74/11.00 Prover 8: Warning: ignoring some quantifiers % 79.74/11.00 Prover 13: Warning: ignoring some quantifiers % 79.74/11.01 Prover 8: Constructing countermodel ... % 79.74/11.01 Prover 10: Constructing countermodel ... % 79.74/11.02 Prover 13: Constructing countermodel ... % 80.70/11.08 Prover 11: Warning: ignoring some quantifiers % 80.70/11.11 Prover 11: Constructing countermodel ... % 110.54/14.92 Prover 13: stopped % 110.54/14.93 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 111.58/15.06 Prover 16: Preprocessing ... % 112.82/15.21 Prover 16: Warning: ignoring some quantifiers % 112.82/15.23 Prover 16: Constructing countermodel ... % 118.27/15.95 Prover 1: stopped % 118.70/15.96 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 119.32/16.06 Prover 19: Preprocessing ... % 120.54/16.24 Prover 19: Warning: ignoring some quantifiers % 120.54/16.25 Prover 19: Constructing countermodel ... % 146.76/19.70 Prover 19: stopped % 148.70/20.01 Prover 16: stopped % 190.72/27.93 Prover 4: stopped % 200.77/30.28 Prover 7: stopped % 230.54/39.07 Prover 10: Found proof (size 6596) % 230.54/39.07 Prover 10: proved (28370ms) % 230.54/39.08 Prover 8: stopped % 230.54/39.08 Prover 11: stopped % 230.54/39.08 % 230.54/39.08 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 230.54/39.08 % 230.94/39.21 % SZS output start Proof for theBenchmark % 230.94/39.23 Assumptions after simplification: % 230.94/39.23 --------------------------------- % 230.94/39.23 % 230.94/39.23 (finite_domain_1) % 230.94/39.23 $i(n1) & $i(n0) & ! [v0: $i] : (v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0, % 230.94/39.23 n1) | ~ leq(n0, v0)) % 230.94/39.23 % 230.94/39.23 (finite_domain_2) % 230.94/39.23 $i(n2) & $i(n1) & $i(n0) & ! [v0: $i] : (v0 = n2 | v0 = n1 | v0 = n0 | ~ % 230.94/39.23 $i(v0) | ~ leq(v0, n2) | ~ leq(n0, v0)) % 230.94/39.23 % 230.94/39.23 (finite_domain_5) % 230.94/39.24 $i(n5) & $i(n4) & $i(n3) & $i(n2) & $i(n1) & $i(n0) & ! [v0: $i] : (v0 = n5 | % 230.94/39.24 v0 = n4 | v0 = n3 | v0 = n2 | v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0, n5) % 230.94/39.24 | ~ leq(n0, v0)) % 230.94/39.24 % 230.94/39.24 (irreflexivity_gt) % 230.94/39.24 ! [v0: $i] : ( ~ $i(v0) | ~ gt(v0, v0)) % 230.94/39.24 % 230.94/39.24 (leq_gt2) % 230.94/39.24 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ leq(v0, v1) % 230.94/39.24 | gt(v1, v0)) % 230.94/39.24 % 230.94/39.24 (leq_gt_pred) % 231.21/39.27 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (pred(v1) = v2) | ~ $i(v1) | ~ % 231.21/39.27 $i(v0) | ~ leq(v0, v2) | gt(v1, v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 231.21/39.27 $i] : ( ~ (pred(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ gt(v1, v0) | leq(v0, % 231.21/39.27 v2)) % 231.21/39.27 % 231.21/39.27 (pred_minus_1) % 231.21/39.27 $i(n1) & ! [v0: $i] : ! [v1: $i] : ( ~ (minus(v0, n1) = v1) | ~ $i(v0) | % 231.21/39.27 (pred(v0) = v1 & $i(v1))) % 231.21/39.27 % 231.21/39.27 (pred_succ) % 231.21/39.27 ! [v0: $i] : ! [v1: $i] : ( ~ (succ(v0) = v1) | ~ $i(v0) | pred(v1) = v0) % 231.21/39.27 % 231.21/39.27 (quaternion_ds1_symm_0008) % 231.33/39.28 $i(id_ds1_filter) & $i(pminus_ds1_filter) & $i(r_ds1_filter) & % 231.33/39.28 $i(q_ds1_filter) & $i(n6) & $i(n999) & $i(pv5) & $i(n3) & $i(n1) & $i(n0) & ? % 231.33/39.28 [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] % 231.33/39.28 : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? % 231.33/39.28 [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : ? [v15: $i] : ? % 231.33/39.28 [v16: $i] : ? [v17: $i] : ? [v18: $i] : ? [v19: $i] : ? [v20: $i] : ? % 231.33/39.28 [v21: $i] : ? [v22: $i] : (minus(n6, n1) = v1 & minus(n999, n1) = v0 & % 231.33/39.28 minus(n3, n1) = v2 & $i(v20) & $i(v19) & $i(v16) & $i(v15) & $i(v12) & % 231.33/39.28 $i(v11) & $i(v8) & $i(v7) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & % 231.33/39.28 leq(pv5, v0) & leq(n0, pv5) & ! [v23: $i] : ! [v24: $i] : ! [v25: $i] : ( % 231.33/39.28 ~ (a_select3(id_ds1_filter, v23, v24) = v25) | ~ $i(v24) | ~ $i(v23) | % 231.33/39.28 ~ leq(v24, v1) | ~ leq(v23, v1) | ~ leq(n0, v24) | ~ leq(n0, v23) | % 231.33/39.28 (a_select3(id_ds1_filter, v24, v23) = v25 & $i(v25))) & ! [v23: $i] : ! % 231.33/39.28 [v24: $i] : ! [v25: $i] : ( ~ (a_select3(pminus_ds1_filter, v23, v24) = % 231.33/39.28 v25) | ~ $i(v24) | ~ $i(v23) | ~ leq(v24, v1) | ~ leq(v23, v1) | ~ % 231.33/39.28 leq(n0, v24) | ~ leq(n0, v23) | (a_select3(pminus_ds1_filter, v24, v23) = % 231.33/39.28 v25 & $i(v25))) & ! [v23: $i] : ! [v24: $i] : ! [v25: $i] : ( ~ % 231.33/39.28 (a_select3(r_ds1_filter, v23, v24) = v25) | ~ $i(v24) | ~ $i(v23) | ~ % 231.33/39.28 leq(v24, v2) | ~ leq(v23, v2) | ~ leq(n0, v24) | ~ leq(n0, v23) | % 231.33/39.28 (a_select3(r_ds1_filter, v24, v23) = v25 & $i(v25))) & ! [v23: $i] : ! % 231.33/39.28 [v24: $i] : ! [v25: $i] : ( ~ (a_select3(q_ds1_filter, v23, v24) = v25) | % 231.33/39.28 ~ $i(v24) | ~ $i(v23) | ~ leq(v24, v1) | ~ leq(v23, v1) | ~ leq(n0, % 231.33/39.28 v24) | ~ leq(n0, v23) | (a_select3(q_ds1_filter, v24, v23) = v25 & % 231.33/39.28 $i(v25))) & (( ~ (v22 = v21) & a_select3(q_ds1_filter, v20, v19) = v22 & % 231.33/39.28 a_select3(q_ds1_filter, v19, v20) = v21 & $i(v22) & $i(v21) & leq(v20, % 231.33/39.28 v1) & leq(v19, v1) & leq(n0, v20) & leq(n0, v19)) | ( ~ (v18 = v17) & % 231.33/39.29 a_select3(r_ds1_filter, v16, v15) = v18 & a_select3(r_ds1_filter, v15, % 231.33/39.29 v16) = v17 & $i(v18) & $i(v17) & leq(v16, v2) & leq(v15, v2) & leq(n0, % 231.33/39.29 v16) & leq(n0, v15)) | ( ~ (v14 = v13) & a_select3(pminus_ds1_filter, % 231.33/39.29 v12, v11) = v14 & a_select3(pminus_ds1_filter, v11, v12) = v13 & % 231.33/39.29 $i(v14) & $i(v13) & leq(v12, v1) & leq(v11, v1) & leq(n0, v12) & leq(n0, % 231.33/39.29 v11)) | ( ~ (v10 = v9) & a_select3(pminus_ds1_filter, v8, v7) = v10 & % 231.33/39.29 a_select3(pminus_ds1_filter, v7, v8) = v9 & $i(v10) & $i(v9) & leq(v8, % 231.33/39.29 v1) & leq(v7, v1) & leq(n0, v8) & leq(n0, v7)) | ( ~ (v6 = v5) & % 231.33/39.29 a_select3(id_ds1_filter, v4, v3) = v6 & a_select3(id_ds1_filter, v3, v4) % 231.33/39.29 = v5 & $i(v6) & $i(v5) & leq(v4, v1) & leq(v3, v1) & leq(n0, v4) & % 231.33/39.29 leq(n0, v3)))) % 231.33/39.29 % 231.33/39.29 (successor_1) % 231.33/39.29 succ(n0) = n1 & $i(n1) & $i(n0) % 231.33/39.29 % 231.33/39.29 (successor_2) % 231.33/39.29 $i(n2) & $i(n0) & ? [v0: $i] : (succ(v0) = n2 & succ(n0) = v0 & $i(v0)) % 231.33/39.29 % 231.33/39.29 (successor_3) % 231.33/39.29 $i(n3) & $i(n0) & ? [v0: $i] : ? [v1: $i] : (succ(v1) = n3 & succ(v0) = v1 & % 231.33/39.29 succ(n0) = v0 & $i(v1) & $i(v0)) % 231.33/39.29 % 231.33/39.29 (successor_4) % 231.33/39.29 $i(n4) & $i(n0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (succ(v2) = n4 & % 231.33/39.29 succ(v1) = v2 & succ(v0) = v1 & succ(n0) = v0 & $i(v2) & $i(v1) & $i(v0)) % 231.33/39.29 % 231.33/39.29 (successor_5) % 231.33/39.29 $i(n5) & $i(n0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 231.33/39.29 (succ(v3) = n5 & succ(v2) = v3 & succ(v1) = v2 & succ(v0) = v1 & succ(n0) = v0 % 231.33/39.29 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 231.33/39.29 % 231.33/39.29 (successor_6) % 231.33/39.29 $i(n6) & $i(n0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? % 231.33/39.29 [v4: $i] : (succ(v4) = n6 & succ(v3) = v4 & succ(v2) = v3 & succ(v1) = v2 & % 231.33/39.29 succ(v0) = v1 & succ(n0) = v0 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 231.33/39.29 % 231.33/39.29 (function-axioms) % 231.33/39.30 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 231.33/39.30 $i] : (v1 = v0 | ~ (tptp_update3(v5, v4, v3, v2) = v1) | ~ % 231.33/39.30 (tptp_update3(v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 231.33/39.30 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_update2(v4, v3, v2) = % 231.33/39.30 v1) | ~ (tptp_update2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 231.33/39.30 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (sum(v4, v3, v2) = v1) | % 231.33/39.30 ~ (sum(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 231.33/39.30 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_const_array2(v4, v3, v2) = v1) | % 231.33/39.30 ~ (tptp_const_array2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 231.33/39.30 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (a_select3(v4, v3, v2) = % 231.33/39.30 v1) | ~ (a_select3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 231.33/39.30 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (minus(v3, v2) = v1) | ~ (minus(v3, % 231.33/39.30 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 231.33/39.30 = v0 | ~ (plus(v3, v2) = v1) | ~ (plus(v3, v2) = v0)) & ! [v0: $i] : ! % 231.33/39.31 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (tptp_mmul(v3, v2) = v1) % 231.33/39.31 | ~ (tptp_mmul(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 231.33/39.31 ! [v3: $i] : (v1 = v0 | ~ (tptp_msub(v3, v2) = v1) | ~ (tptp_msub(v3, v2) = % 231.33/39.31 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 231.33/39.31 ~ (tptp_madd(v3, v2) = v1) | ~ (tptp_madd(v3, v2) = v0)) & ! [v0: $i] : ! % 231.33/39.31 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (dim(v3, v2) = v1) | ~ % 231.33/39.31 (dim(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 231.33/39.31 : (v1 = v0 | ~ (tptp_const_array1(v3, v2) = v1) | ~ (tptp_const_array1(v3, % 231.33/39.31 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 231.33/39.31 = v0 | ~ (a_select2(v3, v2) = v1) | ~ (a_select2(v3, v2) = v0)) & ! [v0: % 231.33/39.31 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 231.33/39.31 (uniform_int_rnd(v3, v2) = v1) | ~ (uniform_int_rnd(v3, v2) = v0)) & ! % 231.33/39.31 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (inv(v2) = v1) | ~ % 231.33/39.31 (inv(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 231.33/39.31 (trans(v2) = v1) | ~ (trans(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 231.33/39.31 [v2: $i] : (v1 = v0 | ~ (succ(v2) = v1) | ~ (succ(v2) = v0)) & ! [v0: $i] : % 231.33/39.31 ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (pred(v2) = v1) | ~ (pred(v2) = % 231.33/39.31 v0)) % 231.33/39.31 % 231.33/39.31 Further assumptions not needed in the proof: % 231.33/39.31 -------------------------------------------- % 231.33/39.31 const_array1_select, const_array2_select, defuse, finite_domain_0, % 231.33/39.31 finite_domain_3, finite_domain_4, finite_domain_6, gt_0_tptp_minus_1, gt_1_0, % 231.33/39.31 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, % 231.33/39.31 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, % 231.33/39.31 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, % 231.33/39.31 gt_6_3, gt_6_4, gt_6_5, gt_6_tptp_minus_1, gt_999_0, gt_999_1, gt_999_2, % 231.33/39.31 gt_999_3, gt_999_4, gt_999_5, gt_999_6, gt_999_tptp_minus_1, gt_succ, leq_geq, % 231.33/39.31 leq_gt1, leq_minus, leq_succ, leq_succ_gt, leq_succ_gt_equiv, leq_succ_succ, % 231.33/39.31 lt_gt, matrix_symm_aba1, matrix_symm_aba2, matrix_symm_add, matrix_symm_inv, % 231.33/39.31 matrix_symm_joseph_update, matrix_symm_sub, matrix_symm_trans, % 231.33/39.31 matrix_symm_update_diagonal, reflexivity_leq, sel2_update_1, sel2_update_2, % 231.33/39.31 sel2_update_3, sel3_update_1, sel3_update_2, sel3_update_3, succ_plus_1_l, % 231.33/39.31 succ_plus_1_r, succ_plus_2_l, succ_plus_2_r, succ_plus_3_l, succ_plus_3_r, % 231.33/39.31 succ_plus_4_l, succ_plus_4_r, succ_plus_5_l, succ_plus_5_r, succ_pred, % 231.33/39.31 succ_tptp_minus_1, sum_plus_base, sum_plus_base_float, totality, % 231.33/39.31 transitivity_gt, transitivity_leq, ttrue, uniform_int_rand_ranges_hi, % 231.33/39.31 uniform_int_rand_ranges_lo % 231.33/39.31 % 231.33/39.31 Those formulas are unsatisfiable: % 231.33/39.31 --------------------------------- % 231.33/39.31 % 231.33/39.31 Begin of proof % 231.33/39.31 | % 231.33/39.31 | ALPHA: (leq_gt_pred) implies: % 231.33/39.31 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (pred(v1) = v2) | ~ % 231.33/39.31 | $i(v1) | ~ $i(v0) | ~ gt(v1, v0) | leq(v0, v2)) % 231.33/39.31 | % 231.33/39.31 | ALPHA: (pred_minus_1) implies: % 231.33/39.31 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (minus(v0, n1) = v1) | ~ $i(v0) | % 231.33/39.31 | (pred(v0) = v1 & $i(v1))) % 231.33/39.31 | % 231.33/39.31 | ALPHA: (finite_domain_5) implies: % 231.33/39.31 | (3) ! [v0: $i] : (v0 = n5 | v0 = n4 | v0 = n3 | v0 = n2 | v0 = n1 | v0 = % 231.33/39.31 | n0 | ~ $i(v0) | ~ leq(v0, n5) | ~ leq(n0, v0)) % 231.33/39.31 | % 231.33/39.31 | ALPHA: (finite_domain_1) implies: % 231.33/39.31 | (4) ! [v0: $i] : (v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0, n1) | ~ % 231.33/39.31 | leq(n0, v0)) % 231.33/39.31 | % 231.33/39.31 | ALPHA: (finite_domain_2) implies: % 231.33/39.31 | (5) ! [v0: $i] : (v0 = n2 | v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0, n2) % 231.33/39.31 | | ~ leq(n0, v0)) % 231.33/39.31 | % 231.33/39.31 | ALPHA: (successor_4) implies: % 231.33/39.32 | (6) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (succ(v2) = n4 & succ(v1) = % 231.33/39.32 | v2 & succ(v0) = v1 & succ(n0) = v0 & $i(v2) & $i(v1) & $i(v0)) % 231.33/39.32 | % 231.33/39.32 | ALPHA: (successor_5) implies: % 231.33/39.32 | (7) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (succ(v3) = n5 % 231.33/39.32 | & succ(v2) = v3 & succ(v1) = v2 & succ(v0) = v1 & succ(n0) = v0 & % 231.33/39.32 | $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 231.33/39.32 | % 231.33/39.32 | ALPHA: (successor_6) implies: % 231.33/39.32 | (8) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 231.33/39.32 | (succ(v4) = n6 & succ(v3) = v4 & succ(v2) = v3 & succ(v1) = v2 & % 231.33/39.32 | succ(v0) = v1 & succ(n0) = v0 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & % 231.33/39.32 | $i(v0)) % 231.33/39.32 | % 231.33/39.32 | ALPHA: (successor_1) implies: % 231.33/39.32 | (9) succ(n0) = n1 % 231.33/39.32 | % 231.33/39.32 | ALPHA: (successor_2) implies: % 231.33/39.32 | (10) ? [v0: $i] : (succ(v0) = n2 & succ(n0) = v0 & $i(v0)) % 231.33/39.32 | % 231.33/39.32 | ALPHA: (successor_3) implies: % 231.33/39.33 | (11) ? [v0: $i] : ? [v1: $i] : (succ(v1) = n3 & succ(v0) = v1 & succ(n0) % 231.33/39.33 | = v0 & $i(v1) & $i(v0)) % 231.33/39.33 | % 231.33/39.33 | ALPHA: (quaternion_ds1_symm_0008) implies: % 231.60/39.33 | (12) $i(n0) % 231.60/39.33 | (13) $i(n6) % 231.60/39.35 | (14) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 231.60/39.35 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : % 231.60/39.35 | ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: % 231.60/39.35 | $i] : ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? [v18: $i] : ? % 231.60/39.35 | [v19: $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : (minus(n6, % 231.60/39.35 | n1) = v1 & minus(n999, n1) = v0 & minus(n3, n1) = v2 & $i(v20) & % 231.60/39.35 | $i(v19) & $i(v16) & $i(v15) & $i(v12) & $i(v11) & $i(v8) & $i(v7) & % 231.60/39.35 | $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & leq(pv5, v0) & leq(n0, % 231.60/39.35 | pv5) & ! [v23: $i] : ! [v24: $i] : ! [v25: $i] : ( ~ % 231.60/39.35 | (a_select3(id_ds1_filter, v23, v24) = v25) | ~ $i(v24) | ~ % 231.60/39.35 | $i(v23) | ~ leq(v24, v1) | ~ leq(v23, v1) | ~ leq(n0, v24) | ~ % 231.60/39.35 | leq(n0, v23) | (a_select3(id_ds1_filter, v24, v23) = v25 & % 231.60/39.35 | $i(v25))) & ! [v23: $i] : ! [v24: $i] : ! [v25: $i] : ( ~ % 231.60/39.35 | (a_select3(pminus_ds1_filter, v23, v24) = v25) | ~ $i(v24) | ~ % 231.60/39.35 | $i(v23) | ~ leq(v24, v1) | ~ leq(v23, v1) | ~ leq(n0, v24) | ~ % 231.60/39.35 | leq(n0, v23) | (a_select3(pminus_ds1_filter, v24, v23) = v25 & % 231.60/39.35 | $i(v25))) & ! [v23: $i] : ! [v24: $i] : ! [v25: $i] : ( ~ % 231.60/39.35 | (a_select3(r_ds1_filter, v23, v24) = v25) | ~ $i(v24) | ~ % 231.60/39.35 | $i(v23) | ~ leq(v24, v2) | ~ leq(v23, v2) | ~ leq(n0, v24) | ~ % 231.60/39.35 | leq(n0, v23) | (a_select3(r_ds1_filter, v24, v23) = v25 & % 231.60/39.35 | $i(v25))) & ! [v23: $i] : ! [v24: $i] : ! [v25: $i] : ( ~ % 231.60/39.35 | (a_select3(q_ds1_filter, v23, v24) = v25) | ~ $i(v24) | ~ % 231.60/39.35 | $i(v23) | ~ leq(v24, v1) | ~ leq(v23, v1) | ~ leq(n0, v24) | ~ % 231.60/39.35 | leq(n0, v23) | (a_select3(q_ds1_filter, v24, v23) = v25 & % 231.60/39.35 | $i(v25))) & (( ~ (v22 = v21) & a_select3(q_ds1_filter, v20, v19) % 231.60/39.35 | = v22 & a_select3(q_ds1_filter, v19, v20) = v21 & $i(v22) & % 231.60/39.35 | $i(v21) & leq(v20, v1) & leq(v19, v1) & leq(n0, v20) & leq(n0, % 231.60/39.35 | v19)) | ( ~ (v18 = v17) & a_select3(r_ds1_filter, v16, v15) = % 231.60/39.35 | v18 & a_select3(r_ds1_filter, v15, v16) = v17 & $i(v18) & % 231.60/39.35 | $i(v17) & leq(v16, v2) & leq(v15, v2) & leq(n0, v16) & leq(n0, % 231.60/39.35 | v15)) | ( ~ (v14 = v13) & a_select3(pminus_ds1_filter, v12, % 231.60/39.35 | v11) = v14 & a_select3(pminus_ds1_filter, v11, v12) = v13 & % 231.60/39.35 | $i(v14) & $i(v13) & leq(v12, v1) & leq(v11, v1) & leq(n0, v12) & % 231.60/39.35 | leq(n0, v11)) | ( ~ (v10 = v9) & a_select3(pminus_ds1_filter, % 231.60/39.35 | v8, v7) = v10 & a_select3(pminus_ds1_filter, v7, v8) = v9 & % 231.60/39.35 | $i(v10) & $i(v9) & leq(v8, v1) & leq(v7, v1) & leq(n0, v8) & % 231.60/39.35 | leq(n0, v7)) | ( ~ (v6 = v5) & a_select3(id_ds1_filter, v4, v3) % 231.60/39.35 | = v6 & a_select3(id_ds1_filter, v3, v4) = v5 & $i(v6) & $i(v5) & % 231.60/39.35 | leq(v4, v1) & leq(v3, v1) & leq(n0, v4) & leq(n0, v3)))) % 231.60/39.35 | % 231.60/39.35 | ALPHA: (function-axioms) implies: % 231.60/39.35 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (pred(v2) = % 231.60/39.35 | v1) | ~ (pred(v2) = v0)) % 231.60/39.35 | (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (succ(v2) = % 231.60/39.35 | v1) | ~ (succ(v2) = v0)) % 231.60/39.35 | (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 231.60/39.35 | (v1 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) % 231.60/39.35 | = v0)) % 231.60/39.35 | % 231.60/39.35 | DELTA: instantiating (10) with fresh symbol all_55_0 gives: % 231.73/39.35 | (18) succ(all_55_0) = n2 & succ(n0) = all_55_0 & $i(all_55_0) % 231.73/39.35 | % 231.73/39.36 | ALPHA: (18) implies: % 231.73/39.36 | (19) $i(all_55_0) % 231.73/39.36 | (20) succ(n0) = all_55_0 % 231.73/39.36 | (21) succ(all_55_0) = n2 % 231.73/39.36 | % 231.73/39.36 | DELTA: instantiating (11) with fresh symbols all_57_0, all_57_1 gives: % 231.73/39.36 | (22) succ(all_57_0) = n3 & succ(all_57_1) = all_57_0 & succ(n0) = all_57_1 % 231.73/39.36 | & $i(all_57_0) & $i(all_57_1) % 231.73/39.36 | % 231.73/39.36 | ALPHA: (22) implies: % 231.73/39.36 | (23) $i(all_57_0) % 231.73/39.36 | (24) succ(n0) = all_57_1 % 231.73/39.36 | (25) succ(all_57_1) = all_57_0 % 231.73/39.36 | (26) succ(all_57_0) = n3 % 231.73/39.36 | % 231.73/39.36 | DELTA: instantiating (6) with fresh symbols all_60_0, all_60_1, all_60_2 % 231.73/39.36 | gives: % 231.73/39.36 | (27) succ(all_60_0) = n4 & succ(all_60_1) = all_60_0 & succ(all_60_2) = % 231.73/39.36 | all_60_1 & succ(n0) = all_60_2 & $i(all_60_0) & $i(all_60_1) & % 231.73/39.36 | $i(all_60_2) % 231.73/39.36 | % 231.73/39.36 | ALPHA: (27) implies: % 231.73/39.36 | (28) $i(all_60_0) % 231.73/39.36 | (29) succ(n0) = all_60_2 % 231.73/39.36 | (30) succ(all_60_2) = all_60_1 % 231.73/39.36 | (31) succ(all_60_1) = all_60_0 % 231.73/39.36 | (32) succ(all_60_0) = n4 % 231.73/39.36 | % 231.73/39.36 | DELTA: instantiating (7) with fresh symbols all_62_0, all_62_1, all_62_2, % 231.73/39.36 | all_62_3 gives: % 231.73/39.36 | (33) succ(all_62_0) = n5 & succ(all_62_1) = all_62_0 & succ(all_62_2) = % 231.73/39.36 | all_62_1 & succ(all_62_3) = all_62_2 & succ(n0) = all_62_3 & % 231.73/39.36 | $i(all_62_0) & $i(all_62_1) & $i(all_62_2) & $i(all_62_3) % 231.73/39.36 | % 231.73/39.36 | ALPHA: (33) implies: % 231.73/39.36 | (34) $i(all_62_0) % 231.73/39.36 | (35) succ(n0) = all_62_3 % 231.73/39.36 | (36) succ(all_62_3) = all_62_2 % 231.73/39.36 | (37) succ(all_62_2) = all_62_1 % 231.73/39.36 | (38) succ(all_62_1) = all_62_0 % 231.73/39.36 | (39) succ(all_62_0) = n5 % 231.73/39.36 | % 231.73/39.36 | DELTA: instantiating (8) with fresh symbols all_64_0, all_64_1, all_64_2, % 231.73/39.36 | all_64_3, all_64_4 gives: % 231.73/39.37 | (40) succ(all_64_0) = n6 & succ(all_64_1) = all_64_0 & succ(all_64_2) = % 231.73/39.37 | all_64_1 & succ(all_64_3) = all_64_2 & succ(all_64_4) = all_64_3 & % 231.73/39.37 | succ(n0) = all_64_4 & $i(all_64_0) & $i(all_64_1) & $i(all_64_2) & % 231.73/39.37 | $i(all_64_3) & $i(all_64_4) % 231.73/39.37 | % 231.73/39.37 | ALPHA: (40) implies: % 231.73/39.37 | (41) $i(all_64_0) % 231.73/39.37 | (42) succ(n0) = all_64_4 % 231.73/39.37 | (43) succ(all_64_4) = all_64_3 % 231.73/39.37 | (44) succ(all_64_3) = all_64_2 % 231.73/39.37 | (45) succ(all_64_2) = all_64_1 % 231.73/39.37 | (46) succ(all_64_1) = all_64_0 % 231.73/39.37 | (47) succ(all_64_0) = n6 % 231.73/39.37 | % 231.73/39.37 | DELTA: instantiating (14) with fresh symbols all_74_0, all_74_1, all_74_2, % 231.73/39.37 | all_74_3, all_74_4, all_74_5, all_74_6, all_74_7, all_74_8, all_74_9, % 231.73/39.37 | all_74_10, all_74_11, all_74_12, all_74_13, all_74_14, all_74_15, % 231.73/39.37 | all_74_16, all_74_17, all_74_18, all_74_19, all_74_20, all_74_21, % 231.73/39.37 | all_74_22 gives: % 231.73/39.38 | (48) minus(n6, n1) = all_74_21 & minus(n999, n1) = all_74_22 & minus(n3, % 231.73/39.38 | n1) = all_74_20 & $i(all_74_2) & $i(all_74_3) & $i(all_74_6) & % 231.73/39.38 | $i(all_74_7) & $i(all_74_10) & $i(all_74_11) & $i(all_74_14) & % 231.73/39.38 | $i(all_74_15) & $i(all_74_18) & $i(all_74_19) & $i(all_74_20) & % 231.73/39.38 | $i(all_74_21) & $i(all_74_22) & leq(pv5, all_74_22) & leq(n0, pv5) & % 231.73/39.38 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (a_select3(id_ds1_filter, % 231.73/39.38 | v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ leq(v1, all_74_21) | % 231.73/39.38 | ~ leq(v0, all_74_21) | ~ leq(n0, v1) | ~ leq(n0, v0) | % 231.73/39.38 | (a_select3(id_ds1_filter, v1, v0) = v2 & $i(v2))) & ! [v0: $i] : ! % 231.73/39.38 | [v1: $i] : ! [v2: $i] : ( ~ (a_select3(pminus_ds1_filter, v0, v1) = % 231.73/39.38 | v2) | ~ $i(v1) | ~ $i(v0) | ~ leq(v1, all_74_21) | ~ leq(v0, % 231.73/39.38 | all_74_21) | ~ leq(n0, v1) | ~ leq(n0, v0) | % 231.73/39.38 | (a_select3(pminus_ds1_filter, v1, v0) = v2 & $i(v2))) & ! [v0: $i] % 231.73/39.38 | : ! [v1: $i] : ! [v2: $i] : ( ~ (a_select3(r_ds1_filter, v0, v1) = % 231.73/39.38 | v2) | ~ $i(v1) | ~ $i(v0) | ~ leq(v1, all_74_20) | ~ leq(v0, % 231.73/39.38 | all_74_20) | ~ leq(n0, v1) | ~ leq(n0, v0) | % 231.73/39.38 | (a_select3(r_ds1_filter, v1, v0) = v2 & $i(v2))) & ! [v0: $i] : ! % 231.73/39.38 | [v1: $i] : ! [v2: $i] : ( ~ (a_select3(q_ds1_filter, v0, v1) = v2) | % 231.73/39.38 | ~ $i(v1) | ~ $i(v0) | ~ leq(v1, all_74_21) | ~ leq(v0, all_74_21) % 231.73/39.38 | | ~ leq(n0, v1) | ~ leq(n0, v0) | (a_select3(q_ds1_filter, v1, v0) % 231.73/39.38 | = v2 & $i(v2))) & (( ~ (all_74_0 = all_74_1) & % 231.73/39.38 | a_select3(q_ds1_filter, all_74_2, all_74_3) = all_74_0 & % 231.73/39.38 | a_select3(q_ds1_filter, all_74_3, all_74_2) = all_74_1 & % 231.73/39.38 | $i(all_74_0) & $i(all_74_1) & leq(all_74_2, all_74_21) & % 231.73/39.38 | leq(all_74_3, all_74_21) & leq(n0, all_74_2) & leq(n0, all_74_3)) % 231.73/39.38 | | ( ~ (all_74_4 = all_74_5) & a_select3(r_ds1_filter, all_74_6, % 231.73/39.38 | all_74_7) = all_74_4 & a_select3(r_ds1_filter, all_74_7, % 231.73/39.38 | all_74_6) = all_74_5 & $i(all_74_4) & $i(all_74_5) & % 231.73/39.38 | leq(all_74_6, all_74_20) & leq(all_74_7, all_74_20) & leq(n0, % 231.73/39.38 | all_74_6) & leq(n0, all_74_7)) | ( ~ (all_74_8 = all_74_9) & % 231.73/39.38 | a_select3(pminus_ds1_filter, all_74_10, all_74_11) = all_74_8 & % 231.73/39.38 | a_select3(pminus_ds1_filter, all_74_11, all_74_10) = all_74_9 & % 231.73/39.38 | $i(all_74_8) & $i(all_74_9) & leq(all_74_10, all_74_21) & % 231.73/39.38 | leq(all_74_11, all_74_21) & leq(n0, all_74_10) & leq(n0, % 231.73/39.38 | all_74_11)) | ( ~ (all_74_12 = all_74_13) & % 231.73/39.38 | a_select3(pminus_ds1_filter, all_74_14, all_74_15) = all_74_12 & % 231.73/39.38 | a_select3(pminus_ds1_filter, all_74_15, all_74_14) = all_74_13 & % 231.73/39.38 | $i(all_74_12) & $i(all_74_13) & leq(all_74_14, all_74_21) & % 231.73/39.38 | leq(all_74_15, all_74_21) & leq(n0, all_74_14) & leq(n0, % 231.73/39.38 | all_74_15)) | ( ~ (all_74_16 = all_74_17) & % 231.73/39.38 | a_select3(id_ds1_filter, all_74_18, all_74_19) = all_74_16 & % 231.73/39.38 | a_select3(id_ds1_filter, all_74_19, all_74_18) = all_74_17 & % 231.73/39.38 | $i(all_74_16) & $i(all_74_17) & leq(all_74_18, all_74_21) & % 231.73/39.38 | leq(all_74_19, all_74_21) & leq(n0, all_74_18) & leq(n0, % 231.73/39.38 | all_74_19))) % 231.73/39.38 | % 231.73/39.38 | ALPHA: (48) implies: % 231.73/39.39 | (49) $i(all_74_19) % 231.73/39.39 | (50) $i(all_74_18) % 231.73/39.39 | (51) $i(all_74_15) % 231.73/39.39 | (52) $i(all_74_14) % 231.73/39.39 | (53) $i(all_74_11) % 231.73/39.39 | (54) $i(all_74_10) % 231.73/39.39 | (55) $i(all_74_7) % 231.73/39.39 | (56) $i(all_74_6) % 231.73/39.39 | (57) $i(all_74_3) % 231.73/39.39 | (58) $i(all_74_2) % 231.73/39.39 | (59) minus(n3, n1) = all_74_20 % 231.73/39.39 | (60) minus(n6, n1) = all_74_21 % 231.73/39.39 | (61) ( ~ (all_74_0 = all_74_1) & a_select3(q_ds1_filter, all_74_2, % 231.73/39.39 | all_74_3) = all_74_0 & a_select3(q_ds1_filter, all_74_3, all_74_2) % 231.73/39.39 | = all_74_1 & $i(all_74_0) & $i(all_74_1) & leq(all_74_2, all_74_21) % 231.73/39.39 | & leq(all_74_3, all_74_21) & leq(n0, all_74_2) & leq(n0, all_74_3)) % 231.73/39.39 | | ( ~ (all_74_4 = all_74_5) & a_select3(r_ds1_filter, all_74_6, % 231.73/39.39 | all_74_7) = all_74_4 & a_select3(r_ds1_filter, all_74_7, all_74_6) % 231.73/39.39 | = all_74_5 & $i(all_74_4) & $i(all_74_5) & leq(all_74_6, all_74_20) % 231.73/39.39 | & leq(all_74_7, all_74_20) & leq(n0, all_74_6) & leq(n0, all_74_7)) % 231.73/39.39 | | ( ~ (all_74_8 = all_74_9) & a_select3(pminus_ds1_filter, all_74_10, % 231.73/39.39 | all_74_11) = all_74_8 & a_select3(pminus_ds1_filter, all_74_11, % 231.73/39.39 | all_74_10) = all_74_9 & $i(all_74_8) & $i(all_74_9) & % 231.73/39.39 | leq(all_74_10, all_74_21) & leq(all_74_11, all_74_21) & leq(n0, % 231.73/39.39 | all_74_10) & leq(n0, all_74_11)) | ( ~ (all_74_12 = all_74_13) & % 231.73/39.39 | a_select3(pminus_ds1_filter, all_74_14, all_74_15) = all_74_12 & % 231.73/39.39 | a_select3(pminus_ds1_filter, all_74_15, all_74_14) = all_74_13 & % 231.73/39.39 | $i(all_74_12) & $i(all_74_13) & leq(all_74_14, all_74_21) & % 231.73/39.39 | leq(all_74_15, all_74_21) & leq(n0, all_74_14) & leq(n0, all_74_15)) % 231.73/39.39 | | ( ~ (all_74_16 = all_74_17) & a_select3(id_ds1_filter, all_74_18, % 231.73/39.39 | all_74_19) = all_74_16 & a_select3(id_ds1_filter, all_74_19, % 231.73/39.39 | all_74_18) = all_74_17 & $i(all_74_16) & $i(all_74_17) & % 231.73/39.39 | leq(all_74_18, all_74_21) & leq(all_74_19, all_74_21) & leq(n0, % 231.73/39.39 | all_74_18) & leq(n0, all_74_19)) % 231.73/39.39 | (62) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (a_select3(q_ds1_filter, % 231.73/39.39 | v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ leq(v1, all_74_21) | % 231.73/39.39 | ~ leq(v0, all_74_21) | ~ leq(n0, v1) | ~ leq(n0, v0) | % 231.73/39.39 | (a_select3(q_ds1_filter, v1, v0) = v2 & $i(v2))) % 231.73/39.39 | (63) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (a_select3(r_ds1_filter, % 231.73/39.39 | v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ leq(v1, all_74_20) | % 231.73/39.39 | ~ leq(v0, all_74_20) | ~ leq(n0, v1) | ~ leq(n0, v0) | % 231.73/39.39 | (a_select3(r_ds1_filter, v1, v0) = v2 & $i(v2))) % 231.73/39.40 | (64) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 231.73/39.40 | (a_select3(pminus_ds1_filter, v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) % 231.73/39.40 | | ~ leq(v1, all_74_21) | ~ leq(v0, all_74_21) | ~ leq(n0, v1) | % 231.73/39.40 | ~ leq(n0, v0) | (a_select3(pminus_ds1_filter, v1, v0) = v2 & % 231.73/39.40 | $i(v2))) % 231.73/39.40 | (65) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 231.73/39.40 | (a_select3(id_ds1_filter, v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 231.73/39.40 | leq(v1, all_74_21) | ~ leq(v0, all_74_21) | ~ leq(n0, v1) | ~ % 231.73/39.40 | leq(n0, v0) | (a_select3(id_ds1_filter, v1, v0) = v2 & $i(v2))) % 231.73/39.40 | % 231.73/39.40 | GROUND_INST: instantiating (16) with all_60_2, all_62_3, n0, simplifying with % 231.73/39.40 | (29), (35) gives: % 231.73/39.40 | (66) all_62_3 = all_60_2 % 231.73/39.40 | % 231.73/39.40 | GROUND_INST: instantiating (16) with all_57_1, all_62_3, n0, simplifying with % 231.73/39.40 | (24), (35) gives: % 231.73/39.40 | (67) all_62_3 = all_57_1 % 231.73/39.40 | % 231.73/39.40 | GROUND_INST: instantiating (16) with all_55_0, all_62_3, n0, simplifying with % 231.73/39.40 | (20), (35) gives: % 231.73/39.40 | (68) all_62_3 = all_55_0 % 231.73/39.40 | % 231.73/39.40 | GROUND_INST: instantiating (16) with all_57_1, all_64_4, n0, simplifying with % 231.73/39.40 | (24), (42) gives: % 231.73/39.40 | (69) all_64_4 = all_57_1 % 231.73/39.40 | % 231.73/39.40 | GROUND_INST: instantiating (16) with n1, all_64_4, n0, simplifying with (9), % 231.73/39.40 | (42) gives: % 231.73/39.40 | (70) all_64_4 = n1 % 231.73/39.40 | % 231.73/39.40 | COMBINE_EQS: (69), (70) imply: % 231.73/39.40 | (71) all_57_1 = n1 % 231.73/39.40 | % 231.73/39.40 | SIMP: (71) implies: % 231.73/39.40 | (72) all_57_1 = n1 % 231.73/39.40 | % 231.73/39.40 | COMBINE_EQS: (66), (68) imply: % 231.73/39.40 | (73) all_60_2 = all_55_0 % 231.73/39.40 | % 231.73/39.40 | COMBINE_EQS: (66), (67) imply: % 231.73/39.40 | (74) all_60_2 = all_57_1 % 231.73/39.40 | % 231.73/39.40 | COMBINE_EQS: (73), (74) imply: % 231.73/39.40 | (75) all_57_1 = all_55_0 % 231.73/39.40 | % 231.73/39.40 | SIMP: (75) implies: % 231.73/39.40 | (76) all_57_1 = all_55_0 % 231.73/39.40 | % 231.73/39.40 | COMBINE_EQS: (72), (76) imply: % 231.73/39.40 | (77) all_55_0 = n1 % 231.73/39.40 | % 231.73/39.40 | COMBINE_EQS: (73), (77) imply: % 231.73/39.40 | (78) all_60_2 = n1 % 231.73/39.40 | % 231.73/39.40 | COMBINE_EQS: (66), (78) imply: % 231.73/39.40 | (79) all_62_3 = n1 % 231.73/39.40 | % 231.73/39.40 | REDUCE: (43), (70) imply: % 231.73/39.40 | (80) succ(n1) = all_64_3 % 231.73/39.40 | % 231.73/39.40 | REDUCE: (36), (79) imply: % 231.73/39.40 | (81) succ(n1) = all_62_2 % 231.73/39.40 | % 231.73/39.40 | REDUCE: (30), (78) imply: % 231.73/39.40 | (82) succ(n1) = all_60_1 % 231.73/39.40 | % 231.73/39.41 | REDUCE: (25), (72) imply: % 231.73/39.41 | (83) succ(n1) = all_57_0 % 231.73/39.41 | % 231.73/39.41 | REDUCE: (21), (77) imply: % 231.73/39.41 | (84) succ(n1) = n2 % 231.73/39.41 | % 231.73/39.41 | REDUCE: (19), (77) imply: % 231.73/39.41 | (85) $i(n1) % 231.73/39.41 | % 231.73/39.41 | GROUND_INST: instantiating (16) with all_60_1, all_62_2, n1, simplifying with % 231.73/39.41 | (81), (82) gives: % 231.73/39.41 | (86) all_62_2 = all_60_1 % 231.73/39.41 | % 231.73/39.41 | GROUND_INST: instantiating (16) with all_57_0, all_62_2, n1, simplifying with % 231.73/39.41 | (81), (83) gives: % 231.73/39.41 | (87) all_62_2 = all_57_0 % 231.73/39.41 | % 231.73/39.41 | GROUND_INST: instantiating (16) with all_60_1, all_64_3, n1, simplifying with % 231.73/39.41 | (80), (82) gives: % 231.73/39.41 | (88) all_64_3 = all_60_1 % 231.73/39.41 | % 231.73/39.41 | GROUND_INST: instantiating (16) with n2, all_64_3, n1, simplifying with (80), % 231.73/39.41 | (84) gives: % 231.73/39.41 | (89) all_64_3 = n2 % 231.73/39.41 | % 231.73/39.41 | COMBINE_EQS: (88), (89) imply: % 231.73/39.41 | (90) all_60_1 = n2 % 231.73/39.41 | % 231.73/39.41 | SIMP: (90) implies: % 231.73/39.41 | (91) all_60_1 = n2 % 231.73/39.41 | % 231.73/39.41 | COMBINE_EQS: (86), (87) imply: % 231.73/39.41 | (92) all_60_1 = all_57_0 % 231.73/39.41 | % 231.73/39.41 | SIMP: (92) implies: % 231.73/39.41 | (93) all_60_1 = all_57_0 % 231.73/39.41 | % 231.73/39.41 | COMBINE_EQS: (91), (93) imply: % 231.73/39.41 | (94) all_57_0 = n2 % 231.73/39.41 | % 231.73/39.41 | SIMP: (94) implies: % 231.73/39.41 | (95) all_57_0 = n2 % 231.73/39.41 | % 231.73/39.41 | COMBINE_EQS: (87), (95) imply: % 231.73/39.41 | (96) all_62_2 = n2 % 231.73/39.41 | % 231.73/39.41 | REDUCE: (44), (89) imply: % 231.73/39.41 | (97) succ(n2) = all_64_2 % 231.73/39.41 | % 231.73/39.41 | REDUCE: (37), (96) imply: % 231.73/39.41 | (98) succ(n2) = all_62_1 % 231.73/39.41 | % 231.73/39.41 | REDUCE: (31), (91) imply: % 231.73/39.41 | (99) succ(n2) = all_60_0 % 231.73/39.41 | % 231.73/39.41 | REDUCE: (26), (95) imply: % 231.73/39.41 | (100) succ(n2) = n3 % 231.73/39.41 | % 231.73/39.41 | REDUCE: (23), (95) imply: % 231.73/39.41 | (101) $i(n2) % 231.73/39.41 | % 231.73/39.41 | GROUND_INST: instantiating (16) with all_60_0, all_62_1, n2, simplifying with % 231.73/39.41 | (98), (99) gives: % 231.73/39.41 | (102) all_62_1 = all_60_0 % 231.73/39.41 | % 231.73/39.41 | GROUND_INST: instantiating (16) with all_62_1, all_64_2, n2, simplifying with % 231.73/39.41 | (97), (98) gives: % 231.73/39.41 | (103) all_64_2 = all_62_1 % 231.73/39.41 | % 231.73/39.41 | GROUND_INST: instantiating (16) with n3, all_64_2, n2, simplifying with (97), % 231.73/39.41 | (100) gives: % 231.73/39.41 | (104) all_64_2 = n3 % 231.73/39.41 | % 231.73/39.41 | COMBINE_EQS: (103), (104) imply: % 231.73/39.41 | (105) all_62_1 = n3 % 231.73/39.41 | % 231.73/39.41 | SIMP: (105) implies: % 231.73/39.41 | (106) all_62_1 = n3 % 231.73/39.41 | % 231.73/39.41 | COMBINE_EQS: (102), (106) imply: % 231.73/39.41 | (107) all_60_0 = n3 % 231.73/39.41 | % 231.73/39.41 | SIMP: (107) implies: % 231.73/39.41 | (108) all_60_0 = n3 % 231.73/39.41 | % 231.73/39.41 | REDUCE: (45), (104) imply: % 231.73/39.41 | (109) succ(n3) = all_64_1 % 231.73/39.41 | % 231.73/39.41 | REDUCE: (38), (106) imply: % 231.73/39.42 | (110) succ(n3) = all_62_0 % 231.73/39.42 | % 231.73/39.42 | REDUCE: (32), (108) imply: % 231.73/39.42 | (111) succ(n3) = n4 % 231.73/39.42 | % 231.73/39.42 | REDUCE: (28), (108) imply: % 231.73/39.42 | (112) $i(n3) % 231.73/39.42 | % 231.73/39.42 | GROUND_INST: instantiating (16) with all_62_0, all_64_1, n3, simplifying with % 231.73/39.42 | (109), (110) gives: % 231.73/39.42 | (113) all_64_1 = all_62_0 % 231.73/39.42 | % 231.73/39.42 | GROUND_INST: instantiating (16) with n4, all_64_1, n3, simplifying with (109), % 231.73/39.42 | (111) gives: % 231.73/39.42 | (114) all_64_1 = n4 % 231.73/39.42 | % 231.73/39.42 | COMBINE_EQS: (113), (114) imply: % 231.73/39.42 | (115) all_62_0 = n4 % 231.73/39.42 | % 231.73/39.42 | SIMP: (115) implies: % 231.73/39.42 | (116) all_62_0 = n4 % 231.73/39.42 | % 231.73/39.42 | REDUCE: (46), (114) imply: % 231.73/39.42 | (117) succ(n4) = all_64_0 % 231.73/39.42 | % 231.73/39.42 | REDUCE: (39), (116) imply: % 231.73/39.42 | (118) succ(n4) = n5 % 231.73/39.42 | % 231.73/39.42 | REDUCE: (34), (116) imply: % 231.73/39.42 | (119) $i(n4) % 231.73/39.42 | % 231.73/39.42 | GROUND_INST: instantiating (16) with n5, all_64_0, n4, simplifying with (117), % 231.73/39.42 | (118) gives: % 231.73/39.42 | (120) all_64_0 = n5 % 231.73/39.42 | % 231.73/39.42 | REDUCE: (47), (120) imply: % 231.73/39.42 | (121) succ(n5) = n6 % 231.73/39.42 | % 231.73/39.42 | REDUCE: (41), (120) imply: % 231.73/39.42 | (122) $i(n5) % 231.73/39.42 | % 231.73/39.42 | GROUND_INST: instantiating (pred_succ) with n1, n2, simplifying with (84), % 231.73/39.42 | (85) gives: % 231.73/39.42 | (123) pred(n2) = n1 % 231.73/39.42 | % 231.73/39.42 | GROUND_INST: instantiating (pred_succ) with n2, n3, simplifying with (100), % 231.73/39.42 | (101) gives: % 231.73/39.42 | (124) pred(n3) = n2 % 231.73/39.42 | % 231.73/39.42 | GROUND_INST: instantiating (pred_succ) with n3, n4, simplifying with (111), % 231.73/39.42 | (112) gives: % 231.73/39.42 | (125) pred(n4) = n3 % 231.73/39.42 | % 231.73/39.42 | GROUND_INST: instantiating (pred_succ) with n4, n5, simplifying with (118), % 231.73/39.42 | (119) gives: % 231.73/39.42 | (126) pred(n5) = n4 % 231.73/39.42 | % 231.73/39.42 | GROUND_INST: instantiating (pred_succ) with n5, n6, simplifying with (121), % 231.73/39.42 | (122) gives: % 231.73/39.42 | (127) pred(n6) = n5 % 231.73/39.42 | % 231.73/39.42 | GROUND_INST: instantiating (2) with n3, all_74_20, simplifying with (59), % 231.73/39.42 | (112) gives: % 231.73/39.42 | (128) pred(n3) = all_74_20 & $i(all_74_20) % 231.73/39.42 | % 231.73/39.42 | ALPHA: (128) implies: % 231.73/39.42 | (129) $i(all_74_20) % 231.73/39.42 | (130) pred(n3) = all_74_20 % 231.73/39.42 | % 231.73/39.42 | GROUND_INST: instantiating (2) with n6, all_74_21, simplifying with (13), (60) % 231.73/39.42 | gives: % 231.73/39.42 | (131) pred(n6) = all_74_21 & $i(all_74_21) % 231.73/39.42 | % 231.73/39.42 | ALPHA: (131) implies: % 231.73/39.42 | (132) $i(all_74_21) % 231.73/39.42 | (133) pred(n6) = all_74_21 % 231.73/39.42 | % 231.73/39.42 | GROUND_INST: instantiating (15) with n2, all_74_20, n3, simplifying with % 231.73/39.42 | (124), (130) gives: % 231.73/39.42 | (134) all_74_20 = n2 % 231.73/39.42 | % 231.73/39.42 | GROUND_INST: instantiating (15) with n5, all_74_21, n6, simplifying with % 231.73/39.42 | (127), (133) gives: % 231.73/39.42 | (135) all_74_21 = n5 % 231.73/39.42 | % 231.73/39.42 | BETA: splitting (61) gives: % 231.73/39.42 | % 231.73/39.43 | Case 1: % 231.73/39.43 | | % 231.73/39.43 | | (136) ( ~ (all_74_0 = all_74_1) & a_select3(q_ds1_filter, all_74_2, % 231.73/39.43 | | all_74_3) = all_74_0 & a_select3(q_ds1_filter, all_74_3, % 231.73/39.43 | | all_74_2) = all_74_1 & $i(all_74_0) & $i(all_74_1) & % 231.73/39.43 | | leq(all_74_2, all_74_21) & leq(all_74_3, all_74_21) & leq(n0, % 231.73/39.43 | | all_74_2) & leq(n0, all_74_3)) | ( ~ (all_74_4 = all_74_5) & % 231.73/39.43 | | a_select3(r_ds1_filter, all_74_6, all_74_7) = all_74_4 & % 231.73/39.43 | | a_select3(r_ds1_filter, all_74_7, all_74_6) = all_74_5 & % 231.73/39.43 | | $i(all_74_4) & $i(all_74_5) & leq(all_74_6, all_74_20) & % 231.73/39.43 | | leq(all_74_7, all_74_20) & leq(n0, all_74_6) & leq(n0, all_74_7)) % 231.73/39.43 | | % 231.73/39.43 | | BETA: splitting (136) gives: % 231.73/39.43 | | % 231.73/39.43 | | Case 1: % 231.73/39.43 | | | % 231.73/39.43 | | | (137) ~ (all_74_0 = all_74_1) & a_select3(q_ds1_filter, all_74_2, % 231.73/39.43 | | | all_74_3) = all_74_0 & a_select3(q_ds1_filter, all_74_3, % 231.73/39.43 | | | all_74_2) = all_74_1 & $i(all_74_0) & $i(all_74_1) & % 231.73/39.43 | | | leq(all_74_2, all_74_21) & leq(all_74_3, all_74_21) & leq(n0, % 231.73/39.43 | | | all_74_2) & leq(n0, all_74_3) % 231.73/39.43 | | | % 231.73/39.43 | | | ALPHA: (137) implies: % 231.73/39.43 | | | (138) ~ (all_74_0 = all_74_1) % 231.73/39.43 | | | (139) leq(n0, all_74_3) % 231.73/39.43 | | | (140) leq(n0, all_74_2) % 231.73/39.43 | | | (141) leq(all_74_3, all_74_21) % 231.73/39.43 | | | (142) leq(all_74_2, all_74_21) % 231.73/39.43 | | | (143) a_select3(q_ds1_filter, all_74_3, all_74_2) = all_74_1 % 231.73/39.43 | | | (144) a_select3(q_ds1_filter, all_74_2, all_74_3) = all_74_0 % 231.73/39.43 | | | % 231.73/39.43 | | | REDUCE: (135), (142) imply: % 231.73/39.43 | | | (145) leq(all_74_2, n5) % 231.73/39.43 | | | % 231.73/39.43 | | | REDUCE: (135), (141) imply: % 231.73/39.43 | | | (146) leq(all_74_3, n5) % 231.73/39.43 | | | % 231.73/39.43 | | | GROUND_INST: instantiating (leq_gt2) with n0, all_74_3, simplifying with % 231.73/39.43 | | | (12), (57), (139) gives: % 231.73/39.43 | | | (147) all_74_3 = n0 | gt(all_74_3, n0) % 231.73/39.43 | | | % 231.73/39.43 | | | GROUND_INST: instantiating (leq_gt2) with n0, all_74_2, simplifying with % 231.73/39.43 | | | (12), (58), (140) gives: % 231.73/39.43 | | | (148) all_74_2 = n0 | gt(all_74_2, n0) % 231.73/39.43 | | | % 231.73/39.43 | | | GROUND_INST: instantiating (3) with all_74_3, simplifying with (57), % 231.73/39.43 | | | (139), (146) gives: % 232.07/39.43 | | | (149) all_74_3 = n5 | all_74_3 = n4 | all_74_3 = n3 | all_74_3 = n2 | % 232.07/39.43 | | | all_74_3 = n1 | all_74_3 = n0 % 232.07/39.43 | | | % 232.07/39.43 | | | GROUND_INST: instantiating (leq_gt2) with all_74_3, n5, simplifying with % 232.07/39.43 | | | (57), (122), (146) gives: % 232.07/39.43 | | | (150) all_74_3 = n5 | gt(n5, all_74_3) % 232.07/39.43 | | | % 232.07/39.43 | | | GROUND_INST: instantiating (3) with all_74_2, simplifying with (58), % 232.07/39.43 | | | (140), (145) gives: % 232.07/39.43 | | | (151) all_74_2 = n5 | all_74_2 = n4 | all_74_2 = n3 | all_74_2 = n2 | % 232.07/39.43 | | | all_74_2 = n1 | all_74_2 = n0 % 232.07/39.43 | | | % 232.07/39.43 | | | GROUND_INST: instantiating (leq_gt2) with all_74_2, n5, simplifying with % 232.07/39.43 | | | (58), (122), (145) gives: % 232.07/39.43 | | | (152) all_74_2 = n5 | gt(n5, all_74_2) % 232.07/39.43 | | | % 232.07/39.43 | | | BETA: splitting (148) gives: % 232.07/39.43 | | | % 232.07/39.43 | | | Case 1: % 232.07/39.43 | | | | % 232.07/39.43 | | | | (153) gt(all_74_2, n0) % 232.07/39.43 | | | | % 232.07/39.43 | | | | BETA: splitting (147) gives: % 232.07/39.43 | | | | % 232.07/39.43 | | | | Case 1: % 232.07/39.43 | | | | | % 232.07/39.43 | | | | | (154) gt(all_74_3, n0) % 232.07/39.43 | | | | | % 232.07/39.43 | | | | | BETA: splitting (150) gives: % 232.07/39.43 | | | | | % 232.07/39.43 | | | | | Case 1: % 232.07/39.43 | | | | | | % 232.07/39.43 | | | | | | (155) gt(n5, all_74_3) % 232.07/39.43 | | | | | | % 232.07/39.43 | | | | | | GROUND_INST: instantiating (1) with all_74_3, n5, n4, simplifying % 232.07/39.43 | | | | | | with (57), (122), (126), (155) gives: % 232.07/39.43 | | | | | | (156) leq(all_74_3, n4) % 232.07/39.43 | | | | | | % 232.07/39.44 | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_3, n4, simplifying % 232.07/39.44 | | | | | | with (57), (119), (156) gives: % 232.07/39.44 | | | | | | (157) all_74_3 = n4 | gt(n4, all_74_3) % 232.07/39.44 | | | | | | % 232.07/39.44 | | | | | | BETA: splitting (152) gives: % 232.07/39.44 | | | | | | % 232.07/39.44 | | | | | | Case 1: % 232.07/39.44 | | | | | | | % 232.07/39.44 | | | | | | | (158) gt(n5, all_74_2) % 232.07/39.44 | | | | | | | % 232.07/39.44 | | | | | | | GROUND_INST: instantiating (1) with all_74_2, n5, n4, simplifying % 232.07/39.44 | | | | | | | with (58), (122), (126), (158) gives: % 232.07/39.44 | | | | | | | (159) leq(all_74_2, n4) % 232.07/39.44 | | | | | | | % 232.07/39.44 | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_2, n4, % 232.07/39.44 | | | | | | | simplifying with (58), (119), (159) gives: % 232.07/39.44 | | | | | | | (160) all_74_2 = n4 | gt(n4, all_74_2) % 232.07/39.44 | | | | | | | % 232.07/39.44 | | | | | | | BETA: splitting (151) gives: % 232.07/39.44 | | | | | | | % 232.07/39.44 | | | | | | | Case 1: % 232.07/39.44 | | | | | | | | % 232.07/39.44 | | | | | | | | (161) all_74_2 = n0 % 232.07/39.44 | | | | | | | | % 232.07/39.44 | | | | | | | | REF_CLOSE: (58), (153), (161), (irreflexivity_gt) are % 232.07/39.44 | | | | | | | | inconsistent by sub-proof #58. % 232.07/39.44 | | | | | | | | % 232.07/39.44 | | | | | | | Case 2: % 232.07/39.44 | | | | | | | | % 232.07/39.44 | | | | | | | | (162) ~ (all_74_2 = n0) % 232.07/39.44 | | | | | | | | % 232.07/39.44 | | | | | | | | BETA: splitting (149) gives: % 232.07/39.44 | | | | | | | | % 232.07/39.44 | | | | | | | | Case 1: % 232.07/39.44 | | | | | | | | | % 232.07/39.44 | | | | | | | | | (163) all_74_3 = n0 % 232.07/39.44 | | | | | | | | | % 232.07/39.44 | | | | | | | | | REF_CLOSE: (57), (154), (163), (irreflexivity_gt) are % 232.07/39.44 | | | | | | | | | inconsistent by sub-proof #57. % 232.07/39.44 | | | | | | | | | % 232.07/39.44 | | | | | | | | Case 2: % 232.07/39.44 | | | | | | | | | % 232.07/39.44 | | | | | | | | | (164) ~ (all_74_3 = n0) % 232.07/39.44 | | | | | | | | | % 232.07/39.44 | | | | | | | | | BETA: splitting (157) gives: % 232.07/39.44 | | | | | | | | | % 232.07/39.44 | | | | | | | | | Case 1: % 232.07/39.44 | | | | | | | | | | % 232.07/39.44 | | | | | | | | | | (165) gt(n4, all_74_3) % 232.07/39.44 | | | | | | | | | | % 232.07/39.44 | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_3, n4, n3, % 232.07/39.44 | | | | | | | | | | simplifying with (57), (119), (125), (165) gives: % 232.07/39.44 | | | | | | | | | | (166) leq(all_74_3, n3) % 232.07/39.44 | | | | | | | | | | % 232.07/39.44 | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_3, n3, % 232.07/39.44 | | | | | | | | | | simplifying with (57), (112), (166) gives: % 232.07/39.44 | | | | | | | | | | (167) all_74_3 = n3 | gt(n3, all_74_3) % 232.07/39.44 | | | | | | | | | | % 232.07/39.44 | | | | | | | | | | BETA: splitting (160) gives: % 232.07/39.44 | | | | | | | | | | % 232.07/39.44 | | | | | | | | | | Case 1: % 232.07/39.44 | | | | | | | | | | | % 232.07/39.44 | | | | | | | | | | | (168) gt(n4, all_74_2) % 232.07/39.44 | | | | | | | | | | | % 232.07/39.44 | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_2, n4, n3, % 232.07/39.44 | | | | | | | | | | | simplifying with (58), (119), (125), (168) gives: % 232.07/39.44 | | | | | | | | | | | (169) leq(all_74_2, n3) % 232.07/39.44 | | | | | | | | | | | % 232.07/39.44 | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_2, n3, % 232.07/39.44 | | | | | | | | | | | simplifying with (58), (112), (169) gives: % 232.07/39.44 | | | | | | | | | | | (170) all_74_2 = n3 | gt(n3, all_74_2) % 232.07/39.44 | | | | | | | | | | | % 232.07/39.44 | | | | | | | | | | | BETA: splitting (167) gives: % 232.07/39.44 | | | | | | | | | | | % 232.07/39.44 | | | | | | | | | | | Case 1: % 232.07/39.44 | | | | | | | | | | | | % 232.07/39.44 | | | | | | | | | | | | (171) gt(n3, all_74_3) % 232.07/39.44 | | | | | | | | | | | | % 232.07/39.44 | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_3, n3, n2, % 232.07/39.44 | | | | | | | | | | | | simplifying with (57), (112), (124), (171) gives: % 232.07/39.44 | | | | | | | | | | | | (172) leq(all_74_3, n2) % 232.07/39.44 | | | | | | | | | | | | % 232.07/39.44 | | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_3, n2, % 232.07/39.44 | | | | | | | | | | | | simplifying with (57), (101), (172) gives: % 232.07/39.44 | | | | | | | | | | | | (173) all_74_3 = n2 | gt(n2, all_74_3) % 232.07/39.44 | | | | | | | | | | | | % 232.07/39.44 | | | | | | | | | | | | BETA: splitting (170) gives: % 232.07/39.44 | | | | | | | | | | | | % 232.07/39.44 | | | | | | | | | | | | Case 1: % 232.07/39.44 | | | | | | | | | | | | | % 232.07/39.44 | | | | | | | | | | | | | (174) gt(n3, all_74_2) % 232.07/39.44 | | | | | | | | | | | | | % 232.07/39.44 | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_2, n3, n2, % 232.07/39.44 | | | | | | | | | | | | | simplifying with (58), (112), (124), (174) gives: % 232.07/39.44 | | | | | | | | | | | | | (175) leq(all_74_2, n2) % 232.07/39.44 | | | | | | | | | | | | | % 232.07/39.45 | | | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_2, n2, % 232.07/39.45 | | | | | | | | | | | | | simplifying with (58), (101), (175) gives: % 232.07/39.45 | | | | | | | | | | | | | (176) all_74_2 = n2 | gt(n2, all_74_2) % 232.07/39.45 | | | | | | | | | | | | | % 232.07/39.45 | | | | | | | | | | | | | BETA: splitting (173) gives: % 232.07/39.45 | | | | | | | | | | | | | % 232.07/39.45 | | | | | | | | | | | | | Case 1: % 232.07/39.45 | | | | | | | | | | | | | | % 232.07/39.45 | | | | | | | | | | | | | | (177) gt(n2, all_74_3) % 232.07/39.45 | | | | | | | | | | | | | | % 232.07/39.45 | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_3, n2, n1, % 232.07/39.45 | | | | | | | | | | | | | | simplifying with (57), (101), (123), (177) gives: % 232.07/39.45 | | | | | | | | | | | | | | (178) leq(all_74_3, n1) % 232.07/39.45 | | | | | | | | | | | | | | % 232.07/39.45 | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_74_3, simplifying with % 232.07/39.45 | | | | | | | | | | | | | | (57), (139), (178) gives: % 232.07/39.45 | | | | | | | | | | | | | | (179) all_74_3 = n1 | all_74_3 = n0 % 232.07/39.45 | | | | | | | | | | | | | | % 232.07/39.45 | | | | | | | | | | | | | | BETA: splitting (179) gives: % 232.07/39.45 | | | | | | | | | | | | | | % 232.07/39.45 | | | | | | | | | | | | | | Case 1: % 232.07/39.45 | | | | | | | | | | | | | | | % 232.07/39.45 | | | | | | | | | | | | | | | (180) all_74_3 = n0 % 232.07/39.45 | | | | | | | | | | | | | | | % 232.07/39.45 | | | | | | | | | | | | | | | REDUCE: (164), (180) imply: % 232.07/39.45 | | | | | | | | | | | | | | | (181) $false % 232.07/39.45 | | | | | | | | | | | | | | | % 232.07/39.45 | | | | | | | | | | | | | | | CLOSE: (181) is inconsistent. % 232.07/39.45 | | | | | | | | | | | | | | | % 232.07/39.45 | | | | | | | | | | | | | | Case 2: % 232.07/39.45 | | | | | | | | | | | | | | | % 232.07/39.45 | | | | | | | | | | | | | | | (182) all_74_3 = n1 % 232.07/39.45 | | | | | | | | | | | | | | | % 232.07/39.45 | | | | | | | | | | | | | | | REDUCE: (144), (182) imply: % 232.07/39.45 | | | | | | | | | | | | | | | (183) a_select3(q_ds1_filter, all_74_2, n1) = all_74_0 % 232.07/39.45 | | | | | | | | | | | | | | | % 232.07/39.45 | | | | | | | | | | | | | | | REDUCE: (143), (182) imply: % 232.07/39.45 | | | | | | | | | | | | | | | (184) a_select3(q_ds1_filter, n1, all_74_2) = all_74_1 % 232.07/39.45 | | | | | | | | | | | | | | | % 232.07/39.45 | | | | | | | | | | | | | | | REDUCE: (146), (182) imply: % 232.07/39.45 | | | | | | | | | | | | | | | (185) leq(n1, n5) % 232.07/39.45 | | | | | | | | | | | | | | | % 232.07/39.45 | | | | | | | | | | | | | | | REDUCE: (139), (182) imply: % 232.07/39.45 | | | | | | | | | | | | | | | (186) leq(n0, n1) % 232.07/39.45 | | | | | | | | | | | | | | | % 232.07/39.45 | | | | | | | | | | | | | | | BETA: splitting (176) gives: % 232.07/39.45 | | | | | | | | | | | | | | | % 232.07/39.45 | | | | | | | | | | | | | | | Case 1: % 232.07/39.45 | | | | | | | | | | | | | | | | % 232.07/39.45 | | | | | | | | | | | | | | | | (187) gt(n2, all_74_2) % 232.07/39.45 | | | | | | | | | | | | | | | | % 232.07/39.45 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_2, n2, n1, % 232.07/39.45 | | | | | | | | | | | | | | | | simplifying with (58), (101), (123), (187) gives: % 232.07/39.45 | | | | | | | | | | | | | | | | (188) leq(all_74_2, n1) % 232.07/39.45 | | | | | | | | | | | | | | | | % 232.07/39.45 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_74_2, simplifying with % 232.07/39.45 | | | | | | | | | | | | | | | | (58), (140), (188) gives: % 232.07/39.45 | | | | | | | | | | | | | | | | (189) all_74_2 = n1 | all_74_2 = n0 % 232.07/39.45 | | | | | | | | | | | | | | | | % 232.07/39.45 | | | | | | | | | | | | | | | | BETA: splitting (189) gives: % 232.07/39.45 | | | | | | | | | | | | | | | | % 232.07/39.45 | | | | | | | | | | | | | | | | Case 1: % 232.07/39.45 | | | | | | | | | | | | | | | | | % 232.07/39.45 | | | | | | | | | | | | | | | | | (190) all_74_2 = n0 % 232.07/39.45 | | | | | | | | | | | | | | | | | % 232.07/39.45 | | | | | | | | | | | | | | | | | REDUCE: (162), (190) imply: % 232.07/39.45 | | | | | | | | | | | | | | | | | (191) $false % 232.07/39.45 | | | | | | | | | | | | | | | | | % 232.07/39.45 | | | | | | | | | | | | | | | | | CLOSE: (191) is inconsistent. % 232.07/39.45 | | | | | | | | | | | | | | | | | % 232.07/39.45 | | | | | | | | | | | | | | | | Case 2: % 232.07/39.45 | | | | | | | | | | | | | | | | | % 232.07/39.45 | | | | | | | | | | | | | | | | | (192) all_74_2 = n1 % 232.07/39.45 | | | | | | | | | | | | | | | | | % 232.07/39.45 | | | | | | | | | | | | | | | | | REDUCE: (183), (192) imply: % 232.07/39.45 | | | | | | | | | | | | | | | | | (193) a_select3(q_ds1_filter, n1, n1) = all_74_0 % 232.07/39.45 | | | | | | | | | | | | | | | | | % 232.07/39.45 | | | | | | | | | | | | | | | | | REDUCE: (184), (192) imply: % 232.07/39.45 | | | | | | | | | | | | | | | | | (194) a_select3(q_ds1_filter, n1, n1) = all_74_1 % 232.07/39.45 | | | | | | | | | | | | | | | | | % 232.07/39.45 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_74_1, all_74_0, n1, % 232.07/39.45 | | | | | | | | | | | | | | | | | n1, q_ds1_filter, simplifying with (193), (194) % 232.07/39.45 | | | | | | | | | | | | | | | | | gives: % 232.07/39.45 | | | | | | | | | | | | | | | | | (195) all_74_0 = all_74_1 % 232.07/39.45 | | | | | | | | | | | | | | | | | % 232.07/39.45 | | | | | | | | | | | | | | | | | REDUCE: (138), (195) imply: % 232.07/39.45 | | | | | | | | | | | | | | | | | (196) $false % 232.07/39.45 | | | | | | | | | | | | | | | | | % 232.07/39.45 | | | | | | | | | | | | | | | | | CLOSE: (196) is inconsistent. % 232.07/39.45 | | | | | | | | | | | | | | | | | % 232.07/39.45 | | | | | | | | | | | | | | | | End of split % 232.07/39.45 | | | | | | | | | | | | | | | | % 232.07/39.45 | | | | | | | | | | | | | | | Case 2: % 232.07/39.45 | | | | | | | | | | | | | | | | % 232.07/39.45 | | | | | | | | | | | | | | | | (197) all_74_2 = n2 % 232.07/39.45 | | | | | | | | | | | | | | | | % 232.07/39.45 | | | | | | | | | | | | | | | | REDUCE: (183), (197) imply: % 232.07/39.45 | | | | | | | | | | | | | | | | (198) a_select3(q_ds1_filter, n2, n1) = all_74_0 % 232.07/39.45 | | | | | | | | | | | | | | | | % 232.07/39.45 | | | | | | | | | | | | | | | | REDUCE: (184), (197) imply: % 232.07/39.45 | | | | | | | | | | | | | | | | (199) a_select3(q_ds1_filter, n1, n2) = all_74_1 % 232.07/39.45 | | | | | | | | | | | | | | | | % 232.07/39.45 | | | | | | | | | | | | | | | | REDUCE: (145), (197) imply: % 232.07/39.45 | | | | | | | | | | | | | | | | (200) leq(n2, n5) % 232.07/39.45 | | | | | | | | | | | | | | | | % 232.07/39.45 | | | | | | | | | | | | | | | | REDUCE: (140), (197) imply: % 232.07/39.45 | | | | | | | | | | | | | | | | (201) leq(n0, n2) % 232.07/39.45 | | | | | | | | | | | | | | | | % 232.07/39.45 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (62) with n1, n2, all_74_1, % 232.07/39.45 | | | | | | | | | | | | | | | | simplifying with (85), (101), (186), (199), (201) % 232.07/39.45 | | | | | | | | | | | | | | | | gives: % 232.07/39.45 | | | | | | | | | | | | | | | | (202) ~ leq(n2, all_74_21) | ~ leq(n1, all_74_21) | % 232.07/39.45 | | | | | | | | | | | | | | | | (a_select3(q_ds1_filter, n2, n1) = all_74_1 & % 232.07/39.45 | | | | | | | | | | | | | | | | $i(all_74_1)) % 232.07/39.45 | | | | | | | | | | | | | | | | % 232.07/39.45 | | | | | | | | | | | | | | | | BETA: splitting (202) gives: % 232.07/39.45 | | | | | | | | | | | | | | | | % 232.07/39.45 | | | | | | | | | | | | | | | | Case 1: % 232.07/39.45 | | | | | | | | | | | | | | | | | % 232.07/39.45 | | | | | | | | | | | | | | | | | (203) ~ leq(n2, all_74_21) % 232.07/39.45 | | | | | | | | | | | | | | | | | % 232.07/39.45 | | | | | | | | | | | | | | | | | REDUCE: (135), (203) imply: % 232.07/39.45 | | | | | | | | | | | | | | | | | (204) ~ leq(n2, n5) % 232.07/39.45 | | | | | | | | | | | | | | | | | % 232.07/39.45 | | | | | | | | | | | | | | | | | PRED_UNIFY: (200), (204) imply: % 232.07/39.45 | | | | | | | | | | | | | | | | | (205) $false % 232.07/39.45 | | | | | | | | | | | | | | | | | % 232.07/39.45 | | | | | | | | | | | | | | | | | CLOSE: (205) is inconsistent. % 232.07/39.45 | | | | | | | | | | | | | | | | | % 232.07/39.45 | | | | | | | | | | | | | | | | Case 2: % 232.07/39.45 | | | | | | | | | | | | | | | | | % 232.07/39.45 | | | | | | | | | | | | | | | | | (206) ~ leq(n1, all_74_21) | (a_select3(q_ds1_filter, % 232.07/39.45 | | | | | | | | | | | | | | | | | n2, n1) = all_74_1 & $i(all_74_1)) % 232.07/39.45 | | | | | | | | | | | | | | | | | % 232.07/39.45 | | | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 232.07/39.45 | | | | | | | | | | | | | | | | | % 232.07/39.45 | | | | | | | | | | | | | | | | | Case 1: % 232.07/39.45 | | | | | | | | | | | | | | | | | | % 232.07/39.45 | | | | | | | | | | | | | | | | | | (207) ~ leq(n1, all_74_21) % 232.07/39.45 | | | | | | | | | | | | | | | | | | % 232.07/39.45 | | | | | | | | | | | | | | | | | | REDUCE: (135), (207) imply: % 232.07/39.45 | | | | | | | | | | | | | | | | | | (208) ~ leq(n1, n5) % 232.07/39.45 | | | | | | | | | | | | | | | | | | % 232.07/39.45 | | | | | | | | | | | | | | | | | | PRED_UNIFY: (185), (208) imply: % 232.07/39.45 | | | | | | | | | | | | | | | | | | (209) $false % 232.07/39.45 | | | | | | | | | | | | | | | | | | % 232.07/39.45 | | | | | | | | | | | | | | | | | | CLOSE: (209) is inconsistent. % 232.07/39.45 | | | | | | | | | | | | | | | | | | % 232.07/39.45 | | | | | | | | | | | | | | | | | Case 2: % 232.07/39.45 | | | | | | | | | | | | | | | | | | % 232.07/39.45 | | | | | | | | | | | | | | | | | | (210) a_select3(q_ds1_filter, n2, n1) = all_74_1 & % 232.07/39.45 | | | | | | | | | | | | | | | | | | $i(all_74_1) % 232.07/39.45 | | | | | | | | | | | | | | | | | | % 232.07/39.45 | | | | | | | | | | | | | | | | | | ALPHA: (210) implies: % 232.07/39.45 | | | | | | | | | | | | | | | | | | (211) a_select3(q_ds1_filter, n2, n1) = all_74_1 % 232.07/39.45 | | | | | | | | | | | | | | | | | | % 232.07/39.45 | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (138), (198), (211) are inconsistent by % 232.07/39.45 | | | | | | | | | | | | | | | | | | sub-proof #56. % 232.07/39.45 | | | | | | | | | | | | | | | | | | % 232.07/39.45 | | | | | | | | | | | | | | | | | End of split % 232.07/39.45 | | | | | | | | | | | | | | | | | % 232.07/39.45 | | | | | | | | | | | | | | | | End of split % 232.07/39.45 | | | | | | | | | | | | | | | | % 232.07/39.46 | | | | | | | | | | | | | | | End of split % 232.07/39.46 | | | | | | | | | | | | | | | % 232.07/39.46 | | | | | | | | | | | | | | End of split % 232.07/39.46 | | | | | | | | | | | | | | % 232.07/39.46 | | | | | | | | | | | | | Case 2: % 232.07/39.46 | | | | | | | | | | | | | | % 232.07/39.46 | | | | | | | | | | | | | | (212) all_74_3 = n2 % 232.07/39.46 | | | | | | | | | | | | | | % 232.07/39.46 | | | | | | | | | | | | | | REDUCE: (144), (212) imply: % 232.07/39.46 | | | | | | | | | | | | | | (213) a_select3(q_ds1_filter, all_74_2, n2) = all_74_0 % 232.07/39.46 | | | | | | | | | | | | | | % 232.07/39.46 | | | | | | | | | | | | | | REDUCE: (143), (212) imply: % 232.07/39.46 | | | | | | | | | | | | | | (214) a_select3(q_ds1_filter, n2, all_74_2) = all_74_1 % 232.07/39.46 | | | | | | | | | | | | | | % 232.07/39.46 | | | | | | | | | | | | | | REDUCE: (146), (212) imply: % 232.07/39.46 | | | | | | | | | | | | | | (215) leq(n2, n5) % 232.07/39.46 | | | | | | | | | | | | | | % 232.07/39.46 | | | | | | | | | | | | | | REDUCE: (139), (212) imply: % 232.07/39.46 | | | | | | | | | | | | | | (216) leq(n0, n2) % 232.07/39.46 | | | | | | | | | | | | | | % 232.07/39.46 | | | | | | | | | | | | | | BETA: splitting (176) gives: % 232.07/39.46 | | | | | | | | | | | | | | % 232.07/39.46 | | | | | | | | | | | | | | Case 1: % 232.07/39.46 | | | | | | | | | | | | | | | % 232.07/39.46 | | | | | | | | | | | | | | | (217) gt(n2, all_74_2) % 232.07/39.46 | | | | | | | | | | | | | | | % 232.07/39.46 | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_2, n2, n1, % 232.07/39.46 | | | | | | | | | | | | | | | simplifying with (58), (101), (123), (217) gives: % 232.07/39.46 | | | | | | | | | | | | | | | (218) leq(all_74_2, n1) % 232.07/39.46 | | | | | | | | | | | | | | | % 232.07/39.46 | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_74_2, simplifying with % 232.07/39.46 | | | | | | | | | | | | | | | (58), (140), (218) gives: % 232.07/39.46 | | | | | | | | | | | | | | | (219) all_74_2 = n1 | all_74_2 = n0 % 232.07/39.46 | | | | | | | | | | | | | | | % 232.07/39.46 | | | | | | | | | | | | | | | BETA: splitting (219) gives: % 232.07/39.46 | | | | | | | | | | | | | | | % 232.07/39.46 | | | | | | | | | | | | | | | Case 1: % 232.07/39.46 | | | | | | | | | | | | | | | | % 232.07/39.46 | | | | | | | | | | | | | | | | (220) all_74_2 = n0 % 232.07/39.46 | | | | | | | | | | | | | | | | % 232.07/39.46 | | | | | | | | | | | | | | | | REDUCE: (162), (220) imply: % 232.07/39.46 | | | | | | | | | | | | | | | | (221) $false % 232.07/39.46 | | | | | | | | | | | | | | | | % 232.07/39.46 | | | | | | | | | | | | | | | | CLOSE: (221) is inconsistent. % 232.07/39.46 | | | | | | | | | | | | | | | | % 232.07/39.46 | | | | | | | | | | | | | | | Case 2: % 232.07/39.46 | | | | | | | | | | | | | | | | % 232.07/39.46 | | | | | | | | | | | | | | | | (222) all_74_2 = n1 % 232.07/39.46 | | | | | | | | | | | | | | | | % 232.07/39.46 | | | | | | | | | | | | | | | | REDUCE: (213), (222) imply: % 232.07/39.46 | | | | | | | | | | | | | | | | (223) a_select3(q_ds1_filter, n1, n2) = all_74_0 % 232.07/39.46 | | | | | | | | | | | | | | | | % 232.07/39.46 | | | | | | | | | | | | | | | | REDUCE: (214), (222) imply: % 232.07/39.46 | | | | | | | | | | | | | | | | (224) a_select3(q_ds1_filter, n2, n1) = all_74_1 % 232.07/39.46 | | | | | | | | | | | | | | | | % 232.07/39.46 | | | | | | | | | | | | | | | | REDUCE: (145), (222) imply: % 232.07/39.46 | | | | | | | | | | | | | | | | (225) leq(n1, n5) % 232.07/39.46 | | | | | | | | | | | | | | | | % 232.07/39.46 | | | | | | | | | | | | | | | | REDUCE: (140), (222) imply: % 232.07/39.46 | | | | | | | | | | | | | | | | (226) leq(n0, n1) % 232.07/39.46 | | | | | | | | | | | | | | | | % 232.07/39.46 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (62) with n1, n2, all_74_0, % 232.07/39.46 | | | | | | | | | | | | | | | | simplifying with (85), (101), (216), (223), (226) % 232.07/39.46 | | | | | | | | | | | | | | | | gives: % 232.07/39.46 | | | | | | | | | | | | | | | | (227) ~ leq(n2, all_74_21) | ~ leq(n1, all_74_21) | % 232.07/39.46 | | | | | | | | | | | | | | | | (a_select3(q_ds1_filter, n2, n1) = all_74_0 & % 232.07/39.46 | | | | | | | | | | | | | | | | $i(all_74_0)) % 232.07/39.46 | | | | | | | | | | | | | | | | % 232.07/39.46 | | | | | | | | | | | | | | | | BETA: splitting (227) gives: % 232.07/39.46 | | | | | | | | | | | | | | | | % 232.07/39.46 | | | | | | | | | | | | | | | | Case 1: % 232.07/39.46 | | | | | | | | | | | | | | | | | % 232.07/39.46 | | | | | | | | | | | | | | | | | (228) ~ leq(n2, all_74_21) % 232.07/39.46 | | | | | | | | | | | | | | | | | % 232.07/39.46 | | | | | | | | | | | | | | | | | REDUCE: (135), (228) imply: % 232.07/39.46 | | | | | | | | | | | | | | | | | (229) ~ leq(n2, n5) % 232.07/39.46 | | | | | | | | | | | | | | | | | % 232.07/39.46 | | | | | | | | | | | | | | | | | PRED_UNIFY: (215), (229) imply: % 232.07/39.46 | | | | | | | | | | | | | | | | | (230) $false % 232.07/39.46 | | | | | | | | | | | | | | | | | % 232.07/39.46 | | | | | | | | | | | | | | | | | CLOSE: (230) is inconsistent. % 232.07/39.46 | | | | | | | | | | | | | | | | | % 232.07/39.46 | | | | | | | | | | | | | | | | Case 2: % 232.07/39.46 | | | | | | | | | | | | | | | | | % 232.07/39.46 | | | | | | | | | | | | | | | | | (231) ~ leq(n1, all_74_21) | (a_select3(q_ds1_filter, % 232.07/39.46 | | | | | | | | | | | | | | | | | n2, n1) = all_74_0 & $i(all_74_0)) % 232.07/39.46 | | | | | | | | | | | | | | | | | % 232.07/39.46 | | | | | | | | | | | | | | | | | BETA: splitting (231) gives: % 232.07/39.46 | | | | | | | | | | | | | | | | | % 232.07/39.46 | | | | | | | | | | | | | | | | | Case 1: % 232.07/39.46 | | | | | | | | | | | | | | | | | | % 232.07/39.46 | | | | | | | | | | | | | | | | | | (232) ~ leq(n1, all_74_21) % 232.07/39.46 | | | | | | | | | | | | | | | | | | % 232.07/39.46 | | | | | | | | | | | | | | | | | | REDUCE: (135), (232) imply: % 232.07/39.46 | | | | | | | | | | | | | | | | | | (233) ~ leq(n1, n5) % 232.07/39.46 | | | | | | | | | | | | | | | | | | % 232.07/39.46 | | | | | | | | | | | | | | | | | | PRED_UNIFY: (225), (233) imply: % 232.07/39.46 | | | | | | | | | | | | | | | | | | (234) $false % 232.07/39.46 | | | | | | | | | | | | | | | | | | % 232.07/39.46 | | | | | | | | | | | | | | | | | | CLOSE: (234) is inconsistent. % 232.07/39.46 | | | | | | | | | | | | | | | | | | % 232.07/39.46 | | | | | | | | | | | | | | | | | Case 2: % 232.07/39.46 | | | | | | | | | | | | | | | | | | % 232.07/39.46 | | | | | | | | | | | | | | | | | | (235) a_select3(q_ds1_filter, n2, n1) = all_74_0 & % 232.07/39.46 | | | | | | | | | | | | | | | | | | $i(all_74_0) % 232.07/39.46 | | | | | | | | | | | | | | | | | | % 232.07/39.46 | | | | | | | | | | | | | | | | | | ALPHA: (235) implies: % 232.07/39.46 | | | | | | | | | | | | | | | | | | (236) a_select3(q_ds1_filter, n2, n1) = all_74_0 % 232.07/39.46 | | | | | | | | | | | | | | | | | | % 232.07/39.46 | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (138), (224), (236) are inconsistent by % 232.07/39.46 | | | | | | | | | | | | | | | | | | sub-proof #56. % 232.07/39.46 | | | | | | | | | | | | | | | | | | % 232.07/39.46 | | | | | | | | | | | | | | | | | End of split % 232.07/39.46 | | | | | | | | | | | | | | | | | % 232.07/39.46 | | | | | | | | | | | | | | | | End of split % 232.07/39.46 | | | | | | | | | | | | | | | | % 232.07/39.46 | | | | | | | | | | | | | | | End of split % 232.07/39.46 | | | | | | | | | | | | | | | % 232.07/39.46 | | | | | | | | | | | | | | Case 2: % 232.07/39.46 | | | | | | | | | | | | | | | % 232.07/39.46 | | | | | | | | | | | | | | | (237) all_74_2 = n2 % 232.07/39.46 | | | | | | | | | | | | | | | % 232.07/39.46 | | | | | | | | | | | | | | | REDUCE: (213), (237) imply: % 232.07/39.46 | | | | | | | | | | | | | | | (238) a_select3(q_ds1_filter, n2, n2) = all_74_0 % 232.07/39.46 | | | | | | | | | | | | | | | % 232.07/39.46 | | | | | | | | | | | | | | | REDUCE: (214), (237) imply: % 232.07/39.46 | | | | | | | | | | | | | | | (239) a_select3(q_ds1_filter, n2, n2) = all_74_1 % 232.07/39.46 | | | | | | | | | | | | | | | % 232.07/39.46 | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_74_1, all_74_0, n2, % 232.07/39.46 | | | | | | | | | | | | | | | n2, q_ds1_filter, simplifying with (238), (239) % 232.07/39.46 | | | | | | | | | | | | | | | gives: % 232.07/39.46 | | | | | | | | | | | | | | | (240) all_74_0 = all_74_1 % 232.07/39.46 | | | | | | | | | | | | | | | % 232.07/39.46 | | | | | | | | | | | | | | | REDUCE: (138), (240) imply: % 232.07/39.46 | | | | | | | | | | | | | | | (241) $false % 232.07/39.46 | | | | | | | | | | | | | | | % 232.07/39.46 | | | | | | | | | | | | | | | CLOSE: (241) is inconsistent. % 232.07/39.46 | | | | | | | | | | | | | | | % 232.07/39.46 | | | | | | | | | | | | | | End of split % 232.07/39.46 | | | | | | | | | | | | | | % 232.07/39.46 | | | | | | | | | | | | | End of split % 232.07/39.46 | | | | | | | | | | | | | % 232.07/39.46 | | | | | | | | | | | | Case 2: % 232.07/39.46 | | | | | | | | | | | | | % 232.07/39.46 | | | | | | | | | | | | | (242) all_74_2 = n3 % 232.07/39.46 | | | | | | | | | | | | | % 232.07/39.46 | | | | | | | | | | | | | REDUCE: (144), (242) imply: % 232.07/39.46 | | | | | | | | | | | | | (243) a_select3(q_ds1_filter, n3, all_74_3) = all_74_0 % 232.07/39.46 | | | | | | | | | | | | | % 232.07/39.46 | | | | | | | | | | | | | REDUCE: (143), (242) imply: % 232.07/39.46 | | | | | | | | | | | | | (244) a_select3(q_ds1_filter, all_74_3, n3) = all_74_1 % 232.07/39.46 | | | | | | | | | | | | | % 232.07/39.46 | | | | | | | | | | | | | REDUCE: (145), (242) imply: % 232.07/39.46 | | | | | | | | | | | | | (245) leq(n3, n5) % 232.07/39.46 | | | | | | | | | | | | | % 232.07/39.46 | | | | | | | | | | | | | REDUCE: (140), (242) imply: % 232.07/39.46 | | | | | | | | | | | | | (246) leq(n0, n3) % 232.07/39.46 | | | | | | | | | | | | | % 232.07/39.46 | | | | | | | | | | | | | BETA: splitting (173) gives: % 232.07/39.46 | | | | | | | | | | | | | % 232.07/39.46 | | | | | | | | | | | | | Case 1: % 232.07/39.46 | | | | | | | | | | | | | | % 232.07/39.46 | | | | | | | | | | | | | | (247) gt(n2, all_74_3) % 232.07/39.46 | | | | | | | | | | | | | | % 232.07/39.46 | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_3, n2, n1, % 232.07/39.46 | | | | | | | | | | | | | | simplifying with (57), (101), (123), (247) gives: % 232.07/39.46 | | | | | | | | | | | | | | (248) leq(all_74_3, n1) % 232.07/39.46 | | | | | | | | | | | | | | % 232.07/39.46 | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_74_3, simplifying with % 232.07/39.46 | | | | | | | | | | | | | | (57), (139), (248) gives: % 232.07/39.46 | | | | | | | | | | | | | | (249) all_74_3 = n1 | all_74_3 = n0 % 232.07/39.46 | | | | | | | | | | | | | | % 232.07/39.46 | | | | | | | | | | | | | | BETA: splitting (249) gives: % 232.07/39.46 | | | | | | | | | | | | | | % 232.07/39.46 | | | | | | | | | | | | | | Case 1: % 232.07/39.46 | | | | | | | | | | | | | | | % 232.07/39.46 | | | | | | | | | | | | | | | (250) all_74_3 = n0 % 232.07/39.46 | | | | | | | | | | | | | | | % 232.07/39.46 | | | | | | | | | | | | | | | REDUCE: (164), (250) imply: % 232.07/39.46 | | | | | | | | | | | | | | | (251) $false % 232.07/39.46 | | | | | | | | | | | | | | | % 232.07/39.46 | | | | | | | | | | | | | | | CLOSE: (251) is inconsistent. % 232.07/39.46 | | | | | | | | | | | | | | | % 232.07/39.46 | | | | | | | | | | | | | | Case 2: % 232.07/39.46 | | | | | | | | | | | | | | | % 232.07/39.46 | | | | | | | | | | | | | | | (252) all_74_3 = n1 % 232.07/39.46 | | | | | | | | | | | | | | | % 232.07/39.46 | | | | | | | | | | | | | | | REDUCE: (244), (252) imply: % 232.07/39.46 | | | | | | | | | | | | | | | (253) a_select3(q_ds1_filter, n1, n3) = all_74_1 % 232.07/39.46 | | | | | | | | | | | | | | | % 232.07/39.46 | | | | | | | | | | | | | | | REDUCE: (243), (252) imply: % 232.07/39.46 | | | | | | | | | | | | | | | (254) a_select3(q_ds1_filter, n3, n1) = all_74_0 % 232.07/39.46 | | | | | | | | | | | | | | | % 232.07/39.46 | | | | | | | | | | | | | | | REDUCE: (146), (252) imply: % 232.07/39.46 | | | | | | | | | | | | | | | (255) leq(n1, n5) % 232.07/39.46 | | | | | | | | | | | | | | | % 232.07/39.46 | | | | | | | | | | | | | | | REDUCE: (139), (252) imply: % 232.07/39.46 | | | | | | | | | | | | | | | (256) leq(n0, n1) % 232.07/39.46 | | | | | | | | | | | | | | | % 232.07/39.46 | | | | | | | | | | | | | | | GROUND_INST: instantiating (62) with n1, n3, all_74_1, % 232.07/39.46 | | | | | | | | | | | | | | | simplifying with (85), (112), (246), (253), (256) % 232.07/39.46 | | | | | | | | | | | | | | | gives: % 232.07/39.46 | | | | | | | | | | | | | | | (257) ~ leq(n3, all_74_21) | ~ leq(n1, all_74_21) | % 232.07/39.46 | | | | | | | | | | | | | | | (a_select3(q_ds1_filter, n3, n1) = all_74_1 & % 232.07/39.46 | | | | | | | | | | | | | | | $i(all_74_1)) % 232.07/39.46 | | | | | | | | | | | | | | | % 232.07/39.46 | | | | | | | | | | | | | | | BETA: splitting (257) gives: % 232.07/39.46 | | | | | | | | | | | | | | | % 232.07/39.46 | | | | | | | | | | | | | | | Case 1: % 232.07/39.46 | | | | | | | | | | | | | | | | % 232.07/39.46 | | | | | | | | | | | | | | | | (258) ~ leq(n3, all_74_21) % 232.07/39.46 | | | | | | | | | | | | | | | | % 232.07/39.46 | | | | | | | | | | | | | | | | REDUCE: (135), (258) imply: % 232.07/39.46 | | | | | | | | | | | | | | | | (259) ~ leq(n3, n5) % 232.07/39.46 | | | | | | | | | | | | | | | | % 232.07/39.46 | | | | | | | | | | | | | | | | PRED_UNIFY: (245), (259) imply: % 232.07/39.46 | | | | | | | | | | | | | | | | (260) $false % 232.07/39.46 | | | | | | | | | | | | | | | | % 232.07/39.46 | | | | | | | | | | | | | | | | CLOSE: (260) is inconsistent. % 232.07/39.46 | | | | | | | | | | | | | | | | % 232.07/39.46 | | | | | | | | | | | | | | | Case 2: % 232.07/39.46 | | | | | | | | | | | | | | | | % 232.07/39.47 | | | | | | | | | | | | | | | | (261) ~ leq(n1, all_74_21) | (a_select3(q_ds1_filter, % 232.07/39.47 | | | | | | | | | | | | | | | | n3, n1) = all_74_1 & $i(all_74_1)) % 232.07/39.47 | | | | | | | | | | | | | | | | % 232.07/39.47 | | | | | | | | | | | | | | | | BETA: splitting (261) gives: % 232.07/39.47 | | | | | | | | | | | | | | | | % 232.07/39.47 | | | | | | | | | | | | | | | | Case 1: % 232.07/39.47 | | | | | | | | | | | | | | | | | % 232.07/39.47 | | | | | | | | | | | | | | | | | (262) ~ leq(n1, all_74_21) % 232.07/39.47 | | | | | | | | | | | | | | | | | % 232.07/39.47 | | | | | | | | | | | | | | | | | REDUCE: (135), (262) imply: % 232.07/39.47 | | | | | | | | | | | | | | | | | (263) ~ leq(n1, n5) % 232.07/39.47 | | | | | | | | | | | | | | | | | % 232.07/39.47 | | | | | | | | | | | | | | | | | PRED_UNIFY: (255), (263) imply: % 232.07/39.47 | | | | | | | | | | | | | | | | | (264) $false % 232.07/39.47 | | | | | | | | | | | | | | | | | % 232.07/39.47 | | | | | | | | | | | | | | | | | CLOSE: (264) is inconsistent. % 232.07/39.47 | | | | | | | | | | | | | | | | | % 232.07/39.47 | | | | | | | | | | | | | | | | Case 2: % 232.07/39.47 | | | | | | | | | | | | | | | | | % 232.07/39.47 | | | | | | | | | | | | | | | | | (265) a_select3(q_ds1_filter, n3, n1) = all_74_1 & % 232.07/39.47 | | | | | | | | | | | | | | | | | $i(all_74_1) % 232.07/39.47 | | | | | | | | | | | | | | | | | % 232.07/39.47 | | | | | | | | | | | | | | | | | ALPHA: (265) implies: % 232.07/39.47 | | | | | | | | | | | | | | | | | (266) a_select3(q_ds1_filter, n3, n1) = all_74_1 % 232.07/39.47 | | | | | | | | | | | | | | | | | % 232.07/39.47 | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (138), (254), (266) are inconsistent by % 232.07/39.47 | | | | | | | | | | | | | | | | | sub-proof #55. % 232.07/39.47 | | | | | | | | | | | | | | | | | % 232.07/39.47 | | | | | | | | | | | | | | | | End of split % 232.07/39.47 | | | | | | | | | | | | | | | | % 232.07/39.47 | | | | | | | | | | | | | | | End of split % 232.07/39.47 | | | | | | | | | | | | | | | % 232.07/39.47 | | | | | | | | | | | | | | End of split % 232.07/39.47 | | | | | | | | | | | | | | % 232.07/39.47 | | | | | | | | | | | | | Case 2: % 232.07/39.47 | | | | | | | | | | | | | | % 232.07/39.47 | | | | | | | | | | | | | | (267) all_74_3 = n2 % 232.07/39.47 | | | | | | | | | | | | | | % 232.07/39.47 | | | | | | | | | | | | | | REDUCE: (244), (267) imply: % 232.07/39.47 | | | | | | | | | | | | | | (268) a_select3(q_ds1_filter, n2, n3) = all_74_1 % 232.07/39.47 | | | | | | | | | | | | | | % 232.07/39.47 | | | | | | | | | | | | | | REDUCE: (243), (267) imply: % 232.07/39.47 | | | | | | | | | | | | | | (269) a_select3(q_ds1_filter, n3, n2) = all_74_0 % 232.07/39.47 | | | | | | | | | | | | | | % 232.07/39.47 | | | | | | | | | | | | | | REDUCE: (146), (267) imply: % 232.07/39.47 | | | | | | | | | | | | | | (270) leq(n2, n5) % 232.07/39.47 | | | | | | | | | | | | | | % 232.07/39.47 | | | | | | | | | | | | | | REDUCE: (139), (267) imply: % 232.07/39.47 | | | | | | | | | | | | | | (271) leq(n0, n2) % 232.07/39.47 | | | | | | | | | | | | | | % 232.07/39.47 | | | | | | | | | | | | | | GROUND_INST: instantiating (62) with n2, n3, all_74_1, % 232.07/39.47 | | | | | | | | | | | | | | simplifying with (101), (112), (246), (268), (271) % 232.07/39.47 | | | | | | | | | | | | | | gives: % 232.07/39.47 | | | | | | | | | | | | | | (272) ~ leq(n3, all_74_21) | ~ leq(n2, all_74_21) | % 232.07/39.47 | | | | | | | | | | | | | | (a_select3(q_ds1_filter, n3, n2) = all_74_1 & % 232.07/39.47 | | | | | | | | | | | | | | $i(all_74_1)) % 232.07/39.47 | | | | | | | | | | | | | | % 232.07/39.47 | | | | | | | | | | | | | | BETA: splitting (272) gives: % 232.07/39.47 | | | | | | | | | | | | | | % 232.07/39.47 | | | | | | | | | | | | | | Case 1: % 232.07/39.47 | | | | | | | | | | | | | | | % 232.07/39.47 | | | | | | | | | | | | | | | (273) ~ leq(n3, all_74_21) % 232.07/39.47 | | | | | | | | | | | | | | | % 232.07/39.47 | | | | | | | | | | | | | | | REDUCE: (135), (273) imply: % 232.07/39.47 | | | | | | | | | | | | | | | (274) ~ leq(n3, n5) % 232.07/39.47 | | | | | | | | | | | | | | | % 232.07/39.47 | | | | | | | | | | | | | | | PRED_UNIFY: (245), (274) imply: % 232.07/39.47 | | | | | | | | | | | | | | | (275) $false % 232.07/39.47 | | | | | | | | | | | | | | | % 232.07/39.47 | | | | | | | | | | | | | | | CLOSE: (275) is inconsistent. % 232.07/39.47 | | | | | | | | | | | | | | | % 232.07/39.47 | | | | | | | | | | | | | | Case 2: % 232.07/39.47 | | | | | | | | | | | | | | | % 232.07/39.47 | | | | | | | | | | | | | | | (276) ~ leq(n2, all_74_21) | (a_select3(q_ds1_filter, % 232.07/39.47 | | | | | | | | | | | | | | | n3, n2) = all_74_1 & $i(all_74_1)) % 232.07/39.47 | | | | | | | | | | | | | | | % 232.07/39.47 | | | | | | | | | | | | | | | BETA: splitting (276) gives: % 232.07/39.47 | | | | | | | | | | | | | | | % 232.07/39.47 | | | | | | | | | | | | | | | Case 1: % 232.07/39.47 | | | | | | | | | | | | | | | | % 232.07/39.47 | | | | | | | | | | | | | | | | (277) ~ leq(n2, all_74_21) % 232.07/39.47 | | | | | | | | | | | | | | | | % 232.07/39.47 | | | | | | | | | | | | | | | | REDUCE: (135), (277) imply: % 232.07/39.47 | | | | | | | | | | | | | | | | (278) ~ leq(n2, n5) % 232.07/39.47 | | | | | | | | | | | | | | | | % 232.07/39.47 | | | | | | | | | | | | | | | | PRED_UNIFY: (270), (278) imply: % 232.07/39.47 | | | | | | | | | | | | | | | | (279) $false % 232.07/39.47 | | | | | | | | | | | | | | | | % 232.07/39.47 | | | | | | | | | | | | | | | | CLOSE: (279) is inconsistent. % 232.07/39.47 | | | | | | | | | | | | | | | | % 232.07/39.47 | | | | | | | | | | | | | | | Case 2: % 232.07/39.47 | | | | | | | | | | | | | | | | % 232.07/39.47 | | | | | | | | | | | | | | | | (280) a_select3(q_ds1_filter, n3, n2) = all_74_1 & % 232.07/39.47 | | | | | | | | | | | | | | | | $i(all_74_1) % 232.07/39.47 | | | | | | | | | | | | | | | | % 232.07/39.47 | | | | | | | | | | | | | | | | ALPHA: (280) implies: % 232.07/39.47 | | | | | | | | | | | | | | | | (281) a_select3(q_ds1_filter, n3, n2) = all_74_1 % 232.07/39.47 | | | | | | | | | | | | | | | | % 232.07/39.47 | | | | | | | | | | | | | | | | REF_CLOSE: (17), (138), (269), (281) are inconsistent by % 232.07/39.47 | | | | | | | | | | | | | | | | sub-proof #54. % 232.07/39.47 | | | | | | | | | | | | | | | | % 232.07/39.47 | | | | | | | | | | | | | | | End of split % 232.07/39.47 | | | | | | | | | | | | | | | % 232.07/39.47 | | | | | | | | | | | | | | End of split % 232.07/39.47 | | | | | | | | | | | | | | % 232.07/39.47 | | | | | | | | | | | | | End of split % 232.07/39.47 | | | | | | | | | | | | | % 232.07/39.47 | | | | | | | | | | | | End of split % 232.07/39.47 | | | | | | | | | | | | % 232.07/39.47 | | | | | | | | | | | Case 2: % 232.07/39.47 | | | | | | | | | | | | % 232.07/39.47 | | | | | | | | | | | | (282) all_74_3 = n3 % 232.07/39.47 | | | | | | | | | | | | % 232.07/39.47 | | | | | | | | | | | | REDUCE: (144), (282) imply: % 232.07/39.47 | | | | | | | | | | | | (283) a_select3(q_ds1_filter, all_74_2, n3) = all_74_0 % 232.07/39.47 | | | | | | | | | | | | % 232.07/39.47 | | | | | | | | | | | | REDUCE: (143), (282) imply: % 232.07/39.47 | | | | | | | | | | | | (284) a_select3(q_ds1_filter, n3, all_74_2) = all_74_1 % 232.07/39.47 | | | | | | | | | | | | % 232.07/39.47 | | | | | | | | | | | | REDUCE: (146), (282) imply: % 232.07/39.47 | | | | | | | | | | | | (285) leq(n3, n5) % 232.07/39.47 | | | | | | | | | | | | % 232.07/39.47 | | | | | | | | | | | | REDUCE: (139), (282) imply: % 232.07/39.47 | | | | | | | | | | | | (286) leq(n0, n3) % 232.07/39.47 | | | | | | | | | | | | % 232.07/39.47 | | | | | | | | | | | | BETA: splitting (170) gives: % 232.07/39.47 | | | | | | | | | | | | % 232.07/39.47 | | | | | | | | | | | | Case 1: % 232.07/39.47 | | | | | | | | | | | | | % 232.07/39.47 | | | | | | | | | | | | | (287) gt(n3, all_74_2) % 232.07/39.47 | | | | | | | | | | | | | % 232.07/39.47 | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_2, n3, n2, % 232.07/39.47 | | | | | | | | | | | | | simplifying with (58), (112), (124), (287) gives: % 232.07/39.47 | | | | | | | | | | | | | (288) leq(all_74_2, n2) % 232.07/39.47 | | | | | | | | | | | | | % 232.07/39.47 | | | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_2, n2, % 232.07/39.47 | | | | | | | | | | | | | simplifying with (58), (101), (288) gives: % 232.07/39.47 | | | | | | | | | | | | | (289) all_74_2 = n2 | gt(n2, all_74_2) % 232.07/39.47 | | | | | | | | | | | | | % 232.07/39.47 | | | | | | | | | | | | | BETA: splitting (289) gives: % 232.07/39.47 | | | | | | | | | | | | | % 232.07/39.47 | | | | | | | | | | | | | Case 1: % 232.07/39.47 | | | | | | | | | | | | | | % 232.07/39.47 | | | | | | | | | | | | | | (290) gt(n2, all_74_2) % 232.07/39.47 | | | | | | | | | | | | | | % 232.07/39.47 | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_2, n2, n1, % 232.07/39.47 | | | | | | | | | | | | | | simplifying with (58), (101), (123), (290) gives: % 232.07/39.47 | | | | | | | | | | | | | | (291) leq(all_74_2, n1) % 232.07/39.47 | | | | | | | | | | | | | | % 232.07/39.47 | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_74_2, simplifying with % 232.07/39.47 | | | | | | | | | | | | | | (58), (140), (291) gives: % 232.07/39.47 | | | | | | | | | | | | | | (292) all_74_2 = n1 | all_74_2 = n0 % 232.07/39.47 | | | | | | | | | | | | | | % 232.07/39.47 | | | | | | | | | | | | | | BETA: splitting (292) gives: % 232.07/39.47 | | | | | | | | | | | | | | % 232.07/39.47 | | | | | | | | | | | | | | Case 1: % 232.07/39.47 | | | | | | | | | | | | | | | % 232.07/39.47 | | | | | | | | | | | | | | | (293) all_74_2 = n0 % 232.07/39.47 | | | | | | | | | | | | | | | % 232.07/39.47 | | | | | | | | | | | | | | | REDUCE: (162), (293) imply: % 232.07/39.47 | | | | | | | | | | | | | | | (294) $false % 232.07/39.47 | | | | | | | | | | | | | | | % 232.07/39.47 | | | | | | | | | | | | | | | CLOSE: (294) is inconsistent. % 232.07/39.47 | | | | | | | | | | | | | | | % 232.07/39.47 | | | | | | | | | | | | | | Case 2: % 232.07/39.47 | | | | | | | | | | | | | | | % 232.07/39.47 | | | | | | | | | | | | | | | (295) all_74_2 = n1 % 232.07/39.47 | | | | | | | | | | | | | | | % 232.07/39.47 | | | | | | | | | | | | | | | REDUCE: (283), (295) imply: % 232.07/39.47 | | | | | | | | | | | | | | | (296) a_select3(q_ds1_filter, n1, n3) = all_74_0 % 232.07/39.47 | | | | | | | | | | | | | | | % 232.07/39.47 | | | | | | | | | | | | | | | REDUCE: (284), (295) imply: % 232.07/39.47 | | | | | | | | | | | | | | | (297) a_select3(q_ds1_filter, n3, n1) = all_74_1 % 232.07/39.47 | | | | | | | | | | | | | | | % 232.07/39.47 | | | | | | | | | | | | | | | REDUCE: (145), (295) imply: % 232.07/39.47 | | | | | | | | | | | | | | | (298) leq(n1, n5) % 232.07/39.47 | | | | | | | | | | | | | | | % 232.07/39.47 | | | | | | | | | | | | | | | REDUCE: (140), (295) imply: % 232.07/39.47 | | | | | | | | | | | | | | | (299) leq(n0, n1) % 232.07/39.47 | | | | | | | | | | | | | | | % 232.07/39.47 | | | | | | | | | | | | | | | GROUND_INST: instantiating (62) with n1, n3, all_74_0, % 232.07/39.47 | | | | | | | | | | | | | | | simplifying with (85), (112), (286), (296), (299) % 232.07/39.47 | | | | | | | | | | | | | | | gives: % 232.07/39.47 | | | | | | | | | | | | | | | (300) ~ leq(n3, all_74_21) | ~ leq(n1, all_74_21) | % 232.07/39.47 | | | | | | | | | | | | | | | (a_select3(q_ds1_filter, n3, n1) = all_74_0 & % 232.07/39.47 | | | | | | | | | | | | | | | $i(all_74_0)) % 232.07/39.47 | | | | | | | | | | | | | | | % 232.07/39.47 | | | | | | | | | | | | | | | BETA: splitting (300) gives: % 232.07/39.47 | | | | | | | | | | | | | | | % 232.07/39.47 | | | | | | | | | | | | | | | Case 1: % 232.07/39.47 | | | | | | | | | | | | | | | | % 232.07/39.47 | | | | | | | | | | | | | | | | (301) ~ leq(n3, all_74_21) % 232.07/39.47 | | | | | | | | | | | | | | | | % 232.07/39.47 | | | | | | | | | | | | | | | | REDUCE: (135), (301) imply: % 232.07/39.47 | | | | | | | | | | | | | | | | (302) ~ leq(n3, n5) % 232.07/39.47 | | | | | | | | | | | | | | | | % 232.07/39.47 | | | | | | | | | | | | | | | | PRED_UNIFY: (285), (302) imply: % 232.07/39.47 | | | | | | | | | | | | | | | | (303) $false % 232.07/39.47 | | | | | | | | | | | | | | | | % 232.07/39.47 | | | | | | | | | | | | | | | | CLOSE: (303) is inconsistent. % 232.07/39.47 | | | | | | | | | | | | | | | | % 232.24/39.47 | | | | | | | | | | | | | | | Case 2: % 232.24/39.47 | | | | | | | | | | | | | | | | % 232.24/39.47 | | | | | | | | | | | | | | | | (304) ~ leq(n1, all_74_21) | (a_select3(q_ds1_filter, % 232.24/39.47 | | | | | | | | | | | | | | | | n3, n1) = all_74_0 & $i(all_74_0)) % 232.24/39.47 | | | | | | | | | | | | | | | | % 232.24/39.47 | | | | | | | | | | | | | | | | BETA: splitting (304) gives: % 232.24/39.47 | | | | | | | | | | | | | | | | % 232.24/39.47 | | | | | | | | | | | | | | | | Case 1: % 232.24/39.47 | | | | | | | | | | | | | | | | | % 232.24/39.47 | | | | | | | | | | | | | | | | | (305) ~ leq(n1, all_74_21) % 232.24/39.47 | | | | | | | | | | | | | | | | | % 232.24/39.47 | | | | | | | | | | | | | | | | | REDUCE: (135), (305) imply: % 232.24/39.47 | | | | | | | | | | | | | | | | | (306) ~ leq(n1, n5) % 232.24/39.47 | | | | | | | | | | | | | | | | | % 232.24/39.47 | | | | | | | | | | | | | | | | | PRED_UNIFY: (298), (306) imply: % 232.24/39.47 | | | | | | | | | | | | | | | | | (307) $false % 232.24/39.47 | | | | | | | | | | | | | | | | | % 232.24/39.47 | | | | | | | | | | | | | | | | | CLOSE: (307) is inconsistent. % 232.24/39.47 | | | | | | | | | | | | | | | | | % 232.24/39.47 | | | | | | | | | | | | | | | | Case 2: % 232.24/39.47 | | | | | | | | | | | | | | | | | % 232.24/39.47 | | | | | | | | | | | | | | | | | (308) a_select3(q_ds1_filter, n3, n1) = all_74_0 & % 232.24/39.47 | | | | | | | | | | | | | | | | | $i(all_74_0) % 232.24/39.47 | | | | | | | | | | | | | | | | | % 232.24/39.47 | | | | | | | | | | | | | | | | | ALPHA: (308) implies: % 232.24/39.47 | | | | | | | | | | | | | | | | | (309) a_select3(q_ds1_filter, n3, n1) = all_74_0 % 232.24/39.47 | | | | | | | | | | | | | | | | | % 232.24/39.47 | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (138), (297), (309) are inconsistent by % 232.24/39.47 | | | | | | | | | | | | | | | | | sub-proof #55. % 232.24/39.47 | | | | | | | | | | | | | | | | | % 232.24/39.47 | | | | | | | | | | | | | | | | End of split % 232.24/39.47 | | | | | | | | | | | | | | | | % 232.24/39.47 | | | | | | | | | | | | | | | End of split % 232.24/39.47 | | | | | | | | | | | | | | | % 232.24/39.47 | | | | | | | | | | | | | | End of split % 232.24/39.47 | | | | | | | | | | | | | | % 232.24/39.47 | | | | | | | | | | | | | Case 2: % 232.24/39.47 | | | | | | | | | | | | | | % 232.24/39.47 | | | | | | | | | | | | | | (310) all_74_2 = n2 % 232.24/39.47 | | | | | | | | | | | | | | % 232.24/39.47 | | | | | | | | | | | | | | REDUCE: (283), (310) imply: % 232.24/39.47 | | | | | | | | | | | | | | (311) a_select3(q_ds1_filter, n2, n3) = all_74_0 % 232.24/39.47 | | | | | | | | | | | | | | % 232.24/39.47 | | | | | | | | | | | | | | REDUCE: (284), (310) imply: % 232.24/39.48 | | | | | | | | | | | | | | (312) a_select3(q_ds1_filter, n3, n2) = all_74_1 % 232.24/39.48 | | | | | | | | | | | | | | % 232.24/39.48 | | | | | | | | | | | | | | REDUCE: (145), (310) imply: % 232.24/39.48 | | | | | | | | | | | | | | (313) leq(n2, n5) % 232.24/39.48 | | | | | | | | | | | | | | % 232.24/39.48 | | | | | | | | | | | | | | REDUCE: (140), (310) imply: % 232.24/39.48 | | | | | | | | | | | | | | (314) leq(n0, n2) % 232.24/39.48 | | | | | | | | | | | | | | % 232.24/39.48 | | | | | | | | | | | | | | GROUND_INST: instantiating (62) with n2, n3, all_74_0, % 232.24/39.48 | | | | | | | | | | | | | | simplifying with (101), (112), (286), (311), (314) % 232.24/39.48 | | | | | | | | | | | | | | gives: % 232.24/39.48 | | | | | | | | | | | | | | (315) ~ leq(n3, all_74_21) | ~ leq(n2, all_74_21) | % 232.24/39.48 | | | | | | | | | | | | | | (a_select3(q_ds1_filter, n3, n2) = all_74_0 & % 232.24/39.48 | | | | | | | | | | | | | | $i(all_74_0)) % 232.24/39.48 | | | | | | | | | | | | | | % 232.24/39.48 | | | | | | | | | | | | | | BETA: splitting (315) gives: % 232.24/39.48 | | | | | | | | | | | | | | % 232.24/39.48 | | | | | | | | | | | | | | Case 1: % 232.24/39.48 | | | | | | | | | | | | | | | % 232.24/39.48 | | | | | | | | | | | | | | | (316) ~ leq(n3, all_74_21) % 232.24/39.48 | | | | | | | | | | | | | | | % 232.24/39.48 | | | | | | | | | | | | | | | REDUCE: (135), (316) imply: % 232.24/39.48 | | | | | | | | | | | | | | | (317) ~ leq(n3, n5) % 232.24/39.48 | | | | | | | | | | | | | | | % 232.24/39.48 | | | | | | | | | | | | | | | PRED_UNIFY: (285), (317) imply: % 232.24/39.48 | | | | | | | | | | | | | | | (318) $false % 232.24/39.48 | | | | | | | | | | | | | | | % 232.24/39.48 | | | | | | | | | | | | | | | CLOSE: (318) is inconsistent. % 232.24/39.48 | | | | | | | | | | | | | | | % 232.24/39.48 | | | | | | | | | | | | | | Case 2: % 232.24/39.48 | | | | | | | | | | | | | | | % 232.24/39.48 | | | | | | | | | | | | | | | (319) ~ leq(n2, all_74_21) | (a_select3(q_ds1_filter, % 232.24/39.48 | | | | | | | | | | | | | | | n3, n2) = all_74_0 & $i(all_74_0)) % 232.24/39.48 | | | | | | | | | | | | | | | % 232.24/39.48 | | | | | | | | | | | | | | | BETA: splitting (319) gives: % 232.24/39.48 | | | | | | | | | | | | | | | % 232.24/39.48 | | | | | | | | | | | | | | | Case 1: % 232.24/39.48 | | | | | | | | | | | | | | | | % 232.24/39.48 | | | | | | | | | | | | | | | | (320) ~ leq(n2, all_74_21) % 232.24/39.48 | | | | | | | | | | | | | | | | % 232.24/39.48 | | | | | | | | | | | | | | | | REDUCE: (135), (320) imply: % 232.24/39.48 | | | | | | | | | | | | | | | | (321) ~ leq(n2, n5) % 232.24/39.48 | | | | | | | | | | | | | | | | % 232.24/39.48 | | | | | | | | | | | | | | | | PRED_UNIFY: (313), (321) imply: % 232.24/39.48 | | | | | | | | | | | | | | | | (322) $false % 232.24/39.48 | | | | | | | | | | | | | | | | % 232.24/39.48 | | | | | | | | | | | | | | | | CLOSE: (322) is inconsistent. % 232.24/39.48 | | | | | | | | | | | | | | | | % 232.24/39.48 | | | | | | | | | | | | | | | Case 2: % 232.24/39.48 | | | | | | | | | | | | | | | | % 232.24/39.48 | | | | | | | | | | | | | | | | (323) a_select3(q_ds1_filter, n3, n2) = all_74_0 & % 232.24/39.48 | | | | | | | | | | | | | | | | $i(all_74_0) % 232.24/39.48 | | | | | | | | | | | | | | | | % 232.24/39.48 | | | | | | | | | | | | | | | | ALPHA: (323) implies: % 232.24/39.48 | | | | | | | | | | | | | | | | (324) a_select3(q_ds1_filter, n3, n2) = all_74_0 % 232.24/39.48 | | | | | | | | | | | | | | | | % 232.24/39.48 | | | | | | | | | | | | | | | | REF_CLOSE: (17), (138), (312), (324) are inconsistent by % 232.24/39.48 | | | | | | | | | | | | | | | | sub-proof #54. % 232.24/39.48 | | | | | | | | | | | | | | | | % 232.24/39.48 | | | | | | | | | | | | | | | End of split % 232.24/39.48 | | | | | | | | | | | | | | | % 232.24/39.48 | | | | | | | | | | | | | | End of split % 232.24/39.48 | | | | | | | | | | | | | | % 232.24/39.48 | | | | | | | | | | | | | End of split % 232.24/39.48 | | | | | | | | | | | | | % 232.24/39.48 | | | | | | | | | | | | Case 2: % 232.24/39.48 | | | | | | | | | | | | | % 232.24/39.48 | | | | | | | | | | | | | (325) all_74_2 = n3 % 232.24/39.48 | | | | | | | | | | | | | % 232.24/39.48 | | | | | | | | | | | | | REDUCE: (283), (325) imply: % 232.24/39.48 | | | | | | | | | | | | | (326) a_select3(q_ds1_filter, n3, n3) = all_74_0 % 232.24/39.48 | | | | | | | | | | | | | % 232.24/39.48 | | | | | | | | | | | | | REDUCE: (284), (325) imply: % 232.24/39.48 | | | | | | | | | | | | | (327) a_select3(q_ds1_filter, n3, n3) = all_74_1 % 232.24/39.48 | | | | | | | | | | | | | % 232.24/39.48 | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_74_1, all_74_0, n3, % 232.24/39.48 | | | | | | | | | | | | | n3, q_ds1_filter, simplifying with (326), (327) % 232.24/39.48 | | | | | | | | | | | | | gives: % 232.24/39.48 | | | | | | | | | | | | | (328) all_74_0 = all_74_1 % 232.24/39.48 | | | | | | | | | | | | | % 232.24/39.48 | | | | | | | | | | | | | REDUCE: (138), (328) imply: % 232.24/39.48 | | | | | | | | | | | | | (329) $false % 232.24/39.48 | | | | | | | | | | | | | % 232.24/39.48 | | | | | | | | | | | | | CLOSE: (329) is inconsistent. % 232.24/39.48 | | | | | | | | | | | | | % 232.24/39.48 | | | | | | | | | | | | End of split % 232.24/39.48 | | | | | | | | | | | | % 232.24/39.48 | | | | | | | | | | | End of split % 232.24/39.48 | | | | | | | | | | | % 232.24/39.48 | | | | | | | | | | Case 2: % 232.24/39.48 | | | | | | | | | | | % 232.24/39.48 | | | | | | | | | | | (330) all_74_2 = n4 % 232.24/39.48 | | | | | | | | | | | % 232.24/39.48 | | | | | | | | | | | REDUCE: (144), (330) imply: % 232.24/39.48 | | | | | | | | | | | (331) a_select3(q_ds1_filter, n4, all_74_3) = all_74_0 % 232.24/39.48 | | | | | | | | | | | % 232.24/39.48 | | | | | | | | | | | REDUCE: (143), (330) imply: % 232.24/39.48 | | | | | | | | | | | (332) a_select3(q_ds1_filter, all_74_3, n4) = all_74_1 % 232.24/39.48 | | | | | | | | | | | % 232.24/39.48 | | | | | | | | | | | REDUCE: (145), (330) imply: % 232.24/39.48 | | | | | | | | | | | (333) leq(n4, n5) % 232.24/39.48 | | | | | | | | | | | % 232.24/39.48 | | | | | | | | | | | REDUCE: (140), (330) imply: % 232.24/39.48 | | | | | | | | | | | (334) leq(n0, n4) % 232.24/39.48 | | | | | | | | | | | % 232.24/39.48 | | | | | | | | | | | BETA: splitting (167) gives: % 232.24/39.48 | | | | | | | | | | | % 232.24/39.48 | | | | | | | | | | | Case 1: % 232.24/39.48 | | | | | | | | | | | | % 232.24/39.48 | | | | | | | | | | | | (335) gt(n3, all_74_3) % 232.24/39.48 | | | | | | | | | | | | % 232.24/39.48 | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_3, n3, n2, % 232.24/39.48 | | | | | | | | | | | | simplifying with (57), (112), (124), (335) gives: % 232.24/39.48 | | | | | | | | | | | | (336) leq(all_74_3, n2) % 232.24/39.48 | | | | | | | | | | | | % 232.24/39.48 | | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_3, n2, % 232.24/39.48 | | | | | | | | | | | | simplifying with (57), (101), (336) gives: % 232.24/39.48 | | | | | | | | | | | | (337) all_74_3 = n2 | gt(n2, all_74_3) % 232.24/39.48 | | | | | | | | | | | | % 232.24/39.48 | | | | | | | | | | | | BETA: splitting (337) gives: % 232.24/39.48 | | | | | | | | | | | | % 232.24/39.48 | | | | | | | | | | | | Case 1: % 232.24/39.48 | | | | | | | | | | | | | % 232.24/39.48 | | | | | | | | | | | | | (338) gt(n2, all_74_3) % 232.24/39.48 | | | | | | | | | | | | | % 232.24/39.48 | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_3, n2, n1, % 232.24/39.48 | | | | | | | | | | | | | simplifying with (57), (101), (123), (338) gives: % 232.24/39.48 | | | | | | | | | | | | | (339) leq(all_74_3, n1) % 232.24/39.48 | | | | | | | | | | | | | % 232.24/39.48 | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_74_3, simplifying with % 232.24/39.48 | | | | | | | | | | | | | (57), (139), (339) gives: % 232.24/39.48 | | | | | | | | | | | | | (340) all_74_3 = n1 | all_74_3 = n0 % 232.24/39.48 | | | | | | | | | | | | | % 232.24/39.48 | | | | | | | | | | | | | BETA: splitting (340) gives: % 232.24/39.48 | | | | | | | | | | | | | % 232.24/39.48 | | | | | | | | | | | | | Case 1: % 232.24/39.48 | | | | | | | | | | | | | | % 232.24/39.48 | | | | | | | | | | | | | | (341) all_74_3 = n0 % 232.24/39.48 | | | | | | | | | | | | | | % 232.24/39.48 | | | | | | | | | | | | | | REDUCE: (164), (341) imply: % 232.24/39.48 | | | | | | | | | | | | | | (342) $false % 232.24/39.48 | | | | | | | | | | | | | | % 232.24/39.48 | | | | | | | | | | | | | | CLOSE: (342) is inconsistent. % 232.24/39.48 | | | | | | | | | | | | | | % 232.24/39.48 | | | | | | | | | | | | | Case 2: % 232.24/39.48 | | | | | | | | | | | | | | % 232.24/39.48 | | | | | | | | | | | | | | (343) all_74_3 = n1 % 232.24/39.48 | | | | | | | | | | | | | | % 232.24/39.48 | | | | | | | | | | | | | | REDUCE: (332), (343) imply: % 232.24/39.48 | | | | | | | | | | | | | | (344) a_select3(q_ds1_filter, n1, n4) = all_74_1 % 232.24/39.48 | | | | | | | | | | | | | | % 232.24/39.48 | | | | | | | | | | | | | | REDUCE: (331), (343) imply: % 232.24/39.48 | | | | | | | | | | | | | | (345) a_select3(q_ds1_filter, n4, n1) = all_74_0 % 232.24/39.48 | | | | | | | | | | | | | | % 232.24/39.48 | | | | | | | | | | | | | | REDUCE: (146), (343) imply: % 232.24/39.48 | | | | | | | | | | | | | | (346) leq(n1, n5) % 232.24/39.48 | | | | | | | | | | | | | | % 232.24/39.48 | | | | | | | | | | | | | | REDUCE: (139), (343) imply: % 232.24/39.48 | | | | | | | | | | | | | | (347) leq(n0, n1) % 232.24/39.48 | | | | | | | | | | | | | | % 232.24/39.48 | | | | | | | | | | | | | | GROUND_INST: instantiating (62) with n1, n4, all_74_1, % 232.24/39.48 | | | | | | | | | | | | | | simplifying with (85), (119), (334), (344), (347) % 232.24/39.48 | | | | | | | | | | | | | | gives: % 232.24/39.48 | | | | | | | | | | | | | | (348) ~ leq(n4, all_74_21) | ~ leq(n1, all_74_21) | % 232.24/39.48 | | | | | | | | | | | | | | (a_select3(q_ds1_filter, n4, n1) = all_74_1 & % 232.24/39.48 | | | | | | | | | | | | | | $i(all_74_1)) % 232.24/39.48 | | | | | | | | | | | | | | % 232.24/39.48 | | | | | | | | | | | | | | BETA: splitting (348) gives: % 232.24/39.48 | | | | | | | | | | | | | | % 232.24/39.48 | | | | | | | | | | | | | | Case 1: % 232.24/39.48 | | | | | | | | | | | | | | | % 232.24/39.48 | | | | | | | | | | | | | | | (349) ~ leq(n4, all_74_21) % 232.24/39.48 | | | | | | | | | | | | | | | % 232.24/39.48 | | | | | | | | | | | | | | | REDUCE: (135), (349) imply: % 232.24/39.48 | | | | | | | | | | | | | | | (350) ~ leq(n4, n5) % 232.24/39.48 | | | | | | | | | | | | | | | % 232.24/39.48 | | | | | | | | | | | | | | | PRED_UNIFY: (333), (350) imply: % 232.24/39.48 | | | | | | | | | | | | | | | (351) $false % 232.24/39.48 | | | | | | | | | | | | | | | % 232.24/39.48 | | | | | | | | | | | | | | | CLOSE: (351) is inconsistent. % 232.24/39.48 | | | | | | | | | | | | | | | % 232.24/39.48 | | | | | | | | | | | | | | Case 2: % 232.24/39.48 | | | | | | | | | | | | | | | % 232.24/39.48 | | | | | | | | | | | | | | | (352) ~ leq(n1, all_74_21) | (a_select3(q_ds1_filter, % 232.24/39.48 | | | | | | | | | | | | | | | n4, n1) = all_74_1 & $i(all_74_1)) % 232.24/39.48 | | | | | | | | | | | | | | | % 232.24/39.48 | | | | | | | | | | | | | | | BETA: splitting (352) gives: % 232.24/39.48 | | | | | | | | | | | | | | | % 232.24/39.48 | | | | | | | | | | | | | | | Case 1: % 232.24/39.48 | | | | | | | | | | | | | | | | % 232.24/39.48 | | | | | | | | | | | | | | | | (353) ~ leq(n1, all_74_21) % 232.24/39.48 | | | | | | | | | | | | | | | | % 232.24/39.48 | | | | | | | | | | | | | | | | REDUCE: (135), (353) imply: % 232.24/39.48 | | | | | | | | | | | | | | | | (354) ~ leq(n1, n5) % 232.24/39.48 | | | | | | | | | | | | | | | | % 232.24/39.48 | | | | | | | | | | | | | | | | PRED_UNIFY: (346), (354) imply: % 232.24/39.48 | | | | | | | | | | | | | | | | (355) $false % 232.24/39.48 | | | | | | | | | | | | | | | | % 232.24/39.48 | | | | | | | | | | | | | | | | CLOSE: (355) is inconsistent. % 232.24/39.48 | | | | | | | | | | | | | | | | % 232.24/39.48 | | | | | | | | | | | | | | | Case 2: % 232.24/39.48 | | | | | | | | | | | | | | | | % 232.24/39.48 | | | | | | | | | | | | | | | | (356) a_select3(q_ds1_filter, n4, n1) = all_74_1 & % 232.24/39.48 | | | | | | | | | | | | | | | | $i(all_74_1) % 232.24/39.48 | | | | | | | | | | | | | | | | % 232.24/39.48 | | | | | | | | | | | | | | | | ALPHA: (356) implies: % 232.24/39.48 | | | | | | | | | | | | | | | | (357) a_select3(q_ds1_filter, n4, n1) = all_74_1 % 232.24/39.48 | | | | | | | | | | | | | | | | % 232.24/39.48 | | | | | | | | | | | | | | | | REF_CLOSE: (17), (138), (345), (357) are inconsistent by % 232.24/39.48 | | | | | | | | | | | | | | | | sub-proof #53. % 232.24/39.48 | | | | | | | | | | | | | | | | % 232.24/39.48 | | | | | | | | | | | | | | | End of split % 232.24/39.48 | | | | | | | | | | | | | | | % 232.24/39.48 | | | | | | | | | | | | | | End of split % 232.24/39.48 | | | | | | | | | | | | | | % 232.24/39.48 | | | | | | | | | | | | | End of split % 232.24/39.48 | | | | | | | | | | | | | % 232.24/39.48 | | | | | | | | | | | | Case 2: % 232.24/39.48 | | | | | | | | | | | | | % 232.24/39.48 | | | | | | | | | | | | | (358) all_74_3 = n2 % 232.24/39.48 | | | | | | | | | | | | | % 232.24/39.48 | | | | | | | | | | | | | REDUCE: (332), (358) imply: % 232.24/39.48 | | | | | | | | | | | | | (359) a_select3(q_ds1_filter, n2, n4) = all_74_1 % 232.24/39.48 | | | | | | | | | | | | | % 232.24/39.48 | | | | | | | | | | | | | REDUCE: (331), (358) imply: % 232.24/39.48 | | | | | | | | | | | | | (360) a_select3(q_ds1_filter, n4, n2) = all_74_0 % 232.24/39.48 | | | | | | | | | | | | | % 232.24/39.48 | | | | | | | | | | | | | REDUCE: (146), (358) imply: % 232.24/39.48 | | | | | | | | | | | | | (361) leq(n2, n5) % 232.24/39.48 | | | | | | | | | | | | | % 232.24/39.48 | | | | | | | | | | | | | REDUCE: (139), (358) imply: % 232.24/39.48 | | | | | | | | | | | | | (362) leq(n0, n2) % 232.24/39.48 | | | | | | | | | | | | | % 232.24/39.48 | | | | | | | | | | | | | GROUND_INST: instantiating (62) with n2, n4, all_74_1, % 232.24/39.48 | | | | | | | | | | | | | simplifying with (101), (119), (334), (359), (362) % 232.24/39.48 | | | | | | | | | | | | | gives: % 232.24/39.49 | | | | | | | | | | | | | (363) ~ leq(n4, all_74_21) | ~ leq(n2, all_74_21) | % 232.24/39.49 | | | | | | | | | | | | | (a_select3(q_ds1_filter, n4, n2) = all_74_1 & % 232.24/39.49 | | | | | | | | | | | | | $i(all_74_1)) % 232.24/39.49 | | | | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | | | | BETA: splitting (363) gives: % 232.24/39.49 | | | | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | | | | Case 1: % 232.24/39.49 | | | | | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | | | | | (364) ~ leq(n4, all_74_21) % 232.24/39.49 | | | | | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | | | | | REDUCE: (135), (364) imply: % 232.24/39.49 | | | | | | | | | | | | | | (365) ~ leq(n4, n5) % 232.24/39.49 | | | | | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | | | | | PRED_UNIFY: (333), (365) imply: % 232.24/39.49 | | | | | | | | | | | | | | (366) $false % 232.24/39.49 | | | | | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | | | | | CLOSE: (366) is inconsistent. % 232.24/39.49 | | | | | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | | | | Case 2: % 232.24/39.49 | | | | | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | | | | | (367) ~ leq(n2, all_74_21) | (a_select3(q_ds1_filter, % 232.24/39.49 | | | | | | | | | | | | | | n4, n2) = all_74_1 & $i(all_74_1)) % 232.24/39.49 | | | | | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | | | | | BETA: splitting (367) gives: % 232.24/39.49 | | | | | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | | | | | Case 1: % 232.24/39.49 | | | | | | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | | | | | | (368) ~ leq(n2, all_74_21) % 232.24/39.49 | | | | | | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | | | | | | REDUCE: (135), (368) imply: % 232.24/39.49 | | | | | | | | | | | | | | | (369) ~ leq(n2, n5) % 232.24/39.49 | | | | | | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | | | | | | PRED_UNIFY: (361), (369) imply: % 232.24/39.49 | | | | | | | | | | | | | | | (370) $false % 232.24/39.49 | | | | | | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | | | | | | CLOSE: (370) is inconsistent. % 232.24/39.49 | | | | | | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | | | | | Case 2: % 232.24/39.49 | | | | | | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | | | | | | (371) a_select3(q_ds1_filter, n4, n2) = all_74_1 & % 232.24/39.49 | | | | | | | | | | | | | | | $i(all_74_1) % 232.24/39.49 | | | | | | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | | | | | | ALPHA: (371) implies: % 232.24/39.49 | | | | | | | | | | | | | | | (372) a_select3(q_ds1_filter, n4, n2) = all_74_1 % 232.24/39.49 | | | | | | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | | | | | | REF_CLOSE: (17), (138), (360), (372) are inconsistent by % 232.24/39.49 | | | | | | | | | | | | | | | sub-proof #52. % 232.24/39.49 | | | | | | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | | | | | End of split % 232.24/39.49 | | | | | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | | | | End of split % 232.24/39.49 | | | | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | | | End of split % 232.24/39.49 | | | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | | Case 2: % 232.24/39.49 | | | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | | | (373) all_74_3 = n3 % 232.24/39.49 | | | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | | | REDUCE: (332), (373) imply: % 232.24/39.49 | | | | | | | | | | | | (374) a_select3(q_ds1_filter, n3, n4) = all_74_1 % 232.24/39.49 | | | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | | | REDUCE: (331), (373) imply: % 232.24/39.49 | | | | | | | | | | | | (375) a_select3(q_ds1_filter, n4, n3) = all_74_0 % 232.24/39.49 | | | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | | | REDUCE: (146), (373) imply: % 232.24/39.49 | | | | | | | | | | | | (376) leq(n3, n5) % 232.24/39.49 | | | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | | | REDUCE: (139), (373) imply: % 232.24/39.49 | | | | | | | | | | | | (377) leq(n0, n3) % 232.24/39.49 | | | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | | | GROUND_INST: instantiating (62) with n3, n4, all_74_1, % 232.24/39.49 | | | | | | | | | | | | simplifying with (112), (119), (334), (374), (377) % 232.24/39.49 | | | | | | | | | | | | gives: % 232.24/39.49 | | | | | | | | | | | | (378) ~ leq(n4, all_74_21) | ~ leq(n3, all_74_21) | % 232.24/39.49 | | | | | | | | | | | | (a_select3(q_ds1_filter, n4, n3) = all_74_1 & % 232.24/39.49 | | | | | | | | | | | | $i(all_74_1)) % 232.24/39.49 | | | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | | | BETA: splitting (378) gives: % 232.24/39.49 | | | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | | | Case 1: % 232.24/39.49 | | | | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | | | | (379) ~ leq(n4, all_74_21) % 232.24/39.49 | | | | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | | | | REDUCE: (135), (379) imply: % 232.24/39.49 | | | | | | | | | | | | | (380) ~ leq(n4, n5) % 232.24/39.49 | | | | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | | | | PRED_UNIFY: (333), (380) imply: % 232.24/39.49 | | | | | | | | | | | | | (381) $false % 232.24/39.49 | | | | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | | | | CLOSE: (381) is inconsistent. % 232.24/39.49 | | | | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | | | Case 2: % 232.24/39.49 | | | | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | | | | (382) ~ leq(n3, all_74_21) | (a_select3(q_ds1_filter, % 232.24/39.49 | | | | | | | | | | | | | n4, n3) = all_74_1 & $i(all_74_1)) % 232.24/39.49 | | | | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | | | | BETA: splitting (382) gives: % 232.24/39.49 | | | | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | | | | Case 1: % 232.24/39.49 | | | | | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | | | | | (383) ~ leq(n3, all_74_21) % 232.24/39.49 | | | | | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | | | | | REDUCE: (135), (383) imply: % 232.24/39.49 | | | | | | | | | | | | | | (384) ~ leq(n3, n5) % 232.24/39.49 | | | | | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | | | | | PRED_UNIFY: (376), (384) imply: % 232.24/39.49 | | | | | | | | | | | | | | (385) $false % 232.24/39.49 | | | | | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | | | | | CLOSE: (385) is inconsistent. % 232.24/39.49 | | | | | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | | | | Case 2: % 232.24/39.49 | | | | | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | | | | | (386) a_select3(q_ds1_filter, n4, n3) = all_74_1 & % 232.24/39.49 | | | | | | | | | | | | | | $i(all_74_1) % 232.24/39.49 | | | | | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | | | | | ALPHA: (386) implies: % 232.24/39.49 | | | | | | | | | | | | | | (387) a_select3(q_ds1_filter, n4, n3) = all_74_1 % 232.24/39.49 | | | | | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | | | | | REF_CLOSE: (17), (138), (375), (387) are inconsistent by % 232.24/39.49 | | | | | | | | | | | | | | sub-proof #51. % 232.24/39.49 | | | | | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | | | | End of split % 232.24/39.49 | | | | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | | | End of split % 232.24/39.49 | | | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | | End of split % 232.24/39.49 | | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | End of split % 232.24/39.49 | | | | | | | | | | % 232.24/39.49 | | | | | | | | | Case 2: % 232.24/39.49 | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | (388) all_74_3 = n4 % 232.24/39.49 | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | REDUCE: (144), (388) imply: % 232.24/39.49 | | | | | | | | | | (389) a_select3(q_ds1_filter, all_74_2, n4) = all_74_0 % 232.24/39.49 | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | REDUCE: (143), (388) imply: % 232.24/39.49 | | | | | | | | | | (390) a_select3(q_ds1_filter, n4, all_74_2) = all_74_1 % 232.24/39.49 | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | REDUCE: (146), (388) imply: % 232.24/39.49 | | | | | | | | | | (391) leq(n4, n5) % 232.24/39.49 | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | REDUCE: (139), (388) imply: % 232.24/39.49 | | | | | | | | | | (392) leq(n0, n4) % 232.24/39.49 | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | BETA: splitting (160) gives: % 232.24/39.49 | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | Case 1: % 232.24/39.49 | | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | | (393) gt(n4, all_74_2) % 232.24/39.49 | | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_2, n4, n3, % 232.24/39.49 | | | | | | | | | | | simplifying with (58), (119), (125), (393) gives: % 232.24/39.49 | | | | | | | | | | | (394) leq(all_74_2, n3) % 232.24/39.49 | | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_2, n3, % 232.24/39.49 | | | | | | | | | | | simplifying with (58), (112), (394) gives: % 232.24/39.49 | | | | | | | | | | | (395) all_74_2 = n3 | gt(n3, all_74_2) % 232.24/39.49 | | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | | BETA: splitting (395) gives: % 232.24/39.49 | | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | | Case 1: % 232.24/39.49 | | | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | | | (396) gt(n3, all_74_2) % 232.24/39.49 | | | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_2, n3, n2, % 232.24/39.49 | | | | | | | | | | | | simplifying with (58), (112), (124), (396) gives: % 232.24/39.49 | | | | | | | | | | | | (397) leq(all_74_2, n2) % 232.24/39.49 | | | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_2, n2, % 232.24/39.49 | | | | | | | | | | | | simplifying with (58), (101), (397) gives: % 232.24/39.49 | | | | | | | | | | | | (398) all_74_2 = n2 | gt(n2, all_74_2) % 232.24/39.49 | | | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | | | BETA: splitting (398) gives: % 232.24/39.49 | | | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | | | Case 1: % 232.24/39.49 | | | | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | | | | (399) gt(n2, all_74_2) % 232.24/39.49 | | | | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_2, n2, n1, % 232.24/39.49 | | | | | | | | | | | | | simplifying with (58), (101), (123), (399) gives: % 232.24/39.49 | | | | | | | | | | | | | (400) leq(all_74_2, n1) % 232.24/39.49 | | | | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_74_2, simplifying with % 232.24/39.49 | | | | | | | | | | | | | (58), (140), (400) gives: % 232.24/39.49 | | | | | | | | | | | | | (401) all_74_2 = n1 | all_74_2 = n0 % 232.24/39.49 | | | | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | | | | BETA: splitting (401) gives: % 232.24/39.49 | | | | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | | | | Case 1: % 232.24/39.49 | | | | | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | | | | | (402) all_74_2 = n0 % 232.24/39.49 | | | | | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | | | | | REDUCE: (162), (402) imply: % 232.24/39.49 | | | | | | | | | | | | | | (403) $false % 232.24/39.49 | | | | | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | | | | | CLOSE: (403) is inconsistent. % 232.24/39.49 | | | | | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | | | | Case 2: % 232.24/39.49 | | | | | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | | | | | (404) all_74_2 = n1 % 232.24/39.49 | | | | | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | | | | | REDUCE: (389), (404) imply: % 232.24/39.49 | | | | | | | | | | | | | | (405) a_select3(q_ds1_filter, n1, n4) = all_74_0 % 232.24/39.49 | | | | | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | | | | | REDUCE: (390), (404) imply: % 232.24/39.49 | | | | | | | | | | | | | | (406) a_select3(q_ds1_filter, n4, n1) = all_74_1 % 232.24/39.49 | | | | | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | | | | | REDUCE: (145), (404) imply: % 232.24/39.49 | | | | | | | | | | | | | | (407) leq(n1, n5) % 232.24/39.49 | | | | | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | | | | | REDUCE: (140), (404) imply: % 232.24/39.49 | | | | | | | | | | | | | | (408) leq(n0, n1) % 232.24/39.49 | | | | | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | | | | | GROUND_INST: instantiating (62) with n1, n4, all_74_0, % 232.24/39.49 | | | | | | | | | | | | | | simplifying with (85), (119), (392), (405), (408) % 232.24/39.49 | | | | | | | | | | | | | | gives: % 232.24/39.49 | | | | | | | | | | | | | | (409) ~ leq(n4, all_74_21) | ~ leq(n1, all_74_21) | % 232.24/39.49 | | | | | | | | | | | | | | (a_select3(q_ds1_filter, n4, n1) = all_74_0 & % 232.24/39.49 | | | | | | | | | | | | | | $i(all_74_0)) % 232.24/39.49 | | | | | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | | | | | BETA: splitting (409) gives: % 232.24/39.49 | | | | | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | | | | | Case 1: % 232.24/39.49 | | | | | | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | | | | | | (410) ~ leq(n4, all_74_21) % 232.24/39.49 | | | | | | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | | | | | | REDUCE: (135), (410) imply: % 232.24/39.49 | | | | | | | | | | | | | | | (411) ~ leq(n4, n5) % 232.24/39.49 | | | | | | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | | | | | | PRED_UNIFY: (391), (411) imply: % 232.24/39.49 | | | | | | | | | | | | | | | (412) $false % 232.24/39.49 | | | | | | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | | | | | | CLOSE: (412) is inconsistent. % 232.24/39.49 | | | | | | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | | | | | Case 2: % 232.24/39.49 | | | | | | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | | | | | | (413) ~ leq(n1, all_74_21) | (a_select3(q_ds1_filter, % 232.24/39.49 | | | | | | | | | | | | | | | n4, n1) = all_74_0 & $i(all_74_0)) % 232.24/39.49 | | | | | | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | | | | | | BETA: splitting (413) gives: % 232.24/39.49 | | | | | | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | | | | | | Case 1: % 232.24/39.49 | | | | | | | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | | | | | | | (414) ~ leq(n1, all_74_21) % 232.24/39.49 | | | | | | | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | | | | | | | REDUCE: (135), (414) imply: % 232.24/39.49 | | | | | | | | | | | | | | | | (415) ~ leq(n1, n5) % 232.24/39.49 | | | | | | | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | | | | | | | PRED_UNIFY: (407), (415) imply: % 232.24/39.49 | | | | | | | | | | | | | | | | (416) $false % 232.24/39.49 | | | | | | | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | | | | | | | CLOSE: (416) is inconsistent. % 232.24/39.49 | | | | | | | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | | | | | | Case 2: % 232.24/39.49 | | | | | | | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | | | | | | | (417) a_select3(q_ds1_filter, n4, n1) = all_74_0 & % 232.24/39.49 | | | | | | | | | | | | | | | | $i(all_74_0) % 232.24/39.49 | | | | | | | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | | | | | | | ALPHA: (417) implies: % 232.24/39.49 | | | | | | | | | | | | | | | | (418) a_select3(q_ds1_filter, n4, n1) = all_74_0 % 232.24/39.49 | | | | | | | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | | | | | | | REF_CLOSE: (17), (138), (406), (418) are inconsistent by % 232.24/39.49 | | | | | | | | | | | | | | | | sub-proof #53. % 232.24/39.49 | | | | | | | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | | | | | | End of split % 232.24/39.49 | | | | | | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | | | | | End of split % 232.24/39.49 | | | | | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | | | | End of split % 232.24/39.49 | | | | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | | | Case 2: % 232.24/39.49 | | | | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | | | | (419) all_74_2 = n2 % 232.24/39.49 | | | | | | | | | | | | | % 232.24/39.49 | | | | | | | | | | | | | REDUCE: (389), (419) imply: % 232.24/39.50 | | | | | | | | | | | | | (420) a_select3(q_ds1_filter, n2, n4) = all_74_0 % 232.24/39.50 | | | | | | | | | | | | | % 232.24/39.50 | | | | | | | | | | | | | REDUCE: (390), (419) imply: % 232.24/39.50 | | | | | | | | | | | | | (421) a_select3(q_ds1_filter, n4, n2) = all_74_1 % 232.24/39.50 | | | | | | | | | | | | | % 232.24/39.50 | | | | | | | | | | | | | REDUCE: (145), (419) imply: % 232.24/39.50 | | | | | | | | | | | | | (422) leq(n2, n5) % 232.24/39.50 | | | | | | | | | | | | | % 232.24/39.50 | | | | | | | | | | | | | REDUCE: (140), (419) imply: % 232.24/39.50 | | | | | | | | | | | | | (423) leq(n0, n2) % 232.24/39.50 | | | | | | | | | | | | | % 232.24/39.50 | | | | | | | | | | | | | GROUND_INST: instantiating (62) with n2, n4, all_74_0, % 232.24/39.50 | | | | | | | | | | | | | simplifying with (101), (119), (392), (420), (423) % 232.24/39.50 | | | | | | | | | | | | | gives: % 232.24/39.50 | | | | | | | | | | | | | (424) ~ leq(n4, all_74_21) | ~ leq(n2, all_74_21) | % 232.24/39.50 | | | | | | | | | | | | | (a_select3(q_ds1_filter, n4, n2) = all_74_0 & % 232.24/39.50 | | | | | | | | | | | | | $i(all_74_0)) % 232.24/39.50 | | | | | | | | | | | | | % 232.24/39.50 | | | | | | | | | | | | | BETA: splitting (424) gives: % 232.24/39.50 | | | | | | | | | | | | | % 232.24/39.50 | | | | | | | | | | | | | Case 1: % 232.24/39.50 | | | | | | | | | | | | | | % 232.24/39.50 | | | | | | | | | | | | | | (425) ~ leq(n4, all_74_21) % 232.24/39.50 | | | | | | | | | | | | | | % 232.24/39.50 | | | | | | | | | | | | | | REDUCE: (135), (425) imply: % 232.24/39.50 | | | | | | | | | | | | | | (426) ~ leq(n4, n5) % 232.24/39.50 | | | | | | | | | | | | | | % 232.24/39.50 | | | | | | | | | | | | | | PRED_UNIFY: (391), (426) imply: % 232.24/39.50 | | | | | | | | | | | | | | (427) $false % 232.24/39.50 | | | | | | | | | | | | | | % 232.24/39.50 | | | | | | | | | | | | | | CLOSE: (427) is inconsistent. % 232.24/39.50 | | | | | | | | | | | | | | % 232.24/39.50 | | | | | | | | | | | | | Case 2: % 232.24/39.50 | | | | | | | | | | | | | | % 232.24/39.50 | | | | | | | | | | | | | | (428) ~ leq(n2, all_74_21) | (a_select3(q_ds1_filter, % 232.24/39.50 | | | | | | | | | | | | | | n4, n2) = all_74_0 & $i(all_74_0)) % 232.24/39.50 | | | | | | | | | | | | | | % 232.24/39.50 | | | | | | | | | | | | | | BETA: splitting (428) gives: % 232.24/39.50 | | | | | | | | | | | | | | % 232.24/39.50 | | | | | | | | | | | | | | Case 1: % 232.24/39.50 | | | | | | | | | | | | | | | % 232.24/39.50 | | | | | | | | | | | | | | | (429) ~ leq(n2, all_74_21) % 232.24/39.50 | | | | | | | | | | | | | | | % 232.24/39.50 | | | | | | | | | | | | | | | REDUCE: (135), (429) imply: % 232.24/39.50 | | | | | | | | | | | | | | | (430) ~ leq(n2, n5) % 232.24/39.50 | | | | | | | | | | | | | | | % 232.24/39.50 | | | | | | | | | | | | | | | PRED_UNIFY: (422), (430) imply: % 232.24/39.50 | | | | | | | | | | | | | | | (431) $false % 232.24/39.50 | | | | | | | | | | | | | | | % 232.24/39.50 | | | | | | | | | | | | | | | CLOSE: (431) is inconsistent. % 232.24/39.50 | | | | | | | | | | | | | | | % 232.24/39.50 | | | | | | | | | | | | | | Case 2: % 232.24/39.50 | | | | | | | | | | | | | | | % 232.24/39.50 | | | | | | | | | | | | | | | (432) a_select3(q_ds1_filter, n4, n2) = all_74_0 & % 232.24/39.50 | | | | | | | | | | | | | | | $i(all_74_0) % 232.24/39.50 | | | | | | | | | | | | | | | % 232.24/39.50 | | | | | | | | | | | | | | | ALPHA: (432) implies: % 232.24/39.50 | | | | | | | | | | | | | | | (433) a_select3(q_ds1_filter, n4, n2) = all_74_0 % 232.24/39.50 | | | | | | | | | | | | | | | % 232.24/39.50 | | | | | | | | | | | | | | | REF_CLOSE: (17), (138), (421), (433) are inconsistent by % 232.24/39.50 | | | | | | | | | | | | | | | sub-proof #52. % 232.24/39.50 | | | | | | | | | | | | | | | % 232.24/39.50 | | | | | | | | | | | | | | End of split % 232.24/39.50 | | | | | | | | | | | | | | % 232.24/39.50 | | | | | | | | | | | | | End of split % 232.24/39.50 | | | | | | | | | | | | | % 232.24/39.50 | | | | | | | | | | | | End of split % 232.24/39.50 | | | | | | | | | | | | % 232.24/39.50 | | | | | | | | | | | Case 2: % 232.24/39.50 | | | | | | | | | | | | % 232.24/39.50 | | | | | | | | | | | | (434) all_74_2 = n3 % 232.24/39.50 | | | | | | | | | | | | % 232.24/39.50 | | | | | | | | | | | | REDUCE: (389), (434) imply: % 232.24/39.50 | | | | | | | | | | | | (435) a_select3(q_ds1_filter, n3, n4) = all_74_0 % 232.24/39.50 | | | | | | | | | | | | % 232.24/39.50 | | | | | | | | | | | | REDUCE: (390), (434) imply: % 232.24/39.50 | | | | | | | | | | | | (436) a_select3(q_ds1_filter, n4, n3) = all_74_1 % 232.24/39.50 | | | | | | | | | | | | % 232.24/39.50 | | | | | | | | | | | | REDUCE: (145), (434) imply: % 232.24/39.50 | | | | | | | | | | | | (437) leq(n3, n5) % 232.24/39.50 | | | | | | | | | | | | % 232.24/39.50 | | | | | | | | | | | | REDUCE: (140), (434) imply: % 232.24/39.50 | | | | | | | | | | | | (438) leq(n0, n3) % 232.24/39.50 | | | | | | | | | | | | % 232.24/39.50 | | | | | | | | | | | | GROUND_INST: instantiating (62) with n3, n4, all_74_0, % 232.24/39.50 | | | | | | | | | | | | simplifying with (112), (119), (392), (435), (438) % 232.24/39.50 | | | | | | | | | | | | gives: % 232.24/39.50 | | | | | | | | | | | | (439) ~ leq(n4, all_74_21) | ~ leq(n3, all_74_21) | % 232.24/39.50 | | | | | | | | | | | | (a_select3(q_ds1_filter, n4, n3) = all_74_0 & % 232.24/39.50 | | | | | | | | | | | | $i(all_74_0)) % 232.24/39.50 | | | | | | | | | | | | % 232.24/39.50 | | | | | | | | | | | | BETA: splitting (439) gives: % 232.24/39.50 | | | | | | | | | | | | % 232.24/39.50 | | | | | | | | | | | | Case 1: % 232.24/39.50 | | | | | | | | | | | | | % 232.24/39.50 | | | | | | | | | | | | | (440) ~ leq(n4, all_74_21) % 232.24/39.50 | | | | | | | | | | | | | % 232.24/39.50 | | | | | | | | | | | | | REDUCE: (135), (440) imply: % 232.24/39.50 | | | | | | | | | | | | | (441) ~ leq(n4, n5) % 232.24/39.50 | | | | | | | | | | | | | % 232.24/39.50 | | | | | | | | | | | | | PRED_UNIFY: (391), (441) imply: % 232.24/39.50 | | | | | | | | | | | | | (442) $false % 232.24/39.50 | | | | | | | | | | | | | % 232.24/39.50 | | | | | | | | | | | | | CLOSE: (442) is inconsistent. % 232.24/39.50 | | | | | | | | | | | | | % 232.24/39.50 | | | | | | | | | | | | Case 2: % 232.24/39.50 | | | | | | | | | | | | | % 232.24/39.50 | | | | | | | | | | | | | (443) ~ leq(n3, all_74_21) | (a_select3(q_ds1_filter, % 232.24/39.50 | | | | | | | | | | | | | n4, n3) = all_74_0 & $i(all_74_0)) % 232.24/39.50 | | | | | | | | | | | | | % 232.24/39.50 | | | | | | | | | | | | | BETA: splitting (443) gives: % 232.24/39.50 | | | | | | | | | | | | | % 232.24/39.50 | | | | | | | | | | | | | Case 1: % 232.24/39.50 | | | | | | | | | | | | | | % 232.24/39.50 | | | | | | | | | | | | | | (444) ~ leq(n3, all_74_21) % 232.24/39.50 | | | | | | | | | | | | | | % 232.24/39.50 | | | | | | | | | | | | | | REDUCE: (135), (444) imply: % 232.24/39.50 | | | | | | | | | | | | | | (445) ~ leq(n3, n5) % 232.24/39.50 | | | | | | | | | | | | | | % 232.24/39.50 | | | | | | | | | | | | | | PRED_UNIFY: (437), (445) imply: % 232.24/39.50 | | | | | | | | | | | | | | (446) $false % 232.24/39.50 | | | | | | | | | | | | | | % 232.24/39.50 | | | | | | | | | | | | | | CLOSE: (446) is inconsistent. % 232.24/39.50 | | | | | | | | | | | | | | % 232.24/39.50 | | | | | | | | | | | | | Case 2: % 232.24/39.50 | | | | | | | | | | | | | | % 232.24/39.50 | | | | | | | | | | | | | | (447) a_select3(q_ds1_filter, n4, n3) = all_74_0 & % 232.24/39.50 | | | | | | | | | | | | | | $i(all_74_0) % 232.24/39.50 | | | | | | | | | | | | | | % 232.24/39.50 | | | | | | | | | | | | | | ALPHA: (447) implies: % 232.24/39.50 | | | | | | | | | | | | | | (448) a_select3(q_ds1_filter, n4, n3) = all_74_0 % 232.24/39.50 | | | | | | | | | | | | | | % 232.24/39.50 | | | | | | | | | | | | | | REF_CLOSE: (17), (138), (436), (448) are inconsistent by % 232.24/39.50 | | | | | | | | | | | | | | sub-proof #51. % 232.24/39.50 | | | | | | | | | | | | | | % 232.24/39.50 | | | | | | | | | | | | | End of split % 232.24/39.50 | | | | | | | | | | | | | % 232.24/39.50 | | | | | | | | | | | | End of split % 232.24/39.50 | | | | | | | | | | | | % 232.24/39.50 | | | | | | | | | | | End of split % 232.24/39.50 | | | | | | | | | | | % 232.24/39.50 | | | | | | | | | | Case 2: % 232.24/39.50 | | | | | | | | | | | % 232.24/39.50 | | | | | | | | | | | (449) all_74_2 = n4 % 232.24/39.50 | | | | | | | | | | | % 232.24/39.50 | | | | | | | | | | | REDUCE: (389), (449) imply: % 232.24/39.50 | | | | | | | | | | | (450) a_select3(q_ds1_filter, n4, n4) = all_74_0 % 232.24/39.50 | | | | | | | | | | | % 232.24/39.50 | | | | | | | | | | | REDUCE: (390), (449) imply: % 232.24/39.50 | | | | | | | | | | | (451) a_select3(q_ds1_filter, n4, n4) = all_74_1 % 232.24/39.50 | | | | | | | | | | | % 232.24/39.50 | | | | | | | | | | | GROUND_INST: instantiating (17) with all_74_1, all_74_0, n4, % 232.24/39.50 | | | | | | | | | | | n4, q_ds1_filter, simplifying with (450), (451) % 232.24/39.50 | | | | | | | | | | | gives: % 232.24/39.50 | | | | | | | | | | | (452) all_74_0 = all_74_1 % 232.24/39.50 | | | | | | | | | | | % 232.24/39.50 | | | | | | | | | | | REDUCE: (138), (452) imply: % 232.24/39.50 | | | | | | | | | | | (453) $false % 232.24/39.50 | | | | | | | | | | | % 232.24/39.50 | | | | | | | | | | | CLOSE: (453) is inconsistent. % 232.24/39.50 | | | | | | | | | | | % 232.24/39.50 | | | | | | | | | | End of split % 232.24/39.50 | | | | | | | | | | % 232.24/39.50 | | | | | | | | | End of split % 232.24/39.50 | | | | | | | | | % 232.24/39.50 | | | | | | | | End of split % 232.24/39.50 | | | | | | | | % 232.24/39.50 | | | | | | | End of split % 232.24/39.50 | | | | | | | % 232.24/39.50 | | | | | | Case 2: % 232.24/39.50 | | | | | | | % 232.24/39.50 | | | | | | | (454) all_74_2 = n5 % 232.24/39.50 | | | | | | | % 232.24/39.50 | | | | | | | REDUCE: (144), (454) imply: % 232.24/39.50 | | | | | | | (455) a_select3(q_ds1_filter, n5, all_74_3) = all_74_0 % 232.24/39.50 | | | | | | | % 232.24/39.50 | | | | | | | REDUCE: (143), (454) imply: % 232.24/39.50 | | | | | | | (456) a_select3(q_ds1_filter, all_74_3, n5) = all_74_1 % 232.24/39.50 | | | | | | | % 232.24/39.50 | | | | | | | REDUCE: (145), (454) imply: % 232.24/39.50 | | | | | | | (457) leq(n5, n5) % 232.24/39.50 | | | | | | | % 232.24/39.50 | | | | | | | REDUCE: (140), (454) imply: % 232.24/39.50 | | | | | | | (458) leq(n0, n5) % 232.24/39.50 | | | | | | | % 232.24/39.50 | | | | | | | BETA: splitting (149) gives: % 232.24/39.50 | | | | | | | % 232.24/39.50 | | | | | | | Case 1: % 232.24/39.50 | | | | | | | | % 232.24/39.50 | | | | | | | | (459) all_74_3 = n0 % 232.24/39.50 | | | | | | | | % 232.24/39.50 | | | | | | | | REF_CLOSE: (57), (154), (459), (irreflexivity_gt) are % 232.24/39.50 | | | | | | | | inconsistent by sub-proof #57. % 232.24/39.50 | | | | | | | | % 232.24/39.50 | | | | | | | Case 2: % 232.24/39.50 | | | | | | | | % 232.24/39.50 | | | | | | | | (460) ~ (all_74_3 = n0) % 232.24/39.50 | | | | | | | | % 232.24/39.50 | | | | | | | | BETA: splitting (157) gives: % 232.24/39.50 | | | | | | | | % 232.24/39.50 | | | | | | | | Case 1: % 232.24/39.50 | | | | | | | | | % 232.24/39.50 | | | | | | | | | (461) gt(n4, all_74_3) % 232.24/39.50 | | | | | | | | | % 232.24/39.50 | | | | | | | | | GROUND_INST: instantiating (1) with all_74_3, n4, n3, % 232.24/39.50 | | | | | | | | | simplifying with (57), (119), (125), (461) gives: % 232.24/39.50 | | | | | | | | | (462) leq(all_74_3, n3) % 232.24/39.50 | | | | | | | | | % 232.24/39.50 | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_3, n3, % 232.24/39.50 | | | | | | | | | simplifying with (57), (112), (462) gives: % 232.24/39.50 | | | | | | | | | (463) all_74_3 = n3 | gt(n3, all_74_3) % 232.24/39.50 | | | | | | | | | % 232.24/39.50 | | | | | | | | | BETA: splitting (463) gives: % 232.24/39.50 | | | | | | | | | % 232.24/39.50 | | | | | | | | | Case 1: % 232.24/39.50 | | | | | | | | | | % 232.24/39.50 | | | | | | | | | | (464) gt(n3, all_74_3) % 232.24/39.50 | | | | | | | | | | % 232.24/39.50 | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_3, n3, n2, % 232.24/39.50 | | | | | | | | | | simplifying with (57), (112), (124), (464) gives: % 232.24/39.50 | | | | | | | | | | (465) leq(all_74_3, n2) % 232.24/39.50 | | | | | | | | | | % 232.24/39.50 | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_3, n2, % 232.24/39.50 | | | | | | | | | | simplifying with (57), (101), (465) gives: % 232.24/39.50 | | | | | | | | | | (466) all_74_3 = n2 | gt(n2, all_74_3) % 232.24/39.50 | | | | | | | | | | % 232.24/39.50 | | | | | | | | | | BETA: splitting (466) gives: % 232.24/39.50 | | | | | | | | | | % 232.24/39.50 | | | | | | | | | | Case 1: % 232.24/39.50 | | | | | | | | | | | % 232.24/39.50 | | | | | | | | | | | (467) gt(n2, all_74_3) % 232.24/39.50 | | | | | | | | | | | % 232.24/39.50 | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_3, n2, n1, % 232.24/39.50 | | | | | | | | | | | simplifying with (57), (101), (123), (467) gives: % 232.24/39.50 | | | | | | | | | | | (468) leq(all_74_3, n1) % 232.24/39.50 | | | | | | | | | | | % 232.24/39.50 | | | | | | | | | | | GROUND_INST: instantiating (4) with all_74_3, simplifying with % 232.24/39.50 | | | | | | | | | | | (57), (139), (468) gives: % 232.24/39.50 | | | | | | | | | | | (469) all_74_3 = n1 | all_74_3 = n0 % 232.24/39.50 | | | | | | | | | | | % 232.24/39.50 | | | | | | | | | | | BETA: splitting (469) gives: % 232.24/39.50 | | | | | | | | | | | % 232.24/39.50 | | | | | | | | | | | Case 1: % 232.24/39.50 | | | | | | | | | | | | % 232.24/39.50 | | | | | | | | | | | | (470) all_74_3 = n0 % 232.24/39.50 | | | | | | | | | | | | % 232.24/39.50 | | | | | | | | | | | | REDUCE: (460), (470) imply: % 232.24/39.50 | | | | | | | | | | | | (471) $false % 232.24/39.50 | | | | | | | | | | | | % 232.24/39.50 | | | | | | | | | | | | CLOSE: (471) is inconsistent. % 232.24/39.50 | | | | | | | | | | | | % 232.24/39.50 | | | | | | | | | | | Case 2: % 232.24/39.50 | | | | | | | | | | | | % 232.24/39.50 | | | | | | | | | | | | (472) all_74_3 = n1 % 232.24/39.50 | | | | | | | | | | | | % 232.24/39.50 | | | | | | | | | | | | REDUCE: (456), (472) imply: % 232.24/39.50 | | | | | | | | | | | | (473) a_select3(q_ds1_filter, n1, n5) = all_74_1 % 232.24/39.50 | | | | | | | | | | | | % 232.24/39.50 | | | | | | | | | | | | REDUCE: (455), (472) imply: % 232.24/39.50 | | | | | | | | | | | | (474) a_select3(q_ds1_filter, n5, n1) = all_74_0 % 232.24/39.50 | | | | | | | | | | | | % 232.24/39.50 | | | | | | | | | | | | REDUCE: (146), (472) imply: % 232.24/39.50 | | | | | | | | | | | | (475) leq(n1, n5) % 232.24/39.50 | | | | | | | | | | | | % 232.24/39.50 | | | | | | | | | | | | REDUCE: (139), (472) imply: % 232.24/39.50 | | | | | | | | | | | | (476) leq(n0, n1) % 232.24/39.50 | | | | | | | | | | | | % 232.24/39.50 | | | | | | | | | | | | GROUND_INST: instantiating (62) with n1, n5, all_74_1, % 232.24/39.50 | | | | | | | | | | | | simplifying with (85), (122), (458), (473), (476) % 232.24/39.50 | | | | | | | | | | | | gives: % 232.24/39.51 | | | | | | | | | | | | (477) ~ leq(n5, all_74_21) | ~ leq(n1, all_74_21) | % 232.24/39.51 | | | | | | | | | | | | (a_select3(q_ds1_filter, n5, n1) = all_74_1 & % 232.24/39.51 | | | | | | | | | | | | $i(all_74_1)) % 232.24/39.51 | | | | | | | | | | | | % 232.24/39.51 | | | | | | | | | | | | BETA: splitting (477) gives: % 232.24/39.51 | | | | | | | | | | | | % 232.24/39.51 | | | | | | | | | | | | Case 1: % 232.24/39.51 | | | | | | | | | | | | | % 232.24/39.51 | | | | | | | | | | | | | (478) ~ leq(n5, all_74_21) % 232.24/39.51 | | | | | | | | | | | | | % 232.24/39.51 | | | | | | | | | | | | | REDUCE: (135), (478) imply: % 232.24/39.51 | | | | | | | | | | | | | (479) ~ leq(n5, n5) % 232.24/39.51 | | | | | | | | | | | | | % 232.24/39.51 | | | | | | | | | | | | | PRED_UNIFY: (457), (479) imply: % 232.24/39.51 | | | | | | | | | | | | | (480) $false % 232.24/39.51 | | | | | | | | | | | | | % 232.24/39.51 | | | | | | | | | | | | | CLOSE: (480) is inconsistent. % 232.24/39.51 | | | | | | | | | | | | | % 232.24/39.51 | | | | | | | | | | | | Case 2: % 232.24/39.51 | | | | | | | | | | | | | % 232.24/39.51 | | | | | | | | | | | | | (481) ~ leq(n1, all_74_21) | (a_select3(q_ds1_filter, % 232.24/39.51 | | | | | | | | | | | | | n5, n1) = all_74_1 & $i(all_74_1)) % 232.24/39.51 | | | | | | | | | | | | | % 232.24/39.51 | | | | | | | | | | | | | BETA: splitting (481) gives: % 232.24/39.51 | | | | | | | | | | | | | % 232.24/39.51 | | | | | | | | | | | | | Case 1: % 232.24/39.51 | | | | | | | | | | | | | | % 232.24/39.51 | | | | | | | | | | | | | | (482) ~ leq(n1, all_74_21) % 232.24/39.51 | | | | | | | | | | | | | | % 232.24/39.51 | | | | | | | | | | | | | | REDUCE: (135), (482) imply: % 232.24/39.51 | | | | | | | | | | | | | | (483) ~ leq(n1, n5) % 232.24/39.51 | | | | | | | | | | | | | | % 232.24/39.51 | | | | | | | | | | | | | | PRED_UNIFY: (475), (483) imply: % 232.24/39.51 | | | | | | | | | | | | | | (484) $false % 232.24/39.51 | | | | | | | | | | | | | | % 232.24/39.51 | | | | | | | | | | | | | | CLOSE: (484) is inconsistent. % 232.24/39.51 | | | | | | | | | | | | | | % 232.24/39.51 | | | | | | | | | | | | | Case 2: % 232.24/39.51 | | | | | | | | | | | | | | % 232.24/39.51 | | | | | | | | | | | | | | (485) a_select3(q_ds1_filter, n5, n1) = all_74_1 & % 232.24/39.51 | | | | | | | | | | | | | | $i(all_74_1) % 232.24/39.51 | | | | | | | | | | | | | | % 232.24/39.51 | | | | | | | | | | | | | | ALPHA: (485) implies: % 232.24/39.51 | | | | | | | | | | | | | | (486) a_select3(q_ds1_filter, n5, n1) = all_74_1 % 232.24/39.51 | | | | | | | | | | | | | | % 232.24/39.51 | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_74_0, all_74_1, n1, % 232.24/39.51 | | | | | | | | | | | | | | n5, q_ds1_filter, simplifying with (474), (486) % 232.24/39.51 | | | | | | | | | | | | | | gives: % 232.24/39.51 | | | | | | | | | | | | | | (487) all_74_0 = all_74_1 % 232.24/39.51 | | | | | | | | | | | | | | % 232.24/39.51 | | | | | | | | | | | | | | REDUCE: (138), (487) imply: % 232.24/39.51 | | | | | | | | | | | | | | (488) $false % 232.24/39.51 | | | | | | | | | | | | | | % 232.24/39.51 | | | | | | | | | | | | | | CLOSE: (488) is inconsistent. % 232.24/39.51 | | | | | | | | | | | | | | % 232.24/39.51 | | | | | | | | | | | | | End of split % 232.24/39.51 | | | | | | | | | | | | | % 232.24/39.51 | | | | | | | | | | | | End of split % 232.24/39.51 | | | | | | | | | | | | % 232.24/39.51 | | | | | | | | | | | End of split % 232.24/39.51 | | | | | | | | | | | % 232.24/39.51 | | | | | | | | | | Case 2: % 232.24/39.51 | | | | | | | | | | | % 232.24/39.51 | | | | | | | | | | | (489) all_74_3 = n2 % 232.24/39.51 | | | | | | | | | | | % 232.24/39.51 | | | | | | | | | | | REDUCE: (456), (489) imply: % 232.24/39.51 | | | | | | | | | | | (490) a_select3(q_ds1_filter, n2, n5) = all_74_1 % 232.24/39.51 | | | | | | | | | | | % 232.24/39.51 | | | | | | | | | | | REDUCE: (455), (489) imply: % 232.24/39.51 | | | | | | | | | | | (491) a_select3(q_ds1_filter, n5, n2) = all_74_0 % 232.24/39.51 | | | | | | | | | | | % 232.24/39.51 | | | | | | | | | | | REDUCE: (146), (489) imply: % 232.24/39.51 | | | | | | | | | | | (492) leq(n2, n5) % 232.24/39.51 | | | | | | | | | | | % 232.24/39.51 | | | | | | | | | | | REDUCE: (139), (489) imply: % 232.24/39.51 | | | | | | | | | | | (493) leq(n0, n2) % 232.24/39.51 | | | | | | | | | | | % 232.24/39.51 | | | | | | | | | | | GROUND_INST: instantiating (62) with n2, n5, all_74_1, % 232.24/39.51 | | | | | | | | | | | simplifying with (101), (122), (458), (490), (493) % 232.24/39.51 | | | | | | | | | | | gives: % 232.24/39.51 | | | | | | | | | | | (494) ~ leq(n5, all_74_21) | ~ leq(n2, all_74_21) | % 232.24/39.51 | | | | | | | | | | | (a_select3(q_ds1_filter, n5, n2) = all_74_1 & % 232.24/39.51 | | | | | | | | | | | $i(all_74_1)) % 232.24/39.51 | | | | | | | | | | | % 232.24/39.51 | | | | | | | | | | | BETA: splitting (494) gives: % 232.24/39.51 | | | | | | | | | | | % 232.24/39.51 | | | | | | | | | | | Case 1: % 232.24/39.51 | | | | | | | | | | | | % 232.24/39.51 | | | | | | | | | | | | (495) ~ leq(n5, all_74_21) % 232.24/39.51 | | | | | | | | | | | | % 232.24/39.51 | | | | | | | | | | | | REDUCE: (135), (495) imply: % 232.24/39.51 | | | | | | | | | | | | (496) ~ leq(n5, n5) % 232.24/39.51 | | | | | | | | | | | | % 232.24/39.51 | | | | | | | | | | | | PRED_UNIFY: (457), (496) imply: % 232.24/39.51 | | | | | | | | | | | | (497) $false % 232.24/39.51 | | | | | | | | | | | | % 232.24/39.51 | | | | | | | | | | | | CLOSE: (497) is inconsistent. % 232.24/39.51 | | | | | | | | | | | | % 232.24/39.51 | | | | | | | | | | | Case 2: % 232.24/39.51 | | | | | | | | | | | | % 232.24/39.51 | | | | | | | | | | | | (498) ~ leq(n2, all_74_21) | (a_select3(q_ds1_filter, % 232.24/39.51 | | | | | | | | | | | | n5, n2) = all_74_1 & $i(all_74_1)) % 232.24/39.51 | | | | | | | | | | | | % 232.24/39.51 | | | | | | | | | | | | BETA: splitting (498) gives: % 232.24/39.51 | | | | | | | | | | | | % 232.24/39.51 | | | | | | | | | | | | Case 1: % 232.24/39.51 | | | | | | | | | | | | | % 232.24/39.51 | | | | | | | | | | | | | (499) ~ leq(n2, all_74_21) % 232.24/39.51 | | | | | | | | | | | | | % 232.24/39.51 | | | | | | | | | | | | | REDUCE: (135), (499) imply: % 232.24/39.51 | | | | | | | | | | | | | (500) ~ leq(n2, n5) % 232.24/39.51 | | | | | | | | | | | | | % 232.24/39.51 | | | | | | | | | | | | | PRED_UNIFY: (492), (500) imply: % 232.24/39.51 | | | | | | | | | | | | | (501) $false % 232.24/39.51 | | | | | | | | | | | | | % 232.24/39.51 | | | | | | | | | | | | | CLOSE: (501) is inconsistent. % 232.24/39.51 | | | | | | | | | | | | | % 232.24/39.51 | | | | | | | | | | | | Case 2: % 232.24/39.51 | | | | | | | | | | | | | % 232.24/39.51 | | | | | | | | | | | | | (502) a_select3(q_ds1_filter, n5, n2) = all_74_1 & % 232.24/39.51 | | | | | | | | | | | | | $i(all_74_1) % 232.24/39.51 | | | | | | | | | | | | | % 232.24/39.51 | | | | | | | | | | | | | ALPHA: (502) implies: % 232.24/39.51 | | | | | | | | | | | | | (503) a_select3(q_ds1_filter, n5, n2) = all_74_1 % 232.24/39.51 | | | | | | | | | | | | | % 232.24/39.51 | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_74_0, all_74_1, n2, % 232.24/39.51 | | | | | | | | | | | | | n5, q_ds1_filter, simplifying with (491), (503) % 232.24/39.51 | | | | | | | | | | | | | gives: % 232.24/39.51 | | | | | | | | | | | | | (504) all_74_0 = all_74_1 % 232.24/39.51 | | | | | | | | | | | | | % 232.24/39.51 | | | | | | | | | | | | | REDUCE: (138), (504) imply: % 232.24/39.51 | | | | | | | | | | | | | (505) $false % 232.24/39.51 | | | | | | | | | | | | | % 232.24/39.51 | | | | | | | | | | | | | CLOSE: (505) is inconsistent. % 232.24/39.51 | | | | | | | | | | | | | % 232.24/39.51 | | | | | | | | | | | | End of split % 232.24/39.51 | | | | | | | | | | | | % 232.24/39.51 | | | | | | | | | | | End of split % 232.24/39.51 | | | | | | | | | | | % 232.24/39.51 | | | | | | | | | | End of split % 232.24/39.51 | | | | | | | | | | % 232.24/39.51 | | | | | | | | | Case 2: % 232.24/39.51 | | | | | | | | | | % 232.24/39.51 | | | | | | | | | | (506) all_74_3 = n3 % 232.24/39.51 | | | | | | | | | | % 232.24/39.51 | | | | | | | | | | REDUCE: (456), (506) imply: % 232.24/39.51 | | | | | | | | | | (507) a_select3(q_ds1_filter, n3, n5) = all_74_1 % 232.24/39.51 | | | | | | | | | | % 232.24/39.51 | | | | | | | | | | REDUCE: (455), (506) imply: % 232.24/39.51 | | | | | | | | | | (508) a_select3(q_ds1_filter, n5, n3) = all_74_0 % 232.24/39.51 | | | | | | | | | | % 232.24/39.51 | | | | | | | | | | REDUCE: (146), (506) imply: % 232.24/39.51 | | | | | | | | | | (509) leq(n3, n5) % 232.24/39.51 | | | | | | | | | | % 232.24/39.51 | | | | | | | | | | REDUCE: (139), (506) imply: % 232.24/39.51 | | | | | | | | | | (510) leq(n0, n3) % 232.24/39.51 | | | | | | | | | | % 232.24/39.51 | | | | | | | | | | REF_CLOSE: (17), (62), (112), (122), (135), (138), (457), % 232.24/39.51 | | | | | | | | | | (458), (507), (508), (509), (510) are inconsistent % 232.24/39.51 | | | | | | | | | | by sub-proof #50. % 232.24/39.51 | | | | | | | | | | % 232.24/39.51 | | | | | | | | | End of split % 232.24/39.51 | | | | | | | | | % 232.24/39.51 | | | | | | | | Case 2: % 232.24/39.51 | | | | | | | | | % 232.24/39.51 | | | | | | | | | (511) all_74_3 = n4 % 232.24/39.51 | | | | | | | | | % 232.24/39.51 | | | | | | | | | REDUCE: (456), (511) imply: % 232.24/39.51 | | | | | | | | | (512) a_select3(q_ds1_filter, n4, n5) = all_74_1 % 232.24/39.51 | | | | | | | | | % 232.24/39.51 | | | | | | | | | REDUCE: (455), (511) imply: % 232.24/39.51 | | | | | | | | | (513) a_select3(q_ds1_filter, n5, n4) = all_74_0 % 232.24/39.51 | | | | | | | | | % 232.24/39.51 | | | | | | | | | REDUCE: (146), (511) imply: % 232.24/39.51 | | | | | | | | | (514) leq(n4, n5) % 232.24/39.51 | | | | | | | | | % 232.24/39.51 | | | | | | | | | REDUCE: (139), (511) imply: % 232.24/39.51 | | | | | | | | | (515) leq(n0, n4) % 232.24/39.51 | | | | | | | | | % 232.24/39.51 | | | | | | | | | GROUND_INST: instantiating (62) with n4, n5, all_74_1, % 232.24/39.51 | | | | | | | | | simplifying with (119), (122), (458), (512), (515) % 232.24/39.51 | | | | | | | | | gives: % 232.24/39.51 | | | | | | | | | (516) ~ leq(n5, all_74_21) | ~ leq(n4, all_74_21) | % 232.24/39.51 | | | | | | | | | (a_select3(q_ds1_filter, n5, n4) = all_74_1 & % 232.24/39.51 | | | | | | | | | $i(all_74_1)) % 232.24/39.51 | | | | | | | | | % 232.24/39.51 | | | | | | | | | BETA: splitting (516) gives: % 232.24/39.51 | | | | | | | | | % 232.24/39.51 | | | | | | | | | Case 1: % 232.24/39.51 | | | | | | | | | | % 232.24/39.51 | | | | | | | | | | (517) ~ leq(n5, all_74_21) % 232.24/39.51 | | | | | | | | | | % 232.24/39.51 | | | | | | | | | | REDUCE: (135), (517) imply: % 232.24/39.51 | | | | | | | | | | (518) ~ leq(n5, n5) % 232.24/39.51 | | | | | | | | | | % 232.24/39.51 | | | | | | | | | | PRED_UNIFY: (457), (518) imply: % 232.24/39.51 | | | | | | | | | | (519) $false % 232.24/39.51 | | | | | | | | | | % 232.24/39.51 | | | | | | | | | | CLOSE: (519) is inconsistent. % 232.24/39.51 | | | | | | | | | | % 232.24/39.51 | | | | | | | | | Case 2: % 232.24/39.51 | | | | | | | | | | % 232.24/39.51 | | | | | | | | | | (520) ~ leq(n4, all_74_21) | (a_select3(q_ds1_filter, % 232.24/39.51 | | | | | | | | | | n5, n4) = all_74_1 & $i(all_74_1)) % 232.24/39.51 | | | | | | | | | | % 232.24/39.51 | | | | | | | | | | BETA: splitting (520) gives: % 232.24/39.51 | | | | | | | | | | % 232.24/39.51 | | | | | | | | | | Case 1: % 232.24/39.51 | | | | | | | | | | | % 232.24/39.51 | | | | | | | | | | | (521) ~ leq(n4, all_74_21) % 232.24/39.51 | | | | | | | | | | | % 232.24/39.51 | | | | | | | | | | | REDUCE: (135), (521) imply: % 232.24/39.51 | | | | | | | | | | | (522) ~ leq(n4, n5) % 232.24/39.51 | | | | | | | | | | | % 232.24/39.51 | | | | | | | | | | | PRED_UNIFY: (514), (522) imply: % 232.24/39.51 | | | | | | | | | | | (523) $false % 232.24/39.51 | | | | | | | | | | | % 232.24/39.51 | | | | | | | | | | | CLOSE: (523) is inconsistent. % 232.24/39.51 | | | | | | | | | | | % 232.24/39.51 | | | | | | | | | | Case 2: % 232.24/39.51 | | | | | | | | | | | % 232.24/39.51 | | | | | | | | | | | (524) a_select3(q_ds1_filter, n5, n4) = all_74_1 & % 232.24/39.51 | | | | | | | | | | | $i(all_74_1) % 232.24/39.51 | | | | | | | | | | | % 232.24/39.51 | | | | | | | | | | | ALPHA: (524) implies: % 232.24/39.51 | | | | | | | | | | | (525) a_select3(q_ds1_filter, n5, n4) = all_74_1 % 232.24/39.51 | | | | | | | | | | | % 232.24/39.51 | | | | | | | | | | | REF_CLOSE: (17), (138), (513), (525) are inconsistent by % 232.24/39.51 | | | | | | | | | | | sub-proof #49. % 232.24/39.51 | | | | | | | | | | | % 232.24/39.51 | | | | | | | | | | End of split % 232.24/39.51 | | | | | | | | | | % 232.24/39.51 | | | | | | | | | End of split % 232.24/39.51 | | | | | | | | | % 232.24/39.51 | | | | | | | | End of split % 232.24/39.51 | | | | | | | | % 232.24/39.51 | | | | | | | End of split % 232.24/39.51 | | | | | | | % 232.24/39.51 | | | | | | End of split % 232.24/39.51 | | | | | | % 232.24/39.51 | | | | | Case 2: % 232.24/39.51 | | | | | | % 232.24/39.51 | | | | | | (526) all_74_3 = n5 % 232.24/39.51 | | | | | | % 232.24/39.51 | | | | | | REDUCE: (144), (526) imply: % 232.24/39.51 | | | | | | (527) a_select3(q_ds1_filter, all_74_2, n5) = all_74_0 % 232.24/39.51 | | | | | | % 232.24/39.51 | | | | | | REDUCE: (143), (526) imply: % 232.24/39.51 | | | | | | (528) a_select3(q_ds1_filter, n5, all_74_2) = all_74_1 % 232.24/39.51 | | | | | | % 232.24/39.51 | | | | | | REDUCE: (146), (526) imply: % 232.24/39.51 | | | | | | (529) leq(n5, n5) % 232.24/39.51 | | | | | | % 232.24/39.51 | | | | | | REDUCE: (139), (526) imply: % 232.24/39.51 | | | | | | (530) leq(n0, n5) % 232.24/39.51 | | | | | | % 232.24/39.51 | | | | | | BETA: splitting (152) gives: % 232.24/39.51 | | | | | | % 232.24/39.51 | | | | | | Case 1: % 232.24/39.51 | | | | | | | % 232.24/39.51 | | | | | | | (531) gt(n5, all_74_2) % 232.24/39.51 | | | | | | | % 232.24/39.51 | | | | | | | GROUND_INST: instantiating (1) with all_74_2, n5, n4, simplifying % 232.24/39.51 | | | | | | | with (58), (122), (126), (531) gives: % 232.24/39.51 | | | | | | | (532) leq(all_74_2, n4) % 232.24/39.51 | | | | | | | % 232.24/39.51 | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_2, n4, % 232.24/39.51 | | | | | | | simplifying with (58), (119), (532) gives: % 232.24/39.51 | | | | | | | (533) all_74_2 = n4 | gt(n4, all_74_2) % 232.24/39.51 | | | | | | | % 232.24/39.51 | | | | | | | BETA: splitting (151) gives: % 232.24/39.51 | | | | | | | % 232.24/39.51 | | | | | | | Case 1: % 232.24/39.51 | | | | | | | | % 232.24/39.51 | | | | | | | | (534) all_74_2 = n0 % 232.24/39.52 | | | | | | | | % 232.24/39.52 | | | | | | | | REF_CLOSE: (58), (153), (534), (irreflexivity_gt) are % 232.24/39.52 | | | | | | | | inconsistent by sub-proof #58. % 232.24/39.52 | | | | | | | | % 232.24/39.52 | | | | | | | Case 2: % 232.24/39.52 | | | | | | | | % 232.24/39.52 | | | | | | | | (535) ~ (all_74_2 = n0) % 232.24/39.52 | | | | | | | | % 232.24/39.52 | | | | | | | | BETA: splitting (533) gives: % 232.24/39.52 | | | | | | | | % 232.24/39.52 | | | | | | | | Case 1: % 232.24/39.52 | | | | | | | | | % 232.24/39.52 | | | | | | | | | (536) gt(n4, all_74_2) % 232.24/39.52 | | | | | | | | | % 232.24/39.52 | | | | | | | | | GROUND_INST: instantiating (1) with all_74_2, n4, n3, % 232.24/39.52 | | | | | | | | | simplifying with (58), (119), (125), (536) gives: % 232.24/39.52 | | | | | | | | | (537) leq(all_74_2, n3) % 232.24/39.52 | | | | | | | | | % 232.24/39.52 | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_2, n3, % 232.24/39.52 | | | | | | | | | simplifying with (58), (112), (537) gives: % 232.24/39.52 | | | | | | | | | (538) all_74_2 = n3 | gt(n3, all_74_2) % 232.24/39.52 | | | | | | | | | % 232.24/39.52 | | | | | | | | | BETA: splitting (538) gives: % 232.24/39.52 | | | | | | | | | % 232.24/39.52 | | | | | | | | | Case 1: % 232.24/39.52 | | | | | | | | | | % 232.24/39.52 | | | | | | | | | | (539) gt(n3, all_74_2) % 232.24/39.52 | | | | | | | | | | % 232.24/39.52 | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_2, n3, n2, % 232.24/39.52 | | | | | | | | | | simplifying with (58), (112), (124), (539) gives: % 232.24/39.52 | | | | | | | | | | (540) leq(all_74_2, n2) % 232.24/39.52 | | | | | | | | | | % 232.24/39.52 | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_2, n2, % 232.24/39.52 | | | | | | | | | | simplifying with (58), (101), (540) gives: % 232.24/39.52 | | | | | | | | | | (541) all_74_2 = n2 | gt(n2, all_74_2) % 232.24/39.52 | | | | | | | | | | % 232.24/39.52 | | | | | | | | | | BETA: splitting (541) gives: % 232.24/39.52 | | | | | | | | | | % 232.24/39.52 | | | | | | | | | | Case 1: % 232.24/39.52 | | | | | | | | | | | % 232.24/39.52 | | | | | | | | | | | (542) gt(n2, all_74_2) % 232.24/39.52 | | | | | | | | | | | % 232.24/39.52 | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_2, n2, n1, % 232.24/39.52 | | | | | | | | | | | simplifying with (58), (101), (123), (542) gives: % 232.24/39.52 | | | | | | | | | | | (543) leq(all_74_2, n1) % 232.24/39.52 | | | | | | | | | | | % 232.24/39.52 | | | | | | | | | | | GROUND_INST: instantiating (4) with all_74_2, simplifying with % 232.24/39.52 | | | | | | | | | | | (58), (140), (543) gives: % 232.24/39.52 | | | | | | | | | | | (544) all_74_2 = n1 | all_74_2 = n0 % 232.24/39.52 | | | | | | | | | | | % 232.24/39.52 | | | | | | | | | | | BETA: splitting (544) gives: % 232.24/39.52 | | | | | | | | | | | % 232.24/39.52 | | | | | | | | | | | Case 1: % 232.24/39.52 | | | | | | | | | | | | % 232.24/39.52 | | | | | | | | | | | | (545) all_74_2 = n0 % 232.24/39.52 | | | | | | | | | | | | % 232.24/39.52 | | | | | | | | | | | | REDUCE: (535), (545) imply: % 232.24/39.52 | | | | | | | | | | | | (546) $false % 232.24/39.52 | | | | | | | | | | | | % 232.24/39.52 | | | | | | | | | | | | CLOSE: (546) is inconsistent. % 232.24/39.52 | | | | | | | | | | | | % 232.24/39.52 | | | | | | | | | | | Case 2: % 232.24/39.52 | | | | | | | | | | | | % 232.24/39.52 | | | | | | | | | | | | (547) all_74_2 = n1 % 232.24/39.52 | | | | | | | | | | | | % 232.24/39.52 | | | | | | | | | | | | REDUCE: (527), (547) imply: % 232.24/39.52 | | | | | | | | | | | | (548) a_select3(q_ds1_filter, n1, n5) = all_74_0 % 232.24/39.52 | | | | | | | | | | | | % 232.24/39.52 | | | | | | | | | | | | REDUCE: (528), (547) imply: % 232.24/39.52 | | | | | | | | | | | | (549) a_select3(q_ds1_filter, n5, n1) = all_74_1 % 232.24/39.52 | | | | | | | | | | | | % 232.24/39.52 | | | | | | | | | | | | REDUCE: (145), (547) imply: % 232.24/39.52 | | | | | | | | | | | | (550) leq(n1, n5) % 232.24/39.52 | | | | | | | | | | | | % 232.24/39.52 | | | | | | | | | | | | REDUCE: (140), (547) imply: % 232.24/39.52 | | | | | | | | | | | | (551) leq(n0, n1) % 232.24/39.52 | | | | | | | | | | | | % 232.24/39.52 | | | | | | | | | | | | GROUND_INST: instantiating (62) with n1, n5, all_74_0, % 232.24/39.52 | | | | | | | | | | | | simplifying with (85), (122), (530), (548), (551) % 232.24/39.52 | | | | | | | | | | | | gives: % 232.24/39.52 | | | | | | | | | | | | (552) ~ leq(n5, all_74_21) | ~ leq(n1, all_74_21) | % 232.24/39.52 | | | | | | | | | | | | (a_select3(q_ds1_filter, n5, n1) = all_74_0 & % 232.24/39.52 | | | | | | | | | | | | $i(all_74_0)) % 232.24/39.52 | | | | | | | | | | | | % 232.24/39.52 | | | | | | | | | | | | BETA: splitting (552) gives: % 232.24/39.52 | | | | | | | | | | | | % 232.24/39.52 | | | | | | | | | | | | Case 1: % 232.24/39.52 | | | | | | | | | | | | | % 232.24/39.52 | | | | | | | | | | | | | (553) ~ leq(n5, all_74_21) % 232.24/39.52 | | | | | | | | | | | | | % 232.24/39.52 | | | | | | | | | | | | | REDUCE: (135), (553) imply: % 232.24/39.52 | | | | | | | | | | | | | (554) ~ leq(n5, n5) % 232.24/39.52 | | | | | | | | | | | | | % 232.24/39.52 | | | | | | | | | | | | | PRED_UNIFY: (529), (554) imply: % 232.24/39.52 | | | | | | | | | | | | | (555) $false % 232.24/39.52 | | | | | | | | | | | | | % 232.24/39.52 | | | | | | | | | | | | | CLOSE: (555) is inconsistent. % 232.24/39.52 | | | | | | | | | | | | | % 232.24/39.52 | | | | | | | | | | | | Case 2: % 232.24/39.52 | | | | | | | | | | | | | % 232.24/39.52 | | | | | | | | | | | | | (556) ~ leq(n1, all_74_21) | (a_select3(q_ds1_filter, % 232.24/39.52 | | | | | | | | | | | | | n5, n1) = all_74_0 & $i(all_74_0)) % 232.24/39.52 | | | | | | | | | | | | | % 232.24/39.52 | | | | | | | | | | | | | BETA: splitting (556) gives: % 232.24/39.52 | | | | | | | | | | | | | % 232.24/39.52 | | | | | | | | | | | | | Case 1: % 232.24/39.52 | | | | | | | | | | | | | | % 232.24/39.52 | | | | | | | | | | | | | | (557) ~ leq(n1, all_74_21) % 232.24/39.52 | | | | | | | | | | | | | | % 232.24/39.52 | | | | | | | | | | | | | | REDUCE: (135), (557) imply: % 232.24/39.52 | | | | | | | | | | | | | | (558) ~ leq(n1, n5) % 232.24/39.52 | | | | | | | | | | | | | | % 232.24/39.52 | | | | | | | | | | | | | | PRED_UNIFY: (550), (558) imply: % 232.24/39.52 | | | | | | | | | | | | | | (559) $false % 232.24/39.52 | | | | | | | | | | | | | | % 232.24/39.52 | | | | | | | | | | | | | | CLOSE: (559) is inconsistent. % 232.24/39.52 | | | | | | | | | | | | | | % 232.24/39.52 | | | | | | | | | | | | | Case 2: % 232.24/39.52 | | | | | | | | | | | | | | % 232.24/39.52 | | | | | | | | | | | | | | (560) a_select3(q_ds1_filter, n5, n1) = all_74_0 & % 232.24/39.52 | | | | | | | | | | | | | | $i(all_74_0) % 232.24/39.52 | | | | | | | | | | | | | | % 232.24/39.52 | | | | | | | | | | | | | | ALPHA: (560) implies: % 232.24/39.52 | | | | | | | | | | | | | | (561) a_select3(q_ds1_filter, n5, n1) = all_74_0 % 232.24/39.52 | | | | | | | | | | | | | | % 232.24/39.52 | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_74_0, all_74_1, n1, % 232.24/39.52 | | | | | | | | | | | | | | n5, q_ds1_filter, simplifying with (549), (561) % 232.24/39.52 | | | | | | | | | | | | | | gives: % 232.24/39.52 | | | | | | | | | | | | | | (562) all_74_0 = all_74_1 % 232.24/39.52 | | | | | | | | | | | | | | % 232.24/39.52 | | | | | | | | | | | | | | REDUCE: (138), (562) imply: % 232.24/39.52 | | | | | | | | | | | | | | (563) $false % 232.24/39.52 | | | | | | | | | | | | | | % 232.24/39.52 | | | | | | | | | | | | | | CLOSE: (563) is inconsistent. % 232.24/39.52 | | | | | | | | | | | | | | % 232.24/39.52 | | | | | | | | | | | | | End of split % 232.24/39.52 | | | | | | | | | | | | | % 232.24/39.52 | | | | | | | | | | | | End of split % 232.24/39.52 | | | | | | | | | | | | % 232.24/39.52 | | | | | | | | | | | End of split % 232.24/39.52 | | | | | | | | | | | % 232.24/39.52 | | | | | | | | | | Case 2: % 232.24/39.52 | | | | | | | | | | | % 232.24/39.52 | | | | | | | | | | | (564) all_74_2 = n2 % 232.24/39.52 | | | | | | | | | | | % 232.24/39.52 | | | | | | | | | | | REDUCE: (527), (564) imply: % 232.24/39.52 | | | | | | | | | | | (565) a_select3(q_ds1_filter, n2, n5) = all_74_0 % 232.24/39.52 | | | | | | | | | | | % 232.24/39.52 | | | | | | | | | | | REDUCE: (528), (564) imply: % 232.24/39.52 | | | | | | | | | | | (566) a_select3(q_ds1_filter, n5, n2) = all_74_1 % 232.24/39.52 | | | | | | | | | | | % 232.24/39.52 | | | | | | | | | | | REDUCE: (145), (564) imply: % 232.24/39.52 | | | | | | | | | | | (567) leq(n2, n5) % 232.24/39.52 | | | | | | | | | | | % 232.24/39.52 | | | | | | | | | | | REDUCE: (140), (564) imply: % 232.24/39.52 | | | | | | | | | | | (568) leq(n0, n2) % 232.24/39.52 | | | | | | | | | | | % 232.24/39.52 | | | | | | | | | | | GROUND_INST: instantiating (62) with n2, n5, all_74_0, % 232.24/39.52 | | | | | | | | | | | simplifying with (101), (122), (530), (565), (568) % 232.24/39.52 | | | | | | | | | | | gives: % 232.24/39.52 | | | | | | | | | | | (569) ~ leq(n5, all_74_21) | ~ leq(n2, all_74_21) | % 232.24/39.52 | | | | | | | | | | | (a_select3(q_ds1_filter, n5, n2) = all_74_0 & % 232.24/39.52 | | | | | | | | | | | $i(all_74_0)) % 232.24/39.52 | | | | | | | | | | | % 232.24/39.52 | | | | | | | | | | | BETA: splitting (569) gives: % 232.24/39.52 | | | | | | | | | | | % 232.24/39.52 | | | | | | | | | | | Case 1: % 232.24/39.52 | | | | | | | | | | | | % 232.24/39.52 | | | | | | | | | | | | (570) ~ leq(n5, all_74_21) % 232.24/39.52 | | | | | | | | | | | | % 232.24/39.52 | | | | | | | | | | | | REDUCE: (135), (570) imply: % 232.24/39.52 | | | | | | | | | | | | (571) ~ leq(n5, n5) % 232.24/39.52 | | | | | | | | | | | | % 232.24/39.52 | | | | | | | | | | | | PRED_UNIFY: (529), (571) imply: % 232.24/39.52 | | | | | | | | | | | | (572) $false % 232.24/39.52 | | | | | | | | | | | | % 232.24/39.52 | | | | | | | | | | | | CLOSE: (572) is inconsistent. % 232.24/39.52 | | | | | | | | | | | | % 232.24/39.52 | | | | | | | | | | | Case 2: % 232.24/39.52 | | | | | | | | | | | | % 232.24/39.52 | | | | | | | | | | | | (573) ~ leq(n2, all_74_21) | (a_select3(q_ds1_filter, % 232.24/39.52 | | | | | | | | | | | | n5, n2) = all_74_0 & $i(all_74_0)) % 232.24/39.52 | | | | | | | | | | | | % 232.24/39.52 | | | | | | | | | | | | BETA: splitting (573) gives: % 232.24/39.52 | | | | | | | | | | | | % 232.24/39.52 | | | | | | | | | | | | Case 1: % 232.24/39.52 | | | | | | | | | | | | | % 232.24/39.52 | | | | | | | | | | | | | (574) ~ leq(n2, all_74_21) % 232.24/39.52 | | | | | | | | | | | | | % 232.24/39.52 | | | | | | | | | | | | | REDUCE: (135), (574) imply: % 232.24/39.52 | | | | | | | | | | | | | (575) ~ leq(n2, n5) % 232.24/39.52 | | | | | | | | | | | | | % 232.24/39.52 | | | | | | | | | | | | | PRED_UNIFY: (567), (575) imply: % 232.24/39.52 | | | | | | | | | | | | | (576) $false % 232.24/39.52 | | | | | | | | | | | | | % 232.24/39.52 | | | | | | | | | | | | | CLOSE: (576) is inconsistent. % 232.24/39.52 | | | | | | | | | | | | | % 232.24/39.52 | | | | | | | | | | | | Case 2: % 232.24/39.52 | | | | | | | | | | | | | % 232.24/39.52 | | | | | | | | | | | | | (577) a_select3(q_ds1_filter, n5, n2) = all_74_0 & % 232.24/39.52 | | | | | | | | | | | | | $i(all_74_0) % 232.24/39.52 | | | | | | | | | | | | | % 232.24/39.52 | | | | | | | | | | | | | ALPHA: (577) implies: % 232.24/39.52 | | | | | | | | | | | | | (578) a_select3(q_ds1_filter, n5, n2) = all_74_0 % 232.24/39.52 | | | | | | | | | | | | | % 232.24/39.52 | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_74_0, all_74_1, n2, % 232.24/39.52 | | | | | | | | | | | | | n5, q_ds1_filter, simplifying with (566), (578) % 232.24/39.52 | | | | | | | | | | | | | gives: % 232.24/39.52 | | | | | | | | | | | | | (579) all_74_0 = all_74_1 % 232.24/39.52 | | | | | | | | | | | | | % 232.24/39.52 | | | | | | | | | | | | | REDUCE: (138), (579) imply: % 232.24/39.52 | | | | | | | | | | | | | (580) $false % 232.24/39.52 | | | | | | | | | | | | | % 232.24/39.52 | | | | | | | | | | | | | CLOSE: (580) is inconsistent. % 232.24/39.52 | | | | | | | | | | | | | % 232.24/39.52 | | | | | | | | | | | | End of split % 232.24/39.52 | | | | | | | | | | | | % 232.24/39.52 | | | | | | | | | | | End of split % 232.24/39.52 | | | | | | | | | | | % 232.24/39.52 | | | | | | | | | | End of split % 232.24/39.52 | | | | | | | | | | % 232.24/39.52 | | | | | | | | | Case 2: % 232.24/39.52 | | | | | | | | | | % 232.24/39.52 | | | | | | | | | | (581) all_74_2 = n3 % 232.24/39.52 | | | | | | | | | | % 232.24/39.52 | | | | | | | | | | REDUCE: (527), (581) imply: % 232.24/39.52 | | | | | | | | | | (582) a_select3(q_ds1_filter, n3, n5) = all_74_0 % 232.24/39.52 | | | | | | | | | | % 232.24/39.52 | | | | | | | | | | REDUCE: (528), (581) imply: % 232.24/39.52 | | | | | | | | | | (583) a_select3(q_ds1_filter, n5, n3) = all_74_1 % 232.24/39.52 | | | | | | | | | | % 232.24/39.52 | | | | | | | | | | REDUCE: (145), (581) imply: % 232.24/39.52 | | | | | | | | | | (584) leq(n3, n5) % 232.24/39.52 | | | | | | | | | | % 232.24/39.52 | | | | | | | | | | REDUCE: (140), (581) imply: % 232.24/39.52 | | | | | | | | | | (585) leq(n0, n3) % 232.24/39.52 | | | | | | | | | | % 232.24/39.52 | | | | | | | | | | GROUND_INST: instantiating (62) with n3, n5, all_74_0, % 232.24/39.52 | | | | | | | | | | simplifying with (112), (122), (530), (582), (585) % 232.24/39.52 | | | | | | | | | | gives: % 232.24/39.52 | | | | | | | | | | (586) ~ leq(n5, all_74_21) | ~ leq(n3, all_74_21) | % 232.24/39.52 | | | | | | | | | | (a_select3(q_ds1_filter, n5, n3) = all_74_0 & % 232.24/39.52 | | | | | | | | | | $i(all_74_0)) % 232.24/39.52 | | | | | | | | | | % 232.24/39.52 | | | | | | | | | | GROUND_INST: instantiating (62) with n5, n3, all_74_1, % 232.24/39.52 | | | | | | | | | | simplifying with (112), (122), (530), (583), (585) % 232.24/39.52 | | | | | | | | | | gives: % 232.24/39.52 | | | | | | | | | | (587) ~ leq(n5, all_74_21) | ~ leq(n3, all_74_21) | % 232.24/39.52 | | | | | | | | | | (a_select3(q_ds1_filter, n3, n5) = all_74_1 & % 232.24/39.52 | | | | | | | | | | $i(all_74_1)) % 232.24/39.52 | | | | | | | | | | % 232.24/39.52 | | | | | | | | | | BETA: splitting (586) gives: % 232.24/39.52 | | | | | | | | | | % 232.24/39.52 | | | | | | | | | | Case 1: % 232.24/39.52 | | | | | | | | | | | % 232.24/39.52 | | | | | | | | | | | (588) ~ leq(n5, all_74_21) % 232.24/39.52 | | | | | | | | | | | % 232.24/39.52 | | | | | | | | | | | REDUCE: (135), (588) imply: % 232.24/39.52 | | | | | | | | | | | (589) ~ leq(n5, n5) % 232.24/39.52 | | | | | | | | | | | % 232.24/39.52 | | | | | | | | | | | PRED_UNIFY: (529), (589) imply: % 232.24/39.52 | | | | | | | | | | | (590) $false % 232.24/39.52 | | | | | | | | | | | % 232.24/39.52 | | | | | | | | | | | CLOSE: (590) is inconsistent. % 232.24/39.52 | | | | | | | | | | | % 232.24/39.53 | | | | | | | | | | Case 2: % 232.24/39.53 | | | | | | | | | | | % 232.24/39.53 | | | | | | | | | | | (591) leq(n5, all_74_21) % 232.24/39.53 | | | | | | | | | | | (592) ~ leq(n3, all_74_21) | (a_select3(q_ds1_filter, % 232.24/39.53 | | | | | | | | | | | n5, n3) = all_74_0 & $i(all_74_0)) % 232.24/39.53 | | | | | | | | | | | % 232.24/39.53 | | | | | | | | | | | BETA: splitting (587) gives: % 232.24/39.53 | | | | | | | | | | | % 232.24/39.53 | | | | | | | | | | | Case 1: % 232.24/39.53 | | | | | | | | | | | | % 232.24/39.53 | | | | | | | | | | | | (593) ~ leq(n5, all_74_21) % 232.24/39.53 | | | | | | | | | | | | % 232.24/39.53 | | | | | | | | | | | | REDUCE: (135), (593) imply: % 232.24/39.53 | | | | | | | | | | | | (594) ~ leq(n5, n5) % 232.24/39.53 | | | | | | | | | | | | % 232.24/39.53 | | | | | | | | | | | | PRED_UNIFY: (529), (594) imply: % 232.24/39.53 | | | | | | | | | | | | (595) $false % 232.24/39.53 | | | | | | | | | | | | % 232.24/39.53 | | | | | | | | | | | | CLOSE: (595) is inconsistent. % 232.24/39.53 | | | | | | | | | | | | % 232.24/39.53 | | | | | | | | | | | Case 2: % 232.24/39.53 | | | | | | | | | | | | % 232.24/39.53 | | | | | | | | | | | | (596) ~ leq(n3, all_74_21) | (a_select3(q_ds1_filter, % 232.24/39.53 | | | | | | | | | | | | n3, n5) = all_74_1 & $i(all_74_1)) % 232.24/39.53 | | | | | | | | | | | | % 232.24/39.53 | | | | | | | | | | | | BETA: splitting (596) gives: % 232.24/39.53 | | | | | | | | | | | | % 232.24/39.53 | | | | | | | | | | | | Case 1: % 232.24/39.53 | | | | | | | | | | | | | % 232.24/39.53 | | | | | | | | | | | | | (597) ~ leq(n3, all_74_21) % 232.24/39.53 | | | | | | | | | | | | | % 232.24/39.53 | | | | | | | | | | | | | REDUCE: (135), (597) imply: % 232.24/39.53 | | | | | | | | | | | | | (598) ~ leq(n3, n5) % 232.24/39.53 | | | | | | | | | | | | | % 232.24/39.53 | | | | | | | | | | | | | PRED_UNIFY: (584), (598) imply: % 232.24/39.53 | | | | | | | | | | | | | (599) $false % 232.24/39.53 | | | | | | | | | | | | | % 232.24/39.53 | | | | | | | | | | | | | CLOSE: (599) is inconsistent. % 232.24/39.53 | | | | | | | | | | | | | % 232.24/39.53 | | | | | | | | | | | | Case 2: % 232.24/39.53 | | | | | | | | | | | | | % 232.24/39.53 | | | | | | | | | | | | | (600) leq(n3, all_74_21) % 232.24/39.53 | | | | | | | | | | | | | (601) a_select3(q_ds1_filter, n3, n5) = all_74_1 & % 232.24/39.53 | | | | | | | | | | | | | $i(all_74_1) % 232.24/39.53 | | | | | | | | | | | | | % 232.24/39.53 | | | | | | | | | | | | | ALPHA: (601) implies: % 232.24/39.53 | | | | | | | | | | | | | (602) a_select3(q_ds1_filter, n3, n5) = all_74_1 % 232.24/39.53 | | | | | | | | | | | | | % 232.24/39.53 | | | | | | | | | | | | | BETA: splitting (592) gives: % 232.24/39.53 | | | | | | | | | | | | | % 232.24/39.53 | | | | | | | | | | | | | Case 1: % 232.24/39.53 | | | | | | | | | | | | | | % 232.24/39.53 | | | | | | | | | | | | | | (603) ~ leq(n3, all_74_21) % 232.24/39.53 | | | | | | | | | | | | | | % 232.24/39.53 | | | | | | | | | | | | | | REDUCE: (135), (603) imply: % 232.24/39.53 | | | | | | | | | | | | | | (604) ~ leq(n3, n5) % 232.24/39.53 | | | | | | | | | | | | | | % 232.24/39.53 | | | | | | | | | | | | | | PRED_UNIFY: (584), (604) imply: % 232.24/39.53 | | | | | | | | | | | | | | (605) $false % 232.24/39.53 | | | | | | | | | | | | | | % 232.24/39.53 | | | | | | | | | | | | | | CLOSE: (605) is inconsistent. % 232.24/39.53 | | | | | | | | | | | | | | % 232.24/39.53 | | | | | | | | | | | | | Case 2: % 232.24/39.53 | | | | | | | | | | | | | | % 232.24/39.53 | | | | | | | | | | | | | | (606) a_select3(q_ds1_filter, n5, n3) = all_74_0 & % 232.24/39.53 | | | | | | | | | | | | | | $i(all_74_0) % 232.24/39.53 | | | | | | | | | | | | | | % 232.24/39.53 | | | | | | | | | | | | | | ALPHA: (606) implies: % 232.24/39.53 | | | | | | | | | | | | | | (607) a_select3(q_ds1_filter, n5, n3) = all_74_0 % 232.24/39.53 | | | | | | | | | | | | | | % 232.24/39.53 | | | | | | | | | | | | | | REF_CLOSE: (17), (62), (112), (122), (135), (138), (529), % 232.24/39.53 | | | | | | | | | | | | | | (530), (584), (585), (602), (607) are inconsistent % 232.24/39.53 | | | | | | | | | | | | | | by sub-proof #50. % 232.24/39.53 | | | | | | | | | | | | | | % 232.24/39.53 | | | | | | | | | | | | | End of split % 232.24/39.53 | | | | | | | | | | | | | % 232.24/39.53 | | | | | | | | | | | | End of split % 232.24/39.53 | | | | | | | | | | | | % 232.24/39.53 | | | | | | | | | | | End of split % 232.24/39.53 | | | | | | | | | | | % 232.24/39.53 | | | | | | | | | | End of split % 232.24/39.53 | | | | | | | | | | % 232.24/39.53 | | | | | | | | | End of split % 232.24/39.53 | | | | | | | | | % 232.24/39.53 | | | | | | | | Case 2: % 232.24/39.53 | | | | | | | | | % 232.24/39.53 | | | | | | | | | (608) all_74_2 = n4 % 232.24/39.53 | | | | | | | | | % 232.24/39.53 | | | | | | | | | REDUCE: (527), (608) imply: % 232.24/39.53 | | | | | | | | | (609) a_select3(q_ds1_filter, n4, n5) = all_74_0 % 232.24/39.53 | | | | | | | | | % 232.24/39.53 | | | | | | | | | REDUCE: (528), (608) imply: % 232.24/39.53 | | | | | | | | | (610) a_select3(q_ds1_filter, n5, n4) = all_74_1 % 232.24/39.53 | | | | | | | | | % 232.24/39.53 | | | | | | | | | REDUCE: (145), (608) imply: % 232.24/39.53 | | | | | | | | | (611) leq(n4, n5) % 232.24/39.53 | | | | | | | | | % 232.24/39.53 | | | | | | | | | REDUCE: (140), (608) imply: % 232.24/39.53 | | | | | | | | | (612) leq(n0, n4) % 232.24/39.53 | | | | | | | | | % 232.24/39.53 | | | | | | | | | GROUND_INST: instantiating (62) with n4, n5, all_74_0, % 232.24/39.53 | | | | | | | | | simplifying with (119), (122), (530), (609), (612) % 232.24/39.53 | | | | | | | | | gives: % 232.24/39.53 | | | | | | | | | (613) ~ leq(n5, all_74_21) | ~ leq(n4, all_74_21) | % 232.24/39.53 | | | | | | | | | (a_select3(q_ds1_filter, n5, n4) = all_74_0 & % 232.24/39.53 | | | | | | | | | $i(all_74_0)) % 232.24/39.53 | | | | | | | | | % 232.24/39.53 | | | | | | | | | BETA: splitting (613) gives: % 232.24/39.53 | | | | | | | | | % 232.24/39.53 | | | | | | | | | Case 1: % 232.24/39.53 | | | | | | | | | | % 232.24/39.53 | | | | | | | | | | (614) ~ leq(n5, all_74_21) % 232.24/39.53 | | | | | | | | | | % 232.24/39.53 | | | | | | | | | | REDUCE: (135), (614) imply: % 232.24/39.53 | | | | | | | | | | (615) ~ leq(n5, n5) % 232.24/39.53 | | | | | | | | | | % 232.24/39.53 | | | | | | | | | | PRED_UNIFY: (529), (615) imply: % 232.24/39.53 | | | | | | | | | | (616) $false % 232.24/39.53 | | | | | | | | | | % 232.24/39.53 | | | | | | | | | | CLOSE: (616) is inconsistent. % 232.24/39.53 | | | | | | | | | | % 232.24/39.53 | | | | | | | | | Case 2: % 232.24/39.53 | | | | | | | | | | % 232.24/39.53 | | | | | | | | | | (617) ~ leq(n4, all_74_21) | (a_select3(q_ds1_filter, % 232.24/39.53 | | | | | | | | | | n5, n4) = all_74_0 & $i(all_74_0)) % 232.24/39.53 | | | | | | | | | | % 232.24/39.53 | | | | | | | | | | BETA: splitting (617) gives: % 232.24/39.53 | | | | | | | | | | % 232.24/39.53 | | | | | | | | | | Case 1: % 232.24/39.53 | | | | | | | | | | | % 232.24/39.53 | | | | | | | | | | | (618) ~ leq(n4, all_74_21) % 232.24/39.53 | | | | | | | | | | | % 232.24/39.53 | | | | | | | | | | | REDUCE: (135), (618) imply: % 232.24/39.53 | | | | | | | | | | | (619) ~ leq(n4, n5) % 232.24/39.53 | | | | | | | | | | | % 232.24/39.53 | | | | | | | | | | | PRED_UNIFY: (611), (619) imply: % 232.24/39.53 | | | | | | | | | | | (620) $false % 232.24/39.53 | | | | | | | | | | | % 232.24/39.53 | | | | | | | | | | | CLOSE: (620) is inconsistent. % 232.24/39.53 | | | | | | | | | | | % 232.24/39.53 | | | | | | | | | | Case 2: % 232.24/39.53 | | | | | | | | | | | % 232.24/39.53 | | | | | | | | | | | (621) a_select3(q_ds1_filter, n5, n4) = all_74_0 & % 232.24/39.53 | | | | | | | | | | | $i(all_74_0) % 232.24/39.53 | | | | | | | | | | | % 232.24/39.53 | | | | | | | | | | | ALPHA: (621) implies: % 232.24/39.53 | | | | | | | | | | | (622) a_select3(q_ds1_filter, n5, n4) = all_74_0 % 232.24/39.53 | | | | | | | | | | | % 232.24/39.53 | | | | | | | | | | | REF_CLOSE: (17), (138), (610), (622) are inconsistent by % 232.24/39.53 | | | | | | | | | | | sub-proof #49. % 232.24/39.53 | | | | | | | | | | | % 232.24/39.53 | | | | | | | | | | End of split % 232.24/39.53 | | | | | | | | | | % 232.24/39.53 | | | | | | | | | End of split % 232.24/39.53 | | | | | | | | | % 232.24/39.53 | | | | | | | | End of split % 232.24/39.53 | | | | | | | | % 232.24/39.53 | | | | | | | End of split % 232.24/39.53 | | | | | | | % 232.24/39.53 | | | | | | Case 2: % 232.24/39.53 | | | | | | | % 232.24/39.53 | | | | | | | (623) all_74_2 = n5 % 232.24/39.53 | | | | | | | % 232.24/39.53 | | | | | | | REDUCE: (527), (623) imply: % 232.24/39.53 | | | | | | | (624) a_select3(q_ds1_filter, n5, n5) = all_74_0 % 232.24/39.53 | | | | | | | % 232.24/39.53 | | | | | | | REDUCE: (528), (623) imply: % 232.24/39.53 | | | | | | | (625) a_select3(q_ds1_filter, n5, n5) = all_74_1 % 232.24/39.53 | | | | | | | % 232.24/39.53 | | | | | | | GROUND_INST: instantiating (17) with all_74_1, all_74_0, n5, n5, % 232.24/39.53 | | | | | | | q_ds1_filter, simplifying with (624), (625) gives: % 232.24/39.53 | | | | | | | (626) all_74_0 = all_74_1 % 232.24/39.53 | | | | | | | % 232.24/39.53 | | | | | | | REDUCE: (138), (626) imply: % 232.24/39.53 | | | | | | | (627) $false % 232.24/39.53 | | | | | | | % 232.24/39.53 | | | | | | | CLOSE: (627) is inconsistent. % 232.24/39.53 | | | | | | | % 232.24/39.53 | | | | | | End of split % 232.24/39.53 | | | | | | % 232.24/39.53 | | | | | End of split % 232.24/39.53 | | | | | % 232.24/39.53 | | | | Case 2: % 232.24/39.53 | | | | | % 232.24/39.53 | | | | | (628) all_74_3 = n0 % 232.24/39.53 | | | | | (629) ~ gt(all_74_3, n0) % 232.24/39.53 | | | | | % 232.24/39.53 | | | | | REDUCE: (144), (628) imply: % 232.24/39.53 | | | | | (630) a_select3(q_ds1_filter, all_74_2, n0) = all_74_0 % 232.24/39.53 | | | | | % 232.24/39.53 | | | | | REDUCE: (143), (628) imply: % 232.24/39.53 | | | | | (631) a_select3(q_ds1_filter, n0, all_74_2) = all_74_1 % 232.24/39.53 | | | | | % 232.24/39.53 | | | | | REDUCE: (146), (628) imply: % 232.24/39.53 | | | | | (632) leq(n0, n5) % 232.24/39.53 | | | | | % 232.24/39.53 | | | | | REDUCE: (139), (628) imply: % 232.24/39.53 | | | | | (633) leq(n0, n0) % 232.24/39.53 | | | | | % 232.24/39.53 | | | | | REDUCE: (628), (629) imply: % 232.24/39.53 | | | | | (634) ~ gt(n0, n0) % 232.24/39.53 | | | | | % 232.24/39.53 | | | | | BETA: splitting (152) gives: % 232.24/39.53 | | | | | % 232.24/39.53 | | | | | Case 1: % 232.24/39.53 | | | | | | % 232.24/39.53 | | | | | | (635) gt(n5, all_74_2) % 232.24/39.53 | | | | | | % 232.24/39.53 | | | | | | GROUND_INST: instantiating (1) with all_74_2, n5, n4, simplifying % 232.24/39.53 | | | | | | with (58), (122), (126), (635) gives: % 232.24/39.53 | | | | | | (636) leq(all_74_2, n4) % 232.24/39.53 | | | | | | % 232.24/39.53 | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_2, n4, simplifying % 232.24/39.53 | | | | | | with (58), (119), (636) gives: % 232.24/39.53 | | | | | | (637) all_74_2 = n4 | gt(n4, all_74_2) % 232.24/39.53 | | | | | | % 232.24/39.53 | | | | | | BETA: splitting (151) gives: % 232.24/39.53 | | | | | | % 232.24/39.53 | | | | | | Case 1: % 232.24/39.53 | | | | | | | % 232.24/39.53 | | | | | | | (638) all_74_2 = n0 % 232.24/39.53 | | | | | | | % 232.24/39.53 | | | | | | | REDUCE: (153), (638) imply: % 232.24/39.53 | | | | | | | (639) gt(n0, n0) % 232.24/39.53 | | | | | | | % 232.24/39.53 | | | | | | | PRED_UNIFY: (634), (639) imply: % 232.24/39.53 | | | | | | | (640) $false % 232.24/39.53 | | | | | | | % 232.24/39.53 | | | | | | | CLOSE: (640) is inconsistent. % 232.24/39.53 | | | | | | | % 232.24/39.53 | | | | | | Case 2: % 232.24/39.53 | | | | | | | % 232.24/39.53 | | | | | | | (641) ~ (all_74_2 = n0) % 232.24/39.53 | | | | | | | % 232.24/39.53 | | | | | | | BETA: splitting (637) gives: % 232.24/39.53 | | | | | | | % 232.24/39.53 | | | | | | | Case 1: % 232.24/39.53 | | | | | | | | % 232.24/39.53 | | | | | | | | (642) gt(n4, all_74_2) % 232.24/39.53 | | | | | | | | % 232.24/39.53 | | | | | | | | GROUND_INST: instantiating (1) with all_74_2, n4, n3, % 232.24/39.53 | | | | | | | | simplifying with (58), (119), (125), (642) gives: % 232.24/39.53 | | | | | | | | (643) leq(all_74_2, n3) % 232.24/39.53 | | | | | | | | % 232.24/39.53 | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_2, n3, % 232.24/39.53 | | | | | | | | simplifying with (58), (112), (643) gives: % 232.24/39.53 | | | | | | | | (644) all_74_2 = n3 | gt(n3, all_74_2) % 232.24/39.53 | | | | | | | | % 232.24/39.53 | | | | | | | | BETA: splitting (644) gives: % 232.24/39.53 | | | | | | | | % 232.24/39.53 | | | | | | | | Case 1: % 232.24/39.53 | | | | | | | | | % 232.24/39.53 | | | | | | | | | (645) gt(n3, all_74_2) % 232.24/39.53 | | | | | | | | | % 232.24/39.53 | | | | | | | | | GROUND_INST: instantiating (1) with all_74_2, n3, n2, % 232.24/39.53 | | | | | | | | | simplifying with (58), (112), (124), (645) gives: % 232.24/39.53 | | | | | | | | | (646) leq(all_74_2, n2) % 232.24/39.53 | | | | | | | | | % 232.24/39.53 | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_2, n2, % 232.24/39.53 | | | | | | | | | simplifying with (58), (101), (646) gives: % 232.24/39.53 | | | | | | | | | (647) all_74_2 = n2 | gt(n2, all_74_2) % 232.24/39.53 | | | | | | | | | % 232.24/39.53 | | | | | | | | | BETA: splitting (647) gives: % 232.24/39.53 | | | | | | | | | % 232.24/39.53 | | | | | | | | | Case 1: % 232.24/39.53 | | | | | | | | | | % 232.24/39.53 | | | | | | | | | | (648) gt(n2, all_74_2) % 232.24/39.53 | | | | | | | | | | % 232.24/39.53 | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_2, n2, n1, % 232.24/39.53 | | | | | | | | | | simplifying with (58), (101), (123), (648) gives: % 232.24/39.53 | | | | | | | | | | (649) leq(all_74_2, n1) % 232.24/39.53 | | | | | | | | | | % 232.24/39.53 | | | | | | | | | | GROUND_INST: instantiating (4) with all_74_2, simplifying with % 232.24/39.53 | | | | | | | | | | (58), (140), (649) gives: % 232.24/39.54 | | | | | | | | | | (650) all_74_2 = n1 | all_74_2 = n0 % 232.24/39.54 | | | | | | | | | | % 232.24/39.54 | | | | | | | | | | BETA: splitting (650) gives: % 232.24/39.54 | | | | | | | | | | % 232.24/39.54 | | | | | | | | | | Case 1: % 232.24/39.54 | | | | | | | | | | | % 232.24/39.54 | | | | | | | | | | | (651) all_74_2 = n0 % 232.24/39.54 | | | | | | | | | | | % 232.24/39.54 | | | | | | | | | | | REDUCE: (641), (651) imply: % 232.24/39.54 | | | | | | | | | | | (652) $false % 232.24/39.54 | | | | | | | | | | | % 232.24/39.54 | | | | | | | | | | | CLOSE: (652) is inconsistent. % 232.24/39.54 | | | | | | | | | | | % 232.24/39.54 | | | | | | | | | | Case 2: % 232.24/39.54 | | | | | | | | | | | % 232.24/39.54 | | | | | | | | | | | (653) all_74_2 = n1 % 232.24/39.54 | | | | | | | | | | | % 232.24/39.54 | | | | | | | | | | | REDUCE: (630), (653) imply: % 232.24/39.54 | | | | | | | | | | | (654) a_select3(q_ds1_filter, n1, n0) = all_74_0 % 232.24/39.54 | | | | | | | | | | | % 232.24/39.54 | | | | | | | | | | | REDUCE: (631), (653) imply: % 232.24/39.54 | | | | | | | | | | | (655) a_select3(q_ds1_filter, n0, n1) = all_74_1 % 232.24/39.54 | | | | | | | | | | | % 232.24/39.54 | | | | | | | | | | | REDUCE: (145), (653) imply: % 232.24/39.54 | | | | | | | | | | | (656) leq(n1, n5) % 232.24/39.54 | | | | | | | | | | | % 232.24/39.54 | | | | | | | | | | | REDUCE: (140), (653) imply: % 232.24/39.54 | | | | | | | | | | | (657) leq(n0, n1) % 232.24/39.54 | | | | | | | | | | | % 232.24/39.54 | | | | | | | | | | | GROUND_INST: instantiating (62) with n0, n1, all_74_1, % 232.24/39.54 | | | | | | | | | | | simplifying with (12), (85), (633), (655), (657) % 232.24/39.54 | | | | | | | | | | | gives: % 232.24/39.54 | | | | | | | | | | | (658) ~ leq(n1, all_74_21) | ~ leq(n0, all_74_21) | % 232.24/39.54 | | | | | | | | | | | (a_select3(q_ds1_filter, n1, n0) = all_74_1 & % 232.24/39.54 | | | | | | | | | | | $i(all_74_1)) % 232.24/39.54 | | | | | | | | | | | % 232.24/39.54 | | | | | | | | | | | BETA: splitting (658) gives: % 232.24/39.54 | | | | | | | | | | | % 232.24/39.54 | | | | | | | | | | | Case 1: % 232.24/39.54 | | | | | | | | | | | | % 232.24/39.54 | | | | | | | | | | | | (659) ~ leq(n0, all_74_21) % 232.24/39.54 | | | | | | | | | | | | % 232.24/39.54 | | | | | | | | | | | | REDUCE: (135), (659) imply: % 232.24/39.54 | | | | | | | | | | | | (660) ~ leq(n0, n5) % 232.24/39.54 | | | | | | | | | | | | % 232.24/39.54 | | | | | | | | | | | | PRED_UNIFY: (632), (660) imply: % 232.24/39.54 | | | | | | | | | | | | (661) $false % 232.24/39.54 | | | | | | | | | | | | % 232.24/39.54 | | | | | | | | | | | | CLOSE: (661) is inconsistent. % 232.24/39.54 | | | | | | | | | | | | % 232.24/39.54 | | | | | | | | | | | Case 2: % 232.24/39.54 | | | | | | | | | | | | % 232.24/39.54 | | | | | | | | | | | | (662) ~ leq(n1, all_74_21) | (a_select3(q_ds1_filter, % 232.24/39.54 | | | | | | | | | | | | n1, n0) = all_74_1 & $i(all_74_1)) % 232.24/39.54 | | | | | | | | | | | | % 232.24/39.54 | | | | | | | | | | | | BETA: splitting (662) gives: % 232.24/39.54 | | | | | | | | | | | | % 232.24/39.54 | | | | | | | | | | | | Case 1: % 232.24/39.54 | | | | | | | | | | | | | % 232.24/39.54 | | | | | | | | | | | | | (663) ~ leq(n1, all_74_21) % 232.24/39.54 | | | | | | | | | | | | | % 232.24/39.54 | | | | | | | | | | | | | REDUCE: (135), (663) imply: % 232.24/39.54 | | | | | | | | | | | | | (664) ~ leq(n1, n5) % 232.24/39.54 | | | | | | | | | | | | | % 232.24/39.54 | | | | | | | | | | | | | PRED_UNIFY: (656), (664) imply: % 232.24/39.54 | | | | | | | | | | | | | (665) $false % 232.24/39.54 | | | | | | | | | | | | | % 232.24/39.54 | | | | | | | | | | | | | CLOSE: (665) is inconsistent. % 232.24/39.54 | | | | | | | | | | | | | % 232.24/39.54 | | | | | | | | | | | | Case 2: % 232.24/39.54 | | | | | | | | | | | | | % 232.24/39.54 | | | | | | | | | | | | | (666) a_select3(q_ds1_filter, n1, n0) = all_74_1 & % 232.24/39.54 | | | | | | | | | | | | | $i(all_74_1) % 232.24/39.54 | | | | | | | | | | | | | % 232.24/39.54 | | | | | | | | | | | | | ALPHA: (666) implies: % 232.24/39.54 | | | | | | | | | | | | | (667) a_select3(q_ds1_filter, n1, n0) = all_74_1 % 232.24/39.54 | | | | | | | | | | | | | % 232.24/39.54 | | | | | | | | | | | | | REF_CLOSE: (17), (138), (654), (667) are inconsistent by % 232.24/39.54 | | | | | | | | | | | | | sub-proof #48. % 232.24/39.54 | | | | | | | | | | | | | % 232.24/39.54 | | | | | | | | | | | | End of split % 232.24/39.54 | | | | | | | | | | | | % 232.24/39.54 | | | | | | | | | | | End of split % 232.24/39.54 | | | | | | | | | | | % 232.24/39.54 | | | | | | | | | | End of split % 232.24/39.54 | | | | | | | | | | % 232.24/39.54 | | | | | | | | | Case 2: % 232.24/39.54 | | | | | | | | | | % 232.24/39.54 | | | | | | | | | | (668) all_74_2 = n2 % 232.24/39.54 | | | | | | | | | | % 232.24/39.54 | | | | | | | | | | REDUCE: (630), (668) imply: % 232.24/39.54 | | | | | | | | | | (669) a_select3(q_ds1_filter, n2, n0) = all_74_0 % 232.24/39.54 | | | | | | | | | | % 232.24/39.54 | | | | | | | | | | REDUCE: (631), (668) imply: % 232.24/39.54 | | | | | | | | | | (670) a_select3(q_ds1_filter, n0, n2) = all_74_1 % 232.24/39.54 | | | | | | | | | | % 232.24/39.54 | | | | | | | | | | REDUCE: (145), (668) imply: % 232.50/39.54 | | | | | | | | | | (671) leq(n2, n5) % 232.50/39.54 | | | | | | | | | | % 232.50/39.54 | | | | | | | | | | REDUCE: (140), (668) imply: % 232.50/39.54 | | | | | | | | | | (672) leq(n0, n2) % 232.50/39.54 | | | | | | | | | | % 232.50/39.54 | | | | | | | | | | GROUND_INST: instantiating (62) with n0, n2, all_74_1, % 232.50/39.54 | | | | | | | | | | simplifying with (12), (101), (633), (670), (672) % 232.50/39.54 | | | | | | | | | | gives: % 232.50/39.54 | | | | | | | | | | (673) ~ leq(n2, all_74_21) | ~ leq(n0, all_74_21) | % 232.50/39.54 | | | | | | | | | | (a_select3(q_ds1_filter, n2, n0) = all_74_1 & % 232.50/39.54 | | | | | | | | | | $i(all_74_1)) % 232.50/39.54 | | | | | | | | | | % 232.50/39.54 | | | | | | | | | | BETA: splitting (673) gives: % 232.50/39.54 | | | | | | | | | | % 232.50/39.54 | | | | | | | | | | Case 1: % 232.50/39.54 | | | | | | | | | | | % 232.50/39.54 | | | | | | | | | | | (674) ~ leq(n0, all_74_21) % 232.50/39.54 | | | | | | | | | | | % 232.50/39.54 | | | | | | | | | | | REDUCE: (135), (674) imply: % 232.50/39.54 | | | | | | | | | | | (675) ~ leq(n0, n5) % 232.50/39.54 | | | | | | | | | | | % 232.50/39.54 | | | | | | | | | | | PRED_UNIFY: (632), (675) imply: % 232.50/39.54 | | | | | | | | | | | (676) $false % 232.50/39.54 | | | | | | | | | | | % 232.50/39.54 | | | | | | | | | | | CLOSE: (676) is inconsistent. % 232.50/39.54 | | | | | | | | | | | % 232.50/39.54 | | | | | | | | | | Case 2: % 232.50/39.54 | | | | | | | | | | | % 232.50/39.54 | | | | | | | | | | | (677) ~ leq(n2, all_74_21) | (a_select3(q_ds1_filter, % 232.50/39.54 | | | | | | | | | | | n2, n0) = all_74_1 & $i(all_74_1)) % 232.50/39.54 | | | | | | | | | | | % 232.50/39.54 | | | | | | | | | | | BETA: splitting (677) gives: % 232.50/39.54 | | | | | | | | | | | % 232.50/39.54 | | | | | | | | | | | Case 1: % 232.50/39.54 | | | | | | | | | | | | % 232.50/39.54 | | | | | | | | | | | | (678) ~ leq(n2, all_74_21) % 232.50/39.54 | | | | | | | | | | | | % 232.50/39.54 | | | | | | | | | | | | REDUCE: (135), (678) imply: % 232.50/39.54 | | | | | | | | | | | | (679) ~ leq(n2, n5) % 232.50/39.54 | | | | | | | | | | | | % 232.50/39.54 | | | | | | | | | | | | PRED_UNIFY: (671), (679) imply: % 232.50/39.54 | | | | | | | | | | | | (680) $false % 232.50/39.54 | | | | | | | | | | | | % 232.50/39.54 | | | | | | | | | | | | CLOSE: (680) is inconsistent. % 232.50/39.54 | | | | | | | | | | | | % 232.50/39.54 | | | | | | | | | | | Case 2: % 232.50/39.54 | | | | | | | | | | | | % 232.50/39.54 | | | | | | | | | | | | (681) a_select3(q_ds1_filter, n2, n0) = all_74_1 & % 232.50/39.54 | | | | | | | | | | | | $i(all_74_1) % 232.50/39.54 | | | | | | | | | | | | % 232.50/39.54 | | | | | | | | | | | | ALPHA: (681) implies: % 232.50/39.54 | | | | | | | | | | | | (682) a_select3(q_ds1_filter, n2, n0) = all_74_1 % 232.50/39.54 | | | | | | | | | | | | % 232.50/39.54 | | | | | | | | | | | | REF_CLOSE: (17), (138), (669), (682) are inconsistent by % 232.50/39.54 | | | | | | | | | | | | sub-proof #47. % 232.50/39.54 | | | | | | | | | | | | % 232.50/39.54 | | | | | | | | | | | End of split % 232.50/39.54 | | | | | | | | | | | % 232.50/39.54 | | | | | | | | | | End of split % 232.50/39.54 | | | | | | | | | | % 232.50/39.54 | | | | | | | | | End of split % 232.50/39.54 | | | | | | | | | % 232.50/39.54 | | | | | | | | Case 2: % 232.50/39.54 | | | | | | | | | % 232.50/39.54 | | | | | | | | | (683) all_74_2 = n3 % 232.50/39.54 | | | | | | | | | % 232.50/39.54 | | | | | | | | | REDUCE: (630), (683) imply: % 232.50/39.54 | | | | | | | | | (684) a_select3(q_ds1_filter, n3, n0) = all_74_0 % 232.50/39.54 | | | | | | | | | % 232.50/39.54 | | | | | | | | | REDUCE: (631), (683) imply: % 232.50/39.54 | | | | | | | | | (685) a_select3(q_ds1_filter, n0, n3) = all_74_1 % 232.50/39.54 | | | | | | | | | % 232.50/39.54 | | | | | | | | | REDUCE: (145), (683) imply: % 232.50/39.54 | | | | | | | | | (686) leq(n3, n5) % 232.50/39.54 | | | | | | | | | % 232.50/39.54 | | | | | | | | | REDUCE: (140), (683) imply: % 232.50/39.54 | | | | | | | | | (687) leq(n0, n3) % 232.50/39.54 | | | | | | | | | % 232.50/39.54 | | | | | | | | | GROUND_INST: instantiating (62) with n0, n3, all_74_1, % 232.50/39.54 | | | | | | | | | simplifying with (12), (112), (633), (685), (687) % 232.50/39.54 | | | | | | | | | gives: % 232.50/39.54 | | | | | | | | | (688) ~ leq(n3, all_74_21) | ~ leq(n0, all_74_21) | % 232.50/39.54 | | | | | | | | | (a_select3(q_ds1_filter, n3, n0) = all_74_1 & % 232.50/39.54 | | | | | | | | | $i(all_74_1)) % 232.50/39.54 | | | | | | | | | % 232.50/39.54 | | | | | | | | | BETA: splitting (688) gives: % 232.50/39.54 | | | | | | | | | % 232.50/39.54 | | | | | | | | | Case 1: % 232.50/39.54 | | | | | | | | | | % 232.50/39.54 | | | | | | | | | | (689) ~ leq(n0, all_74_21) % 232.50/39.54 | | | | | | | | | | % 232.50/39.54 | | | | | | | | | | REDUCE: (135), (689) imply: % 232.50/39.54 | | | | | | | | | | (690) ~ leq(n0, n5) % 232.50/39.54 | | | | | | | | | | % 232.50/39.54 | | | | | | | | | | PRED_UNIFY: (632), (690) imply: % 232.50/39.54 | | | | | | | | | | (691) $false % 232.50/39.54 | | | | | | | | | | % 232.50/39.54 | | | | | | | | | | CLOSE: (691) is inconsistent. % 232.50/39.54 | | | | | | | | | | % 232.50/39.54 | | | | | | | | | Case 2: % 232.50/39.54 | | | | | | | | | | % 232.50/39.54 | | | | | | | | | | (692) ~ leq(n3, all_74_21) | (a_select3(q_ds1_filter, % 232.50/39.54 | | | | | | | | | | n3, n0) = all_74_1 & $i(all_74_1)) % 232.50/39.54 | | | | | | | | | | % 232.50/39.54 | | | | | | | | | | BETA: splitting (692) gives: % 232.50/39.54 | | | | | | | | | | % 232.50/39.54 | | | | | | | | | | Case 1: % 232.50/39.54 | | | | | | | | | | | % 232.50/39.54 | | | | | | | | | | | (693) ~ leq(n3, all_74_21) % 232.50/39.54 | | | | | | | | | | | % 232.50/39.54 | | | | | | | | | | | REDUCE: (135), (693) imply: % 232.50/39.54 | | | | | | | | | | | (694) ~ leq(n3, n5) % 232.50/39.54 | | | | | | | | | | | % 232.50/39.54 | | | | | | | | | | | PRED_UNIFY: (686), (694) imply: % 232.50/39.54 | | | | | | | | | | | (695) $false % 232.50/39.54 | | | | | | | | | | | % 232.50/39.54 | | | | | | | | | | | CLOSE: (695) is inconsistent. % 232.50/39.54 | | | | | | | | | | | % 232.50/39.54 | | | | | | | | | | Case 2: % 232.50/39.54 | | | | | | | | | | | % 232.50/39.54 | | | | | | | | | | | (696) a_select3(q_ds1_filter, n3, n0) = all_74_1 & % 232.50/39.54 | | | | | | | | | | | $i(all_74_1) % 232.50/39.54 | | | | | | | | | | | % 232.50/39.54 | | | | | | | | | | | ALPHA: (696) implies: % 232.50/39.54 | | | | | | | | | | | (697) a_select3(q_ds1_filter, n3, n0) = all_74_1 % 232.50/39.54 | | | | | | | | | | | % 232.50/39.54 | | | | | | | | | | | GROUND_INST: instantiating (17) with all_74_1, all_74_0, n0, % 232.50/39.54 | | | | | | | | | | | n3, q_ds1_filter, simplifying with (684), (697) % 232.50/39.54 | | | | | | | | | | | gives: % 232.50/39.54 | | | | | | | | | | | (698) all_74_0 = all_74_1 % 232.50/39.54 | | | | | | | | | | | % 232.50/39.54 | | | | | | | | | | | REDUCE: (138), (698) imply: % 232.50/39.54 | | | | | | | | | | | (699) $false % 232.50/39.54 | | | | | | | | | | | % 232.50/39.54 | | | | | | | | | | | CLOSE: (699) is inconsistent. % 232.50/39.54 | | | | | | | | | | | % 232.50/39.54 | | | | | | | | | | End of split % 232.50/39.54 | | | | | | | | | | % 232.50/39.54 | | | | | | | | | End of split % 232.50/39.54 | | | | | | | | | % 232.50/39.54 | | | | | | | | End of split % 232.50/39.54 | | | | | | | | % 232.50/39.54 | | | | | | | Case 2: % 232.50/39.54 | | | | | | | | % 232.50/39.54 | | | | | | | | (700) all_74_2 = n4 % 232.50/39.54 | | | | | | | | % 232.50/39.54 | | | | | | | | REDUCE: (630), (700) imply: % 232.50/39.54 | | | | | | | | (701) a_select3(q_ds1_filter, n4, n0) = all_74_0 % 232.50/39.54 | | | | | | | | % 232.50/39.54 | | | | | | | | REDUCE: (631), (700) imply: % 232.50/39.54 | | | | | | | | (702) a_select3(q_ds1_filter, n0, n4) = all_74_1 % 232.50/39.54 | | | | | | | | % 232.50/39.54 | | | | | | | | REDUCE: (145), (700) imply: % 232.50/39.54 | | | | | | | | (703) leq(n4, n5) % 232.50/39.54 | | | | | | | | % 232.50/39.54 | | | | | | | | REDUCE: (140), (700) imply: % 232.50/39.54 | | | | | | | | (704) leq(n0, n4) % 232.50/39.54 | | | | | | | | % 232.50/39.54 | | | | | | | | GROUND_INST: instantiating (62) with n0, n4, all_74_1, % 232.50/39.54 | | | | | | | | simplifying with (12), (119), (633), (702), (704) % 232.50/39.54 | | | | | | | | gives: % 232.50/39.54 | | | | | | | | (705) ~ leq(n4, all_74_21) | ~ leq(n0, all_74_21) | % 232.50/39.54 | | | | | | | | (a_select3(q_ds1_filter, n4, n0) = all_74_1 & % 232.50/39.54 | | | | | | | | $i(all_74_1)) % 232.50/39.54 | | | | | | | | % 232.50/39.54 | | | | | | | | BETA: splitting (705) gives: % 232.50/39.54 | | | | | | | | % 232.50/39.54 | | | | | | | | Case 1: % 232.50/39.54 | | | | | | | | | % 232.50/39.54 | | | | | | | | | (706) ~ leq(n0, all_74_21) % 232.50/39.54 | | | | | | | | | % 232.50/39.54 | | | | | | | | | REDUCE: (135), (706) imply: % 232.50/39.54 | | | | | | | | | (707) ~ leq(n0, n5) % 232.50/39.54 | | | | | | | | | % 232.50/39.54 | | | | | | | | | PRED_UNIFY: (632), (707) imply: % 232.50/39.54 | | | | | | | | | (708) $false % 232.50/39.54 | | | | | | | | | % 232.50/39.54 | | | | | | | | | CLOSE: (708) is inconsistent. % 232.50/39.54 | | | | | | | | | % 232.50/39.54 | | | | | | | | Case 2: % 232.50/39.54 | | | | | | | | | % 232.50/39.54 | | | | | | | | | (709) ~ leq(n4, all_74_21) | (a_select3(q_ds1_filter, n4, % 232.50/39.54 | | | | | | | | | n0) = all_74_1 & $i(all_74_1)) % 232.50/39.54 | | | | | | | | | % 232.50/39.54 | | | | | | | | | BETA: splitting (709) gives: % 232.50/39.54 | | | | | | | | | % 232.50/39.54 | | | | | | | | | Case 1: % 232.50/39.54 | | | | | | | | | | % 232.50/39.54 | | | | | | | | | | (710) ~ leq(n4, all_74_21) % 232.50/39.54 | | | | | | | | | | % 232.50/39.54 | | | | | | | | | | REDUCE: (135), (710) imply: % 232.50/39.54 | | | | | | | | | | (711) ~ leq(n4, n5) % 232.50/39.54 | | | | | | | | | | % 232.50/39.54 | | | | | | | | | | PRED_UNIFY: (703), (711) imply: % 232.50/39.54 | | | | | | | | | | (712) $false % 232.50/39.54 | | | | | | | | | | % 232.50/39.54 | | | | | | | | | | CLOSE: (712) is inconsistent. % 232.50/39.54 | | | | | | | | | | % 232.50/39.54 | | | | | | | | | Case 2: % 232.50/39.54 | | | | | | | | | | % 232.50/39.54 | | | | | | | | | | (713) a_select3(q_ds1_filter, n4, n0) = all_74_1 & % 232.50/39.54 | | | | | | | | | | $i(all_74_1) % 232.50/39.54 | | | | | | | | | | % 232.50/39.54 | | | | | | | | | | ALPHA: (713) implies: % 232.50/39.55 | | | | | | | | | | (714) a_select3(q_ds1_filter, n4, n0) = all_74_1 % 232.50/39.55 | | | | | | | | | | % 232.50/39.55 | | | | | | | | | | REF_CLOSE: (17), (138), (701), (714) are inconsistent by % 232.50/39.55 | | | | | | | | | | sub-proof #46. % 232.50/39.55 | | | | | | | | | | % 232.50/39.55 | | | | | | | | | End of split % 232.50/39.55 | | | | | | | | | % 232.50/39.55 | | | | | | | | End of split % 232.50/39.55 | | | | | | | | % 232.50/39.55 | | | | | | | End of split % 232.50/39.55 | | | | | | | % 232.50/39.55 | | | | | | End of split % 232.50/39.55 | | | | | | % 232.50/39.55 | | | | | Case 2: % 232.50/39.55 | | | | | | % 232.50/39.55 | | | | | | (715) all_74_2 = n5 % 232.50/39.55 | | | | | | % 232.50/39.55 | | | | | | REDUCE: (630), (715) imply: % 232.50/39.55 | | | | | | (716) a_select3(q_ds1_filter, n5, n0) = all_74_0 % 232.50/39.55 | | | | | | % 232.50/39.55 | | | | | | REDUCE: (631), (715) imply: % 232.50/39.55 | | | | | | (717) a_select3(q_ds1_filter, n0, n5) = all_74_1 % 232.50/39.55 | | | | | | % 232.50/39.55 | | | | | | REDUCE: (145), (715) imply: % 232.50/39.55 | | | | | | (718) leq(n5, n5) % 232.50/39.55 | | | | | | % 232.50/39.55 | | | | | | GROUND_INST: instantiating (62) with n0, n5, all_74_1, simplifying % 232.50/39.55 | | | | | | with (12), (122), (632), (633), (717) gives: % 232.50/39.55 | | | | | | (719) ~ leq(n5, all_74_21) | ~ leq(n0, all_74_21) | % 232.50/39.55 | | | | | | (a_select3(q_ds1_filter, n5, n0) = all_74_1 & $i(all_74_1)) % 232.50/39.55 | | | | | | % 232.50/39.55 | | | | | | BETA: splitting (719) gives: % 232.50/39.55 | | | | | | % 232.50/39.55 | | | | | | Case 1: % 232.50/39.55 | | | | | | | % 232.50/39.55 | | | | | | | (720) ~ leq(n0, all_74_21) % 232.50/39.55 | | | | | | | % 232.50/39.55 | | | | | | | REDUCE: (135), (720) imply: % 232.50/39.55 | | | | | | | (721) ~ leq(n0, n5) % 232.50/39.55 | | | | | | | % 232.50/39.55 | | | | | | | PRED_UNIFY: (632), (721) imply: % 232.50/39.55 | | | | | | | (722) $false % 232.50/39.55 | | | | | | | % 232.50/39.55 | | | | | | | CLOSE: (722) is inconsistent. % 232.50/39.55 | | | | | | | % 232.50/39.55 | | | | | | Case 2: % 232.50/39.55 | | | | | | | % 232.50/39.55 | | | | | | | (723) ~ leq(n5, all_74_21) | (a_select3(q_ds1_filter, n5, n0) % 232.50/39.55 | | | | | | | = all_74_1 & $i(all_74_1)) % 232.50/39.55 | | | | | | | % 232.50/39.55 | | | | | | | BETA: splitting (723) gives: % 232.50/39.55 | | | | | | | % 232.50/39.55 | | | | | | | Case 1: % 232.50/39.55 | | | | | | | | % 232.50/39.55 | | | | | | | | (724) ~ leq(n5, all_74_21) % 232.50/39.55 | | | | | | | | % 232.50/39.55 | | | | | | | | REDUCE: (135), (724) imply: % 232.50/39.55 | | | | | | | | (725) ~ leq(n5, n5) % 232.50/39.55 | | | | | | | | % 232.50/39.55 | | | | | | | | PRED_UNIFY: (718), (725) imply: % 232.50/39.55 | | | | | | | | (726) $false % 232.50/39.55 | | | | | | | | % 232.50/39.55 | | | | | | | | CLOSE: (726) is inconsistent. % 232.50/39.55 | | | | | | | | % 232.50/39.55 | | | | | | | Case 2: % 232.50/39.55 | | | | | | | | % 232.50/39.55 | | | | | | | | (727) a_select3(q_ds1_filter, n5, n0) = all_74_1 & % 232.50/39.55 | | | | | | | | $i(all_74_1) % 232.50/39.55 | | | | | | | | % 232.50/39.55 | | | | | | | | ALPHA: (727) implies: % 232.50/39.55 | | | | | | | | (728) a_select3(q_ds1_filter, n5, n0) = all_74_1 % 232.50/39.55 | | | | | | | | % 232.50/39.55 | | | | | | | | REF_CLOSE: (17), (138), (716), (728) are inconsistent by % 232.50/39.55 | | | | | | | | sub-proof #45. % 232.50/39.55 | | | | | | | | % 232.50/39.55 | | | | | | | End of split % 232.50/39.55 | | | | | | | % 232.50/39.55 | | | | | | End of split % 232.50/39.55 | | | | | | % 232.50/39.55 | | | | | End of split % 232.50/39.55 | | | | | % 232.50/39.55 | | | | End of split % 232.50/39.55 | | | | % 232.50/39.55 | | | Case 2: % 232.50/39.55 | | | | % 232.50/39.55 | | | | (729) all_74_2 = n0 % 232.50/39.55 | | | | (730) ~ gt(all_74_2, n0) % 232.50/39.55 | | | | % 232.50/39.55 | | | | REDUCE: (144), (729) imply: % 232.50/39.55 | | | | (731) a_select3(q_ds1_filter, n0, all_74_3) = all_74_0 % 232.50/39.55 | | | | % 232.50/39.55 | | | | REDUCE: (143), (729) imply: % 232.50/39.55 | | | | (732) a_select3(q_ds1_filter, all_74_3, n0) = all_74_1 % 232.50/39.55 | | | | % 232.50/39.55 | | | | REDUCE: (145), (729) imply: % 232.50/39.55 | | | | (733) leq(n0, n5) % 232.50/39.55 | | | | % 232.50/39.55 | | | | REDUCE: (140), (729) imply: % 232.50/39.55 | | | | (734) leq(n0, n0) % 232.50/39.55 | | | | % 232.50/39.55 | | | | REDUCE: (729), (730) imply: % 232.50/39.55 | | | | (735) ~ gt(n0, n0) % 232.50/39.55 | | | | % 232.50/39.55 | | | | BETA: splitting (147) gives: % 232.50/39.55 | | | | % 232.50/39.55 | | | | Case 1: % 232.50/39.55 | | | | | % 232.50/39.55 | | | | | (736) gt(all_74_3, n0) % 232.50/39.55 | | | | | % 232.50/39.55 | | | | | BETA: splitting (150) gives: % 232.50/39.55 | | | | | % 232.50/39.55 | | | | | Case 1: % 232.50/39.55 | | | | | | % 232.50/39.55 | | | | | | (737) gt(n5, all_74_3) % 232.50/39.55 | | | | | | % 232.50/39.55 | | | | | | GROUND_INST: instantiating (1) with all_74_3, n5, n4, simplifying % 232.50/39.55 | | | | | | with (57), (122), (126), (737) gives: % 232.50/39.55 | | | | | | (738) leq(all_74_3, n4) % 232.50/39.55 | | | | | | % 232.50/39.55 | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_3, n4, simplifying % 232.50/39.55 | | | | | | with (57), (119), (738) gives: % 232.50/39.55 | | | | | | (739) all_74_3 = n4 | gt(n4, all_74_3) % 232.50/39.55 | | | | | | % 232.50/39.55 | | | | | | BETA: splitting (149) gives: % 232.50/39.55 | | | | | | % 232.50/39.55 | | | | | | Case 1: % 232.50/39.55 | | | | | | | % 232.50/39.55 | | | | | | | (740) all_74_3 = n0 % 232.50/39.55 | | | | | | | % 232.50/39.55 | | | | | | | REDUCE: (736), (740) imply: % 232.50/39.55 | | | | | | | (741) gt(n0, n0) % 232.50/39.55 | | | | | | | % 232.50/39.55 | | | | | | | PRED_UNIFY: (735), (741) imply: % 232.50/39.55 | | | | | | | (742) $false % 232.50/39.55 | | | | | | | % 232.50/39.55 | | | | | | | CLOSE: (742) is inconsistent. % 232.50/39.55 | | | | | | | % 232.50/39.55 | | | | | | Case 2: % 232.50/39.55 | | | | | | | % 232.50/39.55 | | | | | | | (743) ~ (all_74_3 = n0) % 232.50/39.55 | | | | | | | % 232.50/39.55 | | | | | | | BETA: splitting (739) gives: % 232.50/39.55 | | | | | | | % 232.50/39.55 | | | | | | | Case 1: % 232.50/39.55 | | | | | | | | % 232.50/39.55 | | | | | | | | (744) gt(n4, all_74_3) % 232.50/39.55 | | | | | | | | % 232.50/39.55 | | | | | | | | GROUND_INST: instantiating (1) with all_74_3, n4, n3, % 232.50/39.55 | | | | | | | | simplifying with (57), (119), (125), (744) gives: % 232.50/39.55 | | | | | | | | (745) leq(all_74_3, n3) % 232.50/39.55 | | | | | | | | % 232.50/39.55 | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_3, n3, % 232.50/39.55 | | | | | | | | simplifying with (57), (112), (745) gives: % 232.50/39.55 | | | | | | | | (746) all_74_3 = n3 | gt(n3, all_74_3) % 232.50/39.55 | | | | | | | | % 232.50/39.55 | | | | | | | | BETA: splitting (746) gives: % 232.50/39.55 | | | | | | | | % 232.50/39.55 | | | | | | | | Case 1: % 232.50/39.55 | | | | | | | | | % 232.50/39.55 | | | | | | | | | (747) gt(n3, all_74_3) % 232.50/39.55 | | | | | | | | | % 232.50/39.55 | | | | | | | | | GROUND_INST: instantiating (1) with all_74_3, n3, n2, % 232.50/39.55 | | | | | | | | | simplifying with (57), (112), (124), (747) gives: % 232.50/39.55 | | | | | | | | | (748) leq(all_74_3, n2) % 232.50/39.55 | | | | | | | | | % 232.50/39.55 | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_3, n2, % 232.50/39.55 | | | | | | | | | simplifying with (57), (101), (748) gives: % 232.50/39.55 | | | | | | | | | (749) all_74_3 = n2 | gt(n2, all_74_3) % 232.50/39.55 | | | | | | | | | % 232.50/39.55 | | | | | | | | | BETA: splitting (749) gives: % 232.50/39.55 | | | | | | | | | % 232.50/39.55 | | | | | | | | | Case 1: % 232.50/39.55 | | | | | | | | | | % 232.50/39.55 | | | | | | | | | | (750) gt(n2, all_74_3) % 232.50/39.55 | | | | | | | | | | % 232.50/39.55 | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_3, n2, n1, % 232.50/39.55 | | | | | | | | | | simplifying with (57), (101), (123), (750) gives: % 232.50/39.55 | | | | | | | | | | (751) leq(all_74_3, n1) % 232.50/39.55 | | | | | | | | | | % 232.50/39.55 | | | | | | | | | | GROUND_INST: instantiating (4) with all_74_3, simplifying with % 232.50/39.55 | | | | | | | | | | (57), (139), (751) gives: % 232.50/39.55 | | | | | | | | | | (752) all_74_3 = n1 | all_74_3 = n0 % 232.50/39.55 | | | | | | | | | | % 232.50/39.55 | | | | | | | | | | BETA: splitting (752) gives: % 232.50/39.55 | | | | | | | | | | % 232.50/39.55 | | | | | | | | | | Case 1: % 232.50/39.55 | | | | | | | | | | | % 232.50/39.55 | | | | | | | | | | | (753) all_74_3 = n0 % 232.50/39.55 | | | | | | | | | | | % 232.50/39.55 | | | | | | | | | | | REDUCE: (743), (753) imply: % 232.50/39.55 | | | | | | | | | | | (754) $false % 232.50/39.55 | | | | | | | | | | | % 232.50/39.55 | | | | | | | | | | | CLOSE: (754) is inconsistent. % 232.50/39.55 | | | | | | | | | | | % 232.50/39.55 | | | | | | | | | | Case 2: % 232.50/39.55 | | | | | | | | | | | % 232.50/39.55 | | | | | | | | | | | (755) all_74_3 = n1 % 232.50/39.55 | | | | | | | | | | | % 232.50/39.55 | | | | | | | | | | | REDUCE: (732), (755) imply: % 232.50/39.55 | | | | | | | | | | | (756) a_select3(q_ds1_filter, n1, n0) = all_74_1 % 232.50/39.55 | | | | | | | | | | | % 232.50/39.55 | | | | | | | | | | | REDUCE: (731), (755) imply: % 232.50/39.55 | | | | | | | | | | | (757) a_select3(q_ds1_filter, n0, n1) = all_74_0 % 232.50/39.55 | | | | | | | | | | | % 232.50/39.55 | | | | | | | | | | | REDUCE: (146), (755) imply: % 232.50/39.55 | | | | | | | | | | | (758) leq(n1, n5) % 232.50/39.55 | | | | | | | | | | | % 232.50/39.55 | | | | | | | | | | | REDUCE: (139), (755) imply: % 232.50/39.55 | | | | | | | | | | | (759) leq(n0, n1) % 232.50/39.55 | | | | | | | | | | | % 232.50/39.55 | | | | | | | | | | | GROUND_INST: instantiating (62) with n0, n1, all_74_0, % 232.50/39.55 | | | | | | | | | | | simplifying with (12), (85), (734), (757), (759) % 232.50/39.55 | | | | | | | | | | | gives: % 232.50/39.55 | | | | | | | | | | | (760) ~ leq(n1, all_74_21) | ~ leq(n0, all_74_21) | % 232.50/39.55 | | | | | | | | | | | (a_select3(q_ds1_filter, n1, n0) = all_74_0 & % 232.50/39.55 | | | | | | | | | | | $i(all_74_0)) % 232.50/39.55 | | | | | | | | | | | % 232.50/39.55 | | | | | | | | | | | BETA: splitting (760) gives: % 232.50/39.55 | | | | | | | | | | | % 232.50/39.55 | | | | | | | | | | | Case 1: % 232.50/39.55 | | | | | | | | | | | | % 232.50/39.55 | | | | | | | | | | | | (761) ~ leq(n0, all_74_21) % 232.50/39.55 | | | | | | | | | | | | % 232.50/39.55 | | | | | | | | | | | | REDUCE: (135), (761) imply: % 232.50/39.55 | | | | | | | | | | | | (762) ~ leq(n0, n5) % 232.50/39.55 | | | | | | | | | | | | % 232.50/39.55 | | | | | | | | | | | | PRED_UNIFY: (733), (762) imply: % 232.50/39.55 | | | | | | | | | | | | (763) $false % 232.50/39.55 | | | | | | | | | | | | % 232.50/39.55 | | | | | | | | | | | | CLOSE: (763) is inconsistent. % 232.50/39.55 | | | | | | | | | | | | % 232.50/39.55 | | | | | | | | | | | Case 2: % 232.50/39.55 | | | | | | | | | | | | % 232.50/39.55 | | | | | | | | | | | | (764) ~ leq(n1, all_74_21) | (a_select3(q_ds1_filter, % 232.50/39.55 | | | | | | | | | | | | n1, n0) = all_74_0 & $i(all_74_0)) % 232.50/39.55 | | | | | | | | | | | | % 232.50/39.55 | | | | | | | | | | | | BETA: splitting (764) gives: % 232.50/39.55 | | | | | | | | | | | | % 232.50/39.55 | | | | | | | | | | | | Case 1: % 232.50/39.55 | | | | | | | | | | | | | % 232.50/39.55 | | | | | | | | | | | | | (765) ~ leq(n1, all_74_21) % 232.50/39.55 | | | | | | | | | | | | | % 232.50/39.55 | | | | | | | | | | | | | REDUCE: (135), (765) imply: % 232.50/39.55 | | | | | | | | | | | | | (766) ~ leq(n1, n5) % 232.50/39.55 | | | | | | | | | | | | | % 232.50/39.55 | | | | | | | | | | | | | PRED_UNIFY: (758), (766) imply: % 232.50/39.55 | | | | | | | | | | | | | (767) $false % 232.50/39.55 | | | | | | | | | | | | | % 232.50/39.55 | | | | | | | | | | | | | CLOSE: (767) is inconsistent. % 232.50/39.55 | | | | | | | | | | | | | % 232.50/39.55 | | | | | | | | | | | | Case 2: % 232.50/39.55 | | | | | | | | | | | | | % 232.50/39.55 | | | | | | | | | | | | | (768) a_select3(q_ds1_filter, n1, n0) = all_74_0 & % 232.50/39.55 | | | | | | | | | | | | | $i(all_74_0) % 232.50/39.55 | | | | | | | | | | | | | % 232.50/39.55 | | | | | | | | | | | | | ALPHA: (768) implies: % 232.50/39.55 | | | | | | | | | | | | | (769) a_select3(q_ds1_filter, n1, n0) = all_74_0 % 232.50/39.55 | | | | | | | | | | | | | % 232.50/39.55 | | | | | | | | | | | | | REF_CLOSE: (17), (138), (756), (769) are inconsistent by % 232.50/39.55 | | | | | | | | | | | | | sub-proof #48. % 232.50/39.55 | | | | | | | | | | | | | % 232.50/39.55 | | | | | | | | | | | | End of split % 232.50/39.55 | | | | | | | | | | | | % 232.50/39.55 | | | | | | | | | | | End of split % 232.50/39.55 | | | | | | | | | | | % 232.50/39.55 | | | | | | | | | | End of split % 232.50/39.55 | | | | | | | | | | % 232.50/39.55 | | | | | | | | | Case 2: % 232.50/39.55 | | | | | | | | | | % 232.50/39.55 | | | | | | | | | | (770) all_74_3 = n2 % 232.50/39.55 | | | | | | | | | | % 232.50/39.55 | | | | | | | | | | REDUCE: (732), (770) imply: % 232.50/39.55 | | | | | | | | | | (771) a_select3(q_ds1_filter, n2, n0) = all_74_1 % 232.50/39.55 | | | | | | | | | | % 232.50/39.55 | | | | | | | | | | REDUCE: (731), (770) imply: % 232.50/39.55 | | | | | | | | | | (772) a_select3(q_ds1_filter, n0, n2) = all_74_0 % 232.50/39.55 | | | | | | | | | | % 232.50/39.55 | | | | | | | | | | REDUCE: (146), (770) imply: % 232.50/39.55 | | | | | | | | | | (773) leq(n2, n5) % 232.50/39.55 | | | | | | | | | | % 232.50/39.55 | | | | | | | | | | REDUCE: (139), (770) imply: % 232.50/39.55 | | | | | | | | | | (774) leq(n0, n2) % 232.50/39.55 | | | | | | | | | | % 232.50/39.55 | | | | | | | | | | GROUND_INST: instantiating (62) with n0, n2, all_74_0, % 232.50/39.55 | | | | | | | | | | simplifying with (12), (101), (734), (772), (774) % 232.50/39.55 | | | | | | | | | | gives: % 232.50/39.55 | | | | | | | | | | (775) ~ leq(n2, all_74_21) | ~ leq(n0, all_74_21) | % 232.50/39.55 | | | | | | | | | | (a_select3(q_ds1_filter, n2, n0) = all_74_0 & % 232.50/39.55 | | | | | | | | | | $i(all_74_0)) % 232.50/39.55 | | | | | | | | | | % 232.50/39.55 | | | | | | | | | | BETA: splitting (775) gives: % 232.50/39.55 | | | | | | | | | | % 232.50/39.55 | | | | | | | | | | Case 1: % 232.50/39.55 | | | | | | | | | | | % 232.50/39.55 | | | | | | | | | | | (776) ~ leq(n0, all_74_21) % 232.50/39.55 | | | | | | | | | | | % 232.50/39.55 | | | | | | | | | | | REDUCE: (135), (776) imply: % 232.50/39.55 | | | | | | | | | | | (777) ~ leq(n0, n5) % 232.50/39.55 | | | | | | | | | | | % 232.50/39.55 | | | | | | | | | | | PRED_UNIFY: (733), (777) imply: % 232.50/39.55 | | | | | | | | | | | (778) $false % 232.50/39.55 | | | | | | | | | | | % 232.50/39.55 | | | | | | | | | | | CLOSE: (778) is inconsistent. % 232.50/39.55 | | | | | | | | | | | % 232.50/39.55 | | | | | | | | | | Case 2: % 232.50/39.55 | | | | | | | | | | | % 232.50/39.56 | | | | | | | | | | | (779) ~ leq(n2, all_74_21) | (a_select3(q_ds1_filter, % 232.50/39.56 | | | | | | | | | | | n2, n0) = all_74_0 & $i(all_74_0)) % 232.50/39.56 | | | | | | | | | | | % 232.50/39.56 | | | | | | | | | | | BETA: splitting (779) gives: % 232.50/39.56 | | | | | | | | | | | % 232.50/39.56 | | | | | | | | | | | Case 1: % 232.50/39.56 | | | | | | | | | | | | % 232.50/39.56 | | | | | | | | | | | | (780) ~ leq(n2, all_74_21) % 232.50/39.56 | | | | | | | | | | | | % 232.50/39.56 | | | | | | | | | | | | REDUCE: (135), (780) imply: % 232.50/39.56 | | | | | | | | | | | | (781) ~ leq(n2, n5) % 232.50/39.56 | | | | | | | | | | | | % 232.50/39.56 | | | | | | | | | | | | PRED_UNIFY: (773), (781) imply: % 232.50/39.56 | | | | | | | | | | | | (782) $false % 232.50/39.56 | | | | | | | | | | | | % 232.50/39.56 | | | | | | | | | | | | CLOSE: (782) is inconsistent. % 232.50/39.56 | | | | | | | | | | | | % 232.50/39.56 | | | | | | | | | | | Case 2: % 232.50/39.56 | | | | | | | | | | | | % 232.50/39.56 | | | | | | | | | | | | (783) a_select3(q_ds1_filter, n2, n0) = all_74_0 & % 232.50/39.56 | | | | | | | | | | | | $i(all_74_0) % 232.50/39.56 | | | | | | | | | | | | % 232.50/39.56 | | | | | | | | | | | | ALPHA: (783) implies: % 232.50/39.56 | | | | | | | | | | | | (784) a_select3(q_ds1_filter, n2, n0) = all_74_0 % 232.50/39.56 | | | | | | | | | | | | % 232.50/39.56 | | | | | | | | | | | | REF_CLOSE: (17), (138), (771), (784) are inconsistent by % 232.50/39.56 | | | | | | | | | | | | sub-proof #47. % 232.50/39.56 | | | | | | | | | | | | % 232.50/39.56 | | | | | | | | | | | End of split % 232.50/39.56 | | | | | | | | | | | % 232.50/39.56 | | | | | | | | | | End of split % 232.50/39.56 | | | | | | | | | | % 232.50/39.56 | | | | | | | | | End of split % 232.50/39.56 | | | | | | | | | % 232.50/39.56 | | | | | | | | Case 2: % 232.50/39.56 | | | | | | | | | % 232.50/39.56 | | | | | | | | | (785) all_74_3 = n3 % 232.50/39.56 | | | | | | | | | % 232.50/39.56 | | | | | | | | | REDUCE: (732), (785) imply: % 232.50/39.56 | | | | | | | | | (786) a_select3(q_ds1_filter, n3, n0) = all_74_1 % 232.50/39.56 | | | | | | | | | % 232.50/39.56 | | | | | | | | | REDUCE: (731), (785) imply: % 232.50/39.56 | | | | | | | | | (787) a_select3(q_ds1_filter, n0, n3) = all_74_0 % 232.50/39.56 | | | | | | | | | % 232.50/39.56 | | | | | | | | | REDUCE: (146), (785) imply: % 232.50/39.56 | | | | | | | | | (788) leq(n3, n5) % 232.50/39.56 | | | | | | | | | % 232.50/39.56 | | | | | | | | | REDUCE: (139), (785) imply: % 232.50/39.56 | | | | | | | | | (789) leq(n0, n3) % 232.50/39.56 | | | | | | | | | % 232.50/39.56 | | | | | | | | | GROUND_INST: instantiating (62) with n0, n3, all_74_0, % 232.50/39.56 | | | | | | | | | simplifying with (12), (112), (734), (787), (789) % 232.50/39.56 | | | | | | | | | gives: % 232.50/39.56 | | | | | | | | | (790) ~ leq(n3, all_74_21) | ~ leq(n0, all_74_21) | % 232.50/39.56 | | | | | | | | | (a_select3(q_ds1_filter, n3, n0) = all_74_0 & % 232.50/39.56 | | | | | | | | | $i(all_74_0)) % 232.50/39.56 | | | | | | | | | % 232.50/39.56 | | | | | | | | | BETA: splitting (790) gives: % 232.50/39.56 | | | | | | | | | % 232.50/39.56 | | | | | | | | | Case 1: % 232.50/39.56 | | | | | | | | | | % 232.50/39.56 | | | | | | | | | | (791) ~ leq(n0, all_74_21) % 232.50/39.56 | | | | | | | | | | % 232.50/39.56 | | | | | | | | | | REDUCE: (135), (791) imply: % 232.50/39.56 | | | | | | | | | | (792) ~ leq(n0, n5) % 232.50/39.56 | | | | | | | | | | % 232.50/39.56 | | | | | | | | | | PRED_UNIFY: (733), (792) imply: % 232.50/39.56 | | | | | | | | | | (793) $false % 232.50/39.56 | | | | | | | | | | % 232.50/39.56 | | | | | | | | | | CLOSE: (793) is inconsistent. % 232.50/39.56 | | | | | | | | | | % 232.50/39.56 | | | | | | | | | Case 2: % 232.50/39.56 | | | | | | | | | | % 232.50/39.56 | | | | | | | | | | (794) ~ leq(n3, all_74_21) | (a_select3(q_ds1_filter, % 232.50/39.56 | | | | | | | | | | n3, n0) = all_74_0 & $i(all_74_0)) % 232.50/39.56 | | | | | | | | | | % 232.50/39.56 | | | | | | | | | | BETA: splitting (794) gives: % 232.50/39.56 | | | | | | | | | | % 232.50/39.56 | | | | | | | | | | Case 1: % 232.50/39.56 | | | | | | | | | | | % 232.50/39.56 | | | | | | | | | | | (795) ~ leq(n3, all_74_21) % 232.50/39.56 | | | | | | | | | | | % 232.50/39.56 | | | | | | | | | | | REDUCE: (135), (795) imply: % 232.50/39.56 | | | | | | | | | | | (796) ~ leq(n3, n5) % 232.50/39.56 | | | | | | | | | | | % 232.50/39.56 | | | | | | | | | | | PRED_UNIFY: (788), (796) imply: % 232.50/39.56 | | | | | | | | | | | (797) $false % 232.50/39.56 | | | | | | | | | | | % 232.50/39.56 | | | | | | | | | | | CLOSE: (797) is inconsistent. % 