%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWV112+1 : TPTP v8.1.2. Bugfixed v3.3.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n005.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Thu Aug 31 22:54:57 EDT 2023 % Result : Theorem 93.52s 12.98s % Output : Proof 263.42s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWV112+1 : TPTP v8.1.2. Bugfixed v3.3.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.34 % Computer : n005.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Tue Aug 29 03:53:52 EDT 2023 % 0.14/0.34 % CPUTime : % 0.20/0.60 ________ _____ % 0.20/0.60 ___ __ \_________(_)________________________________ % 0.20/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.60 % 0.20/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.60 (2023-06-19) % 0.20/0.60 % 0.20/0.60 (c) Philipp Rümmer, 2009-2023 % 0.20/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.60 Amanda Stjerna. % 0.20/0.60 Free software under BSD-3-Clause. % 0.20/0.60 % 0.20/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.60 % 0.20/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.20/0.61 Running up to 7 provers in parallel. % 0.20/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 5.20/1.44 Prover 4: Preprocessing ... % 5.20/1.44 Prover 5: Preprocessing ... % 5.20/1.44 Prover 6: Preprocessing ... % 5.20/1.44 Prover 2: Preprocessing ... % 5.20/1.46 Prover 3: Preprocessing ... % 5.20/1.47 Prover 1: Preprocessing ... % 5.20/1.47 Prover 0: Preprocessing ... % 11.97/2.34 Prover 1: Warning: ignoring some quantifiers % 12.53/2.38 Prover 6: Proving ... % 12.53/2.40 Prover 4: Warning: ignoring some quantifiers % 12.53/2.42 Prover 3: Warning: ignoring some quantifiers % 12.53/2.43 Prover 1: Constructing countermodel ... % 12.53/2.45 Prover 3: Constructing countermodel ... % 13.43/2.51 Prover 2: Proving ... % 13.43/2.51 Prover 4: Constructing countermodel ... % 14.74/2.68 Prover 0: Proving ... % 14.93/2.71 Prover 5: Proving ... % 73.01/10.29 Prover 2: stopped % 73.36/10.30 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 73.82/10.47 Prover 7: Preprocessing ... % 76.08/10.71 Prover 7: Warning: ignoring some quantifiers % 76.08/10.73 Prover 7: Constructing countermodel ... % 93.52/12.97 Prover 3: proved (12351ms) % 93.52/12.97 % 93.52/12.98 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 93.52/12.98 % 93.52/12.99 Prover 5: stopped % 93.52/12.99 Prover 6: stopped % 93.52/12.99 Prover 0: stopped % 93.52/12.99 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 93.52/12.99 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 93.52/12.99 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 93.52/12.99 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 93.72/13.09 Prover 13: Preprocessing ... % 94.84/13.12 Prover 8: Preprocessing ... % 94.84/13.12 Prover 10: Preprocessing ... % 94.84/13.16 Prover 11: Preprocessing ... % 95.33/13.23 Prover 10: Warning: ignoring some quantifiers % 95.33/13.24 Prover 10: Constructing countermodel ... % 96.09/13.29 Prover 8: Warning: ignoring some quantifiers % 96.34/13.30 Prover 8: Constructing countermodel ... % 96.34/13.33 Prover 13: Warning: ignoring some quantifiers % 96.61/13.33 Prover 11: Warning: ignoring some quantifiers % 96.61/13.35 Prover 13: Constructing countermodel ... % 96.61/13.36 Prover 11: Constructing countermodel ... % 116.26/15.97 Prover 1: stopped % 116.26/15.97 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 117.23/16.07 Prover 16: Preprocessing ... % 118.01/16.25 Prover 16: Warning: ignoring some quantifiers % 118.01/16.26 Prover 16: Constructing countermodel ... % 125.29/17.07 Prover 13: stopped % 125.29/17.08 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 125.85/17.14 Prover 19: Preprocessing ... % 127.61/17.40 Prover 19: Warning: ignoring some quantifiers % 127.61/17.43 Prover 19: Constructing countermodel ... % 151.80/20.79 Prover 16: stopped % 152.30/20.81 Prover 19: stopped % 191.09/27.96 Prover 4: stopped % 201.48/30.40 Prover 7: stopped % 240.87/42.37 Prover 11: stopped % 245.79/44.60 Prover 8: stopped % 259.17/55.93 Prover 10: Found proof (size 11348) % 259.17/55.93 Prover 10: proved (42945ms) % 259.17/55.93 % 259.17/55.93 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 259.17/55.93 % 259.29/56.12 % SZS output start Proof for theBenchmark % 259.29/56.15 Assumptions after simplification: % 259.29/56.15 --------------------------------- % 259.29/56.15 % 259.29/56.15 (finite_domain_0) % 259.29/56.15 $i(n0) & ! [v0: $i] : (v0 = n0 | ~ $i(v0) | ~ leq(v0, n0) | ~ leq(n0, v0)) % 259.29/56.15 % 259.29/56.15 (finite_domain_1) % 259.29/56.15 $i(n1) & $i(n0) & ! [v0: $i] : (v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0, % 259.29/56.15 n1) | ~ leq(n0, v0)) % 259.29/56.15 % 259.29/56.15 (finite_domain_2) % 259.29/56.16 $i(n2) & $i(n1) & $i(n0) & ! [v0: $i] : (v0 = n2 | v0 = n1 | v0 = n0 | ~ % 259.29/56.16 $i(v0) | ~ leq(v0, n2) | ~ leq(n0, v0)) % 259.29/56.16 % 259.29/56.16 (finite_domain_3) % 259.29/56.16 $i(n3) & $i(n2) & $i(n1) & $i(n0) & ! [v0: $i] : (v0 = n3 | v0 = n2 | v0 = n1 % 259.29/56.16 | v0 = n0 | ~ $i(v0) | ~ leq(v0, n3) | ~ leq(n0, v0)) % 259.29/56.16 % 259.29/56.16 (finite_domain_4) % 259.29/56.16 $i(n4) & $i(n3) & $i(n2) & $i(n1) & $i(n0) & ! [v0: $i] : (v0 = n4 | v0 = n3 % 259.29/56.16 | v0 = n2 | v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0, n4) | ~ leq(n0, v0)) % 259.29/56.16 % 259.29/56.16 (finite_domain_5) % 259.29/56.16 $i(n5) & $i(n4) & $i(n3) & $i(n2) & $i(n1) & $i(n0) & ! [v0: $i] : (v0 = n5 | % 259.29/56.16 v0 = n4 | v0 = n3 | v0 = n2 | v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0, n5) % 259.29/56.16 | ~ leq(n0, v0)) % 259.29/56.16 % 259.29/56.16 (finite_domain_6) % 259.29/56.16 $i(n6) & $i(n5) & $i(n4) & $i(n3) & $i(n2) & $i(n1) & $i(n0) & ! [v0: $i] : % 259.29/56.16 (v0 = n6 | v0 = n5 | v0 = n4 | v0 = n3 | v0 = n2 | v0 = n1 | v0 = n0 | ~ % 259.29/56.16 $i(v0) | ~ leq(v0, n6) | ~ leq(n0, v0)) % 259.29/56.16 % 259.29/56.17 (gt_6_5) % 259.29/56.17 $i(n6) & $i(n5) & gt(n6, n5) % 259.29/56.17 % 259.29/56.17 (gt_succ) % 259.66/56.19 ! [v0: $i] : ! [v1: $i] : ( ~ (succ(v0) = v1) | ~ $i(v0) | gt(v1, v0)) % 259.66/56.19 % 259.66/56.19 (irreflexivity_gt) % 259.66/56.19 ! [v0: $i] : ( ~ $i(v0) | ~ gt(v0, v0)) % 259.66/56.19 % 259.66/56.19 (leq_gt1) % 259.66/56.19 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ gt(v1, v0) | leq(v0, % 259.66/56.19 v1)) % 259.66/56.19 % 259.66/56.19 (leq_gt2) % 259.66/56.19 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ leq(v0, v1) % 259.66/56.19 | gt(v1, v0)) % 259.66/56.19 % 259.66/56.19 (leq_gt_pred) % 259.66/56.20 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (pred(v1) = v2) | ~ $i(v1) | ~ % 259.66/56.20 $i(v0) | ~ leq(v0, v2) | gt(v1, v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 259.66/56.20 $i] : ( ~ (pred(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ gt(v1, v0) | leq(v0, % 259.66/56.20 v2)) % 259.66/56.20 % 259.66/56.20 (leq_succ) % 259.66/56.20 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (succ(v1) = v2) | ~ $i(v1) | ~ % 259.66/56.20 $i(v0) | ~ leq(v0, v1) | leq(v0, v2)) % 259.66/56.20 % 259.66/56.20 (leq_succ_gt) % 259.66/56.20 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (succ(v0) = v2) | ~ $i(v1) | ~ % 259.66/56.20 $i(v0) | ~ leq(v2, v1) | gt(v1, v0)) % 259.66/56.20 % 259.66/56.20 (leq_succ_gt_equiv) % 259.66/56.20 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (succ(v1) = v2) | ~ $i(v1) | ~ % 259.66/56.20 $i(v0) | ~ leq(v0, v1) | gt(v2, v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 259.66/56.20 $i] : ( ~ (succ(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ gt(v2, v0) | leq(v0, % 259.66/56.20 v1)) % 259.66/56.20 % 259.66/56.20 (leq_succ_succ) % 259.66/56.20 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (succ(v1) = v3) | % 259.66/56.20 ~ (succ(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ leq(v2, v3) | leq(v0, v1)) & % 259.66/56.20 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (succ(v1) = v3) | % 259.66/56.20 ~ (succ(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ leq(v0, v1) | leq(v2, v3)) % 259.66/56.20 % 259.66/56.20 (pred_minus_1) % 259.66/56.21 $i(n1) & ! [v0: $i] : ! [v1: $i] : ( ~ (minus(v0, n1) = v1) | ~ $i(v0) | % 259.66/56.21 (pred(v0) = v1 & $i(v1))) % 259.66/56.21 % 259.66/56.21 (pred_succ) % 259.66/56.21 ! [v0: $i] : ! [v1: $i] : ( ~ (succ(v0) = v1) | ~ $i(v0) | pred(v1) = v0) % 259.66/56.21 % 259.66/56.21 (quaternion_ds1_symm_0005) % 260.18/56.22 $i(id_ds1_filter) & $i(pminus_ds1_filter) & $i(r_ds1_filter) & % 260.18/56.22 $i(q_ds1_filter) & $i(n6) & $i(n999) & $i(pv57) & $i(pv5) & $i(n3) & $i(n1) & % 260.18/56.22 $i(n0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 260.18/56.22 ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: % 260.18/56.22 $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : ? [v15: % 260.18/56.22 $i] : ? [v16: $i] : ? [v17: $i] : ? [v18: $i] : ? [v19: $i] : ? [v20: % 260.18/56.22 $i] : ? [v21: $i] : (minus(n6, n1) = v1 & minus(n999, n1) = v0 & % 260.18/56.22 minus(pv57, n1) = v3 & minus(n3, n1) = v2 & $i(v19) & $i(v18) & $i(v15) & % 260.18/56.22 $i(v14) & $i(v11) & $i(v10) & $i(v7) & $i(v6) & $i(v3) & $i(v2) & $i(v1) & % 260.18/56.22 $i(v0) & leq(pv57, v1) & leq(pv5, v0) & leq(n0, pv57) & leq(n0, pv5) & ! % 260.18/56.22 [v22: $i] : ! [v23: $i] : ! [v24: $i] : ( ~ (a_select3(id_ds1_filter, v22, % 260.18/56.22 v23) = v24) | ~ $i(v23) | ~ $i(v22) | ~ leq(v23, v1) | ~ leq(v22, % 260.18/56.22 v3) | ~ leq(n0, v23) | ~ leq(n0, v22) | (a_select3(id_ds1_filter, v23, % 260.18/56.22 v22) = v24 & $i(v24))) & ! [v22: $i] : ! [v23: $i] : ! [v24: $i] : % 260.18/56.22 ( ~ (a_select3(id_ds1_filter, v22, v23) = v24) | ~ $i(v23) | ~ $i(v22) | % 260.18/56.22 ~ leq(v23, v1) | ~ leq(v22, pv57) | ~ leq(n0, v23) | ~ leq(n0, v22) | % 260.18/56.22 (a_select3(id_ds1_filter, v23, v22) = v24 & $i(v24))) & ! [v22: $i] : ! % 260.18/56.22 [v23: $i] : ! [v24: $i] : ( ~ (a_select3(pminus_ds1_filter, v22, v23) = % 260.18/56.22 v24) | ~ $i(v23) | ~ $i(v22) | ~ leq(v23, v1) | ~ leq(v22, v1) | ~ % 260.18/56.22 leq(n0, v23) | ~ leq(n0, v22) | (a_select3(pminus_ds1_filter, v23, v22) = % 260.18/56.22 v24 & $i(v24))) & ! [v22: $i] : ! [v23: $i] : ! [v24: $i] : ( ~ % 260.18/56.22 (a_select3(r_ds1_filter, v22, v23) = v24) | ~ $i(v23) | ~ $i(v22) | ~ % 260.18/56.22 leq(v23, v2) | ~ leq(v22, v2) | ~ leq(n0, v23) | ~ leq(n0, v22) | % 260.18/56.22 (a_select3(r_ds1_filter, v23, v22) = v24 & $i(v24))) & ! [v22: $i] : ! % 260.18/56.22 [v23: $i] : ! [v24: $i] : ( ~ (a_select3(q_ds1_filter, v22, v23) = v24) | % 260.18/56.22 ~ $i(v23) | ~ $i(v22) | ~ leq(v23, v1) | ~ leq(v22, v1) | ~ leq(n0, % 260.18/56.22 v23) | ~ leq(n0, v22) | (a_select3(q_ds1_filter, v23, v22) = v24 & % 260.18/56.22 $i(v24))) & (( ~ (v21 = v20) & a_select3(q_ds1_filter, v19, v18) = v21 & % 260.18/56.22 a_select3(q_ds1_filter, v18, v19) = v20 & $i(v21) & $i(v20) & leq(v19, % 260.18/56.22 v1) & leq(v18, v1) & leq(n0, v19) & leq(n0, v18)) | ( ~ (v17 = v16) & % 260.18/56.22 a_select3(r_ds1_filter, v15, v14) = v17 & a_select3(r_ds1_filter, v14, % 260.18/56.22 v15) = v16 & $i(v17) & $i(v16) & leq(v15, v2) & leq(v14, v2) & leq(n0, % 260.18/56.22 v15) & leq(n0, v14)) | ( ~ (v13 = v12) & a_select3(pminus_ds1_filter, % 260.18/56.22 v11, v10) = v13 & a_select3(pminus_ds1_filter, v10, v11) = v12 & % 260.18/56.22 $i(v13) & $i(v12) & leq(v11, v1) & leq(v10, v1) & leq(n0, v11) & leq(n0, % 260.18/56.22 v10)) | ( ~ (v9 = v8) & minus(v4, n1) = v5 & plus(n1, pv57) = v4 & % 260.18/56.22 a_select3(id_ds1_filter, v7, v6) = v9 & a_select3(id_ds1_filter, v6, v7) % 260.18/56.22 = v8 & $i(v9) & $i(v8) & $i(v5) & $i(v4) & leq(v7, v1) & leq(v6, v5) & % 260.18/56.22 leq(n0, v7) & leq(n0, v6)))) % 260.18/56.22 % 260.18/56.22 (succ_plus_1_l) % 260.18/56.22 $i(n1) & ! [v0: $i] : ! [v1: $i] : ( ~ (plus(n1, v0) = v1) | ~ $i(v0) | % 260.18/56.22 (succ(v0) = v1 & $i(v1))) % 260.18/56.22 % 260.18/56.22 (succ_pred) % 260.18/56.22 ! [v0: $i] : ! [v1: $i] : ( ~ (pred(v0) = v1) | ~ $i(v0) | succ(v1) = v0) % 260.18/56.22 % 260.18/56.22 (successor_1) % 260.18/56.23 succ(n0) = n1 & $i(n1) & $i(n0) % 260.18/56.23 % 260.18/56.23 (successor_2) % 260.18/56.23 $i(n2) & $i(n0) & ? [v0: $i] : (succ(v0) = n2 & succ(n0) = v0 & $i(v0)) % 260.18/56.23 % 260.18/56.23 (successor_3) % 260.18/56.23 $i(n3) & $i(n0) & ? [v0: $i] : ? [v1: $i] : (succ(v1) = n3 & succ(v0) = v1 & % 260.18/56.23 succ(n0) = v0 & $i(v1) & $i(v0)) % 260.18/56.23 % 260.18/56.23 (successor_4) % 260.18/56.23 $i(n4) & $i(n0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (succ(v2) = n4 & % 260.18/56.23 succ(v1) = v2 & succ(v0) = v1 & succ(n0) = v0 & $i(v2) & $i(v1) & $i(v0)) % 260.18/56.23 % 260.18/56.23 (successor_5) % 260.18/56.23 $i(n5) & $i(n0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 260.18/56.23 (succ(v3) = n5 & succ(v2) = v3 & succ(v1) = v2 & succ(v0) = v1 & succ(n0) = v0 % 260.18/56.23 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 260.18/56.23 % 260.18/56.23 (successor_6) % 260.18/56.23 $i(n6) & $i(n0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? % 260.18/56.23 [v4: $i] : (succ(v4) = n6 & succ(v3) = v4 & succ(v2) = v3 & succ(v1) = v2 & % 260.18/56.23 succ(v0) = v1 & succ(n0) = v0 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 260.18/56.23 % 260.18/56.23 (transitivity_gt) % 260.18/56.23 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 260.18/56.23 ~ gt(v1, v2) | ~ gt(v0, v1) | gt(v0, v2)) % 260.18/56.23 % 260.18/56.23 (transitivity_leq) % 260.18/56.23 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 260.18/56.23 ~ leq(v1, v2) | ~ leq(v0, v1) | leq(v0, v2)) % 260.18/56.23 % 260.18/56.23 (function-axioms) % 260.18/56.24 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 260.18/56.24 $i] : (v1 = v0 | ~ (tptp_update3(v5, v4, v3, v2) = v1) | ~ % 260.18/56.24 (tptp_update3(v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 260.18/56.24 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_update2(v4, v3, v2) = % 260.18/56.24 v1) | ~ (tptp_update2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 260.18/56.24 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (sum(v4, v3, v2) = v1) | % 260.18/56.24 ~ (sum(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 260.18/56.24 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_const_array2(v4, v3, v2) = v1) | % 260.18/56.24 ~ (tptp_const_array2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 260.18/56.24 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (a_select3(v4, v3, v2) = % 260.18/56.24 v1) | ~ (a_select3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 260.18/56.24 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (minus(v3, v2) = v1) | ~ (minus(v3, % 260.18/56.24 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 260.18/56.24 = v0 | ~ (plus(v3, v2) = v1) | ~ (plus(v3, v2) = v0)) & ! [v0: $i] : ! % 260.18/56.24 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (tptp_mmul(v3, v2) = v1) % 260.18/56.24 | ~ (tptp_mmul(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 260.18/56.24 ! [v3: $i] : (v1 = v0 | ~ (tptp_msub(v3, v2) = v1) | ~ (tptp_msub(v3, v2) = % 260.18/56.24 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 260.18/56.24 ~ (tptp_madd(v3, v2) = v1) | ~ (tptp_madd(v3, v2) = v0)) & ! [v0: $i] : ! % 260.18/56.24 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (dim(v3, v2) = v1) | ~ % 260.18/56.24 (dim(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 260.18/56.24 : (v1 = v0 | ~ (tptp_const_array1(v3, v2) = v1) | ~ (tptp_const_array1(v3, % 260.18/56.24 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 260.18/56.24 = v0 | ~ (a_select2(v3, v2) = v1) | ~ (a_select2(v3, v2) = v0)) & ! [v0: % 260.18/56.24 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 260.18/56.24 (uniform_int_rnd(v3, v2) = v1) | ~ (uniform_int_rnd(v3, v2) = v0)) & ! % 260.18/56.24 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (inv(v2) = v1) | ~ % 260.18/56.24 (inv(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 260.18/56.24 (trans(v2) = v1) | ~ (trans(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 260.18/56.24 [v2: $i] : (v1 = v0 | ~ (succ(v2) = v1) | ~ (succ(v2) = v0)) & ! [v0: $i] : % 260.18/56.24 ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (pred(v2) = v1) | ~ (pred(v2) = % 260.18/56.24 v0)) % 260.18/56.24 % 260.18/56.24 Further assumptions not needed in the proof: % 260.18/56.24 -------------------------------------------- % 260.18/56.24 const_array1_select, const_array2_select, defuse, gt_0_tptp_minus_1, gt_1_0, % 260.18/56.24 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, % 260.18/56.24 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, % 260.18/56.24 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, % 260.18/56.24 gt_6_3, gt_6_4, gt_6_tptp_minus_1, gt_999_0, gt_999_1, gt_999_2, gt_999_3, % 260.18/56.24 gt_999_4, gt_999_5, gt_999_6, gt_999_tptp_minus_1, leq_geq, leq_minus, lt_gt, % 260.18/56.24 matrix_symm_aba1, matrix_symm_aba2, matrix_symm_add, matrix_symm_inv, % 260.18/56.24 matrix_symm_joseph_update, matrix_symm_sub, matrix_symm_trans, % 260.18/56.24 matrix_symm_update_diagonal, reflexivity_leq, sel2_update_1, sel2_update_2, % 260.18/56.24 sel2_update_3, sel3_update_1, sel3_update_2, sel3_update_3, succ_plus_1_r, % 260.18/56.24 succ_plus_2_l, succ_plus_2_r, succ_plus_3_l, succ_plus_3_r, succ_plus_4_l, % 260.18/56.24 succ_plus_4_r, succ_plus_5_l, succ_plus_5_r, succ_tptp_minus_1, sum_plus_base, % 260.18/56.24 sum_plus_base_float, totality, ttrue, uniform_int_rand_ranges_hi, % 260.18/56.24 uniform_int_rand_ranges_lo % 260.18/56.24 % 260.18/56.24 Those formulas are unsatisfiable: % 260.18/56.24 --------------------------------- % 260.18/56.24 % 260.18/56.24 Begin of proof % 260.18/56.25 | % 260.18/56.25 | ALPHA: (leq_gt_pred) implies: % 260.18/56.25 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (pred(v1) = v2) | ~ % 260.18/56.25 | $i(v1) | ~ $i(v0) | ~ gt(v1, v0) | leq(v0, v2)) % 260.18/56.25 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (pred(v1) = v2) | ~ % 260.18/56.25 | $i(v1) | ~ $i(v0) | ~ leq(v0, v2) | gt(v1, v0)) % 260.18/56.25 | % 260.18/56.25 | ALPHA: (leq_succ_gt_equiv) implies: % 260.18/56.25 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (succ(v1) = v2) | ~ % 260.18/56.25 | $i(v1) | ~ $i(v0) | ~ leq(v0, v1) | gt(v2, v0)) % 260.18/56.25 | % 260.18/56.25 | ALPHA: (succ_plus_1_l) implies: % 260.18/56.25 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (plus(n1, v0) = v1) | ~ $i(v0) | % 260.18/56.25 | (succ(v0) = v1 & $i(v1))) % 260.18/56.25 | % 260.18/56.25 | ALPHA: (pred_minus_1) implies: % 260.18/56.25 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (minus(v0, n1) = v1) | ~ $i(v0) | % 260.18/56.25 | (pred(v0) = v1 & $i(v1))) % 260.18/56.25 | % 260.18/56.25 | ALPHA: (leq_succ_succ) implies: % 260.18/56.25 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (succ(v1) = % 260.18/56.25 | v3) | ~ (succ(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ leq(v0, v1) | % 260.18/56.25 | leq(v2, v3)) % 260.18/56.25 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (succ(v1) = % 260.18/56.25 | v3) | ~ (succ(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ leq(v2, v3) | % 260.18/56.25 | leq(v0, v1)) % 260.18/56.25 | % 260.18/56.25 | ALPHA: (gt_6_5) implies: % 260.18/56.25 | (8) gt(n6, n5) % 260.18/56.25 | % 260.18/56.25 | ALPHA: (finite_domain_4) implies: % 260.18/56.25 | (9) ! [v0: $i] : (v0 = n4 | v0 = n3 | v0 = n2 | v0 = n1 | v0 = n0 | ~ % 260.18/56.25 | $i(v0) | ~ leq(v0, n4) | ~ leq(n0, v0)) % 260.18/56.25 | % 260.18/56.25 | ALPHA: (finite_domain_5) implies: % 260.18/56.25 | (10) ! [v0: $i] : (v0 = n5 | v0 = n4 | v0 = n3 | v0 = n2 | v0 = n1 | v0 = % 260.18/56.25 | n0 | ~ $i(v0) | ~ leq(v0, n5) | ~ leq(n0, v0)) % 260.18/56.25 | % 260.18/56.25 | ALPHA: (finite_domain_6) implies: % 260.18/56.26 | (11) ! [v0: $i] : (v0 = n6 | v0 = n5 | v0 = n4 | v0 = n3 | v0 = n2 | v0 = % 260.18/56.26 | n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0, n6) | ~ leq(n0, v0)) % 260.18/56.26 | % 260.18/56.26 | ALPHA: (finite_domain_0) implies: % 260.18/56.26 | (12) ! [v0: $i] : (v0 = n0 | ~ $i(v0) | ~ leq(v0, n0) | ~ leq(n0, v0)) % 260.18/56.26 | % 260.18/56.26 | ALPHA: (finite_domain_1) implies: % 260.18/56.26 | (13) ! [v0: $i] : (v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0, n1) | ~ % 260.18/56.26 | leq(n0, v0)) % 260.18/56.26 | % 260.18/56.26 | ALPHA: (finite_domain_2) implies: % 260.42/56.26 | (14) ! [v0: $i] : (v0 = n2 | v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0, % 260.42/56.26 | n2) | ~ leq(n0, v0)) % 260.42/56.26 | % 260.42/56.26 | ALPHA: (finite_domain_3) implies: % 260.42/56.26 | (15) ! [v0: $i] : (v0 = n3 | v0 = n2 | v0 = n1 | v0 = n0 | ~ $i(v0) | ~ % 260.42/56.26 | leq(v0, n3) | ~ leq(n0, v0)) % 260.42/56.26 | % 260.42/56.26 | ALPHA: (successor_4) implies: % 260.42/56.26 | (16) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (succ(v2) = n4 & succ(v1) = % 260.42/56.26 | v2 & succ(v0) = v1 & succ(n0) = v0 & $i(v2) & $i(v1) & $i(v0)) % 260.42/56.26 | % 260.42/56.26 | ALPHA: (successor_5) implies: % 260.42/56.26 | (17) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (succ(v3) = n5 % 260.42/56.26 | & succ(v2) = v3 & succ(v1) = v2 & succ(v0) = v1 & succ(n0) = v0 & % 260.42/56.26 | $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 260.42/56.26 | % 260.42/56.26 | ALPHA: (successor_6) implies: % 260.42/56.26 | (18) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 260.42/56.26 | (succ(v4) = n6 & succ(v3) = v4 & succ(v2) = v3 & succ(v1) = v2 & % 260.42/56.26 | succ(v0) = v1 & succ(n0) = v0 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & % 260.42/56.26 | $i(v0)) % 260.42/56.26 | % 260.42/56.26 | ALPHA: (successor_1) implies: % 260.42/56.26 | (19) succ(n0) = n1 % 260.42/56.26 | % 260.42/56.26 | ALPHA: (successor_2) implies: % 260.42/56.26 | (20) ? [v0: $i] : (succ(v0) = n2 & succ(n0) = v0 & $i(v0)) % 260.42/56.26 | % 260.42/56.26 | ALPHA: (successor_3) implies: % 260.42/56.26 | (21) ? [v0: $i] : ? [v1: $i] : (succ(v1) = n3 & succ(v0) = v1 & succ(n0) % 260.42/56.26 | = v0 & $i(v1) & $i(v0)) % 260.42/56.26 | % 260.42/56.26 | ALPHA: (quaternion_ds1_symm_0005) implies: % 260.42/56.26 | (22) $i(n0) % 260.42/56.26 | (23) $i(pv5) % 260.42/56.26 | (24) $i(pv57) % 260.42/56.26 | (25) $i(n6) % 260.42/56.27 | (26) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 260.42/56.27 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : % 260.42/56.27 | ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: % 260.42/56.27 | $i] : ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? [v18: $i] : ? % 260.42/56.27 | [v19: $i] : ? [v20: $i] : ? [v21: $i] : (minus(n6, n1) = v1 & % 260.42/56.27 | minus(n999, n1) = v0 & minus(pv57, n1) = v3 & minus(n3, n1) = v2 & % 260.42/56.27 | $i(v19) & $i(v18) & $i(v15) & $i(v14) & $i(v11) & $i(v10) & $i(v7) & % 260.42/56.27 | $i(v6) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & leq(pv57, v1) & % 260.42/56.27 | leq(pv5, v0) & leq(n0, pv57) & leq(n0, pv5) & ! [v22: $i] : ! % 260.42/56.27 | [v23: $i] : ! [v24: $i] : ( ~ (a_select3(id_ds1_filter, v22, v23) = % 260.42/56.27 | v24) | ~ $i(v23) | ~ $i(v22) | ~ leq(v23, v1) | ~ leq(v22, % 260.42/56.27 | v3) | ~ leq(n0, v23) | ~ leq(n0, v22) | % 260.42/56.27 | (a_select3(id_ds1_filter, v23, v22) = v24 & $i(v24))) & ! [v22: % 260.42/56.27 | $i] : ! [v23: $i] : ! [v24: $i] : ( ~ (a_select3(id_ds1_filter, % 260.42/56.27 | v22, v23) = v24) | ~ $i(v23) | ~ $i(v22) | ~ leq(v23, v1) | % 260.42/56.27 | ~ leq(v22, pv57) | ~ leq(n0, v23) | ~ leq(n0, v22) | % 260.42/56.27 | (a_select3(id_ds1_filter, v23, v22) = v24 & $i(v24))) & ! [v22: % 260.42/56.27 | $i] : ! [v23: $i] : ! [v24: $i] : ( ~ % 260.42/56.27 | (a_select3(pminus_ds1_filter, v22, v23) = v24) | ~ $i(v23) | ~ % 260.42/56.27 | $i(v22) | ~ leq(v23, v1) | ~ leq(v22, v1) | ~ leq(n0, v23) | ~ % 260.42/56.27 | leq(n0, v22) | (a_select3(pminus_ds1_filter, v23, v22) = v24 & % 260.42/56.27 | $i(v24))) & ! [v22: $i] : ! [v23: $i] : ! [v24: $i] : ( ~ % 260.42/56.27 | (a_select3(r_ds1_filter, v22, v23) = v24) | ~ $i(v23) | ~ % 260.42/56.27 | $i(v22) | ~ leq(v23, v2) | ~ leq(v22, v2) | ~ leq(n0, v23) | ~ % 260.42/56.27 | leq(n0, v22) | (a_select3(r_ds1_filter, v23, v22) = v24 & % 260.42/56.27 | $i(v24))) & ! [v22: $i] : ! [v23: $i] : ! [v24: $i] : ( ~ % 260.42/56.27 | (a_select3(q_ds1_filter, v22, v23) = v24) | ~ $i(v23) | ~ % 260.42/56.27 | $i(v22) | ~ leq(v23, v1) | ~ leq(v22, v1) | ~ leq(n0, v23) | ~ % 260.42/56.27 | leq(n0, v22) | (a_select3(q_ds1_filter, v23, v22) = v24 & % 260.42/56.27 | $i(v24))) & (( ~ (v21 = v20) & a_select3(q_ds1_filter, v19, v18) % 260.42/56.27 | = v21 & a_select3(q_ds1_filter, v18, v19) = v20 & $i(v21) & % 260.42/56.27 | $i(v20) & leq(v19, v1) & leq(v18, v1) & leq(n0, v19) & leq(n0, % 260.42/56.27 | v18)) | ( ~ (v17 = v16) & a_select3(r_ds1_filter, v15, v14) = % 260.42/56.27 | v17 & a_select3(r_ds1_filter, v14, v15) = v16 & $i(v17) & % 260.42/56.27 | $i(v16) & leq(v15, v2) & leq(v14, v2) & leq(n0, v15) & leq(n0, % 260.42/56.27 | v14)) | ( ~ (v13 = v12) & a_select3(pminus_ds1_filter, v11, % 260.42/56.27 | v10) = v13 & a_select3(pminus_ds1_filter, v10, v11) = v12 & % 260.42/56.27 | $i(v13) & $i(v12) & leq(v11, v1) & leq(v10, v1) & leq(n0, v11) & % 260.42/56.27 | leq(n0, v10)) | ( ~ (v9 = v8) & minus(v4, n1) = v5 & plus(n1, % 260.42/56.27 | pv57) = v4 & a_select3(id_ds1_filter, v7, v6) = v9 & % 260.42/56.27 | a_select3(id_ds1_filter, v6, v7) = v8 & $i(v9) & $i(v8) & $i(v5) % 260.42/56.27 | & $i(v4) & leq(v7, v1) & leq(v6, v5) & leq(n0, v7) & leq(n0, % 260.42/56.27 | v6)))) % 260.42/56.27 | % 260.42/56.27 | ALPHA: (function-axioms) implies: % 260.42/56.28 | (27) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (pred(v2) = % 260.42/56.28 | v1) | ~ (pred(v2) = v0)) % 260.42/56.28 | (28) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (succ(v2) = % 260.42/56.28 | v1) | ~ (succ(v2) = v0)) % 260.42/56.28 | (29) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 260.42/56.28 | (minus(v3, v2) = v1) | ~ (minus(v3, v2) = v0)) % 260.42/56.28 | (30) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 260.42/56.28 | (v1 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) % 260.42/56.28 | = v0)) % 260.42/56.28 | % 260.42/56.28 | DELTA: instantiating (20) with fresh symbol all_55_0 gives: % 260.42/56.28 | (31) succ(all_55_0) = n2 & succ(n0) = all_55_0 & $i(all_55_0) % 260.42/56.28 | % 260.42/56.28 | ALPHA: (31) implies: % 260.42/56.28 | (32) $i(all_55_0) % 260.42/56.28 | (33) succ(n0) = all_55_0 % 260.42/56.28 | (34) succ(all_55_0) = n2 % 260.42/56.28 | % 260.42/56.28 | DELTA: instantiating (21) with fresh symbols all_57_0, all_57_1 gives: % 260.42/56.28 | (35) succ(all_57_0) = n3 & succ(all_57_1) = all_57_0 & succ(n0) = all_57_1 % 260.42/56.28 | & $i(all_57_0) & $i(all_57_1) % 260.42/56.28 | % 260.42/56.28 | ALPHA: (35) implies: % 260.42/56.28 | (36) $i(all_57_0) % 260.42/56.28 | (37) succ(n0) = all_57_1 % 260.42/56.28 | (38) succ(all_57_1) = all_57_0 % 260.42/56.28 | (39) succ(all_57_0) = n3 % 260.42/56.28 | % 260.42/56.28 | DELTA: instantiating (16) with fresh symbols all_60_0, all_60_1, all_60_2 % 260.42/56.28 | gives: % 260.42/56.28 | (40) succ(all_60_0) = n4 & succ(all_60_1) = all_60_0 & succ(all_60_2) = % 260.42/56.28 | all_60_1 & succ(n0) = all_60_2 & $i(all_60_0) & $i(all_60_1) & % 260.42/56.28 | $i(all_60_2) % 260.42/56.28 | % 260.42/56.28 | ALPHA: (40) implies: % 260.42/56.28 | (41) $i(all_60_0) % 260.42/56.28 | (42) succ(n0) = all_60_2 % 260.42/56.28 | (43) succ(all_60_2) = all_60_1 % 260.42/56.28 | (44) succ(all_60_1) = all_60_0 % 260.42/56.28 | (45) succ(all_60_0) = n4 % 260.42/56.28 | % 260.42/56.28 | DELTA: instantiating (17) with fresh symbols all_62_0, all_62_1, all_62_2, % 260.42/56.28 | all_62_3 gives: % 260.42/56.28 | (46) succ(all_62_0) = n5 & succ(all_62_1) = all_62_0 & succ(all_62_2) = % 260.42/56.28 | all_62_1 & succ(all_62_3) = all_62_2 & succ(n0) = all_62_3 & % 260.42/56.28 | $i(all_62_0) & $i(all_62_1) & $i(all_62_2) & $i(all_62_3) % 260.42/56.28 | % 260.42/56.28 | ALPHA: (46) implies: % 260.42/56.28 | (47) $i(all_62_0) % 260.42/56.28 | (48) succ(n0) = all_62_3 % 260.42/56.28 | (49) succ(all_62_3) = all_62_2 % 260.42/56.28 | (50) succ(all_62_2) = all_62_1 % 260.42/56.28 | (51) succ(all_62_1) = all_62_0 % 260.42/56.28 | (52) succ(all_62_0) = n5 % 260.42/56.28 | % 260.42/56.28 | DELTA: instantiating (18) with fresh symbols all_64_0, all_64_1, all_64_2, % 260.42/56.28 | all_64_3, all_64_4 gives: % 260.42/56.28 | (53) succ(all_64_0) = n6 & succ(all_64_1) = all_64_0 & succ(all_64_2) = % 260.42/56.28 | all_64_1 & succ(all_64_3) = all_64_2 & succ(all_64_4) = all_64_3 & % 260.42/56.28 | succ(n0) = all_64_4 & $i(all_64_0) & $i(all_64_1) & $i(all_64_2) & % 260.42/56.28 | $i(all_64_3) & $i(all_64_4) % 260.42/56.28 | % 260.42/56.28 | ALPHA: (53) implies: % 260.42/56.28 | (54) $i(all_64_0) % 260.42/56.28 | (55) succ(n0) = all_64_4 % 260.42/56.29 | (56) succ(all_64_4) = all_64_3 % 260.42/56.29 | (57) succ(all_64_3) = all_64_2 % 260.42/56.29 | (58) succ(all_64_2) = all_64_1 % 260.42/56.29 | (59) succ(all_64_1) = all_64_0 % 260.42/56.29 | (60) succ(all_64_0) = n6 % 260.42/56.29 | % 260.42/56.29 | DELTA: instantiating (26) with fresh symbols all_74_0, all_74_1, all_74_2, % 260.42/56.29 | all_74_3, all_74_4, all_74_5, all_74_6, all_74_7, all_74_8, all_74_9, % 260.42/56.29 | all_74_10, all_74_11, all_74_12, all_74_13, all_74_14, all_74_15, % 260.42/56.29 | all_74_16, all_74_17, all_74_18, all_74_19, all_74_20, all_74_21 gives: % 260.42/56.29 | (61) minus(n6, n1) = all_74_20 & minus(n999, n1) = all_74_21 & minus(pv57, % 260.42/56.29 | n1) = all_74_18 & minus(n3, n1) = all_74_19 & $i(all_74_2) & % 260.42/56.29 | $i(all_74_3) & $i(all_74_6) & $i(all_74_7) & $i(all_74_10) & % 260.42/56.29 | $i(all_74_11) & $i(all_74_14) & $i(all_74_15) & $i(all_74_18) & % 260.42/56.29 | $i(all_74_19) & $i(all_74_20) & $i(all_74_21) & leq(pv57, all_74_20) & % 260.42/56.29 | leq(pv5, all_74_21) & leq(n0, pv57) & leq(n0, pv5) & ! [v0: $i] : ! % 260.42/56.29 | [v1: $i] : ! [v2: $i] : ( ~ (a_select3(id_ds1_filter, v0, v1) = v2) | % 260.42/56.29 | ~ $i(v1) | ~ $i(v0) | ~ leq(v1, all_74_20) | ~ leq(v0, % 260.42/56.29 | all_74_18) | ~ leq(n0, v1) | ~ leq(n0, v0) | % 260.42/56.29 | (a_select3(id_ds1_filter, v1, v0) = v2 & $i(v2))) & ! [v0: $i] : ! % 260.42/56.29 | [v1: $i] : ! [v2: $i] : ( ~ (a_select3(id_ds1_filter, v0, v1) = v2) | % 260.42/56.29 | ~ $i(v1) | ~ $i(v0) | ~ leq(v1, all_74_20) | ~ leq(v0, pv57) | % 260.42/56.29 | ~ leq(n0, v1) | ~ leq(n0, v0) | (a_select3(id_ds1_filter, v1, v0) = % 260.42/56.29 | v2 & $i(v2))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 260.42/56.29 | (a_select3(pminus_ds1_filter, v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) % 260.42/56.29 | | ~ leq(v1, all_74_20) | ~ leq(v0, all_74_20) | ~ leq(n0, v1) | % 260.42/56.29 | ~ leq(n0, v0) | (a_select3(pminus_ds1_filter, v1, v0) = v2 & % 260.42/56.30 | $i(v2))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 260.42/56.30 | (a_select3(r_ds1_filter, v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 260.42/56.30 | leq(v1, all_74_19) | ~ leq(v0, all_74_19) | ~ leq(n0, v1) | ~ % 260.42/56.30 | leq(n0, v0) | (a_select3(r_ds1_filter, v1, v0) = v2 & $i(v2))) & ! % 260.42/56.30 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (a_select3(q_ds1_filter, % 260.42/56.30 | v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ leq(v1, all_74_20) | % 260.42/56.30 | ~ leq(v0, all_74_20) | ~ leq(n0, v1) | ~ leq(n0, v0) | % 260.42/56.30 | (a_select3(q_ds1_filter, v1, v0) = v2 & $i(v2))) & (( ~ (all_74_0 = % 260.42/56.30 | all_74_1) & a_select3(q_ds1_filter, all_74_2, all_74_3) = % 260.42/56.30 | all_74_0 & a_select3(q_ds1_filter, all_74_3, all_74_2) = all_74_1 % 260.42/56.30 | & $i(all_74_0) & $i(all_74_1) & leq(all_74_2, all_74_20) & % 260.42/56.30 | leq(all_74_3, all_74_20) & leq(n0, all_74_2) & leq(n0, all_74_3)) % 260.42/56.30 | | ( ~ (all_74_4 = all_74_5) & a_select3(r_ds1_filter, all_74_6, % 260.42/56.30 | all_74_7) = all_74_4 & a_select3(r_ds1_filter, all_74_7, % 260.42/56.30 | all_74_6) = all_74_5 & $i(all_74_4) & $i(all_74_5) & % 260.42/56.30 | leq(all_74_6, all_74_19) & leq(all_74_7, all_74_19) & leq(n0, % 260.42/56.30 | all_74_6) & leq(n0, all_74_7)) | ( ~ (all_74_8 = all_74_9) & % 260.42/56.30 | a_select3(pminus_ds1_filter, all_74_10, all_74_11) = all_74_8 & % 260.42/56.30 | a_select3(pminus_ds1_filter, all_74_11, all_74_10) = all_74_9 & % 260.42/56.30 | $i(all_74_8) & $i(all_74_9) & leq(all_74_10, all_74_20) & % 260.42/56.30 | leq(all_74_11, all_74_20) & leq(n0, all_74_10) & leq(n0, % 260.42/56.30 | all_74_11)) | ( ~ (all_74_12 = all_74_13) & minus(all_74_17, n1) % 260.42/56.30 | = all_74_16 & plus(n1, pv57) = all_74_17 & % 260.42/56.30 | a_select3(id_ds1_filter, all_74_14, all_74_15) = all_74_12 & % 260.42/56.30 | a_select3(id_ds1_filter, all_74_15, all_74_14) = all_74_13 & % 260.42/56.30 | $i(all_74_12) & $i(all_74_13) & $i(all_74_16) & $i(all_74_17) & % 260.42/56.30 | leq(all_74_14, all_74_20) & leq(all_74_15, all_74_16) & leq(n0, % 260.42/56.30 | all_74_14) & leq(n0, all_74_15))) % 260.42/56.30 | % 260.42/56.30 | ALPHA: (61) implies: % 260.42/56.30 | (62) leq(n0, pv5) % 260.42/56.30 | (63) leq(n0, pv57) % 260.42/56.30 | (64) leq(pv57, all_74_20) % 260.42/56.30 | (65) $i(all_74_20) % 260.42/56.30 | (66) $i(all_74_15) % 260.42/56.30 | (67) $i(all_74_14) % 260.42/56.30 | (68) $i(all_74_11) % 260.42/56.30 | (69) $i(all_74_10) % 260.42/56.30 | (70) $i(all_74_7) % 260.42/56.30 | (71) $i(all_74_6) % 260.42/56.30 | (72) $i(all_74_3) % 260.42/56.30 | (73) $i(all_74_2) % 260.42/56.30 | (74) minus(n3, n1) = all_74_19 % 260.42/56.30 | (75) minus(pv57, n1) = all_74_18 % 260.42/56.30 | (76) minus(n6, n1) = all_74_20 % 260.42/56.30 | (77) ( ~ (all_74_0 = all_74_1) & a_select3(q_ds1_filter, all_74_2, % 260.42/56.30 | all_74_3) = all_74_0 & a_select3(q_ds1_filter, all_74_3, all_74_2) % 260.42/56.30 | = all_74_1 & $i(all_74_0) & $i(all_74_1) & leq(all_74_2, all_74_20) % 260.42/56.30 | & leq(all_74_3, all_74_20) & leq(n0, all_74_2) & leq(n0, all_74_3)) % 260.42/56.30 | | ( ~ (all_74_4 = all_74_5) & a_select3(r_ds1_filter, all_74_6, % 260.42/56.30 | all_74_7) = all_74_4 & a_select3(r_ds1_filter, all_74_7, all_74_6) % 260.42/56.30 | = all_74_5 & $i(all_74_4) & $i(all_74_5) & leq(all_74_6, all_74_19) % 260.42/56.30 | & leq(all_74_7, all_74_19) & leq(n0, all_74_6) & leq(n0, all_74_7)) % 260.42/56.30 | | ( ~ (all_74_8 = all_74_9) & a_select3(pminus_ds1_filter, all_74_10, % 260.42/56.30 | all_74_11) = all_74_8 & a_select3(pminus_ds1_filter, all_74_11, % 260.42/56.30 | all_74_10) = all_74_9 & $i(all_74_8) & $i(all_74_9) & % 260.42/56.30 | leq(all_74_10, all_74_20) & leq(all_74_11, all_74_20) & leq(n0, % 260.42/56.30 | all_74_10) & leq(n0, all_74_11)) | ( ~ (all_74_12 = all_74_13) & % 260.42/56.30 | minus(all_74_17, n1) = all_74_16 & plus(n1, pv57) = all_74_17 & % 260.42/56.30 | a_select3(id_ds1_filter, all_74_14, all_74_15) = all_74_12 & % 260.42/56.30 | a_select3(id_ds1_filter, all_74_15, all_74_14) = all_74_13 & % 260.42/56.30 | $i(all_74_12) & $i(all_74_13) & $i(all_74_16) & $i(all_74_17) & % 260.42/56.30 | leq(all_74_14, all_74_20) & leq(all_74_15, all_74_16) & leq(n0, % 260.42/56.30 | all_74_14) & leq(n0, all_74_15)) % 260.42/56.30 | (78) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (a_select3(q_ds1_filter, % 260.42/56.30 | v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ leq(v1, all_74_20) | % 260.42/56.30 | ~ leq(v0, all_74_20) | ~ leq(n0, v1) | ~ leq(n0, v0) | % 260.42/56.30 | (a_select3(q_ds1_filter, v1, v0) = v2 & $i(v2))) % 260.42/56.30 | (79) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (a_select3(r_ds1_filter, % 260.42/56.30 | v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ leq(v1, all_74_19) | % 260.42/56.30 | ~ leq(v0, all_74_19) | ~ leq(n0, v1) | ~ leq(n0, v0) | % 260.42/56.30 | (a_select3(r_ds1_filter, v1, v0) = v2 & $i(v2))) % 260.42/56.31 | (80) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 260.42/56.31 | (a_select3(pminus_ds1_filter, v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) % 260.42/56.31 | | ~ leq(v1, all_74_20) | ~ leq(v0, all_74_20) | ~ leq(n0, v1) | % 260.42/56.31 | ~ leq(n0, v0) | (a_select3(pminus_ds1_filter, v1, v0) = v2 & % 260.42/56.31 | $i(v2))) % 260.42/56.31 | (81) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 260.42/56.31 | (a_select3(id_ds1_filter, v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 260.42/56.31 | leq(v1, all_74_20) | ~ leq(v0, pv57) | ~ leq(n0, v1) | ~ leq(n0, % 260.42/56.31 | v0) | (a_select3(id_ds1_filter, v1, v0) = v2 & $i(v2))) % 260.42/56.31 | (82) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 260.42/56.31 | (a_select3(id_ds1_filter, v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 260.42/56.31 | leq(v1, all_74_20) | ~ leq(v0, all_74_18) | ~ leq(n0, v1) | ~ % 260.42/56.31 | leq(n0, v0) | (a_select3(id_ds1_filter, v1, v0) = v2 & $i(v2))) % 260.42/56.31 | % 260.42/56.31 | GROUND_INST: instantiating (28) with all_60_2, all_62_3, n0, simplifying with % 260.42/56.31 | (42), (48) gives: % 260.42/56.31 | (83) all_62_3 = all_60_2 % 260.42/56.31 | % 260.42/56.31 | GROUND_INST: instantiating (28) with all_57_1, all_62_3, n0, simplifying with % 260.42/56.31 | (37), (48) gives: % 260.42/56.31 | (84) all_62_3 = all_57_1 % 260.42/56.31 | % 260.42/56.31 | GROUND_INST: instantiating (28) with all_55_0, all_62_3, n0, simplifying with % 260.42/56.31 | (33), (48) gives: % 260.42/56.31 | (85) all_62_3 = all_55_0 % 260.42/56.31 | % 260.42/56.31 | GROUND_INST: instantiating (28) with all_57_1, all_64_4, n0, simplifying with % 260.42/56.31 | (37), (55) gives: % 260.42/56.31 | (86) all_64_4 = all_57_1 % 260.42/56.31 | % 260.42/56.31 | GROUND_INST: instantiating (28) with n1, all_64_4, n0, simplifying with (19), % 260.42/56.31 | (55) gives: % 260.42/56.31 | (87) all_64_4 = n1 % 260.42/56.31 | % 260.42/56.31 | COMBINE_EQS: (86), (87) imply: % 260.42/56.31 | (88) all_57_1 = n1 % 260.42/56.31 | % 260.42/56.31 | SIMP: (88) implies: % 260.42/56.31 | (89) all_57_1 = n1 % 260.42/56.31 | % 260.42/56.31 | COMBINE_EQS: (83), (85) imply: % 260.42/56.31 | (90) all_60_2 = all_55_0 % 260.42/56.31 | % 260.42/56.31 | COMBINE_EQS: (83), (84) imply: % 260.42/56.31 | (91) all_60_2 = all_57_1 % 260.42/56.31 | % 260.42/56.31 | COMBINE_EQS: (90), (91) imply: % 260.42/56.31 | (92) all_57_1 = all_55_0 % 260.42/56.31 | % 260.42/56.31 | SIMP: (92) implies: % 260.42/56.31 | (93) all_57_1 = all_55_0 % 260.42/56.31 | % 260.42/56.31 | COMBINE_EQS: (89), (93) imply: % 260.42/56.31 | (94) all_55_0 = n1 % 260.42/56.31 | % 260.42/56.31 | COMBINE_EQS: (90), (94) imply: % 260.42/56.31 | (95) all_60_2 = n1 % 260.42/56.31 | % 260.42/56.31 | COMBINE_EQS: (83), (95) imply: % 260.42/56.31 | (96) all_62_3 = n1 % 260.42/56.31 | % 260.42/56.31 | REDUCE: (56), (87) imply: % 260.42/56.31 | (97) succ(n1) = all_64_3 % 260.42/56.31 | % 260.42/56.31 | REDUCE: (49), (96) imply: % 260.42/56.31 | (98) succ(n1) = all_62_2 % 260.42/56.31 | % 260.42/56.31 | REDUCE: (43), (95) imply: % 260.42/56.31 | (99) succ(n1) = all_60_1 % 260.42/56.31 | % 260.42/56.31 | REDUCE: (38), (89) imply: % 260.42/56.31 | (100) succ(n1) = all_57_0 % 260.42/56.31 | % 260.42/56.31 | REDUCE: (34), (94) imply: % 260.42/56.31 | (101) succ(n1) = n2 % 260.42/56.31 | % 260.42/56.31 | REDUCE: (32), (94) imply: % 260.42/56.31 | (102) $i(n1) % 260.42/56.31 | % 260.42/56.32 | GROUND_INST: instantiating (28) with all_60_1, all_62_2, n1, simplifying with % 260.42/56.32 | (98), (99) gives: % 260.42/56.32 | (103) all_62_2 = all_60_1 % 260.42/56.32 | % 260.42/56.32 | GROUND_INST: instantiating (28) with all_57_0, all_62_2, n1, simplifying with % 260.42/56.32 | (98), (100) gives: % 260.42/56.32 | (104) all_62_2 = all_57_0 % 260.42/56.32 | % 260.42/56.32 | GROUND_INST: instantiating (28) with all_60_1, all_64_3, n1, simplifying with % 260.42/56.32 | (97), (99) gives: % 260.42/56.32 | (105) all_64_3 = all_60_1 % 260.42/56.32 | % 260.42/56.32 | GROUND_INST: instantiating (28) with n2, all_64_3, n1, simplifying with (97), % 260.42/56.32 | (101) gives: % 260.42/56.32 | (106) all_64_3 = n2 % 260.42/56.32 | % 260.42/56.32 | COMBINE_EQS: (105), (106) imply: % 260.42/56.32 | (107) all_60_1 = n2 % 260.42/56.32 | % 260.42/56.32 | SIMP: (107) implies: % 260.42/56.32 | (108) all_60_1 = n2 % 260.42/56.32 | % 260.42/56.32 | COMBINE_EQS: (103), (104) imply: % 260.42/56.32 | (109) all_60_1 = all_57_0 % 260.42/56.32 | % 260.42/56.32 | SIMP: (109) implies: % 260.42/56.32 | (110) all_60_1 = all_57_0 % 260.42/56.32 | % 260.42/56.32 | COMBINE_EQS: (108), (110) imply: % 260.42/56.32 | (111) all_57_0 = n2 % 260.42/56.32 | % 260.42/56.32 | SIMP: (111) implies: % 260.42/56.32 | (112) all_57_0 = n2 % 260.42/56.32 | % 260.42/56.32 | COMBINE_EQS: (104), (112) imply: % 260.42/56.32 | (113) all_62_2 = n2 % 260.42/56.32 | % 260.42/56.32 | REDUCE: (57), (106) imply: % 260.42/56.32 | (114) succ(n2) = all_64_2 % 260.42/56.32 | % 260.42/56.32 | REDUCE: (50), (113) imply: % 260.42/56.32 | (115) succ(n2) = all_62_1 % 260.42/56.32 | % 260.42/56.32 | REDUCE: (44), (108) imply: % 260.42/56.32 | (116) succ(n2) = all_60_0 % 260.42/56.32 | % 260.42/56.32 | REDUCE: (39), (112) imply: % 260.42/56.32 | (117) succ(n2) = n3 % 260.42/56.32 | % 260.42/56.32 | REDUCE: (36), (112) imply: % 260.42/56.32 | (118) $i(n2) % 260.42/56.32 | % 260.42/56.32 | GROUND_INST: instantiating (28) with all_60_0, all_62_1, n2, simplifying with % 260.42/56.32 | (115), (116) gives: % 260.42/56.32 | (119) all_62_1 = all_60_0 % 260.42/56.32 | % 260.42/56.32 | GROUND_INST: instantiating (28) with all_62_1, all_64_2, n2, simplifying with % 260.42/56.32 | (114), (115) gives: % 260.42/56.32 | (120) all_64_2 = all_62_1 % 260.42/56.32 | % 260.42/56.32 | GROUND_INST: instantiating (28) with n3, all_64_2, n2, simplifying with (114), % 260.42/56.32 | (117) gives: % 260.42/56.32 | (121) all_64_2 = n3 % 260.42/56.32 | % 260.42/56.32 | COMBINE_EQS: (120), (121) imply: % 260.42/56.32 | (122) all_62_1 = n3 % 260.42/56.32 | % 260.42/56.32 | SIMP: (122) implies: % 260.42/56.32 | (123) all_62_1 = n3 % 260.42/56.32 | % 260.42/56.32 | COMBINE_EQS: (119), (123) imply: % 260.42/56.32 | (124) all_60_0 = n3 % 260.42/56.32 | % 260.42/56.32 | SIMP: (124) implies: % 260.42/56.32 | (125) all_60_0 = n3 % 260.42/56.32 | % 260.42/56.32 | REDUCE: (58), (121) imply: % 260.42/56.32 | (126) succ(n3) = all_64_1 % 260.42/56.32 | % 260.42/56.32 | REDUCE: (51), (123) imply: % 260.42/56.32 | (127) succ(n3) = all_62_0 % 260.42/56.32 | % 260.42/56.32 | REDUCE: (45), (125) imply: % 260.42/56.32 | (128) succ(n3) = n4 % 260.42/56.32 | % 260.42/56.32 | REDUCE: (41), (125) imply: % 260.42/56.32 | (129) $i(n3) % 260.42/56.32 | % 260.42/56.32 | GROUND_INST: instantiating (28) with all_62_0, all_64_1, n3, simplifying with % 260.42/56.32 | (126), (127) gives: % 260.42/56.32 | (130) all_64_1 = all_62_0 % 260.42/56.32 | % 260.42/56.32 | GROUND_INST: instantiating (28) with n4, all_64_1, n3, simplifying with (126), % 260.42/56.32 | (128) gives: % 260.42/56.32 | (131) all_64_1 = n4 % 260.42/56.32 | % 260.42/56.32 | COMBINE_EQS: (130), (131) imply: % 260.42/56.32 | (132) all_62_0 = n4 % 260.42/56.32 | % 260.42/56.32 | SIMP: (132) implies: % 260.42/56.32 | (133) all_62_0 = n4 % 260.42/56.32 | % 260.42/56.32 | REDUCE: (59), (131) imply: % 260.42/56.32 | (134) succ(n4) = all_64_0 % 260.42/56.32 | % 260.42/56.32 | REDUCE: (52), (133) imply: % 260.42/56.32 | (135) succ(n4) = n5 % 260.42/56.32 | % 260.42/56.32 | REDUCE: (47), (133) imply: % 260.42/56.32 | (136) $i(n4) % 260.42/56.32 | % 260.42/56.33 | GROUND_INST: instantiating (28) with n5, all_64_0, n4, simplifying with (134), % 260.42/56.33 | (135) gives: % 260.42/56.33 | (137) all_64_0 = n5 % 260.42/56.33 | % 260.42/56.33 | REDUCE: (60), (137) imply: % 260.42/56.33 | (138) succ(n5) = n6 % 260.42/56.33 | % 260.42/56.33 | REDUCE: (54), (137) imply: % 260.42/56.33 | (139) $i(n5) % 260.42/56.33 | % 260.42/56.33 | GROUND_INST: instantiating (leq_gt1) with n5, n6, simplifying with (8), (25), % 260.42/56.33 | (139) gives: % 260.42/56.33 | (140) leq(n5, n6) % 260.42/56.33 | % 260.42/56.33 | GROUND_INST: instantiating (leq_gt2) with n0, pv5, simplifying with (22), % 260.42/56.33 | (23), (62) gives: % 260.42/56.33 | (141) pv5 = n0 | gt(pv5, n0) % 260.42/56.33 | % 260.42/56.33 | GROUND_INST: instantiating (leq_gt2) with n0, pv57, simplifying with (22), % 260.42/56.33 | (24), (63) gives: % 260.42/56.33 | (142) pv57 = n0 | gt(pv57, n0) % 260.42/56.33 | % 260.42/56.33 | GROUND_INST: instantiating (leq_gt2) with pv57, all_74_20, simplifying with % 260.42/56.33 | (24), (64), (65) gives: % 260.42/56.33 | (143) all_74_20 = pv57 | gt(all_74_20, pv57) % 260.42/56.33 | % 260.42/56.33 | GROUND_INST: instantiating (pred_succ) with n0, n1, simplifying with (19), % 260.42/56.33 | (22) gives: % 260.42/56.33 | (144) pred(n1) = n0 % 260.42/56.33 | % 260.42/56.33 | GROUND_INST: instantiating (pred_succ) with n1, n2, simplifying with (101), % 260.42/56.33 | (102) gives: % 260.42/56.33 | (145) pred(n2) = n1 % 260.42/56.33 | % 260.42/56.33 | GROUND_INST: instantiating (pred_succ) with n2, n3, simplifying with (117), % 260.42/56.33 | (118) gives: % 260.42/56.33 | (146) pred(n3) = n2 % 260.42/56.33 | % 260.42/56.33 | GROUND_INST: instantiating (pred_succ) with n3, n4, simplifying with (128), % 260.42/56.33 | (129) gives: % 260.42/56.33 | (147) pred(n4) = n3 % 260.42/56.33 | % 260.42/56.33 | GROUND_INST: instantiating (pred_succ) with n4, n5, simplifying with (135), % 260.42/56.33 | (136) gives: % 260.42/56.33 | (148) pred(n5) = n4 % 260.42/56.33 | % 260.42/56.33 | GROUND_INST: instantiating (pred_succ) with n5, n6, simplifying with (138), % 260.42/56.33 | (139) gives: % 260.42/56.33 | (149) pred(n6) = n5 % 260.42/56.33 | % 260.42/56.33 | GROUND_INST: instantiating (5) with n3, all_74_19, simplifying with (74), % 260.42/56.33 | (129) gives: % 260.42/56.33 | (150) pred(n3) = all_74_19 & $i(all_74_19) % 260.42/56.33 | % 260.42/56.33 | ALPHA: (150) implies: % 260.42/56.33 | (151) $i(all_74_19) % 260.42/56.33 | (152) pred(n3) = all_74_19 % 260.42/56.33 | % 260.42/56.33 | GROUND_INST: instantiating (5) with pv57, all_74_18, simplifying with (24), % 260.42/56.33 | (75) gives: % 260.42/56.33 | (153) pred(pv57) = all_74_18 & $i(all_74_18) % 260.42/56.33 | % 260.42/56.33 | ALPHA: (153) implies: % 260.42/56.33 | (154) $i(all_74_18) % 260.42/56.33 | (155) pred(pv57) = all_74_18 % 260.42/56.33 | % 260.42/56.33 | GROUND_INST: instantiating (5) with n6, all_74_20, simplifying with (25), (76) % 260.42/56.33 | gives: % 260.42/56.33 | (156) pred(n6) = all_74_20 & $i(all_74_20) % 260.42/56.33 | % 260.42/56.33 | ALPHA: (156) implies: % 260.42/56.33 | (157) pred(n6) = all_74_20 % 260.42/56.33 | % 260.42/56.33 | GROUND_INST: instantiating (27) with n2, all_74_19, n3, simplifying with % 260.42/56.33 | (146), (152) gives: % 260.42/56.33 | (158) all_74_19 = n2 % 260.42/56.33 | % 260.42/56.33 | GROUND_INST: instantiating (27) with n5, all_74_20, n6, simplifying with % 260.42/56.33 | (149), (157) gives: % 260.42/56.33 | (159) all_74_20 = n5 % 260.42/56.33 | % 260.42/56.33 | REDUCE: (76), (159) imply: % 260.42/56.33 | (160) minus(n6, n1) = n5 % 260.42/56.33 | % 260.42/56.33 | REDUCE: (74), (158) imply: % 260.42/56.33 | (161) minus(n3, n1) = n2 % 260.42/56.33 | % 260.42/56.33 | REDUCE: (64), (159) imply: % 260.42/56.33 | (162) leq(pv57, n5) % 260.42/56.33 | % 260.42/56.34 | GROUND_INST: instantiating (transitivity_leq) with pv57, n5, n6, simplifying % 260.42/56.34 | with (24), (25), (139), (140), (162) gives: % 260.42/56.34 | (163) leq(pv57, n6) % 260.42/56.34 | % 260.42/56.34 | GROUND_INST: instantiating (10) with pv57, simplifying with (24), (63), (162) % 260.42/56.34 | gives: % 260.42/56.34 | (164) pv57 = n5 | pv57 = n4 | pv57 = n3 | pv57 = n2 | pv57 = n1 | pv57 = n0 % 260.42/56.34 | % 260.42/56.34 | GROUND_INST: instantiating (succ_pred) with pv57, all_74_18, simplifying with % 260.42/56.34 | (24), (155) gives: % 260.42/56.34 | (165) succ(all_74_18) = pv57 % 260.42/56.34 | % 260.42/56.34 | GROUND_INST: instantiating (11) with pv57, simplifying with (24), (63), (163) % 260.42/56.34 | gives: % 260.42/56.34 | (166) n6 = pv57 | pv57 = n5 | pv57 = n4 | pv57 = n3 | pv57 = n2 | pv57 = n1 % 260.42/56.34 | | pv57 = n0 % 260.42/56.34 | % 260.42/56.34 | GROUND_INST: instantiating (7) with all_74_18, n5, pv57, n6, simplifying with % 260.42/56.34 | (138), (139), (154), (163), (165) gives: % 260.42/56.34 | (167) leq(all_74_18, n5) % 260.42/56.34 | % 260.42/56.34 | GROUND_INST: instantiating (7) with all_74_18, n4, pv57, n5, simplifying with % 260.42/56.34 | (135), (136), (154), (162), (165) gives: % 260.42/56.34 | (168) leq(all_74_18, n4) % 260.42/56.34 | % 260.42/56.34 | GROUND_INST: instantiating (gt_succ) with all_74_18, pv57, simplifying with % 260.42/56.34 | (154), (165) gives: % 260.42/56.34 | (169) gt(pv57, all_74_18) % 260.42/56.34 | % 260.42/56.34 | GROUND_INST: instantiating (1) with all_74_18, pv57, all_74_18, simplifying % 260.42/56.34 | with (24), (154), (155), (169) gives: % 260.42/56.34 | (170) leq(all_74_18, all_74_18) % 260.42/56.34 | % 260.42/56.34 | GROUND_INST: instantiating (leq_gt1) with all_74_18, pv57, simplifying with % 260.42/56.34 | (24), (154), (169) gives: % 260.42/56.34 | (171) leq(all_74_18, pv57) % 260.42/56.34 | % 260.42/56.34 | GROUND_INST: instantiating (transitivity_leq) with all_74_18, n5, n6, % 260.42/56.34 | simplifying with (25), (139), (140), (154), (167) gives: % 260.42/56.34 | (172) leq(all_74_18, n6) % 260.42/56.34 | % 260.42/56.34 | GROUND_INST: instantiating (6) with all_74_18, all_74_18, pv57, pv57, % 260.42/56.34 | simplifying with (154), (165), (170) gives: % 260.42/56.34 | (173) leq(pv57, pv57) % 260.42/56.34 | % 260.42/56.34 | BETA: splitting (77) gives: % 260.42/56.34 | % 260.42/56.34 | Case 1: % 260.42/56.34 | | % 260.42/56.34 | | (174) ( ~ (all_74_0 = all_74_1) & a_select3(q_ds1_filter, all_74_2, % 260.42/56.34 | | all_74_3) = all_74_0 & a_select3(q_ds1_filter, all_74_3, % 260.42/56.34 | | all_74_2) = all_74_1 & $i(all_74_0) & $i(all_74_1) & % 260.42/56.34 | | leq(all_74_2, all_74_20) & leq(all_74_3, all_74_20) & leq(n0, % 260.42/56.34 | | all_74_2) & leq(n0, all_74_3)) | ( ~ (all_74_4 = all_74_5) & % 260.42/56.34 | | a_select3(r_ds1_filter, all_74_6, all_74_7) = all_74_4 & % 260.42/56.34 | | a_select3(r_ds1_filter, all_74_7, all_74_6) = all_74_5 & % 260.42/56.34 | | $i(all_74_4) & $i(all_74_5) & leq(all_74_6, all_74_19) & % 260.42/56.34 | | leq(all_74_7, all_74_19) & leq(n0, all_74_6) & leq(n0, all_74_7)) % 260.42/56.34 | | % 260.42/56.34 | | BETA: splitting (174) gives: % 260.42/56.34 | | % 260.42/56.34 | | Case 1: % 260.42/56.34 | | | % 260.42/56.34 | | | (175) ~ (all_74_0 = all_74_1) & a_select3(q_ds1_filter, all_74_2, % 260.42/56.34 | | | all_74_3) = all_74_0 & a_select3(q_ds1_filter, all_74_3, % 260.42/56.34 | | | all_74_2) = all_74_1 & $i(all_74_0) & $i(all_74_1) & % 260.42/56.34 | | | leq(all_74_2, all_74_20) & leq(all_74_3, all_74_20) & leq(n0, % 260.42/56.34 | | | all_74_2) & leq(n0, all_74_3) % 260.42/56.34 | | | % 260.42/56.34 | | | ALPHA: (175) implies: % 260.42/56.34 | | | (176) ~ (all_74_0 = all_74_1) % 260.42/56.34 | | | (177) leq(n0, all_74_3) % 260.42/56.34 | | | (178) leq(n0, all_74_2) % 260.42/56.34 | | | (179) leq(all_74_3, all_74_20) % 260.85/56.34 | | | (180) leq(all_74_2, all_74_20) % 260.85/56.34 | | | (181) a_select3(q_ds1_filter, all_74_3, all_74_2) = all_74_1 % 260.85/56.34 | | | (182) a_select3(q_ds1_filter, all_74_2, all_74_3) = all_74_0 % 260.85/56.34 | | | % 260.85/56.34 | | | REDUCE: (159), (180) imply: % 260.85/56.34 | | | (183) leq(all_74_2, n5) % 260.85/56.34 | | | % 260.85/56.34 | | | REDUCE: (159), (179) imply: % 260.85/56.34 | | | (184) leq(all_74_3, n5) % 260.85/56.34 | | | % 260.85/56.35 | | | GROUND_INST: instantiating (leq_gt2) with n0, all_74_3, simplifying with % 260.85/56.35 | | | (22), (72), (177) gives: % 260.85/56.35 | | | (185) all_74_3 = n0 | gt(all_74_3, n0) % 260.85/56.35 | | | % 260.85/56.35 | | | GROUND_INST: instantiating (leq_gt2) with n0, all_74_2, simplifying with % 260.85/56.35 | | | (22), (73), (178) gives: % 260.85/56.35 | | | (186) all_74_2 = n0 | gt(all_74_2, n0) % 260.85/56.35 | | | % 260.85/56.35 | | | GROUND_INST: instantiating (transitivity_leq) with all_74_3, n5, n6, % 260.85/56.35 | | | simplifying with (25), (72), (139), (140), (184) gives: % 260.85/56.35 | | | (187) leq(all_74_3, n6) % 260.85/56.35 | | | % 260.85/56.35 | | | GROUND_INST: instantiating (10) with all_74_3, simplifying with (72), % 260.85/56.35 | | | (177), (184) gives: % 260.85/56.35 | | | (188) all_74_3 = n5 | all_74_3 = n4 | all_74_3 = n3 | all_74_3 = n2 | % 260.85/56.35 | | | all_74_3 = n1 | all_74_3 = n0 % 260.85/56.35 | | | % 260.85/56.35 | | | GROUND_INST: instantiating (leq_gt2) with all_74_3, n5, simplifying with % 260.85/56.35 | | | (72), (139), (184) gives: % 260.85/56.35 | | | (189) all_74_3 = n5 | gt(n5, all_74_3) % 260.85/56.35 | | | % 260.85/56.35 | | | GROUND_INST: instantiating (transitivity_leq) with all_74_2, n5, n6, % 260.85/56.35 | | | simplifying with (25), (73), (139), (140), (183) gives: % 260.85/56.35 | | | (190) leq(all_74_2, n6) % 260.85/56.35 | | | % 260.85/56.35 | | | GROUND_INST: instantiating (10) with all_74_2, simplifying with (73), % 260.85/56.35 | | | (178), (183) gives: % 260.85/56.35 | | | (191) all_74_2 = n5 | all_74_2 = n4 | all_74_2 = n3 | all_74_2 = n2 | % 260.85/56.35 | | | all_74_2 = n1 | all_74_2 = n0 % 260.85/56.35 | | | % 260.85/56.35 | | | GROUND_INST: instantiating (leq_gt2) with all_74_2, n5, simplifying with % 260.85/56.35 | | | (73), (139), (183) gives: % 260.85/56.35 | | | (192) all_74_2 = n5 | gt(n5, all_74_2) % 260.85/56.35 | | | % 260.85/56.35 | | | GROUND_INST: instantiating (11) with all_74_3, simplifying with (72), % 260.85/56.35 | | | (177), (187) gives: % 260.85/56.35 | | | (193) all_74_3 = n6 | all_74_3 = n5 | all_74_3 = n4 | all_74_3 = n3 | % 260.85/56.35 | | | all_74_3 = n2 | all_74_3 = n1 | all_74_3 = n0 % 260.85/56.35 | | | % 260.85/56.35 | | | GROUND_INST: instantiating (11) with all_74_2, simplifying with (73), % 260.85/56.35 | | | (178), (190) gives: % 260.85/56.35 | | | (194) all_74_2 = n6 | all_74_2 = n5 | all_74_2 = n4 | all_74_2 = n3 | % 260.85/56.35 | | | all_74_2 = n2 | all_74_2 = n1 | all_74_2 = n0 % 260.85/56.35 | | | % 260.85/56.35 | | | BETA: splitting (142) gives: % 260.85/56.35 | | | % 260.85/56.35 | | | Case 1: % 260.85/56.35 | | | | % 260.85/56.35 | | | | (195) gt(pv57, n0) % 260.85/56.35 | | | | % 260.85/56.35 | | | | GROUND_INST: instantiating (1) with n0, pv57, all_74_18, simplifying % 260.85/56.35 | | | | with (22), (24), (155), (195) gives: % 260.85/56.35 | | | | (196) leq(n0, all_74_18) % 260.85/56.35 | | | | % 260.85/56.35 | | | | GROUND_INST: instantiating (leq_gt2) with n0, all_74_18, simplifying % 260.85/56.35 | | | | with (22), (154), (196) gives: % 260.85/56.35 | | | | (197) all_74_18 = n0 | gt(all_74_18, n0) % 260.85/56.35 | | | | % 260.85/56.35 | | | | BETA: splitting (164) gives: % 260.85/56.35 | | | | % 260.85/56.35 | | | | Case 1: % 260.85/56.35 | | | | | % 260.85/56.35 | | | | | (198) pv57 = n0 % 260.85/56.35 | | | | | % 260.85/56.35 | | | | | REF_CLOSE: (24), (195), (198), (irreflexivity_gt) are inconsistent by % 260.85/56.35 | | | | | sub-proof #95. % 260.85/56.35 | | | | | % 260.85/56.35 | | | | Case 2: % 260.85/56.35 | | | | | % 260.85/56.35 | | | | | (199) ~ (pv57 = n0) % 260.85/56.35 | | | | | (200) pv57 = n5 | pv57 = n4 | pv57 = n3 | pv57 = n2 | pv57 = n1 % 260.85/56.35 | | | | | % 260.85/56.35 | | | | | BETA: splitting (166) gives: % 260.85/56.35 | | | | | % 260.85/56.35 | | | | | Case 1: % 260.85/56.35 | | | | | | % 260.85/56.35 | | | | | | (201) pv57 = n0 % 260.85/56.35 | | | | | | % 260.85/56.35 | | | | | | REDUCE: (199), (201) imply: % 260.85/56.35 | | | | | | (202) $false % 260.85/56.35 | | | | | | % 260.85/56.35 | | | | | | CLOSE: (202) is inconsistent. % 260.85/56.35 | | | | | | % 260.85/56.35 | | | | | Case 2: % 260.85/56.35 | | | | | | % 260.85/56.35 | | | | | | (203) n6 = pv57 | pv57 = n5 | pv57 = n4 | pv57 = n3 | pv57 = n2 | % 260.85/56.35 | | | | | | pv57 = n1 % 260.85/56.35 | | | | | | % 260.85/56.35 | | | | | | BETA: splitting (186) gives: % 260.85/56.35 | | | | | | % 260.85/56.35 | | | | | | Case 1: % 260.85/56.35 | | | | | | | % 260.85/56.36 | | | | | | | (204) gt(all_74_2, n0) % 260.85/56.36 | | | | | | | % 260.85/56.36 | | | | | | | BETA: splitting (185) gives: % 260.85/56.36 | | | | | | | % 260.85/56.36 | | | | | | | Case 1: % 260.85/56.36 | | | | | | | | % 260.85/56.36 | | | | | | | | (205) gt(all_74_3, n0) % 260.85/56.36 | | | | | | | | % 260.85/56.36 | | | | | | | | BETA: splitting (192) gives: % 260.85/56.36 | | | | | | | | % 260.85/56.36 | | | | | | | | Case 1: % 260.85/56.36 | | | | | | | | | % 260.85/56.36 | | | | | | | | | (206) gt(n5, all_74_2) % 260.85/56.36 | | | | | | | | | % 260.85/56.36 | | | | | | | | | BETA: splitting (189) gives: % 260.85/56.36 | | | | | | | | | % 260.85/56.36 | | | | | | | | | Case 1: % 260.85/56.36 | | | | | | | | | | % 260.85/56.36 | | | | | | | | | | (207) gt(n5, all_74_3) % 260.85/56.36 | | | | | | | | | | % 260.85/56.36 | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_3, n5, n4, % 260.85/56.36 | | | | | | | | | | simplifying with (72), (139), (148), (207) gives: % 260.85/56.36 | | | | | | | | | | (208) leq(all_74_3, n4) % 260.85/56.36 | | | | | | | | | | % 260.85/56.36 | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_2, n5, n4, % 260.85/56.36 | | | | | | | | | | simplifying with (73), (139), (148), (206) gives: % 260.85/56.36 | | | | | | | | | | (209) leq(all_74_2, n4) % 260.85/56.36 | | | | | | | | | | % 260.85/56.36 | | | | | | | | | | BETA: splitting (188) gives: % 260.85/56.36 | | | | | | | | | | % 260.85/56.36 | | | | | | | | | | Case 1: % 260.85/56.36 | | | | | | | | | | | % 260.85/56.36 | | | | | | | | | | | (210) all_74_3 = n0 % 260.85/56.36 | | | | | | | | | | | % 260.85/56.36 | | | | | | | | | | | REF_CLOSE: (72), (205), (210), (irreflexivity_gt) are % 260.85/56.36 | | | | | | | | | | | inconsistent by sub-proof #94. % 260.85/56.36 | | | | | | | | | | | % 260.85/56.36 | | | | | | | | | | Case 2: % 260.85/56.36 | | | | | | | | | | | % 260.85/56.36 | | | | | | | | | | | (211) ~ (all_74_3 = n0) % 260.85/56.36 | | | | | | | | | | | % 260.85/56.36 | | | | | | | | | | | BETA: splitting (191) gives: % 260.85/56.36 | | | | | | | | | | | % 260.85/56.36 | | | | | | | | | | | Case 1: % 260.85/56.36 | | | | | | | | | | | | % 260.85/56.36 | | | | | | | | | | | | (212) all_74_2 = n0 % 260.85/56.36 | | | | | | | | | | | | % 260.85/56.36 | | | | | | | | | | | | REF_CLOSE: (73), (204), (212), (irreflexivity_gt) are % 260.85/56.36 | | | | | | | | | | | | inconsistent by sub-proof #93. % 260.85/56.36 | | | | | | | | | | | | % 260.85/56.36 | | | | | | | | | | | Case 2: % 260.85/56.36 | | | | | | | | | | | | % 260.85/56.36 | | | | | | | | | | | | (213) ~ (all_74_2 = n0) % 260.85/56.36 | | | | | | | | | | | | % 260.85/56.36 | | | | | | | | | | | | BETA: splitting (193) gives: % 260.85/56.36 | | | | | | | | | | | | % 260.85/56.36 | | | | | | | | | | | | Case 1: % 260.85/56.36 | | | | | | | | | | | | | % 260.85/56.36 | | | | | | | | | | | | | (214) all_74_3 = n0 % 260.85/56.36 | | | | | | | | | | | | | % 260.85/56.36 | | | | | | | | | | | | | REDUCE: (211), (214) imply: % 260.85/56.36 | | | | | | | | | | | | | (215) $false % 260.85/56.36 | | | | | | | | | | | | | % 260.85/56.36 | | | | | | | | | | | | | CLOSE: (215) is inconsistent. % 260.85/56.36 | | | | | | | | | | | | | % 260.85/56.36 | | | | | | | | | | | | Case 2: % 260.85/56.36 | | | | | | | | | | | | | % 260.85/56.36 | | | | | | | | | | | | | % 260.85/56.36 | | | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_3, n4, % 260.85/56.36 | | | | | | | | | | | | | simplifying with (72), (136), (208) gives: % 260.85/56.36 | | | | | | | | | | | | | (216) all_74_3 = n4 | gt(n4, all_74_3) % 260.85/56.36 | | | | | | | | | | | | | % 260.85/56.36 | | | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_2, n4, % 260.85/56.36 | | | | | | | | | | | | | simplifying with (73), (136), (209) gives: % 260.85/56.36 | | | | | | | | | | | | | (217) all_74_2 = n4 | gt(n4, all_74_2) % 260.85/56.36 | | | | | | | | | | | | | % 260.85/56.36 | | | | | | | | | | | | | REF_CLOSE: (1), (13), (30), (72), (73), (78), (118), (129), % 260.85/56.36 | | | | | | | | | | | | | (136), (145), (146), (147), (159), (176), (177), % 260.85/56.36 | | | | | | | | | | | | | (178), (181), (182), (183), (184), (211), (213), % 260.85/56.36 | | | | | | | | | | | | | (216), (217), (leq_gt2) are inconsistent by % 260.85/56.36 | | | | | | | | | | | | | sub-proof #87. % 260.85/56.36 | | | | | | | | | | | | | % 260.85/56.36 | | | | | | | | | | | | End of split % 260.85/56.36 | | | | | | | | | | | | % 260.85/56.36 | | | | | | | | | | | End of split % 260.85/56.36 | | | | | | | | | | | % 260.85/56.36 | | | | | | | | | | End of split % 260.85/56.36 | | | | | | | | | | % 260.85/56.36 | | | | | | | | | Case 2: % 260.85/56.36 | | | | | | | | | | % 260.85/56.36 | | | | | | | | | | (218) all_74_3 = n5 % 260.85/56.36 | | | | | | | | | | % 260.85/56.36 | | | | | | | | | | REDUCE: (182), (218) imply: % 260.85/56.36 | | | | | | | | | | (219) a_select3(q_ds1_filter, all_74_2, n5) = all_74_0 % 260.85/56.36 | | | | | | | | | | % 260.85/56.36 | | | | | | | | | | REDUCE: (181), (218) imply: % 260.85/56.36 | | | | | | | | | | (220) a_select3(q_ds1_filter, n5, all_74_2) = all_74_1 % 260.85/56.36 | | | | | | | | | | % 260.85/56.36 | | | | | | | | | | REDUCE: (184), (218) imply: % 260.85/56.36 | | | | | | | | | | (221) leq(n5, n5) % 260.85/56.36 | | | | | | | | | | % 260.85/56.36 | | | | | | | | | | REDUCE: (177), (218) imply: % 260.85/56.36 | | | | | | | | | | (222) leq(n0, n5) % 260.85/56.36 | | | | | | | | | | % 260.85/56.36 | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_2, n5, n4, % 260.85/56.36 | | | | | | | | | | simplifying with (73), (139), (148), (206) gives: % 260.85/56.36 | | | | | | | | | | (223) leq(all_74_2, n4) % 260.85/56.36 | | | | | | | | | | % 260.85/56.36 | | | | | | | | | | BETA: splitting (191) gives: % 260.85/56.36 | | | | | | | | | | % 260.85/56.36 | | | | | | | | | | Case 1: % 260.85/56.36 | | | | | | | | | | | % 260.85/56.36 | | | | | | | | | | | (224) all_74_2 = n0 % 260.85/56.36 | | | | | | | | | | | % 260.85/56.36 | | | | | | | | | | | REF_CLOSE: (73), (204), (224), (irreflexivity_gt) are % 260.85/56.36 | | | | | | | | | | | inconsistent by sub-proof #93. % 260.85/56.36 | | | | | | | | | | | % 260.85/56.36 | | | | | | | | | | Case 2: % 260.85/56.36 | | | | | | | | | | | % 260.85/56.36 | | | | | | | | | | | (225) ~ (all_74_2 = n0) % 260.85/56.36 | | | | | | | | | | | % 260.85/56.36 | | | | | | | | | | | BETA: splitting (194) gives: % 260.85/56.36 | | | | | | | | | | | % 260.85/56.36 | | | | | | | | | | | Case 1: % 260.85/56.36 | | | | | | | | | | | | % 260.85/56.36 | | | | | | | | | | | | (226) all_74_2 = n0 % 260.85/56.36 | | | | | | | | | | | | % 260.85/56.36 | | | | | | | | | | | | REDUCE: (225), (226) imply: % 260.85/56.36 | | | | | | | | | | | | (227) $false % 260.85/56.36 | | | | | | | | | | | | % 260.85/56.36 | | | | | | | | | | | | CLOSE: (227) is inconsistent. % 260.85/56.36 | | | | | | | | | | | | % 260.85/56.36 | | | | | | | | | | | Case 2: % 260.85/56.36 | | | | | | | | | | | | % 260.85/56.36 | | | | | | | | | | | | % 260.85/56.36 | | | | | | | | | | | | GROUND_INST: instantiating (9) with all_74_2, simplifying with % 260.85/56.36 | | | | | | | | | | | | (73), (178), (223) gives: % 260.85/56.36 | | | | | | | | | | | | (228) all_74_2 = n4 | all_74_2 = n3 | all_74_2 = n2 | % 260.85/56.36 | | | | | | | | | | | | all_74_2 = n1 | all_74_2 = n0 % 260.85/56.36 | | | | | | | | | | | | % 260.85/56.36 | | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_2, n4, % 260.85/56.36 | | | | | | | | | | | | simplifying with (73), (136), (223) gives: % 260.85/56.36 | | | | | | | | | | | | (229) all_74_2 = n4 | gt(n4, all_74_2) % 260.85/56.36 | | | | | | | | | | | | % 260.85/56.36 | | | | | | | | | | | | REF_CLOSE: (1), (13), (30), (73), (78), (118), (129), (136), % 260.85/56.36 | | | | | | | | | | | | (139), (145), (146), (147), (159), (176), (178), % 260.85/56.36 | | | | | | | | | | | | (183), (219), (220), (221), (222), (225), (228), % 260.85/56.36 | | | | | | | | | | | | (229), (leq_gt2) are inconsistent by sub-proof % 260.85/56.36 | | | | | | | | | | | | #83. % 260.85/56.36 | | | | | | | | | | | | % 260.85/56.36 | | | | | | | | | | | End of split % 260.85/56.36 | | | | | | | | | | | % 260.85/56.36 | | | | | | | | | | End of split % 260.85/56.36 | | | | | | | | | | % 260.85/56.36 | | | | | | | | | End of split % 260.85/56.36 | | | | | | | | | % 260.85/56.36 | | | | | | | | Case 2: % 260.85/56.36 | | | | | | | | | % 260.85/56.36 | | | | | | | | | (230) all_74_2 = n5 % 260.85/56.36 | | | | | | | | | % 260.85/56.36 | | | | | | | | | REDUCE: (182), (230) imply: % 260.85/56.36 | | | | | | | | | (231) a_select3(q_ds1_filter, n5, all_74_3) = all_74_0 % 260.85/56.36 | | | | | | | | | % 260.85/56.36 | | | | | | | | | REDUCE: (181), (230) imply: % 260.85/56.36 | | | | | | | | | (232) a_select3(q_ds1_filter, all_74_3, n5) = all_74_1 % 260.85/56.36 | | | | | | | | | % 260.85/56.36 | | | | | | | | | REDUCE: (183), (230) imply: % 260.85/56.36 | | | | | | | | | (233) leq(n5, n5) % 260.85/56.36 | | | | | | | | | % 260.85/56.36 | | | | | | | | | REDUCE: (178), (230) imply: % 260.85/56.36 | | | | | | | | | (234) leq(n0, n5) % 260.85/56.36 | | | | | | | | | % 260.85/56.36 | | | | | | | | | BETA: splitting (189) gives: % 260.85/56.36 | | | | | | | | | % 260.85/56.36 | | | | | | | | | Case 1: % 260.85/56.36 | | | | | | | | | | % 260.85/56.36 | | | | | | | | | | (235) gt(n5, all_74_3) % 260.85/56.36 | | | | | | | | | | % 260.85/56.36 | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_3, n5, n4, % 260.85/56.36 | | | | | | | | | | simplifying with (72), (139), (148), (235) gives: % 260.85/56.36 | | | | | | | | | | (236) leq(all_74_3, n4) % 260.85/56.36 | | | | | | | | | | % 260.85/56.36 | | | | | | | | | | BETA: splitting (188) gives: % 260.85/56.36 | | | | | | | | | | % 260.85/56.36 | | | | | | | | | | Case 1: % 260.85/56.36 | | | | | | | | | | | % 260.85/56.37 | | | | | | | | | | | (237) all_74_3 = n0 % 260.85/56.37 | | | | | | | | | | | % 260.85/56.37 | | | | | | | | | | | REF_CLOSE: (72), (205), (237), (irreflexivity_gt) are % 260.85/56.37 | | | | | | | | | | | inconsistent by sub-proof #94. % 260.85/56.37 | | | | | | | | | | | % 260.85/56.37 | | | | | | | | | | Case 2: % 260.85/56.37 | | | | | | | | | | | % 260.85/56.37 | | | | | | | | | | | (238) ~ (all_74_3 = n0) % 260.85/56.37 | | | | | | | | | | | % 260.85/56.37 | | | | | | | | | | | REF_CLOSE: (1), (13), (30), (72), (78), (118), (129), (136), % 260.85/56.37 | | | | | | | | | | | (139), (145), (146), (147), (159), (176), (177), % 260.85/56.37 | | | | | | | | | | | (184), (193), (231), (232), (233), (234), (236), % 260.85/56.37 | | | | | | | | | | | (238), (leq_gt2) are inconsistent by sub-proof % 260.85/56.37 | | | | | | | | | | | #82. % 260.85/56.37 | | | | | | | | | | | % 260.85/56.37 | | | | | | | | | | End of split % 260.85/56.37 | | | | | | | | | | % 260.85/56.37 | | | | | | | | | Case 2: % 260.85/56.37 | | | | | | | | | | % 260.85/56.37 | | | | | | | | | | (239) all_74_3 = n5 % 260.85/56.37 | | | | | | | | | | % 260.85/56.37 | | | | | | | | | | REDUCE: (232), (239) imply: % 260.85/56.37 | | | | | | | | | | (240) a_select3(q_ds1_filter, n5, n5) = all_74_1 % 260.85/56.37 | | | | | | | | | | % 260.85/56.37 | | | | | | | | | | REDUCE: (231), (239) imply: % 260.85/56.37 | | | | | | | | | | (241) a_select3(q_ds1_filter, n5, n5) = all_74_0 % 260.85/56.37 | | | | | | | | | | % 260.85/56.37 | | | | | | | | | | GROUND_INST: instantiating (30) with all_74_1, all_74_0, n5, % 260.85/56.37 | | | | | | | | | | n5, q_ds1_filter, simplifying with (240), (241) % 260.85/56.37 | | | | | | | | | | gives: % 260.85/56.37 | | | | | | | | | | (242) all_74_0 = all_74_1 % 260.85/56.37 | | | | | | | | | | % 260.85/56.37 | | | | | | | | | | REDUCE: (176), (242) imply: % 260.85/56.37 | | | | | | | | | | (243) $false % 260.85/56.37 | | | | | | | | | | % 260.85/56.37 | | | | | | | | | | CLOSE: (243) is inconsistent. % 260.85/56.37 | | | | | | | | | | % 260.85/56.37 | | | | | | | | | End of split % 260.85/56.37 | | | | | | | | | % 260.85/56.37 | | | | | | | | End of split % 260.85/56.37 | | | | | | | | % 260.85/56.37 | | | | | | | Case 2: % 260.85/56.37 | | | | | | | | % 260.85/56.37 | | | | | | | | (244) all_74_3 = n0 % 260.85/56.37 | | | | | | | | (245) ~ gt(all_74_3, n0) % 260.85/56.37 | | | | | | | | % 260.85/56.37 | | | | | | | | REDUCE: (244), (245) imply: % 260.85/56.37 | | | | | | | | (246) ~ gt(n0, n0) % 260.85/56.37 | | | | | | | | % 260.85/56.37 | | | | | | | | REF_CLOSE: (1), (9), (13), (19), (27), (28), (30), (72), (73), % 260.85/56.37 | | | | | | | | (78), (118), (129), (136), (139), (144), (145), % 260.85/56.37 | | | | | | | | (146), (147), (148), (154), (155), (159), (165), % 260.85/56.37 | | | | | | | | (167), (176), (177), (178), (181), (182), (183), % 260.85/56.37 | | | | | | | | (184), (185), (188), (189), (191), (192), (193), % 260.85/56.37 | | | | | | | | (196), (197), (200), (203), (204), (246), (leq_gt2) % 260.85/56.37 | | | | | | | | are inconsistent by sub-proof #70. % 260.85/56.37 | | | | | | | | % 260.85/56.37 | | | | | | | End of split % 260.85/56.37 | | | | | | | % 260.85/56.37 | | | | | | Case 2: % 260.85/56.37 | | | | | | | % 260.85/56.37 | | | | | | | (247) all_74_2 = n0 % 260.85/56.37 | | | | | | | (248) ~ gt(all_74_2, n0) % 260.85/56.37 | | | | | | | % 260.85/56.37 | | | | | | | REDUCE: (247), (248) imply: % 260.85/56.37 | | | | | | | (249) ~ gt(n0, n0) % 260.85/56.37 | | | | | | | % 260.85/56.37 | | | | | | | BETA: splitting (186) gives: % 260.85/56.37 | | | | | | | % 260.85/56.37 | | | | | | | Case 1: % 260.85/56.37 | | | | | | | | % 260.85/56.37 | | | | | | | | (250) gt(all_74_2, n0) % 260.85/56.37 | | | | | | | | % 260.85/56.37 | | | | | | | | REF_CLOSE: (1), (9), (13), (19), (27), (28), (30), (72), (73), % 260.85/56.37 | | | | | | | | (78), (118), (129), (136), (139), (144), (145), % 260.85/56.37 | | | | | | | | (146), (147), (148), (154), (155), (159), (165), % 260.85/56.37 | | | | | | | | (167), (176), (177), (178), (181), (182), (183), % 260.85/56.37 | | | | | | | | (184), (185), (188), (189), (191), (192), (193), % 260.85/56.37 | | | | | | | | (196), (197), (200), (203), (249), (250), (leq_gt2) % 260.85/56.37 | | | | | | | | are inconsistent by sub-proof #70. % 260.85/56.37 | | | | | | | | % 260.85/56.37 | | | | | | | Case 2: % 260.85/56.37 | | | | | | | | % 260.85/56.37 | | | | | | | | % 260.85/56.37 | | | | | | | | REDUCE: (182), (247) imply: % 260.85/56.37 | | | | | | | | (251) a_select3(q_ds1_filter, n0, all_74_3) = all_74_0 % 260.85/56.37 | | | | | | | | % 260.85/56.37 | | | | | | | | REDUCE: (181), (247) imply: % 260.85/56.37 | | | | | | | | (252) a_select3(q_ds1_filter, all_74_3, n0) = all_74_1 % 260.85/56.37 | | | | | | | | % 260.85/56.37 | | | | | | | | REDUCE: (183), (247) imply: % 260.85/56.37 | | | | | | | | (253) leq(n0, n5) % 260.85/56.37 | | | | | | | | % 260.85/56.37 | | | | | | | | REDUCE: (178), (247) imply: % 260.85/56.37 | | | | | | | | (254) leq(n0, n0) % 260.85/56.37 | | | | | | | | % 260.85/56.37 | | | | | | | | BETA: splitting (185) gives: % 260.85/56.37 | | | | | | | | % 260.85/56.37 | | | | | | | | Case 1: % 260.85/56.37 | | | | | | | | | % 260.85/56.37 | | | | | | | | | (255) gt(all_74_3, n0) % 260.85/56.37 | | | | | | | | | % 260.85/56.37 | | | | | | | | | BETA: splitting (189) gives: % 260.85/56.37 | | | | | | | | | % 260.85/56.37 | | | | | | | | | Case 1: % 260.85/56.37 | | | | | | | | | | % 260.85/56.37 | | | | | | | | | | (256) gt(n5, all_74_3) % 260.85/56.37 | | | | | | | | | | % 260.85/56.37 | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_3, n5, n4, % 260.85/56.37 | | | | | | | | | | simplifying with (72), (139), (148), (256) gives: % 260.85/56.37 | | | | | | | | | | (257) leq(all_74_3, n4) % 260.85/56.37 | | | | | | | | | | % 260.85/56.37 | | | | | | | | | | REF_CLOSE: (1), (13), (22), (30), (72), (78), (118), (129), % 260.85/56.37 | | | | | | | | | | (136), (145), (146), (147), (159), (176), (177), % 260.85/56.37 | | | | | | | | | | (184), (188), (249), (251), (252), (253), (254), % 260.85/56.37 | | | | | | | | | | (255), (257), (leq_gt2) are inconsistent by % 260.85/56.37 | | | | | | | | | | sub-proof #69. % 260.85/56.37 | | | | | | | | | | % 260.85/56.37 | | | | | | | | | Case 2: % 260.85/56.37 | | | | | | | | | | % 260.85/56.37 | | | | | | | | | | (258) all_74_3 = n5 % 260.85/56.37 | | | | | | | | | | % 260.85/56.37 | | | | | | | | | | REDUCE: (252), (258) imply: % 260.85/56.37 | | | | | | | | | | (259) a_select3(q_ds1_filter, n5, n0) = all_74_1 % 260.85/56.37 | | | | | | | | | | % 260.85/56.37 | | | | | | | | | | REDUCE: (251), (258) imply: % 260.85/56.37 | | | | | | | | | | (260) a_select3(q_ds1_filter, n0, n5) = all_74_0 % 260.85/56.37 | | | | | | | | | | % 260.85/56.37 | | | | | | | | | | REDUCE: (184), (258) imply: % 260.85/56.37 | | | | | | | | | | (261) leq(n5, n5) % 260.85/56.37 | | | | | | | | | | % 260.85/56.37 | | | | | | | | | | REF_CLOSE: (22), (27), (30), (78), (139), (144), (154), % 260.85/56.37 | | | | | | | | | | (155), (159), (167), (176), (196), (197), (200), % 260.85/56.37 | | | | | | | | | | (203), (249), (253), (254), (259), (260), (261) % 260.85/56.37 | | | | | | | | | | are inconsistent by sub-proof #72. % 260.85/56.37 | | | | | | | | | | % 260.85/56.37 | | | | | | | | | End of split % 260.85/56.37 | | | | | | | | | % 260.85/56.37 | | | | | | | | Case 2: % 260.85/56.37 | | | | | | | | | % 260.85/56.37 | | | | | | | | | (262) all_74_3 = n0 % 260.85/56.37 | | | | | | | | | % 260.85/56.37 | | | | | | | | | REDUCE: (252), (262) imply: % 260.85/56.37 | | | | | | | | | (263) a_select3(q_ds1_filter, n0, n0) = all_74_1 % 260.85/56.37 | | | | | | | | | % 260.85/56.37 | | | | | | | | | REDUCE: (251), (262) imply: % 260.85/56.37 | | | | | | | | | (264) a_select3(q_ds1_filter, n0, n0) = all_74_0 % 260.85/56.37 | | | | | | | | | % 260.85/56.37 | | | | | | | | | GROUND_INST: instantiating (30) with all_74_1, all_74_0, n0, % 260.85/56.37 | | | | | | | | | n0, q_ds1_filter, simplifying with (263), (264) % 260.85/56.37 | | | | | | | | | gives: % 260.85/56.37 | | | | | | | | | (265) all_74_0 = all_74_1 % 260.85/56.37 | | | | | | | | | % 260.85/56.37 | | | | | | | | | REDUCE: (176), (265) imply: % 260.85/56.37 | | | | | | | | | (266) $false % 260.85/56.37 | | | | | | | | | % 260.85/56.37 | | | | | | | | | CLOSE: (266) is inconsistent. % 260.85/56.37 | | | | | | | | | % 260.85/56.37 | | | | | | | | End of split % 260.85/56.37 | | | | | | | | % 260.85/56.38 | | | | | | | End of split % 260.85/56.38 | | | | | | | % 260.85/56.38 | | | | | | End of split % 260.85/56.38 | | | | | | % 260.85/56.38 | | | | | End of split % 260.85/56.38 | | | | | % 260.85/56.38 | | | | End of split % 260.85/56.38 | | | | % 260.85/56.38 | | | Case 2: % 260.85/56.38 | | | | % 260.85/56.38 | | | | (267) pv57 = n0 % 260.85/56.38 | | | | (268) ~ gt(pv57, n0) % 260.85/56.38 | | | | % 260.85/56.38 | | | | REDUCE: (267), (268) imply: % 260.85/56.38 | | | | (269) ~ gt(n0, n0) % 260.85/56.38 | | | | % 260.85/56.38 | | | | BETA: splitting (186) gives: % 260.85/56.38 | | | | % 260.85/56.38 | | | | Case 1: % 260.85/56.38 | | | | | % 260.85/56.38 | | | | | (270) gt(all_74_2, n0) % 260.85/56.38 | | | | | % 260.85/56.38 | | | | | BETA: splitting (185) gives: % 260.85/56.38 | | | | | % 260.85/56.38 | | | | | Case 1: % 260.85/56.38 | | | | | | % 260.85/56.38 | | | | | | (271) gt(all_74_3, n0) % 260.85/56.38 | | | | | | % 260.85/56.38 | | | | | | REF_CLOSE: (1), (9), (13), (30), (72), (73), (78), (118), (129), % 260.85/56.38 | | | | | | (136), (139), (145), (146), (147), (148), (159), (176), % 260.85/56.38 | | | | | | (177), (178), (181), (182), (183), (184), (188), (189), % 260.85/56.38 | | | | | | (191), (192), (193), (269), (270), (271), (leq_gt2) are % 260.85/56.38 | | | | | | inconsistent by sub-proof #81. % 260.85/56.38 | | | | | | % 260.85/56.38 | | | | | Case 2: % 260.85/56.38 | | | | | | % 260.85/56.38 | | | | | | (272) all_74_3 = n0 % 260.85/56.38 | | | | | | (273) ~ gt(all_74_3, n0) % 260.85/56.38 | | | | | | % 260.85/56.38 | | | | | | REDUCE: (182), (272) imply: % 260.85/56.38 | | | | | | (274) a_select3(q_ds1_filter, all_74_2, n0) = all_74_0 % 260.85/56.38 | | | | | | % 260.85/56.38 | | | | | | REDUCE: (181), (272) imply: % 260.85/56.38 | | | | | | (275) a_select3(q_ds1_filter, n0, all_74_2) = all_74_1 % 260.85/56.38 | | | | | | % 260.85/56.38 | | | | | | REDUCE: (184), (272) imply: % 260.85/56.38 | | | | | | (276) leq(n0, n5) % 260.85/56.38 | | | | | | % 260.85/56.38 | | | | | | REDUCE: (177), (272) imply: % 260.85/56.38 | | | | | | (277) leq(n0, n0) % 260.85/56.38 | | | | | | % 260.85/56.38 | | | | | | BETA: splitting (192) gives: % 260.85/56.38 | | | | | | % 260.85/56.38 | | | | | | Case 1: % 260.85/56.38 | | | | | | | % 260.85/56.38 | | | | | | | (278) gt(n5, all_74_2) % 260.85/56.38 | | | | | | | % 260.85/56.38 | | | | | | | GROUND_INST: instantiating (1) with all_74_2, n5, n4, simplifying % 260.85/56.38 | | | | | | | with (73), (139), (148), (278) gives: % 260.85/56.38 | | | | | | | (279) leq(all_74_2, n4) % 260.85/56.38 | | | | | | | % 260.85/56.38 | | | | | | | REF_CLOSE: (1), (9), (13), (22), (30), (73), (78), (118), (129), % 260.85/56.38 | | | | | | | (136), (145), (146), (147), (159), (176), (178), (183), % 260.85/56.38 | | | | | | | (191), (269), (270), (274), (275), (276), (277), (279), % 260.85/56.38 | | | | | | | (leq_gt2) are inconsistent by sub-proof #76. % 260.85/56.38 | | | | | | | % 260.85/56.38 | | | | | | Case 2: % 260.85/56.38 | | | | | | | % 260.85/56.38 | | | | | | | (280) all_74_2 = n5 % 260.85/56.38 | | | | | | | % 260.85/56.38 | | | | | | | REDUCE: (274), (280) imply: % 260.85/56.38 | | | | | | | (281) a_select3(q_ds1_filter, n5, n0) = all_74_0 % 260.85/56.38 | | | | | | | % 260.85/56.38 | | | | | | | REDUCE: (275), (280) imply: % 260.85/56.38 | | | | | | | (282) a_select3(q_ds1_filter, n0, n5) = all_74_1 % 260.85/56.38 | | | | | | | % 260.85/56.38 | | | | | | | REDUCE: (183), (280) imply: % 260.85/56.38 | | | | | | | (283) leq(n5, n5) % 260.85/56.38 | | | | | | | % 260.85/56.38 | | | | | | | GROUND_INST: instantiating (78) with n0, n5, all_74_1, simplifying % 260.85/56.38 | | | | | | | with (22), (139), (276), (277), (282) gives: % 260.85/56.38 | | | | | | | (284) ~ leq(n5, all_74_20) | ~ leq(n0, all_74_20) | % 260.85/56.38 | | | | | | | (a_select3(q_ds1_filter, n5, n0) = all_74_1 & % 260.85/56.38 | | | | | | | $i(all_74_1)) % 260.85/56.38 | | | | | | | % 260.85/56.38 | | | | | | | BETA: splitting (284) gives: % 260.85/56.38 | | | | | | | % 260.85/56.38 | | | | | | | Case 1: % 260.85/56.38 | | | | | | | | % 260.85/56.38 | | | | | | | | (285) ~ leq(n0, all_74_20) % 260.85/56.38 | | | | | | | | % 260.85/56.38 | | | | | | | | REDUCE: (159), (285) imply: % 260.85/56.38 | | | | | | | | (286) ~ leq(n0, n5) % 260.85/56.38 | | | | | | | | % 260.85/56.38 | | | | | | | | PRED_UNIFY: (276), (286) imply: % 260.85/56.38 | | | | | | | | (287) $false % 260.85/56.38 | | | | | | | | % 260.85/56.38 | | | | | | | | CLOSE: (287) is inconsistent. % 260.85/56.38 | | | | | | | | % 260.85/56.38 | | | | | | | Case 2: % 260.85/56.38 | | | | | | | | % 260.85/56.38 | | | | | | | | (288) ~ leq(n5, all_74_20) | (a_select3(q_ds1_filter, n5, % 260.85/56.38 | | | | | | | | n0) = all_74_1 & $i(all_74_1)) % 260.85/56.38 | | | | | | | | % 260.85/56.38 | | | | | | | | BETA: splitting (288) gives: % 260.85/56.38 | | | | | | | | % 260.85/56.38 | | | | | | | | Case 1: % 260.85/56.38 | | | | | | | | | % 260.85/56.38 | | | | | | | | | (289) ~ leq(n5, all_74_20) % 260.85/56.38 | | | | | | | | | % 260.85/56.38 | | | | | | | | | REDUCE: (159), (289) imply: % 260.85/56.38 | | | | | | | | | (290) ~ leq(n5, n5) % 260.85/56.38 | | | | | | | | | % 260.85/56.38 | | | | | | | | | PRED_UNIFY: (283), (290) imply: % 260.85/56.38 | | | | | | | | | (291) $false % 260.85/56.38 | | | | | | | | | % 260.85/56.38 | | | | | | | | | CLOSE: (291) is inconsistent. % 260.85/56.38 | | | | | | | | | % 260.85/56.38 | | | | | | | | Case 2: % 260.85/56.38 | | | | | | | | | % 260.85/56.38 | | | | | | | | | (292) a_select3(q_ds1_filter, n5, n0) = all_74_1 & % 260.85/56.38 | | | | | | | | | $i(all_74_1) % 260.85/56.38 | | | | | | | | | % 260.85/56.38 | | | | | | | | | ALPHA: (292) implies: % 260.85/56.38 | | | | | | | | | (293) a_select3(q_ds1_filter, n5, n0) = all_74_1 % 260.85/56.38 | | | | | | | | | % 260.85/56.38 | | | | | | | | | REF_CLOSE: (30), (176), (281), (293) are inconsistent by % 260.85/56.38 | | | | | | | | | sub-proof #74. % 260.85/56.38 | | | | | | | | | % 260.85/56.38 | | | | | | | | End of split % 260.85/56.38 | | | | | | | | % 260.85/56.38 | | | | | | | End of split % 260.85/56.38 | | | | | | | % 260.85/56.38 | | | | | | End of split % 260.85/56.38 | | | | | | % 260.85/56.38 | | | | | End of split % 260.85/56.38 | | | | | % 260.85/56.38 | | | | Case 2: % 260.85/56.38 | | | | | % 260.85/56.38 | | | | | (294) all_74_2 = n0 % 260.85/56.38 | | | | | (295) ~ gt(all_74_2, n0) % 260.85/56.38 | | | | | % 260.85/56.38 | | | | | REDUCE: (182), (294) imply: % 260.85/56.38 | | | | | (296) a_select3(q_ds1_filter, n0, all_74_3) = all_74_0 % 260.85/56.38 | | | | | % 260.85/56.38 | | | | | REDUCE: (181), (294) imply: % 260.85/56.38 | | | | | (297) a_select3(q_ds1_filter, all_74_3, n0) = all_74_1 % 260.85/56.38 | | | | | % 260.85/56.38 | | | | | REDUCE: (183), (294) imply: % 260.85/56.38 | | | | | (298) leq(n0, n5) % 260.85/56.38 | | | | | % 260.85/56.38 | | | | | REDUCE: (178), (294) imply: % 260.85/56.38 | | | | | (299) leq(n0, n0) % 260.85/56.38 | | | | | % 260.85/56.38 | | | | | BETA: splitting (185) gives: % 260.85/56.38 | | | | | % 260.85/56.38 | | | | | Case 1: % 260.85/56.38 | | | | | | % 260.85/56.38 | | | | | | (300) gt(all_74_3, n0) % 260.85/56.38 | | | | | | % 260.85/56.38 | | | | | | BETA: splitting (189) gives: % 260.85/56.38 | | | | | | % 260.85/56.38 | | | | | | Case 1: % 260.85/56.38 | | | | | | | % 260.85/56.38 | | | | | | | (301) gt(n5, all_74_3) % 260.85/56.38 | | | | | | | % 260.85/56.38 | | | | | | | GROUND_INST: instantiating (1) with all_74_3, n5, n4, simplifying % 260.85/56.38 | | | | | | | with (72), (139), (148), (301) gives: % 260.85/56.38 | | | | | | | (302) leq(all_74_3, n4) % 260.85/56.38 | | | | | | | % 260.85/56.38 | | | | | | | REF_CLOSE: (1), (13), (22), (30), (72), (78), (118), (129), (136), % 260.85/56.38 | | | | | | | (145), (146), (147), (159), (176), (177), (184), (188), % 260.85/56.38 | | | | | | | (269), (296), (297), (298), (299), (300), (302), % 260.85/56.38 | | | | | | | (leq_gt2) are inconsistent by sub-proof #69. % 260.85/56.38 | | | | | | | % 260.85/56.38 | | | | | | Case 2: % 260.85/56.38 | | | | | | | % 260.85/56.38 | | | | | | | (303) all_74_3 = n5 % 260.85/56.38 | | | | | | | % 260.85/56.38 | | | | | | | REDUCE: (297), (303) imply: % 260.85/56.38 | | | | | | | (304) a_select3(q_ds1_filter, n5, n0) = all_74_1 % 260.85/56.38 | | | | | | | % 260.85/56.38 | | | | | | | REDUCE: (296), (303) imply: % 260.85/56.38 | | | | | | | (305) a_select3(q_ds1_filter, n0, n5) = all_74_0 % 260.85/56.38 | | | | | | | % 260.85/56.38 | | | | | | | REDUCE: (184), (303) imply: % 261.05/56.38 | | | | | | | (306) leq(n5, n5) % 261.05/56.38 | | | | | | | % 261.05/56.38 | | | | | | | GROUND_INST: instantiating (78) with n0, n5, all_74_0, simplifying % 261.05/56.38 | | | | | | | with (22), (139), (298), (299), (305) gives: % 261.05/56.39 | | | | | | | (307) ~ leq(n5, all_74_20) | ~ leq(n0, all_74_20) | % 261.05/56.39 | | | | | | | (a_select3(q_ds1_filter, n5, n0) = all_74_0 & % 261.05/56.39 | | | | | | | $i(all_74_0)) % 261.05/56.39 | | | | | | | % 261.05/56.39 | | | | | | | REF_CLOSE: (30), (159), (176), (298), (304), (306), (307) are % 261.05/56.39 | | | | | | | inconsistent by sub-proof #73. % 261.05/56.39 | | | | | | | % 261.05/56.39 | | | | | | End of split % 261.05/56.39 | | | | | | % 261.05/56.39 | | | | | Case 2: % 261.05/56.39 | | | | | | % 261.05/56.39 | | | | | | (308) all_74_3 = n0 % 261.05/56.39 | | | | | | % 261.05/56.39 | | | | | | REDUCE: (297), (308) imply: % 261.05/56.39 | | | | | | (309) a_select3(q_ds1_filter, n0, n0) = all_74_1 % 261.05/56.39 | | | | | | % 261.05/56.39 | | | | | | REDUCE: (296), (308) imply: % 261.05/56.39 | | | | | | (310) a_select3(q_ds1_filter, n0, n0) = all_74_0 % 261.05/56.39 | | | | | | % 261.05/56.39 | | | | | | GROUND_INST: instantiating (30) with all_74_1, all_74_0, n0, n0, % 261.05/56.39 | | | | | | q_ds1_filter, simplifying with (309), (310) gives: % 261.05/56.39 | | | | | | (311) all_74_0 = all_74_1 % 261.05/56.39 | | | | | | % 261.05/56.39 | | | | | | REDUCE: (176), (311) imply: % 261.05/56.39 | | | | | | (312) $false % 261.05/56.39 | | | | | | % 261.05/56.39 | | | | | | CLOSE: (312) is inconsistent. % 261.05/56.39 | | | | | | % 261.05/56.39 | | | | | End of split % 261.05/56.39 | | | | | % 261.05/56.39 | | | | End of split % 261.05/56.39 | | | | % 261.05/56.39 | | | End of split % 261.05/56.39 | | | % 261.05/56.39 | | Case 2: % 261.05/56.39 | | | % 261.05/56.39 | | | (313) ~ (all_74_4 = all_74_5) & a_select3(r_ds1_filter, all_74_6, % 261.05/56.39 | | | all_74_7) = all_74_4 & a_select3(r_ds1_filter, all_74_7, % 261.05/56.39 | | | all_74_6) = all_74_5 & $i(all_74_4) & $i(all_74_5) & % 261.05/56.39 | | | leq(all_74_6, all_74_19) & leq(all_74_7, all_74_19) & leq(n0, % 261.05/56.39 | | | all_74_6) & leq(n0, all_74_7) % 261.05/56.39 | | | % 261.05/56.39 | | | ALPHA: (313) implies: % 261.05/56.39 | | | (314) ~ (all_74_4 = all_74_5) % 261.05/56.39 | | | (315) leq(n0, all_74_7) % 261.05/56.39 | | | (316) leq(n0, all_74_6) % 261.05/56.39 | | | (317) leq(all_74_7, all_74_19) % 261.05/56.39 | | | (318) leq(all_74_6, all_74_19) % 261.05/56.39 | | | (319) a_select3(r_ds1_filter, all_74_7, all_74_6) = all_74_5 % 261.05/56.39 | | | (320) a_select3(r_ds1_filter, all_74_6, all_74_7) = all_74_4 % 261.05/56.39 | | | % 261.05/56.39 | | | REDUCE: (158), (318) imply: % 261.05/56.39 | | | (321) leq(all_74_6, n2) % 261.05/56.39 | | | % 261.05/56.39 | | | REDUCE: (158), (317) imply: % 261.05/56.39 | | | (322) leq(all_74_7, n2) % 261.05/56.39 | | | % 261.05/56.39 | | | GROUND_INST: instantiating (leq_gt2) with n0, all_74_7, simplifying with % 261.05/56.39 | | | (22), (70), (315) gives: % 261.05/56.39 | | | (323) all_74_7 = n0 | gt(all_74_7, n0) % 261.05/56.39 | | | % 261.05/56.39 | | | GROUND_INST: instantiating (leq_gt2) with n0, all_74_6, simplifying with % 261.05/56.39 | | | (22), (71), (316) gives: % 261.05/56.39 | | | (324) all_74_6 = n0 | gt(all_74_6, n0) % 261.05/56.39 | | | % 261.05/56.39 | | | GROUND_INST: instantiating (14) with all_74_7, simplifying with (70), % 261.05/56.39 | | | (315), (322) gives: % 261.05/56.39 | | | (325) all_74_7 = n2 | all_74_7 = n1 | all_74_7 = n0 % 261.05/56.39 | | | % 261.05/56.39 | | | GROUND_INST: instantiating (leq_gt2) with all_74_7, n2, simplifying with % 261.05/56.39 | | | (70), (118), (322) gives: % 261.05/56.39 | | | (326) all_74_7 = n2 | gt(n2, all_74_7) % 261.05/56.39 | | | % 261.05/56.39 | | | GROUND_INST: instantiating (14) with all_74_6, simplifying with (71), % 261.05/56.39 | | | (316), (321) gives: % 261.05/56.39 | | | (327) all_74_6 = n2 | all_74_6 = n1 | all_74_6 = n0 % 261.05/56.39 | | | % 261.05/56.39 | | | GROUND_INST: instantiating (leq_gt2) with all_74_6, n2, simplifying with % 261.05/56.39 | | | (71), (118), (321) gives: % 261.05/56.39 | | | (328) all_74_6 = n2 | gt(n2, all_74_6) % 261.05/56.39 | | | % 261.05/56.39 | | | BETA: splitting (324) gives: % 261.05/56.39 | | | % 261.05/56.39 | | | Case 1: % 261.05/56.39 | | | | % 261.05/56.39 | | | | (329) gt(all_74_6, n0) % 261.05/56.39 | | | | % 261.05/56.39 | | | | BETA: splitting (323) gives: % 261.05/56.39 | | | | % 261.05/56.39 | | | | Case 1: % 261.05/56.39 | | | | | % 261.05/56.39 | | | | | (330) gt(all_74_7, n0) % 261.05/56.39 | | | | | % 261.05/56.39 | | | | | BETA: splitting (328) gives: % 261.05/56.39 | | | | | % 261.05/56.39 | | | | | Case 1: % 261.05/56.39 | | | | | | % 261.05/56.39 | | | | | | (331) gt(n2, all_74_6) % 261.05/56.39 | | | | | | % 261.05/56.39 | | | | | | BETA: splitting (326) gives: % 261.05/56.39 | | | | | | % 261.05/56.39 | | | | | | Case 1: % 261.05/56.39 | | | | | | | % 261.05/56.39 | | | | | | | (332) gt(n2, all_74_7) % 261.05/56.39 | | | | | | | % 261.05/56.39 | | | | | | | BETA: splitting (327) gives: % 261.05/56.39 | | | | | | | % 261.05/56.39 | | | | | | | Case 1: % 261.05/56.39 | | | | | | | | % 261.05/56.39 | | | | | | | | (333) all_74_6 = n0 % 261.05/56.39 | | | | | | | | % 261.05/56.39 | | | | | | | | REF_CLOSE: (71), (329), (333), (irreflexivity_gt) are % 261.05/56.39 | | | | | | | | inconsistent by sub-proof #68. % 261.05/56.39 | | | | | | | | % 261.05/56.39 | | | | | | | Case 2: % 261.05/56.39 | | | | | | | | % 261.05/56.39 | | | | | | | | (334) ~ (all_74_6 = n0) % 261.05/56.39 | | | | | | | | % 261.05/56.39 | | | | | | | | BETA: splitting (325) gives: % 261.05/56.39 | | | | | | | | % 261.05/56.39 | | | | | | | | Case 1: % 261.05/56.39 | | | | | | | | | % 261.05/56.39 | | | | | | | | | (335) all_74_7 = n0 % 261.05/56.39 | | | | | | | | | % 261.05/56.39 | | | | | | | | | REF_CLOSE: (70), (330), (335), (irreflexivity_gt) are % 261.05/56.39 | | | | | | | | | inconsistent by sub-proof #67. % 261.05/56.39 | | | | | | | | | % 261.05/56.39 | | | | | | | | Case 2: % 261.05/56.39 | | | | | | | | | % 261.05/56.39 | | | | | | | | | (336) ~ (all_74_7 = n0) % 261.05/56.39 | | | | | | | | | % 261.05/56.39 | | | | | | | | | GROUND_INST: instantiating (1) with all_74_7, n2, n1, % 261.05/56.39 | | | | | | | | | simplifying with (70), (118), (145), (332) gives: % 261.05/56.39 | | | | | | | | | (337) leq(all_74_7, n1) % 261.05/56.39 | | | | | | | | | % 261.05/56.39 | | | | | | | | | GROUND_INST: instantiating (1) with all_74_6, n2, n1, % 261.05/56.39 | | | | | | | | | simplifying with (71), (118), (145), (331) gives: % 261.05/56.39 | | | | | | | | | (338) leq(all_74_6, n1) % 261.05/56.39 | | | | | | | | | % 261.05/56.39 | | | | | | | | | GROUND_INST: instantiating (13) with all_74_7, simplifying with % 261.05/56.39 | | | | | | | | | (70), (315), (337) gives: % 261.05/56.39 | | | | | | | | | (339) all_74_7 = n1 | all_74_7 = n0 % 261.05/56.39 | | | | | | | | | % 261.05/56.39 | | | | | | | | | GROUND_INST: instantiating (13) with all_74_6, simplifying with % 261.05/56.39 | | | | | | | | | (71), (316), (338) gives: % 261.05/56.39 | | | | | | | | | (340) all_74_6 = n1 | all_74_6 = n0 % 261.05/56.39 | | | | | | | | | % 261.05/56.39 | | | | | | | | | BETA: splitting (340) gives: % 261.05/56.39 | | | | | | | | | % 261.05/56.39 | | | | | | | | | Case 1: % 261.05/56.39 | | | | | | | | | | % 261.05/56.39 | | | | | | | | | | (341) all_74_6 = n0 % 261.05/56.39 | | | | | | | | | | % 261.05/56.39 | | | | | | | | | | REDUCE: (334), (341) imply: % 261.05/56.39 | | | | | | | | | | (342) $false % 261.05/56.39 | | | | | | | | | | % 261.05/56.39 | | | | | | | | | | CLOSE: (342) is inconsistent. % 261.05/56.39 | | | | | | | | | | % 261.05/56.39 | | | | | | | | | Case 2: % 261.05/56.39 | | | | | | | | | | % 261.05/56.39 | | | | | | | | | | (343) all_74_6 = n1 % 261.05/56.39 | | | | | | | | | | % 261.05/56.39 | | | | | | | | | | REDUCE: (320), (343) imply: % 261.05/56.39 | | | | | | | | | | (344) a_select3(r_ds1_filter, n1, all_74_7) = all_74_4 % 261.05/56.39 | | | | | | | | | | % 261.05/56.39 | | | | | | | | | | REDUCE: (319), (343) imply: % 261.05/56.39 | | | | | | | | | | (345) a_select3(r_ds1_filter, all_74_7, n1) = all_74_5 % 261.05/56.39 | | | | | | | | | | % 261.05/56.39 | | | | | | | | | | BETA: splitting (339) gives: % 261.05/56.39 | | | | | | | | | | % 261.05/56.39 | | | | | | | | | | Case 1: % 261.05/56.39 | | | | | | | | | | | % 261.05/56.39 | | | | | | | | | | | (346) all_74_7 = n0 % 261.05/56.39 | | | | | | | | | | | % 261.05/56.39 | | | | | | | | | | | REDUCE: (336), (346) imply: % 261.05/56.39 | | | | | | | | | | | (347) $false % 261.05/56.39 | | | | | | | | | | | % 261.05/56.39 | | | | | | | | | | | CLOSE: (347) is inconsistent. % 261.05/56.39 | | | | | | | | | | | % 261.05/56.39 | | | | | | | | | | Case 2: % 261.05/56.39 | | | | | | | | | | | % 261.05/56.39 | | | | | | | | | | | (348) all_74_7 = n1 % 261.05/56.39 | | | | | | | | | | | % 261.05/56.39 | | | | | | | | | | | REDUCE: (345), (348) imply: % 261.05/56.39 | | | | | | | | | | | (349) a_select3(r_ds1_filter, n1, n1) = all_74_5 % 261.05/56.39 | | | | | | | | | | | % 261.05/56.39 | | | | | | | | | | | REDUCE: (344), (348) imply: % 261.05/56.39 | | | | | | | | | | | (350) a_select3(r_ds1_filter, n1, n1) = all_74_4 % 261.05/56.39 | | | | | | | | | | | % 261.05/56.39 | | | | | | | | | | | GROUND_INST: instantiating (30) with all_74_5, all_74_4, n1, % 261.05/56.39 | | | | | | | | | | | n1, r_ds1_filter, simplifying with (349), (350) % 261.05/56.39 | | | | | | | | | | | gives: % 261.05/56.39 | | | | | | | | | | | (351) all_74_4 = all_74_5 % 261.05/56.39 | | | | | | | | | | | % 261.05/56.39 | | | | | | | | | | | REDUCE: (314), (351) imply: % 261.05/56.39 | | | | | | | | | | | (352) $false % 261.05/56.39 | | | | | | | | | | | % 261.05/56.39 | | | | | | | | | | | CLOSE: (352) is inconsistent. % 261.05/56.39 | | | | | | | | | | | % 261.05/56.39 | | | | | | | | | | End of split % 261.05/56.39 | | | | | | | | | | % 261.05/56.39 | | | | | | | | | End of split % 261.05/56.39 | | | | | | | | | % 261.05/56.39 | | | | | | | | End of split % 261.05/56.39 | | | | | | | | % 261.05/56.39 | | | | | | | End of split % 261.05/56.39 | | | | | | | % 261.05/56.39 | | | | | | Case 2: % 261.05/56.39 | | | | | | | % 261.05/56.39 | | | | | | | (353) all_74_7 = n2 % 261.05/56.40 | | | | | | | % 261.05/56.40 | | | | | | | REDUCE: (320), (353) imply: % 261.05/56.40 | | | | | | | (354) a_select3(r_ds1_filter, all_74_6, n2) = all_74_4 % 261.05/56.40 | | | | | | | % 261.05/56.40 | | | | | | | REDUCE: (319), (353) imply: % 261.05/56.40 | | | | | | | (355) a_select3(r_ds1_filter, n2, all_74_6) = all_74_5 % 261.05/56.40 | | | | | | | % 261.05/56.40 | | | | | | | REDUCE: (322), (353) imply: % 261.05/56.40 | | | | | | | (356) leq(n2, n2) % 261.05/56.40 | | | | | | | % 261.05/56.40 | | | | | | | REDUCE: (315), (353) imply: % 261.05/56.40 | | | | | | | (357) leq(n0, n2) % 261.05/56.40 | | | | | | | % 261.05/56.40 | | | | | | | BETA: splitting (327) gives: % 261.05/56.40 | | | | | | | % 261.05/56.40 | | | | | | | Case 1: % 261.05/56.40 | | | | | | | | % 261.05/56.40 | | | | | | | | (358) all_74_6 = n0 % 261.05/56.40 | | | | | | | | % 261.05/56.40 | | | | | | | | REF_CLOSE: (71), (329), (358), (irreflexivity_gt) are % 261.05/56.40 | | | | | | | | inconsistent by sub-proof #68. % 261.05/56.40 | | | | | | | | % 261.05/56.40 | | | | | | | Case 2: % 261.05/56.40 | | | | | | | | % 261.05/56.40 | | | | | | | | (359) ~ (all_74_6 = n0) % 261.05/56.40 | | | | | | | | % 261.05/56.40 | | | | | | | | GROUND_INST: instantiating (1) with all_74_6, n2, n1, % 261.05/56.40 | | | | | | | | simplifying with (71), (118), (145), (331) gives: % 261.05/56.40 | | | | | | | | (360) leq(all_74_6, n1) % 261.05/56.40 | | | | | | | | % 261.05/56.40 | | | | | | | | GROUND_INST: instantiating (13) with all_74_6, simplifying with % 261.05/56.40 | | | | | | | | (71), (316), (360) gives: % 261.05/56.40 | | | | | | | | (361) all_74_6 = n1 | all_74_6 = n0 % 261.05/56.40 | | | | | | | | % 261.05/56.40 | | | | | | | | BETA: splitting (361) gives: % 261.05/56.40 | | | | | | | | % 261.05/56.40 | | | | | | | | Case 1: % 261.05/56.40 | | | | | | | | | % 261.05/56.40 | | | | | | | | | (362) all_74_6 = n0 % 261.05/56.40 | | | | | | | | | % 261.05/56.40 | | | | | | | | | REDUCE: (359), (362) imply: % 261.05/56.40 | | | | | | | | | (363) $false % 261.05/56.40 | | | | | | | | | % 261.05/56.40 | | | | | | | | | CLOSE: (363) is inconsistent. % 261.05/56.40 | | | | | | | | | % 261.05/56.40 | | | | | | | | Case 2: % 261.05/56.40 | | | | | | | | | % 261.05/56.40 | | | | | | | | | (364) all_74_6 = n1 % 261.05/56.40 | | | | | | | | | % 261.05/56.40 | | | | | | | | | REDUCE: (354), (364) imply: % 261.05/56.40 | | | | | | | | | (365) a_select3(r_ds1_filter, n1, n2) = all_74_4 % 261.05/56.40 | | | | | | | | | % 261.05/56.40 | | | | | | | | | REDUCE: (355), (364) imply: % 261.05/56.40 | | | | | | | | | (366) a_select3(r_ds1_filter, n2, n1) = all_74_5 % 261.05/56.40 | | | | | | | | | % 261.05/56.40 | | | | | | | | | REDUCE: (321), (364) imply: % 261.05/56.40 | | | | | | | | | (367) leq(n1, n2) % 261.05/56.40 | | | | | | | | | % 261.05/56.40 | | | | | | | | | REDUCE: (316), (364) imply: % 261.05/56.40 | | | | | | | | | (368) leq(n0, n1) % 261.05/56.40 | | | | | | | | | % 261.05/56.40 | | | | | | | | | GROUND_INST: instantiating (79) with n1, n2, all_74_4, % 261.05/56.40 | | | | | | | | | simplifying with (102), (118), (357), (365), (368) % 261.05/56.40 | | | | | | | | | gives: % 261.05/56.40 | | | | | | | | | (369) ~ leq(n2, all_74_19) | ~ leq(n1, all_74_19) | % 261.05/56.40 | | | | | | | | | (a_select3(r_ds1_filter, n2, n1) = all_74_4 & % 261.05/56.40 | | | | | | | | | $i(all_74_4)) % 261.05/56.40 | | | | | | | | | % 261.05/56.40 | | | | | | | | | BETA: splitting (369) gives: % 261.05/56.40 | | | | | | | | | % 261.05/56.40 | | | | | | | | | Case 1: % 261.05/56.40 | | | | | | | | | | % 261.05/56.40 | | | | | | | | | | (370) ~ leq(n2, all_74_19) % 261.05/56.40 | | | | | | | | | | % 261.05/56.40 | | | | | | | | | | REDUCE: (158), (370) imply: % 261.05/56.40 | | | | | | | | | | (371) ~ leq(n2, n2) % 261.05/56.40 | | | | | | | | | | % 261.05/56.40 | | | | | | | | | | PRED_UNIFY: (356), (371) imply: % 261.05/56.40 | | | | | | | | | | (372) $false % 261.05/56.40 | | | | | | | | | | % 261.05/56.40 | | | | | | | | | | CLOSE: (372) is inconsistent. % 261.05/56.40 | | | | | | | | | | % 261.05/56.40 | | | | | | | | | Case 2: % 261.05/56.40 | | | | | | | | | | % 261.05/56.40 | | | | | | | | | | (373) ~ leq(n1, all_74_19) | (a_select3(r_ds1_filter, % 261.05/56.40 | | | | | | | | | | n2, n1) = all_74_4 & $i(all_74_4)) % 261.05/56.40 | | | | | | | | | | % 261.05/56.40 | | | | | | | | | | BETA: splitting (373) gives: % 261.05/56.40 | | | | | | | | | | % 261.05/56.40 | | | | | | | | | | Case 1: % 261.05/56.40 | | | | | | | | | | | % 261.05/56.40 | | | | | | | | | | | (374) ~ leq(n1, all_74_19) % 261.05/56.40 | | | | | | | | | | | % 261.05/56.40 | | | | | | | | | | | REDUCE: (158), (374) imply: % 261.05/56.40 | | | | | | | | | | | (375) ~ leq(n1, n2) % 261.05/56.40 | | | | | | | | | | | % 261.05/56.40 | | | | | | | | | | | PRED_UNIFY: (367), (375) imply: % 261.05/56.40 | | | | | | | | | | | (376) $false % 261.05/56.40 | | | | | | | | | | | % 261.05/56.40 | | | | | | | | | | | CLOSE: (376) is inconsistent. % 261.05/56.40 | | | | | | | | | | | % 261.05/56.40 | | | | | | | | | | Case 2: % 261.05/56.40 | | | | | | | | | | | % 261.05/56.40 | | | | | | | | | | | (377) a_select3(r_ds1_filter, n2, n1) = all_74_4 & % 261.05/56.40 | | | | | | | | | | | $i(all_74_4) % 261.05/56.40 | | | | | | | | | | | % 261.05/56.40 | | | | | | | | | | | ALPHA: (377) implies: % 261.05/56.40 | | | | | | | | | | | (378) a_select3(r_ds1_filter, n2, n1) = all_74_4 % 261.05/56.40 | | | | | | | | | | | % 261.05/56.40 | | | | | | | | | | | REF_CLOSE: (30), (314), (366), (378) are inconsistent by % 261.05/56.40 | | | | | | | | | | | sub-proof #66. % 261.05/56.40 | | | | | | | | | | | % 261.05/56.40 | | | | | | | | | | End of split % 261.05/56.40 | | | | | | | | | | % 261.05/56.40 | | | | | | | | | End of split % 261.05/56.40 | | | | | | | | | % 261.05/56.40 | | | | | | | | End of split % 261.05/56.40 | | | | | | | | % 261.05/56.40 | | | | | | | End of split % 261.05/56.40 | | | | | | | % 261.05/56.40 | | | | | | End of split % 261.05/56.40 | | | | | | % 261.05/56.40 | | | | | Case 2: % 261.05/56.40 | | | | | | % 261.05/56.40 | | | | | | (379) all_74_6 = n2 % 261.05/56.40 | | | | | | % 261.05/56.40 | | | | | | REDUCE: (320), (379) imply: % 261.05/56.40 | | | | | | (380) a_select3(r_ds1_filter, n2, all_74_7) = all_74_4 % 261.05/56.40 | | | | | | % 261.05/56.40 | | | | | | REDUCE: (319), (379) imply: % 261.05/56.40 | | | | | | (381) a_select3(r_ds1_filter, all_74_7, n2) = all_74_5 % 261.05/56.40 | | | | | | % 261.05/56.40 | | | | | | REDUCE: (321), (379) imply: % 261.05/56.40 | | | | | | (382) leq(n2, n2) % 261.05/56.40 | | | | | | % 261.05/56.40 | | | | | | REDUCE: (316), (379) imply: % 261.05/56.40 | | | | | | (383) leq(n0, n2) % 261.05/56.40 | | | | | | % 261.05/56.40 | | | | | | BETA: splitting (326) gives: % 261.05/56.40 | | | | | | % 261.05/56.40 | | | | | | Case 1: % 261.05/56.40 | | | | | | | % 261.05/56.40 | | | | | | | (384) gt(n2, all_74_7) % 261.05/56.40 | | | | | | | % 261.05/56.40 | | | | | | | BETA: splitting (325) gives: % 261.05/56.40 | | | | | | | % 261.05/56.40 | | | | | | | Case 1: % 261.05/56.40 | | | | | | | | % 261.05/56.40 | | | | | | | | (385) all_74_7 = n0 % 261.05/56.40 | | | | | | | | % 261.05/56.40 | | | | | | | | REF_CLOSE: (70), (330), (385), (irreflexivity_gt) are % 261.05/56.40 | | | | | | | | inconsistent by sub-proof #67. % 261.05/56.40 | | | | | | | | % 261.05/56.40 | | | | | | | Case 2: % 261.05/56.40 | | | | | | | | % 261.05/56.40 | | | | | | | | (386) ~ (all_74_7 = n0) % 261.05/56.40 | | | | | | | | % 261.05/56.40 | | | | | | | | GROUND_INST: instantiating (1) with all_74_7, n2, n1, % 261.05/56.40 | | | | | | | | simplifying with (70), (118), (145), (384) gives: % 261.05/56.40 | | | | | | | | (387) leq(all_74_7, n1) % 261.05/56.40 | | | | | | | | % 261.05/56.40 | | | | | | | | GROUND_INST: instantiating (13) with all_74_7, simplifying with % 261.05/56.40 | | | | | | | | (70), (315), (387) gives: % 261.05/56.40 | | | | | | | | (388) all_74_7 = n1 | all_74_7 = n0 % 261.05/56.40 | | | | | | | | % 261.05/56.40 | | | | | | | | BETA: splitting (388) gives: % 261.05/56.40 | | | | | | | | % 261.05/56.40 | | | | | | | | Case 1: % 261.05/56.40 | | | | | | | | | % 261.05/56.40 | | | | | | | | | (389) all_74_7 = n0 % 261.05/56.40 | | | | | | | | | % 261.05/56.40 | | | | | | | | | REDUCE: (386), (389) imply: % 261.05/56.40 | | | | | | | | | (390) $false % 261.05/56.40 | | | | | | | | | % 261.05/56.40 | | | | | | | | | CLOSE: (390) is inconsistent. % 261.05/56.40 | | | | | | | | | % 261.05/56.40 | | | | | | | | Case 2: % 261.05/56.40 | | | | | | | | | % 261.05/56.40 | | | | | | | | | (391) all_74_7 = n1 % 261.05/56.40 | | | | | | | | | % 261.05/56.40 | | | | | | | | | REDUCE: (381), (391) imply: % 261.05/56.40 | | | | | | | | | (392) a_select3(r_ds1_filter, n1, n2) = all_74_5 % 261.05/56.40 | | | | | | | | | % 261.05/56.40 | | | | | | | | | REDUCE: (380), (391) imply: % 261.05/56.40 | | | | | | | | | (393) a_select3(r_ds1_filter, n2, n1) = all_74_4 % 261.05/56.40 | | | | | | | | | % 261.05/56.40 | | | | | | | | | REDUCE: (322), (391) imply: % 261.05/56.40 | | | | | | | | | (394) leq(n1, n2) % 261.05/56.40 | | | | | | | | | % 261.05/56.40 | | | | | | | | | REDUCE: (315), (391) imply: % 261.05/56.40 | | | | | | | | | (395) leq(n0, n1) % 261.05/56.40 | | | | | | | | | % 261.05/56.40 | | | | | | | | | GROUND_INST: instantiating (79) with n1, n2, all_74_5, % 261.05/56.40 | | | | | | | | | simplifying with (102), (118), (383), (392), (395) % 261.05/56.40 | | | | | | | | | gives: % 261.05/56.40 | | | | | | | | | (396) ~ leq(n2, all_74_19) | ~ leq(n1, all_74_19) | % 261.05/56.40 | | | | | | | | | (a_select3(r_ds1_filter, n2, n1) = all_74_5 & % 261.05/56.40 | | | | | | | | | $i(all_74_5)) % 261.05/56.40 | | | | | | | | | % 261.05/56.40 | | | | | | | | | BETA: splitting (396) gives: % 261.05/56.40 | | | | | | | | | % 261.05/56.40 | | | | | | | | | Case 1: % 261.05/56.40 | | | | | | | | | | % 261.05/56.40 | | | | | | | | | | (397) ~ leq(n2, all_74_19) % 261.05/56.40 | | | | | | | | | | % 261.05/56.40 | | | | | | | | | | REDUCE: (158), (397) imply: % 261.05/56.40 | | | | | | | | | | (398) ~ leq(n2, n2) % 261.05/56.40 | | | | | | | | | | % 261.05/56.40 | | | | | | | | | | PRED_UNIFY: (382), (398) imply: % 261.05/56.40 | | | | | | | | | | (399) $false % 261.05/56.40 | | | | | | | | | | % 261.05/56.40 | | | | | | | | | | CLOSE: (399) is inconsistent. % 261.05/56.40 | | | | | | | | | | % 261.05/56.40 | | | | | | | | | Case 2: % 261.05/56.40 | | | | | | | | | | % 261.05/56.40 | | | | | | | | | | (400) ~ leq(n1, all_74_19) | (a_select3(r_ds1_filter, % 261.05/56.40 | | | | | | | | | | n2, n1) = all_74_5 & $i(all_74_5)) % 261.05/56.40 | | | | | | | | | | % 261.05/56.40 | | | | | | | | | | BETA: splitting (400) gives: % 261.05/56.40 | | | | | | | | | | % 261.05/56.40 | | | | | | | | | | Case 1: % 261.05/56.40 | | | | | | | | | | | % 261.05/56.40 | | | | | | | | | | | (401) ~ leq(n1, all_74_19) % 261.05/56.40 | | | | | | | | | | | % 261.05/56.40 | | | | | | | | | | | REDUCE: (158), (401) imply: % 261.05/56.40 | | | | | | | | | | | (402) ~ leq(n1, n2) % 261.05/56.40 | | | | | | | | | | | % 261.05/56.40 | | | | | | | | | | | PRED_UNIFY: (394), (402) imply: % 261.05/56.40 | | | | | | | | | | | (403) $false % 261.05/56.40 | | | | | | | | | | | % 261.05/56.40 | | | | | | | | | | | CLOSE: (403) is inconsistent. % 261.05/56.40 | | | | | | | | | | | % 261.05/56.40 | | | | | | | | | | Case 2: % 261.05/56.40 | | | | | | | | | | | % 261.05/56.40 | | | | | | | | | | | (404) a_select3(r_ds1_filter, n2, n1) = all_74_5 & % 261.05/56.40 | | | | | | | | | | | $i(all_74_5) % 261.05/56.40 | | | | | | | | | | | % 261.05/56.40 | | | | | | | | | | | ALPHA: (404) implies: % 261.05/56.40 | | | | | | | | | | | (405) a_select3(r_ds1_filter, n2, n1) = all_74_5 % 261.05/56.40 | | | | | | | | | | | % 261.05/56.40 | | | | | | | | | | | REF_CLOSE: (30), (314), (393), (405) are inconsistent by % 261.05/56.40 | | | | | | | | | | | sub-proof #66. % 261.05/56.40 | | | | | | | | | | | % 261.05/56.40 | | | | | | | | | | End of split % 261.05/56.40 | | | | | | | | | | % 261.05/56.40 | | | | | | | | | End of split % 261.05/56.40 | | | | | | | | | % 261.05/56.40 | | | | | | | | End of split % 261.05/56.40 | | | | | | | | % 261.05/56.40 | | | | | | | End of split % 261.05/56.40 | | | | | | | % 261.05/56.40 | | | | | | Case 2: % 261.05/56.40 | | | | | | | % 261.05/56.40 | | | | | | | (406) all_74_7 = n2 % 261.05/56.40 | | | | | | | % 261.05/56.40 | | | | | | | REDUCE: (381), (406) imply: % 261.05/56.41 | | | | | | | (407) a_select3(r_ds1_filter, n2, n2) = all_74_5 % 261.05/56.41 | | | | | | | % 261.05/56.41 | | | | | | | REDUCE: (380), (406) imply: % 261.05/56.41 | | | | | | | (408) a_select3(r_ds1_filter, n2, n2) = all_74_4 % 261.05/56.41 | | | | | | | % 261.05/56.41 | | | | | | | GROUND_INST: instantiating (30) with all_74_5, all_74_4, n2, n2, % 261.05/56.41 | | | | | | | r_ds1_filter, simplifying with (407), (408) gives: % 261.05/56.41 | | | | | | | (409) all_74_4 = all_74_5 % 261.05/56.41 | | | | | | | % 261.05/56.41 | | | | | | | REDUCE: (314), (409) imply: % 261.05/56.41 | | | | | | | (410) $false % 261.05/56.41 | | | | | | | % 261.05/56.41 | | | | | | | CLOSE: (410) is inconsistent. % 261.05/56.41 | | | | | | | % 261.05/56.41 | | | | | | End of split % 261.05/56.41 | | | | | | % 261.05/56.41 | | | | | End of split % 261.05/56.41 | | | | | % 261.05/56.41 | | | | Case 2: % 261.05/56.41 | | | | | % 261.05/56.41 | | | | | (411) all_74_7 = n0 % 261.05/56.41 | | | | | (412) ~ gt(all_74_7, n0) % 261.05/56.41 | | | | | % 261.05/56.41 | | | | | REDUCE: (320), (411) imply: % 261.05/56.41 | | | | | (413) a_select3(r_ds1_filter, all_74_6, n0) = all_74_4 % 261.05/56.41 | | | | | % 261.05/56.41 | | | | | REDUCE: (319), (411) imply: % 261.05/56.41 | | | | | (414) a_select3(r_ds1_filter, n0, all_74_6) = all_74_5 % 261.05/56.41 | | | | | % 261.05/56.41 | | | | | REDUCE: (322), (411) imply: % 261.05/56.41 | | | | | (415) leq(n0, n2) % 261.05/56.41 | | | | | % 261.05/56.41 | | | | | REDUCE: (315), (411) imply: % 261.05/56.41 | | | | | (416) leq(n0, n0) % 261.05/56.41 | | | | | % 261.05/56.41 | | | | | REDUCE: (411), (412) imply: % 261.05/56.41 | | | | | (417) ~ gt(n0, n0) % 261.05/56.41 | | | | | % 261.05/56.41 | | | | | BETA: splitting (328) gives: % 261.05/56.41 | | | | | % 261.05/56.41 | | | | | Case 1: % 261.05/56.41 | | | | | | % 261.05/56.41 | | | | | | (418) gt(n2, all_74_6) % 261.05/56.41 | | | | | | % 261.05/56.41 | | | | | | BETA: splitting (327) gives: % 261.05/56.41 | | | | | | % 261.05/56.41 | | | | | | Case 1: % 261.05/56.41 | | | | | | | % 261.05/56.41 | | | | | | | (419) all_74_6 = n0 % 261.05/56.41 | | | | | | | % 261.05/56.41 | | | | | | | REDUCE: (329), (419) imply: % 261.05/56.41 | | | | | | | (420) gt(n0, n0) % 261.05/56.41 | | | | | | | % 261.05/56.41 | | | | | | | PRED_UNIFY: (417), (420) imply: % 261.05/56.41 | | | | | | | (421) $false % 261.05/56.41 | | | | | | | % 261.05/56.41 | | | | | | | CLOSE: (421) is inconsistent. % 261.05/56.41 | | | | | | | % 261.05/56.41 | | | | | | Case 2: % 261.05/56.41 | | | | | | | % 261.05/56.41 | | | | | | | (422) ~ (all_74_6 = n0) % 261.05/56.41 | | | | | | | % 261.05/56.41 | | | | | | | GROUND_INST: instantiating (1) with all_74_6, n2, n1, simplifying % 261.05/56.41 | | | | | | | with (71), (118), (145), (418) gives: % 261.05/56.41 | | | | | | | (423) leq(all_74_6, n1) % 261.05/56.41 | | | | | | | % 261.05/56.41 | | | | | | | GROUND_INST: instantiating (13) with all_74_6, simplifying with % 261.05/56.41 | | | | | | | (71), (316), (423) gives: % 261.05/56.41 | | | | | | | (424) all_74_6 = n1 | all_74_6 = n0 % 261.05/56.41 | | | | | | | % 261.05/56.41 | | | | | | | BETA: splitting (424) gives: % 261.05/56.41 | | | | | | | % 261.05/56.41 | | | | | | | Case 1: % 261.05/56.41 | | | | | | | | % 261.05/56.41 | | | | | | | | (425) all_74_6 = n0 % 261.05/56.41 | | | | | | | | % 261.05/56.41 | | | | | | | | REDUCE: (422), (425) imply: % 261.05/56.41 | | | | | | | | (426) $false % 261.05/56.41 | | | | | | | | % 261.05/56.41 | | | | | | | | CLOSE: (426) is inconsistent. % 261.05/56.41 | | | | | | | | % 261.05/56.41 | | | | | | | Case 2: % 261.05/56.41 | | | | | | | | % 261.05/56.41 | | | | | | | | (427) all_74_6 = n1 % 261.05/56.41 | | | | | | | | % 261.05/56.41 | | | | | | | | REDUCE: (413), (427) imply: % 261.05/56.41 | | | | | | | | (428) a_select3(r_ds1_filter, n1, n0) = all_74_4 % 261.05/56.41 | | | | | | | | % 261.05/56.41 | | | | | | | | REDUCE: (414), (427) imply: % 261.05/56.41 | | | | | | | | (429) a_select3(r_ds1_filter, n0, n1) = all_74_5 % 261.05/56.41 | | | | | | | | % 261.05/56.41 | | | | | | | | REDUCE: (321), (427) imply: % 261.05/56.41 | | | | | | | | (430) leq(n1, n2) % 261.05/56.41 | | | | | | | | % 261.05/56.41 | | | | | | | | REDUCE: (316), (427) imply: % 261.05/56.41 | | | | | | | | (431) leq(n0, n1) % 261.05/56.41 | | | | | | | | % 261.05/56.41 | | | | | | | | GROUND_INST: instantiating (79) with n0, n1, all_74_5, % 261.05/56.41 | | | | | | | | simplifying with (22), (102), (416), (429), (431) % 261.05/56.41 | | | | | | | | gives: % 261.05/56.41 | | | | | | | | (432) ~ leq(n1, all_74_19) | ~ leq(n0, all_74_19) | % 261.05/56.41 | | | | | | | | (a_select3(r_ds1_filter, n1, n0) = all_74_5 & % 261.05/56.41 | | | | | | | | $i(all_74_5)) % 261.05/56.41 | | | | | | | | % 261.05/56.41 | | | | | | | | BETA: splitting (432) gives: % 261.05/56.41 | | | | | | | | % 261.05/56.41 | | | | | | | | Case 1: % 261.05/56.41 | | | | | | | | | % 261.05/56.41 | | | | | | | | | (433) ~ leq(n0, all_74_19) % 261.05/56.41 | | | | | | | | | % 261.05/56.41 | | | | | | | | | REDUCE: (158), (433) imply: % 261.05/56.41 | | | | | | | | | (434) ~ leq(n0, n2) % 261.05/56.41 | | | | | | | | | % 261.05/56.41 | | | | | | | | | PRED_UNIFY: (415), (434) imply: % 261.05/56.41 | | | | | | | | | (435) $false % 261.05/56.41 | | | | | | | | | % 261.05/56.41 | | | | | | | | | CLOSE: (435) is inconsistent. % 261.05/56.41 | | | | | | | | | % 261.05/56.41 | | | | | | | | Case 2: % 261.05/56.41 | | | | | | | | | % 261.05/56.41 | | | | | | | | | (436) ~ leq(n1, all_74_19) | (a_select3(r_ds1_filter, n1, % 261.05/56.41 | | | | | | | | | n0) = all_74_5 & $i(all_74_5)) % 261.05/56.41 | | | | | | | | | % 261.05/56.41 | | | | | | | | | BETA: splitting (436) gives: % 261.05/56.41 | | | | | | | | | % 261.05/56.41 | | | | | | | | | Case 1: % 261.05/56.41 | | | | | | | | | | % 261.05/56.41 | | | | | | | | | | (437) ~ leq(n1, all_74_19) % 261.05/56.41 | | | | | | | | | | % 261.05/56.41 | | | | | | | | | | REDUCE: (158), (437) imply: % 261.05/56.41 | | | | | | | | | | (438) ~ leq(n1, n2) % 261.05/56.41 | | | | | | | | | | % 261.05/56.41 | | | | | | | | | | PRED_UNIFY: (430), (438) imply: % 261.05/56.41 | | | | | | | | | | (439) $false % 261.05/56.41 | | | | | | | | | | % 261.05/56.41 | | | | | | | | | | CLOSE: (439) is inconsistent. % 261.05/56.41 | | | | | | | | | | % 261.05/56.41 | | | | | | | | | Case 2: % 261.05/56.41 | | | | | | | | | | % 261.05/56.41 | | | | | | | | | | (440) a_select3(r_ds1_filter, n1, n0) = all_74_5 & % 261.05/56.41 | | | | | | | | | | $i(all_74_5) % 261.05/56.41 | | | | | | | | | | % 261.05/56.41 | | | | | | | | | | ALPHA: (440) implies: % 261.05/56.41 | | | | | | | | | | (441) a_select3(r_ds1_filter, n1, n0) = all_74_5 % 261.05/56.41 | | | | | | | | | | % 261.05/56.41 | | | | | | | | | | REF_CLOSE: (30), (314), (428), (441) are inconsistent by % 261.05/56.41 | | | | | | | | | | sub-proof #65. % 261.05/56.41 | | | | | | | | | | % 261.05/56.41 | | | | | | | | | End of split % 261.05/56.41 | | | | | | | | | % 261.05/56.41 | | | | | | | | End of split % 261.05/56.41 | | | | | | | | % 261.05/56.41 | | | | | | | End of split % 261.05/56.41 | | | | | | | % 261.05/56.41 | | | | | | End of split % 261.05/56.41 | | | | | | % 261.05/56.41 | | | | | Case 2: % 261.05/56.41 | | | | | | % 261.05/56.41 | | | | | | (442) all_74_6 = n2 % 261.05/56.41 | | | | | | % 261.05/56.41 | | | | | | REDUCE: (413), (442) imply: % 261.05/56.41 | | | | | | (443) a_select3(r_ds1_filter, n2, n0) = all_74_4 % 261.05/56.41 | | | | | | % 261.05/56.41 | | | | | | REDUCE: (414), (442) imply: % 261.05/56.41 | | | | | | (444) a_select3(r_ds1_filter, n0, n2) = all_74_5 % 261.05/56.41 | | | | | | % 261.05/56.41 | | | | | | REDUCE: (321), (442) imply: % 261.05/56.41 | | | | | | (445) leq(n2, n2) % 261.05/56.41 | | | | | | % 261.05/56.41 | | | | | | GROUND_INST: instantiating (79) with n0, n2, all_74_5, simplifying % 261.05/56.41 | | | | | | with (22), (118), (415), (416), (444) gives: % 261.05/56.41 | | | | | | (446) ~ leq(n2, all_74_19) | ~ leq(n0, all_74_19) | % 261.05/56.41 | | | | | | (a_select3(r_ds1_filter, n2, n0) = all_74_5 & $i(all_74_5)) % 261.05/56.41 | | | | | | % 261.05/56.41 | | | | | | BETA: splitting (446) gives: % 261.05/56.41 | | | | | | % 261.05/56.41 | | | | | | Case 1: % 261.05/56.41 | | | | | | | % 261.05/56.41 | | | | | | | (447) ~ leq(n0, all_74_19) % 261.05/56.41 | | | | | | | % 261.05/56.41 | | | | | | | REDUCE: (158), (447) imply: % 261.05/56.41 | | | | | | | (448) ~ leq(n0, n2) % 261.05/56.41 | | | | | | | % 261.05/56.41 | | | | | | | PRED_UNIFY: (415), (448) imply: % 261.05/56.41 | | | | | | | (449) $false % 261.05/56.41 | | | | | | | % 261.05/56.41 | | | | | | | CLOSE: (449) is inconsistent. % 261.05/56.41 | | | | | | | % 261.05/56.41 | | | | | | Case 2: % 261.05/56.41 | | | | | | | % 261.05/56.41 | | | | | | | (450) ~ leq(n2, all_74_19) | (a_select3(r_ds1_filter, n2, n0) % 261.05/56.41 | | | | | | | = all_74_5 & $i(all_74_5)) % 261.05/56.41 | | | | | | | % 261.05/56.41 | | | | | | | BETA: splitting (450) gives: % 261.05/56.41 | | | | | | | % 261.05/56.41 | | | | | | | Case 1: % 261.05/56.41 | | | | | | | | % 261.05/56.41 | | | | | | | | (451) ~ leq(n2, all_74_19) % 261.05/56.41 | | | | | | | | % 261.05/56.41 | | | | | | | | REDUCE: (158), (451) imply: % 261.05/56.41 | | | | | | | | (452) ~ leq(n2, n2) % 261.05/56.41 | | | | | | | | % 261.05/56.41 | | | | | | | | PRED_UNIFY: (445), (452) imply: % 261.05/56.41 | | | | | | | | (453) $false % 261.05/56.41 | | | | | | | | % 261.05/56.41 | | | | | | | | CLOSE: (453) is inconsistent. % 261.05/56.41 | | | | | | | | % 261.05/56.41 | | | | | | | Case 2: % 261.05/56.41 | | | | | | | | % 261.05/56.41 | | | | | | | | (454) a_select3(r_ds1_filter, n2, n0) = all_74_5 & % 261.05/56.41 | | | | | | | | $i(all_74_5) % 261.05/56.41 | | | | | | | | % 261.05/56.41 | | | | | | | | ALPHA: (454) implies: % 261.05/56.41 | | | | | | | | (455) a_select3(r_ds1_filter, n2, n0) = all_74_5 % 261.05/56.41 | | | | | | | | % 261.05/56.41 | | | | | | | | GROUND_INST: instantiating (30) with all_74_5, all_74_4, n0, n2, % 261.05/56.41 | | | | | | | | r_ds1_filter, simplifying with (443), (455) gives: % 261.05/56.41 | | | | | | | | (456) all_74_4 = all_74_5 % 261.05/56.41 | | | | | | | | % 261.05/56.41 | | | | | | | | REDUCE: (314), (456) imply: % 261.05/56.41 | | | | | | | | (457) $false % 261.05/56.41 | | | | | | | | % 261.05/56.41 | | | | | | | | CLOSE: (457) is inconsistent. % 261.05/56.41 | | | | | | | | % 261.05/56.41 | | | | | | | End of split % 261.05/56.41 | | | | | | | % 261.05/56.41 | | | | | | End of split % 261.05/56.41 | | | | | | % 261.05/56.41 | | | | | End of split % 261.05/56.41 | | | | | % 261.05/56.41 | | | | End of split % 261.05/56.41 | | | | % 261.05/56.41 | | | Case 2: % 261.05/56.41 | | | | % 261.05/56.41 | | | | (458) all_74_6 = n0 % 261.05/56.41 | | | | (459) ~ gt(all_74_6, n0) % 261.05/56.41 | | | | % 261.05/56.41 | | | | REDUCE: (320), (458) imply: % 261.05/56.41 | | | | (460) a_select3(r_ds1_filter, n0, all_74_7) = all_74_4 % 261.05/56.41 | | | | % 261.05/56.41 | | | | REDUCE: (319), (458) imply: % 261.05/56.41 | | | | (461) a_select3(r_ds1_filter, all_74_7, n0) = all_74_5 % 261.05/56.41 | | | | % 261.05/56.41 | | | | REDUCE: (321), (458) imply: % 261.05/56.41 | | | | (462) leq(n0, n2) % 261.05/56.41 | | | | % 261.05/56.42 | | | | REDUCE: (316), (458) imply: % 261.05/56.42 | | | | (463) leq(n0, n0) % 261.05/56.42 | | | | % 261.05/56.42 | | | | REDUCE: (458), (459) imply: % 261.05/56.42 | | | | (464) ~ gt(n0, n0) % 261.05/56.42 | | | | % 261.05/56.42 | | | | BETA: splitting (323) gives: % 261.05/56.42 | | | | % 261.05/56.42 | | | | Case 1: % 261.05/56.42 | | | | | % 261.05/56.42 | | | | | (465) gt(all_74_7, n0) % 261.05/56.42 | | | | | % 261.05/56.42 | | | | | BETA: splitting (326) gives: % 261.05/56.42 | | | | | % 261.05/56.42 | | | | | Case 1: % 261.05/56.42 | | | | | | % 261.05/56.42 | | | | | | (466) gt(n2, all_74_7) % 261.05/56.42 | | | | | | % 261.05/56.42 | | | | | | GROUND_INST: instantiating (1) with all_74_7, n2, n1, simplifying % 261.05/56.42 | | | | | | with (70), (118), (145), (466) gives: % 261.05/56.42 | | | | | | (467) leq(all_74_7, n1) % 261.05/56.42 | | | | | | % 261.05/56.42 | | | | | | BETA: splitting (325) gives: % 261.05/56.42 | | | | | | % 261.05/56.42 | | | | | | Case 1: % 261.05/56.42 | | | | | | | % 261.05/56.42 | | | | | | | (468) all_74_7 = n0 % 261.05/56.42 | | | | | | | % 261.05/56.42 | | | | | | | REDUCE: (465), (468) imply: % 261.05/56.42 | | | | | | | (469) gt(n0, n0) % 261.05/56.42 | | | | | | | % 261.05/56.42 | | | | | | | PRED_UNIFY: (464), (469) imply: % 261.05/56.42 | | | | | | | (470) $false % 261.05/56.42 | | | | | | | % 261.05/56.42 | | | | | | | CLOSE: (470) is inconsistent. % 261.05/56.42 | | | | | | | % 261.05/56.42 | | | | | | Case 2: % 261.05/56.42 | | | | | | | % 261.05/56.42 | | | | | | | (471) ~ (all_74_7 = n0) % 261.05/56.42 | | | | | | | % 261.05/56.42 | | | | | | | GROUND_INST: instantiating (13) with all_74_7, simplifying with % 261.05/56.42 | | | | | | | (70), (315), (467) gives: % 261.05/56.42 | | | | | | | (472) all_74_7 = n1 | all_74_7 = n0 % 261.05/56.42 | | | | | | | % 261.05/56.42 | | | | | | | BETA: splitting (472) gives: % 261.05/56.42 | | | | | | | % 261.05/56.42 | | | | | | | Case 1: % 261.05/56.42 | | | | | | | | % 261.05/56.42 | | | | | | | | (473) all_74_7 = n0 % 261.05/56.42 | | | | | | | | % 261.05/56.42 | | | | | | | | REDUCE: (471), (473) imply: % 261.05/56.42 | | | | | | | | (474) $false % 261.05/56.42 | | | | | | | | % 261.05/56.42 | | | | | | | | CLOSE: (474) is inconsistent. % 261.05/56.42 | | | | | | | | % 261.05/56.42 | | | | | | | Case 2: % 261.05/56.42 | | | | | | | | % 261.05/56.42 | | | | | | | | (475) all_74_7 = n1 % 261.05/56.42 | | | | | | | | % 261.05/56.42 | | | | | | | | REDUCE: (461), (475) imply: % 261.05/56.42 | | | | | | | | (476) a_select3(r_ds1_filter, n1, n0) = all_74_5 % 261.05/56.42 | | | | | | | | % 261.05/56.42 | | | | | | | | REDUCE: (460), (475) imply: % 261.05/56.42 | | | | | | | | (477) a_select3(r_ds1_filter, n0, n1) = all_74_4 % 261.05/56.42 | | | | | | | | % 261.05/56.42 | | | | | | | | REDUCE: (322), (475) imply: % 261.05/56.42 | | | | | | | | (478) leq(n1, n2) % 261.05/56.42 | | | | | | | | % 261.05/56.42 | | | | | | | | REDUCE: (315), (475) imply: % 261.05/56.42 | | | | | | | | (479) leq(n0, n1) % 261.05/56.42 | | | | | | | | % 261.05/56.42 | | | | | | | | GROUND_INST: instantiating (79) with n0, n1, all_74_4, % 261.05/56.42 | | | | | | | | simplifying with (22), (102), (463), (477), (479) % 261.05/56.42 | | | | | | | | gives: % 261.05/56.42 | | | | | | | | (480) ~ leq(n1, all_74_19) | ~ leq(n0, all_74_19) | % 261.05/56.42 | | | | | | | | (a_select3(r_ds1_filter, n1, n0) = all_74_4 & % 261.05/56.42 | | | | | | | | $i(all_74_4)) % 261.05/56.42 | | | | | | | | % 261.05/56.42 | | | | | | | | BETA: splitting (480) gives: % 261.05/56.42 | | | | | | | | % 261.05/56.42 | | | | | | | | Case 1: % 261.05/56.42 | | | | | | | | | % 261.05/56.42 | | | | | | | | | (481) ~ leq(n0, all_74_19) % 261.05/56.42 | | | | | | | | | % 261.05/56.42 | | | | | | | | | REDUCE: (158), (481) imply: % 261.05/56.42 | | | | | | | | | (482) ~ leq(n0, n2) % 261.05/56.42 | | | | | | | | | % 261.05/56.42 | | | | | | | | | PRED_UNIFY: (462), (482) imply: % 261.05/56.42 | | | | | | | | | (483) $false % 261.05/56.42 | | | | | | | | | % 261.05/56.42 | | | | | | | | | CLOSE: (483) is inconsistent. % 261.05/56.42 | | | | | | | | | % 261.05/56.42 | | | | | | | | Case 2: % 261.05/56.42 | | | | | | | | | % 261.05/56.42 | | | | | | | | | (484) ~ leq(n1, all_74_19) | (a_select3(r_ds1_filter, n1, % 261.05/56.42 | | | | | | | | | n0) = all_74_4 & $i(all_74_4)) % 261.05/56.42 | | | | | | | | | % 261.05/56.42 | | | | | | | | | BETA: splitting (484) gives: % 261.05/56.42 | | | | | | | | | % 261.05/56.42 | | | | | | | | | Case 1: % 261.05/56.42 | | | | | | | | | | % 261.05/56.42 | | | | | | | | | | (485) ~ leq(n1, all_74_19) % 261.05/56.42 | | | | | | | | | | % 261.05/56.42 | | | | | | | | | | REDUCE: (158), (485) imply: % 261.05/56.42 | | | | | | | | | | (486) ~ leq(n1, n2) % 261.05/56.42 | | | | | | | | | | % 261.05/56.42 | | | | | | | | | | PRED_UNIFY: (478), (486) imply: % 261.05/56.42 | | | | | | | | | | (487) $false % 261.05/56.42 | | | | | | | | | | % 261.05/56.42 | | | | | | | | | | CLOSE: (487) is inconsistent. % 261.05/56.42 | | | | | | | | | | % 261.05/56.42 | | | | | | | | | Case 2: % 261.05/56.42 | | | | | | | | | | % 261.05/56.42 | | | | | | | | | | (488) a_select3(r_ds1_filter, n1, n0) = all_74_4 & % 261.05/56.42 | | | | | | | | | | $i(all_74_4) % 261.05/56.42 | | | | | | | | | | % 261.05/56.42 | | | | | | | | | | ALPHA: (488) implies: % 261.05/56.42 | | | | | | | | | | (489) a_select3(r_ds1_filter, n1, n0) = all_74_4 % 261.05/56.42 | | | | | | | | | | % 261.05/56.42 | | | | | | | | | | REF_CLOSE: (30), (314), (476), (489) are inconsistent by % 261.05/56.42 | | | | | | | | | | sub-proof #65. % 261.05/56.42 | | | | | | | | | | % 261.05/56.42 | | | | | | | | | End of split % 261.05/56.42 | | | | | | | | | % 261.05/56.42 | | | | | | | | End of split % 261.05/56.42 | | | | | | | | % 261.05/56.42 | | | | | | | End of split % 261.05/56.42 | | | | | | | % 261.05/56.42 | | | | | | End of split % 261.05/56.42 | | | | | | % 261.05/56.42 | | | | | Case 2: % 261.05/56.42 | | | | | | % 261.05/56.42 | | | | | | (490) all_74_7 = n2 % 261.05/56.42 | | | | | | % 261.05/56.42 | | | | | | REDUCE: (461), (490) imply: % 261.05/56.42 | | | | | | (491) a_select3(r_ds1_filter, n2, n0) = all_74_5 % 261.05/56.42 | | | | | | % 261.05/56.42 | | | | | | REDUCE: (460), (490) imply: % 261.05/56.42 | | | | | | (492) a_select3(r_ds1_filter, n0, n2) = all_74_4 % 261.05/56.42 | | | | | | % 261.05/56.42 | | | | | | REDUCE: (322), (490) imply: % 261.05/56.42 | | | | | | (493) leq(n2, n2) % 261.05/56.42 | | | | | | % 261.05/56.42 | | | | | | GROUND_INST: instantiating (79) with n0, n2, all_74_4, simplifying % 261.05/56.42 | | | | | | with (22), (118), (462), (463), (492) gives: % 261.05/56.42 | | | | | | (494) ~ leq(n2, all_74_19) | ~ leq(n0, all_74_19) | % 261.05/56.42 | | | | | | (a_select3(r_ds1_filter, n2, n0) = all_74_4 & $i(all_74_4)) % 261.05/56.42 | | | | | | % 261.05/56.42 | | | | | | BETA: splitting (494) gives: % 261.05/56.42 | | | | | | % 261.05/56.42 | | | | | | Case 1: % 261.05/56.42 | | | | | | | % 261.05/56.42 | | | | | | | (495) ~ leq(n0, all_74_19) % 261.05/56.42 | | | | | | | % 261.05/56.42 | | | | | | | REDUCE: (158), (495) imply: % 261.05/56.42 | | | | | | | (496) ~ leq(n0, n2) % 261.05/56.42 | | | | | | | % 261.05/56.42 | | | | | | | PRED_UNIFY: (462), (496) imply: % 261.05/56.42 | | | | | | | (497) $false % 261.05/56.42 | | | | | | | % 261.05/56.42 | | | | | | | CLOSE: (497) is inconsistent. % 261.05/56.42 | | | | | | | % 261.05/56.42 | | | | | | Case 2: % 261.05/56.42 | | | | | | | % 261.05/56.42 | | | | | | | (498) ~ leq(n2, all_74_19) | (a_select3(r_ds1_filter, n2, n0) % 261.05/56.42 | | | | | | | = all_74_4 & $i(all_74_4)) % 261.05/56.42 | | | | | | | % 261.05/56.42 | | | | | | | BETA: splitting (498) gives: % 261.05/56.42 | | | | | | | % 261.05/56.42 | | | | | | | Case 1: % 261.05/56.42 | | | | | | | | % 261.05/56.42 | | | | | | | | (499) ~ leq(n2, all_74_19) % 261.05/56.42 | | | | | | | | % 261.05/56.42 | | | | | | | | REDUCE: (158), (499) imply: % 261.05/56.42 | | | | | | | | (500) ~ leq(n2, n2) % 261.05/56.42 | | | | | | | | % 261.05/56.42 | | | | | | | | PRED_UNIFY: (493), (500) imply: % 261.05/56.42 | | | | | | | | (501) $false % 261.05/56.42 | | | | | | | | % 261.05/56.42 | | | | | | | | CLOSE: (501) is inconsistent. % 261.05/56.42 | | | | | | | | % 261.05/56.42 | | | | | | | Case 2: % 261.05/56.42 | | | | | | | | % 261.05/56.42 | | | | | | | | (502) a_select3(r_ds1_filter, n2, n0) = all_74_4 & % 261.05/56.42 | | | | | | | | $i(all_74_4) % 261.05/56.42 | | | | | | | | % 261.05/56.42 | | | | | | | | ALPHA: (502) implies: % 261.05/56.42 | | | | | | | | (503) a_select3(r_ds1_filter, n2, n0) = all_74_4 % 261.05/56.42 | | | | | | | | % 261.05/56.42 | | | | | | | | GROUND_INST: instantiating (30) with all_74_5, all_74_4, n0, n2, % 261.05/56.42 | | | | | | | | r_ds1_filter, simplifying with (491), (503) gives: % 261.05/56.42 | | | | | | | | (504) all_74_4 = all_74_5 % 261.05/56.42 | | | | | | | | % 261.05/56.42 | | | | | | | | REDUCE: (314), (504) imply: % 261.05/56.42 | | | | | | | | (505) $false % 261.05/56.42 | | | | | | | | % 261.05/56.42 | | | | | | | | CLOSE: (505) is inconsistent. % 261.05/56.42 | | | | | | | | % 261.05/56.42 | | | | | | | End of split % 261.05/56.42 | | | | | | | % 261.05/56.42 | | | | | | End of split % 261.05/56.42 | | | | | | % 261.05/56.42 | | | | | End of split % 261.05/56.42 | | | | | % 261.05/56.42 | | | | Case 2: % 261.05/56.42 | | | | | % 261.05/56.42 | | | | | (506) all_74_7 = n0 % 261.05/56.42 | | | | | % 261.05/56.42 | | | | | REDUCE: (461), (506) imply: % 261.05/56.42 | | | | | (507) a_select3(r_ds1_filter, n0, n0) = all_74_5 % 261.05/56.42 | | | | | % 261.05/56.42 | | | | | REDUCE: (460), (506) imply: % 261.05/56.42 | | | | | (508) a_select3(r_ds1_filter, n0, n0) = all_74_4 % 261.05/56.42 | | | | | % 261.05/56.42 | | | | | GROUND_INST: instantiating (30) with all_74_5, all_74_4, n0, n0, % 261.05/56.42 | | | | | r_ds1_filter, simplifying with (507), (508) gives: % 261.05/56.42 | | | | | (509) all_74_4 = all_74_5 % 261.05/56.42 | | | | | % 261.05/56.42 | | | | | REDUCE: (314), (509) imply: % 261.05/56.42 | | | | | (510) $false % 261.05/56.42 | | | | | % 261.05/56.42 | | | | | CLOSE: (510) is inconsistent. % 261.05/56.42 | | | | | % 261.05/56.42 | | | | End of split % 261.05/56.42 | | | | % 261.05/56.42 | | | End of split % 261.05/56.42 | | | % 261.05/56.42 | | End of split % 261.05/56.42 | | % 261.05/56.42 | Case 2: % 261.05/56.42 | | % 261.05/56.42 | | (511) ( ~ (all_74_8 = all_74_9) & a_select3(pminus_ds1_filter, all_74_10, % 261.05/56.42 | | all_74_11) = all_74_8 & a_select3(pminus_ds1_filter, all_74_11, % 261.05/56.42 | | all_74_10) = all_74_9 & $i(all_74_8) & $i(all_74_9) & % 261.05/56.42 | | leq(all_74_10, all_74_20) & leq(all_74_11, all_74_20) & leq(n0, % 261.05/56.42 | | all_74_10) & leq(n0, all_74_11)) | ( ~ (all_74_12 = all_74_13) % 261.05/56.42 | | & minus(all_74_17, n1) = all_74_16 & plus(n1, pv57) = all_74_17 & % 261.05/56.42 | | a_select3(id_ds1_filter, all_74_14, all_74_15) = all_74_12 & % 261.05/56.42 | | a_select3(id_ds1_filter, all_74_15, all_74_14) = all_74_13 & % 261.05/56.42 | | $i(all_74_12) & $i(all_74_13) & $i(all_74_16) & $i(all_74_17) & % 261.05/56.42 | | leq(all_74_14, all_74_20) & leq(all_74_15, all_74_16) & leq(n0, % 261.05/56.42 | | all_74_14) & leq(n0, all_74_15)) % 261.05/56.42 | | % 261.05/56.42 | | BETA: splitting (511) gives: % 261.05/56.42 | | % 261.05/56.42 | | Case 1: % 261.05/56.42 | | | % 261.05/56.43 | | | (512) ~ (all_74_8 = all_74_9) & a_select3(pminus_ds1_filter, % 261.05/56.43 | | | all_74_10, all_74_11) = all_74_8 & a_select3(pminus_ds1_filter, % 261.05/56.43 | | | all_74_11, all_74_10) = all_74_9 & $i(all_74_8) & $i(all_74_9) % 261.05/56.43 | | | & leq(all_74_10, all_74_20) & leq(all_74_11, all_74_20) & leq(n0, % 261.05/56.43 | | | all_74_10) & leq(n0, all_74_11) % 261.05/56.43 | | | % 261.05/56.43 | | | ALPHA: (512) implies: % 261.05/56.43 | | | (513) ~ (all_74_8 = all_74_9) % 261.05/56.43 | | | (514) leq(n0, all_74_11) % 261.05/56.43 | | | (515) leq(n0, all_74_10) % 261.05/56.43 | | | (516) leq(all_74_11, all_74_20) % 261.05/56.43 | | | (517) leq(all_74_10, all_74_20) % 261.05/56.43 | | | (518) a_select3(pminus_ds1_filter, all_74_11, all_74_10) = all_74_9 % 261.05/56.43 | | | (519) a_select3(pminus_ds1_filter, all_74_10, all_74_11) = all_74_8 % 261.05/56.43 | | | % 261.05/56.43 | | | REDUCE: (159), (517) imply: % 261.05/56.43 | | | (520) leq(all_74_10, n5) % 261.05/56.43 | | | % 261.05/56.43 | | | REDUCE: (159), (516) imply: % 261.05/56.43 | | | (521) leq(all_74_11, n5) % 261.05/56.43 | | | % 261.05/56.43 | | | GROUND_INST: instantiating (leq_gt2) with n0, all_74_11, simplifying with % 261.05/56.43 | | | (22), (68), (514) gives: % 261.05/56.43 | | | (522) all_74_11 = n0 | gt(all_74_11, n0) % 261.05/56.43 | | | % 261.05/56.43 | | | GROUND_INST: instantiating (leq_gt2) with n0, all_74_10, simplifying with % 261.05/56.43 | | | (22), (69), (515) gives: % 261.05/56.43 | | | (523) all_74_10 = n0 | gt(all_74_10, n0) % 261.05/56.43 | | | % 261.05/56.43 | | | GROUND_INST: instantiating (transitivity_leq) with all_74_11, n5, n6, % 261.05/56.43 | | | simplifying with (25), (68), (139), (140), (521) gives: % 261.05/56.43 | | | (524) leq(all_74_11, n6) % 261.05/56.43 | | | % 261.05/56.43 | | | GROUND_INST: instantiating (10) with all_74_11, simplifying with (68), % 261.05/56.43 | | | (514), (521) gives: % 261.05/56.43 | | | (525) all_74_11 = n5 | all_74_11 = n4 | all_74_11 = n3 | all_74_11 = n2 % 261.05/56.43 | | | | all_74_11 = n1 | all_74_11 = n0 % 261.05/56.43 | | | % 261.05/56.43 | | | GROUND_INST: instantiating (leq_gt2) with all_74_11, n5, simplifying with % 261.05/56.43 | | | (68), (139), (521) gives: % 261.05/56.43 | | | (526) all_74_11 = n5 | gt(n5, all_74_11) % 261.05/56.43 | | | % 261.05/56.43 | | | GROUND_INST: instantiating (transitivity_leq) with all_74_10, n5, n6, % 261.05/56.43 | | | simplifying with (25), (69), (139), (140), (520) gives: % 261.05/56.43 | | | (527) leq(all_74_10, n6) % 261.05/56.43 | | | % 261.05/56.43 | | | GROUND_INST: instantiating (10) with all_74_10, simplifying with (69), % 261.05/56.43 | | | (515), (520) gives: % 261.05/56.43 | | | (528) all_74_10 = n5 | all_74_10 = n4 | all_74_10 = n3 | all_74_10 = n2 % 261.05/56.43 | | | | all_74_10 = n1 | all_74_10 = n0 % 261.05/56.43 | | | % 261.05/56.43 | | | GROUND_INST: instantiating (leq_gt2) with all_74_10, n5, simplifying with % 261.05/56.43 | | | (69), (139), (520) gives: % 261.05/56.43 | | | (529) all_74_10 = n5 | gt(n5, all_74_10) % 261.05/56.43 | | | % 261.05/56.43 | | | GROUND_INST: instantiating (11) with all_74_11, simplifying with (68), % 261.05/56.43 | | | (514), (524) gives: % 261.05/56.43 | | | (530) all_74_11 = n6 | all_74_11 = n5 | all_74_11 = n4 | all_74_11 = n3 % 261.05/56.43 | | | | all_74_11 = n2 | all_74_11 = n1 | all_74_11 = n0 % 261.05/56.43 | | | % 261.05/56.43 | | | GROUND_INST: instantiating (11) with all_74_10, simplifying with (69), % 261.05/56.43 | | | (515), (527) gives: % 261.05/56.43 | | | (531) all_74_10 = n6 | all_74_10 = n5 | all_74_10 = n4 | all_74_10 = n3 % 261.05/56.43 | | | | all_74_10 = n2 | all_74_10 = n1 | all_74_10 = n0 % 261.05/56.43 | | | % 261.05/56.43 | | | BETA: splitting (142) gives: % 261.05/56.43 | | | % 261.05/56.43 | | | Case 1: % 261.05/56.43 | | | | % 261.05/56.43 | | | | (532) gt(pv57, n0) % 261.05/56.43 | | | | % 261.05/56.43 | | | | GROUND_INST: instantiating (1) with n0, pv57, all_74_18, simplifying % 261.05/56.43 | | | | with (22), (24), (155), (532) gives: % 261.05/56.43 | | | | (533) leq(n0, all_74_18) % 261.05/56.43 | | | | % 261.05/56.43 | | | | GROUND_INST: instantiating (11) with all_74_18, simplifying with (154), % 261.05/56.43 | | | | (172), (533) gives: % 261.05/56.43 | | | | (534) all_74_18 = n6 | all_74_18 = n5 | all_74_18 = n4 | all_74_18 = % 261.05/56.43 | | | | n3 | all_74_18 = n2 | all_74_18 = n1 | all_74_18 = n0 % 261.05/56.43 | | | | % 261.05/56.43 | | | | GROUND_INST: instantiating (9) with all_74_18, simplifying with (154), % 261.05/56.43 | | | | (168), (533) gives: % 261.05/56.43 | | | | (535) all_74_18 = n4 | all_74_18 = n3 | all_74_18 = n2 | all_74_18 = % 261.05/56.43 | | | | n1 | all_74_18 = n0 % 261.05/56.43 | | | | % 261.05/56.43 | | | | GROUND_INST: instantiating (leq_gt2) with n0, all_74_18, simplifying % 261.05/56.43 | | | | with (22), (154), (533) gives: % 261.05/56.43 | | | | (536) all_74_18 = n0 | gt(all_74_18, n0) % 261.05/56.43 | | | | % 261.05/56.43 | | | | BETA: splitting (523) gives: % 261.05/56.43 | | | | % 261.05/56.43 | | | | Case 1: % 261.05/56.43 | | | | | % 261.05/56.43 | | | | | (537) gt(all_74_10, n0) % 261.05/56.43 | | | | | % 261.05/56.43 | | | | | BETA: splitting (522) gives: % 261.05/56.43 | | | | | % 261.05/56.43 | | | | | Case 1: % 261.05/56.43 | | | | | | % 261.05/56.43 | | | | | | (538) gt(all_74_11, n0) % 261.05/56.43 | | | | | | % 261.05/56.43 | | | | | | BETA: splitting (526) gives: % 261.05/56.43 | | | | | | % 261.05/56.43 | | | | | | Case 1: % 261.05/56.43 | | | | | | | % 261.05/56.43 | | | | | | | (539) gt(n5, all_74_11) % 261.05/56.43 | | | | | | | % 261.05/56.43 | | | | | | | BETA: splitting (529) gives: % 261.05/56.43 | | | | | | | % 261.05/56.43 | | | | | | | Case 1: % 261.05/56.43 | | | | | | | | % 261.05/56.43 | | | | | | | | (540) gt(n5, all_74_10) % 261.05/56.43 | | | | | | | | % 261.05/56.43 | | | | | | | | GROUND_INST: instantiating (1) with all_74_11, n5, n4, % 261.05/56.43 | | | | | | | | simplifying with (68), (139), (148), (539) gives: % 261.05/56.43 | | | | | | | | (541) leq(all_74_11, n4) % 261.05/56.43 | | | | | | | | % 261.05/56.43 | | | | | | | | GROUND_INST: instantiating (1) with all_74_10, n5, n4, % 261.05/56.43 | | | | | | | | simplifying with (69), (139), (148), (540) gives: % 261.05/56.43 | | | | | | | | (542) leq(all_74_10, n4) % 261.05/56.43 | | | | | | | | % 261.05/56.43 | | | | | | | | BETA: splitting (528) gives: % 261.05/56.43 | | | | | | | | % 261.05/56.43 | | | | | | | | Case 1: % 261.05/56.43 | | | | | | | | | % 261.05/56.43 | | | | | | | | | (543) all_74_10 = n0 % 261.05/56.43 | | | | | | | | | % 261.05/56.43 | | | | | | | | | REF_CLOSE: (69), (537), (543), (irreflexivity_gt) are % 261.05/56.43 | | | | | | | | | inconsistent by sub-proof #64. % 261.05/56.43 | | | | | | | | | % 261.05/56.43 | | | | | | | | Case 2: % 261.05/56.43 | | | | | | | | | % 261.05/56.43 | | | | | | | | | (544) ~ (all_74_10 = n0) % 261.05/56.43 | | | | | | | | | % 261.05/56.43 | | | | | | | | | BETA: splitting (525) gives: % 261.05/56.43 | | | | | | | | | % 261.05/56.43 | | | | | | | | | Case 1: % 261.05/56.43 | | | | | | | | | | % 261.05/56.43 | | | | | | | | | | (545) all_74_11 = n0 % 261.05/56.43 | | | | | | | | | | % 261.05/56.43 | | | | | | | | | | REF_CLOSE: (68), (538), (545), (irreflexivity_gt) are % 261.05/56.43 | | | | | | | | | | inconsistent by sub-proof #63. % 261.05/56.43 | | | | | | | | | | % 261.05/56.43 | | | | | | | | | Case 2: % 261.05/56.43 | | | | | | | | | | % 261.05/56.43 | | | | | | | | | | (546) ~ (all_74_11 = n0) % 261.05/56.43 | | | | | | | | | | % 261.05/56.43 | | | | | | | | | | BETA: splitting (530) gives: % 261.05/56.43 | | | | | | | | | | % 261.05/56.43 | | | | | | | | | | Case 1: % 261.05/56.43 | | | | | | | | | | | % 261.05/56.43 | | | | | | | | | | | (547) all_74_11 = n0 % 261.05/56.43 | | | | | | | | | | | % 261.05/56.43 | | | | | | | | | | | REDUCE: (546), (547) imply: % 261.05/56.43 | | | | | | | | | | | (548) $false % 261.05/56.43 | | | | | | | | | | | % 261.05/56.43 | | | | | | | | | | | CLOSE: (548) is inconsistent. % 261.05/56.43 | | | | | | | | | | | % 261.05/56.43 | | | | | | | | | | Case 2: % 261.05/56.43 | | | | | | | | | | | % 261.05/56.43 | | | | | | | | | | | % 261.05/56.43 | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_11, n4, % 261.05/56.43 | | | | | | | | | | | simplifying with (68), (136), (541) gives: % 261.05/56.43 | | | | | | | | | | | (549) all_74_11 = n4 | gt(n4, all_74_11) % 261.05/56.43 | | | | | | | | | | | % 261.05/56.43 | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_10, n4, % 261.05/56.43 | | | | | | | | | | | simplifying with (69), (136), (542) gives: % 261.05/56.43 | | | | | | | | | | | (550) all_74_10 = n4 | gt(n4, all_74_10) % 261.05/56.43 | | | | | | | | | | | % 261.05/56.43 | | | | | | | | | | | REF_CLOSE: (1), (13), (30), (68), (69), (80), (118), (129), % 261.05/56.43 | | | | | | | | | | | (136), (145), (146), (147), (159), (513), (514), % 261.05/56.43 | | | | | | | | | | | (515), (518), (519), (520), (521), (544), (546), % 261.05/56.43 | | | | | | | | | | | (549), (550), (leq_gt2) are inconsistent by % 261.05/56.43 | | | | | | | | | | | sub-proof #58. % 261.05/56.43 | | | | | | | | | | | % 261.05/56.43 | | | | | | | | | | End of split % 261.05/56.43 | | | | | | | | | | % 261.05/56.43 | | | | | | | | | End of split % 261.05/56.43 | | | | | | | | | % 261.05/56.43 | | | | | | | | End of split % 261.05/56.43 | | | | | | | | % 261.05/56.43 | | | | | | | Case 2: % 261.05/56.43 | | | | | | | | % 261.05/56.43 | | | | | | | | (551) all_74_10 = n5 % 261.05/56.43 | | | | | | | | % 261.05/56.43 | | | | | | | | REDUCE: (519), (551) imply: % 261.05/56.43 | | | | | | | | (552) a_select3(pminus_ds1_filter, n5, all_74_11) = all_74_8 % 261.05/56.43 | | | | | | | | % 261.05/56.43 | | | | | | | | REDUCE: (518), (551) imply: % 261.05/56.43 | | | | | | | | (553) a_select3(pminus_ds1_filter, all_74_11, n5) = all_74_9 % 261.05/56.43 | | | | | | | | % 261.05/56.43 | | | | | | | | REDUCE: (520), (551) imply: % 261.05/56.43 | | | | | | | | (554) leq(n5, n5) % 261.05/56.43 | | | | | | | | % 261.05/56.43 | | | | | | | | REDUCE: (515), (551) imply: % 261.05/56.43 | | | | | | | | (555) leq(n0, n5) % 261.05/56.43 | | | | | | | | % 261.05/56.44 | | | | | | | | GROUND_INST: instantiating (1) with all_74_11, n5, n4, % 261.05/56.44 | | | | | | | | simplifying with (68), (139), (148), (539) gives: % 261.05/56.44 | | | | | | | | (556) leq(all_74_11, n4) % 261.05/56.44 | | | | | | | | % 261.05/56.44 | | | | | | | | BETA: splitting (525) gives: % 261.05/56.44 | | | | | | | | % 261.05/56.44 | | | | | | | | Case 1: % 261.05/56.44 | | | | | | | | | % 261.05/56.44 | | | | | | | | | (557) all_74_11 = n0 % 261.05/56.44 | | | | | | | | | % 261.05/56.44 | | | | | | | | | REF_CLOSE: (68), (538), (557), (irreflexivity_gt) are % 261.05/56.44 | | | | | | | | | inconsistent by sub-proof #63. % 261.05/56.44 | | | | | | | | | % 261.05/56.44 | | | | | | | | Case 2: % 261.05/56.44 | | | | | | | | | % 261.05/56.44 | | | | | | | | | (558) ~ (all_74_11 = n0) % 261.05/56.44 | | | | | | | | | % 261.05/56.44 | | | | | | | | | BETA: splitting (530) gives: % 261.05/56.44 | | | | | | | | | % 261.05/56.44 | | | | | | | | | Case 1: % 261.05/56.44 | | | | | | | | | | % 261.05/56.44 | | | | | | | | | | (559) all_74_11 = n0 % 261.05/56.44 | | | | | | | | | | % 261.05/56.44 | | | | | | | | | | REDUCE: (558), (559) imply: % 261.05/56.44 | | | | | | | | | | (560) $false % 261.05/56.44 | | | | | | | | | | % 261.05/56.44 | | | | | | | | | | CLOSE: (560) is inconsistent. % 261.05/56.44 | | | | | | | | | | % 261.05/56.44 | | | | | | | | | Case 2: % 261.05/56.44 | | | | | | | | | | % 261.05/56.44 | | | | | | | | | | % 261.05/56.44 | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_11, n4, % 261.05/56.44 | | | | | | | | | | simplifying with (68), (136), (556) gives: % 261.05/56.44 | | | | | | | | | | (561) all_74_11 = n4 | gt(n4, all_74_11) % 261.05/56.44 | | | | | | | | | | % 261.05/56.44 | | | | | | | | | | REF_CLOSE: (1), (13), (30), (68), (80), (118), (129), (136), % 261.05/56.44 | | | | | | | | | | (139), (145), (146), (147), (159), (513), (514), % 261.05/56.44 | | | | | | | | | | (521), (552), (553), (554), (555), (558), (561), % 261.05/56.44 | | | | | | | | | | (leq_gt2) are inconsistent by sub-proof #54. % 261.05/56.44 | | | | | | | | | | % 261.05/56.44 | | | | | | | | | End of split % 261.05/56.44 | | | | | | | | | % 261.05/56.44 | | | | | | | | End of split % 261.05/56.44 | | | | | | | | % 261.05/56.44 | | | | | | | End of split % 261.05/56.44 | | | | | | | % 261.05/56.44 | | | | | | Case 2: % 261.05/56.44 | | | | | | | % 261.05/56.44 | | | | | | | (562) all_74_11 = n5 % 261.05/56.44 | | | | | | | % 261.05/56.44 | | | | | | | REDUCE: (519), (562) imply: % 261.05/56.44 | | | | | | | (563) a_select3(pminus_ds1_filter, all_74_10, n5) = all_74_8 % 261.05/56.44 | | | | | | | % 261.05/56.44 | | | | | | | REDUCE: (518), (562) imply: % 261.05/56.44 | | | | | | | (564) a_select3(pminus_ds1_filter, n5, all_74_10) = all_74_9 % 261.05/56.44 | | | | | | | % 261.05/56.44 | | | | | | | REDUCE: (521), (562) imply: % 261.05/56.44 | | | | | | | (565) leq(n5, n5) % 261.05/56.44 | | | | | | | % 261.05/56.44 | | | | | | | REDUCE: (514), (562) imply: % 261.05/56.44 | | | | | | | (566) leq(n0, n5) % 261.05/56.44 | | | | | | | % 261.29/56.44 | | | | | | | BETA: splitting (529) gives: % 261.29/56.44 | | | | | | | % 261.29/56.44 | | | | | | | Case 1: % 261.29/56.44 | | | | | | | | % 261.29/56.44 | | | | | | | | (567) gt(n5, all_74_10) % 261.29/56.44 | | | | | | | | % 261.29/56.44 | | | | | | | | GROUND_INST: instantiating (1) with all_74_10, n5, n4, % 261.29/56.44 | | | | | | | | simplifying with (69), (139), (148), (567) gives: % 261.29/56.44 | | | | | | | | (568) leq(all_74_10, n4) % 261.29/56.44 | | | | | | | | % 261.29/56.44 | | | | | | | | BETA: splitting (528) gives: % 261.29/56.44 | | | | | | | | % 261.29/56.44 | | | | | | | | Case 1: % 261.29/56.44 | | | | | | | | | % 261.29/56.44 | | | | | | | | | (569) all_74_10 = n0 % 261.29/56.44 | | | | | | | | | % 261.29/56.44 | | | | | | | | | REF_CLOSE: (69), (537), (569), (irreflexivity_gt) are % 261.29/56.44 | | | | | | | | | inconsistent by sub-proof #64. % 261.29/56.44 | | | | | | | | | % 261.29/56.44 | | | | | | | | Case 2: % 261.29/56.44 | | | | | | | | | % 261.29/56.44 | | | | | | | | | (570) ~ (all_74_10 = n0) % 261.29/56.44 | | | | | | | | | % 261.29/56.44 | | | | | | | | | BETA: splitting (531) gives: % 261.29/56.44 | | | | | | | | | % 261.29/56.44 | | | | | | | | | Case 1: % 261.29/56.44 | | | | | | | | | | % 261.29/56.44 | | | | | | | | | | (571) all_74_10 = n0 % 261.29/56.44 | | | | | | | | | | % 261.29/56.44 | | | | | | | | | | REDUCE: (570), (571) imply: % 261.29/56.44 | | | | | | | | | | (572) $false % 261.29/56.44 | | | | | | | | | | % 261.29/56.44 | | | | | | | | | | CLOSE: (572) is inconsistent. % 261.29/56.44 | | | | | | | | | | % 261.29/56.44 | | | | | | | | | Case 2: % 261.29/56.44 | | | | | | | | | | % 261.29/56.44 | | | | | | | | | | % 261.29/56.44 | | | | | | | | | | REF_CLOSE: (1), (9), (13), (30), (69), (80), (118), (129), % 261.29/56.44 | | | | | | | | | | (136), (139), (145), (146), (147), (159), (513), % 261.29/56.44 | | | | | | | | | | (515), (520), (563), (564), (565), (566), (568), % 261.29/56.44 | | | | | | | | | | (570), (leq_gt2) are inconsistent by sub-proof % 261.29/56.44 | | | | | | | | | | #53. % 261.29/56.44 | | | | | | | | | | % 261.29/56.44 | | | | | | | | | End of split % 261.29/56.44 | | | | | | | | | % 261.29/56.44 | | | | | | | | End of split % 261.29/56.44 | | | | | | | | % 261.29/56.44 | | | | | | | Case 2: % 261.29/56.44 | | | | | | | | % 261.29/56.44 | | | | | | | | (573) all_74_10 = n5 % 261.29/56.44 | | | | | | | | % 261.29/56.44 | | | | | | | | REDUCE: (563), (573) imply: % 261.29/56.44 | | | | | | | | (574) a_select3(pminus_ds1_filter, n5, n5) = all_74_8 % 261.29/56.44 | | | | | | | | % 261.29/56.44 | | | | | | | | REDUCE: (564), (573) imply: % 261.29/56.44 | | | | | | | | (575) a_select3(pminus_ds1_filter, n5, n5) = all_74_9 % 261.29/56.44 | | | | | | | | % 261.29/56.44 | | | | | | | | GROUND_INST: instantiating (30) with all_74_9, all_74_8, n5, n5, % 261.29/56.44 | | | | | | | | pminus_ds1_filter, simplifying with (574), (575) % 261.29/56.44 | | | | | | | | gives: % 261.29/56.44 | | | | | | | | (576) all_74_8 = all_74_9 % 261.29/56.44 | | | | | | | | % 261.29/56.44 | | | | | | | | REDUCE: (513), (576) imply: % 261.29/56.44 | | | | | | | | (577) $false % 261.29/56.44 | | | | | | | | % 261.29/56.44 | | | | | | | | CLOSE: (577) is inconsistent. % 261.29/56.44 | | | | | | | | % 261.29/56.44 | | | | | | | End of split % 261.29/56.44 | | | | | | | % 261.29/56.44 | | | | | | End of split % 261.29/56.44 | | | | | | % 261.29/56.44 | | | | | Case 2: % 261.29/56.44 | | | | | | % 261.29/56.44 | | | | | | (578) all_74_11 = n0 % 261.29/56.44 | | | | | | (579) ~ gt(all_74_11, n0) % 261.29/56.44 | | | | | | % 261.29/56.44 | | | | | | REDUCE: (578), (579) imply: % 261.29/56.44 | | | | | | (580) ~ gt(n0, n0) % 261.29/56.44 | | | | | | % 261.29/56.44 | | | | | | REF_CLOSE: (1), (9), (13), (30), (68), (69), (80), (118), (129), % 261.29/56.44 | | | | | | (136), (139), (145), (146), (147), (148), (154), (159), % 261.29/56.44 | | | | | | (167), (513), (514), (515), (518), (519), (520), (521), % 261.29/56.44 | | | | | | (522), (525), (526), (528), (529), (533), (534), (535), % 261.29/56.44 | | | | | | (536), (537), (580), (leq_gt2) are inconsistent by % 261.29/56.44 | | | | | | sub-proof #44. % 261.29/56.44 | | | | | | % 261.29/56.44 | | | | | End of split % 261.29/56.44 | | | | | % 261.29/56.44 | | | | Case 2: % 261.29/56.44 | | | | | % 261.29/56.44 | | | | | (581) all_74_10 = n0 % 261.29/56.44 | | | | | (582) ~ gt(all_74_10, n0) % 261.29/56.44 | | | | | % 261.29/56.44 | | | | | REDUCE: (581), (582) imply: % 261.29/56.44 | | | | | (583) ~ gt(n0, n0) % 261.29/56.44 | | | | | % 261.29/56.44 | | | | | BETA: splitting (523) gives: % 261.29/56.44 | | | | | % 261.29/56.44 | | | | | Case 1: % 261.29/56.44 | | | | | | % 261.29/56.44 | | | | | | (584) gt(all_74_10, n0) % 261.29/56.44 | | | | | | % 261.29/56.44 | | | | | | REF_CLOSE: (1), (9), (13), (30), (68), (69), (80), (118), (129), % 261.29/56.44 | | | | | | (136), (139), (145), (146), (147), (148), (154), (159), % 261.29/56.44 | | | | | | (167), (513), (514), (515), (518), (519), (520), (521), % 261.29/56.44 | | | | | | (522), (525), (526), (528), (529), (533), (534), (535), % 261.29/56.44 | | | | | | (536), (583), (584), (leq_gt2) are inconsistent by % 261.29/56.44 | | | | | | sub-proof #44. % 261.29/56.44 | | | | | | % 261.29/56.44 | | | | | Case 2: % 261.29/56.44 | | | | | | % 261.29/56.44 | | | | | | % 261.29/56.44 | | | | | | REDUCE: (519), (581) imply: % 261.29/56.44 | | | | | | (585) a_select3(pminus_ds1_filter, n0, all_74_11) = all_74_8 % 261.29/56.44 | | | | | | % 261.29/56.44 | | | | | | REDUCE: (518), (581) imply: % 261.29/56.44 | | | | | | (586) a_select3(pminus_ds1_filter, all_74_11, n0) = all_74_9 % 261.29/56.44 | | | | | | % 261.29/56.44 | | | | | | REDUCE: (520), (581) imply: % 261.29/56.44 | | | | | | (587) leq(n0, n5) % 261.29/56.44 | | | | | | % 261.29/56.44 | | | | | | REDUCE: (515), (581) imply: % 261.29/56.44 | | | | | | (588) leq(n0, n0) % 261.29/56.44 | | | | | | % 261.29/56.44 | | | | | | BETA: splitting (522) gives: % 261.29/56.44 | | | | | | % 261.29/56.44 | | | | | | Case 1: % 261.29/56.44 | | | | | | | % 261.29/56.44 | | | | | | | (589) gt(all_74_11, n0) % 261.29/56.44 | | | | | | | % 261.29/56.44 | | | | | | | BETA: splitting (526) gives: % 261.29/56.44 | | | | | | | % 261.29/56.44 | | | | | | | Case 1: % 261.29/56.44 | | | | | | | | % 261.29/56.44 | | | | | | | | (590) gt(n5, all_74_11) % 261.29/56.44 | | | | | | | | % 261.29/56.44 | | | | | | | | GROUND_INST: instantiating (1) with all_74_11, n5, n4, % 261.29/56.44 | | | | | | | | simplifying with (68), (139), (148), (590) gives: % 261.29/56.44 | | | | | | | | (591) leq(all_74_11, n4) % 261.29/56.44 | | | | | | | | % 261.29/56.44 | | | | | | | | REF_CLOSE: (1), (13), (22), (30), (68), (80), (118), (129), % 261.29/56.44 | | | | | | | | (136), (145), (146), (147), (159), (513), (514), % 261.29/56.44 | | | | | | | | (521), (525), (583), (585), (586), (587), (588), % 261.29/56.44 | | | | | | | | (589), (591), (leq_gt2) are inconsistent by sub-proof % 261.29/56.44 | | | | | | | | #43. % 261.29/56.44 | | | | | | | | % 261.29/56.44 | | | | | | | Case 2: % 261.29/56.44 | | | | | | | | % 261.29/56.44 | | | | | | | | (592) all_74_11 = n5 % 261.29/56.44 | | | | | | | | % 261.29/56.44 | | | | | | | | REDUCE: (586), (592) imply: % 261.29/56.44 | | | | | | | | (593) a_select3(pminus_ds1_filter, n5, n0) = all_74_9 % 261.29/56.44 | | | | | | | | % 261.29/56.44 | | | | | | | | REDUCE: (585), (592) imply: % 261.29/56.44 | | | | | | | | (594) a_select3(pminus_ds1_filter, n0, n5) = all_74_8 % 261.29/56.44 | | | | | | | | % 261.29/56.44 | | | | | | | | REDUCE: (521), (592) imply: % 261.29/56.44 | | | | | | | | (595) leq(n5, n5) % 261.29/56.44 | | | | | | | | % 261.29/56.44 | | | | | | | | BETA: splitting (536) gives: % 261.29/56.44 | | | | | | | | % 261.29/56.44 | | | | | | | | Case 1: % 261.29/56.44 | | | | | | | | | % 261.29/56.44 | | | | | | | | | (596) gt(all_74_18, n0) % 261.29/56.44 | | | | | | | | | % 261.29/56.44 | | | | | | | | | BETA: splitting (535) gives: % 261.29/56.44 | | | | | | | | | % 261.29/56.44 | | | | | | | | | Case 1: % 261.29/56.44 | | | | | | | | | | % 261.29/56.44 | | | | | | | | | | (597) all_74_18 = n0 % 261.29/56.44 | | | | | | | | | | % 261.29/56.44 | | | | | | | | | | REDUCE: (596), (597) imply: % 261.29/56.44 | | | | | | | | | | (598) gt(n0, n0) % 261.29/56.44 | | | | | | | | | | % 261.29/56.44 | | | | | | | | | | PRED_UNIFY: (583), (598) imply: % 261.29/56.44 | | | | | | | | | | (599) $false % 261.29/56.44 | | | | | | | | | | % 261.29/56.44 | | | | | | | | | | CLOSE: (599) is inconsistent. % 261.29/56.44 | | | | | | | | | | % 261.29/56.44 | | | | | | | | | Case 2: % 261.29/56.44 | | | | | | | | | | % 261.29/56.44 | | | | | | | | | | (600) ~ (all_74_18 = n0) % 261.29/56.44 | | | | | | | | | | % 261.29/56.44 | | | | | | | | | | BETA: splitting (534) gives: % 261.29/56.44 | | | | | | | | | | % 261.29/56.44 | | | | | | | | | | Case 1: % 261.29/56.44 | | | | | | | | | | | % 261.29/56.44 | | | | | | | | | | | (601) all_74_18 = n0 % 261.29/56.44 | | | | | | | | | | | % 261.29/56.44 | | | | | | | | | | | REDUCE: (600), (601) imply: % 261.29/56.44 | | | | | | | | | | | (602) $false % 261.29/56.44 | | | | | | | | | | | % 261.29/56.44 | | | | | | | | | | | CLOSE: (602) is inconsistent. % 261.29/56.44 | | | | | | | | | | | % 261.29/56.44 | | | | | | | | | | Case 2: % 261.29/56.44 | | | | | | | | | | | % 261.29/56.45 | | | | | | | | | | | % 261.29/56.45 | | | | | | | | | | | GROUND_INST: instantiating (80) with n0, n5, all_74_8, % 261.29/56.45 | | | | | | | | | | | simplifying with (22), (139), (587), (588), (594) % 261.29/56.45 | | | | | | | | | | | gives: % 261.29/56.45 | | | | | | | | | | | (603) ~ leq(n5, all_74_20) | ~ leq(n0, all_74_20) | % 261.29/56.45 | | | | | | | | | | | (a_select3(pminus_ds1_filter, n5, n0) = all_74_8 & % 261.29/56.45 | | | | | | | | | | | $i(all_74_8)) % 261.29/56.45 | | | | | | | | | | | % 261.29/56.45 | | | | | | | | | | | REF_CLOSE: (30), (159), (513), (587), (593), (595), (603) are % 261.29/56.45 | | | | | | | | | | | inconsistent by sub-proof #42. % 261.29/56.45 | | | | | | | | | | | % 261.29/56.45 | | | | | | | | | | End of split % 261.29/56.45 | | | | | | | | | | % 261.29/56.45 | | | | | | | | | End of split % 261.29/56.45 | | | | | | | | | % 261.29/56.45 | | | | | | | | Case 2: % 261.29/56.45 | | | | | | | | | % 261.29/56.45 | | | | | | | | | (604) all_74_18 = n0 % 261.29/56.45 | | | | | | | | | % 261.36/56.45 | | | | | | | | | GROUND_INST: instantiating (80) with n0, n5, all_74_8, % 261.36/56.45 | | | | | | | | | simplifying with (22), (139), (587), (588), (594) % 261.36/56.45 | | | | | | | | | gives: % 261.36/56.45 | | | | | | | | | (605) ~ leq(n5, all_74_20) | ~ leq(n0, all_74_20) | % 261.36/56.45 | | | | | | | | | (a_select3(pminus_ds1_filter, n5, n0) = all_74_8 & % 261.36/56.45 | | | | | | | | | $i(all_74_8)) % 261.36/56.45 | | | | | | | | | % 261.36/56.45 | | | | | | | | | REF_CLOSE: (30), (159), (513), (587), (593), (595), (605) are % 261.36/56.45 | | | | | | | | | inconsistent by sub-proof #42. % 261.36/56.45 | | | | | | | | | % 261.36/56.45 | | | | | | | | End of split % 261.36/56.45 | | | | | | | | % 261.36/56.45 | | | | | | | End of split % 261.36/56.45 | | | | | | | % 261.36/56.45 | | | | | | Case 2: % 261.36/56.45 | | | | | | | % 261.36/56.45 | | | | | | | (606) all_74_11 = n0 % 261.36/56.45 | | | | | | | % 261.36/56.45 | | | | | | | REDUCE: (586), (606) imply: % 261.36/56.45 | | | | | | | (607) a_select3(pminus_ds1_filter, n0, n0) = all_74_9 % 261.36/56.45 | | | | | | | % 261.36/56.45 | | | | | | | REDUCE: (585), (606) imply: % 261.36/56.45 | | | | | | | (608) a_select3(pminus_ds1_filter, n0, n0) = all_74_8 % 261.36/56.45 | | | | | | | % 261.36/56.45 | | | | | | | GROUND_INST: instantiating (30) with all_74_9, all_74_8, n0, n0, % 261.36/56.45 | | | | | | | pminus_ds1_filter, simplifying with (607), (608) % 261.36/56.45 | | | | | | | gives: % 261.36/56.45 | | | | | | | (609) all_74_8 = all_74_9 % 261.36/56.45 | | | | | | | % 261.36/56.45 | | | | | | | REDUCE: (513), (609) imply: % 261.36/56.45 | | | | | | | (610) $false % 261.36/56.45 | | | | | | | % 261.36/56.45 | | | | | | | CLOSE: (610) is inconsistent. % 261.36/56.45 | | | | | | | % 261.36/56.45 | | | | | | End of split % 261.36/56.45 | | | | | | % 261.36/56.45 | | | | | End of split % 261.36/56.45 | | | | | % 261.36/56.45 | | | | End of split % 261.36/56.45 | | | | % 261.36/56.45 | | | Case 2: % 261.36/56.45 | | | | % 261.36/56.45 | | | | (611) pv57 = n0 % 261.36/56.45 | | | | (612) ~ gt(pv57, n0) % 261.36/56.45 | | | | % 261.36/56.45 | | | | REDUCE: (611), (612) imply: % 261.36/56.45 | | | | (613) ~ gt(n0, n0) % 261.36/56.45 | | | | % 261.36/56.45 | | | | BETA: splitting (523) gives: % 261.36/56.45 | | | | % 261.36/56.45 | | | | Case 1: % 261.36/56.45 | | | | | % 261.36/56.45 | | | | | (614) gt(all_74_10, n0) % 261.36/56.45 | | | | | % 261.36/56.45 | | | | | BETA: splitting (522) gives: % 261.36/56.45 | | | | | % 261.36/56.45 | | | | | Case 1: % 261.36/56.45 | | | | | | % 261.36/56.45 | | | | | | (615) gt(all_74_11, n0) % 261.36/56.45 | | | | | | % 261.36/56.45 | | | | | | REF_CLOSE: (1), (9), (13), (30), (68), (69), (80), (118), (129), % 261.36/56.45 | | | | | | (136), (139), (145), (146), (147), (148), (159), (513), % 261.36/56.45 | | | | | | (514), (515), (518), (519), (520), (521), (525), (526), % 261.36/56.45 | | | | | | (528), (529), (613), (614), (615), (leq_gt2) are % 261.36/56.45 | | | | | | inconsistent by sub-proof #52. % 261.36/56.45 | | | | | | % 261.36/56.45 | | | | | Case 2: % 261.36/56.45 | | | | | | % 261.36/56.45 | | | | | | (616) all_74_11 = n0 % 261.36/56.46 | | | | | | (617) ~ gt(all_74_11, n0) % 261.36/56.46 | | | | | | % 261.36/56.46 | | | | | | REDUCE: (519), (616) imply: % 261.36/56.46 | | | | | | (618) a_select3(pminus_ds1_filter, all_74_10, n0) = all_74_8 % 261.36/56.46 | | | | | | % 261.36/56.46 | | | | | | REDUCE: (518), (616) imply: % 261.36/56.46 | | | | | | (619) a_select3(pminus_ds1_filter, n0, all_74_10) = all_74_9 % 261.36/56.46 | | | | | | % 261.36/56.46 | | | | | | REDUCE: (521), (616) imply: % 261.36/56.46 | | | | | | (620) leq(n0, n5) % 261.36/56.46 | | | | | | % 261.36/56.46 | | | | | | REDUCE: (514), (616) imply: % 261.36/56.46 | | | | | | (621) leq(n0, n0) % 261.36/56.46 | | | | | | % 261.36/56.46 | | | | | | BETA: splitting (529) gives: % 261.36/56.46 | | | | | | % 261.36/56.46 | | | | | | Case 1: % 261.36/56.46 | | | | | | | % 261.36/56.46 | | | | | | | (622) gt(n5, all_74_10) % 261.36/56.46 | | | | | | | % 261.36/56.46 | | | | | | | GROUND_INST: instantiating (1) with all_74_10, n5, n4, simplifying % 261.36/56.46 | | | | | | | with (69), (139), (148), (622) gives: % 261.36/56.46 | | | | | | | (623) leq(all_74_10, n4) % 261.36/56.46 | | | | | | | % 261.36/56.46 | | | | | | | REF_CLOSE: (1), (13), (22), (30), (69), (80), (118), (129), (136), % 261.36/56.46 | | | | | | | (145), (146), (147), (159), (513), (515), (520), (528), % 261.36/56.46 | | | | | | | (613), (614), (618), (619), (620), (621), (623), % 261.36/56.46 | | | | | | | (leq_gt2) are inconsistent by sub-proof #47. % 261.36/56.46 | | | | | | | % 261.36/56.46 | | | | | | Case 2: % 261.36/56.46 | | | | | | | % 261.36/56.46 | | | | | | | (624) all_74_10 = n5 % 261.36/56.46 | | | | | | | % 261.36/56.46 | | | | | | | REDUCE: (618), (624) imply: % 261.36/56.46 | | | | | | | (625) a_select3(pminus_ds1_filter, n5, n0) = all_74_8 % 261.36/56.46 | | | | | | | % 261.36/56.46 | | | | | | | REDUCE: (619), (624) imply: % 261.36/56.46 | | | | | | | (626) a_select3(pminus_ds1_filter, n0, n5) = all_74_9 % 261.36/56.46 | | | | | | | % 261.36/56.46 | | | | | | | REDUCE: (520), (624) imply: % 261.36/56.46 | | | | | | | (627) leq(n5, n5) % 261.36/56.46 | | | | | | | % 261.36/56.46 | | | | | | | GROUND_INST: instantiating (80) with n0, n5, all_74_9, simplifying % 261.36/56.46 | | | | | | | with (22), (139), (620), (621), (626) gives: % 261.36/56.46 | | | | | | | (628) ~ leq(n5, all_74_20) | ~ leq(n0, all_74_20) | % 261.36/56.46 | | | | | | | (a_select3(pminus_ds1_filter, n5, n0) = all_74_9 & % 261.36/56.46 | | | | | | | $i(all_74_9)) % 261.36/56.46 | | | | | | | % 261.36/56.46 | | | | | | | REF_CLOSE: (30), (159), (513), (620), (625), (627), (628) are % 261.36/56.46 | | | | | | | inconsistent by sub-proof #45. % 261.36/56.46 | | | | | | | % 261.36/56.46 | | | | | | End of split % 261.36/56.46 | | | | | | % 261.36/56.46 | | | | | End of split % 261.36/56.46 | | | | | % 261.36/56.46 | | | | Case 2: % 261.36/56.46 | | | | | % 261.36/56.46 | | | | | (629) all_74_10 = n0 % 261.36/56.46 | | | | | (630) ~ gt(all_74_10, n0) % 261.36/56.46 | | | | | % 261.36/56.46 | | | | | REDUCE: (519), (629) imply: % 261.36/56.46 | | | | | (631) a_select3(pminus_ds1_filter, n0, all_74_11) = all_74_8 % 261.36/56.46 | | | | | % 261.36/56.46 | | | | | REDUCE: (518), (629) imply: % 261.36/56.46 | | | | | (632) a_select3(pminus_ds1_filter, all_74_11, n0) = all_74_9 % 261.36/56.46 | | | | | % 261.36/56.46 | | | | | REDUCE: (520), (629) imply: % 261.36/56.46 | | | | | (633) leq(n0, n5) % 261.36/56.46 | | | | | % 261.36/56.46 | | | | | REDUCE: (515), (629) imply: % 261.36/56.46 | | | | | (634) leq(n0, n0) % 261.36/56.46 | | | | | % 261.36/56.46 | | | | | BETA: splitting (522) gives: % 261.36/56.46 | | | | | % 261.36/56.46 | | | | | Case 1: % 261.36/56.46 | | | | | | % 261.36/56.46 | | | | | | (635) gt(all_74_11, n0) % 261.36/56.46 | | | | | | % 261.36/56.46 | | | | | | BETA: splitting (526) gives: % 261.36/56.46 | | | | | | % 261.36/56.46 | | | | | | Case 1: % 261.36/56.46 | | | | | | | % 261.36/56.46 | | | | | | | (636) gt(n5, all_74_11) % 261.36/56.46 | | | | | | | % 261.36/56.46 | | | | | | | GROUND_INST: instantiating (1) with all_74_11, n5, n4, simplifying % 261.36/56.46 | | | | | | | with (68), (139), (148), (636) gives: % 261.36/56.46 | | | | | | | (637) leq(all_74_11, n4) % 261.36/56.46 | | | | | | | % 261.36/56.46 | | | | | | | REF_CLOSE: (1), (13), (22), (30), (68), (80), (118), (129), (136), % 261.36/56.46 | | | | | | | (145), (146), (147), (159), (513), (514), (521), (525), % 261.36/56.46 | | | | | | | (613), (631), (632), (633), (634), (635), (637), % 261.36/56.46 | | | | | | | (leq_gt2) are inconsistent by sub-proof #43. % 261.36/56.46 | | | | | | | % 261.36/56.46 | | | | | | Case 2: % 261.36/56.46 | | | | | | | % 261.36/56.46 | | | | | | | (638) all_74_11 = n5 % 261.36/56.46 | | | | | | | % 261.36/56.46 | | | | | | | REDUCE: (632), (638) imply: % 261.36/56.46 | | | | | | | (639) a_select3(pminus_ds1_filter, n5, n0) = all_74_9 % 261.36/56.46 | | | | | | | % 261.36/56.46 | | | | | | | REDUCE: (631), (638) imply: % 261.36/56.46 | | | | | | | (640) a_select3(pminus_ds1_filter, n0, n5) = all_74_8 % 261.36/56.46 | | | | | | | % 261.36/56.46 | | | | | | | REDUCE: (521), (638) imply: % 261.36/56.46 | | | | | | | (641) leq(n5, n5) % 261.36/56.46 | | | | | | | % 261.36/56.46 | | | | | | | GROUND_INST: instantiating (80) with n0, n5, all_74_8, simplifying % 261.36/56.46 | | | | | | | with (22), (139), (633), (634), (640) gives: % 261.36/56.46 | | | | | | | (642) ~ leq(n5, all_74_20) | ~ leq(n0, all_74_20) | % 261.36/56.46 | | | | | | | (a_select3(pminus_ds1_filter, n5, n0) = all_74_8 & % 261.36/56.46 | | | | | | | $i(all_74_8)) % 261.36/56.46 | | | | | | | % 261.36/56.46 | | | | | | | REF_CLOSE: (30), (159), (513), (633), (639), (641), (642) are % 261.36/56.46 | | | | | | | inconsistent by sub-proof #42. % 261.36/56.46 | | | | | | | % 261.36/56.46 | | | | | | End of split % 261.36/56.46 | | | | | | % 261.36/56.46 | | | | | Case 2: % 261.36/56.46 | | | | | | % 261.36/56.46 | | | | | | (643) all_74_11 = n0 % 261.36/56.46 | | | | | | % 261.36/56.46 | | | | | | REDUCE: (632), (643) imply: % 261.36/56.46 | | | | | | (644) a_select3(pminus_ds1_filter, n0, n0) = all_74_9 % 261.36/56.46 | | | | | | % 261.36/56.46 | | | | | | REDUCE: (631), (643) imply: % 261.36/56.46 | | | | | | (645) a_select3(pminus_ds1_filter, n0, n0) = all_74_8 % 261.36/56.46 | | | | | | % 261.36/56.46 | | | | | | GROUND_INST: instantiating (30) with all_74_9, all_74_8, n0, n0, % 261.36/56.46 | | | | | | pminus_ds1_filter, simplifying with (644), (645) gives: % 261.36/56.46 | | | | | | (646) all_74_8 = all_74_9 % 261.36/56.46 | | | | | | % 261.36/56.46 | | | | | | REDUCE: (513), (646) imply: % 261.36/56.46 | | | | | | (647) $false % 261.36/56.46 | | | | | | % 261.36/56.46 | | | | | | CLOSE: (647) is inconsistent. % 261.36/56.46 | | | | | | % 261.36/56.46 | | | | | End of split % 261.36/56.46 | | | | | % 261.36/56.46 | | | | End of split % 261.36/56.46 | | | | % 261.36/56.46 | | | End of split % 261.36/56.46 | | | % 261.36/56.46 | | Case 2: % 261.36/56.46 | | | % 261.36/56.46 | | | (648) ~ (all_74_12 = all_74_13) & minus(all_74_17, n1) = all_74_16 & % 261.36/56.46 | | | plus(n1, pv57) = all_74_17 & a_select3(id_ds1_filter, all_74_14, % 261.36/56.46 | | | all_74_15) = all_74_12 & a_select3(id_ds1_filter, all_74_15, % 261.36/56.46 | | | all_74_14) = all_74_13 & $i(all_74_12) & $i(all_74_13) & % 261.36/56.46 | | | $i(all_74_16) & $i(all_74_17) & leq(all_74_14, all_74_20) & % 261.36/56.46 | | | leq(all_74_15, all_74_16) & leq(n0, all_74_14) & leq(n0, % 261.36/56.46 | | | all_74_15) % 261.36/56.46 | | | % 261.36/56.46 | | | ALPHA: (648) implies: % 261.36/56.46 | | | (649) ~ (all_74_12 = all_74_13) % 261.36/56.46 | | | (650) leq(n0, all_74_15) % 261.36/56.46 | | | (651) leq(n0, all_74_14) % 261.36/56.46 | | | (652) leq(all_74_15, all_74_16) % 261.36/56.46 | | | (653) leq(all_74_14, all_74_20) % 261.36/56.46 | | | (654) $i(all_74_16) % 261.36/56.46 | | | (655) a_select3(id_ds1_filter, all_74_15, all_74_14) = all_74_13 % 261.36/56.46 | | | (656) a_select3(id_ds1_filter, all_74_14, all_74_15) = all_74_12 % 261.36/56.46 | | | (657) plus(n1, pv57) = all_74_17 % 261.36/56.46 | | | (658) minus(all_74_17, n1) = all_74_16 % 261.36/56.46 | | | % 261.36/56.46 | | | REDUCE: (159), (653) imply: % 261.36/56.46 | | | (659) leq(all_74_14, n5) % 261.36/56.46 | | | % 261.36/56.46 | | | GROUND_INST: instantiating (leq_gt2) with n0, all_74_15, simplifying with % 261.36/56.46 | | | (22), (66), (650) gives: % 261.36/56.46 | | | (660) all_74_15 = n0 | gt(all_74_15, n0) % 261.36/56.46 | | | % 261.36/56.46 | | | GROUND_INST: instantiating (leq_gt2) with n0, all_74_14, simplifying with % 261.36/56.46 | | | (22), (67), (651) gives: % 261.36/56.46 | | | (661) all_74_14 = n0 | gt(all_74_14, n0) % 261.36/56.46 | | | % 261.36/56.46 | | | GROUND_INST: instantiating (transitivity_leq) with n0, all_74_15, % 261.36/56.46 | | | all_74_16, simplifying with (22), (66), (650), (652), (654) % 261.36/56.46 | | | gives: % 261.36/56.46 | | | (662) leq(n0, all_74_16) % 261.36/56.46 | | | % 261.36/56.46 | | | GROUND_INST: instantiating (leq_gt2) with all_74_15, all_74_16, % 261.36/56.46 | | | simplifying with (66), (652), (654) gives: % 261.36/56.46 | | | (663) all_74_15 = all_74_16 | gt(all_74_16, all_74_15) % 261.36/56.46 | | | % 261.36/56.46 | | | GROUND_INST: instantiating (transitivity_leq) with all_74_14, n5, n6, % 261.36/56.46 | | | simplifying with (25), (67), (139), (140), (659) gives: % 261.36/56.46 | | | (664) leq(all_74_14, n6) % 261.36/56.46 | | | % 261.36/56.46 | | | GROUND_INST: instantiating (10) with all_74_14, simplifying with (67), % 261.36/56.46 | | | (651), (659) gives: % 261.36/56.46 | | | (665) all_74_14 = n5 | all_74_14 = n4 | all_74_14 = n3 | all_74_14 = n2 % 261.36/56.46 | | | | all_74_14 = n1 | all_74_14 = n0 % 261.36/56.46 | | | % 261.36/56.46 | | | GROUND_INST: instantiating (leq_gt2) with all_74_14, n5, simplifying with % 261.36/56.46 | | | (67), (139), (659) gives: % 261.36/56.46 | | | (666) all_74_14 = n5 | gt(n5, all_74_14) % 261.36/56.46 | | | % 261.36/56.46 | | | GROUND_INST: instantiating (4) with pv57, all_74_17, simplifying with % 261.36/56.46 | | | (24), (657) gives: % 261.36/56.46 | | | (667) succ(pv57) = all_74_17 & $i(all_74_17) % 261.36/56.46 | | | % 261.36/56.46 | | | ALPHA: (667) implies: % 261.36/56.46 | | | (668) $i(all_74_17) % 261.36/56.46 | | | (669) succ(pv57) = all_74_17 % 261.36/56.46 | | | % 261.36/56.46 | | | GROUND_INST: instantiating (5) with all_74_17, all_74_16, simplifying with % 261.36/56.46 | | | (658), (668) gives: % 261.36/56.47 | | | (670) pred(all_74_17) = all_74_16 & $i(all_74_16) % 261.36/56.47 | | | % 261.36/56.47 | | | ALPHA: (670) implies: % 261.36/56.47 | | | (671) pred(all_74_17) = all_74_16 % 261.36/56.47 | | | % 261.36/56.47 | | | GROUND_INST: instantiating (11) with all_74_14, simplifying with (67), % 261.36/56.47 | | | (651), (664) gives: % 261.36/56.47 | | | (672) all_74_14 = n6 | all_74_14 = n5 | all_74_14 = n4 | all_74_14 = n3 % 261.36/56.47 | | | | all_74_14 = n2 | all_74_14 = n1 | all_74_14 = n0 % 261.36/56.47 | | | % 261.36/56.47 | | | GROUND_INST: instantiating (succ_pred) with all_74_17, all_74_16, % 261.36/56.47 | | | simplifying with (668), (671) gives: % 261.36/56.47 | | | (673) succ(all_74_16) = all_74_17 % 261.36/56.47 | | | % 261.36/56.47 | | | GROUND_INST: instantiating (6) with pv57, n5, all_74_17, n6, simplifying % 261.36/56.47 | | | with (24), (138), (139), (162), (669) gives: % 261.36/56.47 | | | (674) leq(all_74_17, n6) % 261.36/56.47 | | | % 261.36/56.47 | | | GROUND_INST: instantiating (leq_succ) with pv57, pv57, all_74_17, % 261.36/56.47 | | | simplifying with (24), (173), (669) gives: % 261.36/56.47 | | | (675) leq(pv57, all_74_17) % 261.36/56.47 | | | % 261.36/56.47 | | | GROUND_INST: instantiating (leq_succ) with n0, pv57, all_74_17, % 261.36/56.47 | | | simplifying with (22), (24), (63), (669) gives: % 261.36/56.47 | | | (676) leq(n0, all_74_17) % 261.36/56.47 | | | % 261.36/56.47 | | | GROUND_INST: instantiating (3) with n0, pv57, all_74_17, simplifying with % 261.36/56.47 | | | (22), (24), (63), (669) gives: % 261.36/56.47 | | | (677) gt(all_74_17, n0) % 261.36/56.47 | | | % 261.36/56.47 | | | GROUND_INST: instantiating (pred_succ) with pv57, all_74_17, simplifying % 261.36/56.47 | | | with (24), (669) gives: % 261.36/56.47 | | | (678) pred(all_74_17) = pv57 % 261.36/56.47 | | | % 261.36/56.47 | | | GROUND_INST: instantiating (27) with all_74_16, pv57, all_74_17, % 261.36/56.47 | | | simplifying with (671), (678) gives: % 261.36/56.47 | | | (679) all_74_16 = pv57 % 261.36/56.47 | | | % 261.36/56.47 | | | REDUCE: (658), (679) imply: % 261.36/56.47 | | | (680) minus(all_74_17, n1) = pv57 % 261.36/56.47 | | | % 261.36/56.47 | | | REDUCE: (652), (679) imply: % 261.36/56.47 | | | (681) leq(all_74_15, pv57) % 261.36/56.47 | | | % 261.36/56.47 | | | GROUND_INST: instantiating (11) with all_74_17, simplifying with (668), % 261.36/56.47 | | | (674), (676) gives: % 261.36/56.47 | | | (682) all_74_17 = n6 | all_74_17 = n5 | all_74_17 = n4 | all_74_17 = n3 % 261.36/56.47 | | | | all_74_17 = n2 | all_74_17 = n1 | all_74_17 = n0 % 261.36/56.47 | | | % 261.36/56.47 | | | GROUND_INST: instantiating (transitivity_leq) with all_74_15, pv57, n6, % 261.36/56.47 | | | simplifying with (24), (25), (66), (163), (681) gives: % 261.36/56.47 | | | (683) leq(all_74_15, n6) % 261.36/56.47 | | | % 261.36/56.47 | | | GROUND_INST: instantiating (transitivity_leq) with all_74_15, pv57, n5, % 261.36/56.47 | | | simplifying with (24), (66), (139), (162), (681) gives: % 261.36/56.47 | | | (684) leq(all_74_15, n5) % 261.36/56.47 | | | % 261.36/56.47 | | | GROUND_INST: instantiating (transitivity_leq) with all_74_15, pv57, % 261.36/56.47 | | | all_74_17, simplifying with (24), (66), (668), (675), (681) % 261.36/56.47 | | | gives: % 261.36/56.47 | | | (685) leq(all_74_15, all_74_17) % 261.36/56.47 | | | % 261.36/56.47 | | | GROUND_INST: instantiating (2) with all_74_15, n6, n5, simplifying with % 261.36/56.47 | | | (25), (66), (149), (684) gives: % 261.36/56.47 | | | (686) gt(n6, all_74_15) % 261.36/56.47 | | | % 261.36/56.47 | | | GROUND_INST: instantiating (10) with all_74_15, simplifying with (66), % 261.36/56.47 | | | (650), (684) gives: % 261.36/56.47 | | | (687) all_74_15 = n5 | all_74_15 = n4 | all_74_15 = n3 | all_74_15 = n2 % 261.36/56.47 | | | | all_74_15 = n1 | all_74_15 = n0 % 261.36/56.47 | | | % 261.36/56.47 | | | GROUND_INST: instantiating (11) with all_74_15, simplifying with (66), % 261.36/56.47 | | | (650), (683) gives: % 261.36/56.47 | | | (688) all_74_15 = n6 | all_74_15 = n5 | all_74_15 = n4 | all_74_15 = n3 % 261.36/56.47 | | | | all_74_15 = n2 | all_74_15 = n1 | all_74_15 = n0 % 261.36/56.47 | | | % 261.36/56.47 | | | BETA: splitting (142) gives: % 261.36/56.47 | | | % 261.36/56.47 | | | Case 1: % 261.36/56.47 | | | | % 261.36/56.47 | | | | (689) gt(pv57, n0) % 261.36/56.47 | | | | % 261.36/56.47 | | | | GROUND_INST: instantiating (1) with n0, pv57, all_74_18, simplifying % 261.36/56.47 | | | | with (22), (24), (155), (689) gives: % 261.36/56.47 | | | | (690) leq(n0, all_74_18) % 261.36/56.47 | | | | % 261.36/56.47 | | | | BETA: splitting (143) gives: % 261.36/56.47 | | | | % 261.36/56.47 | | | | Case 1: % 261.36/56.47 | | | | | % 261.36/56.47 | | | | | (691) gt(all_74_20, pv57) % 261.36/56.47 | | | | | % 261.36/56.47 | | | | | REDUCE: (159), (691) imply: % 261.36/56.47 | | | | | (692) gt(n5, pv57) % 261.36/56.47 | | | | | % 261.36/56.47 | | | | | GROUND_INST: instantiating (1) with pv57, n5, n4, simplifying with % 261.36/56.47 | | | | | (24), (139), (148), (692) gives: % 261.36/56.47 | | | | | (693) leq(pv57, n4) % 261.36/56.47 | | | | | % 261.36/56.47 | | | | | GROUND_INST: instantiating (6) with n0, all_74_18, n1, pv57, % 261.36/56.47 | | | | | simplifying with (19), (22), (154), (165), (690) gives: % 261.36/56.47 | | | | | (694) leq(n1, pv57) % 261.36/56.47 | | | | | % 261.36/56.47 | | | | | GROUND_INST: instantiating (11) with all_74_18, simplifying with % 261.36/56.47 | | | | | (154), (172), (690) gives: % 261.36/56.47 | | | | | (695) all_74_18 = n6 | all_74_18 = n5 | all_74_18 = n4 | all_74_18 % 261.36/56.47 | | | | | = n3 | all_74_18 = n2 | all_74_18 = n1 | all_74_18 = n0 % 261.36/56.47 | | | | | % 261.36/56.47 | | | | | GROUND_INST: instantiating (9) with all_74_18, simplifying with (154), % 261.36/56.47 | | | | | (168), (690) gives: % 261.36/56.47 | | | | | (696) all_74_18 = n4 | all_74_18 = n3 | all_74_18 = n2 | all_74_18 % 261.36/56.47 | | | | | = n1 | all_74_18 = n0 % 261.36/56.47 | | | | | % 261.36/56.47 | | | | | GROUND_INST: instantiating (leq_gt2) with n0, all_74_18, simplifying % 261.36/56.47 | | | | | with (22), (154), (690) gives: % 261.36/56.47 | | | | | (697) all_74_18 = n0 | gt(all_74_18, n0) % 261.36/56.47 | | | | | % 261.36/56.47 | | | | | GROUND_INST: instantiating (6) with n1, pv57, n2, all_74_17, % 261.36/56.47 | | | | | simplifying with (24), (101), (102), (669), (694) gives: % 261.36/56.47 | | | | | (698) leq(n2, all_74_17) % 261.36/56.47 | | | | | % 261.36/56.47 | | | | | GROUND_INST: instantiating (leq_gt2) with n1, pv57, simplifying with % 261.36/56.47 | | | | | (24), (102), (694) gives: % 261.36/56.47 | | | | | (699) pv57 = n1 | gt(pv57, n1) % 261.36/56.47 | | | | | % 261.36/56.47 | | | | | GROUND_INST: instantiating (6) with pv57, n4, all_74_17, n5, % 261.36/56.47 | | | | | simplifying with (24), (135), (136), (669), (693) gives: % 261.36/56.47 | | | | | (700) leq(all_74_17, n5) % 261.36/56.47 | | | | | % 261.36/56.47 | | | | | GROUND_INST: instantiating (7) with all_74_18, n3, pv57, n4, % 261.36/56.47 | | | | | simplifying with (128), (129), (154), (165), (693) gives: % 261.36/56.47 | | | | | (701) leq(all_74_18, n3) % 261.36/56.47 | | | | | % 261.36/56.47 | | | | | GROUND_INST: instantiating (transitivity_leq) with all_74_15, pv57, % 261.36/56.47 | | | | | n4, simplifying with (24), (66), (136), (681), (693) % 261.36/56.47 | | | | | gives: % 261.36/56.47 | | | | | (702) leq(all_74_15, n4) % 261.36/56.47 | | | | | % 261.36/56.47 | | | | | GROUND_INST: instantiating (leq_gt2) with pv57, n4, simplifying with % 261.36/56.47 | | | | | (24), (136), (693) gives: % 261.36/56.47 | | | | | (703) pv57 = n4 | gt(n4, pv57) % 261.36/56.47 | | | | | % 261.36/56.47 | | | | | BETA: splitting (164) gives: % 261.36/56.47 | | | | | % 261.36/56.47 | | | | | Case 1: % 261.36/56.47 | | | | | | % 261.36/56.47 | | | | | | (704) pv57 = n0 % 261.36/56.47 | | | | | | % 261.36/56.47 | | | | | | REF_CLOSE: (24), (689), (704), (irreflexivity_gt) are inconsistent % 261.36/56.47 | | | | | | by sub-proof #95. % 261.36/56.47 | | | | | | % 261.36/56.47 | | | | | Case 2: % 261.36/56.47 | | | | | | % 261.36/56.47 | | | | | | (705) ~ (pv57 = n0) % 261.36/56.47 | | | | | | (706) pv57 = n5 | pv57 = n4 | pv57 = n3 | pv57 = n2 | pv57 = n1 % 261.36/56.47 | | | | | | % 261.36/56.47 | | | | | | GROUND_INST: instantiating (leq_gt2) with n2, all_74_17, simplifying % 261.36/56.47 | | | | | | with (118), (668), (698) gives: % 261.36/56.47 | | | | | | (707) all_74_17 = n2 | gt(all_74_17, n2) % 261.36/56.47 | | | | | | % 261.36/56.47 | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_18, n3, simplifying % 261.36/56.47 | | | | | | with (129), (154), (701) gives: % 261.36/56.47 | | | | | | (708) all_74_18 = n3 | gt(n3, all_74_18) % 261.36/56.47 | | | | | | % 261.36/56.47 | | | | | | GROUND_INST: instantiating (2) with all_74_15, n5, n4, simplifying % 261.36/56.47 | | | | | | with (66), (139), (148), (702) gives: % 261.36/56.47 | | | | | | (709) gt(n5, all_74_15) % 261.36/56.47 | | | | | | % 261.36/56.47 | | | | | | GROUND_INST: instantiating (9) with all_74_15, simplifying with % 261.36/56.47 | | | | | | (66), (650), (702) gives: % 261.36/56.47 | | | | | | (710) all_74_15 = n4 | all_74_15 = n3 | all_74_15 = n2 | % 261.36/56.47 | | | | | | all_74_15 = n1 | all_74_15 = n0 % 261.36/56.47 | | | | | | % 261.36/56.47 | | | | | | BETA: splitting (661) gives: % 261.36/56.47 | | | | | | % 261.36/56.47 | | | | | | Case 1: % 261.36/56.47 | | | | | | | % 261.36/56.47 | | | | | | | (711) gt(all_74_14, n0) % 261.36/56.47 | | | | | | | % 261.36/56.47 | | | | | | | BETA: splitting (660) gives: % 261.36/56.47 | | | | | | | % 261.36/56.47 | | | | | | | Case 1: % 261.36/56.47 | | | | | | | | % 261.36/56.47 | | | | | | | | (712) gt(all_74_15, n0) % 261.36/56.47 | | | | | | | | % 261.36/56.47 | | | | | | | | BETA: splitting (663) gives: % 261.36/56.47 | | | | | | | | % 261.36/56.47 | | | | | | | | Case 1: % 261.36/56.47 | | | | | | | | | % 261.36/56.47 | | | | | | | | | (713) gt(all_74_16, all_74_15) % 261.36/56.47 | | | | | | | | | % 261.36/56.47 | | | | | | | | | REDUCE: (679), (713) imply: % 261.36/56.47 | | | | | | | | | (714) gt(pv57, all_74_15) % 261.36/56.47 | | | | | | | | | % 261.36/56.47 | | | | | | | | | BETA: splitting (666) gives: % 261.36/56.47 | | | | | | | | | % 261.36/56.47 | | | | | | | | | Case 1: % 261.36/56.47 | | | | | | | | | | % 261.36/56.47 | | | | | | | | | | (715) gt(n5, all_74_14) % 261.36/56.47 | | | | | | | | | | % 261.36/56.47 | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_14, n5, n4, % 261.36/56.47 | | | | | | | | | | simplifying with (67), (139), (148), (715) gives: % 261.36/56.47 | | | | | | | | | | (716) leq(all_74_14, n4) % 261.36/56.47 | | | | | | | | | | % 261.36/56.47 | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_15, pv57, all_74_18, % 261.36/56.47 | | | | | | | | | | simplifying with (24), (66), (155), (714) gives: % 261.36/56.47 | | | | | | | | | | (717) leq(all_74_15, all_74_18) % 261.36/56.47 | | | | | | | | | | % 261.36/56.47 | | | | | | | | | | BETA: splitting (665) gives: % 261.36/56.47 | | | | | | | | | | % 261.36/56.47 | | | | | | | | | | Case 1: % 261.36/56.47 | | | | | | | | | | | % 261.36/56.47 | | | | | | | | | | | (718) all_74_14 = n0 % 261.36/56.47 | | | | | | | | | | | % 261.36/56.47 | | | | | | | | | | | REF_CLOSE: (67), (711), (718), (irreflexivity_gt) are % 261.36/56.47 | | | | | | | | | | | inconsistent by sub-proof #41. % 261.36/56.47 | | | | | | | | | | | % 261.36/56.47 | | | | | | | | | | Case 2: % 261.36/56.47 | | | | | | | | | | | % 261.36/56.47 | | | | | | | | | | | (719) ~ (all_74_14 = n0) % 261.36/56.47 | | | | | | | | | | | (720) all_74_14 = n5 | all_74_14 = n4 | all_74_14 = n3 | % 261.36/56.47 | | | | | | | | | | | all_74_14 = n2 | all_74_14 = n1 % 261.36/56.47 | | | | | | | | | | | % 261.36/56.47 | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_15, all_74_18, % 261.36/56.47 | | | | | | | | | | | simplifying with (66), (154), (717) gives: % 261.36/56.48 | | | | | | | | | | | (721) all_74_15 = all_74_18 | gt(all_74_18, all_74_15) % 261.36/56.48 | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_14, n4, % 261.36/56.48 | | | | | | | | | | | simplifying with (67), (136), (716) gives: % 261.36/56.48 | | | | | | | | | | | (722) all_74_14 = n4 | gt(n4, all_74_14) % 261.36/56.48 | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | BETA: splitting (682) gives: % 261.36/56.48 | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | Case 1: % 261.36/56.48 | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | (723) all_74_17 = n0 % 261.36/56.48 | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | REDUCE: (677), (723) imply: % 261.36/56.48 | | | | | | | | | | | | (724) gt(n0, n0) % 261.36/56.48 | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | GROUND_INST: instantiating (irreflexivity_gt) with n0, % 261.36/56.48 | | | | | | | | | | | | simplifying with (22), (724) gives: % 261.36/56.48 | | | | | | | | | | | | (725) $false % 261.36/56.48 | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | CLOSE: (725) is inconsistent. % 261.36/56.48 | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | Case 2: % 261.36/56.48 | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | (726) all_74_17 = n6 | all_74_17 = n5 | all_74_17 = n4 | % 261.36/56.48 | | | | | | | | | | | | all_74_17 = n3 | all_74_17 = n2 | all_74_17 = n1 % 261.36/56.48 | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | BETA: splitting (687) gives: % 261.36/56.48 | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | Case 1: % 261.36/56.48 | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | (727) all_74_15 = n0 % 261.36/56.48 | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | REF_CLOSE: (66), (712), (727), (irreflexivity_gt) are % 261.36/56.48 | | | | | | | | | | | | | inconsistent by sub-proof #40. % 261.36/56.48 | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | Case 2: % 261.36/56.48 | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | (728) ~ (all_74_15 = n0) % 261.36/56.48 | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | BETA: splitting (688) gives: % 261.36/56.48 | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | Case 1: % 261.36/56.48 | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | (729) all_74_15 = n0 % 261.36/56.48 | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | REDUCE: (728), (729) imply: % 261.36/56.48 | | | | | | | | | | | | | | (730) $false % 261.36/56.48 | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | CLOSE: (730) is inconsistent. % 261.36/56.48 | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | Case 2: % 261.36/56.48 | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | (731) all_74_15 = n6 | all_74_15 = n5 | all_74_15 = n4 | % 261.36/56.48 | | | | | | | | | | | | | | all_74_15 = n3 | all_74_15 = n2 | all_74_15 = n1 % 261.36/56.48 | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | BETA: splitting (697) gives: % 261.36/56.48 | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | Case 1: % 261.36/56.48 | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | (732) gt(all_74_18, n0) % 261.36/56.48 | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | BETA: splitting (696) gives: % 261.36/56.48 | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | Case 1: % 261.36/56.48 | | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | | (733) all_74_18 = n0 % 261.36/56.48 | | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | | REF_CLOSE: (154), (732), (733), (irreflexivity_gt) are % 261.36/56.48 | | | | | | | | | | | | | | | | inconsistent by sub-proof #39. % 261.36/56.48 | | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | Case 2: % 261.36/56.48 | | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | | (734) ~ (all_74_18 = n0) % 261.36/56.48 | | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | | BETA: splitting (699) gives: % 261.36/56.48 | | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | | Case 1: % 261.36/56.48 | | | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | | | (735) gt(pv57, n1) % 261.36/56.48 | | | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with n1, pv57, all_74_18, % 261.36/56.48 | | | | | | | | | | | | | | | | | simplifying with (24), (102), (155), (735) gives: % 261.36/56.48 | | | | | | | | | | | | | | | | | (736) leq(n1, all_74_18) % 261.36/56.48 | | | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | | | BETA: splitting (703) gives: % 261.36/56.48 | | | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | | | Case 1: % 261.36/56.48 | | | | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | | | | (737) gt(n4, pv57) % 261.36/56.48 | | | | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | | | | BETA: splitting (708) gives: % 261.36/56.48 | | | | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | | | | Case 1: % 261.36/56.48 | | | | | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | | | | | (738) gt(n3, all_74_18) % 261.36/56.48 | | | | | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_18, n3, n2, % 261.36/56.48 | | | | | | | | | | | | | | | | | | | simplifying with (129), (146), (154), (738) gives: % 261.36/56.48 | | | | | | | | | | | | | | | | | | | (739) leq(all_74_18, n2) % 261.36/56.48 | | | | | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with pv57, n4, n3, simplifying % 261.36/56.48 | | | | | | | | | | | | | | | | | | | with (24), (136), (147), (737) gives: % 261.36/56.48 | | | | | | | | | | | | | | | | | | | (740) leq(pv57, n3) % 261.36/56.48 | | | | | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with n1, all_74_18, % 261.36/56.48 | | | | | | | | | | | | | | | | | | | simplifying with (102), (154), (736) gives: % 261.36/56.48 | | | | | | | | | | | | | | | | | | | (741) all_74_18 = n1 | gt(all_74_18, n1) % 261.36/56.48 | | | | | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | | | | | BETA: splitting (706) gives: % 261.36/56.48 | | | | | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | | | | | Case 1: % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | (742) pv57 = n1 % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (27), (144), (155), (734), (742) are inconsistent % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | by sub-proof #38. % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | | | | | Case 2: % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | (743) ~ (pv57 = n1) % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | (744) pv57 = n5 | pv57 = n4 | pv57 = n3 | pv57 = n2 % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | BETA: splitting (722) gives: % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | Case 1: % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | (745) gt(n4, all_74_14) % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (721) gives: % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | (746) gt(all_74_18, all_74_15) % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_14, n4, n3, % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | simplifying with (67), (136), (147), (745) gives: % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | (747) leq(all_74_14, n3) % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (15) with pv57, simplifying with % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | (24), (63), (740) gives: % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | (748) pv57 = n3 | pv57 = n2 | pv57 = n1 | pv57 = n0 % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with pv57, n3, simplifying % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | with (24), (129), (740) gives: % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | (749) pv57 = n3 | gt(n3, pv57) % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (731) gives: % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | (750) all_74_15 = n6 % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (684), (750) imply: % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | (751) leq(n6, n5) % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (726) gives: % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | (752) all_74_17 = n6 % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (680), (752) imply: % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | (753) minus(n6, n1) = pv57 % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (29) with n5, pv57, n1, n6, % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (160), (753) gives: % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | (754) pv57 = n5 % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (692), (754) imply: % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | (755) gt(n5, n5) % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (irreflexivity_gt) with n5, % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (139), (755) gives: % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | (756) $false % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (756) is inconsistent. % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (leq_succ_gt) with n5, n5, n6, % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (138), (139), (751) gives: % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | (757) gt(n5, n5) % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (irreflexivity_gt) with n5, % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (139), (757) gives: % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | (758) $false % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (758) is inconsistent. % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | End of split % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_14, n3, % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | simplifying with (67), (129), (747) gives: % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | (759) all_74_14 = n3 | gt(n3, all_74_14) % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (741) gives: % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | (760) gt(all_74_18, n1) % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (744) gives: % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | (761) pv57 = n3 % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (75), (761) imply: % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | (762) minus(n3, n1) = all_74_18 % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (155), (761) imply: % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | (763) pred(n3) = all_74_18 % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (681), (761) imply: % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | (764) leq(all_74_15, n3) % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (29) with n2, all_74_18, n1, n3, % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (161), (762) gives: % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | (765) all_74_18 = n2 % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (717), (765) imply: % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | (766) leq(all_74_15, n2) % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (746), (765) imply: % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | (767) gt(n2, all_74_15) % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_15, n2, n1, % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (66), (118), (145), (767) gives: % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | (768) leq(all_74_15, n1) % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_74_15, simplifying % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | with (66), (650), (768) gives: % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | (769) all_74_15 = n1 | all_74_15 = n0 % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (769) gives: % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | | (770) all_74_15 = n0 % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (728), (770) imply: % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | | (771) $false % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (771) is inconsistent. % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | | (772) all_74_15 = n1 % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (656), (772) imply: % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | | (773) a_select3(id_ds1_filter, all_74_14, n1) = % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | | all_74_12 % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (655), (772) imply: % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | | (774) a_select3(id_ds1_filter, n1, all_74_14) = % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | | all_74_13 % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (764), (772) imply: % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | | (775) leq(n1, n3) % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (766), (772) imply: % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | | (776) leq(n1, n2) % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (650), (772) imply: % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | | (777) leq(n0, n1) % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (759) gives: % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | (778) gt(n3, all_74_14) % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_14, n3, n2, % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (67), (129), (146), (778) gives: % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | (779) leq(all_74_14, n2) % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_14, n2, % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (67), (118), (779) gives: % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | (780) all_74_14 = n2 | gt(n2, all_74_14) % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (780) gives: % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (781) gt(n2, all_74_14) % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_14, n2, n1, % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (67), (118), (145), (781) gives: % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (782) leq(all_74_14, n1) % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (30), (67), (649), (651), (719), (773), % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (774), (782) are inconsistent by sub-proof #37. % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (783) all_74_14 = n2 % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (773), (783) imply: % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (784) a_select3(id_ds1_filter, n2, n1) = all_74_12 % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (774), (783) imply: % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (785) a_select3(id_ds1_filter, n1, n2) = all_74_13 % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (659), (783) imply: % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (786) leq(n2, n5) % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (651), (783) imply: % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (787) leq(n0, n2) % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (82) with n1, n2, all_74_13, % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (102), (118), (777), (785), (787) % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (788) ~ leq(n2, all_74_20) | ~ leq(n1, all_74_18) | % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (a_select3(id_ds1_filter, n2, n1) = all_74_13 & % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_74_13)) % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (788) gives: % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (789) ~ leq(n2, all_74_20) % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (159), (789) imply: % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (790) ~ leq(n2, n5) % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (786), (790) imply: % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (791) $false % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (791) is inconsistent. % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (792) ~ leq(n1, all_74_18) | (a_select3(id_ds1_filter, % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | n2, n1) = all_74_13 & $i(all_74_13)) % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (792) gives: % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (793) ~ leq(n1, all_74_18) % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (765), (793) imply: % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (794) ~ leq(n1, n2) % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (776), (794) imply: % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (795) $false % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (795) is inconsistent. % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (796) a_select3(id_ds1_filter, n2, n1) = all_74_13 & % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_74_13) % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (796) implies: % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (797) a_select3(id_ds1_filter, n2, n1) = all_74_13 % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (649), (784), (797) are inconsistent by % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #36. % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | (798) all_74_14 = n3 % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (773), (798) imply: % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | (799) a_select3(id_ds1_filter, n3, n1) = all_74_12 % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (774), (798) imply: % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | (800) a_select3(id_ds1_filter, n1, n3) = all_74_13 % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (659), (798) imply: % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | (801) leq(n3, n5) % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (651), (798) imply: % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | (802) leq(n0, n3) % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (81) with n1, n3, all_74_13, % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (102), (129), (777), (800), (802) % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | (803) ~ leq(n3, all_74_20) | ~ leq(n1, pv57) | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | (a_select3(id_ds1_filter, n3, n1) = all_74_13 & % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_74_13)) % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (803) gives: % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (804) ~ leq(n3, all_74_20) % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (159), (804) imply: % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (805) ~ leq(n3, n5) % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (801), (805) imply: % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (806) $false % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (806) is inconsistent. % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (807) ~ leq(n1, pv57) | (a_select3(id_ds1_filter, n3, % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | n1) = all_74_13 & $i(all_74_13)) % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (807) gives: % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (808) ~ leq(n1, pv57) % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (761), (808) imply: % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (809) ~ leq(n1, n3) % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (775), (809) imply: % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (810) $false % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (810) is inconsistent. % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (811) a_select3(id_ds1_filter, n3, n1) = all_74_13 & % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_74_13) % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (811) implies: % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (812) a_select3(id_ds1_filter, n3, n1) = all_74_13 % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (649), (799), (812) are inconsistent by % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #35. % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | (813) ~ (pv57 = n3) % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (24), (27), (145), (154), (155), (705), (743), % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | (744), (748), (749), (760), (813), % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | (irreflexivity_gt) are inconsistent by sub-proof % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | #33. % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | (814) all_74_18 = n1 % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | (815) ~ gt(all_74_18, n1) % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (717), (814) imply: % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | (816) leq(all_74_15, n1) % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (746), (814) imply: % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | (817) gt(n1, all_74_15) % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (814), (815) imply: % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | (818) ~ gt(n1, n1) % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (66), (650), (728), (816), (817), (818) are % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #32. % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | End of split % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | End of split % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | (819) all_74_15 = all_74_18 % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | (820) ~ gt(all_74_18, all_74_15) % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (656), (819) imply: % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | (821) a_select3(id_ds1_filter, all_74_14, all_74_18) = % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | all_74_12 % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (655), (819) imply: % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | (822) a_select3(id_ds1_filter, all_74_18, all_74_14) = % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | all_74_13 % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (686), (819) imply: % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | (823) gt(n6, all_74_18) % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (819), (820) imply: % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | (824) ~ gt(all_74_18, all_74_18) % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_14, n4, n3, % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | simplifying with (67), (136), (147), (745) gives: % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | (825) leq(all_74_14, n3) % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (15) with pv57, simplifying with % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | (24), (63), (740) gives: % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | (826) pv57 = n3 | pv57 = n2 | pv57 = n1 | pv57 = n0 % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with pv57, n3, simplifying % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | with (24), (129), (740) gives: % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | (827) pv57 = n3 | gt(n3, pv57) % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (731) gives: % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | (828) all_74_15 = n6 % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (819), (828) imply: % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | (829) all_74_18 = n6 % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (823), (829) imply: % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | (830) gt(n6, n6) % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (824), (829) imply: % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | (831) ~ gt(n6, n6) % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (830), (831) imply: % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | (832) $false % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (832) is inconsistent. % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_14, n3, % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | simplifying with (67), (129), (825) gives: % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | (833) all_74_14 = n3 | gt(n3, all_74_14) % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (741) gives: % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | (834) gt(all_74_18, n1) % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (744) gives: % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | (835) pv57 = n3 % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (75), (835) imply: % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | (836) minus(n3, n1) = all_74_18 % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (155), (835) imply: % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | (837) pred(n3) = all_74_18 % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (29) with n2, all_74_18, n1, n3, % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (161), (836) gives: % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | (838) all_74_18 = n2 % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (821), (838) imply: % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | (839) a_select3(id_ds1_filter, all_74_14, n2) = % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | all_74_12 % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (822), (838) imply: % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | (840) a_select3(id_ds1_filter, n2, all_74_14) = % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | all_74_13 % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (167), (838) imply: % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | (841) leq(n2, n5) % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (739), (838) imply: % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | (842) leq(n2, n2) % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (690), (838) imply: % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | (843) leq(n0, n2) % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (833) gives: % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | (844) gt(n3, all_74_14) % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_14, n3, n2, % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (67), (129), (146), (844) gives: % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | (845) leq(all_74_14, n2) % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_14, n2, % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (67), (118), (845) gives: % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | (846) all_74_14 = n2 | gt(n2, all_74_14) % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (846) gives: % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | (847) gt(n2, all_74_14) % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_14, n2, n1, % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (67), (118), (145), (847) gives: % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | (848) leq(all_74_14, n1) % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_74_14, simplifying % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | with (67), (651), (848) gives: % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | (849) all_74_14 = n1 | all_74_14 = n0 % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (849) gives: % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (850) all_74_14 = n0 % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (719), (850) imply: % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (851) $false % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (851) is inconsistent. % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (852) all_74_14 = n1 % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (839), (852) imply: % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (853) a_select3(id_ds1_filter, n1, n2) = all_74_12 % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (840), (852) imply: % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (854) a_select3(id_ds1_filter, n2, n1) = all_74_13 % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (845), (852) imply: % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (855) leq(n1, n2) % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (651), (852) imply: % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (856) leq(n0, n1) % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (82) with n1, n2, all_74_12, % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (102), (118), (843), (853), (856) % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (857) ~ leq(n2, all_74_20) | ~ leq(n1, all_74_18) | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (a_select3(id_ds1_filter, n2, n1) = all_74_12 & % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_74_12)) % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (857) gives: % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (858) ~ leq(n2, all_74_20) % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (159), (858) imply: % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (859) ~ leq(n2, n5) % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (841), (859) imply: % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (860) $false % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (860) is inconsistent. % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (861) ~ leq(n1, all_74_18) | (a_select3(id_ds1_filter, % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | n2, n1) = all_74_12 & $i(all_74_12)) % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (861) gives: % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (862) ~ leq(n1, all_74_18) % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (838), (862) imply: % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (863) ~ leq(n1, n2) % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (855), (863) imply: % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (864) $false % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (864) is inconsistent. % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (865) a_select3(id_ds1_filter, n2, n1) = all_74_12 & % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_74_12) % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (865) implies: % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (866) a_select3(id_ds1_filter, n2, n1) = all_74_12 % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (649), (854), (866) are inconsistent by % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #36. % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | (867) all_74_14 = n2 % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (839), (867) imply: % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | (868) a_select3(id_ds1_filter, n2, n2) = all_74_12 % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (840), (867) imply: % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | (869) a_select3(id_ds1_filter, n2, n2) = all_74_13 % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (649), (868), (869) are inconsistent by % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #31. % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | (870) all_74_14 = n3 % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (839), (870) imply: % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | (871) a_select3(id_ds1_filter, n3, n2) = all_74_12 % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (840), (870) imply: % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | (872) a_select3(id_ds1_filter, n2, n3) = all_74_13 % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (659), (870) imply: % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | (873) leq(n3, n5) % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (651), (870) imply: % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | (874) leq(n0, n3) % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (82) with n2, n3, all_74_13, % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (118), (129), (843), (872), (874) % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | (875) ~ leq(n3, all_74_20) | ~ leq(n2, all_74_18) | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | (a_select3(id_ds1_filter, n3, n2) = all_74_13 & % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_74_13)) % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (875) gives: % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | (876) ~ leq(n3, all_74_20) % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (159), (876) imply: % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | (877) ~ leq(n3, n5) % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (873), (877) imply: % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | (878) $false % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (878) is inconsistent. % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | (879) ~ leq(n2, all_74_18) | (a_select3(id_ds1_filter, % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | n3, n2) = all_74_13 & $i(all_74_13)) % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (879) gives: % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (880) ~ leq(n2, all_74_18) % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (838), (880) imply: % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (881) ~ leq(n2, n2) % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (842), (881) imply: % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (882) $false % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (882) is inconsistent. % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (883) a_select3(id_ds1_filter, n3, n2) = all_74_13 & % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_74_13) % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (883) implies: % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (884) a_select3(id_ds1_filter, n3, n2) = all_74_13 % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (649), (871), (884) are inconsistent by % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #30. % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | (885) ~ (pv57 = n3) % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (24), (27), (145), (154), (155), (705), (743), % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | (744), (826), (827), (834), (885), % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | (irreflexivity_gt) are inconsistent by sub-proof % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | #33. % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | (886) all_74_18 = n1 % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (821), (886) imply: % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | (887) a_select3(id_ds1_filter, all_74_14, n1) = % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | all_74_12 % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (822), (886) imply: % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | (888) a_select3(id_ds1_filter, n1, all_74_14) = % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | all_74_13 % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (165), (886) imply: % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | (889) succ(n1) = pv57 % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (155), (886) imply: % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | (890) pred(pv57) = n1 % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (736), (886) imply: % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | (891) leq(n1, n1) % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (690), (886) imply: % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | (892) leq(n0, n1) % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (28) with n2, pv57, n1, simplifying % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | with (101), (889) gives: % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | (893) pv57 = n2 % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (669), (893) imply: % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | (894) succ(n2) = all_74_17 % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (678), (893) imply: % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | (895) pred(all_74_17) = n2 % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (28) with n3, all_74_17, n2, % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (117), (894) gives: % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | (896) all_74_17 = n3 % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (833) gives: % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | (897) gt(n3, all_74_14) % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_14, n3, n2, % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (67), (129), (146), (897) gives: % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | (898) leq(all_74_14, n2) % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_14, n2, % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (67), (118), (898) gives: % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | (899) all_74_14 = n2 | gt(n2, all_74_14) % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (899) gives: % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | (900) gt(n2, all_74_14) % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_14, n2, n1, % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (67), (118), (145), (900) gives: % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | (901) leq(all_74_14, n1) % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (30), (67), (649), (651), (719), (887), % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | (888), (901) are inconsistent by sub-proof #37. % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | (902) all_74_14 = n2 % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (887), (902) imply: % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | (903) a_select3(id_ds1_filter, n2, n1) = all_74_12 % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (888), (902) imply: % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | (904) a_select3(id_ds1_filter, n1, n2) = all_74_13 % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (659), (902) imply: % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | (905) leq(n2, n5) % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (651), (902) imply: % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | (906) leq(n0, n2) % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (82) with n1, n2, all_74_13, % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (102), (118), (892), (904), (906) % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | (907) ~ leq(n2, all_74_20) | ~ leq(n1, all_74_18) | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | (a_select3(id_ds1_filter, n2, n1) = all_74_13 & % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_74_13)) % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (907) gives: % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | (908) ~ leq(n2, all_74_20) % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (159), (908) imply: % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | (909) ~ leq(n2, n5) % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (905), (909) imply: % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | (910) $false % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (910) is inconsistent. % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | (911) ~ leq(n1, all_74_18) | (a_select3(id_ds1_filter, % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | n2, n1) = all_74_13 & $i(all_74_13)) % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (911) gives: % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (912) ~ leq(n1, all_74_18) % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (886), (912) imply: % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (913) ~ leq(n1, n1) % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (891), (913) imply: % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (914) $false % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (914) is inconsistent. % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (915) a_select3(id_ds1_filter, n2, n1) = all_74_13 & % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_74_13) % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (915) implies: % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (916) a_select3(id_ds1_filter, n2, n1) = all_74_13 % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (649), (903), (916) are inconsistent by % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #36. % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | (917) all_74_14 = n3 % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (887), (917) imply: % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | (918) a_select3(id_ds1_filter, n3, n1) = all_74_12 % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (888), (917) imply: % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | (919) a_select3(id_ds1_filter, n1, n3) = all_74_13 % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (659), (917) imply: % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | (920) leq(n3, n5) % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (651), (917) imply: % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | (921) leq(n0, n3) % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (82) with n1, n3, all_74_13, % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (102), (129), (892), (919), (921) % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | (922) ~ leq(n3, all_74_20) | ~ leq(n1, all_74_18) | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | (a_select3(id_ds1_filter, n3, n1) = all_74_13 & % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_74_13)) % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (922) gives: % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | (923) ~ leq(n3, all_74_20) % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (159), (923) imply: % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | (924) ~ leq(n3, n5) % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (920), (924) imply: % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | (925) $false % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (925) is inconsistent. % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | (926) ~ leq(n1, all_74_18) | (a_select3(id_ds1_filter, % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | n3, n1) = all_74_13 & $i(all_74_13)) % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (926) gives: % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | (927) ~ leq(n1, all_74_18) % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (886), (927) imply: % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | (928) ~ leq(n1, n1) % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (891), (928) imply: % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | (929) $false % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (929) is inconsistent. % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | (930) a_select3(id_ds1_filter, n3, n1) = all_74_13 & % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_74_13) % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (930) implies: % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | (931) a_select3(id_ds1_filter, n3, n1) = all_74_13 % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (649), (918), (931) are inconsistent by % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #35. % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | End of split % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | End of split % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | End of split % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | Case 2: % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | (932) all_74_14 = n4 % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | REDUCE: (656), (932) imply: % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | (933) a_select3(id_ds1_filter, n4, all_74_15) = % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | all_74_12 % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | REDUCE: (655), (932) imply: % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | (934) a_select3(id_ds1_filter, all_74_15, n4) = % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | all_74_13 % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | REDUCE: (659), (932) imply: % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | (935) leq(n4, n5) % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | REDUCE: (651), (932) imply: % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | (936) leq(n0, n4) % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (721) gives: % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | (937) gt(all_74_18, all_74_15) % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (15) with pv57, simplifying with % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | (24), (63), (740) gives: % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | (938) pv57 = n3 | pv57 = n2 | pv57 = n1 | pv57 = n0 % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with pv57, n3, simplifying % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | with (24), (129), (740) gives: % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | (939) pv57 = n3 | gt(n3, pv57) % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (741) gives: % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | (940) gt(all_74_18, n1) % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (744) gives: % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | (941) pv57 = n3 % 261.36/56.50 | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (75), (941) imply: % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | (942) minus(n3, n1) = all_74_18 % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (669), (941) imply: % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | (943) succ(n3) = all_74_17 % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (28) with n4, all_74_17, n3, % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (128), (943) gives: % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | (944) all_74_17 = n4 % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (29) with n2, all_74_18, n1, n3, % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (161), (942) gives: % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | (945) all_74_18 = n2 % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (717), (945) imply: % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | (946) leq(all_74_15, n2) % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (937), (945) imply: % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | (947) gt(n2, all_74_15) % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_15, n2, n1, % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (66), (118), (145), (947) gives: % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | (948) leq(all_74_15, n1) % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_74_15, simplifying % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | with (66), (650), (948) gives: % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | (949) all_74_15 = n1 | all_74_15 = n0 % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (949) gives: % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | (950) all_74_15 = n0 % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (728), (950) imply: % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | (951) $false % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (951) is inconsistent. % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | (952) all_74_15 = n1 % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (934), (952) imply: % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | (953) a_select3(id_ds1_filter, n1, n4) = all_74_13 % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (933), (952) imply: % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | (954) a_select3(id_ds1_filter, n4, n1) = all_74_12 % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (946), (952) imply: % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | (955) leq(n1, n2) % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (650), (952) imply: % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | (956) leq(n0, n1) % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (82) with n1, n4, all_74_13, % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (102), (136), (936), (953), (956) % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | (957) ~ leq(n4, all_74_20) | ~ leq(n1, all_74_18) | % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | (a_select3(id_ds1_filter, n4, n1) = all_74_13 & % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_74_13)) % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (957) gives: % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | | (958) ~ leq(n4, all_74_20) % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (159), (958) imply: % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | | (959) ~ leq(n4, n5) % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (935), (959) imply: % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | | (960) $false % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (960) is inconsistent. % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | | (961) ~ leq(n1, all_74_18) | (a_select3(id_ds1_filter, % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | | n4, n1) = all_74_13 & $i(all_74_13)) % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (961) gives: % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | (962) ~ leq(n1, all_74_18) % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (945), (962) imply: % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | (963) ~ leq(n1, n2) % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (955), (963) imply: % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | (964) $false % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (964) is inconsistent. % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | (965) a_select3(id_ds1_filter, n4, n1) = all_74_13 & % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_74_13) % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (965) implies: % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | (966) a_select3(id_ds1_filter, n4, n1) = all_74_13 % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (649), (954), (966) are inconsistent by % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #29. % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | (967) ~ (pv57 = n3) % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (24), (27), (145), (154), (155), (705), (743), % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | (744), (938), (939), (940), (967), % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | (irreflexivity_gt) are inconsistent by sub-proof % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | #33. % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | End of split % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | (968) all_74_18 = n1 % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | (969) ~ gt(all_74_18, n1) % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (66), (650), (717), (728), (937), (968), % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | (969) are inconsistent by sub-proof #28. % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | End of split % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | (970) all_74_15 = all_74_18 % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (934), (970) imply: % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | (971) a_select3(id_ds1_filter, all_74_18, n4) = % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | all_74_13 % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (933), (970) imply: % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | (972) a_select3(id_ds1_filter, n4, all_74_18) = % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | all_74_12 % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (15) with pv57, simplifying with % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | (24), (63), (740) gives: % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | (973) pv57 = n3 | pv57 = n2 | pv57 = n1 | pv57 = n0 % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with pv57, n3, simplifying % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | with (24), (129), (740) gives: % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | (974) pv57 = n3 | gt(n3, pv57) % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (741) gives: % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | (975) gt(all_74_18, n1) % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (744) gives: % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | (976) pv57 = n3 % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (75), (976) imply: % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | (977) minus(n3, n1) = all_74_18 % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (669), (976) imply: % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | (978) succ(n3) = all_74_17 % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (28) with n4, all_74_17, n3, % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (128), (978) gives: % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | (979) all_74_17 = n4 % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (29) with n2, all_74_18, n1, n3, % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (161), (977) gives: % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | (980) all_74_18 = n2 % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (971), (980) imply: % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | (981) a_select3(id_ds1_filter, n2, n4) = all_74_13 % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (972), (980) imply: % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | (982) a_select3(id_ds1_filter, n4, n2) = all_74_12 % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (739), (980) imply: % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | (983) leq(n2, n2) % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (690), (980) imply: % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | (984) leq(n0, n2) % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (82) with n2, n4, all_74_13, % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (118), (136), (936), (981), (984) % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | gives: % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | (985) ~ leq(n4, all_74_20) | ~ leq(n2, all_74_18) | % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | (a_select3(id_ds1_filter, n4, n2) = all_74_13 & % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_74_13)) % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (985) gives: % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | (986) ~ leq(n4, all_74_20) % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (159), (986) imply: % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | (987) ~ leq(n4, n5) % 261.36/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (935), (987) imply: % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | (988) $false % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (988) is inconsistent. % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | (989) ~ leq(n2, all_74_18) | (a_select3(id_ds1_filter, % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | n4, n2) = all_74_13 & $i(all_74_13)) % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (989) gives: % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | | (990) ~ leq(n2, all_74_18) % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (980), (990) imply: % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | | (991) ~ leq(n2, n2) % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (983), (991) imply: % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | | (992) $false % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (992) is inconsistent. % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | | (993) a_select3(id_ds1_filter, n4, n2) = all_74_13 & % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_74_13) % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (993) implies: % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | | (994) a_select3(id_ds1_filter, n4, n2) = all_74_13 % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (649), (982), (994) are inconsistent by % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #27. % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | | (995) ~ (pv57 = n3) % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (24), (27), (145), (154), (155), (705), (743), % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | | (744), (973), (974), (975), (995), % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | | (irreflexivity_gt) are inconsistent by sub-proof % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | | #33. % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | End of split % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | (996) all_74_18 = n1 % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (971), (996) imply: % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | (997) a_select3(id_ds1_filter, n1, n4) = all_74_13 % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (972), (996) imply: % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | (998) a_select3(id_ds1_filter, n4, n1) = all_74_12 % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (736), (996) imply: % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | (999) leq(n1, n1) % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (690), (996) imply: % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | (1000) leq(n0, n1) % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (82) with n1, n4, all_74_13, % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | simplifying with (102), (136), (936), (997), % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | (1000) gives: % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | (1001) ~ leq(n4, all_74_20) | ~ leq(n1, all_74_18) | % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | (a_select3(id_ds1_filter, n4, n1) = all_74_13 & % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | $i(all_74_13)) % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1001) gives: % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | | (1002) ~ leq(n4, all_74_20) % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (159), (1002) imply: % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | | (1003) ~ leq(n4, n5) % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (935), (1003) imply: % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | | (1004) $false % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1004) is inconsistent. % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | | (1005) ~ leq(n1, all_74_18) | (a_select3(id_ds1_filter, % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | | n4, n1) = all_74_13 & $i(all_74_13)) % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1005) gives: % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | (1006) ~ leq(n1, all_74_18) % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (996), (1006) imply: % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | (1007) ~ leq(n1, n1) % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (999), (1007) imply: % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | (1008) $false % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1008) is inconsistent. % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | (1009) a_select3(id_ds1_filter, n4, n1) = all_74_13 & % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_74_13) % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1009) implies: % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | (1010) a_select3(id_ds1_filter, n4, n1) = all_74_13 % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (649), (998), (1010) are inconsistent by % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #29. % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | End of split % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | End of split % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | End of split % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | | % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | End of split % 261.63/56.51 | | | | | | | | | | | | | | | | | | | | % 261.63/56.51 | | | | | | | | | | | | | | | | | | | End of split % 261.63/56.51 | | | | | | | | | | | | | | | | | | | % 261.63/56.51 | | | | | | | | | | | | | | | | | | Case 2: % 261.63/56.51 | | | | | | | | | | | | | | | | | | | % 261.63/56.51 | | | | | | | | | | | | | | | | | | | (1011) all_74_18 = n3 % 261.63/56.51 | | | | | | | | | | | | | | | | | | | % 261.63/56.51 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (24), (28), (128), (165), (737), (1011), % 261.63/56.51 | | | | | | | | | | | | | | | | | | | (irreflexivity_gt) are inconsistent by sub-proof % 261.63/56.51 | | | | | | | | | | | | | | | | | | | #26. % 261.63/56.51 | | | | | | | | | | | | | | | | | | | % 261.63/56.51 | | | | | | | | | | | | | | | | | | End of split % 261.63/56.51 | | | | | | | | | | | | | | | | | | % 261.63/56.51 | | | | | | | | | | | | | | | | | Case 2: % 261.63/56.51 | | | | | | | | | | | | | | | | | | % 261.63/56.51 | | | | | | | | | | | | | | | | | | (1012) pv57 = n4 % 261.63/56.51 | | | | | | | | | | | | | | | | | | (1013) ~ gt(n4, pv57) % 261.63/56.51 | | | | | | | | | | | | | | | | | | % 261.63/56.51 | | | | | | | | | | | | | | | | | | REDUCE: (669), (1012) imply: % 261.63/56.51 | | | | | | | | | | | | | | | | | | (1014) succ(n4) = all_74_17 % 261.63/56.51 | | | | | | | | | | | | | | | | | | % 261.63/56.51 | | | | | | | | | | | | | | | | | | REDUCE: (155), (1012) imply: % 261.63/56.51 | | | | | | | | | | | | | | | | | | (1015) pred(n4) = all_74_18 % 261.63/56.51 | | | | | | | | | | | | | | | | | | % 261.63/56.51 | | | | | | | | | | | | | | | | | | REDUCE: (1012), (1013) imply: % 261.63/56.51 | | | | | | | | | | | | | | | | | | (1016) ~ gt(n4, n4) % 261.63/56.51 | | | | | | | | | | | | | | | | | | % 261.63/56.51 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (27) with n3, all_74_18, n4, % 261.63/56.51 | | | | | | | | | | | | | | | | | | simplifying with (147), (1015) gives: % 261.63/56.51 | | | | | | | | | | | | | | | | | | (1017) all_74_18 = n3 % 261.63/56.51 | | | | | | | | | | | | | | | | | | % 261.63/56.51 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (28) with n5, all_74_17, n4, % 261.63/56.51 | | | | | | | | | | | | | | | | | | simplifying with (135), (1014) gives: % 261.63/56.51 | | | | | | | | | | | | | | | | | | (1018) all_74_17 = n5 % 261.63/56.51 | | | | | | | | | | | | | | | | | | % 261.63/56.51 | | | | | | | | | | | | | | | | | | REDUCE: (717), (1017) imply: % 261.63/56.51 | | | | | | | | | | | | | | | | | | (1019) leq(all_74_15, n3) % 261.63/56.51 | | | | | | | | | | | | | | | | | | % 261.63/56.51 | | | | | | | | | | | | | | | | | | BETA: splitting (722) gives: % 261.63/56.51 | | | | | | | | | | | | | | | | | | % 261.63/56.51 | | | | | | | | | | | | | | | | | | Case 1: % 261.63/56.51 | | | | | | | | | | | | | | | | | | | % 261.63/56.51 | | | | | | | | | | | | | | | | | | | (1020) gt(n4, all_74_14) % 261.63/56.51 | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_14, n4, n3, % 261.63/56.52 | | | | | | | | | | | | | | | | | | | simplifying with (67), (136), (147), (1020) gives: % 261.63/56.52 | | | | | | | | | | | | | | | | | | | (1021) leq(all_74_14, n3) % 261.63/56.52 | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_14, n3, % 261.63/56.52 | | | | | | | | | | | | | | | | | | | simplifying with (67), (129), (1021) gives: % 261.63/56.52 | | | | | | | | | | | | | | | | | | | (1022) all_74_14 = n3 | gt(n3, all_74_14) % 261.63/56.52 | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | BETA: splitting (721) gives: % 261.63/56.52 | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | Case 1: % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | (1023) gt(all_74_18, all_74_15) % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | REDUCE: (1017), (1023) imply: % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | (1024) gt(n3, all_74_15) % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_15, n3, n2, % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | simplifying with (66), (129), (146), (1024) gives: % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | (1025) leq(all_74_15, n2) % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | BETA: splitting (720) gives: % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | Case 1: % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | (1026) all_74_14 = n5 % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | REDUCE: (716), (1026) imply: % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | (1027) leq(n5, n4) % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (leq_succ_gt) with n4, n4, n5, % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | simplifying with (135), (136), (1016), (1027) % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | gives: % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | (1028) $false % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | CLOSE: (1028) is inconsistent. % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | Case 2: % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_15, n2, % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | simplifying with (66), (118), (1025) gives: % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | (1029) all_74_15 = n2 | gt(n2, all_74_15) % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1022) gives: % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | (1030) gt(n3, all_74_14) % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_14, n3, n2, % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | simplifying with (67), (129), (146), (1030) gives: % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | (1031) leq(all_74_14, n2) % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_14, n2, % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | simplifying with (67), (118), (1031) gives: % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | (1032) all_74_14 = n2 | gt(n2, all_74_14) % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1029) gives: % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | (1033) gt(n2, all_74_15) % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_15, n2, n1, % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | simplifying with (66), (118), (145), (1033) gives: % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | (1034) leq(all_74_15, n1) % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_74_15, simplifying % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | with (66), (650), (1034) gives: % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | (1035) all_74_15 = n1 | all_74_15 = n0 % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1035) gives: % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | (1036) all_74_15 = n0 % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (728), (1036) imply: % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | (1037) $false % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1037) is inconsistent. % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | (1038) all_74_15 = n1 % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (656), (1038) imply: % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | (1039) a_select3(id_ds1_filter, all_74_14, n1) = % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | all_74_12 % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (655), (1038) imply: % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | (1040) a_select3(id_ds1_filter, n1, all_74_14) = % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | all_74_13 % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1019), (1038) imply: % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | (1041) leq(n1, n3) % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (650), (1038) imply: % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | (1042) leq(n0, n1) % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1032) gives: % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | (1043) gt(n2, all_74_14) % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_14, n2, n1, % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (67), (118), (145), (1043) gives: % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | (1044) leq(all_74_14, n1) % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (30), (67), (649), (651), (719), (1039), % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | (1040), (1044) are inconsistent by sub-proof #37. % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | (1045) all_74_14 = n2 % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1039), (1045) imply: % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | (1046) a_select3(id_ds1_filter, n2, n1) = all_74_12 % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1040), (1045) imply: % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | (1047) a_select3(id_ds1_filter, n1, n2) = all_74_13 % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (659), (1045) imply: % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | (1048) leq(n2, n5) % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (651), (1045) imply: % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | (1049) leq(n0, n2) % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (82) with n1, n2, all_74_13, % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (102), (118), (1042), (1047), % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | (1049) gives: % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | (1050) ~ leq(n2, all_74_20) | ~ leq(n1, all_74_18) | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | (a_select3(id_ds1_filter, n2, n1) = all_74_13 & % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_74_13)) % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1050) gives: % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | | (1051) ~ leq(n2, all_74_20) % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (159), (1051) imply: % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | | (1052) ~ leq(n2, n5) % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1048), (1052) imply: % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | | (1053) $false % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1053) is inconsistent. % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | | (1054) ~ leq(n1, all_74_18) | (a_select3(id_ds1_filter, % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | | n2, n1) = all_74_13 & $i(all_74_13)) % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1054) gives: % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1055) ~ leq(n1, all_74_18) % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1017), (1055) imply: % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1056) ~ leq(n1, n3) % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1041), (1056) imply: % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1057) $false % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1057) is inconsistent. % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1058) a_select3(id_ds1_filter, n2, n1) = all_74_13 & % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_74_13) % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1058) implies: % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1059) a_select3(id_ds1_filter, n2, n1) = all_74_13 % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (649), (1046), (1059) are inconsistent by % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #36. % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | End of split % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | (1060) all_74_15 = n2 % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (656), (1060) imply: % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | (1061) a_select3(id_ds1_filter, all_74_14, n2) = % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | all_74_12 % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (655), (1060) imply: % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | (1062) a_select3(id_ds1_filter, n2, all_74_14) = % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | all_74_13 % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (684), (1060) imply: % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | (1063) leq(n2, n5) % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (650), (1060) imply: % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | (1064) leq(n0, n2) % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1032) gives: % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | (1065) gt(n2, all_74_14) % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_14, n2, n1, % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (67), (118), (145), (1065) gives: % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | (1066) leq(all_74_14, n1) % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_74_14, simplifying % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | with (67), (651), (1066) gives: % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | (1067) all_74_14 = n1 | all_74_14 = n0 % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1067) gives: % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | (1068) all_74_14 = n0 % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (719), (1068) imply: % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | (1069) $false % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1069) is inconsistent. % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | (1070) all_74_14 = n1 % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1061), (1070) imply: % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | (1071) a_select3(id_ds1_filter, n1, n2) = all_74_12 % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1062), (1070) imply: % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | (1072) a_select3(id_ds1_filter, n2, n1) = all_74_13 % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1021), (1070) imply: % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | (1073) leq(n1, n3) % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (651), (1070) imply: % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | (1074) leq(n0, n1) % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (82) with n1, n2, all_74_12, % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (102), (118), (1064), (1071), % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | (1074) gives: % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | (1075) ~ leq(n2, all_74_20) | ~ leq(n1, all_74_18) | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | (a_select3(id_ds1_filter, n2, n1) = all_74_12 & % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_74_12)) % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1075) gives: % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | | (1076) ~ leq(n2, all_74_20) % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (159), (1076) imply: % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | | (1077) ~ leq(n2, n5) % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1063), (1077) imply: % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | | (1078) $false % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1078) is inconsistent. % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | | (1079) ~ leq(n1, all_74_18) | (a_select3(id_ds1_filter, % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | | n2, n1) = all_74_12 & $i(all_74_12)) % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1079) gives: % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1080) ~ leq(n1, all_74_18) % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1017), (1080) imply: % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1081) ~ leq(n1, n3) % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1073), (1081) imply: % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1082) $false % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1082) is inconsistent. % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1083) a_select3(id_ds1_filter, n2, n1) = all_74_12 & % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_74_12) % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1083) implies: % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1084) a_select3(id_ds1_filter, n2, n1) = all_74_12 % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (649), (1072), (1084) are inconsistent by % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #36. % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | (1085) all_74_14 = n2 % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1061), (1085) imply: % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | (1086) a_select3(id_ds1_filter, n2, n2) = all_74_12 % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1062), (1085) imply: % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | (1087) a_select3(id_ds1_filter, n2, n2) = all_74_13 % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (30) with all_74_13, all_74_12, n2, % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | n2, id_ds1_filter, simplifying with (1086), (1087) % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | gives: % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | (1088) all_74_12 = all_74_13 % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (649), (1088) imply: % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | (1089) $false % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1089) is inconsistent. % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | End of split % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | End of split % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | (1090) all_74_14 = n3 % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (656), (1090) imply: % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | (1091) a_select3(id_ds1_filter, n3, all_74_15) = % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | all_74_12 % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (655), (1090) imply: % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | (1092) a_select3(id_ds1_filter, all_74_15, n3) = % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | all_74_13 % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (659), (1090) imply: % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | (1093) leq(n3, n5) % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (651), (1090) imply: % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | (1094) leq(n0, n3) % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1029) gives: % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | (1095) gt(n2, all_74_15) % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_15, n2, n1, % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | simplifying with (66), (118), (145), (1095) gives: % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | (1096) leq(all_74_15, n1) % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_74_15, simplifying % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | with (66), (650), (1096) gives: % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | (1097) all_74_15 = n1 | all_74_15 = n0 % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1097) gives: % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | (1098) all_74_15 = n0 % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (728), (1098) imply: % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | (1099) $false % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1099) is inconsistent. % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | (1100) all_74_15 = n1 % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1092), (1100) imply: % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | (1101) a_select3(id_ds1_filter, n1, n3) = all_74_13 % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1091), (1100) imply: % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | (1102) a_select3(id_ds1_filter, n3, n1) = all_74_12 % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (702), (1100) imply: % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | (1103) leq(n1, n4) % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (650), (1100) imply: % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | (1104) leq(n0, n1) % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (81) with n1, n3, all_74_13, % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (102), (129), (1094), (1101), % 261.63/56.52 | | | | | | | | | | | | | | | | | | | | | | | | (1104) gives: % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | (1105) ~ leq(n3, all_74_20) | ~ leq(n1, pv57) | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | (a_select3(id_ds1_filter, n3, n1) = all_74_13 & % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_74_13)) % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1105) gives: % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | | (1106) ~ leq(n3, all_74_20) % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (159), (1106) imply: % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | | (1107) ~ leq(n3, n5) % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1093), (1107) imply: % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | | (1108) $false % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1108) is inconsistent. % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | | (1109) ~ leq(n1, pv57) | (a_select3(id_ds1_filter, n3, % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | | n1) = all_74_13 & $i(all_74_13)) % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1109) gives: % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | | | (1110) ~ leq(n1, pv57) % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1012), (1110) imply: % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | | | (1111) ~ leq(n1, n4) % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1103), (1111) imply: % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | | | (1112) $false % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1112) is inconsistent. % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | | | (1113) a_select3(id_ds1_filter, n3, n1) = all_74_13 & % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_74_13) % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1113) implies: % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | | | (1114) a_select3(id_ds1_filter, n3, n1) = all_74_13 % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (649), (1102), (1114) are inconsistent by % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #35. % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | End of split % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | (1115) all_74_15 = n2 % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1092), (1115) imply: % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | (1116) a_select3(id_ds1_filter, n2, n3) = all_74_13 % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1091), (1115) imply: % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | (1117) a_select3(id_ds1_filter, n3, n2) = all_74_12 % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (702), (1115) imply: % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | (1118) leq(n2, n4) % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (650), (1115) imply: % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | (1119) leq(n0, n2) % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (81) with n2, n3, all_74_13, % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | simplifying with (118), (129), (1094), (1116), % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | (1119) gives: % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | (1120) ~ leq(n3, all_74_20) | ~ leq(n2, pv57) | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | (a_select3(id_ds1_filter, n3, n2) = all_74_13 & % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | $i(all_74_13)) % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1120) gives: % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | (1121) ~ leq(n3, all_74_20) % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (159), (1121) imply: % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | (1122) ~ leq(n3, n5) % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1093), (1122) imply: % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | (1123) $false % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1123) is inconsistent. % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | (1124) ~ leq(n2, pv57) | (a_select3(id_ds1_filter, n3, % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | n2) = all_74_13 & $i(all_74_13)) % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1124) gives: % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | | (1125) ~ leq(n2, pv57) % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1012), (1125) imply: % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | | (1126) ~ leq(n2, n4) % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1118), (1126) imply: % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | | (1127) $false % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1127) is inconsistent. % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | | (1128) a_select3(id_ds1_filter, n3, n2) = all_74_13 & % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_74_13) % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1128) implies: % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | | (1129) a_select3(id_ds1_filter, n3, n2) = all_74_13 % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (649), (1117), (1129) are inconsistent by % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #30. % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | End of split % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | End of split % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | End of split % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | End of split % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | Case 2: % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | (1130) all_74_15 = all_74_18 % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1017), (1130) imply: % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | (1131) all_74_15 = n3 % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | REDUCE: (656), (1131) imply: % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | (1132) a_select3(id_ds1_filter, all_74_14, n3) = % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | all_74_12 % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | REDUCE: (655), (1131) imply: % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | (1133) a_select3(id_ds1_filter, n3, all_74_14) = % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | all_74_13 % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | REDUCE: (684), (1131) imply: % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | (1134) leq(n3, n5) % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | REDUCE: (650), (1131) imply: % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | (1135) leq(n0, n3) % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | BETA: splitting (1022) gives: % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | Case 1: % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | (1136) gt(n3, all_74_14) % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_14, n3, n2, % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | simplifying with (67), (129), (146), (1136) gives: % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | (1137) leq(all_74_14, n2) % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_14, n2, % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | simplifying with (67), (118), (1137) gives: % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | (1138) all_74_14 = n2 | gt(n2, all_74_14) % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1138) gives: % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | (1139) gt(n2, all_74_14) % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_14, n2, n1, % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | simplifying with (67), (118), (145), (1139) gives: % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | (1140) leq(all_74_14, n1) % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_74_14, simplifying % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | with (67), (651), (1140) gives: % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | (1141) all_74_14 = n1 | all_74_14 = n0 % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1141) gives: % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | (1142) all_74_14 = n0 % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (719), (1142) imply: % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | (1143) $false % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1143) is inconsistent. % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | (1144) all_74_14 = n1 % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1132), (1144) imply: % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | (1145) a_select3(id_ds1_filter, n1, n3) = all_74_12 % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1133), (1144) imply: % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | (1146) a_select3(id_ds1_filter, n3, n1) = all_74_13 % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (716), (1144) imply: % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | (1147) leq(n1, n4) % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (651), (1144) imply: % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | (1148) leq(n0, n1) % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (81) with n1, n3, all_74_12, % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | simplifying with (102), (129), (1135), (1145), % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | (1148) gives: % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | (1149) ~ leq(n3, all_74_20) | ~ leq(n1, pv57) | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | (a_select3(id_ds1_filter, n3, n1) = all_74_12 & % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | $i(all_74_12)) % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1149) gives: % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | (1150) ~ leq(n3, all_74_20) % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (159), (1150) imply: % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | (1151) ~ leq(n3, n5) % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1134), (1151) imply: % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | (1152) $false % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1152) is inconsistent. % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | (1153) ~ leq(n1, pv57) | (a_select3(id_ds1_filter, n3, % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | n1) = all_74_12 & $i(all_74_12)) % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1153) gives: % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | | (1154) ~ leq(n1, pv57) % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1012), (1154) imply: % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | | (1155) ~ leq(n1, n4) % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1147), (1155) imply: % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | | (1156) $false % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1156) is inconsistent. % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | | (1157) a_select3(id_ds1_filter, n3, n1) = all_74_12 & % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_74_12) % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1157) implies: % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | | (1158) a_select3(id_ds1_filter, n3, n1) = all_74_12 % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (30) with all_74_13, all_74_12, n1, % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | | n3, id_ds1_filter, simplifying with (1146), (1158) % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | | (1159) all_74_12 = all_74_13 % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (649), (1159) imply: % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | | (1160) $false % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1160) is inconsistent. % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | End of split % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | End of split % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | (1161) all_74_14 = n2 % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1132), (1161) imply: % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | (1162) a_select3(id_ds1_filter, n2, n3) = all_74_12 % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1133), (1161) imply: % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | (1163) a_select3(id_ds1_filter, n3, n2) = all_74_13 % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (716), (1161) imply: % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | (1164) leq(n2, n4) % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (651), (1161) imply: % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | (1165) leq(n0, n2) % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (81) with n2, n3, all_74_12, % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | simplifying with (118), (129), (1135), (1162), % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | (1165) gives: % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | (1166) ~ leq(n3, all_74_20) | ~ leq(n2, pv57) | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | (a_select3(id_ds1_filter, n3, n2) = all_74_12 & % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | $i(all_74_12)) % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1166) gives: % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | (1167) ~ leq(n3, all_74_20) % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (159), (1167) imply: % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | (1168) ~ leq(n3, n5) % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1134), (1168) imply: % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | (1169) $false % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1169) is inconsistent. % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | (1170) ~ leq(n2, pv57) | (a_select3(id_ds1_filter, n3, % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | n2) = all_74_12 & $i(all_74_12)) % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1170) gives: % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | (1171) ~ leq(n2, pv57) % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1012), (1171) imply: % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | (1172) ~ leq(n2, n4) % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1164), (1172) imply: % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | (1173) $false % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1173) is inconsistent. % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | (1174) a_select3(id_ds1_filter, n3, n2) = all_74_12 & % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_74_12) % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1174) implies: % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | (1175) a_select3(id_ds1_filter, n3, n2) = all_74_12 % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (649), (1163), (1175) are inconsistent by % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #30. % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | End of split % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | End of split % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | End of split % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | Case 2: % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | (1176) all_74_14 = n3 % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | REDUCE: (1132), (1176) imply: % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | (1177) a_select3(id_ds1_filter, n3, n3) = all_74_12 % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | REDUCE: (1133), (1176) imply: % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | (1178) a_select3(id_ds1_filter, n3, n3) = all_74_13 % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (30) with all_74_13, all_74_12, n3, % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | n3, id_ds1_filter, simplifying with (1177), (1178) % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | gives: % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | (1179) all_74_12 = all_74_13 % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | REDUCE: (649), (1179) imply: % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | (1180) $false % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | CLOSE: (1180) is inconsistent. % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | End of split % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | End of split % 261.63/56.53 | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | Case 2: % 261.63/56.53 | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | (1181) all_74_14 = n4 % 261.63/56.53 | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | REDUCE: (656), (1181) imply: % 261.63/56.53 | | | | | | | | | | | | | | | | | | | (1182) a_select3(id_ds1_filter, n4, all_74_15) = % 261.63/56.53 | | | | | | | | | | | | | | | | | | | all_74_12 % 261.63/56.53 | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | REDUCE: (655), (1181) imply: % 261.63/56.53 | | | | | | | | | | | | | | | | | | | (1183) a_select3(id_ds1_filter, all_74_15, n4) = % 261.63/56.53 | | | | | | | | | | | | | | | | | | | all_74_13 % 261.63/56.53 | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | REDUCE: (659), (1181) imply: % 261.63/56.53 | | | | | | | | | | | | | | | | | | | (1184) leq(n4, n5) % 261.63/56.53 | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | REDUCE: (651), (1181) imply: % 261.63/56.53 | | | | | | | | | | | | | | | | | | | (1185) leq(n0, n4) % 261.63/56.53 | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | BETA: splitting (721) gives: % 261.63/56.53 | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | Case 1: % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | (1186) gt(all_74_18, all_74_15) % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | REDUCE: (1017), (1186) imply: % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | (1187) gt(n3, all_74_15) % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_15, n3, n2, % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | simplifying