232.50/39.56 | | | | | | | | | | | % 232.50/39.56 | | | | | | | | | | Case 2: % 232.50/39.56 | | | | | | | | | | | % 232.50/39.56 | | | | | | | | | | | (798) a_select3(q_ds1_filter, n3, n0) = all_74_0 & % 232.50/39.56 | | | | | | | | | | | $i(all_74_0) % 232.50/39.56 | | | | | | | | | | | % 232.50/39.56 | | | | | | | | | | | ALPHA: (798) implies: % 232.50/39.56 | | | | | | | | | | | (799) a_select3(q_ds1_filter, n3, n0) = all_74_0 % 232.50/39.56 | | | | | | | | | | | % 232.50/39.56 | | | | | | | | | | | GROUND_INST: instantiating (17) with all_74_1, all_74_0, n0, % 232.50/39.56 | | | | | | | | | | | n3, q_ds1_filter, simplifying with (786), (799) % 232.50/39.56 | | | | | | | | | | | gives: % 232.50/39.56 | | | | | | | | | | | (800) all_74_0 = all_74_1 % 232.50/39.56 | | | | | | | | | | | % 232.50/39.56 | | | | | | | | | | | REDUCE: (138), (800) imply: % 232.50/39.56 | | | | | | | | | | | (801) $false % 232.50/39.56 | | | | | | | | | | | % 232.50/39.56 | | | | | | | | | | | CLOSE: (801) is inconsistent. % 232.50/39.56 | | | | | | | | | | | % 232.50/39.56 | | | | | | | | | | End of split % 232.50/39.56 | | | | | | | | | | % 232.50/39.56 | | | | | | | | | End of split % 232.50/39.56 | | | | | | | | | % 232.50/39.56 | | | | | | | | End of split % 232.50/39.56 | | | | | | | | % 232.50/39.56 | | | | | | | Case 2: % 232.50/39.56 | | | | | | | | % 232.50/39.56 | | | | | | | | (802) all_74_3 = n4 % 232.50/39.56 | | | | | | | | % 232.50/39.56 | | | | | | | | REDUCE: (732), (802) imply: % 232.50/39.56 | | | | | | | | (803) a_select3(q_ds1_filter, n4, n0) = all_74_1 % 232.50/39.56 | | | | | | | | % 232.50/39.56 | | | | | | | | REDUCE: (731), (802) imply: % 232.50/39.56 | | | | | | | | (804) a_select3(q_ds1_filter, n0, n4) = all_74_0 % 232.50/39.56 | | | | | | | | % 232.50/39.56 | | | | | | | | REDUCE: (146), (802) imply: % 232.50/39.56 | | | | | | | | (805) leq(n4, n5) % 232.50/39.56 | | | | | | | | % 232.50/39.56 | | | | | | | | REDUCE: (139), (802) imply: % 232.50/39.56 | | | | | | | | (806) leq(n0, n4) % 232.50/39.56 | | | | | | | | % 232.50/39.56 | | | | | | | | GROUND_INST: instantiating (62) with n0, n4, all_74_0, % 232.50/39.56 | | | | | | | | simplifying with (12), (119), (734), (804), (806) % 232.50/39.56 | | | | | | | | gives: % 232.50/39.56 | | | | | | | | (807) ~ leq(n4, all_74_21) | ~ leq(n0, all_74_21) | % 232.50/39.56 | | | | | | | | (a_select3(q_ds1_filter, n4, n0) = all_74_0 & % 232.50/39.56 | | | | | | | | $i(all_74_0)) % 232.50/39.56 | | | | | | | | % 232.50/39.56 | | | | | | | | BETA: splitting (807) gives: % 232.50/39.56 | | | | | | | | % 232.50/39.56 | | | | | | | | Case 1: % 232.50/39.56 | | | | | | | | | % 232.50/39.56 | | | | | | | | | (808) ~ leq(n0, all_74_21) % 232.50/39.56 | | | | | | | | | % 232.50/39.56 | | | | | | | | | REDUCE: (135), (808) imply: % 232.50/39.56 | | | | | | | | | (809) ~ leq(n0, n5) % 232.50/39.56 | | | | | | | | | % 232.50/39.56 | | | | | | | | | PRED_UNIFY: (733), (809) imply: % 232.50/39.56 | | | | | | | | | (810) $false % 232.50/39.56 | | | | | | | | | % 232.50/39.56 | | | | | | | | | CLOSE: (810) is inconsistent. % 232.50/39.56 | | | | | | | | | % 232.50/39.56 | | | | | | | | Case 2: % 232.50/39.56 | | | | | | | | | % 232.50/39.56 | | | | | | | | | (811) ~ leq(n4, all_74_21) | (a_select3(q_ds1_filter, n4, % 232.50/39.56 | | | | | | | | | n0) = all_74_0 & $i(all_74_0)) % 232.50/39.56 | | | | | | | | | % 232.50/39.56 | | | | | | | | | BETA: splitting (811) gives: % 232.50/39.56 | | | | | | | | | % 232.50/39.56 | | | | | | | | | Case 1: % 232.50/39.56 | | | | | | | | | | % 232.50/39.56 | | | | | | | | | | (812) ~ leq(n4, all_74_21) % 232.50/39.56 | | | | | | | | | | % 232.50/39.56 | | | | | | | | | | REDUCE: (135), (812) imply: % 232.50/39.56 | | | | | | | | | | (813) ~ leq(n4, n5) % 232.50/39.56 | | | | | | | | | | % 232.50/39.56 | | | | | | | | | | PRED_UNIFY: (805), (813) imply: % 232.50/39.56 | | | | | | | | | | (814) $false % 232.50/39.56 | | | | | | | | | | % 232.50/39.56 | | | | | | | | | | CLOSE: (814) is inconsistent. % 232.50/39.56 | | | | | | | | | | % 232.50/39.56 | | | | | | | | | Case 2: % 232.50/39.56 | | | | | | | | | | % 232.50/39.56 | | | | | | | | | | (815) a_select3(q_ds1_filter, n4, n0) = all_74_0 & % 232.50/39.56 | | | | | | | | | | $i(all_74_0) % 232.50/39.56 | | | | | | | | | | % 232.50/39.56 | | | | | | | | | | ALPHA: (815) implies: % 232.50/39.56 | | | | | | | | | | (816) a_select3(q_ds1_filter, n4, n0) = all_74_0 % 232.50/39.56 | | | | | | | | | | % 232.50/39.56 | | | | | | | | | | REF_CLOSE: (17), (138), (803), (816) are inconsistent by % 232.50/39.56 | | | | | | | | | | sub-proof #46. % 232.50/39.56 | | | | | | | | | | % 232.50/39.56 | | | | | | | | | End of split % 232.50/39.56 | | | | | | | | | % 232.50/39.56 | | | | | | | | End of split % 232.50/39.56 | | | | | | | | % 232.50/39.56 | | | | | | | End of split % 232.50/39.56 | | | | | | | % 232.50/39.56 | | | | | | End of split % 232.50/39.56 | | | | | | % 232.50/39.56 | | | | | Case 2: % 232.50/39.56 | | | | | | % 232.50/39.56 | | | | | | (817) all_74_3 = n5 % 232.50/39.56 | | | | | | % 232.50/39.56 | | | | | | REDUCE: (732), (817) imply: % 232.50/39.56 | | | | | | (818) a_select3(q_ds1_filter, n5, n0) = all_74_1 % 232.50/39.56 | | | | | | % 232.50/39.56 | | | | | | REDUCE: (731), (817) imply: % 232.50/39.56 | | | | | | (819) a_select3(q_ds1_filter, n0, n5) = all_74_0 % 232.50/39.56 | | | | | | % 232.50/39.56 | | | | | | REDUCE: (146), (817) imply: % 232.50/39.56 | | | | | | (820) leq(n5, n5) % 232.50/39.56 | | | | | | % 232.50/39.56 | | | | | | GROUND_INST: instantiating (62) with n0, n5, all_74_0, simplifying % 232.50/39.56 | | | | | | with (12), (122), (733), (734), (819) gives: % 232.50/39.56 | | | | | | (821) ~ leq(n5, all_74_21) | ~ leq(n0, all_74_21) | % 232.50/39.56 | | | | | | (a_select3(q_ds1_filter, n5, n0) = all_74_0 & $i(all_74_0)) % 232.50/39.56 | | | | | | % 232.50/39.56 | | | | | | BETA: splitting (821) gives: % 232.50/39.56 | | | | | | % 232.50/39.56 | | | | | | Case 1: % 232.50/39.56 | | | | | | | % 232.50/39.56 | | | | | | | (822) ~ leq(n0, all_74_21) % 232.50/39.56 | | | | | | | % 232.60/39.56 | | | | | | | REDUCE: (135), (822) imply: % 232.60/39.56 | | | | | | | (823) ~ leq(n0, n5) % 232.60/39.56 | | | | | | | % 232.60/39.56 | | | | | | | PRED_UNIFY: (733), (823) imply: % 232.60/39.56 | | | | | | | (824) $false % 232.60/39.56 | | | | | | | % 232.60/39.56 | | | | | | | CLOSE: (824) is inconsistent. % 232.60/39.56 | | | | | | | % 232.60/39.56 | | | | | | Case 2: % 232.60/39.56 | | | | | | | % 232.60/39.56 | | | | | | | (825) ~ leq(n5, all_74_21) | (a_select3(q_ds1_filter, n5, n0) % 232.60/39.56 | | | | | | | = all_74_0 & $i(all_74_0)) % 232.60/39.56 | | | | | | | % 232.60/39.56 | | | | | | | BETA: splitting (825) gives: % 232.60/39.56 | | | | | | | % 232.60/39.56 | | | | | | | Case 1: % 232.60/39.56 | | | | | | | | % 232.60/39.56 | | | | | | | | (826) ~ leq(n5, all_74_21) % 232.60/39.56 | | | | | | | | % 232.60/39.56 | | | | | | | | REDUCE: (135), (826) imply: % 232.60/39.56 | | | | | | | | (827) ~ leq(n5, n5) % 232.60/39.56 | | | | | | | | % 232.60/39.56 | | | | | | | | PRED_UNIFY: (820), (827) imply: % 232.60/39.56 | | | | | | | | (828) $false % 232.60/39.56 | | | | | | | | % 232.60/39.56 | | | | | | | | CLOSE: (828) is inconsistent. % 232.60/39.56 | | | | | | | | % 232.60/39.56 | | | | | | | Case 2: % 232.60/39.56 | | | | | | | | % 232.60/39.56 | | | | | | | | (829) a_select3(q_ds1_filter, n5, n0) = all_74_0 & % 232.60/39.56 | | | | | | | | $i(all_74_0) % 232.60/39.56 | | | | | | | | % 232.60/39.56 | | | | | | | | ALPHA: (829) implies: % 232.60/39.56 | | | | | | | | (830) a_select3(q_ds1_filter, n5, n0) = all_74_0 % 232.60/39.56 | | | | | | | | % 232.60/39.56 | | | | | | | | REF_CLOSE: (17), (138), (818), (830) are inconsistent by % 232.60/39.56 | | | | | | | | sub-proof #45. % 232.60/39.56 | | | | | | | | % 232.60/39.56 | | | | | | | End of split % 232.60/39.56 | | | | | | | % 232.60/39.56 | | | | | | End of split % 232.60/39.56 | | | | | | % 232.60/39.56 | | | | | End of split % 232.60/39.56 | | | | | % 232.60/39.56 | | | | Case 2: % 232.60/39.56 | | | | | % 232.60/39.56 | | | | | (831) all_74_3 = n0 % 232.60/39.56 | | | | | % 232.60/39.56 | | | | | REDUCE: (732), (831) imply: % 232.60/39.56 | | | | | (832) a_select3(q_ds1_filter, n0, n0) = all_74_1 % 232.60/39.56 | | | | | % 232.60/39.56 | | | | | REDUCE: (731), (831) imply: % 232.60/39.56 | | | | | (833) a_select3(q_ds1_filter, n0, n0) = all_74_0 % 232.60/39.56 | | | | | % 232.60/39.56 | | | | | GROUND_INST: instantiating (17) with all_74_1, all_74_0, n0, n0, % 232.60/39.56 | | | | | q_ds1_filter, simplifying with (832), (833) gives: % 232.60/39.56 | | | | | (834) all_74_0 = all_74_1 % 232.60/39.56 | | | | | % 232.60/39.56 | | | | | REDUCE: (138), (834) imply: % 232.60/39.56 | | | | | (835) $false % 232.60/39.56 | | | | | % 232.60/39.56 | | | | | CLOSE: (835) is inconsistent. % 232.60/39.56 | | | | | % 232.60/39.56 | | | | End of split % 232.60/39.56 | | | | % 232.60/39.56 | | | End of split % 232.60/39.56 | | | % 232.60/39.56 | | Case 2: % 232.60/39.56 | | | % 232.60/39.56 | | | (836) ~ (all_74_4 = all_74_5) & a_select3(r_ds1_filter, all_74_6, % 232.60/39.56 | | | all_74_7) = all_74_4 & a_select3(r_ds1_filter, all_74_7, % 232.60/39.56 | | | all_74_6) = all_74_5 & $i(all_74_4) & $i(all_74_5) & % 232.60/39.56 | | | leq(all_74_6, all_74_20) & leq(all_74_7, all_74_20) & leq(n0, % 232.60/39.56 | | | all_74_6) & leq(n0, all_74_7) % 232.60/39.56 | | | % 232.60/39.56 | | | ALPHA: (836) implies: % 232.60/39.56 | | | (837) ~ (all_74_4 = all_74_5) % 232.60/39.56 | | | (838) leq(n0, all_74_7) % 232.60/39.56 | | | (839) leq(n0, all_74_6) % 232.60/39.56 | | | (840) leq(all_74_7, all_74_20) % 232.60/39.56 | | | (841) leq(all_74_6, all_74_20) % 232.60/39.56 | | | (842) a_select3(r_ds1_filter, all_74_7, all_74_6) = all_74_5 % 232.60/39.56 | | | (843) a_select3(r_ds1_filter, all_74_6, all_74_7) = all_74_4 % 232.60/39.56 | | | % 232.60/39.56 | | | REDUCE: (134), (841) imply: % 232.60/39.56 | | | (844) leq(all_74_6, n2) % 232.60/39.56 | | | % 232.60/39.56 | | | REDUCE: (134), (840) imply: % 232.60/39.57 | | | (845) leq(all_74_7, n2) % 232.60/39.57 | | | % 232.60/39.57 | | | GROUND_INST: instantiating (leq_gt2) with n0, all_74_7, simplifying with % 232.60/39.57 | | | (12), (55), (838) gives: % 232.60/39.57 | | | (846) all_74_7 = n0 | gt(all_74_7, n0) % 232.60/39.57 | | | % 232.60/39.57 | | | GROUND_INST: instantiating (leq_gt2) with n0, all_74_6, simplifying with % 232.60/39.57 | | | (12), (56), (839) gives: % 232.60/39.57 | | | (847) all_74_6 = n0 | gt(all_74_6, n0) % 232.60/39.57 | | | % 232.60/39.57 | | | GROUND_INST: instantiating (5) with all_74_7, simplifying with (55), % 232.60/39.57 | | | (838), (845) gives: % 232.60/39.57 | | | (848) all_74_7 = n2 | all_74_7 = n1 | all_74_7 = n0 % 232.60/39.57 | | | % 232.60/39.57 | | | GROUND_INST: instantiating (leq_gt2) with all_74_7, n2, simplifying with % 232.60/39.57 | | | (55), (101), (845) gives: % 232.60/39.57 | | | (849) all_74_7 = n2 | gt(n2, all_74_7) % 232.60/39.57 | | | % 232.60/39.57 | | | GROUND_INST: instantiating (5) with all_74_6, simplifying with (56), % 232.60/39.57 | | | (839), (844) gives: % 232.60/39.57 | | | (850) all_74_6 = n2 | all_74_6 = n1 | all_74_6 = n0 % 232.60/39.57 | | | % 232.60/39.57 | | | GROUND_INST: instantiating (leq_gt2) with all_74_6, n2, simplifying with % 232.60/39.57 | | | (56), (101), (844) gives: % 232.60/39.57 | | | (851) all_74_6 = n2 | gt(n2, all_74_6) % 232.60/39.57 | | | % 232.60/39.57 | | | BETA: splitting (846) gives: % 232.60/39.57 | | | % 232.60/39.57 | | | Case 1: % 232.60/39.57 | | | | % 232.60/39.57 | | | | (852) gt(all_74_7, n0) % 232.60/39.57 | | | | % 232.60/39.57 | | | | BETA: splitting (847) gives: % 232.60/39.57 | | | | % 232.60/39.57 | | | | Case 1: % 232.60/39.57 | | | | | % 232.60/39.57 | | | | | (853) gt(all_74_6, n0) % 232.60/39.57 | | | | | % 232.60/39.57 | | | | | BETA: splitting (851) gives: % 232.60/39.57 | | | | | % 232.60/39.57 | | | | | Case 1: % 232.60/39.57 | | | | | | % 232.60/39.57 | | | | | | (854) gt(n2, all_74_6) % 232.60/39.57 | | | | | | % 232.60/39.57 | | | | | | GROUND_INST: instantiating (1) with all_74_6, n2, n1, simplifying % 232.60/39.57 | | | | | | with (56), (101), (123), (854) gives: % 232.60/39.57 | | | | | | (855) leq(all_74_6, n1) % 232.60/39.57 | | | | | | % 232.60/39.57 | | | | | | GROUND_INST: instantiating (4) with all_74_6, simplifying with (56), % 232.60/39.57 | | | | | | (839), (855) gives: % 232.60/39.57 | | | | | | (856) all_74_6 = n1 | all_74_6 = n0 % 232.60/39.57 | | | | | | % 232.60/39.57 | | | | | | BETA: splitting (849) gives: % 232.60/39.57 | | | | | | % 232.60/39.57 | | | | | | Case 1: % 232.60/39.57 | | | | | | | % 232.60/39.57 | | | | | | | (857) gt(n2, all_74_7) % 232.60/39.57 | | | | | | | % 232.60/39.57 | | | | | | | GROUND_INST: instantiating (1) with all_74_7, n2, n1, simplifying % 232.60/39.57 | | | | | | | with (55), (101), (123), (857) gives: % 232.60/39.57 | | | | | | | (858) leq(all_74_7, n1) % 232.60/39.57 | | | | | | | % 232.60/39.57 | | | | | | | GROUND_INST: instantiating (4) with all_74_7, simplifying with % 232.60/39.57 | | | | | | | (55), (838), (858) gives: % 232.60/39.57 | | | | | | | (859) all_74_7 = n1 | all_74_7 = n0 % 232.60/39.57 | | | | | | | % 232.60/39.57 | | | | | | | BETA: splitting (848) gives: % 232.60/39.57 | | | | | | | % 232.60/39.57 | | | | | | | Case 1: % 232.60/39.57 | | | | | | | | % 232.60/39.57 | | | | | | | | (860) all_74_7 = n0 % 232.60/39.57 | | | | | | | | % 232.60/39.57 | | | | | | | | REF_CLOSE: (55), (852), (860), (irreflexivity_gt) are % 232.60/39.57 | | | | | | | | inconsistent by sub-proof #44. % 232.60/39.57 | | | | | | | | % 232.60/39.57 | | | | | | | Case 2: % 232.60/39.57 | | | | | | | | % 232.60/39.57 | | | | | | | | (861) ~ (all_74_7 = n0) % 232.60/39.57 | | | | | | | | % 232.60/39.57 | | | | | | | | BETA: splitting (859) gives: % 232.60/39.57 | | | | | | | | % 232.60/39.57 | | | | | | | | Case 1: % 232.60/39.57 | | | | | | | | | % 232.60/39.57 | | | | | | | | | (862) all_74_7 = n0 % 232.60/39.57 | | | | | | | | | % 232.60/39.57 | | | | | | | | | REDUCE: (861), (862) imply: % 232.60/39.57 | | | | | | | | | (863) $false % 232.60/39.57 | | | | | | | | | % 232.60/39.57 | | | | | | | | | CLOSE: (863) is inconsistent. % 232.60/39.57 | | | | | | | | | % 232.60/39.57 | | | | | | | | Case 2: % 232.60/39.57 | | | | | | | | | % 232.60/39.57 | | | | | | | | | (864) all_74_7 = n1 % 232.60/39.57 | | | | | | | | | % 232.60/39.57 | | | | | | | | | REDUCE: (843), (864) imply: % 232.60/39.57 | | | | | | | | | (865) a_select3(r_ds1_filter, all_74_6, n1) = all_74_4 % 232.60/39.57 | | | | | | | | | % 232.60/39.57 | | | | | | | | | REDUCE: (842), (864) imply: % 232.60/39.57 | | | | | | | | | (866) a_select3(r_ds1_filter, n1, all_74_6) = all_74_5 % 232.60/39.57 | | | | | | | | | % 232.60/39.57 | | | | | | | | | BETA: splitting (850) gives: % 232.60/39.57 | | | | | | | | | % 232.60/39.57 | | | | | | | | | Case 1: % 232.60/39.57 | | | | | | | | | | % 232.60/39.57 | | | | | | | | | | (867) all_74_6 = n0 % 232.60/39.57 | | | | | | | | | | % 232.60/39.57 | | | | | | | | | | REF_CLOSE: (56), (853), (867), (irreflexivity_gt) are % 232.60/39.57 | | | | | | | | | | inconsistent by sub-proof #43. % 232.60/39.57 | | | | | | | | | | % 232.60/39.57 | | | | | | | | | Case 2: % 232.60/39.57 | | | | | | | | | | % 232.60/39.57 | | | | | | | | | | (868) ~ (all_74_6 = n0) % 232.60/39.57 | | | | | | | | | | % 232.60/39.57 | | | | | | | | | | BETA: splitting (856) gives: % 232.60/39.57 | | | | | | | | | | % 232.60/39.57 | | | | | | | | | | Case 1: % 232.60/39.57 | | | | | | | | | | | % 232.60/39.57 | | | | | | | | | | | (869) all_74_6 = n0 % 232.60/39.57 | | | | | | | | | | | % 232.60/39.57 | | | | | | | | | | | REDUCE: (868), (869) imply: % 232.60/39.57 | | | | | | | | | | | (870) $false % 232.60/39.57 | | | | | | | | | | | % 232.60/39.57 | | | | | | | | | | | CLOSE: (870) is inconsistent. % 232.60/39.57 | | | | | | | | | | | % 232.60/39.57 | | | | | | | | | | Case 2: % 232.60/39.57 | | | | | | | | | | | % 232.60/39.57 | | | | | | | | | | | (871) all_74_6 = n1 % 232.60/39.57 | | | | | | | | | | | % 232.60/39.57 | | | | | | | | | | | REDUCE: (865), (871) imply: % 232.60/39.57 | | | | | | | | | | | (872) a_select3(r_ds1_filter, n1, n1) = all_74_4 % 232.60/39.57 | | | | | | | | | | | % 232.60/39.57 | | | | | | | | | | | REDUCE: (866), (871) imply: % 232.60/39.57 | | | | | | | | | | | (873) a_select3(r_ds1_filter, n1, n1) = all_74_5 % 232.60/39.57 | | | | | | | | | | | % 232.60/39.57 | | | | | | | | | | | GROUND_INST: instantiating (17) with all_74_5, all_74_4, n1, % 232.60/39.57 | | | | | | | | | | | n1, r_ds1_filter, simplifying with (872), (873) % 232.60/39.57 | | | | | | | | | | | gives: % 232.60/39.57 | | | | | | | | | | | (874) all_74_4 = all_74_5 % 232.60/39.57 | | | | | | | | | | | % 232.60/39.57 | | | | | | | | | | | REDUCE: (837), (874) imply: % 232.60/39.57 | | | | | | | | | | | (875) $false % 232.60/39.57 | | | | | | | | | | | % 232.60/39.57 | | | | | | | | | | | CLOSE: (875) is inconsistent. % 232.60/39.57 | | | | | | | | | | | % 232.60/39.57 | | | | | | | | | | End of split % 232.60/39.57 | | | | | | | | | | % 232.60/39.57 | | | | | | | | | End of split % 232.60/39.57 | | | | | | | | | % 232.60/39.57 | | | | | | | | End of split % 232.60/39.57 | | | | | | | | % 232.60/39.57 | | | | | | | End of split % 232.60/39.57 | | | | | | | % 232.60/39.57 | | | | | | Case 2: % 232.60/39.57 | | | | | | | % 232.60/39.57 | | | | | | | (876) all_74_7 = n2 % 232.60/39.57 | | | | | | | % 232.60/39.57 | | | | | | | REDUCE: (843), (876) imply: % 232.60/39.57 | | | | | | | (877) a_select3(r_ds1_filter, all_74_6, n2) = all_74_4 % 232.60/39.57 | | | | | | | % 232.60/39.57 | | | | | | | REDUCE: (842), (876) imply: % 232.60/39.57 | | | | | | | (878) a_select3(r_ds1_filter, n2, all_74_6) = all_74_5 % 232.60/39.57 | | | | | | | % 232.60/39.57 | | | | | | | REDUCE: (845), (876) imply: % 232.60/39.57 | | | | | | | (879) leq(n2, n2) % 232.60/39.57 | | | | | | | % 232.60/39.57 | | | | | | | REDUCE: (838), (876) imply: % 232.60/39.57 | | | | | | | (880) leq(n0, n2) % 232.60/39.57 | | | | | | | % 232.60/39.57 | | | | | | | BETA: splitting (850) gives: % 232.60/39.57 | | | | | | | % 232.60/39.57 | | | | | | | Case 1: % 232.60/39.57 | | | | | | | | % 232.60/39.57 | | | | | | | | (881) all_74_6 = n0 % 232.60/39.57 | | | | | | | | % 232.60/39.57 | | | | | | | | REF_CLOSE: (56), (853), (881), (irreflexivity_gt) are % 232.60/39.57 | | | | | | | | inconsistent by sub-proof #43. % 232.60/39.57 | | | | | | | | % 232.60/39.57 | | | | | | | Case 2: % 232.60/39.57 | | | | | | | | % 232.60/39.57 | | | | | | | | (882) ~ (all_74_6 = n0) % 232.60/39.57 | | | | | | | | % 232.60/39.57 | | | | | | | | BETA: splitting (856) gives: % 232.60/39.57 | | | | | | | | % 232.60/39.57 | | | | | | | | Case 1: % 232.60/39.57 | | | | | | | | | % 232.60/39.57 | | | | | | | | | (883) all_74_6 = n0 % 232.60/39.57 | | | | | | | | | % 232.60/39.57 | | | | | | | | | REDUCE: (882), (883) imply: % 232.60/39.57 | | | | | | | | | (884) $false % 232.60/39.57 | | | | | | | | | % 232.60/39.57 | | | | | | | | | CLOSE: (884) is inconsistent. % 232.60/39.57 | | | | | | | | | % 232.60/39.57 | | | | | | | | Case 2: % 232.60/39.57 | | | | | | | | | % 232.60/39.57 | | | | | | | | | (885) all_74_6 = n1 % 232.60/39.57 | | | | | | | | | % 232.60/39.57 | | | | | | | | | REDUCE: (877), (885) imply: % 232.60/39.57 | | | | | | | | | (886) a_select3(r_ds1_filter, n1, n2) = all_74_4 % 232.60/39.57 | | | | | | | | | % 232.60/39.57 | | | | | | | | | REDUCE: (878), (885) imply: % 232.60/39.57 | | | | | | | | | (887) a_select3(r_ds1_filter, n2, n1) = all_74_5 % 232.60/39.57 | | | | | | | | | % 232.60/39.57 | | | | | | | | | REDUCE: (844), (885) imply: % 232.60/39.57 | | | | | | | | | (888) leq(n1, n2) % 232.60/39.57 | | | | | | | | | % 232.60/39.57 | | | | | | | | | REDUCE: (839), (885) imply: % 232.60/39.57 | | | | | | | | | (889) leq(n0, n1) % 232.60/39.57 | | | | | | | | | % 232.60/39.57 | | | | | | | | | GROUND_INST: instantiating (63) with n1, n2, all_74_4, % 232.60/39.57 | | | | | | | | | simplifying with (85), (101), (880), (886), (889) % 232.60/39.57 | | | | | | | | | gives: % 232.60/39.57 | | | | | | | | | (890) ~ leq(n2, all_74_20) | ~ leq(n1, all_74_20) | % 232.60/39.57 | | | | | | | | | (a_select3(r_ds1_filter, n2, n1) = all_74_4 & % 232.60/39.57 | | | | | | | | | $i(all_74_4)) % 232.60/39.57 | | | | | | | | | % 232.60/39.57 | | | | | | | | | BETA: splitting (890) gives: % 232.60/39.57 | | | | | | | | | % 232.60/39.57 | | | | | | | | | Case 1: % 232.60/39.57 | | | | | | | | | | % 232.60/39.57 | | | | | | | | | | (891) ~ leq(n2, all_74_20) % 232.60/39.57 | | | | | | | | | | % 232.60/39.57 | | | | | | | | | | REDUCE: (134), (891) imply: % 232.60/39.57 | | | | | | | | | | (892) ~ leq(n2, n2) % 232.60/39.57 | | | | | | | | | | % 232.60/39.57 | | | | | | | | | | PRED_UNIFY: (879), (892) imply: % 232.60/39.57 | | | | | | | | | | (893) $false % 232.60/39.57 | | | | | | | | | | % 232.60/39.57 | | | | | | | | | | CLOSE: (893) is inconsistent. % 232.60/39.57 | | | | | | | | | | % 232.60/39.57 | | | | | | | | | Case 2: % 232.60/39.57 | | | | | | | | | | % 232.60/39.57 | | | | | | | | | | (894) ~ leq(n1, all_74_20) | (a_select3(r_ds1_filter, % 232.60/39.57 | | | | | | | | | | n2, n1) = all_74_4 & $i(all_74_4)) % 232.60/39.57 | | | | | | | | | | % 232.60/39.57 | | | | | | | | | | BETA: splitting (894) gives: % 232.60/39.57 | | | | | | | | | | % 232.60/39.57 | | | | | | | | | | Case 1: % 232.60/39.57 | | | | | | | | | | | % 232.60/39.57 | | | | | | | | | | | (895) ~ leq(n1, all_74_20) % 232.60/39.57 | | | | | | | | | | | % 232.60/39.57 | | | | | | | | | | | REDUCE: (134), (895) imply: % 232.60/39.57 | | | | | | | | | | | (896) ~ leq(n1, n2) % 232.60/39.57 | | | | | | | | | | | % 232.60/39.57 | | | | | | | | | | | PRED_UNIFY: (888), (896) imply: % 232.60/39.57 | | | | | | | | | | | (897) $false % 232.60/39.57 | | | | | | | | | | | % 232.60/39.57 | | | | | | | | | | | CLOSE: (897) is inconsistent. % 232.60/39.57 | | | | | | | | | | | % 232.60/39.57 | | | | | | | | | | Case 2: % 232.60/39.57 | | | | | | | | | | | % 232.60/39.57 | | | | | | | | | | | (898) a_select3(r_ds1_filter, n2, n1) = all_74_4 & % 232.60/39.57 | | | | | | | | | | | $i(all_74_4) % 232.60/39.57 | | | | | | | | | | | % 232.60/39.57 | | | | | | | | | | | ALPHA: (898) implies: % 232.60/39.57 | | | | | | | | | | | (899) a_select3(r_ds1_filter, n2, n1) = all_74_4 % 232.60/39.57 | | | | | | | | | | | % 232.60/39.57 | | | | | | | | | | | REF_CLOSE: (17), (837), (887), (899) are inconsistent by % 232.60/39.57 | | | | | | | | | | | sub-proof #42. % 232.60/39.57 | | | | | | | | | | | % 232.60/39.57 | | | | | | | | | | End of split % 232.60/39.57 | | | | | | | | | | % 232.60/39.57 | | | | | | | | | End of split % 232.60/39.57 | | | | | | | | | % 232.60/39.57 | | | | | | | | End of split % 232.60/39.57 | | | | | | | | % 232.60/39.57 | | | | | | | End of split % 232.60/39.57 | | | | | | | % 232.60/39.57 | | | | | | End of split % 232.60/39.57 | | | | | | % 232.60/39.57 | | | | | Case 2: % 232.60/39.57 | | | | | | % 232.60/39.57 | | | | | | (900) all_74_6 = n2 % 232.60/39.57 | | | | | | % 232.60/39.57 | | | | | | REDUCE: (843), (900) imply: % 232.60/39.57 | | | | | | (901) a_select3(r_ds1_filter, n2, all_74_7) = all_74_4 % 232.60/39.57 | | | | | | % 232.60/39.57 | | | | | | REDUCE: (842), (900) imply: % 232.60/39.57 | | | | | | (902) a_select3(r_ds1_filter, all_74_7, n2) = all_74_5 % 232.60/39.57 | | | | | | % 232.60/39.57 | | | | | | REDUCE: (844), (900) imply: % 232.60/39.57 | | | | | | (903) leq(n2, n2) % 232.60/39.57 | | | | | | % 232.60/39.57 | | | | | | REDUCE: (839), (900) imply: % 232.60/39.57 | | | | | | (904) leq(n0, n2) % 232.60/39.57 | | | | | | % 232.60/39.57 | | | | | | BETA: splitting (849) gives: % 232.60/39.57 | | | | | | % 232.60/39.57 | | | | | | Case 1: % 232.60/39.57 | | | | | | | % 232.60/39.57 | | | | | | | (905) gt(n2, all_74_7) % 232.60/39.57 | | | | | | | % 232.60/39.57 | | | | | | | GROUND_INST: instantiating (1) with all_74_7, n2, n1, simplifying % 232.60/39.57 | | | | | | | with (55), (101), (123), (905) gives: % 232.60/39.57 | | | | | | | (906) leq(all_74_7, n1) % 232.60/39.57 | | | | | | | % 232.60/39.57 | | | | | | | GROUND_INST: instantiating (4) with all_74_7, simplifying with % 232.60/39.57 | | | | | | | (55), (838), (906) gives: % 232.60/39.57 | | | | | | | (907) all_74_7 = n1 | all_74_7 = n0 % 232.60/39.57 | | | | | | | % 232.60/39.57 | | | | | | | BETA: splitting (848) gives: % 232.60/39.57 | | | | | | | % 232.60/39.57 | | | | | | | Case 1: % 232.60/39.57 | | | | | | | | % 232.60/39.57 | | | | | | | | (908) all_74_7 = n0 % 232.60/39.57 | | | | | | | | % 232.60/39.57 | | | | | | | | REF_CLOSE: (55), (852), (908), (irreflexivity_gt) are % 232.60/39.57 | | | | | | | | inconsistent by sub-proof #44. % 232.60/39.57 | | | | | | | | % 232.60/39.57 | | | | | | | Case 2: % 232.60/39.57 | | | | | | | | % 232.60/39.57 | | | | | | | | (909) ~ (all_74_7 = n0) % 232.60/39.57 | | | | | | | | % 232.60/39.57 | | | | | | | | BETA: splitting (907) gives: % 232.60/39.57 | | | | | | | | % 232.60/39.57 | | | | | | | | Case 1: % 232.60/39.57 | | | | | | | | | % 232.60/39.57 | | | | | | | | | (910) all_74_7 = n0 % 232.60/39.57 | | | | | | | | | % 232.60/39.57 | | | | | | | | | REDUCE: (909), (910) imply: % 232.60/39.57 | | | | | | | | | (911) $false % 232.60/39.57 | | | | | | | | | % 232.60/39.57 | | | | | | | | | CLOSE: (911) is inconsistent. % 232.60/39.57 | | | | | | | | | % 232.60/39.57 | | | | | | | | Case 2: % 232.60/39.57 | | | | | | | | | % 232.60/39.57 | | | | | | | | | (912) all_74_7 = n1 % 232.60/39.57 | | | | | | | | | % 232.60/39.57 | | | | | | | | | REDUCE: (902), (912) imply: % 232.60/39.57 | | | | | | | | | (913) a_select3(r_ds1_filter, n1, n2) = all_74_5 % 232.60/39.57 | | | | | | | | | % 232.60/39.57 | | | | | | | | | REDUCE: (901), (912) imply: % 232.60/39.57 | | | | | | | | | (914) a_select3(r_ds1_filter, n2, n1) = all_74_4 % 232.60/39.57 | | | | | | | | | % 232.60/39.57 | | | | | | | | | REDUCE: (845), (912) imply: % 232.60/39.58 | | | | | | | | | (915) leq(n1, n2) % 232.60/39.58 | | | | | | | | | % 232.60/39.58 | | | | | | | | | REDUCE: (838), (912) imply: % 232.60/39.58 | | | | | | | | | (916) leq(n0, n1) % 232.60/39.58 | | | | | | | | | % 232.60/39.58 | | | | | | | | | GROUND_INST: instantiating (63) with n1, n2, all_74_5, % 232.60/39.58 | | | | | | | | | simplifying with (85), (101), (904), (913), (916) % 232.60/39.58 | | | | | | | | | gives: % 232.60/39.58 | | | | | | | | | (917) ~ leq(n2, all_74_20) | ~ leq(n1, all_74_20) | % 232.60/39.58 | | | | | | | | | (a_select3(r_ds1_filter, n2, n1) = all_74_5 & % 232.60/39.58 | | | | | | | | | $i(all_74_5)) % 232.60/39.58 | | | | | | | | | % 232.60/39.58 | | | | | | | | | BETA: splitting (917) gives: % 232.60/39.58 | | | | | | | | | % 232.60/39.58 | | | | | | | | | Case 1: % 232.60/39.58 | | | | | | | | | | % 232.60/39.58 | | | | | | | | | | (918) ~ leq(n2, all_74_20) % 232.60/39.58 | | | | | | | | | | % 232.60/39.58 | | | | | | | | | | REDUCE: (134), (918) imply: % 232.60/39.58 | | | | | | | | | | (919) ~ leq(n2, n2) % 232.60/39.58 | | | | | | | | | | % 232.60/39.58 | | | | | | | | | | PRED_UNIFY: (903), (919) imply: % 232.60/39.58 | | | | | | | | | | (920) $false % 232.60/39.58 | | | | | | | | | | % 232.60/39.58 | | | | | | | | | | CLOSE: (920) is inconsistent. % 232.60/39.58 | | | | | | | | | | % 232.60/39.58 | | | | | | | | | Case 2: % 232.60/39.58 | | | | | | | | | | % 232.60/39.58 | | | | | | | | | | (921) ~ leq(n1, all_74_20) | (a_select3(r_ds1_filter, % 232.60/39.58 | | | | | | | | | | n2, n1) = all_74_5 & $i(all_74_5)) % 232.60/39.58 | | | | | | | | | | % 232.60/39.58 | | | | | | | | | | BETA: splitting (921) gives: % 232.60/39.58 | | | | | | | | | | % 232.60/39.58 | | | | | | | | | | Case 1: % 232.60/39.58 | | | | | | | | | | | % 232.60/39.58 | | | | | | | | | | | (922) ~ leq(n1, all_74_20) % 232.60/39.58 | | | | | | | | | | | % 232.60/39.58 | | | | | | | | | | | REDUCE: (134), (922) imply: % 232.60/39.58 | | | | | | | | | | | (923) ~ leq(n1, n2) % 232.60/39.58 | | | | | | | | | | | % 232.60/39.58 | | | | | | | | | | | PRED_UNIFY: (915), (923) imply: % 232.60/39.58 | | | | | | | | | | | (924) $false % 232.60/39.58 | | | | | | | | | | | % 232.60/39.58 | | | | | | | | | | | CLOSE: (924) is inconsistent. % 232.60/39.58 | | | | | | | | | | | % 232.60/39.58 | | | | | | | | | | Case 2: % 232.60/39.58 | | | | | | | | | | | % 232.60/39.58 | | | | | | | | | | | (925) a_select3(r_ds1_filter, n2, n1) = all_74_5 & % 232.60/39.58 | | | | | | | | | | | $i(all_74_5) % 232.60/39.58 | | | | | | | | | | | % 232.60/39.58 | | | | | | | | | | | ALPHA: (925) implies: % 232.60/39.58 | | | | | | | | | | | (926) a_select3(r_ds1_filter, n2, n1) = all_74_5 % 232.60/39.58 | | | | | | | | | | | % 232.60/39.58 | | | | | | | | | | | REF_CLOSE: (17), (837), (914), (926) are inconsistent by % 232.60/39.58 | | | | | | | | | | | sub-proof #42. % 232.60/39.58 | | | | | | | | | | | % 232.60/39.58 | | | | | | | | | | End of split % 232.60/39.58 | | | | | | | | | | % 232.60/39.58 | | | | | | | | | End of split % 232.60/39.58 | | | | | | | | | % 232.60/39.58 | | | | | | | | End of split % 232.60/39.58 | | | | | | | | % 232.60/39.58 | | | | | | | End of split % 232.60/39.58 | | | | | | | % 232.60/39.58 | | | | | | Case 2: % 232.60/39.58 | | | | | | | % 232.60/39.58 | | | | | | | (927) all_74_7 = n2 % 232.60/39.58 | | | | | | | % 232.60/39.58 | | | | | | | REDUCE: (902), (927) imply: % 232.60/39.58 | | | | | | | (928) a_select3(r_ds1_filter, n2, n2) = all_74_5 % 232.60/39.58 | | | | | | | % 232.60/39.58 | | | | | | | REDUCE: (901), (927) imply: % 232.60/39.58 | | | | | | | (929) a_select3(r_ds1_filter, n2, n2) = all_74_4 % 232.60/39.58 | | | | | | | % 232.60/39.58 | | | | | | | GROUND_INST: instantiating (17) with all_74_5, all_74_4, n2, n2, % 232.60/39.58 | | | | | | | r_ds1_filter, simplifying with (928), (929) gives: % 232.60/39.58 | | | | | | | (930) all_74_4 = all_74_5 % 232.60/39.58 | | | | | | | % 232.60/39.58 | | | | | | | REDUCE: (837), (930) imply: % 232.60/39.58 | | | | | | | (931) $false % 232.60/39.58 | | | | | | | % 232.60/39.58 | | | | | | | CLOSE: (931) is inconsistent. % 232.60/39.58 | | | | | | | % 232.60/39.58 | | | | | | End of split % 232.60/39.58 | | | | | | % 232.60/39.58 | | | | | End of split % 232.60/39.58 | | | | | % 232.60/39.58 | | | | Case 2: % 232.60/39.58 | | | | | % 232.60/39.58 | | | | | (932) all_74_6 = n0 % 232.60/39.58 | | | | | (933) ~ gt(all_74_6, n0) % 232.60/39.58 | | | | | % 232.60/39.58 | | | | | REDUCE: (843), (932) imply: % 232.60/39.58 | | | | | (934) a_select3(r_ds1_filter, n0, all_74_7) = all_74_4 % 232.60/39.58 | | | | | % 232.60/39.58 | | | | | REDUCE: (842), (932) imply: % 232.60/39.58 | | | | | (935) a_select3(r_ds1_filter, all_74_7, n0) = all_74_5 % 232.60/39.58 | | | | | % 232.60/39.58 | | | | | REDUCE: (844), (932) imply: % 232.60/39.58 | | | | | (936) leq(n0, n2) % 232.60/39.58 | | | | | % 232.60/39.58 | | | | | REDUCE: (839), (932) imply: % 232.60/39.58 | | | | | (937) leq(n0, n0) % 232.60/39.58 | | | | | % 232.60/39.58 | | | | | REDUCE: (932), (933) imply: % 232.60/39.58 | | | | | (938) ~ gt(n0, n0) % 232.60/39.58 | | | | | % 232.60/39.58 | | | | | BETA: splitting (849) gives: % 232.60/39.58 | | | | | % 232.60/39.58 | | | | | Case 1: % 232.60/39.58 | | | | | | % 232.60/39.58 | | | | | | (939) gt(n2, all_74_7) % 232.60/39.58 | | | | | | % 232.60/39.58 | | | | | | GROUND_INST: instantiating (1) with all_74_7, n2, n1, simplifying % 232.60/39.58 | | | | | | with (55), (101), (123), (939) gives: % 232.60/39.58 | | | | | | (940) leq(all_74_7, n1) % 232.60/39.58 | | | | | | % 232.60/39.58 | | | | | | GROUND_INST: instantiating (4) with all_74_7, simplifying with (55), % 232.60/39.58 | | | | | | (838), (940) gives: % 232.60/39.58 | | | | | | (941) all_74_7 = n1 | all_74_7 = n0 % 232.60/39.58 | | | | | | % 232.60/39.58 | | | | | | BETA: splitting (848) gives: % 232.60/39.58 | | | | | | % 232.60/39.58 | | | | | | Case 1: % 232.60/39.58 | | | | | | | % 232.60/39.58 | | | | | | | (942) all_74_7 = n0 % 232.60/39.58 | | | | | | | % 232.60/39.58 | | | | | | | REDUCE: (852), (942) imply: % 232.60/39.58 | | | | | | | (943) gt(n0, n0) % 232.60/39.58 | | | | | | | % 232.60/39.58 | | | | | | | PRED_UNIFY: (938), (943) imply: % 232.60/39.58 | | | | | | | (944) $false % 232.60/39.58 | | | | | | | % 232.60/39.58 | | | | | | | CLOSE: (944) is inconsistent. % 232.60/39.58 | | | | | | | % 232.60/39.58 | | | | | | Case 2: % 232.60/39.58 | | | | | | | % 232.60/39.58 | | | | | | | (945) ~ (all_74_7 = n0) % 232.60/39.58 | | | | | | | % 232.60/39.58 | | | | | | | BETA: splitting (941) gives: % 232.60/39.58 | | | | | | | % 232.60/39.58 | | | | | | | Case 1: % 232.60/39.58 | | | | | | | | % 232.60/39.58 | | | | | | | | (946) all_74_7 = n0 % 232.60/39.58 | | | | | | | | % 232.60/39.58 | | | | | | | | REDUCE: (945), (946) imply: % 232.60/39.58 | | | | | | | | (947) $false % 232.60/39.58 | | | | | | | | % 232.60/39.58 | | | | | | | | CLOSE: (947) is inconsistent. % 232.60/39.58 | | | | | | | | % 232.60/39.58 | | | | | | | Case 2: % 232.60/39.58 | | | | | | | | % 232.60/39.58 | | | | | | | | (948) all_74_7 = n1 % 232.60/39.58 | | | | | | | | % 232.60/39.58 | | | | | | | | REDUCE: (935), (948) imply: % 232.60/39.58 | | | | | | | | (949) a_select3(r_ds1_filter, n1, n0) = all_74_5 % 232.60/39.58 | | | | | | | | % 232.60/39.58 | | | | | | | | REDUCE: (934), (948) imply: % 232.60/39.58 | | | | | | | | (950) a_select3(r_ds1_filter, n0, n1) = all_74_4 % 232.60/39.58 | | | | | | | | % 232.60/39.58 | | | | | | | | REDUCE: (845), (948) imply: % 232.60/39.58 | | | | | | | | (951) leq(n1, n2) % 232.60/39.58 | | | | | | | | % 232.60/39.58 | | | | | | | | REDUCE: (838), (948) imply: % 232.60/39.58 | | | | | | | | (952) leq(n0, n1) % 232.60/39.58 | | | | | | | | % 232.60/39.58 | | | | | | | | GROUND_INST: instantiating (63) with n0, n1, all_74_4, % 232.60/39.58 | | | | | | | | simplifying with (12), (85), (937), (950), (952) % 232.60/39.58 | | | | | | | | gives: % 232.60/39.58 | | | | | | | | (953) ~ leq(n1, all_74_20) | ~ leq(n0, all_74_20) | % 232.60/39.58 | | | | | | | | (a_select3(r_ds1_filter, n1, n0) = all_74_4 & % 232.60/39.58 | | | | | | | | $i(all_74_4)) % 232.60/39.58 | | | | | | | | % 232.60/39.58 | | | | | | | | BETA: splitting (953) gives: % 232.60/39.58 | | | | | | | | % 232.60/39.58 | | | | | | | | Case 1: % 232.60/39.58 | | | | | | | | | % 232.60/39.58 | | | | | | | | | (954) ~ leq(n0, all_74_20) % 232.60/39.58 | | | | | | | | | % 232.60/39.58 | | | | | | | | | REDUCE: (134), (954) imply: % 232.60/39.58 | | | | | | | | | (955) ~ leq(n0, n2) % 232.60/39.58 | | | | | | | | | % 232.60/39.58 | | | | | | | | | PRED_UNIFY: (936), (955) imply: % 232.60/39.58 | | | | | | | | | (956) $false % 232.60/39.58 | | | | | | | | | % 232.60/39.58 | | | | | | | | | CLOSE: (956) is inconsistent. % 232.60/39.58 | | | | | | | | | % 232.60/39.58 | | | | | | | | Case 2: % 232.60/39.58 | | | | | | | | | % 232.60/39.58 | | | | | | | | | (957) ~ leq(n1, all_74_20) | (a_select3(r_ds1_filter, n1, % 232.60/39.58 | | | | | | | | | n0) = all_74_4 & $i(all_74_4)) % 232.60/39.58 | | | | | | | | | % 232.60/39.58 | | | | | | | | | BETA: splitting (957) gives: % 232.60/39.58 | | | | | | | | | % 232.60/39.58 | | | | | | | | | Case 1: % 232.60/39.58 | | | | | | | | | | % 232.60/39.58 | | | | | | | | | | (958) ~ leq(n1, all_74_20) % 232.60/39.58 | | | | | | | | | | % 232.60/39.58 | | | | | | | | | | REDUCE: (134), (958) imply: % 232.60/39.58 | | | | | | | | | | (959) ~ leq(n1, n2) % 232.60/39.58 | | | | | | | | | | % 232.60/39.58 | | | | | | | | | | PRED_UNIFY: (951), (959) imply: % 232.60/39.58 | | | | | | | | | | (960) $false % 232.60/39.58 | | | | | | | | | | % 232.60/39.58 | | | | | | | | | | CLOSE: (960) is inconsistent. % 232.60/39.58 | | | | | | | | | | % 232.60/39.58 | | | | | | | | | Case 2: % 232.60/39.58 | | | | | | | | | | % 232.60/39.58 | | | | | | | | | | (961) a_select3(r_ds1_filter, n1, n0) = all_74_4 & % 232.60/39.58 | | | | | | | | | | $i(all_74_4) % 232.60/39.58 | | | | | | | | | | % 232.60/39.58 | | | | | | | | | | ALPHA: (961) implies: % 232.60/39.58 | | | | | | | | | | (962) a_select3(r_ds1_filter, n1, n0) = all_74_4 % 232.60/39.58 | | | | | | | | | | % 232.60/39.58 | | | | | | | | | | REF_CLOSE: (17), (837), (949), (962) are inconsistent by % 232.60/39.58 | | | | | | | | | | sub-proof #41. % 232.60/39.58 | | | | | | | | | | % 232.60/39.58 | | | | | | | | | End of split % 232.60/39.58 | | | | | | | | | % 232.60/39.58 | | | | | | | | End of split % 232.60/39.58 | | | | | | | | % 232.60/39.58 | | | | | | | End of split % 232.60/39.58 | | | | | | | % 232.60/39.58 | | | | | | End of split % 232.60/39.58 | | | | | | % 232.60/39.58 | | | | | Case 2: % 232.60/39.58 | | | | | | % 232.60/39.58 | | | | | | (963) all_74_7 = n2 % 232.60/39.58 | | | | | | % 232.60/39.58 | | | | | | REDUCE: (935), (963) imply: % 232.60/39.58 | | | | | | (964) a_select3(r_ds1_filter, n2, n0) = all_74_5 % 232.60/39.58 | | | | | | % 232.60/39.58 | | | | | | REDUCE: (934), (963) imply: % 232.60/39.58 | | | | | | (965) a_select3(r_ds1_filter, n0, n2) = all_74_4 % 232.60/39.58 | | | | | | % 232.60/39.58 | | | | | | REDUCE: (845), (963) imply: % 232.60/39.58 | | | | | | (966) leq(n2, n2) % 232.60/39.58 | | | | | | % 232.60/39.58 | | | | | | GROUND_INST: instantiating (63) with n0, n2, all_74_4, simplifying % 232.60/39.58 | | | | | | with (12), (101), (936), (937), (965) gives: % 232.60/39.58 | | | | | | (967) ~ leq(n2, all_74_20) | ~ leq(n0, all_74_20) | % 232.60/39.58 | | | | | | (a_select3(r_ds1_filter, n2, n0) = all_74_4 & $i(all_74_4)) % 232.60/39.58 | | | | | | % 232.60/39.58 | | | | | | BETA: splitting (967) gives: % 232.60/39.58 | | | | | | % 232.60/39.58 | | | | | | Case 1: % 232.60/39.58 | | | | | | | % 232.60/39.58 | | | | | | | (968) ~ leq(n0, all_74_20) % 232.60/39.58 | | | | | | | % 232.60/39.58 | | | | | | | REDUCE: (134), (968) imply: % 232.60/39.58 | | | | | | | (969) ~ leq(n0, n2) % 232.60/39.58 | | | | | | | % 232.60/39.58 | | | | | | | PRED_UNIFY: (936), (969) imply: % 232.60/39.58 | | | | | | | (970) $false % 232.60/39.58 | | | | | | | % 232.60/39.58 | | | | | | | CLOSE: (970) is inconsistent. % 232.60/39.58 | | | | | | | % 232.60/39.58 | | | | | | Case 2: % 232.60/39.58 | | | | | | | % 232.60/39.58 | | | | | | | (971) ~ leq(n2, all_74_20) | (a_select3(r_ds1_filter, n2, n0) % 232.60/39.58 | | | | | | | = all_74_4 & $i(all_74_4)) % 232.60/39.58 | | | | | | | % 232.60/39.58 | | | | | | | BETA: splitting (971) gives: % 232.60/39.58 | | | | | | | % 232.60/39.58 | | | | | | | Case 1: % 232.60/39.58 | | | | | | | | % 232.60/39.58 | | | | | | | | (972) ~ leq(n2, all_74_20) % 232.60/39.58 | | | | | | | | % 232.60/39.58 | | | | | | | | REDUCE: (134), (972) imply: % 232.60/39.58 | | | | | | | | (973) ~ leq(n2, n2) % 232.60/39.58 | | | | | | | | % 232.60/39.58 | | | | | | | | PRED_UNIFY: (966), (973) imply: % 232.60/39.58 | | | | | | | | (974) $false % 232.60/39.58 | | | | | | | | % 232.60/39.58 | | | | | | | | CLOSE: (974) is inconsistent. % 232.60/39.58 | | | | | | | | % 232.60/39.58 | | | | | | | Case 2: % 232.60/39.58 | | | | | | | | % 232.60/39.58 | | | | | | | | (975) a_select3(r_ds1_filter, n2, n0) = all_74_4 & % 232.60/39.58 | | | | | | | | $i(all_74_4) % 232.60/39.58 | | | | | | | | % 232.60/39.58 | | | | | | | | ALPHA: (975) implies: % 232.60/39.58 | | | | | | | | (976) a_select3(r_ds1_filter, n2, n0) = all_74_4 % 232.60/39.58 | | | | | | | | % 232.60/39.58 | | | | | | | | GROUND_INST: instantiating (17) with all_74_5, all_74_4, n0, n2, % 232.60/39.58 | | | | | | | | r_ds1_filter, simplifying with (964), (976) gives: % 232.60/39.58 | | | | | | | | (977) all_74_4 = all_74_5 % 232.60/39.58 | | | | | | | | % 232.60/39.58 | | | | | | | | REDUCE: (837), (977) imply: % 232.60/39.58 | | | | | | | | (978) $false % 232.60/39.58 | | | | | | | | % 232.60/39.58 | | | | | | | | CLOSE: (978) is inconsistent. % 232.60/39.58 | | | | | | | | % 232.60/39.58 | | | | | | | End of split % 232.60/39.58 | | | | | | | % 232.60/39.58 | | | | | | End of split % 232.60/39.58 | | | | | | % 232.60/39.58 | | | | | End of split % 232.60/39.58 | | | | | % 232.60/39.58 | | | | End of split % 232.60/39.58 | | | | % 232.60/39.58 | | | Case 2: % 232.60/39.58 | | | | % 232.60/39.58 | | | | (979) all_74_7 = n0 % 232.60/39.58 | | | | (980) ~ gt(all_74_7, n0) % 232.60/39.58 | | | | % 232.60/39.58 | | | | REDUCE: (843), (979) imply: % 232.60/39.58 | | | | (981) a_select3(r_ds1_filter, all_74_6, n0) = all_74_4 % 232.60/39.58 | | | | % 232.60/39.58 | | | | REDUCE: (842), (979) imply: % 232.60/39.58 | | | | (982) a_select3(r_ds1_filter, n0, all_74_6) = all_74_5 % 232.60/39.58 | | | | % 232.60/39.58 | | | | REDUCE: (845), (979) imply: % 232.60/39.58 | | | | (983) leq(n0, n2) % 232.60/39.58 | | | | % 232.60/39.58 | | | | REDUCE: (838), (979) imply: % 232.60/39.58 | | | | (984) leq(n0, n0) % 232.60/39.58 | | | | % 232.60/39.58 | | | | REDUCE: (979), (980) imply: % 232.60/39.58 | | | | (985) ~ gt(n0, n0) % 232.60/39.58 | | | | % 232.60/39.58 | | | | BETA: splitting (847) gives: % 232.60/39.58 | | | | % 232.60/39.58 | | | | Case 1: % 232.60/39.58 | | | | | % 232.60/39.58 | | | | | (986) gt(all_74_6, n0) % 232.60/39.58 | | | | | % 232.60/39.58 | | | | | BETA: splitting (851) gives: % 232.60/39.58 | | | | | % 232.60/39.58 | | | | | Case 1: % 232.60/39.58 | | | | | | % 232.60/39.58 | | | | | | (987) gt(n2, all_74_6) % 232.60/39.58 | | | | | | % 232.60/39.59 | | | | | | GROUND_INST: instantiating (1) with all_74_6, n2, n1, simplifying % 232.60/39.59 | | | | | | with (56), (101), (123), (987) gives: % 232.60/39.59 | | | | | | (988) leq(all_74_6, n1) % 232.60/39.59 | | | | | | % 232.60/39.59 | | | | | | GROUND_INST: instantiating (4) with all_74_6, simplifying with (56), % 232.60/39.59 | | | | | | (839), (988) gives: % 232.60/39.59 | | | | | | (989) all_74_6 = n1 | all_74_6 = n0 % 232.60/39.59 | | | | | | % 232.60/39.59 | | | | | | BETA: splitting (850) gives: % 232.60/39.59 | | | | | | % 232.60/39.59 | | | | | | Case 1: % 232.60/39.59 | | | | | | | % 232.60/39.59 | | | | | | | (990) all_74_6 = n0 % 232.60/39.59 | | | | | | | % 232.60/39.59 | | | | | | | REDUCE: (986), (990) imply: % 232.60/39.59 | | | | | | | (991) gt(n0, n0) % 232.60/39.59 | | | | | | | % 232.60/39.59 | | | | | | | PRED_UNIFY: (985), (991) imply: % 232.60/39.59 | | | | | | | (992) $false % 232.60/39.59 | | | | | | | % 232.60/39.59 | | | | | | | CLOSE: (992) is inconsistent. % 232.60/39.59 | | | | | | | % 232.60/39.59 | | | | | | Case 2: % 232.60/39.59 | | | | | | | % 232.60/39.59 | | | | | | | (993) ~ (all_74_6 = n0) % 232.60/39.59 | | | | | | | % 232.60/39.59 | | | | | | | BETA: splitting (989) gives: % 232.60/39.59 | | | | | | | % 232.60/39.59 | | | | | | | Case 1: % 232.60/39.59 | | | | | | | | % 232.60/39.59 | | | | | | | | (994) all_74_6 = n0 % 232.60/39.59 | | | | | | | | % 232.60/39.59 | | | | | | | | REDUCE: (993), (994) imply: % 232.60/39.59 | | | | | | | | (995) $false % 232.60/39.59 | | | | | | | | % 232.60/39.59 | | | | | | | | CLOSE: (995) is inconsistent. % 232.60/39.59 | | | | | | | | % 232.60/39.59 | | | | | | | Case 2: % 232.60/39.59 | | | | | | | | % 232.60/39.59 | | | | | | | | (996) all_74_6 = n1 % 232.60/39.59 | | | | | | | | % 232.60/39.59 | | | | | | | | REDUCE: (981), (996) imply: % 232.60/39.59 | | | | | | | | (997) a_select3(r_ds1_filter, n1, n0) = all_74_4 % 232.60/39.59 | | | | | | | | % 232.60/39.59 | | | | | | | | REDUCE: (982), (996) imply: % 232.60/39.59 | | | | | | | | (998) a_select3(r_ds1_filter, n0, n1) = all_74_5 % 232.60/39.59 | | | | | | | | % 232.60/39.59 | | | | | | | | REDUCE: (844), (996) imply: % 232.60/39.59 | | | | | | | | (999) leq(n1, n2) % 232.60/39.59 | | | | | | | | % 232.60/39.59 | | | | | | | | REDUCE: (839), (996) imply: % 232.60/39.59 | | | | | | | | (1000) leq(n0, n1) % 232.60/39.59 | | | | | | | | % 232.60/39.59 | | | | | | | | GROUND_INST: instantiating (63) with n0, n1, all_74_5, % 232.60/39.59 | | | | | | | | simplifying with (12), (85), (984), (998), (1000) % 232.60/39.59 | | | | | | | | gives: % 232.60/39.59 | | | | | | | | (1001) ~ leq(n1, all_74_20) | ~ leq(n0, all_74_20) | % 232.60/39.59 | | | | | | | | (a_select3(r_ds1_filter, n1, n0) = all_74_5 & % 232.60/39.59 | | | | | | | | $i(all_74_5)) % 232.60/39.59 | | | | | | | | % 232.60/39.59 | | | | | | | | BETA: splitting (1001) gives: % 232.60/39.59 | | | | | | | | % 232.60/39.59 | | | | | | | | Case 1: % 232.60/39.59 | | | | | | | | | % 232.60/39.59 | | | | | | | | | (1002) ~ leq(n0, all_74_20) % 232.60/39.59 | | | | | | | | | % 232.60/39.59 | | | | | | | | | REDUCE: (134), (1002) imply: % 232.60/39.59 | | | | | | | | | (1003) ~ leq(n0, n2) % 232.60/39.59 | | | | | | | | | % 232.60/39.59 | | | | | | | | | PRED_UNIFY: (983), (1003) imply: % 232.60/39.59 | | | | | | | | | (1004) $false % 232.60/39.59 | | | | | | | | | % 232.60/39.59 | | | | | | | | | CLOSE: (1004) is inconsistent. % 232.60/39.59 | | | | | | | | | % 232.60/39.59 | | | | | | | | Case 2: % 232.60/39.59 | | | | | | | | | % 232.60/39.59 | | | | | | | | | (1005) ~ leq(n1, all_74_20) | (a_select3(r_ds1_filter, n1, % 232.60/39.59 | | | | | | | | | n0) = all_74_5 & $i(all_74_5)) % 232.60/39.59 | | | | | | | | | % 232.60/39.59 | | | | | | | | | BETA: splitting (1005) gives: % 232.60/39.59 | | | | | | | | | % 232.60/39.59 | | | | | | | | | Case 1: % 232.60/39.59 | | | | | | | | | | % 232.60/39.59 | | | | | | | | | | (1006) ~ leq(n1, all_74_20) % 232.60/39.59 | | | | | | | | | | % 232.60/39.59 | | | | | | | | | | REDUCE: (134), (1006) imply: % 232.60/39.59 | | | | | | | | | | (1007) ~ leq(n1, n2) % 232.60/39.59 | | | | | | | | | | % 232.60/39.59 | | | | | | | | | | PRED_UNIFY: (999), (1007) imply: % 232.60/39.59 | | | | | | | | | | (1008) $false % 232.60/39.59 | | | | | | | | | | % 232.60/39.59 | | | | | | | | | | CLOSE: (1008) is inconsistent. % 232.60/39.59 | | | | | | | | | | % 232.60/39.59 | | | | | | | | | Case 2: % 232.60/39.59 | | | | | | | | | | % 232.60/39.59 | | | | | | | | | | (1009) a_select3(r_ds1_filter, n1, n0) = all_74_5 & % 232.60/39.59 | | | | | | | | | | $i(all_74_5) % 232.60/39.59 | | | | | | | | | | % 232.60/39.59 | | | | | | | | | | ALPHA: (1009) implies: % 232.60/39.59 | | | | | | | | | | (1010) a_select3(r_ds1_filter, n1, n0) = all_74_5 % 232.60/39.59 | | | | | | | | | | % 232.60/39.59 | | | | | | | | | | REF_CLOSE: (17), (837), (997), (1010) are inconsistent by % 232.60/39.59 | | | | | | | | | | sub-proof #41. % 232.60/39.59 | | | | | | | | | | % 232.60/39.59 | | | | | | | | | End of split % 232.60/39.59 | | | | | | | | | % 232.60/39.59 | | | | | | | | End of split % 232.60/39.59 | | | | | | | | % 232.60/39.59 | | | | | | | End of split % 232.60/39.59 | | | | | | | % 232.60/39.59 | | | | | | End of split % 232.60/39.59 | | | | | | % 232.60/39.59 | | | | | Case 2: % 232.60/39.59 | | | | | | % 232.60/39.59 | | | | | | (1011) all_74_6 = n2 % 232.60/39.59 | | | | | | % 232.60/39.59 | | | | | | REDUCE: (981), (1011) imply: % 232.60/39.59 | | | | | | (1012) a_select3(r_ds1_filter, n2, n0) = all_74_4 % 232.60/39.59 | | | | | | % 232.60/39.59 | | | | | | REDUCE: (982), (1011) imply: % 232.60/39.59 | | | | | | (1013) a_select3(r_ds1_filter, n0, n2) = all_74_5 % 232.60/39.59 | | | | | | % 232.60/39.59 | | | | | | REDUCE: (844), (1011) imply: % 232.60/39.59 | | | | | | (1014) leq(n2, n2) % 232.60/39.59 | | | | | | % 232.60/39.59 | | | | | | GROUND_INST: instantiating (63) with n0, n2, all_74_5, simplifying % 232.60/39.59 | | | | | | with (12), (101), (983), (984), (1013) gives: % 232.60/39.59 | | | | | | (1015) ~ leq(n2, all_74_20) | ~ leq(n0, all_74_20) | % 232.60/39.59 | | | | | | (a_select3(r_ds1_filter, n2, n0) = all_74_5 & % 232.60/39.59 | | | | | | $i(all_74_5)) % 232.60/39.59 | | | | | | % 232.60/39.59 | | | | | | BETA: splitting (1015) gives: % 232.60/39.59 | | | | | | % 232.60/39.59 | | | | | | Case 1: % 232.60/39.59 | | | | | | | % 232.60/39.59 | | | | | | | (1016) ~ leq(n0, all_74_20) % 232.60/39.59 | | | | | | | % 232.60/39.59 | | | | | | | REDUCE: (134), (1016) imply: % 232.60/39.59 | | | | | | | (1017) ~ leq(n0, n2) % 232.60/39.59 | | | | | | | % 232.60/39.59 | | | | | | | PRED_UNIFY: (983), (1017) imply: % 232.60/39.59 | | | | | | | (1018) $false % 232.60/39.59 | | | | | | | % 232.60/39.59 | | | | | | | CLOSE: (1018) is inconsistent. % 232.60/39.59 | | | | | | | % 232.60/39.59 | | | | | | Case 2: % 232.60/39.59 | | | | | | | % 232.60/39.59 | | | | | | | (1019) ~ leq(n2, all_74_20) | (a_select3(r_ds1_filter, n2, n0) % 232.60/39.59 | | | | | | | = all_74_5 & $i(all_74_5)) % 232.60/39.59 | | | | | | | % 232.60/39.59 | | | | | | | BETA: splitting (1019) gives: % 232.60/39.59 | | | | | | | % 232.60/39.59 | | | | | | | Case 1: % 232.60/39.59 | | | | | | | | % 232.60/39.59 | | | | | | | | (1020) ~ leq(n2, all_74_20) % 232.60/39.59 | | | | | | | | % 232.60/39.59 | | | | | | | | REDUCE: (134), (1020) imply: % 232.60/39.59 | | | | | | | | (1021) ~ leq(n2, n2) % 232.60/39.59 | | | | | | | | % 232.60/39.59 | | | | | | | | PRED_UNIFY: (1014), (1021) imply: % 232.60/39.59 | | | | | | | | (1022) $false % 232.60/39.59 | | | | | | | | % 232.60/39.59 | | | | | | | | CLOSE: (1022) is inconsistent. % 232.60/39.59 | | | | | | | | % 232.60/39.59 | | | | | | | Case 2: % 232.60/39.59 | | | | | | | | % 232.60/39.59 | | | | | | | | (1023) a_select3(r_ds1_filter, n2, n0) = all_74_5 & % 232.60/39.59 | | | | | | | | $i(all_74_5) % 232.60/39.59 | | | | | | | | % 232.60/39.59 | | | | | | | | ALPHA: (1023) implies: % 232.60/39.59 | | | | | | | | (1024) a_select3(r_ds1_filter, n2, n0) = all_74_5 % 232.60/39.59 | | | | | | | | % 232.60/39.59 | | | | | | | | GROUND_INST: instantiating (17) with all_74_5, all_74_4, n0, n2, % 232.60/39.59 | | | | | | | | r_ds1_filter, simplifying with (1012), (1024) % 232.60/39.59 | | | | | | | | gives: % 232.60/39.59 | | | | | | | | (1025) all_74_4 = all_74_5 % 232.60/39.59 | | | | | | | | % 232.60/39.59 | | | | | | | | REDUCE: (837), (1025) imply: % 232.60/39.59 | | | | | | | | (1026) $false % 232.60/39.59 | | | | | | | | % 232.60/39.59 | | | | | | | | CLOSE: (1026) is inconsistent. % 232.60/39.59 | | | | | | | | % 232.60/39.59 | | | | | | | End of split % 232.60/39.59 | | | | | | | % 232.60/39.59 | | | | | | End of split % 232.60/39.59 | | | | | | % 232.60/39.59 | | | | | End of split % 232.60/39.59 | | | | | % 232.60/39.59 | | | | Case 2: % 232.60/39.59 | | | | | % 232.60/39.59 | | | | | (1027) all_74_6 = n0 % 232.60/39.59 | | | | | % 232.60/39.59 | | | | | REDUCE: (981), (1027) imply: % 232.60/39.59 | | | | | (1028) a_select3(r_ds1_filter, n0, n0) = all_74_4 % 232.60/39.59 | | | | | % 232.60/39.59 | | | | | REDUCE: (982), (1027) imply: % 232.60/39.59 | | | | | (1029) a_select3(r_ds1_filter, n0, n0) = all_74_5 % 232.60/39.59 | | | | | % 232.60/39.59 | | | | | GROUND_INST: instantiating (17) with all_74_5, all_74_4, n0, n0, % 232.60/39.59 | | | | | r_ds1_filter, simplifying with (1028), (1029) gives: % 232.60/39.59 | | | | | (1030) all_74_4 = all_74_5 % 232.60/39.59 | | | | | % 232.60/39.59 | | | | | REDUCE: (837), (1030) imply: % 232.60/39.59 | | | | | (1031) $false % 232.60/39.59 | | | | | % 232.60/39.59 | | | | | CLOSE: (1031) is inconsistent. % 232.60/39.59 | | | | | % 232.60/39.59 | | | | End of split % 232.60/39.59 | | | | % 232.60/39.59 | | | End of split % 232.60/39.59 | | | % 232.60/39.59 | | End of split % 232.60/39.59 | | % 232.60/39.59 | Case 2: % 232.60/39.59 | | % 232.60/39.59 | | (1032) ( ~ (all_74_8 = all_74_9) & a_select3(pminus_ds1_filter, % 232.60/39.59 | | all_74_10, all_74_11) = all_74_8 & % 232.60/39.59 | | a_select3(pminus_ds1_filter, all_74_11, all_74_10) = all_74_9 & % 232.60/39.59 | | $i(all_74_8) & $i(all_74_9) & leq(all_74_10, all_74_21) & % 232.60/39.59 | | leq(all_74_11, all_74_21) & leq(n0, all_74_10) & leq(n0, % 232.60/39.59 | | all_74_11)) | ( ~ (all_74_12 = all_74_13) & % 232.60/39.59 | | a_select3(pminus_ds1_filter, all_74_14, all_74_15) = all_74_12 & % 232.60/39.59 | | a_select3(pminus_ds1_filter, all_74_15, all_74_14) = all_74_13 & % 232.60/39.59 | | $i(all_74_12) & $i(all_74_13) & leq(all_74_14, all_74_21) & % 232.60/39.59 | | leq(all_74_15, all_74_21) & leq(n0, all_74_14) & leq(n0, % 232.60/39.59 | | all_74_15)) | ( ~ (all_74_16 = all_74_17) & % 232.60/39.59 | | a_select3(id_ds1_filter, all_74_18, all_74_19) = all_74_16 & % 232.60/39.59 | | a_select3(id_ds1_filter, all_74_19, all_74_18) = all_74_17 & % 232.60/39.59 | | $i(all_74_16) & $i(all_74_17) & leq(all_74_18, all_74_21) & % 232.60/39.59 | | leq(all_74_19, all_74_21) & leq(n0, all_74_18) & leq(n0, % 232.60/39.59 | | all_74_19)) % 232.60/39.59 | | % 232.60/39.59 | | BETA: splitting (1032) gives: % 232.60/39.59 | | % 232.60/39.59 | | Case 1: % 232.60/39.59 | | | % 232.60/39.59 | | | (1033) ~ (all_74_8 = all_74_9) & a_select3(pminus_ds1_filter, % 232.60/39.59 | | | all_74_10, all_74_11) = all_74_8 & % 232.60/39.59 | | | a_select3(pminus_ds1_filter, all_74_11, all_74_10) = all_74_9 & % 232.60/39.59 | | | $i(all_74_8) & $i(all_74_9) & leq(all_74_10, all_74_21) & % 232.60/39.59 | | | leq(all_74_11, all_74_21) & leq(n0, all_74_10) & leq(n0, % 232.60/39.59 | | | all_74_11) % 232.60/39.59 | | | % 232.60/39.59 | | | ALPHA: (1033) implies: % 232.60/39.59 | | | (1034) ~ (all_74_8 = all_74_9) % 232.60/39.59 | | | (1035) leq(n0, all_74_11) % 232.60/39.59 | | | (1036) leq(n0, all_74_10) % 232.60/39.59 | | | (1037) leq(all_74_11, all_74_21) % 232.60/39.59 | | | (1038) leq(all_74_10, all_74_21) % 232.60/39.59 | | | (1039) a_select3(pminus_ds1_filter, all_74_11, all_74_10) = all_74_9 % 232.60/39.59 | | | (1040) a_select3(pminus_ds1_filter, all_74_10, all_74_11) = all_74_8 % 232.60/39.59 | | | % 232.60/39.59 | | | REDUCE: (135), (1038) imply: % 232.60/39.59 | | | (1041) leq(all_74_10, n5) % 232.60/39.59 | | | % 232.60/39.59 | | | REDUCE: (135), (1037) imply: % 232.60/39.59 | | | (1042) leq(all_74_11, n5) % 232.60/39.59 | | | % 232.60/39.59 | | | GROUND_INST: instantiating (leq_gt2) with n0, all_74_11, simplifying with % 232.60/39.59 | | | (12), (53), (1035) gives: % 232.60/39.59 | | | (1043) all_74_11 = n0 | gt(all_74_11, n0) % 232.60/39.59 | | | % 232.60/39.59 | | | GROUND_INST: instantiating (leq_gt2) with n0, all_74_10, simplifying with % 232.60/39.59 | | | (12), (54), (1036) gives: % 232.60/39.59 | | | (1044) all_74_10 = n0 | gt(all_74_10, n0) % 232.60/39.59 | | | % 232.60/39.59 | | | GROUND_INST: instantiating (3) with all_74_11, simplifying with (53), % 232.60/39.59 | | | (1035), (1042) gives: % 232.60/39.59 | | | (1045) all_74_11 = n5 | all_74_11 = n4 | all_74_11 = n3 | all_74_11 = % 232.60/39.59 | | | n2 | all_74_11 = n1 | all_74_11 = n0 % 232.60/39.59 | | | % 232.60/39.59 | | | GROUND_INST: instantiating (leq_gt2) with all_74_11, n5, simplifying with % 232.60/39.59 | | | (53), (122), (1042) gives: % 232.60/39.59 | | | (1046) all_74_11 = n5 | gt(n5, all_74_11) % 232.60/39.59 | | | % 232.60/39.59 | | | GROUND_INST: instantiating (3) with all_74_10, simplifying with (54), % 232.60/39.59 | | | (1036), (1041) gives: % 232.60/39.60 | | | (1047) all_74_10 = n5 | all_74_10 = n4 | all_74_10 = n3 | all_74_10 = % 232.60/39.60 | | | n2 | all_74_10 = n1 | all_74_10 = n0 % 232.60/39.60 | | | % 232.60/39.60 | | | GROUND_INST: instantiating (leq_gt2) with all_74_10, n5, simplifying with % 232.60/39.60 | | | (54), (122), (1041) gives: % 232.60/39.60 | | | (1048) all_74_10 = n5 | gt(n5, all_74_10) % 232.60/39.60 | | | % 232.60/39.60 | | | BETA: splitting (1044) gives: % 232.60/39.60 | | | % 232.60/39.60 | | | Case 1: % 232.60/39.60 | | | | % 232.60/39.60 | | | | (1049) gt(all_74_10, n0) % 232.60/39.60 | | | | % 232.60/39.60 | | | | BETA: splitting (1043) gives: % 232.60/39.60 | | | | % 232.60/39.60 | | | | Case 1: % 232.60/39.60 | | | | | % 232.60/39.60 | | | | | (1050) gt(all_74_11, n0) % 232.60/39.60 | | | | | % 232.60/39.60 | | | | | BETA: splitting (1046) gives: % 232.60/39.60 | | | | | % 232.60/39.60 | | | | | Case 1: % 232.60/39.60 | | | | | | % 232.60/39.60 | | | | | | (1051) gt(n5, all_74_11) % 232.60/39.60 | | | | | | % 232.60/39.60 | | | | | | GROUND_INST: instantiating (1) with all_74_11, n5, n4, simplifying % 232.60/39.60 | | | | | | with (53), (122), (126), (1051) gives: % 232.60/39.60 | | | | | | (1052) leq(all_74_11, n4) % 232.60/39.60 | | | | | | % 232.60/39.60 | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_11, n4, simplifying % 232.60/39.60 | | | | | | with (53), (119), (1052) gives: % 232.60/39.60 | | | | | | (1053) all_74_11 = n4 | gt(n4, all_74_11) % 232.60/39.60 | | | | | | % 232.60/39.60 | | | | | | BETA: splitting (1048) gives: % 232.60/39.60 | | | | | | % 232.60/39.60 | | | | | | Case 1: % 232.60/39.60 | | | | | | | % 232.60/39.60 | | | | | | | (1054) gt(n5, all_74_10) % 232.60/39.60 | | | | | | | % 232.60/39.60 | | | | | | | GROUND_INST: instantiating (1) with all_74_10, n5, n4, simplifying % 232.60/39.60 | | | | | | | with (54), (122), (126), (1054) gives: % 232.60/39.60 | | | | | | | (1055) leq(all_74_10, n4) % 232.60/39.60 | | | | | | | % 232.60/39.60 | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_10, n4, % 232.60/39.60 | | | | | | | simplifying with (54), (119), (1055) gives: % 232.60/39.60 | | | | | | | (1056) all_74_10 = n4 | gt(n4, all_74_10) % 232.60/39.60 | | | | | | | % 232.60/39.60 | | | | | | | BETA: splitting (1047) gives: % 232.60/39.60 | | | | | | | % 232.60/39.60 | | | | | | | Case 1: % 232.60/39.60 | | | | | | | | % 232.60/39.60 | | | | | | | | (1057) all_74_10 = n0 % 232.60/39.60 | | | | | | | | % 232.60/39.60 | | | | | | | | REF_CLOSE: (54), (1049), (1057), (irreflexivity_gt) are % 232.60/39.60 | | | | | | | | inconsistent by sub-proof #40. % 232.60/39.60 | | | | | | | | % 232.60/39.60 | | | | | | | Case 2: % 232.60/39.60 | | | | | | | | % 232.60/39.60 | | | | | | | | (1058) ~ (all_74_10 = n0) % 232.60/39.60 | | | | | | | | % 232.60/39.60 | | | | | | | | BETA: splitting (1045) gives: % 232.60/39.60 | | | | | | | | % 232.60/39.60 | | | | | | | | Case 1: % 232.60/39.60 | | | | | | | | | % 232.60/39.60 | | | | | | | | | (1059) all_74_11 = n0 % 232.60/39.60 | | | | | | | | | % 232.60/39.60 | | | | | | | | | REF_CLOSE: (53), (1050), (1059), (irreflexivity_gt) are % 232.60/39.60 | | | | | | | | | inconsistent by sub-proof #39. % 232.60/39.60 | | | | | | | | | % 232.60/39.60 | | | | | | | | Case 2: % 232.60/39.60 | | | | | | | | | % 232.60/39.60 | | | | | | | | | (1060) ~ (all_74_11 = n0) % 232.60/39.60 | | | | | | | | | % 232.60/39.60 | | | | | | | | | BETA: splitting (1053) gives: % 232.60/39.60 | | | | | | | | | % 232.60/39.60 | | | | | | | | | Case 1: % 232.60/39.60 | | | | | | | | | | % 232.60/39.60 | | | | | | | | | | (1061) gt(n4, all_74_11) % 232.60/39.60 | | | | | | | | | | % 232.60/39.60 | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_11, n4, n3, % 232.60/39.60 | | | | | | | | | | simplifying with (53), (119), (125), (1061) gives: % 232.60/39.60 | | | | | | | | | | (1062) leq(all_74_11, n3) % 232.60/39.60 | | | | | | | | | | % 232.60/39.60 | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_11, n3, % 232.60/39.60 | | | | | | | | | | simplifying with (53), (112), (1062) gives: % 232.60/39.60 | | | | | | | | | | (1063) all_74_11 = n3 | gt(n3, all_74_11) % 232.60/39.60 | | | | | | | | | | % 232.60/39.60 | | | | | | | | | | BETA: splitting (1056) gives: % 232.60/39.60 | | | | | | | | | | % 232.60/39.60 | | | | | | | | | | Case 1: % 232.60/39.60 | | | | | | | | | | | % 232.60/39.60 | | | | | | | | | | | (1064) gt(n4, all_74_10) % 232.60/39.60 | | | | | | | | | | | % 232.60/39.60 | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_10, n4, n3, % 232.60/39.60 | | | | | | | | | | | simplifying with (54), (119), (125), (1064) gives: % 232.60/39.60 | | | | | | | | | | | (1065) leq(all_74_10, n3) % 232.60/39.60 | | | | | | | | | | | % 232.60/39.60 | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_10, n3, % 232.60/39.60 | | | | | | | | | | | simplifying with (54), (112), (1065) gives: % 232.60/39.60 | | | | | | | | | | | (1066) all_74_10 = n3 | gt(n3, all_74_10) % 232.60/39.60 | | | | | | | | | | | % 232.60/39.60 | | | | | | | | | | | BETA: splitting (1063) gives: % 232.60/39.60 | | | | | | | | | | | % 232.60/39.60 | | | | | | | | | | | Case 1: % 232.60/39.60 | | | | | | | | | | | | % 232.60/39.60 | | | | | | | | | | | | (1067) gt(n3, all_74_11) % 232.60/39.60 | | | | | | | | | | | | % 232.60/39.60 | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_11, n3, n2, % 232.60/39.60 | | | | | | | | | | | | simplifying with (53), (112), (124), (1067) gives: % 232.60/39.60 | | | | | | | | | | | | (1068) leq(all_74_11, n2) % 232.60/39.60 | | | | | | | | | | | | % 232.60/39.60 | | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_11, n2, % 232.60/39.60 | | | | | | | | | | | | simplifying with (53), (101), (1068) gives: % 232.60/39.60 | | | | | | | | | | | | (1069) all_74_11 = n2 | gt(n2, all_74_11) % 232.60/39.60 | | | | | | | | | | | | % 232.60/39.60 | | | | | | | | | | | | BETA: splitting (1066) gives: % 232.60/39.60 | | | | | | | | | | | | % 232.60/39.60 | | | | | | | | | | | | Case 1: % 232.60/39.60 | | | | | | | | | | | | | % 232.60/39.60 | | | | | | | | | | | | | (1070) gt(n3, all_74_10) % 232.60/39.60 | | | | | | | | | | | | | % 232.60/39.60 | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_10, n3, n2, % 232.60/39.60 | | | | | | | | | | | | | simplifying with (54), (112), (124), (1070) gives: % 232.60/39.60 | | | | | | | | | | | | | (1071) leq(all_74_10, n2) % 232.60/39.60 | | | | | | | | | | | | | % 232.60/39.60 | | | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_10, n2, % 232.60/39.60 | | | | | | | | | | | | | simplifying with (54), (101), (1071) gives: % 232.60/39.60 | | | | | | | | | | | | | (1072) all_74_10 = n2 | gt(n2, all_74_10) % 232.60/39.60 | | | | | | | | | | | | | % 232.60/39.60 | | | | | | | | | | | | | BETA: splitting (1069) gives: % 232.60/39.60 | | | | | | | | | | | | | % 232.60/39.60 | | | | | | | | | | | | | Case 1: % 232.60/39.60 | | | | | | | | | | | | | | % 232.60/39.60 | | | | | | | | | | | | | | (1073) gt(n2, all_74_11) % 232.60/39.60 | | | | | | | | | | | | | | % 232.60/39.60 | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_11, n2, n1, % 232.60/39.60 | | | | | | | | | | | | | | simplifying with (53), (101), (123), (1073) gives: % 232.60/39.60 | | | | | | | | | | | | | | (1074) leq(all_74_11, n1) % 232.60/39.60 | | | | | | | | | | | | | | % 232.60/39.60 | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_74_11, simplifying with % 232.60/39.60 | | | | | | | | | | | | | | (53), (1035), (1074) gives: % 232.60/39.60 | | | | | | | | | | | | | | (1075) all_74_11 = n1 | all_74_11 = n0 % 232.60/39.60 | | | | | | | | | | | | | | % 232.60/39.60 | | | | | | | | | | | | | | BETA: splitting (1075) gives: % 232.60/39.60 | | | | | | | | | | | | | | % 232.60/39.60 | | | | | | | | | | | | | | Case 1: % 232.60/39.60 | | | | | | | | | | | | | | | % 232.60/39.60 | | | | | | | | | | | | | | | (1076) all_74_11 = n0 % 232.60/39.60 | | | | | | | | | | | | | | | % 232.60/39.60 | | | | | | | | | | | | | | | REDUCE: (1060), (1076) imply: % 232.60/39.60 | | | | | | | | | | | | | | | (1077) $false % 232.60/39.60 | | | | | | | | | | | | | | | % 232.60/39.60 | | | | | | | | | | | | | | | CLOSE: (1077) is inconsistent. % 232.60/39.60 | | | | | | | | | | | | | | | % 232.60/39.60 | | | | | | | | | | | | | | Case 2: % 232.60/39.60 | | | | | | | | | | | | | | | % 232.60/39.60 | | | | | | | | | | | | | | | (1078) all_74_11 = n1 % 232.60/39.60 | | | | | | | | | | | | | | | % 232.60/39.60 | | | | | | | | | | | | | | | REDUCE: (1040), (1078) imply: % 232.60/39.60 | | | | | | | | | | | | | | | (1079) a_select3(pminus_ds1_filter, all_74_10, n1) = % 232.60/39.60 | | | | | | | | | | | | | | | all_74_8 % 232.60/39.60 | | | | | | | | | | | | | | | % 232.60/39.60 | | | | | | | | | | | | | | | REDUCE: (1039), (1078) imply: % 232.60/39.60 | | | | | | | | | | | | | | | (1080) a_select3(pminus_ds1_filter, n1, all_74_10) = % 232.60/39.60 | | | | | | | | | | | | | | | all_74_9 % 232.60/39.60 | | | | | | | | | | | | | | | % 232.60/39.60 | | | | | | | | | | | | | | | REDUCE: (1042), (1078) imply: % 232.60/39.60 | | | | | | | | | | | | | | | (1081) leq(n1, n5) % 232.60/39.60 | | | | | | | | | | | | | | | % 232.60/39.60 | | | | | | | | | | | | | | | REDUCE: (1035), (1078) imply: % 232.60/39.60 | | | | | | | | | | | | | | | (1082) leq(n0, n1) % 232.60/39.60 | | | | | | | | | | | | | | | % 232.60/39.60 | | | | | | | | | | | | | | | BETA: splitting (1072) gives: % 232.60/39.60 | | | | | | | | | | | | | | | % 232.60/39.60 | | | | | | | | | | | | | | | Case 1: % 232.60/39.60 | | | | | | | | | | | | | | | | % 232.60/39.60 | | | | | | | | | | | | | | | | (1083) gt(n2, all_74_10) % 232.60/39.60 | | | | | | | | | | | | | | | | % 232.60/39.60 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_10, n2, n1, % 232.60/39.60 | | | | | | | | | | | | | | | | simplifying with (54), (101), (123), (1083) gives: % 232.60/39.60 | | | | | | | | | | | | | | | | (1084) leq(all_74_10, n1) % 232.60/39.60 | | | | | | | | | | | | | | | | % 232.60/39.60 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_74_10, simplifying with % 232.60/39.60 | | | | | | | | | | | | | | | | (54), (1036), (1084) gives: % 232.60/39.60 | | | | | | | | | | | | | | | | (1085) all_74_10 = n1 | all_74_10 = n0 % 232.60/39.60 | | | | | | | | | | | | | | | | % 232.60/39.60 | | | | | | | | | | | | | | | | BETA: splitting (1085) gives: % 232.60/39.60 | | | | | | | | | | | | | | | | % 232.60/39.60 | | | | | | | | | | | | | | | | Case 1: % 232.60/39.60 | | | | | | | | | | | | | | | | | % 232.60/39.60 | | | | | | | | | | | | | | | | | (1086) all_74_10 = n0 % 232.60/39.60 | | | | | | | | | | | | | | | | | % 232.60/39.60 | | | | | | | | | | | | | | | | | REDUCE: (1058), (1086) imply: % 232.60/39.60 | | | | | | | | | | | | | | | | | (1087) $false % 232.60/39.60 | | | | | | | | | | | | | | | | | % 232.60/39.60 | | | | | | | | | | | | | | | | | CLOSE: (1087) is inconsistent. % 232.60/39.60 | | | | | | | | | | | | | | | | | % 232.60/39.60 | | | | | | | | | | | | | | | | Case 2: % 232.60/39.60 | | | | | | | | | | | | | | | | | % 232.60/39.60 | | | | | | | | | | | | | | | | | (1088) all_74_10 = n1 % 232.60/39.60 | | | | | | | | | | | | | | | | | % 232.60/39.60 | | | | | | | | | | | | | | | | | REDUCE: (1079), (1088) imply: % 232.60/39.60 | | | | | | | | | | | | | | | | | (1089) a_select3(pminus_ds1_filter, n1, n1) = all_74_8 % 232.60/39.60 | | | | | | | | | | | | | | | | | % 232.60/39.60 | | | | | | | | | | | | | | | | | REDUCE: (1080), (1088) imply: % 232.60/39.60 | | | | | | | | | | | | | | | | | (1090) a_select3(pminus_ds1_filter, n1, n1) = all_74_9 % 232.60/39.60 | | | | | | | | | | | | | | | | | % 232.60/39.60 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_74_9, all_74_8, n1, % 232.60/39.60 | | | | | | | | | | | | | | | | | n1, pminus_ds1_filter, simplifying with (1089), % 232.60/39.60 | | | | | | | | | | | | | | | | | (1090) gives: % 232.60/39.60 | | | | | | | | | | | | | | | | | (1091) all_74_8 = all_74_9 % 232.60/39.60 | | | | | | | | | | | | | | | | | % 232.60/39.60 | | | | | | | | | | | | | | | | | REDUCE: (1034), (1091) imply: % 232.60/39.60 | | | | | | | | | | | | | | | | | (1092) $false % 232.60/39.60 | | | | | | | | | | | | | | | | | % 232.60/39.60 | | | | | | | | | | | | | | | | | CLOSE: (1092) is inconsistent. % 232.60/39.60 | | | | | | | | | | | | | | | | | % 232.60/39.60 | | | | | | | | | | | | | | | | End of split % 232.60/39.60 | | | | | | | | | | | | | | | | % 232.60/39.60 | | | | | | | | | | | | | | | Case 2: % 232.60/39.60 | | | | | | | | | | | | | | | | % 232.60/39.60 | | | | | | | | | | | | | | | | (1093) all_74_10 = n2 % 232.60/39.60 | | | | | | | | | | | | | | | | % 232.60/39.60 | | | | | | | | | | | | | | | | REDUCE: (1079), (1093) imply: % 232.60/39.60 | | | | | | | | | | | | | | | | (1094) a_select3(pminus_ds1_filter, n2, n1) = all_74_8 % 232.60/39.60 | | | | | | | | | | | | | | | | % 232.60/39.60 | | | | | | | | | | | | | | | | REDUCE: (1080), (1093) imply: % 232.60/39.60 | | | | | | | | | | | | | | | | (1095) a_select3(pminus_ds1_filter, n1, n2) = all_74_9 % 232.60/39.60 | | | | | | | | | | | | | | | | % 232.60/39.60 | | | | | | | | | | | | | | | | REDUCE: (1041), (1093) imply: % 232.60/39.60 | | | | | | | | | | | | | | | | (1096) leq(n2, n5) % 232.60/39.60 | | | | | | | | | | | | | | | | % 232.60/39.60 | | | | | | | | | | | | | | | | REDUCE: (1036), (1093) imply: % 232.60/39.60 | | | | | | | | | | | | | | | | (1097) leq(n0, n2) % 232.60/39.60 | | | | | | | | | | | | | | | | % 232.60/39.60 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (64) with n1, n2, all_74_9, % 232.60/39.60 | | | | | | | | | | | | | | | | simplifying with (85), (101), (1082), (1095), % 232.60/39.60 | | | | | | | | | | | | | | | | (1097) gives: % 232.60/39.60 | | | | | | | | | | | | | | | | (1098) ~ leq(n2, all_74_21) | ~ leq(n1, all_74_21) | % 232.60/39.60 | | | | | | | | | | | | | | | | (a_select3(pminus_ds1_filter, n2, n1) = all_74_9 & % 232.60/39.60 | | | | | | | | | | | | | | | | $i(all_74_9)) % 232.60/39.60 | | | | | | | | | | | | | | | | % 232.60/39.60 | | | | | | | | | | | | | | | | BETA: splitting (1098) gives: % 232.60/39.60 | | | | | | | | | | | | | | | | % 232.60/39.60 | | | | | | | | | | | | | | | | Case 1: % 232.60/39.60 | | | | | | | | | | | | | | | | | % 232.60/39.60 | | | | | | | | | | | | | | | | | (1099) ~ leq(n2, all_74_21) % 232.60/39.60 | | | | | | | | | | | | | | | | | % 232.60/39.60 | | | | | | | | | | | | | | | | | REDUCE: (135), (1099) imply: % 232.60/39.60 | | | | | | | | | | | | | | | | | (1100) ~ leq(n2, n5) % 232.60/39.60 | | | | | | | | | | | | | | | | | % 232.60/39.60 | | | | | | | | | | | | | | | | | PRED_UNIFY: (1096), (1100) imply: % 232.60/39.60 | | | | | | | | | | | | | | | | | (1101) $false % 232.60/39.60 | | | | | | | | | | | | | | | | | % 232.60/39.60 | | | | | | | | | | | | | | | | | CLOSE: (1101) is inconsistent. % 232.60/39.60 | | | | | | | | | | | | | | | | | % 232.60/39.60 | | | | | | | | | | | | | | | | Case 2: % 232.60/39.60 | | | | | | | | | | | | | | | | | % 232.60/39.60 | | | | | | | | | | | | | | | | | (1102) ~ leq(n1, all_74_21) | % 232.60/39.60 | | | | | | | | | | | | | | | | | (a_select3(pminus_ds1_filter, n2, n1) = all_74_9 & % 232.60/39.60 | | | | | | | | | | | | | | | | | $i(all_74_9)) % 232.60/39.60 | | | | | | | | | | | | | | | | | % 232.60/39.60 | | | | | | | | | | | | | | | | | BETA: splitting (1102) gives: % 232.60/39.60 | | | | | | | | | | | | | | | | | % 232.60/39.60 | | | | | | | | | | | | | | | | | Case 1: % 232.60/39.60 | | | | | | | | | | | | | | | | | | % 232.60/39.60 | | | | | | | | | | | | | | | | | | (1103) ~ leq(n1, all_74_21) % 232.60/39.60 | | | | | | | | | | | | | | | | | | % 232.60/39.60 | | | | | | | | | | | | | | | | | | REDUCE: (135), (1103) imply: % 232.60/39.60 | | | | | | | | | | | | | | | | | | (1104) ~ leq(n1, n5) % 232.60/39.60 | | | | | | | | | | | | | | | | | | % 232.60/39.60 | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1081), (1104) imply: % 232.60/39.60 | | | | | | | | | | | | | | | | | | (1105) $false % 232.60/39.60 | | | | | | | | | | | | | | | | | | % 232.60/39.60 | | | | | | | | | | | | | | | | | | CLOSE: (1105) is inconsistent. % 232.60/39.60 | | | | | | | | | | | | | | | | | | % 232.60/39.60 | | | | | | | | | | | | | | | | | Case 2: % 232.60/39.60 | | | | | | | | | | | | | | | | | | % 232.60/39.60 | | | | | | | | | | | | | | | | | | (1106) a_select3(pminus_ds1_filter, n2, n1) = all_74_9 & % 232.60/39.60 | | | | | | | | | | | | | | | | | | $i(all_74_9) % 232.60/39.60 | | | | | | | | | | | | | | | | | | % 232.60/39.60 | | | | | | | | | | | | | | | | | | ALPHA: (1106) implies: % 232.60/39.60 | | | | | | | | | | | | | | | | | | (1107) a_select3(pminus_ds1_filter, n2, n1) = all_74_9 % 232.60/39.60 | | | | | | | | | | | | | | | | | | % 232.60/39.60 | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (1034), (1094), (1107) are inconsistent by % 232.60/39.60 | | | | | | | | | | | | | | | | | | sub-proof #38. % 232.60/39.60 | | | | | | | | | | | | | | | | | | % 232.60/39.60 | | | | | | | | | | | | | | | | | End of split % 232.60/39.60 | | | | | | | | | | | | | | | | | % 232.60/39.60 | | | | | | | | | | | | | | | | End of split % 232.60/39.60 | | | | | | | | | | | | | | | | % 232.60/39.60 | | | | | | | | | | | | | | | End of split % 232.60/39.60 | | | | | | | | | | | | | | | % 232.60/39.60 | | | | | | | | | | | | | | End of split % 232.60/39.60 | | | | | | | | | | | | | | % 232.60/39.60 | | | | | | | | | | | | | Case 2: % 232.60/39.60 | | | | | | | | | | | | | | % 232.60/39.60 | | | | | | | | | | | | | | (1108) all_74_11 = n2 % 232.60/39.60 | | | | | | | | | | | | | | % 232.60/39.60 | | | | | | | | | | | | | | REDUCE: (1040), (1108) imply: % 232.60/39.60 | | | | | | | | | | | | | | (1109) a_select3(pminus_ds1_filter, all_74_10, n2) = % 232.60/39.60 | | | | | | | | | | | | | | all_74_8 % 232.60/39.60 | | | | | | | | | | | | | | % 232.60/39.60 | | | | | | | | | | | | | | REDUCE: (1039), (1108) imply: % 232.60/39.60 | | | | | | | | | | | | | | (1110) a_select3(pminus_ds1_filter, n2, all_74_10) = % 232.60/39.60 | | | | | | | | | | | | | | all_74_9 % 232.60/39.60 | | | | | | | | | | | | | | % 232.60/39.60 | | | | | | | | | | | | | | REDUCE: (1042), (1108) imply: % 232.60/39.60 | | | | | | | | | | | | | | (1111) leq(n2, n5) % 232.60/39.60 | | | | | | | | | | | | | | % 232.60/39.60 | | | | | | | | | | | | | | REDUCE: (1035), (1108) imply: % 232.60/39.60 | | | | | | | | | | | | | | (1112) leq(n0, n2) % 232.60/39.60 | | | | | | | | | | | | | | % 232.60/39.60 | | | | | | | | | | | | | | BETA: splitting (1072) gives: % 232.60/39.60 | | | | | | | | | | | | | | % 232.60/39.60 | | | | | | | | | | | | | | Case 1: % 232.60/39.60 | | | | | | | | | | | | | | | % 232.60/39.60 | | | | | | | | | | | | | | | (1113) gt(n2, all_74_10) % 232.60/39.60 | | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_10, n2, n1, % 232.60/39.61 | | | | | | | | | | | | | | | simplifying with (54), (101), (123), (1113) gives: % 232.60/39.61 | | | | | | | | | | | | | | | (1114) leq(all_74_10, n1) % 232.60/39.61 | | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_74_10, simplifying with % 232.60/39.61 | | | | | | | | | | | | | | | (54), (1036), (1114) gives: % 232.60/39.61 | | | | | | | | | | | | | | | (1115) all_74_10 = n1 | all_74_10 = n0 % 232.60/39.61 | | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | | BETA: splitting (1115) gives: % 232.60/39.61 | | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | | Case 1: % 232.60/39.61 | | | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | | | (1116) all_74_10 = n0 % 232.60/39.61 | | | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | | | REDUCE: (1058), (1116) imply: % 232.60/39.61 | | | | | | | | | | | | | | | | (1117) $false % 232.60/39.61 | | | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | | | CLOSE: (1117) is inconsistent. % 232.60/39.61 | | | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | | Case 2: % 232.60/39.61 | | | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | | | (1118) all_74_10 = n1 % 232.60/39.61 | | | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | | | REDUCE: (1109), (1118) imply: % 232.60/39.61 | | | | | | | | | | | | | | | | (1119) a_select3(pminus_ds1_filter, n1, n2) = all_74_8 % 232.60/39.61 | | | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | | | REDUCE: (1110), (1118) imply: % 232.60/39.61 | | | | | | | | | | | | | | | | (1120) a_select3(pminus_ds1_filter, n2, n1) = all_74_9 % 232.60/39.61 | | | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | | | REDUCE: (1041), (1118) imply: % 232.60/39.61 | | | | | | | | | | | | | | | | (1121) leq(n1, n5) % 232.60/39.61 | | | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | | | REDUCE: (1036), (1118) imply: % 232.60/39.61 | | | | | | | | | | | | | | | | (1122) leq(n0, n1) % 232.60/39.61 | | | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (64) with n1, n2, all_74_8, % 232.60/39.61 | | | | | | | | | | | | | | | | simplifying with (85), (101), (1112), (1119), % 232.60/39.61 | | | | | | | | | | | | | | | | (1122) gives: % 232.60/39.61 | | | | | | | | | | | | | | | | (1123) ~ leq(n2, all_74_21) | ~ leq(n1, all_74_21) | % 232.60/39.61 | | | | | | | | | | | | | | | | (a_select3(pminus_ds1_filter, n2, n1) = all_74_8 & % 232.60/39.61 | | | | | | | | | | | | | | | | $i(all_74_8)) % 232.60/39.61 | | | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | | | BETA: splitting (1123) gives: % 232.60/39.61 | | | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | | | Case 1: % 232.60/39.61 | | | | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | | | | (1124) ~ leq(n2, all_74_21) % 232.60/39.61 | | | | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | | | | REDUCE: (135), (1124) imply: % 232.60/39.61 | | | | | | | | | | | | | | | | | (1125) ~ leq(n2, n5) % 232.60/39.61 | | | | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | | | | PRED_UNIFY: (1111), (1125) imply: % 232.60/39.61 | | | | | | | | | | | | | | | | | (1126) $false % 232.60/39.61 | | | | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | | | | CLOSE: (1126) is inconsistent. % 232.60/39.61 | | | | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | | | Case 2: % 232.60/39.61 | | | | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | | | | (1127) ~ leq(n1, all_74_21) | % 232.60/39.61 | | | | | | | | | | | | | | | | | (a_select3(pminus_ds1_filter, n2, n1) = all_74_8 & % 232.60/39.61 | | | | | | | | | | | | | | | | | $i(all_74_8)) % 232.60/39.61 | | | | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | | | | BETA: splitting (1127) gives: % 232.60/39.61 | | | | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | | | | Case 1: % 232.60/39.61 | | | | | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | | | | | (1128) ~ leq(n1, all_74_21) % 232.60/39.61 | | | | | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | | | | | REDUCE: (135), (1128) imply: % 232.60/39.61 | | | | | | | | | | | | | | | | | | (1129) ~ leq(n1, n5) % 232.60/39.61 | | | | | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1121), (1129) imply: % 232.60/39.61 | | | | | | | | | | | | | | | | | | (1130) $false % 232.60/39.61 | | | | | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | | | | | CLOSE: (1130) is inconsistent. % 232.60/39.61 | | | | | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | | | | Case 2: % 232.60/39.61 | | | | | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | | | | | (1131) a_select3(pminus_ds1_filter, n2, n1) = all_74_8 & % 232.60/39.61 | | | | | | | | | | | | | | | | | | $i(all_74_8) % 232.60/39.61 | | | | | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | | | | | ALPHA: (1131) implies: % 232.60/39.61 | | | | | | | | | | | | | | | | | | (1132) a_select3(pminus_ds1_filter, n2, n1) = all_74_8 % 232.60/39.61 | | | | | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (1034), (1120), (1132) are inconsistent by % 232.60/39.61 | | | | | | | | | | | | | | | | | | sub-proof #38. % 232.60/39.61 | | | | | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | | | | End of split % 232.60/39.61 | | | | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | | | End of split % 232.60/39.61 | | | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | | End of split % 232.60/39.61 | | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | Case 2: % 232.60/39.61 | | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | | (1133) all_74_10 = n2 % 232.60/39.61 | | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | | REDUCE: (1109), (1133) imply: % 232.60/39.61 | | | | | | | | | | | | | | | (1134) a_select3(pminus_ds1_filter, n2, n2) = all_74_8 % 232.60/39.61 | | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | | REDUCE: (1110), (1133) imply: % 232.60/39.61 | | | | | | | | | | | | | | | (1135) a_select3(pminus_ds1_filter, n2, n2) = all_74_9 % 232.60/39.61 | | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_74_9, all_74_8, n2, % 232.60/39.61 | | | | | | | | | | | | | | | n2, pminus_ds1_filter, simplifying with (1134), % 232.60/39.61 | | | | | | | | | | | | | | | (1135) gives: % 232.60/39.61 | | | | | | | | | | | | | | | (1136) all_74_8 = all_74_9 % 232.60/39.61 | | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | | REDUCE: (1034), (1136) imply: % 232.60/39.61 | | | | | | | | | | | | | | | (1137) $false % 232.60/39.61 | | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | | CLOSE: (1137) is inconsistent. % 232.60/39.61 | | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | End of split % 232.60/39.61 | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | End of split % 232.60/39.61 | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | Case 2: % 232.60/39.61 | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | (1138) all_74_10 = n3 % 232.60/39.61 | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | REDUCE: (1040), (1138) imply: % 232.60/39.61 | | | | | | | | | | | | | (1139) a_select3(pminus_ds1_filter, n3, all_74_11) = % 232.60/39.61 | | | | | | | | | | | | | all_74_8 % 232.60/39.61 | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | REDUCE: (1039), (1138) imply: % 232.60/39.61 | | | | | | | | | | | | | (1140) a_select3(pminus_ds1_filter, all_74_11, n3) = % 232.60/39.61 | | | | | | | | | | | | | all_74_9 % 232.60/39.61 | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | REDUCE: (1041), (1138) imply: % 232.60/39.61 | | | | | | | | | | | | | (1141) leq(n3, n5) % 232.60/39.61 | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | REDUCE: (1036), (1138) imply: % 232.60/39.61 | | | | | | | | | | | | | (1142) leq(n0, n3) % 232.60/39.61 | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | BETA: splitting (1069) gives: % 232.60/39.61 | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | Case 1: % 232.60/39.61 | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | (1143) gt(n2, all_74_11) % 232.60/39.61 | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_11, n2, n1, % 232.60/39.61 | | | | | | | | | | | | | | simplifying with (53), (101), (123), (1143) gives: % 232.60/39.61 | | | | | | | | | | | | | | (1144) leq(all_74_11, n1) % 232.60/39.61 | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_74_11, simplifying with % 232.60/39.61 | | | | | | | | | | | | | | (53), (1035), (1144) gives: % 232.60/39.61 | | | | | | | | | | | | | | (1145) all_74_11 = n1 | all_74_11 = n0 % 232.60/39.61 | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | BETA: splitting (1145) gives: % 232.60/39.61 | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | Case 1: % 232.60/39.61 | | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | | (1146) all_74_11 = n0 % 232.60/39.61 | | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | | REDUCE: (1060), (1146) imply: % 232.60/39.61 | | | | | | | | | | | | | | | (1147) $false % 232.60/39.61 | | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | | CLOSE: (1147) is inconsistent. % 232.60/39.61 | | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | Case 2: % 232.60/39.61 | | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | | (1148) all_74_11 = n1 % 232.60/39.61 | | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | | REDUCE: (1140), (1148) imply: % 232.60/39.61 | | | | | | | | | | | | | | | (1149) a_select3(pminus_ds1_filter, n1, n3) = all_74_9 % 232.60/39.61 | | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | | REDUCE: (1139), (1148) imply: % 232.60/39.61 | | | | | | | | | | | | | | | (1150) a_select3(pminus_ds1_filter, n3, n1) = all_74_8 % 232.60/39.61 | | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | | REDUCE: (1042), (1148) imply: % 232.60/39.61 | | | | | | | | | | | | | | | (1151) leq(n1, n5) % 232.60/39.61 | | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | | REDUCE: (1035), (1148) imply: % 232.60/39.61 | | | | | | | | | | | | | | | (1152) leq(n0, n1) % 232.60/39.61 | | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | | GROUND_INST: instantiating (64) with n1, n3, all_74_9, % 232.60/39.61 | | | | | | | | | | | | | | | simplifying with (85), (112), (1142), (1149), % 232.60/39.61 | | | | | | | | | | | | | | | (1152) gives: % 232.60/39.61 | | | | | | | | | | | | | | | (1153) ~ leq(n3, all_74_21) | ~ leq(n1, all_74_21) | % 232.60/39.61 | | | | | | | | | | | | | | | (a_select3(pminus_ds1_filter, n3, n1) = all_74_9 & % 232.60/39.61 | | | | | | | | | | | | | | | $i(all_74_9)) % 232.60/39.61 | | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | | BETA: splitting (1153) gives: % 232.60/39.61 | | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | | Case 1: % 232.60/39.61 | | | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | | | (1154) ~ leq(n3, all_74_21) % 232.60/39.61 | | | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | | | REDUCE: (135), (1154) imply: % 232.60/39.61 | | | | | | | | | | | | | | | | (1155) ~ leq(n3, n5) % 232.60/39.61 | | | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | | | PRED_UNIFY: (1141), (1155) imply: % 232.60/39.61 | | | | | | | | | | | | | | | | (1156) $false % 232.60/39.61 | | | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | | | CLOSE: (1156) is inconsistent. % 232.60/39.61 | | | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | | Case 2: % 232.60/39.61 | | | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | | | (1157) ~ leq(n1, all_74_21) | % 232.60/39.61 | | | | | | | | | | | | | | | | (a_select3(pminus_ds1_filter, n3, n1) = all_74_9 & % 232.60/39.61 | | | | | | | | | | | | | | | | $i(all_74_9)) % 232.60/39.61 | | | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | | | BETA: splitting (1157) gives: % 232.60/39.61 | | | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | | | Case 1: % 232.60/39.61 | | | | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | | | | (1158) ~ leq(n1, all_74_21) % 232.60/39.61 | | | | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | | | | REDUCE: (135), (1158) imply: % 232.60/39.61 | | | | | | | | | | | | | | | | | (1159) ~ leq(n1, n5) % 232.60/39.61 | | | | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | | | | PRED_UNIFY: (1151), (1159) imply: % 232.60/39.61 | | | | | | | | | | | | | | | | | (1160) $false % 232.60/39.61 | | | | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | | | | CLOSE: (1160) is inconsistent. % 232.60/39.61 | | | | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | | | Case 2: % 232.60/39.61 | | | | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | | | | (1161) a_select3(pminus_ds1_filter, n3, n1) = all_74_9 & % 232.60/39.61 | | | | | | | | | | | | | | | | | $i(all_74_9) % 232.60/39.61 | | | | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | | | | ALPHA: (1161) implies: % 232.60/39.61 | | | | | | | | | | | | | | | | | (1162) a_select3(pminus_ds1_filter, n3, n1) = all_74_9 % 232.60/39.61 | | | | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (1034), (1150), (1162) are inconsistent by % 232.60/39.61 | | | | | | | | | | | | | | | | | sub-proof #37. % 232.60/39.61 | | | | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | | | End of split % 232.60/39.61 | | | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | | End of split % 232.60/39.61 | | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | End of split % 232.60/39.61 | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | Case 2: % 232.60/39.61 | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | (1163) all_74_11 = n2 % 232.60/39.61 | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | REDUCE: (1140), (1163) imply: % 232.60/39.61 | | | | | | | | | | | | | | (1164) a_select3(pminus_ds1_filter, n2, n3) = all_74_9 % 232.60/39.61 | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | REDUCE: (1139), (1163) imply: % 232.60/39.61 | | | | | | | | | | | | | | (1165) a_select3(pminus_ds1_filter, n3, n2) = all_74_8 % 232.60/39.61 | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | REDUCE: (1042), (1163) imply: % 232.60/39.61 | | | | | | | | | | | | | | (1166) leq(n2, n5) % 232.60/39.61 | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | REDUCE: (1035), (1163) imply: % 232.60/39.61 | | | | | | | | | | | | | | (1167) leq(n0, n2) % 232.60/39.61 | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | GROUND_INST: instantiating (64) with n2, n3, all_74_9, % 232.60/39.61 | | | | | | | | | | | | | | simplifying with (101), (112), (1142), (1164), % 232.60/39.61 | | | | | | | | | | | | | | (1167) gives: % 232.60/39.61 | | | | | | | | | | | | | | (1168) ~ leq(n3, all_74_21) | ~ leq(n2, all_74_21) | % 232.60/39.61 | | | | | | | | | | | | | | (a_select3(pminus_ds1_filter, n3, n2) = all_74_9 & % 232.60/39.61 | | | | | | | | | | | | | | $i(all_74_9)) % 232.60/39.61 | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | BETA: splitting (1168) gives: % 232.60/39.61 | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | Case 1: % 232.60/39.61 | | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | | (1169) ~ leq(n3, all_74_21) % 232.60/39.61 | | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | | REDUCE: (135), (1169) imply: % 232.60/39.61 | | | | | | | | | | | | | | | (1170) ~ leq(n3, n5) % 232.60/39.61 | | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | | PRED_UNIFY: (1141), (1170) imply: % 232.60/39.61 | | | | | | | | | | | | | | | (1171) $false % 232.60/39.61 | | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | | CLOSE: (1171) is inconsistent. % 232.60/39.61 | | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | Case 2: % 232.60/39.61 | | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | | (1172) ~ leq(n2, all_74_21) | % 232.60/39.61 | | | | | | | | | | | | | | | (a_select3(pminus_ds1_filter, n3, n2) = all_74_9 & % 232.60/39.61 | | | | | | | | | | | | | | | $i(all_74_9)) % 232.60/39.61 | | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | | BETA: splitting (1172) gives: % 232.60/39.61 | | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | | Case 1: % 232.60/39.61 | | | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | | | (1173) ~ leq(n2, all_74_21) % 232.60/39.61 | | | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | | | REDUCE: (135), (1173) imply: % 232.60/39.61 | | | | | | | | | | | | | | | | (1174) ~ leq(n2, n5) % 232.60/39.61 | | | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | | | PRED_UNIFY: (1166), (1174) imply: % 232.60/39.61 | | | | | | | | | | | | | | | | (1175) $false % 232.60/39.61 | | | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | | | CLOSE: (1175) is inconsistent. % 232.60/39.61 | | | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | | Case 2: % 232.60/39.61 | | | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | | | (1176) a_select3(pminus_ds1_filter, n3, n2) = all_74_9 & % 232.60/39.61 | | | | | | | | | | | | | | | | $i(all_74_9) % 232.60/39.61 | | | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | | | ALPHA: (1176) implies: % 232.60/39.61 | | | | | | | | | | | | | | | | (1177) a_select3(pminus_ds1_filter, n3, n2) = all_74_9 % 232.60/39.61 | | | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | | | REF_CLOSE: (17), (1034), (1165), (1177) are inconsistent by % 232.60/39.61 | | | | | | | | | | | | | | | | sub-proof #36. % 232.60/39.61 | | | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | | End of split % 232.60/39.61 | | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | | End of split % 232.60/39.61 | | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | End of split % 232.60/39.61 | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | End of split % 232.60/39.61 | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | Case 2: % 232.60/39.61 | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | (1178) all_74_11 = n3 % 232.60/39.61 | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | REDUCE: (1040), (1178) imply: % 232.60/39.61 | | | | | | | | | | | | (1179) a_select3(pminus_ds1_filter, all_74_10, n3) = % 232.60/39.61 | | | | | | | | | | | | all_74_8 % 232.60/39.61 | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | REDUCE: (1039), (1178) imply: % 232.60/39.61 | | | | | | | | | | | | (1180) a_select3(pminus_ds1_filter, n3, all_74_10) = % 232.60/39.61 | | | | | | | | | | | | all_74_9 % 232.60/39.61 | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | REDUCE: (1042), (1178) imply: % 232.60/39.61 | | | | | | | | | | | | (1181) leq(n3, n5) % 232.60/39.61 | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | REDUCE: (1035), (1178) imply: % 232.60/39.61 | | | | | | | | | | | | (1182) leq(n0, n3) % 232.60/39.61 | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | BETA: splitting (1066) gives: % 232.60/39.61 | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | Case 1: % 232.60/39.61 | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | (1183) gt(n3, all_74_10) % 232.60/39.61 | | | | | | | | | | | | | % 232.60/39.61 | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_10, n3, n2, % 232.60/39.61 | | | | | | | | | | | | | simplifying with (54), (112), (124), (1183) gives: % 232.60/39.61 | | | | | | | | | | | | | (1184) leq(all_74_10, n2) % 232.60/39.61 | | | | | | | | | | | | | % 232.60/39.62 | | | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_10, n2, % 232.60/39.62 | | | | | | | | | | | | | simplifying with (54), (101), (1184) gives: % 232.60/39.62 | | | | | | | | | | | | | (1185) all_74_10 = n2 | gt(n2, all_74_10) % 232.60/39.62 | | | | | | | | | | | | | % 232.60/39.62 | | | | | | | | | | | | | BETA: splitting (1185) gives: % 232.60/39.62 | | | | | | | | | | | | | % 232.60/39.62 | | | | | | | | | | | | | Case 1: % 232.60/39.62 | | | | | | | | | | | | | | % 232.60/39.62 | | | | | | | | | | | | | | (1186) gt(n2, all_74_10) % 232.60/39.62 | | | | | | | | | | | | | | % 232.60/39.62 | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_10, n2, n1, % 232.60/39.62 | | | | | | | | | | | | | | simplifying with (54), (101), (123), (1186) gives: % 232.60/39.62 | | | | | | | | | | | | | | (1187) leq(all_74_10, n1) % 232.60/39.62 | | | | | | | | | | | | | | % 232.60/39.62 | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_74_10, simplifying with % 232.60/39.62 | | | | | | | | | | | | | | (54), (1036), (1187) gives: % 232.60/39.62 | | | | | | | | | | | | | | (1188) all_74_10 = n1 | all_74_10 = n0 % 232.60/39.62 | | | | | | | | | | | | | | % 232.60/39.62 | | | | | | | | | | | | | | BETA: splitting (1188) gives: % 232.60/39.62 | | | | | | | | | | | | | | % 232.60/39.62 | | | | | | | | | | | | | | Case 1: % 232.60/39.62 | | | | | | | | | | | | | | | % 232.60/39.62 | | | | | | | | | | | | | | | (1189) all_74_10 = n0 % 232.60/39.62 | | | | | | | | | | | | | | | % 232.60/39.62 | | | | | | | | | | | | | | | REDUCE: (1058), (1189) imply: % 232.60/39.62 | | | | | | | | | | | | | | | (1190) $false % 232.60/39.62 | | | | | | | | | | | | | | | % 232.60/39.62 | | | | | | | | | | | | | | | CLOSE: (1190) is inconsistent. % 232.60/39.62 | | | | | | | | | | | | | | | % 232.60/39.62 | | | | | | | | | | | | | | Case 2: % 232.60/39.62 | | | | | | | | | | | | | | | % 232.60/39.62 | | | | | | | | | | | | | | | (1191) all_74_10 = n1 % 232.60/39.62 | | | | | | | | | | | | | | | % 232.60/39.62 | | | | | | | | | | | | | | | REDUCE: (1179), (1191) imply: % 232.60/39.62 | | | | | | | | | | | | | | | (1192) a_select3(pminus_ds1_filter, n1, n3) = all_74_8 % 232.60/39.62 | | | | | | | | | | | | | | | % 232.60/39.62 | | | | | | | | | | | | | | | REDUCE: (1180), (1191) imply: % 232.60/39.62 | | | | | | | | | | | | | | | (1193) a_select3(pminus_ds1_filter, n3, n1) = all_74_9 % 232.60/39.62 | | | | | | | | | | | | | | | % 232.60/39.62 | | | | | | | | | | | | | | | REDUCE: (1041), (1191) imply: % 232.60/39.62 | | | | | | | | | | | | | | | (1194) leq(n1, n5) % 232.60/39.62 | | | | | | | | | | | | | | | % 232.60/39.62 | | | | | | | | | | | | | | | REDUCE: (1036), (1191) imply: % 232.60/39.62 | | | | | | | | | | | | | | | (1195) leq(n0, n1) % 232.60/39.62 | | | | | | | | | | | | | | | % 232.60/39.62 | | | | | | | | | | | | | | | GROUND_INST: instantiating (64) with n1, n3, all_74_8, % 232.60/39.62 | | | | | | | | | | | | | | | simplifying with (85), (112), (1182), (1192), % 232.60/39.62 | | | | | | | | | | | | | | | (1195) gives: % 232.60/39.62 | | | | | | | | | | | | | | | (1196) ~ leq(n3, all_74_21) | ~ leq(n1, all_74_21) | % 232.60/39.62 | | | | | | | | | | | | | | | (a_select3(pminus_ds1_filter, n3, n1) = all_74_8 & % 232.60/39.62 | | | | | | | | | | | | | | | $i(all_74_8)) % 232.60/39.62 | | | | | | | | | | | | | | | % 232.60/39.62 | | | | | | | | | | | | | | | BETA: splitting (1196) gives: % 232.60/39.62 | | | | | | | | | | | | | | | % 232.60/39.62 | | | | | | | | | | | | | | | Case 1: % 232.60/39.62 | | | | | | | | | | | | | | | | % 232.60/39.62 | | | | | | | | | | | | | | | | (1197) ~ leq(n3, all_74_21) % 232.60/39.62 | | | | | | | | | | | | | | | | % 232.60/39.62 | | | | | | | | | | | | | | | | REDUCE: (135), (1197) imply: % 232.60/39.62 | | | | | | | | | | | | | | | | (1198) ~ leq(n3, n5) % 232.60/39.62 | | | | | | | | | | | | | | | | % 232.60/39.62 | | | | | | | | | | | | | | | | PRED_UNIFY: (1181), (1198) imply: % 232.60/39.62 | | | | | | | | | | | | | | | | (1199) $false % 232.60/39.62 | | | | | | | | | | | | | | | | % 232.60/39.62 | | | | | | | | | | | | | | | | CLOSE: (1199) is inconsistent. % 232.60/39.62 | | | | | | | | | | | | | | | | % 232.60/39.62 | | | | | | | | | | | | | | | Case 2: % 232.60/39.62 | | | | | | | | | | | | | | | | % 232.60/39.62 | | | | | | | | | | | | | | | | (1200) ~ leq(n1, all_74_21) | % 232.60/39.62 | | | | | | | | | | | | | | | | (a_select3(pminus_ds1_filter, n3, n1) = all_74_8 & % 232.60/39.62 | | | | | | | | | | | | | | | | $i(all_74_8)) % 232.60/39.62 | | | | | | | | | | | | | | | | % 232.60/39.62 | | | | | | | | | | | | | | | | BETA: splitting (1200) gives: % 232.60/39.62 | | | | | | | | | | | | | | | | % 232.60/39.62 | | | | | | | | | | | | | | | | Case 1: % 232.60/39.62 | | | | | | | | | | | | | | | | | % 232.60/39.62 | | | | | | | | | | | | | | | | | (1201) ~ leq(n1, all_74_21) % 232.60/39.62 | | | | | | | | | | | | | | | | | % 232.60/39.62 | | | | | | | | | | | | | | | | | REDUCE: (135), (1201) imply: % 232.60/39.62 | | | | | | | | | | | | | | | | | (1202) ~ leq(n1, n5) % 232.60/39.62 | | | | | | | | | | | | | | | | | % 232.60/39.62 | | | | | | | | | | | | | | | | | PRED_UNIFY: (1194), (1202) imply: % 232.60/39.62 | | | | | | | | | | | | | | | | | (1203) $false % 232.60/39.62 | | | | | | | | | | | | | | | | | % 232.60/39.62 | | | | | | | | | | | | | | | | | CLOSE: (1203) is inconsistent. % 232.60/39.62 | | | | | | | | | | | | | | | | | % 232.60/39.62 | | | | | | | | | | | | | | | | Case 2: % 232.60/39.62 | | | | | | | | | | | | | | | | | % 232.60/39.62 | | | | | | | | | | | | | | | | | (1204) a_select3(pminus_ds1_filter, n3, n1) = all_74_8 & % 232.60/39.62 | | | | | | | | | | | | | | | | | $i(all_74_8) % 232.60/39.62 | | | | | | | | | | | | | | | | | % 232.60/39.62 | | | | | | | | | | | | | | | | | ALPHA: (1204) implies: % 232.60/39.62 | | | | | | | | | | | | | | | | | (1205) a_select3(pminus_ds1_filter, n3, n1) = all_74_8 % 232.60/39.62 | | | | | | | | | | | | | | | | | % 232.60/39.62 | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (1034), (1193), (1205) are inconsistent by % 232.60/39.62 | | | | | | | | | | | | | | | | | sub-proof #37. % 232.60/39.62 | | | | | | | | | | | | | | | | | % 232.60/39.62 | | | | | | | | | | | | | | | | End of split % 232.60/39.62 | | | | | | | | | | | | | | | | % 232.60/39.62 | | | | | | | | | | | | | | | End of split % 232.60/39.62 | | | | | | | | | | | | | | | % 232.60/39.62 | | | | | | | | | | | | | | End of split % 232.60/39.62 | | | | | | | | | | | | | | % 232.60/39.62 | | | | | | | | | | | | | Case 2: % 232.60/39.62 | | | | | | | | | | | | | | % 232.60/39.62 | | | | | | | | | | | | | | (1206) all_74_10 = n2 % 232.60/39.62 | | | | | | | | | | | | | | % 232.60/39.62 | | | | | | | | | | | | | | REDUCE: (1179), (1206) imply: % 232.60/39.62 | | | | | | | | | | | | | | (1207) a_select3(pminus_ds1_filter, n2, n3) = all_74_8 % 232.60/39.62 | | | | | | | | | | | | | | % 232.60/39.62 | | | | | | | | | | | | | | REDUCE: (1180), (1206) imply: % 232.60/39.62 | | | | | | | | | | | | | | (1208) a_select3(pminus_ds1_filter, n3, n2) = all_74_9 % 232.60/39.62 | | | | | | | | | | | | | | % 232.60/39.62 | | | | | | | | | | | | | | REDUCE: (1041), (1206) imply: % 232.60/39.62 | | | | | | | | | | | | | | (1209) leq(n2, n5) % 232.60/39.62 | | | | | | | | | | | | | | % 232.60/39.62 | | | | | | | | | | | | | | REDUCE: (1036), (1206) imply: % 232.60/39.62 | | | | | | | | | | | | | | (1210) leq(n0, n2) % 232.60/39.62 | | | | | | | | | | | | | | % 232.60/39.62 | | | | | | | | | | | | | | GROUND_INST: instantiating (64) with n2, n3, all_74_8, % 232.60/39.62 | | | | | | | | | | | | | | simplifying with (101), (112), (1182), (1207), % 232.60/39.62 | | | | | | | | | | | | | | (1210) gives: % 232.60/39.62 | | | | | | | | | | | | | | (1211) ~ leq(n3, all_74_21) | ~ leq(n2, all_74_21) | % 232.60/39.62 | | | | | | | | | | | | | | (a_select3(pminus_ds1_filter, n3, n2) = all_74_8 & % 232.60/39.62 | | | | | | | | | | | | | | $i(all_74_8)) % 232.60/39.62 | | | | | | | | | | | | | | % 232.60/39.62 | | | | | | | | | | | | | | BETA: splitting (1211) gives: % 232.60/39.62 | | | | | | | | | | | | | | % 232.60/39.62 | | | | | | | | | | | | | | Case 1: % 232.60/39.62 | | | | | | | | | | | | | | | % 232.60/39.62 | | | | | | | | | | | | | | | (1212) ~ leq(n3, all_74_21) % 232.60/39.62 | | | | | | | | | | | | | | | % 232.60/39.62 | | | | | | | | | | | | | | | REDUCE: (135), (1212) imply: % 232.60/39.62 | | | | | | | | | | | | | | | (1213) ~ leq(n3, n5) % 232.60/39.62 | | | | | | | | | | | | | | | % 232.60/39.62 | | | | | | | | | | | | | | | PRED_UNIFY: (1181), (1213) imply: % 232.60/39.62 | | | | | | | | | | | | | | | (1214) $false % 232.60/39.62 | | | | | | | | | | | | | | | % 232.60/39.62 | | | | | | | | | | | | | | | CLOSE: (1214) is inconsistent. % 232.60/39.62 | | | | | | | | | | | | | | | % 232.60/39.62 | | | | | | | | | | | | | | Case 2: % 232.60/39.62 | | | | | | | | | | | | | | | % 232.60/39.62 | | | | | | | | | | | | | | | (1215) ~ leq(n2, all_74_21) | % 232.60/39.62 | | | | | | | | | | | | | | | (a_select3(pminus_ds1_filter, n3, n2) = all_74_8 & % 232.60/39.62 | | | | | | | | | | | | | | | $i(all_74_8)) % 232.60/39.62 | | | | | | | | | | | | | | | % 232.60/39.62 | | | | | | | | | | | | | | | BETA: splitting (1215) gives: % 232.60/39.62 | | | | | | | | | | | | | | | % 232.60/39.62 | | | | | | | | | | | | | | | Case 1: % 232.60/39.62 | | | | | | | | | | | | | | | | % 232.60/39.62 | | | | | | | | | | | | | | | | (1216) ~ leq(n2, all_74_21) % 232.60/39.62 | | | | | | | | | | | | | | | | % 232.60/39.62 | | | | | | | | | | | | | | | | REDUCE: (135), (1216) imply: % 232.60/39.62 | | | | | | | | | | | | | | | | (1217) ~ leq(n2, n5) % 232.60/39.62 | | | | | | | | | | | | | | | | % 232.60/39.62 | | | | | | | | | | | | | | | | PRED_UNIFY: (1209), (1217) imply: % 232.60/39.62 | | | | | | | | | | | | | | | | (1218) $false % 232.60/39.62 | | | | | | | | | | | | | | | | % 232.60/39.62 | | | | | | | | | | | | | | | | CLOSE: (1218) is inconsistent. % 232.60/39.62 | | | | | | | | | | | | | | | | % 232.60/39.62 | | | | | | | | | | | | | | | Case 2: % 232.60/39.62 | | | | | | | | | | | | | | | | % 232.60/39.62 | | | | | | | | | | | | | | | | (1219) a_select3(pminus_ds1_filter, n3, n2) = all_74_8 & % 232.60/39.62 | | | | | | | | | | | | | | | | $i(all_74_8) % 232.60/39.62 | | | | | | | | | | | | | | | | % 232.60/39.62 | | | | | | | | | | | | | | | | ALPHA: (1219) implies: % 232.86/39.62 | | | | | | | | | | | | | | | | (1220) a_select3(pminus_ds1_filter, n3, n2) = all_74_8 % 232.86/39.62 | | | | | | | | | | | | | | | | % 232.86/39.62 | | | | | | | | | | | | | | | | REF_CLOSE: (17), (1034), (1208), (1220) are inconsistent by % 232.86/39.62 | | | | | | | | | | | | | | | | sub-proof #36. % 232.86/39.62 | | | | | | | | | | | | | | | | % 232.86/39.62 | | | | | | | | | | | | | | | End of split % 232.86/39.62 | | | | | | | | | | | | | | | % 232.86/39.62 | | | | | | | | | | | | | | End of split % 232.86/39.62 | | | | | | | | | | | | | | % 232.86/39.62 | | | | | | | | | | | | | End of split % 232.86/39.62 | | | | | | | | | | | | | % 232.86/39.62 | | | | | | | | | | | | Case 2: % 232.86/39.62 | | | | | | | | | | | | | % 232.86/39.62 | | | | | | | | | | | | | (1221) all_74_10 = n3 % 232.86/39.62 | | | | | | | | | | | | | % 232.86/39.62 | | | | | | | | | | | | | REDUCE: (1179), (1221) imply: % 232.86/39.62 | | | | | | | | | | | | | (1222) a_select3(pminus_ds1_filter, n3, n3) = all_74_8 % 232.86/39.62 | | | | | | | | | | | | | % 232.86/39.62 | | | | | | | | | | | | | REDUCE: (1180), (1221) imply: % 232.86/39.62 | | | | | | | | | | | | | (1223) a_select3(pminus_ds1_filter, n3, n3) = all_74_9 % 232.86/39.62 | | | | | | | | | | | | | % 232.86/39.62 | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_74_9, all_74_8, n3, % 232.86/39.62 | | | | | | | | | | | | | n3, pminus_ds1_filter, simplifying with (1222), % 232.86/39.62 | | | | | | | | | | | | | (1223) gives: % 232.86/39.62 | | | | | | | | | | | | | (1224) all_74_8 = all_74_9 % 232.86/39.62 | | | | | | | | | | | | | % 232.86/39.62 | | | | | | | | | | | | | REDUCE: (1034), (1224) imply: % 232.86/39.62 | | | | | | | | | | | | | (1225) $false % 232.86/39.62 | | | | | | | | | | | | | % 232.86/39.62 | | | | | | | | | | | | | CLOSE: (1225) is inconsistent. % 232.86/39.62 | | | | | | | | | | | | | % 232.86/39.62 | | | | | | | | | | | | End of split % 232.86/39.62 | | | | | | | | | | | | % 232.86/39.62 | | | | | | | | | | | End of split % 232.86/39.62 | | | | | | | | | | | % 232.86/39.62 | | | | | | | | | | Case 2: % 232.86/39.62 | | | | | | | | | | | % 232.86/39.62 | | | | | | | | | | | (1226) all_74_10 = n4 % 232.86/39.62 | | | | | | | | | | | % 232.86/39.62 | | | | | | | | | | | REDUCE: (1040), (1226) imply: % 232.86/39.62 | | | | | | | | | | | (1227) a_select3(pminus_ds1_filter, n4, all_74_11) = % 232.86/39.62 | | | | | | | | | | | all_74_8 % 232.86/39.62 | | | | | | | | | | | % 232.86/39.62 | | | | | | | | | | | REDUCE: (1039), (1226) imply: % 232.86/39.62 | | | | | | | | | | | (1228) a_select3(pminus_ds1_filter, all_74_11, n4) = % 232.86/39.62 | | | | | | | | | | | all_74_9 % 232.86/39.62 | | | | | | | | | | | % 232.86/39.62 | | | | | | | | | | | REDUCE: (1041), (1226) imply: % 232.86/39.62 | | | | | | | | | | | (1229) leq(n4, n5) % 232.86/39.62 | | | | | | | | | | | % 232.86/39.62 | | | | | | | | | | | REDUCE: (1036), (1226) imply: % 232.86/39.62 | | | | | | | | | | | (1230) leq(n0, n4) % 232.86/39.62 | | | | | | | | | | | % 232.86/39.62 | | | | | | | | | | | BETA: splitting (1063) gives: % 232.86/39.62 | | | | | | | | | | | % 232.86/39.62 | | | | | | | | | | | Case 1: % 232.86/39.62 | | | | | | | | | | | | % 232.86/39.62 | | | | | | | | | | | | (1231) gt(n3, all_74_11) % 232.86/39.62 | | | | | | | | | | | | % 232.86/39.62 | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_11, n3, n2, % 232.86/39.62 | | | | | | | | | | | | simplifying with (53), (112), (124), (1231) gives: % 232.86/39.62 | | | | | | | | | | | | (1232) leq(all_74_11, n2) % 232.86/39.62 | | | | | | | | | | | | % 232.86/39.62 | | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_11, n2, % 232.86/39.62 | | | | | | | | | | | | simplifying with (53), (101), (1232) gives: % 232.86/39.62 | | | | | | | | | | | | (1233) all_74_11 = n2 | gt(n2, all_74_11) % 232.86/39.62 | | | | | | | | | | | | % 232.86/39.62 | | | | | | | | | | | | BETA: splitting (1233) gives: % 232.86/39.62 | | | | | | | | | | | | % 232.86/39.62 | | | | | | | | | | | | Case 1: % 232.86/39.62 | | | | | | | | | | | | | % 232.86/39.62 | | | | | | | | | | | | | (1234) gt(n2, all_74_11) % 232.86/39.62 | | | | | | | | | | | | | % 232.86/39.62 | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_11, n2, n1, % 232.86/39.62 | | | | | | | | | | | | | simplifying with (53), (101), (123), (1234) gives: % 232.86/39.62 | | | | | | | | | | | | | (1235) leq(all_74_11, n1) % 232.86/39.62 | | | | | | | | | | | | | % 232.86/39.62 | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_74_11, simplifying with % 232.86/39.62 | | | | | | | | | | | | | (53), (1035), (1235) gives: % 232.86/39.62 | | | | | | | | | | | | | (1236) all_74_11 = n1 | all_74_11 = n0 % 232.86/39.62 | | | | | | | | | | | | | % 232.86/39.62 | | | | | | | | | | | | | BETA: splitting (1236) gives: % 232.86/39.62 | | | | | | | | | | | | | % 232.86/39.62 | | | | | | | | | | | | | Case 1: % 232.86/39.62 | | | | | | | | | | | | | | % 232.86/39.62 | | | | | | | | | | | | | | (1237) all_74_11 = n0 % 232.86/39.62 | | | | | | | | | | | | | | % 232.86/39.62 | | | | | | | | | | | | | | REDUCE: (1060), (1237) imply: % 232.86/39.62 | | | | | | | | | | | | | | (1238) $false % 232.86/39.62 | | | | | | | | | | | | | | % 232.86/39.62 | | | | | | | | | | | | | | CLOSE: (1238) is inconsistent. % 232.86/39.62 | | | | | | | | | | | | | | % 232.86/39.62 | | | | | | | | | | | | | Case 2: % 232.86/39.62 | | | | | | | | | | | | | | % 232.86/39.62 | | | | | | | | | | | | | | (1239) all_74_11 = n1 % 232.86/39.62 | | | | | | | | | | | | | | % 232.86/39.62 | | | | | | | | | | | | | | REDUCE: (1228), (1239) imply: % 232.86/39.62 | | | | | | | | | | | | | | (1240) a_select3(pminus_ds1_filter, n1, n4) = all_74_9 % 232.86/39.62 | | | | | | | | | | | | | | % 232.86/39.62 | | | | | | | | | | | | | | REDUCE: (1227), (1239) imply: % 232.86/39.62 | | | | | | | | | | | | | | (1241) a_select3(pminus_ds1_filter, n4, n1) = all_74_8 % 232.86/39.62 | | | | | | | | | | | | | | % 232.86/39.62 | | | | | | | | | | | | | | REDUCE: (1042), (1239) imply: % 232.86/39.62 | | | | | | | | | | | | | | (1242) leq(n1, n5) % 232.86/39.62 | | | | | | | | | | | | | | % 232.86/39.62 | | | | | | | | | | | | | | REDUCE: (1035), (1239) imply: % 232.86/39.62 | | | | | | | | | | | | | | (1243) leq(n0, n1) % 232.86/39.62 | | | | | | | | | | | | | | % 232.86/39.62 | | | | | | | | | | | | | | GROUND_INST: instantiating (64) with n1, n4, all_74_9, % 232.86/39.62 | | | | | | | | | | | | | | simplifying with (85), (119), (1230), (1240), % 232.86/39.62 | | | | | | | | | | | | | | (1243) gives: % 232.86/39.62 | | | | | | | | | | | | | | (1244) ~ leq(n4, all_74_21) | ~ leq(n1, all_74_21) | % 232.86/39.62 | | | | | | | | | | | | | | (a_select3(pminus_ds1_filter, n4, n1) = all_74_9 & % 232.86/39.62 | | | | | | | | | | | | | | $i(all_74_9)) % 232.86/39.62 | | | | | | | | | | | | | | % 232.86/39.62 | | | | | | | | | | | | | | BETA: splitting (1244) gives: % 232.86/39.62 | | | | | | | | | | | | | | % 232.86/39.62 | | | | | | | | | | | | | | Case 1: % 232.86/39.62 | | | | | | | | | | | | | | | % 232.86/39.62 | | | | | | | | | | | | | | | (1245) ~ leq(n4, all_74_21) % 232.86/39.62 | | | | | | | | | | | | | | | % 232.86/39.62 | | | | | | | | | | | | | | | REDUCE: (135), (1245) imply: % 232.86/39.62 | | | | | | | | | | | | | | | (1246) ~ leq(n4, n5) % 232.86/39.62 | | | | | | | | | | | | | | | % 232.86/39.62 | | | | | | | | | | | | | | | PRED_UNIFY: (1229), (1246) imply: % 232.86/39.62 | | | | | | | | | | | | | | | (1247) $false % 232.86/39.62 | | | | | | | | | | | | | | | % 232.86/39.62 | | | | | | | | | | | | | | | CLOSE: (1247) is inconsistent. % 232.86/39.62 | | | | | | | | | | | | | | | % 232.86/39.62 | | | | | | | | | | | | | | Case 2: % 232.86/39.62 | | | | | | | | | | | | | | | % 232.86/39.62 | | | | | | | | | | | | | | | (1248) ~ leq(n1, all_74_21) | % 232.86/39.62 | | | | | | | | | | | | | | | (a_select3(pminus_ds1_filter, n4, n1) = all_74_9 & % 232.86/39.62 | | | | | | | | | | | | | | | $i(all_74_9)) % 232.86/39.62 | | | | | | | | | | | | | | | % 232.86/39.62 | | | | | | | | | | | | | | | BETA: splitting (1248) gives: % 232.86/39.62 | | | | | | | | | | | | | | | % 232.86/39.62 | | | | | | | | | | | | | | | Case 1: % 232.86/39.62 | | | | | | | | | | | | | | | | % 232.86/39.62 | | | | | | | | | | | | | | | | (1249) ~ leq(n1, all_74_21) % 232.86/39.62 | | | | | | | | | | | | | | | | % 232.86/39.62 | | | | | | | | | | | | | | | | REDUCE: (135), (1249) imply: % 232.86/39.62 | | | | | | | | | | | | | | | | (1250) ~ leq(n1, n5) % 232.86/39.62 | | | | | | | | | | | | | | | | % 232.86/39.62 | | | | | | | | | | | | | | | | PRED_UNIFY: (1242), (1250) imply: % 232.86/39.62 | | | | | | | | | | | | | | | | (1251) $false % 232.86/39.62 | | | | | | | | | | | | | | | | % 232.86/39.62 | | | | | | | | | | | | | | | | CLOSE: (1251) is inconsistent. % 232.86/39.62 | | | | | | | | | | | | | | | | % 232.86/39.62 | | | | | | | | | | | | | | | Case 2: % 232.86/39.62 | | | | | | | | | | | | | | | | % 232.86/39.62 | | | | | | | | | | | | | | | | (1252) a_select3(pminus_ds1_filter, n4, n1) = all_74_9 & % 232.86/39.62 | | | | | | | | | | | | | | | | $i(all_74_9) % 232.86/39.62 | | | | | | | | | | | | | | | | % 232.86/39.62 | | | | | | | | | | | | | | | | ALPHA: (1252) implies: % 232.86/39.62 | | | | | | | | | | | | | | | | (1253) a_select3(pminus_ds1_filter, n4, n1) = all_74_9 % 232.86/39.62 | | | | | | | | | | | | | | | | % 232.86/39.62 | | | | | | | | | | | | | | | | REF_CLOSE: (17), (1034), (1241), (1253) are inconsistent by % 232.86/39.62 | | | | | | | | | | | | | | | | sub-proof #35. % 232.86/39.62 | | | | | | | | | | | | | | | | % 232.86/39.62 | | | | | | | | | | | | | | | End of split % 232.86/39.62 | | | | | | | | | | | | | | | % 232.86/39.62 | | | | | | | | | | | | | | End of split % 232.86/39.62 | | | | | | | | | | | | | | % 232.86/39.62 | | | | | | | | | | | | | End of split % 232.86/39.62 | | | | | | | | | | | | | % 232.86/39.62 | | | | | | | | | | | | Case 2: % 232.86/39.62 | | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | | (1254) all_74_11 = n2 % 232.86/39.63 | | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | | REDUCE: (1228), (1254) imply: % 232.86/39.63 | | | | | | | | | | | | | (1255) a_select3(pminus_ds1_filter, n2, n4) = all_74_9 % 232.86/39.63 | | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | | REDUCE: (1227), (1254) imply: % 232.86/39.63 | | | | | | | | | | | | | (1256) a_select3(pminus_ds1_filter, n4, n2) = all_74_8 % 232.86/39.63 | | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | | REDUCE: (1042), (1254) imply: % 232.86/39.63 | | | | | | | | | | | | | (1257) leq(n2, n5) % 232.86/39.63 | | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | | REDUCE: (1035), (1254) imply: % 232.86/39.63 | | | | | | | | | | | | | (1258) leq(n0, n2) % 232.86/39.63 | | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | | GROUND_INST: instantiating (64) with n2, n4, all_74_9, % 232.86/39.63 | | | | | | | | | | | | | simplifying with (101), (119), (1230), (1255), % 232.86/39.63 | | | | | | | | | | | | | (1258) gives: % 232.86/39.63 | | | | | | | | | | | | | (1259) ~ leq(n4, all_74_21) | ~ leq(n2, all_74_21) | % 232.86/39.63 | | | | | | | | | | | | | (a_select3(pminus_ds1_filter, n4, n2) = all_74_9 & % 232.86/39.63 | | | | | | | | | | | | | $i(all_74_9)) % 232.86/39.63 | | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | | BETA: splitting (1259) gives: % 232.86/39.63 | | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | | Case 1: % 232.86/39.63 | | | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | | | (1260) ~ leq(n4, all_74_21) % 232.86/39.63 | | | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | | | REDUCE: (135), (1260) imply: % 232.86/39.63 | | | | | | | | | | | | | | (1261) ~ leq(n4, n5) % 232.86/39.63 | | | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | | | PRED_UNIFY: (1229), (1261) imply: % 232.86/39.63 | | | | | | | | | | | | | | (1262) $false % 232.86/39.63 | | | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | | | CLOSE: (1262) is inconsistent. % 232.86/39.63 | | | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | | Case 2: % 232.86/39.63 | | | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | | | (1263) ~ leq(n2, all_74_21) | % 232.86/39.63 | | | | | | | | | | | | | | (a_select3(pminus_ds1_filter, n4, n2) = all_74_9 & % 232.86/39.63 | | | | | | | | | | | | | | $i(all_74_9)) % 232.86/39.63 | | | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | | | BETA: splitting (1263) gives: % 232.86/39.63 | | | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | | | Case 1: % 232.86/39.63 | | | | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | | | | (1264) ~ leq(n2, all_74_21) % 232.86/39.63 | | | | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | | | | REDUCE: (135), (1264) imply: % 232.86/39.63 | | | | | | | | | | | | | | | (1265) ~ leq(n2, n5) % 232.86/39.63 | | | | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | | | | PRED_UNIFY: (1257), (1265) imply: % 232.86/39.63 | | | | | | | | | | | | | | | (1266) $false % 232.86/39.63 | | | | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | | | | CLOSE: (1266) is inconsistent. % 232.86/39.63 | | | | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | | | Case 2: % 232.86/39.63 | | | | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | | | | (1267) a_select3(pminus_ds1_filter, n4, n2) = all_74_9 & % 232.86/39.63 | | | | | | | | | | | | | | | $i(all_74_9) % 232.86/39.63 | | | | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | | | | ALPHA: (1267) implies: % 232.86/39.63 | | | | | | | | | | | | | | | (1268) a_select3(pminus_ds1_filter, n4, n2) = all_74_9 % 232.86/39.63 | | | | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_74_8, all_74_9, n2, % 232.86/39.63 | | | | | | | | | | | | | | | n4, pminus_ds1_filter, simplifying with (1256), % 232.86/39.63 | | | | | | | | | | | | | | | (1268) gives: % 232.86/39.63 | | | | | | | | | | | | | | | (1269) all_74_8 = all_74_9 % 232.86/39.63 | | | | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | | | | REDUCE: (1034), (1269) imply: % 232.86/39.63 | | | | | | | | | | | | | | | (1270) $false % 232.86/39.63 | | | | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | | | | CLOSE: (1270) is inconsistent. % 232.86/39.63 | | | | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | | | End of split % 232.86/39.63 | | | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | | End of split % 232.86/39.63 | | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | End of split % 232.86/39.63 | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | Case 2: % 232.86/39.63 | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | (1271) all_74_11 = n3 % 232.86/39.63 | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | REDUCE: (1228), (1271) imply: % 232.86/39.63 | | | | | | | | | | | | (1272) a_select3(pminus_ds1_filter, n3, n4) = all_74_9 % 232.86/39.63 | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | REDUCE: (1227), (1271) imply: % 232.86/39.63 | | | | | | | | | | | | (1273) a_select3(pminus_ds1_filter, n4, n3) = all_74_8 % 232.86/39.63 | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | REDUCE: (1042), (1271) imply: % 232.86/39.63 | | | | | | | | | | | | (1274) leq(n3, n5) % 232.86/39.63 | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | REDUCE: (1035), (1271) imply: % 232.86/39.63 | | | | | | | | | | | | (1275) leq(n0, n3) % 232.86/39.63 | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | GROUND_INST: instantiating (64) with n3, n4, all_74_9, % 232.86/39.63 | | | | | | | | | | | | simplifying with (112), (119), (1230), (1272), % 232.86/39.63 | | | | | | | | | | | | (1275) gives: % 232.86/39.63 | | | | | | | | | | | | (1276) ~ leq(n4, all_74_21) | ~ leq(n3, all_74_21) | % 232.86/39.63 | | | | | | | | | | | | (a_select3(pminus_ds1_filter, n4, n3) = all_74_9 & % 232.86/39.63 | | | | | | | | | | | | $i(all_74_9)) % 232.86/39.63 | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | BETA: splitting (1276) gives: % 232.86/39.63 | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | Case 1: % 232.86/39.63 | | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | | (1277) ~ leq(n4, all_74_21) % 232.86/39.63 | | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | | REDUCE: (135), (1277) imply: % 232.86/39.63 | | | | | | | | | | | | | (1278) ~ leq(n4, n5) % 232.86/39.63 | | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | | PRED_UNIFY: (1229), (1278) imply: % 232.86/39.63 | | | | | | | | | | | | | (1279) $false % 232.86/39.63 | | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | | CLOSE: (1279) is inconsistent. % 232.86/39.63 | | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | Case 2: % 232.86/39.63 | | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | | (1280) ~ leq(n3, all_74_21) | % 232.86/39.63 | | | | | | | | | | | | | (a_select3(pminus_ds1_filter, n4, n3) = all_74_9 & % 232.86/39.63 | | | | | | | | | | | | | $i(all_74_9)) % 232.86/39.63 | | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | | BETA: splitting (1280) gives: % 232.86/39.63 | | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | | Case 1: % 232.86/39.63 | | | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | | | (1281) ~ leq(n3, all_74_21) % 232.86/39.63 | | | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | | | REDUCE: (135), (1281) imply: % 232.86/39.63 | | | | | | | | | | | | | | (1282) ~ leq(n3, n5) % 232.86/39.63 | | | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | | | PRED_UNIFY: (1274), (1282) imply: % 232.86/39.63 | | | | | | | | | | | | | | (1283) $false % 232.86/39.63 | | | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | | | CLOSE: (1283) is inconsistent. % 232.86/39.63 | | | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | | Case 2: % 232.86/39.63 | | | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | | | (1284) a_select3(pminus_ds1_filter, n4, n3) = all_74_9 & % 232.86/39.63 | | | | | | | | | | | | | | $i(all_74_9) % 232.86/39.63 | | | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | | | ALPHA: (1284) implies: % 232.86/39.63 | | | | | | | | | | | | | | (1285) a_select3(pminus_ds1_filter, n4, n3) = all_74_9 % 232.86/39.63 | | | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | | | REF_CLOSE: (17), (1034), (1273), (1285) are inconsistent by % 232.86/39.63 | | | | | | | | | | | | | | sub-proof #34. % 232.86/39.63 | | | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | | End of split % 232.86/39.63 | | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | End of split % 232.86/39.63 | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | End of split % 232.86/39.63 | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | End of split % 232.86/39.63 | | | | | | | | | | % 232.86/39.63 | | | | | | | | | Case 2: % 232.86/39.63 | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | (1286) all_74_11 = n4 % 232.86/39.63 | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | REDUCE: (1040), (1286) imply: % 232.86/39.63 | | | | | | | | | | (1287) a_select3(pminus_ds1_filter, all_74_10, n4) = % 232.86/39.63 | | | | | | | | | | all_74_8 % 232.86/39.63 | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | REDUCE: (1039), (1286) imply: % 232.86/39.63 | | | | | | | | | | (1288) a_select3(pminus_ds1_filter, n4, all_74_10) = % 232.86/39.63 | | | | | | | | | | all_74_9 % 232.86/39.63 | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | REDUCE: (1042), (1286) imply: % 232.86/39.63 | | | | | | | | | | (1289) leq(n4, n5) % 232.86/39.63 | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | REDUCE: (1035), (1286) imply: % 232.86/39.63 | | | | | | | | | | (1290) leq(n0, n4) % 232.86/39.63 | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | BETA: splitting (1056) gives: % 232.86/39.63 | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | Case 1: % 232.86/39.63 | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | (1291) gt(n4, all_74_10) % 232.86/39.63 | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_10, n4, n3, % 232.86/39.63 | | | | | | | | | | | simplifying with (54), (119), (125), (1291) gives: % 232.86/39.63 | | | | | | | | | | | (1292) leq(all_74_10, n3) % 232.86/39.63 | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_10, n3, % 232.86/39.63 | | | | | | | | | | | simplifying with (54), (112), (1292) gives: % 232.86/39.63 | | | | | | | | | | | (1293) all_74_10 = n3 | gt(n3, all_74_10) % 232.86/39.63 | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | BETA: splitting (1293) gives: % 232.86/39.63 | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | Case 1: % 232.86/39.63 | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | (1294) gt(n3, all_74_10) % 232.86/39.63 | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_10, n3, n2, % 232.86/39.63 | | | | | | | | | | | | simplifying with (54), (112), (124), (1294) gives: % 232.86/39.63 | | | | | | | | | | | | (1295) leq(all_74_10, n2) % 232.86/39.63 | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_10, n2, % 232.86/39.63 | | | | | | | | | | | | simplifying with (54), (101), (1295) gives: % 232.86/39.63 | | | | | | | | | | | | (1296) all_74_10 = n2 | gt(n2, all_74_10) % 232.86/39.63 | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | BETA: splitting (1296) gives: % 232.86/39.63 | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | Case 1: % 232.86/39.63 | | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | | (1297) gt(n2, all_74_10) % 232.86/39.63 | | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_10, n2, n1, % 232.86/39.63 | | | | | | | | | | | | | simplifying with (54), (101), (123), (1297) gives: % 232.86/39.63 | | | | | | | | | | | | | (1298) leq(all_74_10, n1) % 232.86/39.63 | | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_74_10, simplifying with % 232.86/39.63 | | | | | | | | | | | | | (54), (1036), (1298) gives: % 232.86/39.63 | | | | | | | | | | | | | (1299) all_74_10 = n1 | all_74_10 = n0 % 232.86/39.63 | | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | | BETA: splitting (1299) gives: % 232.86/39.63 | | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | | Case 1: % 232.86/39.63 | | | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | | | (1300) all_74_10 = n0 % 232.86/39.63 | | | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | | | REDUCE: (1058), (1300) imply: % 232.86/39.63 | | | | | | | | | | | | | | (1301) $false % 232.86/39.63 | | | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | | | CLOSE: (1301) is inconsistent. % 232.86/39.63 | | | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | | Case 2: % 232.86/39.63 | | | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | | | (1302) all_74_10 = n1 % 232.86/39.63 | | | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | | | REDUCE: (1287), (1302) imply: % 232.86/39.63 | | | | | | | | | | | | | | (1303) a_select3(pminus_ds1_filter, n1, n4) = all_74_8 % 232.86/39.63 | | | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | | | REDUCE: (1288), (1302) imply: % 232.86/39.63 | | | | | | | | | | | | | | (1304) a_select3(pminus_ds1_filter, n4, n1) = all_74_9 % 232.86/39.63 | | | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | | | REDUCE: (1041), (1302) imply: % 232.86/39.63 | | | | | | | | | | | | | | (1305) leq(n1, n5) % 232.86/39.63 | | | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | | | REDUCE: (1036), (1302) imply: % 232.86/39.63 | | | | | | | | | | | | | | (1306) leq(n0, n1) % 232.86/39.63 | | | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | | | GROUND_INST: instantiating (64) with n1, n4, all_74_8, % 232.86/39.63 | | | | | | | | | | | | | | simplifying with (85), (119), (1290), (1303), % 232.86/39.63 | | | | | | | | | | | | | | (1306) gives: % 232.86/39.63 | | | | | | | | | | | | | | (1307) ~ leq(n4, all_74_21) | ~ leq(n1, all_74_21) | % 232.86/39.63 | | | | | | | | | | | | | | (a_select3(pminus_ds1_filter, n4, n1) = all_74_8 & % 232.86/39.63 | | | | | | | | | | | | | | $i(all_74_8)) % 232.86/39.63 | | | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | | | BETA: splitting (1307) gives: % 232.86/39.63 | | | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | | | Case 1: % 232.86/39.63 | | | | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | | | | (1308) ~ leq(n4, all_74_21) % 232.86/39.63 | | | | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | | | | REDUCE: (135), (1308) imply: % 232.86/39.63 | | | | | | | | | | | | | | | (1309) ~ leq(n4, n5) % 232.86/39.63 | | | | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | | | | PRED_UNIFY: (1289), (1309) imply: % 232.86/39.63 | | | | | | | | | | | | | | | (1310) $false % 232.86/39.63 | | | | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | | | | CLOSE: (1310) is inconsistent. % 232.86/39.63 | | | | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | | | Case 2: % 232.86/39.63 | | | | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | | | | (1311) ~ leq(n1, all_74_21) | % 232.86/39.63 | | | | | | | | | | | | | | | (a_select3(pminus_ds1_filter, n4, n1) = all_74_8 & % 232.86/39.63 | | | | | | | | | | | | | | | $i(all_74_8)) % 232.86/39.63 | | | | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | | | | BETA: splitting (1311) gives: % 232.86/39.63 | | | | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | | | | Case 1: % 232.86/39.63 | | | | | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | | | | | (1312) ~ leq(n1, all_74_21) % 232.86/39.63 | | | | | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | | | | | REDUCE: (135), (1312) imply: % 232.86/39.63 | | | | | | | | | | | | | | | | (1313) ~ leq(n1, n5) % 232.86/39.63 | | | | | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | | | | | PRED_UNIFY: (1305), (1313) imply: % 232.86/39.63 | | | | | | | | | | | | | | | | (1314) $false % 232.86/39.63 | | | | | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | | | | | CLOSE: (1314) is inconsistent. % 232.86/39.63 | | | | | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | | | | Case 2: % 232.86/39.63 | | | | | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | | | | | (1315) a_select3(pminus_ds1_filter, n4, n1) = all_74_8 & % 232.86/39.63 | | | | | | | | | | | | | | | | $i(all_74_8) % 232.86/39.63 | | | | | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | | | | | ALPHA: (1315) implies: % 232.86/39.63 | | | | | | | | | | | | | | | | (1316) a_select3(pminus_ds1_filter, n4, n1) = all_74_8 % 232.86/39.63 | | | | | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | | | | | REF_CLOSE: (17), (1034), (1304), (1316) are inconsistent by % 232.86/39.63 | | | | | | | | | | | | | | | | sub-proof #35. % 232.86/39.63 | | | | | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | | | | End of split % 232.86/39.63 | | | | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | | | End of split % 232.86/39.63 | | | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | | End of split % 232.86/39.63 | | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | Case 2: % 232.86/39.63 | | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | | (1317) all_74_10 = n2 % 232.86/39.63 | | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | | REDUCE: (1287), (1317) imply: % 232.86/39.63 | | | | | | | | | | | | | (1318) a_select3(pminus_ds1_filter, n2, n4) = all_74_8 % 232.86/39.63 | | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | | REDUCE: (1288), (1317) imply: % 232.86/39.63 | | | | | | | | | | | | | (1319) a_select3(pminus_ds1_filter, n4, n2) = all_74_9 % 232.86/39.63 | | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | | REDUCE: (1041), (1317) imply: % 232.86/39.63 | | | | | | | | | | | | | (1320) leq(n2, n5) % 232.86/39.63 | | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | | REDUCE: (1036), (1317) imply: % 232.86/39.63 | | | | | | | | | | | | | (1321) leq(n0, n2) % 232.86/39.63 | | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | | GROUND_INST: instantiating (64) with n2, n4, all_74_8, % 232.86/39.63 | | | | | | | | | | | | | simplifying with (101), (119), (1290), (1318), % 232.86/39.63 | | | | | | | | | | | | | (1321) gives: % 232.86/39.63 | | | | | | | | | | | | | (1322) ~ leq(n4, all_74_21) | ~ leq(n2, all_74_21) | % 232.86/39.63 | | | | | | | | | | | | | (a_select3(pminus_ds1_filter, n4, n2) = all_74_8 & % 232.86/39.63 | | | | | | | | | | | | | $i(all_74_8)) % 232.86/39.63 | | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | | BETA: splitting (1322) gives: % 232.86/39.63 | | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | | Case 1: % 232.86/39.63 | | | | | | | | | | | | | | % 232.86/39.63 | | | | | | | | | | | | | | (1323) ~ leq(n4, all_74_21) % 232.86/39.63 | | | | | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | | | | | REDUCE: (135), (1323) imply: % 232.86/39.64 | | | | | | | | | | | | | | (1324) ~ leq(n4, n5) % 232.86/39.64 | | | | | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | | | | | PRED_UNIFY: (1289), (1324) imply: % 232.86/39.64 | | | | | | | | | | | | | | (1325) $false % 232.86/39.64 | | | | | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | | | | | CLOSE: (1325) is inconsistent. % 232.86/39.64 | | | | | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | | | | Case 2: % 232.86/39.64 | | | | | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | | | | | (1326) ~ leq(n2, all_74_21) | % 232.86/39.64 | | | | | | | | | | | | | | (a_select3(pminus_ds1_filter, n4, n2) = all_74_8 & % 232.86/39.64 | | | | | | | | | | | | | | $i(all_74_8)) % 232.86/39.64 | | | | | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | | | | | BETA: splitting (1326) gives: % 232.86/39.64 | | | | | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | | | | | Case 1: % 232.86/39.64 | | | | | | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | | | | | | (1327) ~ leq(n2, all_74_21) % 232.86/39.64 | | | | | | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | | | | | | REDUCE: (135), (1327) imply: % 232.86/39.64 | | | | | | | | | | | | | | | (1328) ~ leq(n2, n5) % 232.86/39.64 | | | | | | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | | | | | | PRED_UNIFY: (1320), (1328) imply: % 232.86/39.64 | | | | | | | | | | | | | | | (1329) $false % 232.86/39.64 | | | | | | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | | | | | | CLOSE: (1329) is inconsistent. % 232.86/39.64 | | | | | | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | | | | | Case 2: % 232.86/39.64 | | | | | | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | | | | | | (1330) a_select3(pminus_ds1_filter, n4, n2) = all_74_8 & % 232.86/39.64 | | | | | | | | | | | | | | | $i(all_74_8) % 232.86/39.64 | | | | | | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | | | | | | ALPHA: (1330) implies: % 232.86/39.64 | | | | | | | | | | | | | | | (1331) a_select3(pminus_ds1_filter, n4, n2) = all_74_8 % 232.86/39.64 | | | | | | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_74_8, all_74_9, n2, % 232.86/39.64 | | | | | | | | | | | | | | | n4, pminus_ds1_filter, simplifying with (1319), % 232.86/39.64 | | | | | | | | | | | | | | | (1331) gives: % 232.86/39.64 | | | | | | | | | | | | | | | (1332) all_74_8 = all_74_9 % 232.86/39.64 | | | | | | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | | | | | | REDUCE: (1034), (1332) imply: % 232.86/39.64 | | | | | | | | | | | | | | | (1333) $false % 232.86/39.64 | | | | | | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | | | | | | CLOSE: (1333) is inconsistent. % 232.86/39.64 | | | | | | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | | | | | End of split % 232.86/39.64 | | | | | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | | | | End of split % 232.86/39.64 | | | | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | | | End of split % 232.86/39.64 | | | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | | Case 2: % 232.86/39.64 | | | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | | | (1334) all_74_10 = n3 % 232.86/39.64 | | | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | | | REDUCE: (1287), (1334) imply: % 232.86/39.64 | | | | | | | | | | | | (1335) a_select3(pminus_ds1_filter, n3, n4) = all_74_8 % 232.86/39.64 | | | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | | | REDUCE: (1288), (1334) imply: % 232.86/39.64 | | | | | | | | | | | | (1336) a_select3(pminus_ds1_filter, n4, n3) = all_74_9 % 232.86/39.64 | | | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | | | REDUCE: (1041), (1334) imply: % 232.86/39.64 | | | | | | | | | | | | (1337) leq(n3, n5) % 232.86/39.64 | | | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | | | REDUCE: (1036), (1334) imply: % 232.86/39.64 | | | | | | | | | | | | (1338) leq(n0, n3) % 232.86/39.64 | | | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | | | GROUND_INST: instantiating (64) with n3, n4, all_74_8, % 232.86/39.64 | | | | | | | | | | | | simplifying with (112), (119), (1290), (1335), % 232.86/39.64 | | | | | | | | | | | | (1338) gives: % 232.86/39.64 | | | | | | | | | | | | (1339) ~ leq(n4, all_74_21) | ~ leq(n3, all_74_21) | % 232.86/39.64 | | | | | | | | | | | | (a_select3(pminus_ds1_filter, n4, n3) = all_74_8 & % 232.86/39.64 | | | | | | | | | | | | $i(all_74_8)) % 232.86/39.64 | | | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | | | BETA: splitting (1339) gives: % 232.86/39.64 | | | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | | | Case 1: % 232.86/39.64 | | | | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | | | | (1340) ~ leq(n4, all_74_21) % 232.86/39.64 | | | | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | | | | REDUCE: (135), (1340) imply: % 232.86/39.64 | | | | | | | | | | | | | (1341) ~ leq(n4, n5) % 232.86/39.64 | | | | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | | | | PRED_UNIFY: (1289), (1341) imply: % 232.86/39.64 | | | | | | | | | | | | | (1342) $false % 232.86/39.64 | | | | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | | | | CLOSE: (1342) is inconsistent. % 232.86/39.64 | | | | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | | | Case 2: % 232.86/39.64 | | | | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | | | | (1343) ~ leq(n3, all_74_21) | % 232.86/39.64 | | | | | | | | | | | | | (a_select3(pminus_ds1_filter, n4, n3) = all_74_8 & % 232.86/39.64 | | | | | | | | | | | | | $i(all_74_8)) % 232.86/39.64 | | | | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | | | | BETA: splitting (1343) gives: % 232.86/39.64 | | | | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | | | | Case 1: % 232.86/39.64 | | | | | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | | | | | (1344) ~ leq(n3, all_74_21) % 232.86/39.64 | | | | | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | | | | | REDUCE: (135), (1344) imply: % 232.86/39.64 | | | | | | | | | | | | | | (1345) ~ leq(n3, n5) % 232.86/39.64 | | | | | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | | | | | PRED_UNIFY: (1337), (1345) imply: % 232.86/39.64 | | | | | | | | | | | | | | (1346) $false % 232.86/39.64 | | | | | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | | | | | CLOSE: (1346) is inconsistent. % 232.86/39.64 | | | | | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | | | | Case 2: % 232.86/39.64 | | | | | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | | | | | (1347) a_select3(pminus_ds1_filter, n4, n3) = all_74_8 & % 232.86/39.64 | | | | | | | | | | | | | | $i(all_74_8) % 232.86/39.64 | | | | | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | | | | | ALPHA: (1347) implies: % 232.86/39.64 | | | | | | | | | | | | | | (1348) a_select3(pminus_ds1_filter, n4, n3) = all_74_8 % 232.86/39.64 | | | | | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | | | | | REF_CLOSE: (17), (1034), (1336), (1348) are inconsistent by % 232.86/39.64 | | | | | | | | | | | | | | sub-proof #34. % 232.86/39.64 | | | | | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | | | | End of split % 232.86/39.64 | | | | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | | | End of split % 232.86/39.64 | | | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | | End of split % 232.86/39.64 | | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | Case 2: % 232.86/39.64 | | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | | (1349) all_74_10 = n4 % 232.86/39.64 | | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | | REDUCE: (1287), (1349) imply: % 232.86/39.64 | | | | | | | | | | | (1350) a_select3(pminus_ds1_filter, n4, n4) = all_74_8 % 232.86/39.64 | | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | | REDUCE: (1288), (1349) imply: % 232.86/39.64 | | | | | | | | | | | (1351) a_select3(pminus_ds1_filter, n4, n4) = all_74_9 % 232.86/39.64 | | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | | GROUND_INST: instantiating (17) with all_74_9, all_74_8, n4, % 232.86/39.64 | | | | | | | | | | | n4, pminus_ds1_filter, simplifying with (1350), % 232.86/39.64 | | | | | | | | | | | (1351) gives: % 232.86/39.64 | | | | | | | | | | | (1352) all_74_8 = all_74_9 % 232.86/39.64 | | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | | REDUCE: (1034), (1352) imply: % 232.86/39.64 | | | | | | | | | | | (1353) $false % 232.86/39.64 | | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | | CLOSE: (1353) is inconsistent. % 232.86/39.64 | | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | End of split % 232.86/39.64 | | | | | | | | | | % 232.86/39.64 | | | | | | | | | End of split % 232.86/39.64 | | | | | | | | | % 232.86/39.64 | | | | | | | | End of split % 232.86/39.64 | | | | | | | | % 232.86/39.64 | | | | | | | End of split % 232.86/39.64 | | | | | | | % 232.86/39.64 | | | | | | Case 2: % 232.86/39.64 | | | | | | | % 232.86/39.64 | | | | | | | (1354) all_74_10 = n5 % 232.86/39.64 | | | | | | | % 232.86/39.64 | | | | | | | REDUCE: (1040), (1354) imply: % 232.86/39.64 | | | | | | | (1355) a_select3(pminus_ds1_filter, n5, all_74_11) = all_74_8 % 232.86/39.64 | | | | | | | % 232.86/39.64 | | | | | | | REDUCE: (1039), (1354) imply: % 232.86/39.64 | | | | | | | (1356) a_select3(pminus_ds1_filter, all_74_11, n5) = all_74_9 % 232.86/39.64 | | | | | | | % 232.86/39.64 | | | | | | | REDUCE: (1041), (1354) imply: % 232.86/39.64 | | | | | | | (1357) leq(n5, n5) % 232.86/39.64 | | | | | | | % 232.86/39.64 | | | | | | | REDUCE: (1036), (1354) imply: % 232.86/39.64 | | | | | | | (1358) leq(n0, n5) % 232.86/39.64 | | | | | | | % 232.86/39.64 | | | | | | | BETA: splitting (1045) gives: % 232.86/39.64 | | | | | | | % 232.86/39.64 | | | | | | | Case 1: % 232.86/39.64 | | | | | | | | % 232.86/39.64 | | | | | | | | (1359) all_74_11 = n0 % 232.86/39.64 | | | | | | | | % 232.86/39.64 | | | | | | | | REF_CLOSE: (53), (1050), (1359), (irreflexivity_gt) are % 232.86/39.64 | | | | | | | | inconsistent by sub-proof #39. % 232.86/39.64 | | | | | | | | % 232.86/39.64 | | | | | | | Case 2: % 232.86/39.64 | | | | | | | | % 232.86/39.64 | | | | | | | | (1360) ~ (all_74_11 = n0) % 232.86/39.64 | | | | | | | | % 232.86/39.64 | | | | | | | | BETA: splitting (1053) gives: % 232.86/39.64 | | | | | | | | % 232.86/39.64 | | | | | | | | Case 1: % 232.86/39.64 | | | | | | | | | % 232.86/39.64 | | | | | | | | | (1361) gt(n4, all_74_11) % 232.86/39.64 | | | | | | | | | % 232.86/39.64 | | | | | | | | | GROUND_INST: instantiating (1) with all_74_11, n4, n3, % 232.86/39.64 | | | | | | | | | simplifying with (53), (119), (125), (1361) gives: % 232.86/39.64 | | | | | | | | | (1362) leq(all_74_11, n3) % 232.86/39.64 | | | | | | | | | % 232.86/39.64 | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_11, n3, % 232.86/39.64 | | | | | | | | | simplifying with (53), (112), (1362) gives: % 232.86/39.64 | | | | | | | | | (1363) all_74_11 = n3 | gt(n3, all_74_11) % 232.86/39.64 | | | | | | | | | % 232.86/39.64 | | | | | | | | | BETA: splitting (1363) gives: % 232.86/39.64 | | | | | | | | | % 232.86/39.64 | | | | | | | | | Case 1: % 232.86/39.64 | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | (1364) gt(n3, all_74_11) % 232.86/39.64 | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_11, n3, n2, % 232.86/39.64 | | | | | | | | | | simplifying with (53), (112), (124), (1364) gives: % 232.86/39.64 | | | | | | | | | | (1365) leq(all_74_11, n2) % 232.86/39.64 | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_11, n2, % 232.86/39.64 | | | | | | | | | | simplifying with (53), (101), (1365) gives: % 232.86/39.64 | | | | | | | | | | (1366) all_74_11 = n2 | gt(n2, all_74_11) % 232.86/39.64 | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | BETA: splitting (1366) gives: % 232.86/39.64 | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | Case 1: % 232.86/39.64 | | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | | (1367) gt(n2, all_74_11) % 232.86/39.64 | | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_11, n2, n1, % 232.86/39.64 | | | | | | | | | | | simplifying with (53), (101), (123), (1367) gives: % 232.86/39.64 | | | | | | | | | | | (1368) leq(all_74_11, n1) % 232.86/39.64 | | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | | GROUND_INST: instantiating (4) with all_74_11, simplifying with % 232.86/39.64 | | | | | | | | | | | (53), (1035), (1368) gives: % 232.86/39.64 | | | | | | | | | | | (1369) all_74_11 = n1 | all_74_11 = n0 % 232.86/39.64 | | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | | BETA: splitting (1369) gives: % 232.86/39.64 | | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | | Case 1: % 232.86/39.64 | | | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | | | (1370) all_74_11 = n0 % 232.86/39.64 | | | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | | | REDUCE: (1360), (1370) imply: % 232.86/39.64 | | | | | | | | | | | | (1371) $false % 232.86/39.64 | | | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | | | CLOSE: (1371) is inconsistent. % 232.86/39.64 | | | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | | Case 2: % 232.86/39.64 | | | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | | | (1372) all_74_11 = n1 % 232.86/39.64 | | | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | | | REDUCE: (1356), (1372) imply: % 232.86/39.64 | | | | | | | | | | | | (1373) a_select3(pminus_ds1_filter, n1, n5) = all_74_9 % 232.86/39.64 | | | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | | | REDUCE: (1355), (1372) imply: % 232.86/39.64 | | | | | | | | | | | | (1374) a_select3(pminus_ds1_filter, n5, n1) = all_74_8 % 232.86/39.64 | | | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | | | REDUCE: (1042), (1372) imply: % 232.86/39.64 | | | | | | | | | | | | (1375) leq(n1, n5) % 232.86/39.64 | | | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | | | REDUCE: (1035), (1372) imply: % 232.86/39.64 | | | | | | | | | | | | (1376) leq(n0, n1) % 232.86/39.64 | | | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | | | GROUND_INST: instantiating (64) with n1, n5, all_74_9, % 232.86/39.64 | | | | | | | | | | | | simplifying with (85), (122), (1358), (1373), % 232.86/39.64 | | | | | | | | | | | | (1376) gives: % 232.86/39.64 | | | | | | | | | | | | (1377) ~ leq(n5, all_74_21) | ~ leq(n1, all_74_21) | % 232.86/39.64 | | | | | | | | | | | | (a_select3(pminus_ds1_filter, n5, n1) = all_74_9 & % 232.86/39.64 | | | | | | | | | | | | $i(all_74_9)) % 232.86/39.64 | | | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | | | BETA: splitting (1377) gives: % 232.86/39.64 | | | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | | | Case 1: % 232.86/39.64 | | | | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | | | | (1378) ~ leq(n5, all_74_21) % 232.86/39.64 | | | | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | | | | REDUCE: (135), (1378) imply: % 232.86/39.64 | | | | | | | | | | | | | (1379) ~ leq(n5, n5) % 232.86/39.64 | | | | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | | | | PRED_UNIFY: (1357), (1379) imply: % 232.86/39.64 | | | | | | | | | | | | | (1380) $false % 232.86/39.64 | | | | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | | | | CLOSE: (1380) is inconsistent. % 232.86/39.64 | | | | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | | | Case 2: % 232.86/39.64 | | | | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | | | | (1381) ~ leq(n1, all_74_21) | % 232.86/39.64 | | | | | | | | | | | | | (a_select3(pminus_ds1_filter, n5, n1) = all_74_9 & % 232.86/39.64 | | | | | | | | | | | | | $i(all_74_9)) % 232.86/39.64 | | | | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | | | | BETA: splitting (1381) gives: % 232.86/39.64 | | | | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | | | | Case 1: % 232.86/39.64 | | | | | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | | | | | (1382) ~ leq(n1, all_74_21) % 232.86/39.64 | | | | | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | | | | | REDUCE: (135), (1382) imply: % 232.86/39.64 | | | | | | | | | | | | | | (1383) ~ leq(n1, n5) % 232.86/39.64 | | | | | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | | | | | PRED_UNIFY: (1375), (1383) imply: % 232.86/39.64 | | | | | | | | | | | | | | (1384) $false % 232.86/39.64 | | | | | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | | | | | CLOSE: (1384) is inconsistent. % 232.86/39.64 | | | | | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | | | | Case 2: % 232.86/39.64 | | | | | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | | | | | (1385) a_select3(pminus_ds1_filter, n5, n1) = all_74_9 & % 232.86/39.64 | | | | | | | | | | | | | | $i(all_74_9) % 232.86/39.64 | | | | | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | | | | | ALPHA: (1385) implies: % 232.86/39.64 | | | | | | | | | | | | | | (1386) a_select3(pminus_ds1_filter, n5, n1) = all_74_9 % 232.86/39.64 | | | | | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_74_9, all_74_8, n1, % 232.86/39.64 | | | | | | | | | | | | | | n5, pminus_ds1_filter, simplifying with (1374), % 232.86/39.64 | | | | | | | | | | | | | | (1386) gives: % 232.86/39.64 | | | | | | | | | | | | | | (1387) all_74_8 = all_74_9 % 232.86/39.64 | | | | | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | | | | | REDUCE: (1034), (1387) imply: % 232.86/39.64 | | | | | | | | | | | | | | (1388) $false % 232.86/39.64 | | | | | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | | | | | CLOSE: (1388) is inconsistent. % 232.86/39.64 | | | | | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | | | | End of split % 232.86/39.64 | | | | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | | | End of split % 232.86/39.64 | | | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | | End of split % 232.86/39.64 | | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | Case 2: % 232.86/39.64 | | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | | (1389) all_74_11 = n2 % 232.86/39.64 | | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | | REDUCE: (1356), (1389) imply: % 232.86/39.64 | | | | | | | | | | | (1390) a_select3(pminus_ds1_filter, n2, n5) = all_74_9 % 232.86/39.64 | | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | | REDUCE: (1355), (1389) imply: % 232.86/39.64 | | | | | | | | | | | (1391) a_select3(pminus_ds1_filter, n5, n2) = all_74_8 % 232.86/39.64 | | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | | REDUCE: (1042), (1389) imply: % 232.86/39.64 | | | | | | | | | | | (1392) leq(n2, n5) % 232.86/39.64 | | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | | REDUCE: (1035), (1389) imply: % 232.86/39.64 | | | | | | | | | | | (1393) leq(n0, n2) % 232.86/39.64 | | | | | | | | | | | % 232.86/39.64 | | | | | | | | | | | GROUND_INST: instantiating (64) with n2, n5, all_74_9, % 232.86/39.64 | | | | | | | | | | | simplifying with (101), (122), (1358), (1390), % 232.86/39.65 | | | | | | | | | | | (1393) gives: % 232.86/39.65 | | | | | | | | | | | (1394) ~ leq(n5, all_74_21) | ~ leq(n2, all_74_21) | % 232.86/39.65 | | | | | | | | | | | (a_select3(pminus_ds1_filter, n5, n2) = all_74_9 & % 232.86/39.65 | | | | | | | | | | | $i(all_74_9)) % 232.86/39.65 | | | | | | | | | | | % 232.86/39.65 | | | | | | | | | | | BETA: splitting (1394) gives: % 232.86/39.65 | | | | | | | | | | | % 232.86/39.65 | | | | | | | | | | | Case 1: % 232.86/39.65 | | | | | | | | | | | | % 232.86/39.65 | | | | | | | | | | | | (1395) ~ leq(n5, all_74_21) % 232.86/39.65 | | | | | | | | | | | | % 232.86/39.65 | | | | | | | | | | | | REDUCE: (135), (1395) imply: % 232.86/39.65 | | | | | | | | | | | | (1396) ~ leq(n5, n5) % 232.86/39.65 | | | | | | | | | | | | % 232.86/39.65 | | | | | | | | | | | | PRED_UNIFY: (1357), (1396) imply: % 232.86/39.65 | | | | | | | | | | | | (1397) $false % 232.86/39.65 | | | | | | | | | | | | % 232.86/39.65 | | | | | | | | | | | | CLOSE: (1397) is inconsistent. % 232.86/39.65 | | | | | | | | | | | | % 232.86/39.65 | | | | | | | | | | | Case 2: % 232.86/39.65 | | | | | | | | | | | | % 232.86/39.65 | | | | | | | | | | | | (1398) ~ leq(n2, all_74_21) | % 232.86/39.65 | | | | | | | | | | | | (a_select3(pminus_ds1_filter, n5, n2) = all_74_9 & % 232.86/39.65 | | | | | | | | | | | | $i(all_74_9)) % 232.86/39.65 | | | | | | | | | | | | % 232.86/39.65 | | | | | | | | | | | | BETA: splitting (1398) gives: % 232.86/39.65 | | | | | | | | | | | | % 232.86/39.65 | | | | | | | | | | | | Case 1: % 232.86/39.65 | | | | | | | | | | | | | % 232.86/39.65 | | | | | | | | | | | | | (1399) ~ leq(n2, all_74_21) % 232.86/39.65 | | | | | | | | | | | | | % 232.86/39.65 | | | | | | | | | | | | | REDUCE: (135), (1399) imply: % 232.86/39.65 | | | | | | | | | | | | | (1400) ~ leq(n2, n5) % 232.86/39.65 | | | | | | | | | | | | | % 232.86/39.65 | | | | | | | | | | | | | PRED_UNIFY: (1392), (1400) imply: % 232.86/39.65 | | | | | | | | | | | | | (1401) $false % 232.86/39.65 | | | | | | | | | | | | | % 232.86/39.65 | | | | | | | | | | | | | CLOSE: (1401) is inconsistent. % 232.86/39.65 | | | | | | | | | | | | | % 232.86/39.65 | | | | | | | | | | | | Case 2: % 232.86/39.65 | | | | | | | | | | | | | % 232.86/39.65 | | | | | | | | | | | | | (1402) a_select3(pminus_ds1_filter, n5, n2) = all_74_9 & % 232.86/39.65 | | | | | | | | | | | | | $i(all_74_9) % 232.86/39.65 | | | | | | | | | | | | | % 232.86/39.65 | | | | | | | | | | | | | ALPHA: (1402) implies: % 232.86/39.65 | | | | | | | | | | | | | (1403) a_select3(pminus_ds1_filter, n5, n2) = all_74_9 % 232.86/39.65 | | | | | | | | | | | | | % 232.86/39.65 | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_74_9, all_74_8, n2, % 232.86/39.65 | | | | | | | | | | | | | n5, pminus_ds1_filter, simplifying with (1391), % 232.86/39.65 | | | | | | | | | | | | | (1403) gives: % 232.86/39.65 | | | | | | | | | | | | | (1404) all_74_8 = all_74_9 % 232.86/39.65 | | | | | | | | | | | | | % 232.86/39.65 | | | | | | | | | | | | | REDUCE: (1034), (1404) imply: % 232.86/39.65 | | | | | | | | | | | | | (1405) $false % 232.86/39.65 | | | | | | | | | | | | | % 232.86/39.65 | | | | | | | | | | | | | CLOSE: (1405) is inconsistent. % 232.86/39.65 | | | | | | | | | | | | | % 232.86/39.65 | | | | | | | | | | | | End of split % 232.86/39.65 | | | | | | | | | | | | % 232.86/39.65 | | | | | | | | | | | End of split % 232.86/39.65 | | | | | | | | | | | % 232.86/39.65 | | | | | | | | | | End of split % 232.86/39.65 | | | | | | | | | | % 232.86/39.65 | | | | | | | | | Case 2: % 232.86/39.65 | | | | | | | | | | % 232.86/39.65 | | | | | | | | | | (1406) all_74_11 = n3 % 232.86/39.65 | | | | | | | | | | % 232.86/39.65 | | | | | | | | | | REDUCE: (1356), (1406) imply: % 232.86/39.65 | | | | | | | | | | (1407) a_select3(pminus_ds1_filter, n3, n5) = all_74_9 % 232.86/39.65 | | | | | | | | | | % 232.86/39.65 | | | | | | | | | | REDUCE: (1355), (1406) imply: % 232.86/39.65 | | | | | | | | | | (1408) a_select3(pminus_ds1_filter, n5, n3) = all_74_8 % 232.86/39.65 | | | | | | | | | | % 232.86/39.65 | | | | | | | | | | REDUCE: (1042), (1406) imply: % 232.86/39.65 | | | | | | | | | | (1409) leq(n3, n5) % 232.86/39.65 | | | | | | | | | | % 232.86/39.65 | | | | | | | | | | REDUCE: (1035), (1406) imply: % 232.86/39.65 | | | | | | | | | | (1410) leq(n0, n3) % 232.86/39.65 | | | | | | | | | | % 232.86/39.65 | | | | | | | | | | GROUND_INST: instantiating (64) with n3, n5, all_74_9, % 232.86/39.65 | | | | | | | | | | simplifying with (112), (122), (1358), (1407), % 232.86/39.65 | | | | | | | | | | (1410) gives: % 232.86/39.65 | | | | | | | | | | (1411) ~ leq(n5, all_74_21) | ~ leq(n3, all_74_21) | % 232.86/39.65 | | | | | | | | | | (a_select3(pminus_ds1_filter, n5, n3) = all_74_9 & % 232.86/39.65 | | | | | | | | | | $i(all_74_9)) % 232.86/39.65 | | | | | | | | | | % 232.86/39.65 | | | | | | | | | | BETA: splitting (1411) gives: % 232.86/39.65 | | | | | | | | | | % 232.86/39.65 | | | | | | | | | | Case 1: % 232.86/39.65 | | | | | | | | | | | % 232.86/39.65 | | | | | | | | | | | (1412) ~ leq(n5, all_74_21) % 232.86/39.65 | | | | | | | | | | | % 232.86/39.65 | | | | | | | | | | | REDUCE: (135), (1412) imply: % 232.86/39.65 | | | | | | | | | | | (1413) ~ leq(n5, n5) % 232.86/39.65 | | | | | | | | | | | % 232.86/39.65 | | | | | | | | | | | PRED_UNIFY: (1357), (1413) imply: % 232.86/39.65 | | | | | | | | | | | (1414) $false % 232.86/39.65 | | | | | | | | | | | % 232.86/39.65 | | | | | | | | | | | CLOSE: (1414) is inconsistent. % 232.86/39.65 | | | | | | | | | | | % 232.86/39.65 | | | | | | | | | | Case 2: % 232.86/39.65 | | | | | | | | | | | % 232.86/39.65 | | | | | | | | | | | (1415) ~ leq(n3, all_74_21) | % 232.86/39.65 | | | | | | | | | | | (a_select3(pminus_ds1_filter, n5, n3) = all_74_9 & % 232.86/39.65 | | | | | | | | | | | $i(all_74_9)) % 232.86/39.65 | | | | | | | | | | | % 232.86/39.65 | | | | | | | | | | | BETA: splitting (1415) gives: % 232.86/39.65 | | | | | | | | | | | % 232.86/39.65 | | | | | | | | | | | Case 1: % 232.86/39.65 | | | | | | | | | | | | % 232.86/39.65 | | | | | | | | | | | | (1416) ~ leq(n3, all_74_21) % 232.86/39.65 | | | | | | | | | | | | % 232.86/39.65 | | | | | | | | | | | | REDUCE: (135), (1416) imply: % 232.86/39.65 | | | | | | | | | | | | (1417) ~ leq(n3, n5) % 232.86/39.65 | | | | | | | | | | | | % 232.86/39.65 | | | | | | | | | | | | PRED_UNIFY: (1409), (1417) imply: % 232.86/39.65 | | | | | | | | | | | | (1418) $false % 232.86/39.65 | | | | | | | | | | | | % 232.86/39.65 | | | | | | | | | | | | CLOSE: (1418) is inconsistent. % 232.86/39.65 | | | | | | | | | | | | % 232.86/39.65 | | | | | | | | | | | Case 2: % 232.86/39.65 | | | | | | | | | | | | % 232.86/39.65 | | | | | | | | | | | | (1419) a_select3(pminus_ds1_filter, n5, n3) = all_74_9 & % 232.86/39.65 | | | | | | | | | | | | $i(all_74_9) % 232.86/39.65 | | | | | | | | | | | | % 232.86/39.65 | | | | | | | | | | | | ALPHA: (1419) implies: % 232.86/39.65 | | | | | | | | | | | | (1420) a_select3(pminus_ds1_filter, n5, n3) = all_74_9 % 232.86/39.65 | | | | | | | | | | | | % 232.86/39.65 | | | | | | | | | | | | REF_CLOSE: (17), (1034), (1408), (1420) are inconsistent by % 232.86/39.65 | | | | | | | | | | | | sub-proof #33. % 232.86/39.65 | | | | | | | | | | | | % 232.86/39.65 | | | | | | | | | | | End of split % 232.86/39.65 | | | | | | | | | | | % 232.86/39.65 | | | | | | | | | | End of split % 232.86/39.65 | | | | | | | | | | % 232.86/39.65 | | | | | | | | | End of split % 232.86/39.65 | | | | | | | | | % 232.86/39.65 | | | | | | | | Case 2: % 232.86/39.65 | | | | | | | | | % 232.86/39.65 | | | | | | | | | (1421) all_74_11 = n4 % 232.86/39.65 | | | | | | | | | % 232.86/39.65 | | | | | | | | | REDUCE: (1356), (1421) imply: % 232.86/39.65 | | | | | | | | | (1422) a_select3(pminus_ds1_filter, n4, n5) = all_74_9 % 232.86/39.65 | | | | | | | | | % 232.86/39.65 | | | | | | | | | REDUCE: (1355), (1421) imply: % 232.86/39.65 | | | | | | | | | (1423) a_select3(pminus_ds1_filter, n5, n4) = all_74_8 % 232.86/39.65 | | | | | | | | | % 232.86/39.65 | | | | | | | | | REDUCE: (1042), (1421) imply: % 232.86/39.65 | | | | | | | | | (1424) leq(n4, n5) % 232.86/39.65 | | | | | | | | | % 232.86/39.65 | | | | | | | | | REDUCE: (1035), (1421) imply: % 232.86/39.65 | | | | | | | | | (1425) leq(n0, n4) % 232.86/39.65 | | | | | | | | | % 232.86/39.65 | | | | | | | | | GROUND_INST: instantiating (64) with n4, n5, all_74_9, % 232.86/39.65 | | | | | | | | | simplifying with (119), (122), (1358), (1422), % 232.86/39.65 | | | | | | | | | (1425) gives: % 232.86/39.65 | | | | | | | | | (1426) ~ leq(n5, all_74_21) | ~ leq(n4, all_74_21) | % 232.86/39.65 | | | | | | | | | (a_select3(pminus_ds1_filter, n5, n4) = all_74_9 & % 232.86/39.65 | | | | | | | | | $i(all_74_9)) % 232.86/39.65 | | | | | | | | | % 232.86/39.65 | | | | | | | | | BETA: splitting (1426) gives: % 232.86/39.65 | | | | | | | | | % 232.86/39.65 | | | | | | | | | Case 1: % 232.86/39.65 | | | | | | | | | | % 232.86/39.65 | | | | | | | | | | (1427) ~ leq(n5, all_74_21) % 232.86/39.65 | | | | | | | | | | % 232.86/39.65 | | | | | | | | | | REDUCE: (135), (1427) imply: % 232.86/39.65 | | | | | | | | | | (1428) ~ leq(n5, n5) % 232.86/39.65 | | | | | | | | | | % 232.86/39.65 | | | | | | | | | | PRED_UNIFY: (1357), (1428) imply: % 232.86/39.65 | | | | | | | | | | (1429) $false % 232.86/39.65 | | | | | | | | | | % 232.86/39.65 | | | | | | | | | | CLOSE: (1429) is inconsistent. % 232.86/39.65 | | | | | | | | | | % 232.86/39.65 | | | | | | | | | Case 2: % 232.86/39.65 | | | | | | | | | | % 232.86/39.65 | | | | | | | | | | (1430) ~ leq(n4, all_74_21) | % 232.86/39.65 | | | | | | | | | | (a_select3(pminus_ds1_filter, n5, n4) = all_74_9 & % 232.86/39.65 | | | | | | | | | | $i(all_74_9)) % 232.86/39.65 | | | | | | | | | | % 232.86/39.65 | | | | | | | | | | BETA: splitting (1430) gives: % 232.86/39.65 | | | | | | | | | | % 232.86/39.65 | | | | | | | | | | Case 1: % 232.86/39.65 | | | | | | | | | | | % 232.86/39.65 | | | | | | | | | | | (1431) ~ leq(n4, all_74_21) % 232.86/39.65 | | | | | | | | | | | % 232.86/39.65 | | | | | | | | | | | REDUCE: (135), (1431) imply: % 232.86/39.65 | | | | | | | | | | | (1432) ~ leq(n4, n5) % 232.86/39.65 | | | | | | | | | | | % 232.86/39.65 | | | | | | | | | | | PRED_UNIFY: (1424), (1432) imply: % 232.86/39.65 | | | | | | | | | | | (1433) $false % 232.86/39.65 | | | | | | | | | | | % 232.86/39.65 | | | | | | | | | | | CLOSE: (1433) is inconsistent. % 232.86/39.65 | | | | | | | | | | | % 232.86/39.65 | | | | | | | | | | Case 2: % 232.86/39.65 | | | | | | | | | | | % 232.86/39.65 | | | | | | | | | | | (1434) a_select3(pminus_ds1_filter, n5, n4) = all_74_9 & % 232.86/39.65 | | | | | | | | | | | $i(all_74_9) % 232.86/39.65 | | | | | | | | | | | % 232.86/39.65 | | | | | | | | | | | ALPHA: (1434) implies: % 232.86/39.65 | | | | | | | | | | | (1435) a_select3(pminus_ds1_filter, n5, n4) = all_74_9 % 232.86/39.65 | | | | | | | | | | | % 232.86/39.65 | | | | | | | | | | | REF_CLOSE: (17), (1034), (1423), (1435) are inconsistent by % 232.86/39.65 | | | | | | | | | | | sub-proof #32. % 232.86/39.65 | | | | | | | | | | | % 232.86/39.65 | | | | | | | | | | End of split % 232.86/39.65 | | | | | | | | | | % 232.86/39.65 | | | | | | | | | End of split % 232.86/39.65 | | | | | | | | | % 232.86/39.65 | | | | | | | | End of split % 232.86/39.65 | | | | | | | | % 232.86/39.65 | | | | | | | End of split % 232.86/39.65 | | | | | | | % 232.86/39.65 | | | | | | End of split % 232.86/39.65 | | | | | | % 232.86/39.65 | | | | | Case 2: % 232.86/39.65 | | | | | | % 232.86/39.65 | | | | | | (1436) all_74_11 = n5 % 232.86/39.65 | | | | | | % 232.86/39.65 | | | | | | REDUCE: (1040), (1436) imply: % 232.86/39.65 | | | | | | (1437) a_select3(pminus_ds1_filter, all_74_10, n5) = all_74_8 % 232.86/39.65 | | | | | | % 232.86/39.65 | | | | | | REDUCE: (1039), (1436) imply: % 232.86/39.65 | | | | | | (1438) a_select3(pminus_ds1_filter, n5, all_74_10) = all_74_9 % 232.86/39.65 | | | | | | % 232.86/39.65 | | | | | | REDUCE: (1042), (1436) imply: % 232.86/39.65 | | | | | | (1439) leq(n5, n5) % 232.86/39.65 | | | | | | % 232.86/39.65 | | | | | | REDUCE: (1035), (1436) imply: % 232.86/39.65 | | | | | | (1440) leq(n0, n5) % 232.86/39.65 | | | | | | % 232.86/39.65 | | | | | | BETA: splitting (1048) gives: % 232.86/39.65 | | | | | | % 232.86/39.65 | | | | | | Case 1: % 232.86/39.65 | | | | | | | % 232.86/39.65 | | | | | | | (1441) gt(n5, all_74_10) % 232.86/39.65 | | | | | | | % 232.86/39.65 | | | | | | | GROUND_INST: instantiating (1) with all_74_10, n5, n4, simplifying % 232.86/39.65 | | | | | | | with (54), (122), (126), (1441) gives: % 232.86/39.65 | | | | | | | (1442) leq(all_74_10, n4) % 232.86/39.65 | | | | | | | % 232.86/39.65 | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_10, n4, % 232.86/39.65 | | | | | | | simplifying with (54), (119), (1442) gives: % 232.86/39.65 | | | | | | | (1443) all_74_10 = n4 | gt(n4, all_74_10) % 232.86/39.65 | | | | | | | % 232.86/39.65 | | | | | | | BETA: splitting (1047) gives: % 232.86/39.65 | | | | | | | % 232.86/39.65 | | | | | | | Case 1: % 232.86/39.65 | | | | | | | | % 232.86/39.65 | | | | | | | | (1444) all_74_10 = n0 % 232.86/39.65 | | | | | | | | % 232.86/39.65 | | | | | | | | REF_CLOSE: (54), (1049), (1444), (irreflexivity_gt) are % 232.86/39.65 | | | | | | | | inconsistent by sub-proof #40. % 232.86/39.65 | | | | | | | | % 232.86/39.65 | | | | | | | Case 2: % 232.86/39.65 | | | | | | | | % 232.86/39.65 | | | | | | | | (1445) ~ (all_74_10 = n0) % 232.86/39.65 | | | | | | | | % 232.86/39.65 | | | | | | | | BETA: splitting (1443) gives: % 232.86/39.65 | | | | | | | | % 232.86/39.65 | | | | | | | | Case 1: % 232.86/39.65 | | | | | | | | | % 232.86/39.65 | | | | | | | | | (1446) gt(n4, all_74_10) % 232.86/39.65 | | | | | | | | | % 232.86/39.65 | | | | | | | | | GROUND_INST: instantiating (1) with all_74_10, n4, n3, % 232.86/39.65 | | | | | | | | | simplifying with (54), (119), (125), (1446) gives: % 232.86/39.65 | | | | | | | | | (1447) leq(all_74_10, n3) % 232.86/39.65 | | | | | | | | | % 232.86/39.65 | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_10, n3, % 232.86/39.65 | | | | | | | | | simplifying with (54), (112), (1447) gives: % 232.86/39.65 | | | | | | | | | (1448) all_74_10 = n3 | gt(n3, all_74_10) % 232.86/39.65 | | | | | | | | | % 232.86/39.65 | | | | | | | | | BETA: splitting (1448) gives: % 232.86/39.65 | | | | | | | | | % 232.86/39.65 | | | | | | | | | Case 1: % 232.86/39.65 | | | | | | | | | | % 232.86/39.65 | | | | | | | | | | (1449) gt(n3, all_74_10) % 232.86/39.65 | | | | | | | | | | % 232.86/39.65 | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_10, n3, n2, % 232.86/39.65 | | | | | | | | | | simplifying with (54), (112), (124), (1449) gives: % 232.86/39.65 | | | | | | | | | | (1450) leq(all_74_10, n2) % 232.86/39.65 | | | | | | | | | | % 232.86/39.65 | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_10, n2, % 232.86/39.65 | | | | | | | | | | simplifying with (54), (101), (1450) gives: % 232.86/39.65 | | | | | | | | | | (1451) all_74_10 = n2 | gt(n2, all_74_10) % 232.86/39.65 | | | | | | | | | | % 232.86/39.65 | | | | | | | | | | BETA: splitting (1451) gives: % 232.86/39.65 | | | | | | | | | | % 232.86/39.65 | | | | | | | | | | Case 1: % 232.86/39.65 | | | | | | | | | | | % 232.86/39.65 | | | | | | | | | | | (1452) gt(n2, all_74_10) % 232.86/39.65 | | | | | | | | | | | % 232.86/39.65 | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_10, n2, n1, % 232.86/39.65 | | | | | | | | | | | simplifying with (54), (101), (123), (1452) gives: % 232.86/39.65 | | | | | | | | | | | (1453) leq(all_74_10, n1) % 232.86/39.65 | | | | | | | | | | | % 232.86/39.65 | | | | | | | | | | | GROUND_INST: instantiating (4) with all_74_10, simplifying with % 232.86/39.65 | | | | | | | | | | | (54), (1036), (1453) gives: % 232.86/39.65 | | | | | | | | | | | (1454) all_74_10 = n1 | all_74_10 = n0 % 232.86/39.65 | | | | | | | | | | | % 232.86/39.65 | | | | | | | | | | | BETA: splitting (1454) gives: % 232.86/39.65 | | | | | | | | | | | % 232.86/39.65 | | | | | | | | | | | Case 1: % 232.86/39.65 | | | | | | | | | | | | % 232.86/39.65 | | | | | | | | | | | | (1455) all_74_10 = n0 % 232.86/39.65 | | | | | | | | | | | | % 232.86/39.65 | | | | | | | | | | | | REDUCE: (1445), (1455) imply: % 232.86/39.65 | | | | | | | | | | | | (1456) $false % 232.86/39.65 | | | | | | | | | | | | % 232.86/39.65 | | | | | | | | | | | | CLOSE: (1456) is inconsistent. % 232.86/39.65 | | | | | | | | | | | | % 232.86/39.65 | | | | | | | | | | | Case 2: % 232.86/39.65 | | | | | | | | | | | | % 232.86/39.65 | | | | | | | | | | | | (1457) all_74_10 = n1 % 232.86/39.65 | | | | | | | | | | | | % 232.86/39.65 | | | | | | | | | | | | REDUCE: (1437), (1457) imply: % 232.86/39.65 | | | | | | | | | | | | (1458) a_select3(pminus_ds1_filter, n1, n5) = all_74_8 % 232.86/39.65 | | | | | | | | | | | | % 232.86/39.65 | | | | | | | | | | | | REDUCE: (1438), (1457) imply: % 232.86/39.65 | | | | | | | | | | | | (1459) a_select3(pminus_ds1_filter, n5, n1) = all_74_9 % 232.86/39.65 | | | | | | | | | | | | % 232.86/39.65 | | | | | | | | | | | | REDUCE: (1041), (1457) imply: % 232.86/39.65 | | | | | | | | | | | | (1460) leq(n1, n5) % 232.86/39.65 | | | | | | | | | | | | % 232.86/39.65 | | | | | | | | | | | | REDUCE: (1036), (1457) imply: % 232.86/39.65 | | | | | | | | | | | | (1461) leq(n0, n1) % 232.86/39.65 | | | | | | | | | | | | % 232.86/39.65 | | | | | | | | | | | | GROUND_INST: instantiating (64) with n1, n5, all_74_8, % 232.86/39.65 | | | | | | | | | | | | simplifying with (85), (122), (1440), (1458), % 232.86/39.65 | | | | | | | | | | | | (1461) gives: % 232.86/39.65 | | | | | | | | | | | | (1462) ~ leq(n5, all_74_21) | ~ leq(n1, all_74_21) | % 232.86/39.65 | | | | | | | | | | | | (a_select3(pminus_ds1_filter, n5, n1) = all_74_8 & % 232.86/39.65 | | | | | | | | | | | | $i(all_74_8)) % 232.86/39.65 | | | | | | | | | | | | % 232.86/39.65 | | | | | | | | | | | | BETA: splitting (1462) gives: % 232.86/39.65 | | | | | | | | | | | | % 232.86/39.65 | | | | | | | | | | | | Case 1: % 232.86/39.65 | | | | | | | | | | | | | % 232.86/39.66 | | | | | | | | | | | | | (1463) ~ leq(n5, all_74_21) % 232.86/39.66 | | | | | | | | | | | | | % 232.86/39.66 | | | | | | | | | | | | | REDUCE: (135), (1463) imply: % 232.86/39.66 | | | | | | | | | | | | | (1464) ~ leq(n5, n5) % 232.86/39.66 | | | | | | | | | | | | | % 232.86/39.66 | | | | | | | | | | | | | PRED_UNIFY: (1439), (1464) imply: % 232.86/39.66 | | | | | | | | | | | | | (1465) $false % 232.86/39.66 | | | | | | | | | | | | | % 232.86/39.66 | | | | | | | | | | | | | CLOSE: (1465) is inconsistent. % 233.00/39.66 | | | | | | | | | | | | | % 233.00/39.66 | | | | | | | | | | | | Case 2: % 233.00/39.66 | | | | | | | | | | | | | % 233.00/39.66 | | | | | | | | | | | | | (1466) ~ leq(n1, all_74_21) | % 233.00/39.66 | | | | | | | | | | | | | (a_select3(pminus_ds1_filter, n5, n1) = all_74_8 & % 233.00/39.66 | | | | | | | | | | | | | $i(all_74_8)) % 233.00/39.66 | | | | | | | | | | | | | % 233.00/39.66 | | | | | | | | | | | | | BETA: splitting (1466) gives: % 233.00/39.66 | | | | | | | | | | | | | % 233.00/39.66 | | | | | | | | | | | | | Case 1: % 233.00/39.66 | | | | | | | | | | | | | | % 233.00/39.66 | | | | | | | | | | | | | | (1467) ~ leq(n1, all_74_21) % 233.00/39.66 | | | | | | | | | | | | | | % 233.00/39.66 | | | | | | | | | | | | | | REDUCE: (135), (1467) imply: % 233.00/39.66 | | | | | | | | | | | | | | (1468) ~ leq(n1, n5) % 233.00/39.66 | | | | | | | | | | | | | | % 233.00/39.66 | | | | | | | | | | | | | | PRED_UNIFY: (1460), (1468) imply: % 233.00/39.66 | | | | | | | | | | | | | | (1469) $false % 233.00/39.66 | | | | | | | | | | | | | | % 233.00/39.66 | | | | | | | | | | | | | | CLOSE: (1469) is inconsistent. % 233.00/39.66 | | | | | | | | | | | | | | % 233.00/39.66 | | | | | | | | | | | | | Case 2: % 233.00/39.66 | | | | | | | | | | | | | | % 233.00/39.66 | | | | | | | | | | | | | | (1470) a_select3(pminus_ds1_filter, n5, n1) = all_74_8 & % 233.00/39.66 | | | | | | | | | | | | | | $i(all_74_8) % 233.00/39.66 | | | | | | | | | | | | | | % 233.00/39.66 | | | | | | | | | | | | | | ALPHA: (1470) implies: % 233.00/39.66 | | | | | | | | | | | | | | (1471) a_select3(pminus_ds1_filter, n5, n1) = all_74_8 % 233.00/39.66 | | | | | | | | | | | | | | % 233.00/39.66 | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_74_9, all_74_8, n1, % 233.00/39.66 | | | | | | | | | | | | | | n5, pminus_ds1_filter, simplifying with (1459), % 233.00/39.66 | | | | | | | | | | | | | | (1471) gives: % 233.00/39.66 | | | | | | | | | | | | | | (1472) all_74_8 = all_74_9 % 233.00/39.66 | | | | | | | | | | | | | | % 233.00/39.66 | | | | | | | | | | | | | | REDUCE: (1034), (1472) imply: % 233.00/39.66 | | | | | | | | | | | | | | (1473) $false % 233.00/39.66 | | | | | | | | | | | | | | % 233.00/39.66 | | | | | | | | | | | | | | CLOSE: (1473) is inconsistent. % 233.00/39.66 | | | | | | | | | | | | | | % 233.00/39.66 | | | | | | | | | | | | | End of split % 233.00/39.66 | | | | | | | | | | | | | % 233.00/39.66 | | | | | | | | | | | | End of split % 233.00/39.66 | | | | | | | | | | | | % 233.00/39.66 | | | | | | | | | | | End of split % 233.00/39.66 | | | | | | | | | | | % 233.00/39.66 | | | | | | | | | | Case 2: % 233.00/39.66 | | | | | | | | | | | % 233.00/39.66 | | | | | | | | | | | (1474) all_74_10 = n2 % 233.00/39.66 | | | | | | | | | | | % 233.00/39.66 | | | | | | | | | | | REDUCE: (1437), (1474) imply: % 233.00/39.66 | | | | | | | | | | | (1475) a_select3(pminus_ds1_filter, n2, n5) = all_74_8 % 233.00/39.66 | | | | | | | | | | | % 233.00/39.66 | | | | | | | | | | | REDUCE: (1438), (1474) imply: % 233.00/39.66 | | | | | | | | | | | (1476) a_select3(pminus_ds1_filter, n5, n2) = all_74_9 % 233.00/39.66 | | | | | | | | | | | % 233.00/39.66 | | | | | | | | | | | REDUCE: (1041), (1474) imply: % 233.00/39.66 | | | | | | | | | | | (1477) leq(n2, n5) % 233.00/39.66 | | | | | | | | | | | % 233.00/39.66 | | | | | | | | | | | REDUCE: (1036), (1474) imply: % 233.00/39.66 | | | | | | | | | | | (1478) leq(n0, n2) % 233.00/39.66 | | | | | | | | | | | % 233.00/39.66 | | | | | | | | | | | GROUND_INST: instantiating (64) with n2, n5, all_74_8, % 233.00/39.66 | | | | | | | | | | | simplifying with (101), (122), (1440), (1475), % 233.00/39.66 | | | | | | | | | | | (1478) gives: % 233.00/39.66 | | | | | | | | | | | (1479) ~ leq(n5, all_74_21) | ~ leq(n2, all_74_21) | % 233.00/39.66 | | | | | | | | | | | (a_select3(pminus_ds1_filter, n5, n2) = all_74_8 & % 233.00/39.66 | | | | | | | | | | | $i(all_74_8)) % 233.00/39.66 | | | | | | | | | | | % 233.00/39.66 | | | | | | | | | | | BETA: splitting (1479) gives: % 233.00/39.66 | | | | | | | | | | | % 233.00/39.66 | | | | | | | | | | | Case 1: % 233.00/39.66 | | | | | | | | | | | | % 233.00/39.66 | | | | | | | | | | | | (1480) ~ leq(n5, all_74_21) % 233.00/39.66 | | | | | | | | | | | | % 233.00/39.66 | | | | | | | | | | | | REDUCE: (135), (1480) imply: % 233.00/39.66 | | | | | | | | | | | | (1481) ~ leq(n5, n5) % 233.00/39.66 | | | | | | | | | | | | % 233.00/39.66 | | | | | | | | | | | | PRED_UNIFY: (1439), (1481) imply: % 233.00/39.66 | | | | | | | | | | | | (1482) $false % 233.00/39.66 | | | | | | | | | | | | % 233.00/39.66 | | | | | | | | | | | | CLOSE: (1482) is inconsistent. % 233.00/39.66 | | | | | | | | | | | | % 233.00/39.66 | | | | | | | | | | | Case 2: % 233.00/39.66 | | | | | | | | | | | | % 233.00/39.66 | | | | | | | | | | | | (1483) ~ leq(n2, all_74_21) | % 233.00/39.66 | | | | | | | | | | | | (a_select3(pminus_ds1_filter, n5, n2) = all_74_8 & % 233.00/39.66 | | | | | | | | | | | | $i(all_74_8)) % 233.00/39.66 | | | | | | | | | | | | % 233.00/39.66 | | | | | | | | | | | | BETA: splitting (1483) gives: % 233.00/39.66 | | | | | | | | | | | | % 233.00/39.66 | | | | | | | | | | | | Case 1: % 233.00/39.66 | | | | | | | | | | | | | % 233.00/39.66 | | | | | | | | | | | | | (1484) ~ leq(n2, all_74_21) % 233.00/39.66 | | | | | | | | | | | | | % 233.00/39.66 | | | | | | | | | | | | | REDUCE: (135), (1484) imply: % 233.00/39.66 | | | | | | | | | | | | | (1485) ~ leq(n2, n5) % 233.00/39.66 | | | | | | | | | | | | | % 233.00/39.66 | | | | | | | | | | | | | PRED_UNIFY: (1477), (1485) imply: % 233.00/39.66 | | | | | | | | | | | | | (1486) $false % 233.00/39.66 | | | | | | | | | | | | | % 233.00/39.66 | | | | | | | | | | | | | CLOSE: (1486) is inconsistent. % 233.00/39.66 | | | | | | | | | | | | | % 233.00/39.66 | | | | | | | | | | | | Case 2: % 233.00/39.66 | | | | | | | | | | | | | % 233.00/39.66 | | | | | | | | | | | | | (1487) a_select3(pminus_ds1_filter, n5, n2) = all_74_8 & % 233.00/39.66 | | | | | | | | | | | | | $i(all_74_8) % 233.00/39.66 | | | | | | | | | | | | | % 233.00/39.66 | | | | | | | | | | | | | ALPHA: (1487) implies: % 233.00/39.66 | | | | | | | | | | | | | (1488) a_select3(pminus_ds1_filter, n5, n2) = all_74_8 % 233.00/39.66 | | | | | | | | | | | | | % 233.00/39.66 | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_74_9, all_74_8, n2, % 233.00/39.66 | | | | | | | | | | | | | n5, pminus_ds1_filter, simplifying with (1476), % 233.00/39.66 | | | | | | | | | | | | | (1488) gives: % 233.00/39.66 | | | | | | | | | | | | | (1489) all_74_8 = all_74_9 % 233.00/39.66 | | | | | | | | | | | | | % 233.00/39.66 | | | | | | | | | | | | | REDUCE: (1034), (1489) imply: % 233.00/39.66 | | | | | | | | | | | | | (1490) $false % 233.00/39.66 | | | | | | | | | | | | | % 233.00/39.66 | | | | | | | | | | | | | CLOSE: (1490) is inconsistent. % 233.00/39.66 | | | | | | | | | | | | | % 233.00/39.66 | | | | | | | | | | | | End of split % 233.00/39.66 | | | | | | | | | | | | % 233.00/39.66 | | | | | | | | | | | End of split % 233.00/39.66 | | | | | | | | | | | % 233.00/39.66 | | | | | | | | | | End of split % 233.00/39.66 | | | | | | | | | | % 233.00/39.66 | | | | | | | | | Case 2: % 233.00/39.66 | | | | | | | | | | % 233.00/39.66 | | | | | | | | | | (1491) all_74_10 = n3 % 233.00/39.66 | | | | | | | | | | % 233.00/39.66 | | | | | | | | | | REDUCE: (1437), (1491) imply: % 233.00/39.66 | | | | | | | | | | (1492) a_select3(pminus_ds1_filter, n3, n5) = all_74_8 % 233.00/39.66 | | | | | | | | | | % 233.00/39.66 | | | | | | | | | | REDUCE: (1438), (1491) imply: % 233.00/39.66 | | | | | | | | | | (1493) a_select3(pminus_ds1_filter, n5, n3) = all_74_9 % 233.00/39.66 | | | | | | | | | | % 233.00/39.66 | | | | | | | | | | REDUCE: (1041), (1491) imply: % 233.00/39.66 | | | | | | | | | | (1494) leq(n3, n5) % 233.00/39.66 | | | | | | | | | | % 233.00/39.66 | | | | | | | | | | REDUCE: (1036), (1491) imply: % 233.00/39.66 | | | | | | | | | | (1495) leq(n0, n3) % 233.00/39.66 | | | | | | | | | | % 233.00/39.66 | | | | | | | | | | GROUND_INST: instantiating (64) with n3, n5, all_74_8, % 233.00/39.66 | | | | | | | | | | simplifying with (112), (122), (1440), (1492), % 233.00/39.66 | | | | | | | | | | (1495) gives: % 233.00/39.66 | | | | | | | | | | (1496) ~ leq(n5, all_74_21) | ~ leq(n3, all_74_21) | % 233.00/39.66 | | | | | | | | | | (a_select3(pminus_ds1_filter, n5, n3) = all_74_8 & % 233.00/39.66 | | | | | | | | | | $i(all_74_8)) % 233.00/39.66 | | | | | | | | | | % 233.00/39.66 | | | | | | | | | | BETA: splitting (1496) gives: % 233.00/39.66 | | | | | | | | | | % 233.00/39.66 | | | | | | | | | | Case 1: % 233.00/39.66 | | | | | | | | | | | % 233.00/39.66 | | | | | | | | | | | (1497) ~ leq(n5, all_74_21) % 233.00/39.66 | | | | | | | | | | | % 233.00/39.66 | | | | | | | | | | | REDUCE: (135), (1497) imply: % 233.00/39.66 | | | | | | | | | | | (1498) ~ leq(n5, n5) % 233.00/39.66 | | | | | | | | | | | % 233.00/39.66 | | | | | | | | | | | PRED_UNIFY: (1439), (1498) imply: % 233.00/39.66 | | | | | | | | | | | (1499) $false % 233.00/39.66 | | | | | | | | | | | % 233.00/39.66 | | | | | | | | | | | CLOSE: (1499) is inconsistent. % 233.00/39.66 | | | | | | | | | | | % 233.00/39.66 | | | | | | | | | | Case 2: % 233.00/39.66 | | | | | | | | | | | % 233.00/39.66 | | | | | | | | | | | (1500) ~ leq(n3, all_74_21) | % 233.00/39.66 | | | | | | | | | | | (a_select3(pminus_ds1_filter, n5, n3) = all_74_8 & % 233.00/39.66 | | | | | | | | | | | $i(all_74_8)) % 233.00/39.66 | | | | | | | | | | | % 233.00/39.66 | | | | | | | | | | | BETA: splitting (1500) gives: % 233.00/39.66 | | | | | | | | | | | % 233.00/39.66 | | | | | | | | | | | Case 1: % 233.00/39.66 | | | | | | | | | | | | % 233.00/39.66 | | | | | | | | | | | | (1501) ~ leq(n3, all_74_21) % 233.00/39.66 | | | | | | | | | | | | % 233.00/39.66 | | | | | | | | | | | | REDUCE: (135), (1501) imply: % 233.00/39.66 | | | | | | | | | | | | (1502) ~ leq(n3, n5) % 233.00/39.66 | | | | | | | | | | | | % 233.00/39.66 | | | | | | | | | | | | PRED_UNIFY: (1494), (1502) imply: % 233.00/39.66 | | | | | | | | | | | | (1503) $false % 233.00/39.66 | | | | | | | | | | | | % 233.00/39.66 | | | | | | | | | | | | CLOSE: (1503) is inconsistent. % 233.00/39.66 | | | | | | | | | | | | % 233.00/39.66 | | | | | | | | | | | Case 2: % 233.00/39.66 | | | | | | | | | | | | % 233.00/39.66 | | | | | | | | | | | | (1504) a_select3(pminus_ds1_filter, n5, n3) = all_74_8 & % 233.00/39.66 | | | | | | | | | | | | $i(all_74_8) % 233.00/39.66 | | | | | | | | | | | | % 233.00/39.66 | | | | | | | | | | | | ALPHA: (1504) implies: % 233.00/39.66 | | | | | | | | | | | | (1505) a_select3(pminus_ds1_filter, n5, n3) = all_74_8 % 233.00/39.66 | | | | | | | | | | | | % 233.00/39.66 | | | | | | | | | | | | REF_CLOSE: (17), (1034), (1493), (1505) are inconsistent by % 233.00/39.66 | | | | | | | | | | | | sub-proof #33. % 233.00/39.66 | | | | | | | | | | | | % 233.00/39.66 | | | | | | | | | | | End of split % 233.00/39.66 | | | | | | | | | | | % 233.00/39.66 | | | | | | | | | | End of split % 233.00/39.66 | | | | | | | | | | % 233.00/39.66 | | | | | | | | | End of split % 233.00/39.66 | | | | | | | | | % 233.00/39.66 | | | | | | | | Case 2: % 233.00/39.66 | | | | | | | | | % 233.00/39.66 | | | | | | | | | (1506) all_74_10 = n4 % 233.00/39.66 | | | | | | | | | % 233.00/39.66 | | | | | | | | | REDUCE: (1437), (1506) imply: % 233.00/39.66 | | | | | | | | | (1507) a_select3(pminus_ds1_filter, n4, n5) = all_74_8 % 233.00/39.66 | | | | | | | | | % 233.00/39.66 | | | | | | | | | REDUCE: (1438), (1506) imply: % 233.00/39.66 | | | | | | | | | (1508) a_select3(pminus_ds1_filter, n5, n4) = all_74_9 % 233.00/39.66 | | | | | | | | | % 233.00/39.66 | | | | | | | | | REDUCE: (1041), (1506) imply: % 233.00/39.66 | | | | | | | | | (1509) leq(n4, n5) % 233.00/39.66 | | | | | | | | | % 233.00/39.66 | | | | | | | | | REDUCE: (1036), (1506) imply: % 233.00/39.66 | | | | | | | | | (1510) leq(n0, n4) % 233.00/39.66 | | | | | | | | | % 233.00/39.66 | | | | | | | | | GROUND_INST: instantiating (64) with n4, n5, all_74_8, % 233.00/39.66 | | | | | | | | | simplifying with (119), (122), (1440), (1507), % 233.00/39.66 | | | | | | | | | (1510) gives: % 233.00/39.66 | | | | | | | | | (1511) ~ leq(n5, all_74_21) | ~ leq(n4, all_74_21) | % 233.00/39.66 | | | | | | | | | (a_select3(pminus_ds1_filter, n5, n4) = all_74_8 & % 233.00/39.66 | | | | | | | | | $i(all_74_8)) % 233.00/39.66 | | | | | | | | | % 233.00/39.66 | | | | | | | | | BETA: splitting (1511) gives: % 233.00/39.66 | | | | | | | | | % 233.00/39.66 | | | | | | | | | Case 1: % 233.00/39.66 | | | | | | | | | | % 233.00/39.66 | | | | | | | | | | (1512) ~ leq(n5, all_74_21) % 233.00/39.66 | | | | | | | | | | % 233.00/39.66 | | | | | | | | | | REDUCE: (135), (1512) imply: % 233.00/39.66 | | | | | | | | | | (1513) ~ leq(n5, n5) % 233.00/39.66 | | | | | | | | | | % 233.00/39.66 | | | | | | | | | | PRED_UNIFY: (1439), (1513) imply: % 233.00/39.66 | | | | | | | | | | (1514) $false % 233.00/39.66 | | | | | | | | | | % 233.00/39.66 | | | | | | | | | | CLOSE: (1514) is inconsistent. % 233.00/39.66 | | | | | | | | | | % 233.00/39.66 | | | | | | | | | Case 2: % 233.00/39.66 | | | | | | | | | | % 233.00/39.66 | | | | | | | | | | (1515) ~ leq(n4, all_74_21) | % 233.00/39.66 | | | | | | | | | | (a_select3(pminus_ds1_filter, n5, n4) = all_74_8 & % 233.00/39.66 | | | | | | | | | | $i(all_74_8)) % 233.00/39.66 | | | | | | | | | | % 233.00/39.66 | | | | | | | | | | BETA: splitting (1515) gives: % 233.00/39.66 | | | | | | | | | | % 233.00/39.66 | | | | | | | | | | Case 1: % 233.00/39.66 | | | | | | | | | | | % 233.00/39.66 | | | | | | | | | | | (1516) ~ leq(n4, all_74_21) % 233.00/39.66 | | | | | | | | | | | % 233.00/39.66 | | | | | | | | | | | REDUCE: (135), (1516) imply: % 233.00/39.66 | | | | | | | | | | | (1517) ~ leq(n4, n5) % 233.00/39.66 | | | | | | | | | | | % 233.00/39.66 | | | | | | | | | | | PRED_UNIFY: (1509), (1517) imply: % 233.00/39.66 | | | | | | | | | | | (1518) $false % 233.00/39.66 | | | | | | | | | | | % 233.00/39.66 | | | | | | | | | | | CLOSE: (1518) is inconsistent. % 233.00/39.66 | | | | | | | | | | | % 233.00/39.66 | | | | | | | | | | Case 2: % 233.00/39.66 | | | | | | | | | | | % 233.00/39.66 | | | | | | | | | | | (1519) a_select3(pminus_ds1_filter, n5, n4) = all_74_8 & % 233.00/39.66 | | | | | | | | | | | $i(all_74_8) % 233.00/39.66 | | | | | | | | | | | % 233.00/39.66 | | | | | | | | | | | ALPHA: (1519) implies: % 233.00/39.66 | | | | | | | | | | | (1520) a_select3(pminus_ds1_filter, n5, n4) = all_74_8 % 233.00/39.66 | | | | | | | | | | | % 233.00/39.66 | | | | | | | | | | | REF_CLOSE: (17), (1034), (1508), (1520) are inconsistent by % 233.00/39.66 | | | | | | | | | | | sub-proof #32. % 233.00/39.66 | | | | | | | | | | | % 233.00/39.66 | | | | | | | | | | End of split % 233.00/39.66 | | | | | | | | | | % 233.00/39.66 | | | | | | | | | End of split % 233.00/39.66 | | | | | | | | | % 233.00/39.66 | | | | | | | | End of split % 233.00/39.66 | | | | | | | | % 233.00/39.66 | | | | | | | End of split % 233.00/39.66 | | | | | | | % 233.00/39.66 | | | | | | Case 2: % 233.00/39.66 | | | | | | | % 233.00/39.66 | | | | | | | (1521) all_74_10 = n5 % 233.00/39.66 | | | | | | | % 233.00/39.66 | | | | | | | REDUCE: (1437), (1521) imply: % 233.00/39.66 | | | | | | | (1522) a_select3(pminus_ds1_filter, n5, n5) = all_74_8 % 233.00/39.66 | | | | | | | % 233.00/39.66 | | | | | | | REDUCE: (1438), (1521) imply: % 233.00/39.66 | | | | | | | (1523) a_select3(pminus_ds1_filter, n5, n5) = all_74_9 % 233.00/39.66 | | | | | | | % 233.00/39.66 | | | | | | | GROUND_INST: instantiating (17) with all_74_9, all_74_8, n5, n5, % 233.00/39.66 | | | | | | | pminus_ds1_filter, simplifying with (1522), (1523) % 233.00/39.66 | | | | | | | gives: % 233.00/39.66 | | | | | | | (1524) all_74_8 = all_74_9 % 233.00/39.66 | | | | | | | % 233.00/39.66 | | | | | | | REDUCE: (1034), (1524) imply: % 233.00/39.66 | | | | | | | (1525) $false % 233.00/39.66 | | | | | | | % 233.00/39.66 | | | | | | | CLOSE: (1525) is inconsistent. % 233.00/39.66 | | | | | | | % 233.00/39.66 | | | | | | End of split % 233.00/39.66 | | | | | | % 233.00/39.66 | | | | | End of split % 233.00/39.66 | | | | | % 233.00/39.66 | | | | Case 2: % 233.00/39.66 | | | | | % 233.00/39.66 | | | | | (1526) all_74_11 = n0 % 233.00/39.66 | | | | | (1527) ~ gt(all_74_11, n0) % 233.00/39.66 | | | | | % 233.00/39.66 | | | | | REDUCE: (1040), (1526) imply: % 233.00/39.66 | | | | | (1528) a_select3(pminus_ds1_filter, all_74_10, n0) = all_74_8 % 233.00/39.66 | | | | | % 233.00/39.66 | | | | | REDUCE: (1039), (1526) imply: % 233.00/39.66 | | | | | (1529) a_select3(pminus_ds1_filter, n0, all_74_10) = all_74_9 % 233.00/39.66 | | | | | % 233.00/39.66 | | | | | REDUCE: (1042), (1526) imply: % 233.00/39.66 | | | | | (1530) leq(n0, n5) % 233.00/39.66 | | | | | % 233.00/39.66 | | | | | REDUCE: (1035), (1526) imply: % 233.00/39.66 | | | | | (1531) leq(n0, n0) % 233.00/39.66 | | | | | % 233.00/39.66 | | | | | REDUCE: (1526), (1527) imply: % 233.00/39.66 | | | | | (1532) ~ gt(n0, n0) % 233.00/39.66 | | | | | % 233.00/39.66 | | | | | BETA: splitting (1048) gives: % 233.00/39.66 | | | | | % 233.00/39.66 | | | | | Case 1: % 233.00/39.66 | | | | | | % 233.00/39.66 | | | | | | (1533) gt(n5, all_74_10) % 233.00/39.66 | | | | | | % 233.00/39.66 | | | | | | GROUND_INST: instantiating (1) with all_74_10, n5, n4, simplifying % 233.00/39.66 | | | | | | with (54), (122), (126), (1533) gives: % 233.00/39.66 | | | | | | (1534) leq(all_74_10, n4) % 233.00/39.66 | | | | | | % 233.00/39.66 | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_10, n4, simplifying % 233.00/39.66 | | | | | | with (54), (119), (1534) gives: % 233.00/39.67 | | | | | | (1535) all_74_10 = n4 | gt(n4, all_74_10) % 233.00/39.67 | | | | | | % 233.00/39.67 | | | | | | BETA: splitting (1047) gives: % 233.00/39.67 | | | | | | % 233.00/39.67 | | | | | | Case 1: % 233.00/39.67 | | | | | | | % 233.00/39.67 | | | | | | | (1536) all_74_10 = n0 % 233.00/39.67 | | | | | | | % 233.00/39.67 | | | | | | | REDUCE: (1049), (1536) imply: % 233.00/39.67 | | | | | | | (1537) gt(n0, n0) % 233.00/39.67 | | | | | | | % 233.00/39.67 | | | | | | | PRED_UNIFY: (1532), (1537) imply: % 233.00/39.67 | | | | | | | (1538) $false % 233.00/39.67 | | | | | | | % 233.00/39.67 | | | | | | | CLOSE: (1538) is inconsistent. % 233.00/39.67 | | | | | | | % 233.00/39.67 | | | | | | Case 2: % 233.00/39.67 | | | | | | | % 233.00/39.67 | | | | | | | (1539) ~ (all_74_10 = n0) % 233.00/39.67 | | | | | | | % 233.00/39.67 | | | | | | | BETA: splitting (1535) gives: % 233.00/39.67 | | | | | | | % 233.00/39.67 | | | | | | | Case 1: % 233.00/39.67 | | | | | | | | % 233.00/39.67 | | | | | | | | (1540) gt(n4, all_74_10) % 233.00/39.67 | | | | | | | | % 233.00/39.67 | | | | | | | | GROUND_INST: instantiating (1) with all_74_10, n4, n3, % 233.00/39.67 | | | | | | | | simplifying with (54), (119), (125), (1540) gives: % 233.00/39.67 | | | | | | | | (1541) leq(all_74_10, n3) % 233.00/39.67 | | | | | | | | % 233.00/39.67 | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_10, n3, % 233.00/39.67 | | | | | | | | simplifying with (54), (112), (1541) gives: % 233.00/39.67 | | | | | | | | (1542) all_74_10 = n3 | gt(n3, all_74_10) % 233.00/39.67 | | | | | | | | % 233.00/39.67 | | | | | | | | BETA: splitting (1542) gives: % 233.00/39.67 | | | | | | | | % 233.00/39.67 | | | | | | | | Case 1: % 233.00/39.67 | | | | | | | | | % 233.00/39.67 | | | | | | | | | (1543) gt(n3, all_74_10) % 233.00/39.67 | | | | | | | | | % 233.00/39.67 | | | | | | | | | GROUND_INST: instantiating (1) with all_74_10, n3, n2, % 233.00/39.67 | | | | | | | | | simplifying with (54), (112), (124), (1543) gives: % 233.00/39.67 | | | | | | | | | (1544) leq(all_74_10, n2) % 233.00/39.67 | | | | | | | | | % 233.00/39.67 | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_10, n2, % 233.00/39.67 | | | | | | | | | simplifying with (54), (101), (1544) gives: % 233.00/39.67 | | | | | | | | | (1545) all_74_10 = n2 | gt(n2, all_74_10) % 233.00/39.67 | | | | | | | | | % 233.00/39.67 | | | | | | | | | BETA: splitting (1545) gives: % 233.00/39.67 | | | | | | | | | % 233.00/39.67 | | | | | | | | | Case 1: % 233.00/39.67 | | | | | | | | | | % 233.00/39.67 | | | | | | | | | | (1546) gt(n2, all_74_10) % 233.00/39.67 | | | | | | | | | | % 233.00/39.67 | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_10, n2, n1, % 233.00/39.67 | | | | | | | | | | simplifying with (54), (101), (123), (1546) gives: % 233.00/39.67 | | | | | | | | | | (1547) leq(all_74_10, n1) % 233.00/39.67 | | | | | | | | | | % 233.00/39.67 | | | | | | | | | | GROUND_INST: instantiating (4) with all_74_10, simplifying with % 233.00/39.67 | | | | | | | | | | (54), (1036), (1547) gives: % 233.00/39.67 | | | | | | | | | | (1548) all_74_10 = n1 | all_74_10 = n0 % 233.00/39.67 | | | | | | | | | | % 233.00/39.67 | | | | | | | | | | BETA: splitting (1548) gives: % 233.00/39.67 | | | | | | | | | | % 233.00/39.67 | | | | | | | | | | Case 1: % 233.00/39.67 | | | | | | | | | | | % 233.00/39.67 | | | | | | | | | | | (1549) all_74_10 = n0 % 233.00/39.67 | | | | | | | | | | | % 233.00/39.67 | | | | | | | | | | | REDUCE: (1539), (1549) imply: % 233.00/39.67 | | | | | | | | | | | (1550) $false % 233.00/39.67 | | | | | | | | | | | % 233.00/39.67 | | | | | | | | | | | CLOSE: (1550) is inconsistent. % 233.00/39.67 | | | | | | | | | | | % 233.00/39.67 | | | | | | | | | | Case 2: % 233.00/39.67 | | | | | | | | | | | % 233.00/39.67 | | | | | | | | | | | (1551) all_74_10 = n1 % 233.00/39.67 | | | | | | | | | | | % 233.00/39.67 | | | | | | | | | | | REDUCE: (1528), (1551) imply: % 233.00/39.67 | | | | | | | | | | | (1552) a_select3(pminus_ds1_filter, n1, n0) = all_74_8 % 233.00/39.67 | | | | | | | | | | | % 233.00/39.67 | | | | | | | | | | | REDUCE: (1529), (1551) imply: % 233.00/39.67 | | | | | | | | | | | (1553) a_select3(pminus_ds1_filter, n0, n1) = all_74_9 % 233.00/39.67 | | | | | | | | | | | % 233.00/39.67 | | | | | | | | | | | REDUCE: (1041), (1551) imply: % 233.00/39.67 | | | | | | | | | | | (1554) leq(n1, n5) % 233.00/39.67 | | | | | | | | | | | % 233.00/39.67 | | | | | | | | | | | REDUCE: (1036), (1551) imply: % 233.00/39.67 | | | | | | | | | | | (1555) leq(n0, n1) % 233.00/39.67 | | | | | | | | | | | % 233.00/39.67 | | | | | | | | | | | GROUND_INST: instantiating (64) with n0, n1, all_74_9, % 233.00/39.67 | | | | | | | | | | | simplifying with (12), (85), (1531), (1553), % 233.00/39.67 | | | | | | | | | | | (1555) gives: % 233.00/39.67 | | | | | | | | | | | (1556) ~ leq(n1, all_74_21) | ~ leq(n0, all_74_21) | % 233.00/39.67 | | | | | | | | | | | (a_select3(pminus_ds1_filter, n1, n0) = all_74_9 & % 233.00/39.67 | | | | | | | | | | | $i(all_74_9)) % 233.00/39.67 | | | | | | | | | | | % 233.00/39.67 | | | | | | | | | | | BETA: splitting (1556) gives: % 233.00/39.67 | | | | | | | | | | | % 233.00/39.67 | | | | | | | | | | | Case 1: % 233.00/39.67 | | | | | | | | | | | | % 233.00/39.67 | | | | | | | | | | | | (1557) ~ leq(n0, all_74_21) % 233.00/39.67 | | | | | | | | | | | | % 233.00/39.67 | | | | | | | | | | | | REDUCE: (135), (1557) imply: % 233.00/39.67 | | | | | | | | | | | | (1558) ~ leq(n0, n5) % 233.00/39.67 | | | | | | | | | | | | % 233.00/39.67 | | | | | | | | | | | | PRED_UNIFY: (1530), (1558) imply: % 233.00/39.67 | | | | | | | | | | | | (1559) $false % 233.00/39.67 | | | | | | | | | | | | % 233.00/39.67 | | | | | | | | | | | | CLOSE: (1559) is inconsistent. % 233.00/39.67 | | | | | | | | | | | | % 233.00/39.67 | | | | | | | | | | | Case 2: % 233.00/39.67 | | | | | | | | | | | | % 233.00/39.67 | | | | | | | | | | | | (1560) ~ leq(n1, all_74_21) | % 233.00/39.67 | | | | | | | | | | | | (a_select3(pminus_ds1_filter, n1, n0) = all_74_9 & % 233.00/39.67 | | | | | | | | | | | | $i(all_74_9)) % 233.00/39.67 | | | | | | | | | | | | % 233.00/39.67 | | | | | | | | | | | | BETA: splitting (1560) gives: % 233.00/39.67 | | | | | | | | | | | | % 233.00/39.67 | | | | | | | | | | | | Case 1: % 233.00/39.67 | | | | | | | | | | | | | % 233.00/39.67 | | | | | | | | | | | | | (1561) ~ leq(n1, all_74_21) % 233.00/39.67 | | | | | | | | | | | | | % 233.00/39.67 | | | | | | | | | | | | | REDUCE: (135), (1561) imply: % 233.00/39.67 | | | | | | | | | | | | | (1562) ~ leq(n1, n5) % 233.00/39.67 | | | | | | | | | | | | | % 233.00/39.67 | | | | | | | | | | | | | PRED_UNIFY: (1554), (1562) imply: % 233.00/39.67 | | | | | | | | | | | | | (1563) $false % 233.00/39.67 | | | | | | | | | | | | | % 233.00/39.67 | | | | | | | | | | | | | CLOSE: (1563) is inconsistent. % 233.00/39.67 | | | | | | | | | | | | | % 233.00/39.67 | | | | | | | | | | | | Case 2: % 233.00/39.67 | | | | | | | | | | | | | % 233.00/39.67 | | | | | | | | | | | | | (1564) a_select3(pminus_ds1_filter, n1, n0) = all_74_9 & % 233.00/39.67 | | | | | | | | | | | | | $i(all_74_9) % 233.00/39.67 | | | | | | | | | | | | | % 233.00/39.67 | | | | | | | | | | | | | ALPHA: (1564) implies: % 233.00/39.67 | | | | | | | | | | | | | (1565) a_select3(pminus_ds1_filter, n1, n0) = all_74_9 % 233.00/39.67 | | | | | | | | | | | | | % 233.00/39.67 | | | | | | | | | | | | | REF_CLOSE: (17), (1034), (1552), (1565) are inconsistent by % 233.00/39.67 | | | | | | | | | | | | | sub-proof #31. % 233.00/39.67 | | | | | | | | | | | | | % 233.00/39.67 | | | | | | | | | | | | End of split % 233.00/39.67 | | | | | | | | | | | | % 233.00/39.67 | | | | | | | | | | | End of split % 233.00/39.67 | | | | | | | | | | | % 233.00/39.67 | | | | | | | | | | End of split % 233.00/39.67 | | | | | | | | | | % 233.00/39.67 | | | | | | | | | Case 2: % 233.00/39.67 | | | | | | | | | | % 233.00/39.67 | | | | | | | | | | (1566) all_74_10 = n2 % 233.00/39.67 | | | | | | | | | | % 233.00/39.67 | | | | | | | | | | REDUCE: (1528), (1566) imply: % 233.00/39.67 | | | | | | | | | | (1567) a_select3(pminus_ds1_filter, n2, n0) = all_74_8 % 233.00/39.67 | | | | | | | | | | % 233.00/39.67 | | | | | | | | | | REDUCE: (1529), (1566) imply: % 233.00/39.67 | | | | | | | | | | (1568) a_select3(pminus_ds1_filter, n0, n2) = all_74_9 % 233.00/39.67 | | | | | | | | | | % 233.00/39.67 | | | | | | | | | | REDUCE: (1041), (1566) imply: % 233.00/39.67 | | | | | | | | | | (1569) leq(n2, n5) % 233.00/39.67 | | | | | | | | | | % 233.00/39.67 | | | | | | | | | | REDUCE: (1036), (1566) imply: % 233.00/39.67 | | | | | | | | | | (1570) leq(n0, n2) % 233.00/39.67 | | | | | | | | | | % 233.00/39.67 | | | | | | | | | | GROUND_INST: instantiating (64) with n0, n2, all_74_9, % 233.00/39.67 | | | | | | | | | | simplifying with (12), (101), (1531), (1568), % 233.00/39.67 | | | | | | | | | | (1570) gives: % 233.00/39.67 | | | | | | | | | | (1571) ~ leq(n2, all_74_21) | ~ leq(n0, all_74_21) | % 233.00/39.67 | | | | | | | | | | (a_select3(pminus_ds1_filter, n2, n0) = all_74_9 & % 233.00/39.67 | | | | | | | | | | $i(all_74_9)) % 233.00/39.67 | | | | | | | | | | % 233.00/39.67 | | | | | | | | | | BETA: splitting (1571) gives: % 233.00/39.67 | | | | | | | | | | % 233.00/39.67 | | | | | | | | | | Case 1: % 233.00/39.67 | | | | | | | | | | | % 233.00/39.67 | | | | | | | | | | | (1572) ~ leq(n0, all_74_21) % 233.00/39.67 | | | | | | | | | | | % 233.00/39.67 | | | | | | | | | | | REDUCE: (135), (1572) imply: % 233.00/39.67 | | | | | | | | | | | (1573) ~ leq(n0, n5) % 233.00/39.67 | | | | | | | | | | | % 233.00/39.67 | | | | | | | | | | | PRED_UNIFY: (1530), (1573) imply: % 233.00/39.67 | | | | | | | | | | | (1574) $false % 233.00/39.67 | | | | | | | | | | | % 233.00/39.67 | | | | | | | | | | | CLOSE: (1574) is inconsistent. % 233.00/39.67 | | | | | | | | | | | % 233.00/39.67 | | | | | | | | | | Case 2: % 233.00/39.67 | | | | | | | | | | | % 233.00/39.67 | | | | | | | | | | | (1575) ~ leq(n2, all_74_21) | % 233.00/39.67 | | | | | | | | | | | (a_select3(pminus_ds1_filter, n2, n0) = all_74_9 & % 233.00/39.67 | | | | | | | | | | | $i(all_74_9)) % 233.00/39.67 | | | | | | | | | | | % 233.00/39.67 | | | | | | | | | | | BETA: splitting (1575) gives: % 233.00/39.67 | | | | | | | | | | | % 233.00/39.67 | | | | | | | | | | | Case 1: % 233.00/39.67 | | | | | | | | | | | | % 233.00/39.67 | | | | | | | | | | | | (1576) ~ leq(n2, all_74_21) % 233.00/39.67 | | | | | | | | | | | | % 233.00/39.67 | | | | | | | | | | | | REDUCE: (135), (1576) imply: % 233.00/39.67 | | | | | | | | | | | | (1577) ~ leq(n2, n5) % 233.00/39.67 | | | | | | | | | | | | % 233.00/39.67 | | | | | | | | | | | | PRED_UNIFY: (1569), (1577) imply: % 233.00/39.67 | | | | | | | | | | | | (1578) $false % 233.00/39.67 | | | | | | | | | | | | % 233.00/39.67 | | | | | | | | | | | | CLOSE: (1578) is inconsistent. % 233.00/39.67 | | | | | | | | | | | | % 233.00/39.67 | | | | | | | | | | | Case 2: % 233.00/39.67 | | | | | | | | | | | | % 233.00/39.67 | | | | | | | | | | | | (1579) a_select3(pminus_ds1_filter, n2, n0) = all_74_9 & % 233.00/39.67 | | | | | | | | | | | | $i(all_74_9) % 233.00/39.67 | | | | | | | | | | | | % 233.00/39.67 | | | | | | | | | | | | ALPHA: (1579) implies: % 233.00/39.67 | | | | | | | | | | | | (1580) a_select3(pminus_ds1_filter, n2, n0) = all_74_9 % 233.00/39.67 | | | | | | | | | | | | % 233.00/39.67 | | | | | | | | | | | | REF_CLOSE: (17), (1034), (1567), (1580) are inconsistent by % 233.00/39.67 | | | | | | | | | | | | sub-proof #30. % 233.00/39.67 | | | | | | | | | | | | % 233.00/39.67 | | | | | | | | | | | End of split % 233.00/39.67 | | | | | | | | | | | % 233.00/39.67 | | | | | | | | | | End of split % 233.00/39.67 | | | | | | | | | | % 233.00/39.67 | | | | | | | | | End of split % 233.00/39.67 | | | | | | | | | % 233.00/39.67 | | | | | | | | Case 2: % 233.00/39.67 | | | | | | | | | % 233.00/39.67 | | | | | | | | | (1581) all_74_10 = n3 % 233.00/39.67 | | | | | | | | | % 233.00/39.67 | | | | | | | | | REDUCE: (1528), (1581) imply: % 233.00/39.67 | | | | | | | | | (1582) a_select3(pminus_ds1_filter, n3, n0) = all_74_8 % 233.00/39.67 | | | | | | | | | % 233.00/39.67 | | | | | | | | | REDUCE: (1529), (1581) imply: % 233.00/39.67 | | | | | | | | | (1583) a_select3(pminus_ds1_filter, n0, n3) = all_74_9 % 233.00/39.67 | | | | | | | | | % 233.00/39.67 | | | | | | | | | REDUCE: (1041), (1581) imply: % 233.00/39.67 | | | | | | | | | (1584) leq(n3, n5) % 233.00/39.67 | | | | | | | | | % 233.00/39.67 | | | | | | | | | REDUCE: (1036), (1581) imply: % 233.00/39.67 | | | | | | | | | (1585) leq(n0, n3) % 233.00/39.67 | | | | | | | | | % 233.00/39.67 | | | | | | | | | GROUND_INST: instantiating (64) with n0, n3, all_74_9, % 233.00/39.67 | | | | | | | | | simplifying with (12), (112), (1531), (1583), % 233.00/39.67 | | | | | | | | | (1585) gives: % 233.00/39.67 | | | | | | | | | (1586) ~ leq(n3, all_74_21) | ~ leq(n0, all_74_21) | % 233.00/39.67 | | | | | | | | | (a_select3(pminus_ds1_filter, n3, n0) = all_74_9 & % 233.00/39.67 | | | | | | | | | $i(all_74_9)) % 233.00/39.67 | | | | | | | | | % 233.00/39.67 | | | | | | | | | BETA: splitting (1586) gives: % 233.00/39.67 | | | | | | | | | % 233.00/39.67 | | | | | | | | | Case 1: % 233.00/39.67 | | | | | | | | | | % 233.00/39.67 | | | | | | | | | | (1587) ~ leq(n0, all_74_21) % 233.00/39.67 | | | | | | | | | | % 233.00/39.67 | | | | | | | | | | REDUCE: (135), (1587) imply: % 233.00/39.67 | | | | | | | | | | (1588) ~ leq(n0, n5) % 233.00/39.67 | | | | | | | | | | % 233.00/39.67 | | | | | | | | | | PRED_UNIFY: (1530), (1588) imply: % 233.00/39.67 | | | | | | | | | | (1589) $false % 233.00/39.67 | | | | | | | | | | % 233.00/39.67 | | | | | | | | | | CLOSE: (1589) is inconsistent. % 233.00/39.67 | | | | | | | | | | % 233.00/39.67 | | | | | | | | | Case 2: % 233.00/39.67 | | | | | | | | | | % 233.00/39.67 | | | | | | | | | | (1590) ~ leq(n3, all_74_21) | % 233.00/39.67 | | | | | | | | | | (a_select3(pminus_ds1_filter, n3, n0) = all_74_9 & % 233.00/39.67 | | | | | | | | | | $i(all_74_9)) % 233.00/39.67 | | | | | | | | | | % 233.00/39.67 | | | | | | | | | | BETA: splitting (1590) gives: % 233.00/39.67 | | | | | | | | | | % 233.00/39.67 | | | | | | | | | | Case 1: % 233.00/39.67 | | | | | | | | | | | % 233.00/39.67 | | | | | | | | | | | (1591) ~ leq(n3, all_74_21) % 233.00/39.67 | | | | | | | | | | | % 233.00/39.67 | | | | | | | | | | | REDUCE: (135), (1591) imply: % 233.00/39.67 | | | | | | | | | | | (1592) ~ leq(n3, n5) % 233.00/39.67 | | | | | | | | | | | % 233.00/39.67 | | | | | | | | | | | PRED_UNIFY: (1584), (1592) imply: % 233.00/39.67 | | | | | | | | | | | (1593) $false % 233.00/39.67 | | | | | | | | | | | % 233.00/39.67 | | | | | | | | | | | CLOSE: (1593) is inconsistent. % 233.00/39.67 | | | | | | | | | | | % 233.00/39.67 | | | | | | | | | | Case 2: % 233.00/39.67 | | | | | | | | | | | % 233.00/39.67 | | | | | | | | | | | (1594) a_select3(pminus_ds1_filter, n3, n0) = all_74_9 & % 233.00/39.67 | | | | | | | | | | | $i(all_74_9) % 233.00/39.67 | | | | | | | | | | | % 233.00/39.67 | | | | | | | | | | | ALPHA: (1594) implies: % 233.00/39.67 | | | | | | | | | | | (1595) a_select3(pminus_ds1_filter, n3, n0) = all_74_9 % 233.00/39.67 | | | | | | | | | | | % 233.00/39.67 | | | | | | | | | | | GROUND_INST: instantiating (17) with all_74_8, all_74_9, n0, % 233.00/39.67 | | | | | | | | | | | n3, pminus_ds1_filter, simplifying with (1582), % 233.00/39.67 | | | | | | | | | | | (1595) gives: % 233.00/39.67 | | | | | | | | | | | (1596) all_74_8 = all_74_9 % 233.00/39.67 | | | | | | | | | | | % 233.00/39.67 | | | | | | | | | | | REDUCE: (1034), (1596) imply: % 233.00/39.67 | | | | | | | | | | | (1597) $false % 233.00/39.67 | | | | | | | | | | | % 233.00/39.67 | | | | | | | | | | | CLOSE: (1597) is inconsistent. % 233.00/39.67 | | | | | | | | | | | % 233.00/39.67 | | | | | | | | | | End of split % 233.00/39.67 | | | | | | | | | | % 233.00/39.67 | | | | | | | | | End of split % 233.00/39.67 | | | | | | | | | % 233.00/39.67 | | | | | | | | End of split % 233.00/39.67 | | | | | | | | % 233.00/39.67 | | | | | | | Case 2: % 233.00/39.67 | | | | | | | | % 233.00/39.67 | | | | | | | | (1598) all_74_10 = n4 % 233.00/39.67 | | | | | | | | % 233.00/39.67 | | | | | | | | REDUCE: (1528), (1598) imply: % 233.00/39.67 | | | | | | | | (1599) a_select3(pminus_ds1_filter, n4, n0) = all_74_8 % 233.00/39.67 | | | | | | | | % 233.00/39.67 | | | | | | | | REDUCE: (1529), (1598) imply: % 233.00/39.67 | | | | | | | | (1600) a_select3(pminus_ds1_filter, n0, n4) = all_74_9 % 233.00/39.67 | | | | | | | | % 233.00/39.67 | | | | | | | | REDUCE: (1041), (1598) imply: % 233.00/39.67 | | | | | | | | (1601) leq(n4, n5) % 233.00/39.67 | | | | | | | | % 233.00/39.67 | | | | | | | | REDUCE: (1036), (1598) imply: % 233.00/39.67 | | | | | | | | (1602) leq(n0, n4) % 233.00/39.67 | | | | | | | | % 233.00/39.67 | | | | | | | | GROUND_INST: instantiating (64) with n0, n4, all_74_9, % 233.00/39.67 | | | | | | | | simplifying with (12), (119), (1531), (1600), % 233.00/39.67 | | | | | | | | (1602) gives: % 233.00/39.67 | | | | | | | | (1603) ~ leq(n4, all_74_21) | ~ leq(n0, all_74_21) | % 233.00/39.67 | | | | | | | | (a_select3(pminus_ds1_filter, n4, n0) = all_74_9 & % 233.00/39.67 | | | | | | | | $i(all_74_9)) % 233.00/39.67 | | | | | | | | % 233.00/39.67 | | | | | | | | BETA: splitting (1603) gives: % 233.00/39.67 | | | | | | | | % 233.00/39.67 | | | | | | | | Case 1: % 233.00/39.67 | | | | | | | | | % 233.00/39.67 | | | | | | | | | (1604) ~ leq(n0, all_74_21) % 233.00/39.67 | | | | | | | | | % 233.00/39.67 | | | | | | | | | REDUCE: (135), (1604) imply: % 233.00/39.67 | | | | | | | | | (1605) ~ leq(n0, n5) % 233.00/39.67 | | | | | | | | | % 233.00/39.67 | | | | | | | | | PRED_UNIFY: (1530), (1605) imply: % 233.00/39.68 | | | | | | | | | (1606) $false % 233.00/39.68 | | | | | | | | | % 233.00/39.68 | | | | | | | | | CLOSE: (1606) is inconsistent. % 233.00/39.68 | | | | | | | | | % 233.00/39.68 | | | | | | | | Case 2: % 233.00/39.68 | | | | | | | | | % 233.00/39.68 | | | | | | | | | (1607) ~ leq(n4, all_74_21) | % 233.00/39.68 | | | | | | | | | (a_select3(pminus_ds1_filter, n4, n0) = all_74_9 & % 233.00/39.68 | | | | | | | | | $i(all_74_9)) % 233.00/39.68 | | | | | | | | | % 233.00/39.68 | | | | | | | | | BETA: splitting (1607) gives: % 233.00/39.68 | | | | | | | | | % 233.00/39.68 | | | | | | | | | Case 1: % 233.00/39.68 | | | | | | | | | | % 233.00/39.68 | | | | | | | | | | (1608) ~ leq(n4, all_74_21) % 233.00/39.68 | | | | | | | | | | % 233.00/39.68 | | | | | | | | | | REDUCE: (135), (1608) imply: % 233.00/39.68 | | | | | | | | | | (1609) ~ leq(n4, n5) % 233.00/39.68 | | | | | | | | | | % 233.00/39.68 | | | | | | | | | | PRED_UNIFY: (1601), (1609) imply: % 233.00/39.68 | | | | | | | | | | (1610) $false % 233.00/39.68 | | | | | | | | | | % 233.00/39.68 | | | | | | | | | | CLOSE: (1610) is inconsistent. % 233.00/39.68 | | | | | | | | | | % 233.00/39.68 | | | | | | | | | Case 2: % 233.00/39.68 | | | | | | | | | | % 233.00/39.68 | | | | | | | | | | (1611) a_select3(pminus_ds1_filter, n4, n0) = all_74_9 & % 233.00/39.68 | | | | | | | | | | $i(all_74_9) % 233.00/39.68 | | | | | | | | | | % 233.00/39.68 | | | | | | | | | | ALPHA: (1611) implies: % 233.00/39.68 | | | | | | | | | | (1612) a_select3(pminus_ds1_filter, n4, n0) = all_74_9 % 233.00/39.68 | | | | | | | | | | % 233.00/39.68 | | | | | | | | | | REF_CLOSE: (17), (1034), (1599), (1612) are inconsistent by % 233.00/39.68 | | | | | | | | | | sub-proof #29. % 233.00/39.68 | | | | | | | | | | % 233.00/39.68 | | | | | | | | | End of split % 233.00/39.68 | | | | | | | | | % 233.00/39.68 | | | | | | | | End of split % 233.00/39.68 | | | | | | | | % 233.00/39.68 | | | | | | | End of split % 233.00/39.68 | | | | | | | % 233.00/39.68 | | | | | | End of split % 233.00/39.68 | | | | | | % 233.00/39.68 | | | | | Case 2: % 233.00/39.68 | | | | | | % 233.00/39.68 | | | | | | (1613) all_74_10 = n5 % 233.00/39.68 | | | | | | % 233.00/39.68 | | | | | | REDUCE: (1528), (1613) imply: % 233.00/39.68 | | | | | | (1614) a_select3(pminus_ds1_filter, n5, n0) = all_74_8 % 233.00/39.68 | | | | | | % 233.00/39.68 | | | | | | REDUCE: (1529), (1613) imply: % 233.00/39.68 | | | | | | (1615) a_select3(pminus_ds1_filter, n0, n5) = all_74_9 % 233.00/39.68 | | | | | | % 233.00/39.68 | | | | | | REDUCE: (1041), (1613) imply: % 233.00/39.68 | | | | | | (1616) leq(n5, n5) % 233.00/39.68 | | | | | | % 233.00/39.68 | | | | | | GROUND_INST: instantiating (64) with n0, n5, all_74_9, simplifying % 233.00/39.68 | | | | | | with (12), (122), (1530), (1531), (1615) gives: % 233.00/39.68 | | | | | | (1617) ~ leq(n5, all_74_21) | ~ leq(n0, all_74_21) | % 233.00/39.68 | | | | | | (a_select3(pminus_ds1_filter, n5, n0) = all_74_9 & % 233.00/39.68 | | | | | | $i(all_74_9)) % 233.00/39.68 | | | | | | % 233.00/39.68 | | | | | | BETA: splitting (1617) gives: % 233.00/39.68 | | | | | | % 233.00/39.68 | | | | | | Case 1: % 233.00/39.68 | | | | | | | % 233.00/39.68 | | | | | | | (1618) ~ leq(n0, all_74_21) % 233.00/39.68 | | | | | | | % 233.00/39.68 | | | | | | | REDUCE: (135), (1618) imply: % 233.00/39.68 | | | | | | | (1619) ~ leq(n0, n5) % 233.00/39.68 | | | | | | | % 233.00/39.68 | | | | | | | PRED_UNIFY: (1530), (1619) imply: % 233.00/39.68 | | | | | | | (1620) $false % 233.00/39.68 | | | | | | | % 233.00/39.68 | | | | | | | CLOSE: (1620) is inconsistent. % 233.00/39.68 | | | | | | | % 233.00/39.68 | | | | | | Case 2: % 233.00/39.68 | | | | | | | % 233.00/39.68 | | | | | | | (1621) ~ leq(n5, all_74_21) | (a_select3(pminus_ds1_filter, % 233.00/39.68 | | | | | | | n5, n0) = all_74_9 & $i(all_74_9)) % 233.00/39.68 | | | | | | | % 233.00/39.68 | | | | | | | BETA: splitting (1621) gives: % 233.00/39.68 | | | | | | | % 233.00/39.68 | | | | | | | Case 1: % 233.00/39.68 | | | | | | | | % 233.00/39.68 | | | | | | | | (1622) ~ leq(n5, all_74_21) % 233.00/39.68 | | | | | | | | % 233.00/39.68 | | | | | | | | REDUCE: (135), (1622) imply: % 233.00/39.68 | | | | | | | | (1623) ~ leq(n5, n5) % 233.00/39.68 | | | | | | | | % 233.00/39.68 | | | | | | | | PRED_UNIFY: (1616), (1623) imply: % 233.00/39.68 | | | | | | | | (1624) $false % 233.00/39.68 | | | | | | | | % 233.00/39.68 | | | | | | | | CLOSE: (1624) is inconsistent. % 233.00/39.68 | | | | | | | | % 233.00/39.68 | | | | | | | Case 2: % 233.00/39.68 | | | | | | | | % 233.00/39.68 | | | | | | | | (1625) a_select3(pminus_ds1_filter, n5, n0) = all_74_9 & % 233.00/39.68 | | | | | | | | $i(all_74_9) % 