with (66), (129), (146), (1187) gives: % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | (1188) leq(all_74_15, n2) % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_15, n2, % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | simplifying with (66), (118), (1188) gives: % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | (1189) all_74_15 = n2 | gt(n2, all_74_15) % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | BETA: splitting (1189) gives: % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | Case 1: % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | (1190) gt(n2, all_74_15) % 261.63/56.53 | | | | | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_15, n2, n1, % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | simplifying with (66), (118), (145), (1190) gives: % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | (1191) leq(all_74_15, n1) % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_74_15, simplifying % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | with (66), (650), (1191) gives: % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | (1192) all_74_15 = n1 | all_74_15 = n0 % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1192) gives: % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | (1193) all_74_15 = n0 % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (728), (1193) imply: % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | (1194) $false % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1194) is inconsistent. % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | (1195) all_74_15 = n1 % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1183), (1195) imply: % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | (1196) a_select3(id_ds1_filter, n1, n4) = all_74_13 % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1182), (1195) imply: % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | (1197) a_select3(id_ds1_filter, n4, n1) = all_74_12 % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (702), (1195) imply: % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | (1198) leq(n1, n4) % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (650), (1195) imply: % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | (1199) leq(n0, n1) % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (81) with n1, n4, all_74_13, % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | simplifying with (102), (136), (1185), (1196), % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | (1199) gives: % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | (1200) ~ leq(n4, all_74_20) | ~ leq(n1, pv57) | % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | (a_select3(id_ds1_filter, n4, n1) = all_74_13 & % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | $i(all_74_13)) % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1200) gives: % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | | (1201) ~ leq(n4, all_74_20) % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (159), (1201) imply: % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | | (1202) ~ leq(n4, n5) % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1184), (1202) imply: % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | | (1203) $false % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1203) is inconsistent. % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | | (1204) ~ leq(n1, pv57) | (a_select3(id_ds1_filter, n4, % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | | n1) = all_74_13 & $i(all_74_13)) % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1204) gives: % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | | | (1205) ~ leq(n1, pv57) % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1012), (1205) imply: % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | | | (1206) ~ leq(n1, n4) % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1198), (1206) imply: % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | | | (1207) $false % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1207) is inconsistent. % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | | | (1208) a_select3(id_ds1_filter, n4, n1) = all_74_13 & % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_74_13) % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1208) implies: % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | | | (1209) a_select3(id_ds1_filter, n4, n1) = all_74_13 % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (649), (1197), (1209) are inconsistent by % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #29. % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | | End of split % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | End of split % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | End of split % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | Case 2: % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | (1210) all_74_15 = n2 % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | REDUCE: (1183), (1210) imply: % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | (1211) a_select3(id_ds1_filter, n2, n4) = all_74_13 % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | REDUCE: (1182), (1210) imply: % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | (1212) a_select3(id_ds1_filter, n4, n2) = all_74_12 % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | REDUCE: (702), (1210) imply: % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | (1213) leq(n2, n4) % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | REDUCE: (650), (1210) imply: % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | (1214) leq(n0, n2) % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (81) with n2, n4, all_74_13, % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | simplifying with (118), (136), (1185), (1211), % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | (1214) gives: % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | (1215) ~ leq(n4, all_74_20) | ~ leq(n2, pv57) | % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | (a_select3(id_ds1_filter, n4, n2) = all_74_13 & % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | $i(all_74_13)) % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1215) gives: % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | (1216) ~ leq(n4, all_74_20) % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (159), (1216) imply: % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | (1217) ~ leq(n4, n5) % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1184), (1217) imply: % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | (1218) $false % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1218) is inconsistent. % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | (1219) ~ leq(n2, pv57) | (a_select3(id_ds1_filter, n4, % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | n2) = all_74_13 & $i(all_74_13)) % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1219) gives: % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | | (1220) ~ leq(n2, pv57) % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1012), (1220) imply: % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | | (1221) ~ leq(n2, n4) % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1213), (1221) imply: % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | | (1222) $false % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1222) is inconsistent. % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | | (1223) a_select3(id_ds1_filter, n4, n2) = all_74_13 & % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | | $i(all_74_13) % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1223) implies: % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | | (1224) a_select3(id_ds1_filter, n4, n2) = all_74_13 % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (30) with all_74_12, all_74_13, n2, % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | | n4, id_ds1_filter, simplifying with (1212), (1224) % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | | gives: % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | | (1225) all_74_12 = all_74_13 % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (649), (1225) imply: % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | | (1226) $false % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1226) is inconsistent. % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | End of split % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | End of split % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | End of split % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | | | Case 2: % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | (1227) all_74_15 = all_74_18 % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1017), (1227) imply: % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | (1228) all_74_15 = n3 % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | REDUCE: (1183), (1228) imply: % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | (1229) a_select3(id_ds1_filter, n3, n4) = all_74_13 % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | REDUCE: (1182), (1228) imply: % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | (1230) a_select3(id_ds1_filter, n4, n3) = all_74_12 % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | REDUCE: (1019), (1228) imply: % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | (1231) leq(n3, n3) % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | REDUCE: (650), (1228) imply: % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | (1232) leq(n0, n3) % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (82) with n3, n4, all_74_13, % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | simplifying with (129), (136), (1185), (1229), % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | (1232) gives: % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | (1233) ~ leq(n4, all_74_20) | ~ leq(n3, all_74_18) | % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | (a_select3(id_ds1_filter, n4, n3) = all_74_13 & % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | $i(all_74_13)) % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | BETA: splitting (1233) gives: % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | Case 1: % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | (1234) ~ leq(n4, all_74_20) % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | REDUCE: (159), (1234) imply: % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | (1235) ~ leq(n4, n5) % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1184), (1235) imply: % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | (1236) $false % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | CLOSE: (1236) is inconsistent. % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | Case 2: % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | (1237) ~ leq(n3, all_74_18) | (a_select3(id_ds1_filter, % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | n4, n3) = all_74_13 & $i(all_74_13)) % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1237) gives: % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | (1238) ~ leq(n3, all_74_18) % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1017), (1238) imply: % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | (1239) ~ leq(n3, n3) % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1231), (1239) imply: % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | (1240) $false % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1240) is inconsistent. % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | (1241) a_select3(id_ds1_filter, n4, n3) = all_74_13 & % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | $i(all_74_13) % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1241) implies: % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | (1242) a_select3(id_ds1_filter, n4, n3) = all_74_13 % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (649), (1230), (1242) are inconsistent by % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | sub-proof #25. % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | End of split % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | End of split % 261.63/56.54 | | | | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | | | End of split % 261.63/56.54 | | | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | | End of split % 261.63/56.54 | | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | End of split % 261.63/56.54 | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | Case 2: % 261.63/56.54 | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | (1243) pv57 = n1 % 261.63/56.54 | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | REDUCE: (155), (1243) imply: % 261.63/56.54 | | | | | | | | | | | | | | | | | (1244) pred(n1) = all_74_18 % 261.63/56.54 | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (27) with n0, all_74_18, n1, % 261.63/56.54 | | | | | | | | | | | | | | | | | simplifying with (144), (1244) gives: % 261.63/56.54 | | | | | | | | | | | | | | | | | (1245) all_74_18 = n0 % 261.63/56.54 | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | REDUCE: (734), (1245) imply: % 261.63/56.54 | | | | | | | | | | | | | | | | | (1246) $false % 261.63/56.54 | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | CLOSE: (1246) is inconsistent. % 261.63/56.54 | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | End of split % 261.63/56.54 | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | End of split % 261.63/56.54 | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | Case 2: % 261.63/56.54 | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | (1247) all_74_18 = n0 % 261.63/56.54 | | | | | | | | | | | | | | | (1248) ~ gt(all_74_18, n0) % 261.63/56.54 | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | REDUCE: (1247), (1248) imply: % 261.63/56.54 | | | | | | | | | | | | | | | (1249) ~ gt(n0, n0) % 261.63/56.54 | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | REF_CLOSE: (22), (66), (712), (721), (728), (1247), (1249), % 261.63/56.54 | | | | | | | | | | | | | | | (transitivity_gt) are inconsistent by sub-proof % 261.63/56.54 | | | | | | | | | | | | | | | #24. % 261.63/56.54 | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | End of split % 261.63/56.54 | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | End of split % 261.63/56.54 | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | End of split % 261.63/56.54 | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | End of split % 261.63/56.54 | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | End of split % 261.63/56.54 | | | | | | | | | | % 261.63/56.54 | | | | | | | | | Case 2: % 261.63/56.54 | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | (1250) all_74_14 = n5 % 261.63/56.54 | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | REDUCE: (656), (1250) imply: % 261.63/56.54 | | | | | | | | | | (1251) a_select3(id_ds1_filter, n5, all_74_15) = % 261.63/56.54 | | | | | | | | | | all_74_12 % 261.63/56.54 | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | REDUCE: (655), (1250) imply: % 261.63/56.54 | | | | | | | | | | (1252) a_select3(id_ds1_filter, all_74_15, n5) = % 261.63/56.54 | | | | | | | | | | all_74_13 % 261.63/56.54 | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | REDUCE: (659), (1250) imply: % 261.63/56.54 | | | | | | | | | | (1253) leq(n5, n5) % 261.63/56.54 | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | REDUCE: (651), (1250) imply: % 261.63/56.54 | | | | | | | | | | (1254) leq(n0, n5) % 261.63/56.54 | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_15, pv57, all_74_18, % 261.63/56.54 | | | | | | | | | | simplifying with (24), (66), (155), (714) gives: % 261.63/56.54 | | | | | | | | | | (1255) leq(all_74_15, all_74_18) % 261.63/56.54 | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_15, all_74_18, % 261.63/56.54 | | | | | | | | | | simplifying with (66), (154), (1255) gives: % 261.63/56.54 | | | | | | | | | | (1256) all_74_15 = all_74_18 | gt(all_74_18, all_74_15) % 261.63/56.54 | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | BETA: splitting (687) gives: % 261.63/56.54 | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | Case 1: % 261.63/56.54 | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | (1257) all_74_15 = n0 % 261.63/56.54 | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | REF_CLOSE: (66), (712), (1257), (irreflexivity_gt) are % 261.63/56.54 | | | | | | | | | | | inconsistent by sub-proof #40. % 261.63/56.54 | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | Case 2: % 261.63/56.54 | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | (1258) ~ (all_74_15 = n0) % 261.63/56.54 | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | BETA: splitting (697) gives: % 261.63/56.54 | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | Case 1: % 261.63/56.54 | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | (1259) gt(all_74_18, n0) % 261.63/56.54 | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | BETA: splitting (696) gives: % 261.63/56.54 | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | Case 1: % 261.63/56.54 | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | (1260) all_74_18 = n0 % 261.63/56.54 | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | REF_CLOSE: (154), (1259), (1260), (irreflexivity_gt) are % 261.63/56.54 | | | | | | | | | | | | | inconsistent by sub-proof #39. % 261.63/56.54 | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | Case 2: % 261.63/56.54 | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | (1261) ~ (all_74_18 = n0) % 261.63/56.54 | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | BETA: splitting (699) gives: % 261.63/56.54 | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | Case 1: % 261.63/56.54 | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | (1262) gt(pv57, n1) % 261.63/56.54 | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | BETA: splitting (703) gives: % 261.63/56.54 | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | Case 1: % 261.63/56.54 | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | (1263) gt(n4, pv57) % 261.63/56.54 | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with pv57, n4, n3, simplifying % 261.63/56.54 | | | | | | | | | | | | | | | with (24), (136), (147), (1263) gives: % 261.63/56.54 | | | | | | | | | | | | | | | (1264) leq(pv57, n3) % 261.63/56.54 | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with n1, pv57, all_74_18, % 261.63/56.54 | | | | | | | | | | | | | | | simplifying with (24), (102), (155), (1262) gives: % 261.63/56.54 | | | | | | | | | | | | | | | (1265) leq(n1, all_74_18) % 261.63/56.54 | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with n1, all_74_18, % 261.63/56.54 | | | | | | | | | | | | | | | simplifying with (102), (154), (1265) gives: % 261.63/56.54 | | | | | | | | | | | | | | | (1266) all_74_18 = n1 | gt(all_74_18, n1) % 261.63/56.54 | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with all_74_18, n2, pv57, n3, % 261.63/56.54 | | | | | | | | | | | | | | | simplifying with (117), (118), (154), (165), % 261.63/56.54 | | | | | | | | | | | | | | | (1264) gives: % 261.63/56.54 | | | | | | | | | | | | | | | (1267) leq(all_74_18, n2) % 261.63/56.54 | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | GROUND_INST: instantiating (15) with pv57, simplifying with % 261.63/56.54 | | | | | | | | | | | | | | | (24), (63), (1264) gives: % 261.63/56.54 | | | | | | | | | | | | | | | (1268) pv57 = n3 | pv57 = n2 | pv57 = n1 | pv57 = n0 % 261.63/56.54 | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with pv57, n3, simplifying % 261.63/56.54 | | | | | | | | | | | | | | | with (24), (129), (1264) gives: % 261.63/56.54 | | | | | | | | | | | | | | | (1269) pv57 = n3 | gt(n3, pv57) % 261.63/56.54 | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | BETA: splitting (706) gives: % 261.63/56.54 | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | Case 1: % 261.63/56.54 | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | (1270) pv57 = n1 % 261.63/56.54 | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | REF_CLOSE: (27), (144), (155), (1261), (1270) are % 261.63/56.54 | | | | | | | | | | | | | | | | inconsistent by sub-proof #38. % 261.63/56.54 | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | Case 2: % 261.63/56.54 | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | (1271) ~ (pv57 = n1) % 261.63/56.54 | | | | | | | | | | | | | | | | (1272) pv57 = n5 | pv57 = n4 | pv57 = n3 | pv57 = n2 % 261.63/56.54 | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | BETA: splitting (1256) gives: % 261.63/56.54 | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | Case 1: % 261.63/56.54 | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | (1273) gt(all_74_18, all_74_15) % 261.63/56.54 | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | BETA: splitting (1266) gives: % 261.63/56.54 | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | Case 1: % 261.63/56.54 | | | | | | | | | | | | | | | | | | % 261.63/56.54 | | | | | | | | | | | | | | | | | | (1274) gt(all_74_18, n1) % 261.63/56.55 | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | BETA: splitting (1269) gives: % 261.63/56.55 | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | Case 1: % 261.63/56.55 | | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | | (1275) gt(n3, pv57) % 261.63/56.55 | | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (24), (27), (145), (154), (155), (705), (1268), % 261.63/56.55 | | | | | | | | | | | | | | | | | | | (1271), (1272), (1274), (1275), (irreflexivity_gt) % 261.63/56.55 | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #34. % 261.63/56.55 | | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | Case 2: % 261.63/56.55 | | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | | (1276) pv57 = n3 % 261.63/56.55 | | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | | REDUCE: (75), (1276) imply: % 261.63/56.55 | | | | | | | | | | | | | | | | | | | (1277) minus(n3, n1) = all_74_18 % 261.63/56.55 | | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (29) with n2, all_74_18, n1, n3, % 261.63/56.55 | | | | | | | | | | | | | | | | | | | simplifying with (161), (1277) gives: % 261.63/56.55 | | | | | | | | | | | | | | | | | | | (1278) all_74_18 = n2 % 261.63/56.55 | | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | | REDUCE: (1255), (1278) imply: % 261.63/56.55 | | | | | | | | | | | | | | | | | | | (1279) leq(all_74_15, n2) % 261.63/56.55 | | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | | REDUCE: (1273), (1278) imply: % 261.63/56.55 | | | | | | | | | | | | | | | | | | | (1280) gt(n2, all_74_15) % 261.63/56.55 | | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_15, n2, n1, % 261.63/56.55 | | | | | | | | | | | | | | | | | | | simplifying with (66), (118), (145), (1280) gives: % 261.63/56.55 | | | | | | | | | | | | | | | | | | | (1281) leq(all_74_15, n1) % 261.63/56.55 | | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_74_15, simplifying % 261.63/56.55 | | | | | | | | | | | | | | | | | | | with (66), (650), (1281) gives: % 261.63/56.55 | | | | | | | | | | | | | | | | | | | (1282) all_74_15 = n1 | all_74_15 = n0 % 261.63/56.55 | | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | | BETA: splitting (1282) gives: % 261.63/56.55 | | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | | Case 1: % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | (1283) all_74_15 = n0 % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | REDUCE: (1258), (1283) imply: % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | (1284) $false % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | CLOSE: (1284) is inconsistent. % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | | Case 2: % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | (1285) all_74_15 = n1 % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | REDUCE: (1252), (1285) imply: % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | (1286) a_select3(id_ds1_filter, n1, n5) = all_74_13 % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | REDUCE: (1251), (1285) imply: % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | (1287) a_select3(id_ds1_filter, n5, n1) = all_74_12 % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | REDUCE: (1279), (1285) imply: % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | (1288) leq(n1, n2) % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | REDUCE: (650), (1285) imply: % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | (1289) leq(n0, n1) % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (82) with n1, n5, all_74_13, % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | simplifying with (102), (139), (1254), (1286), % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | (1289) gives: % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | (1290) ~ leq(n5, all_74_20) | ~ leq(n1, all_74_18) | % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | (a_select3(id_ds1_filter, n5, n1) = all_74_13 & % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | $i(all_74_13)) % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | BETA: splitting (1290) gives: % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | Case 1: % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | | (1291) ~ leq(n5, all_74_20) % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | | REDUCE: (159), (1291) imply: % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | | (1292) ~ leq(n5, n5) % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1253), (1292) imply: % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | | (1293) $false % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | | CLOSE: (1293) is inconsistent. % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | Case 2: % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | | (1294) ~ leq(n1, all_74_18) | (a_select3(id_ds1_filter, % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | | n5, n1) = all_74_13 & $i(all_74_13)) % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1294) gives: % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | | | (1295) ~ leq(n1, all_74_18) % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1278), (1295) imply: % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | | | (1296) ~ leq(n1, n2) % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1288), (1296) imply: % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | | | (1297) $false % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1297) is inconsistent. % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | | | (1298) a_select3(id_ds1_filter, n5, n1) = all_74_13 & % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | | | $i(all_74_13) % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1298) implies: % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | | | (1299) a_select3(id_ds1_filter, n5, n1) = all_74_13 % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (649), (1287), (1299) are inconsistent by % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | | | sub-proof #23. % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | | End of split % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | End of split % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | | End of split % 261.63/56.55 | | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | End of split % 261.63/56.55 | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | Case 2: % 261.63/56.55 | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | (1300) all_74_18 = n1 % 261.63/56.55 | | | | | | | | | | | | | | | | | | (1301) ~ gt(all_74_18, n1) % 261.63/56.55 | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (66), (650), (1255), (1258), (1273), (1300), % 261.63/56.55 | | | | | | | | | | | | | | | | | | (1301) are inconsistent by sub-proof #28. % 261.63/56.55 | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | End of split % 261.63/56.55 | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | Case 2: % 261.63/56.55 | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | (1302) all_74_15 = all_74_18 % 261.63/56.55 | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | REDUCE: (1252), (1302) imply: % 261.63/56.55 | | | | | | | | | | | | | | | | | (1303) a_select3(id_ds1_filter, all_74_18, n5) = % 261.63/56.55 | | | | | | | | | | | | | | | | | all_74_13 % 261.63/56.55 | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | REDUCE: (1251), (1302) imply: % 261.63/56.55 | | | | | | | | | | | | | | | | | (1304) a_select3(id_ds1_filter, n5, all_74_18) = % 261.63/56.55 | | | | | | | | | | | | | | | | | all_74_12 % 261.63/56.55 | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | BETA: splitting (1266) gives: % 261.63/56.55 | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | Case 1: % 261.63/56.55 | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | (1305) gt(all_74_18, n1) % 261.63/56.55 | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | BETA: splitting (1269) gives: % 261.63/56.55 | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | Case 1: % 261.63/56.55 | | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | | (1306) gt(n3, pv57) % 261.63/56.55 | | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (24), (27), (145), (154), (155), (705), (1268), % 261.63/56.55 | | | | | | | | | | | | | | | | | | | (1271), (1272), (1305), (1306), (irreflexivity_gt) % 261.63/56.55 | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #34. % 261.63/56.55 | | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | Case 2: % 261.63/56.55 | | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | | (1307) pv57 = n3 % 261.63/56.55 | | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | | REDUCE: (75), (1307) imply: % 261.63/56.55 | | | | | | | | | | | | | | | | | | | (1308) minus(n3, n1) = all_74_18 % 261.63/56.55 | | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (29) with n2, all_74_18, n1, n3, % 261.63/56.55 | | | | | | | | | | | | | | | | | | | simplifying with (161), (1308) gives: % 261.63/56.55 | | | | | | | | | | | | | | | | | | | (1309) all_74_18 = n2 % 261.63/56.55 | | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | | REDUCE: (1303), (1309) imply: % 261.63/56.55 | | | | | | | | | | | | | | | | | | | (1310) a_select3(id_ds1_filter, n2, n5) = all_74_13 % 261.63/56.55 | | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | | REDUCE: (1304), (1309) imply: % 261.63/56.55 | | | | | | | | | | | | | | | | | | | (1311) a_select3(id_ds1_filter, n5, n2) = all_74_12 % 261.63/56.55 | | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | | REDUCE: (1267), (1309) imply: % 261.63/56.55 | | | | | | | | | | | | | | | | | | | (1312) leq(n2, n2) % 261.63/56.55 | | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | | REDUCE: (690), (1309) imply: % 261.63/56.55 | | | | | | | | | | | | | | | | | | | (1313) leq(n0, n2) % 261.63/56.55 | | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (82) with n2, n5, all_74_13, % 261.63/56.55 | | | | | | | | | | | | | | | | | | | simplifying with (118), (139), (1254), (1310), % 261.63/56.55 | | | | | | | | | | | | | | | | | | | (1313) gives: % 261.63/56.55 | | | | | | | | | | | | | | | | | | | (1314) ~ leq(n5, all_74_20) | ~ leq(n2, all_74_18) | % 261.63/56.55 | | | | | | | | | | | | | | | | | | | (a_select3(id_ds1_filter, n5, n2) = all_74_13 & % 261.63/56.55 | | | | | | | | | | | | | | | | | | | $i(all_74_13)) % 261.63/56.55 | | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | | BETA: splitting (1314) gives: % 261.63/56.55 | | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | | Case 1: % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | (1315) ~ leq(n5, all_74_20) % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | REDUCE: (159), (1315) imply: % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | (1316) ~ leq(n5, n5) % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1253), (1316) imply: % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | (1317) $false % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | CLOSE: (1317) is inconsistent. % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | | Case 2: % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | (1318) ~ leq(n2, all_74_18) | (a_select3(id_ds1_filter, % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | n5, n2) = all_74_13 & $i(all_74_13)) % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | BETA: splitting (1318) gives: % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | Case 1: % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | | (1319) ~ leq(n2, all_74_18) % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | | REDUCE: (1309), (1319) imply: % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | | (1320) ~ leq(n2, n2) % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1312), (1320) imply: % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | | (1321) $false % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | | CLOSE: (1321) is inconsistent. % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | Case 2: % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | | (1322) a_select3(id_ds1_filter, n5, n2) = all_74_13 & % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | | $i(all_74_13) % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | | ALPHA: (1322) implies: % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | | (1323) a_select3(id_ds1_filter, n5, n2) = all_74_13 % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (649), (1311), (1323) are inconsistent by % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | | sub-proof #22. % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | End of split % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | | End of split % 261.63/56.55 | | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | End of split % 261.63/56.55 | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | Case 2: % 261.63/56.55 | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | (1324) all_74_18 = n1 % 261.63/56.55 | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | REDUCE: (1303), (1324) imply: % 261.63/56.55 | | | | | | | | | | | | | | | | | | (1325) a_select3(id_ds1_filter, n1, n5) = all_74_13 % 261.63/56.55 | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | REDUCE: (1304), (1324) imply: % 261.63/56.55 | | | | | | | | | | | | | | | | | | (1326) a_select3(id_ds1_filter, n5, n1) = all_74_12 % 261.63/56.55 | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | REDUCE: (1265), (1324) imply: % 261.63/56.55 | | | | | | | | | | | | | | | | | | (1327) leq(n1, n1) % 261.63/56.55 | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | REDUCE: (690), (1324) imply: % 261.63/56.55 | | | | | | | | | | | | | | | | | | (1328) leq(n0, n1) % 261.63/56.55 | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (82) with n1, n5, all_74_13, % 261.63/56.55 | | | | | | | | | | | | | | | | | | simplifying with (102), (139), (1254), (1325), % 261.63/56.55 | | | | | | | | | | | | | | | | | | (1328) gives: % 261.63/56.55 | | | | | | | | | | | | | | | | | | (1329) ~ leq(n5, all_74_20) | ~ leq(n1, all_74_18) | % 261.63/56.55 | | | | | | | | | | | | | | | | | | (a_select3(id_ds1_filter, n5, n1) = all_74_13 & % 261.63/56.55 | | | | | | | | | | | | | | | | | | $i(all_74_13)) % 261.63/56.55 | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | BETA: splitting (1329) gives: % 261.63/56.55 | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | Case 1: % 261.63/56.55 | | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | | (1330) ~ leq(n5, all_74_20) % 261.63/56.55 | | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | | REDUCE: (159), (1330) imply: % 261.63/56.55 | | | | | | | | | | | | | | | | | | | (1331) ~ leq(n5, n5) % 261.63/56.55 | | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1253), (1331) imply: % 261.63/56.55 | | | | | | | | | | | | | | | | | | | (1332) $false % 261.63/56.55 | | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | | CLOSE: (1332) is inconsistent. % 261.63/56.55 | | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | Case 2: % 261.63/56.55 | | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | | (1333) ~ leq(n1, all_74_18) | (a_select3(id_ds1_filter, % 261.63/56.55 | | | | | | | | | | | | | | | | | | | n5, n1) = all_74_13 & $i(all_74_13)) % 261.63/56.55 | | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | | BETA: splitting (1333) gives: % 261.63/56.55 | | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | | Case 1: % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | (1334) ~ leq(n1, all_74_18) % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | REDUCE: (1324), (1334) imply: % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | (1335) ~ leq(n1, n1) % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1327), (1335) imply: % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | (1336) $false % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | CLOSE: (1336) is inconsistent. % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | | Case 2: % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | (1337) a_select3(id_ds1_filter, n5, n1) = all_74_13 & % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | $i(all_74_13) % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | ALPHA: (1337) implies: % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | (1338) a_select3(id_ds1_filter, n5, n1) = all_74_13 % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (649), (1326), (1338) are inconsistent by % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | sub-proof #23. % 261.63/56.55 | | | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | | End of split % 261.63/56.55 | | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | End of split % 261.63/56.55 | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | End of split % 261.63/56.55 | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | End of split % 261.63/56.55 | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | End of split % 261.63/56.55 | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | Case 2: % 261.63/56.55 | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | (1339) pv57 = n4 % 261.63/56.55 | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | REDUCE: (669), (1339) imply: % 261.63/56.55 | | | | | | | | | | | | | | | (1340) succ(n4) = all_74_17 % 261.63/56.55 | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | REDUCE: (155), (1339) imply: % 261.63/56.55 | | | | | | | | | | | | | | | (1341) pred(n4) = all_74_18 % 261.63/56.55 | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | GROUND_INST: instantiating (27) with n3, all_74_18, n4, % 261.63/56.55 | | | | | | | | | | | | | | | simplifying with (147), (1341) gives: % 261.63/56.55 | | | | | | | | | | | | | | | (1342) all_74_18 = n3 % 261.63/56.55 | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | GROUND_INST: instantiating (28) with n5, all_74_17, n4, % 261.63/56.55 | | | | | | | | | | | | | | | simplifying with (135), (1340) gives: % 261.63/56.55 | | | | | | | | | | | | | | | (1343) all_74_17 = n5 % 261.63/56.55 | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | REDUCE: (1255), (1342) imply: % 261.63/56.55 | | | | | | | | | | | | | | | (1344) leq(all_74_15, n3) % 261.63/56.55 | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | BETA: splitting (1256) gives: % 261.63/56.55 | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | Case 1: % 261.63/56.55 | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | (1345) gt(all_74_18, all_74_15) % 261.63/56.55 | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | REDUCE: (1342), (1345) imply: % 261.63/56.55 | | | | | | | | | | | | | | | | (1346) gt(n3, all_74_15) % 261.63/56.55 | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_15, n3, n2, % 261.63/56.55 | | | | | | | | | | | | | | | | simplifying with (66), (129), (146), (1346) gives: % 261.63/56.55 | | | | | | | | | | | | | | | | (1347) leq(all_74_15, n2) % 261.63/56.55 | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_15, n2, % 261.63/56.55 | | | | | | | | | | | | | | | | simplifying with (66), (118), (1347) gives: % 261.63/56.55 | | | | | | | | | | | | | | | | (1348) all_74_15 = n2 | gt(n2, all_74_15) % 261.63/56.55 | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | BETA: splitting (1348) gives: % 261.63/56.55 | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | Case 1: % 261.63/56.55 | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | (1349) gt(n2, all_74_15) % 261.63/56.55 | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_15, n2, n1, % 261.63/56.55 | | | | | | | | | | | | | | | | | simplifying with (66), (118), (145), (1349) gives: % 261.63/56.55 | | | | | | | | | | | | | | | | | (1350) leq(all_74_15, n1) % 261.63/56.55 | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_74_15, simplifying % 261.63/56.55 | | | | | | | | | | | | | | | | | with (66), (650), (1350) gives: % 261.63/56.55 | | | | | | | | | | | | | | | | | (1351) all_74_15 = n1 | all_74_15 = n0 % 261.63/56.55 | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | BETA: splitting (1351) gives: % 261.63/56.55 | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | Case 1: % 261.63/56.55 | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | (1352) all_74_15 = n0 % 261.63/56.55 | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | REDUCE: (1258), (1352) imply: % 261.63/56.55 | | | | | | | | | | | | | | | | | | (1353) $false % 261.63/56.55 | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | CLOSE: (1353) is inconsistent. % 261.63/56.55 | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | Case 2: % 261.63/56.55 | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | (1354) all_74_15 = n1 % 261.63/56.55 | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | REDUCE: (1252), (1354) imply: % 261.63/56.55 | | | | | | | | | | | | | | | | | | (1355) a_select3(id_ds1_filter, n1, n5) = all_74_13 % 261.63/56.55 | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | REDUCE: (1251), (1354) imply: % 261.63/56.55 | | | | | | | | | | | | | | | | | | (1356) a_select3(id_ds1_filter, n5, n1) = all_74_12 % 261.63/56.55 | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | REDUCE: (1344), (1354) imply: % 261.63/56.55 | | | | | | | | | | | | | | | | | | (1357) leq(n1, n3) % 261.63/56.55 | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | REDUCE: (650), (1354) imply: % 261.63/56.55 | | | | | | | | | | | | | | | | | | (1358) leq(n0, n1) % 261.63/56.55 | | | | | | | | | | | | | | | | | | % 261.63/56.55 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (82) with n1, n5, all_74_13, % 261.63/56.56 | | | | | | | | | | | | | | | | | | simplifying with (102), (139), (1254), (1355), % 261.63/56.56 | | | | | | | | | | | | | | | | | | (1358) gives: % 261.63/56.56 | | | | | | | | | | | | | | | | | | (1359) ~ leq(n5, all_74_20) | ~ leq(n1, all_74_18) | % 261.63/56.56 | | | | | | | | | | | | | | | | | | (a_select3(id_ds1_filter, n5, n1) = all_74_13 & % 261.63/56.56 | | | | | | | | | | | | | | | | | | $i(all_74_13)) % 261.63/56.56 | | | | | | | | | | | | | | | | | | % 261.63/56.56 | | | | | | | | | | | | | | | | | | BETA: splitting (1359) gives: % 261.63/56.56 | | | | | | | | | | | | | | | | | | % 261.63/56.56 | | | | | | | | | | | | | | | | | | Case 1: % 261.63/56.56 | | | | | | | | | | | | | | | | | | | % 261.63/56.56 | | | | | | | | | | | | | | | | | | | (1360) ~ leq(n5, all_74_20) % 261.63/56.56 | | | | | | | | | | | | | | | | | | | % 261.63/56.56 | | | | | | | | | | | | | | | | | | | REDUCE: (159), (1360) imply: % 261.63/56.56 | | | | | | | | | | | | | | | | | | | (1361) ~ leq(n5, n5) % 261.63/56.56 | | | | | | | | | | | | | | | | | | | % 261.63/56.56 | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1253), (1361) imply: % 261.63/56.56 | | | | | | | | | | | | | | | | | | | (1362) $false % 261.63/56.56 | | | | | | | | | | | | | | | | | | | % 261.63/56.56 | | | | | | | | | | | | | | | | | | | CLOSE: (1362) is inconsistent. % 261.63/56.56 | | | | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | | | Case 2: % 261.81/56.56 | | | | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | | | | (1363) ~ leq(n1, all_74_18) | (a_select3(id_ds1_filter, % 261.81/56.56 | | | | | | | | | | | | | | | | | | | n5, n1) = all_74_13 & $i(all_74_13)) % 261.81/56.56 | | | | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | | | | BETA: splitting (1363) gives: % 261.81/56.56 | | | | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | | | | Case 1: % 261.81/56.56 | | | | | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | | | | | (1364) ~ leq(n1, all_74_18) % 261.81/56.56 | | | | | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | | | | | REDUCE: (1342), (1364) imply: % 261.81/56.56 | | | | | | | | | | | | | | | | | | | | (1365) ~ leq(n1, n3) % 261.81/56.56 | | | | | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1357), (1365) imply: % 261.81/56.56 | | | | | | | | | | | | | | | | | | | | (1366) $false % 261.81/56.56 | | | | | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | | | | | CLOSE: (1366) is inconsistent. % 261.81/56.56 | | | | | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | | | | Case 2: % 261.81/56.56 | | | | | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | | | | | (1367) a_select3(id_ds1_filter, n5, n1) = all_74_13 & % 261.81/56.56 | | | | | | | | | | | | | | | | | | | | $i(all_74_13) % 261.81/56.56 | | | | | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | | | | | ALPHA: (1367) implies: % 261.81/56.56 | | | | | | | | | | | | | | | | | | | | (1368) a_select3(id_ds1_filter, n5, n1) = all_74_13 % 261.81/56.56 | | | | | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (30) with all_74_12, all_74_13, n1, % 261.81/56.56 | | | | | | | | | | | | | | | | | | | | n5, id_ds1_filter, simplifying with (1356), (1368) % 261.81/56.56 | | | | | | | | | | | | | | | | | | | | gives: % 261.81/56.56 | | | | | | | | | | | | | | | | | | | | (1369) all_74_12 = all_74_13 % 261.81/56.56 | | | | | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | | | | | REDUCE: (649), (1369) imply: % 261.81/56.56 | | | | | | | | | | | | | | | | | | | | (1370) $false % 261.81/56.56 | | | | | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | | | | | CLOSE: (1370) is inconsistent. % 261.81/56.56 | | | | | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | | | | End of split % 261.81/56.56 | | | | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | | | End of split % 261.81/56.56 | | | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | | End of split % 261.81/56.56 | | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | Case 2: % 261.81/56.56 | | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | | (1371) all_74_15 = n2 % 261.81/56.56 | | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | | REDUCE: (1252), (1371) imply: % 261.81/56.56 | | | | | | | | | | | | | | | | | (1372) a_select3(id_ds1_filter, n2, n5) = all_74_13 % 261.81/56.56 | | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | | REDUCE: (1251), (1371) imply: % 261.81/56.56 | | | | | | | | | | | | | | | | | (1373) a_select3(id_ds1_filter, n5, n2) = all_74_12 % 261.81/56.56 | | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | | REDUCE: (702), (1371) imply: % 261.81/56.56 | | | | | | | | | | | | | | | | | (1374) leq(n2, n4) % 261.81/56.56 | | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | | REDUCE: (650), (1371) imply: % 261.81/56.56 | | | | | | | | | | | | | | | | | (1375) leq(n0, n2) % 261.81/56.56 | | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (81) with n2, n5, all_74_13, % 261.81/56.56 | | | | | | | | | | | | | | | | | simplifying with (118), (139), (1254), (1372), % 261.81/56.56 | | | | | | | | | | | | | | | | | (1375) gives: % 261.81/56.56 | | | | | | | | | | | | | | | | | (1376) ~ leq(n5, all_74_20) | ~ leq(n2, pv57) | % 261.81/56.56 | | | | | | | | | | | | | | | | | (a_select3(id_ds1_filter, n5, n2) = all_74_13 & % 261.81/56.56 | | | | | | | | | | | | | | | | | $i(all_74_13)) % 261.81/56.56 | | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | | BETA: splitting (1376) gives: % 261.81/56.56 | | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | | Case 1: % 261.81/56.56 | | | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | | | (1377) ~ leq(n5, all_74_20) % 261.81/56.56 | | | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | | | REDUCE: (159), (1377) imply: % 261.81/56.56 | | | | | | | | | | | | | | | | | | (1378) ~ leq(n5, n5) % 261.81/56.56 | | | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1253), (1378) imply: % 261.81/56.56 | | | | | | | | | | | | | | | | | | (1379) $false % 261.81/56.56 | | | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | | | CLOSE: (1379) is inconsistent. % 261.81/56.56 | | | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | | Case 2: % 261.81/56.56 | | | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | | | (1380) ~ leq(n2, pv57) | (a_select3(id_ds1_filter, n5, % 261.81/56.56 | | | | | | | | | | | | | | | | | | n2) = all_74_13 & $i(all_74_13)) % 261.81/56.56 | | | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | | | BETA: splitting (1380) gives: % 261.81/56.56 | | | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | | | Case 1: % 261.81/56.56 | | | | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | | | | (1381) ~ leq(n2, pv57) % 261.81/56.56 | | | | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | | | | REDUCE: (1339), (1381) imply: % 261.81/56.56 | | | | | | | | | | | | | | | | | | | (1382) ~ leq(n2, n4) % 261.81/56.56 | | | | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1374), (1382) imply: % 261.81/56.56 | | | | | | | | | | | | | | | | | | | (1383) $false % 261.81/56.56 | | | | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | | | | CLOSE: (1383) is inconsistent. % 261.81/56.56 | | | | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | | | Case 2: % 261.81/56.56 | | | | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | | | | (1384) a_select3(id_ds1_filter, n5, n2) = all_74_13 & % 261.81/56.56 | | | | | | | | | | | | | | | | | | | $i(all_74_13) % 261.81/56.56 | | | | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | | | | ALPHA: (1384) implies: % 261.81/56.56 | | | | | | | | | | | | | | | | | | | (1385) a_select3(id_ds1_filter, n5, n2) = all_74_13 % 261.81/56.56 | | | | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (30) with all_74_12, all_74_13, n2, % 261.81/56.56 | | | | | | | | | | | | | | | | | | | n5, id_ds1_filter, simplifying with (1373), (1385) % 261.81/56.56 | | | | | | | | | | | | | | | | | | | gives: % 261.81/56.56 | | | | | | | | | | | | | | | | | | | (1386) all_74_12 = all_74_13 % 261.81/56.56 | | | | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | | | | REDUCE: (649), (1386) imply: % 261.81/56.56 | | | | | | | | | | | | | | | | | | | (1387) $false % 261.81/56.56 | | | | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | | | | CLOSE: (1387) is inconsistent. % 261.81/56.56 | | | | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | | | End of split % 261.81/56.56 | | | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | | End of split % 261.81/56.56 | | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | End of split % 261.81/56.56 | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | Case 2: % 261.81/56.56 | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | (1388) all_74_15 = all_74_18 % 261.81/56.56 | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | COMBINE_EQS: (1342), (1388) imply: % 261.81/56.56 | | | | | | | | | | | | | | | | (1389) all_74_15 = n3 % 261.81/56.56 | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | REDUCE: (1252), (1389) imply: % 261.81/56.56 | | | | | | | | | | | | | | | | (1390) a_select3(id_ds1_filter, n3, n5) = all_74_13 % 261.81/56.56 | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | REDUCE: (1251), (1389) imply: % 261.81/56.56 | | | | | | | | | | | | | | | | (1391) a_select3(id_ds1_filter, n5, n3) = all_74_12 % 261.81/56.56 | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | REDUCE: (702), (1389) imply: % 261.81/56.56 | | | | | | | | | | | | | | | | (1392) leq(n3, n4) % 261.81/56.56 | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | REDUCE: (650), (1389) imply: % 261.81/56.56 | | | | | | | | | | | | | | | | (1393) leq(n0, n3) % 261.81/56.56 | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (81) with n3, n5, all_74_13, % 261.81/56.56 | | | | | | | | | | | | | | | | simplifying with (129), (139), (1254), (1390), % 261.81/56.56 | | | | | | | | | | | | | | | | (1393) gives: % 261.81/56.56 | | | | | | | | | | | | | | | | (1394) ~ leq(n5, all_74_20) | ~ leq(n3, pv57) | % 261.81/56.56 | | | | | | | | | | | | | | | | (a_select3(id_ds1_filter, n5, n3) = all_74_13 & % 261.81/56.56 | | | | | | | | | | | | | | | | $i(all_74_13)) % 261.81/56.56 | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | BETA: splitting (1394) gives: % 261.81/56.56 | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | Case 1: % 261.81/56.56 | | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | | (1395) ~ leq(n5, all_74_20) % 261.81/56.56 | | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | | REDUCE: (159), (1395) imply: % 261.81/56.56 | | | | | | | | | | | | | | | | | (1396) ~ leq(n5, n5) % 261.81/56.56 | | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | | PRED_UNIFY: (1253), (1396) imply: % 261.81/56.56 | | | | | | | | | | | | | | | | | (1397) $false % 261.81/56.56 | | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | | CLOSE: (1397) is inconsistent. % 261.81/56.56 | | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | Case 2: % 261.81/56.56 | | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | | (1398) ~ leq(n3, pv57) | (a_select3(id_ds1_filter, n5, % 261.81/56.56 | | | | | | | | | | | | | | | | | n3) = all_74_13 & $i(all_74_13)) % 261.81/56.56 | | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | | BETA: splitting (1398) gives: % 261.81/56.56 | | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | | Case 1: % 261.81/56.56 | | | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | | | (1399) ~ leq(n3, pv57) % 261.81/56.56 | | | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | | | REDUCE: (1339), (1399) imply: % 261.81/56.56 | | | | | | | | | | | | | | | | | | (1400) ~ leq(n3, n4) % 261.81/56.56 | | | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1392), (1400) imply: % 261.81/56.56 | | | | | | | | | | | | | | | | | | (1401) $false % 261.81/56.56 | | | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | | | CLOSE: (1401) is inconsistent. % 261.81/56.56 | | | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | | Case 2: % 261.81/56.56 | | | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | | | (1402) a_select3(id_ds1_filter, n5, n3) = all_74_13 & % 261.81/56.56 | | | | | | | | | | | | | | | | | | $i(all_74_13) % 261.81/56.56 | | | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | | | ALPHA: (1402) implies: % 261.81/56.56 | | | | | | | | | | | | | | | | | | (1403) a_select3(id_ds1_filter, n5, n3) = all_74_13 % 261.81/56.56 | | | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (30) with all_74_12, all_74_13, n3, % 261.81/56.56 | | | | | | | | | | | | | | | | | | n5, id_ds1_filter, simplifying with (1391), (1403) % 261.81/56.56 | | | | | | | | | | | | | | | | | | gives: % 261.81/56.56 | | | | | | | | | | | | | | | | | | (1404) all_74_12 = all_74_13 % 261.81/56.56 | | | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | | | REDUCE: (649), (1404) imply: % 261.81/56.56 | | | | | | | | | | | | | | | | | | (1405) $false % 261.81/56.56 | | | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | | | CLOSE: (1405) is inconsistent. % 261.81/56.56 | | | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | | End of split % 261.81/56.56 | | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | End of split % 261.81/56.56 | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | End of split % 261.81/56.56 | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | End of split % 261.81/56.56 | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | Case 2: % 261.81/56.56 | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | (1406) pv57 = n1 % 261.81/56.56 | | | | | | | | | | | | | | (1407) ~ gt(pv57, n1) % 261.81/56.56 | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | REF_CLOSE: (13), (66), (650), (681), (714), (1258), (1406), % 261.81/56.56 | | | | | | | | | | | | | | (1407) are inconsistent by sub-proof #21. % 261.81/56.56 | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | End of split % 261.81/56.56 | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | End of split % 261.81/56.56 | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | Case 2: % 261.81/56.56 | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | (1408) all_74_18 = n0 % 261.81/56.56 | | | | | | | | | | | | (1409) ~ gt(all_74_18, n0) % 261.81/56.56 | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | REDUCE: (1408), (1409) imply: % 261.81/56.56 | | | | | | | | | | | | (1410) ~ gt(n0, n0) % 261.81/56.56 | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | REF_CLOSE: (22), (66), (712), (1256), (1258), (1408), (1410), % 261.81/56.56 | | | | | | | | | | | | (transitivity_gt) are inconsistent by sub-proof % 261.81/56.56 | | | | | | | | | | | | #24. % 261.81/56.56 | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | End of split % 261.81/56.56 | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | End of split % 261.81/56.56 | | | | | | | | | | % 261.81/56.56 | | | | | | | | | End of split % 261.81/56.56 | | | | | | | | | % 261.81/56.56 | | | | | | | | Case 2: % 261.81/56.56 | | | | | | | | | % 261.81/56.56 | | | | | | | | | (1411) all_74_15 = all_74_16 % 261.81/56.56 | | | | | | | | | (1412) ~ gt(all_74_16, all_74_15) % 261.81/56.56 | | | | | | | | | % 261.81/56.56 | | | | | | | | | COMBINE_EQS: (679), (1411) imply: % 261.81/56.56 | | | | | | | | | (1413) all_74_15 = pv57 % 261.81/56.56 | | | | | | | | | % 261.81/56.56 | | | | | | | | | REDUCE: (656), (1413) imply: % 261.81/56.56 | | | | | | | | | (1414) a_select3(id_ds1_filter, all_74_14, pv57) = % 261.81/56.56 | | | | | | | | | all_74_12 % 261.81/56.56 | | | | | | | | | % 261.81/56.56 | | | | | | | | | REDUCE: (655), (1413) imply: % 261.81/56.56 | | | | | | | | | (1415) a_select3(id_ds1_filter, pv57, all_74_14) = % 261.81/56.56 | | | | | | | | | all_74_13 % 261.81/56.56 | | | | | | | | | % 261.81/56.56 | | | | | | | | | REDUCE: (679), (1412), (1413) imply: % 261.81/56.56 | | | | | | | | | (1416) ~ gt(pv57, pv57) % 261.81/56.56 | | | | | | | | | % 261.81/56.56 | | | | | | | | | BETA: splitting (666) gives: % 261.81/56.56 | | | | | | | | | % 261.81/56.56 | | | | | | | | | Case 1: % 261.81/56.56 | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | (1417) gt(n5, all_74_14) % 261.81/56.56 | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_14, n5, n4, % 261.81/56.56 | | | | | | | | | | simplifying with (67), (139), (148), (1417) gives: % 261.81/56.56 | | | | | | | | | | (1418) leq(all_74_14, n4) % 261.81/56.56 | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | BETA: splitting (665) gives: % 261.81/56.56 | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | Case 1: % 261.81/56.56 | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | (1419) all_74_14 = n0 % 261.81/56.56 | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | REF_CLOSE: (67), (711), (1419), (irreflexivity_gt) are % 261.81/56.56 | | | | | | | | | | | inconsistent by sub-proof #41. % 261.81/56.56 | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | Case 2: % 261.81/56.56 | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | (1420) ~ (all_74_14 = n0) % 261.81/56.56 | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | BETA: splitting (672) gives: % 261.81/56.56 | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | Case 1: % 261.81/56.56 | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | (1421) all_74_14 = n0 % 261.81/56.56 | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | REDUCE: (1420), (1421) imply: % 261.81/56.56 | | | | | | | | | | | | (1422) $false % 261.81/56.56 | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | CLOSE: (1422) is inconsistent. % 261.81/56.56 | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | Case 2: % 261.81/56.56 | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_14, n4, % 261.81/56.56 | | | | | | | | | | | | simplifying with (67), (136), (1418) gives: % 261.81/56.56 | | | | | | | | | | | | (1423) all_74_14 = n4 | gt(n4, all_74_14) % 261.81/56.56 | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | BETA: splitting (687) gives: % 261.81/56.56 | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | Case 1: % 261.81/56.56 | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | (1424) all_74_15 = n0 % 261.81/56.56 | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | COMBINE_EQS: (1413), (1424) imply: % 261.81/56.56 | | | | | | | | | | | | | (1425) pv57 = n0 % 261.81/56.56 | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | REDUCE: (705), (1425) imply: % 261.81/56.56 | | | | | | | | | | | | | (1426) $false % 261.81/56.56 | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | CLOSE: (1426) is inconsistent. % 261.81/56.56 | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | Case 2: % 261.81/56.56 | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | (1427) ~ (all_74_15 = n0) % 261.81/56.56 | | | | | | | | | | | | | (1428) all_74_15 = n5 | all_74_15 = n4 | all_74_15 = n3 | % 261.81/56.56 | | | | | | | | | | | | | all_74_15 = n2 | all_74_15 = n1 % 261.81/56.56 | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | BETA: splitting (697) gives: % 261.81/56.56 | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | Case 1: % 261.81/56.56 | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | (1429) gt(all_74_18, n0) % 261.81/56.56 | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | BETA: splitting (696) gives: % 261.81/56.56 | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | Case 1: % 261.81/56.56 | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | (1430) all_74_18 = n0 % 261.81/56.56 | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | REF_CLOSE: (154), (1429), (1430), (irreflexivity_gt) are % 261.81/56.56 | | | | | | | | | | | | | | | inconsistent by sub-proof #39. % 261.81/56.56 | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | Case 2: % 261.81/56.56 | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | (1431) ~ (all_74_18 = n0) % 261.81/56.56 | | | | | | | | | | | | | | | (1432) all_74_18 = n4 | all_74_18 = n3 | all_74_18 = n2 | % 261.81/56.56 | | | | | | | | | | | | | | | all_74_18 = n1 % 261.81/56.56 | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | BETA: splitting (699) gives: % 261.81/56.56 | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | Case 1: % 261.81/56.56 | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | (1433) gt(pv57, n1) % 261.81/56.56 | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | BETA: splitting (703) gives: % 261.81/56.56 | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | Case 1: % 261.81/56.56 | | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | | (1434) gt(n4, pv57) % 261.81/56.56 | | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | | BETA: splitting (695) gives: % 261.81/56.56 | | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | | Case 1: % 261.81/56.56 | | | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | | | (1435) all_74_18 = n0 % 261.81/56.56 | | | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | | | REDUCE: (1431), (1435) imply: % 261.81/56.56 | | | | | | | | | | | | | | | | | | (1436) $false % 261.81/56.56 | | | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | | | CLOSE: (1436) is inconsistent. % 261.81/56.56 | | | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | | Case 2: % 261.81/56.56 | | | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with pv57, n4, n3, simplifying % 261.81/56.56 | | | | | | | | | | | | | | | | | | with (24), (136), (147), (1434) gives: % 261.81/56.56 | | | | | | | | | | | | | | | | | | (1437) leq(pv57, n3) % 261.81/56.56 | | | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with n1, pv57, all_74_18, % 261.81/56.56 | | | | | | | | | | | | | | | | | | simplifying with (24), (102), (155), (1433) gives: % 261.81/56.56 | | | | | | | | | | | | | | | | | | (1438) leq(n1, all_74_18) % 261.81/56.56 | | | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | | | BETA: splitting (706) gives: % 261.81/56.56 | | | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | | | Case 1: % 261.81/56.56 | | | | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | | | | (1439) pv57 = n1 % 261.81/56.56 | | | | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1416), (1433), (1439) are inconsistent by % 261.81/56.56 | | | | | | | | | | | | | | | | | | | sub-proof #20. % 261.81/56.56 | | | | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | | | Case 2: % 261.81/56.56 | | | | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | | | | (1440) ~ (pv57 = n1) % 261.81/56.56 | | | | | | | | | | | | | | | | | | | (1441) pv57 = n5 | pv57 = n4 | pv57 = n3 | pv57 = n2 % 261.81/56.56 | | | | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | | | | BETA: splitting (710) gives: % 261.81/56.56 | | | | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | | | | Case 1: % 261.81/56.56 | | | | | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | | | | | (1442) all_74_15 = n0 % 261.81/56.56 | | | | | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1413), (1442) imply: % 261.81/56.56 | | | | | | | | | | | | | | | | | | | | (1443) pv57 = n0 % 261.81/56.56 | | | | | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | | | | | REDUCE: (705), (1443) imply: % 261.81/56.56 | | | | | | | | | | | | | | | | | | | | (1444) $false % 261.81/56.56 | | | | | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | | | | | CLOSE: (1444) is inconsistent. % 261.81/56.56 | | | | | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | | | | Case 2: % 261.81/56.56 | | | | | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with n1, all_74_18, n2, pv57, % 261.81/56.56 | | | | | | | | | | | | | | | | | | | | simplifying with (101), (102), (154), (165), % 261.81/56.56 | | | | | | | | | | | | | | | | | | | | (1438) gives: % 261.81/56.56 | | | | | | | | | | | | | | | | | | | | (1445) leq(n2, pv57) % 261.81/56.56 | | | | | | | | | | | | | | | | | | | | % 261.81/56.56 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (15) with pv57, simplifying with % 261.81/56.56 | | | | | | | | | | | | | | | | | | | | (24), (63), (1437) gives: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | (1446) pv57 = n3 | pv57 = n2 | pv57 = n1 | pv57 = n0 % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | BETA: splitting (1423) gives: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | Case 1: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | (1447) gt(n4, all_74_14) % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_14, n4, n3, % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | simplifying with (67), (136), (147), (1447) gives: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | (1448) leq(all_74_14, n3) % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1428) gives: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | (1449) all_74_15 = n5 % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1413), (1449) imply: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | (1450) pv57 = n5 % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (692), (1450) imply: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | (1451) gt(n5, n5) % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1416), (1450) imply: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | (1452) ~ gt(n5, n5) % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1451), (1452) imply: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | (1453) $false % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1453) is inconsistent. % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | (1454) ~ (all_74_15 = n5) % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1413), (1454) imply: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | (1455) ~ (pv57 = n5) % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1432) gives: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | (1456) all_74_18 = n4 % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (165), (1456) imply: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | (1457) succ(n4) = pv57 % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (28) with n5, pv57, n4, simplifying % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | with (135), (1457) gives: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | (1458) pv57 = n5 % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1455), (1458) imply: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | (1459) $false % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1459) is inconsistent. % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_14, n3, % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | simplifying with (67), (129), (1448) gives: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | (1460) all_74_14 = n3 | gt(n3, all_74_14) % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1441) gives: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | (1461) pv57 = n3 % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (75), (1461) imply: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | (1462) minus(n3, n1) = all_74_18 % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1414), (1461) imply: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | (1463) a_select3(id_ds1_filter, all_74_14, n3) = % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | all_74_12 % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1415), (1461) imply: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | (1464) a_select3(id_ds1_filter, n3, all_74_14) = % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | all_74_13 % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (155), (1461) imply: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | (1465) pred(n3) = all_74_18 % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (162), (1461) imply: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | (1466) leq(n3, n5) % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (63), (1461) imply: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | (1467) leq(n0, n3) % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (29) with n2, all_74_18, n1, n3, % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (161), (1462) gives: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | (1468) all_74_18 = n2 % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1460) gives: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | (1469) gt(n3, all_74_14) % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_14, n3, n2, % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (67), (129), (146), (1469) gives: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | (1470) leq(all_74_14, n2) % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_14, n2, % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (67), (118), (1470) gives: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | (1471) all_74_14 = n2 | gt(n2, all_74_14) % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1471) gives: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | (1472) gt(n2, all_74_14) % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_14, n2, n1, % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (67), (118), (145), (1472) gives: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | (1473) leq(all_74_14, n1) % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_74_14, simplifying % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | with (67), (651), (1473) gives: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | (1474) all_74_14 = n1 | all_74_14 = n0 % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1474) gives: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1475) all_74_14 = n0 % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1420), (1475) imply: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1476) $false % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1476) is inconsistent. % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1477) all_74_14 = n1 % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1463), (1477) imply: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1478) a_select3(id_ds1_filter, n1, n3) = all_74_12 % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1464), (1477) imply: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1479) a_select3(id_ds1_filter, n3, n1) = all_74_13 % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1470), (1477) imply: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1480) leq(n1, n2) % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (651), (1477) imply: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1481) leq(n0, n1) % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (82) with n1, n3, all_74_12, % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (102), (129), (1467), (1478), % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1481) gives: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1482) ~ leq(n3, all_74_20) | ~ leq(n1, all_74_18) | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | (a_select3(id_ds1_filter, n3, n1) = all_74_12 & % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_74_12)) % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1482) gives: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1483) ~ leq(n3, all_74_20) % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (159), (1483) imply: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1484) ~ leq(n3, n5) % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1466), (1484) imply: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1485) $false % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1485) is inconsistent. % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1486) ~ leq(n1, all_74_18) | (a_select3(id_ds1_filter, % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | n3, n1) = all_74_12 & $i(all_74_12)) % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1486) gives: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1487) ~ leq(n1, all_74_18) % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1468), (1487) imply: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1488) ~ leq(n1, n2) % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1480), (1488) imply: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1489) $false % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1489) is inconsistent. % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1490) a_select3(id_ds1_filter, n3, n1) = all_74_12 & % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_74_12) % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1490) implies: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1491) a_select3(id_ds1_filter, n3, n1) = all_74_12 % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (649), (1479), (1491) are inconsistent by % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #35. % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | (1492) all_74_14 = n2 % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1463), (1492) imply: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | (1493) a_select3(id_ds1_filter, n2, n3) = all_74_12 % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1464), (1492) imply: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | (1494) a_select3(id_ds1_filter, n3, n2) = all_74_13 % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1448), (1492) imply: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | (1495) leq(n2, n3) % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (651), (1492) imply: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | (1496) leq(n0, n2) % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (81) with n2, n3, all_74_12, % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (118), (129), (1467), (1493), % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | (1496) gives: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | (1497) ~ leq(n3, all_74_20) | ~ leq(n2, pv57) | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | (a_select3(id_ds1_filter, n3, n2) = all_74_12 & % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_74_12)) % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1497) gives: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1498) ~ leq(n3, all_74_20) % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (159), (1498) imply: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1499) ~ leq(n3, n5) % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1466), (1499) imply: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1500) $false % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1500) is inconsistent. % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1501) ~ leq(n2, pv57) | (a_select3(id_ds1_filter, n3, % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | n2) = all_74_12 & $i(all_74_12)) % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1501) gives: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1502) ~ leq(n2, pv57) % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1461), (1502) imply: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1503) ~ leq(n2, n3) % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1495), (1503) imply: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1504) $false % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1504) is inconsistent. % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1505) a_select3(id_ds1_filter, n3, n2) = all_74_12 & % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_74_12) % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1505) implies: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1506) a_select3(id_ds1_filter, n3, n2) = all_74_12 % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (649), (1494), (1506) are inconsistent by % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #30. % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | (1507) all_74_14 = n3 % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1463), (1507) imply: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | (1508) a_select3(id_ds1_filter, n3, n3) = all_74_12 % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1464), (1507) imply: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | (1509) a_select3(id_ds1_filter, n3, n3) = all_74_13 % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (649), (1508), (1509) are inconsistent by % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #19. % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | (1510) ~ (pv57 = n3) % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1446) gives: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | (1511) pv57 = n0 % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (705), (1511) imply: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | (1512) $false % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1512) is inconsistent. % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | (1513) pv57 = n3 | pv57 = n2 | pv57 = n1 % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1513) gives: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | (1514) pv57 = n1 % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1440), (1514) imply: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | (1515) $false % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1515) is inconsistent. % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | (1516) pv57 = n3 | pv57 = n2 % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1516) gives: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1517) pv57 = n3 % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1510), (1517) imply: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1518) $false % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1518) is inconsistent. % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1519) pv57 = n2 % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1414), (1519) imply: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1520) a_select3(id_ds1_filter, all_74_14, n2) = % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_74_12 % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1415), (1519) imply: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1521) a_select3(id_ds1_filter, n2, all_74_14) = % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_74_13 % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (669), (1519) imply: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1522) succ(n2) = all_74_17 % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (678), (1519) imply: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1523) pred(all_74_17) = n2 % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (155), (1519) imply: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1524) pred(n2) = all_74_18 % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (162), (1519) imply: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1525) leq(n2, n5) % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1445), (1519) imply: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1526) leq(n2, n2) % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (63), (1519) imply: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1527) leq(n0, n2) % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (27) with n1, all_74_18, n2, % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (145), (1524) gives: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1528) all_74_18 = n1 % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (28) with n3, all_74_17, n2, % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (117), (1522) gives: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1529) all_74_17 = n3 % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1460) gives: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1530) gt(n3, all_74_14) % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_14, n3, n2, % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (67), (129), (146), (1530) gives: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1531) leq(all_74_14, n2) % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_14, n2, % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (67), (118), (1531) gives: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1532) all_74_14 = n2 | gt(n2, all_74_14) % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1532) gives: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1533) gt(n2, all_74_14) % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_14, n2, n1, % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (67), (118), (145), (1533) gives: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1534) leq(all_74_14, n1) % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_74_14, simplifying % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | with (67), (651), (1534) gives: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1535) all_74_14 = n1 | all_74_14 = n0 % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1535) gives: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1536) all_74_14 = n0 % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1420), (1536) imply: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1537) $false % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1537) is inconsistent. % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1538) all_74_14 = n1 % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1520), (1538) imply: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1539) a_select3(id_ds1_filter, n1, n2) = all_74_12 % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1521), (1538) imply: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1540) a_select3(id_ds1_filter, n2, n1) = all_74_13 % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1534), (1538) imply: % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1541) leq(n1, n1) % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (651), (1538) imply: % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1542) leq(n0, n1) % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (82) with n1, n2, all_74_12, % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (102), (118), (1527), (1539), % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1542) gives: % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1543) ~ leq(n2, all_74_20) | ~ leq(n1, all_74_18) | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (a_select3(id_ds1_filter, n2, n1) = all_74_12 & % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_74_12)) % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1543) gives: % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1544) ~ leq(n2, all_74_20) % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (159), (1544) imply: % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1545) ~ leq(n2, n5) % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1525), (1545) imply: % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1546) $false % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1546) is inconsistent. % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1547) ~ leq(n1, all_74_18) | (a_select3(id_ds1_filter, % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | n2, n1) = all_74_12 & $i(all_74_12)) % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1547) gives: % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1548) ~ leq(n1, all_74_18) % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1528), (1548) imply: % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1549) ~ leq(n1, n1) % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1541), (1549) imply: % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1550) $false % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1550) is inconsistent. % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1551) a_select3(id_ds1_filter, n2, n1) = all_74_12 & % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_74_12) % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1551) implies: % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1552) a_select3(id_ds1_filter, n2, n1) = all_74_12 % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (649), (1540), (1552) are inconsistent by % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #36. % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1553) all_74_14 = n2 % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1520), (1553) imply: % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1554) a_select3(id_ds1_filter, n2, n2) = all_74_12 % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1521), (1553) imply: % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1555) a_select3(id_ds1_filter, n2, n2) = all_74_13 % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (649), (1554), (1555) are inconsistent by % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #31. % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1556) all_74_14 = n3 % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1520), (1556) imply: % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1557) a_select3(id_ds1_filter, n3, n2) = all_74_12 % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1521), (1556) imply: % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1558) a_select3(id_ds1_filter, n2, n3) = all_74_13 % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (659), (1556) imply: % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1559) leq(n3, n5) % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (651), (1556) imply: % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1560) leq(n0, n3) % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (81) with n2, n3, all_74_13, % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (118), (129), (1527), (1558), % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1560) gives: % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1561) ~ leq(n3, all_74_20) | ~ leq(n2, pv57) | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (a_select3(id_ds1_filter, n3, n2) = all_74_13 & % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_74_13)) % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1561) gives: % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1562) ~ leq(n3, all_74_20) % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (159), (1562) imply: % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1563) ~ leq(n3, n5) % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1559), (1563) imply: % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1564) $false % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1564) is inconsistent. % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1565) ~ leq(n2, pv57) | (a_select3(id_ds1_filter, n3, % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | n2) = all_74_13 & $i(all_74_13)) % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1565) gives: % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1566) ~ leq(n2, pv57) % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1519), (1566) imply: % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1567) ~ leq(n2, n2) % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1526), (1567) imply: % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1568) $false % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1568) is inconsistent. % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1569) a_select3(id_ds1_filter, n3, n2) = all_74_13 & % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_74_13) % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1569) implies: % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1570) a_select3(id_ds1_filter, n3, n2) = all_74_13 % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (649), (1557), (1570) are inconsistent by % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #30. % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | End of split % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | End of split % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | End of split % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | Case 2: % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | (1571) all_74_14 = n4 % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | REDUCE: (1414), (1571) imply: % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | (1572) a_select3(id_ds1_filter, n4, pv57) = all_74_12 % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | REDUCE: (1415), (1571) imply: % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | (1573) a_select3(id_ds1_filter, pv57, n4) = all_74_13 % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | REDUCE: (659), (1571) imply: % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | (1574) leq(n4, n5) % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | REDUCE: (651), (1571) imply: % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | (1575) leq(n0, n4) % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1441) gives: % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | (1576) pv57 = n3 % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1573), (1576) imply: % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | (1577) a_select3(id_ds1_filter, n3, n4) = all_74_13 % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1572), (1576) imply: % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | (1578) a_select3(id_ds1_filter, n4, n3) = all_74_12 % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (669), (1576) imply: % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | (1579) succ(n3) = all_74_17 % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1437), (1576) imply: % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | (1580) leq(n3, n3) % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (63), (1576) imply: % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | (1581) leq(n0, n3) % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (28) with n4, all_74_17, n3, % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | simplifying with (128), (1579) gives: % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | (1582) all_74_17 = n4 % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (81) with