233.00/39.68 | | | | | | | | % 233.00/39.68 | | | | | | | | ALPHA: (1625) implies: % 233.00/39.68 | | | | | | | | (1626) a_select3(pminus_ds1_filter, n5, n0) = all_74_9 % 233.00/39.68 | | | | | | | | % 233.00/39.68 | | | | | | | | REF_CLOSE: (17), (1034), (1614), (1626) are inconsistent by % 233.00/39.68 | | | | | | | | sub-proof #28. % 233.00/39.68 | | | | | | | | % 233.00/39.68 | | | | | | | End of split % 233.00/39.68 | | | | | | | % 233.00/39.68 | | | | | | End of split % 233.00/39.68 | | | | | | % 233.00/39.68 | | | | | End of split % 233.00/39.68 | | | | | % 233.00/39.68 | | | | End of split % 233.00/39.68 | | | | % 233.00/39.68 | | | Case 2: % 233.00/39.68 | | | | % 233.00/39.68 | | | | (1627) all_74_10 = n0 % 233.00/39.68 | | | | (1628) ~ gt(all_74_10, n0) % 233.00/39.68 | | | | % 233.00/39.68 | | | | REDUCE: (1040), (1627) imply: % 233.00/39.68 | | | | (1629) a_select3(pminus_ds1_filter, n0, all_74_11) = all_74_8 % 233.00/39.68 | | | | % 233.00/39.68 | | | | REDUCE: (1039), (1627) imply: % 233.00/39.68 | | | | (1630) a_select3(pminus_ds1_filter, all_74_11, n0) = all_74_9 % 233.00/39.68 | | | | % 233.00/39.68 | | | | REDUCE: (1041), (1627) imply: % 233.00/39.68 | | | | (1631) leq(n0, n5) % 233.00/39.68 | | | | % 233.00/39.68 | | | | REDUCE: (1036), (1627) imply: % 233.00/39.68 | | | | (1632) leq(n0, n0) % 233.00/39.68 | | | | % 233.00/39.68 | | | | REDUCE: (1627), (1628) imply: % 233.00/39.68 | | | | (1633) ~ gt(n0, n0) % 233.00/39.68 | | | | % 233.00/39.68 | | | | BETA: splitting (1043) gives: % 233.00/39.68 | | | | % 233.00/39.68 | | | | Case 1: % 233.00/39.68 | | | | | % 233.00/39.68 | | | | | (1634) gt(all_74_11, n0) % 233.00/39.68 | | | | | % 233.00/39.68 | | | | | BETA: splitting (1046) gives: % 233.00/39.68 | | | | | % 233.00/39.68 | | | | | Case 1: % 233.00/39.68 | | | | | | % 233.00/39.68 | | | | | | (1635) gt(n5, all_74_11) % 233.00/39.68 | | | | | | % 233.00/39.68 | | | | | | GROUND_INST: instantiating (1) with all_74_11, n5, n4, simplifying % 233.00/39.68 | | | | | | with (53), (122), (126), (1635) gives: % 233.00/39.68 | | | | | | (1636) leq(all_74_11, n4) % 233.00/39.68 | | | | | | % 233.00/39.68 | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_11, n4, simplifying % 233.00/39.68 | | | | | | with (53), (119), (1636) gives: % 233.00/39.68 | | | | | | (1637) all_74_11 = n4 | gt(n4, all_74_11) % 233.00/39.68 | | | | | | % 233.00/39.68 | | | | | | BETA: splitting (1045) gives: % 233.00/39.68 | | | | | | % 233.00/39.68 | | | | | | Case 1: % 233.00/39.68 | | | | | | | % 233.00/39.68 | | | | | | | (1638) all_74_11 = n0 % 233.00/39.68 | | | | | | | % 233.00/39.68 | | | | | | | REDUCE: (1634), (1638) imply: % 233.00/39.68 | | | | | | | (1639) gt(n0, n0) % 233.00/39.68 | | | | | | | % 233.00/39.68 | | | | | | | PRED_UNIFY: (1633), (1639) imply: % 233.00/39.68 | | | | | | | (1640) $false % 233.00/39.68 | | | | | | | % 233.00/39.68 | | | | | | | CLOSE: (1640) is inconsistent. % 233.00/39.68 | | | | | | | % 233.00/39.68 | | | | | | Case 2: % 233.00/39.68 | | | | | | | % 233.00/39.68 | | | | | | | (1641) ~ (all_74_11 = n0) % 233.00/39.68 | | | | | | | % 233.00/39.68 | | | | | | | BETA: splitting (1637) gives: % 233.00/39.68 | | | | | | | % 233.00/39.68 | | | | | | | Case 1: % 233.00/39.68 | | | | | | | | % 233.00/39.68 | | | | | | | | (1642) gt(n4, all_74_11) % 233.00/39.68 | | | | | | | | % 233.00/39.68 | | | | | | | | GROUND_INST: instantiating (1) with all_74_11, n4, n3, % 233.00/39.68 | | | | | | | | simplifying with (53), (119), (125), (1642) gives: % 233.00/39.68 | | | | | | | | (1643) leq(all_74_11, n3) % 233.00/39.68 | | | | | | | | % 233.00/39.68 | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_11, n3, % 233.00/39.68 | | | | | | | | simplifying with (53), (112), (1643) gives: % 233.00/39.68 | | | | | | | | (1644) all_74_11 = n3 | gt(n3, all_74_11) % 233.00/39.68 | | | | | | | | % 233.00/39.68 | | | | | | | | BETA: splitting (1644) gives: % 233.00/39.68 | | | | | | | | % 233.00/39.68 | | | | | | | | Case 1: % 233.00/39.68 | | | | | | | | | % 233.00/39.68 | | | | | | | | | (1645) gt(n3, all_74_11) % 233.00/39.68 | | | | | | | | | % 233.00/39.68 | | | | | | | | | GROUND_INST: instantiating (1) with all_74_11, n3, n2, % 233.00/39.68 | | | | | | | | | simplifying with (53), (112), (124), (1645) gives: % 233.00/39.68 | | | | | | | | | (1646) leq(all_74_11, n2) % 233.00/39.68 | | | | | | | | | % 233.00/39.68 | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_11, n2, % 233.00/39.68 | | | | | | | | | simplifying with (53), (101), (1646) gives: % 233.00/39.68 | | | | | | | | | (1647) all_74_11 = n2 | gt(n2, all_74_11) % 233.00/39.68 | | | | | | | | | % 233.00/39.68 | | | | | | | | | BETA: splitting (1647) gives: % 233.00/39.68 | | | | | | | | | % 233.00/39.68 | | | | | | | | | Case 1: % 233.00/39.68 | | | | | | | | | | % 233.00/39.68 | | | | | | | | | | (1648) gt(n2, all_74_11) % 233.00/39.68 | | | | | | | | | | % 233.00/39.68 | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_11, n2, n1, % 233.00/39.68 | | | | | | | | | | simplifying with (53), (101), (123), (1648) gives: % 233.00/39.68 | | | | | | | | | | (1649) leq(all_74_11, n1) % 233.00/39.68 | | | | | | | | | | % 233.00/39.68 | | | | | | | | | | GROUND_INST: instantiating (4) with all_74_11, simplifying with % 233.00/39.68 | | | | | | | | | | (53), (1035), (1649) gives: % 233.00/39.68 | | | | | | | | | | (1650) all_74_11 = n1 | all_74_11 = n0 % 233.00/39.68 | | | | | | | | | | % 233.00/39.68 | | | | | | | | | | BETA: splitting (1650) gives: % 233.00/39.68 | | | | | | | | | | % 233.00/39.68 | | | | | | | | | | Case 1: % 233.00/39.68 | | | | | | | | | | | % 233.00/39.68 | | | | | | | | | | | (1651) all_74_11 = n0 % 233.00/39.68 | | | | | | | | | | | % 233.00/39.68 | | | | | | | | | | | REDUCE: (1641), (1651) imply: % 233.00/39.68 | | | | | | | | | | | (1652) $false % 233.00/39.68 | | | | | | | | | | | % 233.00/39.68 | | | | | | | | | | | CLOSE: (1652) is inconsistent. % 233.00/39.68 | | | | | | | | | | | % 233.00/39.68 | | | | | | | | | | Case 2: % 233.00/39.68 | | | | | | | | | | | % 233.00/39.68 | | | | | | | | | | | (1653) all_74_11 = n1 % 233.00/39.68 | | | | | | | | | | | % 233.00/39.68 | | | | | | | | | | | REDUCE: (1630), (1653) imply: % 233.00/39.68 | | | | | | | | | | | (1654) a_select3(pminus_ds1_filter, n1, n0) = all_74_9 % 233.00/39.68 | | | | | | | | | | | % 233.00/39.68 | | | | | | | | | | | REDUCE: (1629), (1653) imply: % 233.00/39.68 | | | | | | | | | | | (1655) a_select3(pminus_ds1_filter, n0, n1) = all_74_8 % 233.00/39.68 | | | | | | | | | | | % 233.00/39.68 | | | | | | | | | | | REDUCE: (1042), (1653) imply: % 233.00/39.68 | | | | | | | | | | | (1656) leq(n1, n5) % 233.00/39.68 | | | | | | | | | | | % 233.00/39.68 | | | | | | | | | | | REDUCE: (1035), (1653) imply: % 233.00/39.68 | | | | | | | | | | | (1657) leq(n0, n1) % 233.00/39.68 | | | | | | | | | | | % 233.00/39.68 | | | | | | | | | | | GROUND_INST: instantiating (64) with n0, n1, all_74_8, % 233.00/39.68 | | | | | | | | | | | simplifying with (12), (85), (1632), (1655), % 233.00/39.68 | | | | | | | | | | | (1657) gives: % 233.00/39.68 | | | | | | | | | | | (1658) ~ leq(n1, all_74_21) | ~ leq(n0, all_74_21) | % 233.00/39.68 | | | | | | | | | | | (a_select3(pminus_ds1_filter, n1, n0) = all_74_8 & % 233.00/39.68 | | | | | | | | | | | $i(all_74_8)) % 233.00/39.68 | | | | | | | | | | | % 233.00/39.68 | | | | | | | | | | | BETA: splitting (1658) gives: % 233.00/39.68 | | | | | | | | | | | % 233.00/39.68 | | | | | | | | | | | Case 1: % 233.00/39.68 | | | | | | | | | | | | % 233.00/39.68 | | | | | | | | | | | | (1659) ~ leq(n0, all_74_21) % 233.00/39.68 | | | | | | | | | | | | % 233.00/39.68 | | | | | | | | | | | | REDUCE: (135), (1659) imply: % 233.00/39.68 | | | | | | | | | | | | (1660) ~ leq(n0, n5) % 233.00/39.68 | | | | | | | | | | | | % 233.00/39.68 | | | | | | | | | | | | PRED_UNIFY: (1631), (1660) imply: % 233.00/39.68 | | | | | | | | | | | | (1661) $false % 233.00/39.68 | | | | | | | | | | | | % 233.00/39.68 | | | | | | | | | | | | CLOSE: (1661) is inconsistent. % 233.00/39.68 | | | | | | | | | | | | % 233.00/39.68 | | | | | | | | | | | Case 2: % 233.00/39.68 | | | | | | | | | | | | % 233.00/39.68 | | | | | | | | | | | | (1662) ~ leq(n1, all_74_21) | % 233.00/39.68 | | | | | | | | | | | | (a_select3(pminus_ds1_filter, n1, n0) = all_74_8 & % 233.00/39.68 | | | | | | | | | | | | $i(all_74_8)) % 233.00/39.68 | | | | | | | | | | | | % 233.00/39.68 | | | | | | | | | | | | BETA: splitting (1662) gives: % 233.00/39.68 | | | | | | | | | | | | % 233.00/39.68 | | | | | | | | | | | | Case 1: % 233.00/39.68 | | | | | | | | | | | | | % 233.00/39.68 | | | | | | | | | | | | | (1663) ~ leq(n1, all_74_21) % 233.00/39.68 | | | | | | | | | | | | | % 233.00/39.68 | | | | | | | | | | | | | REDUCE: (135), (1663) imply: % 233.00/39.68 | | | | | | | | | | | | | (1664) ~ leq(n1, n5) % 233.00/39.68 | | | | | | | | | | | | | % 233.00/39.68 | | | | | | | | | | | | | PRED_UNIFY: (1656), (1664) imply: % 233.00/39.68 | | | | | | | | | | | | | (1665) $false % 233.00/39.68 | | | | | | | | | | | | | % 233.00/39.68 | | | | | | | | | | | | | CLOSE: (1665) is inconsistent. % 233.00/39.68 | | | | | | | | | | | | | % 233.00/39.68 | | | | | | | | | | | | Case 2: % 233.00/39.68 | | | | | | | | | | | | | % 233.00/39.68 | | | | | | | | | | | | | (1666) a_select3(pminus_ds1_filter, n1, n0) = all_74_8 & % 233.00/39.68 | | | | | | | | | | | | | $i(all_74_8) % 233.00/39.68 | | | | | | | | | | | | | % 233.00/39.68 | | | | | | | | | | | | | ALPHA: (1666) implies: % 233.00/39.68 | | | | | | | | | | | | | (1667) a_select3(pminus_ds1_filter, n1, n0) = all_74_8 % 233.00/39.68 | | | | | | | | | | | | | % 233.00/39.68 | | | | | | | | | | | | | REF_CLOSE: (17), (1034), (1654), (1667) are inconsistent by % 233.00/39.68 | | | | | | | | | | | | | sub-proof #31. % 233.00/39.68 | | | | | | | | | | | | | % 233.00/39.68 | | | | | | | | | | | | End of split % 233.00/39.68 | | | | | | | | | | | | % 233.00/39.68 | | | | | | | | | | | End of split % 233.00/39.68 | | | | | | | | | | | % 233.00/39.68 | | | | | | | | | | End of split % 233.00/39.68 | | | | | | | | | | % 233.00/39.68 | | | | | | | | | Case 2: % 233.00/39.68 | | | | | | | | | | % 233.00/39.68 | | | | | | | | | | (1668) all_74_11 = n2 % 233.00/39.68 | | | | | | | | | | % 233.00/39.68 | | | | | | | | | | REDUCE: (1630), (1668) imply: % 233.00/39.68 | | | | | | | | | | (1669) a_select3(pminus_ds1_filter, n2, n0) = all_74_9 % 233.00/39.68 | | | | | | | | | | % 233.00/39.68 | | | | | | | | | | REDUCE: (1629), (1668) imply: % 233.00/39.68 | | | | | | | | | | (1670) a_select3(pminus_ds1_filter, n0, n2) = all_74_8 % 233.00/39.68 | | | | | | | | | | % 233.00/39.68 | | | | | | | | | | REDUCE: (1042), (1668) imply: % 233.00/39.68 | | | | | | | | | | (1671) leq(n2, n5) % 233.00/39.68 | | | | | | | | | | % 233.00/39.68 | | | | | | | | | | REDUCE: (1035), (1668) imply: % 233.00/39.68 | | | | | | | | | | (1672) leq(n0, n2) % 233.00/39.68 | | | | | | | | | | % 233.00/39.68 | | | | | | | | | | GROUND_INST: instantiating (64) with n0, n2, all_74_8, % 233.00/39.68 | | | | | | | | | | simplifying with (12), (101), (1632), (1670), % 233.00/39.68 | | | | | | | | | | (1672) gives: % 233.00/39.68 | | | | | | | | | | (1673) ~ leq(n2, all_74_21) | ~ leq(n0, all_74_21) | % 233.00/39.68 | | | | | | | | | | (a_select3(pminus_ds1_filter, n2, n0) = all_74_8 & % 233.00/39.68 | | | | | | | | | | $i(all_74_8)) % 233.00/39.68 | | | | | | | | | | % 233.00/39.68 | | | | | | | | | | BETA: splitting (1673) gives: % 233.00/39.68 | | | | | | | | | | % 233.00/39.68 | | | | | | | | | | Case 1: % 233.00/39.68 | | | | | | | | | | | % 233.00/39.68 | | | | | | | | | | | (1674) ~ leq(n0, all_74_21) % 233.00/39.68 | | | | | | | | | | | % 233.00/39.68 | | | | | | | | | | | REDUCE: (135), (1674) imply: % 233.00/39.68 | | | | | | | | | | | (1675) ~ leq(n0, n5) % 233.00/39.68 | | | | | | | | | | | % 233.00/39.68 | | | | | | | | | | | PRED_UNIFY: (1631), (1675) imply: % 233.00/39.68 | | | | | | | | | | | (1676) $false % 233.00/39.68 | | | | | | | | | | | % 233.00/39.68 | | | | | | | | | | | CLOSE: (1676) is inconsistent. % 233.00/39.68 | | | | | | | | | | | % 233.00/39.68 | | | | | | | | | | Case 2: % 233.00/39.68 | | | | | | | | | | | % 233.00/39.68 | | | | | | | | | | | (1677) ~ leq(n2, all_74_21) | % 233.00/39.68 | | | | | | | | | | | (a_select3(pminus_ds1_filter, n2, n0) = all_74_8 & % 233.00/39.68 | | | | | | | | | | | $i(all_74_8)) % 233.00/39.68 | | | | | | | | | | | % 233.00/39.68 | | | | | | | | | | | BETA: splitting (1677) gives: % 233.00/39.68 | | | | | | | | | | | % 233.00/39.68 | | | | | | | | | | | Case 1: % 233.00/39.68 | | | | | | | | | | | | % 233.00/39.69 | | | | | | | | | | | | (1678) ~ leq(n2, all_74_21) % 233.00/39.69 | | | | | | | | | | | | % 233.00/39.69 | | | | | | | | | | | | REDUCE: (135), (1678) imply: % 233.00/39.69 | | | | | | | | | | | | (1679) ~ leq(n2, n5) % 233.00/39.69 | | | | | | | | | | | | % 233.00/39.69 | | | | | | | | | | | | PRED_UNIFY: (1671), (1679) imply: % 233.00/39.69 | | | | | | | | | | | | (1680) $false % 233.00/39.69 | | | | | | | | | | | | % 233.00/39.69 | | | | | | | | | | | | CLOSE: (1680) is inconsistent. % 233.00/39.69 | | | | | | | | | | | | % 233.00/39.69 | | | | | | | | | | | Case 2: % 233.00/39.69 | | | | | | | | | | | | % 233.00/39.69 | | | | | | | | | | | | (1681) a_select3(pminus_ds1_filter, n2, n0) = all_74_8 & % 233.00/39.69 | | | | | | | | | | | | $i(all_74_8) % 233.00/39.69 | | | | | | | | | | | | % 233.00/39.69 | | | | | | | | | | | | ALPHA: (1681) implies: % 233.00/39.69 | | | | | | | | | | | | (1682) a_select3(pminus_ds1_filter, n2, n0) = all_74_8 % 233.00/39.69 | | | | | | | | | | | | % 233.00/39.69 | | | | | | | | | | | | REF_CLOSE: (17), (1034), (1669), (1682) are inconsistent by % 233.00/39.69 | | | | | | | | | | | | sub-proof #30. % 233.00/39.69 | | | | | | | | | | | | % 233.00/39.69 | | | | | | | | | | | End of split % 233.00/39.69 | | | | | | | | | | | % 233.00/39.69 | | | | | | | | | | End of split % 233.00/39.69 | | | | | | | | | | % 233.00/39.69 | | | | | | | | | End of split % 233.00/39.69 | | | | | | | | | % 233.00/39.69 | | | | | | | | Case 2: % 233.00/39.69 | | | | | | | | | % 233.00/39.69 | | | | | | | | | (1683) all_74_11 = n3 % 233.00/39.69 | | | | | | | | | % 233.00/39.69 | | | | | | | | | REDUCE: (1630), (1683) imply: % 233.00/39.69 | | | | | | | | | (1684) a_select3(pminus_ds1_filter, n3, n0) = all_74_9 % 233.00/39.69 | | | | | | | | | % 233.00/39.69 | | | | | | | | | REDUCE: (1629), (1683) imply: % 233.00/39.69 | | | | | | | | | (1685) a_select3(pminus_ds1_filter, n0, n3) = all_74_8 % 233.00/39.69 | | | | | | | | | % 233.00/39.69 | | | | | | | | | REDUCE: (1042), (1683) imply: % 233.00/39.69 | | | | | | | | | (1686) leq(n3, n5) % 233.00/39.69 | | | | | | | | | % 233.00/39.69 | | | | | | | | | REDUCE: (1035), (1683) imply: % 233.00/39.69 | | | | | | | | | (1687) leq(n0, n3) % 233.00/39.69 | | | | | | | | | % 233.00/39.69 | | | | | | | | | GROUND_INST: instantiating (64) with n0, n3, all_74_8, % 233.00/39.69 | | | | | | | | | simplifying with (12), (112), (1632), (1685), % 233.00/39.69 | | | | | | | | | (1687) gives: % 233.00/39.69 | | | | | | | | | (1688) ~ leq(n3, all_74_21) | ~ leq(n0, all_74_21) | % 233.00/39.69 | | | | | | | | | (a_select3(pminus_ds1_filter, n3, n0) = all_74_8 & % 233.00/39.69 | | | | | | | | | $i(all_74_8)) % 233.00/39.69 | | | | | | | | | % 233.00/39.69 | | | | | | | | | BETA: splitting (1688) gives: % 233.00/39.69 | | | | | | | | | % 233.00/39.69 | | | | | | | | | Case 1: % 233.00/39.69 | | | | | | | | | | % 233.00/39.69 | | | | | | | | | | (1689) ~ leq(n0, all_74_21) % 233.00/39.69 | | | | | | | | | | % 233.00/39.69 | | | | | | | | | | REDUCE: (135), (1689) imply: % 233.00/39.69 | | | | | | | | | | (1690) ~ leq(n0, n5) % 233.00/39.69 | | | | | | | | | | % 233.00/39.69 | | | | | | | | | | PRED_UNIFY: (1631), (1690) imply: % 233.00/39.69 | | | | | | | | | | (1691) $false % 233.00/39.69 | | | | | | | | | | % 233.00/39.69 | | | | | | | | | | CLOSE: (1691) is inconsistent. % 233.00/39.69 | | | | | | | | | | % 233.00/39.69 | | | | | | | | | Case 2: % 233.00/39.69 | | | | | | | | | | % 233.00/39.69 | | | | | | | | | | (1692) ~ leq(n3, all_74_21) | % 233.00/39.69 | | | | | | | | | | (a_select3(pminus_ds1_filter, n3, n0) = all_74_8 & % 233.00/39.69 | | | | | | | | | | $i(all_74_8)) % 233.00/39.69 | | | | | | | | | | % 233.00/39.69 | | | | | | | | | | BETA: splitting (1692) gives: % 233.00/39.69 | | | | | | | | | | % 233.00/39.69 | | | | | | | | | | Case 1: % 233.00/39.69 | | | | | | | | | | | % 233.00/39.69 | | | | | | | | | | | (1693) ~ leq(n3, all_74_21) % 233.00/39.69 | | | | | | | | | | | % 233.00/39.69 | | | | | | | | | | | REDUCE: (135), (1693) imply: % 233.00/39.69 | | | | | | | | | | | (1694) ~ leq(n3, n5) % 233.00/39.69 | | | | | | | | | | | % 233.00/39.69 | | | | | | | | | | | PRED_UNIFY: (1686), (1694) imply: % 233.00/39.69 | | | | | | | | | | | (1695) $false % 233.00/39.69 | | | | | | | | | | | % 233.00/39.69 | | | | | | | | | | | CLOSE: (1695) is inconsistent. % 233.00/39.69 | | | | | | | | | | | % 233.00/39.69 | | | | | | | | | | Case 2: % 233.00/39.69 | | | | | | | | | | | % 233.00/39.69 | | | | | | | | | | | (1696) a_select3(pminus_ds1_filter, n3, n0) = all_74_8 & % 233.00/39.69 | | | | | | | | | | | $i(all_74_8) % 233.00/39.69 | | | | | | | | | | | % 233.00/39.69 | | | | | | | | | | | ALPHA: (1696) implies: % 233.00/39.69 | | | | | | | | | | | (1697) a_select3(pminus_ds1_filter, n3, n0) = all_74_8 % 233.00/39.69 | | | | | | | | | | | % 233.00/39.69 | | | | | | | | | | | GROUND_INST: instantiating (17) with all_74_8, all_74_9, n0, % 233.00/39.69 | | | | | | | | | | | n3, pminus_ds1_filter, simplifying with (1684), % 233.00/39.69 | | | | | | | | | | | (1697) gives: % 233.00/39.69 | | | | | | | | | | | (1698) all_74_8 = all_74_9 % 233.00/39.69 | | | | | | | | | | | % 233.00/39.69 | | | | | | | | | | | REDUCE: (1034), (1698) imply: % 233.00/39.69 | | | | | | | | | | | (1699) $false % 233.00/39.69 | | | | | | | | | | | % 233.00/39.69 | | | | | | | | | | | CLOSE: (1699) is inconsistent. % 233.00/39.69 | | | | | | | | | | | % 233.00/39.69 | | | | | | | | | | End of split % 233.00/39.69 | | | | | | | | | | % 233.00/39.69 | | | | | | | | | End of split % 233.00/39.69 | | | | | | | | | % 233.00/39.69 | | | | | | | | End of split % 233.00/39.69 | | | | | | | | % 233.00/39.69 | | | | | | | Case 2: % 233.00/39.69 | | | | | | | | % 233.00/39.69 | | | | | | | | (1700) all_74_11 = n4 % 233.00/39.69 | | | | | | | | % 233.00/39.69 | | | | | | | | REDUCE: (1630), (1700) imply: % 233.00/39.69 | | | | | | | | (1701) a_select3(pminus_ds1_filter, n4, n0) = all_74_9 % 233.00/39.69 | | | | | | | | % 233.00/39.69 | | | | | | | | REDUCE: (1629), (1700) imply: % 233.00/39.69 | | | | | | | | (1702) a_select3(pminus_ds1_filter, n0, n4) = all_74_8 % 233.00/39.69 | | | | | | | | % 233.00/39.69 | | | | | | | | REDUCE: (1042), (1700) imply: % 233.00/39.69 | | | | | | | | (1703) leq(n4, n5) % 233.00/39.69 | | | | | | | | % 233.00/39.69 | | | | | | | | REDUCE: (1035), (1700) imply: % 233.00/39.69 | | | | | | | | (1704) leq(n0, n4) % 233.00/39.69 | | | | | | | | % 233.00/39.69 | | | | | | | | GROUND_INST: instantiating (64) with n0, n4, all_74_8, % 233.00/39.69 | | | | | | | | simplifying with (12), (119), (1632), (1702), % 233.00/39.69 | | | | | | | | (1704) gives: % 233.00/39.69 | | | | | | | | (1705) ~ leq(n4, all_74_21) | ~ leq(n0, all_74_21) | % 233.00/39.69 | | | | | | | | (a_select3(pminus_ds1_filter, n4, n0) = all_74_8 & % 233.00/39.69 | | | | | | | | $i(all_74_8)) % 233.00/39.69 | | | | | | | | % 233.00/39.69 | | | | | | | | BETA: splitting (1705) gives: % 233.00/39.69 | | | | | | | | % 233.00/39.69 | | | | | | | | Case 1: % 233.00/39.69 | | | | | | | | | % 233.00/39.69 | | | | | | | | | (1706) ~ leq(n0, all_74_21) % 233.00/39.69 | | | | | | | | | % 233.00/39.69 | | | | | | | | | REDUCE: (135), (1706) imply: % 233.00/39.69 | | | | | | | | | (1707) ~ leq(n0, n5) % 233.00/39.69 | | | | | | | | | % 233.00/39.69 | | | | | | | | | PRED_UNIFY: (1631), (1707) imply: % 233.00/39.69 | | | | | | | | | (1708) $false % 233.00/39.69 | | | | | | | | | % 233.00/39.69 | | | | | | | | | CLOSE: (1708) is inconsistent. % 233.00/39.69 | | | | | | | | | % 233.00/39.69 | | | | | | | | Case 2: % 233.00/39.69 | | | | | | | | | % 233.00/39.69 | | | | | | | | | (1709) ~ leq(n4, all_74_21) | % 233.00/39.69 | | | | | | | | | (a_select3(pminus_ds1_filter, n4, n0) = all_74_8 & % 233.00/39.69 | | | | | | | | | $i(all_74_8)) % 233.00/39.69 | | | | | | | | | % 233.00/39.69 | | | | | | | | | BETA: splitting (1709) gives: % 233.00/39.69 | | | | | | | | | % 233.00/39.69 | | | | | | | | | Case 1: % 233.00/39.69 | | | | | | | | | | % 233.00/39.69 | | | | | | | | | | (1710) ~ leq(n4, all_74_21) % 233.00/39.69 | | | | | | | | | | % 233.00/39.69 | | | | | | | | | | REDUCE: (135), (1710) imply: % 233.00/39.69 | | | | | | | | | | (1711) ~ leq(n4, n5) % 233.00/39.69 | | | | | | | | | | % 233.00/39.69 | | | | | | | | | | PRED_UNIFY: (1703), (1711) imply: % 233.00/39.69 | | | | | | | | | | (1712) $false % 233.00/39.69 | | | | | | | | | | % 233.00/39.69 | | | | | | | | | | CLOSE: (1712) is inconsistent. % 233.00/39.69 | | | | | | | | | | % 233.00/39.69 | | | | | | | | | Case 2: % 233.00/39.69 | | | | | | | | | | % 233.00/39.69 | | | | | | | | | | (1713) a_select3(pminus_ds1_filter, n4, n0) = all_74_8 & % 233.00/39.69 | | | | | | | | | | $i(all_74_8) % 233.00/39.69 | | | | | | | | | | % 233.00/39.69 | | | | | | | | | | ALPHA: (1713) implies: % 233.00/39.69 | | | | | | | | | | (1714) a_select3(pminus_ds1_filter, n4, n0) = all_74_8 % 233.00/39.69 | | | | | | | | | | % 233.00/39.69 | | | | | | | | | | REF_CLOSE: (17), (1034), (1701), (1714) are inconsistent by % 233.00/39.69 | | | | | | | | | | sub-proof #29. % 233.00/39.69 | | | | | | | | | | % 233.00/39.69 | | | | | | | | | End of split % 233.00/39.69 | | | | | | | | | % 233.00/39.69 | | | | | | | | End of split % 233.00/39.69 | | | | | | | | % 233.00/39.69 | | | | | | | End of split % 233.00/39.69 | | | | | | | % 233.00/39.69 | | | | | | End of split % 233.00/39.69 | | | | | | % 233.00/39.69 | | | | | Case 2: % 233.00/39.69 | | | | | | % 233.00/39.69 | | | | | | (1715) all_74_11 = n5 % 233.00/39.69 | | | | | | % 233.00/39.69 | | | | | | REDUCE: (1630), (1715) imply: % 233.00/39.69 | | | | | | (1716) a_select3(pminus_ds1_filter, n5, n0) = all_74_9 % 233.00/39.69 | | | | | | % 233.00/39.69 | | | | | | REDUCE: (1629), (1715) imply: % 233.00/39.69 | | | | | | (1717) a_select3(pminus_ds1_filter, n0, n5) = all_74_8 % 233.00/39.69 | | | | | | % 233.00/39.69 | | | | | | REDUCE: (1042), (1715) imply: % 233.00/39.69 | | | | | | (1718) leq(n5, n5) % 233.00/39.69 | | | | | | % 233.00/39.69 | | | | | | GROUND_INST: instantiating (64) with n0, n5, all_74_8, simplifying % 233.00/39.69 | | | | | | with (12), (122), (1631), (1632), (1717) gives: % 233.00/39.69 | | | | | | (1719) ~ leq(n5, all_74_21) | ~ leq(n0, all_74_21) | % 233.00/39.69 | | | | | | (a_select3(pminus_ds1_filter, n5, n0) = all_74_8 & % 233.00/39.69 | | | | | | $i(all_74_8)) % 233.00/39.69 | | | | | | % 233.00/39.69 | | | | | | BETA: splitting (1719) gives: % 233.00/39.69 | | | | | | % 233.00/39.69 | | | | | | Case 1: % 233.00/39.69 | | | | | | | % 233.00/39.69 | | | | | | | (1720) ~ leq(n0, all_74_21) % 233.00/39.69 | | | | | | | % 233.00/39.69 | | | | | | | REDUCE: (135), (1720) imply: % 233.00/39.69 | | | | | | | (1721) ~ leq(n0, n5) % 233.00/39.69 | | | | | | | % 233.00/39.69 | | | | | | | PRED_UNIFY: (1631), (1721) imply: % 233.00/39.69 | | | | | | | (1722) $false % 233.00/39.69 | | | | | | | % 233.00/39.69 | | | | | | | CLOSE: (1722) is inconsistent. % 233.00/39.69 | | | | | | | % 233.00/39.69 | | | | | | Case 2: % 233.00/39.69 | | | | | | | % 233.00/39.69 | | | | | | | (1723) ~ leq(n5, all_74_21) | (a_select3(pminus_ds1_filter, % 233.00/39.69 | | | | | | | n5, n0) = all_74_8 & $i(all_74_8)) % 233.00/39.69 | | | | | | | % 233.00/39.69 | | | | | | | BETA: splitting (1723) gives: % 233.00/39.69 | | | | | | | % 233.00/39.69 | | | | | | | Case 1: % 233.00/39.69 | | | | | | | | % 233.00/39.69 | | | | | | | | (1724) ~ leq(n5, all_74_21) % 233.00/39.69 | | | | | | | | % 233.00/39.69 | | | | | | | | REDUCE: (135), (1724) imply: % 233.00/39.69 | | | | | | | | (1725) ~ leq(n5, n5) % 233.00/39.69 | | | | | | | | % 233.00/39.69 | | | | | | | | PRED_UNIFY: (1718), (1725) imply: % 233.00/39.69 | | | | | | | | (1726) $false % 233.00/39.69 | | | | | | | | % 233.00/39.69 | | | | | | | | CLOSE: (1726) is inconsistent. % 233.00/39.69 | | | | | | | | % 233.00/39.69 | | | | | | | Case 2: % 233.00/39.69 | | | | | | | | % 233.00/39.69 | | | | | | | | (1727) a_select3(pminus_ds1_filter, n5, n0) = all_74_8 & % 233.00/39.69 | | | | | | | | $i(all_74_8) % 233.00/39.69 | | | | | | | | % 233.00/39.69 | | | | | | | | ALPHA: (1727) implies: % 233.00/39.69 | | | | | | | | (1728) a_select3(pminus_ds1_filter, n5, n0) = all_74_8 % 233.00/39.69 | | | | | | | | % 233.00/39.69 | | | | | | | | REF_CLOSE: (17), (1034), (1716), (1728) are inconsistent by % 233.00/39.69 | | | | | | | | sub-proof #28. % 233.00/39.69 | | | | | | | | % 233.00/39.69 | | | | | | | End of split % 233.00/39.69 | | | | | | | % 233.00/39.69 | | | | | | End of split % 233.00/39.69 | | | | | | % 233.00/39.69 | | | | | End of split % 233.00/39.69 | | | | | % 233.00/39.69 | | | | Case 2: % 233.00/39.69 | | | | | % 233.00/39.69 | | | | | (1729) all_74_11 = n0 % 233.00/39.69 | | | | | % 233.00/39.69 | | | | | REDUCE: (1630), (1729) imply: % 233.00/39.69 | | | | | (1730) a_select3(pminus_ds1_filter, n0, n0) = all_74_9 % 233.00/39.69 | | | | | % 233.00/39.69 | | | | | REDUCE: (1629), (1729) imply: % 233.00/39.69 | | | | | (1731) a_select3(pminus_ds1_filter, n0, n0) = all_74_8 % 233.00/39.69 | | | | | % 233.00/39.69 | | | | | GROUND_INST: instantiating (17) with all_74_9, all_74_8, n0, n0, % 233.00/39.69 | | | | | pminus_ds1_filter, simplifying with (1730), (1731) gives: % 233.00/39.69 | | | | | (1732) all_74_8 = all_74_9 % 233.00/39.69 | | | | | % 233.00/39.69 | | | | | REDUCE: (1034), (1732) imply: % 233.00/39.69 | | | | | (1733) $false % 233.00/39.69 | | | | | % 233.00/39.69 | | | | | CLOSE: (1733) is inconsistent. % 233.00/39.69 | | | | | % 233.00/39.69 | | | | End of split % 233.00/39.69 | | | | % 233.00/39.69 | | | End of split % 233.00/39.69 | | | % 233.00/39.69 | | Case 2: % 233.00/39.69 | | | % 233.00/39.69 | | | (1734) ( ~ (all_74_12 = all_74_13) & a_select3(pminus_ds1_filter, % 233.00/39.69 | | | all_74_14, all_74_15) = all_74_12 & % 233.00/39.69 | | | a_select3(pminus_ds1_filter, all_74_15, all_74_14) = all_74_13 % 233.00/39.69 | | | & $i(all_74_12) & $i(all_74_13) & leq(all_74_14, all_74_21) & % 233.00/39.69 | | | leq(all_74_15, all_74_21) & leq(n0, all_74_14) & leq(n0, % 233.00/39.69 | | | all_74_15)) | ( ~ (all_74_16 = all_74_17) & % 233.00/39.69 | | | a_select3(id_ds1_filter, all_74_18, all_74_19) = all_74_16 & % 233.00/39.69 | | | a_select3(id_ds1_filter, all_74_19, all_74_18) = all_74_17 & % 233.00/39.69 | | | $i(all_74_16) & $i(all_74_17) & leq(all_74_18, all_74_21) & % 233.00/39.69 | | | leq(all_74_19, all_74_21) & leq(n0, all_74_18) & leq(n0, % 233.00/39.69 | | | all_74_19)) % 233.00/39.69 | | | % 233.00/39.69 | | | BETA: splitting (1734) gives: % 233.00/39.69 | | | % 233.00/39.69 | | | Case 1: % 233.00/39.69 | | | | % 233.00/39.69 | | | | (1735) ~ (all_74_12 = all_74_13) & a_select3(pminus_ds1_filter, % 233.00/39.69 | | | | all_74_14, all_74_15) = all_74_12 & % 233.00/39.69 | | | | a_select3(pminus_ds1_filter, all_74_15, all_74_14) = all_74_13 % 233.00/39.69 | | | | & $i(all_74_12) & $i(all_74_13) & leq(all_74_14, all_74_21) & % 233.00/39.69 | | | | leq(all_74_15, all_74_21) & leq(n0, all_74_14) & leq(n0, % 233.00/39.69 | | | | all_74_15) % 233.00/39.69 | | | | % 233.00/39.69 | | | | ALPHA: (1735) implies: % 233.00/39.69 | | | | (1736) ~ (all_74_12 = all_74_13) % 233.00/39.69 | | | | (1737) leq(n0, all_74_15) % 233.00/39.69 | | | | (1738) leq(n0, all_74_14) % 233.00/39.69 | | | | (1739) leq(all_74_15, all_74_21) % 233.00/39.69 | | | | (1740) leq(all_74_14, all_74_21) % 233.00/39.69 | | | | (1741) a_select3(pminus_ds1_filter, all_74_15, all_74_14) = all_74_13 % 233.00/39.69 | | | | (1742) a_select3(pminus_ds1_filter, all_74_14, all_74_15) = all_74_12 % 233.00/39.69 | | | | % 233.00/39.69 | | | | REDUCE: (135), (1740) imply: % 233.00/39.69 | | | | (1743) leq(all_74_14, n5) % 233.00/39.69 | | | | % 233.00/39.69 | | | | REDUCE: (135), (1739) imply: % 233.00/39.70 | | | | (1744) leq(all_74_15, n5) % 233.00/39.70 | | | | % 233.00/39.70 | | | | GROUND_INST: instantiating (leq_gt2) with n0, all_74_15, simplifying % 233.00/39.70 | | | | with (12), (51), (1737) gives: % 233.00/39.70 | | | | (1745) all_74_15 = n0 | gt(all_74_15, n0) % 233.00/39.70 | | | | % 233.00/39.70 | | | | GROUND_INST: instantiating (leq_gt2) with n0, all_74_14, simplifying % 233.00/39.70 | | | | with (12), (52), (1738) gives: % 233.00/39.70 | | | | (1746) all_74_14 = n0 | gt(all_74_14, n0) % 233.00/39.70 | | | | % 233.00/39.70 | | | | GROUND_INST: instantiating (3) with all_74_15, simplifying with (51), % 233.00/39.70 | | | | (1737), (1744) gives: % 233.00/39.70 | | | | (1747) all_74_15 = n5 | all_74_15 = n4 | all_74_15 = n3 | all_74_15 = % 233.00/39.70 | | | | n2 | all_74_15 = n1 | all_74_15 = n0 % 233.00/39.70 | | | | % 233.00/39.70 | | | | GROUND_INST: instantiating (leq_gt2) with all_74_15, n5, simplifying % 233.00/39.70 | | | | with (51), (122), (1744) gives: % 233.00/39.70 | | | | (1748) all_74_15 = n5 | gt(n5, all_74_15) % 233.00/39.70 | | | | % 233.00/39.70 | | | | GROUND_INST: instantiating (3) with all_74_14, simplifying with (52), % 233.00/39.70 | | | | (1738), (1743) gives: % 233.00/39.70 | | | | (1749) all_74_14 = n5 | all_74_14 = n4 | all_74_14 = n3 | all_74_14 = % 233.00/39.70 | | | | n2 | all_74_14 = n1 | all_74_14 = n0 % 233.00/39.70 | | | | % 233.00/39.70 | | | | GROUND_INST: instantiating (leq_gt2) with all_74_14, n5, simplifying % 233.00/39.70 | | | | with (52), (122), (1743) gives: % 233.00/39.70 | | | | (1750) all_74_14 = n5 | gt(n5, all_74_14) % 233.00/39.70 | | | | % 233.00/39.70 | | | | BETA: splitting (1746) gives: % 233.00/39.70 | | | | % 233.00/39.70 | | | | Case 1: % 233.00/39.70 | | | | | % 233.00/39.70 | | | | | (1751) gt(all_74_14, n0) % 233.00/39.70 | | | | | % 233.00/39.70 | | | | | BETA: splitting (1745) gives: % 233.00/39.70 | | | | | % 233.00/39.70 | | | | | Case 1: % 233.00/39.70 | | | | | | % 233.00/39.70 | | | | | | (1752) gt(all_74_15, n0) % 233.00/39.70 | | | | | | % 233.00/39.70 | | | | | | BETA: splitting (1748) gives: % 233.00/39.70 | | | | | | % 233.00/39.70 | | | | | | Case 1: % 233.00/39.70 | | | | | | | % 233.00/39.70 | | | | | | | (1753) gt(n5, all_74_15) % 233.00/39.70 | | | | | | | % 233.00/39.70 | | | | | | | GROUND_INST: instantiating (1) with all_74_15, n5, n4, simplifying % 233.00/39.70 | | | | | | | with (51), (122), (126), (1753) gives: % 233.00/39.70 | | | | | | | (1754) leq(all_74_15, n4) % 233.00/39.70 | | | | | | | % 233.00/39.70 | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_15, n4, % 233.00/39.70 | | | | | | | simplifying with (51), (119), (1754) gives: % 233.00/39.70 | | | | | | | (1755) all_74_15 = n4 | gt(n4, all_74_15) % 233.00/39.70 | | | | | | | % 233.00/39.70 | | | | | | | BETA: splitting (1750) gives: % 233.00/39.70 | | | | | | | % 233.00/39.70 | | | | | | | Case 1: % 233.00/39.70 | | | | | | | | % 233.00/39.70 | | | | | | | | (1756) gt(n5, all_74_14) % 233.00/39.70 | | | | | | | | % 233.00/39.70 | | | | | | | | GROUND_INST: instantiating (1) with all_74_14, n5, n4, % 233.00/39.70 | | | | | | | | simplifying with (52), (122), (126), (1756) gives: % 233.00/39.70 | | | | | | | | (1757) leq(all_74_14, n4) % 233.00/39.70 | | | | | | | | % 233.00/39.70 | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_14, n4, % 233.00/39.70 | | | | | | | | simplifying with (52), (119), (1757) gives: % 233.00/39.70 | | | | | | | | (1758) all_74_14 = n4 | gt(n4, all_74_14) % 233.00/39.70 | | | | | | | | % 233.00/39.70 | | | | | | | | BETA: splitting (1749) gives: % 233.00/39.70 | | | | | | | | % 233.00/39.70 | | | | | | | | Case 1: % 233.00/39.70 | | | | | | | | | % 233.00/39.70 | | | | | | | | | (1759) all_74_14 = n0 % 233.00/39.70 | | | | | | | | | % 233.00/39.70 | | | | | | | | | REDUCE: (1751), (1759) imply: % 233.00/39.70 | | | | | | | | | (1760) gt(n0, n0) % 233.00/39.70 | | | | | | | | | % 233.00/39.70 | | | | | | | | | GROUND_INST: instantiating (irreflexivity_gt) with n0, % 233.00/39.70 | | | | | | | | | simplifying with (12), (1760) gives: % 233.00/39.70 | | | | | | | | | (1761) $false % 233.00/39.70 | | | | | | | | | % 233.00/39.70 | | | | | | | | | CLOSE: (1761) is inconsistent. % 233.00/39.70 | | | | | | | | | % 233.00/39.70 | | | | | | | | Case 2: % 233.00/39.70 | | | | | | | | | % 233.00/39.70 | | | | | | | | | (1762) ~ (all_74_14 = n0) % 233.00/39.70 | | | | | | | | | % 233.00/39.70 | | | | | | | | | BETA: splitting (1747) gives: % 233.00/39.70 | | | | | | | | | % 233.00/39.70 | | | | | | | | | Case 1: % 233.00/39.70 | | | | | | | | | | % 233.00/39.70 | | | | | | | | | | (1763) all_74_15 = n0 % 233.00/39.70 | | | | | | | | | | % 233.00/39.70 | | | | | | | | | | REF_CLOSE: (51), (1752), (1763), (irreflexivity_gt) are % 233.00/39.70 | | | | | | | | | | inconsistent by sub-proof #27. % 233.00/39.70 | | | | | | | | | | % 233.00/39.70 | | | | | | | | | Case 2: % 233.00/39.70 | | | | | | | | | | % 233.00/39.70 | | | | | | | | | | (1764) ~ (all_74_15 = n0) % 233.00/39.70 | | | | | | | | | | % 233.00/39.70 | | | | | | | | | | REF_CLOSE: (1), (4), (17), (51), (52), (64), (101), (112), % 233.00/39.70 | | | | | | | | | | (119), (123), (124), (125), (135), (1736), (1737), % 233.00/39.70 | | | | | | | | | | (1738), (1741), (1742), (1743), (1744), (1755), % 233.00/39.70 | | | | | | | | | | (1758), (1762), (1764), (leq_gt2) are inconsistent % 233.00/39.70 | | | | | | | | | | by sub-proof #23. % 233.00/39.70 | | | | | | | | | | % 233.00/39.70 | | | | | | | | | End of split % 233.00/39.70 | | | | | | | | | % 233.00/39.70 | | | | | | | | End of split % 233.00/39.70 | | | | | | | | % 233.00/39.70 | | | | | | | Case 2: % 233.00/39.70 | | | | | | | | % 233.00/39.70 | | | | | | | | (1765) all_74_14 = n5 % 233.00/39.70 | | | | | | | | % 233.00/39.70 | | | | | | | | REDUCE: (1742), (1765) imply: % 233.00/39.70 | | | | | | | | (1766) a_select3(pminus_ds1_filter, n5, all_74_15) = % 233.00/39.70 | | | | | | | | all_74_12 % 233.00/39.70 | | | | | | | | % 233.00/39.70 | | | | | | | | REDUCE: (1741), (1765) imply: % 233.00/39.70 | | | | | | | | (1767) a_select3(pminus_ds1_filter, all_74_15, n5) = % 233.00/39.70 | | | | | | | | all_74_13 % 233.00/39.70 | | | | | | | | % 233.00/39.70 | | | | | | | | REDUCE: (1743), (1765) imply: % 233.00/39.70 | | | | | | | | (1768) leq(n5, n5) % 233.00/39.70 | | | | | | | | % 233.00/39.70 | | | | | | | | REDUCE: (1738), (1765) imply: % 233.00/39.70 | | | | | | | | (1769) leq(n0, n5) % 233.00/39.70 | | | | | | | | % 233.00/39.70 | | | | | | | | BETA: splitting (1747) gives: % 233.00/39.70 | | | | | | | | % 233.00/39.70 | | | | | | | | Case 1: % 233.00/39.70 | | | | | | | | | % 233.00/39.70 | | | | | | | | | (1770) all_74_15 = n0 % 233.00/39.70 | | | | | | | | | % 233.00/39.70 | | | | | | | | | REF_CLOSE: (51), (1752), (1770), (irreflexivity_gt) are % 233.00/39.70 | | | | | | | | | inconsistent by sub-proof #27. % 233.00/39.70 | | | | | | | | | % 233.00/39.70 | | | | | | | | Case 2: % 233.00/39.70 | | | | | | | | | % 233.00/39.70 | | | | | | | | | (1771) ~ (all_74_15 = n0) % 233.00/39.70 | | | | | | | | | % 233.00/39.70 | | | | | | | | | REF_CLOSE: (1), (4), (17), (51), (64), (101), (112), (119), % 233.00/39.70 | | | | | | | | | (122), (123), (124), (125), (135), (1736), (1737), % 233.00/39.70 | | | | | | | | | (1744), (1755), (1766), (1767), (1768), (1769), % 233.00/39.70 | | | | | | | | | (1771), (leq_gt2) are inconsistent by sub-proof % 233.00/39.70 | | | | | | | | | #21. % 233.00/39.70 | | | | | | | | | % 233.00/39.70 | | | | | | | | End of split % 233.00/39.70 | | | | | | | | % 233.00/39.70 | | | | | | | End of split % 233.00/39.70 | | | | | | | % 233.00/39.70 | | | | | | Case 2: % 233.00/39.70 | | | | | | | % 233.00/39.70 | | | | | | | (1772) all_74_15 = n5 % 233.00/39.70 | | | | | | | % 233.00/39.70 | | | | | | | REDUCE: (1742), (1772) imply: % 233.00/39.70 | | | | | | | (1773) a_select3(pminus_ds1_filter, all_74_14, n5) = all_74_12 % 233.00/39.70 | | | | | | | % 233.00/39.70 | | | | | | | REDUCE: (1741), (1772) imply: % 233.00/39.70 | | | | | | | (1774) a_select3(pminus_ds1_filter, n5, all_74_14) = all_74_13 % 233.00/39.70 | | | | | | | % 233.00/39.70 | | | | | | | REDUCE: (1744), (1772) imply: % 233.00/39.70 | | | | | | | (1775) leq(n5, n5) % 233.00/39.70 | | | | | | | % 233.00/39.70 | | | | | | | REDUCE: (1737), (1772) imply: % 233.00/39.70 | | | | | | | (1776) leq(n0, n5) % 233.00/39.70 | | | | | | | % 233.00/39.70 | | | | | | | BETA: splitting (1750) gives: % 233.00/39.70 | | | | | | | % 233.00/39.70 | | | | | | | Case 1: % 233.00/39.70 | | | | | | | | % 233.00/39.70 | | | | | | | | (1777) gt(n5, all_74_14) % 233.00/39.70 | | | | | | | | % 233.00/39.70 | | | | | | | | GROUND_INST: instantiating (1) with all_74_14, n5, n4, % 233.00/39.70 | | | | | | | | simplifying with (52), (122), (126), (1777) gives: % 233.00/39.70 | | | | | | | | (1778) leq(all_74_14, n4) % 233.00/39.70 | | | | | | | | % 233.00/39.70 | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_14, n4, % 233.00/39.70 | | | | | | | | simplifying with (52), (119), (1778) gives: % 233.00/39.70 | | | | | | | | (1779) all_74_14 = n4 | gt(n4, all_74_14) % 233.00/39.70 | | | | | | | | % 233.00/39.70 | | | | | | | | BETA: splitting (1749) gives: % 233.00/39.70 | | | | | | | | % 233.00/39.70 | | | | | | | | Case 1: % 233.00/39.70 | | | | | | | | | % 233.00/39.70 | | | | | | | | | (1780) all_74_14 = n0 % 233.00/39.70 | | | | | | | | | % 233.00/39.70 | | | | | | | | | REDUCE: (1751), (1780) imply: % 233.00/39.70 | | | | | | | | | (1781) gt(n0, n0) % 233.00/39.70 | | | | | | | | | % 233.00/39.70 | | | | | | | | | GROUND_INST: instantiating (irreflexivity_gt) with n0, % 233.00/39.70 | | | | | | | | | simplifying with (12), (1781) gives: % 233.00/39.70 | | | | | | | | | (1782) $false % 233.00/39.70 | | | | | | | | | % 233.00/39.70 | | | | | | | | | CLOSE: (1782) is inconsistent. % 233.00/39.70 | | | | | | | | | % 233.00/39.70 | | | | | | | | Case 2: % 233.00/39.70 | | | | | | | | | % 233.00/39.70 | | | | | | | | | (1783) ~ (all_74_14 = n0) % 233.00/39.70 | | | | | | | | | % 233.00/39.70 | | | | | | | | | REF_CLOSE: (1), (4), (17), (52), (64), (101), (112), (119), % 233.00/39.70 | | | | | | | | | (122), (123), (124), (125), (135), (1736), (1738), % 233.00/39.70 | | | | | | | | | (1743), (1773), (1774), (1775), (1776), (1779), % 233.00/39.70 | | | | | | | | | (1783), (leq_gt2) are inconsistent by sub-proof % 233.00/39.70 | | | | | | | | | #20. % 233.00/39.70 | | | | | | | | | % 233.00/39.70 | | | | | | | | End of split % 233.00/39.70 | | | | | | | | % 233.00/39.70 | | | | | | | Case 2: % 233.00/39.70 | | | | | | | | % 233.00/39.70 | | | | | | | | (1784) all_74_14 = n5 % 233.00/39.70 | | | | | | | | % 233.00/39.70 | | | | | | | | REDUCE: (1773), (1784) imply: % 233.00/39.70 | | | | | | | | (1785) a_select3(pminus_ds1_filter, n5, n5) = all_74_12 % 233.00/39.70 | | | | | | | | % 233.00/39.70 | | | | | | | | REDUCE: (1774), (1784) imply: % 233.00/39.70 | | | | | | | | (1786) a_select3(pminus_ds1_filter, n5, n5) = all_74_13 % 233.00/39.70 | | | | | | | | % 233.00/39.70 | | | | | | | | GROUND_INST: instantiating (17) with all_74_13, all_74_12, n5, % 233.00/39.70 | | | | | | | | n5, pminus_ds1_filter, simplifying with (1785), % 233.00/39.70 | | | | | | | | (1786) gives: % 233.00/39.70 | | | | | | | | (1787) all_74_12 = all_74_13 % 233.00/39.70 | | | | | | | | % 233.00/39.70 | | | | | | | | REDUCE: (1736), (1787) imply: % 233.00/39.70 | | | | | | | | (1788) $false % 233.00/39.70 | | | | | | | | % 233.00/39.70 | | | | | | | | CLOSE: (1788) is inconsistent. % 233.00/39.70 | | | | | | | | % 233.00/39.70 | | | | | | | End of split % 233.00/39.70 | | | | | | | % 233.00/39.70 | | | | | | End of split % 233.00/39.70 | | | | | | % 233.00/39.70 | | | | | Case 2: % 233.00/39.70 | | | | | | % 233.00/39.70 | | | | | | (1789) all_74_15 = n0 % 233.00/39.70 | | | | | | (1790) ~ gt(all_74_15, n0) % 233.00/39.70 | | | | | | % 233.00/39.70 | | | | | | REDUCE: (1789), (1790) imply: % 233.00/39.70 | | | | | | (1791) ~ gt(n0, n0) % 233.00/39.70 | | | | | | % 233.00/39.70 | | | | | | REF_CLOSE: (1), (4), (17), (51), (52), (64), (101), (112), (119), % 233.00/39.70 | | | | | | (122), (123), (124), (125), (126), (135), (1736), (1737), % 233.00/39.70 | | | | | | (1738), (1741), (1742), (1743), (1744), (1745), (1747), % 233.00/39.70 | | | | | | (1748), (1749), (1750), (1751), (1791), (leq_gt2) are % 233.00/39.70 | | | | | | inconsistent by sub-proof #15. % 233.00/39.70 | | | | | | % 233.00/39.70 | | | | | End of split % 233.00/39.70 | | | | | % 233.00/39.70 | | | | Case 2: % 233.00/39.70 | | | | | % 233.00/39.70 | | | | | (1792) all_74_14 = n0 % 233.00/39.70 | | | | | (1793) ~ gt(all_74_14, n0) % 233.00/39.70 | | | | | % 233.00/39.70 | | | | | REDUCE: (1792), (1793) imply: % 233.00/39.70 | | | | | (1794) ~ gt(n0, n0) % 233.00/39.70 | | | | | % 233.00/39.70 | | | | | BETA: splitting (1746) gives: % 233.00/39.70 | | | | | % 233.00/39.70 | | | | | Case 1: % 233.00/39.70 | | | | | | % 233.00/39.70 | | | | | | (1795) gt(all_74_14, n0) % 233.00/39.70 | | | | | | % 233.00/39.70 | | | | | | REF_CLOSE: (1), (4), (17), (51), (52), (64), (101), (112), (119), % 233.00/39.70 | | | | | | (122), (123), (124), (125), (126), (135), (1736), (1737), % 233.00/39.70 | | | | | | (1738), (1741), (1742), (1743), (1744), (1745), (1747), % 233.00/39.70 | | | | | | (1748), (1749), (1750), (1794), (1795), (leq_gt2) are % 233.00/39.70 | | | | | | inconsistent by sub-proof #15. % 233.00/39.70 | | | | | | % 233.00/39.70 | | | | | Case 2: % 233.00/39.70 | | | | | | % 233.00/39.70 | | | | | | % 233.00/39.70 | | | | | | REDUCE: (1742), (1792) imply: % 233.00/39.70 | | | | | | (1796) a_select3(pminus_ds1_filter, n0, all_74_15) = all_74_12 % 233.00/39.70 | | | | | | % 233.00/39.70 | | | | | | REDUCE: (1741), (1792) imply: % 233.00/39.70 | | | | | | (1797) a_select3(pminus_ds1_filter, all_74_15, n0) = all_74_13 % 233.00/39.70 | | | | | | % 233.00/39.70 | | | | | | REDUCE: (1743), (1792) imply: % 233.00/39.70 | | | | | | (1798) leq(n0, n5) % 233.00/39.70 | | | | | | % 233.00/39.70 | | | | | | REDUCE: (1738), (1792) imply: % 233.00/39.70 | | | | | | (1799) leq(n0, n0) % 233.00/39.70 | | | | | | % 233.00/39.70 | | | | | | BETA: splitting (1745) gives: % 233.00/39.71 | | | | | | % 233.00/39.71 | | | | | | Case 1: % 233.00/39.71 | | | | | | | % 233.00/39.71 | | | | | | | (1800) gt(all_74_15, n0) % 233.00/39.71 | | | | | | | % 233.00/39.71 | | | | | | | BETA: splitting (1748) gives: % 233.00/39.71 | | | | | | | % 233.00/39.71 | | | | | | | Case 1: % 233.00/39.71 | | | | | | | | % 233.00/39.71 | | | | | | | | (1801) gt(n5, all_74_15) % 233.00/39.71 | | | | | | | | % 233.00/39.71 | | | | | | | | GROUND_INST: instantiating (1) with all_74_15, n5, n4, % 233.00/39.71 | | | | | | | | simplifying with (51), (122), (126), (1801) gives: % 233.00/39.71 | | | | | | | | (1802) leq(all_74_15, n4) % 233.00/39.71 | | | | | | | | % 233.00/39.71 | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_15, n4, % 233.00/39.71 | | | | | | | | simplifying with (51), (119), (1802) gives: % 233.00/39.71 | | | | | | | | (1803) all_74_15 = n4 | gt(n4, all_74_15) % 233.00/39.71 | | | | | | | | % 233.00/39.71 | | | | | | | | BETA: splitting (1747) gives: % 233.00/39.71 | | | | | | | | % 233.00/39.71 | | | | | | | | Case 1: % 233.00/39.71 | | | | | | | | | % 233.00/39.71 | | | | | | | | | (1804) all_74_15 = n0 % 233.00/39.71 | | | | | | | | | % 233.00/39.71 | | | | | | | | | REDUCE: (1800), (1804) imply: % 233.00/39.71 | | | | | | | | | (1805) gt(n0, n0) % 233.00/39.71 | | | | | | | | | % 233.00/39.71 | | | | | | | | | PRED_UNIFY: (1794), (1805) imply: % 233.00/39.71 | | | | | | | | | (1806) $false % 233.00/39.71 | | | | | | | | | % 233.00/39.71 | | | | | | | | | CLOSE: (1806) is inconsistent. % 233.00/39.71 | | | | | | | | | % 233.00/39.71 | | | | | | | | Case 2: % 233.00/39.71 | | | | | | | | | % 233.00/39.71 | | | | | | | | | (1807) ~ (all_74_15 = n0) % 233.00/39.71 | | | | | | | | | % 233.00/39.71 | | | | | | | | | BETA: splitting (1803) gives: % 233.00/39.71 | | | | | | | | | % 233.00/39.71 | | | | | | | | | Case 1: % 233.00/39.71 | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | (1808) gt(n4, all_74_15) % 233.00/39.71 | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_15, n4, n3, % 233.00/39.71 | | | | | | | | | | simplifying with (51), (119), (125), (1808) gives: % 233.00/39.71 | | | | | | | | | | (1809) leq(all_74_15, n3) % 233.00/39.71 | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_15, n3, % 233.00/39.71 | | | | | | | | | | simplifying with (51), (112), (1809) gives: % 233.00/39.71 | | | | | | | | | | (1810) all_74_15 = n3 | gt(n3, all_74_15) % 233.00/39.71 | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | BETA: splitting (1810) gives: % 233.00/39.71 | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | Case 1: % 233.00/39.71 | | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | | (1811) gt(n3, all_74_15) % 233.00/39.71 | | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_15, n3, n2, % 233.00/39.71 | | | | | | | | | | | simplifying with (51), (112), (124), (1811) gives: % 233.00/39.71 | | | | | | | | | | | (1812) leq(all_74_15, n2) % 233.00/39.71 | | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_15, n2, % 233.00/39.71 | | | | | | | | | | | simplifying with (51), (101), (1812) gives: % 233.00/39.71 | | | | | | | | | | | (1813) all_74_15 = n2 | gt(n2, all_74_15) % 233.00/39.71 | | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | | BETA: splitting (1813) gives: % 233.00/39.71 | | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | | Case 1: % 233.00/39.71 | | | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | | | (1814) gt(n2, all_74_15) % 233.00/39.71 | | | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_15, n2, n1, % 233.00/39.71 | | | | | | | | | | | | simplifying with (51), (101), (123), (1814) gives: % 233.00/39.71 | | | | | | | | | | | | (1815) leq(all_74_15, n1) % 233.00/39.71 | | | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_74_15, simplifying with % 233.00/39.71 | | | | | | | | | | | | (51), (1737), (1815) gives: % 233.00/39.71 | | | | | | | | | | | | (1816) all_74_15 = n1 | all_74_15 = n0 % 233.00/39.71 | | | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | | | BETA: splitting (1816) gives: % 233.00/39.71 | | | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | | | Case 1: % 233.00/39.71 | | | | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | | | | (1817) all_74_15 = n0 % 233.00/39.71 | | | | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | | | | REDUCE: (1807), (1817) imply: % 233.00/39.71 | | | | | | | | | | | | | (1818) $false % 233.00/39.71 | | | | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | | | | CLOSE: (1818) is inconsistent. % 233.00/39.71 | | | | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | | | Case 2: % 233.00/39.71 | | | | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | | | | (1819) all_74_15 = n1 % 233.00/39.71 | | | | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | | | | REDUCE: (1797), (1819) imply: % 233.00/39.71 | | | | | | | | | | | | | (1820) a_select3(pminus_ds1_filter, n1, n0) = all_74_13 % 233.00/39.71 | | | | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | | | | REDUCE: (1796), (1819) imply: % 233.00/39.71 | | | | | | | | | | | | | (1821) a_select3(pminus_ds1_filter, n0, n1) = all_74_12 % 233.00/39.71 | | | | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | | | | REDUCE: (1744), (1819) imply: % 233.00/39.71 | | | | | | | | | | | | | (1822) leq(n1, n5) % 233.00/39.71 | | | | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | | | | REDUCE: (1737), (1819) imply: % 233.00/39.71 | | | | | | | | | | | | | (1823) leq(n0, n1) % 233.00/39.71 | | | | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | | | | GROUND_INST: instantiating (64) with n0, n1, all_74_12, % 233.00/39.71 | | | | | | | | | | | | | simplifying with (12), (85), (1799), (1821), % 233.00/39.71 | | | | | | | | | | | | | (1823) gives: % 233.00/39.71 | | | | | | | | | | | | | (1824) ~ leq(n1, all_74_21) | ~ leq(n0, all_74_21) | % 233.00/39.71 | | | | | | | | | | | | | (a_select3(pminus_ds1_filter, n1, n0) = all_74_12 % 233.00/39.71 | | | | | | | | | | | | | & $i(all_74_12)) % 233.00/39.71 | | | | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | | | | BETA: splitting (1824) gives: % 233.00/39.71 | | | | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | | | | Case 1: % 233.00/39.71 | | | | | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | | | | | (1825) ~ leq(n0, all_74_21) % 233.00/39.71 | | | | | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | | | | | REDUCE: (135), (1825) imply: % 233.00/39.71 | | | | | | | | | | | | | | (1826) ~ leq(n0, n5) % 233.00/39.71 | | | | | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | | | | | PRED_UNIFY: (1798), (1826) imply: % 233.00/39.71 | | | | | | | | | | | | | | (1827) $false % 233.00/39.71 | | | | | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | | | | | CLOSE: (1827) is inconsistent. % 233.00/39.71 | | | | | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | | | | Case 2: % 233.00/39.71 | | | | | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | | | | | (1828) ~ leq(n1, all_74_21) | % 233.00/39.71 | | | | | | | | | | | | | | (a_select3(pminus_ds1_filter, n1, n0) = all_74_12 % 233.00/39.71 | | | | | | | | | | | | | | & $i(all_74_12)) % 233.00/39.71 | | | | | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | | | | | BETA: splitting (1828) gives: % 233.00/39.71 | | | | | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | | | | | Case 1: % 233.00/39.71 | | | | | | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | | | | | | (1829) ~ leq(n1, all_74_21) % 233.00/39.71 | | | | | | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | | | | | | REDUCE: (135), (1829) imply: % 233.00/39.71 | | | | | | | | | | | | | | | (1830) ~ leq(n1, n5) % 233.00/39.71 | | | | | | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | | | | | | PRED_UNIFY: (1822), (1830) imply: % 233.00/39.71 | | | | | | | | | | | | | | | (1831) $false % 233.00/39.71 | | | | | | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | | | | | | CLOSE: (1831) is inconsistent. % 233.00/39.71 | | | | | | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | | | | | Case 2: % 233.00/39.71 | | | | | | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | | | | | | (1832) a_select3(pminus_ds1_filter, n1, n0) = all_74_12 & % 233.00/39.71 | | | | | | | | | | | | | | | $i(all_74_12) % 233.00/39.71 | | | | | | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | | | | | | ALPHA: (1832) implies: % 233.00/39.71 | | | | | | | | | | | | | | | (1833) a_select3(pminus_ds1_filter, n1, n0) = all_74_12 % 233.00/39.71 | | | | | | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | | | | | | REF_CLOSE: (17), (1736), (1820), (1833) are inconsistent by % 233.00/39.71 | | | | | | | | | | | | | | | sub-proof #19. % 233.00/39.71 | | | | | | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | | | | | End of split % 233.00/39.71 | | | | | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | | | | End of split % 233.00/39.71 | | | | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | | | End of split % 233.00/39.71 | | | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | | Case 2: % 233.00/39.71 | | | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | | | (1834) all_74_15 = n2 % 233.00/39.71 | | | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | | | REDUCE: (1797), (1834) imply: % 233.00/39.71 | | | | | | | | | | | | (1835) a_select3(pminus_ds1_filter, n2, n0) = all_74_13 % 233.00/39.71 | | | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | | | REDUCE: (1796), (1834) imply: % 233.00/39.71 | | | | | | | | | | | | (1836) a_select3(pminus_ds1_filter, n0, n2) = all_74_12 % 233.00/39.71 | | | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | | | REDUCE: (1744), (1834) imply: % 233.00/39.71 | | | | | | | | | | | | (1837) leq(n2, n5) % 233.00/39.71 | | | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | | | REDUCE: (1737), (1834) imply: % 233.00/39.71 | | | | | | | | | | | | (1838) leq(n0, n2) % 233.00/39.71 | | | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | | | GROUND_INST: instantiating (64) with n0, n2, all_74_12, % 233.00/39.71 | | | | | | | | | | | | simplifying with (12), (101), (1799), (1836), % 233.00/39.71 | | | | | | | | | | | | (1838) gives: % 233.00/39.71 | | | | | | | | | | | | (1839) ~ leq(n2, all_74_21) | ~ leq(n0, all_74_21) | % 233.00/39.71 | | | | | | | | | | | | (a_select3(pminus_ds1_filter, n2, n0) = all_74_12 % 233.00/39.71 | | | | | | | | | | | | & $i(all_74_12)) % 233.00/39.71 | | | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | | | BETA: splitting (1839) gives: % 233.00/39.71 | | | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | | | Case 1: % 233.00/39.71 | | | | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | | | | (1840) ~ leq(n0, all_74_21) % 233.00/39.71 | | | | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | | | | REDUCE: (135), (1840) imply: % 233.00/39.71 | | | | | | | | | | | | | (1841) ~ leq(n0, n5) % 233.00/39.71 | | | | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | | | | PRED_UNIFY: (1798), (1841) imply: % 233.00/39.71 | | | | | | | | | | | | | (1842) $false % 233.00/39.71 | | | | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | | | | CLOSE: (1842) is inconsistent. % 233.00/39.71 | | | | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | | | Case 2: % 233.00/39.71 | | | | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | | | | (1843) ~ leq(n2, all_74_21) | % 233.00/39.71 | | | | | | | | | | | | | (a_select3(pminus_ds1_filter, n2, n0) = all_74_12 % 233.00/39.71 | | | | | | | | | | | | | & $i(all_74_12)) % 233.00/39.71 | | | | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | | | | BETA: splitting (1843) gives: % 233.00/39.71 | | | | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | | | | Case 1: % 233.00/39.71 | | | | | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | | | | | (1844) ~ leq(n2, all_74_21) % 233.00/39.71 | | | | | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | | | | | REDUCE: (135), (1844) imply: % 233.00/39.71 | | | | | | | | | | | | | | (1845) ~ leq(n2, n5) % 233.00/39.71 | | | | | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | | | | | PRED_UNIFY: (1837), (1845) imply: % 233.00/39.71 | | | | | | | | | | | | | | (1846) $false % 233.00/39.71 | | | | | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | | | | | CLOSE: (1846) is inconsistent. % 233.00/39.71 | | | | | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | | | | Case 2: % 233.00/39.71 | | | | | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | | | | | (1847) a_select3(pminus_ds1_filter, n2, n0) = all_74_12 & % 233.00/39.71 | | | | | | | | | | | | | | $i(all_74_12) % 233.00/39.71 | | | | | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | | | | | ALPHA: (1847) implies: % 233.00/39.71 | | | | | | | | | | | | | | (1848) a_select3(pminus_ds1_filter, n2, n0) = all_74_12 % 233.00/39.71 | | | | | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | | | | | REF_CLOSE: (17), (1736), (1835), (1848) are inconsistent by % 233.00/39.71 | | | | | | | | | | | | | | sub-proof #18. % 233.00/39.71 | | | | | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | | | | End of split % 233.00/39.71 | | | | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | | | End of split % 233.00/39.71 | | | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | | End of split % 233.00/39.71 | | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | Case 2: % 233.00/39.71 | | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | | (1849) all_74_15 = n3 % 233.00/39.71 | | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | | REDUCE: (1797), (1849) imply: % 233.00/39.71 | | | | | | | | | | | (1850) a_select3(pminus_ds1_filter, n3, n0) = all_74_13 % 233.00/39.71 | | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | | REDUCE: (1796), (1849) imply: % 233.00/39.71 | | | | | | | | | | | (1851) a_select3(pminus_ds1_filter, n0, n3) = all_74_12 % 233.00/39.71 | | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | | REDUCE: (1744), (1849) imply: % 233.00/39.71 | | | | | | | | | | | (1852) leq(n3, n5) % 233.00/39.71 | | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | | REDUCE: (1737), (1849) imply: % 233.00/39.71 | | | | | | | | | | | (1853) leq(n0, n3) % 233.00/39.71 | | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | | GROUND_INST: instantiating (64) with n0, n3, all_74_12, % 233.00/39.71 | | | | | | | | | | | simplifying with (12), (112), (1799), (1851), % 233.00/39.71 | | | | | | | | | | | (1853) gives: % 233.00/39.71 | | | | | | | | | | | (1854) ~ leq(n3, all_74_21) | ~ leq(n0, all_74_21) | % 233.00/39.71 | | | | | | | | | | | (a_select3(pminus_ds1_filter, n3, n0) = all_74_12 % 233.00/39.71 | | | | | | | | | | | & $i(all_74_12)) % 233.00/39.71 | | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | | BETA: splitting (1854) gives: % 233.00/39.71 | | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | | Case 1: % 233.00/39.71 | | | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | | | (1855) ~ leq(n0, all_74_21) % 233.00/39.71 | | | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | | | REDUCE: (135), (1855) imply: % 233.00/39.71 | | | | | | | | | | | | (1856) ~ leq(n0, n5) % 233.00/39.71 | | | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | | | PRED_UNIFY: (1798), (1856) imply: % 233.00/39.71 | | | | | | | | | | | | (1857) $false % 233.00/39.71 | | | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | | | CLOSE: (1857) is inconsistent. % 233.00/39.71 | | | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | | Case 2: % 233.00/39.71 | | | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | | | (1858) ~ leq(n3, all_74_21) | % 233.00/39.71 | | | | | | | | | | | | (a_select3(pminus_ds1_filter, n3, n0) = all_74_12 % 233.00/39.71 | | | | | | | | | | | | & $i(all_74_12)) % 233.00/39.71 | | | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | | | BETA: splitting (1858) gives: % 233.00/39.71 | | | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | | | Case 1: % 233.00/39.71 | | | | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | | | | (1859) ~ leq(n3, all_74_21) % 233.00/39.71 | | | | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | | | | REDUCE: (135), (1859) imply: % 233.00/39.71 | | | | | | | | | | | | | (1860) ~ leq(n3, n5) % 233.00/39.71 | | | | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | | | | PRED_UNIFY: (1852), (1860) imply: % 233.00/39.71 | | | | | | | | | | | | | (1861) $false % 233.00/39.71 | | | | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | | | | CLOSE: (1861) is inconsistent. % 233.00/39.71 | | | | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | | | Case 2: % 233.00/39.71 | | | | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | | | | (1862) a_select3(pminus_ds1_filter, n3, n0) = all_74_12 & % 233.00/39.71 | | | | | | | | | | | | | $i(all_74_12) % 233.00/39.71 | | | | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | | | | ALPHA: (1862) implies: % 233.00/39.71 | | | | | | | | | | | | | (1863) a_select3(pminus_ds1_filter, n3, n0) = all_74_12 % 233.00/39.71 | | | | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_74_13, all_74_12, n0, % 233.00/39.71 | | | | | | | | | | | | | n3, pminus_ds1_filter, simplifying with (1850), % 233.00/39.71 | | | | | | | | | | | | | (1863) gives: % 233.00/39.71 | | | | | | | | | | | | | (1864) all_74_12 = all_74_13 % 233.00/39.71 | | | | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | | | | REDUCE: (1736), (1864) imply: % 233.00/39.71 | | | | | | | | | | | | | (1865) $false % 233.00/39.71 | | | | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | | | | CLOSE: (1865) is inconsistent. % 233.00/39.71 | | | | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | | | End of split % 233.00/39.71 | | | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | | End of split % 233.00/39.71 | | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | End of split % 233.00/39.71 | | | | | | | | | | % 233.00/39.71 | | | | | | | | | Case 2: % 233.00/39.71 | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | (1866) all_74_15 = n4 % 233.00/39.71 | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | REDUCE: (1797), (1866) imply: % 233.00/39.71 | | | | | | | | | | (1867) a_select3(pminus_ds1_filter, n4, n0) = all_74_13 % 233.00/39.71 | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | REDUCE: (1796), (1866) imply: % 233.00/39.71 | | | | | | | | | | (1868) a_select3(pminus_ds1_filter, n0, n4) = all_74_12 % 233.00/39.71 | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | REDUCE: (1744), (1866) imply: % 233.00/39.71 | | | | | | | | | | (1869) leq(n4, n5) % 233.00/39.71 | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | REDUCE: (1737), (1866) imply: % 233.00/39.71 | | | | | | | | | | (1870) leq(n0, n4) % 233.00/39.71 | | | | | | | | | | % 233.00/39.71 | | | | | | | | | | GROUND_INST: instantiating (64) with n0, n4, all_74_12, % 233.00/39.71 | | | | | | | | | | simplifying with (12), (119), (1799), (1868), % 233.00/39.71 | | | | | | | | | | (1870) gives: % 233.00/39.72 | | | | | | | | | | (1871) ~ leq(n4, all_74_21) | ~ leq(n0, all_74_21) | % 233.00/39.72 | | | | | | | | | | (a_select3(pminus_ds1_filter, n4, n0) = all_74_12 % 233.00/39.72 | | | | | | | | | | & $i(all_74_12)) % 233.00/39.72 | | | | | | | | | | % 233.00/39.72 | | | | | | | | | | BETA: splitting (1871) gives: % 233.00/39.72 | | | | | | | | | | % 233.00/39.72 | | | | | | | | | | Case 1: % 233.00/39.72 | | | | | | | | | | | % 233.00/39.72 | | | | | | | | | | | (1872) ~ leq(n0, all_74_21) % 233.00/39.72 | | | | | | | | | | | % 233.00/39.72 | | | | | | | | | | | REDUCE: (135), (1872) imply: % 233.00/39.72 | | | | | | | | | | | (1873) ~ leq(n0, n5) % 233.00/39.72 | | | | | | | | | | | % 233.00/39.72 | | | | | | | | | | | PRED_UNIFY: (1798), (1873) imply: % 233.00/39.72 | | | | | | | | | | | (1874) $false % 233.00/39.72 | | | | | | | | | | | % 233.00/39.72 | | | | | | | | | | | CLOSE: (1874) is inconsistent. % 233.00/39.72 | | | | | | | | | | | % 233.00/39.72 | | | | | | | | | | Case 2: % 233.00/39.72 | | | | | | | | | | | % 233.00/39.72 | | | | | | | | | | | (1875) ~ leq(n4, all_74_21) | % 233.00/39.72 | | | | | | | | | | | (a_select3(pminus_ds1_filter, n4, n0) = all_74_12 % 233.00/39.72 | | | | | | | | | | | & $i(all_74_12)) % 233.00/39.72 | | | | | | | | | | | % 233.00/39.72 | | | | | | | | | | | BETA: splitting (1875) gives: % 233.00/39.72 | | | | | | | | | | | % 233.00/39.72 | | | | | | | | | | | Case 1: % 233.00/39.72 | | | | | | | | | | | | % 233.00/39.72 | | | | | | | | | | | | (1876) ~ leq(n4, all_74_21) % 233.00/39.72 | | | | | | | | | | | | % 233.00/39.72 | | | | | | | | | | | | REDUCE: (135), (1876) imply: % 233.00/39.72 | | | | | | | | | | | | (1877) ~ leq(n4, n5) % 233.00/39.72 | | | | | | | | | | | | % 233.00/39.72 | | | | | | | | | | | | PRED_UNIFY: (1869), (1877) imply: % 233.00/39.72 | | | | | | | | | | | | (1878) $false % 233.00/39.72 | | | | | | | | | | | | % 233.00/39.72 | | | | | | | | | | | | CLOSE: (1878) is inconsistent. % 233.00/39.72 | | | | | | | | | | | | % 233.00/39.72 | | | | | | | | | | | Case 2: % 233.00/39.72 | | | | | | | | | | | | % 233.00/39.72 | | | | | | | | | | | | (1879) a_select3(pminus_ds1_filter, n4, n0) = all_74_12 & % 233.00/39.72 | | | | | | | | | | | | $i(all_74_12) % 233.00/39.72 | | | | | | | | | | | | % 233.00/39.72 | | | | | | | | | | | | ALPHA: (1879) implies: % 233.00/39.72 | | | | | | | | | | | | (1880) a_select3(pminus_ds1_filter, n4, n0) = all_74_12 % 233.00/39.72 | | | | | | | | | | | | % 233.00/39.72 | | | | | | | | | | | | REF_CLOSE: (17), (1736), (1867), (1880) are inconsistent by % 233.00/39.72 | | | | | | | | | | | | sub-proof #17. % 233.00/39.72 | | | | | | | | | | | | % 233.00/39.72 | | | | | | | | | | | End of split % 233.00/39.72 | | | | | | | | | | | % 233.00/39.72 | | | | | | | | | | End of split % 233.00/39.72 | | | | | | | | | | % 233.00/39.72 | | | | | | | | | End of split % 233.00/39.72 | | | | | | | | | % 233.00/39.72 | | | | | | | | End of split % 233.00/39.72 | | | | | | | | % 233.00/39.72 | | | | | | | Case 2: % 233.00/39.72 | | | | | | | | % 233.00/39.72 | | | | | | | | (1881) all_74_15 = n5 % 233.00/39.72 | | | | | | | | % 233.00/39.72 | | | | | | | | REDUCE: (1797), (1881) imply: % 233.00/39.72 | | | | | | | | (1882) a_select3(pminus_ds1_filter, n5, n0) = all_74_13 % 233.00/39.72 | | | | | | | | % 233.00/39.72 | | | | | | | | REDUCE: (1796), (1881) imply: % 233.00/39.72 | | | | | | | | (1883) a_select3(pminus_ds1_filter, n0, n5) = all_74_12 % 233.00/39.72 | | | | | | | | % 233.00/39.72 | | | | | | | | REDUCE: (1744), (1881) imply: % 233.00/39.72 | | | | | | | | (1884) leq(n5, n5) % 233.00/39.72 | | | | | | | | % 233.00/39.72 | | | | | | | | GROUND_INST: instantiating (64) with n0, n5, all_74_12, % 233.00/39.72 | | | | | | | | simplifying with (12), (122), (1798), (1799), % 233.00/39.72 | | | | | | | | (1883) gives: % 233.00/39.72 | | | | | | | | (1885) ~ leq(n5, all_74_21) | ~ leq(n0, all_74_21) | % 233.00/39.72 | | | | | | | | (a_select3(pminus_ds1_filter, n5, n0) = all_74_12 & % 233.00/39.72 | | | | | | | | $i(all_74_12)) % 233.00/39.72 | | | | | | | | % 233.00/39.72 | | | | | | | | BETA: splitting (1885) gives: % 233.00/39.72 | | | | | | | | % 233.00/39.72 | | | | | | | | Case 1: % 233.00/39.72 | | | | | | | | | % 233.00/39.72 | | | | | | | | | (1886) ~ leq(n0, all_74_21) % 233.00/39.72 | | | | | | | | | % 233.00/39.72 | | | | | | | | | REDUCE: (135), (1886) imply: % 233.00/39.72 | | | | | | | | | (1887) ~ leq(n0, n5) % 233.00/39.72 | | | | | | | | | % 233.00/39.72 | | | | | | | | | PRED_UNIFY: (1798), (1887) imply: % 233.00/39.72 | | | | | | | | | (1888) $false % 233.00/39.72 | | | | | | | | | % 233.00/39.72 | | | | | | | | | CLOSE: (1888) is inconsistent. % 233.00/39.72 | | | | | | | | | % 233.00/39.72 | | | | | | | | Case 2: % 233.00/39.72 | | | | | | | | | % 233.00/39.72 | | | | | | | | | (1889) ~ leq(n5, all_74_21) | % 233.00/39.72 | | | | | | | | | (a_select3(pminus_ds1_filter, n5, n0) = all_74_12 & % 233.00/39.72 | | | | | | | | | $i(all_74_12)) % 233.00/39.72 | | | | | | | | | % 233.00/39.72 | | | | | | | | | BETA: splitting (1889) gives: % 233.00/39.72 | | | | | | | | | % 233.00/39.72 | | | | | | | | | Case 1: % 233.00/39.72 | | | | | | | | | | % 233.00/39.72 | | | | | | | | | | (1890) ~ leq(n5, all_74_21) % 233.00/39.72 | | | | | | | | | | % 233.00/39.72 | | | | | | | | | | REDUCE: (135), (1890) imply: % 233.00/39.72 | | | | | | | | | | (1891) ~ leq(n5, n5) % 233.00/39.72 | | | | | | | | | | % 233.00/39.72 | | | | | | | | | | PRED_UNIFY: (1884), (1891) imply: % 233.00/39.72 | | | | | | | | | | (1892) $false % 233.00/39.72 | | | | | | | | | | % 233.00/39.72 | | | | | | | | | | CLOSE: (1892) is inconsistent. % 233.00/39.72 | | | | | | | | | | % 233.00/39.72 | | | | | | | | | Case 2: % 233.00/39.72 | | | | | | | | | | % 233.00/39.72 | | | | | | | | | | (1893) a_select3(pminus_ds1_filter, n5, n0) = all_74_12 & % 233.00/39.72 | | | | | | | | | | $i(all_74_12) % 233.00/39.72 | | | | | | | | | | % 233.00/39.72 | | | | | | | | | | ALPHA: (1893) implies: % 233.00/39.72 | | | | | | | | | | (1894) a_select3(pminus_ds1_filter, n5, n0) = all_74_12 % 233.00/39.72 | | | | | | | | | | % 233.00/39.72 | | | | | | | | | | REF_CLOSE: (17), (1736), (1882), (1894) are inconsistent by % 233.00/39.72 | | | | | | | | | | sub-proof #16. % 233.00/39.72 | | | | | | | | | | % 233.00/39.72 | | | | | | | | | End of split % 233.00/39.72 | | | | | | | | | % 233.00/39.72 | | | | | | | | End of split % 233.00/39.72 | | | | | | | | % 233.00/39.72 | | | | | | | End of split % 233.00/39.72 | | | | | | | % 233.00/39.72 | | | | | | Case 2: % 233.00/39.72 | | | | | | | % 233.00/39.72 | | | | | | | (1895) all_74_15 = n0 % 233.00/39.72 | | | | | | | % 233.00/39.72 | | | | | | | REDUCE: (1797), (1895) imply: % 233.00/39.72 | | | | | | | (1896) a_select3(pminus_ds1_filter, n0, n0) = all_74_13 % 233.00/39.72 | | | | | | | % 233.00/39.72 | | | | | | | REDUCE: (1796), (1895) imply: % 233.00/39.72 | | | | | | | (1897) a_select3(pminus_ds1_filter, n0, n0) = all_74_12 % 233.00/39.72 | | | | | | | % 233.00/39.72 | | | | | | | GROUND_INST: instantiating (17) with all_74_13, all_74_12, n0, n0, % 233.00/39.72 | | | | | | | pminus_ds1_filter, simplifying with (1896), (1897) % 233.00/39.72 | | | | | | | gives: % 233.00/39.72 | | | | | | | (1898) all_74_12 = all_74_13 % 233.00/39.72 | | | | | | | % 233.00/39.72 | | | | | | | REDUCE: (1736), (1898) imply: % 233.00/39.72 | | | | | | | (1899) $false % 233.00/39.72 | | | | | | | % 233.00/39.72 | | | | | | | CLOSE: (1899) is inconsistent. % 233.00/39.72 | | | | | | | % 233.00/39.72 | | | | | | End of split % 233.00/39.72 | | | | | | % 233.00/39.72 | | | | | End of split % 233.00/39.72 | | | | | % 233.00/39.72 | | | | End of split % 233.00/39.72 | | | | % 233.00/39.72 | | | Case 2: % 233.00/39.72 | | | | % 233.00/39.72 | | | | (1900) ~ (all_74_16 = all_74_17) & a_select3(id_ds1_filter, % 233.00/39.72 | | | | all_74_18, all_74_19) = all_74_16 & a_select3(id_ds1_filter, % 233.00/39.72 | | | | all_74_19, all_74_18) = all_74_17 & $i(all_74_16) & % 233.00/39.72 | | | | $i(all_74_17) & leq(all_74_18, all_74_21) & leq(all_74_19, % 233.00/39.72 | | | | all_74_21) & leq(n0, all_74_18) & leq(n0, all_74_19) % 233.00/39.72 | | | | % 233.00/39.72 | | | | ALPHA: (1900) implies: % 233.00/39.72 | | | | (1901) ~ (all_74_16 = all_74_17) % 233.00/39.72 | | | | (1902) leq(n0, all_74_19) % 233.00/39.72 | | | | (1903) leq(n0, all_74_18) % 233.00/39.72 | | | | (1904) leq(all_74_19, all_74_21) % 233.00/39.72 | | | | (1905) leq(all_74_18, all_74_21) % 233.00/39.72 | | | | (1906) a_select3(id_ds1_filter, all_74_19, all_74_18) = all_74_17 % 233.00/39.72 | | | | (1907) a_select3(id_ds1_filter, all_74_18, all_74_19) = all_74_16 % 233.00/39.72 | | | | % 233.00/39.72 | | | | REDUCE: (135), (1905) imply: % 233.00/39.72 | | | | (1908) leq(all_74_18, n5) % 233.00/39.72 | | | | % 233.00/39.72 | | | | REDUCE: (135), (1904) imply: % 233.00/39.72 | | | | (1909) leq(all_74_19, n5) % 233.00/39.72 | | | | % 233.00/39.72 | | | | GROUND_INST: instantiating (leq_gt2) with n0, all_74_19, simplifying % 233.00/39.72 | | | | with (12), (49), (1902) gives: % 233.00/39.72 | | | | (1910) all_74_19 = n0 | gt(all_74_19, n0) % 233.00/39.72 | | | | % 233.00/39.72 | | | | GROUND_INST: instantiating (leq_gt2) with n0, all_74_18, simplifying % 233.00/39.72 | | | | with (12), (50), (1903) gives: % 233.00/39.72 | | | | (1911) all_74_18 = n0 | gt(all_74_18, n0) % 233.00/39.72 | | | | % 233.00/39.72 | | | | GROUND_INST: instantiating (3) with all_74_19, simplifying with (49), % 233.00/39.72 | | | | (1902), (1909) gives: % 233.00/39.72 | | | | (1912) all_74_19 = n5 | all_74_19 = n4 | all_74_19 = n3 | all_74_19 = % 233.00/39.72 | | | | n2 | all_74_19 = n1 | all_74_19 = n0 % 233.00/39.72 | | | | % 233.00/39.72 | | | | GROUND_INST: instantiating (leq_gt2) with all_74_19, n5, simplifying % 233.00/39.72 | | | | with (49), (122), (1909) gives: % 233.00/39.72 | | | | (1913) all_74_19 = n5 | gt(n5, all_74_19) % 233.00/39.72 | | | | % 233.00/39.72 | | | | GROUND_INST: instantiating (3) with all_74_18, simplifying with (50), % 233.00/39.72 | | | | (1903), (1908) gives: % 233.00/39.72 | | | | (1914) all_74_18 = n5 | all_74_18 = n4 | all_74_18 = n3 | all_74_18 = % 233.00/39.72 | | | | n2 | all_74_18 = n1 | all_74_18 = n0 % 233.00/39.72 | | | | % 233.00/39.72 | | | | GROUND_INST: instantiating (leq_gt2) with all_74_18, n5, simplifying % 233.00/39.72 | | | | with (50), (122), (1908) gives: % 233.00/39.72 | | | | (1915) all_74_18 = n5 | gt(n5, all_74_18) % 233.00/39.72 | | | | % 233.00/39.72 | | | | BETA: splitting (1911) gives: % 233.00/39.72 | | | | % 233.00/39.72 | | | | Case 1: % 233.00/39.72 | | | | | % 233.00/39.72 | | | | | (1916) gt(all_74_18, n0) % 233.00/39.72 | | | | | % 233.00/39.72 | | | | | BETA: splitting (1910) gives: % 233.00/39.72 | | | | | % 233.00/39.72 | | | | | Case 1: % 233.00/39.72 | | | | | | % 233.00/39.72 | | | | | | (1917) gt(all_74_19, n0) % 233.00/39.72 | | | | | | % 233.00/39.72 | | | | | | BETA: splitting (1913) gives: % 233.00/39.72 | | | | | | % 233.00/39.72 | | | | | | Case 1: % 233.00/39.72 | | | | | | | % 233.00/39.72 | | | | | | | (1918) gt(n5, all_74_19) % 233.00/39.72 | | | | | | | % 233.00/39.72 | | | | | | | GROUND_INST: instantiating (1) with all_74_19, n5, n4, simplifying % 233.00/39.72 | | | | | | | with (49), (122), (126), (1918) gives: % 233.00/39.72 | | | | | | | (1919) leq(all_74_19, n4) % 233.00/39.72 | | | | | | | % 233.00/39.72 | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_19, n4, % 233.00/39.72 | | | | | | | simplifying with (49), (119), (1919) gives: % 233.00/39.72 | | | | | | | (1920) all_74_19 = n4 | gt(n4, all_74_19) % 233.00/39.72 | | | | | | | % 233.00/39.72 | | | | | | | BETA: splitting (1915) gives: % 233.00/39.72 | | | | | | | % 233.00/39.72 | | | | | | | Case 1: % 233.00/39.72 | | | | | | | | % 233.00/39.72 | | | | | | | | (1921) gt(n5, all_74_18) % 233.00/39.72 | | | | | | | | % 233.00/39.72 | | | | | | | | GROUND_INST: instantiating (1) with all_74_18, n5, n4, % 233.00/39.72 | | | | | | | | simplifying with (50), (122), (126), (1921) gives: % 233.00/39.72 | | | | | | | | (1922) leq(all_74_18, n4) % 233.00/39.72 | | | | | | | | % 233.00/39.72 | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_18, n4, % 233.00/39.72 | | | | | | | | simplifying with (50), (119), (1922) gives: % 233.00/39.72 | | | | | | | | (1923) all_74_18 = n4 | gt(n4, all_74_18) % 233.00/39.72 | | | | | | | | % 233.00/39.72 | | | | | | | | BETA: splitting (1914) gives: % 233.00/39.72 | | | | | | | | % 233.00/39.72 | | | | | | | | Case 1: % 233.00/39.72 | | | | | | | | | % 233.00/39.72 | | | | | | | | | (1924) all_74_18 = n0 % 233.00/39.72 | | | | | | | | | % 233.00/39.72 | | | | | | | | | REF_CLOSE: (50), (1916), (1924), (irreflexivity_gt) are % 233.00/39.72 | | | | | | | | | inconsistent by sub-proof #14. % 233.00/39.72 | | | | | | | | | % 233.00/39.72 | | | | | | | | Case 2: % 233.00/39.72 | | | | | | | | | % 233.00/39.72 | | | | | | | | | (1925) ~ (all_74_18 = n0) % 233.00/39.72 | | | | | | | | | % 233.00/39.72 | | | | | | | | | BETA: splitting (1912) gives: % 233.00/39.72 | | | | | | | | | % 233.00/39.72 | | | | | | | | | Case 1: % 233.00/39.72 | | | | | | | | | | % 233.00/39.72 | | | | | | | | | | (1926) all_74_19 = n0 % 233.00/39.72 | | | | | | | | | | % 233.00/39.72 | | | | | | | | | | REF_CLOSE: (49), (1917), (1926), (irreflexivity_gt) are % 233.00/39.72 | | | | | | | | | | inconsistent by sub-proof #13. % 233.00/39.72 | | | | | | | | | | % 233.00/39.72 | | | | | | | | | Case 2: % 233.00/39.72 | | | | | | | | | | % 233.00/39.72 | | | | | | | | | | (1927) ~ (all_74_19 = n0) % 233.00/39.72 | | | | | | | | | | % 233.00/39.72 | | | | | | | | | | REF_CLOSE: (1), (4), (17), (49), (50), (65), (101), (112), % 233.00/39.72 | | | | | | | | | | (119), (123), (124), (125), (135), (1901), (1902), % 233.00/39.72 | | | | | | | | | | (1903), (1906), (1907), (1908), (1909), (1920), % 233.00/39.72 | | | | | | | | | | (1923), (1925), (1927), (leq_gt2) are inconsistent % 233.00/39.72 | | | | | | | | | | by sub-proof #9. % 233.00/39.72 | | | | | | | | | | % 233.00/39.72 | | | | | | | | | End of split % 233.00/39.72 | | | | | | | | | % 233.00/39.72 | | | | | | | | End of split % 233.00/39.72 | | | | | | | | % 233.00/39.72 | | | | | | | Case 2: % 233.00/39.72 | | | | | | | | % 233.00/39.72 | | | | | | | | (1928) all_74_18 = n5 % 233.00/39.72 | | | | | | | | % 233.00/39.72 | | | | | | | | REDUCE: (1907), (1928) imply: % 233.00/39.72 | | | | | | | | (1929) a_select3(id_ds1_filter, n5, all_74_19) = all_74_16 % 233.00/39.72 | | | | | | | | % 233.00/39.72 | | | | | | | | REDUCE: (1906), (1928) imply: % 233.00/39.72 | | | | | | | | (1930) a_select3(id_ds1_filter, all_74_19, n5) = all_74_17 % 233.00/39.72 | | | | | | | | % 233.00/39.72 | | | | | | | | REDUCE: (1908), (1928) imply: % 233.00/39.72 | | | | | | | | (1931) leq(n5, n5) % 233.00/39.72 | | | | | | | | % 233.00/39.72 | | | | | | | | REDUCE: (1903), (1928) imply: % 233.00/39.72 | | | | | | | | (1932) leq(n0, n5) % 233.00/39.72 | | | | | | | | % 233.00/39.72 | | | | | | | | BETA: splitting (1912) gives: % 233.00/39.72 | | | | | | | | % 233.00/39.72 | | | | | | | | Case 1: % 233.00/39.72 | | | | | | | | | % 233.00/39.72 | | | | | | | | | (1933) all_74_19 = n0 % 233.00/39.72 | | | | | | | | | % 233.00/39.72 | | | | | | | | | REF_CLOSE: (49), (1917), (1933), (irreflexivity_gt) are % 233.00/39.72 | | | | | | | | | inconsistent by sub-proof #13. % 233.00/39.72 | | | | | | | | | % 233.00/39.72 | | | | | | | | Case 2: % 233.00/39.72 | | | | | | | | | % 233.00/39.72 | | | | | | | | | (1934) ~ (all_74_19 = n0) % 233.00/39.72 | | | | | | | | | % 233.00/39.72 | | | | | | | | | REF_CLOSE: (1), (4), (17), (49), (65), (101), (112), (119), % 233.00/39.72 | | | | | | | | | (122), (123), (124), (125), (135), (1901), (1902), % 233.00/39.72 | | | | | | | | | (1909), (1920), (1929), (1930), (1931), (1932), % 233.00/39.72 | | | | | | | | | (1934), (leq_gt2) are inconsistent by sub-proof #7. % 233.00/39.72 | | | | | | | | | % 233.00/39.72 | | | | | | | | End of split % 233.00/39.72 | | | | | | | | % 233.00/39.72 | | | | | | | End of split % 233.00/39.72 | | | | | | | % 233.00/39.72 | | | | | | Case 2: % 233.00/39.72 | | | | | | | % 233.00/39.72 | | | | | | | (1935) all_74_19 = n5 % 233.00/39.72 | | | | | | | % 233.00/39.72 | | | | | | | REDUCE: (1907), (1935) imply: % 233.00/39.72 | | | | | | | (1936) a_select3(id_ds1_filter, all_74_18, n5) = all_74_16 % 233.00/39.73 | | | | | | | % 233.00/39.73 | | | | | | | REDUCE: (1906), (1935) imply: % 233.00/39.73 | | | | | | | (1937) a_select3(id_ds1_filter, n5, all_74_18) = all_74_17 % 233.00/39.73 | | | | | | | % 233.00/39.73 | | | | | | | REDUCE: (1909), (1935) imply: % 233.00/39.73 | | | | | | | (1938) leq(n5, n5) % 233.00/39.73 | | | | | | | % 233.00/39.73 | | | | | | | REDUCE: (1902), (1935) imply: % 233.00/39.73 | | | | | | | (1939) leq(n0, n5) % 233.00/39.73 | | | | | | | % 233.00/39.73 | | | | | | | BETA: splitting (1915) gives: % 233.00/39.73 | | | | | | | % 233.00/39.73 | | | | | | | Case 1: % 233.00/39.73 | | | | | | | | % 233.00/39.73 | | | | | | | | (1940) gt(n5, all_74_18) % 233.00/39.73 | | | | | | | | % 233.00/39.73 | | | | | | | | GROUND_INST: instantiating (1) with all_74_18, n5, n4, % 233.00/39.73 | | | | | | | | simplifying with (50), (122), (126), (1940) gives: % 233.00/39.73 | | | | | | | | (1941) leq(all_74_18, n4) % 233.00/39.73 | | | | | | | | % 233.00/39.73 | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_18, n4, % 233.00/39.73 | | | | | | | | simplifying with (50), (119), (1941) gives: % 233.00/39.73 | | | | | | | | (1942) all_74_18 = n4 | gt(n4, all_74_18) % 233.00/39.73 | | | | | | | | % 233.00/39.73 | | | | | | | | BETA: splitting (1914) gives: % 233.00/39.73 | | | | | | | | % 233.00/39.73 | | | | | | | | Case 1: % 233.00/39.73 | | | | | | | | | % 233.00/39.73 | | | | | | | | | (1943) all_74_18 = n0 % 233.00/39.73 | | | | | | | | | % 233.00/39.73 | | | | | | | | | REF_CLOSE: (50), (1916), (1943), (irreflexivity_gt) are % 233.00/39.73 | | | | | | | | | inconsistent by sub-proof #14. % 233.00/39.73 | | | | | | | | | % 233.00/39.73 | | | | | | | | Case 2: % 233.00/39.73 | | | | | | | | | % 233.00/39.73 | | | | | | | | | (1944) ~ (all_74_18 = n0) % 233.00/39.73 | | | | | | | | | % 233.00/39.73 | | | | | | | | | REF_CLOSE: (1), (4), (17), (50), (65), (101), (112), (119), % 233.00/39.73 | | | | | | | | | (122), (123), (124), (125), (135), (1901), (1903), % 233.00/39.73 | | | | | | | | | (1908), (1936), (1937), (1938), (1939), (1942), % 233.00/39.73 | | | | | | | | | (1944), (leq_gt2) are inconsistent by sub-proof #6. % 233.00/39.73 | | | | | | | | | % 233.00/39.73 | | | | | | | | End of split % 233.00/39.73 | | | | | | | | % 233.00/39.73 | | | | | | | Case 2: % 233.00/39.73 | | | | | | | | % 233.00/39.73 | | | | | | | | (1945) all_74_18 = n5 % 233.00/39.73 | | | | | | | | % 233.00/39.73 | | | | | | | | REDUCE: (1936), (1945) imply: % 233.00/39.73 | | | | | | | | (1946) a_select3(id_ds1_filter, n5, n5) = all_74_16 % 233.00/39.73 | | | | | | | | % 233.00/39.73 | | | | | | | | REDUCE: (1937), (1945) imply: % 233.00/39.73 | | | | | | | | (1947) a_select3(id_ds1_filter, n5, n5) = all_74_17 % 233.00/39.73 | | | | | | | | % 233.00/39.73 | | | | | | | | GROUND_INST: instantiating (17) with all_74_17, all_74_16, n5, % 233.00/39.73 | | | | | | | | n5, id_ds1_filter, simplifying with (1946), (1947) % 233.00/39.73 | | | | | | | | gives: % 233.00/39.73 | | | | | | | | (1948) all_74_16 = all_74_17 % 233.00/39.73 | | | | | | | | % 233.00/39.73 | | | | | | | | REDUCE: (1901), (1948) imply: % 233.00/39.73 | | | | | | | | (1949) $false % 233.00/39.73 | | | | | | | | % 233.00/39.73 | | | | | | | | CLOSE: (1949) is inconsistent. % 233.00/39.73 | | | | | | | | % 233.00/39.73 | | | | | | | End of split % 233.00/39.73 | | | | | | | % 233.00/39.73 | | | | | | End of split % 233.00/39.73 | | | | | | % 233.00/39.73 | | | | | Case 2: % 233.00/39.73 | | | | | | % 233.00/39.73 | | | | | | (1950) all_74_19 = n0 % 233.00/39.73 | | | | | | (1951) ~ gt(all_74_19, n0) % 233.00/39.73 | | | | | | % 233.00/39.73 | | | | | | REDUCE: (1950), (1951) imply: % 233.00/39.73 | | | | | | (1952) ~ gt(n0, n0) % 233.00/39.73 | | | | | | % 233.00/39.73 | | | | | | REF_CLOSE: (1), (4), (17), (49), (50), (65), (101), (112), (119), % 233.00/39.73 | | | | | | (122), (123), (124), (125), (126), (135), (1901), (1902), % 233.00/39.73 | | | | | | (1903), (1906), (1907), (1908), (1909), (1910), (1912), % 233.00/39.73 | | | | | | (1913), (1914), (1915), (1916), (1952), (leq_gt2) are % 233.00/39.73 | | | | | | inconsistent by sub-proof #1. % 233.00/39.73 | | | | | | % 233.00/39.73 | | | | | End of split % 233.00/39.73 | | | | | % 233.00/39.73 | | | | Case 2: % 233.00/39.73 | | | | | % 233.00/39.73 | | | | | (1953) all_74_18 = n0 % 233.00/39.73 | | | | | (1954) ~ gt(all_74_18, n0) % 233.00/39.73 | | | | | % 233.00/39.73 | | | | | REDUCE: (1953), (1954) imply: % 233.00/39.73 | | | | | (1955) ~ gt(n0, n0) % 233.00/39.73 | | | | | % 233.00/39.73 | | | | | BETA: splitting (1911) gives: % 233.00/39.73 | | | | | % 233.00/39.73 | | | | | Case 1: % 233.00/39.73 | | | | | | % 233.00/39.73 | | | | | | (1956) gt(all_74_18, n0) % 233.00/39.73 | | | | | | % 233.00/39.73 | | | | | | REF_CLOSE: (1), (4), (17), (49), (50), (65), (101), (112), (119), % 233.00/39.73 | | | | | | (122), (123), (124), (125), (126), (135), (1901), (1902), % 233.00/39.73 | | | | | | (1903), (1906), (1907), (1908), (1909), (1910), (1912), % 233.00/39.73 | | | | | | (1913), (1914), (1915), (1955), (1956), (leq_gt2) are % 233.00/39.73 | | | | | | inconsistent by sub-proof #1. % 233.00/39.73 | | | | | | % 233.00/39.73 | | | | | Case 2: % 233.00/39.73 | | | | | | % 233.00/39.73 | | | | | | % 233.00/39.73 | | | | | | REDUCE: (1907), (1953) imply: % 233.00/39.73 | | | | | | (1957) a_select3(id_ds1_filter, n0, all_74_19) = all_74_16 % 233.00/39.73 | | | | | | % 233.00/39.73 | | | | | | REDUCE: (1906), (1953) imply: % 233.00/39.73 | | | | | | (1958) a_select3(id_ds1_filter, all_74_19, n0) = all_74_17 % 233.00/39.73 | | | | | | % 233.00/39.73 | | | | | | REDUCE: (1908), (1953) imply: % 233.00/39.73 | | | | | | (1959) leq(n0, n5) % 233.00/39.73 | | | | | | % 233.00/39.73 | | | | | | REDUCE: (1903), (1953) imply: % 233.00/39.73 | | | | | | (1960) leq(n0, n0) % 233.00/39.73 | | | | | | % 233.00/39.73 | | | | | | BETA: splitting (1910) gives: % 233.00/39.73 | | | | | | % 233.00/39.73 | | | | | | Case 1: % 233.00/39.73 | | | | | | | % 233.00/39.73 | | | | | | | (1961) gt(all_74_19, n0) % 233.00/39.73 | | | | | | | % 233.00/39.73 | | | | | | | BETA: splitting (1913) gives: % 233.00/39.73 | | | | | | | % 233.00/39.73 | | | | | | | Case 1: % 233.00/39.73 | | | | | | | | % 233.00/39.73 | | | | | | | | (1962) gt(n5, all_74_19) % 233.00/39.73 | | | | | | | | % 233.00/39.73 | | | | | | | | GROUND_INST: instantiating (1) with all_74_19, n5, n4, % 233.00/39.73 | | | | | | | | simplifying with (49), (122), (126), (1962) gives: % 233.00/39.73 | | | | | | | | (1963) leq(all_74_19, n4) % 233.00/39.73 | | | | | | | | % 233.00/39.73 | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_19, n4, % 233.00/39.73 | | | | | | | | simplifying with (49), (119), (1963) gives: % 233.00/39.73 | | | | | | | | (1964) all_74_19 = n4 | gt(n4, all_74_19) % 233.00/39.73 | | | | | | | | % 233.00/39.73 | | | | | | | | BETA: splitting (1912) gives: % 233.00/39.73 | | | | | | | | % 233.00/39.73 | | | | | | | | Case 1: % 233.00/39.73 | | | | | | | | | % 233.00/39.73 | | | | | | | | | (1965) all_74_19 = n0 % 233.00/39.73 | | | | | | | | | % 233.00/39.73 | | | | | | | | | REDUCE: (1961), (1965) imply: % 233.00/39.73 | | | | | | | | | (1966) gt(n0, n0) % 233.00/39.73 | | | | | | | | | % 233.00/39.73 | | | | | | | | | PRED_UNIFY: (1955), (1966) imply: % 233.00/39.73 | | | | | | | | | (1967) $false % 233.00/39.73 | | | | | | | | | % 233.00/39.73 | | | | | | | | | CLOSE: (1967) is inconsistent. % 233.00/39.73 | | | | | | | | | % 233.00/39.73 | | | | | | | | Case 2: % 233.00/39.73 | | | | | | | | | % 233.00/39.73 | | | | | | | | | (1968) ~ (all_74_19 = n0) % 233.00/39.73 | | | | | | | | | % 233.00/39.73 | | | | | | | | | BETA: splitting (1964) gives: % 233.00/39.73 | | | | | | | | | % 233.00/39.73 | | | | | | | | | Case 1: % 233.00/39.73 | | | | | | | | | | % 233.00/39.73 | | | | | | | | | | (1969) gt(n4, all_74_19) % 233.00/39.73 | | | | | | | | | | % 233.00/39.73 | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_19, n4, n3, % 233.00/39.73 | | | | | | | | | | simplifying with (49), (119), (125), (1969) gives: % 233.00/39.73 | | | | | | | | | | (1970) leq(all_74_19, n3) % 233.00/39.73 | | | | | | | | | | % 233.00/39.73 | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_19, n3, % 233.00/39.73 | | | | | | | | | | simplifying with (49), (112), (1970) gives: % 233.00/39.73 | | | | | | | | | | (1971) all_74_19 = n3 | gt(n3, all_74_19) % 233.00/39.73 | | | | | | | | | | % 233.00/39.73 | | | | | | | | | | BETA: splitting (1971) gives: % 233.00/39.73 | | | | | | | | | | % 233.00/39.73 | | | | | | | | | | Case 1: % 233.00/39.73 | | | | | | | | | | | % 233.00/39.73 | | | | | | | | | | | (1972) gt(n3, all_74_19) % 233.00/39.73 | | | | | | | | | | | % 233.00/39.73 | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_19, n3, n2, % 233.00/39.73 | | | | | | | | | | | simplifying with (49), (112), (124), (1972) gives: % 233.00/39.73 | | | | | | | | | | | (1973) leq(all_74_19, n2) % 233.00/39.73 | | | | | | | | | | | % 233.00/39.73 | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_19, n2, % 233.00/39.73 | | | | | | | | | | | simplifying with (49), (101), (1973) gives: % 233.00/39.73 | | | | | | | | | | | (1974) all_74_19 = n2 | gt(n2, all_74_19) % 233.00/39.73 | | | | | | | | | | | % 233.00/39.73 | | | | | | | | | | | BETA: splitting (1974) gives: % 233.00/39.73 | | | | | | | | | | | % 233.00/39.73 | | | | | | | | | | | Case 1: % 233.00/39.73 | | | | | | | | | | | | % 233.00/39.73 | | | | | | | | | | | | (1975) gt(n2, all_74_19) % 233.00/39.73 | | | | | | | | | | | | % 233.00/39.73 | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_19, n2, n1, % 233.00/39.73 | | | | | | | | | | | | simplifying with (49), (101), (123), (1975) gives: % 233.00/39.73 | | | | | | | | | | | | (1976) leq(all_74_19, n1) % 233.00/39.73 | | | | | | | | | | | | % 233.00/39.73 | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_74_19, simplifying with % 233.00/39.73 | | | | | | | | | | | | (49), (1902), (1976) gives: % 233.00/39.73 | | | | | | | | | | | | (1977) all_74_19 = n1 | all_74_19 = n0 % 233.00/39.73 | | | | | | | | | | | | % 233.00/39.73 | | | | | | | | | | | | BETA: splitting (1977) gives: % 233.00/39.73 | | | | | | | | | | | | % 233.00/39.73 | | | | | | | | | | | | Case 1: % 233.00/39.73 | | | | | | | | | | | | | % 233.00/39.73 | | | | | | | | | | | | | (1978) all_74_19 = n0 % 233.00/39.73 | | | | | | | | | | | | | % 233.00/39.73 | | | | | | | | | | | | | REDUCE: (1968), (1978) imply: % 233.00/39.73 | | | | | | | | | | | | | (1979) $false % 233.00/39.73 | | | | | | | | | | | | | % 233.00/39.73 | | | | | | | | | | | | | CLOSE: (1979) is inconsistent. % 233.00/39.73 | | | | | | | | | | | | | % 233.00/39.73 | | | | | | | | | | | | Case 2: % 233.00/39.73 | | | | | | | | | | | | | % 233.00/39.73 | | | | | | | | | | | | | (1980) all_74_19 = n1 % 233.00/39.73 | | | | | | | | | | | | | % 233.00/39.73 | | | | | | | | | | | | | REDUCE: (1958), (1980) imply: % 233.31/39.73 | | | | | | | | | | | | | (1981) a_select3(id_ds1_filter, n1, n0) = all_74_17 % 233.31/39.73 | | | | | | | | | | | | | % 233.31/39.73 | | | | | | | | | | | | | REDUCE: (1957), (1980) imply: % 233.31/39.73 | | | | | | | | | | | | | (1982) a_select3(id_ds1_filter, n0, n1) = all_74_16 % 233.31/39.73 | | | | | | | | | | | | | % 233.31/39.73 | | | | | | | | | | | | | REDUCE: (1909), (1980) imply: % 233.31/39.73 | | | | | | | | | | | | | (1983) leq(n1, n5) % 233.31/39.73 | | | | | | | | | | | | | % 233.31/39.73 | | | | | | | | | | | | | REDUCE: (1902), (1980) imply: % 233.31/39.73 | | | | | | | | | | | | | (1984) leq(n0, n1) % 233.31/39.73 | | | | | | | | | | | | | % 233.31/39.73 | | | | | | | | | | | | | GROUND_INST: instantiating (65) with n0, n1, all_74_16, % 233.31/39.73 | | | | | | | | | | | | | simplifying with (12), (85), (1960), (1982), % 233.31/39.73 | | | | | | | | | | | | | (1984) gives: % 233.31/39.73 | | | | | | | | | | | | | (1985) ~ leq(n1, all_74_21) | ~ leq(n0, all_74_21) | % 233.31/39.73 | | | | | | | | | | | | | (a_select3(id_ds1_filter, n1, n0) = all_74_16 & % 233.31/39.73 | | | | | | | | | | | | | $i(all_74_16)) % 233.31/39.73 | | | | | | | | | | | | | % 233.31/39.73 | | | | | | | | | | | | | BETA: splitting (1985) gives: % 233.31/39.73 | | | | | | | | | | | | | % 233.31/39.73 | | | | | | | | | | | | | Case 1: % 233.31/39.73 | | | | | | | | | | | | | | % 233.31/39.73 | | | | | | | | | | | | | | (1986) ~ leq(n0, all_74_21) % 233.31/39.73 | | | | | | | | | | | | | | % 233.31/39.73 | | | | | | | | | | | | | | REDUCE: (135), (1986) imply: % 233.31/39.73 | | | | | | | | | | | | | | (1987) ~ leq(n0, n5) % 233.31/39.73 | | | | | | | | | | | | | | % 233.31/39.73 | | | | | | | | | | | | | | PRED_UNIFY: (1959), (1987) imply: % 233.31/39.73 | | | | | | | | | | | | | | (1988) $false % 233.31/39.73 | | | | | | | | | | | | | | % 233.31/39.73 | | | | | | | | | | | | | | CLOSE: (1988) is inconsistent. % 233.31/39.73 | | | | | | | | | | | | | | % 233.31/39.73 | | | | | | | | | | | | | Case 2: % 233.31/39.73 | | | | | | | | | | | | | | % 233.31/39.73 | | | | | | | | | | | | | | (1989) ~ leq(n1, all_74_21) | (a_select3(id_ds1_filter, % 233.31/39.73 | | | | | | | | | | | | | | n1, n0) = all_74_16 & $i(all_74_16)) % 233.31/39.73 | | | | | | | | | | | | | | % 233.31/39.73 | | | | | | | | | | | | | | BETA: splitting (1989) gives: % 233.31/39.73 | | | | | | | | | | | | | | % 233.31/39.73 | | | | | | | | | | | | | | Case 1: % 233.31/39.73 | | | | | | | | | | | | | | | % 233.31/39.73 | | | | | | | | | | | | | | | (1990) ~ leq(n1, all_74_21) % 233.31/39.73 | | | | | | | | | | | | | | | % 233.31/39.73 | | | | | | | | | | | | | | | REDUCE: (135), (1990) imply: % 233.31/39.73 | | | | | | | | | | | | | | | (1991) ~ leq(n1, n5) % 233.31/39.73 | | | | | | | | | | | | | | | % 233.31/39.73 | | | | | | | | | | | | | | | PRED_UNIFY: (1983), (1991) imply: % 233.31/39.73 | | | | | | | | | | | | | | | (1992) $false % 233.31/39.73 | | | | | | | | | | | | | | | % 233.31/39.73 | | | | | | | | | | | | | | | CLOSE: (1992) is inconsistent. % 233.31/39.73 | | | | | | | | | | | | | | | % 233.31/39.73 | | | | | | | | | | | | | | Case 2: % 233.31/39.73 | | | | | | | | | | | | | | | % 233.31/39.73 | | | | | | | | | | | | | | | (1993) a_select3(id_ds1_filter, n1, n0) = all_74_16 & % 233.31/39.73 | | | | | | | | | | | | | | | $i(all_74_16) % 233.31/39.73 | | | | | | | | | | | | | | | % 233.31/39.73 | | | | | | | | | | | | | | | ALPHA: (1993) implies: % 233.31/39.73 | | | | | | | | | | | | | | | (1994) a_select3(id_ds1_filter, n1, n0) = all_74_16 % 233.31/39.73 | | | | | | | | | | | | | | | % 233.31/39.73 | | | | | | | | | | | | | | | REF_CLOSE: (17), (1901), (1981), (1994) are inconsistent by % 233.31/39.73 | | | | | | | | | | | | | | | sub-proof #5. % 233.31/39.73 | | | | | | | | | | | | | | | % 233.31/39.73 | | | | | | | | | | | | | | End of split % 233.31/39.73 | | | | | | | | | | | | | | % 233.31/39.73 | | | | | | | | | | | | | End of split % 233.31/39.73 | | | | | | | | | | | | | % 233.31/39.73 | | | | | | | | | | | | End of split % 233.31/39.73 | | | | | | | | | | | | % 233.31/39.73 | | | | | | | | | | | Case 2: % 233.31/39.73 | | | | | | | | | | | | % 233.31/39.73 | | | | | | | | | | | | (1995) all_74_19 = n2 % 233.31/39.73 | | | | | | | | | | | | % 233.31/39.73 | | | | | | | | | | | | REDUCE: (1958), (1995) imply: % 233.31/39.73 | | | | | | | | | | | | (1996) a_select3(id_ds1_filter, n2, n0) = all_74_17 % 233.31/39.73 | | | | | | | | | | | | % 233.31/39.73 | | | | | | | | | | | | REDUCE: (1957), (1995) imply: % 233.31/39.73 | | | | | | | | | | | | (1997) a_select3(id_ds1_filter, n0, n2) = all_74_16 % 233.31/39.73 | | | | | | | | | | | | % 233.31/39.73 | | | | | | | | | | | | REDUCE: (1909), (1995) imply: % 233.31/39.73 | | | | | | | | | | | | (1998) leq(n2, n5) % 233.31/39.73 | | | | | | | | | | | | % 233.31/39.73 | | | | | | | | | | | | REDUCE: (1902), (1995) imply: % 233.31/39.73 | | | | | | | | | | | | (1999) leq(n0, n2) % 233.31/39.73 | | | | | | | | | | | | % 233.31/39.73 | | | | | | | | | | | | GROUND_INST: instantiating (65) with n0, n2, all_74_16, % 233.31/39.73 | | | | | | | | | | | | simplifying with (12), (101), (1960), (1997), % 233.31/39.73 | | | | | | | | | | | | (1999) gives: % 233.31/39.73 | | | | | | | | | | | | (2000) ~ leq(n2, all_74_21) | ~ leq(n0, all_74_21) | % 233.31/39.73 | | | | | | | | | | | | (a_select3(id_ds1_filter, n2, n0) = all_74_16 & % 233.31/39.73 | | | | | | | | | | | | $i(all_74_16)) % 233.31/39.73 | | | | | | | | | | | | % 233.31/39.73 | | | | | | | | | | | | BETA: splitting (2000) gives: % 233.31/39.73 | | | | | | | | | | | | % 233.31/39.73 | | | | | | | | | | | | Case 1: % 233.31/39.73 | | | | | | | | | | | | | % 233.31/39.73 | | | | | | | | | | | | | (2001) ~ leq(n0, all_74_21) % 233.31/39.73 | | | | | | | | | | | | | % 233.31/39.73 | | | | | | | | | | | | | REDUCE: (135), (2001) imply: % 233.31/39.73 | | | | | | | | | | | | | (2002) ~ leq(n0, n5) % 233.31/39.73 | | | | | | | | | | | | | % 233.31/39.73 | | | | | | | | | | | | | PRED_UNIFY: (1959), (2002) imply: % 233.31/39.73 | | | | | | | | | | | | | (2003) $false % 233.31/39.73 | | | | | | | | | | | | | % 233.31/39.73 | | | | | | | | | | | | | CLOSE: (2003) is inconsistent. % 233.31/39.73 | | | | | | | | | | | | | % 233.31/39.73 | | | | | | | | | | | | Case 2: % 233.31/39.73 | | | | | | | | | | | | | % 233.31/39.74 | | | | | | | | | | | | | (2004) ~ leq(n2, all_74_21) | (a_select3(id_ds1_filter, % 233.31/39.74 | | | | | | | | | | | | | n2, n0) = all_74_16 & $i(all_74_16)) % 233.31/39.74 | | | | | | | | | | | | | % 233.31/39.74 | | | | | | | | | | | | | BETA: splitting (2004) gives: % 233.31/39.74 | | | | | | | | | | | | | % 233.31/39.74 | | | | | | | | | | | | | Case 1: % 233.31/39.74 | | | | | | | | | | | | | | % 233.31/39.74 | | | | | | | | | | | | | | (2005) ~ leq(n2, all_74_21) % 233.31/39.74 | | | | | | | | | | | | | | % 233.31/39.74 | | | | | | | | | | | | | | REDUCE: (135), (2005) imply: % 233.31/39.74 | | | | | | | | | | | | | | (2006) ~ leq(n2, n5) % 233.31/39.74 | | | | | | | | | | | | | | % 233.31/39.74 | | | | | | | | | | | | | | PRED_UNIFY: (1998), (2006) imply: % 233.31/39.74 | | | | | | | | | | | | | | (2007) $false % 233.31/39.74 | | | | | | | | | | | | | | % 233.31/39.74 | | | | | | | | | | | | | | CLOSE: (2007) is inconsistent. % 233.31/39.74 | | | | | | | | | | | | | | % 233.31/39.74 | | | | | | | | | | | | | Case 2: % 233.31/39.74 | | | | | | | | | | | | | | % 233.31/39.74 | | | | | | | | | | | | | | (2008) a_select3(id_ds1_filter, n2, n0) = all_74_16 & % 233.31/39.74 | | | | | | | | | | | | | | $i(all_74_16) % 233.31/39.74 | | | | | | | | | | | | | | % 233.31/39.74 | | | | | | | | | | | | | | ALPHA: (2008) implies: % 233.31/39.74 | | | | | | | | | | | | | | (2009) a_select3(id_ds1_filter, n2, n0) = all_74_16 % 233.31/39.74 | | | | | | | | | | | | | | % 233.31/39.74 | | | | | | | | | | | | | | REF_CLOSE: (17), (1901), (1996), (2009) are inconsistent by % 233.31/39.74 | | | | | | | | | | | | | | sub-proof #4. % 233.31/39.74 | | | | | | | | | | | | | | % 233.31/39.74 | | | | | | | | | | | | | End of split % 233.31/39.74 | | | | | | | | | | | | | % 233.31/39.74 | | | | | | | | | | | | End of split % 233.31/39.74 | | | | | | | | | | | | % 233.31/39.74 | | | | | | | | | | | End of split % 233.31/39.74 | | | | | | | | | | | % 233.31/39.74 | | | | | | | | | | Case 2: % 233.31/39.74 | | | | | | | | | | | % 233.31/39.74 | | | | | | | | | | | (2010) all_74_19 = n3 % 233.31/39.74 | | | | | | | | | | | % 233.31/39.74 | | | | | | | | | | | REDUCE: (1958), (2010) imply: % 233.31/39.74 | | | | | | | | | | | (2011) a_select3(id_ds1_filter, n3, n0) = all_74_17 % 233.31/39.74 | | | | | | | | | | | % 233.31/39.74 | | | | | | | | | | | REDUCE: (1957), (2010) imply: % 233.31/39.74 | | | | | | | | | | | (2012) a_select3(id_ds1_filter, n0, n3) = all_74_16 % 233.31/39.74 | | | | | | | | | | | % 233.31/39.74 | | | | | | | | | | | REDUCE: (1909), (2010) imply: % 233.31/39.74 | | | | | | | | | | | (2013) leq(n3, n5) % 233.31/39.74 | | | | | | | | | | | % 233.31/39.74 | | | | | | | | | | | REDUCE: (1902), (2010) imply: % 233.31/39.74 | | | | | | | | | | | (2014) leq(n0, n3) % 233.31/39.74 | | | | | | | | | | | % 233.31/39.74 | | | | | | | | | | | GROUND_INST: instantiating (65) with n0, n3, all_74_16, % 233.31/39.74 | | | | | | | | | | | simplifying with (12), (112), (1960), (2012), % 233.31/39.74 | | | | | | | | | | | (2014) gives: % 233.31/39.74 | | | | | | | | | | | (2015) ~ leq(n3, all_74_21) | ~ leq(n0, all_74_21) | % 233.31/39.74 | | | | | | | | | | | (a_select3(id_ds1_filter, n3, n0) = all_74_16 & % 233.31/39.74 | | | | | | | | | | | $i(all_74_16)) % 233.31/39.74 | | | | | | | | | | | % 233.31/39.74 | | | | | | | | | | | BETA: splitting (2015) gives: % 233.31/39.74 | | | | | | | | | | | % 233.31/39.74 | | | | | | | | | | | Case 1: % 233.31/39.74 | | | | | | | | | | | | % 233.31/39.74 | | | | | | | | | | | | (2016) ~ leq(n0, all_74_21) % 233.31/39.74 | | | | | | | | | | | | % 233.31/39.74 | | | | | | | | | | | | REDUCE: (135), (2016) imply: % 233.31/39.74 | | | | | | | | | | | | (2017) ~ leq(n0, n5) % 233.31/39.74 | | | | | | | | | | | | % 233.31/39.74 | | | | | | | | | | | | PRED_UNIFY: (1959), (2017) imply: % 233.31/39.74 | | | | | | | | | | | | (2018) $false % 233.31/39.74 | | | | | | | | | | | | % 233.31/39.74 | | | | | | | | | | | | CLOSE: (2018) is inconsistent. % 233.31/39.74 | | | | | | | | | | | | % 233.31/39.74 | | | | | | | | | | | Case 2: % 233.31/39.74 | | | | | | | | | | | | % 233.31/39.74 | | | | | | | | | | | | (2019) ~ leq(n3, all_74_21) | (a_select3(id_ds1_filter, % 233.31/39.74 | | | | | | | | | | | | n3, n0) = all_74_16 & $i(all_74_16)) % 233.31/39.74 | | | | | | | | | | | | % 233.31/39.74 | | | | | | | | | | | | BETA: splitting (2019) gives: % 233.31/39.74 | | | | | | | | | | | | % 233.31/39.74 | | | | | | | | | | | | Case 1: % 233.31/39.74 | | | | | | | | | | | | | % 233.31/39.74 | | | | | | | | | | | | | (2020) ~ leq(n3, all_74_21) % 233.31/39.74 | | | | | | | | | | | | | % 233.31/39.74 | | | | | | | | | | | | | REDUCE: (135), (2020) imply: % 233.31/39.74 | | | | | | | | | | | | | (2021) ~ leq(n3, n5) % 233.31/39.74 | | | | | | | | | | | | | % 233.31/39.74 | | | | | | | | | | | | | PRED_UNIFY: (2013), (2021) imply: % 233.31/39.74 | | | | | | | | | | | | | (2022) $false % 233.31/39.74 | | | | | | | | | | | | | % 233.31/39.74 | | | | | | | | | | | | | CLOSE: (2022) is inconsistent. % 233.31/39.74 | | | | | | | | | | | | | % 233.31/39.74 | | | | | | | | | | | | Case 2: % 233.31/39.74 | | | | | | | | | | | | | % 233.31/39.74 | | | | | | | | | | | | | (2023) a_select3(id_ds1_filter, n3, n0) = all_74_16 & % 233.31/39.74 | | | | | | | | | | | | | $i(all_74_16) % 233.31/39.74 | | | | | | | | | | | | | % 233.31/39.74 | | | | | | | | | | | | | ALPHA: (2023) implies: % 233.31/39.74 | | | | | | | | | | | | | (2024) a_select3(id_ds1_filter, n3, n0) = all_74_16 % 233.31/39.74 | | | | | | | | | | | | | % 233.31/39.74 | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_74_17, all_74_16, n0, % 233.31/39.74 | | | | | | | | | | | | | n3, id_ds1_filter, simplifying with (2011), (2024) % 233.31/39.74 | | | | | | | | | | | | | gives: % 233.31/39.74 | | | | | | | | | | | | | (2025) all_74_16 = all_74_17 % 233.31/39.74 | | | | | | | | | | | | | % 233.31/39.74 | | | | | | | | | | | | | REDUCE: (1901), (2025) imply: % 233.31/39.74 | | | | | | | | | | | | | (2026) $false % 233.31/39.74 | | | | | | | | | | | | | % 233.31/39.74 | | | | | | | | | | | | | CLOSE: (2026) is inconsistent. % 233.31/39.74 | | | | | | | | | | | | | % 233.31/39.74 | | | | | | | | | | | | End of split % 233.31/39.74 | | | | | | | | | | | | % 233.31/39.74 | | | | | | | | | | | End of split % 233.31/39.74 | | | | | | | | | | | % 233.31/39.74 | | | | | | | | | | End of split % 233.31/39.74 | | | | | | | | | | % 233.31/39.74 | | | | | | | | | Case 2: % 233.31/39.74 | | | | | | | | | | % 233.31/39.74 | | | | | | | | | | (2027) all_74_19 = n4 % 233.31/39.74 | | | | | | | | | | % 233.31/39.74 | | | | | | | | | | REDUCE: (1958), (2027) imply: % 233.31/39.74 | | | | | | | | | | (2028) a_select3(id_ds1_filter, n4, n0) = all_74_17 % 233.31/39.74 | | | | | | | | | | % 233.31/39.74 | | | | | | | | | | REDUCE: (1957), (2027) imply: % 233.31/39.74 | | | | | | | | | | (2029) a_select3(id_ds1_filter, n0, n4) = all_74_16 % 233.31/39.74 | | | | | | | | | | % 233.31/39.74 | | | | | | | | | | REDUCE: (1909), (2027) imply: % 233.31/39.74 | | | | | | | | | | (2030) leq(n4, n5) % 233.31/39.74 | | | | | | | | | | % 233.31/39.74 | | | | | | | | | | REDUCE: (1902), (2027) imply: % 233.31/39.74 | | | | | | | | | | (2031) leq(n0, n4) % 233.31/39.74 | | | | | | | | | | % 233.31/39.74 | | | | | | | | | | GROUND_INST: instantiating (65) with n0, n4, all_74_16, % 233.31/39.74 | | | | | | | | | | simplifying with (12), (119), (1960), (2029), % 233.31/39.74 | | | | | | | | | | (2031) gives: % 233.31/39.74 | | | | | | | | | | (2032) ~ leq(n4, all_74_21) | ~ leq(n0, all_74_21) | % 233.31/39.74 | | | | | | | | | | (a_select3(id_ds1_filter, n4, n0) = all_74_16 & % 233.31/39.74 | | | | | | | | | | $i(all_74_16)) % 233.31/39.74 | | | | | | | | | | % 233.31/39.74 | | | | | | | | | | BETA: splitting (2032) gives: % 233.31/39.74 | | | | | | | | | | % 233.31/39.74 | | | | | | | | | | Case 1: % 233.31/39.74 | | | | | | | | | | | % 233.31/39.74 | | | | | | | | | | | (2033) ~ leq(n0, all_74_21) % 233.31/39.74 | | | | | | | | | | | % 233.31/39.74 | | | | | | | | | | | REDUCE: (135), (2033) imply: % 233.31/39.74 | | | | | | | | | | | (2034) ~ leq(n0, n5) % 233.31/39.74 | | | | | | | | | | | % 233.31/39.74 | | | | | | | | | | | PRED_UNIFY: (1959), (2034) imply: % 233.31/39.74 | | | | | | | | | | | (2035) $false % 233.31/39.74 | | | | | | | | | | | % 233.31/39.74 | | | | | | | | | | | CLOSE: (2035) is inconsistent. % 233.31/39.74 | | | | | | | | | | | % 233.31/39.74 | | | | | | | | | | Case 2: % 233.31/39.74 | | | | | | | | | | | % 233.31/39.74 | | | | | | | | | | | (2036) ~ leq(n4, all_74_21) | (a_select3(id_ds1_filter, % 233.31/39.74 | | | | | | | | | | | n4, n0) = all_74_16 & $i(all_74_16)) % 233.31/39.74 | | | | | | | | | | | % 233.31/39.74 | | | | | | | | | | | BETA: splitting (2036) gives: % 233.31/39.74 | | | | | | | | | | | % 233.31/39.74 | | | | | | | | | | | Case 1: % 233.31/39.74 | | | | | | | | | | | | % 233.31/39.74 | | | | | | | | | | | | (2037) ~ leq(n4, all_74_21) % 233.31/39.74 | | | | | | | | | | | | % 233.31/39.74 | | | | | | | | | | | | REDUCE: (135), (2037) imply: % 233.31/39.74 | | | | | | | | | | | | (2038) ~ leq(n4, n5) % 233.31/39.74 | | | | | | | | | | | | % 233.31/39.74 | | | | | | | | | | | | PRED_UNIFY: (2030), (2038) imply: % 233.31/39.74 | | | | | | | | | | | | (2039) $false % 233.31/39.74 | | | | | | | | | | | | % 233.31/39.74 | | | | | | | | | | | | CLOSE: (2039) is inconsistent. % 233.31/39.74 | | | | | | | | | | | | % 233.31/39.74 | | | | | | | | | | | Case 2: % 233.31/39.74 | | | | | | | | | | | | % 233.31/39.74 | | | | | | | | | | | | (2040) a_select3(id_ds1_filter, n4, n0) = all_74_16 & % 233.31/39.74 | | | | | | | | | | | | $i(all_74_16) % 233.31/39.74 | | | | | | | | | | | | % 233.31/39.74 | | | | | | | | | | | | ALPHA: (2040) implies: % 233.31/39.74 | | | | | | | | | | | | (2041) a_select3(id_ds1_filter, n4, n0) = all_74_16 % 233.31/39.74 | | | | | | | | | | | | % 233.31/39.74 | | | | | | | | | | | | REF_CLOSE: (17), (1901), (2028), (2041) are inconsistent by % 233.31/39.74 | | | | | | | | | | | | sub-proof #3. % 233.31/39.74 | | | | | | | | | | | | % 233.31/39.74 | | | | | | | | | | | End of split % 233.31/39.74 | | | | | | | | | | | % 233.31/39.74 | | | | | | | | | | End of split % 233.31/39.74 | | | | | | | | | | % 233.31/39.74 | | | | | | | | | End of split % 233.31/39.74 | | | | | | | | | % 233.31/39.74 | | | | | | | | End of split % 233.31/39.74 | | | | | | | | % 233.31/39.74 | | | | | | | Case 2: % 233.31/39.74 | | | | | | | | % 233.31/39.74 | | | | | | | | (2042) all_74_19 = n5 % 233.31/39.74 | | | | | | | | % 233.31/39.74 | | | | | | | | REDUCE: (1958), (2042) imply: % 233.31/39.74 | | | | | | | | (2043) a_select3(id_ds1_filter, n5, n0) = all_74_17 % 233.31/39.74 | | | | | | | | % 233.31/39.74 | | | | | | | | REDUCE: (1957), (2042) imply: % 233.31/39.74 | | | | | | | | (2044) a_select3(id_ds1_filter, n0, n5) = all_74_16 % 233.31/39.74 | | | | | | | | % 233.31/39.74 | | | | | | | | REDUCE: (1909), (2042) imply: % 233.31/39.74 | | | | | | | | (2045) leq(n5, n5) % 233.31/39.74 | | | | | | | | % 233.31/39.74 | | | | | | | | GROUND_INST: instantiating (65) with n0, n5, all_74_16, % 233.31/39.74 | | | | | | | | simplifying with (12), (122), (1959), (1960), % 233.31/39.74 | | | | | | | | (2044) gives: % 233.31/39.74 | | | | | | | | (2046) ~ leq(n5, all_74_21) | ~ leq(n0, all_74_21) | % 233.31/39.74 | | | | | | | | (a_select3(id_ds1_filter, n5, n0) = all_74_16 & % 233.31/39.74 | | | | | | | | $i(all_74_16)) % 233.31/39.74 | | | | | | | | % 233.31/39.74 | | | | | | | | BETA: splitting (2046) gives: % 233.31/39.74 | | | | | | | | % 233.31/39.74 | | | | | | | | Case 1: % 233.31/39.74 | | | | | | | | | % 233.31/39.74 | | | | | | | | | (2047) ~ leq(n0, all_74_21) % 233.31/39.74 | | | | | | | | | % 233.31/39.74 | | | | | | | | | REDUCE: (135), (2047) imply: % 233.31/39.74 | | | | | | | | | (2048) ~ leq(n0, n5) % 233.31/39.74 | | | | | | | | | % 233.31/39.74 | | | | | | | | | PRED_UNIFY: (1959), (2048) imply: % 233.31/39.74 | | | | | | | | | (2049) $false % 233.31/39.74 | | | | | | | | | % 233.31/39.74 | | | | | | | | | CLOSE: (2049) is inconsistent. % 233.31/39.74 | | | | | | | | | % 233.31/39.74 | | | | | | | | Case 2: % 233.31/39.74 | | | | | | | | | % 233.31/39.74 | | | | | | | | | (2050) ~ leq(n5, all_74_21) | (a_select3(id_ds1_filter, % 233.31/39.74 | | | | | | | | | n5, n0) = all_74_16 & $i(all_74_16)) % 233.31/39.74 | | | | | | | | | % 233.31/39.74 | | | | | | | | | BETA: splitting (2050) gives: % 233.31/39.74 | | | | | | | | | % 233.31/39.74 | | | | | | | | | Case 1: % 233.31/39.74 | | | | | | | | | | % 233.31/39.74 | | | | | | | | | | (2051) ~ leq(n5, all_74_21) % 233.31/39.74 | | | | | | | | | | % 233.31/39.74 | | | | | | | | | | REDUCE: (135), (2051) imply: % 233.31/39.74 | | | | | | | | | | (2052) ~ leq(n5, n5) % 233.31/39.74 | | | | | | | | | | % 233.31/39.74 | | | | | | | | | | PRED_UNIFY: (2045), (2052) imply: % 233.31/39.74 | | | | | | | | | | (2053) $false % 233.31/39.74 | | | | | | | | | | % 233.31/39.74 | | | | | | | | | | CLOSE: (2053) is inconsistent. % 233.31/39.74 | | | | | | | | | | % 233.31/39.74 | | | | | | | | | Case 2: % 233.31/39.74 | | | | | | | | | | % 233.31/39.74 | | | | | | | | | | (2054) a_select3(id_ds1_filter, n5, n0) = all_74_16 & % 233.31/39.74 | | | | | | | | | | $i(all_74_16) % 233.31/39.74 | | | | | | | | | | % 233.31/39.74 | | | | | | | | | | ALPHA: (2054) implies: % 233.31/39.74 | | | | | | | | | | (2055) a_select3(id_ds1_filter, n5, n0) = all_74_16 % 233.31/39.74 | | | | | | | | | | % 233.31/39.74 | | | | | | | | | | REF_CLOSE: (17), (1901), (2043), (2055) are inconsistent by % 233.31/39.74 | | | | | | | | | | sub-proof #2. % 233.31/39.74 | | | | | | | | | | % 233.31/39.74 | | | | | | | | | End of split % 233.31/39.74 | | | | | | | | | % 233.31/39.74 | | | | | | | | End of split % 233.31/39.74 | | | | | | | | % 233.31/39.74 | | | | | | | End of split % 233.31/39.74 | | | | | | | % 233.31/39.74 | | | | | | Case 2: % 233.31/39.74 | | | | | | | % 233.31/39.74 | | | | | | | (2056) all_74_19 = n0 % 233.31/39.74 | | | | | | | % 233.31/39.74 | | | | | | | REDUCE: (1958), (2056) imply: % 233.31/39.74 | | | | | | | (2057) a_select3(id_ds1_filter, n0, n0) = all_74_17 % 233.31/39.74 | | | | | | | % 233.31/39.74 | | | | | | | REDUCE: (1957), (2056) imply: % 233.31/39.74 | | | | | | | (2058) a_select3(id_ds1_filter, n0, n0) = all_74_16 % 233.31/39.74 | | | | | | | % 233.31/39.74 | | | | | | | GROUND_INST: instantiating (17) with all_74_17, all_74_16, n0, n0, % 233.31/39.74 | | | | | | | id_ds1_filter, simplifying with (2057), (2058) gives: % 233.31/39.74 | | | | | | | (2059) all_74_16 = all_74_17 % 233.31/39.74 | | | | | | | % 233.31/39.74 | | | | | | | REDUCE: (1901), (2059) imply: % 233.31/39.74 | | | | | | | (2060) $false % 233.31/39.74 | | | | | | | % 233.31/39.74 | | | | | | | CLOSE: (2060) is inconsistent. % 233.31/39.74 | | | | | | | % 233.31/39.74 | | | | | | End of split % 233.31/39.74 | | | | | | % 233.31/39.74 | | | | | End of split % 233.31/39.74 | | | | | % 233.31/39.74 | | | | End of split % 233.31/39.74 | | | | % 233.31/39.74 | | | End of split % 233.31/39.74 | | | % 233.31/39.74 | | End of split % 233.31/39.74 | | % 233.31/39.74 | End of split % 233.31/39.74 | % 233.31/39.74 End of proof % 233.31/39.74 % 233.31/39.74 Sub-proof #1 shows that the following formulas are inconsistent: % 233.31/39.74 ---------------------------------------------------------------- % 233.31/39.74 (1) $i(all_74_19) % 233.31/39.74 (2) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ leq(v0, % 233.31/39.74 v1) | gt(v1, v0)) % 233.31/39.74 (3) all_74_19 = n5 | all_74_19 = n4 | all_74_19 = n3 | all_74_19 = n2 | % 233.31/39.74 all_74_19 = n1 | all_74_19 = n0 % 233.31/39.74 (4) leq(all_74_18, n5) % 233.31/39.74 (5) all_74_19 = n5 | gt(n5, all_74_19) % 233.31/39.74 (6) all_74_19 = n0 | gt(all_74_19, n0) % 233.31/39.74 (7) all_74_21 = n5 % 233.31/39.75 (8) all_74_18 = n5 | all_74_18 = n4 | all_74_18 = n3 | all_74_18 = n2 | % 233.31/39.75 all_74_18 = n1 | all_74_18 = n0 % 233.31/39.75 (9) pred(n4) = n3 % 233.31/39.75 (10) ~ gt(n0, n0) % 233.31/39.75 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (pred(v1) = v2) | ~ % 233.31/39.75 $i(v1) | ~ $i(v0) | ~ gt(v1, v0) | leq(v0, v2)) % 233.31/39.75 (12) $i(n2) % 233.31/39.75 (13) pred(n5) = n4 % 233.31/39.75 (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 233.31/39.75 (v1 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 233.31/39.75 v0)) % 233.31/39.75 (15) pred(n2) = n1 % 233.31/39.75 (16) $i(n5) % 233.31/39.75 (17) $i(all_74_18) % 233.31/39.75 (18) $i(n3) % 233.31/39.75 (19) ~ (all_74_16 = all_74_17) % 233.31/39.75 (20) a_select3(id_ds1_filter, all_74_19, all_74_18) = all_74_17 % 233.31/39.75 (21) pred(n3) = n2 % 233.31/39.75 (22) $i(n4) % 233.31/39.75 (23) all_74_18 = n5 | gt(n5, all_74_18) % 233.31/39.75 (24) a_select3(id_ds1_filter, all_74_18, all_74_19) = all_74_16 % 233.31/39.75 (25) leq(all_74_19, n5) % 233.31/39.75 (26) leq(n0, all_74_19) % 233.31/39.75 (27) gt(all_74_18, n0) % 233.31/39.75 (28) leq(n0, all_74_18) % 233.31/39.75 (29) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (a_select3(id_ds1_filter, % 233.31/39.75 v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ leq(v1, all_74_21) | ~ % 233.31/39.75 leq(v0, all_74_21) | ~ leq(n0, v1) | ~ leq(n0, v0) | % 233.31/39.75 (a_select3(id_ds1_filter, v1, v0) = v2 & $i(v2))) % 233.31/39.75 (30) ! [v0: $i] : (v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0, n1) | ~ % 233.31/39.75 leq(n0, v0)) % 233.31/39.75 % 233.31/39.75 Begin of proof % 233.31/39.75 | % 233.31/39.75 | BETA: splitting (6) gives: % 233.31/39.75 | % 233.31/39.75 | Case 1: % 233.31/39.75 | | % 233.31/39.75 | | (31) gt(all_74_19, n0) % 233.31/39.75 | | % 233.31/39.75 | | BETA: splitting (5) gives: % 233.31/39.75 | | % 233.31/39.75 | | Case 1: % 233.31/39.75 | | | % 233.31/39.75 | | | (32) gt(n5, all_74_19) % 233.31/39.75 | | | % 233.31/39.75 | | | GROUND_INST: instantiating (11) with all_74_19, n5, n4, simplifying with % 233.31/39.75 | | | (1), (13), (16), (32) gives: % 233.31/39.75 | | | (33) leq(all_74_19, n4) % 233.31/39.75 | | | % 233.31/39.75 | | | GROUND_INST: instantiating (2) with all_74_19, n4, simplifying with (1), % 233.31/39.75 | | | (22), (33) gives: % 233.31/39.75 | | | (34) all_74_19 = n4 | gt(n4, all_74_19) % 233.31/39.75 | | | % 233.31/39.75 | | | BETA: splitting (23) gives: % 233.31/39.75 | | | % 233.31/39.75 | | | Case 1: % 233.31/39.75 | | | | % 233.31/39.75 | | | | (35) gt(n5, all_74_18) % 233.31/39.75 | | | | % 233.31/39.75 | | | | GROUND_INST: instantiating (11) with all_74_18, n5, n4, simplifying with % 233.31/39.75 | | | | (13), (16), (17), (35) gives: % 233.31/39.75 | | | | (36) leq(all_74_18, n4) % 233.31/39.75 | | | | % 233.31/39.75 | | | | GROUND_INST: instantiating (2) with all_74_18, n4, simplifying with % 233.31/39.75 | | | | (17), (22), (36) gives: % 233.31/39.75 | | | | (37) all_74_18 = n4 | gt(n4, all_74_18) % 233.31/39.75 | | | | % 233.31/39.75 | | | | BETA: splitting (8) gives: % 233.31/39.75 | | | | % 233.31/39.75 | | | | Case 1: % 233.31/39.75 | | | | | % 233.31/39.75 | | | | | (38) all_74_18 = n0 % 233.31/39.75 | | | | | % 233.31/39.75 | | | | | REDUCE: (27), (38) imply: % 233.31/39.75 | | | | | (39) gt(n0, n0) % 233.31/39.75 | | | | | % 233.31/39.75 | | | | | PRED_UNIFY: (10), (39) imply: % 233.31/39.75 | | | | | (40) $false % 233.31/39.75 | | | | | % 233.31/39.75 | | | | | CLOSE: (40) is inconsistent. % 233.31/39.75 | | | | | % 233.31/39.75 | | | | Case 2: % 233.31/39.75 | | | | | % 233.31/39.75 | | | | | (41) ~ (all_74_18 = n0) % 233.31/39.75 | | | | | % 233.31/39.75 | | | | | BETA: splitting (3) gives: % 233.31/39.75 | | | | | % 233.31/39.75 | | | | | Case 1: % 233.31/39.75 | | | | | | % 233.31/39.75 | | | | | | (42) all_74_19 = n0 % 233.31/39.75 | | | | | | % 233.31/39.75 | | | | | | REDUCE: (31), (42) imply: % 233.31/39.75 | | | | | | (43) gt(n0, n0) % 233.31/39.75 | | | | | | % 233.31/39.75 | | | | | | PRED_UNIFY: (10), (43) imply: % 233.31/39.75 | | | | | | (44) $false % 233.31/39.75 | | | | | | % 233.31/39.75 | | | | | | CLOSE: (44) is inconsistent. % 233.31/39.75 | | | | | | % 233.31/39.75 | | | | | Case 2: % 233.31/39.75 | | | | | | % 233.31/39.75 | | | | | | (45) ~ (all_74_19 = n0) % 233.31/39.75 | | | | | | % 233.31/39.75 | | | | | | REF_CLOSE: (1), (2), (4), (7), (9), (11), (12), (14), (15), (17), % 233.31/39.75 | | | | | | (18), (19), (20), (21), (22), (24), (25), (26), (28), % 233.31/39.75 | | | | | | (29), (30), (34), (37), (41), (45) are inconsistent by % 233.31/39.75 | | | | | | sub-proof #9. % 233.31/39.75 | | | | | | % 233.31/39.75 | | | | | End of split % 233.31/39.75 | | | | | % 233.31/39.75 | | | | End of split % 233.31/39.75 | | | | % 233.31/39.75 | | | Case 2: % 233.31/39.75 | | | | % 233.31/39.75 | | | | (46) all_74_18 = n5 % 233.31/39.75 | | | | % 233.31/39.75 | | | | REDUCE: (24), (46) imply: % 233.31/39.75 | | | | (47) a_select3(id_ds1_filter, n5, all_74_19) = all_74_16 % 233.31/39.75 | | | | % 233.31/39.75 | | | | REDUCE: (20), (46) imply: % 233.31/39.75 | | | | (48) a_select3(id_ds1_filter, all_74_19, n5) = all_74_17 % 233.31/39.75 | | | | % 233.31/39.75 | | | | REDUCE: (4), (46) imply: % 233.31/39.75 | | | | (49) leq(n5, n5) % 233.31/39.75 | | | | % 233.31/39.75 | | | | REDUCE: (28), (46) imply: % 233.31/39.75 | | | | (50) leq(n0, n5) % 233.31/39.75 | | | | % 233.31/39.75 | | | | BETA: splitting (3) gives: % 233.31/39.75 | | | | % 233.31/39.75 | | | | Case 1: % 233.31/39.75 | | | | | % 233.31/39.75 | | | | | (51) all_74_19 = n0 % 233.31/39.75 | | | | | % 233.31/39.75 | | | | | REDUCE: (31), (51) imply: % 233.31/39.75 | | | | | (52) gt(n0, n0) % 233.31/39.75 | | | | | % 233.31/39.75 | | | | | PRED_UNIFY: (10), (52) imply: % 233.31/39.75 | | | | | (53) $false % 233.31/39.75 | | | | | % 233.31/39.75 | | | | | CLOSE: (53) is inconsistent. % 233.31/39.75 | | | | | % 233.31/39.75 | | | | Case 2: % 233.31/39.75 | | | | | % 233.31/39.75 | | | | | (54) ~ (all_74_19 = n0) % 233.31/39.75 | | | | | % 233.31/39.75 | | | | | REF_CLOSE: (1), (2), (7), (9), (11), (12), (14), (15), (16), (18), % 233.31/39.75 | | | | | (19), (21), (22), (25), (26), (29), (30), (34), (47), (48), % 233.31/39.75 | | | | | (49), (50), (54) are inconsistent by sub-proof #7. % 233.31/39.75 | | | | | % 233.31/39.75 | | | | End of split % 233.31/39.75 | | | | % 233.31/39.75 | | | End of split % 233.31/39.75 | | | % 233.31/39.75 | | Case 2: % 233.31/39.75 | | | % 233.31/39.75 | | | (55) all_74_19 = n5 % 233.31/39.75 | | | % 233.31/39.75 | | | REDUCE: (24), (55) imply: % 233.31/39.75 | | | (56) a_select3(id_ds1_filter, all_74_18, n5) = all_74_16 % 233.31/39.75 | | | % 233.31/39.75 | | | REDUCE: (20), (55) imply: % 233.31/39.75 | | | (57) a_select3(id_ds1_filter, n5, all_74_18) = all_74_17 % 233.31/39.75 | | | % 233.31/39.75 | | | REDUCE: (25), (55) imply: % 233.31/39.75 | | | (58) leq(n5, n5) % 233.31/39.75 | | | % 233.31/39.75 | | | REDUCE: (26), (55) imply: % 233.31/39.75 | | | (59) leq(n0, n5) % 233.31/39.75 | | | % 233.31/39.75 | | | BETA: splitting (23) gives: % 233.31/39.75 | | | % 233.31/39.75 | | | Case 1: % 233.31/39.75 | | | | % 233.31/39.75 | | | | (60) gt(n5, all_74_18) % 233.31/39.75 | | | | % 233.31/39.75 | | | | GROUND_INST: instantiating (11) with all_74_18, n5, n4, simplifying with % 233.31/39.75 | | | | (13), (16), (17), (60) gives: % 233.31/39.75 | | | | (61) leq(all_74_18, n4) % 233.31/39.75 | | | | % 233.31/39.75 | | | | GROUND_INST: instantiating (2) with all_74_18, n4, simplifying with % 233.31/39.75 | | | | (17), (22), (61) gives: % 233.31/39.75 | | | | (62) all_74_18 = n4 | gt(n4, all_74_18) % 233.31/39.75 | | | | % 233.31/39.75 | | | | BETA: splitting (8) gives: % 233.31/39.75 | | | | % 233.31/39.75 | | | | Case 1: % 233.31/39.75 | | | | | % 233.31/39.75 | | | | | (63) all_74_18 = n0 % 233.31/39.75 | | | | | % 233.31/39.75 | | | | | REDUCE: (27), (63) imply: % 233.31/39.75 | | | | | (64) gt(n0, n0) % 233.31/39.75 | | | | | % 233.31/39.75 | | | | | PRED_UNIFY: (10), (64) imply: % 233.31/39.75 | | | | | (65) $false % 233.31/39.75 | | | | | % 233.31/39.75 | | | | | CLOSE: (65) is inconsistent. % 233.31/39.75 | | | | | % 233.31/39.75 | | | | Case 2: % 233.31/39.75 | | | | | % 233.31/39.75 | | | | | (66) ~ (all_74_18 = n0) % 233.31/39.75 | | | | | % 233.31/39.75 | | | | | REF_CLOSE: (2), (4), (7), (9), (11), (12), (14), (15), (16), (17), % 233.31/39.75 | | | | | (18), (19), (21), (22), (28), (29), (30), (56), (57), (58), % 233.31/39.75 | | | | | (59), (62), (66) are inconsistent by sub-proof #6. % 233.31/39.75 | | | | | % 233.31/39.75 | | | | End of split % 233.31/39.75 | | | | % 233.31/39.75 | | | Case 2: % 233.31/39.75 | | | | % 233.31/39.75 | | | | (67) all_74_18 = n5 % 233.31/39.75 | | | | % 233.31/39.75 | | | | REDUCE: (56), (67) imply: % 233.31/39.75 | | | | (68) a_select3(id_ds1_filter, n5, n5) = all_74_16 % 233.31/39.75 | | | | % 233.31/39.75 | | | | REDUCE: (57), (67) imply: % 233.31/39.75 | | | | (69) a_select3(id_ds1_filter, n5, n5) = all_74_17 % 233.31/39.75 | | | | % 233.31/39.75 | | | | GROUND_INST: instantiating (14) with all_74_17, all_74_16, n5, n5, % 233.31/39.75 | | | | id_ds1_filter, simplifying with (68), (69) gives: % 233.31/39.75 | | | | (70) all_74_16 = all_74_17 % 233.31/39.75 | | | | % 233.31/39.75 | | | | REDUCE: (19), (70) imply: % 233.31/39.75 | | | | (71) $false % 233.31/39.75 | | | | % 233.31/39.75 | | | | CLOSE: (71) is inconsistent. % 233.31/39.75 | | | | % 233.31/39.75 | | | End of split % 233.31/39.75 | | | % 233.31/39.75 | | End of split % 233.31/39.75 | | % 233.31/39.75 | Case 2: % 233.31/39.75 | | % 233.31/39.75 | | (72) all_74_19 = n0 % 233.31/39.75 | | (73) ~ gt(all_74_19, n0) % 233.31/39.75 | | % 233.31/39.75 | | REDUCE: (24), (72) imply: % 233.31/39.75 | | (74) a_select3(id_ds1_filter, all_74_18, n0) = all_74_16 % 233.31/39.75 | | % 233.31/39.75 | | REDUCE: (20), (72) imply: % 233.31/39.75 | | (75) a_select3(id_ds1_filter, n0, all_74_18) = all_74_17 % 233.31/39.75 | | % 233.31/39.75 | | REDUCE: (1), (72) imply: % 233.31/39.75 | | (76) $i(n0) % 233.31/39.75 | | % 233.31/39.75 | | REDUCE: (25), (72) imply: % 233.31/39.75 | | (77) leq(n0, n5) % 233.31/39.75 | | % 233.31/39.75 | | REDUCE: (26), (72) imply: % 233.31/39.75 | | (78) leq(n0, n0) % 233.31/39.75 | | % 233.31/39.75 | | BETA: splitting (23) gives: % 233.31/39.75 | | % 233.31/39.75 | | Case 1: % 233.31/39.75 | | | % 233.31/39.75 | | | (79) gt(n5, all_74_18) % 233.31/39.75 | | | % 233.31/39.75 | | | GROUND_INST: instantiating (11) with all_74_18, n5, n4, simplifying with % 233.31/39.75 | | | (13), (16), (17), (79) gives: % 233.31/39.75 | | | (80) leq(all_74_18, n4) % 233.31/39.75 | | | % 233.31/39.75 | | | GROUND_INST: instantiating (2) with all_74_18, n4, simplifying with (17), % 233.31/39.75 | | | (22), (80) gives: % 233.31/39.75 | | | (81) all_74_18 = n4 | gt(n4, all_74_18) % 233.31/39.75 | | | % 233.31/39.75 | | | BETA: splitting (8) gives: % 233.31/39.75 | | | % 233.31/39.75 | | | Case 1: % 233.31/39.75 | | | | % 233.31/39.75 | | | | (82) all_74_18 = n0 % 233.31/39.75 | | | | % 233.31/39.75 | | | | REDUCE: (27), (82) imply: % 233.31/39.75 | | | | (83) gt(n0, n0) % 233.31/39.75 | | | | % 233.31/39.75 | | | | PRED_UNIFY: (10), (83) imply: % 233.31/39.75 | | | | (84) $false % 233.31/39.75 | | | | % 233.31/39.75 | | | | CLOSE: (84) is inconsistent. % 233.31/39.75 | | | | % 233.31/39.75 | | | Case 2: % 233.31/39.75 | | | | % 233.31/39.75 | | | | (85) ~ (all_74_18 = n0) % 233.31/39.76 | | | | % 233.31/39.76 | | | | BETA: splitting (81) gives: % 233.31/39.76 | | | | % 233.31/39.76 | | | | Case 1: % 233.31/39.76 | | | | | % 233.31/39.76 | | | | | (86) gt(n4, all_74_18) % 233.31/39.76 | | | | | % 233.31/39.76 | | | | | GROUND_INST: instantiating (11) with all_74_18, n4, n3, simplifying % 233.31/39.76 | | | | | with (9), (17), (22), (86) gives: % 233.31/39.76 | | | | | (87) leq(all_74_18, n3) % 233.31/39.76 | | | | | % 233.31/39.76 | | | | | GROUND_INST: instantiating (2) with all_74_18, n3, simplifying with % 233.31/39.76 | | | | | (17), (18), (87) gives: % 233.31/39.76 | | | | | (88) all_74_18 = n3 | gt(n3, all_74_18) % 233.31/39.76 | | | | | % 233.31/39.76 | | | | | BETA: splitting (88) gives: % 233.31/39.76 | | | | | % 233.31/39.76 | | | | | Case 1: % 233.31/39.76 | | | | | | % 233.31/39.76 | | | | | | (89) gt(n3, all_74_18) % 233.31/39.76 | | | | | | % 233.31/39.76 | | | | | | GROUND_INST: instantiating (11) with all_74_18, n3, n2, simplifying % 233.31/39.76 | | | | | | with (17), (18), (21), (89) gives: % 233.31/39.76 | | | | | | (90) leq(all_74_18, n2) % 233.31/39.76 | | | | | | % 233.31/39.76 | | | | | | GROUND_INST: instantiating (2) with all_74_18, n2, simplifying with % 233.31/39.76 | | | | | | (12), (17), (90) gives: % 233.31/39.76 | | | | | | (91) all_74_18 = n2 | gt(n2, all_74_18) % 233.31/39.76 | | | | | | % 233.31/39.76 | | | | | | BETA: splitting (91) gives: % 233.31/39.76 | | | | | | % 233.31/39.76 | | | | | | Case 1: % 233.31/39.76 | | | | | | | % 233.31/39.76 | | | | | | | (92) gt(n2, all_74_18) % 233.31/39.76 | | | | | | | % 233.31/39.76 | | | | | | | GROUND_INST: instantiating (11) with all_74_18, n2, n1, % 233.31/39.76 | | | | | | | simplifying with (12), (15), (17), (92) gives: % 233.31/39.76 | | | | | | | (93) leq(all_74_18, n1) % 233.31/39.76 | | | | | | | % 233.31/39.76 | | | | | | | GROUND_INST: instantiating (30) with all_74_18, simplifying with % 233.31/39.76 | | | | | | | (17), (28), (93) gives: % 233.31/39.76 | | | | | | | (94) all_74_18 = n1 | all_74_18 = n0 % 233.31/39.76 | | | | | | | % 233.31/39.76 | | | | | | | BETA: splitting (94) gives: % 233.31/39.76 | | | | | | | % 233.31/39.76 | | | | | | | Case 1: % 233.31/39.76 | | | | | | | | % 233.31/39.76 | | | | | | | | (95) all_74_18 = n0 % 233.31/39.76 | | | | | | | | % 233.31/39.76 | | | | | | | | REDUCE: (85), (95) imply: % 233.31/39.76 | | | | | | | | (96) $false % 233.31/39.76 | | | | | | | | % 233.31/39.76 | | | | | | | | CLOSE: (96) is inconsistent. % 233.31/39.76 | | | | | | | | % 233.31/39.76 | | | | | | | Case 2: % 233.31/39.76 | | | | | | | | % 233.31/39.76 | | | | | | | | (97) all_74_18 = n1 % 233.31/39.76 | | | | | | | | % 233.31/39.76 | | | | | | | | REDUCE: (74), (97) imply: % 233.31/39.76 | | | | | | | | (98) a_select3(id_ds1_filter, n1, n0) = all_74_16 % 233.31/39.76 | | | | | | | | % 233.31/39.76 | | | | | | | | REDUCE: (75), (97) imply: % 233.31/39.76 | | | | | | | | (99) a_select3(id_ds1_filter, n0, n1) = all_74_17 % 233.31/39.76 | | | | | | | | % 233.31/39.76 | | | | | | | | REDUCE: (17), (97) imply: % 233.31/39.76 | | | | | | | | (100) $i(n1) % 233.31/39.76 | | | | | | | | % 233.31/39.76 | | | | | | | | REDUCE: (4), (97) imply: % 233.31/39.76 | | | | | | | | (101) leq(n1, n5) % 233.31/39.76 | | | | | | | | % 233.31/39.76 | | | | | | | | REDUCE: (28), (97) imply: % 233.31/39.76 | | | | | | | | (102) leq(n0, n1) % 233.31/39.76 | | | | | | | | % 233.31/39.76 | | | | | | | | GROUND_INST: instantiating (29) with n0, n1, all_74_17, % 233.31/39.76 | | | | | | | | simplifying with (76), (78), (99), (100), (102) % 233.31/39.76 | | | | | | | | gives: % 233.31/39.76 | | | | | | | | (103) ~ leq(n1, all_74_21) | ~ leq(n0, all_74_21) | % 233.31/39.76 | | | | | | | | (a_select3(id_ds1_filter, n1, n0) = all_74_17 & % 233.31/39.76 | | | | | | | | $i(all_74_17)) % 233.31/39.76 | | | | | | | | % 233.31/39.76 | | | | | | | | BETA: splitting (103) gives: % 233.31/39.76 | | | | | | | | % 233.31/39.76 | | | | | | | | Case 1: % 233.31/39.76 | | | | | | | | | % 233.31/39.76 | | | | | | | | | (104) ~ leq(n0, all_74_21) % 233.31/39.76 | | | | | | | | | % 233.31/39.76 | | | | | | | | | REDUCE: (7), (104) imply: % 233.31/39.76 | | | | | | | | | (105) ~ leq(n0, n5) % 233.31/39.76 | | | | | | | | | % 233.31/39.76 | | | | | | | | | PRED_UNIFY: (77), (105) imply: % 233.31/39.76 | | | | | | | | | (106) $false % 233.31/39.76 | | | | | | | | | % 233.31/39.76 | | | | | | | | | CLOSE: (106) is inconsistent. % 233.31/39.76 | | | | | | | | | % 233.31/39.76 | | | | | | | | Case 2: % 233.31/39.76 | | | | | | | | | % 233.31/39.76 | | | | | | | | | (107) ~ leq(n1, all_74_21) | (a_select3(id_ds1_filter, n1, % 233.31/39.76 | | | | | | | | | n0) = all_74_17 & $i(all_74_17)) % 233.31/39.76 | | | | | | | | | % 233.31/39.76 | | | | | | | | | BETA: splitting (107) gives: % 233.31/39.76 | | | | | | | | | % 233.31/39.76 | | | | | | | | | Case 1: % 233.31/39.76 | | | | | | | | | | % 233.31/39.76 | | | | | | | | | | (108) ~ leq(n1, all_74_21) % 233.31/39.76 | | | | | | | | | | % 233.31/39.76 | | | | | | | | | | REDUCE: (7), (108) imply: % 233.31/39.76 | | | | | | | | | | (109) ~ leq(n1, n5) % 233.31/39.76 | | | | | | | | | | % 233.31/39.76 | | | | | | | | | | PRED_UNIFY: (101), (109) imply: % 233.31/39.76 | | | | | | | | | | (110) $false % 233.31/39.76 | | | | | | | | | | % 233.31/39.76 | | | | | | | | | | CLOSE: (110) is inconsistent. % 233.31/39.76 | | | | | | | | | | % 233.31/39.76 | | | | | | | | | Case 2: % 233.31/39.76 | | | | | | | | | | % 233.31/39.76 | | | | | | | | | | (111) a_select3(id_ds1_filter, n1, n0) = all_74_17 & % 233.31/39.76 | | | | | | | | | | $i(all_74_17) % 233.31/39.76 | | | | | | | | | | % 233.31/39.76 | | | | | | | | | | ALPHA: (111) implies: % 233.31/39.76 | | | | | | | | | | (112) a_select3(id_ds1_filter, n1, n0) = all_74_17 % 233.31/39.76 | | | | | | | | | | % 233.31/39.76 | | | | | | | | | | REF_CLOSE: (14), (19), (98), (112) are inconsistent by % 233.31/39.76 | | | | | | | | | | sub-proof #5. % 233.31/39.76 | | | | | | | | | | % 233.31/39.76 | | | | | | | | | End of split % 233.31/39.76 | | | | | | | | | % 233.31/39.76 | | | | | | | | End of split % 233.31/39.76 | | | | | | | | % 233.31/39.76 | | | | | | | End of split % 233.31/39.76 | | | | | | | % 233.31/39.76 | | | | | | Case 2: % 233.31/39.76 | | | | | | | % 233.31/39.76 | | | | | | | (113) all_74_18 = n2 % 233.31/39.76 | | | | | | | % 233.31/39.76 | | | | | | | REDUCE: (74), (113) imply: % 233.31/39.76 | | | | | | | (114) a_select3(id_ds1_filter, n2, n0) = all_74_16 % 233.31/39.76 | | | | | | | % 233.31/39.76 | | | | | | | REDUCE: (75), (113) imply: % 233.31/39.76 | | | | | | | (115) a_select3(id_ds1_filter, n0, n2) = all_74_17 % 233.31/39.76 | | | | | | | % 233.31/39.76 | | | | | | | REDUCE: (4), (113) imply: % 233.31/39.76 | | | | | | | (116) leq(n2, n5) % 233.31/39.76 | | | | | | | % 233.31/39.76 | | | | | | | REDUCE: (28), (113) imply: % 233.31/39.76 | | | | | | | (117) leq(n0, n2) % 233.31/39.76 | | | | | | | % 233.31/39.76 | | | | | | | GROUND_INST: instantiating (29) with n0, n2, all_74_17, % 233.31/39.76 | | | | | | | simplifying with (12), (76), (78), (115), (117) % 233.31/39.76 | | | | | | | gives: % 233.31/39.76 | | | | | | | (118) ~ leq(n2, all_74_21) | ~ leq(n0, all_74_21) | % 233.31/39.76 | | | | | | | (a_select3(id_ds1_filter, n2, n0) = all_74_17 & % 233.31/39.76 | | | | | | | $i(all_74_17)) % 233.31/39.76 | | | | | | | % 233.31/39.76 | | | | | | | BETA: splitting (118) gives: % 233.31/39.76 | | | | | | | % 233.31/39.76 | | | | | | | Case 1: % 233.31/39.76 | | | | | | | | % 233.31/39.76 | | | | | | | | (119) ~ leq(n0, all_74_21) % 233.31/39.76 | | | | | | | | % 233.31/39.76 | | | | | | | | REDUCE: (7), (119) imply: % 233.31/39.76 | | | | | | | | (120) ~ leq(n0, n5) % 233.31/39.76 | | | | | | | | % 233.31/39.76 | | | | | | | | PRED_UNIFY: (77), (120) imply: % 233.31/39.76 | | | | | | | | (121) $false % 233.31/39.76 | | | | | | | | % 233.31/39.76 | | | | | | | | CLOSE: (121) is inconsistent. % 233.31/39.76 | | | | | | | | % 233.31/39.76 | | | | | | | Case 2: % 233.31/39.76 | | | | | | | | % 233.31/39.76 | | | | | | | | (122) ~ leq(n2, all_74_21) | (a_select3(id_ds1_filter, n2, % 233.31/39.76 | | | | | | | | n0) = all_74_17 & $i(all_74_17)) % 233.31/39.76 | | | | | | | | % 233.31/39.76 | | | | | | | | BETA: splitting (122) gives: % 233.31/39.76 | | | | | | | | % 233.31/39.76 | | | | | | | | Case 1: % 233.31/39.76 | | | | | | | | | % 233.31/39.76 | | | | | | | | | (123) ~ leq(n2, all_74_21) % 233.31/39.76 | | | | | | | | | % 233.31/39.76 | | | | | | | | | REDUCE: (7), (123) imply: % 233.31/39.76 | | | | | | | | | (124) ~ leq(n2, n5) % 233.31/39.76 | | | | | | | | | % 233.31/39.76 | | | | | | | | | PRED_UNIFY: (116), (124) imply: % 233.31/39.76 | | | | | | | | | (125) $false % 233.31/39.76 | | | | | | | | | % 233.31/39.76 | | | | | | | | | CLOSE: (125) is inconsistent. % 233.31/39.76 | | | | | | | | | % 233.31/39.76 | | | | | | | | Case 2: % 233.31/39.76 | | | | | | | | | % 233.31/39.76 | | | | | | | | | (126) a_select3(id_ds1_filter, n2, n0) = all_74_17 & % 233.31/39.76 | | | | | | | | | $i(all_74_17) % 233.31/39.76 | | | | | | | | | % 233.31/39.76 | | | | | | | | | ALPHA: (126) implies: % 233.31/39.76 | | | | | | | | | (127) a_select3(id_ds1_filter, n2, n0) = all_74_17 % 233.31/39.76 | | | | | | | | | % 233.31/39.76 | | | | | | | | | REF_CLOSE: (14), (19), (114), (127) are inconsistent by % 233.31/39.76 | | | | | | | | | sub-proof #4. % 233.31/39.76 | | | | | | | | | % 233.31/39.76 | | | | | | | | End of split % 233.31/39.76 | | | | | | | | % 233.31/39.76 | | | | | | | End of split % 233.31/39.76 | | | | | | | % 233.31/39.76 | | | | | | End of split % 233.31/39.76 | | | | | | % 233.31/39.76 | | | | | Case 2: % 233.31/39.76 | | | | | | % 233.31/39.76 | | | | | | (128) all_74_18 = n3 % 233.31/39.76 | | | | | | % 233.31/39.76 | | | | | | REDUCE: (74), (128) imply: % 233.31/39.76 | | | | | | (129) a_select3(id_ds1_filter, n3, n0) = all_74_16 % 233.31/39.76 | | | | | | % 233.31/39.76 | | | | | | REDUCE: (75), (128) imply: % 233.31/39.76 | | | | | | (130) a_select3(id_ds1_filter, n0, n3) = all_74_17 % 233.31/39.76 | | | | | | % 233.31/39.76 | | | | | | REDUCE: (4), (128) imply: % 233.31/39.76 | | | | | | (131) leq(n3, n5) % 233.31/39.76 | | | | | | % 233.31/39.76 | | | | | | REDUCE: (28), (128) imply: % 233.31/39.76 | | | | | | (132) leq(n0, n3) % 233.31/39.76 | | | | | | % 233.31/39.76 | | | | | | GROUND_INST: instantiating (29) with n0, n3, all_74_17, simplifying % 233.31/39.76 | | | | | | with (18), (76), (78), (130), (132) gives: % 233.31/39.76 | | | | | | (133) ~ leq(n3, all_74_21) | ~ leq(n0, all_74_21) | % 233.31/39.76 | | | | | | (a_select3(id_ds1_filter, n3, n0) = all_74_17 & % 233.31/39.76 | | | | | | $i(all_74_17)) % 233.31/39.76 | | | | | | % 233.31/39.76 | | | | | | BETA: splitting (133) gives: % 233.31/39.76 | | | | | | % 233.31/39.76 | | | | | | Case 1: % 233.31/39.76 | | | | | | | % 233.31/39.76 | | | | | | | (134) ~ leq(n0, all_74_21) % 233.31/39.76 | | | | | | | % 233.31/39.76 | | | | | | | REDUCE: (7), (134) imply: % 233.31/39.76 | | | | | | | (135) ~ leq(n0, n5) % 233.31/39.76 | | | | | | | % 233.31/39.76 | | | | | | | PRED_UNIFY: (77), (135) imply: % 233.31/39.76 | | | | | | | (136) $false % 233.31/39.76 | | | | | | | % 233.31/39.76 | | | | | | | CLOSE: (136) is inconsistent. % 233.31/39.76 | | | | | | | % 233.31/39.76 | | | | | | Case 2: % 233.31/39.76 | | | | | | | % 233.31/39.76 | | | | | | | (137) ~ leq(n3, all_74_21) | (a_select3(id_ds1_filter, n3, n0) % 233.31/39.76 | | | | | | | = all_74_17 & $i(all_74_17)) % 233.31/39.76 | | | | | | | % 233.31/39.76 | | | | | | | BETA: splitting (137) gives: % 233.31/39.76 | | | | | | | % 233.31/39.76 | | | | | | | Case 1: % 233.31/39.76 | | | | | | | | % 233.31/39.76 | | | | | | | | (138) ~ leq(n3, all_74_21) % 233.31/39.76 | | | | | | | | % 233.31/39.76 | | | | | | | | REDUCE: (7), (138) imply: % 233.31/39.76 | | | | | | | | (139) ~ leq(n3, n5) % 233.31/39.76 | | | | | | | | % 233.31/39.76 | | | | | | | | PRED_UNIFY: (131), (139) imply: % 233.31/39.76 | | | | | | | | (140) $false % 233.31/39.76 | | | | | | | | % 233.31/39.76 | | | | | | | | CLOSE: (140) is inconsistent. % 233.31/39.76 | | | | | | | | % 233.31/39.76 | | | | | | | Case 2: % 233.31/39.76 | | | | | | | | % 233.31/39.76 | | | | | | | | (141) a_select3(id_ds1_filter, n3, n0) = all_74_17 & % 233.31/39.76 | | | | | | | | $i(all_74_17) % 233.31/39.76 | | | | | | | | % 233.31/39.76 | | | | | | | | ALPHA: (141) implies: % 233.31/39.76 | | | | | | | | (142) a_select3(id_ds1_filter, n3, n0) = all_74_17 % 233.31/39.76 | | | | | | | | % 233.31/39.76 | | | | | | | | GROUND_INST: instantiating (14) with all_74_17, all_74_16, n0, % 233.31/39.76 | | | | | | | | n3, id_ds1_filter, simplifying with (129), (142) % 233.31/39.76 | | | | | | | | gives: % 233.31/39.76 | | | | | | | | (143) all_74_16 = all_74_17 % 233.31/39.76 | | | | | | | | % 233.31/39.76 | | | | | | | | REDUCE: (19), (143) imply: % 233.31/39.76 | | | | | | | | (144) $false % 233.31/39.76 | | | | | | | | % 233.31/39.76 | | | | | | | | CLOSE: (144) is inconsistent. % 233.31/39.76 | | | | | | | | % 233.31/39.76 | | | | | | | End of split % 233.31/39.76 | | | | | | | % 233.31/39.76 | | | | | | End of split % 233.31/39.76 | | | | | | % 233.31/39.76 | | | | | End of split % 233.31/39.76 | | | | | % 233.31/39.76 | | | | Case 2: % 233.31/39.76 | | | | | % 233.31/39.76 | | | | | (145) all_74_18 = n4 % 233.31/39.76 | | | | | % 233.31/39.76 | | | | | REDUCE: (74), (145) imply: % 233.31/39.76 | | | | | (146) a_select3(id_ds1_filter, n4, n0) = all_74_16 % 233.31/39.76 | | | | | % 233.31/39.76 | | | | | REDUCE: (75), (145) imply: % 233.31/39.76 | | | | | (147) a_select3(id_ds1_filter, n0, n4) = all_74_17 % 233.31/39.76 | | | | | % 233.31/39.76 | | | | | REDUCE: (4), (145) imply: % 233.31/39.76 | | | | | (148) leq(n4, n5) % 233.31/39.76 | | | | | % 233.31/39.76 | | | | | REDUCE: (28), (145) imply: % 233.31/39.76 | | | | | (149) leq(n0, n4) % 233.31/39.76 | | | | | % 233.31/39.76 | | | | | GROUND_INST: instantiating (29) with n0, n4, all_74_17, simplifying % 233.31/39.76 | | | | | with (22), (76), (78), (147), (149) gives: % 233.31/39.76 | | | | | (150) ~ leq(n4, all_74_21) | ~ leq(n0, all_74_21) | % 233.31/39.76 | | | | | (a_select3(id_ds1_filter, n4, n0) = all_74_17 & % 233.31/39.76 | | | | | $i(all_74_17)) % 233.31/39.76 | | | | | % 233.31/39.76 | | | | | BETA: splitting (150) gives: % 233.31/39.76 | | | | | % 233.31/39.76 | | | | | Case 1: % 233.31/39.76 | | | | | | % 233.31/39.76 | | | | | | (151) ~ leq(n0, all_74_21) % 233.31/39.76 | | | | | | % 233.31/39.76 | | | | | | REDUCE: (7), (151) imply: % 233.31/39.76 | | | | | | (152) ~ leq(n0, n5) % 233.31/39.76 | | | | | | % 233.31/39.76 | | | | | | PRED_UNIFY: (77), (152) imply: % 233.31/39.76 | | | | | | (153) $false % 233.31/39.76 | | | | | | % 233.31/39.76 | | | | | | CLOSE: (153) is inconsistent. % 233.31/39.76 | | | | | | % 233.31/39.76 | | | | | Case 2: % 233.31/39.76 | | | | | | % 233.31/39.76 | | | | | | (154) ~ leq(n4, all_74_21) | (a_select3(id_ds1_filter, n4, n0) = % 233.31/39.76 | | | | | | all_74_17 & $i(all_74_17)) % 233.31/39.76 | | | | | | % 233.31/39.76 | | | | | | BETA: splitting (154) gives: % 233.31/39.76 | | | | | | % 233.31/39.76 | | | | | | Case 1: % 233.31/39.76 | | | | | | | % 233.31/39.76 | | | | | | | (155) ~ leq(n4, all_74_21) % 233.31/39.76 | | | | | | | % 233.31/39.76 | | | | | | | REDUCE: (7), (155) imply: % 233.31/39.76 | | | | | | | (156) ~ leq(n4, n5) % 233.31/39.76 | | | | | | | % 233.31/39.76 | | | | | | | PRED_UNIFY: (148), (156) imply: % 233.31/39.76 | | | | | | | (157) $false % 233.31/39.76 | | | | | | | % 233.31/39.76 | | | | | | | CLOSE: (157) is inconsistent. % 233.31/39.76 | | | | | | | % 233.31/39.76 | | | | | | Case 2: % 233.31/39.76 | | | | | | | % 233.31/39.76 | | | | | | | (158) a_select3(id_ds1_filter, n4, n0) = all_74_17 & % 233.31/39.76 | | | | | | | $i(all_74_17) % 233.31/39.76 | | | | | | | % 233.31/39.76 | | | | | | | ALPHA: (158) implies: % 233.31/39.76 | | | | | | | (159) a_select3(id_ds1_filter, n4, n0) = all_74_17 % 233.31/39.76 | | | | | | | % 233.31/39.76 | | | | | | | REF_CLOSE: (14), (19), (146), (159) are inconsistent by sub-proof % 233.31/39.76 | | | | | | | #3. % 233.31/39.76 | | | | | | | % 233.31/39.76 | | | | | | End of split % 233.31/39.76 | | | | | | % 233.31/39.76 | | | | | End of split % 233.31/39.76 | | | | | % 233.31/39.76 | | | | End of split % 233.31/39.76 | | | | % 233.31/39.76 | | | End of split % 233.31/39.76 | | | % 233.31/39.76 | | Case 2: % 233.31/39.76 | | | % 233.31/39.76 | | | (160) all_74_18 = n5 % 233.31/39.76 | | | % 233.31/39.77 | | | REDUCE: (74), (160) imply: % 233.31/39.77 | | | (161) a_select3(id_ds1_filter, n5, n0) = all_74_16 % 233.31/39.77 | | | % 233.31/39.77 | | | REDUCE: (75), (160) imply: % 233.31/39.77 | | | (162) a_select3(id_ds1_filter, n0, n5) = all_74_17 % 233.31/39.77 | | | % 233.31/39.77 | | | REDUCE: (4), (160) imply: % 233.31/39.77 | | | (163) leq(n5, n5) % 233.31/39.77 | | | % 233.31/39.77 | | | GROUND_INST: instantiating (29) with n0, n5, all_74_17, simplifying with % 233.31/39.77 | | | (16), (76), (77), (78), (162) gives: % 233.31/39.77 | | | (164) ~ leq(n5, all_74_21) | ~ leq(n0, all_74_21) | % 233.31/39.77 | | | (a_select3(id_ds1_filter, n5, n0) = all_74_17 & $i(all_74_17)) % 233.31/39.77 | | | % 233.31/39.77 | | | BETA: splitting (164) gives: % 233.31/39.77 | | | % 233.31/39.77 | | | Case 1: % 233.31/39.77 | | | | % 233.31/39.77 | | | | (165) ~ leq(n0, all_74_21) % 233.31/39.77 | | | | % 233.31/39.77 | | | | REDUCE: (7), (165) imply: % 233.31/39.77 | | | | (166) ~ leq(n0, n5) % 233.31/39.77 | | | | % 233.31/39.77 | | | | PRED_UNIFY: (77), (166) imply: % 233.31/39.77 | | | | (167) $false % 233.31/39.77 | | | | % 233.31/39.77 | | | | CLOSE: (167) is inconsistent. % 233.31/39.77 | | | | % 233.31/39.77 | | | Case 2: % 233.31/39.77 | | | | % 233.31/39.77 | | | | (168) ~ leq(n5, all_74_21) | (a_select3(id_ds1_filter, n5, n0) = % 233.31/39.77 | | | | all_74_17 & $i(all_74_17)) % 233.31/39.77 | | | | % 233.31/39.77 | | | | BETA: splitting (168) gives: % 233.31/39.77 | | | | % 233.31/39.77 | | | | Case 1: % 233.31/39.77 | | | | | % 233.31/39.77 | | | | | (169) ~ leq(n5, all_74_21) % 233.31/39.77 | | | | | % 233.31/39.77 | | | | | REDUCE: (7), (169) imply: % 233.31/39.77 | | | | | (170) ~ leq(n5, n5) % 233.31/39.77 | | | | | % 233.31/39.77 | | | | | PRED_UNIFY: (163), (170) imply: % 233.31/39.77 | | | | | (171) $false % 233.31/39.77 | | | | | % 233.31/39.77 | | | | | CLOSE: (171) is inconsistent. % 233.31/39.77 | | | | | % 233.31/39.77 | | | | Case 2: % 233.31/39.77 | | | | | % 233.31/39.77 | | | | | (172) a_select3(id_ds1_filter, n5, n0) = all_74_17 & $i(all_74_17) % 233.31/39.77 | | | | | % 233.31/39.77 | | | | | ALPHA: (172) implies: % 233.31/39.77 | | | | | (173) a_select3(id_ds1_filter, n5, n0) = all_74_17 % 233.31/39.77 | | | | | % 233.31/39.77 | | | | | REF_CLOSE: (14), (19), (161), (173) are inconsistent by sub-proof #2. % 233.31/39.77 | | | | | % 233.31/39.77 | | | | End of split % 233.31/39.77 | | | | % 233.31/39.77 | | | End of split % 233.31/39.77 | | | % 233.31/39.77 | | End of split % 233.31/39.77 | | % 233.31/39.77 | End of split % 233.31/39.77 | % 233.31/39.77 End of proof % 233.31/39.77 % 233.31/39.77 Sub-proof #2 shows that the following formulas are inconsistent: % 233.31/39.77 ---------------------------------------------------------------- % 233.31/39.77 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 233.31/39.77 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 233.31/39.77 v0)) % 233.31/39.77 (2) a_select3(id_ds1_filter, n5, n0) = all_74_16 % 233.31/39.77 (3) a_select3(id_ds1_filter, n5, n0) = all_74_17 % 233.31/39.77 (4) ~ (all_74_16 = all_74_17) % 233.31/39.77 % 233.31/39.77 Begin of proof % 233.31/39.77 | % 233.31/39.77 | GROUND_INST: instantiating (1) with all_74_17, all_74_16, n0, n5, % 233.31/39.77 | id_ds1_filter, simplifying with (2), (3) gives: % 233.31/39.77 | (5) all_74_16 = all_74_17 % 233.31/39.77 | % 233.31/39.77 | REDUCE: (4), (5) imply: % 233.31/39.77 | (6) $false % 233.31/39.77 | % 233.31/39.77 | CLOSE: (6) is inconsistent. % 233.31/39.77 | % 233.31/39.77 End of proof % 233.31/39.77 % 233.31/39.77 Sub-proof #3 shows that the following formulas are inconsistent: % 233.31/39.77 ---------------------------------------------------------------- % 233.31/39.77 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 233.31/39.77 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 233.31/39.77 v0)) % 233.31/39.77 (2) a_select3(id_ds1_filter, n4, n0) = all_74_16 % 233.31/39.77 (3) a_select3(id_ds1_filter, n4, n0) = all_74_17 % 233.31/39.77 (4) ~ (all_74_16 = all_74_17) % 233.31/39.77 % 233.31/39.77 Begin of proof % 233.31/39.77 | % 233.31/39.77 | GROUND_INST: instantiating (1) with all_74_17, all_74_16, n0, n4, % 233.31/39.77 | id_ds1_filter, simplifying with (2), (3) gives: % 233.31/39.77 | (5) all_74_16 = all_74_17 % 233.31/39.77 | % 233.31/39.77 | REDUCE: (4), (5) imply: % 233.31/39.77 | (6) $false % 233.31/39.77 | % 233.31/39.77 | CLOSE: (6) is inconsistent. % 233.31/39.77 | % 233.31/39.77 End of proof % 233.31/39.77 % 233.31/39.77 Sub-proof #4 shows that the following formulas are inconsistent: % 233.31/39.77 ---------------------------------------------------------------- % 233.31/39.77 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 233.31/39.77 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 233.31/39.77 v0)) % 233.31/39.77 (2) a_select3(id_ds1_filter, n2, n0) = all_74_16 % 233.31/39.77 (3) a_select3(id_ds1_filter, n2, n0) = all_74_17 % 233.31/39.77 (4) ~ (all_74_16 = all_74_17) % 233.31/39.77 % 233.31/39.77 Begin of proof % 233.31/39.77 | % 233.31/39.77 | GROUND_INST: instantiating (1) with all_74_17, all_74_16, n0, n2, % 233.31/39.77 | id_ds1_filter, simplifying with (2), (3) gives: % 233.31/39.77 | (5) all_74_16 = all_74_17 % 233.31/39.77 | % 233.31/39.77 | REDUCE: (4), (5) imply: % 233.31/39.77 | (6) $false % 233.31/39.77 | % 233.31/39.77 | CLOSE: (6) is inconsistent. % 233.31/39.77 | % 233.31/39.77 End of proof % 233.31/39.77 % 233.31/39.77 Sub-proof #5 shows that the following formulas are inconsistent: % 233.31/39.77 ---------------------------------------------------------------- % 233.31/39.77 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 233.31/39.77 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 233.31/39.77 v0)) % 233.31/39.77 (2) a_select3(id_ds1_filter, n1, n0) = all_74_16 % 233.31/39.77 (3) a_select3(id_ds1_filter, n1, n0) = all_74_17 % 233.31/39.77 (4) ~ (all_74_16 = all_74_17) % 233.31/39.77 % 233.31/39.77 Begin of proof % 233.31/39.77 | % 233.31/39.77 | GROUND_INST: instantiating (1) with all_74_17, all_74_16, n0, n1, % 233.31/39.77 | id_ds1_filter, simplifying with (2), (3) gives: % 233.31/39.77 | (5) all_74_16 = all_74_17 % 233.31/39.77 | % 233.31/39.77 | REDUCE: (4), (5) imply: % 233.31/39.77 | (6) $false % 233.31/39.77 | % 233.31/39.77 | CLOSE: (6) is inconsistent. % 233.31/39.77 | % 233.31/39.77 End of proof % 233.31/39.77 % 233.31/39.77 Sub-proof #6 shows that the following formulas are inconsistent: % 233.31/39.77 ---------------------------------------------------------------- % 233.31/39.77 (1) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ leq(v0, % 233.31/39.77 v1) | gt(v1, v0)) % 233.31/39.77 (2) leq(all_74_18, n5) % 233.31/39.77 (3) all_74_21 = n5 % 233.31/39.77 (4) all_74_18 = n4 | gt(n4, all_74_18) % 233.31/39.77 (5) pred(n4) = n3 % 233.31/39.77 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (pred(v1) = v2) | ~ $i(v1) % 233.31/39.77 | ~ $i(v0) | ~ gt(v1, v0) | leq(v0, v2)) % 233.31/39.77 (7) $i(n2) % 233.31/39.77 (8) a_select3(id_ds1_filter, all_74_18, n5) = all_74_16 % 233.31/39.77 (9) a_select3(id_ds1_filter, n5, all_74_18) = all_74_17 % 233.31/39.77 (10) leq(n5, n5) % 233.31/39.77 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 233.31/39.77 (v1 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 233.31/39.77 v0)) % 233.31/39.77 (12) pred(n2) = n1 % 233.31/39.77 (13) $i(n5) % 233.31/39.77 (14) $i(all_74_18) % 233.31/39.77 (15) $i(n3) % 233.31/39.77 (16) ~ (all_74_16 = all_74_17) % 233.31/39.77 (17) leq(n0, n5) % 233.31/39.77 (18) pred(n3) = n2 % 233.31/39.77 (19) $i(n4) % 233.31/39.77 (20) ~ (all_74_18 = n0) % 233.31/39.77 (21) leq(n0, all_74_18) % 233.31/39.77 (22) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (a_select3(id_ds1_filter, % 233.31/39.77 v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ leq(v1, all_74_21) | ~ % 233.31/39.77 leq(v0, all_74_21) | ~ leq(n0, v1) | ~ leq(n0, v0) | % 233.31/39.77 (a_select3(id_ds1_filter, v1, v0) = v2 & $i(v2))) % 233.31/39.77 (23) ! [v0: $i] : (v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0, n1) | ~ % 233.31/39.77 leq(n0, v0)) % 233.31/39.77 % 233.31/39.77 Begin of proof % 233.31/39.77 | % 233.31/39.77 | BETA: splitting (4) gives: % 233.31/39.77 | % 233.31/39.77 | Case 1: % 233.31/39.77 | | % 233.31/39.77 | | (24) gt(n4, all_74_18) % 233.31/39.77 | | % 233.31/39.77 | | GROUND_INST: instantiating (6) with all_74_18, n4, n3, simplifying with (5), % 233.31/39.77 | | (14), (19), (24) gives: % 233.31/39.77 | | (25) leq(all_74_18, n3) % 233.31/39.77 | | % 233.48/39.77 | | GROUND_INST: instantiating (1) with all_74_18, n3, simplifying with (14), % 233.48/39.77 | | (15), (25) gives: % 233.48/39.77 | | (26) all_74_18 = n3 | gt(n3, all_74_18) % 233.48/39.77 | | % 233.48/39.77 | | BETA: splitting (26) gives: % 233.48/39.77 | | % 233.48/39.77 | | Case 1: % 233.48/39.77 | | | % 233.48/39.77 | | | (27) gt(n3, all_74_18) % 233.48/39.77 | | | % 233.48/39.77 | | | GROUND_INST: instantiating (6) with all_74_18, n3, n2, simplifying with % 233.48/39.77 | | | (14), (15), (18), (27) gives: % 233.48/39.77 | | | (28) leq(all_74_18, n2) % 233.48/39.77 | | | % 233.48/39.77 | | | GROUND_INST: instantiating (1) with all_74_18, n2, simplifying with (7), % 233.48/39.77 | | | (14), (28) gives: % 233.48/39.77 | | | (29) all_74_18 = n2 | gt(n2, all_74_18) % 233.48/39.77 | | | % 233.48/39.77 | | | BETA: splitting (29) gives: % 233.48/39.77 | | | % 233.48/39.77 | | | Case 1: % 233.48/39.77 | | | | % 233.48/39.77 | | | | (30) gt(n2, all_74_18) % 233.48/39.77 | | | | % 233.48/39.77 | | | | GROUND_INST: instantiating (6) with all_74_18, n2, n1, simplifying with % 233.48/39.77 | | | | (7), (12), (14), (30) gives: % 233.48/39.77 | | | | (31) leq(all_74_18, n1) % 233.48/39.77 | | | | % 233.48/39.77 | | | | GROUND_INST: instantiating (23) with all_74_18, simplifying with (14), % 233.48/39.77 | | | | (21), (31) gives: % 233.48/39.77 | | | | (32) all_74_18 = n1 | all_74_18 = n0 % 233.48/39.77 | | | | % 233.48/39.77 | | | | BETA: splitting (32) gives: % 233.48/39.77 | | | | % 233.48/39.77 | | | | Case 1: % 233.48/39.77 | | | | | % 233.48/39.77 | | | | | (33) all_74_18 = n0 % 233.48/39.77 | | | | | % 233.48/39.77 | | | | | REDUCE: (20), (33) imply: % 233.48/39.77 | | | | | (34) $false % 233.48/39.77 | | | | | % 233.48/39.77 | | | | | CLOSE: (34) is inconsistent. % 233.48/39.77 | | | | | % 233.48/39.77 | | | | Case 2: % 233.48/39.77 | | | | | % 233.48/39.77 | | | | | (35) all_74_18 = n1 % 233.48/39.77 | | | | | % 233.48/39.77 | | | | | REDUCE: (8), (35) imply: % 233.48/39.77 | | | | | (36) a_select3(id_ds1_filter, n1, n5) = all_74_16 % 233.48/39.77 | | | | | % 233.48/39.77 | | | | | REDUCE: (9), (35) imply: % 233.48/39.78 | | | | | (37) a_select3(id_ds1_filter, n5, n1) = all_74_17 % 233.48/39.78 | | | | | % 233.48/39.78 | | | | | REDUCE: (14), (35) imply: % 233.48/39.78 | | | | | (38) $i(n1) % 233.48/39.78 | | | | | % 233.48/39.78 | | | | | REDUCE: (2), (35) imply: % 233.48/39.78 | | | | | (39) leq(n1, n5) % 233.48/39.78 | | | | | % 233.48/39.78 | | | | | REDUCE: (21), (35) imply: % 233.48/39.78 | | | | | (40) leq(n0, n1) % 233.48/39.78 | | | | | % 233.48/39.78 | | | | | GROUND_INST: instantiating (22) with n1, n5, all_74_16, simplifying % 233.48/39.78 | | | | | with (13), (17), (36), (38), (40) gives: % 233.48/39.78 | | | | | (41) ~ leq(n5, all_74_21) | ~ leq(n1, all_74_21) | % 233.48/39.78 | | | | | (a_select3(id_ds1_filter, n5, n1) = all_74_16 & $i(all_74_16)) % 233.48/39.78 | | | | | % 233.48/39.78 | | | | | BETA: splitting (41) gives: % 233.48/39.78 | | | | | % 233.48/39.78 | | | | | Case 1: % 233.48/39.78 | | | | | | % 233.48/39.78 | | | | | | (42) ~ leq(n5, all_74_21) % 233.48/39.78 | | | | | | % 233.48/39.78 | | | | | | REDUCE: (3), (42) imply: % 233.48/39.78 | | | | | | (43) ~ leq(n5, n5) % 233.48/39.78 | | | | | | % 233.48/39.78 | | | | | | PRED_UNIFY: (10), (43) imply: % 233.48/39.78 | | | | | | (44) $false % 233.48/39.78 | | | | | | % 233.48/39.78 | | | | | | CLOSE: (44) is inconsistent. % 233.48/39.78 | | | | | | % 233.48/39.78 | | | | | Case 2: % 233.48/39.78 | | | | | | % 233.48/39.78 | | | | | | (45) ~ leq(n1, all_74_21) | (a_select3(id_ds1_filter, n5, n1) = % 233.48/39.78 | | | | | | all_74_16 & $i(all_74_16)) % 233.48/39.78 | | | | | | % 233.48/39.78 | | | | | | BETA: splitting (45) gives: % 233.48/39.78 | | | | | | % 233.48/39.78 | | | | | | Case 1: % 233.48/39.78 | | | | | | | % 233.48/39.78 | | | | | | | (46) ~ leq(n1, all_74_21) % 233.48/39.78 | | | | | | | % 233.48/39.78 | | | | | | | REDUCE: (3), (46) imply: % 233.48/39.78 | | | | | | | (47) ~ leq(n1, n5) % 233.48/39.78 | | | | | | | % 233.48/39.78 | | | | | | | PRED_UNIFY: (39), (47) imply: % 233.48/39.78 | | | | | | | (48) $false % 233.48/39.78 | | | | | | | % 233.48/39.78 | | | | | | | CLOSE: (48) is inconsistent. % 233.48/39.78 | | | | | | | % 233.48/39.78 | | | | | | Case 2: % 233.48/39.78 | | | | | | | % 233.48/39.78 | | | | | | | (49) a_select3(id_ds1_filter, n5, n1) = all_74_16 & % 233.48/39.78 | | | | | | | $i(all_74_16) % 233.48/39.78 | | | | | | | % 233.48/39.78 | | | | | | | ALPHA: (49) implies: % 233.48/39.78 | | | | | | | (50) a_select3(id_ds1_filter, n5, n1) = all_74_16 % 233.48/39.78 | | | | | | | % 233.48/39.78 | | | | | | | GROUND_INST: instantiating (11) with all_74_17, all_74_16, n1, n5, % 233.48/39.78 | | | | | | | id_ds1_filter, simplifying with (37), (50) gives: % 233.48/39.78 | | | | | | | (51) all_74_16 = all_74_17 % 233.48/39.78 | | | | | | | % 233.48/39.78 | | | | | | | REDUCE: (16), (51) imply: % 233.48/39.78 | | | | | | | (52) $false % 233.48/39.78 | | | | | | | % 233.48/39.78 | | | | | | | CLOSE: (52) is inconsistent. % 233.48/39.78 | | | | | | | % 233.48/39.78 | | | | | | End of split % 233.48/39.78 | | | | | | % 233.48/39.78 | | | | | End of split % 233.48/39.78 | | | | | % 233.48/39.78 | | | | End of split % 233.48/39.78 | | | | % 233.48/39.78 | | | Case 2: % 233.48/39.78 | | | | % 233.48/39.78 | | | | (53) all_74_18 = n2 % 233.48/39.78 | | | | % 233.48/39.78 | | | | REDUCE: (8), (53) imply: % 233.48/39.78 | | | | (54) a_select3(id_ds1_filter, n2, n5) = all_74_16 % 233.48/39.78 | | | | % 233.48/39.78 | | | | REDUCE: (9), (53) imply: % 233.48/39.78 | | | | (55) a_select3(id_ds1_filter, n5, n2) = all_74_17 % 233.48/39.78 | | | | % 233.48/39.78 | | | | REDUCE: (2), (53) imply: % 233.48/39.78 | | | | (56) leq(n2, n5) % 233.48/39.78 | | | | % 233.48/39.78 | | | | REDUCE: (21), (53) imply: % 233.48/39.78 | | | | (57) leq(n0, n2) % 233.48/39.78 | | | | % 233.48/39.78 | | | | GROUND_INST: instantiating (22) with n2, n5, all_74_16, simplifying with % 233.48/39.78 | | | | (7), (13), (17), (54), (57) gives: % 233.48/39.78 | | | | (58) ~ leq(n5, all_74_21) | ~ leq(n2, all_74_21) | % 233.48/39.78 | | | | (a_select3(id_ds1_filter, n5, n2) = all_74_16 & $i(all_74_16)) % 233.48/39.78 | | | | % 233.48/39.78 | | | | BETA: splitting (58) gives: % 233.48/39.78 | | | | % 233.48/39.78 | | | | Case 1: % 233.48/39.78 | | | | | % 233.48/39.78 | | | | | (59) ~ leq(n5, all_74_21) % 233.48/39.78 | | | | | % 233.48/39.78 | | | | | REDUCE: (3), (59) imply: % 233.48/39.78 | | | | | (60) ~ leq(n5, n5) % 233.48/39.78 | | | | | % 233.48/39.78 | | | | | PRED_UNIFY: (10), (60) imply: % 233.48/39.78 | | | | | (61) $false % 233.48/39.78 | | | | | % 233.48/39.78 | | | | | CLOSE: (61) is inconsistent. % 233.48/39.78 | | | | | % 233.48/39.78 | | | | Case 2: % 233.48/39.78 | | | | | % 233.48/39.78 | | | | | (62) ~ leq(n2, all_74_21) | (a_select3(id_ds1_filter, n5, n2) = % 233.48/39.78 | | | | | all_74_16 & $i(all_74_16)) % 233.48/39.78 | | | | | % 233.48/39.78 | | | | | BETA: splitting (62) gives: % 233.48/39.78 | | | | | % 233.48/39.78 | | | | | Case 1: % 233.48/39.78 | | | | | | % 233.48/39.78 | | | | | | (63) ~ leq(n2, all_74_21) % 233.48/39.78 | | | | | | % 233.48/39.78 | | | | | | REDUCE: (3), (63) imply: % 233.48/39.78 | | | | | | (64) ~ leq(n2, n5) % 233.48/39.78 | | | | | | % 233.48/39.78 | | | | | | PRED_UNIFY: (56), (64) imply: % 233.48/39.78 | | | | | | (65) $false % 233.48/39.78 | | | | | | % 233.48/39.78 | | | | | | CLOSE: (65) is inconsistent. % 233.48/39.78 | | | | | | % 233.48/39.78 | | | | | Case 2: % 233.48/39.78 | | | | | | % 233.48/39.78 | | | | | | (66) a_select3(id_ds1_filter, n5, n2) = all_74_16 & $i(all_74_16) % 233.48/39.78 | | | | | | % 233.48/39.78 | | | | | | ALPHA: (66) implies: % 233.48/39.78 | | | | | | (67) a_select3(id_ds1_filter, n5, n2) = all_74_16 % 233.48/39.78 | | | | | | % 233.48/39.78 | | | | | | GROUND_INST: instantiating (11) with all_74_17, all_74_16, n2, n5, % 233.48/39.78 | | | | | | id_ds1_filter, simplifying with (55), (67) gives: % 233.48/39.78 | | | | | | (68) all_74_16 = all_74_17 % 233.48/39.78 | | | | | | % 233.48/39.78 | | | | | | REDUCE: (16), (68) imply: % 233.48/39.78 | | | | | | (69) $false % 233.48/39.78 | | | | | | % 233.48/39.78 | | | | | | CLOSE: (69) is inconsistent. % 233.48/39.78 | | | | | | % 233.48/39.78 | | | | | End of split % 233.48/39.78 | | | | | % 233.48/39.78 | | | | End of split % 233.48/39.78 | | | | % 233.48/39.78 | | | End of split % 233.48/39.78 | | | % 233.48/39.78 | | Case 2: % 233.48/39.78 | | | % 233.48/39.78 | | | (70) all_74_18 = n3 % 233.48/39.78 | | | % 233.48/39.78 | | | REDUCE: (8), (70) imply: % 233.48/39.78 | | | (71) a_select3(id_ds1_filter, n3, n5) = all_74_16 % 233.48/39.78 | | | % 233.48/39.78 | | | REDUCE: (9), (70) imply: % 233.48/39.78 | | | (72) a_select3(id_ds1_filter, n5, n3) = all_74_17 % 233.48/39.78 | | | % 233.48/39.78 | | | REDUCE: (2), (70) imply: % 233.48/39.78 | | | (73) leq(n3, n5) % 233.48/39.78 | | | % 233.48/39.78 | | | REDUCE: (21), (70) imply: % 233.48/39.78 | | | (74) leq(n0, n3) % 233.48/39.78 | | | % 233.48/39.78 | | | GROUND_INST: instantiating (22) with n3, n5, all_74_16, simplifying with % 233.48/39.78 | | | (13), (15), (17), (71), (74) gives: % 233.48/39.78 | | | (75) ~ leq(n5, all_74_21) | ~ leq(n3, all_74_21) | % 233.48/39.78 | | | (a_select3(id_ds1_filter, n5, n3) = all_74_16 & $i(all_74_16)) % 233.48/39.78 | | | % 233.48/39.78 | | | BETA: splitting (75) gives: % 233.48/39.78 | | | % 233.48/39.78 | | | Case 1: % 233.48/39.78 | | | | % 233.48/39.78 | | | | (76) ~ leq(n5, all_74_21) % 233.48/39.78 | | | | % 233.48/39.78 | | | | REDUCE: (3), (76) imply: % 233.48/39.78 | | | | (77) ~ leq(n5, n5) % 233.48/39.78 | | | | % 233.48/39.78 | | | | PRED_UNIFY: (10), (77) imply: % 233.48/39.78 | | | | (78) $false % 233.48/39.78 | | | | % 233.48/39.78 | | | | CLOSE: (78) is inconsistent. % 233.48/39.78 | | | | % 233.48/39.78 | | | Case 2: % 233.48/39.78 | | | | % 233.48/39.78 | | | | (79) ~ leq(n3, all_74_21) | (a_select3(id_ds1_filter, n5, n3) = % 233.48/39.78 | | | | all_74_16 & $i(all_74_16)) % 233.48/39.78 | | | | % 233.48/39.78 | | | | BETA: splitting (79) gives: % 233.48/39.78 | | | | % 233.48/39.78 | | | | Case 1: % 233.48/39.78 | | | | | % 233.48/39.78 | | | | | (80) ~ leq(n3, all_74_21) % 233.48/39.78 | | | | | % 233.48/39.78 | | | | | REDUCE: (3), (80) imply: % 233.48/39.78 | | | | | (81) ~ leq(n3, n5) % 233.48/39.78 | | | | | % 233.48/39.78 | | | | | PRED_UNIFY: (73), (81) imply: % 233.48/39.78 | | | | | (82) $false % 233.48/39.78 | | | | | % 233.48/39.78 | | | | | CLOSE: (82) is inconsistent. % 233.48/39.78 | | | | | % 233.48/39.78 | | | | Case 2: % 233.48/39.78 | | | | | % 233.48/39.78 | | | | | (83) a_select3(id_ds1_filter, n5, n3) = all_74_16 & $i(all_74_16) % 233.48/39.78 | | | | | % 233.48/39.78 | | | | | ALPHA: (83) implies: % 233.48/39.78 | | | | | (84) a_select3(id_ds1_filter, n5, n3) = all_74_16 % 233.48/39.78 | | | | | % 233.48/39.78 | | | | | GROUND_INST: instantiating (11) with all_74_17, all_74_16, n3, n5, % 233.48/39.78 | | | | | id_ds1_filter, simplifying with (72), (84) gives: % 233.48/39.78 | | | | | (85) all_74_16 = all_74_17 % 233.48/39.78 | | | | | % 233.48/39.78 | | | | | REDUCE: (16), (85) imply: % 233.48/39.78 | | | | | (86) $false % 233.48/39.78 | | | | | % 233.48/39.78 | | | | | CLOSE: (86) is inconsistent. % 233.48/39.78 | | | | | % 233.48/39.78 | | | | End of split % 233.48/39.78 | | | | % 233.48/39.78 | | | End of split % 233.48/39.78 | | | % 233.48/39.78 | | End of split % 233.48/39.78 | | % 233.48/39.78 | Case 2: % 233.48/39.78 | | % 233.48/39.78 | | (87) all_74_18 = n4 % 233.48/39.78 | | % 233.48/39.78 | | REDUCE: (8), (87) imply: % 233.48/39.78 | | (88) a_select3(id_ds1_filter, n4, n5) = all_74_16 % 233.48/39.78 | | % 233.48/39.78 | | REDUCE: (9), (87) imply: % 233.48/39.78 | | (89) a_select3(id_ds1_filter, n5, n4) = all_74_17 % 233.48/39.78 | | % 233.48/39.78 | | REDUCE: (2), (87) imply: % 233.48/39.78 | | (90) leq(n4, n5) % 233.48/39.78 | | % 233.48/39.78 | | REDUCE: (21), (87) imply: % 233.48/39.78 | | (91) leq(n0, n4) % 233.48/39.78 | | % 233.48/39.78 | | GROUND_INST: instantiating (22) with n4, n5, all_74_16, simplifying with % 233.48/39.78 | | (13), (17), (19), (88), (91) gives: % 233.48/39.78 | | (92) ~ leq(n5, all_74_21) | ~ leq(n4, all_74_21) | % 233.48/39.78 | | (a_select3(id_ds1_filter, n5, n4) = all_74_16 & $i(all_74_16)) % 233.48/39.78 | | % 233.48/39.78 | | BETA: splitting (92) gives: % 233.48/39.78 | | % 233.48/39.78 | | Case 1: % 233.48/39.78 | | | % 233.48/39.78 | | | (93) ~ leq(n5, all_74_21) % 233.48/39.78 | | | % 233.48/39.78 | | | REDUCE: (3), (93) imply: % 233.48/39.78 | | | (94) ~ leq(n5, n5) % 233.48/39.78 | | | % 233.48/39.78 | | | PRED_UNIFY: (10), (94) imply: % 233.48/39.78 | | | (95) $false % 233.48/39.78 | | | % 233.48/39.78 | | | CLOSE: (95) is inconsistent. % 233.48/39.78 | | | % 233.48/39.78 | | Case 2: % 233.48/39.78 | | | % 233.48/39.78 | | | (96) ~ leq(n4, all_74_21) | (a_select3(id_ds1_filter, n5, n4) = % 233.48/39.78 | | | all_74_16 & $i(all_74_16)) % 233.48/39.78 | | | % 233.48/39.78 | | | BETA: splitting (96) gives: % 233.48/39.78 | | | % 233.48/39.78 | | | Case 1: % 233.48/39.78 | | | | % 233.48/39.78 | | | | (97) ~ leq(n4, all_74_21) % 233.48/39.78 | | | | % 233.48/39.78 | | | | REDUCE: (3), (97) imply: % 233.48/39.78 | | | | (98) ~ leq(n4, n5) % 233.48/39.78 | | | | % 233.48/39.78 | | | | PRED_UNIFY: (90), (98) imply: % 233.48/39.78 | | | | (99) $false % 233.48/39.78 | | | | % 233.48/39.78 | | | | CLOSE: (99) is inconsistent. % 233.48/39.78 | | | | % 233.48/39.78 | | | Case 2: % 233.48/39.78 | | | | % 233.48/39.78 | | | | (100) a_select3(id_ds1_filter, n5, n4) = all_74_16 & $i(all_74_16) % 233.48/39.78 | | | | % 233.48/39.78 | | | | ALPHA: (100) implies: % 233.48/39.78 | | | | (101) a_select3(id_ds1_filter, n5, n4) = all_74_16 % 233.48/39.78 | | | | % 233.48/39.78 | | | | REF_CLOSE: (11), (16), (89), (101) are inconsistent by sub-proof #8. % 233.48/39.78 | | | | % 233.48/39.78 | | | End of split % 233.48/39.78 | | | % 233.48/39.78 | | End of split % 233.48/39.78 | | % 233.48/39.78 | End of split % 233.48/39.78 | % 233.48/39.78 End of proof % 233.48/39.78 % 233.48/39.78 Sub-proof #7 shows that the following formulas are inconsistent: % 233.48/39.78 ---------------------------------------------------------------- % 233.48/39.78 (1) $i(all_74_19) % 233.48/39.78 (2) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ leq(v0, % 233.48/39.78 v1) | gt(v1, v0)) % 233.48/39.78 (3) all_74_21 = n5 % 233.48/39.78 (4) pred(n4) = n3 % 233.48/39.78 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (pred(v1) = v2) | ~ $i(v1) % 233.48/39.78 | ~ $i(v0) | ~ gt(v1, v0) | leq(v0, v2)) % 233.48/39.78 (6) a_select3(id_ds1_filter, all_74_19, n5) = all_74_17 % 233.48/39.78 (7) $i(n2) % 233.48/39.78 (8) leq(n5, n5) % 233.48/39.78 (9) all_74_19 = n4 | gt(n4, all_74_19) % 233.48/39.78 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 233.48/39.78 (v1 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 233.48/39.78 v0)) % 233.48/39.78 (11) a_select3(id_ds1_filter, n5, all_74_19) = all_74_16 % 233.48/39.78 (12) pred(n2) = n1 % 233.48/39.78 (13) $i(n5) % 233.48/39.78 (14) ~ (all_74_19 = n0) % 233.48/39.79 (15) $i(n3) % 233.48/39.79 (16) ~ (all_74_16 = all_74_17) % 233.48/39.79 (17) leq(n0, n5) % 233.48/39.79 (18) pred(n3) = n2 % 233.48/39.79 (19) $i(n4) % 233.48/39.79 (20) leq(all_74_19, n5) % 233.48/39.79 (21) leq(n0, all_74_19) % 233.48/39.79 (22) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (a_select3(id_ds1_filter, % 233.48/39.79 v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ leq(v1, all_74_21) | ~ % 233.48/39.79 leq(v0, all_74_21) | ~ leq(n0, v1) | ~ leq(n0, v0) | % 233.48/39.79 (a_select3(id_ds1_filter, v1, v0) = v2 & $i(v2))) % 233.48/39.79 (23) ! [v0: $i] : (v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0, n1) | ~ % 233.48/39.79 leq(n0, v0)) % 233.48/39.79 % 233.48/39.79 Begin of proof % 233.48/39.79 | % 233.48/39.79 | BETA: splitting (9) gives: % 233.48/39.79 | % 233.48/39.79 | Case 1: % 233.48/39.79 | | % 233.48/39.79 | | (24) gt(n4, all_74_19) % 233.48/39.79 | | % 233.48/39.79 | | GROUND_INST: instantiating (5) with all_74_19, n4, n3, simplifying with (1), % 233.48/39.79 | | (4), (19), (24) gives: % 233.48/39.79 | | (25) leq(all_74_19, n3) % 233.48/39.79 | | % 233.48/39.79 | | GROUND_INST: instantiating (2) with all_74_19, n3, simplifying with (1), % 233.48/39.79 | | (15), (25) gives: % 233.48/39.79 | | (26) all_74_19 = n3 | gt(n3, all_74_19) % 233.48/39.79 | | % 233.48/39.79 | | BETA: splitting (26) gives: % 233.48/39.79 | | % 233.48/39.79 | | Case 1: % 233.48/39.79 | | | % 233.48/39.79 | | | (27) gt(n3, all_74_19) % 233.48/39.79 | | | % 233.48/39.79 | | | GROUND_INST: instantiating (5) with all_74_19, n3, n2, simplifying with % 233.48/39.79 | | | (1), (15), (18), (27) gives: % 233.48/39.79 | | | (28) leq(all_74_19, n2) % 233.48/39.79 | | | % 233.48/39.79 | | | GROUND_INST: instantiating (2) with all_74_19, n2, simplifying with (1), % 233.48/39.79 | | | (7), (28) gives: % 233.48/39.79 | | | (29) all_74_19 = n2 | gt(n2, all_74_19) % 233.48/39.79 | | | % 233.48/39.79 | | | BETA: splitting (29) gives: % 233.48/39.79 | | | % 233.48/39.79 | | | Case 1: % 233.48/39.79 | | | | % 233.48/39.79 | | | | (30) gt(n2, all_74_19) % 233.48/39.79 | | | | % 233.48/39.79 | | | | GROUND_INST: instantiating (5) with all_74_19, n2, n1, simplifying with % 233.48/39.79 | | | | (1), (7), (12), (30) gives: % 233.48/39.79 | | | | (31) leq(all_74_19, n1) % 233.48/39.79 | | | | % 233.48/39.79 | | | | GROUND_INST: instantiating (23) with all_74_19, simplifying with (1), % 233.48/39.79 | | | | (21), (31) gives: % 233.48/39.79 | | | | (32) all_74_19 = n1 | all_74_19 = n0 % 233.48/39.79 | | | | % 233.48/39.79 | | | | BETA: splitting (32) gives: % 233.48/39.79 | | | | % 233.48/39.79 | | | | Case 1: % 233.48/39.79 | | | | | % 233.48/39.79 | | | | | (33) all_74_19 = n0 % 233.48/39.79 | | | | | % 233.48/39.79 | | | | | REDUCE: (14), (33) imply: % 233.48/39.79 | | | | | (34) $false % 233.48/39.79 | | | | | % 233.48/39.79 | | | | | CLOSE: (34) is inconsistent. % 233.48/39.79 | | | | | % 233.48/39.79 | | | | Case 2: % 233.48/39.79 | | | | | % 233.48/39.79 | | | | | (35) all_74_19 = n1 % 233.48/39.79 | | | | | % 233.48/39.79 | | | | | REDUCE: (6), (35) imply: % 233.48/39.79 | | | | | (36) a_select3(id_ds1_filter, n1, n5) = all_74_17 % 233.48/39.79 | | | | | % 233.48/39.79 | | | | | REDUCE: (11), (35) imply: % 233.48/39.79 | | | | | (37) a_select3(id_ds1_filter, n5, n1) = all_74_16 % 233.48/39.79 | | | | | % 233.48/39.79 | | | | | REDUCE: (1), (35) imply: % 233.48/39.79 | | | | | (38) $i(n1) % 233.48/39.79 | | | | | % 233.48/39.79 | | | | | REDUCE: (20), (35) imply: % 233.48/39.79 | | | | | (39) leq(n1, n5) % 233.48/39.79 | | | | | % 233.48/39.79 | | | | | REDUCE: (21), (35) imply: % 233.48/39.79 | | | | | (40) leq(n0, n1) % 233.48/39.79 | | | | | % 233.48/39.79 | | | | | GROUND_INST: instantiating (22) with n1, n5, all_74_17, simplifying % 233.48/39.79 | | | | | with (13), (17), (36), (38), (40) gives: % 233.48/39.79 | | | | | (41) ~ leq(n5, all_74_21) | ~ leq(n1, all_74_21) | % 233.48/39.79 | | | | | (a_select3(id_ds1_filter, n5, n1) = all_74_17 & $i(all_74_17)) % 233.48/39.79 | | | | | % 233.48/39.79 | | | | | BETA: splitting (41) gives: % 233.48/39.79 | | | | | % 233.48/39.79 | | | | | Case 1: % 233.48/39.79 | | | | | | % 233.48/39.79 | | | | | | (42) ~ leq(n5, all_74_21) % 233.48/39.79 | | | | | | % 233.48/39.79 | | | | | | REDUCE: (3), (42) imply: % 233.48/39.79 | | | | | | (43) ~ leq(n5, n5) % 233.48/39.79 | | | | | | % 233.48/39.79 | | | | | | PRED_UNIFY: (8), (43) imply: % 233.48/39.79 | | | | | | (44) $false % 233.48/39.79 | | | | | | % 233.48/39.79 | | | | | | CLOSE: (44) is inconsistent. % 233.48/39.79 | | | | | | % 233.48/39.79 | | | | | Case 2: % 233.48/39.79 | | | | | | % 233.48/39.79 | | | | | | (45) ~ leq(n1, all_74_21) | (a_select3(id_ds1_filter, n5, n1) = % 233.48/39.79 | | | | | | all_74_17 & $i(all_74_17)) % 233.48/39.79 | | | | | | % 233.48/39.79 | | | | | | BETA: splitting (45) gives: % 233.48/39.79 | | | | | | % 233.48/39.79 | | | | | | Case 1: % 233.48/39.79 | | | | | | | % 233.48/39.79 | | | | | | | (46) ~ leq(n1, all_74_21) % 233.48/39.79 | | | | | | | % 233.48/39.79 | | | | | | | REDUCE: (3), (46) imply: % 233.48/39.79 | | | | | | | (47) ~ leq(n1, n5) % 233.48/39.79 | | | | | | | % 233.48/39.79 | | | | | | | PRED_UNIFY: (39), (47) imply: % 233.48/39.79 | | | | | | | (48) $false % 233.48/39.79 | | | | | | | % 233.48/39.79 | | | | | | | CLOSE: (48) is inconsistent. % 233.48/39.79 | | | | | | | % 233.48/39.79 | | | | | | Case 2: % 233.48/39.79 | | | | | | | % 233.48/39.79 | | | | | | | (49) a_select3(id_ds1_filter, n5, n1) = all_74_17 & % 233.48/39.79 | | | | | | | $i(all_74_17) % 233.48/39.79 | | | | | | | % 233.48/39.79 | | | | | | | ALPHA: (49) implies: % 233.48/39.79 | | | | | | | (50) a_select3(id_ds1_filter, n5, n1) = all_74_17 % 233.48/39.79 | | | | | | | % 233.48/39.79 | | | | | | | GROUND_INST: instantiating (10) with all_74_17, all_74_16, n1, n5, % 233.48/39.79 | | | | | | | id_ds1_filter, simplifying with (37), (50) gives: % 233.48/39.79 | | | | | | | (51) all_74_16 = all_74_17 % 233.48/39.79 | | | | | | | % 233.48/39.79 | | | | | | | REDUCE: (16), (51) imply: % 233.48/39.79 | | | | | | | (52) $false % 233.48/39.79 | | | | | | | % 233.48/39.79 | | | | | | | CLOSE: (52) is inconsistent. % 233.48/39.79 | | | | | | | % 233.48/39.79 | | | | | | End of split % 233.48/39.79 | | | | | | % 233.48/39.79 | | | | | End of split % 233.48/39.79 | | | | | % 233.48/39.79 | | | | End of split % 233.48/39.79 | | | | % 233.48/39.79 | | | Case 2: % 233.48/39.79 | | | | % 233.48/39.79 | | | | (53) all_74_19 = n2 % 233.48/39.79 | | | | % 233.48/39.79 | | | | REDUCE: (6), (53) imply: % 233.48/39.79 | | | | (54) a_select3(id_ds1_filter, n2, n5) = all_74_17 % 233.48/39.79 | | | | % 233.48/39.79 | | | | REDUCE: (11), (53) imply: % 233.48/39.79 | | | | (55) a_select3(id_ds1_filter, n5, n2) = all_74_16 % 233.48/39.79 | | | | % 233.48/39.79 | | | | REDUCE: (20), (53) imply: % 233.48/39.79 | | | | (56) leq(n2, n5) % 233.48/39.79 | | | | % 233.48/39.79 | | | | REDUCE: (21), (53) imply: % 233.48/39.79 | | | | (57) leq(n0, n2) % 233.48/39.79 | | | | % 233.48/39.79 | | | | GROUND_INST: instantiating (22) with n2, n5, all_74_17, simplifying with % 233.48/39.79 | | | | (7), (13), (17), (54), (57) gives: % 233.48/39.79 | | | | (58) ~ leq(n5, all_74_21) | ~ leq(n2, all_74_21) | % 233.48/39.79 | | | | (a_select3(id_ds1_filter, n5, n2) = all_74_17 & $i(all_74_17)) % 233.48/39.79 | | | | % 233.48/39.79 | | | | BETA: splitting (58) gives: % 233.48/39.79 | | | | % 233.48/39.79 | | | | Case 1: % 233.48/39.79 | | | | | % 233.48/39.79 | | | | | (59) ~ leq(n5, all_74_21) % 233.48/39.79 | | | | | % 233.48/39.79 | | | | | REDUCE: (3), (59) imply: % 233.48/39.79 | | | | | (60) ~ leq(n5, n5) % 233.48/39.79 | | | | | % 233.48/39.79 | | | | | PRED_UNIFY: (8), (60) imply: % 233.48/39.79 | | | | | (61) $false % 233.48/39.79 | | | | | % 233.48/39.79 | | | | | CLOSE: (61) is inconsistent. % 233.48/39.79 | | | | | % 233.48/39.79 | | | | Case 2: % 233.48/39.79 | | | | | % 233.48/39.79 | | | | | (62) ~ leq(n2, all_74_21) | (a_select3(id_ds1_filter, n5, n2) = % 233.48/39.79 | | | | | all_74_17 & $i(all_74_17)) % 233.48/39.79 | | | | | % 233.48/39.79 | | | | | BETA: splitting (62) gives: % 233.48/39.79 | | | | | % 233.48/39.79 | | | | | Case 1: % 233.48/39.79 | | | | | | % 233.48/39.79 | | | | | | (63) ~ leq(n2, all_74_21) % 233.48/39.79 | | | | | | % 233.48/39.79 | | | | | | REDUCE: (3), (63) imply: % 233.48/39.79 | | | | | | (64) ~ leq(n2, n5) % 233.48/39.79 | | | | | | % 233.48/39.79 | | | | | | PRED_UNIFY: (56), (64) imply: % 233.48/39.79 | | | | | | (65) $false % 233.48/39.79 | | | | | | % 233.48/39.79 | | | | | | CLOSE: (65) is inconsistent. % 233.48/39.79 | | | | | | % 233.48/39.79 | | | | | Case 2: % 233.48/39.79 | | | | | | % 233.48/39.79 | | | | | | (66) a_select3(id_ds1_filter, n5, n2) = all_74_17 & $i(all_74_17) % 233.48/39.79 | | | | | | % 233.48/39.79 | | | | | | ALPHA: (66) implies: % 233.48/39.79 | | | | | | (67) a_select3(id_ds1_filter, n5, n2) = all_74_17 % 233.48/39.79 | | | | | | % 233.48/39.79 | | | | | | GROUND_INST: instantiating (10) with all_74_17, all_74_16, n2, n5, % 233.48/39.79 | | | | | | id_ds1_filter, simplifying with (55), (67) gives: % 233.48/39.79 | | | | | | (68) all_74_16 = all_74_17 % 233.48/39.79 | | | | | | % 233.48/39.79 | | | | | | REDUCE: (16), (68) imply: % 233.48/39.79 | | | | | | (69) $false % 233.48/39.79 | | | | | | % 233.48/39.79 | | | | | | CLOSE: (69) is inconsistent. % 233.48/39.79 | | | | | | % 233.48/39.79 | | | | | End of split % 233.48/39.79 | | | | | % 233.48/39.79 | | | | End of split % 233.48/39.79 | | | | % 233.48/39.79 | | | End of split % 233.48/39.79 | | | % 233.48/39.79 | | Case 2: % 233.48/39.79 | | | % 233.48/39.79 | | | (70) all_74_19 = n3 % 233.48/39.79 | | | % 233.48/39.79 | | | REDUCE: (6), (70) imply: % 233.48/39.79 | | | (71) a_select3(id_ds1_filter, n3, n5) = all_74_17 % 233.48/39.79 | | | % 233.48/39.79 | | | REDUCE: (11), (70) imply: % 233.48/39.79 | | | (72) a_select3(id_ds1_filter, n5, n3) = all_74_16 % 233.48/39.79 | | | % 233.48/39.79 | | | REDUCE: (20), (70) imply: % 233.48/39.79 | | | (73) leq(n3, n5) % 233.48/39.79 | | | % 233.48/39.79 | | | REDUCE: (21), (70) imply: % 233.48/39.79 | | | (74) leq(n0, n3) % 233.48/39.79 | | | % 233.48/39.79 | | | GROUND_INST: instantiating (22) with n3, n5, all_74_17, simplifying with % 233.48/39.79 | | | (13), (15), (17), (71), (74) gives: % 233.48/39.79 | | | (75) ~ leq(n5, all_74_21) | ~ leq(n3, all_74_21) | % 233.48/39.79 | | | (a_select3(id_ds1_filter, n5, n3) = all_74_17 & $i(all_74_17)) % 233.48/39.79 | | | % 233.48/39.79 | | | BETA: splitting (75) gives: % 233.48/39.79 | | | % 233.48/39.79 | | | Case 1: % 233.48/39.79 | | | | % 233.48/39.79 | | | | (76) ~ leq(n5, all_74_21) % 233.48/39.79 | | | | % 233.48/39.79 | | | | REDUCE: (3), (76) imply: % 233.48/39.79 | | | | (77) ~ leq(n5, n5) % 233.48/39.79 | | | | % 233.48/39.79 | | | | PRED_UNIFY: (8), (77) imply: % 233.48/39.79 | | | | (78) $false % 233.48/39.79 | | | | % 233.48/39.79 | | | | CLOSE: (78) is inconsistent. % 233.48/39.79 | | | | % 233.48/39.79 | | | Case 2: % 233.48/39.79 | | | | % 233.48/39.79 | | | | (79) ~ leq(n3, all_74_21) | (a_select3(id_ds1_filter, n5, n3) = % 233.48/39.79 | | | | all_74_17 & $i(all_74_17)) % 233.48/39.79 | | | | % 233.48/39.79 | | | | BETA: splitting (79) gives: % 233.48/39.79 | | | | % 233.48/39.79 | | | | Case 1: % 233.48/39.79 | | | | | % 233.48/39.79 | | | | | (80) ~ leq(n3, all_74_21) % 233.48/39.79 | | | | | % 233.48/39.79 | | | | | REDUCE: (3), (80) imply: % 233.48/39.79 | | | | | (81) ~ leq(n3, n5) % 233.48/39.79 | | | | | % 233.48/39.79 | | | | | PRED_UNIFY: (73), (81) imply: % 233.48/39.79 | | | | | (82) $false % 233.48/39.79 | | | | | % 233.48/39.79 | | | | | CLOSE: (82) is inconsistent. % 233.48/39.79 | | | | | % 233.48/39.79 | | | | Case 2: % 233.48/39.79 | | | | | % 233.48/39.79 | | | | | (83) a_select3(id_ds1_filter, n5, n3) = all_74_17 & $i(all_74_17) % 233.48/39.79 | | | | | % 233.48/39.79 | | | | | ALPHA: (83) implies: % 233.48/39.79 | | | | | (84) a_select3(id_ds1_filter, n5, n3) = all_74_17 % 233.48/39.79 | | | | | % 233.48/39.79 | | | | | GROUND_INST: instantiating (10) with all_74_17, all_74_16, n3, n5, % 233.48/39.79 | | | | | id_ds1_filter, simplifying with (72), (84) gives: % 233.48/39.79 | | | | | (85) all_74_16 = all_74_17 % 233.48/39.79 | | | | | % 233.48/39.79 | | | | | REDUCE: (16), (85) imply: % 233.48/39.79 | | | | | (86) $false % 233.48/39.79 | | | | | % 233.48/39.79 | | | | | CLOSE: (86) is inconsistent. % 233.48/39.79 | | | | | % 233.48/39.79 | | | | End of split % 233.48/39.79 | | | | % 233.48/39.79 | | | End of split % 233.48/39.79 | | | % 233.48/39.79 | | End of split % 233.48/39.79 | | % 233.48/39.79 | Case 2: % 233.48/39.79 | | % 233.48/39.79 | | (87) all_74_19 = n4 % 233.48/39.79 | | % 233.48/39.79 | | REDUCE: (6), (87) imply: % 233.48/39.79 | | (88) a_select3(id_ds1_filter, n4, n5) = all_74_17 % 233.48/39.79 | | % 233.48/39.79 | | REDUCE: (11), (87) imply: % 233.48/39.79 | | (89) a_select3(id_ds1_filter, n5, n4) = all_74_16 % 233.48/39.80 | | % 233.48/39.80 | | REDUCE: (20), (87) imply: % 233.48/39.80 | | (90) leq(n4, n5) % 233.48/39.80 | | % 233.48/39.80 | | REDUCE: (21), (87) imply: % 233.48/39.80 | | (91) leq(n0, n4) % 233.48/39.80 | | % 233.48/39.80 | | GROUND_INST: instantiating (22) with n4, n5, all_74_17, simplifying with % 233.48/39.80 | | (13), (17), (19), (88), (91) gives: % 233.48/39.80 | | (92) ~ leq(n5, all_74_21) | ~ leq(n4, all_74_21) | % 233.48/39.80 | | (a_select3(id_ds1_filter, n5, n4) = all_74_17 & $i(all_74_17)) % 233.48/39.80 | | % 233.48/39.80 | | BETA: splitting (92) gives: % 233.48/39.80 | | % 233.48/39.80 | | Case 1: % 233.48/39.80 | | | % 233.48/39.80 | | | (93) ~ leq(n5, all_74_21) % 233.48/39.80 | | | % 233.48/39.80 | | | REDUCE: (3), (93) imply: % 233.48/39.80 | | | (94) ~ leq(n5, n5) % 233.48/39.80 | | | % 233.48/39.80 | | | PRED_UNIFY: (8), (94) imply: % 233.48/39.80 | | | (95) $false % 233.48/39.80 | | | % 233.48/39.80 | | | CLOSE: (95) is inconsistent. % 233.48/39.80 | | | % 233.48/39.80 | | Case 2: % 233.48/39.80 | | | % 233.48/39.80 | | | (96) ~ leq(n4, all_74_21) | (a_select3(id_ds1_filter, n5, n4) = % 233.48/39.80 | | | all_74_17 & $i(all_74_17)) % 233.48/39.80 | | | % 233.48/39.80 | | | BETA: splitting (96) gives: % 233.48/39.80 | | | % 233.48/39.80 | | | Case 1: % 233.48/39.80 | | | | % 233.48/39.80 | | | | (97) ~ leq(n4, all_74_21) % 233.48/39.80 | | | | % 233.48/39.80 | | | | REDUCE: (3), (97) imply: % 233.48/39.80 | | | | (98) ~ leq(n4, n5) % 233.48/39.80 | | | | % 233.48/39.80 | | | | PRED_UNIFY: (90), (98) imply: % 233.48/39.80 | | | | (99) $false % 233.48/39.80 | | | | % 233.48/39.80 | | | | CLOSE: (99) is inconsistent. % 233.48/39.80 | | | | % 233.48/39.80 | | | Case 2: % 233.48/39.80 | | | | % 233.48/39.80 | | | | (100) a_select3(id_ds1_filter, n5, n4) = all_74_17 & $i(all_74_17) % 233.48/39.80 | | | | % 233.48/39.80 | | | | ALPHA: (100) implies: % 233.48/39.80 | | | | (101) a_select3(id_ds1_filter, n5, n4) = all_74_17 % 233.48/39.80 | | | | % 233.48/39.80 | | | | REF_CLOSE: (10), (16), (89), (101) are inconsistent by sub-proof #8. % 233.48/39.80 | | | | % 233.48/39.80 | | | End of split % 233.48/39.80 | | | % 233.48/39.80 | | End of split % 233.48/39.80 | | % 233.48/39.80 | End of split % 233.48/39.80 | % 233.48/39.80 End of proof % 233.48/39.80 % 233.48/39.80 Sub-proof #8 shows that the following formulas are inconsistent: % 233.48/39.80 ---------------------------------------------------------------- % 233.48/39.80 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 233.48/39.80 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 233.48/39.80 v0)) % 233.48/39.80 (2) a_select3(id_ds1_filter, n5, n4) = all_74_16 % 233.48/39.80 (3) a_select3(id_ds1_filter, n5, n4) = all_74_17 % 233.48/39.80 (4) ~ (all_74_16 = all_74_17) % 233.48/39.80 % 233.48/39.80 Begin of proof % 233.48/39.80 | % 233.48/39.80 | GROUND_INST: instantiating (1) with all_74_17, all_74_16, n4, n5, % 233.48/39.80 | id_ds1_filter, simplifying with (2), (3) gives: % 233.48/39.80 | (5) all_74_16 = all_74_17 % 233.48/39.80 | % 233.48/39.80 | REDUCE: (4), (5) imply: % 233.48/39.80 | (6) $false % 233.48/39.80 | % 233.48/39.80 | CLOSE: (6) is inconsistent. % 233.48/39.80 | % 233.48/39.80 End of proof % 233.48/39.80 % 233.48/39.80 Sub-proof #9 shows that the following formulas are inconsistent: % 233.48/39.80 ---------------------------------------------------------------- % 233.48/39.80 (1) $i(all_74_19) % 233.48/39.80 (2) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ leq(v0, % 233.48/39.80 v1) | gt(v1, v0)) % 233.48/39.80 (3) leq(all_74_18, n5) % 233.48/39.80 (4) all_74_21 = n5 % 233.48/39.80 (5) all_74_18 = n4 | gt(n4, all_74_18) % 233.48/39.80 (6) pred(n4) = n3 % 233.48/39.80 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (pred(v1) = v2) | ~ $i(v1) % 233.48/39.80 | ~ $i(v0) | ~ gt(v1, v0) | leq(v0, v2)) % 233.48/39.80 (8) $i(n2) % 233.48/39.80 (9) all_74_19 = n4 | gt(n4, all_74_19) % 233.48/39.80 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 233.48/39.80 (v1 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 233.48/39.80 v0)) % 233.48/39.80 (11) pred(n2) = n1 % 233.48/39.80 (12) $i(all_74_18) % 233.48/39.80 (13) ~ (all_74_19 = n0) % 233.48/39.80 (14) $i(n3) % 233.48/39.80 (15) ~ (all_74_16 = all_74_17) % 233.48/39.80 (16) a_select3(id_ds1_filter, all_74_19, all_74_18) = all_74_17 % 233.48/39.80 (17) pred(n3) = n2 % 233.48/39.80 (18) $i(n4) % 233.48/39.80 (19) a_select3(id_ds1_filter, all_74_18, all_74_19) = all_74_16 % 233.48/39.80 (20) leq(all_74_19, n5) % 233.48/39.80 (21) leq(n0, all_74_19) % 233.48/39.80 (22) ~ (all_74_18 = n0) % 233.48/39.80 (23) leq(n0, all_74_18) % 233.48/39.80 (24) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (a_select3(id_ds1_filter, % 233.48/39.80 v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ leq(v1, all_74_21) | ~ % 233.48/39.80 leq(v0, all_74_21) | ~ leq(n0, v1) | ~ leq(n0, v0) | % 233.48/39.80 (a_select3(id_ds1_filter, v1, v0) = v2 & $i(v2))) % 233.48/39.80 (25) ! [v0: $i] : (v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0, n1) | ~ % 233.48/39.80 leq(n0, v0)) % 233.48/39.80 % 233.48/39.80 Begin of proof % 233.48/39.80 | % 233.48/39.80 | BETA: splitting (9) gives: % 233.48/39.80 | % 233.48/39.80 | Case 1: % 233.48/39.80 | | % 233.48/39.80 | | (26) gt(n4, all_74_19) % 233.48/39.80 | | % 233.48/39.80 | | GROUND_INST: instantiating (7) with all_74_19, n4, n3, simplifying with (1), % 233.48/39.80 | | (6), (18), (26) gives: % 233.48/39.80 | | (27) leq(all_74_19, n3) % 233.48/39.80 | | % 233.48/39.80 | | GROUND_INST: instantiating (2) with all_74_19, n3, simplifying with (1), % 233.48/39.80 | | (14), (27) gives: % 233.48/39.80 | | (28) all_74_19 = n3 | gt(n3, all_74_19) % 233.48/39.80 | | % 233.48/39.80 | | BETA: splitting (5) gives: % 233.48/39.80 | | % 233.48/39.80 | | Case 1: % 233.48/39.80 | | | % 233.48/39.80 | | | (29) gt(n4, all_74_18) % 233.48/39.80 | | | % 233.48/39.80 | | | GROUND_INST: instantiating (7) with all_74_18, n4, n3, simplifying with % 233.48/39.80 | | | (6), (12), (18), (29) gives: % 233.48/39.80 | | | (30) leq(all_74_18, n3) % 233.48/39.80 | | | % 233.48/39.80 | | | GROUND_INST: instantiating (2) with all_74_18, n3, simplifying with (12), % 233.48/39.80 | | | (14), (30) gives: % 233.48/39.80 | | | (31) all_74_18 = n3 | gt(n3, all_74_18) % 233.48/39.80 | | | % 233.48/39.80 | | | BETA: splitting (28) gives: % 233.48/39.80 | | | % 233.48/39.80 | | | Case 1: % 233.48/39.80 | | | | % 233.48/39.80 | | | | (32) gt(n3, all_74_19) % 233.48/39.80 | | | | % 233.48/39.80 | | | | GROUND_INST: instantiating (7) with all_74_19, n3, n2, simplifying with % 233.48/39.80 | | | | (1), (14), (17), (32) gives: % 233.48/39.80 | | | | (33) leq(all_74_19, n2) % 233.48/39.80 | | | | % 233.48/39.80 | | | | GROUND_INST: instantiating (2) with all_74_19, n2, simplifying with (1), % 233.48/39.80 | | | | (8), (33) gives: % 233.48/39.80 | | | | (34) all_74_19 = n2 | gt(n2, all_74_19) % 233.48/39.80 | | | | % 233.48/39.80 | | | | BETA: splitting (31) gives: % 233.48/39.80 | | | | % 233.48/39.80 | | | | Case 1: % 233.48/39.80 | | | | | % 233.48/39.80 | | | | | (35) gt(n3, all_74_18) % 233.48/39.80 | | | | | % 233.48/39.80 | | | | | GROUND_INST: instantiating (7) with all_74_18, n3, n2, simplifying % 233.48/39.80 | | | | | with (12), (14), (17), (35) gives: % 233.48/39.80 | | | | | (36) leq(all_74_18, n2) % 233.48/39.80 | | | | | % 233.48/39.80 | | | | | GROUND_INST: instantiating (2) with all_74_18, n2, simplifying with % 233.48/39.80 | | | | | (8), (12), (36) gives: % 233.48/39.80 | | | | | (37) all_74_18 = n2 | gt(n2, all_74_18) % 233.48/39.80 | | | | | % 233.48/39.80 | | | | | BETA: splitting (34) gives: % 233.48/39.80 | | | | | % 233.48/39.80 | | | | | Case 1: % 233.48/39.80 | | | | | | % 233.48/39.80 | | | | | | (38) gt(n2, all_74_19) % 233.48/39.80 | | | | | | % 233.48/39.80 | | | | | | GROUND_INST: instantiating (7) with all_74_19, n2, n1, simplifying % 233.48/39.80 | | | | | | with (1), (8), (11), (38) gives: % 233.48/39.80 | | | | | | (39) leq(all_74_19, n1) % 233.48/39.80 | | | | | | % 233.48/39.80 | | | | | | GROUND_INST: instantiating (25) with all_74_19, simplifying with % 233.48/39.80 | | | | | | (1), (21), (39) gives: % 233.48/39.80 | | | | | | (40) all_74_19 = n1 | all_74_19 = n0 % 233.48/39.80 | | | | | | % 233.48/39.80 | | | | | | BETA: splitting (40) gives: % 233.48/39.80 | | | | | | % 233.48/39.80 | | | | | | Case 1: % 233.48/39.80 | | | | | | | % 233.48/39.80 | | | | | | | (41) all_74_19 = n0 % 233.48/39.80 | | | | | | | % 233.48/39.80 | | | | | | | REDUCE: (13), (41) imply: % 233.48/39.80 | | | | | | | (42) $false % 233.48/39.80 | | | | | | | % 233.48/39.80 | | | | | | | CLOSE: (42) is inconsistent. % 233.48/39.80 | | | | | | | % 233.48/39.80 | | | | | | Case 2: % 233.48/39.80 | | | | | | | % 233.48/39.80 | | | | | | | (43) all_74_19 = n1 % 233.48/39.80 | | | | | | | % 233.48/39.80 | | | | | | | REDUCE: (19), (43) imply: % 233.48/39.80 | | | | | | | (44) a_select3(id_ds1_filter, all_74_18, n1) = all_74_16 % 233.48/39.80 | | | | | | | % 233.48/39.80 | | | | | | | REDUCE: (16), (43) imply: % 233.48/39.80 | | | | | | | (45) a_select3(id_ds1_filter, n1, all_74_18) = all_74_17 % 233.48/39.80 | | | | | | | % 233.48/39.80 | | | | | | | REDUCE: (1), (43) imply: % 233.48/39.80 | | | | | | | (46) $i(n1) % 233.48/39.80 | | | | | | | % 233.48/39.80 | | | | | | | REDUCE: (20), (43) imply: % 233.48/39.80 | | | | | | | (47) leq(n1, n5) % 233.48/39.80 | | | | | | | % 233.48/39.80 | | | | | | | REDUCE: (21), (43) imply: % 233.48/39.80 | | | | | | | (48) leq(n0, n1) % 233.48/39.80 | | | | | | | % 233.48/39.80 | | | | | | | BETA: splitting (37) gives: % 233.48/39.80 | | | | | | | % 233.48/39.80 | | | | | | | Case 1: % 233.48/39.80 | | | | | | | | % 233.48/39.80 | | | | | | | | (49) gt(n2, all_74_18) % 233.48/39.80 | | | | | | | | % 233.48/39.80 | | | | | | | | GROUND_INST: instantiating (7) with all_74_18, n2, n1, % 233.48/39.80 | | | | | | | | simplifying with (8), (11), (12), (49) gives: % 233.48/39.80 | | | | | | | | (50) leq(all_74_18, n1) % 233.48/39.80 | | | | | | | | % 233.48/39.80 | | | | | | | | GROUND_INST: instantiating (25) with all_74_18, simplifying with % 233.48/39.80 | | | | | | | | (12), (23), (50) gives: % 233.48/39.80 | | | | | | | | (51) all_74_18 = n1 | all_74_18 = n0 % 233.48/39.80 | | | | | | | | % 233.48/39.80 | | | | | | | | BETA: splitting (51) gives: % 233.48/39.80 | | | | | | | | % 233.48/39.80 | | | | | | | | Case 1: % 233.48/39.80 | | | | | | | | | % 233.48/39.80 | | | | | | | | | (52) all_74_18 = n0 % 233.48/39.80 | | | | | | | | | % 233.48/39.80 | | | | | | | | | REDUCE: (22), (52) imply: % 233.48/39.80 | | | | | | | | | (53) $false % 233.48/39.80 | | | | | | | | | % 233.48/39.80 | | | | | | | | | CLOSE: (53) is inconsistent. % 233.48/39.80 | | | | | | | | | % 233.48/39.80 | | | | | | | | Case 2: % 233.48/39.80 | | | | | | | | | % 233.48/39.80 | | | | | | | | | (54) all_74_18 = n1 % 233.48/39.80 | | | | | | | | | % 233.48/39.80 | | | | | | | | | REDUCE: (44), (54) imply: % 233.48/39.80 | | | | | | | | | (55) a_select3(id_ds1_filter, n1, n1) = all_74_16 % 233.48/39.80 | | | | | | | | | % 233.48/39.80 | | | | | | | | | REDUCE: (45), (54) imply: % 233.48/39.80 | | | | | | | | | (56) a_select3(id_ds1_filter, n1, n1) = all_74_17 % 233.48/39.80 | | | | | | | | | % 233.48/39.80 | | | | | | | | | GROUND_INST: instantiating (10) with all_74_17, all_74_16, n1, % 233.48/39.80 | | | | | | | | | n1, id_ds1_filter, simplifying with (55), (56) % 233.48/39.80 | | | | | | | | | gives: % 233.48/39.80 | | | | | | | | | (57) all_74_16 = all_74_17 % 233.48/39.80 | | | | | | | | | % 233.48/39.80 | | | | | | | | | REDUCE: (15), (57) imply: % 233.48/39.80 | | | | | | | | | (58) $false % 233.48/39.80 | | | | | | | | | % 233.48/39.80 | | | | | | | | | CLOSE: (58) is inconsistent. % 233.48/39.80 | | | | | | | | | % 233.48/39.80 | | | | | | | | End of split % 233.48/39.80 | | | | | | | | % 233.48/39.80 | | | | | | | Case 2: % 233.48/39.80 | | | | | | | | % 233.48/39.80 | | | | | | | | (59) all_74_18 = n2 % 233.48/39.80 | | | | | | | | % 233.48/39.80 | | | | | | | | REDUCE: (44), (59) imply: % 233.48/39.80 | | | | | | | | (60) a_select3(id_ds1_filter, n2, n1) = all_74_16 % 233.48/39.80 | | | | | | | | % 233.48/39.80 | | | | | | | | REDUCE: (45), (59) imply: % 233.48/39.81 | | | | | | | | (61) a_select3(id_ds1_filter, n1, n2) = all_74_17 % 233.48/39.81 | | | | | | | | % 233.48/39.81 | | | | | | | | REDUCE: (3), (59) imply: % 233.48/39.81 | | | | | | | | (62) leq(n2, n5) % 233.48/39.81 | | | | | | | | % 233.48/39.81 | | | | | | | | REDUCE: (23), (59) imply: % 233.48/39.81 | | | | | | | | (63) leq(n0, n2) % 233.48/39.81 | | | | | | | | % 233.48/39.81 | | | | | | | | GROUND_INST: instantiating (24) with n1, n2, all_74_17, % 233.48/39.81 | | | | | | | | simplifying with (8), (46), (48), (61), (63) gives: % 233.48/39.81 | | | | | | | | (64) ~ leq(n2, all_74_21) | ~ leq(n1, all_74_21) | % 233.48/39.81 | | | | | | | | (a_select3(id_ds1_filter, n2, n1) = all_74_17 & % 233.48/39.81 | | | | | | | | $i(all_74_17)) % 233.48/39.81 | | | | | | | | % 233.48/39.81 | | | | | | | | BETA: splitting (64) gives: % 233.48/39.81 | | | | | | | | % 233.48/39.81 | | | | | | | | Case 1: % 233.48/39.81 | | | | | | | | | % 233.48/39.81 | | | | | | | | | (65) ~ leq(n2, all_74_21) % 233.48/39.81 | | | | | | | | | % 233.48/39.81 | | | | | | | | | REDUCE: (4), (65) imply: % 233.48/39.81 | | | | | | | | | (66) ~ leq(n2, n5) % 233.48/39.81 | | | | | | | | | % 233.48/39.81 | | | | | | | | | PRED_UNIFY: (62), (66) imply: % 233.48/39.81 | | | | | | | | | (67) $false % 233.48/39.81 | | | | | | | | | % 233.48/39.81 | | | | | | | | | CLOSE: (67) is inconsistent. % 233.48/39.81 | | | | | | | | | % 233.48/39.81 | | | | | | | | Case 2: % 233.48/39.81 | | | | | | | | | % 233.48/39.81 | | | | | | | | | (68) ~ leq(n1, all_74_21) | (a_select3(id_ds1_filter, n2, % 233.48/39.81 | | | | | | | | | n1) = all_74_17 & $i(all_74_17)) % 233.48/39.81 | | | | | | | | | % 233.48/39.81 | | | | | | | | | BETA: splitting (68) gives: % 233.48/39.81 | | | | | | | | | % 233.48/39.81 | | | | | | | | | Case 1: % 233.48/39.81 | | | | | | | | | | % 233.48/39.81 | | | | | | | | | | (69) ~ leq(n1, all_74_21) % 233.48/39.81 | | | | | | | | | | % 233.48/39.81 | | | | | | | | | | REDUCE: (4), (69) imply: % 233.48/39.81 | | | | | | | | | | (70) ~ leq(n1, n5) % 233.48/39.81 | | | | | | | | | | % 233.48/39.81 | | | | | | | | | | PRED_UNIFY: (47), (70) imply: % 233.48/39.81 | | | | | | | | | | (71) $false % 233.48/39.81 | | | | | | | | | | % 233.48/39.81 | | | | | | | | | | CLOSE: (71) is inconsistent. % 233.48/39.81 | | | | | | | | | | % 233.48/39.81 | | | | | | | | | Case 2: % 233.48/39.81 | | | | | | | | | | % 233.48/39.81 | | | | | | | | | | (72) a_select3(id_ds1_filter, n2, n1) = all_74_17 & % 233.48/39.81 | | | | | | | | | | $i(all_74_17) % 233.48/39.81 | | | | | | | | | | % 233.48/39.81 | | | | | | | | | | ALPHA: (72) implies: % 233.48/39.81 | | | | | | | | | | (73) a_select3(id_ds1_filter, n2, n1) = all_74_17 % 233.48/39.81 | | | | | | | | | | % 233.48/39.81 | | | | | | | | | | REF_CLOSE: (10), (15), (60), (73) are inconsistent by % 233.48/39.81 | | | | | | | | | | sub-proof #12. % 233.48/39.81 | | | | | | | | | | % 233.48/39.81 | | | | | | | | | End of split % 233.48/39.81 | | | | | | | | | % 233.48/39.81 | | | | | | | | End of split % 233.48/39.81 | | | | | | | | % 233.48/39.81 | | | | | | | End of split % 233.48/39.81 | | | | | | | % 233.48/39.81 | | | | | | End of split % 233.48/39.81 | | | | | | % 233.48/39.81 | | | | | Case 2: % 233.48/39.81 | | | | | | % 233.48/39.81 | | | | | | (74) all_74_19 = n2 % 233.48/39.81 | | | | | | % 233.48/39.81 | | | | | | REDUCE: (19), (74) imply: % 233.48/39.81 | | | | | | (75) a_select3(id_ds1_filter, all_74_18, n2) = all_74_16 % 233.48/39.81 | | | | | | % 233.48/39.81 | | | | | | REDUCE: (16), (74) imply: % 233.48/39.81 | | | | | | (76) a_select3(id_ds1_filter, n2, all_74_18) = all_74_17 % 233.48/39.81 | | | | | | % 233.48/39.81 | | | | | | REDUCE: (20), (74) imply: % 233.48/39.81 | | | | | | (77) leq(n2, n5) % 233.48/39.81 | | | | | | % 233.48/39.81 | | | | | | REDUCE: (21), (74) imply: % 233.48/39.81 | | | | | | (78) leq(n0, n2) % 233.48/39.81 | | | | | | % 233.48/39.81 | | | | | | BETA: splitting (37) gives: % 233.48/39.81 | | | | | | % 233.48/39.81 | | | | | | Case 1: % 233.48/39.81 | | | | | | | % 233.48/39.81 | | | | | | | (79) gt(n2, all_74_18) % 233.48/39.81 | | | | | | | % 233.48/39.81 | | | | | | | GROUND_INST: instantiating (7) with all_74_18, n2, n1, simplifying % 233.48/39.81 | | | | | | | with (8), (11), (12), (79) gives: % 233.48/39.81 | | | | | | | (80) leq(all_74_18, n1) % 233.48/39.81 | | | | | | | % 233.48/39.81 | | | | | | | GROUND_INST: instantiating (25) with all_74_18, simplifying with % 233.48/39.81 | | | | | | | (12), (23), (80) gives: % 233.48/39.81 | | | | | | | (81) all_74_18 = n1 | all_74_18 = n0 % 233.48/39.81 | | | | | | | % 233.48/39.81 | | | | | | | BETA: splitting (81) gives: % 233.48/39.81 | | | | | | | % 233.48/39.81 | | | | | | | Case 1: % 233.48/39.81 | | | | | | | | % 233.48/39.81 | | | | | | | | (82) all_74_18 = n0 % 233.48/39.81 | | | | | | | | % 233.48/39.81 | | | | | | | | REDUCE: (22), (82) imply: % 233.48/39.81 | | | | | | | | (83) $false % 233.48/39.81 | | | | | | | | % 233.48/39.81 | | | | | | | | CLOSE: (83) is inconsistent. % 233.48/39.81 | | | | | | | | % 233.48/39.81 | | | | | | | Case 2: % 233.48/39.81 | | | | | | | | % 233.48/39.81 | | | | | | | | (84) all_74_18 = n1 % 233.48/39.81 | | | | | | | | % 233.48/39.81 | | | | | | | | REDUCE: (75), (84) imply: % 233.48/39.81 | | | | | | | | (85) a_select3(id_ds1_filter, n1, n2) = all_74_16 % 233.48/39.81 | | | | | | | | % 233.48/39.81 | | | | | | | | REDUCE: (76), (84) imply: % 233.48/39.81 | | | | | | | | (86) a_select3(id_ds1_filter, n2, n1) = all_74_17 % 233.48/39.81 | | | | | | | | % 233.48/39.81 | | | | | | | | REDUCE: (12), (84) imply: % 233.48/39.81 | | | | | | | | (87) $i(n1) % 233.48/39.81 | | | | | | | | % 233.48/39.81 | | | | | | | | REDUCE: (3), (84) imply: % 233.48/39.81 | | | | | | | | (88) leq(n1, n5) % 233.48/39.81 | | | | | | | | % 233.48/39.81 | | | | | | | | REDUCE: (23), (84) imply: % 233.48/39.81 | | | | | | | | (89) leq(n0, n1) % 233.48/39.81 | | | | | | | | % 233.48/39.81 | | | | | | | | GROUND_INST: instantiating (24) with n1, n2, all_74_16, % 233.48/39.81 | | | | | | | | simplifying with (8), (78), (85), (87), (89) gives: % 233.48/39.81 | | | | | | | | (90) ~ leq(n2, all_74_21) | ~ leq(n1, all_74_21) | % 233.48/39.81 | | | | | | | | (a_select3(id_ds1_filter, n2, n1) = all_74_16 & % 233.48/39.81 | | | | | | | | $i(all_74_16)) % 233.48/39.81 | | | | | | | | % 233.48/39.81 | | | | | | | | BETA: splitting (90) gives: % 233.48/39.81 | | | | | | | | % 233.48/39.81 | | | | | | | | Case 1: % 233.48/39.81 | | | | | | | | | % 233.48/39.81 | | | | | | | | | (91) ~ leq(n2, all_74_21) % 233.48/39.81 | | | | | | | | | % 233.48/39.81 | | | | | | | | | REDUCE: (4), (91) imply: % 233.48/39.81 | | | | | | | | | (92) ~ leq(n2, n5) % 233.48/39.81 | | | | | | | | | % 233.48/39.81 | | | | | | | | | PRED_UNIFY: (77), (92) imply: % 233.48/39.81 | | | | | | | | | (93) $false % 233.48/39.81 | | | | | | | | | % 233.48/39.81 | | | | | | | | | CLOSE: (93) is inconsistent. % 233.48/39.81 | | | | | | | | | % 233.48/39.81 | | | | | | | | Case 2: % 233.48/39.81 | | | | | | | | | % 233.48/39.81 | | | | | | | | | (94) ~ leq(n1, all_74_21) | (a_select3(id_ds1_filter, n2, % 233.48/39.81 | | | | | | | | | n1) = all_74_16 & $i(all_74_16)) % 233.48/39.81 | | | | | | | | | % 233.48/39.81 | | | | | | | | | BETA: splitting (94) gives: % 233.48/39.81 | | | | | | | | | % 233.48/39.81 | | | | | | | | | Case 1: % 233.48/39.81 | | | | | | | | | | % 233.48/39.81 | | | | | | | | | | (95) ~ leq(n1, all_74_21) % 233.48/39.81 | | | | | | | | | | % 233.48/39.81 | | | | | | | | | | REDUCE: (4), (95) imply: % 233.48/39.81 | | | | | | | | | | (96) ~ leq(n1, n5) % 233.48/39.81 | | | | | | | | | | % 233.48/39.81 | | | | | | | | | | PRED_UNIFY: (88), (96) imply: % 233.48/39.81 | | | | | | | | | | (97) $false % 233.48/39.81 | | | | | | | | | | % 233.48/39.81 | | | | | | | | | | CLOSE: (97) is inconsistent. % 233.48/39.81 | | | | | | | | | | % 233.48/39.81 | | | | | | | | | Case 2: % 233.48/39.81 | | | | | | | | | | % 233.48/39.81 | | | | | | | | | | (98) a_select3(id_ds1_filter, n2, n1) = all_74_16 & % 233.48/39.81 | | | | | | | | | | $i(all_74_16) % 233.48/39.81 | | | | | | | | | | % 233.48/39.81 | | | | | | | | | | ALPHA: (98) implies: % 233.48/39.81 | | | | | | | | | | (99) a_select3(id_ds1_filter, n2, n1) = all_74_16 % 233.48/39.81 | | | | | | | | | | % 233.48/39.81 | | | | | | | | | | REF_CLOSE: (10), (15), (86), (99) are inconsistent by % 233.48/39.81 | | | | | | | | | | sub-proof #12. % 233.48/39.81 | | | | | | | | | | % 233.48/39.81 | | | | | | | | | End of split % 233.48/39.81 | | | | | | | | | % 233.48/39.81 | | | | | | | | End of split % 233.48/39.81 | | | | | | | | % 233.48/39.81 | | | | | | | End of split % 233.48/39.81 | | | | | | | % 233.48/39.81 | | | | | | Case 2: % 233.48/39.81 | | | | | | | % 233.48/39.81 | | | | | | | (100) all_74_18 = n2 % 233.48/39.81 | | | | | | | % 233.48/39.81 | | | | | | | REDUCE: (75), (100) imply: % 233.48/39.81 | | | | | | | (101) a_select3(id_ds1_filter, n2, n2) = all_74_16 % 233.48/39.81 | | | | | | | % 233.48/39.81 | | | | | | | REDUCE: (76), (100) imply: % 233.48/39.81 | | | | | | | (102) a_select3(id_ds1_filter, n2, n2) = all_74_17 % 233.48/39.81 | | | | | | | % 233.48/39.81 | | | | | | | GROUND_INST: instantiating (10) with all_74_17, all_74_16, n2, n2, % 233.48/39.81 | | | | | | | id_ds1_filter, simplifying with (101), (102) gives: % 233.48/39.81 | | | | | | | (103) all_74_16 = all_74_17 % 233.48/39.81 | | | | | | | % 233.48/39.81 | | | | | | | REDUCE: (15), (103) imply: % 233.48/39.81 | | | | | | | (104) $false % 233.48/39.81 | | | | | | | % 233.48/39.81 | | | | | | | CLOSE: (104) is inconsistent. % 233.48/39.81 | | | | | | | % 233.48/39.81 | | | | | | End of split % 233.48/39.81 | | | | | | % 233.48/39.81 | | | | | End of split % 233.48/39.81 | | | | | % 233.48/39.81 | | | | Case 2: % 233.48/39.81 | | | | | % 233.48/39.81 | | | | | (105) all_74_18 = n3 % 233.48/39.81 | | | | | % 233.48/39.81 | | | | | REDUCE: (19), (105) imply: % 233.48/39.81 | | | | | (106) a_select3(id_ds1_filter, n3, all_74_19) = all_74_16 % 233.48/39.81 | | | | | % 233.48/39.81 | | | | | REDUCE: (16), (105) imply: % 233.48/39.81 | | | | | (107) a_select3(id_ds1_filter, all_74_19, n3) = all_74_17 % 233.48/39.81 | | | | | % 233.48/39.81 | | | | | REDUCE: (3), (105) imply: % 233.48/39.81 | | | | | (108) leq(n3, n5) % 233.48/39.81 | | | | | % 233.48/39.81 | | | | | REDUCE: (23), (105) imply: % 233.48/39.81 | | | | | (109) leq(n0, n3) % 233.48/39.81 | | | | | % 233.48/39.81 | | | | | BETA: splitting (34) gives: % 233.48/39.81 | | | | | % 233.48/39.81 | | | | | Case 1: % 233.48/39.81 | | | | | | % 233.48/39.81 | | | | | | (110) gt(n2, all_74_19) % 233.48/39.81 | | | | | | % 233.48/39.81 | | | | | | GROUND_INST: instantiating (7) with all_74_19, n2, n1, simplifying % 233.48/39.81 | | | | | | with (1), (8), (11), (110) gives: % 233.48/39.81 | | | | | | (111) leq(all_74_19, n1) % 233.48/39.81 | | | | | | % 233.48/39.81 | | | | | | GROUND_INST: instantiating (25) with all_74_19, simplifying with % 233.48/39.81 | | | | | | (1), (21), (111) gives: % 233.48/39.81 | | | | | | (112) all_74_19 = n1 | all_74_19 = n0 % 233.48/39.81 | | | | | | % 233.48/39.81 | | | | | | BETA: splitting (112) gives: % 233.48/39.81 | | | | | | % 233.48/39.81 | | | | | | Case 1: % 233.48/39.81 | | | | | | | % 233.48/39.81 | | | | | | | (113) all_74_19 = n0 % 233.48/39.81 | | | | | | | % 233.48/39.81 | | | | | | | REDUCE: (13), (113) imply: % 233.48/39.81 | | | | | | | (114) $false % 233.48/39.81 | | | | | | | % 233.48/39.81 | | | | | | | CLOSE: (114) is inconsistent. % 233.48/39.81 | | | | | | | % 233.48/39.81 | | | | | | Case 2: % 233.48/39.81 | | | | | | | % 233.48/39.81 | | | | | | | (115) all_74_19 = n1 % 233.48/39.81 | | | | | | | % 233.48/39.81 | | | | | | | REDUCE: (107), (115) imply: % 233.48/39.81 | | | | | | | (116) a_select3(id_ds1_filter, n1, n3) = all_74_17 % 233.48/39.81 | | | | | | | % 233.48/39.81 | | | | | | | REDUCE: (106), (115) imply: % 233.48/39.81 | | | | | | | (117) a_select3(id_ds1_filter, n3, n1) = all_74_16 % 233.48/39.81 | | | | | | | % 233.48/39.81 | | | | | | | REDUCE: (1), (115) imply: % 233.48/39.81 | | | | | | | (118) $i(n1) % 233.48/39.81 | | | | | | | % 233.48/39.81 | | | | | | | REDUCE: (20), (115) imply: % 233.48/39.81 | | | | | | | (119) leq(n1, n5) % 233.48/39.81 | | | | | | | % 233.48/39.81 | | | | | | | REDUCE: (21), (115) imply: % 233.48/39.81 | | | | | | | (120) leq(n0, n1) % 233.48/39.81 | | | | | | | % 233.48/39.81 | | | | | | | GROUND_INST: instantiating (24) with n1, n3, all_74_17, % 233.48/39.81 | | | | | | | simplifying with (14), (109), (116), (118), (120) % 233.48/39.81 | | | | | | | gives: % 233.48/39.81 | | | | | | | (121) ~ leq(n3, all_74_21) | ~ leq(n1, all_74_21) | % 233.48/39.81 | | | | | | | (a_select3(id_ds1_filter, n3, n1) = all_74_17 & % 233.48/39.81 | | | | | | | $i(all_74_17)) % 233.48/39.81 | | | | | | | % 233.48/39.81 | | | | | | | BETA: splitting (121) gives: % 233.48/39.81 | | | | | | | % 233.48/39.81 | | | | | | | Case 1: % 233.48/39.81 | | | | | | | | % 233.48/39.81 | | | | | | | | (122) ~ leq(n3, all_74_21) % 233.48/39.81 | | | | | | | | % 233.48/39.81 | | | | | | | | REDUCE: (4), (122) imply: % 233.48/39.81 | | | | | | | | (123) ~ leq(n3, n5) % 233.48/39.81 | | | | | | | | % 233.48/39.81 | | | | | | | | PRED_UNIFY: (108), (123) imply: % 233.48/39.81 | | | | | | | | (124) $false % 233.48/39.81 | | | | | | | | % 233.48/39.81 | | | | | | | | CLOSE: (124) is inconsistent. % 233.48/39.81 | | | | | | | | % 233.48/39.81 | | | | | | | Case 2: % 233.48/39.81 | | | | | | | | % 233.48/39.81 | | | | | | | | (125) ~ leq(n1, all_74_21) | (a_select3(id_ds1_filter, n3, % 233.48/39.81 | | | | | | | | n1) = all_74_17 & $i(all_74_17)) % 233.48/39.81 | | | | | | | | % 233.48/39.81 | | | | | | | | BETA: splitting (125) gives: % 233.48/39.81 | | | | | | | | % 233.48/39.81 | | | | | | | | Case 1: % 233.48/39.81 | | | | | | | | | % 233.48/39.81 | | | | | | | | | (126) ~ leq(n1, all_74_21) % 233.48/39.81 | | | | | | | | | % 233.48/39.81 | | | | | | | | | REDUCE: (4), (126) imply: % 233.48/39.81 | | | | | | | | | (127) ~ leq(n1, n5) % 233.48/39.81 | | | | | | | | | % 233.48/39.81 | | | | | | | | | PRED_UNIFY: (119), (127) imply: % 233.48/39.81 | | | | | | | | | (128) $false % 233.48/39.81 | | | | | | | | | % 233.48/39.81 | | | | | | | | | CLOSE: (128) is inconsistent. % 233.48/39.81 | | | | | | | | | % 233.48/39.81 | | | | | | | | Case 2: % 233.48/39.81 | | | | | | | | | % 233.48/39.81 | | | | | | | | | (129) a_select3(id_ds1_filter, n3, n1) = all_74_17 & % 233.48/39.81 | | | | | | | | | $i(all_74_17) % 233.48/39.81 | | | | | | | | | % 233.48/39.81 | | | | | | | | | ALPHA: (129) implies: % 233.48/39.81 | | | | | | | | | (130) a_select3(id_ds1_filter, n3, n1) = all_74_17 % 233.48/39.81 | | | | | | | | | % 233.48/39.81 | | | | | | | | | GROUND_INST: instantiating (10) with all_74_17, all_74_16, n1, % 233.48/39.81 | | | | | | | | | n3, id_ds1_filter, simplifying with (117), (130) % 233.48/39.81 | | | | | | | | | gives: % 233.48/39.81 | | | | | | | | | (131) all_74_16 = all_74_17 % 233.48/39.81 | | | | | | | | | % 233.48/39.81 | | | | | | | | | REDUCE: (15), (131) imply: % 233.48/39.81 | | | | | | | | | (132) $false % 233.48/39.81 | | | | | | | | | % 233.48/39.81 | | | | | | | | | CLOSE: (132) is inconsistent. % 233.48/39.81 | | | | | | | | | % 233.48/39.81 | | | | | | | | End of split % 233.48/39.81 | | | | | | | | % 233.48/39.81 | | | | | | | End of split % 233.48/39.81 | | | | | | | % 233.48/39.81 | | | | | | End of split % 233.48/39.81 | | | | | | % 233.48/39.81 | | | | | Case 2: % 233.48/39.81 | | | | | | % 233.48/39.81 | | | | | | (133) all_74_19 = n2 % 233.48/39.81 | | | | | | % 233.48/39.81 | | | | | | REDUCE: (107), (133) imply: % 233.48/39.81 | | | | | | (134) a_select3(id_ds1_filter, n2, n3) = all_74_17 % 233.48/39.81 | | | | | | % 233.48/39.81 | | | | | | REDUCE: (106), (133) imply: % 233.48/39.81 | | | | | | (135) a_select3(id_ds1_filter, n3, n2) = all_74_16 % 233.48/39.81 | | | | | | % 233.48/39.81 | | | | | | REDUCE: (20), (133) imply: % 233.48/39.81 | | | | | | (136) leq(n2, n5) % 233.48/39.81 | | | | | | % 233.48/39.81 | | | | | | REDUCE: (21), (133) imply: % 233.48/39.81 | | | | | | (137) leq(n0, n2) % 233.48/39.81 | | | | | | % 233.48/39.81 | | | | | | GROUND_INST: instantiating (24) with n2, n3, all_74_17, simplifying % 233.48/39.81 | | | | | | with (8), (14), (109), (134), (137) gives: % 233.48/39.81 | | | | | | (138) ~ leq(n3, all_74_21) | ~ leq(n2, all_74_21) | % 233.48/39.81 | | | | | | (a_select3(id_ds1_filter, n3, n2) = all_74_17 & % 233.48/39.81 | | | | | | $i(all_74_17)) % 233.48/39.81 | | | | | | % 233.48/39.81 | | | | | | BETA: splitting (138) gives: % 233.48/39.81 | | | | | | % 233.48/39.81 | | | | | | Case 1: % 233.48/39.81 | | | | | | | % 233.48/39.81 | | | | | | | (139) ~ leq(n3, all_74_21) % 233.48/39.81 | | | | | | | % 233.48/39.81 | | | | | | | REDUCE: (4), (139) imply: % 233.48/39.81 | | | | | | | (140) ~ leq(n3, n5) % 233.48/39.81 | | | | | | | % 233.48/39.81 | | | | | | | PRED_UNIFY: (108), (140) imply: % 233.48/39.81 | | | | | | | (141) $false % 233.48/39.81 | | | | | | | % 233.48/39.81 | | | | | | | CLOSE: (141) is inconsistent. % 233.48/39.81 | | | | | | | % 233.48/39.81 | | | | | | Case 2: % 233.48/39.81 | | | | | | | % 233.48/39.81 | | | | | | | (142) ~ leq(n2, all_74_21) | (a_select3(id_ds1_filter, n3, n2) % 233.48/39.81 | | | | | | | = all_74_17 & $i(all_74_17)) % 233.48/39.81 | | | | | | | % 233.48/39.81 | | | | | | | BETA: splitting (142) gives: % 233.48/39.81 | | | | | | | % 233.48/39.81 | | | | | | | Case 1: % 233.48/39.81 | | | | | | | | % 233.48/39.81 | | | | | | | | (143) ~ leq(n2, all_74_21) % 233.48/39.82 | | | | | | | | % 233.48/39.82 | | | | | | | | REDUCE: (4), (143) imply: % 233.48/39.82 | | | | | | | | (144) ~ leq(n2, n5) % 233.48/39.82 | | | | | | | | % 233.48/39.82 | | | | | | | | PRED_UNIFY: (136), (144) imply: % 233.48/39.82 | | | | | | | | (145) $false % 233.48/39.82 | | | | | | | | % 233.48/39.82 | | | | | | | | CLOSE: (145) is inconsistent. % 233.48/39.82 | | | | | | | | % 233.48/39.82 | | | | | | | Case 2: % 233.48/39.82 | | | | | | | | % 233.48/39.82 | | | | | | | | (146) a_select3(id_ds1_filter, n3, n2) = all_74_17 & % 233.48/39.82 | | | | | | | | $i(all_74_17) % 233.48/39.82 | | | | | | | | % 233.48/39.82 | | | | | | | | ALPHA: (146) implies: % 233.48/39.82 | | | | | | | | (147) a_select3(id_ds1_filter, n3, n2) = all_74_17 % 233.48/39.82 | | | | | | | | % 233.48/39.82 | | | | | | | | REF_CLOSE: (10), (15), (135), (147) are inconsistent by % 233.48/39.82 | | | | | | | | sub-proof #11. % 233.48/39.82 | | | | | | | | % 233.48/39.82 | | | | | | | End of split % 233.48/39.82 | | | | | | | % 233.48/39.82 | | | | | | End of split % 233.48/39.82 | | | | | | % 233.48/39.82 | | | | | End of split % 233.48/39.82 | | | | | % 233.48/39.82 | | | | End of split % 233.48/39.82 | | | | % 233.48/39.82 | | | Case 2: % 233.48/39.82 | | | | % 233.48/39.82 | | | | (148) all_74_19 = n3 % 233.48/39.82 | | | | % 233.48/39.82 | | | | REDUCE: (19), (148) imply: % 233.48/39.82 | | | | (149) a_select3(id_ds1_filter, all_74_18, n3) = all_74_16 % 233.48/39.82 | | | | % 233.48/39.82 | | | | REDUCE: (16), (148) imply: % 233.48/39.82 | | | | (150) a_select3(id_ds1_filter, n3, all_74_18) = all_74_17 % 233.48/39.82 | | | | % 233.48/39.82 | | | | REDUCE: (20), (148) imply: % 233.48/39.82 | | | | (151) leq(n3, n5) % 233.48/39.82 | | | | % 233.48/39.82 | | | | REDUCE: (21), (148) imply: % 233.48/39.82 | | | | (152) leq(n0, n3) % 233.48/39.82 | | | | % 233.48/39.82 | | | | BETA: splitting (31) gives: % 233.48/39.82 | | | | % 233.48/39.82 | | | | Case 1: % 233.48/39.82 | | | | | % 233.48/39.82 | | | | | (153) gt(n3, all_74_18) % 233.48/39.82 | | | | | % 233.48/39.82 | | | | | GROUND_INST: instantiating (7) with all_74_18, n3, n2, simplifying % 233.48/39.82 | | | | | with (12), (14), (17), (153) gives: % 233.48/39.82 | | | | | (154) leq(all_74_18, n2) % 233.48/39.82 | | | | | % 233.48/39.82 | | | | | GROUND_INST: instantiating (2) with all_74_18, n2, simplifying with % 233.48/39.82 | | | | | (8), (12), (154) gives: % 233.48/39.82 | | | | | (155) all_74_18 = n2 | gt(n2, all_74_18) % 233.48/39.82 | | | | | % 233.48/39.82 | | | | | BETA: splitting (155) gives: % 233.48/39.82 | | | | | % 233.48/39.82 | | | | | Case 1: % 233.48/39.82 | | | | | | % 233.48/39.82 | | | | | | (156) gt(n2, all_74_18) % 233.48/39.82 | | | | | | % 233.48/39.82 | | | | | | GROUND_INST: instantiating (7) with all_74_18, n2, n1, simplifying % 233.48/39.82 | | | | | | with (8), (11), (12), (156) gives: % 233.48/39.82 | | | | | | (157) leq(all_74_18, n1) % 233.48/39.82 | | | | | | % 233.48/39.82 | | | | | | GROUND_INST: instantiating (25) with all_74_18, simplifying with % 233.48/39.82 | | | | | | (12), (23), (157) gives: % 233.48/39.82 | | | | | | (158) all_74_18 = n1 | all_74_18 = n0 % 233.48/39.82 | | | | | | % 233.48/39.82 | | | | | | BETA: splitting (158) gives: % 233.48/39.82 | | | | | | % 233.48/39.82 | | | | | | Case 1: % 233.48/39.82 | | | | | | | % 233.48/39.82 | | | | | | | (159) all_74_18 = n0 % 233.48/39.82 | | | | | | | % 233.48/39.82 | | | | | | | REDUCE: (22), (159) imply: % 233.48/39.82 | | | | | | | (160) $false % 233.48/39.82 | | | | | | | % 233.48/39.82 | | | | | | | CLOSE: (160) is inconsistent. % 233.48/39.82 | | | | | | | % 233.48/39.82 | | | | | | Case 2: % 233.48/39.82 | | | | | | | % 233.48/39.82 | | | | | | | (161) all_74_18 = n1 % 233.48/39.82 | | | | | | | % 233.48/39.82 | | | | | | | REDUCE: (149), (161) imply: % 233.48/39.82 | | | | | | | (162) a_select3(id_ds1_filter, n1, n3) = all_74_16 % 233.48/39.82 | | | | | | | % 233.48/39.82 | | | | | | | REDUCE: (150), (161) imply: % 233.48/39.82 | | | | | | | (163) a_select3(id_ds1_filter, n3, n1) = all_74_17 % 233.48/39.82 | | | | | | | % 233.48/39.82 | | | | | | | REDUCE: (12), (161) imply: % 233.48/39.82 | | | | | | | (164) $i(n1) % 233.48/39.82 | | | | | | | % 233.48/39.82 | | | | | | | REDUCE: (3), (161) imply: % 233.48/39.82 | | | | | | | (165) leq(n1, n5) % 233.48/39.82 | | | | | | | % 233.48/39.82 | | | | | | | REDUCE: (23), (161) imply: % 233.48/39.82 | | | | | | | (166) leq(n0, n1) % 233.48/39.82 | | | | | | | % 233.48/39.82 | | | | | | | GROUND_INST: instantiating (24) with n1, n3, all_74_16, % 233.48/39.82 | | | | | | | simplifying with (14), (152), (162), (164), (166) % 233.48/39.82 | | | | | | | gives: % 233.48/39.82 | | | | | | | (167) ~ leq(n3, all_74_21) | ~ leq(n1, all_74_21) | % 233.48/39.82 | | | | | | | (a_select3(id_ds1_filter, n3, n1) = all_74_16 & % 233.48/39.82 | | | | | | | $i(all_74_16)) % 233.48/39.82 | | | | | | | % 233.48/39.82 | | | | | | | BETA: splitting (167) gives: % 233.48/39.82 | | | | | | | % 233.48/39.82 | | | | | | | Case 1: % 233.48/39.82 | | | | | | | | % 233.48/39.82 | | | | | | | | (168) ~ leq(n3, all_74_21) % 233.48/39.82 | | | | | | | | % 233.48/39.82 | | | | | | | | REDUCE: (4), (168) imply: % 233.48/39.82 | | | | | | | | (169) ~ leq(n3, n5) % 233.48/39.82 | | | | | | | | % 233.48/39.82 | | | | | | | | PRED_UNIFY: (151), (169) imply: % 233.48/39.82 | | | | | | | | (170) $false % 233.48/39.82 | | | | | | | | % 233.48/39.82 | | | | | | | | CLOSE: (170) is inconsistent. % 233.48/39.82 | | | | | | | | % 233.48/39.82 | | | | | | | Case 2: % 233.48/39.82 | | | | | | | | % 233.48/39.82 | | | | | | | | (171) ~ leq(n1, all_74_21) | (a_select3(id_ds1_filter, n3, % 233.48/39.82 | | | | | | | | n1) = all_74_16 & $i(all_74_16)) % 233.48/39.82 | | | | | | | | % 233.48/39.82 | | | | | | | | BETA: splitting (171) gives: % 233.48/39.82 | | | | | | | | % 233.48/39.82 | | | | | | | | Case 1: % 233.48/39.82 | | | | | | | | | % 233.48/39.82 | | | | | | | | | (172) ~ leq(n1, all_74_21) % 233.48/39.82 | | | | | | | | | % 233.48/39.82 | | | | | | | | | REDUCE: (4), (172) imply: % 233.48/39.82 | | | | | | | | | (173) ~ leq(n1, n5) % 233.48/39.82 | | | | | | | | | % 233.48/39.82 | | | | | | | | | PRED_UNIFY: (165), (173) imply: % 233.48/39.82 | | | | | | | | | (174) $false % 233.48/39.82 | | | | | | | | | % 233.48/39.82 | | | | | | | | | CLOSE: (174) is inconsistent. % 233.48/39.82 | | | | | | | | | % 233.48/39.82 | | | | | | | | Case 2: % 233.48/39.82 | | | | | | | | | % 233.48/39.82 | | | | | | | | | (175) a_select3(id_ds1_filter, n3, n1) = all_74_16 & % 233.48/39.82 | | | | | | | | | $i(all_74_16) % 233.48/39.82 | | | | | | | | | % 233.48/39.82 | | | | | | | | | ALPHA: (175) implies: % 233.48/39.82 | | | | | | | | | (176) a_select3(id_ds1_filter, n3, n1) = all_74_16 % 233.48/39.82 | | | | | | | | | % 233.48/39.82 | | | | | | | | | GROUND_INST: instantiating (10) with all_74_17, all_74_16, n1, % 233.48/39.82 | | | | | | | | | n3, id_ds1_filter, simplifying with (163), (176) % 233.48/39.82 | | | | | | | | | gives: % 233.48/39.82 | | | | | | | | | (177) all_74_16 = all_74_17 % 233.48/39.82 | | | | | | | | | % 233.48/39.82 | | | | | | | | | REDUCE: (15), (177) imply: % 233.48/39.82 | | | | | | | | | (178) $false % 233.48/39.82 | | | | | | | | | % 233.48/39.82 | | | | | | | | | CLOSE: (178) is inconsistent. % 233.48/39.82 | | | | | | | | | % 233.48/39.82 | | | | | | | | End of split % 233.48/39.82 | | | | | | | | % 233.48/39.82 | | | | | | | End of split % 233.48/39.82 | | | | | | | % 233.48/39.82 | | | | | | End of split % 233.48/39.82 | | | | | | % 233.48/39.82 | | | | | Case 2: % 233.48/39.82 | | | | | | % 233.48/39.82 | | | | | | (179) all_74_18 = n2 % 233.48/39.82 | | | | | | % 233.48/39.82 | | | | | | REDUCE: (149), (179) imply: % 233.48/39.82 | | | | | | (180) a_select3(id_ds1_filter, n2, n3) = all_74_16 % 233.48/39.82 | | | | | | % 233.48/39.82 | | | | | | REDUCE: (150), (179) imply: % 233.48/39.82 | | | | | | (181) a_select3(id_ds1_filter, n3, n2) = all_74_17 % 233.48/39.82 | | | | | | % 233.48/39.82 | | | | | | REDUCE: (3), (179) imply: % 233.48/39.82 | | | | | | (182) leq(n2, n5) % 233.48/39.82 | | | | | | % 233.48/39.82 | | | | | | REDUCE: (23), (179) imply: % 233.48/39.82 | | | | | | (183) leq(n0, n2) % 233.48/39.82 | | | | | | % 233.48/39.82 | | | | | | GROUND_INST: instantiating (24) with n2, n3, all_74_16, simplifying % 233.48/39.82 | | | | | | with (8), (14), (152), (180), (183) gives: % 233.48/39.82 | | | | | | (184) ~ leq(n3, all_74_21) | ~ leq(n2, all_74_21) | % 233.48/39.82 | | | | | | (a_select3(id_ds1_filter, n3, n2) = all_74_16 & % 233.48/39.82 | | | | | | $i(all_74_16)) % 233.48/39.82 | | | | | | % 233.48/39.82 | | | | | | BETA: splitting (184) gives: % 233.48/39.82 | | | | | | % 233.48/39.82 | | | | | | Case 1: % 233.48/39.82 | | | | | | | % 233.48/39.82 | | | | | | | (185) ~ leq(n3, all_74_21) % 233.48/39.82 | | | | | | | % 233.48/39.82 | | | | | | | REDUCE: (4), (185) imply: % 233.48/39.82 | | | | | | | (186) ~ leq(n3, n5) % 233.48/39.82 | | | | | | | % 233.48/39.82 | | | | | | | PRED_UNIFY: (151), (186) imply: % 233.48/39.82 | | | | | | | (187) $false % 233.48/39.82 | | | | | | | % 233.48/39.82 | | | | | | | CLOSE: (187) is inconsistent. % 233.48/39.82 | | | | | | | % 233.48/39.82 | | | | | | Case 2: % 233.48/39.82 | | | | | | | % 233.48/39.82 | | | | | | | (188) ~ leq(n2, all_74_21) | (a_select3(id_ds1_filter, n3, n2) % 233.48/39.82 | | | | | | | = all_74_16 & $i(all_74_16)) % 233.48/39.82 | | | | | | | % 233.48/39.82 | | | | | | | BETA: splitting (188) gives: % 233.48/39.82 | | | | | | | % 233.48/39.82 | | | | | | | Case 1: % 233.48/39.82 | | | | | | | | % 233.48/39.82 | | | | | | | | (189) ~ leq(n2, all_74_21) % 233.48/39.82 | | | | | | | | % 233.48/39.82 | | | | | | | | REDUCE: (4), (189) imply: % 233.48/39.82 | | | | | | | | (190) ~ leq(n2, n5) % 233.48/39.82 | | | | | | | | % 233.48/39.82 | | | | | | | | PRED_UNIFY: (182), (190) imply: % 233.48/39.82 | | | | | | | | (191) $false % 233.48/39.82 | | | | | | | | % 233.48/39.82 | | | | | | | | CLOSE: (191) is inconsistent. % 233.48/39.82 | | | | | | | | % 233.48/39.82 | | | | | | | Case 2: % 233.48/39.82 | | | | | | | | % 233.48/39.82 | | | | | | | | (192) a_select3(id_ds1_filter, n3, n2) = all_74_16 & % 233.48/39.82 | | | | | | | | $i(all_74_16) % 233.48/39.82 | | | | | | | | % 233.48/39.82 | | | | | | | | ALPHA: (192) implies: % 233.48/39.82 | | | | | | | | (193) a_select3(id_ds1_filter, n3, n2) = all_74_16 % 233.48/39.82 | | | | | | | | % 233.48/39.82 | | | | | | | | REF_CLOSE: (10), (15), (181), (193) are inconsistent by % 233.48/39.82 | | | | | | | | sub-proof #11. % 233.48/39.82 | | | | | | | | % 233.48/39.82 | | | | | | | End of split % 233.48/39.82 | | | | | | | % 233.48/39.82 | | | | | | End of split % 233.48/39.82 | | | | | | % 233.48/39.82 | | | | | End of split % 233.48/39.82 | | | | | % 233.48/39.82 | | | | Case 2: % 233.48/39.82 | | | | | % 233.48/39.82 | | | | | (194) all_74_18 = n3 % 233.48/39.82 | | | | | % 233.48/39.82 | | | | | REDUCE: (149), (194) imply: % 233.48/39.82 | | | | | (195) a_select3(id_ds1_filter, n3, n3) = all_74_16 % 233.48/39.82 | | | | | % 233.48/39.82 | | | | | REDUCE: (150), (194) imply: % 233.48/39.82 | | | | | (196) a_select3(id_ds1_filter, n3, n3) = all_74_17 % 233.48/39.82 | | | | | % 233.48/39.82 | | | | | GROUND_INST: instantiating (10) with all_74_17, all_74_16, n3, n3, % 233.48/39.82 | | | | | id_ds1_filter, simplifying with (195), (196) gives: % 233.48/39.82 | | | | | (197) all_74_16 = all_74_17 % 233.48/39.82 | | | | | % 233.48/39.82 | | | | | REDUCE: (15), (197) imply: % 233.48/39.82 | | | | | (198) $false % 233.48/39.82 | | | | | % 233.48/39.82 | | | | | CLOSE: (198) is inconsistent. % 233.48/39.82 | | | | | % 233.48/39.82 | | | | End of split % 233.48/39.82 | | | | % 233.48/39.82 | | | End of split % 233.48/39.82 | | | % 233.48/39.82 | | Case 2: % 233.48/39.82 | | | % 233.48/39.82 | | | (199) all_74_18 = n4 % 233.48/39.82 | | | % 233.48/39.82 | | | REDUCE: (19), (199) imply: % 233.48/39.82 | | | (200) a_select3(id_ds1_filter, n4, all_74_19) = all_74_16 % 233.48/39.82 | | | % 233.48/39.82 | | | REDUCE: (16), (199) imply: % 233.48/39.82 | | | (201) a_select3(id_ds1_filter, all_74_19, n4) = all_74_17 % 233.48/39.82 | | | % 233.48/39.82 | | | REDUCE: (3), (199) imply: % 233.48/39.82 | | | (202) leq(n4, n5) % 233.48/39.82 | | | % 233.48/39.82 | | | REDUCE: (23), (199) imply: % 233.48/39.82 | | | (203) leq(n0, n4) % 233.48/39.82 | | | % 233.48/39.82 | | | BETA: splitting (28) gives: % 233.48/39.82 | | | % 233.48/39.82 | | | Case 1: % 233.48/39.82 | | | | % 233.48/39.82 | | | | (204) gt(n3, all_74_19) % 233.48/39.82 | | | | % 233.48/39.82 | | | | GROUND_INST: instantiating (7) with all_74_19, n3, n2, simplifying with % 233.48/39.82 | | | | (1), (14), (17), (204) gives: % 233.48/39.82 | | | | (205) leq(all_74_19, n2) % 233.48/39.82 | | | | % 233.48/39.82 | | | | GROUND_INST: instantiating (2) with all_74_19, n2, simplifying with (1), % 233.48/39.82 | | | | (8), (205) gives: % 233.48/39.82 | | | | (206) all_74_19 = n2 | gt(n2, all_74_19) % 233.48/39.82 | | | | % 233.48/39.82 | | | | BETA: splitting (206) gives: % 233.48/39.82 | | | | % 233.48/39.82 | | | | Case 1: % 233.48/39.82 | | | | | % 233.48/39.82 | | | | | (207) gt(n2, all_74_19) % 233.48/39.82 | | | | | % 233.48/39.82 | | | | | GROUND_INST: instantiating (7) with all_74_19, n2, n1, simplifying % 233.48/39.82 | | | | | with (1), (8), (11), (207) gives: % 233.48/39.82 | | | | | (208) leq(all_74_19, n1) % 233.48/39.82 | | | | | % 233.48/39.82 | | | | | GROUND_INST: instantiating (25) with all_74_19, simplifying with (1), % 233.48/39.82 | | | | | (21), (208) gives: % 233.48/39.82 | | | | | (209) all_74_19 = n1 | all_74_19 = n0 % 233.48/39.82 | | | | | % 233.48/39.82 | | | | | BETA: splitting (209) gives: % 233.48/39.82 | | | | | % 233.48/39.82 | | | | | Case 1: % 233.48/39.82 | | | | | | % 233.48/39.82 | | | | | | (210) all_74_19 = n0 % 233.48/39.82 | | | | | | % 233.48/39.82 | | | | | | REDUCE: (13), (210) imply: % 233.48/39.82 | | | | | | (211) $false % 233.48/39.82 | | | | | | % 233.48/39.82 | | | | | | CLOSE: (211) is inconsistent. % 233.48/39.82 | | | | | | % 233.48/39.82 | | | | | Case 2: % 233.48/39.82 | | | | | | % 233.48/39.82 | | | | | | (212) all_74_19 = n1 % 233.48/39.82 | | | | | | % 233.48/39.82 | | | | | | REDUCE: (201), (212) imply: % 233.48/39.82 | | | | | | (213) a_select3(id_ds1_filter, n1, n4) = all_74_17 % 233.48/39.82 | | | | | | % 233.48/39.82 | | | | | | REDUCE: (200), (212) imply: % 233.48/39.82 | | | | | | (214) a_select3(id_ds1_filter, n4, n1) = all_74_16 % 233.48/39.82 | | | | | | % 233.48/39.82 | | | | | | REDUCE: (1), (212) imply: % 233.48/39.82 | | | | | | (215) $i(n1) % 233.48/39.82 | | | | | | % 233.48/39.82 | | | | | | REDUCE: (20), (212) imply: % 233.48/39.82 | | | | | | (216) leq(n1, n5) % 233.48/39.82 | | | | | | % 233.48/39.82 | | | | | | REDUCE: (21), (212) imply: % 233.48/39.82 | | | | | | (217) leq(n0, n1) % 233.48/39.82 | | | | | | % 233.48/39.82 | | | | | | GROUND_INST: instantiating (24) with n1, n4, all_74_17, simplifying % 233.48/39.82 | | | | | | with (18), (203), (213), (215), (217) gives: % 233.48/39.82 | | | | | | (218) ~ leq(n4, all_74_21) | ~ leq(n1, all_74_21) | % 233.48/39.82 | | | | | | (a_select3(id_ds1_filter, n4, n1) = all_74_17 & % 233.48/39.82 | | | | | | $i(all_74_17)) % 233.48/39.82 | | | | | | % 233.48/39.82 | | | | | | BETA: splitting (218) gives: % 233.48/39.82 | | | | | | % 233.48/39.82 | | | | | | Case 1: % 233.48/39.82 | | | | | | | % 233.48/39.82 | | | | | | | (219) ~ leq(n4, all_74_21) % 233.48/39.82 | | | | | | | % 233.48/39.82 | | | | | | | REDUCE: (4), (219) imply: % 233.48/39.82 | | | | | | | (220) ~ leq(n4, n5) % 233.48/39.82 | | | | | | | % 233.48/39.82 | | | | | | | PRED_UNIFY: (202), (220) imply: % 233.48/39.82 | | | | | | | (221) $false % 233.48/39.82 | | | | | | | % 233.48/39.82 | | | | | | | CLOSE: (221) is inconsistent. % 233.48/39.82 | | | | | | | % 233.48/39.82 | | | | | | Case 2: % 233.48/39.82 | | | | | | | % 233.48/39.82 | | | | | | | (222) ~ leq(n1, all_74_21) | (a_select3(id_ds1_filter, n4, n1) % 233.48/39.82 | | | | | | | = all_74_17 & $i(all_74_17)) % 233.48/39.82 | | | | | | | % 233.48/39.82 | | | | | | | BETA: splitting (222) gives: % 233.48/39.82 | | | | | | | % 233.48/39.82 | | | | | | | Case 1: % 233.48/39.82 | | | | | | | | % 233.48/39.82 | | | | | | | | (223) ~ leq(n1, all_74_21) % 233.48/39.82 | | | | | | | | % 233.48/39.82 | | | | | | | | REDUCE: (4), (223) imply: % 233.48/39.82 | | | | | | | | (224) ~ leq(n1, n5) % 233.48/39.82 | | | | | | | | % 233.48/39.82 | | | | | | | | PRED_UNIFY: (216), (224) imply: % 233.48/39.82 | | | | | | | | (225) $false % 233.48/39.82 | | | | | | | | % 233.48/39.82 | | | | | | | | CLOSE: (225) is inconsistent. % 233.48/39.82 | | | | | | | | % 233.48/39.82 | | | | | | | Case 2: % 233.48/39.82 | | | | | | | | % 233.48/39.82 | | | | | | | | (226) a_select3(id_ds1_filter, n4, n1) = all_74_17 & % 233.48/39.82 | | | | | | | | $i(all_74_17) % 233.48/39.82 | | | | | | | | % 233.48/39.82 | | | | | | | | ALPHA: (226) implies: % 233.48/39.82 | | | | | | | | (227) a_select3(id_ds1_filter, n4, n1) = all_74_17 % 233.48/39.82 | | | | | | | | % 233.48/39.82 | | | | | | | | GROUND_INST: instantiating (10) with all_74_17, all_74_16, n1, % 233.48/39.82 | | | | | | | | n4, id_ds1_filter, simplifying with (214), (227) % 233.48/39.82 | | | | | | | | gives: % 233.48/39.82 | | | | | | | | (228) all_74_16 = all_74_17 % 233.48/39.82 | | | | | | | | % 233.48/39.82 | | | | | | | | REDUCE: (15), (228) imply: % 233.48/39.82 | | | | | | | | (229) $false % 233.48/39.82 | | | | | | | | % 233.48/39.82 | | | | | | | | CLOSE: (229) is inconsistent. % 233.48/39.82 | | | | | | | | % 233.48/39.82 | | | | | | | End of split % 233.48/39.82 | | | | | | | % 233.48/39.82 | | | | | | End of split % 233.48/39.82 | | | | | | % 233.48/39.82 | | | | | End of split % 233.48/39.82 | | | | | % 233.48/39.82 | | | | Case 2: % 233.48/39.82 | | | | | % 233.48/39.82 | | | | | (230) all_74_19 = n2 % 233.48/39.82 | | | | | % 233.48/39.82 | | | | | REDUCE: (201), (230) imply: % 233.48/39.82 | | | | | (231) a_select3(id_ds1_filter, n2, n4) = all_74_17 % 233.48/39.82 | | | | | % 233.48/39.82 | | | | | REDUCE: (200), (230) imply: % 233.48/39.82 | | | | | (232) a_select3(id_ds1_filter, n4, n2) = all_74_16 % 233.48/39.82 | | | | | % 233.48/39.82 | | | | | REDUCE: (20), (230) imply: % 233.48/39.83 | | | | | (233) leq(n2, n5) % 233.48/39.83 | | | | | % 233.48/39.83 | | | | | REDUCE: (21), (230) imply: % 233.48/39.83 | | | | | (234) leq(n0, n2) % 233.48/39.83 | | | | | % 233.48/39.83 | | | | | GROUND_INST: instantiating (24) with n2, n4, all_74_17, simplifying % 233.48/39.83 | | | | | with (8), (18), (203), (231), (234) gives: % 233.48/39.83 | | | | | (235) ~ leq(n4, all_74_21) | ~ leq(n2, all_74_21) | % 233.48/39.83 | | | | | (a_select3(id_ds1_filter, n4, n2) = all_74_17 & % 233.48/39.83 | | | | | $i(all_74_17)) % 233.48/39.83 | | | | | % 233.48/39.83 | | | | | BETA: splitting (235) gives: % 233.48/39.83 | | | | | % 233.48/39.83 | | | | | Case 1: % 233.48/39.83 | | | | | | % 233.48/39.83 | | | | | | (236) ~ leq(n4, all_74_21) % 233.48/39.83 | | | | | | % 233.48/39.83 | | | | | | REDUCE: (4), (236) imply: % 233.48/39.83 | | | | | | (237) ~ leq(n4, n5) % 233.48/39.83 | | | | | | % 233.48/39.83 | | | | | | PRED_UNIFY: (202), (237) imply: % 233.48/39.83 | | | | | | (238) $false % 233.48/39.83 | | | | | | % 233.48/39.83 | | | | | | CLOSE: (238) is inconsistent. % 233.48/39.83 | | | | | | % 233.48/39.83 | | | | | Case 2: % 233.48/39.83 | | | | | | % 233.48/39.83 | | | | | | (239) ~ leq(n2, all_74_21) | (a_select3(id_ds1_filter, n4, n2) = % 233.48/39.83 | | | | | | all_74_17 & $i(all_74_17)) % 233.48/39.83 | | | | | | % 233.48/39.83 | | | | | | BETA: splitting (239) gives: % 233.48/39.83 | | | | | | % 233.48/39.83 | | | | | | Case 1: % 233.48/39.83 | | | | | | | % 233.48/39.83 | | | | | | | (240) ~ leq(n2, all_74_21) % 233.48/39.83 | | | | | | | % 233.48/39.83 | | | | | | | REDUCE: (4), (240) imply: % 233.48/39.83 | | | | | | | (241) ~ leq(n2, n5) % 233.48/39.83 | | | | | | | % 233.48/39.83 | | | | | | | PRED_UNIFY: (233), (241) imply: % 233.48/39.83 | | | | | | | (242) $false % 233.48/39.83 | | | | | | | % 233.48/39.83 | | | | | | | CLOSE: (242) is inconsistent. % 233.48/39.83 | | | | | | | % 233.48/39.83 | | | | | | Case 2: % 233.48/39.83 | | | | | | | % 233.48/39.83 | | | | | | | (243) a_select3(id_ds1_filter, n4, n2) = all_74_17 & % 233.48/39.83 | | | | | | | $i(all_74_17) % 233.48/39.83 | | | | | | | % 233.48/39.83 | | | | | | | ALPHA: (243) implies: % 233.48/39.83 | | | | | | | (244) a_select3(id_ds1_filter, n4, n2) = all_74_17 % 233.48/39.83 | | | | | | | % 233.48/39.83 | | | | | | | REF_CLOSE: (10), (15), (232), (244) are inconsistent by sub-proof % 233.48/39.83 | | | | | | | #10. % 233.48/39.83 | | | | | | | % 233.48/39.83 | | | | | | End of split % 233.48/39.83 | | | | | | % 233.48/39.83 | | | | | End of split % 233.48/39.83 | | | | | % 233.48/39.83 | | | | End of split % 233.48/39.83 | | | | % 233.48/39.83 | | | Case 2: % 233.48/39.83 | | | | % 233.48/39.83 | | | | (245) all_74_19 = n3 % 233.48/39.83 | | | | % 233.48/39.83 | | | | REDUCE: (201), (245) imply: % 233.48/39.83 | | | | (246) a_select3(id_ds1_filter, n3, n4) = all_74_17 % 233.48/39.83 | | | | % 233.48/39.83 | | | | REDUCE: (200), (245) imply: % 233.48/39.83 | | | | (247) a_select3(id_ds1_filter, n4, n3) = all_74_16 % 233.48/39.83 | | | | % 233.48/39.83 | | | | REDUCE: (20), (245) imply: % 233.48/39.83 | | | | (248) leq(n3, n5) % 233.48/39.83 | | | | % 233.48/39.83 | | | | REDUCE: (21), (245) imply: % 233.48/39.83 | | | | (249) leq(n0, n3) % 233.48/39.83 | | | | % 233.48/39.83 | | | | GROUND_INST: instantiating (24) with n3, n4, all_74_17, simplifying with % 233.48/39.83 | | | | (14), (18), (203), (246), (249) gives: % 233.48/39.83 | | | | (250) ~ leq(n4, all_74_21) | ~ leq(n3, all_74_21) | % 233.48/39.83 | | | | (a_select3(id_ds1_filter, n4, n3) = all_74_17 & $i(all_74_17)) % 233.48/39.83 | | | | % 233.48/39.83 | | | | BETA: splitting (250) gives: % 233.48/39.83 | | | | % 233.48/39.83 | | | | Case 1: % 233.48/39.83 | | | | | % 233.48/39.83 | | | | | (251) ~ leq(n4, all_74_21) % 233.48/39.83 | | | | | % 233.48/39.83 | | | | | REDUCE: (4), (251) imply: % 233.48/39.83 | | | | | (252) ~ leq(n4, n5) % 233.48/39.83 | | | | | % 233.48/39.83 | | | | | PRED_UNIFY: (202), (252) imply: % 233.48/39.83 | | | | | (253) $false % 233.48/39.83 | | | | | % 233.48/39.83 | | | | | CLOSE: (253) is inconsistent. % 233.48/39.83 | | | | | % 233.48/39.83 | | | | Case 2: % 233.48/39.83 | | | | | % 233.48/39.83 | | | | | (254) ~ leq(n3, all_74_21) | (a_select3(id_ds1_filter, n4, n3) = % 233.48/39.83 | | | | | all_74_17 & $i(all_74_17)) % 233.48/39.83 | | | | | % 233.48/39.83 | | | | | BETA: splitting (254) gives: % 233.48/39.83 | | | | | % 233.48/39.83 | | | | | Case 1: % 233.48/39.83 | | | | | | % 233.48/39.83 | | | | | | (255) ~ leq(n3, all_74_21) % 233.48/39.83 | | | | | | % 233.48/39.83 | | | | | | REDUCE: (4), (255) imply: % 233.48/39.83 | | | | | | (256) ~ leq(n3, n5) % 233.48/39.83 | | | | | | % 233.48/39.83 | | | | | | PRED_UNIFY: (248), (256) imply: % 233.48/39.83 | | | | | | (257) $false % 233.48/39.83 | | | | | | % 233.48/39.83 | | | | | | CLOSE: (257) is inconsistent. % 233.48/39.83 | | | | | | % 233.48/39.83 | | | | | Case 2: % 233.48/39.83 | | | | | | % 233.48/39.83 | | | | | | (258) a_select3(id_ds1_filter, n4, n3) = all_74_17 & % 233.48/39.83 | | | | | | $i(all_74_17) % 233.48/39.83 | | | | | | % 233.48/39.83 | | | | | | ALPHA: (258) implies: % 233.48/39.83 | | | | | | (259) a_select3(id_ds1_filter, n4, n3) = all_74_17 % 233.48/39.83 | | | | | | % 233.48/39.83 | | | | | | GROUND_INST: instantiating (10) with all_74_17, all_74_16, n3, n4, % 233.48/39.83 | | | | | | id_ds1_filter, simplifying with (247), (259) gives: % 233.48/39.83 | | | | | | (260) all_74_16 = all_74_17 % 233.48/39.83 | | | | | | % 233.48/39.83 | | | | | | REDUCE: (15), (260) imply: % 233.48/39.83 | | | | | | (261) $false % 233.48/39.83 | | | | | | % 233.48/39.83 | | | | | | CLOSE: (261) is inconsistent. % 233.48/39.83 | | | | | | % 233.48/39.83 | | | | | End of split % 233.48/39.83 | | | | | % 233.48/39.83 | | | | End of split % 233.48/39.83 | | | | % 233.48/39.83 | | | End of split % 233.48/39.83 | | | % 233.48/39.83 | | End of split % 233.48/39.83 | | % 233.48/39.83 | Case 2: % 233.48/39.83 | | % 233.48/39.83 | | (262) all_74_19 = n4 % 233.48/39.83 | | % 233.48/39.83 | | REDUCE: (19), (262) imply: % 233.48/39.83 | | (263) a_select3(id_ds1_filter, all_74_18, n4) = all_74_16 % 233.48/39.83 | | % 233.48/39.83 | | REDUCE: (16), (262) imply: % 233.48/39.83 | | (264) a_select3(id_ds1_filter, n4, all_74_18) = all_74_17 % 233.48/39.83 | | % 233.48/39.83 | | REDUCE: (20), (262) imply: % 233.48/39.83 | | (265) leq(n4, n5) % 233.48/39.83 | | % 233.48/39.83 | | REDUCE: (21), (262) imply: % 233.48/39.83 | | (266) leq(n0, n4) % 233.48/39.83 | | % 233.48/39.83 | | BETA: splitting (5) gives: % 233.48/39.83 | | % 233.48/39.83 | | Case 1: % 233.48/39.83 | | | % 233.48/39.83 | | | (267) gt(n4, all_74_18) % 233.48/39.83 | | | % 233.48/39.83 | | | GROUND_INST: instantiating (7) with all_74_18, n4, n3, simplifying with % 233.48/39.83 | | | (6), (12), (18), (267) gives: % 233.48/39.83 | | | (268) leq(all_74_18, n3) % 233.48/39.83 | | | % 233.48/39.83 | | | GROUND_INST: instantiating (2) with all_74_18, n3, simplifying with (12), % 233.48/39.83 | | | (14), (268) gives: % 233.48/39.83 | | | (269) all_74_18 = n3 | gt(n3, all_74_18) % 233.48/39.83 | | | % 233.48/39.83 | | | BETA: splitting (269) gives: % 233.48/39.83 | | | % 233.48/39.83 | | | Case 1: % 233.48/39.83 | | | | % 233.48/39.83 | | | | (270) gt(n3, all_74_18) % 233.48/39.83 | | | | % 233.48/39.83 | | | | GROUND_INST: instantiating (7) with all_74_18, n3, n2, simplifying with % 233.48/39.83 | | | | (12), (14), (17), (270) gives: % 233.48/39.83 | | | | (271) leq(all_74_18, n2) % 233.48/39.83 | | | | % 233.48/39.83 | | | | GROUND_INST: instantiating (2) with all_74_18, n2, simplifying with (8), % 233.48/39.83 | | | | (12), (271) gives: % 233.48/39.83 | | | | (272) all_74_18 = n2 | gt(n2, all_74_18) % 233.48/39.83 | | | | % 233.48/39.83 | | | | BETA: splitting (272) gives: % 233.48/39.83 | | | | % 233.48/39.83 | | | | Case 1: % 233.48/39.83 | | | | | % 233.48/39.83 | | | | | (273) gt(n2, all_74_18) % 233.48/39.83 | | | | | % 233.48/39.83 | | | | | GROUND_INST: instantiating (7) with all_74_18, n2, n1, simplifying % 233.48/39.83 | | | | | with (8), (11), (12), (273) gives: % 233.48/39.83 | | | | | (274) leq(all_74_18, n1) % 233.48/39.83 | | | | | % 233.48/39.83 | | | | | GROUND_INST: instantiating (25) with all_74_18, simplifying with (12), % 233.48/39.83 | | | | | (23), (274) gives: % 233.48/39.83 | | | | | (275) all_74_18 = n1 | all_74_18 = n0 % 233.48/39.83 | | | | | % 233.48/39.83 | | | | | BETA: splitting (275) gives: % 233.48/39.83 | | | | | % 233.48/39.83 | | | | | Case 1: % 233.48/39.83 | | | | | | % 233.48/39.83 | | | | | | (276) all_74_18 = n0 % 233.48/39.83 | | | | | | % 233.48/39.83 | | | | | | REDUCE: (22), (276) imply: % 233.48/39.83 | | | | | | (277) $false % 233.48/39.83 | | | | | | % 233.48/39.83 | | | | | | CLOSE: (277) is inconsistent. % 233.48/39.83 | | | | | | % 233.48/39.83 | | | | | Case 2: % 233.48/39.83 | | | | | | % 233.48/39.83 | | | | | | (278) all_74_18 = n1 % 233.48/39.83 | | | | | | % 233.48/39.83 | | | | | | REDUCE: (263), (278) imply: % 233.48/39.83 | | | | | | (279) a_select3(id_ds1_filter, n1, n4) = all_74_16 % 233.48/39.83 | | | | | | % 233.48/39.83 | | | | | | REDUCE: (264), (278) imply: % 233.48/39.83 | | | | | | (280) a_select3(id_ds1_filter, n4, n1) = all_74_17 % 233.48/39.83 | | | | | | % 233.48/39.83 | | | | | | REDUCE: (12), (278) imply: % 233.48/39.83 | | | | | | (281) $i(n1) % 233.48/39.83 | | | | | | % 233.48/39.83 | | | | | | REDUCE: (3), (278) imply: % 233.48/39.83 | | | | | | (282) leq(n1, n5) % 233.48/39.83 | | | | | | % 233.48/39.83 | | | | | | REDUCE: (23), (278) imply: % 233.48/39.83 | | | | | | (283) leq(n0, n1) % 233.48/39.83 | | | | | | % 233.48/39.83 | | | | | | GROUND_INST: instantiating (24) with n1, n4, all_74_16, simplifying % 233.48/39.83 | | | | | | with (18), (266), (279), (281), (283) gives: % 233.48/39.83 | | | | | | (284) ~ leq(n4, all_74_21) | ~ leq(n1, all_74_21) | % 233.48/39.83 | | | | | | (a_select3(id_ds1_filter, n4, n1) = all_74_16 & % 233.48/39.83 | | | | | | $i(all_74_16)) % 233.48/39.83 | | | | | | % 233.48/39.83 | | | | | | BETA: splitting (284) gives: % 233.48/39.83 | | | | | | % 233.48/39.83 | | | | | | Case 1: % 233.48/39.83 | | | | | | | % 233.48/39.83 | | | | | | | (285) ~ leq(n4, all_74_21) % 233.48/39.83 | | | | | | | % 233.48/39.83 | | | | | | | REDUCE: (4), (285) imply: % 233.48/39.83 | | | | | | | (286) ~ leq(n4, n5) % 233.48/39.83 | | | | | | | % 233.48/39.83 | | | | | | | PRED_UNIFY: (265), (286) imply: % 233.48/39.83 | | | | | | | (287) $false % 233.48/39.83 | | | | | | | % 233.48/39.83 | | | | | | | CLOSE: (287) is inconsistent. % 233.48/39.83 | | | | | | | % 233.48/39.83 | | | | | | Case 2: % 233.48/39.83 | | | | | | | % 233.48/39.83 | | | | | | | (288) ~ leq(n1, all_74_21) | (a_select3(id_ds1_filter, n4, n1) % 233.48/39.83 | | | | | | | = all_74_16 & $i(all_74_16)) % 233.48/39.83 | | | | | | | % 233.48/39.83 | | | | | | | BETA: splitting (288) gives: % 233.48/39.83 | | | | | | | % 233.48/39.83 | | | | | | | Case 1: % 233.48/39.83 | | | | | | | | % 233.48/39.83 | | | | | | | | (289) ~ leq(n1, all_74_21) % 233.48/39.83 | | | | | | | | % 233.48/39.83 | | | | | | | | REDUCE: (4), (289) imply: % 233.48/39.83 | | | | | | | | (290) ~ leq(n1, n5) % 233.48/39.83 | | | | | | | | % 233.48/39.83 | | | | | | | | PRED_UNIFY: (282), (290) imply: % 233.48/39.83 | | | | | | | | (291) $false % 233.48/39.83 | | | | | | | | % 233.48/39.83 | | | | | | | | CLOSE: (291) is inconsistent. % 233.48/39.83 | | | | | | | | % 233.48/39.83 | | | | | | | Case 2: % 233.48/39.83 | | | | | | | | % 233.48/39.83 | | | | | | | | (292) a_select3(id_ds1_filter, n4, n1) = all_74_16 & % 233.48/39.83 | | | | | | | | $i(all_74_16) % 233.48/39.83 | | | | | | | | % 233.48/39.83 | | | | | | | | ALPHA: (292) implies: % 233.48/39.83 | | | | | | | | (293) a_select3(id_ds1_filter, n4, n1) = all_74_16 % 233.48/39.83 | | | | | | | | % 233.48/39.83 | | | | | | | | GROUND_INST: instantiating (10) with all_74_17, all_74_16, n1, % 233.48/39.83 | | | | | | | | n4, id_ds1_filter, simplifying with (280), (293) % 233.48/39.83 | | | | | | | | gives: % 233.48/39.83 | | | | | | | | (294) all_74_16 = all_74_17 % 233.48/39.83 | | | | | | | | % 233.48/39.83 | | | | | | | | REDUCE: (15), (294) imply: % 233.48/39.83 | | | | | | | | (295) $false % 233.48/39.83 | | | | | | | | % 233.48/39.83 | | | | | | | | CLOSE: (295) is inconsistent. % 233.48/39.83 | | | | | | | | % 233.48/39.83 | | | | | | | End of split % 233.48/39.83 | | | | | | | % 233.48/39.83 | | | | | | End of split % 233.48/39.83 | | | | | | % 233.48/39.83 | | | | | End of split % 233.48/39.83 | | | | | % 233.48/39.83 | | | | Case 2: % 233.48/39.83 | | | | | % 233.48/39.83 | | | | | (296) all_74_18 = n2 % 233.48/39.83 | | | | | % 233.48/39.83 | | | | | REDUCE: (263), (296) imply: % 233.48/39.83 | | | | | (297) a_select3(id_ds1_filter, n2, n4) = all_74_16 % 233.48/39.83 | | | | | % 233.48/39.83 | | | | | REDUCE: (264), (296) imply: % 233.48/39.83 | | | | | (298) a_select3(id_ds1_filter, n4, n2) = all_74_17 % 233.48/39.83 | | | | | % 233.48/39.83 | | | | | REDUCE: (3), (296) imply: % 233.48/39.83 | | | | | (299) leq(n2, n5) % 233.48/39.83 | | | | | % 233.48/39.83 | | | | | REDUCE: (23), (296) imply: % 233.48/39.83 | | | | | (300) leq(n0, n2) % 233.48/39.83 | | | | | % 233.48/39.83 | | | | | GROUND_INST: instantiating (24) with n2, n4, all_74_16, simplifying % 233.48/39.83 | | | | | with (8), (18), (266), (297), (300) gives: % 233.48/39.83 | | | | | (301) ~ leq(n4, all_74_21) | ~ leq(n2, all_74_21) | % 233.48/39.83 | | | | | (a_select3(id_ds1_filter, n4, n2) = all_74_16 & % 233.48/39.83 | | | | | $i(all_74_16)) % 233.48/39.83 | | | | | % 233.48/39.83 | | | | | BETA: splitting (301) gives: % 233.48/39.83 | | | | | % 233.48/39.83 | | | | | Case 1: % 233.48/39.83 | | | | | | % 233.48/39.83 | | | | | | (302) ~ leq(n4, all_74_21) % 233.48/39.83 | | | | | | % 233.48/39.83 | | | | | | REDUCE: (4), (302) imply: % 233.48/39.83 | | | | | | (303) ~ leq(n4, n5) % 233.48/39.83 | | | | | | % 233.48/39.83 | | | | | | PRED_UNIFY: (265), (303) imply: % 233.48/39.83 | | | | | | (304) $false % 233.48/39.83 | | | | | | % 233.48/39.83 | | | | | | CLOSE: (304) is inconsistent. % 233.48/39.83 | | | | | | % 233.48/39.83 | | | | | Case 2: % 233.48/39.83 | | | | | | % 233.48/39.83 | | | | | | (305) ~ leq(n2, all_74_21) | (a_select3(id_ds1_filter, n4, n2) = % 233.48/39.83 | | | | | | all_74_16 & $i(all_74_16)) % 233.48/39.83 | | | | | | % 233.48/39.83 | | | | | | BETA: splitting (305) gives: % 233.48/39.83 | | | | | | % 233.48/39.83 | | | | | | Case 1: % 233.48/39.83 | | | | | | | % 233.48/39.83 | | | | | | | (306) ~ leq(n2, all_74_21) % 233.48/39.83 | | | | | | | % 233.48/39.83 | | | | | | | REDUCE: (4), (306) imply: % 233.48/39.83 | | | | | | | (307) ~ leq(n2, n5) % 233.48/39.83 | | | | | | | % 233.48/39.83 | | | | | | | PRED_UNIFY: (299), (307) imply: % 233.48/39.83 | | | | | | | (308) $false % 233.48/39.83 | | | | | | | % 233.48/39.83 | | | | | | | CLOSE: (308) is inconsistent. % 233.48/39.83 | | | | | | | % 233.48/39.83 | | | | | | Case 2: % 233.48/39.83 | | | | | | | % 233.48/39.83 | | | | | | | (309) a_select3(id_ds1_filter, n4, n2) = all_74_16 & % 233.48/39.83 | | | | | | | $i(all_74_16) % 233.48/39.83 | | | | | | | % 233.48/39.83 | | | | | | | ALPHA: (309) implies: % 233.48/39.83 | | | | | | | (310) a_select3(id_ds1_filter, n4, n2) = all_74_16 % 233.48/39.83 | | | | | | | % 233.48/39.83 | | | | | | | REF_CLOSE: (10), (15), (298), (310) are inconsistent by sub-proof % 233.48/39.83 | | | | | | | #10. % 233.48/39.83 | | | | | | | % 233.48/39.83 | | | | | | End of split % 233.48/39.83 | | | | | | % 233.48/39.83 | | | | | End of split % 233.48/39.83 | | | | | % 233.48/39.83 | | | | End of split % 233.48/39.83 | | | | % 233.48/39.83 | | | Case 2: % 233.48/39.83 | | | | % 233.48/39.83 | | | | (311) all_74_18 = n3 % 233.48/39.83 | | | | % 233.48/39.83 | | | | REDUCE: (263), (311) imply: % 233.48/39.83 | | | | (312) a_select3(id_ds1_filter, n3, n4) = all_74_16 % 233.48/39.83 | | | | % 233.48/39.83 | | | | REDUCE: (264), (311) imply: % 233.48/39.83 | | | | (313) a_select3(id_ds1_filter, n4, n3) = all_74_17 % 233.48/39.83 | | | | % 233.48/39.83 | | | | REDUCE: (3), (311) imply: % 233.48/39.83 | | | | (314) leq(n3, n5) % 233.48/39.83 | | | | % 233.48/39.83 | | | | REDUCE: (23), (311) imply: % 233.48/39.83 | | | | (315) leq(n0, n3) % 233.48/39.83 | | | | % 233.48/39.83 | | | | GROUND_INST: instantiating (24) with n3, n4, all_74_16, simplifying with % 233.48/39.83 | | | | (14), (18), (266), (312), (315) gives: % 233.48/39.83 | | | | (316) ~ leq(n4, all_74_21) | ~ leq(n3, all_74_21) | % 233.48/39.83 | | | | (a_select3(id_ds1_filter, n4, n3) = all_74_16 & $i(all_74_16)) % 233.48/39.83 | | | | % 233.48/39.83 | | | | BETA: splitting (316) gives: % 233.48/39.83 | | | | % 233.48/39.83 | | | | Case 1: % 233.48/39.83 | | | | | % 233.48/39.84 | | | | | (317) ~ leq(n4, all_74_21) % 233.48/39.84 | | | | | % 233.48/39.84 | | | | | REDUCE: (4), (317) imply: % 233.48/39.84 | | | | | (318) ~ leq(n4, n5) % 233.48/39.84 | | | | | % 233.48/39.84 | | | | | PRED_UNIFY: (265), (318) imply: % 233.48/39.84 | | | | | (319) $false % 233.48/39.84 | | | | | % 233.48/39.84 | | | | | CLOSE: (319) is inconsistent. % 233.48/39.84 | | | | | % 233.48/39.84 | | | | Case 2: % 233.48/39.84 | | | | | % 233.48/39.84 | | | | | (320) ~ leq(n3, all_74_21) | (a_select3(id_ds1_filter, n4, n3) = % 233.48/39.84 | | | | | all_74_16 & $i(all_74_16)) % 233.48/39.84 | | | | | % 233.48/39.84 | | | | | BETA: splitting (320) gives: % 233.48/39.84 | | | | | % 233.48/39.84 | | | | | Case 1: % 233.48/39.84 | | | | | | % 233.48/39.84 | | | | | | (321) ~ leq(n3, all_74_21) % 233.48/39.84 | | | | | | % 233.48/39.84 | | | | | | REDUCE: (4), (321) imply: % 233.48/39.84 | | | | | | (322) ~ leq(n3, n5) % 233.48/39.84 | | | | | | % 233.48/39.84 | | | | | | PRED_UNIFY: (314), (322) imply: % 233.48/39.84 | | | | | | (323) $false % 233.48/39.84 | | | | | | % 233.48/39.84 | | | | | | CLOSE: (323) is inconsistent. % 233.48/39.84 | | | | | | % 233.48/39.84 | | | | | Case 2: % 233.48/39.84 | | | | | | % 233.48/39.84 | | | | | | (324) a_select3(id_ds1_filter, n4, n3) = all_74_16 & % 233.48/39.84 | | | | | | $i(all_74_16) % 233.48/39.84 | | | | | | % 233.48/39.84 | | | | | | ALPHA: (324) implies: % 233.48/39.84 | | | | | | (325) a_select3(id_ds1_filter, n4, n3) = all_74_16 % 233.48/39.84 | | | | | | % 233.48/39.84 | | | | | | GROUND_INST: instantiating (10) with all_74_17, all_74_16, n3, n4, % 233.48/39.84 | | | | | | id_ds1_filter, simplifying with (313), (325) gives: % 233.48/39.84 | | | | | | (326) all_74_16 = all_74_17 % 233.48/39.84 | | | | | | % 233.48/39.84 | | | | | | REDUCE: (15), (326) imply: % 233.48/39.84 | | | | | | (327) $false % 233.48/39.84 | | | | | | % 233.48/39.84 | | | | | | CLOSE: (327) is inconsistent. % 233.48/39.84 | | | | | | % 233.48/39.84 | | | | | End of split % 233.48/39.84 | | | | | % 233.48/39.84 | | | | End of split % 233.48/39.84 | | | | % 233.48/39.84 | | | End of split % 233.48/39.84 | | | % 233.48/39.84 | | Case 2: % 233.48/39.84 | | | % 233.48/39.84 | | | (328) all_74_18 = n4 % 233.48/39.84 | | | % 233.48/39.84 | | | REDUCE: (263), (328) imply: % 233.48/39.84 | | | (329) a_select3(id_ds1_filter, n4, n4) = all_74_16 % 233.48/39.84 | | | % 233.48/39.84 | | | REDUCE: (264), (328) imply: % 233.48/39.84 | | | (330) a_select3(id_ds1_filter, n4, n4) = all_74_17 % 233.48/39.84 | | | % 233.48/39.84 | | | GROUND_INST: instantiating (10) with all_74_17, all_74_16, n4, n4, % 233.48/39.84 | | | id_ds1_filter, simplifying with (329), (330) gives: % 233.48/39.84 | | | (331) all_74_16 = all_74_17 % 233.48/39.84 | | | % 233.48/39.84 | | | REDUCE: (15), (331) imply: % 233.48/39.84 | | | (332) $false % 233.48/39.84 | | | % 233.48/39.84 | | | CLOSE: (332) is inconsistent. % 233.48/39.84 | | | % 233.48/39.84 | | End of split % 233.48/39.84 | | % 233.48/39.84 | End of split % 233.48/39.84 | % 233.48/39.84 End of proof % 233.48/39.84 % 233.48/39.84 Sub-proof #10 shows that the following formulas are inconsistent: % 233.48/39.84 ---------------------------------------------------------------- % 233.48/39.84 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 233.48/39.84 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 233.48/39.84 v0)) % 233.48/39.84 (2) a_select3(id_ds1_filter, n4, n2) = all_74_16 % 233.48/39.84 (3) a_select3(id_ds1_filter, n4, n2) = all_74_17 % 233.48/39.84 (4) ~ (all_74_16 = all_74_17) % 233.48/39.84 % 233.48/39.84 Begin of proof % 233.48/39.84 | % 233.48/39.84 | GROUND_INST: instantiating (1) with all_74_17, all_74_16, n2, n4, % 233.48/39.84 | id_ds1_filter, simplifying with (2), (3) gives: % 233.48/39.84 | (5) all_74_16 = all_74_17 % 233.48/39.84 | % 233.48/39.84 | REDUCE: (4), (5) imply: % 233.48/39.84 | (6) $false % 233.48/39.84 | % 233.48/39.84 | CLOSE: (6) is inconsistent. % 233.48/39.84 | % 233.48/39.84 End of proof % 233.48/39.84 % 233.48/39.84 Sub-proof #11 shows that the following formulas are inconsistent: % 233.48/39.84 ---------------------------------------------------------------- % 233.48/39.84 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 233.48/39.84 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 233.48/39.84 v0)) % 233.48/39.84 (2) a_select3(id_ds1_filter, n3, n2) = all_74_16 % 233.48/39.84 (3) a_select3(id_ds1_filter, n3, n2) = all_74_17 % 233.48/39.84 (4) ~ (all_74_16 = all_74_17) % 233.48/39.84 % 233.48/39.84 Begin of proof % 233.48/39.84 | % 233.48/39.84 | GROUND_INST: instantiating (1) with all_74_17, all_74_16, n2, n3, % 233.48/39.84 | id_ds1_filter, simplifying with (2), (3) gives: % 233.48/39.84 | (5) all_74_16 = all_74_17 % 233.48/39.84 | % 233.48/39.84 | REDUCE: (4), (5) imply: % 233.48/39.84 | (6) $false % 233.48/39.84 | % 233.48/39.84 | CLOSE: (6) is inconsistent. % 233.48/39.84 | % 233.48/39.84 End of proof % 233.48/39.84 % 233.48/39.84 Sub-proof #12 shows that the following formulas are inconsistent: % 233.48/39.84 ---------------------------------------------------------------- % 233.48/39.84 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 233.48/39.84 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 233.48/39.84 v0)) % 233.48/39.84 (2) a_select3(id_ds1_filter, n2, n1) = all_74_16 % 233.75/39.84 (3) a_select3(id_ds1_filter, n2, n1) = all_74_17 % 233.75/39.84 (4) ~ (all_74_16 = all_74_17) % 233.75/39.84 % 233.75/39.84 Begin of proof % 233.75/39.84 | % 233.75/39.84 | GROUND_INST: instantiating (1) with all_74_16, all_74_17, n1, n2, % 233.75/39.84 | id_ds1_filter, simplifying with (2), (3) gives: % 233.75/39.84 | (5) all_74_16 = all_74_17 % 233.75/39.84 | % 233.75/39.84 | REDUCE: (4), (5) imply: % 233.75/39.84 | (6) $false % 233.75/39.84 | % 233.75/39.84 | CLOSE: (6) is inconsistent. % 233.75/39.84 | % 233.75/39.84 End of proof % 233.75/39.84 % 233.75/39.84 Sub-proof #13 shows that the following formulas are inconsistent: % 233.75/39.84 ---------------------------------------------------------------- % 233.75/39.84 (1) $i(all_74_19) % 233.75/39.84 (2) all_74_19 = n0 % 233.75/39.84 (3) gt(all_74_19, n0) % 233.75/39.84 (4) ! [v0: $i] : ( ~ $i(v0) | ~ gt(v0, v0)) % 233.75/39.84 % 233.75/39.84 Begin of proof % 233.75/39.84 | % 233.75/39.84 | REDUCE: (1), (2) imply: % 233.75/39.84 | (5) $i(n0) % 233.75/39.84 | % 233.75/39.84 | REDUCE: (2), (3) imply: % 233.75/39.84 | (6) gt(n0, n0) % 233.75/39.84 | % 233.75/39.84 | GROUND_INST: instantiating (4) with n0, simplifying with (5), (6) gives: % 233.75/39.84 | (7) $false % 233.75/39.84 | % 233.75/39.84 | CLOSE: (7) is inconsistent. % 233.75/39.84 | % 233.75/39.84 End of proof % 233.75/39.84 % 233.75/39.84 Sub-proof #14 shows that the following formulas are inconsistent: % 233.75/39.84 ---------------------------------------------------------------- % 233.75/39.84 (1) $i(all_74_18) % 233.75/39.84 (2) all_74_18 = n0 % 233.75/39.84 (3) gt(all_74_18, n0) % 233.75/39.84 (4) ! [v0: $i] : ( ~ $i(v0) | ~ gt(v0, v0)) % 233.75/39.84 % 233.75/39.84 Begin of proof % 233.75/39.84 | % 233.75/39.84 | REDUCE: (1), (2) imply: % 233.75/39.84 | (5) $i(n0) % 233.75/39.84 | % 233.75/39.84 | REDUCE: (2), (3) imply: % 233.75/39.84 | (6) gt(n0, n0) % 233.75/39.84 | % 233.75/39.84 | GROUND_INST: instantiating (4) with n0, simplifying with (5), (6) gives: % 233.75/39.84 | (7) $false % 233.75/39.84 | % 233.75/39.84 | CLOSE: (7) is inconsistent. % 233.75/39.84 | % 233.75/39.84 End of proof % 233.75/39.84 % 233.75/39.84 Sub-proof #15 shows that the following formulas are inconsistent: % 233.75/39.84 ---------------------------------------------------------------- % 233.75/39.84 (1) a_select3(pminus_ds1_filter, all_74_14, all_74_15) = all_74_12 % 233.75/39.84 (2) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ leq(v0, % 233.75/39.84 v1) | gt(v1, v0)) % 233.75/39.84 (3) leq(all_74_14, n5) % 233.75/39.84 (4) ~ (all_74_12 = all_74_13) % 233.75/39.84 (5) all_74_15 = n5 | gt(n5, all_74_15) % 233.75/39.84 (6) a_select3(pminus_ds1_filter, all_74_15, all_74_14) = all_74_13 % 233.75/39.84 (7) all_74_15 = n0 | gt(all_74_15, n0) % 233.75/39.84 (8) all_74_21 = n5 % 233.75/39.84 (9) pred(n4) = n3 % 233.75/39.84 (10) ~ gt(n0, n0) % 233.75/39.84 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (pred(v1) = v2) | ~ % 233.75/39.84 $i(v1) | ~ $i(v0) | ~ gt(v1, v0) | leq(v0, v2)) % 233.75/39.84 (12) $i(n2) % 233.75/39.84 (13) pred(n5) = n4 % 233.75/39.84 (14) all_74_14 = n5 | all_74_14 = n4 | all_74_14 = n3 | all_74_14 = n2 | % 233.75/39.84 all_74_14 = n1 | all_74_14 = n0 % 233.75/39.84 (15) $i(all_74_15) % 233.75/39.84 (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 233.75/39.84 (v1 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 233.75/39.84 v0)) % 233.75/39.84 (17) gt(all_74_14, n0) % 233.75/39.84 (18) leq(n0, all_74_14) % 233.75/39.84 (19) pred(n2) = n1 % 233.75/39.84 (20) $i(n5) % 233.75/39.84 (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 233.75/39.84 (a_select3(pminus_ds1_filter, v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 233.75/39.84 ~ leq(v1, all_74_21) | ~ leq(v0, all_74_21) | ~ leq(n0, v1) | ~ % 233.75/39.84 leq(n0, v0) | (a_select3(pminus_ds1_filter, v1, v0) = v2 & $i(v2))) % 233.75/39.84 (22) leq(all_74_15, n5) % 233.75/39.84 (23) $i(n3) % 233.75/39.84 (24) all_74_14 = n5 | gt(n5, all_74_14) % 233.75/39.84 (25) pred(n3) = n2 % 233.75/39.84 (26) $i(n4) % 233.75/39.84 (27) $i(all_74_14) % 233.75/39.84 (28) leq(n0, all_74_15) % 233.75/39.84 (29) all_74_15 = n5 | all_74_15 = n4 | all_74_15 = n3 | all_74_15 = n2 | % 233.75/39.84 all_74_15 = n1 | all_74_15 = n0 % 233.75/39.84 (30) ! [v0: $i] : (v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0, n1) | ~ % 233.75/39.84 leq(n0, v0)) % 233.75/39.84 % 233.75/39.84 Begin of proof % 233.75/39.84 | % 233.75/39.84 | BETA: splitting (7) gives: % 233.75/39.84 | % 233.75/39.84 | Case 1: % 233.75/39.84 | | % 233.75/39.84 | | (31) gt(all_74_15, n0) % 233.75/39.84 | | % 233.75/39.84 | | BETA: splitting (5) gives: % 233.75/39.84 | | % 233.75/39.84 | | Case 1: % 233.75/39.84 | | | % 233.75/39.84 | | | (32) gt(n5, all_74_15) % 233.75/39.84 | | | % 233.75/39.84 | | | GROUND_INST: instantiating (11) with all_74_15, n5, n4, simplifying with % 233.75/39.84 | | | (13), (15), (20), (32) gives: % 233.75/39.84 | | | (33) leq(all_74_15, n4) % 233.75/39.84 | | | % 233.75/39.84 | | | GROUND_INST: instantiating (2) with all_74_15, n4, simplifying with (15), % 233.75/39.84 | | | (26), (33) gives: % 233.75/39.84 | | | (34) all_74_15 = n4 | gt(n4, all_74_15) % 233.75/39.84 | | | % 233.75/39.84 | | | BETA: splitting (24) gives: % 233.75/39.84 | | | % 233.75/39.84 | | | Case 1: % 233.75/39.84 | | | | % 233.75/39.84 | | | | (35) gt(n5, all_74_14) % 233.75/39.84 | | | | % 233.75/39.84 | | | | GROUND_INST: instantiating (11) with all_74_14, n5, n4, simplifying with % 233.75/39.84 | | | | (13), (20), (27), (35) gives: % 233.75/39.84 | | | | (36) leq(all_74_14, n4) % 233.75/39.84 | | | | % 233.75/39.84 | | | | GROUND_INST: instantiating (2) with all_74_14, n4, simplifying with % 233.75/39.84 | | | | (26), (27), (36) gives: % 233.75/39.84 | | | | (37) all_74_14 = n4 | gt(n4, all_74_14) % 233.75/39.84 | | | | % 233.75/39.84 | | | | BETA: splitting (14) gives: % 233.75/39.84 | | | | % 233.75/39.84 | | | | Case 1: % 233.75/39.84 | | | | | % 233.75/39.84 | | | | | (38) all_74_14 = n0 % 233.75/39.84 | | | | | % 233.75/39.84 | | | | | REDUCE: (17), (38) imply: % 233.75/39.84 | | | | | (39) gt(n0, n0) % 233.75/39.84 | | | | | % 233.75/39.84 | | | | | PRED_UNIFY: (10), (39) imply: % 233.75/39.84 | | | | | (40) $false % 233.75/39.84 | | | | | % 233.75/39.84 | | | | | CLOSE: (40) is inconsistent. % 233.75/39.84 | | | | | % 233.75/39.84 | | | | Case 2: % 233.75/39.84 | | | | | % 233.75/39.84 | | | | | (41) ~ (all_74_14 = n0) % 233.75/39.84 | | | | | % 233.75/39.84 | | | | | BETA: splitting (29) gives: % 233.75/39.84 | | | | | % 233.75/39.84 | | | | | Case 1: % 233.75/39.84 | | | | | | % 233.75/39.84 | | | | | | (42) all_74_15 = n0 % 233.75/39.84 | | | | | | % 233.75/39.84 | | | | | | REDUCE: (31), (42) imply: % 233.75/39.84 | | | | | | (43) gt(n0, n0) % 233.75/39.84 | | | | | | % 233.75/39.84 | | | | | | PRED_UNIFY: (10), (43) imply: % 233.75/39.84 | | | | | | (44) $false % 233.75/39.84 | | | | | | % 233.75/39.84 | | | | | | CLOSE: (44) is inconsistent. % 233.75/39.84 | | | | | | % 233.75/39.84 | | | | | Case 2: % 233.75/39.84 | | | | | | % 233.75/39.84 | | | | | | (45) ~ (all_74_15 = n0) % 233.75/39.84 | | | | | | % 233.75/39.84 | | | | | | REF_CLOSE: (1), (2), (3), (4), (6), (8), (9), (11), (12), (15), % 233.75/39.84 | | | | | | (16), (18), (19), (21), (22), (23), (25), (26), (27), % 233.75/39.84 | | | | | | (28), (30), (34), (37), (41), (45) are inconsistent by % 233.75/39.84 | | | | | | sub-proof #23. % 233.75/39.84 | | | | | | % 233.75/39.84 | | | | | End of split % 233.75/39.84 | | | | | % 233.75/39.84 | | | | End of split % 233.75/39.84 | | | | % 233.75/39.84 | | | Case 2: % 233.75/39.84 | | | | % 233.75/39.84 | | | | (46) all_74_14 = n5 % 233.75/39.84 | | | | % 233.75/39.84 | | | | REDUCE: (1), (46) imply: % 233.75/39.84 | | | | (47) a_select3(pminus_ds1_filter, n5, all_74_15) = all_74_12 % 233.75/39.84 | | | | % 233.75/39.85 | | | | REDUCE: (6), (46) imply: % 233.75/39.85 | | | | (48) a_select3(pminus_ds1_filter, all_74_15, n5) = all_74_13 % 233.75/39.85 | | | | % 233.75/39.85 | | | | REDUCE: (3), (46) imply: % 233.75/39.85 | | | | (49) leq(n5, n5) % 233.75/39.85 | | | | % 233.75/39.85 | | | | REDUCE: (18), (46) imply: % 233.75/39.85 | | | | (50) leq(n0, n5) % 233.75/39.85 | | | | % 233.75/39.85 | | | | BETA: splitting (29) gives: % 233.75/39.85 | | | | % 233.75/39.85 | | | | Case 1: % 233.75/39.85 | | | | | % 233.75/39.85 | | | | | (51) all_74_15 = n0 % 233.75/39.85 | | | | | % 233.75/39.85 | | | | | REDUCE: (31), (51) imply: % 233.75/39.85 | | | | | (52) gt(n0, n0) % 233.75/39.85 | | | | | % 233.75/39.85 | | | | | PRED_UNIFY: (10), (52) imply: % 233.75/39.85 | | | | | (53) $false % 233.75/39.85 | | | | | % 233.75/39.85 | | | | | CLOSE: (53) is inconsistent. % 233.75/39.85 | | | | | % 233.75/39.85 | | | | Case 2: % 233.75/39.85 | | | | | % 233.75/39.85 | | | | | (54) ~ (all_74_15 = n0) % 233.75/39.85 | | | | | % 233.75/39.85 | | | | | REF_CLOSE: (2), (4), (8), (9), (11), (12), (15), (16), (19), (20), % 233.75/39.85 | | | | | (21), (22), (23), (25), (26), (28), (30), (34), (47), (48), % 233.75/39.85 | | | | | (49), (50), (54) are inconsistent by sub-proof #21. % 233.75/39.85 | | | | | % 233.75/39.85 | | | | End of split % 233.75/39.85 | | | | % 233.75/39.85 | | | End of split % 233.75/39.85 | | | % 233.75/39.85 | | Case 2: % 233.75/39.85 | | | % 233.75/39.85 | | | (55) all_74_15 = n5 % 233.75/39.85 | | | % 233.75/39.85 | | | REDUCE: (1), (55) imply: % 233.75/39.85 | | | (56) a_select3(pminus_ds1_filter, all_74_14, n5) = all_74_12 % 233.75/39.85 | | | % 233.75/39.85 | | | REDUCE: (6), (55) imply: % 233.75/39.85 | | | (57) a_select3(pminus_ds1_filter, n5, all_74_14) = all_74_13 % 233.75/39.85 | | | % 233.75/39.85 | | | REDUCE: (22), (55) imply: % 233.75/39.85 | | | (58) leq(n5, n5) % 233.75/39.85 | | | % 233.75/39.85 | | | REDUCE: (28), (55) imply: % 233.75/39.85 | | | (59) leq(n0, n5) % 233.75/39.85 | | | % 233.75/39.85 | | | BETA: splitting (24) gives: % 233.75/39.85 | | | % 233.75/39.85 | | | Case 1: % 233.75/39.85 | | | | % 233.75/39.85 | | | | (60) gt(n5, all_74_14) % 233.75/39.85 | | | | % 233.75/39.85 | | | | GROUND_INST: instantiating (11) with all_74_14, n5, n4, simplifying with % 233.75/39.85 | | | | (13), (20), (27), (60) gives: % 233.75/39.85 | | | | (61) leq(all_74_14, n4) % 233.75/39.85 | | | | % 233.75/39.85 | | | | GROUND_INST: instantiating (2) with all_74_14, n4, simplifying with % 233.75/39.85 | | | | (26), (27), (61) gives: % 233.75/39.85 | | | | (62) all_74_14 = n4 | gt(n4, all_74_14) % 233.75/39.85 | | | | % 233.75/39.85 | | | | BETA: splitting (14) gives: % 233.75/39.85 | | | | % 233.75/39.85 | | | | Case 1: % 233.75/39.85 | | | | | % 233.75/39.85 | | | | | (63) all_74_14 = n0 % 233.75/39.85 | | | | | % 233.75/39.85 | | | | | REDUCE: (17), (63) imply: % 233.75/39.85 | | | | | (64) gt(n0, n0) % 233.75/39.85 | | | | | % 233.75/39.85 | | | | | PRED_UNIFY: (10), (64) imply: % 233.75/39.85 | | | | | (65) $false % 233.75/39.85 | | | | | % 233.75/39.85 | | | | | CLOSE: (65) is inconsistent. % 233.75/39.85 | | | | | % 233.75/39.85 | | | | Case 2: % 233.75/39.85 | | | | | % 233.75/39.85 | | | | | (66) ~ (all_74_14 = n0) % 233.75/39.85 | | | | | % 233.75/39.85 | | | | | REF_CLOSE: (2), (3), (4), (8), (9), (11), (12), (16), (18), (19), % 233.75/39.85 | | | | | (20), (21), (23), (25), (26), (27), (30), (56), (57), (58), % 233.75/39.85 | | | | | (59), (62), (66) are inconsistent by sub-proof #20. % 233.75/39.85 | | | | | % 233.75/39.85 | | | | End of split % 233.75/39.85 | | | | % 233.75/39.85 | | | Case 2: % 233.75/39.85 | | | | % 233.75/39.85 | | | | (67) all_74_14 = n5 % 233.75/39.85 | | | | % 233.75/39.85 | | | | REDUCE: (56), (67) imply: % 233.75/39.85 | | | | (68) a_select3(pminus_ds1_filter, n5, n5) = all_74_12 % 233.75/39.85 | | | | % 233.75/39.85 | | | | REDUCE: (57), (67) imply: % 233.75/39.85 | | | | (69) a_select3(pminus_ds1_filter, n5, n5) = all_74_13 % 233.75/39.85 | | | | % 233.75/39.85 | | | | GROUND_INST: instantiating (16) with all_74_13, all_74_12, n5, n5, % 233.75/39.85 | | | | pminus_ds1_filter, simplifying with (68), (69) gives: % 233.75/39.85 | | | | (70) all_74_12 = all_74_13 % 233.75/39.85 | | | | % 233.75/39.85 | | | | REDUCE: (4), (70) imply: % 233.75/39.85 | | | | (71) $false % 233.75/39.85 | | | | % 233.75/39.85 | | | | CLOSE: (71) is inconsistent. % 233.75/39.85 | | | | % 233.75/39.85 | | | End of split % 233.75/39.85 | | | % 233.75/39.85 | | End of split % 233.75/39.85 | | % 233.75/39.85 | Case 2: % 233.75/39.85 | | % 233.75/39.85 | | (72) all_74_15 = n0 % 233.75/39.85 | | (73) ~ gt(all_74_15, n0) % 233.75/39.85 | | % 233.75/39.85 | | REDUCE: (1), (72) imply: % 233.75/39.85 | | (74) a_select3(pminus_ds1_filter, all_74_14, n0) = all_74_12 % 233.75/39.85 | | % 233.75/39.85 | | REDUCE: (6), (72) imply: % 233.75/39.85 | | (75) a_select3(pminus_ds1_filter, n0, all_74_14) = all_74_13 % 233.75/39.85 | | % 233.75/39.85 | | REDUCE: (15), (72) imply: % 233.75/39.85 | | (76) $i(n0) % 233.75/39.85 | | % 233.75/39.85 | | REDUCE: (22), (72) imply: % 233.75/39.85 | | (77) leq(n0, n5) % 233.75/39.85 | | % 233.75/39.85 | | REDUCE: (28), (72) imply: % 233.75/39.85 | | (78) leq(n0, n0) % 233.75/39.85 | | % 233.75/39.85 | | BETA: splitting (24) gives: % 233.75/39.85 | | % 233.75/39.85 | | Case 1: % 233.75/39.85 | | | % 233.75/39.85 | | | (79) gt(n5, all_74_14) % 233.75/39.85 | | | % 233.75/39.85 | | | GROUND_INST: instantiating (11) with all_74_14, n5, n4, simplifying with % 233.75/39.85 | | | (13), (20), (27), (79) gives: % 233.75/39.85 | | | (80) leq(all_74_14, n4) % 233.75/39.85 | | | % 233.75/39.85 | | | GROUND_INST: instantiating (2) with all_74_14, n4, simplifying with (26), % 233.75/39.85 | | | (27), (80) gives: % 233.75/39.85 | | | (81) all_74_14 = n4 | gt(n4, all_74_14) % 233.75/39.85 | | | % 233.75/39.85 | | | BETA: splitting (14) gives: % 233.75/39.85 | | | % 233.75/39.85 | | | Case 1: % 233.75/39.85 | | | | % 233.75/39.85 | | | | (82) all_74_14 = n0 % 233.75/39.85 | | | | % 233.75/39.85 | | | | REDUCE: (17), (82) imply: % 233.75/39.85 | | | | (83) gt(n0, n0) % 233.75/39.85 | | | | % 233.75/39.85 | | | | PRED_UNIFY: (10), (83) imply: % 233.75/39.85 | | | | (84) $false % 233.75/39.85 | | | | % 233.75/39.85 | | | | CLOSE: (84) is inconsistent. % 233.75/39.85 | | | | % 233.75/39.85 | | | Case 2: % 233.75/39.85 | | | | % 233.75/39.85 | | | | (85) ~ (all_74_14 = n0) % 233.75/39.85 | | | | % 233.75/39.85 | | | | BETA: splitting (81) gives: % 233.75/39.85 | | | | % 233.75/39.85 | | | | Case 1: % 233.75/39.85 | | | | | % 233.75/39.85 | | | | | (86) gt(n4, all_74_14) % 233.75/39.85 | | | | | % 233.75/39.85 | | | | | GROUND_INST: instantiating (11) with all_74_14, n4, n3, simplifying % 233.75/39.85 | | | | | with (9), (26), (27), (86) gives: % 233.75/39.85 | | | | | (87) leq(all_74_14, n3) % 233.75/39.85 | | | | | % 233.75/39.85 | | | | | GROUND_INST: instantiating (2) with all_74_14, n3, simplifying with % 233.75/39.85 | | | | | (23), (27), (87) gives: % 233.75/39.85 | | | | | (88) all_74_14 = n3 | gt(n3, all_74_14) % 233.75/39.85 | | | | | % 233.75/39.85 | | | | | BETA: splitting (88) gives: % 233.75/39.85 | | | | | % 233.75/39.85 | | | | | Case 1: % 233.75/39.85 | | | | | | % 233.75/39.85 | | | | | | (89) gt(n3, all_74_14) % 233.75/39.85 | | | | | | % 233.75/39.85 | | | | | | GROUND_INST: instantiating (11) with all_74_14, n3, n2, simplifying % 233.75/39.85 | | | | | | with (23), (25), (27), (89) gives: % 233.75/39.85 | | | | | | (90) leq(all_74_14, n2) % 233.75/39.85 | | | | | | % 233.75/39.85 | | | | | | GROUND_INST: instantiating (2) with all_74_14, n2, simplifying with % 233.75/39.85 | | | | | | (12), (27), (90) gives: % 233.75/39.85 | | | | | | (91) all_74_14 = n2 | gt(n2, all_74_14) % 233.75/39.85 | | | | | | % 233.75/39.85 | | | | | | BETA: splitting (91) gives: % 233.75/39.85 | | | | | | % 233.75/39.85 | | | | | | Case 1: % 233.75/39.85 | | | | | | | % 233.75/39.85 | | | | | | | (92) gt(n2, all_74_14) % 233.75/39.85 | | | | | | | % 233.75/39.85 | | | | | | | GROUND_INST: instantiating (11) with all_74_14, n2, n1, % 233.75/39.85 | | | | | | | simplifying with (12), (19), (27), (92) gives: % 233.75/39.85 | | | | | | | (93) leq(all_74_14, n1) % 233.75/39.85 | | | | | | | % 233.75/39.85 | | | | | | | GROUND_INST: instantiating (30) with all_74_14, simplifying with % 233.75/39.85 | | | | | | | (18), (27), (93) gives: % 233.75/39.85 | | | | | | | (94) all_74_14 = n1 | all_74_14 = n0 % 233.75/39.85 | | | | | | | % 233.75/39.85 | | | | | | | BETA: splitting (94) gives: % 233.75/39.85 | | | | | | | % 233.75/39.85 | | | | | | | Case 1: % 233.75/39.85 | | | | | | | | % 233.75/39.85 | | | | | | | | (95) all_74_14 = n0 % 233.75/39.85 | | | | | | | | % 233.75/39.85 | | | | | | | | REDUCE: (85), (95) imply: % 233.75/39.85 | | | | | | | | (96) $false % 233.75/39.85 | | | | | | | | % 233.75/39.85 | | | | | | | | CLOSE: (96) is inconsistent. % 233.75/39.85 | | | | | | | | % 233.75/39.85 | | | | | | | Case 2: % 233.75/39.85 | | | | | | | | % 233.75/39.85 | | | | | | | | (97) all_74_14 = n1 % 233.75/39.85 | | | | | | | | % 233.75/39.85 | | | | | | | | REDUCE: (74), (97) imply: % 233.75/39.85 | | | | | | | | (98) a_select3(pminus_ds1_filter, n1, n0) = all_74_12 % 233.75/39.85 | | | | | | | | % 233.75/39.85 | | | | | | | | REDUCE: (75), (97) imply: % 233.75/39.85 | | | | | | | | (99) a_select3(pminus_ds1_filter, n0, n1) = all_74_13 % 233.75/39.85 | | | | | | | | % 233.75/39.85 | | | | | | | | REDUCE: (27), (97) imply: % 233.75/39.85 | | | | | | | | (100) $i(n1) % 233.75/39.85 | | | | | | | | % 233.75/39.85 | | | | | | | | REDUCE: (3), (97) imply: % 233.75/39.85 | | | | | | | | (101) leq(n1, n5) % 233.75/39.85 | | | | | | | | % 233.75/39.85 | | | | | | | | REDUCE: (18), (97) imply: % 233.75/39.85 | | | | | | | | (102) leq(n0, n1) % 233.75/39.85 | | | | | | | | % 233.75/39.85 | | | | | | | | GROUND_INST: instantiating (21) with n0, n1, all_74_13, % 233.75/39.85 | | | | | | | | simplifying with (76), (78), (99), (100), (102) % 233.75/39.85 | | | | | | | | gives: % 233.75/39.85 | | | | | | | | (103) ~ leq(n1, all_74_21) | ~ leq(n0, all_74_21) | % 233.75/39.85 | | | | | | | | (a_select3(pminus_ds1_filter, n1, n0) = all_74_13 & % 233.75/39.85 | | | | | | | | $i(all_74_13)) % 233.75/39.85 | | | | | | | | % 233.75/39.85 | | | | | | | | BETA: splitting (103) gives: % 233.75/39.85 | | | | | | | | % 233.75/39.85 | | | | | | | | Case 1: % 233.75/39.85 | | | | | | | | | % 233.75/39.85 | | | | | | | | | (104) ~ leq(n0, all_74_21) % 233.75/39.85 | | | | | | | | | % 233.75/39.85 | | | | | | | | | REDUCE: (8), (104) imply: % 233.75/39.85 | | | | | | | | | (105) ~ leq(n0, n5) % 233.75/39.85 | | | | | | | | | % 233.75/39.85 | | | | | | | | | PRED_UNIFY: (77), (105) imply: % 233.75/39.85 | | | | | | | | | (106) $false % 233.75/39.85 | | | | | | | | | % 233.75/39.85 | | | | | | | | | CLOSE: (106) is inconsistent. % 233.75/39.85 | | | | | | | | | % 233.75/39.85 | | | | | | | | Case 2: % 233.75/39.85 | | | | | | | | | % 233.75/39.85 | | | | | | | | | (107) ~ leq(n1, all_74_21) | (a_select3(pminus_ds1_filter, % 233.75/39.85 | | | | | | | | | n1, n0) = all_74_13 & $i(all_74_13)) % 233.75/39.85 | | | | | | | | | % 233.75/39.85 | | | | | | | | | BETA: splitting (107) gives: % 233.75/39.85 | | | | | | | | | % 233.75/39.85 | | | | | | | | | Case 1: % 233.75/39.85 | | | | | | | | | | % 233.75/39.85 | | | | | | | | | | (108) ~ leq(n1, all_74_21) % 233.75/39.85 | | | | | | | | | | % 233.75/39.85 | | | | | | | | | | REDUCE: (8), (108) imply: % 233.75/39.85 | | | | | | | | | | (109) ~ leq(n1, n5) % 233.75/39.85 | | | | | | | | | | % 233.75/39.85 | | | | | | | | | | PRED_UNIFY: (101), (109) imply: % 233.75/39.85 | | | | | | | | | | (110) $false % 233.75/39.85 | | | | | | | | | | % 233.75/39.85 | | | | | | | | | | CLOSE: (110) is inconsistent. % 233.75/39.85 | | | | | | | | | | % 233.75/39.85 | | | | | | | | | Case 2: % 233.75/39.85 | | | | | | | | | | % 233.75/39.85 | | | | | | | | | | (111) a_select3(pminus_ds1_filter, n1, n0) = all_74_13 & % 233.75/39.85 | | | | | | | | | | $i(all_74_13) % 233.75/39.85 | | | | | | | | | | % 233.75/39.85 | | | | | | | | | | ALPHA: (111) implies: % 233.75/39.85 | | | | | | | | | | (112) a_select3(pminus_ds1_filter, n1, n0) = all_74_13 % 233.75/39.85 | | | | | | | | | | % 233.75/39.85 | | | | | | | | | | REF_CLOSE: (4), (16), (98), (112) are inconsistent by % 233.75/39.85 | | | | | | | | | | sub-proof #19. % 233.75/39.85 | | | | | | | | | | % 233.75/39.85 | | | | | | | | | End of split % 233.75/39.85 | | | | | | | | | % 233.75/39.85 | | | | | | | | End of split % 233.75/39.85 | | | | | | | | % 233.75/39.85 | | | | | | | End of split % 233.75/39.85 | | | | | | | % 233.75/39.85 | | | | | | Case 2: % 233.75/39.85 | | | | | | | % 233.75/39.85 | | | | | | | (113) all_74_14 = n2 % 233.75/39.85 | | | | | | | % 233.75/39.85 | | | | | | | REDUCE: (74), (113) imply: % 233.75/39.85 | | | | | | | (114) a_select3(pminus_ds1_filter, n2, n0) = all_74_12 % 233.75/39.85 | | | | | | | % 233.75/39.85 | | | | | | | REDUCE: (75), (113) imply: % 233.75/39.85 | | | | | | | (115) a_select3(pminus_ds1_filter, n0, n2) = all_74_13 % 233.75/39.85 | | | | | | | % 233.75/39.85 | | | | | | | REDUCE: (3), (113) imply: % 233.75/39.85 | | | | | | | (116) leq(n2, n5) % 233.75/39.85 | | | | | | | % 233.75/39.85 | | | | | | | REDUCE: (18), (113) imply: % 233.75/39.85 | | | | | | | (117) leq(n0, n2) % 233.75/39.85 | | | | | | | % 233.75/39.85 | | | | | | | GROUND_INST: instantiating (21) with n0, n2, all_74_13, % 233.75/39.85 | | | | | | | simplifying with (12), (76), (78), (115), (117) % 233.75/39.85 | | | | | | | gives: % 233.75/39.85 | | | | | | | (118) ~ leq(n2, all_74_21) | ~ leq(n0, all_74_21) | % 233.75/39.85 | | | | | | | (a_select3(pminus_ds1_filter, n2, n0) = all_74_13 & % 233.75/39.85 | | | | | | | $i(all_74_13)) % 233.75/39.85 | | | | | | | % 233.75/39.85 | | | | | | | BETA: splitting (118) gives: % 233.75/39.85 | | | | | | | % 233.75/39.85 | | | | | | | Case 1: % 233.75/39.85 | | | | | | | | % 233.75/39.85 | | | | | | | | (119) ~ leq(n0, all_74_21) % 233.75/39.85 | | | | | | | | % 233.75/39.85 | | | | | | | | REDUCE: (8), (119) imply: % 233.75/39.85 | | | | | | | | (120) ~ leq(n0, n5) % 233.75/39.85 | | | | | | | | % 233.75/39.85 | | | | | | | | PRED_UNIFY: (77), (120) imply: % 233.75/39.85 | | | | | | | | (121) $false % 233.75/39.85 | | | | | | | | % 233.75/39.85 | | | | | | | | CLOSE: (121) is inconsistent. % 233.75/39.85 | | | | | | | | % 233.75/39.85 | | | | | | | Case 2: % 233.75/39.85 | | | | | | | | % 233.75/39.85 | | | | | | | | (122) ~ leq(n2, all_74_21) | (a_select3(pminus_ds1_filter, % 233.75/39.85 | | | | | | | | n2, n0) = all_74_13 & $i(all_74_13)) % 233.75/39.85 | | | | | | | | % 233.75/39.85 | | | | | | | | BETA: splitting (122) gives: % 233.75/39.85 | | | | | | | | % 233.75/39.85 | | | | | | | | Case 1: % 233.75/39.85 | | | | | | | | | % 233.75/39.85 | | | | | | | | | (123) ~ leq(n2, all_74_21) % 233.75/39.85 | | | | | | | | | % 233.75/39.85 | | | | | | | | | REDUCE: (8), (123) imply: % 233.75/39.85 | | | | | | | | | (124) ~ leq(n2, n5) % 233.75/39.85 | | | | | | | | | % 233.75/39.85 | | | | | | | | | PRED_UNIFY: (116), (124) imply: % 233.75/39.85 | | | | | | | | | (125) $false % 233.75/39.85 | | | | | | | | | % 233.75/39.85 | | | | | | | | | CLOSE: (125) is inconsistent. % 233.75/39.85 | | | | | | | | | % 233.75/39.85 | | | | | | | | Case 2: % 233.75/39.85 | | | | | | | | | % 233.75/39.85 | | | | | | | | | (126) a_select3(pminus_ds1_filter, n2, n0) = all_74_13 & % 233.75/39.85 | | | | | | | | | $i(all_74_13) % 233.75/39.85 | | | | | | | | | % 233.75/39.85 | | | | | | | | | ALPHA: (126) implies: % 233.75/39.85 | | | | | | | | | (127) a_select3(pminus_ds1_filter, n2, n0) = all_74_13 % 233.75/39.85 | | | | | | | | | % 233.75/39.85 | | | | | | | | | REF_CLOSE: (4), (16), (114), (127) are inconsistent by % 233.75/39.85 | | | | | | | | | sub-proof #18. % 233.75/39.85 | | | | | | | | | % 233.75/39.85 | | | | | | | | End of split % 233.75/39.85 | | | | | | | | % 233.75/39.85 | | | | | | | End of split % 233.75/39.85 | | | | | | | % 233.75/39.85 | | | | | | End of split % 233.75/39.85 | | | | | | % 233.75/39.85 | | | | | Case 2: % 233.75/39.85 | | | | | | % 233.75/39.85 | | | | | | (128) all_74_14 = n3 % 233.75/39.85 | | | | | | % 233.75/39.85 | | | | | | REDUCE: (74), (128) imply: % 233.75/39.85 | | | | | | (129) a_select3(pminus_ds1_filter, n3, n0) = all_74_12 % 233.75/39.85 | | | | | | % 233.75/39.85 | | | | | | REDUCE: (75), (128) imply: % 233.75/39.85 | | | | | | (130) a_select3(pminus_ds1_filter, n0, n3) = all_74_13 % 233.75/39.85 | | | | | | % 233.75/39.85 | | | | | | REDUCE: (3), (128) imply: % 233.75/39.85 | | | | | | (131) leq(n3, n5) % 233.75/39.85 | | | | | | % 233.75/39.85 | | | | | | REDUCE: (18), (128) imply: % 233.75/39.85 | | | | | | (132) leq(n0, n3) % 233.75/39.85 | | | | | | % 233.75/39.85 | | | | | | GROUND_INST: instantiating (21) with n0, n3, all_74_13, simplifying % 233.75/39.85 | | | | | | with (23), (76), (78), (130), (132) gives: % 233.75/39.85 | | | | | | (133) ~ leq(n3, all_74_21) | ~ leq(n0, all_74_21) | % 233.75/39.85 | | | | | | (a_select3(pminus_ds1_filter, n3, n0) = all_74_13 & % 233.75/39.85 | | | | | | $i(all_74_13)) % 233.75/39.85 | | | | | | % 233.75/39.85 | | | | | | BETA: splitting (133) gives: % 233.75/39.85 | | | | | | % 233.75/39.85 | | | | | | Case 1: % 233.75/39.85 | | | | | | | % 233.75/39.85 | | | | | | | (134) ~ leq(n0, all_74_21) % 233.75/39.85 | | | | | | | % 233.75/39.85 | | | | | | | REDUCE: (8), (134) imply: % 233.75/39.85 | | | | | | | (135) ~ leq(n0, n5) % 233.75/39.85 | | | | | | | % 233.75/39.85 | | | | | | | PRED_UNIFY: (77), (135) imply: % 233.75/39.85 | | | | | | | (136) $false % 233.75/39.85 | | | | | | | % 233.75/39.85 | | | | | | | CLOSE: (136) is inconsistent. % 233.75/39.85 | | | | | | | % 233.75/39.85 | | | | | | Case 2: % 233.75/39.85 | | | | | | | % 233.75/39.85 | | | | | | | (137) ~ leq(n3, all_74_21) | (a_select3(pminus_ds1_filter, n3, % 233.75/39.85 | | | | | | | n0) = all_74_13 & $i(all_74_13)) % 233.75/39.85 | | | | | | | % 233.75/39.86 | | | | | | | BETA: splitting (137) gives: % 233.75/39.86 | | | | | | | % 233.75/39.86 | | | | | | | Case 1: % 233.75/39.86 | | | | | | | | % 233.75/39.86 | | | | | | | | (138) ~ leq(n3, all_74_21) % 233.75/39.86 | | | | | | | | % 233.75/39.86 | | | | | | | | REDUCE: (8), (138) imply: % 233.75/39.86 | | | | | | | | (139) ~ leq(n3, n5) % 233.75/39.86 | | | | | | | | % 233.75/39.86 | | | | | | | | PRED_UNIFY: (131), (139) imply: % 233.75/39.86 | | | | | | | | (140) $false % 233.75/39.86 | | | | | | | | % 233.75/39.86 | | | | | | | | CLOSE: (140) is inconsistent. % 233.75/39.86 | | | | | | | | % 233.75/39.86 | | | | | | | Case 2: % 233.75/39.86 | | | | | | | | % 233.75/39.86 | | | | | | | | (141) a_select3(pminus_ds1_filter, n3, n0) = all_74_13 & % 233.75/39.86 | | | | | | | | $i(all_74_13) % 233.75/39.86 | | | | | | | | % 233.75/39.86 | | | | | | | | ALPHA: (141) implies: % 233.75/39.86 | | | | | | | | (142) a_select3(pminus_ds1_filter, n3, n0) = all_74_13 % 233.75/39.86 | | | | | | | | % 233.75/39.86 | | | | | | | | GROUND_INST: instantiating (16) with all_74_13, all_74_12, n0, % 233.75/39.86 | | | | | | | | n3, pminus_ds1_filter, simplifying with (129), % 233.75/39.86 | | | | | | | | (142) gives: % 233.75/39.86 | | | | | | | | (143) all_74_12 = all_74_13 % 233.75/39.86 | | | | | | | | % 233.75/39.86 | | | | | | | | REDUCE: (4), (143) imply: % 233.75/39.86 | | | | | | | | (144) $false % 233.75/39.86 | | | | | | | | % 233.75/39.86 | | | | | | | | CLOSE: (144) is inconsistent. % 233.75/39.86 | | | | | | | | % 233.75/39.86 | | | | | | | End of split % 233.75/39.86 | | | | | | | % 233.75/39.86 | | | | | | End of split % 233.75/39.86 | | | | | | % 233.75/39.86 | | | | | End of split % 233.75/39.86 | | | | | % 233.75/39.86 | | | | Case 2: % 233.75/39.86 | | | | | % 233.75/39.86 | | | | | (145) all_74_14 = n4 % 233.75/39.86 | | | | | % 233.75/39.86 | | | | | REDUCE: (74), (145) imply: % 233.75/39.86 | | | | | (146) a_select3(pminus_ds1_filter, n4, n0) = all_74_12 % 233.75/39.86 | | | | | % 233.75/39.86 | | | | | REDUCE: (75), (145) imply: % 233.75/39.86 | | | | | (147) a_select3(pminus_ds1_filter, n0, n4) = all_74_13 % 233.75/39.86 | | | | | % 233.75/39.86 | | | | | REDUCE: (3), (145) imply: % 233.75/39.86 | | | | | (148) leq(n4, n5) % 233.75/39.86 | | | | | % 233.75/39.86 | | | | | REDUCE: (18), (145) imply: % 233.75/39.86 | | | | | (149) leq(n0, n4) % 233.75/39.86 | | | | | % 233.75/39.86 | | | | | GROUND_INST: instantiating (21) with n0, n4, all_74_13, simplifying % 233.75/39.86 | | | | | with (26), (76), (78), (147), (149) gives: % 233.75/39.86 | | | | | (150) ~ leq(n4, all_74_21) | ~ leq(n0, all_74_21) | % 233.75/39.86 | | | | | (a_select3(pminus_ds1_filter, n4, n0) = all_74_13 & % 233.75/39.86 | | | | | $i(all_74_13)) % 233.75/39.86 | | | | | % 233.75/39.86 | | | | | BETA: splitting (150) gives: % 233.75/39.86 | | | | | % 233.75/39.86 | | | | | Case 1: % 233.75/39.86 | | | | | | % 233.75/39.86 | | | | | | (151) ~ leq(n0, all_74_21) % 233.75/39.86 | | | | | | % 233.75/39.86 | | | | | | REDUCE: (8), (151) imply: % 233.75/39.86 | | | | | | (152) ~ leq(n0, n5) % 233.75/39.86 | | | | | | % 233.75/39.86 | | | | | | PRED_UNIFY: (77), (152) imply: % 233.75/39.86 | | | | | | (153) $false % 233.75/39.86 | | | | | | % 233.75/39.86 | | | | | | CLOSE: (153) is inconsistent. % 233.75/39.86 | | | | | | % 233.75/39.86 | | | | | Case 2: % 233.75/39.86 | | | | | | % 233.75/39.86 | | | | | | (154) ~ leq(n4, all_74_21) | (a_select3(pminus_ds1_filter, n4, % 233.75/39.86 | | | | | | n0) = all_74_13 & $i(all_74_13)) % 233.75/39.86 | | | | | | % 233.75/39.86 | | | | | | BETA: splitting (154) gives: % 233.75/39.86 | | | | | | % 233.75/39.86 | | | | | | Case 1: % 233.75/39.86 | | | | | | | % 233.75/39.86 | | | | | | | (155) ~ leq(n4, all_74_21) % 233.75/39.86 | | | | | | | % 233.75/39.86 | | | | | | | REDUCE: (8), (155) imply: % 233.75/39.86 | | | | | | | (156) ~ leq(n4, n5) % 233.75/39.86 | | | | | | | % 233.75/39.86 | | | | | | | PRED_UNIFY: (148), (156) imply: % 233.75/39.86 | | | | | | | (157) $false % 233.75/39.86 | | | | | | | % 233.75/39.86 | | | | | | | CLOSE: (157) is inconsistent. % 233.75/39.86 | | | | | | | % 233.75/39.86 | | | | | | Case 2: % 233.75/39.86 | | | | | | | % 233.75/39.86 | | | | | | | (158) a_select3(pminus_ds1_filter, n4, n0) = all_74_13 & % 233.75/39.86 | | | | | | | $i(all_74_13) % 233.75/39.86 | | | | | | | % 233.75/39.86 | | | | | | | ALPHA: (158) implies: % 233.75/39.86 | | | | | | | (159) a_select3(pminus_ds1_filter, n4, n0) = all_74_13 % 233.75/39.86 | | | | | | | % 233.75/39.86 | | | | | | | REF_CLOSE: (4), (16), (146), (159) are inconsistent by sub-proof % 233.75/39.86 | | | | | | | #17. % 233.75/39.86 | | | | | | | % 233.75/39.86 | | | | | | End of split % 233.75/39.86 | | | | | | % 233.75/39.86 | | | | | End of split % 233.75/39.86 | | | | | % 233.75/39.86 | | | | End of split % 233.75/39.86 | | | | % 233.75/39.86 | | | End of split % 233.75/39.86 | | | % 233.75/39.86 | | Case 2: % 233.75/39.86 | | | % 233.75/39.86 | | | (160) all_74_14 = n5 % 233.75/39.86 | | | % 233.75/39.86 | | | REDUCE: (74), (160) imply: % 233.75/39.86 | | | (161) a_select3(pminus_ds1_filter, n5, n0) = all_74_12 % 233.75/39.86 | | | % 233.75/39.86 | | | REDUCE: (75), (160) imply: % 233.75/39.86 | | | (162) a_select3(pminus_ds1_filter, n0, n5) = all_74_13 % 233.75/39.86 | | | % 233.75/39.86 | | | REDUCE: (3), (160) imply: % 233.75/39.86 | | | (163) leq(n5, n5) % 233.75/39.86 | | | % 233.75/39.86 | | | GROUND_INST: instantiating (21) with n0, n5, all_74_13, simplifying with % 233.75/39.86 | | | (20), (76), (77), (78), (162) gives: % 233.75/39.86 | | | (164) ~ leq(n5, all_74_21) | ~ leq(n0, all_74_21) | % 233.75/39.86 | | | (a_select3(pminus_ds1_filter, n5, n0) = all_74_13 & % 233.75/39.86 | | | $i(all_74_13)) % 233.75/39.86 | | | % 233.75/39.86 | | | BETA: splitting (164) gives: % 233.75/39.86 | | | % 233.75/39.86 | | | Case 1: % 233.75/39.86 | | | | % 233.75/39.86 | | | | (165) ~ leq(n0, all_74_21) % 233.75/39.86 | | | | % 233.75/39.86 | | | | REDUCE: (8), (165) imply: % 233.75/39.86 | | | | (166) ~ leq(n0, n5) % 233.75/39.86 | | | | % 233.75/39.86 | | | | PRED_UNIFY: (77), (166) imply: % 233.75/39.86 | | | | (167) $false % 233.75/39.86 | | | | % 233.75/39.86 | | | | CLOSE: (167) is inconsistent. % 233.75/39.86 | | | | % 233.75/39.86 | | | Case 2: % 233.75/39.86 | | | | % 233.75/39.86 | | | | (168) ~ leq(n5, all_74_21) | (a_select3(pminus_ds1_filter, n5, n0) = % 233.75/39.86 | | | | all_74_13 & $i(all_74_13)) % 233.75/39.86 | | | | % 233.75/39.86 | | | | BETA: splitting (168) gives: % 233.75/39.86 | | | | % 233.75/39.86 | | | | Case 1: % 233.75/39.86 | | | | | % 233.75/39.86 | | | | | (169) ~ leq(n5, all_74_21) % 233.75/39.86 | | | | | % 233.75/39.86 | | | | | REDUCE: (8), (169) imply: % 233.75/39.86 | | | | | (170) ~ leq(n5, n5) % 233.75/39.86 | | | | | % 233.75/39.86 | | | | | PRED_UNIFY: (163), (170) imply: % 233.75/39.86 | | | | | (171) $false % 233.75/39.86 | | | | | % 233.75/39.86 | | | | | CLOSE: (171) is inconsistent. % 233.75/39.86 | | | | | % 233.75/39.86 | | | | Case 2: % 233.75/39.86 | | | | | % 233.75/39.86 | | | | | (172) a_select3(pminus_ds1_filter, n5, n0) = all_74_13 & % 233.75/39.86 | | | | | $i(all_74_13) % 233.75/39.86 | | | | | % 233.75/39.86 | | | | | ALPHA: (172) implies: % 233.75/39.86 | | | | | (173) a_select3(pminus_ds1_filter, n5, n0) = all_74_13 % 233.75/39.86 | | | | | % 233.75/39.86 | | | | | REF_CLOSE: (4), (16), (161), (173) are inconsistent by sub-proof #16. % 233.75/39.86 | | | | | % 233.75/39.86 | | | | End of split % 233.75/39.86 | | | | % 233.75/39.86 | | | End of split % 233.75/39.86 | | | % 233.75/39.86 | | End of split % 233.75/39.86 | | % 233.75/39.86 | End of split % 233.75/39.86 | % 233.75/39.86 End of proof % 233.75/39.86 % 233.75/39.86 Sub-proof #16 shows that the following formulas are inconsistent: % 233.75/39.86 ---------------------------------------------------------------- % 233.75/39.86 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 233.75/39.86 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 233.75/39.86 v0)) % 233.75/39.86 (2) a_select3(pminus_ds1_filter, n5, n0) = all_74_12 % 233.75/39.86 (3) a_select3(pminus_ds1_filter, n5, n0) = all_74_13 % 233.75/39.86 (4) ~ (all_74_12 = all_74_13) % 233.75/39.86 % 233.75/39.86 Begin of proof % 233.75/39.86 | % 233.75/39.86 | GROUND_INST: instantiating (1) with all_74_13, all_74_12, n0, n5, % 233.75/39.86 | pminus_ds1_filter, simplifying with (2), (3) gives: % 233.75/39.86 | (5) all_74_12 = all_74_13 % 233.75/39.86 | % 233.75/39.86 | REDUCE: (4), (5) imply: % 233.75/39.86 | (6) $false % 233.75/39.86 | % 233.75/39.86 | CLOSE: (6) is inconsistent. % 233.75/39.86 | % 233.75/39.86 End of proof % 233.75/39.86 % 233.75/39.86 Sub-proof #17 shows that the following formulas are inconsistent: % 233.75/39.86 ---------------------------------------------------------------- % 233.75/39.86 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 233.75/39.86 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 233.75/39.86 v0)) % 233.75/39.86 (2) a_select3(pminus_ds1_filter, n4, n0) = all_74_12 % 233.75/39.86 (3) a_select3(pminus_ds1_filter, n4, n0) = all_74_13 % 233.75/39.86 (4) ~ (all_74_12 = all_74_13) % 233.75/39.86 % 233.75/39.86 Begin of proof % 233.75/39.86 | % 233.75/39.86 | GROUND_INST: instantiating (1) with all_74_13, all_74_12, n0, n4, % 233.75/39.86 | pminus_ds1_filter, simplifying with (2), (3) gives: % 233.75/39.86 | (5) all_74_12 = all_74_13 % 233.75/39.86 | % 233.75/39.86 | REDUCE: (4), (5) imply: % 233.75/39.86 | (6) $false % 233.75/39.86 | % 233.75/39.86 | CLOSE: (6) is inconsistent. % 233.75/39.86 | % 233.75/39.86 End of proof % 233.75/39.86 % 233.75/39.86 Sub-proof #18 shows that the following formulas are inconsistent: % 233.75/39.86 ---------------------------------------------------------------- % 233.75/39.86 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 233.75/39.86 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 233.75/39.86 v0)) % 233.75/39.86 (2) a_select3(pminus_ds1_filter, n2, n0) = all_74_12 % 233.75/39.86 (3) a_select3(pminus_ds1_filter, n2, n0) = all_74_13 % 233.75/39.86 (4) ~ (all_74_12 = all_74_13) % 233.75/39.86 % 233.75/39.86 Begin of proof % 233.75/39.86 | % 233.75/39.86 | GROUND_INST: instantiating (1) with all_74_13, all_74_12, n0, n2, % 233.75/39.86 | pminus_ds1_filter, simplifying with (2), (3) gives: % 233.75/39.86 | (5) all_74_12 = all_74_13 % 233.75/39.86 | % 233.75/39.86 | REDUCE: (4), (5) imply: % 233.75/39.86 | (6) $false % 233.75/39.86 | % 233.75/39.86 | CLOSE: (6) is inconsistent. % 233.75/39.86 | % 233.75/39.86 End of proof % 233.75/39.86 % 233.75/39.86 Sub-proof #19 shows that the following formulas are inconsistent: % 233.75/39.86 ---------------------------------------------------------------- % 233.75/39.86 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 233.75/39.86 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 233.75/39.86 v0)) % 233.75/39.86 (2) a_select3(pminus_ds1_filter, n1, n0) = all_74_12 % 233.75/39.86 (3) a_select3(pminus_ds1_filter, n1, n0) = all_74_13 % 233.75/39.86 (4) ~ (all_74_12 = all_74_13) % 233.75/39.86 % 233.75/39.86 Begin of proof % 233.75/39.86 | % 233.75/39.86 | GROUND_INST: instantiating (1) with all_74_13, all_74_12, n0, n1, % 233.75/39.86 | pminus_ds1_filter, simplifying with (2), (3) gives: % 233.75/39.86 | (5) all_74_12 = all_74_13 % 233.75/39.86 | % 233.75/39.86 | REDUCE: (4), (5) imply: % 233.75/39.86 | (6) $false % 233.75/39.86 | % 233.75/39.86 | CLOSE: (6) is inconsistent. % 233.75/39.86 | % 233.75/39.86 End of proof % 233.75/39.86 % 233.75/39.86 Sub-proof #20 shows that the following formulas are inconsistent: % 233.75/39.86 ---------------------------------------------------------------- % 233.75/39.86 (1) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ leq(v0, % 233.75/39.86 v1) | gt(v1, v0)) % 233.75/39.86 (2) leq(all_74_14, n5) % 233.75/39.86 (3) ~ (all_74_12 = all_74_13) % 233.75/39.86 (4) all_74_21 = n5 % 233.75/39.86 (5) pred(n4) = n3 % 233.75/39.86 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (pred(v1) = v2) | ~ $i(v1) % 233.75/39.86 | ~ $i(v0) | ~ gt(v1, v0) | leq(v0, v2)) % 233.75/39.86 (7) a_select3(pminus_ds1_filter, all_74_14, n5) = all_74_12 % 233.75/39.86 (8) $i(n2) % 233.75/39.86 (9) leq(n5, n5) % 233.75/39.86 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 233.75/39.86 (v1 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 233.75/39.86 v0)) % 233.75/39.86 (11) leq(n0, all_74_14) % 233.75/39.86 (12) pred(n2) = n1 % 233.75/39.86 (13) $i(n5) % 233.75/39.86 (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 233.75/39.86 (a_select3(pminus_ds1_filter, v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 233.75/39.86 ~ leq(v1, all_74_21) | ~ leq(v0, all_74_21) | ~ leq(n0, v1) | ~ % 233.75/39.86 leq(n0, v0) | (a_select3(pminus_ds1_filter, v1, v0) = v2 & $i(v2))) % 233.75/39.86 (15) a_select3(pminus_ds1_filter, n5, all_74_14) = all_74_13 % 233.75/39.86 (16) $i(n3) % 233.75/39.86 (17) leq(n0, n5) % 233.75/39.86 (18) ~ (all_74_14 = n0) % 233.75/39.86 (19) pred(n3) = n2 % 233.75/39.86 (20) $i(n4) % 233.75/39.86 (21) $i(all_74_14) % 233.75/39.86 (22) all_74_14 = n4 | gt(n4, all_74_14) % 233.75/39.86 (23) ! [v0: $i] : (v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0, n1) | ~ % 233.75/39.86 leq(n0, v0)) % 233.75/39.86 % 233.75/39.86 Begin of proof % 233.75/39.86 | % 233.75/39.86 | BETA: splitting (22) gives: % 233.75/39.86 | % 233.75/39.86 | Case 1: % 233.75/39.86 | | % 233.75/39.86 | | (24) gt(n4, all_74_14) % 233.75/39.86 | | % 233.75/39.86 | | GROUND_INST: instantiating (6) with all_74_14, n4, n3, simplifying with (5), % 233.75/39.86 | | (20), (21), (24) gives: % 233.75/39.86 | | (25) leq(all_74_14, n3) % 233.75/39.86 | | % 233.75/39.86 | | GROUND_INST: instantiating (1) with all_74_14, n3, simplifying with (16), % 233.75/39.86 | | (21), (25) gives: % 233.75/39.86 | | (26) all_74_14 = n3 | gt(n3, all_74_14) % 233.75/39.86 | | % 233.75/39.86 | | BETA: splitting (26) gives: % 233.75/39.86 | | % 233.75/39.86 | | Case 1: % 233.75/39.86 | | | % 233.75/39.86 | | | (27) gt(n3, all_74_14) % 233.75/39.86 | | | % 233.75/39.86 | | | GROUND_INST: instantiating (6) with all_74_14, n3, n2, simplifying with % 233.75/39.86 | | | (16), (19), (21), (27) gives: % 233.75/39.86 | | | (28) leq(all_74_14, n2) % 233.75/39.86 | | | % 233.75/39.86 | | | GROUND_INST: instantiating (1) with all_74_14, n2, simplifying with (8), % 233.75/39.86 | | | (21), (28) gives: % 233.75/39.86 | | | (29) all_74_14 = n2 | gt(n2, all_74_14) % 233.75/39.86 | | | % 233.75/39.86 | | | BETA: splitting (29) gives: % 233.75/39.86 | | | % 233.75/39.86 | | | Case 1: % 233.75/39.86 | | | | % 233.75/39.87 | | | | (30) gt(n2, all_74_14) % 233.75/39.87 | | | | % 233.75/39.87 | | | | GROUND_INST: instantiating (6) with all_74_14, n2, n1, simplifying with % 233.75/39.87 | | | | (8), (12), (21), (30) gives: % 233.75/39.87 | | | | (31) leq(all_74_14, n1) % 233.75/39.87 | | | | % 233.75/39.87 | | | | GROUND_INST: instantiating (23) with all_74_14, simplifying with (11), % 233.75/39.87 | | | | (21), (31) gives: % 233.75/39.87 | | | | (32) all_74_14 = n1 | all_74_14 = n0 % 233.75/39.87 | | | | % 233.75/39.87 | | | | BETA: splitting (32) gives: % 233.75/39.87 | | | | % 233.75/39.87 | | | | Case 1: % 233.75/39.87 | | | | | % 233.75/39.87 | | | | | (33) all_74_14 = n0 % 233.75/39.87 | | | | | % 233.75/39.87 | | | | | REDUCE: (18), (33) imply: % 233.75/39.87 | | | | | (34) $false % 233.75/39.87 | | | | | % 233.75/39.87 | | | | | CLOSE: (34) is inconsistent. % 233.75/39.87 | | | | | % 233.75/39.87 | | | | Case 2: % 233.75/39.87 | | | | | % 233.75/39.87 | | | | | (35) all_74_14 = n1 % 233.75/39.87 | | | | | % 233.75/39.87 | | | | | REDUCE: (7), (35) imply: % 233.75/39.87 | | | | | (36) a_select3(pminus_ds1_filter, n1, n5) = all_74_12 % 233.75/39.87 | | | | | % 233.75/39.87 | | | | | REDUCE: (15), (35) imply: % 233.75/39.87 | | | | | (37) a_select3(pminus_ds1_filter, n5, n1) = all_74_13 % 233.75/39.87 | | | | | % 233.75/39.87 | | | | | REDUCE: (21), (35) imply: % 233.75/39.87 | | | | | (38) $i(n1) % 233.75/39.87 | | | | | % 233.75/39.87 | | | | | REDUCE: (2), (35) imply: % 233.75/39.87 | | | | | (39) leq(n1, n5) % 233.75/39.87 | | | | | % 233.75/39.87 | | | | | REDUCE: (11), (35) imply: % 233.75/39.87 | | | | | (40) leq(n0, n1) % 233.75/39.87 | | | | | % 233.75/39.87 | | | | | GROUND_INST: instantiating (14) with n1, n5, all_74_12, simplifying % 233.75/39.87 | | | | | with (13), (17), (36), (38), (40) gives: % 233.75/39.87 | | | | | (41) ~ leq(n5, all_74_21) | ~ leq(n1, all_74_21) | % 233.75/39.87 | | | | | (a_select3(pminus_ds1_filter, n5, n1) = all_74_12 & % 233.75/39.87 | | | | | $i(all_74_12)) % 233.75/39.87 | | | | | % 233.75/39.87 | | | | | BETA: splitting (41) gives: % 233.75/39.87 | | | | | % 233.75/39.87 | | | | | Case 1: % 233.75/39.87 | | | | | | % 233.75/39.87 | | | | | | (42) ~ leq(n5, all_74_21) % 233.75/39.87 | | | | | | % 233.75/39.87 | | | | | | REDUCE: (4), (42) imply: % 233.75/39.87 | | | | | | (43) ~ leq(n5, n5) % 233.75/39.87 | | | | | | % 233.75/39.87 | | | | | | PRED_UNIFY: (9), (43) imply: % 233.75/39.87 | | | | | | (44) $false % 233.75/39.87 | | | | | | % 233.75/39.87 | | | | | | CLOSE: (44) is inconsistent. % 233.75/39.87 | | | | | | % 233.75/39.87 | | | | | Case 2: % 233.75/39.87 | | | | | | % 233.75/39.87 | | | | | | (45) ~ leq(n1, all_74_21) | (a_select3(pminus_ds1_filter, n5, % 233.75/39.87 | | | | | | n1) = all_74_12 & $i(all_74_12)) % 233.75/39.87 | | | | | | % 233.75/39.87 | | | | | | BETA: splitting (45) gives: % 233.75/39.87 | | | | | | % 233.75/39.87 | | | | | | Case 1: % 233.75/39.87 | | | | | | | % 233.75/39.87 | | | | | | | (46) ~ leq(n1, all_74_21) % 233.75/39.87 | | | | | | | % 233.75/39.87 | | | | | | | REDUCE: (4), (46) imply: % 233.75/39.87 | | | | | | | (47) ~ leq(n1, n5) % 233.75/39.87 | | | | | | | % 233.75/39.87 | | | | | | | PRED_UNIFY: (39), (47) imply: % 233.75/39.87 | | | | | | | (48) $false % 233.75/39.87 | | | | | | | % 233.75/39.87 | | | | | | | CLOSE: (48) is inconsistent. % 233.75/39.87 | | | | | | | % 233.75/39.87 | | | | | | Case 2: % 233.75/39.87 | | | | | | | % 233.75/39.87 | | | | | | | (49) a_select3(pminus_ds1_filter, n5, n1) = all_74_12 & % 233.75/39.87 | | | | | | | $i(all_74_12) % 233.75/39.87 | | | | | | | % 233.75/39.87 | | | | | | | ALPHA: (49) implies: % 233.75/39.87 | | | | | | | (50) a_select3(pminus_ds1_filter, n5, n1) = all_74_12 % 233.75/39.87 | | | | | | | % 233.75/39.87 | | | | | | | GROUND_INST: instantiating (10) with all_74_12, all_74_13, n1, n5, % 233.75/39.87 | | | | | | | pminus_ds1_filter, simplifying with (37), (50) gives: % 233.75/39.87 | | | | | | | (51) all_74_12 = all_74_13 % 233.75/39.87 | | | | | | | % 233.75/39.87 | | | | | | | REDUCE: (3), (51) imply: % 233.75/39.87 | | | | | | | (52) $false % 233.75/39.87 | | | | | | | % 233.75/39.87 | | | | | | | CLOSE: (52) is inconsistent. % 233.75/39.87 | | | | | | | % 233.75/39.87 | | | | | | End of split % 233.75/39.87 | | | | | | % 233.75/39.87 | | | | | End of split % 233.75/39.87 | | | | | % 233.75/39.87 | | | | End of split % 233.75/39.87 | | | | % 233.75/39.87 | | | Case 2: % 233.75/39.87 | | | | % 233.75/39.87 | | | | (53) all_74_14 = n2 % 233.75/39.87 | | | | % 233.75/39.87 | | | | REDUCE: (7), (53) imply: % 233.75/39.87 | | | | (54) a_select3(pminus_ds1_filter, n2, n5) = all_74_12 % 233.75/39.87 | | | | % 233.75/39.87 | | | | REDUCE: (15), (53) imply: % 233.75/39.87 | | | | (55) a_select3(pminus_ds1_filter, n5, n2) = all_74_13 % 233.75/39.87 | | | | % 233.75/39.87 | | | | REDUCE: (2), (53) imply: % 233.75/39.87 | | | | (56) leq(n2, n5) % 233.75/39.87 | | | | % 233.75/39.87 | | | | REDUCE: (11), (53) imply: % 233.75/39.87 | | | | (57) leq(n0, n2) % 233.75/39.87 | | | | % 233.75/39.87 | | | | GROUND_INST: instantiating (14) with n2, n5, all_74_12, simplifying with % 233.75/39.87 | | | | (8), (13), (17), (54), (57) gives: % 233.75/39.87 | | | | (58) ~ leq(n5, all_74_21) | ~ leq(n2, all_74_21) | % 233.75/39.87 | | | | (a_select3(pminus_ds1_filter, n5, n2) = all_74_12 & % 233.75/39.87 | | | | $i(all_74_12)) % 233.75/39.87 | | | | % 233.75/39.87 | | | | BETA: splitting (58) gives: % 233.75/39.87 | | | | % 233.75/39.87 | | | | Case 1: % 233.75/39.87 | | | | | % 233.75/39.87 | | | | | (59) ~ leq(n5, all_74_21) % 233.75/39.87 | | | | | % 233.75/39.87 | | | | | REDUCE: (4), (59) imply: % 233.75/39.87 | | | | | (60) ~ leq(n5, n5) % 233.75/39.87 | | | | | % 233.75/39.87 | | | | | PRED_UNIFY: (9), (60) imply: % 233.75/39.87 | | | | | (61) $false % 233.75/39.87 | | | | | % 233.75/39.87 | | | | | CLOSE: (61) is inconsistent. % 233.75/39.87 | | | | | % 233.75/39.87 | | | | Case 2: % 233.75/39.87 | | | | | % 233.75/39.87 | | | | | (62) ~ leq(n2, all_74_21) | (a_select3(pminus_ds1_filter, n5, n2) % 233.75/39.87 | | | | | = all_74_12 & $i(all_74_12)) % 233.75/39.87 | | | | | % 233.75/39.87 | | | | | BETA: splitting (62) gives: % 233.75/39.87 | | | | | % 233.75/39.87 | | | | | Case 1: % 233.75/39.87 | | | | | | % 233.75/39.87 | | | | | | (63) ~ leq(n2, all_74_21) % 233.75/39.87 | | | | | | % 233.75/39.87 | | | | | | REDUCE: (4), (63) imply: % 233.75/39.87 | | | | | | (64) ~ leq(n2, n5) % 233.75/39.87 | | | | | | % 233.75/39.87 | | | | | | PRED_UNIFY: (56), (64) imply: % 233.75/39.87 | | | | | | (65) $false % 233.75/39.87 | | | | | | % 233.75/39.87 | | | | | | CLOSE: (65) is inconsistent. % 233.75/39.87 | | | | | | % 233.75/39.87 | | | | | Case 2: % 233.75/39.87 | | | | | | % 233.75/39.87 | | | | | | (66) a_select3(pminus_ds1_filter, n5, n2) = all_74_12 & % 233.75/39.87 | | | | | | $i(all_74_12) % 233.75/39.87 | | | | | | % 233.75/39.87 | | | | | | ALPHA: (66) implies: % 233.75/39.87 | | | | | | (67) a_select3(pminus_ds1_filter, n5, n2) = all_74_12 % 233.75/39.87 | | | | | | % 233.75/39.87 | | | | | | GROUND_INST: instantiating (10) with all_74_12, all_74_13, n2, n5, % 233.75/39.87 | | | | | | pminus_ds1_filter, simplifying with (55), (67) gives: % 233.75/39.87 | | | | | | (68) all_74_12 = all_74_13 % 233.75/39.87 | | | | | | % 233.75/39.87 | | | | | | REDUCE: (3), (68) imply: % 233.75/39.87 | | | | | | (69) $false % 233.75/39.87 | | | | | | % 233.75/39.87 | | | | | | CLOSE: (69) is inconsistent. % 233.75/39.87 | | | | | | % 233.75/39.87 | | | | | End of split % 233.75/39.87 | | | | | % 233.75/39.87 | | | | End of split % 233.75/39.87 | | | | % 233.75/39.87 | | | End of split % 233.75/39.87 | | | % 233.75/39.87 | | Case 2: % 233.75/39.87 | | | % 233.75/39.87 | | | (70) all_74_14 = n3 % 233.75/39.87 | | | % 233.75/39.87 | | | REDUCE: (7), (70) imply: % 233.75/39.87 | | | (71) a_select3(pminus_ds1_filter, n3, n5) = all_74_12 % 233.75/39.87 | | | % 233.75/39.87 | | | REDUCE: (15), (70) imply: % 233.75/39.87 | | | (72) a_select3(pminus_ds1_filter, n5, n3) = all_74_13 % 233.75/39.87 | | | % 233.75/39.87 | | | REDUCE: (2), (70) imply: % 233.75/39.87 | | | (73) leq(n3, n5) % 233.75/39.87 | | | % 233.75/39.87 | | | REDUCE: (11), (70) imply: % 233.75/39.87 | | | (74) leq(n0, n3) % 233.75/39.87 | | | % 233.75/39.87 | | | GROUND_INST: instantiating (14) with n3, n5, all_74_12, simplifying with % 233.75/39.87 | | | (13), (16), (17), (71), (74) gives: % 233.75/39.87 | | | (75) ~ leq(n5, all_74_21) | ~ leq(n3, all_74_21) | % 233.75/39.87 | | | (a_select3(pminus_ds1_filter, n5, n3) = all_74_12 & $i(all_74_12)) % 233.75/39.87 | | | % 233.75/39.87 | | | BETA: splitting (75) gives: % 233.75/39.87 | | | % 233.75/39.87 | | | Case 1: % 233.75/39.87 | | | | % 233.75/39.87 | | | | (76) ~ leq(n5, all_74_21) % 233.75/39.87 | | | | % 233.75/39.87 | | | | REDUCE: (4), (76) imply: % 233.75/39.87 | | | | (77) ~ leq(n5, n5) % 233.75/39.87 | | | | % 233.75/39.87 | | | | PRED_UNIFY: (9), (77) imply: % 233.75/39.87 | | | | (78) $false % 233.75/39.87 | | | | % 233.75/39.87 | | | | CLOSE: (78) is inconsistent. % 233.75/39.87 | | | | % 233.75/39.87 | | | Case 2: % 233.75/39.87 | | | | % 233.75/39.87 | | | | (79) ~ leq(n3, all_74_21) | (a_select3(pminus_ds1_filter, n5, n3) = % 233.75/39.87 | | | | all_74_12 & $i(all_74_12)) % 233.75/39.87 | | | | % 233.75/39.87 | | | | BETA: splitting (79) gives: % 233.75/39.87 | | | | % 233.75/39.87 | | | | Case 1: % 233.75/39.87 | | | | | % 233.75/39.87 | | | | | (80) ~ leq(n3, all_74_21) % 233.75/39.87 | | | | | % 233.75/39.87 | | | | | REDUCE: (4), (80) imply: % 233.75/39.87 | | | | | (81) ~ leq(n3, n5) % 233.75/39.87 | | | | | % 233.75/39.87 | | | | | PRED_UNIFY: (73), (81) imply: % 233.75/39.87 | | | | | (82) $false % 233.75/39.87 | | | | | % 233.75/39.87 | | | | | CLOSE: (82) is inconsistent. % 233.75/39.87 | | | | | % 233.75/39.87 | | | | Case 2: % 233.75/39.87 | | | | | % 233.75/39.87 | | | | | (83) a_select3(pminus_ds1_filter, n5, n3) = all_74_12 & % 233.75/39.87 | | | | | $i(all_74_12) % 233.75/39.87 | | | | | % 233.75/39.87 | | | | | ALPHA: (83) implies: % 233.75/39.87 | | | | | (84) a_select3(pminus_ds1_filter, n5, n3) = all_74_12 % 233.75/39.87 | | | | | % 233.75/39.87 | | | | | GROUND_INST: instantiating (10) with all_74_12, all_74_13, n3, n5, % 233.75/39.87 | | | | | pminus_ds1_filter, simplifying with (72), (84) gives: % 233.75/39.87 | | | | | (85) all_74_12 = all_74_13 % 233.75/39.87 | | | | | % 233.75/39.87 | | | | | REDUCE: (3), (85) imply: % 233.75/39.87 | | | | | (86) $false % 233.75/39.87 | | | | | % 233.75/39.87 | | | | | CLOSE: (86) is inconsistent. % 233.75/39.87 | | | | | % 233.75/39.87 | | | | End of split % 233.75/39.87 | | | | % 233.75/39.87 | | | End of split % 233.75/39.87 | | | % 233.75/39.87 | | End of split % 233.75/39.87 | | % 233.75/39.87 | Case 2: % 233.75/39.87 | | % 233.75/39.87 | | (87) all_74_14 = n4 % 233.75/39.87 | | % 233.75/39.87 | | REDUCE: (7), (87) imply: % 233.75/39.87 | | (88) a_select3(pminus_ds1_filter, n4, n5) = all_74_12 % 233.75/39.87 | | % 233.75/39.87 | | REDUCE: (15), (87) imply: % 233.75/39.87 | | (89) a_select3(pminus_ds1_filter, n5, n4) = all_74_13 % 233.75/39.87 | | % 233.75/39.87 | | REDUCE: (2), (87) imply: % 233.75/39.87 | | (90) leq(n4, n5) % 233.75/39.87 | | % 233.75/39.87 | | REDUCE: (11), (87) imply: % 233.75/39.87 | | (91) leq(n0, n4) % 233.75/39.87 | | % 233.75/39.87 | | GROUND_INST: instantiating (14) with n4, n5, all_74_12, simplifying with % 233.75/39.87 | | (13), (17), (20), (88), (91) gives: % 233.75/39.87 | | (92) ~ leq(n5, all_74_21) | ~ leq(n4, all_74_21) | % 233.75/39.87 | | (a_select3(pminus_ds1_filter, n5, n4) = all_74_12 & $i(all_74_12)) % 233.75/39.87 | | % 233.75/39.87 | | BETA: splitting (92) gives: % 233.75/39.87 | | % 233.75/39.87 | | Case 1: % 233.75/39.87 | | | % 233.75/39.87 | | | (93) ~ leq(n5, all_74_21) % 233.75/39.87 | | | % 233.75/39.87 | | | REDUCE: (4), (93) imply: % 233.75/39.87 | | | (94) ~ leq(n5, n5) % 233.75/39.87 | | | % 233.75/39.87 | | | PRED_UNIFY: (9), (94) imply: % 233.75/39.87 | | | (95) $false % 233.75/39.87 | | | % 233.75/39.87 | | | CLOSE: (95) is inconsistent. % 233.75/39.87 | | | % 233.75/39.87 | | Case 2: % 233.75/39.87 | | | % 233.75/39.87 | | | (96) ~ leq(n4, all_74_21) | (a_select3(pminus_ds1_filter, n5, n4) = % 233.75/39.87 | | | all_74_12 & $i(all_74_12)) % 233.75/39.87 | | | % 233.75/39.87 | | | BETA: splitting (96) gives: % 233.75/39.87 | | | % 233.75/39.87 | | | Case 1: % 233.75/39.87 | | | | % 233.75/39.87 | | | | (97) ~ leq(n4, all_74_21) % 233.75/39.87 | | | | % 233.75/39.87 | | | | REDUCE: (4), (97) imply: % 233.75/39.87 | | | | (98) ~ leq(n4, n5) % 233.75/39.87 | | | | % 233.75/39.87 | | | | PRED_UNIFY: (90), (98) imply: % 233.75/39.87 | | | | (99) $false % 233.75/39.87 | | | | % 233.75/39.87 | | | | CLOSE: (99) is inconsistent. % 233.75/39.87 | | | | % 233.75/39.87 | | | Case 2: % 233.75/39.87 | | | | % 233.75/39.87 | | | | (100) a_select3(pminus_ds1_filter, n5, n4) = all_74_12 & % 233.75/39.87 | | | | $i(all_74_12) % 233.75/39.87 | | | | % 233.75/39.87 | | | | ALPHA: (100) implies: % 233.75/39.87 | | | | (101) a_select3(pminus_ds1_filter, n5, n4) = all_74_12 % 233.75/39.87 | | | | % 233.75/39.87 | | | | REF_CLOSE: (3), (10), (89), (101) are inconsistent by sub-proof #22. % 233.75/39.87 | | | | % 233.75/39.87 | | | End of split % 233.75/39.87 | | | % 233.75/39.87 | | End of split % 233.75/39.87 | | % 233.75/39.87 | End of split % 233.75/39.87 | % 233.75/39.87 End of proof % 233.75/39.87 % 233.75/39.87 Sub-proof #21 shows that the following formulas are inconsistent: % 233.75/39.87 ---------------------------------------------------------------- % 233.75/39.87 (1) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ leq(v0, % 233.75/39.87 v1) | gt(v1, v0)) % 233.75/39.87 (2) ~ (all_74_12 = all_74_13) % 233.75/39.87 (3) ~ (all_74_15 = n0) % 233.75/39.87 (4) all_74_15 = n4 | gt(n4, all_74_15) % 233.75/39.87 (5) all_74_21 = n5 % 233.75/39.87 (6) a_select3(pminus_ds1_filter, n5, all_74_15) = all_74_12 % 233.75/39.87 (7) pred(n4) = n3 % 233.75/39.87 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (pred(v1) = v2) | ~ $i(v1) % 233.75/39.87 | ~ $i(v0) | ~ gt(v1, v0) | leq(v0, v2)) % 233.75/39.87 (9) a_select3(pminus_ds1_filter, all_74_15, n5) = all_74_13 % 233.75/39.87 (10) $i(n2) % 233.75/39.87 (11) leq(n5, n5) % 233.75/39.87 (12) $i(all_74_15) % 233.75/39.87 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 233.75/39.87 (v1 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 233.75/39.87 v0)) % 233.75/39.87 (14) pred(n2) = n1 % 233.75/39.87 (15) $i(n5) % 233.75/39.87 (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 233.75/39.87 (a_select3(pminus_ds1_filter, v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 233.75/39.87 ~ leq(v1, all_74_21) | ~ leq(v0, all_74_21) | ~ leq(n0, v1) | ~ % 233.75/39.87 leq(n0, v0) | (a_select3(pminus_ds1_filter, v1, v0) = v2 & $i(v2))) % 233.75/39.87 (17) leq(all_74_15, n5) % 233.75/39.87 (18) $i(n3) % 233.75/39.87 (19) leq(n0, n5) % 233.75/39.87 (20) pred(n3) = n2 % 233.75/39.88 (21) $i(n4) % 233.75/39.88 (22) leq(n0, all_74_15) % 233.75/39.88 (23) ! [v0: $i] : (v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0, n1) | ~ % 233.75/39.88 leq(n0, v0)) % 233.75/39.88 % 233.75/39.88 Begin of proof % 233.75/39.88 | % 233.75/39.88 | BETA: splitting (4) gives: % 233.75/39.88 | % 233.75/39.88 | Case 1: % 233.75/39.88 | | % 233.75/39.88 | | (24) gt(n4, all_74_15) % 233.75/39.88 | | % 233.75/39.88 | | GROUND_INST: instantiating (8) with all_74_15, n4, n3, simplifying with (7), % 233.75/39.88 | | (12), (21), (24) gives: % 233.75/39.88 | | (25) leq(all_74_15, n3) % 233.75/39.88 | | % 233.75/39.88 | | GROUND_INST: instantiating (1) with all_74_15, n3, simplifying with (12), % 233.75/39.88 | | (18), (25) gives: % 233.75/39.88 | | (26) all_74_15 = n3 | gt(n3, all_74_15) % 233.75/39.88 | | % 233.75/39.88 | | BETA: splitting (26) gives: % 233.75/39.88 | | % 233.75/39.88 | | Case 1: % 233.75/39.88 | | | % 233.75/39.88 | | | (27) gt(n3, all_74_15) % 233.75/39.88 | | | % 233.75/39.88 | | | GROUND_INST: instantiating (8) with all_74_15, n3, n2, simplifying with % 233.75/39.88 | | | (12), (18), (20), (27) gives: % 233.75/39.88 | | | (28) leq(all_74_15, n2) % 233.75/39.88 | | | % 233.75/39.88 | | | GROUND_INST: instantiating (1) with all_74_15, n2, simplifying with (10), % 233.75/39.88 | | | (12), (28) gives: % 233.75/39.88 | | | (29) all_74_15 = n2 | gt(n2, all_74_15) % 233.75/39.88 | | | % 233.75/39.88 | | | BETA: splitting (29) gives: % 233.75/39.88 | | | % 233.75/39.88 | | | Case 1: % 233.75/39.88 | | | | % 233.75/39.88 | | | | (30) gt(n2, all_74_15) % 233.75/39.88 | | | | % 233.75/39.88 | | | | GROUND_INST: instantiating (8) with all_74_15, n2, n1, simplifying with % 233.75/39.88 | | | | (10), (12), (14), (30) gives: % 233.75/39.88 | | | | (31) leq(all_74_15, n1) % 233.75/39.88 | | | | % 233.75/39.88 | | | | GROUND_INST: instantiating (23) with all_74_15, simplifying with (12), % 233.75/39.88 | | | | (22), (31) gives: % 233.75/39.88 | | | | (32) all_74_15 = n1 | all_74_15 = n0 % 233.75/39.88 | | | | % 233.75/39.88 | | | | BETA: splitting (32) gives: % 233.75/39.88 | | | | % 233.75/39.88 | | | | Case 1: % 233.75/39.88 | | | | | % 233.75/39.88 | | | | | (33) all_74_15 = n0 % 233.75/39.88 | | | | | % 233.75/39.88 | | | | | REDUCE: (3), (33) imply: % 233.75/39.88 | | | | | (34) $false % 233.75/39.88 | | | | | % 233.75/39.88 | | | | | CLOSE: (34) is inconsistent. % 233.75/39.88 | | | | | % 233.75/39.88 | | | | Case 2: % 233.75/39.88 | | | | | % 233.75/39.88 | | | | | (35) all_74_15 = n1 % 233.75/39.88 | | | | | % 233.75/39.88 | | | | | REDUCE: (9), (35) imply: % 233.75/39.88 | | | | | (36) a_select3(pminus_ds1_filter, n1, n5) = all_74_13 % 233.75/39.88 | | | | | % 233.75/39.88 | | | | | REDUCE: (6), (35) imply: % 233.75/39.88 | | | | | (37) a_select3(pminus_ds1_filter, n5, n1) = all_74_12 % 233.75/39.88 | | | | | % 233.75/39.88 | | | | | REDUCE: (12), (35) imply: % 233.75/39.88 | | | | | (38) $i(n1) % 233.75/39.88 | | | | | % 233.75/39.88 | | | | | REDUCE: (17), (35) imply: % 233.75/39.88 | | | | | (39) leq(n1, n5) % 233.75/39.88 | | | | | % 233.75/39.88 | | | | | REDUCE: (22), (35) imply: % 233.75/39.88 | | | | | (40) leq(n0, n1) % 233.75/39.88 | | | | | % 233.75/39.88 | | | | | GROUND_INST: instantiating (16) with n1, n5, all_74_13, simplifying % 233.75/39.88 | | | | | with (15), (19), (36), (38), (40) gives: % 233.75/39.88 | | | | | (41) ~ leq(n5, all_74_21) | ~ leq(n1, all_74_21) | % 233.75/39.88 | | | | | (a_select3(pminus_ds1_filter, n5, n1) = all_74_13 & % 233.75/39.88 | | | | | $i(all_74_13)) % 233.75/39.88 | | | | | % 233.75/39.88 | | | | | BETA: splitting (41) gives: % 233.75/39.88 | | | | | % 233.75/39.88 | | | | | Case 1: % 233.75/39.88 | | | | | | % 233.75/39.88 | | | | | | (42) ~ leq(n5, all_74_21) % 233.75/39.88 | | | | | | % 233.75/39.88 | | | | | | REDUCE: (5), (42) imply: % 233.75/39.88 | | | | | | (43) ~ leq(n5, n5) % 233.75/39.88 | | | | | | % 233.75/39.88 | | | | | | PRED_UNIFY: (11), (43) imply: % 233.75/39.88 | | | | | | (44) $false % 233.75/39.88 | | | | | | % 233.75/39.88 | | | | | | CLOSE: (44) is inconsistent. % 233.75/39.88 | | | | | | % 233.75/39.88 | | | | | Case 2: % 233.75/39.88 | | | | | | % 233.75/39.88 | | | | | | (45) ~ leq(n1, all_74_21) | (a_select3(pminus_ds1_filter, n5, % 233.75/39.88 | | | | | | n1) = all_74_13 & $i(all_74_13)) % 233.75/39.88 | | | | | | % 233.75/39.88 | | | | | | BETA: splitting (45) gives: % 233.75/39.88 | | | | | | % 233.75/39.88 | | | | | | Case 1: % 233.75/39.88 | | | | | | | % 233.75/39.88 | | | | | | | (46) ~ leq(n1, all_74_21) % 233.75/39.88 | | | | | | | % 233.75/39.88 | | | | | | | REDUCE: (5), (46) imply: % 233.75/39.88 | | | | | | | (47) ~ leq(n1, n5) % 233.75/39.88 | | | | | | | % 233.75/39.88 | | | | | | | PRED_UNIFY: (39), (47) imply: % 233.75/39.88 | | | | | | | (48) $false % 233.75/39.88 | | | | | | | % 233.75/39.88 | | | | | | | CLOSE: (48) is inconsistent. % 233.75/39.88 | | | | | | | % 233.75/39.88 | | | | | | Case 2: % 233.75/39.88 | | | | | | | % 233.75/39.88 | | | | | | | (49) a_select3(pminus_ds1_filter, n5, n1) = all_74_13 & % 233.75/39.88 | | | | | | | $i(all_74_13) % 233.75/39.88 | | | | | | | % 233.75/39.88 | | | | | | | ALPHA: (49) implies: % 233.75/39.88 | | | | | | | (50) a_select3(pminus_ds1_filter, n5, n1) = all_74_13 % 233.75/39.88 | | | | | | | % 233.75/39.88 | | | | | | | GROUND_INST: instantiating (13) with all_74_12, all_74_13, n1, n5, % 233.75/39.88 | | | | | | | pminus_ds1_filter, simplifying with (37), (50) gives: % 233.75/39.88 | | | | | | | (51) all_74_12 = all_74_13 % 233.75/39.88 | | | | | | | % 233.75/39.88 | | | | | | | REDUCE: (2), (51) imply: % 233.75/39.88 | | | | | | | (52) $false % 233.75/39.88 | | | | | | | % 233.75/39.88 | | | | | | | CLOSE: (52) is inconsistent. % 233.75/39.88 | | | | | | | % 233.75/39.88 | | | | | | End of split % 233.75/39.88 | | | | | | % 233.75/39.88 | | | | | End of split % 233.75/39.88 | | | | | % 233.75/39.88 | | | | End of split % 233.75/39.88 | | | | % 233.75/39.88 | | | Case 2: % 233.75/39.88 | | | | % 233.75/39.88 | | | | (53) all_74_15 = n2 % 233.75/39.88 | | | | % 233.75/39.88 | | | | REDUCE: (9), (53) imply: % 233.75/39.88 | | | | (54) a_select3(pminus_ds1_filter, n2, n5) = all_74_13 % 233.75/39.88 | | | | % 233.75/39.88 | | | | REDUCE: (6), (53) imply: % 233.89/39.88 | | | | (55) a_select3(pminus_ds1_filter, n5, n2) = all_74_12 % 233.89/39.88 | | | | % 233.89/39.88 | | | | REDUCE: (17), (53) imply: % 233.89/39.88 | | | | (56) leq(n2, n5) % 233.89/39.88 | | | | % 233.89/39.88 | | | | REDUCE: (22), (53) imply: % 233.89/39.88 | | | | (57) leq(n0, n2) % 233.89/39.88 | | | | % 233.89/39.88 | | | | GROUND_INST: instantiating (16) with n2, n5, all_74_13, simplifying with % 233.89/39.88 | | | | (10), (15), (19), (54), (57) gives: % 233.89/39.88 | | | | (58) ~ leq(n5, all_74_21) | ~ leq(n2, all_74_21) | % 233.89/39.88 | | | | (a_select3(pminus_ds1_filter, n5, n2) = all_74_13 & % 233.89/39.88 | | | | $i(all_74_13)) % 233.89/39.88 | | | | % 233.89/39.88 | | | | BETA: splitting (58) gives: % 233.89/39.88 | | | | % 233.89/39.88 | | | | Case 1: % 233.89/39.88 | | | | | % 233.89/39.88 | | | | | (59) ~ leq(n5, all_74_21) % 233.89/39.88 | | | | | % 233.89/39.88 | | | | | REDUCE: (5), (59) imply: % 233.89/39.88 | | | | | (60) ~ leq(n5, n5) % 233.89/39.88 | | | | | % 233.89/39.88 | | | | | PRED_UNIFY: (11), (60) imply: % 233.89/39.88 | | | | | (61) $false % 233.89/39.88 | | | | | % 233.89/39.88 | | | | | CLOSE: (61) is inconsistent. % 233.89/39.88 | | | | | % 233.89/39.88 | | | | Case 2: % 233.89/39.88 | | | | | % 233.89/39.88 | | | | | (62) ~ leq(n2, all_74_21) | (a_select3(pminus_ds1_filter, n5, n2) % 233.89/39.88 | | | | | = all_74_13 & $i(all_74_13)) % 233.89/39.88 | | | | | % 233.89/39.88 | | | | | BETA: splitting (62) gives: % 233.89/39.88 | | | | | % 233.89/39.88 | | | | | Case 1: % 233.89/39.88 | | | | | | % 233.89/39.88 | | | | | | (63) ~ leq(n2, all_74_21) % 233.89/39.88 | | | | | | % 233.89/39.88 | | | | | | REDUCE: (5), (63) imply: % 233.89/39.88 | | | | | | (64) ~ leq(n2, n5) % 233.89/39.88 | | | | | | % 233.89/39.88 | | | | | | PRED_UNIFY: (56), (64) imply: % 233.89/39.88 | | | | | | (65) $false % 233.89/39.88 | | | | | | % 233.89/39.88 | | | | | | CLOSE: (65) is inconsistent. % 233.89/39.88 | | | | | | % 233.89/39.88 | | | | | Case 2: % 233.89/39.88 | | | | | | % 233.89/39.88 | | | | | | (66) a_select3(pminus_ds1_filter, n5, n2) = all_74_13 & % 233.89/39.88 | | | | | | $i(all_74_13) % 233.89/39.88 | | | | | | % 233.89/39.88 | | | | | | ALPHA: (66) implies: % 233.89/39.88 | | | | | | (67) a_select3(pminus_ds1_filter, n5, n2) = all_74_13 % 233.89/39.88 | | | | | | % 233.89/39.88 | | | | | | GROUND_INST: instantiating (13) with all_74_12, all_74_13, n2, n5, % 233.89/39.88 | | | | | | pminus_ds1_filter, simplifying with (55), (67) gives: % 233.89/39.88 | | | | | | (68) all_74_12 = all_74_13 % 233.89/39.88 | | | | | | % 233.89/39.88 | | | | | | REDUCE: (2), (68) imply: % 233.89/39.88 | | | | | | (69) $false % 233.89/39.88 | | | | | | % 233.89/39.88 | | | | | | CLOSE: (69) is inconsistent. % 233.89/39.88 | | | | | | % 233.89/39.88 | | | | | End of split % 233.89/39.88 | | | | | % 233.89/39.88 | | | | End of split % 233.89/39.88 | | | | % 233.89/39.88 | | | End of split % 233.89/39.88 | | | % 233.89/39.88 | | Case 2: % 233.89/39.88 | | | % 233.89/39.88 | | | (70) all_74_15 = n3 % 233.89/39.88 | | | % 233.89/39.88 | | | REDUCE: (9), (70) imply: % 233.89/39.88 | | | (71) a_select3(pminus_ds1_filter, n3, n5) = all_74_13 % 233.89/39.88 | | | % 233.89/39.88 | | | REDUCE: (6), (70) imply: % 233.89/39.88 | | | (72) a_select3(pminus_ds1_filter, n5, n3) = all_74_12 % 233.89/39.88 | | | % 233.89/39.88 | | | REDUCE: (17), (70) imply: % 233.89/39.88 | | | (73) leq(n3, n5) % 233.89/39.88 | | | % 233.89/39.88 | | | REDUCE: (22), (70) imply: % 233.89/39.88 | | | (74) leq(n0, n3) % 233.89/39.88 | | | % 233.89/39.88 | | | GROUND_INST: instantiating (16) with n3, n5, all_74_13, simplifying with % 233.89/39.88 | | | (15), (18), (19), (71), (74) gives: % 233.89/39.88 | | | (75) ~ leq(n5, all_74_21) | ~ leq(n3, all_74_21) | % 233.89/39.88 | | | (a_select3(pminus_ds1_filter, n5, n3) = all_74_13 & $i(all_74_13)) % 233.89/39.88 | | | % 233.89/39.88 | | | BETA: splitting (75) gives: % 233.89/39.88 | | | % 233.89/39.88 | | | Case 1: % 233.89/39.88 | | | | % 233.89/39.88 | | | | (76) ~ leq(n5, all_74_21) % 233.89/39.88 | | | | % 233.89/39.88 | | | | REDUCE: (5), (76) imply: % 233.89/39.88 | | | | (77) ~ leq(n5, n5) % 233.89/39.88 | | | | % 233.89/39.88 | | | | PRED_UNIFY: (11), (77) imply: % 233.89/39.88 | | | | (78) $false % 233.89/39.88 | | | | % 233.89/39.88 | | | | CLOSE: (78) is inconsistent. % 233.89/39.88 | | | | % 233.89/39.88 | | | Case 2: % 233.89/39.88 | | | | % 233.89/39.88 | | | | (79) ~ leq(n3, all_74_21) | (a_select3(pminus_ds1_filter, n5, n3) = % 233.89/39.88 | | | | all_74_13 & $i(all_74_13)) % 233.89/39.88 | | | | % 233.89/39.88 | | | | BETA: splitting (79) gives: % 233.89/39.88 | | | | % 233.89/39.88 | | | | Case 1: % 233.89/39.88 | | | | | % 233.89/39.88 | | | | | (80) ~ leq(n3, all_74_21) % 233.89/39.88 | | | | | % 233.89/39.88 | | | | | REDUCE: (5), (80) imply: % 233.89/39.88 | | | | | (81) ~ leq(n3, n5) % 233.89/39.88 | | | | | % 233.89/39.88 | | | | | PRED_UNIFY: (73), (81) imply: % 233.89/39.88 | | | | | (82) $false % 233.89/39.88 | | | | | % 233.89/39.88 | | | | | CLOSE: (82) is inconsistent. % 233.89/39.88 | | | | | % 233.89/39.88 | | | | Case 2: % 233.89/39.88 | | | | | % 233.89/39.88 | | | | | (83) a_select3(pminus_ds1_filter, n5, n3) = all_74_13 & % 233.89/39.88 | | | | | $i(all_74_13) % 233.89/39.88 | | | | | % 233.89/39.88 | | | | | ALPHA: (83) implies: % 233.89/39.88 | | | | | (84) a_select3(pminus_ds1_filter, n5, n3) = all_74_13 % 233.89/39.88 | | | | | % 233.89/39.88 | | | | | GROUND_INST: instantiating (13) with all_74_12, all_74_13, n3, n5, % 233.89/39.88 | | | | | pminus_ds1_filter, simplifying with (72), (84) gives: % 233.89/39.88 | | | | | (85) all_74_12 = all_74_13 % 233.89/39.88 | | | | | % 233.89/39.88 | | | | | REDUCE: (2), (85) imply: % 233.89/39.88 | | | | | (86) $false % 233.89/39.88 | | | | | % 233.89/39.88 | | | | | CLOSE: (86) is inconsistent. % 233.89/39.88 | | | | | % 233.89/39.88 | | | | End of split % 233.89/39.88 | | | | % 233.89/39.88 | | | End of split % 233.89/39.88 | | | % 233.89/39.88 | | End of split % 233.89/39.88 | | % 233.89/39.88 | Case 2: % 233.89/39.88 | | % 233.89/39.88 | | (87) all_74_15 = n4 % 233.89/39.88 | | % 233.89/39.88 | | REDUCE: (9), (87) imply: % 233.89/39.88 | | (88) a_select3(pminus_ds1_filter, n4, n5) = all_74_13 % 233.89/39.88 | | % 233.89/39.88 | | REDUCE: (6), (87) imply: % 233.89/39.88 | | (89) a_select3(pminus_ds1_filter, n5, n4) = all_74_12 % 233.89/39.88 | | % 233.89/39.88 | | REDUCE: (17), (87) imply: % 233.89/39.88 | | (90) leq(n4, n5) % 233.89/39.88 | | % 233.89/39.88 | | REDUCE: (22), (87) imply: % 233.89/39.88 | | (91) leq(n0, n4) % 233.89/39.88 | | % 233.89/39.88 | | GROUND_INST: instantiating (16) with n4, n5, all_74_13, simplifying with % 233.89/39.88 | | (15), (19), (21), (88), (91) gives: % 233.89/39.88 | | (92) ~ leq(n5, all_74_21) | ~ leq(n4, all_74_21) | % 233.89/39.88 | | (a_select3(pminus_ds1_filter, n5, n4) = all_74_13 & $i(all_74_13)) % 233.89/39.88 | | % 233.89/39.88 | | BETA: splitting (92) gives: % 233.89/39.88 | | % 233.89/39.88 | | Case 1: % 233.89/39.88 | | | % 233.89/39.88 | | | (93) ~ leq(n5, all_74_21) % 233.89/39.88 | | | % 233.89/39.88 | | | REDUCE: (5), (93) imply: % 233.89/39.88 | | | (94) ~ leq(n5, n5) % 233.89/39.88 | | | % 233.89/39.88 | | | PRED_UNIFY: (11), (94) imply: % 233.89/39.88 | | | (95) $false % 233.89/39.88 | | | % 233.89/39.88 | | | CLOSE: (95) is inconsistent. % 233.89/39.88 | | | % 233.89/39.88 | | Case 2: % 233.89/39.88 | | | % 233.89/39.88 | | | (96) ~ leq(n4, all_74_21) | (a_select3(pminus_ds1_filter, n5, n4) = % 233.89/39.88 | | | all_74_13 & $i(all_74_13)) % 233.89/39.88 | | | % 233.89/39.88 | | | BETA: splitting (96) gives: % 233.89/39.88 | | | % 233.89/39.88 | | | Case 1: % 233.89/39.88 | | | | % 233.89/39.88 | | | | (97) ~ leq(n4, all_74_21) % 233.89/39.88 | | | | % 233.89/39.88 | | | | REDUCE: (5), (97) imply: % 233.89/39.88 | | | | (98) ~ leq(n4, n5) % 233.89/39.88 | | | | % 233.89/39.88 | | | | PRED_UNIFY: (90), (98) imply: % 233.89/39.88 | | | | (99) $false % 233.89/39.88 | | | | % 233.89/39.88 | | | | CLOSE: (99) is inconsistent. % 233.89/39.88 | | | | % 233.89/39.88 | | | Case 2: % 233.89/39.88 | | | | % 233.89/39.88 | | | | (100) a_select3(pminus_ds1_filter, n5, n4) = all_74_13 & % 233.89/39.88 | | | | $i(all_74_13) % 233.89/39.88 | | | | % 233.89/39.88 | | | | ALPHA: (100) implies: % 233.89/39.88 | | | | (101) a_select3(pminus_ds1_filter, n5, n4) = all_74_13 % 233.89/39.88 | | | | % 233.89/39.88 | | | | REF_CLOSE: (2), (13), (89), (101) are inconsistent by sub-proof #22. % 233.89/39.88 | | | | % 233.89/39.88 | | | End of split % 233.89/39.88 | | | % 233.89/39.88 | | End of split % 233.89/39.88 | | % 233.89/39.88 | End of split % 233.89/39.88 | % 233.89/39.88 End of proof % 233.89/39.88 % 233.89/39.88 Sub-proof #22 shows that the following formulas are inconsistent: % 233.89/39.88 ---------------------------------------------------------------- % 233.89/39.88 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 233.89/39.88 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 233.89/39.88 v0)) % 233.89/39.88 (2) a_select3(pminus_ds1_filter, n5, n4) = all_74_12 % 233.89/39.88 (3) a_select3(pminus_ds1_filter, n5, n4) = all_74_13 % 233.89/39.88 (4) ~ (all_74_12 = all_74_13) % 233.89/39.88 % 233.89/39.88 Begin of proof % 233.89/39.88 | % 233.89/39.88 | GROUND_INST: instantiating (1) with all_74_12, all_74_13, n4, n5, % 233.89/39.88 | pminus_ds1_filter, simplifying with (2), (3) gives: % 233.89/39.88 | (5) all_74_12 = all_74_13 % 233.89/39.88 | % 233.89/39.88 | REDUCE: (4), (5) imply: % 233.89/39.88 | (6) $false % 233.89/39.88 | % 233.89/39.88 | CLOSE: (6) is inconsistent. % 233.89/39.88 | % 233.89/39.88 End of proof % 233.89/39.88 % 233.89/39.88 Sub-proof #23 shows that the following formulas are inconsistent: % 233.89/39.88 ---------------------------------------------------------------- % 233.89/39.89 (1) a_select3(pminus_ds1_filter, all_74_14, all_74_15) = all_74_12 % 233.89/39.89 (2) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ leq(v0, % 233.89/39.89 v1) | gt(v1, v0)) % 233.89/39.89 (3) leq(all_74_14, n5) % 233.89/39.89 (4) ~ (all_74_12 = all_74_13) % 233.89/39.89 (5) ~ (all_74_15 = n0) % 233.89/39.89 (6) all_74_15 = n4 | gt(n4, all_74_15) % 233.89/39.89 (7) a_select3(pminus_ds1_filter, all_74_15, all_74_14) = all_74_13 % 233.89/39.89 (8) all_74_21 = n5 % 233.89/39.89 (9) pred(n4) = n3 % 233.89/39.89 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (pred(v1) = v2) | ~ % 233.89/39.89 $i(v1) | ~ $i(v0) | ~ gt(v1, v0) | leq(v0, v2)) % 233.89/39.89 (11) $i(n2) % 233.89/39.89 (12) $i(all_74_15) % 233.89/39.89 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 233.89/39.89 (v1 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 233.89/39.89 v0)) % 233.89/39.89 (14) leq(n0, all_74_14) % 233.89/39.89 (15) pred(n2) = n1 % 233.89/39.89 (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 233.89/39.89 (a_select3(pminus_ds1_filter, v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 233.89/39.89 ~ leq(v1, all_74_21) | ~ leq(v0, all_74_21) | ~ leq(n0, v1) | ~ % 233.89/39.89 leq(n0, v0) | (a_select3(pminus_ds1_filter, v1, v0) = v2 & $i(v2))) % 233.89/39.89 (17) leq(all_74_15, n5) % 233.89/39.89 (18) $i(n3) % 233.89/39.89 (19) ~ (all_74_14 = n0) % 233.89/39.89 (20) pred(n3) = n2 % 233.89/39.89 (21) $i(n4) % 233.89/39.89 (22) $i(all_74_14) % 233.89/39.89 (23) leq(n0, all_74_15) % 233.89/39.89 (24) all_74_14 = n4 | gt(n4, all_74_14) % 233.89/39.89 (25) ! [v0: $i] : (v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0, n1) | ~ % 233.89/39.89 leq(n0, v0)) % 233.89/39.89 % 233.89/39.89 Begin of proof % 233.89/39.89 | % 233.89/39.89 | BETA: splitting (6) gives: % 233.89/39.89 | % 233.89/39.89 | Case 1: % 233.89/39.89 | | % 233.89/39.89 | | (26) gt(n4, all_74_15) % 233.89/39.89 | | % 233.89/39.89 | | GROUND_INST: instantiating (10) with all_74_15, n4, n3, simplifying with % 233.89/39.89 | | (9), (12), (21), (26) gives: % 233.89/39.89 | | (27) leq(all_74_15, n3) % 233.89/39.89 | | % 233.89/39.89 | | GROUND_INST: instantiating (2) with all_74_15, n3, simplifying with (12), % 233.89/39.89 | | (18), (27) gives: % 233.89/39.89 | | (28) all_74_15 = n3 | gt(n3, all_74_15) % 233.89/39.89 | | % 233.89/39.89 | | BETA: splitting (24) gives: % 233.89/39.89 | | % 233.89/39.89 | | Case 1: % 233.89/39.89 | | | % 233.89/39.89 | | | (29) gt(n4, all_74_14) % 233.89/39.89 | | | % 233.89/39.89 | | | GROUND_INST: instantiating (10) with all_74_14, n4, n3, simplifying with % 233.89/39.89 | | | (9), (21), (22), (29) gives: % 233.89/39.89 | | | (30) leq(all_74_14, n3) % 233.89/39.89 | | | % 233.89/39.89 | | | GROUND_INST: instantiating (2) with all_74_14, n3, simplifying with (18), % 233.89/39.89 | | | (22), (30) gives: % 233.89/39.89 | | | (31) all_74_14 = n3 | gt(n3, all_74_14) % 233.89/39.89 | | | % 233.89/39.89 | | | BETA: splitting (28) gives: % 233.89/39.89 | | | % 233.89/39.89 | | | Case 1: % 233.89/39.89 | | | | % 233.89/39.89 | | | | (32) gt(n3, all_74_15) % 233.89/39.89 | | | | % 233.89/39.89 | | | | GROUND_INST: instantiating (10) with all_74_15, n3, n2, simplifying with % 233.89/39.89 | | | | (12), (18), (20), (32) gives: % 233.89/39.89 | | | | (33) leq(all_74_15, n2) % 233.89/39.89 | | | | % 233.89/39.89 | | | | GROUND_INST: instantiating (2) with all_74_15, n2, simplifying with % 233.89/39.89 | | | | (11), (12), (33) gives: % 233.89/39.89 | | | | (34) all_74_15 = n2 | gt(n2, all_74_15) % 233.89/39.89 | | | | % 233.89/39.89 | | | | BETA: splitting (31) gives: % 233.89/39.89 | | | | % 233.89/39.89 | | | | Case 1: % 233.89/39.89 | | | | | % 233.89/39.89 | | | | | (35) gt(n3, all_74_14) % 233.89/39.89 | | | | | % 233.89/39.89 | | | | | GROUND_INST: instantiating (10) with all_74_14, n3, n2, simplifying % 233.89/39.89 | | | | | with (18), (20), (22), (35) gives: % 233.89/39.89 | | | | | (36) leq(all_74_14, n2) % 233.89/39.89 | | | | | % 233.89/39.89 | | | | | GROUND_INST: instantiating (2) with all_74_14, n2, simplifying with % 233.89/39.89 | | | | | (11), (22), (36) gives: % 233.89/39.89 | | | | | (37) all_74_14 = n2 | gt(n2, all_74_14) % 233.89/39.89 | | | | | % 233.89/39.89 | | | | | BETA: splitting (34) gives: % 233.89/39.89 | | | | | % 233.89/39.89 | | | | | Case 1: % 233.89/39.89 | | | | | | % 233.89/39.89 | | | | | | (38) gt(n2, all_74_15) % 233.89/39.89 | | | | | | % 233.89/39.89 | | | | | | GROUND_INST: instantiating (10) with all_74_15, n2, n1, simplifying % 233.89/39.89 | | | | | | with (11), (12), (15), (38) gives: % 233.89/39.89 | | | | | | (39) leq(all_74_15, n1) % 233.89/39.89 | | | | | | % 233.89/39.89 | | | | | | GROUND_INST: instantiating (25) with all_74_15, simplifying with % 233.89/39.89 | | | | | | (12), (23), (39) gives: % 233.89/39.89 | | | | | | (40) all_74_15 = n1 | all_74_15 = n0 % 233.89/39.89 | | | | | | % 233.89/39.89 | | | | | | BETA: splitting (40) gives: % 233.89/39.89 | | | | | | % 233.89/39.89 | | | | | | Case 1: % 233.89/39.89 | | | | | | | % 233.89/39.89 | | | | | | | (41) all_74_15 = n0 % 233.89/39.89 | | | | | | | % 233.89/39.89 | | | | | | | REDUCE: (5), (41) imply: % 233.89/39.89 | | | | | | | (42) $false % 233.89/39.89 | | | | | | | % 233.89/39.89 | | | | | | | CLOSE: (42) is inconsistent. % 233.89/39.89 | | | | | | | % 233.89/39.89 | | | | | | Case 2: % 233.89/39.89 | | | | | | | % 233.89/39.89 | | | | | | | (43) all_74_15 = n1 % 233.89/39.89 | | | | | | | % 233.89/39.89 | | | | | | | REDUCE: (1), (43) imply: % 233.89/39.89 | | | | | | | (44) a_select3(pminus_ds1_filter, all_74_14, n1) = all_74_12 % 233.89/39.89 | | | | | | | % 233.89/39.89 | | | | | | | REDUCE: (7), (43) imply: % 233.89/39.89 | | | | | | | (45) a_select3(pminus_ds1_filter, n1, all_74_14) = all_74_13 % 233.89/39.89 | | | | | | | % 233.89/39.89 | | | | | | | REDUCE: (12), (43) imply: % 233.89/39.89 | | | | | | | (46) $i(n1) % 233.89/39.89 | | | | | | | % 233.89/39.89 | | | | | | | REDUCE: (17), (43) imply: % 233.89/39.89 | | | | | | | (47) leq(n1, n5) % 233.89/39.89 | | | | | | | % 233.89/39.89 | | | | | | | REDUCE: (23), (43) imply: % 233.89/39.89 | | | | | | | (48) leq(n0, n1) % 233.89/39.89 | | | | | | | % 233.89/39.89 | | | | | | | BETA: splitting (37) gives: % 233.89/39.89 | | | | | | | % 233.89/39.89 | | | | | | | Case 1: % 233.89/39.89 | | | | | | | | % 233.89/39.89 | | | | | | | | (49) gt(n2, all_74_14) % 233.89/39.89 | | | | | | | | % 233.89/39.89 | | | | | | | | GROUND_INST: instantiating (10) with all_74_14, n2, n1, % 233.89/39.89 | | | | | | | | simplifying with (11), (15), (22), (49) gives: % 233.89/39.89 | | | | | | | | (50) leq(all_74_14, n1) % 233.89/39.89 | | | | | | | | % 233.89/39.89 | | | | | | | | GROUND_INST: instantiating (25) with all_74_14, simplifying with % 233.89/39.89 | | | | | | | | (14), (22), (50) gives: % 233.89/39.89 | | | | | | | | (51) all_74_14 = n1 | all_74_14 = n0 % 233.89/39.89 | | | | | | | | % 233.89/39.89 | | | | | | | | BETA: splitting (51) gives: % 233.89/39.89 | | | | | | | | % 233.89/39.89 | | | | | | | | Case 1: % 233.89/39.89 | | | | | | | | | % 233.89/39.89 | | | | | | | | | (52) all_74_14 = n0 % 233.89/39.89 | | | | | | | | | % 233.89/39.89 | | | | | | | | | REDUCE: (19), (52) imply: % 233.89/39.89 | | | | | | | | | (53) $false % 233.89/39.89 | | | | | | | | | % 233.89/39.89 | | | | | | | | | CLOSE: (53) is inconsistent. % 233.89/39.89 | | | | | | | | | % 233.89/39.89 | | | | | | | | Case 2: % 233.89/39.89 | | | | | | | | | % 233.89/39.89 | | | | | | | | | (54) all_74_14 = n1 % 233.89/39.89 | | | | | | | | | % 233.89/39.89 | | | | | | | | | REDUCE: (44), (54) imply: % 233.89/39.89 | | | | | | | | | (55) a_select3(pminus_ds1_filter, n1, n1) = all_74_12 % 233.89/39.89 | | | | | | | | | % 233.89/39.89 | | | | | | | | | REDUCE: (45), (54) imply: % 233.89/39.89 | | | | | | | | | (56) a_select3(pminus_ds1_filter, n1, n1) = all_74_13 % 233.89/39.89 | | | | | | | | | % 233.89/39.89 | | | | | | | | | GROUND_INST: instantiating (13) with all_74_13, all_74_12, n1, % 233.89/39.89 | | | | | | | | | n1, pminus_ds1_filter, simplifying with (55), (56) % 233.89/39.89 | | | | | | | | | gives: % 233.89/39.89 | | | | | | | | | (57) all_74_12 = all_74_13 % 233.89/39.89 | | | | | | | | | % 233.89/39.89 | | | | | | | | | REDUCE: (4), (57) imply: % 233.89/39.89 | | | | | | | | | (58) $false % 233.89/39.89 | | | | | | | | | % 233.89/39.89 | | | | | | | | | CLOSE: (58) is inconsistent. % 233.89/39.89 | | | | | | | | | % 233.89/39.89 | | | | | | | | End of split % 233.89/39.89 | | | | | | | | % 233.89/39.89 | | | | | | | Case 2: % 233.89/39.89 | | | | | | | | % 233.89/39.89 | | | | | | | | (59) all_74_14 = n2 % 233.89/39.89 | | | | | | | | % 233.89/39.89 | | | | | | | | REDUCE: (44), (59) imply: % 233.89/39.89 | | | | | | | | (60) a_select3(pminus_ds1_filter, n2, n1) = all_74_12 % 233.89/39.89 | | | | | | | | % 233.89/39.89 | | | | | | | | REDUCE: (45), (59) imply: % 233.89/39.89 | | | | | | | | (61) a_select3(pminus_ds1_filter, n1, n2) = all_74_13 % 233.89/39.89 | | | | | | | | % 233.89/39.89 | | | | | | | | REDUCE: (3), (59) imply: % 233.89/39.89 | | | | | | | | (62) leq(n2, n5) % 233.89/39.89 | | | | | | | | % 233.89/39.89 | | | | | | | | REDUCE: (14), (59) imply: % 233.89/39.89 | | | | | | | | (63) leq(n0, n2) % 233.89/39.89 | | | | | | | | % 233.89/39.89 | | | | | | | | GROUND_INST: instantiating (16) with n1, n2, all_74_13, % 233.89/39.89 | | | | | | | | simplifying with (11), (46), (48), (61), (63) % 233.89/39.89 | | | | | | | | gives: % 233.89/39.89 | | | | | | | | (64) ~ leq(n2, all_74_21) | ~ leq(n1, all_74_21) | % 233.89/39.89 | | | | | | | | (a_select3(pminus_ds1_filter, n2, n1) = all_74_13 & % 233.89/39.89 | | | | | | | | $i(all_74_13)) % 233.89/39.89 | | | | | | | | % 233.89/39.89 | | | | | | | | BETA: splitting (64) gives: % 233.89/39.89 | | | | | | | | % 233.89/39.89 | | | | | | | | Case 1: % 233.89/39.89 | | | | | | | | | % 233.89/39.89 | | | | | | | | | (65) ~ leq(n2, all_74_21) % 233.89/39.89 | | | | | | | | | % 233.89/39.89 | | | | | | | | | REDUCE: (8), (65) imply: % 233.89/39.89 | | | | | | | | | (66) ~ leq(n2, n5) % 233.89/39.89 | | | | | | | | | % 233.89/39.89 | | | | | | | | | PRED_UNIFY: (62), (66) imply: % 233.89/39.89 | | | | | | | | | (67) $false % 233.89/39.89 | | | | | | | | | % 233.89/39.89 | | | | | | | | | CLOSE: (67) is inconsistent. % 233.89/39.89 | | | | | | | | | % 233.89/39.89 | | | | | | | | Case 2: % 233.89/39.89 | | | | | | | | | % 233.89/39.89 | | | | | | | | | (68) ~ leq(n1, all_74_21) | (a_select3(pminus_ds1_filter, % 233.89/39.89 | | | | | | | | | n2, n1) = all_74_13 & $i(all_74_13)) % 233.89/39.89 | | | | | | | | | % 233.89/39.89 | | | | | | | | | BETA: splitting (68) gives: % 233.89/39.89 | | | | | | | | | % 233.89/39.89 | | | | | | | | | Case 1: % 233.89/39.89 | | | | | | | | | | % 233.89/39.89 | | | | | | | | | | (69) ~ leq(n1, all_74_21) % 233.89/39.89 | | | | | | | | | | % 233.89/39.89 | | | | | | | | | | REDUCE: (8), (69) imply: % 233.89/39.89 | | | | | | | | | | (70) ~ leq(n1, n5) % 233.89/39.89 | | | | | | | | | | % 233.89/39.89 | | | | | | | | | | PRED_UNIFY: (47), (70) imply: % 233.89/39.89 | | | | | | | | | | (71) $false % 233.89/39.89 | | | | | | | | | | % 233.89/39.89 | | | | | | | | | | CLOSE: (71) is inconsistent. % 233.89/39.89 | | | | | | | | | | % 233.89/39.89 | | | | | | | | | Case 2: % 233.89/39.89 | | | | | | | | | | % 233.89/39.89 | | | | | | | | | | (72) a_select3(pminus_ds1_filter, n2, n1) = all_74_13 & % 233.89/39.89 | | | | | | | | | | $i(all_74_13) % 233.89/39.89 | | | | | | | | | | % 233.89/39.89 | | | | | | | | | | ALPHA: (72) implies: % 233.89/39.89 | | | | | | | | | | (73) a_select3(pminus_ds1_filter, n2, n1) = all_74_13 % 233.89/39.89 | | | | | | | | | | % 233.89/39.89 | | | | | | | | | | REF_CLOSE: (4), (13), (60), (73) are inconsistent by % 233.89/39.89 | | | | | | | | | | sub-proof #26. % 233.89/39.89 | | | | | | | | | | % 233.89/39.89 | | | | | | | | | End of split % 233.89/39.89 | | | | | | | | | % 233.89/39.89 | | | | | | | | End of split % 233.89/39.89 | | | | | | | | % 233.89/39.89 | | | | | | | End of split % 233.89/39.89 | | | | | | | % 233.89/39.89 | | | | | | End of split % 233.89/39.89 | | | | | | % 233.89/39.89 | | | | | Case 2: % 233.89/39.89 | | | | | | % 233.89/39.89 | | | | | | (74) all_74_15 = n2 % 233.89/39.89 | | | | | | % 233.89/39.89 | | | | | | REDUCE: (1), (74) imply: % 233.89/39.89 | | | | | | (75) a_select3(pminus_ds1_filter, all_74_14, n2) = all_74_12 % 233.89/39.89 | | | | | | % 233.89/39.89 | | | | | | REDUCE: (7), (74) imply: % 233.89/39.89 | | | | | | (76) a_select3(pminus_ds1_filter, n2, all_74_14) = all_74_13 % 233.89/39.89 | | | | | | % 233.89/39.89 | | | | | | REDUCE: (17), (74) imply: % 233.89/39.89 | | | | | | (77) leq(n2, n5) % 233.89/39.89 | | | | | | % 233.89/39.89 | | | | | | REDUCE: (23), (74) imply: % 233.89/39.89 | | | | | | (78) leq(n0, n2) % 233.89/39.89 | | | | | | % 233.89/39.89 | | | | | | BETA: splitting (37) gives: % 233.89/39.89 | | | | | | % 233.89/39.89 | | | | | | Case 1: % 233.89/39.89 | | | | | | | % 233.89/39.89 | | | | | | | (79) gt(n2, all_74_14) % 233.89/39.89 | | | | | | | % 233.89/39.89 | | | | | | | GROUND_INST: instantiating (10) with all_74_14, n2, n1, % 233.89/39.89 | | | | | | | simplifying with (11), (15), (22), (79) gives: % 233.89/39.89 | | | | | | | (80) leq(all_74_14, n1) % 233.89/39.89 | | | | | | | % 233.89/39.89 | | | | | | | GROUND_INST: instantiating (25) with all_74_14, simplifying with % 233.89/39.89 | | | | | | | (14), (22), (80) gives: % 233.89/39.89 | | | | | | | (81) all_74_14 = n1 | all_74_14 = n0 % 233.89/39.89 | | | | | | | % 233.89/39.89 | | | | | | | BETA: splitting (81) gives: % 233.89/39.89 | | | | | | | % 233.89/39.89 | | | | | | | Case 1: % 233.89/39.89 | | | | | | | | % 233.89/39.89 | | | | | | | | (82) all_74_14 = n0 % 233.89/39.89 | | | | | | | | % 233.89/39.89 | | | | | | | | REDUCE: (19), (82) imply: % 233.89/39.89 | | | | | | | | (83) $false % 233.89/39.89 | | | | | | | | % 233.89/39.89 | | | | | | | | CLOSE: (83) is inconsistent. % 233.89/39.89 | | | | | | | | % 233.89/39.89 | | | | | | | Case 2: % 233.89/39.89 | | | | | | | | % 233.89/39.89 | | | | | | | | (84) all_74_14 = n1 % 233.89/39.89 | | | | | | | | % 233.89/39.89 | | | | | | | | REDUCE: (75), (84) imply: % 233.89/39.89 | | | | | | | | (85) a_select3(pminus_ds1_filter, n1, n2) = all_74_12 % 233.89/39.89 | | | | | | | | % 233.89/39.89 | | | | | | | | REDUCE: (76), (84) imply: % 233.89/39.89 | | | | | | | | (86) a_select3(pminus_ds1_filter, n2, n1) = all_74_13 % 233.89/39.89 | | | | | | | | % 233.89/39.89 | | | | | | | | REDUCE: (22), (84) imply: % 233.89/39.89 | | | | | | | | (87) $i(n1) % 233.89/39.89 | | | | | | | | % 233.89/39.89 | | | | | | | | REDUCE: (3), (84) imply: % 233.89/39.89 | | | | | | | | (88) leq(n1, n5) % 233.89/39.89 | | | | | | | | % 233.89/39.89 | | | | | | | | REDUCE: (14), (84) imply: % 233.89/39.89 | | | | | | | | (89) leq(n0, n1) % 233.89/39.89 | | | | | | | | % 233.89/39.89 | | | | | | | | GROUND_INST: instantiating (16) with n1, n2, all_74_12, % 233.89/39.89 | | | | | | | | simplifying with (11), (78), (85), (87), (89) % 233.89/39.89 | | | | | | | | gives: % 233.89/39.89 | | | | | | | | (90) ~ leq(n2, all_74_21) | ~ leq(n1, all_74_21) | % 233.89/39.89 | | | | | | | | (a_select3(pminus_ds1_filter, n2, n1) = all_74_12 & % 233.89/39.89 | | | | | | | | $i(all_74_12)) % 233.89/39.89 | | | | | | | | % 233.89/39.89 | | | | | | | | BETA: splitting (90) gives: % 233.89/39.89 | | | | | | | | % 233.89/39.89 | | | | | | | | Case 1: % 233.89/39.89 | | | | | | | | | % 233.89/39.89 | | | | | | | | | (91) ~ leq(n2, all_74_21) % 233.89/39.89 | | | | | | | | | % 233.89/39.89 | | | | | | | | | REDUCE: (8), (91) imply: % 233.89/39.89 | | | | | | | | | (92) ~ leq(n2, n5) % 233.89/39.89 | | | | | | | | | % 233.89/39.89 | | | | | | | | | PRED_UNIFY: (77), (92) imply: % 233.89/39.89 | | | | | | | | | (93) $false % 233.89/39.89 | | | | | | | | | % 233.89/39.89 | | | | | | | | | CLOSE: (93) is inconsistent. % 233.89/39.89 | | | | | | | | | % 233.89/39.89 | | | | | | | | Case 2: % 233.89/39.89 | | | | | | | | | % 233.89/39.89 | | | | | | | | | (94) ~ leq(n1, all_74_21) | (a_select3(pminus_ds1_filter, % 233.89/39.89 | | | | | | | | | n2, n1) = all_74_12 & $i(all_74_12)) % 233.89/39.89 | | | | | | | | | % 233.89/39.89 | | | | | | | | | BETA: splitting (94) gives: % 233.89/39.89 | | | | | | | | | % 233.89/39.89 | | | | | | | | | Case 1: % 233.89/39.89 | | | | | | | | | | % 233.89/39.89 | | | | | | | | | | (95) ~ leq(n1, all_74_21) % 233.89/39.90 | | | | | | | | | | % 233.89/39.90 | | | | | | | | | | REDUCE: (8), (95) imply: % 233.89/39.90 | | | | | | | | | | (96) ~ leq(n1, n5) % 233.89/39.90 | | | | | | | | | | % 233.89/39.90 | | | | | | | | | | PRED_UNIFY: (88), (96) imply: % 233.89/39.90 | | | | | | | | | | (97) $false % 233.89/39.90 | | | | | | | | | | % 233.89/39.90 | | | | | | | | | | CLOSE: (97) is inconsistent. % 233.89/39.90 | | | | | | | | | | % 233.89/39.90 | | | | | | | | | Case 2: % 233.89/39.90 | | | | | | | | | | % 233.89/39.90 | | | | | | | | | | (98) a_select3(pminus_ds1_filter, n2, n1) = all_74_12 & % 233.89/39.90 | | | | | | | | | | $i(all_74_12) % 233.89/39.90 | | | | | | | | | | % 233.89/39.90 | | | | | | | | | | ALPHA: (98) implies: % 233.89/39.90 | | | | | | | | | | (99) a_select3(pminus_ds1_filter, n2, n1) = all_74_12 % 233.89/39.90 | | | | | | | | | | % 233.89/39.90 | | | | | | | | | | REF_CLOSE: (4), (13), (86), (99) are inconsistent by % 233.89/39.90 | | | | | | | | | | sub-proof #26. % 233.89/39.90 | | | | | | | | | | % 233.89/39.90 | | | | | | | | | End of split % 233.89/39.90 | | | | | | | | | % 233.89/39.90 | | | | | | | | End of split % 233.89/39.90 | | | | | | | | % 233.89/39.90 | | | | | | | End of split % 233.89/39.90 | | | | | | | % 233.89/39.90 | | | | | | Case 2: % 233.89/39.90 | | | | | | | % 233.89/39.90 | | | | | | | (100) all_74_14 = n2 % 233.89/39.90 | | | | | | | % 233.89/39.90 | | | | | | | REDUCE: (75), (100) imply: % 233.89/39.90 | | | | | | | (101) a_select3(pminus_ds1_filter, n2, n2) = all_74_12 % 233.89/39.90 | | | | | | | % 233.89/39.90 | | | | | | | REDUCE: (76), (100) imply: % 233.89/39.90 | | | | | | | (102) a_select3(pminus_ds1_filter, n2, n2) = all_74_13 % 233.89/39.90 | | | | | | | % 233.89/39.90 | | | | | | | GROUND_INST: instantiating (13) with all_74_13, all_74_12, n2, n2, % 233.89/39.90 | | | | | | | pminus_ds1_filter, simplifying with (101), (102) % 233.89/39.90 | | | | | | | gives: % 233.89/39.90 | | | | | | | (103) all_74_12 = all_74_13 % 233.89/39.90 | | | | | | | % 233.89/39.90 | | | | | | | REDUCE: (4), (103) imply: % 233.89/39.90 | | | | | | | (104) $false % 233.89/39.90 | | | | | | | % 233.89/39.90 | | | | | | | CLOSE: (104) is inconsistent. % 233.89/39.90 | | | | | | | % 233.89/39.90 | | | | | | End of split % 233.89/39.90 | | | | | | % 233.89/39.90 | | | | | End of split % 233.89/39.90 | | | | | % 233.89/39.90 | | | | Case 2: % 233.89/39.90 | | | | | % 233.89/39.90 | | | | | (105) all_74_14 = n3 % 233.89/39.90 | | | | | % 233.89/39.90 | | | | | REDUCE: (1), (105) imply: % 233.89/39.90 | | | | | (106) a_select3(pminus_ds1_filter, n3, all_74_15) = all_74_12 % 233.89/39.90 | | | | | % 233.89/39.90 | | | | | REDUCE: (7), (105) imply: % 233.89/39.90 | | | | | (107) a_select3(pminus_ds1_filter, all_74_15, n3) = all_74_13 % 233.89/39.90 | | | | | % 233.89/39.90 | | | | | REDUCE: (3), (105) imply: % 233.89/39.90 | | | | | (108) leq(n3, n5) % 233.89/39.90 | | | | | % 233.89/39.90 | | | | | REDUCE: (14), (105) imply: % 233.89/39.90 | | | | | (109) leq(n0, n3) % 233.89/39.90 | | | | | % 233.89/39.90 | | | | | BETA: splitting (34) gives: % 233.89/39.90 | | | | | % 233.89/39.90 | | | | | Case 1: % 233.89/39.90 | | | | | | % 233.89/39.90 | | | | | | (110) gt(n2, all_74_15) % 233.89/39.90 | | | | | | % 233.89/39.90 | | | | | | GROUND_INST: instantiating (10) with all_74_15, n2, n1, simplifying % 233.89/39.90 | | | | | | with (11), (12), (15), (110) gives: % 233.89/39.90 | | | | | | (111) leq(all_74_15, n1) % 233.89/39.90 | | | | | | % 233.89/39.90 | | | | | | GROUND_INST: instantiating (25) with all_74_15, simplifying with % 233.89/39.90 | | | | | | (12), (23), (111) gives: % 233.89/39.90 | | | | | | (112) all_74_15 = n1 | all_74_15 = n0 % 233.89/39.90 | | | | | | % 233.89/39.90 | | | | | | BETA: splitting (112) gives: % 233.89/39.90 | | | | | | % 233.89/39.90 | | | | | | Case 1: % 233.89/39.90 | | | | | | | % 233.89/39.90 | | | | | | | (113) all_74_15 = n0 % 233.89/39.90 | | | | | | | % 233.89/39.90 | | | | | | | REDUCE: (5), (113) imply: % 233.89/39.90 | | | | | | | (114) $false % 233.89/39.90 | | | | | | | % 233.89/39.90 | | | | | | | CLOSE: (114) is inconsistent. % 233.89/39.90 | | | | | | | % 233.89/39.90 | | | | | | Case 2: % 233.89/39.90 | | | | | | | % 233.89/39.90 | | | | | | | (115) all_74_15 = n1 % 233.89/39.90 | | | | | | | % 233.89/39.90 | | | | | | | REDUCE: (107), (115) imply: % 233.89/39.90 | | | | | | | (116) a_select3(pminus_ds1_filter, n1, n3) = all_74_13 % 233.89/39.90 | | | | | | | % 233.89/39.90 | | | | | | | REDUCE: (106), (115) imply: % 233.89/39.90 | | | | | | | (117) a_select3(pminus_ds1_filter, n3, n1) = all_74_12 % 233.89/39.90 | | | | | | | % 233.89/39.90 | | | | | | | REDUCE: (12), (115) imply: % 233.89/39.90 | | | | | | | (118) $i(n1) % 233.89/39.90 | | | | | | | % 233.89/39.90 | | | | | | | REDUCE: (17), (115) imply: % 233.89/39.90 | | | | | | | (119) leq(n1, n5) % 233.89/39.90 | | | | | | | % 233.89/39.90 | | | | | | | REDUCE: (23), (115) imply: % 233.89/39.90 | | | | | | | (120) leq(n0, n1) % 233.89/39.90 | | | | | | | % 233.89/39.90 | | | | | | | GROUND_INST: instantiating (16) with n1, n3, all_74_13, % 233.89/39.90 | | | | | | | simplifying with (18), (109), (116), (118), (120) % 233.89/39.90 | | | | | | | gives: % 233.89/39.90 | | | | | | | (121) ~ leq(n3, all_74_21) | ~ leq(n1, all_74_21) | % 233.89/39.90 | | | | | | | (a_select3(pminus_ds1_filter, n3, n1) = all_74_13 & % 233.89/39.90 | | | | | | | $i(all_74_13)) % 233.89/39.90 | | | | | | | % 233.89/39.90 | | | | | | | BETA: splitting (121) gives: % 233.89/39.90 | | | | | | | % 233.89/39.90 | | | | | | | Case 1: % 233.89/39.90 | | | | | | | | % 233.89/39.90 | | | | | | | | (122) ~ leq(n3, all_74_21) % 233.89/39.90 | | | | | | | | % 233.89/39.90 | | | | | | | | REDUCE: (8), (122) imply: % 233.89/39.90 | | | | | | | | (123) ~ leq(n3, n5) % 233.89/39.90 | | | | | | | | % 233.89/39.90 | | | | | | | | PRED_UNIFY: (108), (123) imply: % 233.89/39.90 | | | | | | | | (124) $false % 233.89/39.90 | | | | | | | | % 233.89/39.90 | | | | | | | | CLOSE: (124) is inconsistent. % 233.89/39.90 | | | | | | | | % 233.89/39.90 | | | | | | | Case 2: % 233.89/39.90 | | | | | | | | % 233.89/39.90 | | | | | | | | (125) ~ leq(n1, all_74_21) | (a_select3(pminus_ds1_filter, % 233.89/39.90 | | | | | | | | n3, n1) = all_74_13 & $i(all_74_13)) % 233.89/39.90 | | | | | | | | % 233.89/39.90 | | | | | | | | BETA: splitting (125) gives: % 233.89/39.90 | | | | | | | | % 233.89/39.90 | | | | | | | | Case 1: % 233.89/39.90 | | | | | | | | | % 233.89/39.90 | | | | | | | | | (126) ~ leq(n1, all_74_21) % 233.89/39.90 | | | | | | | | | % 233.89/39.90 | | | | | | | | | REDUCE: (8), (126) imply: % 233.89/39.90 | | | | | | | | | (127) ~ leq(n1, n5) % 233.89/39.90 | | | | | | | | | % 233.89/39.90 | | | | | | | | | PRED_UNIFY: (119), (127) imply: % 233.89/39.90 | | | | | | | | | (128) $false % 233.89/39.90 | | | | | | | | | % 233.89/39.90 | | | | | | | | | CLOSE: (128) is inconsistent. % 233.89/39.90 | | | | | | | | | % 233.89/39.90 | | | | | | | | Case 2: % 233.89/39.90 | | | | | | | | | % 233.89/39.90 | | | | | | | | | (129) a_select3(pminus_ds1_filter, n3, n1) = all_74_13 & % 233.89/39.90 | | | | | | | | | $i(all_74_13) % 233.89/39.90 | | | | | | | | | % 233.89/39.90 | | | | | | | | | ALPHA: (129) implies: % 233.89/39.90 | | | | | | | | | (130) a_select3(pminus_ds1_filter, n3, n1) = all_74_13 % 233.89/39.90 | | | | | | | | | % 233.89/39.90 | | | | | | | | | GROUND_INST: instantiating (13) with all_74_12, all_74_13, n1, % 233.89/39.90 | | | | | | | | | n3, pminus_ds1_filter, simplifying with (117), % 233.89/39.90 | | | | | | | | | (130) gives: % 233.89/39.90 | | | | | | | | | (131) all_74_12 = all_74_13 % 233.89/39.90 | | | | | | | | | % 233.89/39.90 | | | | | | | | | REDUCE: (4), (131) imply: % 233.89/39.90 | | | | | | | | | (132) $false % 233.89/39.90 | | | | | | | | | % 233.89/39.90 | | | | | | | | | CLOSE: (132) is inconsistent. % 233.89/39.90 | | | | | | | | | % 233.89/39.90 | | | | | | | | End of split % 233.89/39.90 | | | | | | | | % 233.89/39.90 | | | | | | | End of split % 233.89/39.90 | | | | | | | % 233.89/39.90 | | | | | | End of split % 233.89/39.90 | | | | | | % 233.89/39.90 | | | | | Case 2: % 233.89/39.90 | | | | | | % 233.89/39.90 | | | | | | (133) all_74_15 = n2 % 233.89/39.90 | | | | | | % 233.89/39.90 | | | | | | REDUCE: (107), (133) imply: % 233.89/39.90 | | | | | | (134) a_select3(pminus_ds1_filter, n2, n3) = all_74_13 % 233.89/39.90 | | | | | | % 233.89/39.90 | | | | | | REDUCE: (106), (133) imply: % 233.89/39.90 | | | | | | (135) a_select3(pminus_ds1_filter, n3, n2) = all_74_12 % 233.89/39.90 | | | | | | % 233.89/39.90 | | | | | | REDUCE: (17), (133) imply: % 233.89/39.90 | | | | | | (136) leq(n2, n5) % 233.89/39.90 | | | | | | % 233.89/39.90 | | | | | | REDUCE: (23), (133) imply: % 233.89/39.90 | | | | | | (137) leq(n0, n2) % 233.89/39.90 | | | | | | % 233.89/39.90 | | | | | | GROUND_INST: instantiating (16) with n2, n3, all_74_13, simplifying % 233.89/39.90 | | | | | | with (11), (18), (109), (134), (137) gives: % 233.89/39.90 | | | | | | (138) ~ leq(n3, all_74_21) | ~ leq(n2, all_74_21) | % 233.89/39.90 | | | | | | (a_select3(pminus_ds1_filter, n3, n2) = all_74_13 & % 233.89/39.90 | | | | | | $i(all_74_13)) % 233.89/39.90 | | | | | | % 233.89/39.90 | | | | | | BETA: splitting (138) gives: % 233.89/39.90 | | | | | | % 233.89/39.90 | | | | | | Case 1: % 233.89/39.90 | | | | | | | % 233.89/39.90 | | | | | | | (139) ~ leq(n3, all_74_21) % 233.89/39.90 | | | | | | | % 233.89/39.90 | | | | | | | REDUCE: (8), (139) imply: % 233.89/39.90 | | | | | | | (140) ~ leq(n3, n5) % 233.89/39.90 | | | | | | | % 233.89/39.90 | | | | | | | PRED_UNIFY: (108), (140) imply: % 233.89/39.90 | | | | | | | (141) $false % 233.89/39.90 | | | | | | | % 233.89/39.90 | | | | | | | CLOSE: (141) is inconsistent. % 233.89/39.90 | | | | | | | % 233.89/39.90 | | | | | | Case 2: % 233.89/39.90 | | | | | | | % 233.89/39.90 | | | | | | | (142) ~ leq(n2, all_74_21) | (a_select3(pminus_ds1_filter, n3, % 233.89/39.90 | | | | | | | n2) = all_74_13 & $i(all_74_13)) % 233.89/39.90 | | | | | | | % 233.89/39.90 | | | | | | | BETA: splitting (142) gives: % 233.89/39.90 | | | | | | | % 233.89/39.90 | | | | | | | Case 1: % 233.89/39.90 | | | | | | | | % 233.89/39.90 | | | | | | | | (143) ~ leq(n2, all_74_21) % 233.89/39.90 | | | | | | | | % 233.89/39.90 | | | | | | | | REDUCE: (8), (143) imply: % 233.89/39.90 | | | | | | | | (144) ~ leq(n2, n5) % 233.89/39.90 | | | | | | | | % 233.89/39.90 | | | | | | | | PRED_UNIFY: (136), (144) imply: % 233.89/39.90 | | | | | | | | (145) $false % 233.89/39.90 | | | | | | | | % 233.89/39.90 | | | | | | | | CLOSE: (145) is inconsistent. % 233.89/39.90 | | | | | | | | % 233.89/39.90 | | | | | | | Case 2: % 233.89/39.90 | | | | | | | | % 233.89/39.90 | | | | | | | | (146) a_select3(pminus_ds1_filter, n3, n2) = all_74_13 & % 233.89/39.90 | | | | | | | | $i(all_74_13) % 233.89/39.90 | | | | | | | | % 233.89/39.90 | | | | | | | | ALPHA: (146) implies: % 233.89/39.90 | | | | | | | | (147) a_select3(pminus_ds1_filter, n3, n2) = all_74_13 % 233.89/39.90 | | | | | | | | % 233.89/39.90 | | | | | | | | REF_CLOSE: (4), (13), (135), (147) are inconsistent by sub-proof % 233.89/39.90 | | | | | | | | #25. % 233.89/39.90 | | | | | | | | % 233.89/39.90 | | | | | | | End of split % 233.89/39.90 | | | | | | | % 233.89/39.90 | | | | | | End of split % 233.89/39.90 | | | | | | % 233.89/39.90 | | | | | End of split % 233.89/39.90 | | | | | % 233.89/39.90 | | | | End of split % 233.89/39.90 | | | | % 233.89/39.90 | | | Case 2: % 233.89/39.90 | | | | % 233.89/39.90 | | | | (148) all_74_15 = n3 % 233.89/39.90 | | | | % 233.89/39.90 | | | | REDUCE: (1), (148) imply: % 233.89/39.90 | | | | (149) a_select3(pminus_ds1_filter, all_74_14, n3) = all_74_12 % 233.89/39.90 | | | | % 233.89/39.90 | | | | REDUCE: (7), (148) imply: % 233.89/39.90 | | | | (150) a_select3(pminus_ds1_filter, n3, all_74_14) = all_74_13 % 233.89/39.90 | | | | % 233.89/39.90 | | | | REDUCE: (17), (148) imply: % 233.89/39.90 | | | | (151) leq(n3, n5) % 233.89/39.90 | | | | % 233.89/39.90 | | | | REDUCE: (23), (148) imply: % 233.89/39.90 | | | | (152) leq(n0, n3) % 233.89/39.90 | | | | % 233.89/39.90 | | | | BETA: splitting (31) gives: % 233.89/39.90 | | | | % 233.89/39.90 | | | | Case 1: % 233.89/39.90 | | | | | % 233.89/39.90 | | | | | (153) gt(n3, all_74_14) % 233.89/39.90 | | | | | % 233.89/39.90 | | | | | GROUND_INST: instantiating (10) with all_74_14, n3, n2, simplifying % 233.89/39.90 | | | | | with (18), (20), (22), (153) gives: % 233.89/39.90 | | | | | (154) leq(all_74_14, n2) % 233.89/39.90 | | | | | % 233.89/39.90 | | | | | GROUND_INST: instantiating (2) with all_74_14, n2, simplifying with % 233.89/39.90 | | | | | (11), (22), (154) gives: % 233.89/39.90 | | | | | (155) all_74_14 = n2 | gt(n2, all_74_14) % 233.89/39.90 | | | | | % 233.89/39.90 | | | | | BETA: splitting (155) gives: % 233.89/39.90 | | | | | % 233.89/39.90 | | | | | Case 1: % 233.89/39.90 | | | | | | % 233.89/39.90 | | | | | | (156) gt(n2, all_74_14) % 233.89/39.90 | | | | | | % 233.89/39.90 | | | | | | GROUND_INST: instantiating (10) with all_74_14, n2, n1, simplifying % 233.89/39.90 | | | | | | with (11), (15), (22), (156) gives: % 233.89/39.90 | | | | | | (157) leq(all_74_14, n1) % 233.89/39.90 | | | | | | % 233.89/39.90 | | | | | | GROUND_INST: instantiating (25) with all_74_14, simplifying with % 233.89/39.90 | | | | | | (14), (22), (157) gives: % 233.89/39.90 | | | | | | (158) all_74_14 = n1 | all_74_14 = n0 % 233.89/39.90 | | | | | | % 233.89/39.90 | | | | | | BETA: splitting (158) gives: % 233.89/39.90 | | | | | | % 233.89/39.90 | | | | | | Case 1: % 233.89/39.90 | | | | | | | % 233.89/39.90 | | | | | | | (159) all_74_14 = n0 % 233.89/39.90 | | | | | | | % 233.89/39.90 | | | | | | | REDUCE: (19), (159) imply: % 233.89/39.90 | | | | | | | (160) $false % 233.89/39.90 | | | | | | | % 233.89/39.90 | | | | | | | CLOSE: (160) is inconsistent. % 233.89/39.90 | | | | | | | % 233.89/39.90 | | | | | | Case 2: % 233.89/39.90 | | | | | | | % 233.89/39.90 | | | | | | | (161) all_74_14 = n1 % 233.89/39.90 | | | | | | | % 233.89/39.90 | | | | | | | REDUCE: (149), (161) imply: % 233.89/39.90 | | | | | | | (162) a_select3(pminus_ds1_filter, n1, n3) = all_74_12 % 233.89/39.90 | | | | | | | % 233.89/39.90 | | | | | | | REDUCE: (150), (161) imply: % 233.89/39.90 | | | | | | | (163) a_select3(pminus_ds1_filter, n3, n1) = all_74_13 % 233.89/39.90 | | | | | | | % 233.89/39.90 | | | | | | | REDUCE: (22), (161) imply: % 233.89/39.90 | | | | | | | (164) $i(n1) % 233.89/39.90 | | | | | | | % 233.89/39.90 | | | | | | | REDUCE: (3), (161) imply: % 233.89/39.90 | | | | | | | (165) leq(n1, n5) % 233.89/39.90 | | | | | | | % 233.89/39.90 | | | | | | | REDUCE: (14), (161) imply: % 233.89/39.90 | | | | | | | (166) leq(n0, n1) % 233.89/39.90 | | | | | | | % 233.89/39.90 | | | | | | | GROUND_INST: instantiating (16) with n1, n3, all_74_12, % 233.89/39.90 | | | | | | | simplifying with (18), (152), (162), (164), (166) % 233.89/39.90 | | | | | | | gives: % 233.89/39.90 | | | | | | | (167) ~ leq(n3, all_74_21) | ~ leq(n1, all_74_21) | % 233.89/39.90 | | | | | | | (a_select3(pminus_ds1_filter, n3, n1) = all_74_12 & % 233.89/39.90 | | | | | | | $i(all_74_12)) % 233.89/39.90 | | | | | | | % 233.89/39.90 | | | | | | | BETA: splitting (167) gives: % 233.89/39.90 | | | | | | | % 233.89/39.90 | | | | | | | Case 1: % 233.89/39.90 | | | | | | | | % 233.89/39.90 | | | | | | | | (168) ~ leq(n3, all_74_21) % 233.89/39.90 | | | | | | | | % 233.89/39.90 | | | | | | | | REDUCE: (8), (168) imply: % 233.89/39.90 | | | | | | | | (169) ~ leq(n3, n5) % 233.89/39.90 | | | | | | | | % 233.89/39.90 | | | | | | | | PRED_UNIFY: (151), (169) imply: % 233.89/39.90 | | | | | | | | (170) $false % 233.89/39.90 | | | | | | | | % 233.89/39.90 | | | | | | | | CLOSE: (170) is inconsistent. % 233.89/39.90 | | | | | | | | % 233.89/39.90 | | | | | | | Case 2: % 233.89/39.90 | | | | | | | | % 233.89/39.90 | | | | | | | | (171) ~ leq(n1, all_74_21) | (a_select3(pminus_ds1_filter, % 233.89/39.90 | | | | | | | | n3, n1) = all_74_12 & $i(all_74_12)) % 233.89/39.90 | | | | | | | | % 233.89/39.90 | | | | | | | | BETA: splitting (171) gives: % 233.89/39.90 | | | | | | | | % 233.89/39.90 | | | | | | | | Case 1: % 233.89/39.90 | | | | | | | | | % 233.89/39.90 | | | | | | | | | (172) ~ leq(n1, all_74_21) % 233.89/39.90 | | | | | | | | | % 233.89/39.90 | | | | | | | | | REDUCE: (8), (172) imply: % 233.89/39.90 | | | | | | | | | (173) ~ leq(n1, n5) % 233.89/39.90 | | | | | | | | | % 233.89/39.90 | | | | | | | | | PRED_UNIFY: (165), (173) imply: % 233.89/39.90 | | | | | | | | | (174) $false % 233.89/39.90 | | | | | | | | | % 233.89/39.90 | | | | | | | | | CLOSE: (174) is inconsistent. % 233.89/39.90 | | | | | | | | | % 233.89/39.90 | | | | | | | | Case 2: % 233.89/39.90 | | | | | | | | | % 233.89/39.90 | | | | | | | | | (175) a_select3(pminus_ds1_filter, n3, n1) = all_74_12 & % 233.89/39.90 | | | | | | | | | $i(all_74_12) % 233.89/39.90 | | | | | | | | | % 233.89/39.90 | | | | | | | | | ALPHA: (175) implies: % 233.89/39.90 | | | | | | | | | (176) a_select3(pminus_ds1_filter, n3, n1) = all_74_12 % 233.89/39.90 | | | | | | | | | % 233.89/39.90 | | | | | | | | | GROUND_INST: instantiating (13) with all_74_12, all_74_13, n1, % 233.89/39.90 | | | | | | | | | n3, pminus_ds1_filter, simplifying with (163), % 233.89/39.90 | | | | | | | | | (176) gives: % 233.89/39.90 | | | | | | | | | (177) all_74_12 = all_74_13 % 233.89/39.90 | | | | | | | | | % 233.89/39.90 | | | | | | | | | REDUCE: (4), (177) imply: % 233.89/39.90 | | | | | | | | | (178) $false % 233.89/39.90 | | | | | | | | | % 233.89/39.90 | | | | | | | | | CLOSE: (178) is inconsistent. % 233.89/39.90 | | | | | | | | | % 233.89/39.90 | | | | | | | | End of split % 233.89/39.90 | | | | | | | | % 233.89/39.90 | | | | | | | End of split % 233.89/39.90 | | | | | | | % 233.89/39.90 | | | | | | End of split % 233.89/39.90 | | | | | | % 233.89/39.90 | | | | | Case 2: % 233.89/39.90 | | | | | | % 233.89/39.90 | | | | | | (179) all_74_14 = n2 % 233.89/39.90 | | | | | | % 233.89/39.90 | | | | | | REDUCE: (149), (179) imply: % 233.89/39.90 | | | | | | (180) a_select3(pminus_ds1_filter, n2, n3) = all_74_12 % 233.89/39.90 | | | | | | % 233.89/39.90 | | | | | | REDUCE: (150), (179) imply: % 233.89/39.90 | | | | | | (181) a_select3(pminus_ds1_filter, n3, n2) = all_74_13 % 233.89/39.90 | | | | | | % 233.89/39.90 | | | | | | REDUCE: (3), (179) imply: % 233.89/39.90 | | | | | | (182) leq(n2, n5) % 233.89/39.90 | | | | | | % 233.89/39.90 | | | | | | REDUCE: (14), (179) imply: % 233.89/39.90 | | | | | | (183) leq(n0, n2) % 233.89/39.90 | | | | | | % 233.89/39.90 | | | | | | GROUND_INST: instantiating (16) with n2, n3, all_74_12, simplifying % 233.89/39.90 | | | | | | with (11), (18), (152), (180), (183) gives: % 233.89/39.90 | | | | | | (184) ~ leq(n3, all_74_21) | ~ leq(n2, all_74_21) | % 233.89/39.90 | | | | | | (a_select3(pminus_ds1_filter, n3, n2) = all_74_12 & % 233.89/39.90 | | | | | | $i(all_74_12)) % 233.89/39.90 | | | | | | % 233.89/39.90 | | | | | | BETA: splitting (184) gives: % 233.89/39.90 | | | | | | % 233.89/39.90 | | | | | | Case 1: % 233.89/39.90 | | | | | | | % 233.89/39.90 | | | | | | | (185) ~ leq(n3, all_74_21) % 233.89/39.90 | | | | | | | % 233.89/39.90 | | | | | | | REDUCE: (8), (185) imply: % 233.89/39.90 | | | | | | | (186) ~ leq(n3, n5) % 233.89/39.90 | | | | | | | % 233.89/39.90 | | | | | | | PRED_UNIFY: (151), (186) imply: % 233.89/39.90 | | | | | | | (187) $false % 233.89/39.90 | | | | | | | % 233.89/39.90 | | | | | | | CLOSE: (187) is inconsistent. % 233.89/39.90 | | | | | | | % 233.89/39.90 | | | | | | Case 2: % 233.89/39.90 | | | | | | | % 233.89/39.90 | | | | | | | (188) ~ leq(n2, all_74_21) | (a_select3(pminus_ds1_filter, n3, % 233.89/39.90 | | | | | | | n2) = all_74_12 & $i(all_74_12)) % 233.89/39.90 | | | | | | | % 233.89/39.90 | | | | | | | BETA: splitting (188) gives: % 233.89/39.90 | | | | | | | % 233.89/39.90 | | | | | | | Case 1: % 233.89/39.90 | | | | | | | | % 233.89/39.90 | | | | | | | | (189) ~ leq(n2, all_74_21) % 233.89/39.90 | | | | | | | | % 233.89/39.90 | | | | | | | | REDUCE: (8), (189) imply: % 233.89/39.90 | | | | | | | | (190) ~ leq(n2, n5) % 233.89/39.90 | | | | | | | | % 233.89/39.90 | | | | | | | | PRED_UNIFY: (182), (190) imply: % 233.89/39.90 | | | | | | | | (191) $false % 233.89/39.90 | | | | | | | | % 233.89/39.90 | | | | | | | | CLOSE: (191) is inconsistent. % 233.89/39.90 | | | | | | | | % 233.89/39.90 | | | | | | | Case 2: % 233.89/39.91 | | | | | | | | % 233.89/39.91 | | | | | | | | (192) a_select3(pminus_ds1_filter, n3, n2) = all_74_12 & % 233.89/39.91 | | | | | | | | $i(all_74_12) % 233.89/39.91 | | | | | | | | % 233.89/39.91 | | | | | | | | ALPHA: (192) implies: % 233.89/39.91 | | | | | | | | (193) a_select3(pminus_ds1_filter, n3, n2) = all_74_12 % 233.89/39.91 | | | | | | | | % 233.89/39.91 | | | | | | | | REF_CLOSE: (4), (13), (181), (193) are inconsistent by sub-proof % 233.89/39.91 | | | | | | | | #25. % 233.89/39.91 | | | | | | | | % 233.89/39.91 | | | | | | | End of split % 233.89/39.91 | | | | | | | % 233.89/39.91 | | | | | | End of split % 233.89/39.91 | | | | | | % 233.89/39.91 | | | | | End of split % 233.89/39.91 | | | | | % 233.89/39.91 | | | | Case 2: % 233.89/39.91 | | | | | % 233.89/39.91 | | | | | (194) all_74_14 = n3 % 233.89/39.91 | | | | | % 233.89/39.91 | | | | | REDUCE: (149), (194) imply: % 233.89/39.91 | | | | | (195) a_select3(pminus_ds1_filter, n3, n3) = all_74_12 % 233.89/39.91 | | | | | % 233.89/39.91 | | | | | REDUCE: (150), (194) imply: % 233.89/39.91 | | | | | (196) a_select3(pminus_ds1_filter, n3, n3) = all_74_13 % 233.89/39.91 | | | | | % 233.89/39.91 | | | | | GROUND_INST: instantiating (13) with all_74_13, all_74_12, n3, n3, % 233.89/39.91 | | | | | pminus_ds1_filter, simplifying with (195), (196) gives: % 233.89/39.91 | | | | | (197) all_74_12 = all_74_13 % 233.89/39.91 | | | | | % 233.89/39.91 | | | | | REDUCE: (4), (197) imply: % 233.89/39.91 | | | | | (198) $false % 233.89/39.91 | | | | | % 233.89/39.91 | | | | | CLOSE: (198) is inconsistent. % 233.89/39.91 | | | | | % 233.89/39.91 | | | | End of split % 233.89/39.91 | | | | % 233.89/39.91 | | | End of split % 233.89/39.91 | | | % 233.89/39.91 | | Case 2: % 233.89/39.91 | | | % 233.89/39.91 | | | (199) all_74_14 = n4 % 233.89/39.91 | | | % 233.89/39.91 | | | REDUCE: (1), (199) imply: % 233.89/39.91 | | | (200) a_select3(pminus_ds1_filter, n4, all_74_15) = all_74_12 % 233.89/39.91 | | | % 233.89/39.91 | | | REDUCE: (7), (199) imply: % 233.89/39.91 | | | (201) a_select3(pminus_ds1_filter, all_74_15, n4) = all_74_13 % 233.89/39.91 | | | % 233.89/39.91 | | | REDUCE: (3), (199) imply: % 233.89/39.91 | | | (202) leq(n4, n5) % 233.89/39.91 | | | % 233.89/39.91 | | | REDUCE: (14), (199) imply: % 233.89/39.91 | | | (203) leq(n0, n4) % 233.89/39.91 | | | % 233.89/39.91 | | | BETA: splitting (28) gives: % 233.89/39.91 | | | % 233.89/39.91 | | | Case 1: % 233.89/39.91 | | | | % 233.89/39.91 | | | | (204) gt(n3, all_74_15) % 233.89/39.91 | | | | % 233.89/39.91 | | | | GROUND_INST: instantiating (10) with all_74_15, n3, n2, simplifying with % 233.89/39.91 | | | | (12), (18), (20), (204) gives: % 233.89/39.91 | | | | (205) leq(all_74_15, n2) % 233.89/39.91 | | | | % 233.89/39.91 | | | | GROUND_INST: instantiating (2) with all_74_15, n2, simplifying with % 233.89/39.91 | | | | (11), (12), (205) gives: % 233.89/39.91 | | | | (206) all_74_15 = n2 | gt(n2, all_74_15) % 233.89/39.91 | | | | % 233.89/39.91 | | | | BETA: splitting (206) gives: % 233.89/39.91 | | | | % 233.89/39.91 | | | | Case 1: % 233.89/39.91 | | | | | % 233.89/39.91 | | | | | (207) gt(n2, all_74_15) % 233.89/39.91 | | | | | % 233.89/39.91 | | | | | GROUND_INST: instantiating (10) with all_74_15, n2, n1, simplifying % 233.89/39.91 | | | | | with (11), (12), (15), (207) gives: % 233.89/39.91 | | | | | (208) leq(all_74_15, n1) % 233.89/39.91 | | | | | % 233.89/39.91 | | | | | GROUND_INST: instantiating (25) with all_74_15, simplifying with (12), % 233.89/39.91 | | | | | (23), (208) gives: % 233.89/39.91 | | | | | (209) all_74_15 = n1 | all_74_15 = n0 % 233.89/39.91 | | | | | % 233.89/39.91 | | | | | BETA: splitting (209) gives: % 233.89/39.91 | | | | | % 233.89/39.91 | | | | | Case 1: % 233.89/39.91 | | | | | | % 233.89/39.91 | | | | | | (210) all_74_15 = n0 % 233.89/39.91 | | | | | | % 233.89/39.91 | | | | | | REDUCE: (5), (210) imply: % 233.89/39.91 | | | | | | (211) $false % 233.89/39.91 | | | | | | % 233.89/39.91 | | | | | | CLOSE: (211) is inconsistent. % 233.89/39.91 | | | | | | % 233.89/39.91 | | | | | Case 2: % 233.89/39.91 | | | | | | % 233.89/39.91 | | | | | | (212) all_74_15 = n1 % 233.89/39.91 | | | | | | % 233.89/39.91 | | | | | | REDUCE: (201), (212) imply: % 233.89/39.91 | | | | | | (213) a_select3(pminus_ds1_filter, n1, n4) = all_74_13 % 233.89/39.91 | | | | | | % 233.89/39.91 | | | | | | REDUCE: (200), (212) imply: % 233.89/39.91 | | | | | | (214) a_select3(pminus_ds1_filter, n4, n1) = all_74_12 % 233.89/39.91 | | | | | | % 233.89/39.91 | | | | | | REDUCE: (12), (212) imply: % 233.89/39.91 | | | | | | (215) $i(n1) % 233.89/39.91 | | | | | | % 233.89/39.91 | | | | | | REDUCE: (17), (212) imply: % 233.89/39.91 | | | | | | (216) leq(n1, n5) % 233.89/39.91 | | | | | | % 233.89/39.91 | | | | | | REDUCE: (23), (212) imply: % 233.89/39.91 | | | | | | (217) leq(n0, n1) % 233.89/39.91 | | | | | | % 233.89/39.91 | | | | | | GROUND_INST: instantiating (16) with n1, n4, all_74_13, simplifying % 233.89/39.91 | | | | | | with (21), (203), (213), (215), (217) gives: % 233.89/39.91 | | | | | | (218) ~ leq(n4, all_74_21) | ~ leq(n1, all_74_21) | % 233.89/39.91 | | | | | | (a_select3(pminus_ds1_filter, n4, n1) = all_74_13 & % 233.89/39.91 | | | | | | $i(all_74_13)) % 233.89/39.91 | | | | | | % 233.89/39.91 | | | | | | BETA: splitting (218) gives: % 233.89/39.91 | | | | | | % 233.89/39.91 | | | | | | Case 1: % 233.89/39.91 | | | | | | | % 233.89/39.91 | | | | | | | (219) ~ leq(n4, all_74_21) % 233.89/39.91 | | | | | | | % 233.89/39.91 | | | | | | | REDUCE: (8), (219) imply: % 233.89/39.91 | | | | | | | (220) ~ leq(n4, n5) % 233.89/39.91 | | | | | | | % 233.89/39.91 | | | | | | | PRED_UNIFY: (202), (220) imply: % 233.89/39.91 | | | | | | | (221) $false % 233.89/39.91 | | | | | | | % 233.89/39.91 | | | | | | | CLOSE: (221) is inconsistent. % 233.89/39.91 | | | | | | | % 233.89/39.91 | | | | | | Case 2: % 233.89/39.91 | | | | | | | % 233.89/39.91 | | | | | | | (222) ~ leq(n1, all_74_21) | (a_select3(pminus_ds1_filter, n4, % 233.89/39.91 | | | | | | | n1) = all_74_13 & $i(all_74_13)) % 233.89/39.91 | | | | | | | % 233.89/39.91 | | | | | | | BETA: splitting (222) gives: % 233.89/39.91 | | | | | | | % 233.89/39.91 | | | | | | | Case 1: % 233.89/39.91 | | | | | | | | % 233.89/39.91 | | | | | | | | (223) ~ leq(n1, all_74_21) % 233.89/39.91 | | | | | | | | % 233.89/39.91 | | | | | | | | REDUCE: (8), (223) imply: % 233.89/39.91 | | | | | | | | (224) ~ leq(n1, n5) % 233.89/39.91 | | | | | | | | % 233.89/39.91 | | | | | | | | PRED_UNIFY: (216), (224) imply: % 233.89/39.91 | | | | | | | | (225) $false % 233.89/39.91 | | | | | | | | % 233.89/39.91 | | | | | | | | CLOSE: (225) is inconsistent. % 233.89/39.91 | | | | | | | | % 233.89/39.91 | | | | | | | Case 2: % 233.89/39.91 | | | | | | | | % 233.89/39.91 | | | | | | | | (226) a_select3(pminus_ds1_filter, n4, n1) = all_74_13 & % 233.89/39.91 | | | | | | | | $i(all_74_13) % 233.89/39.91 | | | | | | | | % 233.89/39.91 | | | | | | | | ALPHA: (226) implies: % 233.89/39.91 | | | | | | | | (227) a_select3(pminus_ds1_filter, n4, n1) = all_74_13 % 233.89/39.91 | | | | | | | | % 233.89/39.91 | | | | | | | | GROUND_INST: instantiating (13) with all_74_13, all_74_12, n1, % 233.89/39.91 | | | | | | | | n4, pminus_ds1_filter, simplifying with (214), % 233.89/39.91 | | | | | | | | (227) gives: % 233.89/39.91 | | | | | | | | (228) all_74_12 = all_74_13 % 233.89/39.91 | | | | | | | | % 233.89/39.91 | | | | | | | | REDUCE: (4), (228) imply: % 233.89/39.91 | | | | | | | | (229) $false % 233.89/39.91 | | | | | | | | % 233.89/39.91 | | | | | | | | CLOSE: (229) is inconsistent. % 233.89/39.91 | | | | | | | | % 233.89/39.91 | | | | | | | End of split % 233.89/39.91 | | | | | | | % 233.89/39.91 | | | | | | End of split % 233.89/39.91 | | | | | | % 233.89/39.91 | | | | | End of split % 233.89/39.91 | | | | | % 233.89/39.91 | | | | Case 2: % 233.89/39.91 | | | | | % 233.89/39.91 | | | | | (230) all_74_15 = n2 % 233.89/39.91 | | | | | % 233.89/39.91 | | | | | REDUCE: (201), (230) imply: % 233.89/39.91 | | | | | (231) a_select3(pminus_ds1_filter, n2, n4) = all_74_13 % 233.89/39.91 | | | | | % 233.89/39.91 | | | | | REDUCE: (200), (230) imply: % 233.89/39.91 | | | | | (232) a_select3(pminus_ds1_filter, n4, n2) = all_74_12 % 233.89/39.91 | | | | | % 233.89/39.91 | | | | | REDUCE: (17), (230) imply: % 233.89/39.91 | | | | | (233) leq(n2, n5) % 233.89/39.91 | | | | | % 233.89/39.91 | | | | | REDUCE: (23), (230) imply: % 233.89/39.91 | | | | | (234) leq(n0, n2) % 233.89/39.91 | | | | | % 233.89/39.91 | | | | | GROUND_INST: instantiating (16) with n2, n4, all_74_13, simplifying % 233.89/39.91 | | | | | with (11), (21), (203), (231), (234) gives: % 233.89/39.91 | | | | | (235) ~ leq(n4, all_74_21) | ~ leq(n2, all_74_21) | % 233.89/39.91 | | | | | (a_select3(pminus_ds1_filter, n4, n2) = all_74_13 & % 233.89/39.91 | | | | | $i(all_74_13)) % 233.89/39.91 | | | | | % 233.89/39.91 | | | | | BETA: splitting (235) gives: % 233.89/39.91 | | | | | % 233.89/39.91 | | | | | Case 1: % 233.89/39.91 | | | | | | % 233.89/39.91 | | | | | | (236) ~ leq(n4, all_74_21) % 233.89/39.91 | | | | | | % 233.89/39.91 | | | | | | REDUCE: (8), (236) imply: % 233.89/39.91 | | | | | | (237) ~ leq(n4, n5) % 233.89/39.91 | | | | | | % 233.89/39.91 | | | | | | PRED_UNIFY: (202), (237) imply: % 233.89/39.91 | | | | | | (238) $false % 233.89/39.91 | | | | | | % 233.89/39.91 | | | | | | CLOSE: (238) is inconsistent. % 233.89/39.91 | | | | | | % 233.89/39.91 | | | | | Case 2: % 233.89/39.91 | | | | | | % 233.89/39.91 | | | | | | (239) ~ leq(n2, all_74_21) | (a_select3(pminus_ds1_filter, n4, % 233.89/39.91 | | | | | | n2) = all_74_13 & $i(all_74_13)) % 233.89/39.91 | | | | | | % 233.89/39.91 | | | | | | BETA: splitting (239) gives: % 233.89/39.91 | | | | | | % 233.89/39.91 | | | | | | Case 1: % 233.89/39.91 | | | | | | | % 233.89/39.91 | | | | | | | (240) ~ leq(n2, all_74_21) % 233.89/39.91 | | | | | | | % 233.89/39.91 | | | | | | | REDUCE: (8), (240) imply: % 233.89/39.91 | | | | | | | (241) ~ leq(n2, n5) % 233.89/39.91 | | | | | | | % 233.89/39.91 | | | | | | | PRED_UNIFY: (233), (241) imply: % 233.89/39.91 | | | | | | | (242) $false % 233.89/39.91 | | | | | | | % 233.89/39.91 | | | | | | | CLOSE: (242) is inconsistent. % 233.89/39.91 | | | | | | | % 233.89/39.91 | | | | | | Case 2: % 233.89/39.91 | | | | | | | % 233.89/39.91 | | | | | | | (243) a_select3(pminus_ds1_filter, n4, n2) = all_74_13 & % 233.89/39.91 | | | | | | | $i(all_74_13) % 233.89/39.91 | | | | | | | % 233.89/39.91 | | | | | | | ALPHA: (243) implies: % 233.89/39.91 | | | | | | | (244) a_select3(pminus_ds1_filter, n4, n2) = all_74_13 % 233.89/39.91 | | | | | | | % 233.89/39.91 | | | | | | | REF_CLOSE: (4), (13), (232), (244) are inconsistent by sub-proof % 233.89/39.91 | | | | | | | #24. % 233.89/39.91 | | | | | | | % 233.89/39.91 | | | | | | End of split % 233.89/39.91 | | | | | | % 233.89/39.91 | | | | | End of split % 233.89/39.91 | | | | | % 233.89/39.91 | | | | End of split % 233.89/39.91 | | | | % 233.89/39.91 | | | Case 2: % 233.89/39.91 | | | | % 233.89/39.91 | | | | (245) all_74_15 = n3 % 233.89/39.91 | | | | % 233.89/39.91 | | | | REDUCE: (201), (245) imply: % 233.89/39.91 | | | | (246) a_select3(pminus_ds1_filter, n3, n4) = all_74_13 % 233.89/39.91 | | | | % 233.89/39.91 | | | | REDUCE: (200), (245) imply: % 233.89/39.91 | | | | (247) a_select3(pminus_ds1_filter, n4, n3) = all_74_12 % 233.89/39.91 | | | | % 233.89/39.91 | | | | REDUCE: (17), (245) imply: % 233.89/39.91 | | | | (248) leq(n3, n5) % 233.89/39.91 | | | | % 233.89/39.91 | | | | REDUCE: (23), (245) imply: % 233.89/39.91 | | | | (249) leq(n0, n3) % 233.89/39.91 | | | | % 233.89/39.91 | | | | GROUND_INST: instantiating (16) with n3, n4, all_74_13, simplifying with % 233.89/39.91 | | | | (18), (21), (203), (246), (249) gives: % 233.89/39.91 | | | | (250) ~ leq(n4, all_74_21) | ~ leq(n3, all_74_21) | % 233.89/39.91 | | | | (a_select3(pminus_ds1_filter, n4, n3) = all_74_13 & % 233.89/39.91 | | | | $i(all_74_13)) % 233.89/39.91 | | | | % 233.89/39.91 | | | | BETA: splitting (250) gives: % 233.89/39.91 | | | | % 233.89/39.91 | | | | Case 1: % 233.89/39.91 | | | | | % 233.89/39.91 | | | | | (251) ~ leq(n4, all_74_21) % 233.89/39.91 | | | | | % 233.89/39.91 | | | | | REDUCE: (8), (251) imply: % 233.89/39.91 | | | | | (252) ~ leq(n4, n5) % 233.89/39.91 | | | | | % 233.89/39.91 | | | | | PRED_UNIFY: (202), (252) imply: % 233.89/39.91 | | | | | (253) $false % 233.89/39.91 | | | | | % 233.89/39.91 | | | | | CLOSE: (253) is inconsistent. % 233.89/39.91 | | | | | % 233.89/39.91 | | | | Case 2: % 233.89/39.91 | | | | | % 233.89/39.91 | | | | | (254) ~ leq(n3, all_74_21) | (a_select3(pminus_ds1_filter, n4, n3) % 233.89/39.91 | | | | | = all_74_13 & $i(all_74_13)) % 233.89/39.91 | | | | | % 233.89/39.91 | | | | | BETA: splitting (254) gives: % 233.89/39.91 | | | | | % 233.89/39.91 | | | | | Case 1: % 233.89/39.91 | | | | | | % 233.89/39.91 | | | | | | (255) ~ leq(n3, all_74_21) % 233.89/39.91 | | | | | | % 233.89/39.91 | | | | | | REDUCE: (8), (255) imply: % 233.89/39.91 | | | | | | (256) ~ leq(n3, n5) % 233.89/39.91 | | | | | | % 233.89/39.91 | | | | | | PRED_UNIFY: (248), (256) imply: % 233.89/39.91 | | | | | | (257) $false % 233.89/39.91 | | | | | | % 233.89/39.91 | | | | | | CLOSE: (257) is inconsistent. % 233.89/39.91 | | | | | | % 233.89/39.91 | | | | | Case 2: % 233.89/39.91 | | | | | | % 233.89/39.91 | | | | | | (258) a_select3(pminus_ds1_filter, n4, n3) = all_74_13 & % 233.89/39.91 | | | | | | $i(all_74_13) % 233.89/39.91 | | | | | | % 233.89/39.91 | | | | | | ALPHA: (258) implies: % 233.89/39.91 | | | | | | (259) a_select3(pminus_ds1_filter, n4, n3) = all_74_13 % 233.89/39.91 | | | | | | % 233.89/39.91 | | | | | | GROUND_INST: instantiating (13) with all_74_13, all_74_12, n3, n4, % 233.89/39.91 | | | | | | pminus_ds1_filter, simplifying with (247), (259) gives: % 233.89/39.91 | | | | | | (260) all_74_12 = all_74_13 % 233.89/39.91 | | | | | | % 233.89/39.91 | | | | | | REDUCE: (4), (260) imply: % 233.89/39.91 | | | | | | (261) $false % 233.89/39.91 | | | | | | % 233.89/39.91 | | | | | | CLOSE: (261) is inconsistent. % 233.89/39.91 | | | | | | % 233.89/39.91 | | | | | End of split % 233.89/39.91 | | | | | % 233.89/39.91 | | | | End of split % 233.89/39.91 | | | | % 233.89/39.91 | | | End of split % 233.89/39.91 | | | % 233.89/39.91 | | End of split % 233.89/39.91 | | % 233.89/39.91 | Case 2: % 233.89/39.91 | | % 233.89/39.91 | | (262) all_74_15 = n4 % 233.89/39.91 | | % 233.89/39.91 | | REDUCE: (1), (262) imply: % 233.89/39.91 | | (263) a_select3(pminus_ds1_filter, all_74_14, n4) = all_74_12 % 233.89/39.91 | | % 233.89/39.91 | | REDUCE: (7), (262) imply: % 233.89/39.91 | | (264) a_select3(pminus_ds1_filter, n4, all_74_14) = all_74_13 % 233.89/39.91 | | % 233.89/39.91 | | REDUCE: (17), (262) imply: % 233.89/39.91 | | (265) leq(n4, n5) % 233.89/39.91 | | % 233.89/39.91 | | REDUCE: (23), (262) imply: % 233.89/39.91 | | (266) leq(n0, n4) % 233.89/39.91 | | % 233.89/39.91 | | BETA: splitting (24) gives: % 233.89/39.91 | | % 233.89/39.91 | | Case 1: % 233.89/39.91 | | | % 233.89/39.91 | | | (267) gt(n4, all_74_14) % 233.89/39.91 | | | % 233.89/39.91 | | | GROUND_INST: instantiating (10) with all_74_14, n4, n3, simplifying with % 233.89/39.91 | | | (9), (21), (22), (267) gives: % 233.89/39.91 | | | (268) leq(all_74_14, n3) % 233.89/39.91 | | | % 233.89/39.91 | | | GROUND_INST: instantiating (2) with all_74_14, n3, simplifying with (18), % 233.89/39.91 | | | (22), (268) gives: % 233.89/39.91 | | | (269) all_74_14 = n3 | gt(n3, all_74_14) % 233.89/39.91 | | | % 233.89/39.91 | | | BETA: splitting (269) gives: % 233.89/39.91 | | | % 233.89/39.91 | | | Case 1: % 233.89/39.91 | | | | % 233.89/39.91 | | | | (270) gt(n3, all_74_14) % 233.89/39.91 | | | | % 233.89/39.91 | | | | GROUND_INST: instantiating (10) with all_74_14, n3, n2, simplifying with % 233.89/39.91 | | | | (18), (20), (22), (270) gives: % 233.89/39.91 | | | | (271) leq(all_74_14, n2) % 233.89/39.91 | | | | % 233.89/39.91 | | | | GROUND_INST: instantiating (2) with all_74_14, n2, simplifying with % 233.89/39.91 | | | | (11), (22), (271) gives: % 233.89/39.91 | | | | (272) all_74_14 = n2 | gt(n2, all_74_14) % 233.89/39.91 | | | | % 233.89/39.91 | | | | BETA: splitting (272) gives: % 233.89/39.91 | | | | % 233.89/39.91 | | | | Case 1: % 233.89/39.91 | | | | | % 233.89/39.91 | | | | | (273) gt(n2, all_74_14) % 233.89/39.91 | | | | | % 233.89/39.91 | | | | | GROUND_INST: instantiating (10) with all_74_14, n2, n1, simplifying % 233.89/39.91 | | | | | with (11), (15), (22), (273) gives: % 233.89/39.91 | | | | | (274) leq(all_74_14, n1) % 233.89/39.91 | | | | | % 233.89/39.91 | | | | | GROUND_INST: instantiating (25) with all_74_14, simplifying with (14), % 233.89/39.91 | | | | | (22), (274) gives: % 233.89/39.91 | | | | | (275) all_74_14 = n1 | all_74_14 = n0 % 233.89/39.91 | | | | | % 233.89/39.91 | | | | | BETA: splitting (275) gives: % 233.89/39.91 | | | | | % 233.89/39.91 | | | | | Case 1: % 233.89/39.91 | | | | | | % 233.89/39.91 | | | | | | (276) all_74_14 = n0 % 233.89/39.91 | | | | | | % 233.89/39.91 | | | | | | REDUCE: (19), (276) imply: % 233.89/39.91 | | | | | | (277) $false % 233.89/39.91 | | | | | | % 233.89/39.91 | | | | | | CLOSE: (277) is inconsistent. % 233.89/39.91 | | | | | | % 233.89/39.91 | | | | | Case 2: % 233.89/39.91 | | | | | | % 233.89/39.91 | | | | | | (278) all_74_14 = n1 % 233.89/39.91 | | | | | | % 233.89/39.91 | | | | | | REDUCE: (263), (278) imply: % 233.89/39.91 | | | | | | (279) a_select3(pminus_ds1_filter, n1, n4) = all_74_12 % 233.89/39.91 | | | | | | % 233.89/39.91 | | | | | | REDUCE: (264), (278) imply: % 233.89/39.91 | | | | | | (280) a_select3(pminus_ds1_filter, n4, n1) = all_74_13 % 233.89/39.91 | | | | | | % 233.89/39.91 | | | | | | REDUCE: (22), (278) imply: % 233.89/39.91 | | | | | | (281) $i(n1) % 233.89/39.91 | | | | | | % 233.89/39.91 | | | | | | REDUCE: (3), (278) imply: % 233.89/39.91 | | | | | | (282) leq(n1, n5) % 233.89/39.91 | | | | | | % 233.89/39.91 | | | | | | REDUCE: (14), (278) imply: % 233.89/39.91 | | | | | | (283) leq(n0, n1) % 233.89/39.91 | | | | | | % 233.89/39.91 | | | | | | GROUND_INST: instantiating (16) with n1, n4, all_74_12, simplifying % 233.89/39.91 | | | | | | with (21), (266), (279), (281), (283) gives: % 233.89/39.92 | | | | | | (284) ~ leq(n4, all_74_21) | ~ leq(n1, all_74_21) | % 233.89/39.92 | | | | | | (a_select3(pminus_ds1_filter, n4, n1) = all_74_12 & % 233.89/39.92 | | | | | | $i(all_74_12)) % 233.89/39.92 | | | | | | % 233.89/39.92 | | | | | | BETA: splitting (284) gives: % 233.89/39.92 | | | | | | % 233.89/39.92 | | | | | | Case 1: % 233.89/39.92 | | | | | | | % 233.89/39.92 | | | | | | | (285) ~ leq(n4, all_74_21) % 233.89/39.92 | | | | | | | % 233.89/39.92 | | | | | | | REDUCE: (8), (285) imply: % 233.89/39.92 | | | | | | | (286) ~ leq(n4, n5) % 233.89/39.92 | | | | | | | % 233.89/39.92 | | | | | | | PRED_UNIFY: (265), (286) imply: % 233.89/39.92 | | | | | | | (287) $false % 233.89/39.92 | | | | | | | % 233.89/39.92 | | | | | | | CLOSE: (287) is inconsistent. % 233.89/39.92 | | | | | | | % 233.89/39.92 | | | | | | Case 2: % 233.89/39.92 | | | | | | | % 233.89/39.92 | | | | | | | (288) ~ leq(n1, all_74_21) | (a_select3(pminus_ds1_filter, n4, % 233.89/39.92 | | | | | | | n1) = all_74_12 & $i(all_74_12)) % 233.89/39.92 | | | | | | | % 233.89/39.92 | | | | | | | BETA: splitting (288) gives: % 233.89/39.92 | | | | | | | % 233.89/39.92 | | | | | | | Case 1: % 233.89/39.92 | | | | | | | | % 233.89/39.92 | | | | | | | | (289) ~ leq(n1, all_74_21) % 233.89/39.92 | | | | | | | | % 233.89/39.92 | | | | | | | | REDUCE: (8), (289) imply: % 233.89/39.92 | | | | | | | | (290) ~ leq(n1, n5) % 233.89/39.92 | | | | | | | | % 233.89/39.92 | | | | | | | | PRED_UNIFY: (282), (290) imply: % 233.89/39.92 | | | | | | | | (291) $false % 233.89/39.92 | | | | | | | | % 233.89/39.92 | | | | | | | | CLOSE: (291) is inconsistent. % 233.89/39.92 | | | | | | | | % 233.89/39.92 | | | | | | | Case 2: % 233.89/39.92 | | | | | | | | % 233.89/39.92 | | | | | | | | (292) a_select3(pminus_ds1_filter, n4, n1) = all_74_12 & % 233.89/39.92 | | | | | | | | $i(all_74_12) % 233.89/39.92 | | | | | | | | % 233.89/39.92 | | | | | | | | ALPHA: (292) implies: % 233.89/39.92 | | | | | | | | (293) a_select3(pminus_ds1_filter, n4, n1) = all_74_12 % 233.89/39.92 | | | | | | | | % 233.89/39.92 | | | | | | | | GROUND_INST: instantiating (13) with all_74_13, all_74_12, n1, % 233.89/39.92 | | | | | | | | n4, pminus_ds1_filter, simplifying with (280), % 233.89/39.92 | | | | | | | | (293) gives: % 233.89/39.92 | | | | | | | | (294) all_74_12 = all_74_13 % 233.89/39.92 | | | | | | | | % 233.89/39.92 | | | | | | | | REDUCE: (4), (294) imply: % 233.89/39.92 | | | | | | | | (295) $false % 233.89/39.92 | | | | | | | | % 233.89/39.92 | | | | | | | | CLOSE: (295) is inconsistent. % 233.89/39.92 | | | | | | | | % 233.89/39.92 | | | | | | | End of split % 233.89/39.92 | | | | | | | % 233.89/39.92 | | | | | | End of split % 233.89/39.92 | | | | | | % 233.89/39.92 | | | | | End of split % 233.89/39.92 | | | | | % 233.89/39.92 | | | | Case 2: % 233.89/39.92 | | | | | % 233.89/39.92 | | | | | (296) all_74_14 = n2 % 233.89/39.92 | | | | | % 233.89/39.92 | | | | | REDUCE: (263), (296) imply: % 233.89/39.92 | | | | | (297) a_select3(pminus_ds1_filter, n2, n4) = all_74_12 % 233.89/39.92 | | | | | % 233.89/39.92 | | | | | REDUCE: (264), (296) imply: % 233.89/39.92 | | | | | (298) a_select3(pminus_ds1_filter, n4, n2) = all_74_13 % 233.89/39.92 | | | | | % 233.89/39.92 | | | | | REDUCE: (3), (296) imply: % 233.89/39.92 | | | | | (299) leq(n2, n5) % 233.89/39.92 | | | | | % 233.89/39.92 | | | | | REDUCE: (14), (296) imply: % 233.89/39.92 | | | | | (300) leq(n0, n2) % 233.89/39.92 | | | | | % 233.89/39.92 | | | | | GROUND_INST: instantiating (16) with n2, n4, all_74_12, simplifying % 233.89/39.92 | | | | | with (11), (21), (266), (297), (300) gives: % 233.89/39.92 | | | | | (301) ~ leq(n4, all_74_21) | ~ leq(n2, all_74_21) | % 233.89/39.92 | | | | | (a_select3(pminus_ds1_filter, n4, n2) = all_74_12 & % 233.89/39.92 | | | | | $i(all_74_12)) % 233.89/39.92 | | | | | % 233.89/39.92 | | | | | BETA: splitting (301) gives: % 233.89/39.92 | | | | | % 233.89/39.92 | | | | | Case 1: % 233.89/39.92 | | | | | | % 233.89/39.92 | | | | | | (302) ~ leq(n4, all_74_21) % 233.89/39.92 | | | | | | % 233.89/39.92 | | | | | | REDUCE: (8), (302) imply: % 233.89/39.92 | | | | | | (303) ~ leq(n4, n5) % 233.89/39.92 | | | | | | % 233.89/39.92 | | | | | | PRED_UNIFY: (265), (303) imply: % 233.89/39.92 | | | | | | (304) $false % 233.89/39.92 | | | | | | % 233.89/39.92 | | | | | | CLOSE: (304) is inconsistent. % 233.89/39.92 | | | | | | % 233.89/39.92 | | | | | Case 2: % 233.89/39.92 | | | | | | % 233.89/39.92 | | | | | | (305) ~ leq(n2, all_74_21) | (a_select3(pminus_ds1_filter, n4, % 233.89/39.92 | | | | | | n2) = all_74_12 & $i(all_74_12)) % 233.89/39.92 | | | | | | % 233.89/39.92 | | | | | | BETA: splitting (305) gives: % 233.89/39.92 | | | | | | % 233.89/39.92 | | | | | | Case 1: % 233.89/39.92 | | | | | | | % 233.89/39.92 | | | | | | | (306) ~ leq(n2, all_74_21) % 233.89/39.92 | | | | | | | % 233.89/39.92 | | | | | | | REDUCE: (8), (306) imply: % 233.89/39.92 | | | | | | | (307) ~ leq(n2, n5) % 233.89/39.92 | | | | | | | % 233.89/39.92 | | | | | | | PRED_UNIFY: (299), (307) imply: % 233.89/39.92 | | | | | | | (308) $false % 233.89/39.92 | | | | | | | % 233.89/39.92 | | | | | | | CLOSE: (308) is inconsistent. % 233.89/39.92 | | | | | | | % 233.89/39.92 | | | | | | Case 2: % 233.89/39.92 | | | | | | | % 233.89/39.92 | | | | | | | (309) a_select3(pminus_ds1_filter, n4, n2) = all_74_12 & % 233.89/39.92 | | | | | | | $i(all_74_12) % 233.89/39.92 | | | | | | | % 233.89/39.92 | | | | | | | ALPHA: (309) implies: % 233.89/39.92 | | | | | | | (310) a_select3(pminus_ds1_filter, n4, n2) = all_74_12 % 233.89/39.92 | | | | | | | % 233.89/39.92 | | | | | | | REF_CLOSE: (4), (13), (298), (310) are inconsistent by sub-proof % 233.89/39.92 | | | | | | | #24. % 233.89/39.92 | | | | | | | % 233.89/39.92 | | | | | | End of split % 233.89/39.92 | | | | | | % 233.89/39.92 | | | | | End of split % 233.89/39.92 | | | | | % 233.89/39.92 | | | | End of split % 233.89/39.92 | | | | % 233.89/39.92 | | | Case 2: % 233.89/39.92 | | | | % 233.89/39.92 | | | | (311) all_74_14 = n3 % 233.89/39.92 | | | | % 233.89/39.92 | | | | REDUCE: (263), (311) imply: % 233.89/39.92 | | | | (312) a_select3(pminus_ds1_filter, n3, n4) = all_74_12 % 233.89/39.92 | | | | % 233.89/39.92 | | | | REDUCE: (264), (311) imply: % 233.89/39.92 | | | | (313) a_select3(pminus_ds1_filter, n4, n3) = all_74_13 % 233.89/39.92 | | | | % 233.89/39.92 | | | | REDUCE: (3), (311) imply: % 233.89/39.92 | | | | (314) leq(n3, n5) % 233.89/39.92 | | | | % 233.89/39.92 | | | | REDUCE: (14), (311) imply: % 233.89/39.92 | | | | (315) leq(n0, n3) % 233.89/39.92 | | | | % 233.89/39.92 | | | | GROUND_INST: instantiating (16) with n3, n4, all_74_12, simplifying with % 233.89/39.92 | | | | (18), (21), (266), (312), (315) gives: % 233.89/39.92 | | | | (316) ~ leq(n4, all_74_21) | ~ leq(n3, all_74_21) | % 233.89/39.92 | | | | (a_select3(pminus_ds1_filter, n4, n3) = all_74_12 & % 233.89/39.92 | | | | $i(all_74_12)) % 233.89/39.92 | | | | % 233.89/39.92 | | | | BETA: splitting (316) gives: % 233.89/39.92 | | | | % 233.89/39.92 | | | | Case 1: % 233.89/39.92 | | | | | % 233.89/39.92 | | | | | (317) ~ leq(n4, all_74_21) % 233.89/39.92 | | | | | % 233.89/39.92 | | | | | REDUCE: (8), (317) imply: % 233.89/39.92 | | | | | (318) ~ leq(n4, n5) % 233.89/39.92 | | | | | % 233.89/39.92 | | | | | PRED_UNIFY: (265), (318) imply: % 233.89/39.92 | | | | | (319) $false % 233.89/39.92 | | | | | % 233.89/39.92 | | | | | CLOSE: (319) is inconsistent. % 233.89/39.92 | | | | | % 233.89/39.92 | | | | Case 2: % 233.89/39.92 | | | | | % 233.89/39.92 | | | | | (320) ~ leq(n3, all_74_21) | (a_select3(pminus_ds1_filter, n4, n3) % 233.89/39.92 | | | | | = all_74_12 & $i(all_74_12)) % 233.89/39.92 | | | | | % 233.89/39.92 | | | | | BETA: splitting (320) gives: % 233.89/39.92 | | | | | % 233.89/39.92 | | | | | Case 1: % 233.89/39.92 | | | | | | % 233.89/39.92 | | | | | | (321) ~ leq(n3, all_74_21) % 233.89/39.92 | | | | | | % 233.89/39.92 | | | | | | REDUCE: (8), (321) imply: % 233.89/39.92 | | | | | | (322) ~ leq(n3, n5) % 233.89/39.92 | | | | | | % 233.89/39.92 | | | | | | PRED_UNIFY: (314), (322) imply: % 233.89/39.92 | | | | | | (323) $false % 233.89/39.92 | | | | | | % 233.89/39.92 | | | | | | CLOSE: (323) is inconsistent. % 233.89/39.92 | | | | | | % 233.89/39.92 | | | | | Case 2: % 233.89/39.92 | | | | | | % 233.89/39.92 | | | | | | (324) a_select3(pminus_ds1_filter, n4, n3) = all_74_12 & % 233.89/39.92 | | | | | | $i(all_74_12) % 233.89/39.92 | | | | | | % 233.89/39.92 | | | | | | ALPHA: (324) implies: % 233.89/39.92 | | | | | | (325) a_select3(pminus_ds1_filter, n4, n3) = all_74_12 % 233.89/39.92 | | | | | | % 233.89/39.92 | | | | | | GROUND_INST: instantiating (13) with all_74_13, all_74_12, n3, n4, % 233.89/39.92 | | | | | | pminus_ds1_filter, simplifying with (313), (325) gives: % 233.89/39.92 | | | | | | (326) all_74_12 = all_74_13 % 233.89/39.92 | | | | | | % 233.89/39.92 | | | | | | REDUCE: (4), (326) imply: % 233.89/39.92 | | | | | | (327) $false % 233.89/39.92 | | | | | | % 233.89/39.92 | | | | | | CLOSE: (327) is inconsistent. % 233.89/39.92 | | | | | | % 233.89/39.92 | | | | | End of split % 233.89/39.92 | | | | | % 233.89/39.92 | | | | End of split % 233.89/39.92 | | | | % 233.89/39.92 | | | End of split % 233.89/39.92 | | | % 233.89/39.92 | | Case 2: % 233.89/39.92 | | | % 233.89/39.92 | | | (328) all_74_14 = n4 % 233.89/39.92 | | | % 233.89/39.92 | | | REDUCE: (263), (328) imply: % 233.89/39.92 | | | (329) a_select3(pminus_ds1_filter, n4, n4) = all_74_12 % 233.89/39.92 | | | % 233.89/39.92 | | | REDUCE: (264), (328) imply: % 233.89/39.92 | | | (330) a_select3(pminus_ds1_filter, n4, n4) = all_74_13 % 233.89/39.92 | | | % 233.89/39.92 | | | GROUND_INST: instantiating (13) with all_74_13, all_74_12, n4, n4, % 233.89/39.92 | | | pminus_ds1_filter, simplifying with (329), (330) gives: % 233.89/39.92 | | | (331) all_74_12 = all_74_13 % 233.89/39.92 | | | % 233.89/39.92 | | | REDUCE: (4), (331) imply: % 233.89/39.92 | | | (332) $false % 233.89/39.92 | | | % 233.89/39.92 | | | CLOSE: (332) is inconsistent. % 233.89/39.92 | | | % 233.89/39.92 | | End of split % 233.89/39.92 | | % 233.89/39.92 | End of split % 233.89/39.92 | % 233.89/39.92 End of proof % 233.89/39.92 % 233.89/39.92 Sub-proof #24 shows that the following formulas are inconsistent: % 233.89/39.92 ---------------------------------------------------------------- % 233.89/39.92 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 233.89/39.92 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 233.89/39.92 v0)) % 233.89/39.92 (2) a_select3(pminus_ds1_filter, n4, n2) = all_74_12 % 233.89/39.92 (3) a_select3(pminus_ds1_filter, n4, n2) = all_74_13 % 233.89/39.92 (4) ~ (all_74_12 = all_74_13) % 233.89/39.92 % 233.89/39.92 Begin of proof % 233.89/39.92 | % 233.89/39.92 | GROUND_INST: instantiating (1) with all_74_13, all_74_12, n2, n4, % 233.89/39.92 | pminus_ds1_filter, simplifying with (2), (3) gives: % 233.89/39.92 | (5) all_74_12 = all_74_13 % 233.89/39.92 | % 233.89/39.92 | REDUCE: (4), (5) imply: % 233.89/39.92 | (6) $false % 233.89/39.92 | % 233.89/39.92 | CLOSE: (6) is inconsistent. % 233.89/39.92 | % 233.89/39.92 End of proof % 233.89/39.92 % 233.89/39.92 Sub-proof #25 shows that the following formulas are inconsistent: % 233.89/39.92 ---------------------------------------------------------------- % 233.89/39.92 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 233.89/39.92 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 233.89/39.92 v0)) % 233.89/39.92 (2) a_select3(pminus_ds1_filter, n3, n2) = all_74_12 % 233.89/39.92 (3) a_select3(pminus_ds1_filter, n3, n2) = all_74_13 % 233.89/39.92 (4) ~ (all_74_12 = all_74_13) % 233.89/39.92 % 233.89/39.92 Begin of proof % 233.89/39.92 | % 233.89/39.92 | GROUND_INST: instantiating (1) with all_74_12, all_74_13, n2, n3, % 233.89/39.92 | pminus_ds1_filter, simplifying with (2), (3) gives: % 233.89/39.92 | (5) all_74_12 = all_74_13 % 233.89/39.92 | % 233.89/39.92 | REDUCE: (4), (5) imply: % 233.89/39.92 | (6) $false % 233.89/39.92 | % 233.89/39.92 | CLOSE: (6) is inconsistent. % 233.89/39.92 | % 233.89/39.92 End of proof % 233.89/39.92 % 233.89/39.92 Sub-proof #26 shows that the following formulas are inconsistent: % 233.89/39.92 ---------------------------------------------------------------- % 233.89/39.92 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 233.89/39.92 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 233.89/39.92 v0)) % 233.89/39.92 (2) a_select3(pminus_ds1_filter, n2, n1) = all_74_12 % 233.89/39.92 (3) a_select3(pminus_ds1_filter, n2, n1) = all_74_13 % 233.89/39.92 (4) ~ (all_74_12 = all_74_13) % 233.89/39.92 % 233.89/39.92 Begin of proof % 233.89/39.92 | % 233.89/39.92 | GROUND_INST: instantiating (1) with all_74_13, all_74_12, n1, n2, % 233.89/39.92 | pminus_ds1_filter, simplifying with (2), (3) gives: % 233.89/39.92 | (5) all_74_12 = all_74_13 % 233.89/39.92 | % 233.89/39.92 | REDUCE: (4), (5) imply: % 233.89/39.92 | (6) $false % 233.89/39.92 | % 233.89/39.92 | CLOSE: (6) is inconsistent. % 233.89/39.92 | % 233.89/39.92 End of proof % 233.89/39.92 % 233.89/39.92 Sub-proof #27 shows that the following formulas are inconsistent: % 233.89/39.92 ---------------------------------------------------------------- % 233.89/39.92 (1) $i(all_74_15) % 233.89/39.92 (2) all_74_15 = n0 % 233.89/39.92 (3) gt(all_74_15, n0) % 233.89/39.92 (4) ! [v0: $i] : ( ~ $i(v0) | ~ gt(v0, v0)) % 233.89/39.92 % 233.89/39.92 Begin of proof % 233.89/39.92 | % 233.89/39.92 | REDUCE: (1), (2) imply: % 233.89/39.92 | (5) $i(n0) % 233.89/39.92 | % 233.89/39.92 | REDUCE: (2), (3) imply: % 233.89/39.92 | (6) gt(n0, n0) % 233.89/39.92 | % 233.89/39.92 | GROUND_INST: instantiating (4) with n0, simplifying with (5), (6) gives: % 233.89/39.92 | (7) $false % 233.89/39.92 | % 233.89/39.92 | CLOSE: (7) is inconsistent. % 233.89/39.92 | % 233.89/39.92 End of proof % 233.89/39.92 % 233.89/39.92 Sub-proof #28 shows that the following formulas are inconsistent: % 233.89/39.92 ---------------------------------------------------------------- % 233.89/39.92 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 233.89/39.92 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 233.89/39.92 v0)) % 233.89/39.92 (2) a_select3(pminus_ds1_filter, n5, n0) = all_74_8 % 233.89/39.92 (3) a_select3(pminus_ds1_filter, n5, n0) = all_74_9 % 233.89/39.92 (4) ~ (all_74_8 = all_74_9) % 233.89/39.92 % 233.89/39.92 Begin of proof % 233.89/39.92 | % 233.89/39.92 | GROUND_INST: instantiating (1) with all_74_8, all_74_9, n0, n5, % 233.89/39.92 | pminus_ds1_filter, simplifying with (2), (3) gives: % 233.89/39.92 | (5) all_74_8 = all_74_9 % 233.89/39.92 | % 233.89/39.92 | REDUCE: (4), (5) imply: % 233.89/39.92 | (6) $false % 233.89/39.92 | % 233.89/39.92 | CLOSE: (6) is inconsistent. % 233.89/39.92 | % 233.89/39.92 End of proof % 233.89/39.92 % 233.89/39.92 Sub-proof #29 shows that the following formulas are inconsistent: % 233.89/39.92 ---------------------------------------------------------------- % 233.89/39.92 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 233.89/39.92 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 233.89/39.92 v0)) % 233.89/39.92 (2) a_select3(pminus_ds1_filter, n4, n0) = all_74_8 % 233.89/39.92 (3) a_select3(pminus_ds1_filter, n4, n0) = all_74_9 % 233.89/39.92 (4) ~ (all_74_8 = all_74_9) % 233.89/39.92 % 233.89/39.92 Begin of proof % 233.89/39.92 | % 233.89/39.92 | GROUND_INST: instantiating (1) with all_74_8, all_74_9, n0, n4, % 233.89/39.92 | pminus_ds1_filter, simplifying with (2), (3) gives: % 233.89/39.92 | (5) all_74_8 = all_74_9 % 233.89/39.92 | % 233.89/39.92 | REDUCE: (4), (5) imply: % 233.89/39.92 | (6) $false % 233.89/39.92 | % 233.89/39.92 | CLOSE: (6) is inconsistent. % 233.89/39.92 | % 233.89/39.92 End of proof % 233.89/39.92 % 233.89/39.92 Sub-proof #30 shows that the following formulas are inconsistent: % 233.89/39.92 ---------------------------------------------------------------- % 233.89/39.92 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 233.89/39.92 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 233.89/39.92 v0)) % 233.89/39.92 (2) a_select3(pminus_ds1_filter, n2, n0) = all_74_8 % 233.89/39.93 (3) a_select3(pminus_ds1_filter, n2, n0) = all_74_9 % 233.89/39.93 (4) ~ (all_74_8 = all_74_9) % 233.89/39.93 % 233.89/39.93 Begin of proof % 233.89/39.93 | % 233.89/39.93 | GROUND_INST: instantiating (1) with all_74_8, all_74_9, n0, n2, % 233.89/39.93 | pminus_ds1_filter, simplifying with (2), (3) gives: % 233.89/39.93 | (5) all_74_8 = all_74_9 % 233.89/39.93 | % 233.89/39.93 | REDUCE: (4), (5) imply: % 233.89/39.93 | (6) $false % 233.89/39.93 | % 233.89/39.93 | CLOSE: (6) is inconsistent. % 233.89/39.93 | % 233.89/39.93 End of proof % 233.89/39.93 % 233.89/39.93 Sub-proof #31 shows that the following formulas are inconsistent: % 233.89/39.93 ---------------------------------------------------------------- % 233.89/39.93 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 233.89/39.93 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 233.89/39.93 v0)) % 233.89/39.93 (2) a_select3(pminus_ds1_filter, n1, n0) = all_74_8 % 233.89/39.93 (3) a_select3(pminus_ds1_filter, n1, n0) = all_74_9 % 233.89/39.93 (4) ~ (all_74_8 = all_74_9) % 233.89/39.93 % 233.89/39.93 Begin of proof % 233.89/39.93 | % 233.89/39.93 | GROUND_INST: instantiating (1) with all_74_8, all_74_9, n0, n1, % 233.89/39.93 | pminus_ds1_filter, simplifying with (2), (3) gives: % 233.89/39.93 | (5) all_74_8 = all_74_9 % 233.89/39.93 | % 233.89/39.93 | REDUCE: (4), (5) imply: % 233.89/39.93 | (6) $false % 233.89/39.93 | % 233.89/39.93 | CLOSE: (6) is inconsistent. % 233.89/39.93 | % 233.89/39.93 End of proof % 233.89/39.93 % 233.89/39.93 Sub-proof #32 shows that the following formulas are inconsistent: % 233.89/39.93 ---------------------------------------------------------------- % 233.89/39.93 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 233.89/39.93 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 233.89/39.93 v0)) % 233.89/39.93 (2) a_select3(pminus_ds1_filter, n5, n4) = all_74_8 % 233.89/39.93 (3) a_select3(pminus_ds1_filter, n5, n4) = all_74_9 % 233.89/39.93 (4) ~ (all_74_8 = all_74_9) % 233.89/39.93 % 233.89/39.93 Begin of proof % 233.89/39.93 | % 233.89/39.93 | GROUND_INST: instantiating (1) with all_74_9, all_74_8, n4, n5, % 233.89/39.93 | pminus_ds1_filter, simplifying with (2), (3) gives: % 233.89/39.93 | (5) all_74_8 = all_74_9 % 233.89/39.93 | % 233.89/39.93 | REDUCE: (4), (5) imply: % 233.89/39.93 | (6) $false % 233.89/39.93 | % 233.89/39.93 | CLOSE: (6) is inconsistent. % 233.89/39.93 | % 233.89/39.93 End of proof % 233.89/39.93 % 233.89/39.93 Sub-proof #33 shows that the following formulas are inconsistent: % 233.89/39.93 ---------------------------------------------------------------- % 233.89/39.93 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 233.89/39.93 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 233.89/39.93 v0)) % 233.89/39.93 (2) a_select3(pminus_ds1_filter, n5, n3) = all_74_8 % 233.89/39.93 (3) a_select3(pminus_ds1_filter, n5, n3) = all_74_9 % 233.89/39.93 (4) ~ (all_74_8 = all_74_9) % 233.89/39.93 % 233.89/39.93 Begin of proof % 233.89/39.93 | % 233.89/39.93 | GROUND_INST: instantiating (1) with all_74_9, all_74_8, n3, n5, % 233.89/39.93 | pminus_ds1_filter, simplifying with (2), (3) gives: % 233.89/39.93 | (5) all_74_8 = all_74_9 % 233.89/39.93 | % 233.89/39.93 | REDUCE: (4), (5) imply: % 233.89/39.93 | (6) $false % 233.89/39.93 | % 233.89/39.93 | CLOSE: (6) is inconsistent. % 233.89/39.93 | % 233.89/39.93 End of proof % 233.89/39.93 % 233.89/39.93 Sub-proof #34 shows that the following formulas are inconsistent: % 233.89/39.93 ---------------------------------------------------------------- % 233.89/39.93 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 233.89/39.93 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 233.89/39.93 v0)) % 233.89/39.93 (2) a_select3(pminus_ds1_filter, n4, n3) = all_74_8 % 233.89/39.93 (3) a_select3(pminus_ds1_filter, n4, n3) = all_74_9 % 233.89/39.93 (4) ~ (all_74_8 = all_74_9) % 233.89/39.93 % 233.89/39.93 Begin of proof % 233.89/39.93 | % 233.89/39.93 | GROUND_INST: instantiating (1) with all_74_8, all_74_9, n3, n4, % 233.89/39.93 | pminus_ds1_filter, simplifying with (2), (3) gives: % 233.89/39.93 | (5) all_74_8 = all_74_9 % 233.89/39.93 | % 233.89/39.93 | REDUCE: (4), (5) imply: % 233.89/39.93 | (6) $false % 233.89/39.93 | % 233.89/39.93 | CLOSE: (6) is inconsistent. % 233.89/39.93 | % 233.89/39.93 End of proof % 233.89/39.93 % 233.89/39.93 Sub-proof #35 shows that the following formulas are inconsistent: % 233.89/39.93 ---------------------------------------------------------------- % 233.89/39.93 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 233.89/39.93 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 233.89/39.93 v0)) % 233.89/39.93 (2) a_select3(pminus_ds1_filter, n4, n1) = all_74_8 % 233.89/39.93 (3) a_select3(pminus_ds1_filter, n4, n1) = all_74_9 % 233.89/39.93 (4) ~ (all_74_8 = all_74_9) % 233.89/39.93 % 233.89/39.93 Begin of proof % 233.89/39.93 | % 233.89/39.93 | GROUND_INST: instantiating (1) with all_74_8, all_74_9, n1, n4, % 233.89/39.93 | pminus_ds1_filter, simplifying with (2), (3) gives: % 233.89/39.93 | (5) all_74_8 = all_74_9 % 233.89/39.93 | % 233.89/39.93 | REDUCE: (4), (5) imply: % 233.89/39.93 | (6) $false % 233.89/39.93 | % 233.89/39.93 | CLOSE: (6) is inconsistent. % 233.89/39.93 | % 233.89/39.93 End of proof % 233.89/39.93 % 233.89/39.93 Sub-proof #36 shows that the following formulas are inconsistent: % 233.89/39.93 ---------------------------------------------------------------- % 233.89/39.93 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 233.89/39.93 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 233.89/39.93 v0)) % 233.89/39.93 (2) a_select3(pminus_ds1_filter, n3, n2) = all_74_8 % 233.89/39.93 (3) a_select3(pminus_ds1_filter, n3, n2) = all_74_9 % 233.89/39.93 (4) ~ (all_74_8 = all_74_9) % 233.89/39.93 % 233.89/39.93 Begin of proof % 233.89/39.93 | % 233.89/39.93 | GROUND_INST: instantiating (1) with all_74_8, all_74_9, n2, n3, % 233.89/39.93 | pminus_ds1_filter, simplifying with (2), (3) gives: % 233.89/39.93 | (5) all_74_8 = all_74_9 % 233.89/39.93 | % 233.89/39.93 | REDUCE: (4), (5) imply: % 233.89/39.93 | (6) $false % 233.89/39.93 | % 233.89/39.93 | CLOSE: (6) is inconsistent. % 233.89/39.93 | % 233.89/39.93 End of proof % 233.89/39.93 % 233.89/39.93 Sub-proof #37 shows that the following formulas are inconsistent: % 233.89/39.93 ---------------------------------------------------------------- % 233.89/39.93 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 233.89/39.93 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 233.89/39.93 v0)) % 233.89/39.93 (2) a_select3(pminus_ds1_filter, n3, n1) = all_74_8 % 233.89/39.93 (3) a_select3(pminus_ds1_filter, n3, n1) = all_74_9 % 233.89/39.93 (4) ~ (all_74_8 = all_74_9) % 233.89/39.93 % 233.89/39.93 Begin of proof % 233.89/39.93 | % 233.89/39.93 | GROUND_INST: instantiating (1) with all_74_8, all_74_9, n1, n3, % 233.89/39.93 | pminus_ds1_filter, simplifying with (2), (3) gives: % 233.89/39.93 | (5) all_74_8 = all_74_9 % 233.89/39.93 | % 233.89/39.93 | REDUCE: (4), (5) imply: % 233.89/39.93 | (6) $false % 233.89/39.93 | % 233.89/39.93 | CLOSE: (6) is inconsistent. % 233.89/39.93 | % 233.89/39.93 End of proof % 233.89/39.93 % 233.89/39.93 Sub-proof #38 shows that the following formulas are inconsistent: % 233.89/39.93 ---------------------------------------------------------------- % 233.89/39.93 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 233.89/39.93 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 233.89/39.93 v0)) % 233.89/39.93 (2) a_select3(pminus_ds1_filter, n2, n1) = all_74_8 % 233.89/39.93 (3) a_select3(pminus_ds1_filter, n2, n1) = all_74_9 % 233.89/39.93 (4) ~ (all_74_8 = all_74_9) % 233.89/39.93 % 233.89/39.93 Begin of proof % 233.89/39.93 | % 233.89/39.93 | GROUND_INST: instantiating (1) with all_74_8, all_74_9, n1, n2, % 233.89/39.93 | pminus_ds1_filter, simplifying with (2), (3) gives: % 233.89/39.93 | (5) all_74_8 = all_74_9 % 233.89/39.93 | % 233.89/39.93 | REDUCE: (4), (5) imply: % 233.89/39.93 | (6) $false % 233.89/39.93 | % 233.89/39.93 | CLOSE: (6) is inconsistent. % 233.89/39.93 | % 233.89/39.93 End of proof % 233.89/39.93 % 233.89/39.93 Sub-proof #39 shows that the following formulas are inconsistent: % 233.89/39.93 ---------------------------------------------------------------- % 233.89/39.93 (1) $i(all_74_11) % 233.89/39.93 (2) all_74_11 = n0 % 233.89/39.93 (3) gt(all_74_11, n0) % 233.89/39.93 (4) ! [v0: $i] : ( ~ $i(v0) | ~ gt(v0, v0)) % 233.89/39.93 % 233.89/39.93 Begin of proof % 233.89/39.93 | % 233.89/39.93 | REDUCE: (1), (2) imply: % 233.89/39.93 | (5) $i(n0) % 233.89/39.93 | % 233.89/39.93 | REDUCE: (2), (3) imply: % 233.89/39.93 | (6) gt(n0, n0) % 233.89/39.93 | % 233.89/39.93 | GROUND_INST: instantiating (4) with n0, simplifying with (5), (6) gives: % 233.89/39.93 | (7) $false % 233.89/39.93 | % 233.89/39.93 | CLOSE: (7) is inconsistent. % 233.89/39.93 | % 233.89/39.93 End of proof % 233.89/39.93 % 233.89/39.93 Sub-proof #40 shows that the following formulas are inconsistent: % 233.89/39.93 ---------------------------------------------------------------- % 233.89/39.93 (1) $i(all_74_10) % 233.89/39.93 (2) all_74_10 = n0 % 233.89/39.93 (3) gt(all_74_10, n0) % 233.89/39.93 (4) ! [v0: $i] : ( ~ $i(v0) | ~ gt(v0, v0)) % 233.89/39.93 % 233.89/39.93 Begin of proof % 233.89/39.93 | % 233.89/39.93 | REDUCE: (1), (2) imply: % 233.89/39.93 | (5) $i(n0) % 233.89/39.93 | % 233.89/39.93 | REDUCE: (2), (3) imply: % 233.89/39.93 | (6) gt(n0, n0) % 233.89/39.93 | % 233.89/39.93 | GROUND_INST: instantiating (4) with n0, simplifying with (5), (6) gives: % 233.89/39.93 | (7) $false % 233.89/39.93 | % 233.89/39.93 | CLOSE: (7) is inconsistent. % 233.89/39.93 | % 233.89/39.93 End of proof % 233.89/39.93 % 233.89/39.93 Sub-proof #41 shows that the following formulas are inconsistent: % 233.89/39.93 ---------------------------------------------------------------- % 233.89/39.93 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 233.89/39.93 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 233.89/39.93 v0)) % 233.89/39.93 (2) a_select3(r_ds1_filter, n1, n0) = all_74_4 % 233.89/39.93 (3) a_select3(r_ds1_filter, n1, n0) = all_74_5 % 233.89/39.93 (4) ~ (all_74_4 = all_74_5) % 233.89/39.93 % 233.89/39.93 Begin of proof % 233.89/39.93 | % 233.89/39.93 | GROUND_INST: instantiating (1) with all_74_5, all_74_4, n0, n1, r_ds1_filter, % 233.89/39.93 | simplifying with (2), (3) gives: % 233.89/39.93 | (5) all_74_4 = all_74_5 % 233.89/39.93 | % 233.89/39.93 | REDUCE: (4), (5) imply: % 233.89/39.93 | (6) $false % 233.89/39.93 | % 233.89/39.93 | CLOSE: (6) is inconsistent. % 233.89/39.93 | % 233.89/39.93 End of proof % 233.89/39.93 % 233.89/39.93 Sub-proof #42 shows that the following formulas are inconsistent: % 233.89/39.93 ---------------------------------------------------------------- % 233.89/39.93 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 233.89/39.93 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 233.89/39.93 v0)) % 233.89/39.93 (2) a_select3(r_ds1_filter, n2, n1) = all_74_4 % 233.89/39.93 (3) a_select3(r_ds1_filter, n2, n1) = all_74_5 % 233.89/39.93 (4) ~ (all_74_4 = all_74_5) % 233.89/39.93 % 233.89/39.93 Begin of proof % 233.89/39.93 | % 233.89/39.93 | GROUND_INST: instantiating (1) with all_74_5, all_74_4, n1, n2, r_ds1_filter, % 233.89/39.93 | simplifying with (2), (3) gives: % 233.89/39.93 | (5) all_74_4 = all_74_5 % 233.89/39.93 | % 233.89/39.93 | REDUCE: (4), (5) imply: % 233.89/39.93 | (6) $false % 233.89/39.93 | % 233.89/39.93 | CLOSE: (6) is inconsistent. % 233.89/39.93 | % 233.89/39.93 End of proof % 233.89/39.93 % 233.89/39.93 Sub-proof #43 shows that the following formulas are inconsistent: % 233.89/39.93 ---------------------------------------------------------------- % 233.89/39.93 (1) $i(all_74_6) % 233.89/39.93 (2) all_74_6 = n0 % 233.89/39.93 (3) gt(all_74_6, n0) % 233.89/39.93 (4) ! [v0: $i] : ( ~ $i(v0) | ~ gt(v0, v0)) % 233.89/39.93 % 233.89/39.93 Begin of proof % 233.89/39.93 | % 233.89/39.93 | REDUCE: (1), (2) imply: % 233.89/39.93 | (5) $i(n0) % 233.89/39.93 | % 233.89/39.93 | REDUCE: (2), (3) imply: % 233.89/39.93 | (6) gt(n0, n0) % 233.89/39.93 | % 233.89/39.93 | GROUND_INST: instantiating (4) with n0, simplifying with (5), (6) gives: % 233.89/39.93 | (7) $false % 233.89/39.93 | % 233.89/39.93 | CLOSE: (7) is inconsistent. % 233.89/39.93 | % 233.89/39.93 End of proof % 233.89/39.93 % 233.89/39.93 Sub-proof #44 shows that the following formulas are inconsistent: % 233.89/39.93 ---------------------------------------------------------------- % 233.89/39.93 (1) $i(all_74_7) % 233.89/39.93 (2) all_74_7 = n0 % 233.89/39.93 (3) gt(all_74_7, n0) % 233.89/39.93 (4) ! [v0: $i] : ( ~ $i(v0) | ~ gt(v0, v0)) % 233.89/39.93 % 233.89/39.93 Begin of proof % 233.89/39.93 | % 233.89/39.93 | REDUCE: (1), (2) imply: % 233.89/39.93 | (5) $i(n0) % 233.89/39.93 | % 233.89/39.93 | REDUCE: (2), (3) imply: % 233.89/39.93 | (6) gt(n0, n0) % 233.89/39.93 | % 233.89/39.93 | GROUND_INST: instantiating (4) with n0, simplifying with (5), (6) gives: % 233.89/39.93 | (7) $false % 233.89/39.93 | % 233.89/39.93 | CLOSE: (7) is inconsistent. % 233.89/39.93 | % 233.89/39.93 End of proof % 233.89/39.93 % 233.89/39.93 Sub-proof #45 shows that the following formulas are inconsistent: % 233.89/39.93 ---------------------------------------------------------------- % 233.89/39.93 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 233.89/39.93 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 233.89/39.93 v0)) % 233.89/39.93 (2) a_select3(q_ds1_filter, n5, n0) = all_74_0 % 233.89/39.93 (3) a_select3(q_ds1_filter, n5, n0) = all_74_1 % 233.89/39.94 (4) ~ (all_74_0 = all_74_1) % 233.89/39.94 % 233.89/39.94 Begin of proof % 233.89/39.94 | % 233.89/39.94 | GROUND_INST: instantiating (1) with all_74_1, all_74_0, n0, n5, q_ds1_filter, % 233.89/39.94 | simplifying with (2), (3) gives: % 233.89/39.94 | (5) all_74_0 = all_74_1 % 233.89/39.94 | % 233.89/39.94 | REDUCE: (4), (5) imply: % 233.89/39.94 | (6) $false % 233.89/39.94 | % 233.89/39.94 | CLOSE: (6) is inconsistent. % 233.89/39.94 | % 233.89/39.94 End of proof % 233.89/39.94 % 233.89/39.94 Sub-proof #46 shows that the following formulas are inconsistent: % 233.89/39.94 ---------------------------------------------------------------- % 233.89/39.94 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 233.89/39.94 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 233.89/39.94 v0)) % 233.89/39.94 (2) a_select3(q_ds1_filter, n4, n0) = all_74_0 % 233.89/39.94 (3) a_select3(q_ds1_filter, n4, n0) = all_74_1 % 233.89/39.94 (4) ~ (all_74_0 = all_74_1) % 233.89/39.94 % 233.89/39.94 Begin of proof % 233.89/39.94 | % 233.89/39.94 | GROUND_INST: instantiating (1) with all_74_1, all_74_0, n0, n4, q_ds1_filter, % 233.89/39.94 | simplifying with (2), (3) gives: % 233.89/39.94 | (5) all_74_0 = all_74_1 % 233.89/39.94 | % 233.89/39.94 | REDUCE: (4), (5) imply: % 233.89/39.94 | (6) $false % 233.89/39.94 | % 233.89/39.94 | CLOSE: (6) is inconsistent. % 233.89/39.94 | % 233.89/39.94 End of proof % 233.89/39.94 % 233.89/39.94 Sub-proof #47 shows that the following formulas are inconsistent: % 233.89/39.94 ---------------------------------------------------------------- % 233.89/39.94 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 233.89/39.94 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 233.89/39.94 v0)) % 233.89/39.94 (2) a_select3(q_ds1_filter, n2, n0) = all_74_0 % 233.89/39.94 (3) a_select3(q_ds1_filter, n2, n0) = all_74_1 % 233.89/39.94 (4) ~ (all_74_0 = all_74_1) % 233.89/39.94 % 233.89/39.94 Begin of proof % 233.89/39.94 | % 233.89/39.94 | GROUND_INST: instantiating (1) with all_74_1, all_74_0, n0, n2, q_ds1_filter, % 233.89/39.94 | simplifying with (2), (3) gives: % 233.89/39.94 | (5) all_74_0 = all_74_1 % 233.89/39.94 | % 233.89/39.94 | REDUCE: (4), (5) imply: % 233.89/39.94 | (6) $false % 233.89/39.94 | % 233.89/39.94 | CLOSE: (6) is inconsistent. % 233.89/39.94 | % 233.89/39.94 End of proof % 233.89/39.94 % 233.89/39.94 Sub-proof #48 shows that the following formulas are inconsistent: % 233.89/39.94 ---------------------------------------------------------------- % 233.89/39.94 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 233.89/39.94 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 233.89/39.94 v0)) % 233.89/39.94 (2) a_select3(q_ds1_filter, n1, n0) = all_74_0 % 233.89/39.94 (3) a_select3(q_ds1_filter, n1, n0) = all_74_1 % 233.89/39.94 (4) ~ (all_74_0 = all_74_1) % 233.89/39.94 % 233.89/39.94 Begin of proof % 233.89/39.94 | % 233.89/39.94 | GROUND_INST: instantiating (1) with all_74_1, all_74_0, n0, n1, q_ds1_filter, % 233.89/39.94 | simplifying with (2), (3) gives: % 233.89/39.94 | (5) all_74_0 = all_74_1 % 233.89/39.94 | % 233.89/39.94 | REDUCE: (4), (5) imply: % 233.89/39.94 | (6) $false % 234.14/39.94 | % 234.14/39.94 | CLOSE: (6) is inconsistent. % 234.14/39.94 | % 234.14/39.94 End of proof % 234.14/39.94 % 234.14/39.94 Sub-proof #49 shows that the following formulas are inconsistent: % 234.14/39.94 ---------------------------------------------------------------- % 234.14/39.94 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 234.14/39.94 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 234.14/39.94 v0)) % 234.14/39.94 (2) a_select3(q_ds1_filter, n5, n4) = all_74_0 % 234.14/39.94 (3) a_select3(q_ds1_filter, n5, n4) = all_74_1 % 234.14/39.94 (4) ~ (all_74_0 = all_74_1) % 234.14/39.94 % 234.14/39.94 Begin of proof % 234.14/39.94 | % 234.14/39.94 | GROUND_INST: instantiating (1) with all_74_0, all_74_1, n4, n5, q_ds1_filter, % 234.14/39.94 | simplifying with (2), (3) gives: % 234.14/39.94 | (5) all_74_0 = all_74_1 % 234.14/39.94 | % 234.14/39.94 | REDUCE: (4), (5) imply: % 234.14/39.94 | (6) $false % 234.14/39.94 | % 234.14/39.94 | CLOSE: (6) is inconsistent. % 234.14/39.94 | % 234.14/39.94 End of proof % 234.14/39.94 % 234.14/39.94 Sub-proof #50 shows that the following formulas are inconsistent: % 234.14/39.94 ---------------------------------------------------------------- % 234.14/39.94 (1) a_select3(q_ds1_filter, n3, n5) = all_74_1 % 234.14/39.94 (2) all_74_21 = n5 % 234.14/39.94 (3) leq(n3, n5) % 234.14/39.94 (4) ~ (all_74_0 = all_74_1) % 234.14/39.94 (5) leq(n5, n5) % 234.14/39.94 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 234.14/39.94 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 234.14/39.94 v0)) % 234.14/39.94 (7) leq(n0, n3) % 234.14/39.94 (8) $i(n5) % 234.14/39.94 (9) $i(n3) % 234.14/39.94 (10) leq(n0, n5) % 234.14/39.94 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (a_select3(q_ds1_filter, % 234.14/39.94 v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ leq(v1, all_74_21) | ~ % 234.14/39.94 leq(v0, all_74_21) | ~ leq(n0, v1) | ~ leq(n0, v0) | % 234.14/39.94 (a_select3(q_ds1_filter, v1, v0) = v2 & $i(v2))) % 234.14/39.94 (12) a_select3(q_ds1_filter, n5, n3) = all_74_0 % 234.14/39.94 % 234.14/39.94 Begin of proof % 234.14/39.94 | % 234.14/39.94 | GROUND_INST: instantiating (11) with n3, n5, all_74_1, simplifying with (1), % 234.14/39.94 | (7), (8), (9), (10) gives: % 234.14/39.94 | (13) ~ leq(n5, all_74_21) | ~ leq(n3, all_74_21) | % 234.14/39.94 | (a_select3(q_ds1_filter, n5, n3) = all_74_1 & $i(all_74_1)) % 234.14/39.94 | % 234.14/39.94 | BETA: splitting (13) gives: % 234.14/39.94 | % 234.14/39.94 | Case 1: % 234.14/39.94 | | % 234.14/39.94 | | (14) ~ leq(n5, all_74_21) % 234.14/39.94 | | % 234.14/39.94 | | REDUCE: (2), (14) imply: % 234.14/39.94 | | (15) ~ leq(n5, n5) % 234.14/39.94 | | % 234.14/39.94 | | PRED_UNIFY: (5), (15) imply: % 234.14/39.94 | | (16) $false % 234.14/39.94 | | % 234.14/39.94 | | CLOSE: (16) is inconsistent. % 234.14/39.94 | | % 234.14/39.94 | Case 2: % 234.14/39.94 | | % 234.14/39.94 | | (17) ~ leq(n3, all_74_21) | (a_select3(q_ds1_filter, n5, n3) = all_74_1 % 234.14/39.94 | | & $i(all_74_1)) % 234.14/39.94 | | % 234.14/39.94 | | BETA: splitting (17) gives: % 234.14/39.94 | | % 234.14/39.94 | | Case 1: % 234.14/39.94 | | | % 234.14/39.94 | | | (18) ~ leq(n3, all_74_21) % 234.14/39.94 | | | % 234.14/39.94 | | | REDUCE: (2), (18) imply: % 234.14/39.94 | | | (19) ~ leq(n3, n5) % 234.14/39.94 | | | % 234.14/39.94 | | | PRED_UNIFY: (3), (19) imply: % 234.14/39.94 | | | (20) $false % 234.14/39.94 | | | % 234.14/39.94 | | | CLOSE: (20) is inconsistent. % 234.14/39.94 | | | % 234.14/39.94 | | Case 2: % 234.14/39.94 | | | % 234.14/39.94 | | | (21) a_select3(q_ds1_filter, n5, n3) = all_74_1 & $i(all_74_1) % 234.14/39.94 | | | % 234.14/39.94 | | | ALPHA: (21) implies: % 234.14/39.94 | | | (22) a_select3(q_ds1_filter, n5, n3) = all_74_1 % 234.14/39.94 | | | % 234.14/39.94 | | | GROUND_INST: instantiating (6) with all_74_0, all_74_1, n3, n5, % 234.14/39.94 | | | q_ds1_filter, simplifying with (12), (22) gives: % 234.14/39.94 | | | (23) all_74_0 = all_74_1 % 234.14/39.94 | | | % 234.14/39.94 | | | REDUCE: (4), (23) imply: % 234.14/39.94 | | | (24) $false % 234.14/39.94 | | | % 234.14/39.94 | | | CLOSE: (24) is inconsistent. % 234.14/39.94 | | | % 234.14/39.94 | | End of split % 234.14/39.94 | | % 234.14/39.94 | End of split % 234.14/39.94 | % 234.14/39.94 End of proof % 234.14/39.94 % 234.14/39.94 Sub-proof #51 shows that the following formulas are inconsistent: % 234.14/39.94 ---------------------------------------------------------------- % 234.14/39.94 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 234.14/39.94 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 234.14/39.94 v0)) % 234.14/39.94 (2) a_select3(q_ds1_filter, n4, n3) = all_74_0 % 234.14/39.94 (3) a_select3(q_ds1_filter, n4, n3) = all_74_1 % 234.14/39.94 (4) ~ (all_74_0 = all_74_1) % 234.14/39.94 % 234.14/39.94 Begin of proof % 234.14/39.94 | % 234.14/39.94 | GROUND_INST: instantiating (1) with all_74_1, all_74_0, n3, n4, q_ds1_filter, % 234.14/39.94 | simplifying with (2), (3) gives: % 234.14/39.94 | (5) all_74_0 = all_74_1 % 234.14/39.94 | % 234.14/39.94 | REDUCE: (4), (5) imply: % 234.14/39.94 | (6) $false % 234.14/39.94 | % 234.14/39.94 | CLOSE: (6) is inconsistent. % 234.14/39.94 | % 234.14/39.94 End of proof % 234.14/39.94 % 234.14/39.94 Sub-proof #52 shows that the following formulas are inconsistent: % 234.14/39.94 ---------------------------------------------------------------- % 234.14/39.94 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 234.14/39.94 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 234.14/39.94 v0)) % 234.14/39.94 (2) a_select3(q_ds1_filter, n4, n2) = all_74_0 % 234.14/39.94 (3) a_select3(q_ds1_filter, n4, n2) = all_74_1 % 234.14/39.94 (4) ~ (all_74_0 = all_74_1) % 234.14/39.94 % 234.14/39.94 Begin of proof % 234.14/39.94 | % 234.14/39.94 | GROUND_INST: instantiating (1) with all_74_1, all_74_0, n2, n4, q_ds1_filter, % 234.14/39.94 | simplifying with (2), (3) gives: % 234.14/39.94 | (5) all_74_0 = all_74_1 % 234.14/39.94 | % 234.14/39.94 | REDUCE: (4), (5) imply: % 234.14/39.94 | (6) $false % 234.14/39.94 | % 234.14/39.94 | CLOSE: (6) is inconsistent. % 234.14/39.94 | % 234.14/39.94 End of proof % 234.14/39.94 % 234.14/39.94 Sub-proof #53 shows that the following formulas are inconsistent: % 234.14/39.94 ---------------------------------------------------------------- % 234.14/39.94 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 234.14/39.94 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 234.14/39.94 v0)) % 234.14/39.94 (2) a_select3(q_ds1_filter, n4, n1) = all_74_0 % 234.14/39.94 (3) a_select3(q_ds1_filter, n4, n1) = all_74_1 % 234.14/39.94 (4) ~ (all_74_0 = all_74_1) % 234.14/39.94 % 234.14/39.94 Begin of proof % 234.14/39.94 | % 234.14/39.94 | GROUND_INST: instantiating (1) with all_74_1, all_74_0, n1, n4, q_ds1_filter, % 234.14/39.94 | simplifying with (2), (3) gives: % 234.14/39.94 | (5) all_74_0 = all_74_1 % 234.14/39.94 | % 234.14/39.94 | REDUCE: (4), (5) imply: % 234.14/39.94 | (6) $false % 234.14/39.94 | % 234.14/39.94 | CLOSE: (6) is inconsistent. % 234.14/39.94 | % 234.14/39.94 End of proof % 234.14/39.94 % 234.14/39.94 Sub-proof #54 shows that the following formulas are inconsistent: % 234.14/39.94 ---------------------------------------------------------------- % 234.14/39.94 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 234.14/39.94 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 234.14/39.94 v0)) % 234.14/39.94 (2) a_select3(q_ds1_filter, n3, n2) = all_74_0 % 234.14/39.94 (3) a_select3(q_ds1_filter, n3, n2) = all_74_1 % 234.14/39.94 (4) ~ (all_74_0 = all_74_1) % 234.14/39.94 % 234.14/39.94 Begin of proof % 234.14/39.94 | % 234.14/39.94 | GROUND_INST: instantiating (1) with all_74_0, all_74_1, n2, n3, q_ds1_filter, % 234.14/39.94 | simplifying with (2), (3) gives: % 234.14/39.94 | (5) all_74_0 = all_74_1 % 234.14/39.94 | % 234.14/39.94 | REDUCE: (4), (5) imply: % 234.14/39.94 | (6) $false % 234.14/39.94 | % 234.14/39.94 | CLOSE: (6) is inconsistent. % 234.14/39.94 | % 234.14/39.94 End of proof % 234.14/39.94 % 234.14/39.94 Sub-proof #55 shows that the following formulas are inconsistent: % 234.14/39.94 ---------------------------------------------------------------- % 234.14/39.94 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 234.14/39.94 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 234.14/39.94 v0)) % 234.14/39.94 (2) a_select3(q_ds1_filter, n3, n1) = all_74_0 % 234.14/39.94 (3) a_select3(q_ds1_filter, n3, n1) = all_74_1 % 234.14/39.94 (4) ~ (all_74_0 = all_74_1) % 234.14/39.94 % 234.14/39.94 Begin of proof % 234.14/39.94 | % 234.14/39.94 | GROUND_INST: instantiating (1) with all_74_0, all_74_1, n1, n3, q_ds1_filter, % 234.14/39.94 | simplifying with (2), (3) gives: % 234.14/39.94 | (5) all_74_0 = all_74_1 % 234.14/39.94 | % 234.14/39.94 | REDUCE: (4), (5) imply: % 234.14/39.94 | (6) $false % 234.14/39.94 | % 234.14/39.94 | CLOSE: (6) is inconsistent. % 234.14/39.94 | % 234.14/39.94 End of proof % 234.14/39.94 % 234.14/39.94 Sub-proof #56 shows that the following formulas are inconsistent: % 234.14/39.94 ---------------------------------------------------------------- % 234.14/39.94 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 234.14/39.94 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 234.14/39.94 v0)) % 234.14/39.94 (2) a_select3(q_ds1_filter, n2, n1) = all_74_0 % 234.14/39.94 (3) a_select3(q_ds1_filter, n2, n1) = all_74_1 % 234.14/39.94 (4) ~ (all_74_0 = all_74_1) % 234.14/39.94 % 234.14/39.94 Begin of proof % 234.14/39.94 | % 234.14/39.95 | GROUND_INST: instantiating (1) with all_74_0, all_74_1, n1, n2, q_ds1_filter, % 234.14/39.95 | simplifying with (2), (3) gives: % 234.14/39.95 | (5) all_74_0 = all_74_1 % 234.14/39.95 | % 234.14/39.95 | REDUCE: (4), (5) imply: % 234.14/39.95 | (6) $false % 234.14/39.95 | % 234.14/39.95 | CLOSE: (6) is inconsistent. % 234.14/39.95 | % 234.14/39.95 End of proof % 234.14/39.95 % 234.14/39.95 Sub-proof #57 shows that the following formulas are inconsistent: % 234.14/39.95 ---------------------------------------------------------------- % 234.14/39.95 (1) $i(all_74_3) % 234.14/39.95 (2) all_74_3 = n0 % 234.14/39.95 (3) gt(all_74_3, n0) % 234.14/39.95 (4) ! [v0: $i] : ( ~ $i(v0) | ~ gt(v0, v0)) % 234.14/39.95 % 234.14/39.95 Begin of proof % 234.14/39.95 | % 234.14/39.95 | REDUCE: (1), (2) imply: % 234.14/39.95 | (5) $i(n0) % 234.14/39.95 | % 234.14/39.95 | REDUCE: (2), (3) imply: % 234.14/39.95 | (6) gt(n0, n0) % 234.14/39.95 | % 234.14/39.95 | GROUND_INST: instantiating (4) with n0, simplifying with (5), (6) gives: % 234.14/39.95 | (7) $false % 234.14/39.95 | % 234.14/39.95 | CLOSE: (7) is inconsistent. % 234.14/39.95 | % 234.14/39.95 End of proof % 234.14/39.95 % 234.14/39.95 Sub-proof #58 shows that the following formulas are inconsistent: % 234.14/39.95 ---------------------------------------------------------------- % 234.14/39.95 (1) $i(all_74_2) % 234.14/39.95 (2) all_74_2 = n0 % 234.14/39.95 (3) gt(all_74_2, n0) % 234.14/39.95 (4) ! [v0: $i] : ( ~ $i(v0) | ~ gt(v0, v0)) % 234.14/39.95 % 234.14/39.95 Begin of proof % 234.14/39.95 | % 234.14/39.95 | REDUCE: (1), (2) imply: % 234.14/39.95 | (5) $i(n0) % 234.14/39.95 | % 234.14/39.95 | REDUCE: (2), (3) imply: % 234.14/39.95 | (6) gt(n0, n0) % 234.14/39.95 | % 234.14/39.95 | GROUND_INST: instantiating (4) with n0, simplifying with (5), (6) gives: % 234.14/39.95 | (7) $false % 234.14/39.95 | % 234.14/39.95 | CLOSE: (7) is inconsistent. % 234.14/39.95 | % 234.14/39.95 End of proof % 234.14/39.95 % SZS output end Proof for theBenchmark % 234.14/39.95 % 234.14/39.95 39363ms %------------------------------------------------------------------------------