n3, n4, all_74_13, % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | simplifying with (129), (136), (1575), (1577), % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | (1581) gives: % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | (1583) ~ leq(n4, all_74_20) | ~ leq(n3, pv57) | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | (a_select3(id_ds1_filter, n4, n3) = all_74_13 & % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | $i(all_74_13)) % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1583) gives: % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | (1584) ~ leq(n4, all_74_20) % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (159), (1584) imply: % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | (1585) ~ leq(n4, n5) % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1574), (1585) imply: % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | (1586) $false % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1586) is inconsistent. % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | (1587) ~ leq(n3, pv57) | (a_select3(id_ds1_filter, n4, % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | n3) = all_74_13 & $i(all_74_13)) % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1587) gives: % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | (1588) ~ leq(n3, pv57) % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1576), (1588) imply: % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | (1589) ~ leq(n3, n3) % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1580), (1589) imply: % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | (1590) $false % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1590) is inconsistent. % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | (1591) a_select3(id_ds1_filter, n4, n3) = all_74_13 & % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_74_13) % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1591) implies: % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | (1592) a_select3(id_ds1_filter, n4, n3) = all_74_13 % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (649), (1578), (1592) are inconsistent by % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #25. % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | End of split % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | End of split % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | (1593) ~ (pv57 = n3) % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1446) gives: % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | (1594) pv57 = n0 % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (705), (1594) imply: % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | (1595) $false % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1595) is inconsistent. % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | (1596) pv57 = n3 | pv57 = n2 | pv57 = n1 % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1596) gives: % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | (1597) pv57 = n1 % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1440), (1597) imply: % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | (1598) $false % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1598) is inconsistent. % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | (1599) pv57 = n3 | pv57 = n2 % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1599) gives: % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | (1600) pv57 = n3 % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1593), (1600) imply: % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | (1601) $false % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1601) is inconsistent. % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | (1602) pv57 = n2 % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1573), (1602) imply: % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | (1603) a_select3(id_ds1_filter, n2, n4) = all_74_13 % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1572), (1602) imply: % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | (1604) a_select3(id_ds1_filter, n4, n2) = all_74_12 % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1445), (1602) imply: % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | (1605) leq(n2, n2) % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (63), (1602) imply: % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | (1606) leq(n0, n2) % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (81) with n2, n4, all_74_13, % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (118), (136), (1575), (1603), % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | (1606) gives: % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | (1607) ~ leq(n4, all_74_20) | ~ leq(n2, pv57) | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | (a_select3(id_ds1_filter, n4, n2) = all_74_13 & % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_74_13)) % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1607) gives: % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | (1608) ~ leq(n4, all_74_20) % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (159), (1608) imply: % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | (1609) ~ leq(n4, n5) % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1574), (1609) imply: % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | (1610) $false % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1610) is inconsistent. % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | (1611) ~ leq(n2, pv57) | (a_select3(id_ds1_filter, n4, % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | n2) = all_74_13 & $i(all_74_13)) % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1611) gives: % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1612) ~ leq(n2, pv57) % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1602), (1612) imply: % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1613) ~ leq(n2, n2) % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1605), (1613) imply: % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1614) $false % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1614) is inconsistent. % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1615) a_select3(id_ds1_filter, n4, n2) = all_74_13 & % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_74_13) % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1615) implies: % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1616) a_select3(id_ds1_filter, n4, n2) = all_74_13 % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (649), (1604), (1616) are inconsistent by % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #27. % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | End of split % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | End of split % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | End of split % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | End of split % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | End of split % 261.81/56.58 | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | End of split % 261.81/56.58 | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | End of split % 261.81/56.58 | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | Case 2: % 261.81/56.58 | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | (1617) pv57 = n4 % 261.81/56.58 | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | REDUCE: (1414), (1617) imply: % 261.81/56.58 | | | | | | | | | | | | | | | | | (1618) a_select3(id_ds1_filter, all_74_14, n4) = % 261.81/56.58 | | | | | | | | | | | | | | | | | all_74_12 % 261.81/56.58 | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | REDUCE: (1415), (1617) imply: % 261.81/56.58 | | | | | | | | | | | | | | | | | (1619) a_select3(id_ds1_filter, n4, all_74_14) = % 261.81/56.58 | | | | | | | | | | | | | | | | | all_74_13 % 261.81/56.58 | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | REDUCE: (669), (1617) imply: % 261.81/56.58 | | | | | | | | | | | | | | | | | (1620) succ(n4) = all_74_17 % 261.81/56.58 | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | REDUCE: (155), (1617) imply: % 261.81/56.58 | | | | | | | | | | | | | | | | | (1621) pred(n4) = all_74_18 % 261.81/56.58 | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | REDUCE: (675), (1617) imply: % 261.81/56.58 | | | | | | | | | | | | | | | | | (1622) leq(n4, all_74_17) % 261.81/56.58 | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | REDUCE: (63), (1617) imply: % 261.81/56.58 | | | | | | | | | | | | | | | | | (1623) leq(n0, n4) % 261.81/56.58 | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (27) with n3, all_74_18, n4, % 261.81/56.58 | | | | | | | | | | | | | | | | | simplifying with (147), (1621) gives: % 261.81/56.58 | | | | | | | | | | | | | | | | | (1624) all_74_18 = n3 % 261.81/56.58 | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (28) with n5, all_74_17, n4, % 261.81/56.58 | | | | | | | | | | | | | | | | | simplifying with (135), (1620) gives: % 261.81/56.58 | | | | | | | | | | | | | | | | | (1625) all_74_17 = n5 % 261.81/56.58 | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | REDUCE: (1622), (1625) imply: % 261.81/56.58 | | | | | | | | | | | | | | | | | (1626) leq(n4, n5) % 261.81/56.58 | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | BETA: splitting (1423) gives: % 261.81/56.58 | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | Case 1: % 261.81/56.58 | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | (1627) gt(n4, all_74_14) % 261.81/56.58 | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_14, n4, n3, % 261.81/56.58 | | | | | | | | | | | | | | | | | | simplifying with (67), (136), (147), (1627) gives: % 261.81/56.58 | | | | | | | | | | | | | | | | | | (1628) leq(all_74_14, n3) % 261.81/56.58 | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_14, n3, % 261.81/56.58 | | | | | | | | | | | | | | | | | | simplifying with (67), (129), (1628) gives: % 261.81/56.58 | | | | | | | | | | | | | | | | | | (1629) all_74_14 = n3 | gt(n3, all_74_14) % 261.81/56.58 | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | BETA: splitting (1629) gives: % 261.81/56.58 | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | Case 1: % 261.81/56.58 | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | (1630) gt(n3, all_74_14) % 261.81/56.58 | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_14, n3, n2, % 261.81/56.58 | | | | | | | | | | | | | | | | | | | simplifying with (67), (129), (146), (1630) gives: % 261.81/56.58 | | | | | | | | | | | | | | | | | | | (1631) leq(all_74_14, n2) % 261.81/56.58 | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_14, n2, % 261.81/56.58 | | | | | | | | | | | | | | | | | | | simplifying with (67), (118), (1631) gives: % 261.81/56.58 | | | | | | | | | | | | | | | | | | | (1632) all_74_14 = n2 | gt(n2, all_74_14) % 261.81/56.58 | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | BETA: splitting (1632) gives: % 261.81/56.58 | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | Case 1: % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | % 261.81/56.58 | | | | | | | | | | | | | | | | | | | | (1633) gt(n2, all_74_14) % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_14, n2, n1, % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | simplifying with (67), (118), (145), (1633) gives: % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | (1634) leq(all_74_14, n1) % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_74_14, simplifying % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | with (67), (651), (1634) gives: % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | (1635) all_74_14 = n1 | all_74_14 = n0 % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | BETA: splitting (1635) gives: % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | Case 1: % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | (1636) all_74_14 = n0 % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | REDUCE: (1420), (1636) imply: % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | (1637) $false % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | CLOSE: (1637) is inconsistent. % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | Case 2: % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | (1638) all_74_14 = n1 % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | REDUCE: (1618), (1638) imply: % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | (1639) a_select3(id_ds1_filter, n1, n4) = all_74_12 % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | REDUCE: (1619), (1638) imply: % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | (1640) a_select3(id_ds1_filter, n4, n1) = all_74_13 % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | REDUCE: (1418), (1638) imply: % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | (1641) leq(n1, n4) % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | REDUCE: (651), (1638) imply: % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | (1642) leq(n0, n1) % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (81) with n1, n4, all_74_12, % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | simplifying with (102), (136), (1623), (1639), % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | (1642) gives: % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | (1643) ~ leq(n4, all_74_20) | ~ leq(n1, pv57) | % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | (a_select3(id_ds1_filter, n4, n1) = all_74_12 & % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | $i(all_74_12)) % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1643) gives: % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | | (1644) ~ leq(n4, all_74_20) % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (159), (1644) imply: % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | | (1645) ~ leq(n4, n5) % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1626), (1645) imply: % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | | (1646) $false % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1646) is inconsistent. % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | | (1647) ~ leq(n1, pv57) | (a_select3(id_ds1_filter, n4, % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | | n1) = all_74_12 & $i(all_74_12)) % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1647) gives: % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | | | (1648) ~ leq(n1, pv57) % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1617), (1648) imply: % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | | | (1649) ~ leq(n1, n4) % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1641), (1649) imply: % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | | | (1650) $false % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1650) is inconsistent. % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | | | (1651) a_select3(id_ds1_filter, n4, n1) = all_74_12 & % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | | | $i(all_74_12) % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1651) implies: % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | | | (1652) a_select3(id_ds1_filter, n4, n1) = all_74_12 % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (649), (1640), (1652) are inconsistent by % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #29. % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | | End of split % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | End of split % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | End of split % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | | Case 2: % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | (1653) all_74_14 = n2 % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | REDUCE: (1618), (1653) imply: % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | (1654) a_select3(id_ds1_filter, n2, n4) = all_74_12 % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | REDUCE: (1619), (1653) imply: % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | (1655) a_select3(id_ds1_filter, n4, n2) = all_74_13 % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | REDUCE: (1418), (1653) imply: % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | (1656) leq(n2, n4) % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | REDUCE: (651), (1653) imply: % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | (1657) leq(n0, n2) % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (81) with n2, n4, all_74_12, % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | simplifying with (118), (136), (1623), (1654), % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | (1657) gives: % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | (1658) ~ leq(n4, all_74_20) | ~ leq(n2, pv57) | % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | (a_select3(id_ds1_filter, n4, n2) = all_74_12 & % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | $i(all_74_12)) % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | BETA: splitting (1658) gives: % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | Case 1: % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | (1659) ~ leq(n4, all_74_20) % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | REDUCE: (159), (1659) imply: % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | (1660) ~ leq(n4, n5) % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1626), (1660) imply: % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | (1661) $false % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | CLOSE: (1661) is inconsistent. % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | Case 2: % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | (1662) ~ leq(n2, pv57) | (a_select3(id_ds1_filter, n4, % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | n2) = all_74_12 & $i(all_74_12)) % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1662) gives: % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | | (1663) ~ leq(n2, pv57) % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1617), (1663) imply: % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | | (1664) ~ leq(n2, n4) % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1656), (1664) imply: % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | | (1665) $false % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1665) is inconsistent. % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | | (1666) a_select3(id_ds1_filter, n4, n2) = all_74_12 & % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | | $i(all_74_12) % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1666) implies: % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | | (1667) a_select3(id_ds1_filter, n4, n2) = all_74_12 % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (649), (1655), (1667) are inconsistent by % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | | sub-proof #27. % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | End of split % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | End of split % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | | End of split % 261.81/56.59 | | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | Case 2: % 261.81/56.59 | | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | | (1668) all_74_14 = n3 % 261.81/56.59 | | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | | REDUCE: (1618), (1668) imply: % 261.81/56.59 | | | | | | | | | | | | | | | | | | | (1669) a_select3(id_ds1_filter, n3, n4) = all_74_12 % 261.81/56.59 | | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | | REDUCE: (1619), (1668) imply: % 261.81/56.59 | | | | | | | | | | | | | | | | | | | (1670) a_select3(id_ds1_filter, n4, n3) = all_74_13 % 261.81/56.59 | | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | | REDUCE: (1418), (1668) imply: % 261.81/56.59 | | | | | | | | | | | | | | | | | | | (1671) leq(n3, n4) % 261.81/56.59 | | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | | REDUCE: (651), (1668) imply: % 261.81/56.59 | | | | | | | | | | | | | | | | | | | (1672) leq(n0, n3) % 261.81/56.59 | | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (81) with n3, n4, all_74_12, % 261.81/56.59 | | | | | | | | | | | | | | | | | | | simplifying with (129), (136), (1623), (1669), % 261.81/56.59 | | | | | | | | | | | | | | | | | | | (1672) gives: % 261.81/56.59 | | | | | | | | | | | | | | | | | | | (1673) ~ leq(n4, all_74_20) | ~ leq(n3, pv57) | % 261.81/56.59 | | | | | | | | | | | | | | | | | | | (a_select3(id_ds1_filter, n4, n3) = all_74_12 & % 261.81/56.59 | | | | | | | | | | | | | | | | | | | $i(all_74_12)) % 261.81/56.59 | | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | | BETA: splitting (1673) gives: % 261.81/56.59 | | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | | Case 1: % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | (1674) ~ leq(n4, all_74_20) % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | REDUCE: (159), (1674) imply: % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | (1675) ~ leq(n4, n5) % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1626), (1675) imply: % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | (1676) $false % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | CLOSE: (1676) is inconsistent. % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | | Case 2: % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | (1677) ~ leq(n3, pv57) | (a_select3(id_ds1_filter, n4, % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | n3) = all_74_12 & $i(all_74_12)) % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | BETA: splitting (1677) gives: % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | Case 1: % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | (1678) ~ leq(n3, pv57) % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | REDUCE: (1617), (1678) imply: % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | (1679) ~ leq(n3, n4) % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1671), (1679) imply: % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | (1680) $false % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | CLOSE: (1680) is inconsistent. % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | Case 2: % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | (1681) a_select3(id_ds1_filter, n4, n3) = all_74_12 & % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | $i(all_74_12) % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | ALPHA: (1681) implies: % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | (1682) a_select3(id_ds1_filter, n4, n3) = all_74_12 % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (649), (1670), (1682) are inconsistent by % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | sub-proof #25. % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | End of split % 261.81/56.59 | | | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | | End of split % 261.81/56.59 | | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | End of split % 261.81/56.59 | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | Case 2: % 261.81/56.59 | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | (1683) all_74_14 = n4 % 261.81/56.59 | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | REDUCE: (1618), (1683) imply: % 261.81/56.59 | | | | | | | | | | | | | | | | | | (1684) a_select3(id_ds1_filter, n4, n4) = all_74_12 % 261.81/56.59 | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | REDUCE: (1619), (1683) imply: % 261.81/56.59 | | | | | | | | | | | | | | | | | | (1685) a_select3(id_ds1_filter, n4, n4) = all_74_13 % 261.81/56.59 | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (30) with all_74_13, all_74_12, n4, % 261.81/56.59 | | | | | | | | | | | | | | | | | | n4, id_ds1_filter, simplifying with (1684), (1685) % 261.81/56.59 | | | | | | | | | | | | | | | | | | gives: % 261.81/56.59 | | | | | | | | | | | | | | | | | | (1686) all_74_12 = all_74_13 % 261.81/56.59 | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | REDUCE: (649), (1686) imply: % 261.81/56.59 | | | | | | | | | | | | | | | | | | (1687) $false % 261.81/56.59 | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | CLOSE: (1687) is inconsistent. % 261.81/56.59 | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | End of split % 261.81/56.59 | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | End of split % 261.81/56.59 | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | Case 2: % 261.81/56.59 | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | (1688) pv57 = n1 % 261.81/56.59 | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | REF_CLOSE: (27), (144), (155), (1431), (1688) are % 261.81/56.59 | | | | | | | | | | | | | | | | inconsistent by sub-proof #38. % 261.81/56.59 | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | End of split % 261.81/56.59 | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | End of split % 261.81/56.59 | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | Case 2: % 261.81/56.59 | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | (1689) all_74_18 = n0 % 261.81/56.59 | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | REDUCE: (165), (1689) imply: % 261.81/56.59 | | | | | | | | | | | | | | (1690) succ(n0) = pv57 % 261.81/56.59 | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | GROUND_INST: instantiating (28) with n1, pv57, n0, simplifying % 261.81/56.59 | | | | | | | | | | | | | | with (19), (1690) gives: % 261.81/56.59 | | | | | | | | | | | | | | (1691) pv57 = n1 % 261.81/56.59 | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | REDUCE: (1414), (1691) imply: % 261.81/56.59 | | | | | | | | | | | | | | (1692) a_select3(id_ds1_filter, all_74_14, n1) = % 261.81/56.59 | | | | | | | | | | | | | | all_74_12 % 261.81/56.59 | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | REDUCE: (1415), (1691) imply: % 261.81/56.59 | | | | | | | | | | | | | | (1693) a_select3(id_ds1_filter, n1, all_74_14) = % 261.81/56.59 | | | | | | | | | | | | | | all_74_13 % 261.81/56.59 | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | REDUCE: (669), (1691) imply: % 261.81/56.59 | | | | | | | | | | | | | | (1694) succ(n1) = all_74_17 % 261.81/56.59 | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | REDUCE: (678), (1691) imply: % 261.81/56.59 | | | | | | | | | | | | | | (1695) pred(all_74_17) = n1 % 261.81/56.59 | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | REDUCE: (694), (1691) imply: % 261.81/56.59 | | | | | | | | | | | | | | (1696) leq(n1, n1) % 261.81/56.59 | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | REDUCE: (63), (1691) imply: % 261.81/56.59 | | | | | | | | | | | | | | (1697) leq(n0, n1) % 261.81/56.59 | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | GROUND_INST: instantiating (28) with n2, all_74_17, n1, % 261.81/56.59 | | | | | | | | | | | | | | simplifying with (101), (1694) gives: % 261.81/56.59 | | | | | | | | | | | | | | (1698) all_74_17 = n2 % 261.81/56.59 | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | BETA: splitting (1423) gives: % 261.81/56.59 | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | Case 1: % 261.81/56.59 | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | (1699) gt(n4, all_74_14) % 261.81/56.59 | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_14, n4, n3, % 261.81/56.59 | | | | | | | | | | | | | | | simplifying with (67), (136), (147), (1699) gives: % 261.81/56.59 | | | | | | | | | | | | | | | (1700) leq(all_74_14, n3) % 261.81/56.59 | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_14, n3, % 261.81/56.59 | | | | | | | | | | | | | | | simplifying with (67), (129), (1700) gives: % 261.81/56.59 | | | | | | | | | | | | | | | (1701) all_74_14 = n3 | gt(n3, all_74_14) % 261.81/56.59 | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | BETA: splitting (1701) gives: % 261.81/56.59 | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | Case 1: % 261.81/56.59 | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | (1702) gt(n3, all_74_14) % 261.81/56.59 | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_14, n3, n2, % 261.81/56.59 | | | | | | | | | | | | | | | | simplifying with (67), (129), (146), (1702) gives: % 261.81/56.59 | | | | | | | | | | | | | | | | (1703) leq(all_74_14, n2) % 261.81/56.59 | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_14, n2, % 261.81/56.59 | | | | | | | | | | | | | | | | simplifying with (67), (118), (1703) gives: % 261.81/56.59 | | | | | | | | | | | | | | | | (1704) all_74_14 = n2 | gt(n2, all_74_14) % 261.81/56.59 | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | BETA: splitting (1704) gives: % 261.81/56.59 | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | Case 1: % 261.81/56.59 | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | (1705) gt(n2, all_74_14) % 261.81/56.59 | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_14, n2, n1, % 261.81/56.59 | | | | | | | | | | | | | | | | | simplifying with (67), (118), (145), (1705) gives: % 261.81/56.59 | | | | | | | | | | | | | | | | | (1706) leq(all_74_14, n1) % 261.81/56.59 | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (30), (67), (649), (651), (1420), (1692), % 261.81/56.59 | | | | | | | | | | | | | | | | | (1693), (1706) are inconsistent by sub-proof #37. % 261.81/56.59 | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | Case 2: % 261.81/56.59 | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | (1707) all_74_14 = n2 % 261.81/56.59 | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | REDUCE: (1692), (1707) imply: % 261.81/56.59 | | | | | | | | | | | | | | | | | (1708) a_select3(id_ds1_filter, n2, n1) = all_74_12 % 261.81/56.59 | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | REDUCE: (1693), (1707) imply: % 261.81/56.59 | | | | | | | | | | | | | | | | | (1709) a_select3(id_ds1_filter, n1, n2) = all_74_13 % 261.81/56.59 | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | REDUCE: (659), (1707) imply: % 261.81/56.59 | | | | | | | | | | | | | | | | | (1710) leq(n2, n5) % 261.81/56.59 | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | REDUCE: (651), (1707) imply: % 261.81/56.59 | | | | | | | | | | | | | | | | | (1711) leq(n0, n2) % 261.81/56.59 | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (81) with n1, n2, all_74_13, % 261.81/56.59 | | | | | | | | | | | | | | | | | simplifying with (102), (118), (1697), (1709), % 261.81/56.59 | | | | | | | | | | | | | | | | | (1711) gives: % 261.81/56.59 | | | | | | | | | | | | | | | | | (1712) ~ leq(n2, all_74_20) | ~ leq(n1, pv57) | % 261.81/56.59 | | | | | | | | | | | | | | | | | (a_select3(id_ds1_filter, n2, n1) = all_74_13 & % 261.81/56.59 | | | | | | | | | | | | | | | | | $i(all_74_13)) % 261.81/56.59 | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | BETA: splitting (1712) gives: % 261.81/56.59 | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | Case 1: % 261.81/56.59 | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | (1713) ~ leq(n2, all_74_20) % 261.81/56.59 | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | REDUCE: (159), (1713) imply: % 261.81/56.59 | | | | | | | | | | | | | | | | | | (1714) ~ leq(n2, n5) % 261.81/56.59 | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1710), (1714) imply: % 261.81/56.59 | | | | | | | | | | | | | | | | | | (1715) $false % 261.81/56.59 | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | CLOSE: (1715) is inconsistent. % 261.81/56.59 | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | Case 2: % 261.81/56.59 | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | (1716) ~ leq(n1, pv57) | (a_select3(id_ds1_filter, n2, % 261.81/56.59 | | | | | | | | | | | | | | | | | | n1) = all_74_13 & $i(all_74_13)) % 261.81/56.59 | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | BETA: splitting (1716) gives: % 261.81/56.59 | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | Case 1: % 261.81/56.59 | | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | | (1717) ~ leq(n1, pv57) % 261.81/56.59 | | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | | REDUCE: (1691), (1717) imply: % 261.81/56.59 | | | | | | | | | | | | | | | | | | | (1718) ~ leq(n1, n1) % 261.81/56.59 | | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1696), (1718) imply: % 261.81/56.59 | | | | | | | | | | | | | | | | | | | (1719) $false % 261.81/56.59 | | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | | CLOSE: (1719) is inconsistent. % 261.81/56.59 | | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | Case 2: % 261.81/56.59 | | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | | (1720) a_select3(id_ds1_filter, n2, n1) = all_74_13 & % 261.81/56.59 | | | | | | | | | | | | | | | | | | | $i(all_74_13) % 261.81/56.59 | | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | | ALPHA: (1720) implies: % 261.81/56.59 | | | | | | | | | | | | | | | | | | | (1721) a_select3(id_ds1_filter, n2, n1) = all_74_13 % 261.81/56.59 | | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (649), (1708), (1721) are inconsistent by % 261.81/56.59 | | | | | | | | | | | | | | | | | | | sub-proof #36. % 261.81/56.59 | | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | | End of split % 261.81/56.59 | | | | | | | | | | | | | | | | | | % 261.81/56.59 | | | | | | | | | | | | | | | | | End of split % 261.81/56.59 | | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | End of split % 261.81/56.60 | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | Case 2: % 261.81/56.60 | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | (1722) all_74_14 = n3 % 261.81/56.60 | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | REDUCE: (1692), (1722) imply: % 261.81/56.60 | | | | | | | | | | | | | | | | (1723) a_select3(id_ds1_filter, n3, n1) = all_74_12 % 261.81/56.60 | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | REDUCE: (1693), (1722) imply: % 261.81/56.60 | | | | | | | | | | | | | | | | (1724) a_select3(id_ds1_filter, n1, n3) = all_74_13 % 261.81/56.60 | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | REDUCE: (659), (1722) imply: % 261.81/56.60 | | | | | | | | | | | | | | | | (1725) leq(n3, n5) % 261.81/56.60 | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | REDUCE: (651), (1722) imply: % 261.81/56.60 | | | | | | | | | | | | | | | | (1726) leq(n0, n3) % 261.81/56.60 | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (81) with n1, n3, all_74_13, % 261.81/56.60 | | | | | | | | | | | | | | | | simplifying with (102), (129), (1697), (1724), % 261.81/56.60 | | | | | | | | | | | | | | | | (1726) gives: % 261.81/56.60 | | | | | | | | | | | | | | | | (1727) ~ leq(n3, all_74_20) | ~ leq(n1, pv57) | % 261.81/56.60 | | | | | | | | | | | | | | | | (a_select3(id_ds1_filter, n3, n1) = all_74_13 & % 261.81/56.60 | | | | | | | | | | | | | | | | $i(all_74_13)) % 261.81/56.60 | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | BETA: splitting (1727) gives: % 261.81/56.60 | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | Case 1: % 261.81/56.60 | | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | | (1728) ~ leq(n3, all_74_20) % 261.81/56.60 | | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | | REDUCE: (159), (1728) imply: % 261.81/56.60 | | | | | | | | | | | | | | | | | (1729) ~ leq(n3, n5) % 261.81/56.60 | | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | | PRED_UNIFY: (1725), (1729) imply: % 261.81/56.60 | | | | | | | | | | | | | | | | | (1730) $false % 261.81/56.60 | | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | | CLOSE: (1730) is inconsistent. % 261.81/56.60 | | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | Case 2: % 261.81/56.60 | | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | | (1731) ~ leq(n1, pv57) | (a_select3(id_ds1_filter, n3, % 261.81/56.60 | | | | | | | | | | | | | | | | | n1) = all_74_13 & $i(all_74_13)) % 261.81/56.60 | | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | | BETA: splitting (1731) gives: % 261.81/56.60 | | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | | Case 1: % 261.81/56.60 | | | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | | | (1732) ~ leq(n1, pv57) % 261.81/56.60 | | | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | | | REDUCE: (1691), (1732) imply: % 261.81/56.60 | | | | | | | | | | | | | | | | | | (1733) ~ leq(n1, n1) % 261.81/56.60 | | | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1696), (1733) imply: % 261.81/56.60 | | | | | | | | | | | | | | | | | | (1734) $false % 261.81/56.60 | | | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | | | CLOSE: (1734) is inconsistent. % 261.81/56.60 | | | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | | Case 2: % 261.81/56.60 | | | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | | | (1735) a_select3(id_ds1_filter, n3, n1) = all_74_13 & % 261.81/56.60 | | | | | | | | | | | | | | | | | | $i(all_74_13) % 261.81/56.60 | | | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | | | ALPHA: (1735) implies: % 261.81/56.60 | | | | | | | | | | | | | | | | | | (1736) a_select3(id_ds1_filter, n3, n1) = all_74_13 % 261.81/56.60 | | | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (649), (1723), (1736) are inconsistent by % 261.81/56.60 | | | | | | | | | | | | | | | | | | sub-proof #35. % 261.81/56.60 | | | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | | End of split % 261.81/56.60 | | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | End of split % 261.81/56.60 | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | End of split % 261.81/56.60 | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | Case 2: % 261.81/56.60 | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | (1737) all_74_14 = n4 % 261.81/56.60 | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | REDUCE: (1692), (1737) imply: % 261.81/56.60 | | | | | | | | | | | | | | | (1738) a_select3(id_ds1_filter, n4, n1) = all_74_12 % 261.81/56.60 | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | REDUCE: (1693), (1737) imply: % 261.81/56.60 | | | | | | | | | | | | | | | (1739) a_select3(id_ds1_filter, n1, n4) = all_74_13 % 261.81/56.60 | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | REDUCE: (659), (1737) imply: % 261.81/56.60 | | | | | | | | | | | | | | | (1740) leq(n4, n5) % 261.81/56.60 | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | REDUCE: (651), (1737) imply: % 261.81/56.60 | | | | | | | | | | | | | | | (1741) leq(n0, n4) % 261.81/56.60 | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | GROUND_INST: instantiating (81) with n1, n4, all_74_13, % 261.81/56.60 | | | | | | | | | | | | | | | simplifying with (102), (136), (1697), (1739), % 261.81/56.60 | | | | | | | | | | | | | | | (1741) gives: % 261.81/56.60 | | | | | | | | | | | | | | | (1742) ~ leq(n4, all_74_20) | ~ leq(n1, pv57) | % 261.81/56.60 | | | | | | | | | | | | | | | (a_select3(id_ds1_filter, n4, n1) = all_74_13 & % 261.81/56.60 | | | | | | | | | | | | | | | $i(all_74_13)) % 261.81/56.60 | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | BETA: splitting (1742) gives: % 261.81/56.60 | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | Case 1: % 261.81/56.60 | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | (1743) ~ leq(n4, all_74_20) % 261.81/56.60 | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | REDUCE: (159), (1743) imply: % 261.81/56.60 | | | | | | | | | | | | | | | | (1744) ~ leq(n4, n5) % 261.81/56.60 | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | PRED_UNIFY: (1740), (1744) imply: % 261.81/56.60 | | | | | | | | | | | | | | | | (1745) $false % 261.81/56.60 | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | CLOSE: (1745) is inconsistent. % 261.81/56.60 | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | Case 2: % 261.81/56.60 | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | (1746) ~ leq(n1, pv57) | (a_select3(id_ds1_filter, n4, % 261.81/56.60 | | | | | | | | | | | | | | | | n1) = all_74_13 & $i(all_74_13)) % 261.81/56.60 | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | BETA: splitting (1746) gives: % 261.81/56.60 | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | Case 1: % 261.81/56.60 | | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | | (1747) ~ leq(n1, pv57) % 261.81/56.60 | | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | | REDUCE: (1691), (1747) imply: % 261.81/56.60 | | | | | | | | | | | | | | | | | (1748) ~ leq(n1, n1) % 261.81/56.60 | | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | | PRED_UNIFY: (1696), (1748) imply: % 261.81/56.60 | | | | | | | | | | | | | | | | | (1749) $false % 261.81/56.60 | | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | | CLOSE: (1749) is inconsistent. % 261.81/56.60 | | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | Case 2: % 261.81/56.60 | | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | | (1750) a_select3(id_ds1_filter, n4, n1) = all_74_13 & % 261.81/56.60 | | | | | | | | | | | | | | | | | $i(all_74_13) % 261.81/56.60 | | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | | ALPHA: (1750) implies: % 261.81/56.60 | | | | | | | | | | | | | | | | | (1751) a_select3(id_ds1_filter, n4, n1) = all_74_13 % 261.81/56.60 | | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (649), (1738), (1751) are inconsistent by % 261.81/56.60 | | | | | | | | | | | | | | | | | sub-proof #29. % 261.81/56.60 | | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | End of split % 261.81/56.60 | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | End of split % 261.81/56.60 | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | End of split % 261.81/56.60 | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | End of split % 261.81/56.60 | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | End of split % 261.81/56.60 | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | End of split % 261.81/56.60 | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | End of split % 261.81/56.60 | | | | | | | | | | % 261.81/56.60 | | | | | | | | | Case 2: % 261.81/56.60 | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | (1752) all_74_14 = n5 % 261.81/56.60 | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | REDUCE: (1414), (1752) imply: % 261.81/56.60 | | | | | | | | | | (1753) a_select3(id_ds1_filter, n5, pv57) = all_74_12 % 261.81/56.60 | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | REDUCE: (1415), (1752) imply: % 261.81/56.60 | | | | | | | | | | (1754) a_select3(id_ds1_filter, pv57, n5) = all_74_13 % 261.81/56.60 | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | REDUCE: (659), (1752) imply: % 261.81/56.60 | | | | | | | | | | (1755) leq(n5, n5) % 261.81/56.60 | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | REDUCE: (651), (1752) imply: % 261.81/56.60 | | | | | | | | | | (1756) leq(n0, n5) % 261.81/56.60 | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | BETA: splitting (697) gives: % 261.81/56.60 | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | Case 1: % 261.81/56.60 | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | (1757) gt(all_74_18, n0) % 261.81/56.60 | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | BETA: splitting (696) gives: % 261.81/56.60 | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | Case 1: % 261.81/56.60 | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | (1758) all_74_18 = n0 % 261.81/56.60 | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | REF_CLOSE: (154), (1757), (1758), (irreflexivity_gt) are % 261.81/56.60 | | | | | | | | | | | | inconsistent by sub-proof #39. % 261.81/56.60 | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | Case 2: % 261.81/56.60 | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | (1759) ~ (all_74_18 = n0) % 261.81/56.60 | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | BETA: splitting (699) gives: % 261.81/56.60 | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | Case 1: % 261.81/56.60 | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | (1760) gt(pv57, n1) % 261.81/56.60 | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | BETA: splitting (703) gives: % 261.81/56.60 | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | Case 1: % 261.81/56.60 | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | (1761) gt(n4, pv57) % 261.81/56.60 | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | BETA: splitting (695) gives: % 261.81/56.60 | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | Case 1: % 261.81/56.60 | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | (1762) all_74_18 = n0 % 261.81/56.60 | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | REDUCE: (1759), (1762) imply: % 261.81/56.60 | | | | | | | | | | | | | | | (1763) $false % 261.81/56.60 | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | CLOSE: (1763) is inconsistent. % 261.81/56.60 | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | Case 2: % 261.81/56.60 | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with pv57, n4, n3, simplifying % 261.81/56.60 | | | | | | | | | | | | | | | with (24), (136), (147), (1761) gives: % 261.81/56.60 | | | | | | | | | | | | | | | (1764) leq(pv57, n3) % 261.81/56.60 | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with n1, pv57, all_74_18, % 261.81/56.60 | | | | | | | | | | | | | | | simplifying with (24), (102), (155), (1760) gives: % 261.81/56.60 | | | | | | | | | | | | | | | (1765) leq(n1, all_74_18) % 261.81/56.60 | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | BETA: splitting (707) gives: % 261.81/56.60 | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | Case 1: % 261.81/56.60 | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with n1, all_74_18, n2, pv57, % 261.81/56.60 | | | | | | | | | | | | | | | | simplifying with (101), (102), (154), (165), % 261.81/56.60 | | | | | | | | | | | | | | | | (1765) gives: % 261.81/56.60 | | | | | | | | | | | | | | | | (1766) leq(n2, pv57) % 261.81/56.60 | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with n1, all_74_18, % 261.81/56.60 | | | | | | | | | | | | | | | | simplifying with (102), (154), (1765) gives: % 261.81/56.60 | | | | | | | | | | | | | | | | (1767) all_74_18 = n1 | gt(all_74_18, n1) % 261.81/56.60 | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (15) with pv57, simplifying with % 261.81/56.60 | | | | | | | | | | | | | | | | (24), (63), (1764) gives: % 261.81/56.60 | | | | | | | | | | | | | | | | (1768) pv57 = n3 | pv57 = n2 | pv57 = n1 | pv57 = n0 % 261.81/56.60 | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with pv57, n3, simplifying % 261.81/56.60 | | | | | | | | | | | | | | | | with (24), (129), (1764) gives: % 261.81/56.60 | | | | | | | | | | | | | | | | (1769) pv57 = n3 | gt(n3, pv57) % 261.81/56.60 | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | BETA: splitting (706) gives: % 261.81/56.60 | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | Case 1: % 261.81/56.60 | | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | | (1770) pv57 = n1 % 261.81/56.60 | | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | | REF_CLOSE: (1416), (1760), (1770) are inconsistent by % 261.81/56.60 | | | | | | | | | | | | | | | | | sub-proof #20. % 261.81/56.60 | | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | Case 2: % 261.81/56.60 | | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | | (1771) ~ (pv57 = n1) % 261.81/56.60 | | | | | | | | | | | | | | | | | (1772) pv57 = n5 | pv57 = n4 | pv57 = n3 | pv57 = n2 % 261.81/56.60 | | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | | BETA: splitting (1767) gives: % 261.81/56.60 | | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | | Case 1: % 261.81/56.60 | | | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | | | (1773) gt(all_74_18, n1) % 261.81/56.60 | | | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | | | BETA: splitting (1769) gives: % 261.81/56.60 | | | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | | | Case 1: % 261.81/56.60 | | | | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | | | | (1774) gt(n3, pv57) % 261.81/56.60 | | | | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (24), (27), (145), (154), (155), (705), (1768), % 261.81/56.60 | | | | | | | | | | | | | | | | | | | (1771), (1772), (1773), (1774), (irreflexivity_gt) % 261.81/56.60 | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #34. % 261.81/56.60 | | | | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | | | Case 2: % 261.81/56.60 | | | | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | | | | (1775) pv57 = n3 % 261.81/56.60 | | | | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | | | | REDUCE: (1754), (1775) imply: % 261.81/56.60 | | | | | | | | | | | | | | | | | | | (1776) a_select3(id_ds1_filter, n3, n5) = all_74_13 % 261.81/56.60 | | | | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | | | | REDUCE: (1753), (1775) imply: % 261.81/56.60 | | | | | | | | | | | | | | | | | | | (1777) a_select3(id_ds1_filter, n5, n3) = all_74_12 % 261.81/56.60 | | | | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | | | | REDUCE: (1764), (1775) imply: % 261.81/56.60 | | | | | | | | | | | | | | | | | | | (1778) leq(n3, n3) % 261.81/56.60 | | | | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | | | | REDUCE: (63), (1775) imply: % 261.81/56.60 | | | | | | | | | | | | | | | | | | | (1779) leq(n0, n3) % 261.81/56.60 | | | | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (81) with n3, n5, all_74_13, % 261.81/56.60 | | | | | | | | | | | | | | | | | | | simplifying with (129), (139), (1756), (1776), % 261.81/56.60 | | | | | | | | | | | | | | | | | | | (1779) gives: % 261.81/56.60 | | | | | | | | | | | | | | | | | | | (1780) ~ leq(n5, all_74_20) | ~ leq(n3, pv57) | % 261.81/56.60 | | | | | | | | | | | | | | | | | | | (a_select3(id_ds1_filter, n5, n3) = all_74_13 & % 261.81/56.60 | | | | | | | | | | | | | | | | | | | $i(all_74_13)) % 261.81/56.60 | | | | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | | | | BETA: splitting (1780) gives: % 261.81/56.60 | | | | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | | | | Case 1: % 261.81/56.60 | | | | | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | | | | | (1781) ~ leq(n5, all_74_20) % 261.81/56.60 | | | | | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | | | | | REDUCE: (159), (1781) imply: % 261.81/56.60 | | | | | | | | | | | | | | | | | | | | (1782) ~ leq(n5, n5) % 261.81/56.60 | | | | | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1755), (1782) imply: % 261.81/56.60 | | | | | | | | | | | | | | | | | | | | (1783) $false % 261.81/56.60 | | | | | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | | | | | CLOSE: (1783) is inconsistent. % 261.81/56.60 | | | | | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | | | | Case 2: % 261.81/56.60 | | | | | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | | | | | (1784) ~ leq(n3, pv57) | (a_select3(id_ds1_filter, n5, % 261.81/56.60 | | | | | | | | | | | | | | | | | | | | n3) = all_74_13 & $i(all_74_13)) % 261.81/56.60 | | | | | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | | | | | BETA: splitting (1784) gives: % 261.81/56.60 | | | | | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | | | | | Case 1: % 261.81/56.60 | | | | | | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | | | | | | (1785) ~ leq(n3, pv57) % 261.81/56.60 | | | | | | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | | | | | | REDUCE: (1775), (1785) imply: % 261.81/56.60 | | | | | | | | | | | | | | | | | | | | | (1786) ~ leq(n3, n3) % 261.81/56.60 | | | | | | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1778), (1786) imply: % 261.81/56.60 | | | | | | | | | | | | | | | | | | | | | (1787) $false % 261.81/56.60 | | | | | | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | | | | | | CLOSE: (1787) is inconsistent. % 261.81/56.60 | | | | | | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | | | | | Case 2: % 261.81/56.60 | | | | | | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | | | | | | (1788) a_select3(id_ds1_filter, n5, n3) = all_74_13 & % 261.81/56.60 | | | | | | | | | | | | | | | | | | | | | $i(all_74_13) % 261.81/56.60 | | | | | | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | | | | | | ALPHA: (1788) implies: % 261.81/56.60 | | | | | | | | | | | | | | | | | | | | | (1789) a_select3(id_ds1_filter, n5, n3) = all_74_13 % 261.81/56.60 | | | | | | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (649), (1777), (1789) are inconsistent by % 261.81/56.60 | | | | | | | | | | | | | | | | | | | | | sub-proof #18. % 261.81/56.60 | | | | | | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | | | | | End of split % 261.81/56.60 | | | | | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | | | | End of split % 261.81/56.60 | | | | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | | | End of split % 261.81/56.60 | | | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | | Case 2: % 261.81/56.60 | | | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | | | (1790) all_74_18 = n1 % 261.81/56.60 | | | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | | | REDUCE: (165), (1790) imply: % 261.81/56.60 | | | | | | | | | | | | | | | | | | (1791) succ(n1) = pv57 % 261.81/56.60 | | | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (28) with n2, pv57, n1, simplifying % 261.81/56.60 | | | | | | | | | | | | | | | | | | with (101), (1791) gives: % 261.81/56.60 | | | | | | | | | | | | | | | | | | (1792) pv57 = n2 % 261.81/56.60 | | | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | | | REDUCE: (1754), (1792) imply: % 261.81/56.60 | | | | | | | | | | | | | | | | | | (1793) a_select3(id_ds1_filter, n2, n5) = all_74_13 % 261.81/56.60 | | | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | | | REDUCE: (1753), (1792) imply: % 261.81/56.60 | | | | | | | | | | | | | | | | | | (1794) a_select3(id_ds1_filter, n5, n2) = all_74_12 % 261.81/56.60 | | | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | | | REDUCE: (1766), (1792) imply: % 261.81/56.60 | | | | | | | | | | | | | | | | | | (1795) leq(n2, n2) % 261.81/56.60 | | | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | | | REDUCE: (63), (1792) imply: % 261.81/56.60 | | | | | | | | | | | | | | | | | | (1796) leq(n0, n2) % 261.81/56.60 | | | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (81) with n2, n5, all_74_13, % 261.81/56.60 | | | | | | | | | | | | | | | | | | simplifying with (118), (139), (1756), (1793), % 261.81/56.60 | | | | | | | | | | | | | | | | | | (1796) gives: % 261.81/56.60 | | | | | | | | | | | | | | | | | | (1797) ~ leq(n5, all_74_20) | ~ leq(n2, pv57) | % 261.81/56.60 | | | | | | | | | | | | | | | | | | (a_select3(id_ds1_filter, n5, n2) = all_74_13 & % 261.81/56.60 | | | | | | | | | | | | | | | | | | $i(all_74_13)) % 261.81/56.60 | | | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | | | BETA: splitting (1797) gives: % 261.81/56.60 | | | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | | | Case 1: % 261.81/56.60 | | | | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | | | | (1798) ~ leq(n5, all_74_20) % 261.81/56.60 | | | | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | | | | REDUCE: (159), (1798) imply: % 261.81/56.60 | | | | | | | | | | | | | | | | | | | (1799) ~ leq(n5, n5) % 261.81/56.60 | | | | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1755), (1799) imply: % 261.81/56.60 | | | | | | | | | | | | | | | | | | | (1800) $false % 261.81/56.60 | | | | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | | | | CLOSE: (1800) is inconsistent. % 261.81/56.60 | | | | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | | | Case 2: % 261.81/56.60 | | | | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | | | | (1801) ~ leq(n2, pv57) | (a_select3(id_ds1_filter, n5, % 261.81/56.60 | | | | | | | | | | | | | | | | | | | n2) = all_74_13 & $i(all_74_13)) % 261.81/56.60 | | | | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | | | | BETA: splitting (1801) gives: % 261.81/56.60 | | | | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | | | | Case 1: % 261.81/56.60 | | | | | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | | | | | (1802) ~ leq(n2, pv57) % 261.81/56.60 | | | | | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | | | | | REDUCE: (1792), (1802) imply: % 261.81/56.60 | | | | | | | | | | | | | | | | | | | | (1803) ~ leq(n2, n2) % 261.81/56.60 | | | | | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1795), (1803) imply: % 261.81/56.60 | | | | | | | | | | | | | | | | | | | | (1804) $false % 261.81/56.60 | | | | | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | | | | | CLOSE: (1804) is inconsistent. % 261.81/56.60 | | | | | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | | | | Case 2: % 261.81/56.60 | | | | | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | | | | | (1805) a_select3(id_ds1_filter, n5, n2) = all_74_13 & % 261.81/56.60 | | | | | | | | | | | | | | | | | | | | $i(all_74_13) % 261.81/56.60 | | | | | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | | | | | ALPHA: (1805) implies: % 261.81/56.60 | | | | | | | | | | | | | | | | | | | | (1806) a_select3(id_ds1_filter, n5, n2) = all_74_13 % 261.81/56.60 | | | | | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (649), (1794), (1806) are inconsistent by % 261.81/56.60 | | | | | | | | | | | | | | | | | | | | sub-proof #22. % 261.81/56.60 | | | | | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | | | | End of split % 261.81/56.60 | | | | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | | | End of split % 261.81/56.60 | | | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | | End of split % 261.81/56.60 | | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | End of split % 261.81/56.60 | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | Case 2: % 261.81/56.60 | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | (1807) all_74_17 = n2 % 261.81/56.60 | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | REDUCE: (678), (1807) imply: % 261.81/56.60 | | | | | | | | | | | | | | | | (1808) pred(n2) = pv57 % 261.81/56.60 | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (27) with n1, pv57, n2, simplifying % 261.81/56.60 | | | | | | | | | | | | | | | | with (145), (1808) gives: % 261.81/56.60 | | | | | | | | | | | | | | | | (1809) pv57 = n1 % 261.81/56.60 | | | | | | | | | | | | | | | | % 261.81/56.60 | | | | | | | | | | | | | | | | REDUCE: (1760), (1809) imply: % 261.81/56.60 | | | | | | | | | | | | | | | | (1810) gt(n1, n1) % 261.81/56.60 | | | | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | | | | REDUCE: (1416), (1809) imply: % 261.81/56.61 | | | | | | | | | | | | | | | | (1811) ~ gt(n1, n1) % 261.81/56.61 | | | | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | | | | PRED_UNIFY: (1810), (1811) imply: % 261.81/56.61 | | | | | | | | | | | | | | | | (1812) $false % 261.81/56.61 | | | | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | | | | CLOSE: (1812) is inconsistent. % 261.81/56.61 | | | | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | | | End of split % 261.81/56.61 | | | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | | End of split % 261.81/56.61 | | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | Case 2: % 261.81/56.61 | | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | | (1813) pv57 = n4 % 261.81/56.61 | | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | | REDUCE: (1754), (1813) imply: % 261.81/56.61 | | | | | | | | | | | | | | (1814) a_select3(id_ds1_filter, n4, n5) = all_74_13 % 261.81/56.61 | | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | | REDUCE: (1753), (1813) imply: % 261.81/56.61 | | | | | | | | | | | | | | (1815) a_select3(id_ds1_filter, n5, n4) = all_74_12 % 261.81/56.61 | | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | | REDUCE: (669), (1813) imply: % 261.81/56.61 | | | | | | | | | | | | | | (1816) succ(n4) = all_74_17 % 261.81/56.61 | | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | | REDUCE: (693), (1813) imply: % 261.81/56.61 | | | | | | | | | | | | | | (1817) leq(n4, n4) % 261.81/56.61 | | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | | REDUCE: (63), (1813) imply: % 261.81/56.61 | | | | | | | | | | | | | | (1818) leq(n0, n4) % 261.81/56.61 | | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | | GROUND_INST: instantiating (28) with n5, all_74_17, n4, % 261.81/56.61 | | | | | | | | | | | | | | simplifying with (135), (1816) gives: % 261.81/56.61 | | | | | | | | | | | | | | (1819) all_74_17 = n5 % 261.81/56.61 | | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | | GROUND_INST: instantiating (81) with n4, n5, all_74_13, % 261.81/56.61 | | | | | | | | | | | | | | simplifying with (136), (139), (1756), (1814), % 261.81/56.61 | | | | | | | | | | | | | | (1818) gives: % 261.81/56.61 | | | | | | | | | | | | | | (1820) ~ leq(n5, all_74_20) | ~ leq(n4, pv57) | % 261.81/56.61 | | | | | | | | | | | | | | (a_select3(id_ds1_filter, n5, n4) = all_74_13 & % 261.81/56.61 | | | | | | | | | | | | | | $i(all_74_13)) % 261.81/56.61 | | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | | BETA: splitting (1820) gives: % 261.81/56.61 | | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | | Case 1: % 261.81/56.61 | | | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | | | (1821) ~ leq(n5, all_74_20) % 261.81/56.61 | | | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | | | REDUCE: (159), (1821) imply: % 261.81/56.61 | | | | | | | | | | | | | | | (1822) ~ leq(n5, n5) % 261.81/56.61 | | | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | | | PRED_UNIFY: (1755), (1822) imply: % 261.81/56.61 | | | | | | | | | | | | | | | (1823) $false % 261.81/56.61 | | | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | | | CLOSE: (1823) is inconsistent. % 261.81/56.61 | | | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | | Case 2: % 261.81/56.61 | | | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | | | (1824) ~ leq(n4, pv57) | (a_select3(id_ds1_filter, n5, % 261.81/56.61 | | | | | | | | | | | | | | | n4) = all_74_13 & $i(all_74_13)) % 261.81/56.61 | | | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | | | BETA: splitting (1824) gives: % 261.81/56.61 | | | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | | | Case 1: % 261.81/56.61 | | | | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | | | | (1825) ~ leq(n4, pv57) % 261.81/56.61 | | | | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | | | | REDUCE: (1813), (1825) imply: % 261.81/56.61 | | | | | | | | | | | | | | | | (1826) ~ leq(n4, n4) % 261.81/56.61 | | | | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | | | | PRED_UNIFY: (1817), (1826) imply: % 261.81/56.61 | | | | | | | | | | | | | | | | (1827) $false % 261.81/56.61 | | | | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | | | | CLOSE: (1827) is inconsistent. % 261.81/56.61 | | | | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | | | Case 2: % 261.81/56.61 | | | | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | | | | (1828) a_select3(id_ds1_filter, n5, n4) = all_74_13 & % 261.81/56.61 | | | | | | | | | | | | | | | | $i(all_74_13) % 261.81/56.61 | | | | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | | | | ALPHA: (1828) implies: % 261.81/56.61 | | | | | | | | | | | | | | | | (1829) a_select3(id_ds1_filter, n5, n4) = all_74_13 % 261.81/56.61 | | | | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | | | | REF_CLOSE: (30), (649), (1815), (1829) are inconsistent by % 261.81/56.61 | | | | | | | | | | | | | | | | sub-proof #17. % 261.81/56.61 | | | | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | | | End of split % 261.81/56.61 | | | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | | End of split % 261.81/56.61 | | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | End of split % 261.81/56.61 | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | Case 2: % 261.81/56.61 | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | (1830) pv57 = n1 % 261.81/56.61 | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | REF_CLOSE: (27), (144), (155), (1759), (1830) are % 261.81/56.61 | | | | | | | | | | | | | inconsistent by sub-proof #38. % 261.81/56.61 | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | End of split % 261.81/56.61 | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | End of split % 261.81/56.61 | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | Case 2: % 261.81/56.61 | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | (1831) all_74_18 = n0 % 261.81/56.61 | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | REDUCE: (165), (1831) imply: % 261.81/56.61 | | | | | | | | | | | (1832) succ(n0) = pv57 % 261.81/56.61 | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | GROUND_INST: instantiating (28) with n1, pv57, n0, simplifying % 261.81/56.61 | | | | | | | | | | | with (19), (1832) gives: % 261.81/56.61 | | | | | | | | | | | (1833) pv57 = n1 % 261.81/56.61 | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | REDUCE: (1754), (1833) imply: % 261.81/56.61 | | | | | | | | | | | (1834) a_select3(id_ds1_filter, n1, n5) = all_74_13 % 261.81/56.61 | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | REDUCE: (1753), (1833) imply: % 261.81/56.61 | | | | | | | | | | | (1835) a_select3(id_ds1_filter, n5, n1) = all_74_12 % 261.81/56.61 | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | REDUCE: (694), (1833) imply: % 261.81/56.61 | | | | | | | | | | | (1836) leq(n1, n1) % 261.81/56.61 | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | REDUCE: (63), (1833) imply: % 261.81/56.61 | | | | | | | | | | | (1837) leq(n0, n1) % 261.81/56.61 | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | GROUND_INST: instantiating (81) with n1, n5, all_74_13, % 261.81/56.61 | | | | | | | | | | | simplifying with (102), (139), (1756), (1834), % 261.81/56.61 | | | | | | | | | | | (1837) gives: % 261.81/56.61 | | | | | | | | | | | (1838) ~ leq(n5, all_74_20) | ~ leq(n1, pv57) | % 261.81/56.61 | | | | | | | | | | | (a_select3(id_ds1_filter, n5, n1) = all_74_13 & % 261.81/56.61 | | | | | | | | | | | $i(all_74_13)) % 261.81/56.61 | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | BETA: splitting (1838) gives: % 261.81/56.61 | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | Case 1: % 261.81/56.61 | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | (1839) ~ leq(n5, all_74_20) % 261.81/56.61 | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | REDUCE: (159), (1839) imply: % 261.81/56.61 | | | | | | | | | | | | (1840) ~ leq(n5, n5) % 261.81/56.61 | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | PRED_UNIFY: (1755), (1840) imply: % 261.81/56.61 | | | | | | | | | | | | (1841) $false % 261.81/56.61 | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | CLOSE: (1841) is inconsistent. % 261.81/56.61 | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | Case 2: % 261.81/56.61 | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | (1842) ~ leq(n1, pv57) | (a_select3(id_ds1_filter, n5, % 261.81/56.61 | | | | | | | | | | | | n1) = all_74_13 & $i(all_74_13)) % 261.81/56.61 | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | BETA: splitting (1842) gives: % 261.81/56.61 | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | Case 1: % 261.81/56.61 | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | (1843) ~ leq(n1, pv57) % 261.81/56.61 | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | REDUCE: (1833), (1843) imply: % 261.81/56.61 | | | | | | | | | | | | | (1844) ~ leq(n1, n1) % 261.81/56.61 | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | PRED_UNIFY: (1836), (1844) imply: % 261.81/56.61 | | | | | | | | | | | | | (1845) $false % 261.81/56.61 | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | CLOSE: (1845) is inconsistent. % 261.81/56.61 | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | Case 2: % 261.81/56.61 | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | (1846) a_select3(id_ds1_filter, n5, n1) = all_74_13 & % 261.81/56.61 | | | | | | | | | | | | | $i(all_74_13) % 261.81/56.61 | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | ALPHA: (1846) implies: % 261.81/56.61 | | | | | | | | | | | | | (1847) a_select3(id_ds1_filter, n5, n1) = all_74_13 % 261.81/56.61 | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | REF_CLOSE: (30), (649), (1835), (1847) are inconsistent by % 261.81/56.61 | | | | | | | | | | | | | sub-proof #23. % 261.81/56.61 | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | End of split % 261.81/56.61 | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | End of split % 261.81/56.61 | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | End of split % 261.81/56.61 | | | | | | | | | | % 261.81/56.61 | | | | | | | | | End of split % 261.81/56.61 | | | | | | | | | % 261.81/56.61 | | | | | | | | End of split % 261.81/56.61 | | | | | | | | % 261.81/56.61 | | | | | | | Case 2: % 261.81/56.61 | | | | | | | | % 261.81/56.61 | | | | | | | | (1848) all_74_15 = n0 % 261.81/56.61 | | | | | | | | (1849) ~ gt(all_74_15, n0) % 261.81/56.61 | | | | | | | | % 261.81/56.61 | | | | | | | | REDUCE: (656), (1848) imply: % 261.81/56.61 | | | | | | | | (1850) a_select3(id_ds1_filter, all_74_14, n0) = all_74_12 % 261.81/56.61 | | | | | | | | % 261.81/56.61 | | | | | | | | REDUCE: (655), (1848) imply: % 261.81/56.61 | | | | | | | | (1851) a_select3(id_ds1_filter, n0, all_74_14) = all_74_13 % 261.81/56.61 | | | | | | | | % 261.81/56.61 | | | | | | | | REDUCE: (650), (1848) imply: % 261.81/56.61 | | | | | | | | (1852) leq(n0, n0) % 261.81/56.61 | | | | | | | | % 261.81/56.61 | | | | | | | | REDUCE: (1848), (1849) imply: % 261.81/56.61 | | | | | | | | (1853) ~ gt(n0, n0) % 261.81/56.61 | | | | | | | | % 261.81/56.61 | | | | | | | | BETA: splitting (666) gives: % 261.81/56.61 | | | | | | | | % 261.81/56.61 | | | | | | | | Case 1: % 261.81/56.61 | | | | | | | | | % 261.81/56.61 | | | | | | | | | (1854) gt(n5, all_74_14) % 261.81/56.61 | | | | | | | | | % 261.81/56.61 | | | | | | | | | GROUND_INST: instantiating (1) with all_74_14, n5, n4, % 261.81/56.61 | | | | | | | | | simplifying with (67), (139), (148), (1854) gives: % 261.81/56.61 | | | | | | | | | (1855) leq(all_74_14, n4) % 261.81/56.61 | | | | | | | | | % 261.81/56.61 | | | | | | | | | BETA: splitting (665) gives: % 261.81/56.61 | | | | | | | | | % 261.81/56.61 | | | | | | | | | Case 1: % 261.81/56.61 | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | (1856) all_74_14 = n0 % 261.81/56.61 | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | REDUCE: (711), (1856) imply: % 261.81/56.61 | | | | | | | | | | (1857) gt(n0, n0) % 261.81/56.61 | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | PRED_UNIFY: (1853), (1857) imply: % 261.81/56.61 | | | | | | | | | | (1858) $false % 261.81/56.61 | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | CLOSE: (1858) is inconsistent. % 261.81/56.61 | | | | | | | | | | % 261.81/56.61 | | | | | | | | | Case 2: % 261.81/56.61 | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | (1859) ~ (all_74_14 = n0) % 261.81/56.61 | | | | | | | | | | (1860) all_74_14 = n5 | all_74_14 = n4 | all_74_14 = n3 | % 261.81/56.61 | | | | | | | | | | all_74_14 = n2 | all_74_14 = n1 % 261.81/56.61 | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_14, n4, % 261.81/56.61 | | | | | | | | | | simplifying with (67), (136), (1855) gives: % 261.81/56.61 | | | | | | | | | | (1861) all_74_14 = n4 | gt(n4, all_74_14) % 261.81/56.61 | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | BETA: splitting (697) gives: % 261.81/56.61 | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | Case 1: % 261.81/56.61 | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | (1862) gt(all_74_18, n0) % 261.81/56.61 | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | BETA: splitting (699) gives: % 261.81/56.61 | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | Case 1: % 261.81/56.61 | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | (1863) gt(pv57, n1) % 261.81/56.61 | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | GROUND_INST: instantiating (1) with n1, pv57, all_74_18, % 261.81/56.61 | | | | | | | | | | | | simplifying with (24), (102), (155), (1863) gives: % 261.81/56.61 | | | | | | | | | | | | (1864) leq(n1, all_74_18) % 261.81/56.61 | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | BETA: splitting (703) gives: % 261.81/56.61 | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | Case 1: % 261.81/56.61 | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | (1865) gt(n4, pv57) % 261.81/56.61 | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | GROUND_INST: instantiating (1) with pv57, n4, n3, simplifying % 261.81/56.61 | | | | | | | | | | | | | with (24), (136), (147), (1865) gives: % 261.81/56.61 | | | | | | | | | | | | | (1866) leq(pv57, n3) % 261.81/56.61 | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with n1, all_74_18, % 261.81/56.61 | | | | | | | | | | | | | simplifying with (102), (154), (1864) gives: % 261.81/56.61 | | | | | | | | | | | | | (1867) all_74_18 = n1 | gt(all_74_18, n1) % 261.81/56.61 | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | BETA: splitting (708) gives: % 261.81/56.61 | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | Case 1: % 261.81/56.61 | | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | | GROUND_INST: instantiating (15) with pv57, simplifying with % 261.81/56.61 | | | | | | | | | | | | | | (24), (63), (1866) gives: % 261.81/56.61 | | | | | | | | | | | | | | (1868) pv57 = n3 | pv57 = n2 | pv57 = n1 | pv57 = n0 % 261.81/56.61 | | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with pv57, n3, simplifying % 261.81/56.61 | | | | | | | | | | | | | | with (24), (129), (1866) gives: % 261.81/56.61 | | | | | | | | | | | | | | (1869) pv57 = n3 | gt(n3, pv57) % 261.81/56.61 | | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | | BETA: splitting (706) gives: % 261.81/56.61 | | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | | Case 1: % 261.81/56.61 | | | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | | | (1870) pv57 = n1 % 261.81/56.61 | | | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | | | REF_CLOSE: (27), (144), (155), (1853), (1862), (1870) are % 261.81/56.61 | | | | | | | | | | | | | | | inconsistent by sub-proof #75. % 261.81/56.61 | | | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | | Case 2: % 261.81/56.61 | | | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | | | (1871) ~ (pv57 = n1) % 261.81/56.61 | | | | | | | | | | | | | | | (1872) pv57 = n5 | pv57 = n4 | pv57 = n3 | pv57 = n2 % 261.81/56.61 | | | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | | | BETA: splitting (1861) gives: % 261.81/56.61 | | | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | | | Case 1: % 261.81/56.61 | | | | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | | | | (1873) gt(n4, all_74_14) % 261.81/56.61 | | | | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_14, n4, n3, % 261.81/56.61 | | | | | | | | | | | | | | | | simplifying with (67), (136), (147), (1873) gives: % 261.81/56.61 | | | | | | | | | | | | | | | | (1874) leq(all_74_14, n3) % 261.81/56.61 | | | | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | | | | BETA: splitting (1860) gives: % 261.81/56.61 | | | | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | | | | Case 1: % 261.81/56.61 | | | | | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | | | | | (1875) all_74_14 = n5 % 261.81/56.61 | | | | | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | | | | | REDUCE: (1854), (1875) imply: % 261.81/56.61 | | | | | | | | | | | | | | | | | (1876) gt(n5, n5) % 261.81/56.61 | | | | | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (irreflexivity_gt) with n5, % 261.81/56.61 | | | | | | | | | | | | | | | | | simplifying with (139), (1876) gives: % 261.81/56.61 | | | | | | | | | | | | | | | | | (1877) $false % 261.81/56.61 | | | | | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | | | | | CLOSE: (1877) is inconsistent. % 261.81/56.61 | | | | | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | | | | Case 2: % 261.81/56.61 | | | | | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_14, n3, % 261.81/56.61 | | | | | | | | | | | | | | | | | simplifying with (67), (129), (1874) gives: % 261.81/56.61 | | | | | | | | | | | | | | | | | (1878) all_74_14 = n3 | gt(n3, all_74_14) % 261.81/56.61 | | | | | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | | | | | BETA: splitting (1867) gives: % 261.81/56.61 | | | | | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | | | | | Case 1: % 261.81/56.61 | | | | | | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | | | | | | (1879) gt(all_74_18, n1) % 261.81/56.61 | | | | | | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | | | | | | BETA: splitting (1869) gives: % 261.81/56.61 | | | | | | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | | | | | | Case 1: % 261.81/56.61 | | | | | | | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | | | | | | | (1880) gt(n3, pv57) % 261.81/56.61 | | | | | | | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (24), (27), (145), (154), (155), (705), (1868), % 261.81/56.61 | | | | | | | | | | | | | | | | | | | (1871), (1872), (1879), (1880), (irreflexivity_gt) % 261.81/56.61 | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #34. % 261.81/56.61 | | | | | | | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | | | | | | Case 2: % 261.81/56.61 | | | | | | | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | | | | | | | (1881) pv57 = n3 % 261.81/56.61 | | | | | | | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | | | | | | | REDUCE: (75), (1881) imply: % 261.81/56.61 | | | | | | | | | | | | | | | | | | | (1882) minus(n3, n1) = all_74_18 % 261.81/56.61 | | | | | | | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | | | | | | | REDUCE: (155), (1881) imply: % 261.81/56.61 | | | | | | | | | | | | | | | | | | | (1883) pred(n3) = all_74_18 % 261.81/56.61 | | | | | | | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | | | | | | | REDUCE: (63), (1881) imply: % 261.81/56.61 | | | | | | | | | | | | | | | | | | | (1884) leq(n0, n3) % 261.81/56.61 | | | | | | | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (29) with n2, all_74_18, n1, n3, % 261.81/56.61 | | | | | | | | | | | | | | | | | | | simplifying with (161), (1882) gives: % 261.81/56.61 | | | | | | | | | | | | | | | | | | | (1885) all_74_18 = n2 % 261.81/56.61 | | | | | | | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | | | | | | | REDUCE: (690), (1885) imply: % 261.81/56.61 | | | | | | | | | | | | | | | | | | | (1886) leq(n0, n2) % 261.81/56.61 | | | | | | | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | | | | | | | BETA: splitting (1878) gives: % 261.81/56.61 | | | | | | | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | | | | | | | Case 1: % 261.81/56.61 | | | | | | | | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | | | | | | | | (1887) gt(n3, all_74_14) % 261.81/56.61 | | | | | | | | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_14, n3, n2, % 261.81/56.61 | | | | | | | | | | | | | | | | | | | | simplifying with (67), (129), (146), (1887) gives: % 261.81/56.61 | | | | | | | | | | | | | | | | | | | | (1888) leq(all_74_14, n2) % 261.81/56.61 | | | | | | | | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_14, n2, % 261.81/56.61 | | | | | | | | | | | | | | | | | | | | simplifying with (67), (118), (1888) gives: % 261.81/56.61 | | | | | | | | | | | | | | | | | | | | (1889) all_74_14 = n2 | gt(n2, all_74_14) % 261.81/56.61 | | | | | | | | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | | | | | | | | BETA: splitting (1889) gives: % 261.81/56.61 | | | | | | | | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | | | | | | | | Case 1: % 261.81/56.61 | | | | | | | | | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | | | | | | | | | (1890) gt(n2, all_74_14) % 261.81/56.61 | | | | | | | | | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_14, n2, n1, % 261.81/56.61 | | | | | | | | | | | | | | | | | | | | | simplifying with (67), (118), (145), (1890) gives: % 261.81/56.61 | | | | | | | | | | | | | | | | | | | | | (1891) leq(all_74_14, n1) % 261.81/56.61 | | | | | | | | | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_74_14, simplifying % 261.81/56.61 | | | | | | | | | | | | | | | | | | | | | with (67), (651), (1891) gives: % 261.81/56.61 | | | | | | | | | | | | | | | | | | | | | (1892) all_74_14 = n1 | all_74_14 = n0 % 261.81/56.61 | | | | | | | | | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1892) gives: % 261.81/56.61 | | | | | | | | | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.81/56.61 | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | | | | | | | | | | (1893) all_74_14 = n0 % 261.81/56.61 | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1859), (1893) imply: % 261.81/56.61 | | | | | | | | | | | | | | | | | | | | | | (1894) $false % 261.81/56.61 | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1894) is inconsistent. % 261.81/56.61 | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.81/56.61 | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | | | | | | | | | | (1895) all_74_14 = n1 % 261.81/56.61 | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1850), (1895) imply: % 261.81/56.61 | | | | | | | | | | | | | | | | | | | | | | (1896) a_select3(id_ds1_filter, n1, n0) = all_74_12 % 261.81/56.61 | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1851), (1895) imply: % 261.81/56.61 | | | | | | | | | | | | | | | | | | | | | | (1897) a_select3(id_ds1_filter, n0, n1) = all_74_13 % 261.81/56.61 | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (659), (1895) imply: % 261.81/56.61 | | | | | | | | | | | | | | | | | | | | | | (1898) leq(n1, n5) % 261.81/56.61 | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (651), (1895) imply: % 261.81/56.61 | | | | | | | | | | | | | | | | | | | | | | (1899) leq(n0, n1) % 261.81/56.61 | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.61 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (81) with n0, n1, all_74_13, % 261.81/56.61 | | | | | | | | | | | | | | | | | | | | | | simplifying with (22), (102), (1852), (1897), % 261.81/56.61 | | | | | | | | | | | | | | | | | | | | | | (1899) gives: % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | | (1900) ~ leq(n1, all_74_20) | ~ leq(n0, pv57) | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | | (a_select3(id_ds1_filter, n1, n0) = all_74_13 & % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | | $i(all_74_13)) % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1900) gives: % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | | | (1901) ~ leq(n0, pv57) % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1881), (1901) imply: % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | | | (1902) ~ leq(n0, n3) % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1884), (1902) imply: % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | | | (1903) $false % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1903) is inconsistent. % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | | | (1904) ~ leq(n1, all_74_20) | (a_select3(id_ds1_filter, % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | | | n1, n0) = all_74_13 & $i(all_74_13)) % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (159), (649), (1896), (1898), (1904) are % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #15. % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | | End of split % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | End of split % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | Case 2: % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | (1905) all_74_14 = n2 % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | REDUCE: (1850), (1905) imply: % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | (1906) a_select3(id_ds1_filter, n2, n0) = all_74_12 % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | REDUCE: (1851), (1905) imply: % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | (1907) a_select3(id_ds1_filter, n0, n2) = all_74_13 % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | REDUCE: (659), (1905) imply: % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | (1908) leq(n2, n5) % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (81) with n0, n2, all_74_13, % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | simplifying with (22), (118), (1852), (1886), % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | (1907) gives: % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | (1909) ~ leq(n2, all_74_20) | ~ leq(n0, pv57) | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | (a_select3(id_ds1_filter, n2, n0) = all_74_13 & % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | $i(all_74_13)) % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1909) gives: % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | | (1910) ~ leq(n0, pv57) % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1881), (1910) imply: % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | | (1911) ~ leq(n0, n3) % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1884), (1911) imply: % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | | (1912) $false % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1912) is inconsistent. % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | | (1913) ~ leq(n2, all_74_20) | (a_select3(id_ds1_filter, % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | | n2, n0) = all_74_13 & $i(all_74_13)) % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (159), (649), (1906), (1908), (1913) are % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #13. % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | End of split % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | End of split % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | Case 2: % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | (1914) all_74_14 = n3 % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | REDUCE: (1850), (1914) imply: % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | (1915) a_select3(id_ds1_filter, n3, n0) = all_74_12 % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | REDUCE: (1851), (1914) imply: % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | (1916) a_select3(id_ds1_filter, n0, n3) = all_74_13 % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | REDUCE: (659), (1914) imply: % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | (1917) leq(n3, n5) % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (82) with n0, n3, all_74_13, % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | simplifying with (22), (129), (1852), (1884), % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | (1916) gives: % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | (1918) ~ leq(n3, all_74_20) | ~ leq(n0, all_74_18) | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | (a_select3(id_ds1_filter, n3, n0) = all_74_13 & % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | $i(all_74_13)) % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | BETA: splitting (1918) gives: % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | Case 1: % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | (1919) ~ leq(n0, all_74_18) % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | REDUCE: (1885), (1919) imply: % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | (1920) ~ leq(n0, n2) % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1886), (1920) imply: % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | (1921) $false % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | CLOSE: (1921) is inconsistent. % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | Case 2: % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | (1922) ~ leq(n3, all_74_20) | (a_select3(id_ds1_filter, % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | n3, n0) = all_74_13 & $i(all_74_13)) % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (159), (649), (1915), (1917), (1922) are % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #11. % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | End of split % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | End of split % 261.81/56.62 | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | End of split % 261.81/56.62 | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | Case 2: % 261.81/56.62 | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | (1923) all_74_18 = n1 % 261.81/56.62 | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | REDUCE: (165), (1923) imply: % 261.81/56.62 | | | | | | | | | | | | | | | | | | (1924) succ(n1) = pv57 % 261.81/56.62 | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | REDUCE: (155), (1923) imply: % 261.81/56.62 | | | | | | | | | | | | | | | | | | (1925) pred(pv57) = n1 % 261.81/56.62 | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | REDUCE: (690), (1923) imply: % 261.81/56.62 | | | | | | | | | | | | | | | | | | (1926) leq(n0, n1) % 261.81/56.62 | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (28) with n2, pv57, n1, simplifying % 261.81/56.62 | | | | | | | | | | | | | | | | | | with (101), (1924) gives: % 261.81/56.62 | | | | | | | | | | | | | | | | | | (1927) pv57 = n2 % 261.81/56.62 | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | REDUCE: (669), (1927) imply: % 261.81/56.62 | | | | | | | | | | | | | | | | | | (1928) succ(n2) = all_74_17 % 261.81/56.62 | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | REDUCE: (678), (1927) imply: % 261.81/56.62 | | | | | | | | | | | | | | | | | | (1929) pred(all_74_17) = n2 % 261.81/56.62 | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (28) with n3, all_74_17, n2, % 261.81/56.62 | | | | | | | | | | | | | | | | | | simplifying with (117), (1928) gives: % 261.81/56.62 | | | | | | | | | | | | | | | | | | (1930) all_74_17 = n3 % 261.81/56.62 | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | BETA: splitting (1878) gives: % 261.81/56.62 | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | Case 1: % 261.81/56.62 | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | (1931) gt(n3, all_74_14) % 261.81/56.62 | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_14, n3, n2, % 261.81/56.62 | | | | | | | | | | | | | | | | | | | simplifying with (67), (129), (146), (1931) gives: % 261.81/56.62 | | | | | | | | | | | | | | | | | | | (1932) leq(all_74_14, n2) % 261.81/56.62 | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_14, n2, % 261.81/56.62 | | | | | | | | | | | | | | | | | | | simplifying with (67), (118), (1932) gives: % 261.81/56.62 | | | | | | | | | | | | | | | | | | | (1933) all_74_14 = n2 | gt(n2, all_74_14) % 261.81/56.62 | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | BETA: splitting (1933) gives: % 261.81/56.62 | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | Case 1: % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | (1934) gt(n2, all_74_14) % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_14, n2, n1, % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | simplifying with (67), (118), (145), (1934) gives: % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | (1935) leq(all_74_14, n1) % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_74_14, simplifying % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | with (67), (651), (1935) gives: % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | (1936) all_74_14 = n1 | all_74_14 = n0 % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | BETA: splitting (1936) gives: % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | Case 1: % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | (1937) all_74_14 = n0 % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | REDUCE: (1859), (1937) imply: % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | (1938) $false % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | CLOSE: (1938) is inconsistent. % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | Case 2: % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | (1939) all_74_14 = n1 % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | REDUCE: (1850), (1939) imply: % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | (1940) a_select3(id_ds1_filter, n1, n0) = all_74_12 % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | REDUCE: (1851), (1939) imply: % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | (1941) a_select3(id_ds1_filter, n0, n1) = all_74_13 % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | REDUCE: (659), (1939) imply: % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | (1942) leq(n1, n5) % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (82) with n0, n1, all_74_13, % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | simplifying with (22), (102), (1852), (1926), % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | (1941) gives: % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | (1943) ~ leq(n1, all_74_20) | ~ leq(n0, all_74_18) | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | (a_select3(id_ds1_filter, n1, n0) = all_74_13 & % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | $i(all_74_13)) % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1943) gives: % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | Case 1: % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | | (1944) ~ leq(n0, all_74_18) % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1923), (1944) imply: % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | | (1945) ~ leq(n0, n1) % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1926), (1945) imply: % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | | (1946) $false % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1946) is inconsistent. % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | Case 2: % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | | (1947) ~ leq(n1, all_74_20) | (a_select3(id_ds1_filter, % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | | n1, n0) = all_74_13 & $i(all_74_13)) % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (159), (649), (1940), (1942), (1947) are % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #15. % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | End of split % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | End of split % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | Case 2: % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | (1948) all_74_14 = n2 % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | REDUCE: (1850), (1948) imply: % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | (1949) a_select3(id_ds1_filter, n2, n0) = all_74_12 % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | REDUCE: (1851), (1948) imply: % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | (1950) a_select3(id_ds1_filter, n0, n2) = all_74_13 % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | REDUCE: (659), (1948) imply: % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | (1951) leq(n2, n5) % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | REDUCE: (651), (1948) imply: % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | (1952) leq(n0, n2) % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (82) with n0, n2, all_74_13, % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | simplifying with (22), (118), (1852), (1950), % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | (1952) gives: % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | (1953) ~ leq(n2, all_74_20) | ~ leq(n0, all_74_18) | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | (a_select3(id_ds1_filter, n2, n0) = all_74_13 & % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | $i(all_74_13)) % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | BETA: splitting (1953) gives: % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | Case 1: % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | (1954) ~ leq(n0, all_74_18) % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | REDUCE: (1923), (1954) imply: % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | (1955) ~ leq(n0, n1) % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1926), (1955) imply: % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | (1956) $false % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | CLOSE: (1956) is inconsistent. % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | Case 2: % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | (1957) ~ leq(n2, all_74_20) | (a_select3(id_ds1_filter, % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | n2, n0) = all_74_13 & $i(all_74_13)) % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (159), (649), (1949), (1951), (1957) are % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #13. % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | End of split % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | End of split % 261.81/56.62 | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | Case 2: % 261.81/56.62 | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | (1958) all_74_14 = n3 % 261.81/56.62 | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | REDUCE: (1850), (1958) imply: % 261.81/56.62 | | | | | | | | | | | | | | | | | | | (1959) a_select3(id_ds1_filter, n3, n0) = all_74_12 % 261.81/56.62 | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | REDUCE: (1851), (1958) imply: % 261.81/56.62 | | | | | | | | | | | | | | | | | | | (1960) a_select3(id_ds1_filter, n0, n3) = all_74_13 % 261.81/56.62 | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | REDUCE: (659), (1958) imply: % 261.81/56.62 | | | | | | | | | | | | | | | | | | | (1961) leq(n3, n5) % 261.81/56.62 | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | REDUCE: (651), (1958) imply: % 261.81/56.62 | | | | | | | | | | | | | | | | | | | (1962) leq(n0, n3) % 261.81/56.62 | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (82) with n0, n3, all_74_13, % 261.81/56.62 | | | | | | | | | | | | | | | | | | | simplifying with (22), (129), (1852), (1960), % 261.81/56.62 | | | | | | | | | | | | | | | | | | | (1962) gives: % 261.81/56.62 | | | | | | | | | | | | | | | | | | | (1963) ~ leq(n3, all_74_20) | ~ leq(n0, all_74_18) | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | (a_select3(id_ds1_filter, n3, n0) = all_74_13 & % 261.81/56.62 | | | | | | | | | | | | | | | | | | | $i(all_74_13)) % 261.81/56.62 | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | BETA: splitting (1963) gives: % 261.81/56.62 | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | Case 1: % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | (1964) ~ leq(n0, all_74_18) % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | REDUCE: (1923), (1964) imply: % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | (1965) ~ leq(n0, n1) % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1926), (1965) imply: % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | (1966) $false % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | CLOSE: (1966) is inconsistent. % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | Case 2: % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | (1967) ~ leq(n3, all_74_20) | (a_select3(id_ds1_filter, % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | n3, n0) = all_74_13 & $i(all_74_13)) % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (159), (649), (1959), (1961), (1967) are % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #11. % 261.81/56.62 | | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | End of split % 261.81/56.62 | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | End of split % 261.81/56.62 | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | End of split % 261.81/56.62 | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | End of split % 261.81/56.62 | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | Case 2: % 261.81/56.62 | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | (1968) all_74_14 = n4 % 261.81/56.62 | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | REDUCE: (1850), (1968) imply: % 261.81/56.62 | | | | | | | | | | | | | | | | (1969) a_select3(id_ds1_filter, n4, n0) = all_74_12 % 261.81/56.62 | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | REDUCE: (1851), (1968) imply: % 261.81/56.62 | | | | | | | | | | | | | | | | (1970) a_select3(id_ds1_filter, n0, n4) = all_74_13 % 261.81/56.62 | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | REDUCE: (659), (1968) imply: % 261.81/56.62 | | | | | | | | | | | | | | | | (1971) leq(n4, n5) % 261.81/56.62 | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | REDUCE: (651), (1968) imply: % 261.81/56.62 | | | | | | | | | | | | | | | | (1972) leq(n0, n4) % 261.81/56.62 | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | BETA: splitting (1867) gives: % 261.81/56.62 | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | Case 1: % 261.81/56.62 | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | (1973) gt(all_74_18, n1) % 261.81/56.62 | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | BETA: splitting (1869) gives: % 261.81/56.62 | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | Case 1: % 261.81/56.62 | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | (1974) gt(n3, pv57) % 261.81/56.62 | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | REF_CLOSE: (24), (27), (145), (154), (155), (705), (1868), % 261.81/56.62 | | | | | | | | | | | | | | | | | | (1871), (1872), (1973), (1974), (irreflexivity_gt) % 261.81/56.62 | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #34. % 261.81/56.62 | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | Case 2: % 261.81/56.62 | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | (1975) pv57 = n3 % 261.81/56.62 | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | REDUCE: (75), (1975) imply: % 261.81/56.62 | | | | | | | | | | | | | | | | | | (1976) minus(n3, n1) = all_74_18 % 261.81/56.62 | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | REDUCE: (669), (1975) imply: % 261.81/56.62 | | | | | | | | | | | | | | | | | | (1977) succ(n3) = all_74_17 % 261.81/56.62 | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (28) with n4, all_74_17, n3, % 261.81/56.62 | | | | | | | | | | | | | | | | | | simplifying with (128), (1977) gives: % 261.81/56.62 | | | | | | | | | | | | | | | | | | (1978) all_74_17 = n4 % 261.81/56.62 | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (29) with n2, all_74_18, n1, n3, % 261.81/56.62 | | | | | | | | | | | | | | | | | | simplifying with (161), (1976) gives: % 261.81/56.62 | | | | | | | | | | | | | | | | | | (1979) all_74_18 = n2 % 261.81/56.62 | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | REDUCE: (690), (1979) imply: % 261.81/56.62 | | | | | | | | | | | | | | | | | | (1980) leq(n0, n2) % 261.81/56.62 | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (82) with n0, n4, all_74_13, % 261.81/56.62 | | | | | | | | | | | | | | | | | | simplifying with (22), (136), (1852), (1970), % 261.81/56.62 | | | | | | | | | | | | | | | | | | (1972) gives: % 261.81/56.62 | | | | | | | | | | | | | | | | | | (1981) ~ leq(n4, all_74_20) | ~ leq(n0, all_74_18) | % 261.81/56.62 | | | | | | | | | | | | | | | | | | (a_select3(id_ds1_filter, n4, n0) = all_74_13 & % 261.81/56.62 | | | | | | | | | | | | | | | | | | $i(all_74_13)) % 261.81/56.62 | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | BETA: splitting (1981) gives: % 261.81/56.62 | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | Case 1: % 261.81/56.62 | | | | | | | | | | | | | | | | | | | % 261.81/56.62 | | | | | | | | | | | | | | | | | | | (1982) ~ leq(n0, all_74_18) % 261.81/56.62 | | | | | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | | | | | | REDUCE: (1979), (1982) imply: % 261.81/56.63 | | | | | | | | | | | | | | | | | | | (1983) ~ leq(n0, n2) % 261.81/56.63 | | | | | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1980), (1983) imply: % 261.81/56.63 | | | | | | | | | | | | | | | | | | | (1984) $false % 261.81/56.63 | | | | | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | | | | | | CLOSE: (1984) is inconsistent. % 261.81/56.63 | | | | | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | | | | | Case 2: % 261.81/56.63 | | | | | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | | | | | | (1985) ~ leq(n4, all_74_20) | (a_select3(id_ds1_filter, % 261.81/56.63 | | | | | | | | | | | | | | | | | | | n4, n0) = all_74_13 & $i(all_74_13)) % 261.81/56.63 | | | | | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (159), (649), (1969), (1971), (1985) are % 261.81/56.63 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #9. % 261.81/56.63 | | | | | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | | | | | End of split % 261.81/56.63 | | | | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | | | | End of split % 261.81/56.63 | | | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | | | Case 2: % 261.81/56.63 | | | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | | | | (1986) all_74_18 = n1 % 261.81/56.63 | | | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | | | | REDUCE: (165), (1986) imply: % 261.81/56.63 | | | | | | | | | | | | | | | | | (1987) succ(n1) = pv57 % 261.81/56.63 | | | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (28) with n2, pv57, n1, simplifying % 261.81/56.63 | | | | | | | | | | | | | | | | | with (101), (1987) gives: % 261.81/56.63 | | | | | | | | | | | | | | | | | (1988) pv57 = n2 % 261.81/56.63 | | | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | | | | REDUCE: (63), (1988) imply: % 261.81/56.63 | | | | | | | | | | | | | | | | | (1989) leq(n0, n2) % 261.81/56.63 | | | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (81) with n0, n4, all_74_13, % 261.81/56.63 | | | | | | | | | | | | | | | | | simplifying with (22), (136), (1852), (1970), % 261.81/56.63 | | | | | | | | | | | | | | | | | (1972) gives: % 261.81/56.63 | | | | | | | | | | | | | | | | | (1990) ~ leq(n4, all_74_20) | ~ leq(n0, pv57) | % 261.81/56.63 | | | | | | | | | | | | | | | | | (a_select3(id_ds1_filter, n4, n0) = all_74_13 & % 261.81/56.63 | | | | | | | | | | | | | | | | | $i(all_74_13)) % 261.81/56.63 | | | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | | | | BETA: splitting (1990) gives: % 261.81/56.63 | | | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | | | | Case 1: % 261.81/56.63 | | | | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | | | | | (1991) ~ leq(n0, pv57) % 261.81/56.63 | | | | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | | | | | REDUCE: (1988), (1991) imply: % 261.81/56.63 | | | | | | | | | | | | | | | | | | (1992) ~ leq(n0, n2) % 261.81/56.63 | | | | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1989), (1992) imply: % 261.81/56.63 | | | | | | | | | | | | | | | | | | (1993) $false % 261.81/56.63 | | | | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | | | | | CLOSE: (1993) is inconsistent. % 261.81/56.63 | | | | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | | | | Case 2: % 261.81/56.63 | | | | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | | | | | (1994) ~ leq(n4, all_74_20) | (a_select3(id_ds1_filter, % 261.81/56.63 | | | | | | | | | | | | | | | | | | n4, n0) = all_74_13 & $i(all_74_13)) % 261.81/56.63 | | | | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (159), (649), (1969), (1971), (1994) are % 261.81/56.63 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #9. % 261.81/56.63 | | | | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | | | | End of split % 261.81/56.63 | | | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | | | End of split % 261.81/56.63 | | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | | End of split % 261.81/56.63 | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | End of split % 261.81/56.63 | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | Case 2: % 261.81/56.63 | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | (1995) all_74_18 = n3 % 261.81/56.63 | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | REF_CLOSE: (24), (28), (128), (165), (1865), (1995), % 261.81/56.63 | | | | | | | | | | | | | | (irreflexivity_gt) are inconsistent by sub-proof % 261.81/56.63 | | | | | | | | | | | | | | #26. % 261.81/56.63 | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | End of split % 261.81/56.63 | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | Case 2: % 261.81/56.63 | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | (1996) pv57 = n4 % 261.81/56.63 | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | REDUCE: (155), (1996) imply: % 261.81/56.63 | | | | | | | | | | | | | (1997) pred(n4) = all_74_18 % 261.81/56.63 | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | REDUCE: (63), (1996) imply: % 261.81/56.63 | | | | | | | | | | | | | (1998) leq(n0, n4) % 261.81/56.63 | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | GROUND_INST: instantiating (27) with n3, all_74_18, n4, % 261.81/56.63 | | | | | | | | | | | | | simplifying with (147), (1997) gives: % 261.81/56.63 | | | | | | | | | | | | | (1999) all_74_18 = n3 % 261.81/56.63 | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | REDUCE: (690), (1999) imply: % 261.81/56.63 | | | | | | | | | | | | | (2000) leq(n0, n3) % 261.81/56.63 | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | BETA: splitting (1861) gives: % 261.81/56.63 | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | Case 1: % 261.81/56.63 | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | (2001) gt(n4, all_74_14) % 261.81/56.63 | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_14, n4, n3, % 261.81/56.63 | | | | | | | | | | | | | | simplifying with (67), (136), (147), (2001) gives: % 261.81/56.63 | | | | | | | | | | | | | | (2002) leq(all_74_14, n3) % 261.81/56.63 | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_14, n3, % 261.81/56.63 | | | | | | | | | | | | | | simplifying with (67), (129), (2002) gives: % 261.81/56.63 | | | | | | | | | | | | | | (2003) all_74_14 = n3 | gt(n3, all_74_14) % 261.81/56.63 | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | BETA: splitting (2003) gives: % 261.81/56.63 | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | Case 1: % 261.81/56.63 | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | | (2004) gt(n3, all_74_14) % 261.81/56.63 | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_14, n3, n2, % 261.81/56.63 | | | | | | | | | | | | | | | simplifying with (67), (129), (146), (2004) gives: % 261.81/56.63 | | | | | | | | | | | | | | | (2005) leq(all_74_14, n2) % 261.81/56.63 | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_14, n2, % 261.81/56.63 | | | | | | | | | | | | | | | simplifying with (67), (118), (2005) gives: % 261.81/56.63 | | | | | | | | | | | | | | | (2006) all_74_14 = n2 | gt(n2, all_74_14) % 261.81/56.63 | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | | BETA: splitting (2006) gives: % 261.81/56.63 | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | | Case 1: % 261.81/56.63 | | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | | | (2007) gt(n2, all_74_14) % 261.81/56.63 | | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_14, n2, n1, % 261.81/56.63 | | | | | | | | | | | | | | | | simplifying with (67), (118), (145), (2007) gives: % 261.81/56.63 | | | | | | | | | | | | | | | | (2008) leq(all_74_14, n1) % 261.81/56.63 | | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_74_14, simplifying % 261.81/56.63 | | | | | | | | | | | | | | | | with (67), (651), (2008) gives: % 261.81/56.63 | | | | | | | | | | | | | | | | (2009) all_74_14 = n1 | all_74_14 = n0 % 261.81/56.63 | | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | | | BETA: splitting (2009) gives: % 261.81/56.63 | | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | | | Case 1: % 261.81/56.63 | | | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | | | | (2010) all_74_14 = n0 % 261.81/56.63 | | | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | | | | REDUCE: (1859), (2010) imply: % 261.81/56.63 | | | | | | | | | | | | | | | | | (2011) $false % 261.81/56.63 | | | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | | | | CLOSE: (2011) is inconsistent. % 261.81/56.63 | | | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | | | Case 2: % 261.81/56.63 | | | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | | | | (2012) all_74_14 = n1 % 261.81/56.63 | | | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | | | | REDUCE: (1850), (2012) imply: % 261.81/56.63 | | | | | | | | | | | | | | | | | (2013) a_select3(id_ds1_filter, n1, n0) = all_74_12 % 261.81/56.63 | | | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | | | | REDUCE: (1851), (2012) imply: % 261.81/56.63 | | | | | | | | | | | | | | | | | (2014) a_select3(id_ds1_filter, n0, n1) = all_74_13 % 261.81/56.63 | | | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | | | | REDUCE: (659), (2012) imply: % 261.81/56.63 | | | | | | | | | | | | | | | | | (2015) leq(n1, n5) % 261.81/56.63 | | | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | | | | REDUCE: (651), (2012) imply: % 261.81/56.63 | | | | | | | | | | | | | | | | | (2016) leq(n0, n1) % 261.81/56.63 | | | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (82) with n0, n1, all_74_13, % 261.81/56.63 | | | | | | | | | | | | | | | | | simplifying with (22), (102), (1852), (2014), % 261.81/56.63 | | | | | | | | | | | | | | | | | (2016) gives: % 261.81/56.63 | | | | | | | | | | | | | | | | | (2017) ~ leq(n1, all_74_20) | ~ leq(n0, all_74_18) | % 261.81/56.63 | | | | | | | | | | | | | | | | | (a_select3(id_ds1_filter, n1, n0) = all_74_13 & % 261.81/56.63 | | | | | | | | | | | | | | | | | $i(all_74_13)) % 261.81/56.63 | | | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | | | | BETA: splitting (2017) gives: % 261.81/56.63 | | | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | | | | Case 1: % 261.81/56.63 | | | | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | | | | | (2018) ~ leq(n0, all_74_18) % 261.81/56.63 | | | | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | | | | | REDUCE: (1999), (2018) imply: % 261.81/56.63 | | | | | | | | | | | | | | | | | | (2019) ~ leq(n0, n3) % 261.81/56.63 | | | | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | | | | | PRED_UNIFY: (2000), (2019) imply: % 261.81/56.63 | | | | | | | | | | | | | | | | | | (2020) $false % 261.81/56.63 | | | | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | | | | | CLOSE: (2020) is inconsistent. % 261.81/56.63 | | | | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | | | | Case 2: % 261.81/56.63 | | | | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | | | | | (2021) ~ leq(n1, all_74_20) | (a_select3(id_ds1_filter, % 261.81/56.63 | | | | | | | | | | | | | | | | | | n1, n0) = all_74_13 & $i(all_74_13)) % 261.81/56.63 | | | | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (159), (649), (2013), (2015), (2021) are % 261.81/56.63 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #15. % 261.81/56.63 | | | | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | | | | End of split % 261.81/56.63 | | | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | | | End of split % 261.81/56.63 | | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | | Case 2: % 261.81/56.63 | | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | | | (2022) all_74_14 = n2 % 261.81/56.63 | | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | | | REDUCE: (1850), (2022) imply: % 261.81/56.63 | | | | | | | | | | | | | | | | (2023) a_select3(id_ds1_filter, n2, n0) = all_74_12 % 261.81/56.63 | | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | | | REDUCE: (1851), (2022) imply: % 261.81/56.63 | | | | | | | | | | | | | | | | (2024) a_select3(id_ds1_filter, n0, n2) = all_74_13 % 261.81/56.63 | | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | | | REDUCE: (659), (2022) imply: % 261.81/56.63 | | | | | | | | | | | | | | | | (2025) leq(n2, n5) % 261.81/56.63 | | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | | | REDUCE: (651), (2022) imply: % 261.81/56.63 | | | | | | | | | | | | | | | | (2026) leq(n0, n2) % 261.81/56.63 | | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (81) with n0, n2, all_74_13, % 261.81/56.63 | | | | | | | | | | | | | | | | simplifying with (22), (118), (1852), (2024), % 261.81/56.63 | | | | | | | | | | | | | | | | (2026) gives: % 261.81/56.63 | | | | | | | | | | | | | | | | (2027) ~ leq(n2, all_74_20) | ~ leq(n0, pv57) | % 261.81/56.63 | | | | | | | | | | | | | | | | (a_select3(id_ds1_filter, n2, n0) = all_74_13 & % 261.81/56.63 | | | | | | | | | | | | | | | | $i(all_74_13)) % 261.81/56.63 | | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | | | BETA: splitting (2027) gives: % 261.81/56.63 | | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | | | Case 1: % 261.81/56.63 | | | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | | | | (2028) ~ leq(n0, pv57) % 261.81/56.63 | | | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | | | | REDUCE: (1996), (2028) imply: % 261.81/56.63 | | | | | | | | | | | | | | | | | (2029) ~ leq(n0, n4) % 261.81/56.63 | | | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | | | | PRED_UNIFY: (1998), (2029) imply: % 261.81/56.63 | | | | | | | | | | | | | | | | | (2030) $false % 261.81/56.63 | | | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | | | | CLOSE: (2030) is inconsistent. % 261.81/56.63 | | | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | | | Case 2: % 261.81/56.63 | | | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | | | | (2031) ~ leq(n2, all_74_20) | (a_select3(id_ds1_filter, % 261.81/56.63 | | | | | | | | | | | | | | | | | n2, n0) = all_74_13 & $i(all_74_13)) % 261.81/56.63 | | | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (159), (649), (2023), (2025), (2031) are % 261.81/56.63 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #13. % 261.81/56.63 | | | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | | | End of split % 261.81/56.63 | | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | | End of split % 261.81/56.63 | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | Case 2: % 261.81/56.63 | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | | (2032) all_74_14 = n3 % 261.81/56.63 | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | | REDUCE: (1850), (2032) imply: % 261.81/56.63 | | | | | | | | | | | | | | | (2033) a_select3(id_ds1_filter, n3, n0) = all_74_12 % 261.81/56.63 | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | | REDUCE: (1851), (2032) imply: % 261.81/56.63 | | | | | | | | | | | | | | | (2034) a_select3(id_ds1_filter, n0, n3) = all_74_13 % 261.81/56.63 | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | | REDUCE: (659), (2032) imply: % 261.81/56.63 | | | | | | | | | | | | | | | (2035) leq(n3, n5) % 261.81/56.63 | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | | GROUND_INST: instantiating (81) with n0, n3, all_74_13, % 261.81/56.63 | | | | | | | | | | | | | | | simplifying with (22), (129), (1852), (2000), % 261.81/56.63 | | | | | | | | | | | | | | | (2034) gives: % 261.81/56.63 | | | | | | | | | | | | | | | (2036) ~ leq(n3, all_74_20) | ~ leq(n0, pv57) | % 261.81/56.63 | | | | | | | | | | | | | | | (a_select3(id_ds1_filter, n3, n0) = all_74_13 & % 261.81/56.63 | | | | | | | | | | | | | | | $i(all_74_13)) % 261.81/56.63 | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | | BETA: splitting (2036) gives: % 261.81/56.63 | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | | Case 1: % 261.81/56.63 | | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | | | (2037) ~ leq(n0, pv57) % 261.81/56.63 | | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | | | REDUCE: (1996), (2037) imply: % 261.81/56.63 | | | | | | | | | | | | | | | | (2038) ~ leq(n0, n4) % 261.81/56.63 | | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | | | PRED_UNIFY: (1998), (2038) imply: % 261.81/56.63 | | | | | | | | | | | | | | | | (2039) $false % 261.81/56.63 | | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | | | CLOSE: (2039) is inconsistent. % 261.81/56.63 | | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | | Case 2: % 261.81/56.63 | | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | | | (2040) ~ leq(n3, all_74_20) | (a_select3(id_ds1_filter, % 261.81/56.63 | | | | | | | | | | | | | | | | n3, n0) = all_74_13 & $i(all_74_13)) % 261.81/56.63 | | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | | | REF_CLOSE: (30), (159), (649), (2033), (2035), (2040) are % 261.81/56.63 | | | | | | | | | | | | | | | | inconsistent by sub-proof #11. % 261.81/56.63 | | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | | End of split % 261.81/56.63 | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | End of split % 261.81/56.63 | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | Case 2: % 261.81/56.63 | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | (2041) all_74_14 = n4 % 261.81/56.63 | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | REDUCE: (1850), (2041) imply: % 261.81/56.63 | | | | | | | | | | | | | | (2042) a_select3(id_ds1_filter, n4, n0) = all_74_12 % 261.81/56.63 | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | REDUCE: (1851), (2041) imply: % 261.81/56.63 | | | | | | | | | | | | | | (2043) a_select3(id_ds1_filter, n0, n4) = all_74_13 % 261.81/56.63 | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | REDUCE: (659), (2041) imply: % 261.81/56.63 | | | | | | | | | | | | | | (2044) leq(n4, n5) % 261.81/56.63 | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | REF_CLOSE: (22), (30), (81), (136), (159), (649), (1852), % 261.81/56.63 | | | | | | | | | | | | | | (1996), (1998), (2042), (2043), (2044) are % 261.81/56.63 | | | | | | | | | | | | | | inconsistent by sub-proof #8. % 261.81/56.63 | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | End of split % 261.81/56.63 | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | End of split % 261.81/56.63 | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | Case 2: % 261.81/56.63 | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | (2045) pv57 = n1 % 261.81/56.63 | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | REF_CLOSE: (27), (144), (155), (1853), (1862), (2045) are % 261.81/56.63 | | | | | | | | | | | | inconsistent by sub-proof #75. % 261.81/56.63 | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | End of split % 261.81/56.63 | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | Case 2: % 261.81/56.63 | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | (2046) all_74_18 = n0 % 261.81/56.63 | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | REDUCE: (165), (2046) imply: % 261.81/56.63 | | | | | | | | | | | (2047) succ(n0) = pv57 % 261.81/56.63 | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | GROUND_INST: instantiating (28) with n1, pv57, n0, simplifying % 261.81/56.63 | | | | | | | | | | | with (19), (2047) gives: % 261.81/56.63 | | | | | | | | | | | (2048) pv57 = n1 % 261.81/56.63 | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | REDUCE: (669), (2048) imply: % 261.81/56.63 | | | | | | | | | | | (2049) succ(n1) = all_74_17 % 261.81/56.63 | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | REDUCE: (678), (2048) imply: % 261.81/56.63 | | | | | | | | | | | (2050) pred(all_74_17) = n1 % 261.81/56.63 | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | GROUND_INST: instantiating (28) with n2, all_74_17, n1, % 261.81/56.63 | | | | | | | | | | | simplifying with (101), (2049) gives: % 261.81/56.63 | | | | | | | | | | | (2051) all_74_17 = n2 % 261.81/56.63 | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | BETA: splitting (1861) gives: % 261.81/56.63 | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | Case 1: % 261.81/56.63 | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | (2052) gt(n4, all_74_14) % 261.81/56.63 | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_14, n4, n3, % 261.81/56.63 | | | | | | | | | | | | simplifying with (67), (136), (147), (2052) gives: % 261.81/56.63 | | | | | | | | | | | | (2053) leq(all_74_14, n3) % 261.81/56.63 | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_14, n3, % 261.81/56.63 | | | | | | | | | | | | simplifying with (67), (129), (2053) gives: % 261.81/56.63 | | | | | | | | | | | | (2054) all_74_14 = n3 | gt(n3, all_74_14) % 261.81/56.63 | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | BETA: splitting (2054) gives: % 261.81/56.63 | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | Case 1: % 261.81/56.63 | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | (2055) gt(n3, all_74_14) % 261.81/56.63 | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_14, n3, n2, % 261.81/56.63 | | | | | | | | | | | | | simplifying with (67), (129), (146), (2055) gives: % 261.81/56.63 | | | | | | | | | | | | | (2056) leq(all_74_14, n2) % 261.81/56.63 | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_14, n2, % 261.81/56.63 | | | | | | | | | | | | | simplifying with (67), (118), (2056) gives: % 261.81/56.63 | | | | | | | | | | | | | (2057) all_74_14 = n2 | gt(n2, all_74_14) % 261.81/56.63 | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | BETA: splitting (2057) gives: % 261.81/56.63 | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | Case 1: % 261.81/56.63 | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | (2058) gt(n2, all_74_14) % 261.81/56.63 | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_14, n2, n1, % 261.81/56.63 | | | | | | | | | | | | | | simplifying with (67), (118), (145), (2058) gives: % 261.81/56.63 | | | | | | | | | | | | | | (2059) leq(all_74_14, n1) % 261.81/56.63 | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_74_14, simplifying % 261.81/56.63 | | | | | | | | | | | | | | with (67), (651), (2059) gives: % 261.81/56.63 | | | | | | | | | | | | | | (2060) all_74_14 = n1 | all_74_14 = n0 % 261.81/56.63 | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | BETA: splitting (2060) gives: % 261.81/56.63 | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | Case 1: % 261.81/56.63 | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | | (2061) all_74_14 = n0 % 261.81/56.63 | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | | REDUCE: (1859), (2061) imply: % 261.81/56.63 | | | | | | | | | | | | | | | (2062) $false % 261.81/56.63 | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | | CLOSE: (2062) is inconsistent. % 261.81/56.63 | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | Case 2: % 261.81/56.63 | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | | (2063) all_74_14 = n1 % 261.81/56.63 | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | | REDUCE: (1850), (2063) imply: % 261.81/56.63 | | | | | | | | | | | | | | | (2064) a_select3(id_ds1_filter, n1, n0) = all_74_12 % 261.81/56.63 | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | | REDUCE: (1851), (2063) imply: % 261.81/56.63 | | | | | | | | | | | | | | | (2065) a_select3(id_ds1_filter, n0, n1) = all_74_13 % 261.81/56.63 | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | | REDUCE: (659), (2063) imply: % 261.81/56.63 | | | | | | | | | | | | | | | (2066) leq(n1, n5) % 261.81/56.63 | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | | REDUCE: (651), (2063) imply: % 261.81/56.63 | | | | | | | | | | | | | | | (2067) leq(n0, n1) % 261.81/56.63 | | | | | | | | | | | | | | | % 261.81/56.63 | | | | | | | | | | | | | | | GROUND_INST: instantiating (81) with n0, n1, all_74_13, % 261.81/56.63 | | | | | | | | | | | | | | | simplifying with (22), (102), (1852), (2065), % 261.81/56.63 | | | | | | | | | | | | | | | (2067) gives: % 261.81/56.64 | | | | | | | | | | | | | | | (2068) ~ leq(n1, all_74_20) | ~ leq(n0, pv57) | % 261.81/56.64 | | | | | | | | | | | | | | | (a_select3(id_ds1_filter, n1, n0) = all_74_13 & % 261.81/56.64 | | | | | | | | | | | | | | | $i(all_74_13)) % 261.81/56.64 | | | | | | | | | | | | | | | % 261.81/56.64 | | | | | | | | | | | | | | | BETA: splitting (2068) gives: % 261.81/56.64 | | | | | | | | | | | | | | | % 261.81/56.64 | | | | | | | | | | | | | | | Case 1: % 261.81/56.64 | | | | | | | | | | | | | | | | % 261.81/56.64 | | | | | | | | | | | | | | | | (2069) ~ leq(n0, pv57) % 261.81/56.64 | | | | | | | | | | | | | | | | % 261.81/56.64 | | | | | | | | | | | | | | | | REDUCE: (2048), (2069) imply: % 261.81/56.64 | | | | | | | | | | | | | | | | (2070) ~ leq(n0, n1) % 261.81/56.64 | | | | | | | | | | | | | | | | % 261.81/56.64 | | | | | | | | | | | | | | | | PRED_UNIFY: (2067), (2070) imply: % 261.81/56.64 | | | | | | | | | | | | | | | | (2071) $false % 261.81/56.64 | | | | | | | | | | | | | | | | % 261.81/56.64 | | | | | | | | | | | | | | | | CLOSE: (2071) is inconsistent. % 261.81/56.64 | | | | | | | | | | | | | | | | % 261.81/56.64 | | | | | | | | | | | | | | | Case 2: % 261.81/56.64 | | | | | | | | | | | | | | | | % 261.81/56.64 | | | | | | | | | | | | | | | | (2072) ~ leq(n1, all_74_20) | (a_select3(id_ds1_filter, % 261.81/56.64 | | | | | | | | | | | | | | | | n1, n0) = all_74_13 & $i(all_74_13)) % 261.81/56.64 | | | | | | | | | | | | | | | | % 261.81/56.64 | | | | | | | | | | | | | | | | REF_CLOSE: (30), (159), (649), (2064), (2066), (2072) are % 261.81/56.64 | | | | | | | | | | | | | | | | inconsistent by sub-proof #15. % 261.81/56.64 | | | | | | | | | | | | | | | | % 261.81/56.64 | | | | | | | | | | | | | | | End of split % 261.81/56.64 | | | | | | | | | | | | | | | % 261.81/56.64 | | | | | | | | | | | | | | End of split % 261.81/56.64 | | | | | | | | | | | | | | % 261.81/56.64 | | | | | | | | | | | | | Case 2: % 261.81/56.64 | | | | | | | | | | | | | | % 261.81/56.64 | | | | | | | | | | | | | | (2073) all_74_14 = n2 % 261.81/56.64 | | | | | | | | | | | | | | % 261.81/56.64 | | | | | | | | | | | | | | REDUCE: (1850), (2073) imply: % 261.81/56.64 | | | | | | | | | | | | | | (2074) a_select3(id_ds1_filter, n2, n0) = all_74_12 % 261.81/56.64 | | | | | | | | | | | | | | % 261.81/56.64 | | | | | | | | | | | | | | REDUCE: (1851), (2073) imply: % 261.81/56.64 | | | | | | | | | | | | | | (2075) a_select3(id_ds1_filter, n0, n2) = all_74_13 % 261.81/56.64 | | | | | | | | | | | | | | % 261.81/56.64 | | | | | | | | | | | | | | REDUCE: (659), (2073) imply: % 261.81/56.64 | | | | | | | | | | | | | | (2076) leq(n2, n5) % 261.81/56.64 | | | | | | | | | | | | | | % 261.81/56.64 | | | | | | | | | | | | | | REDUCE: (651), (2073) imply: % 261.81/56.64 | | | | | | | | | | | | | | (2077) leq(n0, n2) % 261.81/56.64 | | | | | | | | | | | | | | % 261.81/56.64 | | | | | | | | | | | | | | GROUND_INST: instantiating (82) with n0, n2, all_74_13, % 261.81/56.64 | | | | | | | | | | | | | | simplifying with (22), (118), (1852), (2075), % 261.81/56.64 | | | | | | | | | | | | | | (2077) gives: % 261.81/56.64 | | | | | | | | | | | | | | (2078) ~ leq(n2, all_74_20) | ~ leq(n0, all_74_18) | % 261.81/56.64 | | | | | | | | | | | | | | (a_select3(id_ds1_filter, n2, n0) = all_74_13 & % 261.81/56.64 | | | | | | | | | | | | | | $i(all_74_13)) % 261.81/56.64 | | | | | | | | | | | | | | % 261.81/56.64 | | | | | | | | | | | | | | BETA: splitting (2078) gives: % 261.81/56.64 | | | | | | | | | | | | | | % 261.81/56.64 | | | | | | | | | | | | | | Case 1: % 261.81/56.64 | | | | | | | | | | | | | | | % 261.81/56.64 | | | | | | | | | | | | | | | (2079) ~ leq(n0, all_74_18) % 261.81/56.64 | | | | | | | | | | | | | | | % 261.81/56.64 | | | | | | | | | | | | | | | REDUCE: (2046), (2079) imply: % 261.81/56.64 | | | | | | | | | | | | | | | (2080) ~ leq(n0, n0) % 261.81/56.64 | | | | | | | | | | | | | | | % 261.81/56.64 | | | | | | | | | | | | | | | PRED_UNIFY: (1852), (2080) imply: % 261.81/56.64 | | | | | | | | | | | | | | | (2081) $false % 261.81/56.64 | | | | | | | | | | | | | | | % 261.81/56.64 | | | | | | | | | | | | | | | CLOSE: (2081) is inconsistent. % 261.81/56.64 | | | | | | | | | | | | | | | % 261.81/56.64 | | | | | | | | | | | | | | Case 2: % 261.81/56.64 | | | | | | | | | | | | | | | % 261.81/56.64 | | | | | | | | | | | | | | | (2082) ~ leq(n2, all_74_20) | (a_select3(id_ds1_filter, % 261.81/56.64 | | | | | | | | | | | | | | | n2, n0) = all_74_13 & $i(all_74_13)) % 261.81/56.64 | | | | | | | | | | | | | | | % 261.81/56.64 | | | | | | | | | | | | | | | REF_CLOSE: (30), (159), (649), (2074), (2076), (2082) are % 261.81/56.64 | | | | | | | | | | | | | | | inconsistent by sub-proof #13. % 261.81/56.64 | | | | | | | | | | | | | | | % 261.81/56.64 | | | | | | | | | | | | | | End of split % 261.81/56.64 | | | | | | | | | | | | | | % 261.81/56.64 | | | | | | | | | | | | | End of split % 261.81/56.64 | | | | | | | | | | | | | % 261.81/56.64 | | | | | | | | | | | | Case 2: % 261.81/56.64 | | | | | | | | | | | | | % 261.81/56.64 | | | | | | | | | | | | | (2083) all_74_14 = n3 % 261.81/56.64 | | | | | | | | | | | | | % 261.81/56.64 | | | | | | | | | | | | | REDUCE: (1850), (2083) imply: % 261.81/56.64 | | | | | | | | | | | | | (2084) a_select3(id_ds1_filter, n3, n0) = all_74_12 % 261.81/56.64 | | | | | | | | | | | | | % 261.81/56.64 | | | | | | | | | | | | | REDUCE: (1851), (2083) imply: % 261.81/56.64 | | | | | | | | | | | | | (2085) a_select3(id_ds1_filter, n0, n3) = all_74_13 % 261.81/56.64 | | | | | | | | | | | | | % 261.81/56.64 | | | | | | | | | | | | | REDUCE: (659), (2083) imply: % 261.81/56.64 | | | | | | | | | | | | | (2086) leq(n3, n5) % 261.81/56.64 | | | | | | | | | | | | | % 261.81/56.64 | | | | | | | | | | | | | REDUCE: (651), (2083) imply: % 261.81/56.64 | | | | | | | | | | | | | (2087) leq(n0, n3) % 261.81/56.64 | | | | | | | | | | | | | % 261.81/56.64 | | | | | | | | | | | | | GROUND_INST: instantiating (82) with n0, n3, all_74_13, % 261.81/56.64 | | | | | | | | | | | | | simplifying with (22), (129), (1852), (2085), % 261.81/56.64 | | | | | | | | | | | | | (2087) gives: % 261.81/56.64 | | | | | | | | | | | | | (2088) ~ leq(n3, all_74_20) | ~ leq(n0, all_74_18) | % 261.81/56.64 | | | | | | | | | | | | | (a_select3(id_ds1_filter, n3, n0) = all_74_13 & % 261.81/56.64 | | | | | | | | | | | | | $i(all_74_13)) % 261.81/56.64 | | | | | | | | | | | | | % 261.81/56.64 | | | | | | | | | | | | | BETA: splitting (2088) gives: % 261.81/56.64 | | | | | | | | | | | | | % 261.81/56.64 | | | | | | | | | | | | | Case 1: % 261.81/56.64 | | | | | | | | | | | | | | % 261.81/56.64 | | | | | | | | | | | | | | (2089) ~ leq(n0, all_74_18) % 261.81/56.64 | | | | | | | | | | | | | | % 261.81/56.64 | | | | | | | | | | | | | | REDUCE: (2046), (2089) imply: % 261.81/56.64 | | | | | | | | | | | | | | (2090) ~ leq(n0, n0) % 261.81/56.64 | | | | | | | | | | | | | | % 261.81/56.64 | | | | | | | | | | | | | | PRED_UNIFY: (1852), (2090) imply: % 261.81/56.64 | | | | | | | | | | | | | | (2091) $false % 261.81/56.64 | | | | | | | | | | | | | | % 261.81/56.64 | | | | | | | | | | | | | | CLOSE: (2091) is inconsistent. % 261.81/56.64 | | | | | | | | | | | | | | % 261.81/56.64 | | | | | | | | | | | | | Case 2: % 261.81/56.64 | | | | | | | | | | | | | | % 261.81/56.64 | | | | | | | | | | | | | | (2092) ~ leq(n3, all_74_20) | (a_select3(id_ds1_filter, % 261.81/56.64 | | | | | | | | | | | | | | n3, n0) = all_74_13 & $i(all_74_13)) % 261.81/56.64 | | | | | | | | | | | | | | % 261.81/56.64 | | | | | | | | | | | | | | REF_CLOSE: (30), (159), (649), (2084), (2086), (2092) are % 261.81/56.64 | | | | | | | | | | | | | | inconsistent by sub-proof #11. % 261.81/56.64 | | | | | | | | | | | | | | % 261.81/56.64 | | | | | | | | | | | | | End of split % 261.81/56.64 | | | | | | | | | | | | | % 261.81/56.64 | | | | | | | | | | | | End of split % 261.81/56.64 | | | | | | | | | | | | % 261.81/56.64 | | | | | | | | | | | Case 2: % 261.81/56.64 | | | | | | | | | | | | % 261.81/56.64 | | | | | | | | | | | | (2093) all_74_14 = n4 % 261.81/56.64 | | | | | | | | | | | | % 261.81/56.64 | | | | | | | | | | | | REDUCE: (1850), (2093) imply: % 261.81/56.64 | | | | | | | | | | | | (2094) a_select3(id_ds1_filter, n4, n0) = all_74_12 % 261.81/56.64 | | | | | | | | | | | | % 261.81/56.64 | | | | | | | | | | | | REDUCE: (1851), (2093) imply: % 261.81/56.64 | | | | | | | | | | | | (2095) a_select3(id_ds1_filter, n0, n4) = all_74_13 % 261.81/56.64 | | | | | | | | | | | | % 261.81/56.64 | | | | | | | | | | | | REDUCE: (659), (2093) imply: % 261.81/56.64 | | | | | | | | | | | | (2096) leq(n4, n5) % 261.81/56.64 | | | | | | | | | | | | % 261.81/56.64 | | | | | | | | | | | | REDUCE: (651), (2093) imply: % 261.81/56.64 | | | | | | | | | | | | (2097) leq(n0, n4) % 261.81/56.64 | | | | | | | | | | | | % 261.81/56.64 | | | | | | | | | | | | GROUND_INST: instantiating (82) with n0, n4, all_74_13, % 261.81/56.64 | | | | | | | | | | | | simplifying with (22), (136), (1852), (2095), % 261.81/56.64 | | | | | | | | | | | | (2097) gives: % 261.81/56.64 | | | | | | | | | | | | (2098) ~ leq(n4, all_74_20) | ~ leq(n0, all_74_18) | % 261.81/56.64 | | | | | | | | | | | | (a_select3(id_ds1_filter, n4, n0) = all_74_13 & % 261.81/56.64 | | | | | | | | | | | | $i(all_74_13)) % 261.81/56.64 | | | | | | | | | | | | % 261.81/56.64 | | | | | | | | | | | | BETA: splitting (2098) gives: % 261.81/56.64 | | | | | | | | | | | | % 261.81/56.64 | | | | | | | | | | | | Case 1: % 261.81/56.64 | | | | | | | | | | | | | % 261.81/56.64 | | | | | | | | | | | | | (2099) ~ leq(n0, all_74_18) % 261.81/56.64 | | | | | | | | | | | | | % 261.81/56.64 | | | | | | | | | | | | | REDUCE: (2046), (2099) imply: % 261.81/56.64 | | | | | | | | | | | | | (2100) ~ leq(n0, n0) % 261.81/56.64 | | | | | | | | | | | | | % 261.81/56.64 | | | | | | | | | | | | | PRED_UNIFY: (1852), (2100) imply: % 261.81/56.64 | | | | | | | | | | | | | (2101) $false % 261.81/56.64 | | | | | | | | | | | | | % 261.81/56.64 | | | | | | | | | | | | | CLOSE: (2101) is inconsistent. % 261.81/56.64 | | | | | | | | | | | | | % 261.81/56.64 | | | | | | | | | | | | Case 2: % 261.81/56.64 | | | | | | | | | | | | | % 261.81/56.64 | | | | | | | | | | | | | (2102) ~ leq(n4, all_74_20) | (a_select3(id_ds1_filter, % 261.81/56.64 | | | | | | | | | | | | | n4, n0) = all_74_13 & $i(all_74_13)) % 261.81/56.64 | | | | | | | | | | | | | % 261.81/56.64 | | | | | | | | | | | | | REF_CLOSE: (30), (159), (649), (2094), (2096), (2102) are % 261.81/56.64 | | | | | | | | | | | | | inconsistent by sub-proof #9. % 261.81/56.64 | | | | | | | | | | | | | % 261.81/56.64 | | | | | | | | | | | | End of split % 261.81/56.64 | | | | | | | | | | | | % 261.81/56.64 | | | | | | | | | | | End of split % 261.81/56.64 | | | | | | | | | | | % 261.81/56.64 | | | | | | | | | | End of split % 261.81/56.64 | | | | | | | | | | % 261.81/56.64 | | | | | | | | | End of split % 261.81/56.64 | | | | | | | | | % 261.81/56.64 | | | | | | | | Case 2: % 261.81/56.64 | | | | | | | | | % 261.81/56.64 | | | | | | | | | (2103) all_74_14 = n5 % 261.81/56.64 | | | | | | | | | % 261.81/56.64 | | | | | | | | | REDUCE: (1850), (2103) imply: % 261.81/56.64 | | | | | | | | | (2104) a_select3(id_ds1_filter, n5, n0) = all_74_12 % 261.81/56.64 | | | | | | | | | % 261.81/56.64 | | | | | | | | | REDUCE: (1851), (2103) imply: % 261.81/56.64 | | | | | | | | | (2105) a_select3(id_ds1_filter, n0, n5) = all_74_13 % 261.81/56.64 | | | | | | | | | % 261.81/56.64 | | | | | | | | | REDUCE: (659), (2103) imply: % 261.81/56.64 | | | | | | | | | (2106) leq(n5, n5) % 261.81/56.64 | | | | | | | | | % 261.81/56.64 | | | | | | | | | REDUCE: (651), (2103) imply: % 261.81/56.64 | | | | | | | | | (2107) leq(n0, n5) % 261.81/56.64 | | | | | | | | | % 261.81/56.64 | | | | | | | | | BETA: splitting (697) gives: % 261.81/56.64 | | | | | | | | | % 261.81/56.64 | | | | | | | | | Case 1: % 261.81/56.64 | | | | | | | | | | % 261.81/56.64 | | | | | | | | | | (2108) gt(all_74_18, n0) % 261.81/56.64 | | | | | | | | | | % 261.81/56.64 | | | | | | | | | | BETA: splitting (699) gives: % 261.81/56.64 | | | | | | | | | | % 261.81/56.64 | | | | | | | | | | Case 1: % 261.81/56.64 | | | | | | | | | | | % 261.81/56.64 | | | | | | | | | | | (2109) gt(pv57, n1) % 261.81/56.64 | | | | | | | | | | | % 261.81/56.64 | | | | | | | | | | | GROUND_INST: instantiating (1) with n1, pv57, all_74_18, % 261.81/56.64 | | | | | | | | | | | simplifying with (24), (102), (155), (2109) gives: % 261.81/56.64 | | | | | | | | | | | (2110) leq(n1, all_74_18) % 261.81/56.64 | | | | | | | | | | | % 261.81/56.64 | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with n1, all_74_18, % 261.81/56.64 | | | | | | | | | | | simplifying with (102), (154), (2110) gives: % 261.81/56.64 | | | | | | | | | | | (2111) all_74_18 = n1 | gt(all_74_18, n1) % 261.81/56.64 | | | | | | | | | | | % 261.81/56.64 | | | | | | | | | | | BETA: splitting (703) gives: % 261.81/56.64 | | | | | | | | | | | % 261.81/56.64 | | | | | | | | | | | Case 1: % 261.81/56.64 | | | | | | | | | | | | % 261.81/56.64 | | | | | | | | | | | | (2112) gt(n4, pv57) % 261.81/56.64 | | | | | | | | | | | | % 261.81/56.64 | | | | | | | | | | | | BETA: splitting (695) gives: % 261.81/56.64 | | | | | | | | | | | | % 261.81/56.64 | | | | | | | | | | | | Case 1: % 261.81/56.64 | | | | | | | | | | | | | % 261.81/56.64 | | | | | | | | | | | | | (2113) all_74_18 = n0 % 261.81/56.64 | | | | | | | | | | | | | % 261.81/56.64 | | | | | | | | | | | | | REF_CLOSE: (22), (30), (82), (139), (159), (649), (1852), % 261.81/56.64 | | | | | | | | | | | | | (2104), (2105), (2106), (2107), (2113) are % 261.81/56.64 | | | | | | | | | | | | | inconsistent by sub-proof #6. % 261.81/56.64 | | | | | | | | | | | | | % 261.81/56.64 | | | | | | | | | | | | Case 2: % 261.81/56.64 | | | | | | | | | | | | | % 261.81/56.64 | | | | | | | | | | | | | % 261.81/56.64 | | | | | | | | | | | | | GROUND_INST: instantiating (1) with pv57, n4, n3, simplifying % 261.81/56.64 | | | | | | | | | | | | | with (24), (136), (147), (2112) gives: % 262.16/56.64 | | | | | | | | | | | | | (2114) leq(pv57, n3) % 262.16/56.64 | | | | | | | | | | | | | % 262.16/56.64 | | | | | | | | | | | | | GROUND_INST: instantiating (15) with pv57, simplifying with % 262.16/56.64 | | | | | | | | | | | | | (24), (63), (2114) gives: % 262.16/56.64 | | | | | | | | | | | | | (2115) pv57 = n3 | pv57 = n2 | pv57 = n1 | pv57 = n0 % 262.16/56.64 | | | | | | | | | | | | | % 262.16/56.64 | | | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with pv57, n3, simplifying % 262.16/56.64 | | | | | | | | | | | | | with (24), (129), (2114) gives: % 262.16/56.64 | | | | | | | | | | | | | (2116) pv57 = n3 | gt(n3, pv57) % 262.16/56.64 | | | | | | | | | | | | | % 262.16/56.64 | | | | | | | | | | | | | BETA: splitting (706) gives: % 262.16/56.64 | | | | | | | | | | | | | % 262.16/56.64 | | | | | | | | | | | | | Case 1: % 262.16/56.64 | | | | | | | | | | | | | | % 262.16/56.64 | | | | | | | | | | | | | | (2117) pv57 = n1 % 262.16/56.64 | | | | | | | | | | | | | | % 262.16/56.64 | | | | | | | | | | | | | | REF_CLOSE: (27), (144), (155), (1853), (2108), (2117) are % 262.16/56.64 | | | | | | | | | | | | | | inconsistent by sub-proof #75. % 262.16/56.64 | | | | | | | | | | | | | | % 262.16/56.64 | | | | | | | | | | | | | Case 2: % 262.16/56.64 | | | | | | | | | | | | | | % 262.16/56.64 | | | | | | | | | | | | | | (2118) ~ (pv57 = n1) % 262.16/56.64 | | | | | | | | | | | | | | (2119) pv57 = n5 | pv57 = n4 | pv57 = n3 | pv57 = n2 % 262.16/56.64 | | | | | | | | | | | | | | % 262.16/56.64 | | | | | | | | | | | | | | BETA: splitting (2111) gives: % 262.16/56.64 | | | | | | | | | | | | | | % 262.16/56.64 | | | | | | | | | | | | | | Case 1: % 262.16/56.64 | | | | | | | | | | | | | | | % 262.16/56.64 | | | | | | | | | | | | | | | (2120) gt(all_74_18, n1) % 262.16/56.64 | | | | | | | | | | | | | | | % 262.16/56.64 | | | | | | | | | | | | | | | BETA: splitting (2116) gives: % 262.16/56.64 | | | | | | | | | | | | | | | % 262.16/56.64 | | | | | | | | | | | | | | | Case 1: % 262.16/56.64 | | | | | | | | | | | | | | | | % 262.16/56.64 | | | | | | | | | | | | | | | | (2121) gt(n3, pv57) % 262.16/56.64 | | | | | | | | | | | | | | | | % 262.16/56.64 | | | | | | | | | | | | | | | | REF_CLOSE: (24), (27), (145), (154), (155), (705), (2115), % 262.16/56.64 | | | | | | | | | | | | | | | | (2118), (2119), (2120), (2121), (irreflexivity_gt) % 262.16/56.64 | | | | | | | | | | | | | | | | are inconsistent by sub-proof #34. % 262.16/56.64 | | | | | | | | | | | | | | | | % 262.16/56.64 | | | | | | | | | | | | | | | Case 2: % 262.16/56.64 | | | | | | | | | | | | | | | | % 262.16/56.64 | | | | | | | | | | | | | | | | (2122) pv57 = n3 % 262.16/56.64 | | | | | | | | | | | | | | | | % 262.16/56.64 | | | | | | | | | | | | | | | | REDUCE: (75), (2122) imply: % 262.16/56.64 | | | | | | | | | | | | | | | | (2123) minus(n3, n1) = all_74_18 % 262.16/56.64 | | | | | | | | | | | | | | | | % 262.16/56.64 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (29) with n2, all_74_18, n1, n3, % 262.16/56.64 | | | | | | | | | | | | | | | | simplifying with (161), (2123) gives: % 262.16/56.64 | | | | | | | | | | | | | | | | (2124) all_74_18 = n2 % 262.16/56.64 | | | | | | | | | | | | | | | | % 262.16/56.64 | | | | | | | | | | | | | | | | REDUCE: (690), (2124) imply: % 262.16/56.64 | | | | | | | | | | | | | | | | (2125) leq(n0, n2) % 262.16/56.64 | | | | | | | | | | | | | | | | % 262.16/56.64 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (82) with n0, n5, all_74_13, % 262.16/56.64 | | | | | | | | | | | | | | | | simplifying with (22), (139), (1852), (2105), % 262.16/56.64 | | | | | | | | | | | | | | | | (2107) gives: % 262.16/56.64 | | | | | | | | | | | | | | | | (2126) ~ leq(n5, all_74_20) | ~ leq(n0, all_74_18) | % 262.16/56.64 | | | | | | | | | | | | | | | | (a_select3(id_ds1_filter, n5, n0) = all_74_13 & % 262.16/56.64 | | | | | | | | | | | | | | | | $i(all_74_13)) % 262.16/56.64 | | | | | | | | | | | | | | | | % 262.16/56.64 | | | | | | | | | | | | | | | | BETA: splitting (2126) gives: % 262.16/56.64 | | | | | | | | | | | | | | | | % 262.16/56.64 | | | | | | | | | | | | | | | | Case 1: % 262.16/56.64 | | | | | | | | | | | | | | | | | % 262.16/56.64 | | | | | | | | | | | | | | | | | (2127) ~ leq(n0, all_74_18) % 262.16/56.64 | | | | | | | | | | | | | | | | | % 262.16/56.64 | | | | | | | | | | | | | | | | | REDUCE: (2124), (2127) imply: % 262.16/56.64 | | | | | | | | | | | | | | | | | (2128) ~ leq(n0, n2) % 262.16/56.64 | | | | | | | | | | | | | | | | | % 262.16/56.64 | | | | | | | | | | | | | | | | | PRED_UNIFY: (2125), (2128) imply: % 262.16/56.64 | | | | | | | | | | | | | | | | | (2129) $false % 262.16/56.64 | | | | | | | | | | | | | | | | | % 262.16/56.64 | | | | | | | | | | | | | | | | | CLOSE: (2129) is inconsistent. % 262.16/56.64 | | | | | | | | | | | | | | | | | % 262.16/56.64 | | | | | | | | | | | | | | | | Case 2: % 262.16/56.64 | | | | | | | | | | | | | | | | | % 262.16/56.64 | | | | | | | | | | | | | | | | | (2130) ~ leq(n5, all_74_20) | (a_select3(id_ds1_filter, % 262.16/56.64 | | | | | | | | | | | | | | | | | n5, n0) = all_74_13 & $i(all_74_13)) % 262.16/56.64 | | | | | | | | | | | | | | | | | % 262.16/56.64 | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (159), (649), (2104), (2106), (2130) are % 262.16/56.64 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #7. % 262.16/56.64 | | | | | | | | | | | | | | | | | % 262.16/56.64 | | | | | | | | | | | | | | | | End of split % 262.16/56.64 | | | | | | | | | | | | | | | | % 262.16/56.64 | | | | | | | | | | | | | | | End of split % 262.16/56.64 | | | | | | | | | | | | | | | % 262.16/56.64 | | | | | | | | | | | | | | Case 2: % 262.16/56.64 | | | | | | | | | | | | | | | % 262.16/56.64 | | | | | | | | | | | | | | | (2131) all_74_18 = n1 % 262.16/56.64 | | | | | | | | | | | | | | | % 262.16/56.64 | | | | | | | | | | | | | | | REDUCE: (690), (2131) imply: % 262.16/56.64 | | | | | | | | | | | | | | | (2132) leq(n0, n1) % 262.16/56.64 | | | | | | | | | | | | | | | % 262.16/56.64 | | | | | | | | | | | | | | | GROUND_INST: instantiating (82) with n0, n5, all_74_13, % 262.16/56.64 | | | | | | | | | | | | | | | simplifying with (22), (139), (1852), (2105), % 262.16/56.64 | | | | | | | | | | | | | | | (2107) gives: % 262.16/56.64 | | | | | | | | | | | | | | | (2133) ~ leq(n5, all_74_20) | ~ leq(n0, all_74_18) | % 262.16/56.64 | | | | | | | | | | | | | | | (a_select3(id_ds1_filter, n5, n0) = all_74_13 & % 262.16/56.64 | | | | | | | | | | | | | | | $i(all_74_13)) % 262.16/56.64 | | | | | | | | | | | | | | | % 262.16/56.64 | | | | | | | | | | | | | | | BETA: splitting (2133) gives: % 262.16/56.64 | | | | | | | | | | | | | | | % 262.16/56.64 | | | | | | | | | | | | | | | Case 1: % 262.16/56.64 | | | | | | | | | | | | | | | | % 262.16/56.64 | | | | | | | | | | | | | | | | (2134) ~ leq(n0, all_74_18) % 262.16/56.64 | | | | | | | | | | | | | | | | % 262.16/56.64 | | | | | | | | | | | | | | | | REDUCE: (2131), (2134) imply: % 262.16/56.64 | | | | | | | | | | | | | | | | (2135) ~ leq(n0, n1) % 262.16/56.64 | | | | | | | | | | | | | | | | % 262.16/56.64 | | | | | | | | | | | | | | | | PRED_UNIFY: (2132), (2135) imply: % 262.16/56.64 | | | | | | | | | | | | | | | | (2136) $false % 262.16/56.64 | | | | | | | | | | | | | | | | % 262.16/56.64 | | | | | | | | | | | | | | | | CLOSE: (2136) is inconsistent. % 262.16/56.64 | | | | | | | | | | | | | | | | % 262.16/56.64 | | | | | | | | | | | | | | | Case 2: % 262.16/56.64 | | | | | | | | | | | | | | | | % 262.16/56.64 | | | | | | | | | | | | | | | | (2137) ~ leq(n5, all_74_20) | (a_select3(id_ds1_filter, % 262.16/56.64 | | | | | | | | | | | | | | | | n5, n0) = all_74_13 & $i(all_74_13)) % 262.16/56.64 | | | | | | | | | | | | | | | | % 262.16/56.64 | | | | | | | | | | | | | | | | REF_CLOSE: (30), (159), (649), (2104), (2106), (2137) are % 262.16/56.64 | | | | | | | | | | | | | | | | inconsistent by sub-proof #7. % 262.16/56.64 | | | | | | | | | | | | | | | | % 262.16/56.64 | | | | | | | | | | | | | | | End of split % 262.16/56.64 | | | | | | | | | | | | | | | % 262.16/56.64 | | | | | | | | | | | | | | End of split % 262.16/56.64 | | | | | | | | | | | | | | % 262.16/56.64 | | | | | | | | | | | | | End of split % 262.16/56.64 | | | | | | | | | | | | | % 262.16/56.64 | | | | | | | | | | | | End of split % 262.16/56.64 | | | | | | | | | | | | % 262.16/56.64 | | | | | | | | | | | Case 2: % 262.16/56.64 | | | | | | | | | | | | % 262.16/56.64 | | | | | | | | | | | | (2138) pv57 = n4 % 262.16/56.64 | | | | | | | | | | | | % 262.16/56.64 | | | | | | | | | | | | REDUCE: (669), (2138) imply: % 262.16/56.64 | | | | | | | | | | | | (2139) succ(n4) = all_74_17 % 262.16/56.64 | | | | | | | | | | | | % 262.16/56.64 | | | | | | | | | | | | REDUCE: (155), (2138) imply: % 262.16/56.64 | | | | | | | | | | | | (2140) pred(n4) = all_74_18 % 262.16/56.64 | | | | | | | | | | | | % 262.16/56.64 | | | | | | | | | | | | GROUND_INST: instantiating (27) with n3, all_74_18, n4, % 262.16/56.64 | | | | | | | | | | | | simplifying with (147), (2140) gives: % 262.16/56.64 | | | | | | | | | | | | (2141) all_74_18 = n3 % 262.16/56.64 | | | | | | | | | | | | % 262.16/56.64 | | | | | | | | | | | | GROUND_INST: instantiating (28) with n5, all_74_17, n4, % 262.16/56.64 | | | | | | | | | | | | simplifying with (135), (2139) gives: % 262.16/56.64 | | | | | | | | | | | | (2142) all_74_17 = n5 % 262.16/56.64 | | | | | | | | | | | | % 262.16/56.64 | | | | | | | | | | | | REDUCE: (690), (2141) imply: % 262.16/56.64 | | | | | | | | | | | | (2143) leq(n0, n3) % 262.16/56.64 | | | | | | | | | | | | % 262.16/56.64 | | | | | | | | | | | | GROUND_INST: instantiating (82) with n0, n5, all_74_13, % 262.16/56.64 | | | | | | | | | | | | simplifying with (22), (139), (1852), (2105), % 262.16/56.64 | | | | | | | | | | | | (2107) gives: % 262.16/56.64 | | | | | | | | | | | | (2144) ~ leq(n5, all_74_20) | ~ leq(n0, all_74_18) | % 262.16/56.64 | | | | | | | | | | | | (a_select3(id_ds1_filter, n5, n0) = all_74_13 & % 262.16/56.64 | | | | | | | | | | | | $i(all_74_13)) % 262.16/56.64 | | | | | | | | | | | | % 262.16/56.64 | | | | | | | | | | | | BETA: splitting (2144) gives: % 262.16/56.64 | | | | | | | | | | | | % 262.16/56.64 | | | | | | | | | | | | Case 1: % 262.16/56.64 | | | | | | | | | | | | | % 262.16/56.64 | | | | | | | | | | | | | (2145) ~ leq(n0, all_74_18) % 262.16/56.64 | | | | | | | | | | | | | % 262.16/56.64 | | | | | | | | | | | | | REDUCE: (2141), (2145) imply: % 262.16/56.64 | | | | | | | | | | | | | (2146) ~ leq(n0, n3) % 262.16/56.64 | | | | | | | | | | | | | % 262.16/56.64 | | | | | | | | | | | | | PRED_UNIFY: (2143), (2146) imply: % 262.16/56.64 | | | | | | | | | | | | | (2147) $false % 262.16/56.64 | | | | | | | | | | | | | % 262.16/56.64 | | | | | | | | | | | | | CLOSE: (2147) is inconsistent. % 262.16/56.64 | | | | | | | | | | | | | % 262.16/56.64 | | | | | | | | | | | | Case 2: % 262.16/56.64 | | | | | | | | | | | | | % 262.16/56.64 | | | | | | | | | | | | | (2148) ~ leq(n5, all_74_20) | (a_select3(id_ds1_filter, % 262.16/56.64 | | | | | | | | | | | | | n5, n0) = all_74_13 & $i(all_74_13)) % 262.16/56.64 | | | | | | | | | | | | | % 262.16/56.64 | | | | | | | | | | | | | REF_CLOSE: (30), (159), (649), (2104), (2106), (2148) are % 262.16/56.64 | | | | | | | | | | | | | inconsistent by sub-proof #7. % 262.16/56.64 | | | | | | | | | | | | | % 262.16/56.64 | | | | | | | | | | | | End of split % 262.16/56.64 | | | | | | | | | | | | % 262.16/56.64 | | | | | | | | | | | End of split % 262.16/56.64 | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | Case 2: % 262.16/56.65 | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | (2149) pv57 = n1 % 262.16/56.65 | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | REF_CLOSE: (27), (144), (155), (1853), (2108), (2149) are % 262.16/56.65 | | | | | | | | | | | inconsistent by sub-proof #75. % 262.16/56.65 | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | End of split % 262.16/56.65 | | | | | | | | | | % 262.16/56.65 | | | | | | | | | Case 2: % 262.16/56.65 | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | (2150) all_74_18 = n0 % 262.16/56.65 | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | REF_CLOSE: (22), (30), (82), (139), (159), (649), (1852), % 262.16/56.65 | | | | | | | | | | (2104), (2105), (2106), (2107), (2150) are % 262.16/56.65 | | | | | | | | | | inconsistent by sub-proof #6. % 262.16/56.65 | | | | | | | | | | % 262.16/56.65 | | | | | | | | | End of split % 262.16/56.65 | | | | | | | | | % 262.16/56.65 | | | | | | | | End of split % 262.16/56.65 | | | | | | | | % 262.16/56.65 | | | | | | | End of split % 262.16/56.65 | | | | | | | % 262.16/56.65 | | | | | | Case 2: % 262.16/56.65 | | | | | | | % 262.16/56.65 | | | | | | | (2151) all_74_14 = n0 % 262.16/56.65 | | | | | | | (2152) ~ gt(all_74_14, n0) % 262.16/56.65 | | | | | | | % 262.16/56.65 | | | | | | | REDUCE: (656), (2151) imply: % 262.16/56.65 | | | | | | | (2153) a_select3(id_ds1_filter, n0, all_74_15) = all_74_12 % 262.16/56.65 | | | | | | | % 262.16/56.65 | | | | | | | REDUCE: (655), (2151) imply: % 262.16/56.65 | | | | | | | (2154) a_select3(id_ds1_filter, all_74_15, n0) = all_74_13 % 262.16/56.65 | | | | | | | % 262.16/56.65 | | | | | | | REDUCE: (651), (2151) imply: % 262.16/56.65 | | | | | | | (2155) leq(n0, n0) % 262.16/56.65 | | | | | | | % 262.16/56.65 | | | | | | | REDUCE: (2151), (2152) imply: % 262.16/56.65 | | | | | | | (2156) ~ gt(n0, n0) % 262.16/56.65 | | | | | | | % 262.16/56.65 | | | | | | | BETA: splitting (660) gives: % 262.16/56.65 | | | | | | | % 262.16/56.65 | | | | | | | Case 1: % 262.16/56.65 | | | | | | | | % 262.16/56.65 | | | | | | | | (2157) gt(all_74_15, n0) % 262.16/56.65 | | | | | | | | % 262.16/56.65 | | | | | | | | BETA: splitting (663) gives: % 262.16/56.65 | | | | | | | | % 262.16/56.65 | | | | | | | | Case 1: % 262.16/56.65 | | | | | | | | | % 262.16/56.65 | | | | | | | | | (2158) gt(all_74_16, all_74_15) % 262.16/56.65 | | | | | | | | | % 262.16/56.65 | | | | | | | | | REDUCE: (679), (2158) imply: % 262.16/56.65 | | | | | | | | | (2159) gt(pv57, all_74_15) % 262.16/56.65 | | | | | | | | | % 262.16/56.65 | | | | | | | | | GROUND_INST: instantiating (1) with all_74_15, pv57, all_74_18, % 262.16/56.65 | | | | | | | | | simplifying with (24), (66), (155), (2159) gives: % 262.16/56.65 | | | | | | | | | (2160) leq(all_74_15, all_74_18) % 262.16/56.65 | | | | | | | | | % 262.16/56.65 | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_15, all_74_18, % 262.16/56.65 | | | | | | | | | simplifying with (66), (154), (2160) gives: % 262.16/56.65 | | | | | | | | | (2161) all_74_15 = all_74_18 | gt(all_74_18, all_74_15) % 262.16/56.65 | | | | | | | | | % 262.16/56.65 | | | | | | | | | BETA: splitting (687) gives: % 262.16/56.65 | | | | | | | | | % 262.16/56.65 | | | | | | | | | Case 1: % 262.16/56.65 | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | (2162) all_74_15 = n0 % 262.16/56.65 | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | REDUCE: (2157), (2162) imply: % 262.16/56.65 | | | | | | | | | | (2163) gt(n0, n0) % 262.16/56.65 | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | PRED_UNIFY: (2156), (2163) imply: % 262.16/56.65 | | | | | | | | | | (2164) $false % 262.16/56.65 | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | CLOSE: (2164) is inconsistent. % 262.16/56.65 | | | | | | | | | | % 262.16/56.65 | | | | | | | | | Case 2: % 262.16/56.65 | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | (2165) ~ (all_74_15 = n0) % 262.16/56.65 | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | BETA: splitting (697) gives: % 262.16/56.65 | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | Case 1: % 262.16/56.65 | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | (2166) gt(all_74_18, n0) % 262.16/56.65 | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | BETA: splitting (699) gives: % 262.16/56.65 | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | Case 1: % 262.16/56.65 | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | (2167) gt(pv57, n1) % 262.16/56.65 | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | BETA: splitting (703) gives: % 262.16/56.65 | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | Case 1: % 262.16/56.65 | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | (2168) gt(n4, pv57) % 262.16/56.65 | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | GROUND_INST: instantiating (1) with pv57, n4, n3, simplifying % 262.16/56.65 | | | | | | | | | | | | | with (24), (136), (147), (2168) gives: % 262.16/56.65 | | | | | | | | | | | | | (2169) leq(pv57, n3) % 262.16/56.65 | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | GROUND_INST: instantiating (1) with n1, pv57, all_74_18, % 262.16/56.65 | | | | | | | | | | | | | simplifying with (24), (102), (155), (2167) gives: % 262.16/56.65 | | | | | | | | | | | | | (2170) leq(n1, all_74_18) % 262.16/56.65 | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with n1, all_74_18, % 262.16/56.65 | | | | | | | | | | | | | simplifying with (102), (154), (2170) gives: % 262.16/56.65 | | | | | | | | | | | | | (2171) all_74_18 = n1 | gt(all_74_18, n1) % 262.16/56.65 | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | GROUND_INST: instantiating (15) with pv57, simplifying with % 262.16/56.65 | | | | | | | | | | | | | (24), (63), (2169) gives: % 262.16/56.65 | | | | | | | | | | | | | (2172) pv57 = n3 | pv57 = n2 | pv57 = n1 | pv57 = n0 % 262.16/56.65 | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with pv57, n3, simplifying % 262.16/56.65 | | | | | | | | | | | | | with (24), (129), (2169) gives: % 262.16/56.65 | | | | | | | | | | | | | (2173) pv57 = n3 | gt(n3, pv57) % 262.16/56.65 | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | BETA: splitting (706) gives: % 262.16/56.65 | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | Case 1: % 262.16/56.65 | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | (2174) pv57 = n1 % 262.16/56.65 | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | REF_CLOSE: (27), (144), (155), (2156), (2166), (2174) are % 262.16/56.65 | | | | | | | | | | | | | | inconsistent by sub-proof #75. % 262.16/56.65 | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | Case 2: % 262.16/56.65 | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | (2175) ~ (pv57 = n1) % 262.16/56.65 | | | | | | | | | | | | | | (2176) pv57 = n5 | pv57 = n4 | pv57 = n3 | pv57 = n2 % 262.16/56.65 | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | BETA: splitting (2161) gives: % 262.16/56.65 | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | Case 1: % 262.16/56.65 | | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | | (2177) gt(all_74_18, all_74_15) % 262.16/56.65 | | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | | BETA: splitting (2171) gives: % 262.16/56.65 | | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | | Case 1: % 262.16/56.65 | | | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | | | (2178) gt(all_74_18, n1) % 262.16/56.65 | | | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | | | BETA: splitting (2173) gives: % 262.16/56.65 | | | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | | | Case 1: % 262.16/56.65 | | | | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | | | | (2179) gt(n3, pv57) % 262.16/56.65 | | | | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | | | | REF_CLOSE: (24), (27), (145), (154), (155), (705), (2172), % 262.16/56.65 | | | | | | | | | | | | | | | | | (2175), (2176), (2178), (2179), (irreflexivity_gt) % 262.16/56.65 | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #34. % 262.16/56.65 | | | | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | | | Case 2: % 262.16/56.65 | | | | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | | | | (2180) pv57 = n3 % 262.16/56.65 | | | | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | | | | REDUCE: (75), (2180) imply: % 262.16/56.65 | | | | | | | | | | | | | | | | | (2181) minus(n3, n1) = all_74_18 % 262.16/56.65 | | | | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (29) with n2, all_74_18, n1, n3, % 262.16/56.65 | | | | | | | | | | | | | | | | | simplifying with (161), (2181) gives: % 262.16/56.65 | | | | | | | | | | | | | | | | | (2182) all_74_18 = n2 % 262.16/56.65 | | | | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | | | | REDUCE: (690), (2182) imply: % 262.16/56.65 | | | | | | | | | | | | | | | | | (2183) leq(n0, n2) % 262.16/56.65 | | | | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | | | | REDUCE: (2177), (2182) imply: % 262.16/56.65 | | | | | | | | | | | | | | | | | (2184) gt(n2, all_74_15) % 262.16/56.65 | | | | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_15, n2, n1, % 262.16/56.65 | | | | | | | | | | | | | | | | | simplifying with (66), (118), (145), (2184) gives: % 262.16/56.65 | | | | | | | | | | | | | | | | | (2185) leq(all_74_15, n1) % 262.16/56.65 | | | | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_74_15, simplifying % 262.16/56.65 | | | | | | | | | | | | | | | | | with (66), (650), (2185) gives: % 262.16/56.65 | | | | | | | | | | | | | | | | | (2186) all_74_15 = n1 | all_74_15 = n0 % 262.16/56.65 | | | | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | | | | BETA: splitting (2186) gives: % 262.16/56.65 | | | | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | | | | Case 1: % 262.16/56.65 | | | | | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | | | | | (2187) all_74_15 = n0 % 262.16/56.65 | | | | | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | | | | | REDUCE: (2165), (2187) imply: % 262.16/56.65 | | | | | | | | | | | | | | | | | | (2188) $false % 262.16/56.65 | | | | | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | | | | | CLOSE: (2188) is inconsistent. % 262.16/56.65 | | | | | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | | | | Case 2: % 262.16/56.65 | | | | | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | | | | | (2189) all_74_15 = n1 % 262.16/56.65 | | | | | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | | | | | REDUCE: (2154), (2189) imply: % 262.16/56.65 | | | | | | | | | | | | | | | | | | (2190) a_select3(id_ds1_filter, n1, n0) = all_74_13 % 262.16/56.65 | | | | | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | | | | | REDUCE: (2153), (2189) imply: % 262.16/56.65 | | | | | | | | | | | | | | | | | | (2191) a_select3(id_ds1_filter, n0, n1) = all_74_12 % 262.16/56.65 | | | | | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | | | | | REDUCE: (684), (2189) imply: % 262.16/56.65 | | | | | | | | | | | | | | | | | | (2192) leq(n1, n5) % 262.16/56.65 | | | | | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | | | | | REDUCE: (650), (2189) imply: % 262.16/56.65 | | | | | | | | | | | | | | | | | | (2193) leq(n0, n1) % 262.16/56.65 | | | | | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (82) with n0, n1, all_74_12, % 262.16/56.65 | | | | | | | | | | | | | | | | | | simplifying with (22), (102), (2155), (2191), % 262.16/56.65 | | | | | | | | | | | | | | | | | | (2193) gives: % 262.16/56.65 | | | | | | | | | | | | | | | | | | (2194) ~ leq(n1, all_74_20) | ~ leq(n0, all_74_18) | % 262.16/56.65 | | | | | | | | | | | | | | | | | | (a_select3(id_ds1_filter, n1, n0) = all_74_12 & % 262.16/56.65 | | | | | | | | | | | | | | | | | | $i(all_74_12)) % 262.16/56.65 | | | | | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | | | | | BETA: splitting (2194) gives: % 262.16/56.65 | | | | | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | | | | | Case 1: % 262.16/56.65 | | | | | | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | | | | | | (2195) ~ leq(n0, all_74_18) % 262.16/56.65 | | | | | | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | | | | | | REDUCE: (2182), (2195) imply: % 262.16/56.65 | | | | | | | | | | | | | | | | | | | (2196) ~ leq(n0, n2) % 262.16/56.65 | | | | | | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (2183), (2196) imply: % 262.16/56.65 | | | | | | | | | | | | | | | | | | | (2197) $false % 262.16/56.65 | | | | | | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | | | | | | CLOSE: (2197) is inconsistent. % 262.16/56.65 | | | | | | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | | | | | Case 2: % 262.16/56.65 | | | | | | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | | | | | | (2198) ~ leq(n1, all_74_20) | (a_select3(id_ds1_filter, % 262.16/56.65 | | | | | | | | | | | | | | | | | | | n1, n0) = all_74_12 & $i(all_74_12)) % 262.16/56.65 | | | | | | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (159), (649), (2190), (2192), (2198) are % 262.16/56.65 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #5. % 262.16/56.65 | | | | | | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | | | | | End of split % 262.16/56.65 | | | | | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | | | | End of split % 262.16/56.65 | | | | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | | | End of split % 262.16/56.65 | | | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | | Case 2: % 262.16/56.65 | | | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | | | (2199) all_74_18 = n1 % 262.16/56.65 | | | | | | | | | | | | | | | | (2200) ~ gt(all_74_18, n1) % 262.16/56.65 | | | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | | | REF_CLOSE: (13), (66), (650), (2160), (2165), (2177), (2199), % 262.16/56.65 | | | | | | | | | | | | | | | | (2200) are inconsistent by sub-proof #28. % 262.16/56.65 | | | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | | End of split % 262.16/56.65 | | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | Case 2: % 262.16/56.65 | | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | | (2201) all_74_15 = all_74_18 % 262.16/56.65 | | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | | REDUCE: (2154), (2201) imply: % 262.16/56.65 | | | | | | | | | | | | | | | (2202) a_select3(id_ds1_filter, all_74_18, n0) = % 262.16/56.65 | | | | | | | | | | | | | | | all_74_13 % 262.16/56.65 | | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | | REDUCE: (2153), (2201) imply: % 262.16/56.65 | | | | | | | | | | | | | | | (2203) a_select3(id_ds1_filter, n0, all_74_18) = % 262.16/56.65 | | | | | | | | | | | | | | | all_74_12 % 262.16/56.65 | | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | | BETA: splitting (2171) gives: % 262.16/56.65 | | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | | Case 1: % 262.16/56.65 | | | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | | | (2204) gt(all_74_18, n1) % 262.16/56.65 | | | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | | | BETA: splitting (2173) gives: % 262.16/56.65 | | | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | | | Case 1: % 262.16/56.65 | | | | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | | | | (2205) gt(n3, pv57) % 262.16/56.65 | | | | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | | | | REF_CLOSE: (24), (27), (145), (154), (155), (705), (2172), % 262.16/56.65 | | | | | | | | | | | | | | | | | (2175), (2176), (2204), (2205), (irreflexivity_gt) % 262.16/56.65 | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #34. % 262.16/56.65 | | | | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | | | Case 2: % 262.16/56.65 | | | | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | | | | (2206) pv57 = n3 % 262.16/56.65 | | | | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | | | | REDUCE: (75), (2206) imply: % 262.16/56.65 | | | | | | | | | | | | | | | | | (2207) minus(n3, n1) = all_74_18 % 262.16/56.65 | | | | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | | | | REDUCE: (63), (2206) imply: % 262.16/56.65 | | | | | | | | | | | | | | | | | (2208) leq(n0, n3) % 262.16/56.65 | | | | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (29) with n2, all_74_18, n1, n3, % 262.16/56.65 | | | | | | | | | | | | | | | | | simplifying with (161), (2207) gives: % 262.16/56.65 | | | | | | | | | | | | | | | | | (2209) all_74_18 = n2 % 262.16/56.65 | | | | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | | | | REDUCE: (2202), (2209) imply: % 262.16/56.65 | | | | | | | | | | | | | | | | | (2210) a_select3(id_ds1_filter, n2, n0) = all_74_13 % 262.16/56.65 | | | | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | | | | REDUCE: (2203), (2209) imply: % 262.16/56.65 | | | | | | | | | | | | | | | | | (2211) a_select3(id_ds1_filter, n0, n2) = all_74_12 % 262.16/56.65 | | | | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | | | | REDUCE: (167), (2209) imply: % 262.16/56.65 | | | | | | | | | | | | | | | | | (2212) leq(n2, n5) % 262.16/56.65 | | | | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | | | | REDUCE: (690), (2209) imply: % 262.16/56.65 | | | | | | | | | | | | | | | | | (2213) leq(n0, n2) % 262.16/56.65 | | | | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (81) with n0, n2, all_74_12, % 262.16/56.65 | | | | | | | | | | | | | | | | | simplifying with (22), (118), (2155), (2211), % 262.16/56.65 | | | | | | | | | | | | | | | | | (2213) gives: % 262.16/56.65 | | | | | | | | | | | | | | | | | (2214) ~ leq(n2, all_74_20) | ~ leq(n0, pv57) | % 262.16/56.65 | | | | | | | | | | | | | | | | | (a_select3(id_ds1_filter, n2, n0) = all_74_12 & % 262.16/56.65 | | | | | | | | | | | | | | | | | $i(all_74_12)) % 262.16/56.65 | | | | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | | | | BETA: splitting (2214) gives: % 262.16/56.65 | | | | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | | | | Case 1: % 262.16/56.65 | | | | | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | | | | | (2215) ~ leq(n0, pv57) % 262.16/56.65 | | | | | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | | | | | REDUCE: (2206), (2215) imply: % 262.16/56.65 | | | | | | | | | | | | | | | | | | (2216) ~ leq(n0, n3) % 262.16/56.65 | | | | | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | | | | | PRED_UNIFY: (2208), (2216) imply: % 262.16/56.65 | | | | | | | | | | | | | | | | | | (2217) $false % 262.16/56.65 | | | | | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | | | | | CLOSE: (2217) is inconsistent. % 262.16/56.65 | | | | | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | | | | Case 2: % 262.16/56.65 | | | | | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | | | | | (2218) ~ leq(n2, all_74_20) | (a_select3(id_ds1_filter, % 262.16/56.65 | | | | | | | | | | | | | | | | | | n2, n0) = all_74_12 & $i(all_74_12)) % 262.16/56.65 | | | | | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (159), (649), (2210), (2212), (2218) are % 262.16/56.65 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #4. % 262.16/56.65 | | | | | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | | | | End of split % 262.16/56.65 | | | | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | | | End of split % 262.16/56.65 | | | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | | Case 2: % 262.16/56.65 | | | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | | | (2219) all_74_18 = n1 % 262.16/56.65 | | | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | | | REDUCE: (2202), (2219) imply: % 262.16/56.65 | | | | | | | | | | | | | | | | (2220) a_select3(id_ds1_filter, n1, n0) = all_74_13 % 262.16/56.65 | | | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | | | REDUCE: (2203), (2219) imply: % 262.16/56.65 | | | | | | | | | | | | | | | | (2221) a_select3(id_ds1_filter, n0, n1) = all_74_12 % 262.16/56.65 | | | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | | | REDUCE: (167), (2219) imply: % 262.16/56.65 | | | | | | | | | | | | | | | | (2222) leq(n1, n5) % 262.16/56.65 | | | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | | | REDUCE: (690), (2219) imply: % 262.16/56.65 | | | | | | | | | | | | | | | | (2223) leq(n0, n1) % 262.16/56.65 | | | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (82) with n0, n1, all_74_12, % 262.16/56.65 | | | | | | | | | | | | | | | | simplifying with (22), (102), (2155), (2221), % 262.16/56.65 | | | | | | | | | | | | | | | | (2223) gives: % 262.16/56.65 | | | | | | | | | | | | | | | | (2224) ~ leq(n1, all_74_20) | ~ leq(n0, all_74_18) | % 262.16/56.65 | | | | | | | | | | | | | | | | (a_select3(id_ds1_filter, n1, n0) = all_74_12 & % 262.16/56.65 | | | | | | | | | | | | | | | | $i(all_74_12)) % 262.16/56.65 | | | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | | | BETA: splitting (2224) gives: % 262.16/56.65 | | | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | | | Case 1: % 262.16/56.65 | | | | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | | | | (2225) ~ leq(n0, all_74_18) % 262.16/56.65 | | | | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | | | | REDUCE: (2219), (2225) imply: % 262.16/56.65 | | | | | | | | | | | | | | | | | (2226) ~ leq(n0, n1) % 262.16/56.65 | | | | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | | | | PRED_UNIFY: (2223), (2226) imply: % 262.16/56.65 | | | | | | | | | | | | | | | | | (2227) $false % 262.16/56.65 | | | | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | | | | CLOSE: (2227) is inconsistent. % 262.16/56.65 | | | | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | | | Case 2: % 262.16/56.65 | | | | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | | | | (2228) ~ leq(n1, all_74_20) | (a_select3(id_ds1_filter, % 262.16/56.65 | | | | | | | | | | | | | | | | | n1, n0) = all_74_12 & $i(all_74_12)) % 262.16/56.65 | | | | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (159), (649), (2220), (2222), (2228) are % 262.16/56.65 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #5. % 262.16/56.65 | | | | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | | | End of split % 262.16/56.65 | | | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | | End of split % 262.16/56.65 | | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | End of split % 262.16/56.65 | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | End of split % 262.16/56.65 | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | Case 2: % 262.16/56.65 | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | (2229) pv57 = n4 % 262.16/56.65 | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | REDUCE: (669), (2229) imply: % 262.16/56.65 | | | | | | | | | | | | | (2230) succ(n4) = all_74_17 % 262.16/56.65 | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | REDUCE: (155), (2229) imply: % 262.16/56.65 | | | | | | | | | | | | | (2231) pred(n4) = all_74_18 % 262.16/56.65 | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | REDUCE: (63), (2229) imply: % 262.16/56.65 | | | | | | | | | | | | | (2232) leq(n0, n4) % 262.16/56.65 | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | GROUND_INST: instantiating (27) with n3, all_74_18, n4, % 262.16/56.65 | | | | | | | | | | | | | simplifying with (147), (2231) gives: % 262.16/56.65 | | | | | | | | | | | | | (2233) all_74_18 = n3 % 262.16/56.65 | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | GROUND_INST: instantiating (28) with n5, all_74_17, n4, % 262.16/56.65 | | | | | | | | | | | | | simplifying with (135), (2230) gives: % 262.16/56.65 | | | | | | | | | | | | | (2234) all_74_17 = n5 % 262.16/56.65 | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | REDUCE: (690), (2233) imply: % 262.16/56.65 | | | | | | | | | | | | | (2235) leq(n0, n3) % 262.16/56.65 | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | BETA: splitting (2161) gives: % 262.16/56.65 | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | Case 1: % 262.16/56.65 | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | (2236) gt(all_74_18, all_74_15) % 262.16/56.65 | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | REDUCE: (2233), (2236) imply: % 262.16/56.65 | | | | | | | | | | | | | | (2237) gt(n3, all_74_15) % 262.16/56.65 | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_15, n3, n2, % 262.16/56.65 | | | | | | | | | | | | | | simplifying with (66), (129), (146), (2237) gives: % 262.16/56.65 | | | | | | | | | | | | | | (2238) leq(all_74_15, n2) % 262.16/56.65 | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_15, n2, % 262.16/56.65 | | | | | | | | | | | | | | simplifying with (66), (118), (2238) gives: % 262.16/56.65 | | | | | | | | | | | | | | (2239) all_74_15 = n2 | gt(n2, all_74_15) % 262.16/56.65 | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | BETA: splitting (2239) gives: % 262.16/56.65 | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | Case 1: % 262.16/56.65 | | | | | | | | | | | | | | | % 262.16/56.65 | | | | | | | | | | | | | | | (2240) gt(n2, all_74_15) % 262.16/56.65 | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_15, n2, n1, % 262.16/56.66 | | | | | | | | | | | | | | | simplifying with (66), (118), (145), (2240) gives: % 262.16/56.66 | | | | | | | | | | | | | | | (2241) leq(all_74_15, n1) % 262.16/56.66 | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_74_15, simplifying % 262.16/56.66 | | | | | | | | | | | | | | | with (66), (650), (2241) gives: % 262.16/56.66 | | | | | | | | | | | | | | | (2242) all_74_15 = n1 | all_74_15 = n0 % 262.16/56.66 | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | | BETA: splitting (2242) gives: % 262.16/56.66 | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | | Case 1: % 262.16/56.66 | | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | | | (2243) all_74_15 = n0 % 262.16/56.66 | | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | | | REDUCE: (2165), (2243) imply: % 262.16/56.66 | | | | | | | | | | | | | | | | (2244) $false % 262.16/56.66 | | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | | | CLOSE: (2244) is inconsistent. % 262.16/56.66 | | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | | Case 2: % 262.16/56.66 | | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | | | (2245) all_74_15 = n1 % 262.16/56.66 | | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | | | REDUCE: (2154), (2245) imply: % 262.16/56.66 | | | | | | | | | | | | | | | | (2246) a_select3(id_ds1_filter, n1, n0) = all_74_13 % 262.16/56.66 | | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | | | REDUCE: (2153), (2245) imply: % 262.16/56.66 | | | | | | | | | | | | | | | | (2247) a_select3(id_ds1_filter, n0, n1) = all_74_12 % 262.16/56.66 | | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | | | REDUCE: (684), (2245) imply: % 262.16/56.66 | | | | | | | | | | | | | | | | (2248) leq(n1, n5) % 262.16/56.66 | | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | | | REDUCE: (650), (2245) imply: % 262.16/56.66 | | | | | | | | | | | | | | | | (2249) leq(n0, n1) % 262.16/56.66 | | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (82) with n0, n1, all_74_12, % 262.16/56.66 | | | | | | | | | | | | | | | | simplifying with (22), (102), (2155), (2247), % 262.16/56.66 | | | | | | | | | | | | | | | | (2249) gives: % 262.16/56.66 | | | | | | | | | | | | | | | | (2250) ~ leq(n1, all_74_20) | ~ leq(n0, all_74_18) | % 262.16/56.66 | | | | | | | | | | | | | | | | (a_select3(id_ds1_filter, n1, n0) = all_74_12 & % 262.16/56.66 | | | | | | | | | | | | | | | | $i(all_74_12)) % 262.16/56.66 | | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | | | BETA: splitting (2250) gives: % 262.16/56.66 | | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | | | Case 1: % 262.16/56.66 | | | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | | | | (2251) ~ leq(n0, all_74_18) % 262.16/56.66 | | | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | | | | REDUCE: (2233), (2251) imply: % 262.16/56.66 | | | | | | | | | | | | | | | | | (2252) ~ leq(n0, n3) % 262.16/56.66 | | | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | | | | PRED_UNIFY: (2235), (2252) imply: % 262.16/56.66 | | | | | | | | | | | | | | | | | (2253) $false % 262.16/56.66 | | | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | | | | CLOSE: (2253) is inconsistent. % 262.16/56.66 | | | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | | | Case 2: % 262.16/56.66 | | | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | | | | (2254) ~ leq(n1, all_74_20) | (a_select3(id_ds1_filter, % 262.16/56.66 | | | | | | | | | | | | | | | | | n1, n0) = all_74_12 & $i(all_74_12)) % 262.16/56.66 | | | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (159), (649), (2246), (2248), (2254) are % 262.16/56.66 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #5. % 262.16/56.66 | | | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | | | End of split % 262.16/56.66 | | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | | End of split % 262.16/56.66 | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | Case 2: % 262.16/56.66 | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | | (2255) all_74_15 = n2 % 262.16/56.66 | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | | REDUCE: (2154), (2255) imply: % 262.16/56.66 | | | | | | | | | | | | | | | (2256) a_select3(id_ds1_filter, n2, n0) = all_74_13 % 262.16/56.66 | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | | REDUCE: (2153), (2255) imply: % 262.16/56.66 | | | | | | | | | | | | | | | (2257) a_select3(id_ds1_filter, n0, n2) = all_74_12 % 262.16/56.66 | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | | REDUCE: (684), (2255) imply: % 262.16/56.66 | | | | | | | | | | | | | | | (2258) leq(n2, n5) % 262.16/56.66 | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | | REDUCE: (650), (2255) imply: % 262.16/56.66 | | | | | | | | | | | | | | | (2259) leq(n0, n2) % 262.16/56.66 | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | | GROUND_INST: instantiating (81) with n0, n2, all_74_12, % 262.16/56.66 | | | | | | | | | | | | | | | simplifying with (22), (118), (2155), (2257), % 262.16/56.66 | | | | | | | | | | | | | | | (2259) gives: % 262.16/56.66 | | | | | | | | | | | | | | | (2260) ~ leq(n2, all_74_20) | ~ leq(n0, pv57) | % 262.16/56.66 | | | | | | | | | | | | | | | (a_select3(id_ds1_filter, n2, n0) = all_74_12 & % 262.16/56.66 | | | | | | | | | | | | | | | $i(all_74_12)) % 262.16/56.66 | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | | BETA: splitting (2260) gives: % 262.16/56.66 | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | | Case 1: % 262.16/56.66 | | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | | | (2261) ~ leq(n0, pv57) % 262.16/56.66 | | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | | | REDUCE: (2229), (2261) imply: % 262.16/56.66 | | | | | | | | | | | | | | | | (2262) ~ leq(n0, n4) % 262.16/56.66 | | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | | | PRED_UNIFY: (2232), (2262) imply: % 262.16/56.66 | | | | | | | | | | | | | | | | (2263) $false % 262.16/56.66 | | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | | | CLOSE: (2263) is inconsistent. % 262.16/56.66 | | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | | Case 2: % 262.16/56.66 | | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | | | (2264) ~ leq(n2, all_74_20) | (a_select3(id_ds1_filter, % 262.16/56.66 | | | | | | | | | | | | | | | | n2, n0) = all_74_12 & $i(all_74_12)) % 262.16/56.66 | | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | | | REF_CLOSE: (30), (159), (649), (2256), (2258), (2264) are % 262.16/56.66 | | | | | | | | | | | | | | | | inconsistent by sub-proof #4. % 262.16/56.66 | | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | | End of split % 262.16/56.66 | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | End of split % 262.16/56.66 | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | Case 2: % 262.16/56.66 | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | (2265) all_74_15 = all_74_18 % 262.16/56.66 | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | COMBINE_EQS: (2233), (2265) imply: % 262.16/56.66 | | | | | | | | | | | | | | (2266) all_74_15 = n3 % 262.16/56.66 | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | REDUCE: (2154), (2266) imply: % 262.16/56.66 | | | | | | | | | | | | | | (2267) a_select3(id_ds1_filter, n3, n0) = all_74_13 % 262.16/56.66 | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | REDUCE: (2153), (2266) imply: % 262.16/56.66 | | | | | | | | | | | | | | (2268) a_select3(id_ds1_filter, n0, n3) = all_74_12 % 262.16/56.66 | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | REDUCE: (684), (2266) imply: % 262.16/56.66 | | | | | | | | | | | | | | (2269) leq(n3, n5) % 262.16/56.66 | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | GROUND_INST: instantiating (81) with n0, n3, all_74_12, % 262.16/56.66 | | | | | | | | | | | | | | simplifying with (22), (129), (2155), (2235), % 262.16/56.66 | | | | | | | | | | | | | | (2268) gives: % 262.16/56.66 | | | | | | | | | | | | | | (2270) ~ leq(n3, all_74_20) | ~ leq(n0, pv57) | % 262.16/56.66 | | | | | | | | | | | | | | (a_select3(id_ds1_filter, n3, n0) = all_74_12 & % 262.16/56.66 | | | | | | | | | | | | | | $i(all_74_12)) % 262.16/56.66 | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | BETA: splitting (2270) gives: % 262.16/56.66 | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | Case 1: % 262.16/56.66 | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | | (2271) ~ leq(n0, pv57) % 262.16/56.66 | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | | REDUCE: (2229), (2271) imply: % 262.16/56.66 | | | | | | | | | | | | | | | (2272) ~ leq(n0, n4) % 262.16/56.66 | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | | PRED_UNIFY: (2232), (2272) imply: % 262.16/56.66 | | | | | | | | | | | | | | | (2273) $false % 262.16/56.66 | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | | CLOSE: (2273) is inconsistent. % 262.16/56.66 | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | Case 2: % 262.16/56.66 | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | | (2274) ~ leq(n3, all_74_20) | (a_select3(id_ds1_filter, % 262.16/56.66 | | | | | | | | | | | | | | | n3, n0) = all_74_12 & $i(all_74_12)) % 262.16/56.66 | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | | REF_CLOSE: (30), (159), (649), (2267), (2269), (2274) are % 262.16/56.66 | | | | | | | | | | | | | | | inconsistent by sub-proof #3. % 262.16/56.66 | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | End of split % 262.16/56.66 | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | End of split % 262.16/56.66 | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | End of split % 262.16/56.66 | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | Case 2: % 262.16/56.66 | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | (2275) pv57 = n1 % 262.16/56.66 | | | | | | | | | | | | (2276) ~ gt(pv57, n1) % 262.16/56.66 | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | REF_CLOSE: (13), (66), (650), (681), (2159), (2165), (2275), % 262.16/56.66 | | | | | | | | | | | | (2276) are inconsistent by sub-proof #21. % 262.16/56.66 | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | End of split % 262.16/56.66 | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | Case 2: % 262.16/56.66 | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | (2277) all_74_18 = n0 % 262.16/56.66 | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | REF_CLOSE: (22), (66), (2156), (2157), (2161), (2165), % 262.16/56.66 | | | | | | | | | | | (2277), (transitivity_gt) are inconsistent by % 262.16/56.66 | | | | | | | | | | | sub-proof #24. % 262.16/56.66 | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | End of split % 262.16/56.66 | | | | | | | | | | % 262.16/56.66 | | | | | | | | | End of split % 262.16/56.66 | | | | | | | | | % 262.16/56.66 | | | | | | | | Case 2: % 262.16/56.66 | | | | | | | | | % 262.16/56.66 | | | | | | | | | (2278) all_74_15 = all_74_16 % 262.16/56.66 | | | | | | | | | (2279) ~ gt(all_74_16, all_74_15) % 262.16/56.66 | | | | | | | | | % 262.16/56.66 | | | | | | | | | COMBINE_EQS: (679), (2278) imply: % 262.16/56.66 | | | | | | | | | (2280) all_74_15 = pv57 % 262.16/56.66 | | | | | | | | | % 262.16/56.66 | | | | | | | | | REDUCE: (2154), (2280) imply: % 262.16/56.66 | | | | | | | | | (2281) a_select3(id_ds1_filter, pv57, n0) = all_74_13 % 262.16/56.66 | | | | | | | | | % 262.16/56.66 | | | | | | | | | REDUCE: (2153), (2280) imply: % 262.16/56.66 | | | | | | | | | (2282) a_select3(id_ds1_filter, n0, pv57) = all_74_12 % 262.16/56.66 | | | | | | | | | % 262.16/56.66 | | | | | | | | | REDUCE: (679), (2279), (2280) imply: % 262.16/56.66 | | | | | | | | | (2283) ~ gt(pv57, pv57) % 262.16/56.66 | | | | | | | | | % 262.16/56.66 | | | | | | | | | BETA: splitting (697) gives: % 262.16/56.66 | | | | | | | | | % 262.16/56.66 | | | | | | | | | Case 1: % 262.16/56.66 | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | (2284) gt(all_74_18, n0) % 262.16/56.66 | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | BETA: splitting (696) gives: % 262.16/56.66 | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | Case 1: % 262.16/56.66 | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | (2285) all_74_18 = n0 % 262.16/56.66 | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | REDUCE: (2284), (2285) imply: % 262.16/56.66 | | | | | | | | | | | (2286) gt(n0, n0) % 262.16/56.66 | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | PRED_UNIFY: (2156), (2286) imply: % 262.16/56.66 | | | | | | | | | | | (2287) $false % 262.16/56.66 | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | CLOSE: (2287) is inconsistent. % 262.16/56.66 | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | Case 2: % 262.16/56.66 | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | (2288) ~ (all_74_18 = n0) % 262.16/56.66 | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | BETA: splitting (699) gives: % 262.16/56.66 | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | Case 1: % 262.16/56.66 | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | (2289) gt(pv57, n1) % 262.16/56.66 | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | GROUND_INST: instantiating (1) with n1, pv57, all_74_18, % 262.16/56.66 | | | | | | | | | | | | simplifying with (24), (102), (155), (2289) gives: % 262.16/56.66 | | | | | | | | | | | | (2290) leq(n1, all_74_18) % 262.16/56.66 | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | BETA: splitting (703) gives: % 262.16/56.66 | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | Case 1: % 262.16/56.66 | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | (2291) gt(n4, pv57) % 262.16/56.66 | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | BETA: splitting (695) gives: % 262.16/56.66 | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | Case 1: % 262.16/56.66 | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | (2292) all_74_18 = n0 % 262.16/56.66 | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | REDUCE: (2288), (2292) imply: % 262.16/56.66 | | | | | | | | | | | | | | (2293) $false % 262.16/56.66 | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | CLOSE: (2293) is inconsistent. % 262.16/56.66 | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | Case 2: % 262.16/56.66 | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with pv57, n4, n3, simplifying % 262.16/56.66 | | | | | | | | | | | | | | with (24), (136), (147), (2291) gives: % 262.16/56.66 | | | | | | | | | | | | | | (2294) leq(pv57, n3) % 262.16/56.66 | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with n1, all_74_18, % 262.16/56.66 | | | | | | | | | | | | | | simplifying with (102), (154), (2290) gives: % 262.16/56.66 | | | | | | | | | | | | | | (2295) all_74_18 = n1 | gt(all_74_18, n1) % 262.16/56.66 | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | GROUND_INST: instantiating (15) with pv57, simplifying with % 262.16/56.66 | | | | | | | | | | | | | | (24), (63), (2294) gives: % 262.16/56.66 | | | | | | | | | | | | | | (2296) pv57 = n3 | pv57 = n2 | pv57 = n1 | pv57 = n0 % 262.16/56.66 | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with pv57, n3, simplifying % 262.16/56.66 | | | | | | | | | | | | | | with (24), (129), (2294) gives: % 262.16/56.66 | | | | | | | | | | | | | | (2297) pv57 = n3 | gt(n3, pv57) % 262.16/56.66 | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | BETA: splitting (706) gives: % 262.16/56.66 | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | Case 1: % 262.16/56.66 | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | | (2298) pv57 = n1 % 262.16/56.66 | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | | REF_CLOSE: (2283), (2289), (2298) are inconsistent by % 262.16/56.66 | | | | | | | | | | | | | | | sub-proof #20. % 262.16/56.66 | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | Case 2: % 262.16/56.66 | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | | (2299) ~ (pv57 = n1) % 262.16/56.66 | | | | | | | | | | | | | | | (2300) pv57 = n5 | pv57 = n4 | pv57 = n3 | pv57 = n2 % 262.16/56.66 | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | | BETA: splitting (2295) gives: % 262.16/56.66 | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | | Case 1: % 262.16/56.66 | | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | | | (2301) gt(all_74_18, n1) % 262.16/56.66 | | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | | | BETA: splitting (2297) gives: % 262.16/56.66 | | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | | | Case 1: % 262.16/56.66 | | | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | | | | (2302) gt(n3, pv57) % 262.16/56.66 | | | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | | | | REF_CLOSE: (24), (27), (145), (154), (155), (705), (2296), % 262.16/56.66 | | | | | | | | | | | | | | | | | (2299), (2300), (2301), (2302), (irreflexivity_gt) % 262.16/56.66 | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #34. % 262.16/56.66 | | | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | | | Case 2: % 262.16/56.66 | | | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | | | | (2303) pv57 = n3 % 262.16/56.66 | | | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | | | | REDUCE: (75), (2303) imply: % 262.16/56.66 | | | | | | | | | | | | | | | | | (2304) minus(n3, n1) = all_74_18 % 262.16/56.66 | | | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | | | | REDUCE: (2281), (2303) imply: % 262.16/56.66 | | | | | | | | | | | | | | | | | (2305) a_select3(id_ds1_filter, n3, n0) = all_74_13 % 262.16/56.66 | | | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | | | | REDUCE: (2282), (2303) imply: % 262.16/56.66 | | | | | | | | | | | | | | | | | (2306) a_select3(id_ds1_filter, n0, n3) = all_74_12 % 262.16/56.66 | | | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | | | | REDUCE: (162), (2303) imply: % 262.16/56.66 | | | | | | | | | | | | | | | | | (2307) leq(n3, n5) % 262.16/56.66 | | | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | | | | REDUCE: (63), (2303) imply: % 262.16/56.66 | | | | | | | | | | | | | | | | | (2308) leq(n0, n3) % 262.16/56.66 | | | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (29) with n2, all_74_18, n1, n3, % 262.16/56.66 | | | | | | | | | | | | | | | | | simplifying with (161), (2304) gives: % 262.16/56.66 | | | | | | | | | | | | | | | | | (2309) all_74_18 = n2 % 262.16/56.66 | | | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | | | | REDUCE: (690), (2309) imply: % 262.16/56.66 | | | | | | | | | | | | | | | | | (2310) leq(n0, n2) % 262.16/56.66 | | | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (82) with n0, n3, all_74_12, % 262.16/56.66 | | | | | | | | | | | | | | | | | simplifying with (22), (129), (2155), (2306), % 262.16/56.66 | | | | | | | | | | | | | | | | | (2308) gives: % 262.16/56.66 | | | | | | | | | | | | | | | | | (2311) ~ leq(n3, all_74_20) | ~ leq(n0, all_74_18) | % 262.16/56.66 | | | | | | | | | | | | | | | | | (a_select3(id_ds1_filter, n3, n0) = all_74_12 & % 262.16/56.66 | | | | | | | | | | | | | | | | | $i(all_74_12)) % 262.16/56.66 | | | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | | | | BETA: splitting (2311) gives: % 262.16/56.66 | | | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | | | | Case 1: % 262.16/56.66 | | | | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | | | | | (2312) ~ leq(n0, all_74_18) % 262.16/56.66 | | | | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | | | | | REDUCE: (2309), (2312) imply: % 262.16/56.66 | | | | | | | | | | | | | | | | | | (2313) ~ leq(n0, n2) % 262.16/56.66 | | | | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | | | | | PRED_UNIFY: (2310), (2313) imply: % 262.16/56.66 | | | | | | | | | | | | | | | | | | (2314) $false % 262.16/56.66 | | | | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | | | | | CLOSE: (2314) is inconsistent. % 262.16/56.66 | | | | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | | | | Case 2: % 262.16/56.66 | | | | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | | | | | (2315) ~ leq(n3, all_74_20) | (a_select3(id_ds1_filter, % 262.16/56.66 | | | | | | | | | | | | | | | | | | n3, n0) = all_74_12 & $i(all_74_12)) % 262.16/56.66 | | | | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (159), (649), (2305), (2307), (2315) are % 262.16/56.66 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #3. % 262.16/56.66 | | | | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | | | | End of split % 262.16/56.66 | | | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | | | End of split % 262.16/56.66 | | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | | Case 2: % 262.16/56.66 | | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | | | (2316) all_74_18 = n1 % 262.16/56.66 | | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | | | REDUCE: (165), (2316) imply: % 262.16/56.66 | | | | | | | | | | | | | | | | (2317) succ(n1) = pv57 % 262.16/56.66 | | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (28) with n2, pv57, n1, simplifying % 262.16/56.66 | | | | | | | | | | | | | | | | with (101), (2317) gives: % 262.16/56.66 | | | | | | | | | | | | | | | | (2318) pv57 = n2 % 262.16/56.66 | | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | | | REDUCE: (2281), (2318) imply: % 262.16/56.66 | | | | | | | | | | | | | | | | (2319) a_select3(id_ds1_filter, n2, n0) = all_74_13 % 262.16/56.66 | | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | | | REDUCE: (2282), (2318) imply: % 262.16/56.66 | | | | | | | | | | | | | | | | (2320) a_select3(id_ds1_filter, n0, n2) = all_74_12 % 262.16/56.66 | | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | | | REDUCE: (162), (2318) imply: % 262.16/56.66 | | | | | | | | | | | | | | | | (2321) leq(n2, n5) % 262.16/56.66 | | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | | | REDUCE: (63), (2318) imply: % 262.16/56.66 | | | | | | | | | | | | | | | | (2322) leq(n0, n2) % 262.16/56.66 | | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (81) with n0, n2, all_74_12, % 262.16/56.66 | | | | | | | | | | | | | | | | simplifying with (22), (118), (2155), (2320), % 262.16/56.66 | | | | | | | | | | | | | | | | (2322) gives: % 262.16/56.66 | | | | | | | | | | | | | | | | (2323) ~ leq(n2, all_74_20) | ~ leq(n0, pv57) | % 262.16/56.66 | | | | | | | | | | | | | | | | (a_select3(id_ds1_filter, n2, n0) = all_74_12 & % 262.16/56.66 | | | | | | | | | | | | | | | | $i(all_74_12)) % 262.16/56.66 | | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | | | BETA: splitting (2323) gives: % 262.16/56.66 | | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | | | Case 1: % 262.16/56.66 | | | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | | | | (2324) ~ leq(n0, pv57) % 262.16/56.66 | | | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | | | | REDUCE: (2318), (2324) imply: % 262.16/56.66 | | | | | | | | | | | | | | | | | (2325) ~ leq(n0, n2) % 262.16/56.66 | | | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | | | | PRED_UNIFY: (2322), (2325) imply: % 262.16/56.66 | | | | | | | | | | | | | | | | | (2326) $false % 262.16/56.66 | | | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | | | | CLOSE: (2326) is inconsistent. % 262.16/56.66 | | | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | | | Case 2: % 262.16/56.66 | | | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | | | | (2327) ~ leq(n2, all_74_20) | (a_select3(id_ds1_filter, % 262.16/56.66 | | | | | | | | | | | | | | | | | n2, n0) = all_74_12 & $i(all_74_12)) % 262.16/56.66 | | | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (159), (649), (2319), (2321), (2327) are % 262.16/56.66 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #4. % 262.16/56.66 | | | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | | | End of split % 262.16/56.66 | | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | | End of split % 262.16/56.66 | | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | | End of split % 262.16/56.66 | | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | End of split % 262.16/56.66 | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | Case 2: % 262.16/56.66 | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | (2328) pv57 = n4 % 262.16/56.66 | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | REDUCE: (2281), (2328) imply: % 262.16/56.66 | | | | | | | | | | | | | (2329) a_select3(id_ds1_filter, n4, n0) = all_74_13 % 262.16/56.66 | | | | | | | | | | | | | % 262.16/56.66 | | | | | | | | | | | | | REDUCE: (2282), (2328) imply: % 262.16/56.67 | | | | | | | | | | | | | (2330) a_select3(id_ds1_filter, n0, n4) = all_74_12 % 262.16/56.67 | | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | | | REDUCE: (669), (2328) imply: % 262.16/56.67 | | | | | | | | | | | | | (2331) succ(n4) = all_74_17 % 262.16/56.67 | | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | | | REDUCE: (675), (2328) imply: % 262.16/56.67 | | | | | | | | | | | | | (2332) leq(n4, all_74_17) % 262.16/56.67 | | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | | | REDUCE: (693), (2328) imply: % 262.16/56.67 | | | | | | | | | | | | | (2333) leq(n4, n4) % 262.16/56.67 | | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | | | REDUCE: (63), (2328) imply: % 262.16/56.67 | | | | | | | | | | | | | (2334) leq(n0, n4) % 262.16/56.67 | | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | | | GROUND_INST: instantiating (28) with n5, all_74_17, n4, % 262.16/56.67 | | | | | | | | | | | | | simplifying with (135), (2331) gives: % 262.16/56.67 | | | | | | | | | | | | | (2335) all_74_17 = n5 % 262.16/56.67 | | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | | | REDUCE: (2332), (2335) imply: % 262.16/56.67 | | | | | | | | | | | | | (2336) leq(n4, n5) % 262.16/56.67 | | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | | | REDUCE: (676), (2335) imply: % 262.16/56.67 | | | | | | | | | | | | | (2337) leq(n0, n5) % 262.16/56.67 | | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | | | GROUND_INST: instantiating (81) with n0, n4, all_74_12, % 262.16/56.67 | | | | | | | | | | | | | simplifying with (22), (136), (2155), (2330), % 262.16/56.67 | | | | | | | | | | | | | (2334) gives: % 262.16/56.67 | | | | | | | | | | | | | (2338) ~ leq(n4, all_74_20) | ~ leq(n0, pv57) | % 262.16/56.67 | | | | | | | | | | | | | (a_select3(id_ds1_filter, n4, n0) = all_74_12 & % 262.16/56.67 | | | | | | | | | | | | | $i(all_74_12)) % 262.16/56.67 | | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | | | GROUND_INST: instantiating (81) with n4, n0, all_74_13, % 262.16/56.67 | | | | | | | | | | | | | simplifying with (22), (136), (2155), (2329), % 262.16/56.67 | | | | | | | | | | | | | (2334) gives: % 262.16/56.67 | | | | | | | | | | | | | (2339) ~ leq(n4, pv57) | ~ leq(n0, all_74_20) | % 262.16/56.67 | | | | | | | | | | | | | (a_select3(id_ds1_filter, n0, n4) = all_74_13 & % 262.16/56.67 | | | | | | | | | | | | | $i(all_74_13)) % 262.16/56.67 | | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | | | BETA: splitting (2338) gives: % 262.16/56.67 | | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | | | Case 1: % 262.16/56.67 | | | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | | | | (2340) ~ leq(n0, pv57) % 262.16/56.67 | | | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | | | | REDUCE: (2328), (2340) imply: % 262.16/56.67 | | | | | | | | | | | | | | (2341) ~ leq(n0, n4) % 262.16/56.67 | | | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | | | | PRED_UNIFY: (2334), (2341) imply: % 262.16/56.67 | | | | | | | | | | | | | | (2342) $false % 262.16/56.67 | | | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | | | | CLOSE: (2342) is inconsistent. % 262.16/56.67 | | | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | | | Case 2: % 262.16/56.67 | | | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | | | | (2343) ~ leq(n4, all_74_20) | (a_select3(id_ds1_filter, % 262.16/56.67 | | | | | | | | | | | | | | n4, n0) = all_74_12 & $i(all_74_12)) % 262.16/56.67 | | | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | | | | BETA: splitting (2339) gives: % 262.16/56.67 | | | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | | | | Case 1: % 262.16/56.67 | | | | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | | | | | (2344) ~ leq(n0, all_74_20) % 262.16/56.67 | | | | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | | | | | REDUCE: (159), (2344) imply: % 262.16/56.67 | | | | | | | | | | | | | | | (2345) ~ leq(n0, n5) % 262.16/56.67 | | | | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | | | | | PRED_UNIFY: (2337), (2345) imply: % 262.16/56.67 | | | | | | | | | | | | | | | (2346) $false % 262.16/56.67 | | | | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | | | | | CLOSE: (2346) is inconsistent. % 262.16/56.67 | | | | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | | | | Case 2: % 262.16/56.67 | | | | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | | | | | (2347) ~ leq(n4, pv57) | (a_select3(id_ds1_filter, n0, % 262.16/56.67 | | | | | | | | | | | | | | | n4) = all_74_13 & $i(all_74_13)) % 262.16/56.67 | | | | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | | | | | BETA: splitting (2347) gives: % 262.16/56.67 | | | | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | | | | | Case 1: % 262.16/56.67 | | | | | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | | | | | | (2348) ~ leq(n4, pv57) % 262.16/56.67 | | | | | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | | | | | | REDUCE: (2328), (2348) imply: % 262.16/56.67 | | | | | | | | | | | | | | | | (2349) ~ leq(n4, n4) % 262.16/56.67 | | | | | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | | | | | | PRED_UNIFY: (2333), (2349) imply: % 262.16/56.67 | | | | | | | | | | | | | | | | (2350) $false % 262.16/56.67 | | | | | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | | | | | | CLOSE: (2350) is inconsistent. % 262.16/56.67 | | | | | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | | | | | Case 2: % 262.16/56.67 | | | | | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | | | | | | (2351) a_select3(id_ds1_filter, n0, n4) = all_74_13 & % 262.16/56.67 | | | | | | | | | | | | | | | | $i(all_74_13) % 262.16/56.67 | | | | | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | | | | | | ALPHA: (2351) implies: % 262.16/56.67 | | | | | | | | | | | | | | | | (2352) a_select3(id_ds1_filter, n0, n4) = all_74_13 % 262.16/56.67 | | | | | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | | | | | | BETA: splitting (2343) gives: % 262.16/56.67 | | | | | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | | | | | | Case 1: % 262.16/56.67 | | | | | | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | | | | | | | (2353) ~ leq(n4, all_74_20) % 262.16/56.67 | | | | | | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | | | | | | | REDUCE: (159), (2353) imply: % 262.16/56.67 | | | | | | | | | | | | | | | | | (2354) ~ leq(n4, n5) % 262.16/56.67 | | | | | | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | | | | | | | PRED_UNIFY: (2336), (2354) imply: % 262.16/56.67 | | | | | | | | | | | | | | | | | (2355) $false % 262.16/56.67 | | | | | | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | | | | | | | CLOSE: (2355) is inconsistent. % 262.16/56.67 | | | | | | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | | | | | | Case 2: % 262.16/56.67 | | | | | | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | | | | | | | (2356) a_select3(id_ds1_filter, n4, n0) = all_74_12 & % 262.16/56.67 | | | | | | | | | | | | | | | | | $i(all_74_12) % 262.16/56.67 | | | | | | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | | | | | | | ALPHA: (2356) implies: % 262.16/56.67 | | | | | | | | | | | | | | | | | (2357) a_select3(id_ds1_filter, n4, n0) = all_74_12 % 262.16/56.67 | | | | | | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | | | | | | | REF_CLOSE: (22), (30), (81), (136), (159), (649), (2155), % 262.16/56.67 | | | | | | | | | | | | | | | | | (2328), (2334), (2336), (2352), (2357) are % 262.16/56.67 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #8. % 262.16/56.67 | | | | | | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | | | | | | End of split % 262.16/56.67 | | | | | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | | | | | End of split % 262.16/56.67 | | | | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | | | | End of split % 262.16/56.67 | | | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | | | End of split % 262.16/56.67 | | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | | End of split % 262.16/56.67 | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | Case 2: % 262.16/56.67 | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | | (2358) pv57 = n1 % 262.16/56.67 | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | | REF_CLOSE: (27), (144), (155), (2156), (2284), (2358) are % 262.16/56.67 | | | | | | | | | | | | inconsistent by sub-proof #75. % 262.16/56.67 | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | End of split % 262.16/56.67 | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | End of split % 262.16/56.67 | | | | | | | | | | % 262.16/56.67 | | | | | | | | | Case 2: % 262.16/56.67 | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | (2359) all_74_18 = n0 % 262.16/56.67 | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | REDUCE: (165), (2359) imply: % 262.16/56.67 | | | | | | | | | | (2360) succ(n0) = pv57 % 262.16/56.67 | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | GROUND_INST: instantiating (28) with n1, pv57, n0, simplifying % 262.16/56.67 | | | | | | | | | | with (19), (2360) gives: % 262.16/56.67 | | | | | | | | | | (2361) pv57 = n1 % 262.16/56.67 | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | REDUCE: (2281), (2361) imply: % 262.16/56.67 | | | | | | | | | | (2362) a_select3(id_ds1_filter, n1, n0) = all_74_13 % 262.16/56.67 | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | REDUCE: (2282), (2361) imply: % 262.16/56.67 | | | | | | | | | | (2363) a_select3(id_ds1_filter, n0, n1) = all_74_12 % 262.16/56.67 | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | REDUCE: (162), (2361) imply: % 262.16/56.67 | | | | | | | | | | (2364) leq(n1, n5) % 262.16/56.67 | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | REDUCE: (63), (2361) imply: % 262.16/56.67 | | | | | | | | | | (2365) leq(n0, n1) % 262.16/56.67 | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | GROUND_INST: instantiating (82) with n0, n1, all_74_12, % 262.16/56.67 | | | | | | | | | | simplifying with (22), (102), (2155), (2363), % 262.16/56.67 | | | | | | | | | | (2365) gives: % 262.16/56.67 | | | | | | | | | | (2366) ~ leq(n1, all_74_20) | ~ leq(n0, all_74_18) | % 262.16/56.67 | | | | | | | | | | (a_select3(id_ds1_filter, n1, n0) = all_74_12 & % 262.16/56.67 | | | | | | | | | | $i(all_74_12)) % 262.16/56.67 | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | BETA: splitting (2366) gives: % 262.16/56.67 | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | Case 1: % 262.16/56.67 | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | (2367) ~ leq(n0, all_74_18) % 262.16/56.67 | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | REDUCE: (2359), (2367) imply: % 262.16/56.67 | | | | | | | | | | | (2368) ~ leq(n0, n0) % 262.16/56.67 | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | PRED_UNIFY: (2155), (2368) imply: % 262.16/56.67 | | | | | | | | | | | (2369) $false % 262.16/56.67 | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | CLOSE: (2369) is inconsistent. % 262.16/56.67 | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | Case 2: % 262.16/56.67 | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | (2370) ~ leq(n1, all_74_20) | (a_select3(id_ds1_filter, % 262.16/56.67 | | | | | | | | | | | n1, n0) = all_74_12 & $i(all_74_12)) % 262.16/56.67 | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | REF_CLOSE: (30), (159), (649), (2362), (2364), (2370) are % 262.16/56.67 | | | | | | | | | | | inconsistent by sub-proof #5. % 262.16/56.67 | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | End of split % 262.16/56.67 | | | | | | | | | | % 262.16/56.67 | | | | | | | | | End of split % 262.16/56.67 | | | | | | | | | % 262.16/56.67 | | | | | | | | End of split % 262.16/56.67 | | | | | | | | % 262.16/56.67 | | | | | | | Case 2: % 262.16/56.67 | | | | | | | | % 262.16/56.67 | | | | | | | | (2371) all_74_15 = n0 % 262.16/56.67 | | | | | | | | % 262.16/56.67 | | | | | | | | REF_CLOSE: (30), (649), (2153), (2154), (2371) are inconsistent % 262.16/56.67 | | | | | | | | by sub-proof #2. % 262.16/56.67 | | | | | | | | % 262.16/56.67 | | | | | | | End of split % 262.16/56.67 | | | | | | | % 262.16/56.67 | | | | | | End of split % 262.16/56.67 | | | | | | % 262.16/56.67 | | | | | End of split % 262.16/56.67 | | | | | % 262.16/56.67 | | | | Case 2: % 262.16/56.67 | | | | | % 262.16/56.67 | | | | | (2372) all_74_20 = pv57 % 262.16/56.67 | | | | | % 262.16/56.67 | | | | | COMBINE_EQS: (159), (2372) imply: % 262.16/56.67 | | | | | (2373) pv57 = n5 % 262.16/56.67 | | | | | % 262.16/56.67 | | | | | SIMP: (2373) implies: % 262.16/56.67 | | | | | (2374) pv57 = n5 % 262.16/56.67 | | | | | % 262.16/56.67 | | | | | COMBINE_EQS: (679), (2374) imply: % 262.16/56.67 | | | | | (2375) all_74_16 = n5 % 262.16/56.67 | | | | | % 262.16/56.67 | | | | | REDUCE: (155), (2374) imply: % 262.16/56.67 | | | | | (2376) pred(n5) = all_74_18 % 262.16/56.67 | | | | | % 262.16/56.67 | | | | | GROUND_INST: instantiating (27) with n4, all_74_18, n5, simplifying % 262.16/56.67 | | | | | with (148), (2376) gives: % 262.16/56.67 | | | | | (2377) all_74_18 = n4 % 262.16/56.67 | | | | | % 262.16/56.67 | | | | | REDUCE: (690), (2377) imply: % 262.16/56.67 | | | | | (2378) leq(n0, n4) % 262.16/56.67 | | | | | % 262.16/56.67 | | | | | BETA: splitting (661) gives: % 262.16/56.67 | | | | | % 262.16/56.67 | | | | | Case 1: % 262.16/56.67 | | | | | | % 262.16/56.67 | | | | | | (2379) gt(all_74_14, n0) % 262.16/56.67 | | | | | | % 262.16/56.67 | | | | | | BETA: splitting (660) gives: % 262.16/56.67 | | | | | | % 262.16/56.67 | | | | | | Case 1: % 262.16/56.67 | | | | | | | % 262.16/56.67 | | | | | | | (2380) gt(all_74_15, n0) % 262.16/56.67 | | | | | | | % 262.16/56.67 | | | | | | | BETA: splitting (663) gives: % 262.16/56.67 | | | | | | | % 262.16/56.67 | | | | | | | Case 1: % 262.16/56.67 | | | | | | | | % 262.16/56.67 | | | | | | | | (2381) gt(all_74_16, all_74_15) % 262.16/56.67 | | | | | | | | % 262.16/56.67 | | | | | | | | REDUCE: (2375), (2381) imply: % 262.16/56.67 | | | | | | | | (2382) gt(n5, all_74_15) % 262.16/56.67 | | | | | | | | % 262.16/56.67 | | | | | | | | BETA: splitting (666) gives: % 262.16/56.67 | | | | | | | | % 262.16/56.67 | | | | | | | | Case 1: % 262.16/56.67 | | | | | | | | | % 262.16/56.67 | | | | | | | | | (2383) gt(n5, all_74_14) % 262.16/56.67 | | | | | | | | | % 262.16/56.67 | | | | | | | | | GROUND_INST: instantiating (1) with all_74_15, n5, n4, % 262.16/56.67 | | | | | | | | | simplifying with (66), (139), (148), (2382) gives: % 262.16/56.67 | | | | | | | | | (2384) leq(all_74_15, n4) % 262.16/56.67 | | | | | | | | | % 262.16/56.67 | | | | | | | | | GROUND_INST: instantiating (1) with all_74_14, n5, n4, % 262.16/56.67 | | | | | | | | | simplifying with (67), (139), (148), (2383) gives: % 262.16/56.67 | | | | | | | | | (2385) leq(all_74_14, n4) % 262.16/56.67 | | | | | | | | | % 262.16/56.67 | | | | | | | | | BETA: splitting (665) gives: % 262.16/56.67 | | | | | | | | | % 262.16/56.67 | | | | | | | | | Case 1: % 262.16/56.67 | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | (2386) all_74_14 = n0 % 262.16/56.67 | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | REF_CLOSE: (67), (2379), (2386), (irreflexivity_gt) are % 262.16/56.67 | | | | | | | | | | inconsistent by sub-proof #41. % 262.16/56.67 | | | | | | | | | | % 262.16/56.67 | | | | | | | | | Case 2: % 262.16/56.67 | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | (2387) ~ (all_74_14 = n0) % 262.16/56.67 | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_15, n4, % 262.16/56.67 | | | | | | | | | | simplifying with (66), (136), (2384) gives: % 262.16/56.67 | | | | | | | | | | (2388) all_74_15 = n4 | gt(n4, all_74_15) % 262.16/56.67 | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_14, n4, % 262.16/56.67 | | | | | | | | | | simplifying with (67), (136), (2385) gives: % 262.16/56.67 | | | | | | | | | | (2389) all_74_14 = n4 | gt(n4, all_74_14) % 262.16/56.67 | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | BETA: splitting (687) gives: % 262.16/56.67 | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | Case 1: % 262.16/56.67 | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | (2390) all_74_15 = n0 % 262.16/56.67 | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | REF_CLOSE: (66), (2380), (2390), (irreflexivity_gt) are % 262.16/56.67 | | | | | | | | | | | inconsistent by sub-proof #40. % 262.16/56.67 | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | Case 2: % 262.16/56.67 | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | (2391) ~ (all_74_15 = n0) % 262.16/56.67 | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | BETA: splitting (2388) gives: % 262.16/56.67 | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | Case 1: % 262.16/56.67 | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | | (2392) gt(n4, all_74_15) % 262.16/56.67 | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_15, n4, n3, % 262.16/56.67 | | | | | | | | | | | | simplifying with (66), (136), (147), (2392) gives: % 262.16/56.67 | | | | | | | | | | | | (2393) leq(all_74_15, n3) % 262.16/56.67 | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_15, n3, % 262.16/56.67 | | | | | | | | | | | | simplifying with (66), (129), (2393) gives: % 262.16/56.67 | | | | | | | | | | | | (2394) all_74_15 = n3 | gt(n3, all_74_15) % 262.16/56.67 | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | | BETA: splitting (2389) gives: % 262.16/56.67 | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | | Case 1: % 262.16/56.67 | | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | | | (2395) gt(n4, all_74_14) % 262.16/56.67 | | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_14, n4, n3, % 262.16/56.67 | | | | | | | | | | | | | simplifying with (67), (136), (147), (2395) gives: % 262.16/56.67 | | | | | | | | | | | | | (2396) leq(all_74_14, n3) % 262.16/56.67 | | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_14, n3, % 262.16/56.67 | | | | | | | | | | | | | simplifying with (67), (129), (2396) gives: % 262.16/56.67 | | | | | | | | | | | | | (2397) all_74_14 = n3 | gt(n3, all_74_14) % 262.16/56.67 | | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | | | BETA: splitting (2397) gives: % 262.16/56.67 | | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | | | Case 1: % 262.16/56.67 | | | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | | | | (2398) gt(n3, all_74_14) % 262.16/56.67 | | | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_14, n3, n2, % 262.16/56.67 | | | | | | | | | | | | | | simplifying with (67), (129), (146), (2398) gives: % 262.16/56.67 | | | | | | | | | | | | | | (2399) leq(all_74_14, n2) % 262.16/56.67 | | | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_14, n2, % 262.16/56.67 | | | | | | | | | | | | | | simplifying with (67), (118), (2399) gives: % 262.16/56.67 | | | | | | | | | | | | | | (2400) all_74_14 = n2 | gt(n2, all_74_14) % 262.16/56.67 | | | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | | | | BETA: splitting (2394) gives: % 262.16/56.67 | | | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | | | | Case 1: % 262.16/56.67 | | | | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | | | | | (2401) gt(n3, all_74_15) % 262.16/56.67 | | | | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_15, n3, n2, % 262.16/56.67 | | | | | | | | | | | | | | | simplifying with (66), (129), (146), (2401) gives: % 262.16/56.67 | | | | | | | | | | | | | | | (2402) leq(all_74_15, n2) % 262.16/56.67 | | | | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_15, n2, % 262.16/56.67 | | | | | | | | | | | | | | | simplifying with (66), (118), (2402) gives: % 262.16/56.67 | | | | | | | | | | | | | | | (2403) all_74_15 = n2 | gt(n2, all_74_15) % 262.16/56.67 | | | | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | | | | | BETA: splitting (2400) gives: % 262.16/56.67 | | | | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | | | | | Case 1: % 262.16/56.67 | | | | | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | | | | | | (2404) gt(n2, all_74_14) % 262.16/56.67 | | | | | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_14, n2, n1, % 262.16/56.67 | | | | | | | | | | | | | | | | simplifying with (67), (118), (145), (2404) gives: % 262.16/56.67 | | | | | | | | | | | | | | | | (2405) leq(all_74_14, n1) % 262.16/56.67 | | | | | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_74_14, simplifying % 262.16/56.67 | | | | | | | | | | | | | | | | with (67), (651), (2405) gives: % 262.16/56.67 | | | | | | | | | | | | | | | | (2406) all_74_14 = n1 | all_74_14 = n0 % 262.16/56.67 | | | | | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | | | | | | BETA: splitting (2406) gives: % 262.16/56.67 | | | | | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | | | | | | Case 1: % 262.16/56.67 | | | | | | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | | | | | | | (2407) all_74_14 = n0 % 262.16/56.67 | | | | | | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | | | | | | | REDUCE: (2387), (2407) imply: % 262.16/56.67 | | | | | | | | | | | | | | | | | (2408) $false % 262.16/56.67 | | | | | | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | | | | | | | CLOSE: (2408) is inconsistent. % 262.16/56.67 | | | | | | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | | | | | | Case 2: % 262.16/56.67 | | | | | | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | | | | | | | (2409) all_74_14 = n1 % 262.16/56.67 | | | | | | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | | | | | | | REDUCE: (656), (2409) imply: % 262.16/56.67 | | | | | | | | | | | | | | | | | (2410) a_select3(id_ds1_filter, n1, all_74_15) = % 262.16/56.67 | | | | | | | | | | | | | | | | | all_74_12 % 262.16/56.67 | | | | | | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | | | | | | | REDUCE: (655), (2409) imply: % 262.16/56.67 | | | | | | | | | | | | | | | | | (2411) a_select3(id_ds1_filter, all_74_15, n1) = % 262.16/56.67 | | | | | | | | | | | | | | | | | all_74_13 % 262.16/56.67 | | | | | | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | | | | | | | REDUCE: (2385), (2409) imply: % 262.16/56.67 | | | | | | | | | | | | | | | | | (2412) leq(n1, n4) % 262.16/56.67 | | | | | | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | | | | | | | REDUCE: (651), (2409) imply: % 262.16/56.67 | | | | | | | | | | | | | | | | | (2413) leq(n0, n1) % 262.16/56.67 | | | | | | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | | | | | | | BETA: splitting (2403) gives: % 262.16/56.67 | | | | | | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | | | | | | | Case 1: % 262.16/56.67 | | | | | | | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | | | | | | | | (2414) gt(n2, all_74_15) % 262.16/56.67 | | | | | | | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_15, n2, n1, % 262.16/56.67 | | | | | | | | | | | | | | | | | | simplifying with (66), (118), (145), (2414) gives: % 262.16/56.67 | | | | | | | | | | | | | | | | | | (2415) leq(all_74_15, n1) % 262.16/56.67 | | | | | | | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_74_15, simplifying % 262.16/56.67 | | | | | | | | | | | | | | | | | | with (66), (650), (2415) gives: % 262.16/56.67 | | | | | | | | | | | | | | | | | | (2416) all_74_15 = n1 | all_74_15 = n0 % 262.16/56.67 | | | | | | | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | | | | | | | | BETA: splitting (2416) gives: % 262.16/56.67 | | | | | | | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | | | | | | | | Case 1: % 262.16/56.67 | | | | | | | | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | | | | | | | | | (2417) all_74_15 = n0 % 262.16/56.67 | | | | | | | | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | | | | | | | | | REDUCE: (2391), (2417) imply: % 262.16/56.67 | | | | | | | | | | | | | | | | | | | (2418) $false % 262.16/56.67 | | | | | | | | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | | | | | | | | | CLOSE: (2418) is inconsistent. % 262.16/56.67 | | | | | | | | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | | | | | | | | Case 2: % 262.16/56.67 | | | | | | | | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | | | | | | | | | (2419) all_74_15 = n1 % 262.16/56.67 | | | | | | | | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | | | | | | | | | REDUCE: (2411), (2419) imply: % 262.16/56.67 | | | | | | | | | | | | | | | | | | | (2420) a_select3(id_ds1_filter, n1, n1) = all_74_13 % 262.16/56.67 | | | | | | | | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | | | | | | | | | REDUCE: (2410), (2419) imply: % 262.16/56.67 | | | | | | | | | | | | | | | | | | | (2421) a_select3(id_ds1_filter, n1, n1) = all_74_12 % 262.16/56.67 | | | | | | | | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (30) with all_74_13, all_74_12, n1, % 262.16/56.67 | | | | | | | | | | | | | | | | | | | n1, id_ds1_filter, simplifying with (2420), (2421) % 262.16/56.67 | | | | | | | | | | | | | | | | | | | gives: % 262.16/56.67 | | | | | | | | | | | | | | | | | | | (2422) all_74_12 = all_74_13 % 262.16/56.67 | | | | | | | | | | | | | | | | | | | % 262.16/56.67 | | | | | | | | | | | | | | | | | | | REDUCE: (649), (2422) imply: % 262.16/56.67 | | | | | | | | | | | | | | | | | | | (2423) $false % 262.16/56.68 | | | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | | | | CLOSE: (2423) is inconsistent. % 262.16/56.68 | | | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | | | End of split % 262.16/56.68 | | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | | Case 2: % 262.16/56.68 | | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | | | (2424) all_74_15 = n2 % 262.16/56.68 | | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | | | REDUCE: (2411), (2424) imply: % 262.16/56.68 | | | | | | | | | | | | | | | | | | (2425) a_select3(id_ds1_filter, n2, n1) = all_74_13 % 262.16/56.68 | | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | | | REDUCE: (2410), (2424) imply: % 262.16/56.68 | | | | | | | | | | | | | | | | | | (2426) a_select3(id_ds1_filter, n1, n2) = all_74_12 % 262.16/56.68 | | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | | | REDUCE: (684), (2424) imply: % 262.16/56.68 | | | | | | | | | | | | | | | | | | (2427) leq(n2, n5) % 262.16/56.68 | | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | | | REDUCE: (650), (2424) imply: % 262.16/56.68 | | | | | | | | | | | | | | | | | | (2428) leq(n0, n2) % 262.16/56.68 | | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (82) with n1, n2, all_74_12, % 262.16/56.68 | | | | | | | | | | | | | | | | | | simplifying with (102), (118), (2413), (2426), % 262.16/56.68 | | | | | | | | | | | | | | | | | | (2428) gives: % 262.16/56.68 | | | | | | | | | | | | | | | | | | (2429) ~ leq(n2, all_74_20) | ~ leq(n1, all_74_18) | % 262.16/56.68 | | | | | | | | | | | | | | | | | | (a_select3(id_ds1_filter, n2, n1) = all_74_12 & % 262.16/56.68 | | | | | | | | | | | | | | | | | | $i(all_74_12)) % 262.16/56.68 | | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | | | BETA: splitting (2429) gives: % 262.16/56.68 | | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | | | Case 1: % 262.16/56.68 | | | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | | | | (2430) ~ leq(n2, all_74_20) % 262.16/56.68 | | | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | | | | REDUCE: (159), (2430) imply: % 262.16/56.68 | | | | | | | | | | | | | | | | | | | (2431) ~ leq(n2, n5) % 262.16/56.68 | | | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (2427), (2431) imply: % 262.16/56.68 | | | | | | | | | | | | | | | | | | | (2432) $false % 262.16/56.68 | | | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | | | | CLOSE: (2432) is inconsistent. % 262.16/56.68 | | | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | | | Case 2: % 262.16/56.68 | | | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | | | | (2433) ~ leq(n1, all_74_18) | (a_select3(id_ds1_filter, % 262.16/56.68 | | | | | | | | | | | | | | | | | | | n2, n1) = all_74_12 & $i(all_74_12)) % 262.16/56.68 | | | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | | | | BETA: splitting (2433) gives: % 262.16/56.68 | | | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | | | | Case 1: % 262.16/56.68 | | | | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | | | | | (2434) ~ leq(n1, all_74_18) % 262.16/56.68 | | | | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | | | | | REDUCE: (2377), (2434) imply: % 262.16/56.68 | | | | | | | | | | | | | | | | | | | | (2435) ~ leq(n1, n4) % 262.16/56.68 | | | | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (2412), (2435) imply: % 262.16/56.68 | | | | | | | | | | | | | | | | | | | | (2436) $false % 262.16/56.68 | | | | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | | | | | CLOSE: (2436) is inconsistent. % 262.16/56.68 | | | | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | | | | Case 2: % 262.16/56.68 | | | | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | | | | | (2437) a_select3(id_ds1_filter, n2, n1) = all_74_12 & % 262.16/56.68 | | | | | | | | | | | | | | | | | | | | $i(all_74_12) % 262.16/56.68 | | | | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | | | | | ALPHA: (2437) implies: % 262.16/56.68 | | | | | | | | | | | | | | | | | | | | (2438) a_select3(id_ds1_filter, n2, n1) = all_74_12 % 262.16/56.68 | | | | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (649), (2425), (2438) are inconsistent by % 262.16/56.68 | | | | | | | | | | | | | | | | | | | | sub-proof #36. % 262.16/56.68 | | | | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | | | | End of split % 262.16/56.68 | | | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | | | End of split % 262.16/56.68 | | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | | End of split % 262.16/56.68 | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | End of split % 262.16/56.68 | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | Case 2: % 262.16/56.68 | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | (2439) all_74_14 = n2 % 262.16/56.68 | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | REDUCE: (656), (2439) imply: % 262.16/56.68 | | | | | | | | | | | | | | | | (2440) a_select3(id_ds1_filter, n2, all_74_15) = % 262.16/56.68 | | | | | | | | | | | | | | | | all_74_12 % 262.16/56.68 | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | REDUCE: (655), (2439) imply: % 262.16/56.68 | | | | | | | | | | | | | | | | (2441) a_select3(id_ds1_filter, all_74_15, n2) = % 262.16/56.68 | | | | | | | | | | | | | | | | all_74_13 % 262.16/56.68 | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | REDUCE: (659), (2439) imply: % 262.16/56.68 | | | | | | | | | | | | | | | | (2442) leq(n2, n5) % 262.16/56.68 | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | REDUCE: (651), (2439) imply: % 262.16/56.68 | | | | | | | | | | | | | | | | (2443) leq(n0, n2) % 262.16/56.68 | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | BETA: splitting (2403) gives: % 262.16/56.68 | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | Case 1: % 262.16/56.68 | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | | (2444) gt(n2, all_74_15) % 262.16/56.68 | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_15, n2, n1, % 262.16/56.68 | | | | | | | | | | | | | | | | | simplifying with (66), (118), (145), (2444) gives: % 262.16/56.68 | | | | | | | | | | | | | | | | | (2445) leq(all_74_15, n1) % 262.16/56.68 | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_74_15, simplifying % 262.16/56.68 | | | | | | | | | | | | | | | | | with (66), (650), (2445) gives: % 262.16/56.68 | | | | | | | | | | | | | | | | | (2446) all_74_15 = n1 | all_74_15 = n0 % 262.16/56.68 | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | | BETA: splitting (2446) gives: % 262.16/56.68 | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | | Case 1: % 262.16/56.68 | | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | | | (2447) all_74_15 = n0 % 262.16/56.68 | | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | | | REDUCE: (2391), (2447) imply: % 262.16/56.68 | | | | | | | | | | | | | | | | | | (2448) $false % 262.16/56.68 | | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | | | CLOSE: (2448) is inconsistent. % 262.16/56.68 | | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | | Case 2: % 262.16/56.68 | | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | | | (2449) all_74_15 = n1 % 262.16/56.68 | | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | | | REDUCE: (2441), (2449) imply: % 262.16/56.68 | | | | | | | | | | | | | | | | | | (2450) a_select3(id_ds1_filter, n1, n2) = all_74_13 % 262.16/56.68 | | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | | | REDUCE: (2440), (2449) imply: % 262.16/56.68 | | | | | | | | | | | | | | | | | | (2451) a_select3(id_ds1_filter, n2, n1) = all_74_12 % 262.16/56.68 | | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | | | REDUCE: (2384), (2449) imply: % 262.16/56.68 | | | | | | | | | | | | | | | | | | (2452) leq(n1, n4) % 262.16/56.68 | | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | | | REDUCE: (650), (2449) imply: % 262.16/56.68 | | | | | | | | | | | | | | | | | | (2453) leq(n0, n1) % 262.16/56.68 | | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (82) with n1, n2, all_74_13, % 262.16/56.68 | | | | | | | | | | | | | | | | | | simplifying with (102), (118), (2443), (2450), % 262.16/56.68 | | | | | | | | | | | | | | | | | | (2453) gives: % 262.16/56.68 | | | | | | | | | | | | | | | | | | (2454) ~ leq(n2, all_74_20) | ~ leq(n1, all_74_18) | % 262.16/56.68 | | | | | | | | | | | | | | | | | | (a_select3(id_ds1_filter, n2, n1) = all_74_13 & % 262.16/56.68 | | | | | | | | | | | | | | | | | | $i(all_74_13)) % 262.16/56.68 | | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | | | BETA: splitting (2454) gives: % 262.16/56.68 | | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | | | Case 1: % 262.16/56.68 | | | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | | | | (2455) ~ leq(n2, all_74_20) % 262.16/56.68 | | | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | | | | REDUCE: (159), (2455) imply: % 262.16/56.68 | | | | | | | | | | | | | | | | | | | (2456) ~ leq(n2, n5) % 262.16/56.68 | | | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (2442), (2456) imply: % 262.16/56.68 | | | | | | | | | | | | | | | | | | | (2457) $false % 262.16/56.68 | | | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | | | | CLOSE: (2457) is inconsistent. % 262.16/56.68 | | | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | | | Case 2: % 262.16/56.68 | | | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | | | | (2458) ~ leq(n1, all_74_18) | (a_select3(id_ds1_filter, % 262.16/56.68 | | | | | | | | | | | | | | | | | | | n2, n1) = all_74_13 & $i(all_74_13)) % 262.16/56.68 | | | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | | | | BETA: splitting (2458) gives: % 262.16/56.68 | | | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | | | | Case 1: % 262.16/56.68 | | | | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | | | | | (2459) ~ leq(n1, all_74_18) % 262.16/56.68 | | | | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | | | | | REDUCE: (2377), (2459) imply: % 262.16/56.68 | | | | | | | | | | | | | | | | | | | | (2460) ~ leq(n1, n4) % 262.16/56.68 | | | | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (2452), (2460) imply: % 262.16/56.68 | | | | | | | | | | | | | | | | | | | | (2461) $false % 262.16/56.68 | | | | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | | | | | CLOSE: (2461) is inconsistent. % 262.16/56.68 | | | | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | | | | Case 2: % 262.16/56.68 | | | | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | | | | | (2462) a_select3(id_ds1_filter, n2, n1) = all_74_13 & % 262.16/56.68 | | | | | | | | | | | | | | | | | | | | $i(all_74_13) % 262.16/56.68 | | | | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | | | | | ALPHA: (2462) implies: % 262.16/56.68 | | | | | | | | | | | | | | | | | | | | (2463) a_select3(id_ds1_filter, n2, n1) = all_74_13 % 262.16/56.68 | | | | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (649), (2451), (2463) are inconsistent by % 262.16/56.68 | | | | | | | | | | | | | | | | | | | | sub-proof #36. % 262.16/56.68 | | | | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | | | | End of split % 262.16/56.68 | | | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | | | End of split % 262.16/56.68 | | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | | End of split % 262.16/56.68 | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | Case 2: % 262.16/56.68 | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | | (2464) all_74_15 = n2 % 262.16/56.68 | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | | REDUCE: (2441), (2464) imply: % 262.16/56.68 | | | | | | | | | | | | | | | | | (2465) a_select3(id_ds1_filter, n2, n2) = all_74_13 % 262.16/56.68 | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | | REDUCE: (2440), (2464) imply: % 262.16/56.68 | | | | | | | | | | | | | | | | | (2466) a_select3(id_ds1_filter, n2, n2) = all_74_12 % 262.16/56.68 | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (649), (2465), (2466) are inconsistent by % 262.16/56.68 | | | | | | | | | | | | | | | | | sub-proof #31. % 262.16/56.68 | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | End of split % 262.16/56.68 | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | End of split % 262.16/56.68 | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | Case 2: % 262.16/56.68 | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | (2467) all_74_15 = n3 % 262.16/56.68 | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | REDUCE: (656), (2467) imply: % 262.16/56.68 | | | | | | | | | | | | | | | (2468) a_select3(id_ds1_filter, all_74_14, n3) = % 262.16/56.68 | | | | | | | | | | | | | | | all_74_12 % 262.16/56.68 | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | REDUCE: (655), (2467) imply: % 262.16/56.68 | | | | | | | | | | | | | | | (2469) a_select3(id_ds1_filter, n3, all_74_14) = % 262.16/56.68 | | | | | | | | | | | | | | | all_74_13 % 262.16/56.68 | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | REDUCE: (684), (2467) imply: % 262.16/56.68 | | | | | | | | | | | | | | | (2470) leq(n3, n5) % 262.16/56.68 | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | REDUCE: (650), (2467) imply: % 262.16/56.68 | | | | | | | | | | | | | | | (2471) leq(n0, n3) % 262.16/56.68 | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | BETA: splitting (2400) gives: % 262.16/56.68 | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | Case 1: % 262.16/56.68 | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | (2472) gt(n2, all_74_14) % 262.16/56.68 | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_14, n2, n1, % 262.16/56.68 | | | | | | | | | | | | | | | | simplifying with (67), (118), (145), (2472) gives: % 262.16/56.68 | | | | | | | | | | | | | | | | (2473) leq(all_74_14, n1) % 262.16/56.68 | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_74_14, simplifying % 262.16/56.68 | | | | | | | | | | | | | | | | with (67), (651), (2473) gives: % 262.16/56.68 | | | | | | | | | | | | | | | | (2474) all_74_14 = n1 | all_74_14 = n0 % 262.16/56.68 | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | BETA: splitting (2474) gives: % 262.16/56.68 | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | Case 1: % 262.16/56.68 | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | | (2475) all_74_14 = n0 % 262.16/56.68 | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | | REDUCE: (2387), (2475) imply: % 262.16/56.68 | | | | | | | | | | | | | | | | | (2476) $false % 262.16/56.68 | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | | CLOSE: (2476) is inconsistent. % 262.16/56.68 | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | Case 2: % 262.16/56.68 | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | | (2477) all_74_14 = n1 % 262.16/56.68 | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | | REDUCE: (2468), (2477) imply: % 262.16/56.68 | | | | | | | | | | | | | | | | | (2478) a_select3(id_ds1_filter, n1, n3) = all_74_12 % 262.16/56.68 | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | | REDUCE: (2469), (2477) imply: % 262.16/56.68 | | | | | | | | | | | | | | | | | (2479) a_select3(id_ds1_filter, n3, n1) = all_74_13 % 262.16/56.68 | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | | REDUCE: (659), (2477) imply: % 262.16/56.68 | | | | | | | | | | | | | | | | | (2480) leq(n1, n5) % 262.16/56.68 | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | | REDUCE: (651), (2477) imply: % 262.16/56.68 | | | | | | | | | | | | | | | | | (2481) leq(n0, n1) % 262.16/56.68 | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (81) with n1, n3, all_74_12, % 262.16/56.68 | | | | | | | | | | | | | | | | | simplifying with (102), (129), (2471), (2478), % 262.16/56.68 | | | | | | | | | | | | | | | | | (2481) gives: % 262.16/56.68 | | | | | | | | | | | | | | | | | (2482) ~ leq(n3, all_74_20) | ~ leq(n1, pv57) | % 262.16/56.68 | | | | | | | | | | | | | | | | | (a_select3(id_ds1_filter, n3, n1) = all_74_12 & % 262.16/56.68 | | | | | | | | | | | | | | | | | $i(all_74_12)) % 262.16/56.68 | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | | BETA: splitting (2482) gives: % 262.16/56.68 | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | | Case 1: % 262.16/56.68 | | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | | | (2483) ~ leq(n3, all_74_20) % 262.16/56.68 | | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | | | REDUCE: (159), (2483) imply: % 262.16/56.68 | | | | | | | | | | | | | | | | | | (2484) ~ leq(n3, n5) % 262.16/56.68 | | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | | | PRED_UNIFY: (2470), (2484) imply: % 262.16/56.68 | | | | | | | | | | | | | | | | | | (2485) $false % 262.16/56.68 | | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | | | CLOSE: (2485) is inconsistent. % 262.16/56.68 | | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | | Case 2: % 262.16/56.68 | | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | | | (2486) ~ leq(n1, pv57) | (a_select3(id_ds1_filter, n3, % 262.16/56.68 | | | | | | | | | | | | | | | | | | n1) = all_74_12 & $i(all_74_12)) % 262.16/56.68 | | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | | | BETA: splitting (2486) gives: % 262.16/56.68 | | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | | | Case 1: % 262.16/56.68 | | | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | | | | (2487) ~ leq(n1, pv57) % 262.16/56.68 | | | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | | | | REDUCE: (2374), (2487) imply: % 262.16/56.68 | | | | | | | | | | | | | | | | | | | (2488) ~ leq(n1, n5) % 262.16/56.68 | | | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (2480), (2488) imply: % 262.16/56.68 | | | | | | | | | | | | | | | | | | | (2489) $false % 262.16/56.68 | | | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | | | | CLOSE: (2489) is inconsistent. % 262.16/56.68 | | | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | | | Case 2: % 262.16/56.68 | | | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | | | | (2490) a_select3(id_ds1_filter, n3, n1) = all_74_12 & % 262.16/56.68 | | | | | | | | | | | | | | | | | | | $i(all_74_12) % 262.16/56.68 | | | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | | | | ALPHA: (2490) implies: % 262.16/56.68 | | | | | | | | | | | | | | | | | | | (2491) a_select3(id_ds1_filter, n3, n1) = all_74_12 % 262.16/56.68 | | | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (649), (2479), (2491) are inconsistent by % 262.16/56.68 | | | | | | | | | | | | | | | | | | | sub-proof #35. % 262.16/56.68 | | | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | | | End of split % 262.16/56.68 | | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | | End of split % 262.16/56.68 | | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | End of split % 262.16/56.68 | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | Case 2: % 262.16/56.68 | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | (2492) all_74_14 = n2 % 262.16/56.68 | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | REDUCE: (2468), (2492) imply: % 262.16/56.68 | | | | | | | | | | | | | | | | (2493) a_select3(id_ds1_filter, n2, n3) = all_74_12 % 262.16/56.68 | | | | | | | | | | | | | | | | % 262.16/56.68 | | | | | | | | | | | | | | | | REDUCE: (2469), (2492) imply: % 262.16/56.68 | | | | | | | | | | | | | | | | (2494) a_select3(id_ds1_filter, n3, n2) = all_74_13 % 262.16/56.68 | | | | | | | | | | | | | | | | % 262.32/56.68 | | | | | | | | | | | | | | | | REDUCE: (659), (2492) imply: % 262.32/56.68 | | | | | | | | | | | | | | | | (2495) leq(n2, n5) % 262.32/56.68 | | | | | | | | | | | | | | | | % 262.32/56.68 | | | | | | | | | | | | | | | | REDUCE: (651), (2492) imply: % 262.32/56.68 | | | | | | | | | | | | | | | | (2496) leq(n0, n2) % 262.32/56.68 | | | | | | | | | | | | | | | | % 262.32/56.68 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (81) with n2, n3, all_74_12, % 262.32/56.68 | | | | | | | | | | | | | | | | simplifying with (118), (129), (2471), (2493), % 262.32/56.68 | | | | | | | | | | | | | | | | (2496) gives: % 262.32/56.68 | | | | | | | | | | | | | | | | (2497) ~ leq(n3, all_74_20) | ~ leq(n2, pv57) | % 262.32/56.68 | | | | | | | | | | | | | | | | (a_select3(id_ds1_filter, n3, n2) = all_74_12 & % 262.32/56.68 | | | | | | | | | | | | | | | | $i(all_74_12)) % 262.32/56.68 | | | | | | | | | | | | | | | | % 262.32/56.68 | | | | | | | | | | | | | | | | BETA: splitting (2497) gives: % 262.32/56.68 | | | | | | | | | | | | | | | | % 262.32/56.68 | | | | | | | | | | | | | | | | Case 1: % 262.32/56.68 | | | | | | | | | | | | | | | | | % 262.32/56.68 | | | | | | | | | | | | | | | | | (2498) ~ leq(n3, all_74_20) % 262.32/56.68 | | | | | | | | | | | | | | | | | % 262.32/56.68 | | | | | | | | | | | | | | | | | REDUCE: (159), (2498) imply: % 262.32/56.68 | | | | | | | | | | | | | | | | | (2499) ~ leq(n3, n5) % 262.32/56.68 | | | | | | | | | | | | | | | | | % 262.32/56.68 | | | | | | | | | | | | | | | | | PRED_UNIFY: (2470), (2499) imply: % 262.32/56.68 | | | | | | | | | | | | | | | | | (2500) $false % 262.32/56.68 | | | | | | | | | | | | | | | | | % 262.32/56.68 | | | | | | | | | | | | | | | | | CLOSE: (2500) is inconsistent. % 262.32/56.68 | | | | | | | | | | | | | | | | | % 262.32/56.68 | | | | | | | | | | | | | | | | Case 2: % 262.32/56.68 | | | | | | | | | | | | | | | | | % 262.32/56.68 | | | | | | | | | | | | | | | | | (2501) ~ leq(n2, pv57) | (a_select3(id_ds1_filter, n3, % 262.32/56.68 | | | | | | | | | | | | | | | | | n2) = all_74_12 & $i(all_74_12)) % 262.32/56.68 | | | | | | | | | | | | | | | | | % 262.32/56.68 | | | | | | | | | | | | | | | | | BETA: splitting (2501) gives: % 262.32/56.68 | | | | | | | | | | | | | | | | | % 262.32/56.68 | | | | | | | | | | | | | | | | | Case 1: % 262.32/56.68 | | | | | | | | | | | | | | | | | | % 262.32/56.68 | | | | | | | | | | | | | | | | | | (2502) ~ leq(n2, pv57) % 262.32/56.68 | | | | | | | | | | | | | | | | | | % 262.32/56.68 | | | | | | | | | | | | | | | | | | REDUCE: (2374), (2502) imply: % 262.32/56.68 | | | | | | | | | | | | | | | | | | (2503) ~ leq(n2, n5) % 262.32/56.68 | | | | | | | | | | | | | | | | | | % 262.32/56.68 | | | | | | | | | | | | | | | | | | PRED_UNIFY: (2495), (2503) imply: % 262.32/56.68 | | | | | | | | | | | | | | | | | | (2504) $false % 262.32/56.68 | | | | | | | | | | | | | | | | | | % 262.32/56.68 | | | | | | | | | | | | | | | | | | CLOSE: (2504) is inconsistent. % 262.32/56.68 | | | | | | | | | | | | | | | | | | % 262.32/56.68 | | | | | | | | | | | | | | | | | Case 2: % 262.32/56.68 | | | | | | | | | | | | | | | | | | % 262.32/56.68 | | | | | | | | | | | | | | | | | | (2505) a_select3(id_ds1_filter, n3, n2) = all_74_12 & % 262.32/56.68 | | | | | | | | | | | | | | | | | | $i(all_74_12) % 262.32/56.68 | | | | | | | | | | | | | | | | | | % 262.32/56.68 | | | | | | | | | | | | | | | | | | ALPHA: (2505) implies: % 262.32/56.68 | | | | | | | | | | | | | | | | | | (2506) a_select3(id_ds1_filter, n3, n2) = all_74_12 % 262.32/56.68 | | | | | | | | | | | | | | | | | | % 262.32/56.68 | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (649), (2494), (2506) are inconsistent by % 262.32/56.68 | | | | | | | | | | | | | | | | | | sub-proof #30. % 262.32/56.68 | | | | | | | | | | | | | | | | | | % 262.32/56.68 | | | | | | | | | | | | | | | | | End of split % 262.32/56.68 | | | | | | | | | | | | | | | | | % 262.32/56.68 | | | | | | | | | | | | | | | | End of split % 262.32/56.68 | | | | | | | | | | | | | | | | % 262.32/56.68 | | | | | | | | | | | | | | | End of split % 262.32/56.68 | | | | | | | | | | | | | | | % 262.32/56.68 | | | | | | | | | | | | | | End of split % 262.32/56.68 | | | | | | | | | | | | | | % 262.32/56.68 | | | | | | | | | | | | | Case 2: % 262.32/56.68 | | | | | | | | | | | | | | % 262.32/56.68 | | | | | | | | | | | | | | (2507) all_74_14 = n3 % 262.32/56.68 | | | | | | | | | | | | | | % 262.32/56.68 | | | | | | | | | | | | | | REDUCE: (656), (2507) imply: % 262.32/56.68 | | | | | | | | | | | | | | (2508) a_select3(id_ds1_filter, n3, all_74_15) = % 262.32/56.68 | | | | | | | | | | | | | | all_74_12 % 262.32/56.68 | | | | | | | | | | | | | | % 262.32/56.68 | | | | | | | | | | | | | | REDUCE: (655), (2507) imply: % 262.32/56.68 | | | | | | | | | | | | | | (2509) a_select3(id_ds1_filter, all_74_15, n3) = % 262.32/56.68 | | | | | | | | | | | | | | all_74_13 % 262.32/56.68 | | | | | | | | | | | | | | % 262.32/56.68 | | | | | | | | | | | | | | REDUCE: (659), (2507) imply: % 262.32/56.68 | | | | | | | | | | | | | | (2510) leq(n3, n5) % 262.32/56.68 | | | | | | | | | | | | | | % 262.32/56.68 | | | | | | | | | | | | | | REDUCE: (651), (2507) imply: % 262.32/56.68 | | | | | | | | | | | | | | (2511) leq(n0, n3) % 262.32/56.68 | | | | | | | | | | | | | | % 262.32/56.68 | | | | | | | | | | | | | | BETA: splitting (2394) gives: % 262.32/56.68 | | | | | | | | | | | | | | % 262.32/56.68 | | | | | | | | | | | | | | Case 1: % 262.32/56.68 | | | | | | | | | | | | | | | % 262.32/56.68 | | | | | | | | | | | | | | | (2512) gt(n3, all_74_15) % 262.32/56.68 | | | | | | | | | | | | | | | % 262.32/56.68 | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_15, n3, n2, % 262.32/56.68 | | | | | | | | | | | | | | | simplifying with (66), (129), (146), (2512) gives: % 262.32/56.68 | | | | | | | | | | | | | | | (2513) leq(all_74_15, n2) % 262.32/56.68 | | | | | | | | | | | | | | | % 262.32/56.68 | | | | | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_15, n2, % 262.32/56.68 | | | | | | | | | | | | | | | simplifying with (66), (118), (2513) gives: % 262.32/56.68 | | | | | | | | | | | | | | | (2514) all_74_15 = n2 | gt(n2, all_74_15) % 262.32/56.68 | | | | | | | | | | | | | | | % 262.32/56.68 | | | | | | | | | | | | | | | BETA: splitting (2514) gives: % 262.32/56.68 | | | | | | | | | | | | | | | % 262.32/56.68 | | | | | | | | | | | | | | | Case 1: % 262.32/56.68 | | | | | | | | | | | | | | | | % 262.32/56.68 | | | | | | | | | | | | | | | | (2515) gt(n2, all_74_15) % 262.32/56.68 | | | | | | | | | | | | | | | | % 262.32/56.68 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_15, n2, n1, % 262.32/56.68 | | | | | | | | | | | | | | | | simplifying with (66), (118), (145), (2515) gives: % 262.32/56.68 | | | | | | | | | | | | | | | | (2516) leq(all_74_15, n1) % 262.32/56.68 | | | | | | | | | | | | | | | | % 262.32/56.68 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_74_15, simplifying % 262.32/56.68 | | | | | | | | | | | | | | | | with (66), (650), (2516) gives: % 262.32/56.68 | | | | | | | | | | | | | | | | (2517) all_74_15 = n1 | all_74_15 = n0 % 262.32/56.68 | | | | | | | | | | | | | | | | % 262.32/56.68 | | | | | | | | | | | | | | | | BETA: splitting (2517) gives: % 262.32/56.68 | | | | | | | | | | | | | | | | % 262.32/56.68 | | | | | | | | | | | | | | | | Case 1: % 262.32/56.68 | | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | | (2518) all_74_15 = n0 % 262.32/56.69 | | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | | REDUCE: (2391), (2518) imply: % 262.32/56.69 | | | | | | | | | | | | | | | | | (2519) $false % 262.32/56.69 | | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | | CLOSE: (2519) is inconsistent. % 262.32/56.69 | | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | Case 2: % 262.32/56.69 | | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | | (2520) all_74_15 = n1 % 262.32/56.69 | | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | | REDUCE: (2509), (2520) imply: % 262.32/56.69 | | | | | | | | | | | | | | | | | (2521) a_select3(id_ds1_filter, n1, n3) = all_74_13 % 262.32/56.69 | | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | | REDUCE: (2508), (2520) imply: % 262.32/56.69 | | | | | | | | | | | | | | | | | (2522) a_select3(id_ds1_filter, n3, n1) = all_74_12 % 262.32/56.69 | | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | | REDUCE: (684), (2520) imply: % 262.32/56.69 | | | | | | | | | | | | | | | | | (2523) leq(n1, n5) % 262.32/56.69 | | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | | REDUCE: (650), (2520) imply: % 262.32/56.69 | | | | | | | | | | | | | | | | | (2524) leq(n0, n1) % 262.32/56.69 | | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (81) with n1, n3, all_74_13, % 262.32/56.69 | | | | | | | | | | | | | | | | | simplifying with (102), (129), (2511), (2521), % 262.32/56.69 | | | | | | | | | | | | | | | | | (2524) gives: % 262.32/56.69 | | | | | | | | | | | | | | | | | (2525) ~ leq(n3, all_74_20) | ~ leq(n1, pv57) | % 262.32/56.69 | | | | | | | | | | | | | | | | | (a_select3(id_ds1_filter, n3, n1) = all_74_13 & % 262.32/56.69 | | | | | | | | | | | | | | | | | $i(all_74_13)) % 262.32/56.69 | | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | | BETA: splitting (2525) gives: % 262.32/56.69 | | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | | Case 1: % 262.32/56.69 | | | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | | | (2526) ~ leq(n3, all_74_20) % 262.32/56.69 | | | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | | | REDUCE: (159), (2526) imply: % 262.32/56.69 | | | | | | | | | | | | | | | | | | (2527) ~ leq(n3, n5) % 262.32/56.69 | | | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | | | PRED_UNIFY: (2510), (2527) imply: % 262.32/56.69 | | | | | | | | | | | | | | | | | | (2528) $false % 262.32/56.69 | | | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | | | CLOSE: (2528) is inconsistent. % 262.32/56.69 | | | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | | Case 2: % 262.32/56.69 | | | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | | | (2529) ~ leq(n1, pv57) | (a_select3(id_ds1_filter, n3, % 262.32/56.69 | | | | | | | | | | | | | | | | | | n1) = all_74_13 & $i(all_74_13)) % 262.32/56.69 | | | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | | | BETA: splitting (2529) gives: % 262.32/56.69 | | | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | | | Case 1: % 262.32/56.69 | | | | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | | | | (2530) ~ leq(n1, pv57) % 262.32/56.69 | | | | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | | | | REDUCE: (2374), (2530) imply: % 262.32/56.69 | | | | | | | | | | | | | | | | | | | (2531) ~ leq(n1, n5) % 262.32/56.69 | | | | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (2523), (2531) imply: % 262.32/56.69 | | | | | | | | | | | | | | | | | | | (2532) $false % 262.32/56.69 | | | | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | | | | CLOSE: (2532) is inconsistent. % 262.32/56.69 | | | | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | | | Case 2: % 262.32/56.69 | | | | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | | | | (2533) a_select3(id_ds1_filter, n3, n1) = all_74_13 & % 262.32/56.69 | | | | | | | | | | | | | | | | | | | $i(all_74_13) % 262.32/56.69 | | | | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | | | | ALPHA: (2533) implies: % 262.32/56.69 | | | | | | | | | | | | | | | | | | | (2534) a_select3(id_ds1_filter, n3, n1) = all_74_13 % 262.32/56.69 | | | | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (649), (2522), (2534) are inconsistent by % 262.32/56.69 | | | | | | | | | | | | | | | | | | | sub-proof #35. % 262.32/56.69 | | | | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | | | End of split % 262.32/56.69 | | | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | | End of split % 262.32/56.69 | | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | End of split % 262.32/56.69 | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | Case 2: % 262.32/56.69 | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | (2535) all_74_15 = n2 % 262.32/56.69 | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | REDUCE: (2509), (2535) imply: % 262.32/56.69 | | | | | | | | | | | | | | | | (2536) a_select3(id_ds1_filter, n2, n3) = all_74_13 % 262.32/56.69 | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | REDUCE: (2508), (2535) imply: % 262.32/56.69 | | | | | | | | | | | | | | | | (2537) a_select3(id_ds1_filter, n3, n2) = all_74_12 % 262.32/56.69 | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | REDUCE: (684), (2535) imply: % 262.32/56.69 | | | | | | | | | | | | | | | | (2538) leq(n2, n5) % 262.32/56.69 | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | REDUCE: (650), (2535) imply: % 262.32/56.69 | | | | | | | | | | | | | | | | (2539) leq(n0, n2) % 262.32/56.69 | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (81) with n2, n3, all_74_13, % 262.32/56.69 | | | | | | | | | | | | | | | | simplifying with (118), (129), (2511), (2536), % 262.32/56.69 | | | | | | | | | | | | | | | | (2539) gives: % 262.32/56.69 | | | | | | | | | | | | | | | | (2540) ~ leq(n3, all_74_20) | ~ leq(n2, pv57) | % 262.32/56.69 | | | | | | | | | | | | | | | | (a_select3(id_ds1_filter, n3, n2) = all_74_13 & % 262.32/56.69 | | | | | | | | | | | | | | | | $i(all_74_13)) % 262.32/56.69 | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | BETA: splitting (2540) gives: % 262.32/56.69 | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | Case 1: % 262.32/56.69 | | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | | (2541) ~ leq(n3, all_74_20) % 262.32/56.69 | | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | | REDUCE: (159), (2541) imply: % 262.32/56.69 | | | | | | | | | | | | | | | | | (2542) ~ leq(n3, n5) % 262.32/56.69 | | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | | PRED_UNIFY: (2510), (2542) imply: % 262.32/56.69 | | | | | | | | | | | | | | | | | (2543) $false % 262.32/56.69 | | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | | CLOSE: (2543) is inconsistent. % 262.32/56.69 | | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | Case 2: % 262.32/56.69 | | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | | (2544) ~ leq(n2, pv57) | (a_select3(id_ds1_filter, n3, % 262.32/56.69 | | | | | | | | | | | | | | | | | n2) = all_74_13 & $i(all_74_13)) % 262.32/56.69 | | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | | BETA: splitting (2544) gives: % 262.32/56.69 | | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | | Case 1: % 262.32/56.69 | | | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | | | (2545) ~ leq(n2, pv57) % 262.32/56.69 | | | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | | | REDUCE: (2374), (2545) imply: % 262.32/56.69 | | | | | | | | | | | | | | | | | | (2546) ~ leq(n2, n5) % 262.32/56.69 | | | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | | | PRED_UNIFY: (2538), (2546) imply: % 262.32/56.69 | | | | | | | | | | | | | | | | | | (2547) $false % 262.32/56.69 | | | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | | | CLOSE: (2547) is inconsistent. % 262.32/56.69 | | | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | | Case 2: % 262.32/56.69 | | | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | | | (2548) a_select3(id_ds1_filter, n3, n2) = all_74_13 & % 262.32/56.69 | | | | | | | | | | | | | | | | | | $i(all_74_13) % 262.32/56.69 | | | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | | | ALPHA: (2548) implies: % 262.32/56.69 | | | | | | | | | | | | | | | | | | (2549) a_select3(id_ds1_filter, n3, n2) = all_74_13 % 262.32/56.69 | | | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (649), (2537), (2549) are inconsistent by % 262.32/56.69 | | | | | | | | | | | | | | | | | | sub-proof #30. % 262.32/56.69 | | | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | | End of split % 262.32/56.69 | | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | End of split % 262.32/56.69 | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | End of split % 262.32/56.69 | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | Case 2: % 262.32/56.69 | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | (2550) all_74_15 = n3 % 262.32/56.69 | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | REDUCE: (2509), (2550) imply: % 262.32/56.69 | | | | | | | | | | | | | | | (2551) a_select3(id_ds1_filter, n3, n3) = all_74_13 % 262.32/56.69 | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | REDUCE: (2508), (2550) imply: % 262.32/56.69 | | | | | | | | | | | | | | | (2552) a_select3(id_ds1_filter, n3, n3) = all_74_12 % 262.32/56.69 | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | REF_CLOSE: (30), (649), (2551), (2552) are inconsistent by % 262.32/56.69 | | | | | | | | | | | | | | | sub-proof #19. % 262.32/56.69 | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | End of split % 262.32/56.69 | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | End of split % 262.32/56.69 | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | Case 2: % 262.32/56.69 | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | (2553) all_74_14 = n4 % 262.32/56.69 | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | REDUCE: (656), (2553) imply: % 262.32/56.69 | | | | | | | | | | | | | (2554) a_select3(id_ds1_filter, n4, all_74_15) = % 262.32/56.69 | | | | | | | | | | | | | all_74_12 % 262.32/56.69 | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | REDUCE: (655), (2553) imply: % 262.32/56.69 | | | | | | | | | | | | | (2555) a_select3(id_ds1_filter, all_74_15, n4) = % 262.32/56.69 | | | | | | | | | | | | | all_74_13 % 262.32/56.69 | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | REDUCE: (659), (2553) imply: % 262.32/56.69 | | | | | | | | | | | | | (2556) leq(n4, n5) % 262.32/56.69 | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | BETA: splitting (2394) gives: % 262.32/56.69 | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | Case 1: % 262.32/56.69 | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | (2557) gt(n3, all_74_15) % 262.32/56.69 | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_15, n3, n2, % 262.32/56.69 | | | | | | | | | | | | | | simplifying with (66), (129), (146), (2557) gives: % 262.32/56.69 | | | | | | | | | | | | | | (2558) leq(all_74_15, n2) % 262.32/56.69 | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_15, n2, % 262.32/56.69 | | | | | | | | | | | | | | simplifying with (66), (118), (2558) gives: % 262.32/56.69 | | | | | | | | | | | | | | (2559) all_74_15 = n2 | gt(n2, all_74_15) % 262.32/56.69 | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | BETA: splitting (2559) gives: % 262.32/56.69 | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | Case 1: % 262.32/56.69 | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | (2560) gt(n2, all_74_15) % 262.32/56.69 | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_15, n2, n1, % 262.32/56.69 | | | | | | | | | | | | | | | simplifying with (66), (118), (145), (2560) gives: % 262.32/56.69 | | | | | | | | | | | | | | | (2561) leq(all_74_15, n1) % 262.32/56.69 | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_74_15, simplifying % 262.32/56.69 | | | | | | | | | | | | | | | with (66), (650), (2561) gives: % 262.32/56.69 | | | | | | | | | | | | | | | (2562) all_74_15 = n1 | all_74_15 = n0 % 262.32/56.69 | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | BETA: splitting (2562) gives: % 262.32/56.69 | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | Case 1: % 262.32/56.69 | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | (2563) all_74_15 = n0 % 262.32/56.69 | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | REDUCE: (2391), (2563) imply: % 262.32/56.69 | | | | | | | | | | | | | | | | (2564) $false % 262.32/56.69 | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | CLOSE: (2564) is inconsistent. % 262.32/56.69 | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | Case 2: % 262.32/56.69 | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | (2565) all_74_15 = n1 % 262.32/56.69 | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | REDUCE: (2555), (2565) imply: % 262.32/56.69 | | | | | | | | | | | | | | | | (2566) a_select3(id_ds1_filter, n1, n4) = all_74_13 % 262.32/56.69 | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | REDUCE: (2554), (2565) imply: % 262.32/56.69 | | | | | | | | | | | | | | | | (2567) a_select3(id_ds1_filter, n4, n1) = all_74_12 % 262.32/56.69 | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | REDUCE: (2384), (2565) imply: % 262.32/56.69 | | | | | | | | | | | | | | | | (2568) leq(n1, n4) % 262.32/56.69 | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | REDUCE: (650), (2565) imply: % 262.32/56.69 | | | | | | | | | | | | | | | | (2569) leq(n0, n1) % 262.32/56.69 | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (82) with n1, n4, all_74_13, % 262.32/56.69 | | | | | | | | | | | | | | | | simplifying with (102), (136), (2378), (2566), % 262.32/56.69 | | | | | | | | | | | | | | | | (2569) gives: % 262.32/56.69 | | | | | | | | | | | | | | | | (2570) ~ leq(n4, all_74_20) | ~ leq(n1, all_74_18) | % 262.32/56.69 | | | | | | | | | | | | | | | | (a_select3(id_ds1_filter, n4, n1) = all_74_13 & % 262.32/56.69 | | | | | | | | | | | | | | | | $i(all_74_13)) % 262.32/56.69 | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | BETA: splitting (2570) gives: % 262.32/56.69 | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | Case 1: % 262.32/56.69 | | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | | (2571) ~ leq(n4, all_74_20) % 262.32/56.69 | | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | | REDUCE: (159), (2571) imply: % 262.32/56.69 | | | | | | | | | | | | | | | | | (2572) ~ leq(n4, n5) % 262.32/56.69 | | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | | PRED_UNIFY: (2556), (2572) imply: % 262.32/56.69 | | | | | | | | | | | | | | | | | (2573) $false % 262.32/56.69 | | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | | CLOSE: (2573) is inconsistent. % 262.32/56.69 | | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | Case 2: % 262.32/56.69 | | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | | (2574) ~ leq(n1, all_74_18) | (a_select3(id_ds1_filter, % 262.32/56.69 | | | | | | | | | | | | | | | | | n4, n1) = all_74_13 & $i(all_74_13)) % 262.32/56.69 | | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | | BETA: splitting (2574) gives: % 262.32/56.69 | | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | | Case 1: % 262.32/56.69 | | | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | | | (2575) ~ leq(n1, all_74_18) % 262.32/56.69 | | | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | | | REDUCE: (2377), (2575) imply: % 262.32/56.69 | | | | | | | | | | | | | | | | | | (2576) ~ leq(n1, n4) % 262.32/56.69 | | | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | | | PRED_UNIFY: (2568), (2576) imply: % 262.32/56.69 | | | | | | | | | | | | | | | | | | (2577) $false % 262.32/56.69 | | | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | | | CLOSE: (2577) is inconsistent. % 262.32/56.69 | | | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | | Case 2: % 262.32/56.69 | | | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | | | (2578) a_select3(id_ds1_filter, n4, n1) = all_74_13 & % 262.32/56.69 | | | | | | | | | | | | | | | | | | $i(all_74_13) % 262.32/56.69 | | | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | | | ALPHA: (2578) implies: % 262.32/56.69 | | | | | | | | | | | | | | | | | | (2579) a_select3(id_ds1_filter, n4, n1) = all_74_13 % 262.32/56.69 | | | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (649), (2567), (2579) are inconsistent by % 262.32/56.69 | | | | | | | | | | | | | | | | | | sub-proof #29. % 262.32/56.69 | | | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | | End of split % 262.32/56.69 | | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | End of split % 262.32/56.69 | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | End of split % 262.32/56.69 | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | Case 2: % 262.32/56.69 | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | (2580) all_74_15 = n2 % 262.32/56.69 | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | REDUCE: (2555), (2580) imply: % 262.32/56.69 | | | | | | | | | | | | | | | (2581) a_select3(id_ds1_filter, n2, n4) = all_74_13 % 262.32/56.69 | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | REDUCE: (2554), (2580) imply: % 262.32/56.69 | | | | | | | | | | | | | | | (2582) a_select3(id_ds1_filter, n4, n2) = all_74_12 % 262.32/56.69 | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | REDUCE: (2384), (2580) imply: % 262.32/56.69 | | | | | | | | | | | | | | | (2583) leq(n2, n4) % 262.32/56.69 | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | REDUCE: (650), (2580) imply: % 262.32/56.69 | | | | | | | | | | | | | | | (2584) leq(n0, n2) % 262.32/56.69 | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | GROUND_INST: instantiating (82) with n2, n4, all_74_13, % 262.32/56.69 | | | | | | | | | | | | | | | simplifying with (118), (136), (2378), (2581), % 262.32/56.69 | | | | | | | | | | | | | | | (2584) gives: % 262.32/56.69 | | | | | | | | | | | | | | | (2585) ~ leq(n4, all_74_20) | ~ leq(n2, all_74_18) | % 262.32/56.69 | | | | | | | | | | | | | | | (a_select3(id_ds1_filter, n4, n2) = all_74_13 & % 262.32/56.69 | | | | | | | | | | | | | | | $i(all_74_13)) % 262.32/56.69 | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | BETA: splitting (2585) gives: % 262.32/56.69 | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | Case 1: % 262.32/56.69 | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | (2586) ~ leq(n4, all_74_20) % 262.32/56.69 | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | REDUCE: (159), (2586) imply: % 262.32/56.69 | | | | | | | | | | | | | | | | (2587) ~ leq(n4, n5) % 262.32/56.69 | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | PRED_UNIFY: (2556), (2587) imply: % 262.32/56.69 | | | | | | | | | | | | | | | | (2588) $false % 262.32/56.69 | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | CLOSE: (2588) is inconsistent. % 262.32/56.69 | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | Case 2: % 262.32/56.69 | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | (2589) ~ leq(n2, all_74_18) | (a_select3(id_ds1_filter, % 262.32/56.69 | | | | | | | | | | | | | | | | n4, n2) = all_74_13 & $i(all_74_13)) % 262.32/56.69 | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | BETA: splitting (2589) gives: % 262.32/56.69 | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | Case 1: % 262.32/56.69 | | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | | (2590) ~ leq(n2, all_74_18) % 262.32/56.69 | | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | | REDUCE: (2377), (2590) imply: % 262.32/56.69 | | | | | | | | | | | | | | | | | (2591) ~ leq(n2, n4) % 262.32/56.69 | | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | | PRED_UNIFY: (2583), (2591) imply: % 262.32/56.69 | | | | | | | | | | | | | | | | | (2592) $false % 262.32/56.69 | | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | | CLOSE: (2592) is inconsistent. % 262.32/56.69 | | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | Case 2: % 262.32/56.69 | | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | | (2593) a_select3(id_ds1_filter, n4, n2) = all_74_13 & % 262.32/56.69 | | | | | | | | | | | | | | | | | $i(all_74_13) % 262.32/56.69 | | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | | ALPHA: (2593) implies: % 262.32/56.69 | | | | | | | | | | | | | | | | | (2594) a_select3(id_ds1_filter, n4, n2) = all_74_13 % 262.32/56.69 | | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (649), (2582), (2594) are inconsistent by % 262.32/56.69 | | | | | | | | | | | | | | | | | sub-proof #27. % 262.32/56.69 | | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | End of split % 262.32/56.69 | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | End of split % 262.32/56.69 | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | End of split % 262.32/56.69 | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | Case 2: % 262.32/56.69 | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | (2595) all_74_15 = n3 % 262.32/56.69 | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | REDUCE: (2555), (2595) imply: % 262.32/56.69 | | | | | | | | | | | | | | (2596) a_select3(id_ds1_filter, n3, n4) = all_74_13 % 262.32/56.69 | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | REDUCE: (2554), (2595) imply: % 262.32/56.69 | | | | | | | | | | | | | | (2597) a_select3(id_ds1_filter, n4, n3) = all_74_12 % 262.32/56.69 | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | REDUCE: (684), (2595) imply: % 262.32/56.69 | | | | | | | | | | | | | | (2598) leq(n3, n5) % 262.32/56.69 | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | REDUCE: (650), (2595) imply: % 262.32/56.69 | | | | | | | | | | | | | | (2599) leq(n0, n3) % 262.32/56.69 | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | GROUND_INST: instantiating (81) with n3, n4, all_74_13, % 262.32/56.69 | | | | | | | | | | | | | | simplifying with (129), (136), (2378), (2596), % 262.32/56.69 | | | | | | | | | | | | | | (2599) gives: % 262.32/56.69 | | | | | | | | | | | | | | (2600) ~ leq(n4, all_74_20) | ~ leq(n3, pv57) | % 262.32/56.69 | | | | | | | | | | | | | | (a_select3(id_ds1_filter, n4, n3) = all_74_13 & % 262.32/56.69 | | | | | | | | | | | | | | $i(all_74_13)) % 262.32/56.69 | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | BETA: splitting (2600) gives: % 262.32/56.69 | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | Case 1: % 262.32/56.69 | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | (2601) ~ leq(n4, all_74_20) % 262.32/56.69 | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | REDUCE: (159), (2601) imply: % 262.32/56.69 | | | | | | | | | | | | | | | (2602) ~ leq(n4, n5) % 262.32/56.69 | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | PRED_UNIFY: (2556), (2602) imply: % 262.32/56.69 | | | | | | | | | | | | | | | (2603) $false % 262.32/56.69 | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | CLOSE: (2603) is inconsistent. % 262.32/56.69 | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | Case 2: % 262.32/56.69 | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | (2604) ~ leq(n3, pv57) | (a_select3(id_ds1_filter, n4, % 262.32/56.69 | | | | | | | | | | | | | | | n3) = all_74_13 & $i(all_74_13)) % 262.32/56.69 | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | BETA: splitting (2604) gives: % 262.32/56.69 | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | Case 1: % 262.32/56.69 | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | (2605) ~ leq(n3, pv57) % 262.32/56.69 | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | REDUCE: (2374), (2605) imply: % 262.32/56.69 | | | | | | | | | | | | | | | | (2606) ~ leq(n3, n5) % 262.32/56.69 | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | PRED_UNIFY: (2598), (2606) imply: % 262.32/56.69 | | | | | | | | | | | | | | | | (2607) $false % 262.32/56.69 | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | CLOSE: (2607) is inconsistent. % 262.32/56.69 | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | Case 2: % 262.32/56.69 | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | (2608) a_select3(id_ds1_filter, n4, n3) = all_74_13 & % 262.32/56.69 | | | | | | | | | | | | | | | | $i(all_74_13) % 262.32/56.69 | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | ALPHA: (2608) implies: % 262.32/56.69 | | | | | | | | | | | | | | | | (2609) a_select3(id_ds1_filter, n4, n3) = all_74_13 % 262.32/56.69 | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | | REF_CLOSE: (30), (649), (2597), (2609) are inconsistent by % 262.32/56.69 | | | | | | | | | | | | | | | | sub-proof #25. % 262.32/56.69 | | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | | End of split % 262.32/56.69 | | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | | End of split % 262.32/56.69 | | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | | End of split % 262.32/56.69 | | | | | | | | | | | | | % 262.32/56.69 | | | | | | | | | | | | End of split % 262.32/56.69 | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | Case 2: % 262.32/56.70 | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | (2610) all_74_15 = n4 % 262.32/56.70 | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | REDUCE: (656), (2610) imply: % 262.32/56.70 | | | | | | | | | | | | (2611) a_select3(id_ds1_filter, all_74_14, n4) = % 262.32/56.70 | | | | | | | | | | | | all_74_12 % 262.32/56.70 | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | REDUCE: (655), (2610) imply: % 262.32/56.70 | | | | | | | | | | | | (2612) a_select3(id_ds1_filter, n4, all_74_14) = % 262.32/56.70 | | | | | | | | | | | | all_74_13 % 262.32/56.70 | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | REDUCE: (684), (2610) imply: % 262.32/56.70 | | | | | | | | | | | | (2613) leq(n4, n5) % 262.32/56.70 | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | BETA: splitting (2389) gives: % 262.32/56.70 | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | Case 1: % 262.32/56.70 | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | (2614) gt(n4, all_74_14) % 262.32/56.70 | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_14, n4, n3, % 262.32/56.70 | | | | | | | | | | | | | simplifying with (67), (136), (147), (2614) gives: % 262.32/56.70 | | | | | | | | | | | | | (2615) leq(all_74_14, n3) % 262.32/56.70 | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_14, n3, % 262.32/56.70 | | | | | | | | | | | | | simplifying with (67), (129), (2615) gives: % 262.32/56.70 | | | | | | | | | | | | | (2616) all_74_14 = n3 | gt(n3, all_74_14) % 262.32/56.70 | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | BETA: splitting (2616) gives: % 262.32/56.70 | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | Case 1: % 262.32/56.70 | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | (2617) gt(n3, all_74_14) % 262.32/56.70 | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_14, n3, n2, % 262.32/56.70 | | | | | | | | | | | | | | simplifying with (67), (129), (146), (2617) gives: % 262.32/56.70 | | | | | | | | | | | | | | (2618) leq(all_74_14, n2) % 262.32/56.70 | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_14, n2, % 262.32/56.70 | | | | | | | | | | | | | | simplifying with (67), (118), (2618) gives: % 262.32/56.70 | | | | | | | | | | | | | | (2619) all_74_14 = n2 | gt(n2, all_74_14) % 262.32/56.70 | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | BETA: splitting (2619) gives: % 262.32/56.70 | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | Case 1: % 262.32/56.70 | | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | | (2620) gt(n2, all_74_14) % 262.32/56.70 | | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_14, n2, n1, % 262.32/56.70 | | | | | | | | | | | | | | | simplifying with (67), (118), (145), (2620) gives: % 262.32/56.70 | | | | | | | | | | | | | | | (2621) leq(all_74_14, n1) % 262.32/56.70 | | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_74_14, simplifying % 262.32/56.70 | | | | | | | | | | | | | | | with (67), (651), (2621) gives: % 262.32/56.70 | | | | | | | | | | | | | | | (2622) all_74_14 = n1 | all_74_14 = n0 % 262.32/56.70 | | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | | BETA: splitting (2622) gives: % 262.32/56.70 | | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | | Case 1: % 262.32/56.70 | | | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | | | (2623) all_74_14 = n0 % 262.32/56.70 | | | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | | | REDUCE: (2387), (2623) imply: % 262.32/56.70 | | | | | | | | | | | | | | | | (2624) $false % 262.32/56.70 | | | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | | | CLOSE: (2624) is inconsistent. % 262.32/56.70 | | | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | | Case 2: % 262.32/56.70 | | | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | | | (2625) all_74_14 = n1 % 262.32/56.70 | | | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | | | REDUCE: (2611), (2625) imply: % 262.32/56.70 | | | | | | | | | | | | | | | | (2626) a_select3(id_ds1_filter, n1, n4) = all_74_12 % 262.32/56.70 | | | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | | | REDUCE: (2612), (2625) imply: % 262.32/56.70 | | | | | | | | | | | | | | | | (2627) a_select3(id_ds1_filter, n4, n1) = all_74_13 % 262.32/56.70 | | | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | | | REDUCE: (2385), (2625) imply: % 262.32/56.70 | | | | | | | | | | | | | | | | (2628) leq(n1, n4) % 262.32/56.70 | | | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | | | REDUCE: (651), (2625) imply: % 262.32/56.70 | | | | | | | | | | | | | | | | (2629) leq(n0, n1) % 262.32/56.70 | | | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (82) with n1, n4, all_74_12, % 262.32/56.70 | | | | | | | | | | | | | | | | simplifying with (102), (136), (2378), (2626), % 262.32/56.70 | | | | | | | | | | | | | | | | (2629) gives: % 262.32/56.70 | | | | | | | | | | | | | | | | (2630) ~ leq(n4, all_74_20) | ~ leq(n1, all_74_18) | % 262.32/56.70 | | | | | | | | | | | | | | | | (a_select3(id_ds1_filter, n4, n1) = all_74_12 & % 262.32/56.70 | | | | | | | | | | | | | | | | $i(all_74_12)) % 262.32/56.70 | | | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | | | BETA: splitting (2630) gives: % 262.32/56.70 | | | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | | | Case 1: % 262.32/56.70 | | | | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | | | | (2631) ~ leq(n4, all_74_20) % 262.32/56.70 | | | | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | | | | REDUCE: (159), (2631) imply: % 262.32/56.70 | | | | | | | | | | | | | | | | | (2632) ~ leq(n4, n5) % 262.32/56.70 | | | | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | | | | PRED_UNIFY: (2613), (2632) imply: % 262.32/56.70 | | | | | | | | | | | | | | | | | (2633) $false % 262.32/56.70 | | | | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | | | | CLOSE: (2633) is inconsistent. % 262.32/56.70 | | | | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | | | Case 2: % 262.32/56.70 | | | | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | | | | (2634) ~ leq(n1, all_74_18) | (a_select3(id_ds1_filter, % 262.32/56.70 | | | | | | | | | | | | | | | | | n4, n1) = all_74_12 & $i(all_74_12)) % 262.32/56.70 | | | | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | | | | BETA: splitting (2634) gives: % 262.32/56.70 | | | | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | | | | Case 1: % 262.32/56.70 | | | | | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | | | | | (2635) ~ leq(n1, all_74_18) % 262.32/56.70 | | | | | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | | | | | REDUCE: (2377), (2635) imply: % 262.32/56.70 | | | | | | | | | | | | | | | | | | (2636) ~ leq(n1, n4) % 262.32/56.70 | | | | | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | | | | | PRED_UNIFY: (2628), (2636) imply: % 262.32/56.70 | | | | | | | | | | | | | | | | | | (2637) $false % 262.32/56.70 | | | | | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | | | | | CLOSE: (2637) is inconsistent. % 262.32/56.70 | | | | | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | | | | Case 2: % 262.32/56.70 | | | | | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | | | | | (2638) a_select3(id_ds1_filter, n4, n1) = all_74_12 & % 262.32/56.70 | | | | | | | | | | | | | | | | | | $i(all_74_12) % 262.32/56.70 | | | | | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | | | | | ALPHA: (2638) implies: % 262.32/56.70 | | | | | | | | | | | | | | | | | | (2639) a_select3(id_ds1_filter, n4, n1) = all_74_12 % 262.32/56.70 | | | | | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (649), (2627), (2639) are inconsistent by % 262.32/56.70 | | | | | | | | | | | | | | | | | | sub-proof #29. % 262.32/56.70 | | | | | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | | | | End of split % 262.32/56.70 | | | | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | | | End of split % 262.32/56.70 | | | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | | End of split % 262.32/56.70 | | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | Case 2: % 262.32/56.70 | | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | | (2640) all_74_14 = n2 % 262.32/56.70 | | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | | REDUCE: (2611), (2640) imply: % 262.32/56.70 | | | | | | | | | | | | | | | (2641) a_select3(id_ds1_filter, n2, n4) = all_74_12 % 262.32/56.70 | | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | | REDUCE: (2612), (2640) imply: % 262.32/56.70 | | | | | | | | | | | | | | | (2642) a_select3(id_ds1_filter, n4, n2) = all_74_13 % 262.32/56.70 | | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | | REDUCE: (2385), (2640) imply: % 262.32/56.70 | | | | | | | | | | | | | | | (2643) leq(n2, n4) % 262.32/56.70 | | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | | REDUCE: (651), (2640) imply: % 262.32/56.70 | | | | | | | | | | | | | | | (2644) leq(n0, n2) % 262.32/56.70 | | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | | GROUND_INST: instantiating (82) with n2, n4, all_74_12, % 262.32/56.70 | | | | | | | | | | | | | | | simplifying with (118), (136), (2378), (2641), % 262.32/56.70 | | | | | | | | | | | | | | | (2644) gives: % 262.32/56.70 | | | | | | | | | | | | | | | (2645) ~ leq(n4, all_74_20) | ~ leq(n2, all_74_18) | % 262.32/56.70 | | | | | | | | | | | | | | | (a_select3(id_ds1_filter, n4, n2) = all_74_12 & % 262.32/56.70 | | | | | | | | | | | | | | | $i(all_74_12)) % 262.32/56.70 | | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | | BETA: splitting (2645) gives: % 262.32/56.70 | | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | | Case 1: % 262.32/56.70 | | | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | | | (2646) ~ leq(n4, all_74_20) % 262.32/56.70 | | | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | | | REDUCE: (159), (2646) imply: % 262.32/56.70 | | | | | | | | | | | | | | | | (2647) ~ leq(n4, n5) % 262.32/56.70 | | | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | | | PRED_UNIFY: (2613), (2647) imply: % 262.32/56.70 | | | | | | | | | | | | | | | | (2648) $false % 262.32/56.70 | | | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | | | CLOSE: (2648) is inconsistent. % 262.32/56.70 | | | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | | Case 2: % 262.32/56.70 | | | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | | | (2649) ~ leq(n2, all_74_18) | (a_select3(id_ds1_filter, % 262.32/56.70 | | | | | | | | | | | | | | | | n4, n2) = all_74_12 & $i(all_74_12)) % 262.32/56.70 | | | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | | | BETA: splitting (2649) gives: % 262.32/56.70 | | | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | | | Case 1: % 262.32/56.70 | | | | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | | | | (2650) ~ leq(n2, all_74_18) % 262.32/56.70 | | | | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | | | | REDUCE: (2377), (2650) imply: % 262.32/56.70 | | | | | | | | | | | | | | | | | (2651) ~ leq(n2, n4) % 262.32/56.70 | | | | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | | | | PRED_UNIFY: (2643), (2651) imply: % 262.32/56.70 | | | | | | | | | | | | | | | | | (2652) $false % 262.32/56.70 | | | | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | | | | CLOSE: (2652) is inconsistent. % 262.32/56.70 | | | | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | | | Case 2: % 262.32/56.70 | | | | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | | | | (2653) a_select3(id_ds1_filter, n4, n2) = all_74_12 & % 262.32/56.70 | | | | | | | | | | | | | | | | | $i(all_74_12) % 262.32/56.70 | | | | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | | | | ALPHA: (2653) implies: % 262.32/56.70 | | | | | | | | | | | | | | | | | (2654) a_select3(id_ds1_filter, n4, n2) = all_74_12 % 262.32/56.70 | | | | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (649), (2642), (2654) are inconsistent by % 262.32/56.70 | | | | | | | | | | | | | | | | | sub-proof #27. % 262.32/56.70 | | | | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | | | End of split % 262.32/56.70 | | | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | | End of split % 262.32/56.70 | | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | End of split % 262.32/56.70 | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | Case 2: % 262.32/56.70 | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | (2655) all_74_14 = n3 % 262.32/56.70 | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | REDUCE: (2611), (2655) imply: % 262.32/56.70 | | | | | | | | | | | | | | (2656) a_select3(id_ds1_filter, n3, n4) = all_74_12 % 262.32/56.70 | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | REDUCE: (2612), (2655) imply: % 262.32/56.70 | | | | | | | | | | | | | | (2657) a_select3(id_ds1_filter, n4, n3) = all_74_13 % 262.32/56.70 | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | REDUCE: (2385), (2655) imply: % 262.32/56.70 | | | | | | | | | | | | | | (2658) leq(n3, n4) % 262.32/56.70 | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | REDUCE: (651), (2655) imply: % 262.32/56.70 | | | | | | | | | | | | | | (2659) leq(n0, n3) % 262.32/56.70 | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | GROUND_INST: instantiating (82) with n3, n4, all_74_12, % 262.32/56.70 | | | | | | | | | | | | | | simplifying with (129), (136), (2378), (2656), % 262.32/56.70 | | | | | | | | | | | | | | (2659) gives: % 262.32/56.70 | | | | | | | | | | | | | | (2660) ~ leq(n4, all_74_20) | ~ leq(n3, all_74_18) | % 262.32/56.70 | | | | | | | | | | | | | | (a_select3(id_ds1_filter, n4, n3) = all_74_12 & % 262.32/56.70 | | | | | | | | | | | | | | $i(all_74_12)) % 262.32/56.70 | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | BETA: splitting (2660) gives: % 262.32/56.70 | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | Case 1: % 262.32/56.70 | | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | | (2661) ~ leq(n4, all_74_20) % 262.32/56.70 | | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | | REDUCE: (159), (2661) imply: % 262.32/56.70 | | | | | | | | | | | | | | | (2662) ~ leq(n4, n5) % 262.32/56.70 | | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | | PRED_UNIFY: (2613), (2662) imply: % 262.32/56.70 | | | | | | | | | | | | | | | (2663) $false % 262.32/56.70 | | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | | CLOSE: (2663) is inconsistent. % 262.32/56.70 | | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | Case 2: % 262.32/56.70 | | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | | (2664) ~ leq(n3, all_74_18) | (a_select3(id_ds1_filter, % 262.32/56.70 | | | | | | | | | | | | | | | n4, n3) = all_74_12 & $i(all_74_12)) % 262.32/56.70 | | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | | BETA: splitting (2664) gives: % 262.32/56.70 | | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | | Case 1: % 262.32/56.70 | | | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | | | (2665) ~ leq(n3, all_74_18) % 262.32/56.70 | | | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | | | REDUCE: (2377), (2665) imply: % 262.32/56.70 | | | | | | | | | | | | | | | | (2666) ~ leq(n3, n4) % 262.32/56.70 | | | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | | | PRED_UNIFY: (2658), (2666) imply: % 262.32/56.70 | | | | | | | | | | | | | | | | (2667) $false % 262.32/56.70 | | | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | | | CLOSE: (2667) is inconsistent. % 262.32/56.70 | | | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | | Case 2: % 262.32/56.70 | | | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | | | (2668) a_select3(id_ds1_filter, n4, n3) = all_74_12 & % 262.32/56.70 | | | | | | | | | | | | | | | | $i(all_74_12) % 262.32/56.70 | | | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | | | ALPHA: (2668) implies: % 262.32/56.70 | | | | | | | | | | | | | | | | (2669) a_select3(id_ds1_filter, n4, n3) = all_74_12 % 262.32/56.70 | | | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | | | REF_CLOSE: (30), (649), (2657), (2669) are inconsistent by % 262.32/56.70 | | | | | | | | | | | | | | | | sub-proof #25. % 262.32/56.70 | | | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | | End of split % 262.32/56.70 | | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | End of split % 262.32/56.70 | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | End of split % 262.32/56.70 | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | Case 2: % 262.32/56.70 | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | (2670) all_74_14 = n4 % 262.32/56.70 | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | REDUCE: (2611), (2670) imply: % 262.32/56.70 | | | | | | | | | | | | | (2671) a_select3(id_ds1_filter, n4, n4) = all_74_12 % 262.32/56.70 | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | REDUCE: (2612), (2670) imply: % 262.32/56.70 | | | | | | | | | | | | | (2672) a_select3(id_ds1_filter, n4, n4) = all_74_13 % 262.32/56.70 | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | GROUND_INST: instantiating (30) with all_74_13, all_74_12, n4, % 262.32/56.70 | | | | | | | | | | | | | n4, id_ds1_filter, simplifying with (2671), (2672) % 262.32/56.70 | | | | | | | | | | | | | gives: % 262.32/56.70 | | | | | | | | | | | | | (2673) all_74_12 = all_74_13 % 262.32/56.70 | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | REDUCE: (649), (2673) imply: % 262.32/56.70 | | | | | | | | | | | | | (2674) $false % 262.32/56.70 | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | CLOSE: (2674) is inconsistent. % 262.32/56.70 | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | End of split % 262.32/56.70 | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | End of split % 262.32/56.70 | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | End of split % 262.32/56.70 | | | | | | | | | | % 262.32/56.70 | | | | | | | | | End of split % 262.32/56.70 | | | | | | | | | % 262.32/56.70 | | | | | | | | Case 2: % 262.32/56.70 | | | | | | | | | % 262.32/56.70 | | | | | | | | | (2675) all_74_14 = n5 % 262.32/56.70 | | | | | | | | | % 262.32/56.70 | | | | | | | | | REDUCE: (656), (2675) imply: % 262.32/56.70 | | | | | | | | | (2676) a_select3(id_ds1_filter, n5, all_74_15) = all_74_12 % 262.32/56.70 | | | | | | | | | % 262.32/56.70 | | | | | | | | | REDUCE: (655), (2675) imply: % 262.32/56.70 | | | | | | | | | (2677) a_select3(id_ds1_filter, all_74_15, n5) = all_74_13 % 262.32/56.70 | | | | | | | | | % 262.32/56.70 | | | | | | | | | REDUCE: (659), (2675) imply: % 262.32/56.70 | | | | | | | | | (2678) leq(n5, n5) % 262.32/56.70 | | | | | | | | | % 262.32/56.70 | | | | | | | | | REDUCE: (651), (2675) imply: % 262.32/56.70 | | | | | | | | | (2679) leq(n0, n5) % 262.32/56.70 | | | | | | | | | % 262.32/56.70 | | | | | | | | | GROUND_INST: instantiating (1) with all_74_15, n5, n4, % 262.32/56.70 | | | | | | | | | simplifying with (66), (139), (148), (2382) gives: % 262.32/56.70 | | | | | | | | | (2680) leq(all_74_15, n4) % 262.32/56.70 | | | | | | | | | % 262.32/56.70 | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_15, n4, % 262.32/56.70 | | | | | | | | | simplifying with (66), (136), (2680) gives: % 262.32/56.70 | | | | | | | | | (2681) all_74_15 = n4 | gt(n4, all_74_15) % 262.32/56.70 | | | | | | | | | % 262.32/56.70 | | | | | | | | | BETA: splitting (687) gives: % 262.32/56.70 | | | | | | | | | % 262.32/56.70 | | | | | | | | | Case 1: % 262.32/56.70 | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | (2682) all_74_15 = n0 % 262.32/56.70 | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | REF_CLOSE: (66), (2380), (2682), (irreflexivity_gt) are % 262.32/56.70 | | | | | | | | | | inconsistent by sub-proof #40. % 262.32/56.70 | | | | | | | | | | % 262.32/56.70 | | | | | | | | | Case 2: % 262.32/56.70 | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | (2683) ~ (all_74_15 = n0) % 262.32/56.70 | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | BETA: splitting (2681) gives: % 262.32/56.70 | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | Case 1: % 262.32/56.70 | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | (2684) gt(n4, all_74_15) % 262.32/56.70 | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_15, n4, n3, % 262.32/56.70 | | | | | | | | | | | simplifying with (66), (136), (147), (2684) gives: % 262.32/56.70 | | | | | | | | | | | (2685) leq(all_74_15, n3) % 262.32/56.70 | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_15, n3, % 262.32/56.70 | | | | | | | | | | | simplifying with (66), (129), (2685) gives: % 262.32/56.70 | | | | | | | | | | | (2686) all_74_15 = n3 | gt(n3, all_74_15) % 262.32/56.70 | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | BETA: splitting (2686) gives: % 262.32/56.70 | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | Case 1: % 262.32/56.70 | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | (2687) gt(n3, all_74_15) % 262.32/56.70 | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_15, n3, n2, % 262.32/56.70 | | | | | | | | | | | | simplifying with (66), (129), (146), (2687) gives: % 262.32/56.70 | | | | | | | | | | | | (2688) leq(all_74_15, n2) % 262.32/56.70 | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_15, n2, % 262.32/56.70 | | | | | | | | | | | | simplifying with (66), (118), (2688) gives: % 262.32/56.70 | | | | | | | | | | | | (2689) all_74_15 = n2 | gt(n2, all_74_15) % 262.32/56.70 | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | BETA: splitting (2689) gives: % 262.32/56.70 | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | Case 1: % 262.32/56.70 | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | (2690) gt(n2, all_74_15) % 262.32/56.70 | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_15, n2, n1, % 262.32/56.70 | | | | | | | | | | | | | simplifying with (66), (118), (145), (2690) gives: % 262.32/56.70 | | | | | | | | | | | | | (2691) leq(all_74_15, n1) % 262.32/56.70 | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_74_15, simplifying % 262.32/56.70 | | | | | | | | | | | | | with (66), (650), (2691) gives: % 262.32/56.70 | | | | | | | | | | | | | (2692) all_74_15 = n1 | all_74_15 = n0 % 262.32/56.70 | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | BETA: splitting (2692) gives: % 262.32/56.70 | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | Case 1: % 262.32/56.70 | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | (2693) all_74_15 = n0 % 262.32/56.70 | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | REDUCE: (2683), (2693) imply: % 262.32/56.70 | | | | | | | | | | | | | | (2694) $false % 262.32/56.70 | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | CLOSE: (2694) is inconsistent. % 262.32/56.70 | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | Case 2: % 262.32/56.70 | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | (2695) all_74_15 = n1 % 262.32/56.70 | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | REDUCE: (2677), (2695) imply: % 262.32/56.70 | | | | | | | | | | | | | | (2696) a_select3(id_ds1_filter, n1, n5) = all_74_13 % 262.32/56.70 | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | REDUCE: (2676), (2695) imply: % 262.32/56.70 | | | | | | | | | | | | | | (2697) a_select3(id_ds1_filter, n5, n1) = all_74_12 % 262.32/56.70 | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | REDUCE: (2680), (2695) imply: % 262.32/56.70 | | | | | | | | | | | | | | (2698) leq(n1, n4) % 262.32/56.70 | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | REDUCE: (650), (2695) imply: % 262.32/56.70 | | | | | | | | | | | | | | (2699) leq(n0, n1) % 262.32/56.70 | | | | | | | | | | | | | | % 262.32/56.70 | | | | | | | | | | | | | | GROUND_INST: instantiating (82) with n1, n5, all_74_13, % 262.32/56.70 | | | | | | | | | | | | | | simplifying with (102), (139), (2679), (2696), % 262.32/56.70 | | | | | | | | | | | | | | (2699) gives: % 262.32/56.71 | | | | | | | | | | | | | | (2700) ~ leq(n5, all_74_20) | ~ leq(n1, all_74_18) | % 262.32/56.71 | | | | | | | | | | | | | | (a_select3(id_ds1_filter, n5, n1) = all_74_13 & % 262.32/56.71 | | | | | | | | | | | | | | $i(all_74_13)) % 262.32/56.71 | | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | | BETA: splitting (2700) gives: % 262.32/56.71 | | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | | Case 1: % 262.32/56.71 | | | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | | | (2701) ~ leq(n5, all_74_20) % 262.32/56.71 | | | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | | | REDUCE: (159), (2701) imply: % 262.32/56.71 | | | | | | | | | | | | | | | (2702) ~ leq(n5, n5) % 262.32/56.71 | | | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | | | PRED_UNIFY: (2678), (2702) imply: % 262.32/56.71 | | | | | | | | | | | | | | | (2703) $false % 262.32/56.71 | | | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | | | CLOSE: (2703) is inconsistent. % 262.32/56.71 | | | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | | Case 2: % 262.32/56.71 | | | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | | | (2704) ~ leq(n1, all_74_18) | (a_select3(id_ds1_filter, % 262.32/56.71 | | | | | | | | | | | | | | | n5, n1) = all_74_13 & $i(all_74_13)) % 262.32/56.71 | | | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | | | BETA: splitting (2704) gives: % 262.32/56.71 | | | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | | | Case 1: % 262.32/56.71 | | | | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | | | | (2705) ~ leq(n1, all_74_18) % 262.32/56.71 | | | | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | | | | REDUCE: (2377), (2705) imply: % 262.32/56.71 | | | | | | | | | | | | | | | | (2706) ~ leq(n1, n4) % 262.32/56.71 | | | | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | | | | PRED_UNIFY: (2698), (2706) imply: % 262.32/56.71 | | | | | | | | | | | | | | | | (2707) $false % 262.32/56.71 | | | | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | | | | CLOSE: (2707) is inconsistent. % 262.32/56.71 | | | | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | | | Case 2: % 262.32/56.71 | | | | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | | | | (2708) a_select3(id_ds1_filter, n5, n1) = all_74_13 & % 262.32/56.71 | | | | | | | | | | | | | | | | $i(all_74_13) % 262.32/56.71 | | | | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | | | | ALPHA: (2708) implies: % 262.32/56.71 | | | | | | | | | | | | | | | | (2709) a_select3(id_ds1_filter, n5, n1) = all_74_13 % 262.32/56.71 | | | | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | | | | REF_CLOSE: (30), (649), (2697), (2709) are inconsistent by % 262.32/56.71 | | | | | | | | | | | | | | | | sub-proof #23. % 262.32/56.71 | | | | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | | | End of split % 262.32/56.71 | | | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | | End of split % 262.32/56.71 | | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | End of split % 262.32/56.71 | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | Case 2: % 262.32/56.71 | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | (2710) all_74_15 = n2 % 262.32/56.71 | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | REDUCE: (2677), (2710) imply: % 262.32/56.71 | | | | | | | | | | | | | (2711) a_select3(id_ds1_filter, n2, n5) = all_74_13 % 262.32/56.71 | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | REDUCE: (2676), (2710) imply: % 262.32/56.71 | | | | | | | | | | | | | (2712) a_select3(id_ds1_filter, n5, n2) = all_74_12 % 262.32/56.71 | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | REDUCE: (2680), (2710) imply: % 262.32/56.71 | | | | | | | | | | | | | (2713) leq(n2, n4) % 262.32/56.71 | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | REDUCE: (650), (2710) imply: % 262.32/56.71 | | | | | | | | | | | | | (2714) leq(n0, n2) % 262.32/56.71 | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | GROUND_INST: instantiating (82) with n2, n5, all_74_13, % 262.32/56.71 | | | | | | | | | | | | | simplifying with (118), (139), (2679), (2711), % 262.32/56.71 | | | | | | | | | | | | | (2714) gives: % 262.32/56.71 | | | | | | | | | | | | | (2715) ~ leq(n5, all_74_20) | ~ leq(n2, all_74_18) | % 262.32/56.71 | | | | | | | | | | | | | (a_select3(id_ds1_filter, n5, n2) = all_74_13 & % 262.32/56.71 | | | | | | | | | | | | | $i(all_74_13)) % 262.32/56.71 | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | BETA: splitting (2715) gives: % 262.32/56.71 | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | Case 1: % 262.32/56.71 | | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | | (2716) ~ leq(n5, all_74_20) % 262.32/56.71 | | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | | REDUCE: (159), (2716) imply: % 262.32/56.71 | | | | | | | | | | | | | | (2717) ~ leq(n5, n5) % 262.32/56.71 | | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | | PRED_UNIFY: (2678), (2717) imply: % 262.32/56.71 | | | | | | | | | | | | | | (2718) $false % 262.32/56.71 | | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | | CLOSE: (2718) is inconsistent. % 262.32/56.71 | | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | Case 2: % 262.32/56.71 | | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | | (2719) ~ leq(n2, all_74_18) | (a_select3(id_ds1_filter, % 262.32/56.71 | | | | | | | | | | | | | | n5, n2) = all_74_13 & $i(all_74_13)) % 262.32/56.71 | | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | | BETA: splitting (2719) gives: % 262.32/56.71 | | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | | Case 1: % 262.32/56.71 | | | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | | | (2720) ~ leq(n2, all_74_18) % 262.32/56.71 | | | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | | | REDUCE: (2377), (2720) imply: % 262.32/56.71 | | | | | | | | | | | | | | | (2721) ~ leq(n2, n4) % 262.32/56.71 | | | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | | | PRED_UNIFY: (2713), (2721) imply: % 262.32/56.71 | | | | | | | | | | | | | | | (2722) $false % 262.32/56.71 | | | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | | | CLOSE: (2722) is inconsistent. % 262.32/56.71 | | | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | | Case 2: % 262.32/56.71 | | | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | | | (2723) a_select3(id_ds1_filter, n5, n2) = all_74_13 & % 262.32/56.71 | | | | | | | | | | | | | | | $i(all_74_13) % 262.32/56.71 | | | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | | | ALPHA: (2723) implies: % 262.32/56.71 | | | | | | | | | | | | | | | (2724) a_select3(id_ds1_filter, n5, n2) = all_74_13 % 262.32/56.71 | | | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | | | REF_CLOSE: (30), (649), (2712), (2724) are inconsistent by % 262.32/56.71 | | | | | | | | | | | | | | | sub-proof #22. % 262.32/56.71 | | | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | | End of split % 262.32/56.71 | | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | End of split % 262.32/56.71 | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | End of split % 262.32/56.71 | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | Case 2: % 262.32/56.71 | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | (2725) all_74_15 = n3 % 262.32/56.71 | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | REDUCE: (2677), (2725) imply: % 262.32/56.71 | | | | | | | | | | | | (2726) a_select3(id_ds1_filter, n3, n5) = all_74_13 % 262.32/56.71 | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | REDUCE: (2676), (2725) imply: % 262.32/56.71 | | | | | | | | | | | | (2727) a_select3(id_ds1_filter, n5, n3) = all_74_12 % 262.32/56.71 | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | REDUCE: (684), (2725) imply: % 262.32/56.71 | | | | | | | | | | | | (2728) leq(n3, n5) % 262.32/56.71 | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | REDUCE: (650), (2725) imply: % 262.32/56.71 | | | | | | | | | | | | (2729) leq(n0, n3) % 262.32/56.71 | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | GROUND_INST: instantiating (81) with n3, n5, all_74_13, % 262.32/56.71 | | | | | | | | | | | | simplifying with (129), (139), (2679), (2726), % 262.32/56.71 | | | | | | | | | | | | (2729) gives: % 262.32/56.71 | | | | | | | | | | | | (2730) ~ leq(n5, all_74_20) | ~ leq(n3, pv57) | % 262.32/56.71 | | | | | | | | | | | | (a_select3(id_ds1_filter, n5, n3) = all_74_13 & % 262.32/56.71 | | | | | | | | | | | | $i(all_74_13)) % 262.32/56.71 | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | BETA: splitting (2730) gives: % 262.32/56.71 | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | Case 1: % 262.32/56.71 | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | (2731) ~ leq(n5, all_74_20) % 262.32/56.71 | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | REDUCE: (159), (2731) imply: % 262.32/56.71 | | | | | | | | | | | | | (2732) ~ leq(n5, n5) % 262.32/56.71 | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | PRED_UNIFY: (2678), (2732) imply: % 262.32/56.71 | | | | | | | | | | | | | (2733) $false % 262.32/56.71 | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | CLOSE: (2733) is inconsistent. % 262.32/56.71 | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | Case 2: % 262.32/56.71 | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | (2734) ~ leq(n3, pv57) | (a_select3(id_ds1_filter, n5, % 262.32/56.71 | | | | | | | | | | | | | n3) = all_74_13 & $i(all_74_13)) % 262.32/56.71 | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | BETA: splitting (2734) gives: % 262.32/56.71 | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | Case 1: % 262.32/56.71 | | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | | (2735) ~ leq(n3, pv57) % 262.32/56.71 | | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | | REDUCE: (2374), (2735) imply: % 262.32/56.71 | | | | | | | | | | | | | | (2736) ~ leq(n3, n5) % 262.32/56.71 | | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | | PRED_UNIFY: (2728), (2736) imply: % 262.32/56.71 | | | | | | | | | | | | | | (2737) $false % 262.32/56.71 | | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | | CLOSE: (2737) is inconsistent. % 262.32/56.71 | | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | Case 2: % 262.32/56.71 | | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | | (2738) a_select3(id_ds1_filter, n5, n3) = all_74_13 & % 262.32/56.71 | | | | | | | | | | | | | | $i(all_74_13) % 262.32/56.71 | | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | | ALPHA: (2738) implies: % 262.32/56.71 | | | | | | | | | | | | | | (2739) a_select3(id_ds1_filter, n5, n3) = all_74_13 % 262.32/56.71 | | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | | REF_CLOSE: (30), (649), (2727), (2739) are inconsistent by % 262.32/56.71 | | | | | | | | | | | | | | sub-proof #18. % 262.32/56.71 | | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | End of split % 262.32/56.71 | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | End of split % 262.32/56.71 | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | End of split % 262.32/56.71 | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | Case 2: % 262.32/56.71 | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | (2740) all_74_15 = n4 % 262.32/56.71 | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | REDUCE: (2677), (2740) imply: % 262.32/56.71 | | | | | | | | | | | (2741) a_select3(id_ds1_filter, n4, n5) = all_74_13 % 262.32/56.71 | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | REDUCE: (2676), (2740) imply: % 262.32/56.71 | | | | | | | | | | | (2742) a_select3(id_ds1_filter, n5, n4) = all_74_12 % 262.32/56.71 | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | REDUCE: (684), (2740) imply: % 262.32/56.71 | | | | | | | | | | | (2743) leq(n4, n5) % 262.32/56.71 | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | GROUND_INST: instantiating (81) with n4, n5, all_74_13, % 262.32/56.71 | | | | | | | | | | | simplifying with (136), (139), (2378), (2679), % 262.32/56.71 | | | | | | | | | | | (2741) gives: % 262.32/56.71 | | | | | | | | | | | (2744) ~ leq(n5, all_74_20) | ~ leq(n4, pv57) | % 262.32/56.71 | | | | | | | | | | | (a_select3(id_ds1_filter, n5, n4) = all_74_13 & % 262.32/56.71 | | | | | | | | | | | $i(all_74_13)) % 262.32/56.71 | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | BETA: splitting (2744) gives: % 262.32/56.71 | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | Case 1: % 262.32/56.71 | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | (2745) ~ leq(n5, all_74_20) % 262.32/56.71 | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | REDUCE: (159), (2745) imply: % 262.32/56.71 | | | | | | | | | | | | (2746) ~ leq(n5, n5) % 262.32/56.71 | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | PRED_UNIFY: (2678), (2746) imply: % 262.32/56.71 | | | | | | | | | | | | (2747) $false % 262.32/56.71 | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | CLOSE: (2747) is inconsistent. % 262.32/56.71 | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | Case 2: % 262.32/56.71 | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | (2748) ~ leq(n4, pv57) | (a_select3(id_ds1_filter, n5, % 262.32/56.71 | | | | | | | | | | | | n4) = all_74_13 & $i(all_74_13)) % 262.32/56.71 | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | BETA: splitting (2748) gives: % 262.32/56.71 | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | Case 1: % 262.32/56.71 | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | (2749) ~ leq(n4, pv57) % 262.32/56.71 | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | REDUCE: (2374), (2749) imply: % 262.32/56.71 | | | | | | | | | | | | | (2750) ~ leq(n4, n5) % 262.32/56.71 | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | PRED_UNIFY: (2743), (2750) imply: % 262.32/56.71 | | | | | | | | | | | | | (2751) $false % 262.32/56.71 | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | CLOSE: (2751) is inconsistent. % 262.32/56.71 | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | Case 2: % 262.32/56.71 | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | (2752) a_select3(id_ds1_filter, n5, n4) = all_74_13 & % 262.32/56.71 | | | | | | | | | | | | | $i(all_74_13) % 262.32/56.71 | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | ALPHA: (2752) implies: % 262.32/56.71 | | | | | | | | | | | | | (2753) a_select3(id_ds1_filter, n5, n4) = all_74_13 % 262.32/56.71 | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | REF_CLOSE: (30), (649), (2742), (2753) are inconsistent by % 262.32/56.71 | | | | | | | | | | | | | sub-proof #17. % 262.32/56.71 | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | End of split % 262.32/56.71 | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | End of split % 262.32/56.71 | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | End of split % 262.32/56.71 | | | | | | | | | | % 262.32/56.71 | | | | | | | | | End of split % 262.32/56.71 | | | | | | | | | % 262.32/56.71 | | | | | | | | End of split % 262.32/56.71 | | | | | | | | % 262.32/56.71 | | | | | | | Case 2: % 262.32/56.71 | | | | | | | | % 262.32/56.71 | | | | | | | | (2754) all_74_15 = all_74_16 % 262.32/56.71 | | | | | | | | % 262.32/56.71 | | | | | | | | COMBINE_EQS: (2375), (2754) imply: % 262.32/56.71 | | | | | | | | (2755) all_74_15 = n5 % 262.32/56.71 | | | | | | | | % 262.32/56.71 | | | | | | | | REDUCE: (656), (2755) imply: % 262.32/56.71 | | | | | | | | (2756) a_select3(id_ds1_filter, all_74_14, n5) = all_74_12 % 262.32/56.71 | | | | | | | | % 262.32/56.71 | | | | | | | | REDUCE: (655), (2755) imply: % 262.32/56.71 | | | | | | | | (2757) a_select3(id_ds1_filter, n5, all_74_14) = all_74_13 % 262.32/56.71 | | | | | | | | % 262.32/56.71 | | | | | | | | REDUCE: (684), (2755) imply: % 262.32/56.71 | | | | | | | | (2758) leq(n5, n5) % 262.32/56.71 | | | | | | | | % 262.32/56.71 | | | | | | | | REDUCE: (650), (2755) imply: % 262.32/56.71 | | | | | | | | (2759) leq(n0, n5) % 262.32/56.71 | | | | | | | | % 262.32/56.71 | | | | | | | | BETA: splitting (666) gives: % 262.32/56.71 | | | | | | | | % 262.32/56.71 | | | | | | | | Case 1: % 262.32/56.71 | | | | | | | | | % 262.32/56.71 | | | | | | | | | (2760) gt(n5, all_74_14) % 262.32/56.71 | | | | | | | | | % 262.32/56.71 | | | | | | | | | GROUND_INST: instantiating (1) with all_74_14, n5, n4, % 262.32/56.71 | | | | | | | | | simplifying with (67), (139), (148), (2760) gives: % 262.32/56.71 | | | | | | | | | (2761) leq(all_74_14, n4) % 262.32/56.71 | | | | | | | | | % 262.32/56.71 | | | | | | | | | BETA: splitting (665) gives: % 262.32/56.71 | | | | | | | | | % 262.32/56.71 | | | | | | | | | Case 1: % 262.32/56.71 | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | (2762) all_74_14 = n0 % 262.32/56.71 | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | REF_CLOSE: (67), (2379), (2762), (irreflexivity_gt) are % 262.32/56.71 | | | | | | | | | | inconsistent by sub-proof #41. % 262.32/56.71 | | | | | | | | | | % 262.32/56.71 | | | | | | | | | Case 2: % 262.32/56.71 | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | (2763) ~ (all_74_14 = n0) % 262.32/56.71 | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_14, n4, % 262.32/56.71 | | | | | | | | | | simplifying with (67), (136), (2761) gives: % 262.32/56.71 | | | | | | | | | | (2764) all_74_14 = n4 | gt(n4, all_74_14) % 262.32/56.71 | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | BETA: splitting (2764) gives: % 262.32/56.71 | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | Case 1: % 262.32/56.71 | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | (2765) gt(n4, all_74_14) % 262.32/56.71 | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_14, n4, n3, % 262.32/56.71 | | | | | | | | | | | simplifying with (67), (136), (147), (2765) gives: % 262.32/56.71 | | | | | | | | | | | (2766) leq(all_74_14, n3) % 262.32/56.71 | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_14, n3, % 262.32/56.71 | | | | | | | | | | | simplifying with (67), (129), (2766) gives: % 262.32/56.71 | | | | | | | | | | | (2767) all_74_14 = n3 | gt(n3, all_74_14) % 262.32/56.71 | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | BETA: splitting (2767) gives: % 262.32/56.71 | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | Case 1: % 262.32/56.71 | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | (2768) gt(n3, all_74_14) % 262.32/56.71 | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_14, n3, n2, % 262.32/56.71 | | | | | | | | | | | | simplifying with (67), (129), (146), (2768) gives: % 262.32/56.71 | | | | | | | | | | | | (2769) leq(all_74_14, n2) % 262.32/56.71 | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_14, n2, % 262.32/56.71 | | | | | | | | | | | | simplifying with (67), (118), (2769) gives: % 262.32/56.71 | | | | | | | | | | | | (2770) all_74_14 = n2 | gt(n2, all_74_14) % 262.32/56.71 | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | BETA: splitting (2770) gives: % 262.32/56.71 | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | Case 1: % 262.32/56.71 | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | (2771) gt(n2, all_74_14) % 262.32/56.71 | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_14, n2, n1, % 262.32/56.71 | | | | | | | | | | | | | simplifying with (67), (118), (145), (2771) gives: % 262.32/56.71 | | | | | | | | | | | | | (2772) leq(all_74_14, n1) % 262.32/56.71 | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_74_14, simplifying % 262.32/56.71 | | | | | | | | | | | | | with (67), (651), (2772) gives: % 262.32/56.71 | | | | | | | | | | | | | (2773) all_74_14 = n1 | all_74_14 = n0 % 262.32/56.71 | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | BETA: splitting (2773) gives: % 262.32/56.71 | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | Case 1: % 262.32/56.71 | | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | | (2774) all_74_14 = n0 % 262.32/56.71 | | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | | REDUCE: (2763), (2774) imply: % 262.32/56.71 | | | | | | | | | | | | | | (2775) $false % 262.32/56.71 | | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | | CLOSE: (2775) is inconsistent. % 262.32/56.71 | | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | Case 2: % 262.32/56.71 | | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | | (2776) all_74_14 = n1 % 262.32/56.71 | | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | | REDUCE: (2756), (2776) imply: % 262.32/56.71 | | | | | | | | | | | | | | (2777) a_select3(id_ds1_filter, n1, n5) = all_74_12 % 262.32/56.71 | | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | | REDUCE: (2757), (2776) imply: % 262.32/56.71 | | | | | | | | | | | | | | (2778) a_select3(id_ds1_filter, n5, n1) = all_74_13 % 262.32/56.71 | | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | | REDUCE: (2761), (2776) imply: % 262.32/56.71 | | | | | | | | | | | | | | (2779) leq(n1, n4) % 262.32/56.71 | | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | | REDUCE: (651), (2776) imply: % 262.32/56.71 | | | | | | | | | | | | | | (2780) leq(n0, n1) % 262.32/56.71 | | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | | GROUND_INST: instantiating (82) with n1, n5, all_74_12, % 262.32/56.71 | | | | | | | | | | | | | | simplifying with (102), (139), (2759), (2777), % 262.32/56.71 | | | | | | | | | | | | | | (2780) gives: % 262.32/56.71 | | | | | | | | | | | | | | (2781) ~ leq(n5, all_74_20) | ~ leq(n1, all_74_18) | % 262.32/56.71 | | | | | | | | | | | | | | (a_select3(id_ds1_filter, n5, n1) = all_74_12 & % 262.32/56.71 | | | | | | | | | | | | | | $i(all_74_12)) % 262.32/56.71 | | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | | BETA: splitting (2781) gives: % 262.32/56.71 | | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | | Case 1: % 262.32/56.71 | | | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | | | (2782) ~ leq(n5, all_74_20) % 262.32/56.71 | | | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | | | REDUCE: (159), (2782) imply: % 262.32/56.71 | | | | | | | | | | | | | | | (2783) ~ leq(n5, n5) % 262.32/56.71 | | | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | | | PRED_UNIFY: (2758), (2783) imply: % 262.32/56.71 | | | | | | | | | | | | | | | (2784) $false % 262.32/56.71 | | | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | | | CLOSE: (2784) is inconsistent. % 262.32/56.71 | | | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | | Case 2: % 262.32/56.71 | | | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | | | (2785) ~ leq(n1, all_74_18) | (a_select3(id_ds1_filter, % 262.32/56.71 | | | | | | | | | | | | | | | n5, n1) = all_74_12 & $i(all_74_12)) % 262.32/56.71 | | | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | | | BETA: splitting (2785) gives: % 262.32/56.71 | | | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | | | Case 1: % 262.32/56.71 | | | | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | | | | (2786) ~ leq(n1, all_74_18) % 262.32/56.71 | | | | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | | | | REDUCE: (2377), (2786) imply: % 262.32/56.71 | | | | | | | | | | | | | | | | (2787) ~ leq(n1, n4) % 262.32/56.71 | | | | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | | | | PRED_UNIFY: (2779), (2787) imply: % 262.32/56.71 | | | | | | | | | | | | | | | | (2788) $false % 262.32/56.71 | | | | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | | | | CLOSE: (2788) is inconsistent. % 262.32/56.71 | | | | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | | | Case 2: % 262.32/56.71 | | | | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | | | | (2789) a_select3(id_ds1_filter, n5, n1) = all_74_12 & % 262.32/56.71 | | | | | | | | | | | | | | | | $i(all_74_12) % 262.32/56.71 | | | | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | | | | ALPHA: (2789) implies: % 262.32/56.71 | | | | | | | | | | | | | | | | (2790) a_select3(id_ds1_filter, n5, n1) = all_74_12 % 262.32/56.71 | | | | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | | | | REF_CLOSE: (30), (649), (2778), (2790) are inconsistent by % 262.32/56.71 | | | | | | | | | | | | | | | | sub-proof #23. % 262.32/56.71 | | | | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | | | End of split % 262.32/56.71 | | | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | | End of split % 262.32/56.71 | | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | End of split % 262.32/56.71 | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | Case 2: % 262.32/56.71 | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | (2791) all_74_14 = n2 % 262.32/56.71 | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | REDUCE: (2756), (2791) imply: % 262.32/56.71 | | | | | | | | | | | | | (2792) a_select3(id_ds1_filter, n2, n5) = all_74_12 % 262.32/56.71 | | | | | | | | | | | | | % 262.32/56.71 | | | | | | | | | | | | | REDUCE: (2757), (2791) imply: % 262.32/56.72 | | | | | | | | | | | | | (2793) a_select3(id_ds1_filter, n5, n2) = all_74_13 % 262.32/56.72 | | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | | REDUCE: (2761), (2791) imply: % 262.32/56.72 | | | | | | | | | | | | | (2794) leq(n2, n4) % 262.32/56.72 | | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | | REDUCE: (651), (2791) imply: % 262.32/56.72 | | | | | | | | | | | | | (2795) leq(n0, n2) % 262.32/56.72 | | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | | GROUND_INST: instantiating (82) with n2, n5, all_74_12, % 262.32/56.72 | | | | | | | | | | | | | simplifying with (118), (139), (2759), (2792), % 262.32/56.72 | | | | | | | | | | | | | (2795) gives: % 262.32/56.72 | | | | | | | | | | | | | (2796) ~ leq(n5, all_74_20) | ~ leq(n2, all_74_18) | % 262.32/56.72 | | | | | | | | | | | | | (a_select3(id_ds1_filter, n5, n2) = all_74_12 & % 262.32/56.72 | | | | | | | | | | | | | $i(all_74_12)) % 262.32/56.72 | | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | | BETA: splitting (2796) gives: % 262.32/56.72 | | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | | Case 1: % 262.32/56.72 | | | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | | | (2797) ~ leq(n5, all_74_20) % 262.32/56.72 | | | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | | | REDUCE: (159), (2797) imply: % 262.32/56.72 | | | | | | | | | | | | | | (2798) ~ leq(n5, n5) % 262.32/56.72 | | | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | | | PRED_UNIFY: (2758), (2798) imply: % 262.32/56.72 | | | | | | | | | | | | | | (2799) $false % 262.32/56.72 | | | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | | | CLOSE: (2799) is inconsistent. % 262.32/56.72 | | | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | | Case 2: % 262.32/56.72 | | | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | | | (2800) ~ leq(n2, all_74_18) | (a_select3(id_ds1_filter, % 262.32/56.72 | | | | | | | | | | | | | | n5, n2) = all_74_12 & $i(all_74_12)) % 262.32/56.72 | | | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | | | BETA: splitting (2800) gives: % 262.32/56.72 | | | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | | | Case 1: % 262.32/56.72 | | | | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | | | | (2801) ~ leq(n2, all_74_18) % 262.32/56.72 | | | | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | | | | REDUCE: (2377), (2801) imply: % 262.32/56.72 | | | | | | | | | | | | | | | (2802) ~ leq(n2, n4) % 262.32/56.72 | | | | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | | | | PRED_UNIFY: (2794), (2802) imply: % 262.32/56.72 | | | | | | | | | | | | | | | (2803) $false % 262.32/56.72 | | | | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | | | | CLOSE: (2803) is inconsistent. % 262.32/56.72 | | | | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | | | Case 2: % 262.32/56.72 | | | | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | | | | (2804) a_select3(id_ds1_filter, n5, n2) = all_74_12 & % 262.32/56.72 | | | | | | | | | | | | | | | $i(all_74_12) % 262.32/56.72 | | | | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | | | | ALPHA: (2804) implies: % 262.32/56.72 | | | | | | | | | | | | | | | (2805) a_select3(id_ds1_filter, n5, n2) = all_74_12 % 262.32/56.72 | | | | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | | | | REF_CLOSE: (30), (649), (2793), (2805) are inconsistent by % 262.32/56.72 | | | | | | | | | | | | | | | sub-proof #22. % 262.32/56.72 | | | | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | | | End of split % 262.32/56.72 | | | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | | End of split % 262.32/56.72 | | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | End of split % 262.32/56.72 | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | Case 2: % 262.32/56.72 | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | (2806) all_74_14 = n3 % 262.32/56.72 | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | REDUCE: (2756), (2806) imply: % 262.32/56.72 | | | | | | | | | | | | (2807) a_select3(id_ds1_filter, n3, n5) = all_74_12 % 262.32/56.72 | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | REDUCE: (2757), (2806) imply: % 262.32/56.72 | | | | | | | | | | | | (2808) a_select3(id_ds1_filter, n5, n3) = all_74_13 % 262.32/56.72 | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | REDUCE: (659), (2806) imply: % 262.32/56.72 | | | | | | | | | | | | (2809) leq(n3, n5) % 262.32/56.72 | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | REDUCE: (651), (2806) imply: % 262.32/56.72 | | | | | | | | | | | | (2810) leq(n0, n3) % 262.32/56.72 | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | GROUND_INST: instantiating (81) with n3, n5, all_74_12, % 262.32/56.72 | | | | | | | | | | | | simplifying with (129), (139), (2759), (2807), % 262.32/56.72 | | | | | | | | | | | | (2810) gives: % 262.32/56.72 | | | | | | | | | | | | (2811) ~ leq(n5, all_74_20) | ~ leq(n3, pv57) | % 262.32/56.72 | | | | | | | | | | | | (a_select3(id_ds1_filter, n5, n3) = all_74_12 & % 262.32/56.72 | | | | | | | | | | | | $i(all_74_12)) % 262.32/56.72 | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | BETA: splitting (2811) gives: % 262.32/56.72 | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | Case 1: % 262.32/56.72 | | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | | (2812) ~ leq(n5, all_74_20) % 262.32/56.72 | | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | | REDUCE: (159), (2812) imply: % 262.32/56.72 | | | | | | | | | | | | | (2813) ~ leq(n5, n5) % 262.32/56.72 | | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | | PRED_UNIFY: (2758), (2813) imply: % 262.32/56.72 | | | | | | | | | | | | | (2814) $false % 262.32/56.72 | | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | | CLOSE: (2814) is inconsistent. % 262.32/56.72 | | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | Case 2: % 262.32/56.72 | | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | | (2815) ~ leq(n3, pv57) | (a_select3(id_ds1_filter, n5, % 262.32/56.72 | | | | | | | | | | | | | n3) = all_74_12 & $i(all_74_12)) % 262.32/56.72 | | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | | BETA: splitting (2815) gives: % 262.32/56.72 | | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | | Case 1: % 262.32/56.72 | | | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | | | (2816) ~ leq(n3, pv57) % 262.32/56.72 | | | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | | | REDUCE: (2374), (2816) imply: % 262.32/56.72 | | | | | | | | | | | | | | (2817) ~ leq(n3, n5) % 262.32/56.72 | | | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | | | PRED_UNIFY: (2809), (2817) imply: % 262.32/56.72 | | | | | | | | | | | | | | (2818) $false % 262.32/56.72 | | | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | | | CLOSE: (2818) is inconsistent. % 262.32/56.72 | | | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | | Case 2: % 262.32/56.72 | | | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | | | (2819) a_select3(id_ds1_filter, n5, n3) = all_74_12 & % 262.32/56.72 | | | | | | | | | | | | | | $i(all_74_12) % 262.32/56.72 | | | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | | | ALPHA: (2819) implies: % 262.32/56.72 | | | | | | | | | | | | | | (2820) a_select3(id_ds1_filter, n5, n3) = all_74_12 % 262.32/56.72 | | | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | | | REF_CLOSE: (30), (649), (2808), (2820) are inconsistent by % 262.32/56.72 | | | | | | | | | | | | | | sub-proof #18. % 262.32/56.72 | | | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | | End of split % 262.32/56.72 | | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | End of split % 262.32/56.72 | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | End of split % 262.32/56.72 | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | Case 2: % 262.32/56.72 | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | (2821) all_74_14 = n4 % 262.32/56.72 | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | REDUCE: (2756), (2821) imply: % 262.32/56.72 | | | | | | | | | | | (2822) a_select3(id_ds1_filter, n4, n5) = all_74_12 % 262.32/56.72 | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | REDUCE: (2757), (2821) imply: % 262.32/56.72 | | | | | | | | | | | (2823) a_select3(id_ds1_filter, n5, n4) = all_74_13 % 262.32/56.72 | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | REDUCE: (659), (2821) imply: % 262.32/56.72 | | | | | | | | | | | (2824) leq(n4, n5) % 262.32/56.72 | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | GROUND_INST: instantiating (81) with n4, n5, all_74_12, % 262.32/56.72 | | | | | | | | | | | simplifying with (136), (139), (2378), (2759), % 262.32/56.72 | | | | | | | | | | | (2822) gives: % 262.32/56.72 | | | | | | | | | | | (2825) ~ leq(n5, all_74_20) | ~ leq(n4, pv57) | % 262.32/56.72 | | | | | | | | | | | (a_select3(id_ds1_filter, n5, n4) = all_74_12 & % 262.32/56.72 | | | | | | | | | | | $i(all_74_12)) % 262.32/56.72 | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | BETA: splitting (2825) gives: % 262.32/56.72 | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | Case 1: % 262.32/56.72 | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | (2826) ~ leq(n5, all_74_20) % 262.32/56.72 | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | REDUCE: (159), (2826) imply: % 262.32/56.72 | | | | | | | | | | | | (2827) ~ leq(n5, n5) % 262.32/56.72 | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | PRED_UNIFY: (2758), (2827) imply: % 262.32/56.72 | | | | | | | | | | | | (2828) $false % 262.32/56.72 | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | CLOSE: (2828) is inconsistent. % 262.32/56.72 | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | Case 2: % 262.32/56.72 | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | (2829) ~ leq(n4, pv57) | (a_select3(id_ds1_filter, n5, % 262.32/56.72 | | | | | | | | | | | | n4) = all_74_12 & $i(all_74_12)) % 262.32/56.72 | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | BETA: splitting (2829) gives: % 262.32/56.72 | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | Case 1: % 262.32/56.72 | | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | | (2830) ~ leq(n4, pv57) % 262.32/56.72 | | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | | REDUCE: (2374), (2830) imply: % 262.32/56.72 | | | | | | | | | | | | | (2831) ~ leq(n4, n5) % 262.32/56.72 | | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | | PRED_UNIFY: (2824), (2831) imply: % 262.32/56.72 | | | | | | | | | | | | | (2832) $false % 262.32/56.72 | | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | | CLOSE: (2832) is inconsistent. % 262.32/56.72 | | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | Case 2: % 262.32/56.72 | | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | | (2833) a_select3(id_ds1_filter, n5, n4) = all_74_12 & % 262.32/56.72 | | | | | | | | | | | | | $i(all_74_12) % 262.32/56.72 | | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | | ALPHA: (2833) implies: % 262.32/56.72 | | | | | | | | | | | | | (2834) a_select3(id_ds1_filter, n5, n4) = all_74_12 % 262.32/56.72 | | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | | REF_CLOSE: (30), (649), (2823), (2834) are inconsistent by % 262.32/56.72 | | | | | | | | | | | | | sub-proof #17. % 262.32/56.72 | | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | End of split % 262.32/56.72 | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | End of split % 262.32/56.72 | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | End of split % 262.32/56.72 | | | | | | | | | | % 262.32/56.72 | | | | | | | | | End of split % 262.32/56.72 | | | | | | | | | % 262.32/56.72 | | | | | | | | Case 2: % 262.32/56.72 | | | | | | | | | % 262.32/56.72 | | | | | | | | | (2835) all_74_14 = n5 % 262.32/56.72 | | | | | | | | | % 262.32/56.72 | | | | | | | | | REDUCE: (2756), (2835) imply: % 262.32/56.72 | | | | | | | | | (2836) a_select3(id_ds1_filter, n5, n5) = all_74_12 % 262.32/56.72 | | | | | | | | | % 262.32/56.72 | | | | | | | | | REDUCE: (2757), (2835) imply: % 262.32/56.72 | | | | | | | | | (2837) a_select3(id_ds1_filter, n5, n5) = all_74_13 % 262.32/56.72 | | | | | | | | | % 262.32/56.72 | | | | | | | | | GROUND_INST: instantiating (30) with all_74_13, all_74_12, n5, % 262.32/56.72 | | | | | | | | | n5, id_ds1_filter, simplifying with (2836), (2837) % 262.32/56.72 | | | | | | | | | gives: % 262.32/56.72 | | | | | | | | | (2838) all_74_12 = all_74_13 % 262.32/56.72 | | | | | | | | | % 262.32/56.72 | | | | | | | | | REDUCE: (649), (2838) imply: % 262.32/56.72 | | | | | | | | | (2839) $false % 262.32/56.72 | | | | | | | | | % 262.32/56.72 | | | | | | | | | CLOSE: (2839) is inconsistent. % 262.32/56.72 | | | | | | | | | % 262.32/56.72 | | | | | | | | End of split % 262.32/56.72 | | | | | | | | % 262.32/56.72 | | | | | | | End of split % 262.32/56.72 | | | | | | | % 262.32/56.72 | | | | | | Case 2: % 262.32/56.72 | | | | | | | % 262.32/56.72 | | | | | | | (2840) all_74_15 = n0 % 262.32/56.72 | | | | | | | (2841) ~ gt(all_74_15, n0) % 262.32/56.72 | | | | | | | % 262.32/56.72 | | | | | | | REDUCE: (656), (2840) imply: % 262.32/56.72 | | | | | | | (2842) a_select3(id_ds1_filter, all_74_14, n0) = all_74_12 % 262.32/56.72 | | | | | | | % 262.32/56.72 | | | | | | | REDUCE: (655), (2840) imply: % 262.32/56.72 | | | | | | | (2843) a_select3(id_ds1_filter, n0, all_74_14) = all_74_13 % 262.32/56.72 | | | | | | | % 262.32/56.72 | | | | | | | REDUCE: (650), (2840) imply: % 262.32/56.72 | | | | | | | (2844) leq(n0, n0) % 262.32/56.72 | | | | | | | % 262.32/56.72 | | | | | | | REDUCE: (2840), (2841) imply: % 262.32/56.72 | | | | | | | (2845) ~ gt(n0, n0) % 262.32/56.72 | | | | | | | % 262.32/56.72 | | | | | | | BETA: splitting (666) gives: % 262.32/56.72 | | | | | | | % 262.32/56.72 | | | | | | | Case 1: % 262.32/56.72 | | | | | | | | % 262.32/56.72 | | | | | | | | (2846) gt(n5, all_74_14) % 262.32/56.72 | | | | | | | | % 262.32/56.72 | | | | | | | | GROUND_INST: instantiating (1) with all_74_14, n5, n4, % 262.32/56.72 | | | | | | | | simplifying with (67), (139), (148), (2846) gives: % 262.32/56.72 | | | | | | | | (2847) leq(all_74_14, n4) % 262.32/56.72 | | | | | | | | % 262.32/56.72 | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_14, n4, % 262.32/56.72 | | | | | | | | simplifying with (67), (136), (2847) gives: % 262.32/56.72 | | | | | | | | (2848) all_74_14 = n4 | gt(n4, all_74_14) % 262.32/56.72 | | | | | | | | % 262.32/56.72 | | | | | | | | BETA: splitting (665) gives: % 262.32/56.72 | | | | | | | | % 262.32/56.72 | | | | | | | | Case 1: % 262.32/56.72 | | | | | | | | | % 262.32/56.72 | | | | | | | | | (2849) all_74_14 = n0 % 262.32/56.72 | | | | | | | | | % 262.32/56.72 | | | | | | | | | REDUCE: (2379), (2849) imply: % 262.32/56.72 | | | | | | | | | (2850) gt(n0, n0) % 262.32/56.72 | | | | | | | | | % 262.32/56.72 | | | | | | | | | PRED_UNIFY: (2845), (2850) imply: % 262.32/56.72 | | | | | | | | | (2851) $false % 262.32/56.72 | | | | | | | | | % 262.32/56.72 | | | | | | | | | CLOSE: (2851) is inconsistent. % 262.32/56.72 | | | | | | | | | % 262.32/56.72 | | | | | | | | Case 2: % 262.32/56.72 | | | | | | | | | % 262.32/56.72 | | | | | | | | | (2852) ~ (all_74_14 = n0) % 262.32/56.72 | | | | | | | | | % 262.32/56.72 | | | | | | | | | BETA: splitting (2848) gives: % 262.32/56.72 | | | | | | | | | % 262.32/56.72 | | | | | | | | | Case 1: % 262.32/56.72 | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | (2853) gt(n4, all_74_14) % 262.32/56.72 | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_14, n4, n3, % 262.32/56.72 | | | | | | | | | | simplifying with (67), (136), (147), (2853) gives: % 262.32/56.72 | | | | | | | | | | (2854) leq(all_74_14, n3) % 262.32/56.72 | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_14, n3, % 262.32/56.72 | | | | | | | | | | simplifying with (67), (129), (2854) gives: % 262.32/56.72 | | | | | | | | | | (2855) all_74_14 = n3 | gt(n3, all_74_14) % 262.32/56.72 | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | BETA: splitting (2855) gives: % 262.32/56.72 | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | Case 1: % 262.32/56.72 | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | (2856) gt(n3, all_74_14) % 262.32/56.72 | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_14, n3, n2, % 262.32/56.72 | | | | | | | | | | | simplifying with (67), (129), (146), (2856) gives: % 262.32/56.72 | | | | | | | | | | | (2857) leq(all_74_14, n2) % 262.32/56.72 | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_14, n2, % 262.32/56.72 | | | | | | | | | | | simplifying with (67), (118), (2857) gives: % 262.32/56.72 | | | | | | | | | | | (2858) all_74_14 = n2 | gt(n2, all_74_14) % 262.32/56.72 | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | BETA: splitting (2858) gives: % 262.32/56.72 | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | Case 1: % 262.32/56.72 | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | (2859) gt(n2, all_74_14) % 262.32/56.72 | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_14, n2, n1, % 262.32/56.72 | | | | | | | | | | | | simplifying with (67), (118), (145), (2859) gives: % 262.32/56.72 | | | | | | | | | | | | (2860) leq(all_74_14, n1) % 262.32/56.72 | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_74_14, simplifying % 262.32/56.72 | | | | | | | | | | | | with (67), (651), (2860) gives: % 262.32/56.72 | | | | | | | | | | | | (2861) all_74_14 = n1 | all_74_14 = n0 % 262.32/56.72 | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | BETA: splitting (2861) gives: % 262.32/56.72 | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | Case 1: % 262.32/56.72 | | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | | (2862) all_74_14 = n0 % 262.32/56.72 | | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | | REDUCE: (2852), (2862) imply: % 262.32/56.72 | | | | | | | | | | | | | (2863) $false % 262.32/56.72 | | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | | CLOSE: (2863) is inconsistent. % 262.32/56.72 | | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | Case 2: % 262.32/56.72 | | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | | (2864) all_74_14 = n1 % 262.32/56.72 | | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | | REDUCE: (2842), (2864) imply: % 262.32/56.72 | | | | | | | | | | | | | (2865) a_select3(id_ds1_filter, n1, n0) = all_74_12 % 262.32/56.72 | | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | | REDUCE: (2843), (2864) imply: % 262.32/56.72 | | | | | | | | | | | | | (2866) a_select3(id_ds1_filter, n0, n1) = all_74_13 % 262.32/56.72 | | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | | REDUCE: (659), (2864) imply: % 262.32/56.72 | | | | | | | | | | | | | (2867) leq(n1, n5) % 262.32/56.72 | | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | | REDUCE: (651), (2864) imply: % 262.32/56.72 | | | | | | | | | | | | | (2868) leq(n0, n1) % 262.32/56.72 | | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | | GROUND_INST: instantiating (82) with n0, n1, all_74_13, % 262.32/56.72 | | | | | | | | | | | | | simplifying with (22), (102), (2844), (2866), % 262.32/56.72 | | | | | | | | | | | | | (2868) gives: % 262.32/56.72 | | | | | | | | | | | | | (2869) ~ leq(n1, all_74_20) | ~ leq(n0, all_74_18) | % 262.32/56.72 | | | | | | | | | | | | | (a_select3(id_ds1_filter, n1, n0) = all_74_13 & % 262.32/56.72 | | | | | | | | | | | | | $i(all_74_13)) % 262.32/56.72 | | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | | BETA: splitting (2869) gives: % 262.32/56.72 | | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | | Case 1: % 262.32/56.72 | | | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | | | (2870) ~ leq(n0, all_74_18) % 262.32/56.72 | | | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | | | REDUCE: (2377), (2870) imply: % 262.32/56.72 | | | | | | | | | | | | | | (2871) ~ leq(n0, n4) % 262.32/56.72 | | | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | | | PRED_UNIFY: (2378), (2871) imply: % 262.32/56.72 | | | | | | | | | | | | | | (2872) $false % 262.32/56.72 | | | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | | | CLOSE: (2872) is inconsistent. % 262.32/56.72 | | | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | | Case 2: % 262.32/56.72 | | | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | | | (2873) ~ leq(n1, all_74_20) | (a_select3(id_ds1_filter, % 262.32/56.72 | | | | | | | | | | | | | | n1, n0) = all_74_13 & $i(all_74_13)) % 262.32/56.72 | | | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | | | REF_CLOSE: (30), (159), (649), (2865), (2867), (2873) are % 262.32/56.72 | | | | | | | | | | | | | | inconsistent by sub-proof #15. % 262.32/56.72 | | | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | | End of split % 262.32/56.72 | | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | End of split % 262.32/56.72 | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | Case 2: % 262.32/56.72 | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | (2874) all_74_14 = n2 % 262.32/56.72 | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | REDUCE: (2842), (2874) imply: % 262.32/56.72 | | | | | | | | | | | | (2875) a_select3(id_ds1_filter, n2, n0) = all_74_12 % 262.32/56.72 | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | REDUCE: (2843), (2874) imply: % 262.32/56.72 | | | | | | | | | | | | (2876) a_select3(id_ds1_filter, n0, n2) = all_74_13 % 262.32/56.72 | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | REDUCE: (659), (2874) imply: % 262.32/56.72 | | | | | | | | | | | | (2877) leq(n2, n5) % 262.32/56.72 | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | REDUCE: (651), (2874) imply: % 262.32/56.72 | | | | | | | | | | | | (2878) leq(n0, n2) % 262.32/56.72 | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | GROUND_INST: instantiating (82) with n0, n2, all_74_13, % 262.32/56.72 | | | | | | | | | | | | simplifying with (22), (118), (2844), (2876), % 262.32/56.72 | | | | | | | | | | | | (2878) gives: % 262.32/56.72 | | | | | | | | | | | | (2879) ~ leq(n2, all_74_20) | ~ leq(n0, all_74_18) | % 262.32/56.72 | | | | | | | | | | | | (a_select3(id_ds1_filter, n2, n0) = all_74_13 & % 262.32/56.72 | | | | | | | | | | | | $i(all_74_13)) % 262.32/56.72 | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | BETA: splitting (2879) gives: % 262.32/56.72 | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | Case 1: % 262.32/56.72 | | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | | (2880) ~ leq(n0, all_74_18) % 262.32/56.72 | | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | | REDUCE: (2377), (2880) imply: % 262.32/56.72 | | | | | | | | | | | | | (2881) ~ leq(n0, n4) % 262.32/56.72 | | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | | PRED_UNIFY: (2378), (2881) imply: % 262.32/56.72 | | | | | | | | | | | | | (2882) $false % 262.32/56.72 | | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | | CLOSE: (2882) is inconsistent. % 262.32/56.72 | | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | Case 2: % 262.32/56.72 | | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | | (2883) ~ leq(n2, all_74_20) | (a_select3(id_ds1_filter, % 262.32/56.72 | | | | | | | | | | | | | n2, n0) = all_74_13 & $i(all_74_13)) % 262.32/56.72 | | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | | REF_CLOSE: (30), (159), (649), (2875), (2877), (2883) are % 262.32/56.72 | | | | | | | | | | | | | inconsistent by sub-proof #13. % 262.32/56.72 | | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | | End of split % 262.32/56.72 | | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | End of split % 262.32/56.72 | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | Case 2: % 262.32/56.72 | | | | | | | | | | | % 262.32/56.72 | | | | | | | | | | | (2884) all_74_14 = n3 % 262.32/56.73 | | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | | REDUCE: (2842), (2884) imply: % 262.32/56.73 | | | | | | | | | | | (2885) a_select3(id_ds1_filter, n3, n0) = all_74_12 % 262.32/56.73 | | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | | REDUCE: (2843), (2884) imply: % 262.32/56.73 | | | | | | | | | | | (2886) a_select3(id_ds1_filter, n0, n3) = all_74_13 % 262.32/56.73 | | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | | REDUCE: (659), (2884) imply: % 262.32/56.73 | | | | | | | | | | | (2887) leq(n3, n5) % 262.32/56.73 | | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | | REDUCE: (651), (2884) imply: % 262.32/56.73 | | | | | | | | | | | (2888) leq(n0, n3) % 262.32/56.73 | | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | | GROUND_INST: instantiating (82) with n0, n3, all_74_13, % 262.32/56.73 | | | | | | | | | | | simplifying with (22), (129), (2844), (2886), % 262.32/56.73 | | | | | | | | | | | (2888) gives: % 262.32/56.73 | | | | | | | | | | | (2889) ~ leq(n3, all_74_20) | ~ leq(n0, all_74_18) | % 262.32/56.73 | | | | | | | | | | | (a_select3(id_ds1_filter, n3, n0) = all_74_13 & % 262.32/56.73 | | | | | | | | | | | $i(all_74_13)) % 262.32/56.73 | | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | | BETA: splitting (2889) gives: % 262.32/56.73 | | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | | Case 1: % 262.32/56.73 | | | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | | | (2890) ~ leq(n0, all_74_18) % 262.32/56.73 | | | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | | | REDUCE: (2377), (2890) imply: % 262.32/56.73 | | | | | | | | | | | | (2891) ~ leq(n0, n4) % 262.32/56.73 | | | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | | | PRED_UNIFY: (2378), (2891) imply: % 262.32/56.73 | | | | | | | | | | | | (2892) $false % 262.32/56.73 | | | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | | | CLOSE: (2892) is inconsistent. % 262.32/56.73 | | | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | | Case 2: % 262.32/56.73 | | | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | | | (2893) ~ leq(n3, all_74_20) | (a_select3(id_ds1_filter, % 262.32/56.73 | | | | | | | | | | | | n3, n0) = all_74_13 & $i(all_74_13)) % 262.32/56.73 | | | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | | | REF_CLOSE: (30), (159), (649), (2885), (2887), (2893) are % 262.32/56.73 | | | | | | | | | | | | inconsistent by sub-proof #11. % 262.32/56.73 | | | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | | End of split % 262.32/56.73 | | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | End of split % 262.32/56.73 | | | | | | | | | | % 262.32/56.73 | | | | | | | | | Case 2: % 262.32/56.73 | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | (2894) all_74_14 = n4 % 262.32/56.73 | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | REDUCE: (2842), (2894) imply: % 262.32/56.73 | | | | | | | | | | (2895) a_select3(id_ds1_filter, n4, n0) = all_74_12 % 262.32/56.73 | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | REDUCE: (2843), (2894) imply: % 262.32/56.73 | | | | | | | | | | (2896) a_select3(id_ds1_filter, n0, n4) = all_74_13 % 262.32/56.73 | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | REDUCE: (659), (2894) imply: % 262.32/56.73 | | | | | | | | | | (2897) leq(n4, n5) % 262.32/56.73 | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | GROUND_INST: instantiating (82) with n0, n4, all_74_13, % 262.32/56.73 | | | | | | | | | | simplifying with (22), (136), (2378), (2844), % 262.32/56.73 | | | | | | | | | | (2896) gives: % 262.32/56.73 | | | | | | | | | | (2898) ~ leq(n4, all_74_20) | ~ leq(n0, all_74_18) | % 262.32/56.73 | | | | | | | | | | (a_select3(id_ds1_filter, n4, n0) = all_74_13 & % 262.32/56.73 | | | | | | | | | | $i(all_74_13)) % 262.32/56.73 | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | BETA: splitting (2898) gives: % 262.32/56.73 | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | Case 1: % 262.32/56.73 | | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | | (2899) ~ leq(n0, all_74_18) % 262.32/56.73 | | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | | REDUCE: (2377), (2899) imply: % 262.32/56.73 | | | | | | | | | | | (2900) ~ leq(n0, n4) % 262.32/56.73 | | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | | PRED_UNIFY: (2378), (2900) imply: % 262.32/56.73 | | | | | | | | | | | (2901) $false % 262.32/56.73 | | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | | CLOSE: (2901) is inconsistent. % 262.32/56.73 | | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | Case 2: % 262.32/56.73 | | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | | (2902) ~ leq(n4, all_74_20) | (a_select3(id_ds1_filter, % 262.32/56.73 | | | | | | | | | | | n4, n0) = all_74_13 & $i(all_74_13)) % 262.32/56.73 | | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | | REF_CLOSE: (30), (159), (649), (2895), (2897), (2902) are % 262.32/56.73 | | | | | | | | | | | inconsistent by sub-proof #9. % 262.32/56.73 | | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | End of split % 262.32/56.73 | | | | | | | | | | % 262.32/56.73 | | | | | | | | | End of split % 262.32/56.73 | | | | | | | | | % 262.32/56.73 | | | | | | | | End of split % 262.32/56.73 | | | | | | | | % 262.32/56.73 | | | | | | | Case 2: % 262.32/56.73 | | | | | | | | % 262.32/56.73 | | | | | | | | (2903) all_74_14 = n5 % 262.32/56.73 | | | | | | | | % 262.32/56.73 | | | | | | | | REDUCE: (2842), (2903) imply: % 262.32/56.73 | | | | | | | | (2904) a_select3(id_ds1_filter, n5, n0) = all_74_12 % 262.32/56.73 | | | | | | | | % 262.32/56.73 | | | | | | | | REDUCE: (2843), (2903) imply: % 262.32/56.73 | | | | | | | | (2905) a_select3(id_ds1_filter, n0, n5) = all_74_13 % 262.32/56.73 | | | | | | | | % 262.32/56.73 | | | | | | | | REDUCE: (659), (2903) imply: % 262.32/56.73 | | | | | | | | (2906) leq(n5, n5) % 262.32/56.73 | | | | | | | | % 262.32/56.73 | | | | | | | | REDUCE: (651), (2903) imply: % 262.32/56.73 | | | | | | | | (2907) leq(n0, n5) % 262.32/56.73 | | | | | | | | % 262.32/56.73 | | | | | | | | GROUND_INST: instantiating (82) with n0, n5, all_74_13, % 262.32/56.73 | | | | | | | | simplifying with (22), (139), (2844), (2905), % 262.32/56.73 | | | | | | | | (2907) gives: % 262.32/56.73 | | | | | | | | (2908) ~ leq(n5, all_74_20) | ~ leq(n0, all_74_18) | % 262.32/56.73 | | | | | | | | (a_select3(id_ds1_filter, n5, n0) = all_74_13 & % 262.32/56.73 | | | | | | | | $i(all_74_13)) % 262.32/56.73 | | | | | | | | % 262.32/56.73 | | | | | | | | BETA: splitting (2908) gives: % 262.32/56.73 | | | | | | | | % 262.32/56.73 | | | | | | | | Case 1: % 262.32/56.73 | | | | | | | | | % 262.32/56.73 | | | | | | | | | (2909) ~ leq(n0, all_74_18) % 262.32/56.73 | | | | | | | | | % 262.32/56.73 | | | | | | | | | REDUCE: (2377), (2909) imply: % 262.32/56.73 | | | | | | | | | (2910) ~ leq(n0, n4) % 262.32/56.73 | | | | | | | | | % 262.32/56.73 | | | | | | | | | PRED_UNIFY: (2378), (2910) imply: % 262.32/56.73 | | | | | | | | | (2911) $false % 262.32/56.73 | | | | | | | | | % 262.32/56.73 | | | | | | | | | CLOSE: (2911) is inconsistent. % 262.32/56.73 | | | | | | | | | % 262.32/56.73 | | | | | | | | Case 2: % 262.32/56.73 | | | | | | | | | % 262.32/56.73 | | | | | | | | | (2912) ~ leq(n5, all_74_20) | (a_select3(id_ds1_filter, % 262.32/56.73 | | | | | | | | | n5, n0) = all_74_13 & $i(all_74_13)) % 262.32/56.73 | | | | | | | | | % 262.32/56.73 | | | | | | | | | REF_CLOSE: (30), (159), (649), (2904), (2906), (2912) are % 262.32/56.73 | | | | | | | | | inconsistent by sub-proof #7. % 262.32/56.73 | | | | | | | | | % 262.32/56.73 | | | | | | | | End of split % 262.32/56.73 | | | | | | | | % 262.32/56.73 | | | | | | | End of split % 262.32/56.73 | | | | | | | % 262.32/56.73 | | | | | | End of split % 262.32/56.73 | | | | | | % 262.32/56.73 | | | | | Case 2: % 262.32/56.73 | | | | | | % 262.32/56.73 | | | | | | (2913) all_74_14 = n0 % 262.32/56.73 | | | | | | (2914) ~ gt(all_74_14, n0) % 262.32/56.73 | | | | | | % 262.32/56.73 | | | | | | REDUCE: (656), (2913) imply: % 262.32/56.73 | | | | | | (2915) a_select3(id_ds1_filter, n0, all_74_15) = all_74_12 % 262.32/56.73 | | | | | | % 262.32/56.73 | | | | | | REDUCE: (655), (2913) imply: % 262.32/56.73 | | | | | | (2916) a_select3(id_ds1_filter, all_74_15, n0) = all_74_13 % 262.32/56.73 | | | | | | % 262.32/56.73 | | | | | | REDUCE: (651), (2913) imply: % 262.32/56.73 | | | | | | (2917) leq(n0, n0) % 262.32/56.73 | | | | | | % 262.32/56.73 | | | | | | REDUCE: (2913), (2914) imply: % 262.32/56.73 | | | | | | (2918) ~ gt(n0, n0) % 262.32/56.73 | | | | | | % 262.32/56.73 | | | | | | BETA: splitting (660) gives: % 262.32/56.73 | | | | | | % 262.32/56.73 | | | | | | Case 1: % 262.32/56.73 | | | | | | | % 262.32/56.73 | | | | | | | (2919) gt(all_74_15, n0) % 262.32/56.73 | | | | | | | % 262.32/56.73 | | | | | | | BETA: splitting (663) gives: % 262.32/56.73 | | | | | | | % 262.32/56.73 | | | | | | | Case 1: % 262.32/56.73 | | | | | | | | % 262.32/56.73 | | | | | | | | (2920) gt(all_74_16, all_74_15) % 262.32/56.73 | | | | | | | | % 262.32/56.73 | | | | | | | | REDUCE: (2375), (2920) imply: % 262.32/56.73 | | | | | | | | (2921) gt(n5, all_74_15) % 262.32/56.73 | | | | | | | | % 262.32/56.73 | | | | | | | | GROUND_INST: instantiating (1) with all_74_15, n5, n4, % 262.32/56.73 | | | | | | | | simplifying with (66), (139), (148), (2921) gives: % 262.32/56.73 | | | | | | | | (2922) leq(all_74_15, n4) % 262.32/56.73 | | | | | | | | % 262.32/56.73 | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_15, n4, % 262.32/56.73 | | | | | | | | simplifying with (66), (136), (2922) gives: % 262.32/56.73 | | | | | | | | (2923) all_74_15 = n4 | gt(n4, all_74_15) % 262.32/56.73 | | | | | | | | % 262.32/56.73 | | | | | | | | BETA: splitting (687) gives: % 262.32/56.73 | | | | | | | | % 262.32/56.73 | | | | | | | | Case 1: % 262.32/56.73 | | | | | | | | | % 262.32/56.73 | | | | | | | | | (2924) all_74_15 = n0 % 262.32/56.73 | | | | | | | | | % 262.32/56.73 | | | | | | | | | REDUCE: (2919), (2924) imply: % 262.32/56.73 | | | | | | | | | (2925) gt(n0, n0) % 262.32/56.73 | | | | | | | | | % 262.32/56.73 | | | | | | | | | PRED_UNIFY: (2918), (2925) imply: % 262.32/56.73 | | | | | | | | | (2926) $false % 262.32/56.73 | | | | | | | | | % 262.32/56.73 | | | | | | | | | CLOSE: (2926) is inconsistent. % 262.32/56.73 | | | | | | | | | % 262.32/56.73 | | | | | | | | Case 2: % 262.32/56.73 | | | | | | | | | % 262.32/56.73 | | | | | | | | | (2927) ~ (all_74_15 = n0) % 262.32/56.73 | | | | | | | | | % 262.32/56.73 | | | | | | | | | BETA: splitting (2923) gives: % 262.32/56.73 | | | | | | | | | % 262.32/56.73 | | | | | | | | | Case 1: % 262.32/56.73 | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | (2928) gt(n4, all_74_15) % 262.32/56.73 | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_15, n4, n3, % 262.32/56.73 | | | | | | | | | | simplifying with (66), (136), (147), (2928) gives: % 262.32/56.73 | | | | | | | | | | (2929) leq(all_74_15, n3) % 262.32/56.73 | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_15, n3, % 262.32/56.73 | | | | | | | | | | simplifying with (66), (129), (2929) gives: % 262.32/56.73 | | | | | | | | | | (2930) all_74_15 = n3 | gt(n3, all_74_15) % 262.32/56.73 | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | BETA: splitting (2930) gives: % 262.32/56.73 | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | Case 1: % 262.32/56.73 | | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | | (2931) gt(n3, all_74_15) % 262.32/56.73 | | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_15, n3, n2, % 262.32/56.73 | | | | | | | | | | | simplifying with (66), (129), (146), (2931) gives: % 262.32/56.73 | | | | | | | | | | | (2932) leq(all_74_15, n2) % 262.32/56.73 | | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_15, n2, % 262.32/56.73 | | | | | | | | | | | simplifying with (66), (118), (2932) gives: % 262.32/56.73 | | | | | | | | | | | (2933) all_74_15 = n2 | gt(n2, all_74_15) % 262.32/56.73 | | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | | BETA: splitting (2933) gives: % 262.32/56.73 | | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | | Case 1: % 262.32/56.73 | | | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | | | (2934) gt(n2, all_74_15) % 262.32/56.73 | | | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_15, n2, n1, % 262.32/56.73 | | | | | | | | | | | | simplifying with (66), (118), (145), (2934) gives: % 262.32/56.73 | | | | | | | | | | | | (2935) leq(all_74_15, n1) % 262.32/56.73 | | | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_74_15, simplifying % 262.32/56.73 | | | | | | | | | | | | with (66), (650), (2935) gives: % 262.32/56.73 | | | | | | | | | | | | (2936) all_74_15 = n1 | all_74_15 = n0 % 262.32/56.73 | | | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | | | BETA: splitting (2936) gives: % 262.32/56.73 | | | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | | | Case 1: % 262.32/56.73 | | | | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | | | | (2937) all_74_15 = n0 % 262.32/56.73 | | | | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | | | | REDUCE: (2927), (2937) imply: % 262.32/56.73 | | | | | | | | | | | | | (2938) $false % 262.32/56.73 | | | | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | | | | CLOSE: (2938) is inconsistent. % 262.32/56.73 | | | | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | | | Case 2: % 262.32/56.73 | | | | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | | | | (2939) all_74_15 = n1 % 262.32/56.73 | | | | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | | | | REDUCE: (2916), (2939) imply: % 262.32/56.73 | | | | | | | | | | | | | (2940) a_select3(id_ds1_filter, n1, n0) = all_74_13 % 262.32/56.73 | | | | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | | | | REDUCE: (2915), (2939) imply: % 262.32/56.73 | | | | | | | | | | | | | (2941) a_select3(id_ds1_filter, n0, n1) = all_74_12 % 262.32/56.73 | | | | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | | | | REDUCE: (684), (2939) imply: % 262.32/56.73 | | | | | | | | | | | | | (2942) leq(n1, n5) % 262.32/56.73 | | | | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | | | | REDUCE: (650), (2939) imply: % 262.32/56.73 | | | | | | | | | | | | | (2943) leq(n0, n1) % 262.32/56.73 | | | | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | | | | GROUND_INST: instantiating (82) with n0, n1, all_74_12, % 262.32/56.73 | | | | | | | | | | | | | simplifying with (22), (102), (2917), (2941), % 262.32/56.73 | | | | | | | | | | | | | (2943) gives: % 262.32/56.73 | | | | | | | | | | | | | (2944) ~ leq(n1, all_74_20) | ~ leq(n0, all_74_18) | % 262.32/56.73 | | | | | | | | | | | | | (a_select3(id_ds1_filter, n1, n0) = all_74_12 & % 262.32/56.73 | | | | | | | | | | | | | $i(all_74_12)) % 262.32/56.73 | | | | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | | | | BETA: splitting (2944) gives: % 262.32/56.73 | | | | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | | | | Case 1: % 262.32/56.73 | | | | | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | | | | | (2945) ~ leq(n0, all_74_18) % 262.32/56.73 | | | | | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | | | | | REDUCE: (2377), (2945) imply: % 262.32/56.73 | | | | | | | | | | | | | | (2946) ~ leq(n0, n4) % 262.32/56.73 | | | | | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | | | | | PRED_UNIFY: (2378), (2946) imply: % 262.32/56.73 | | | | | | | | | | | | | | (2947) $false % 262.32/56.73 | | | | | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | | | | | CLOSE: (2947) is inconsistent. % 262.32/56.73 | | | | | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | | | | Case 2: % 262.32/56.73 | | | | | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | | | | | (2948) ~ leq(n1, all_74_20) | (a_select3(id_ds1_filter, % 262.32/56.73 | | | | | | | | | | | | | | n1, n0) = all_74_12 & $i(all_74_12)) % 262.32/56.73 | | | | | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | | | | | REF_CLOSE: (30), (159), (649), (2940), (2942), (2948) are % 262.32/56.73 | | | | | | | | | | | | | | inconsistent by sub-proof #5. % 262.32/56.73 | | | | | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | | | | End of split % 262.32/56.73 | | | | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | | | End of split % 262.32/56.73 | | | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | | Case 2: % 262.32/56.73 | | | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | | | (2949) all_74_15 = n2 % 262.32/56.73 | | | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | | | REDUCE: (2916), (2949) imply: % 262.32/56.73 | | | | | | | | | | | | (2950) a_select3(id_ds1_filter, n2, n0) = all_74_13 % 262.32/56.73 | | | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | | | REDUCE: (2915), (2949) imply: % 262.32/56.73 | | | | | | | | | | | | (2951) a_select3(id_ds1_filter, n0, n2) = all_74_12 % 262.32/56.73 | | | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | | | REDUCE: (684), (2949) imply: % 262.32/56.73 | | | | | | | | | | | | (2952) leq(n2, n5) % 262.32/56.73 | | | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | | | REDUCE: (650), (2949) imply: % 262.32/56.73 | | | | | | | | | | | | (2953) leq(n0, n2) % 262.32/56.73 | | | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | | | GROUND_INST: instantiating (82) with n0, n2, all_74_12, % 262.32/56.73 | | | | | | | | | | | | simplifying with (22), (118), (2917), (2951), % 262.32/56.73 | | | | | | | | | | | | (2953) gives: % 262.32/56.73 | | | | | | | | | | | | (2954) ~ leq(n2, all_74_20) | ~ leq(n0, all_74_18) | % 262.32/56.73 | | | | | | | | | | | | (a_select3(id_ds1_filter, n2, n0) = all_74_12 & % 262.32/56.73 | | | | | | | | | | | | $i(all_74_12)) % 262.32/56.73 | | | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | | | BETA: splitting (2954) gives: % 262.32/56.73 | | | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | | | Case 1: % 262.32/56.73 | | | | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | | | | (2955) ~ leq(n0, all_74_18) % 262.32/56.73 | | | | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | | | | REDUCE: (2377), (2955) imply: % 262.32/56.73 | | | | | | | | | | | | | (2956) ~ leq(n0, n4) % 262.32/56.73 | | | | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | | | | PRED_UNIFY: (2378), (2956) imply: % 262.32/56.73 | | | | | | | | | | | | | (2957) $false % 262.32/56.73 | | | | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | | | | CLOSE: (2957) is inconsistent. % 262.32/56.73 | | | | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | | | Case 2: % 262.32/56.73 | | | | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | | | | (2958) ~ leq(n2, all_74_20) | (a_select3(id_ds1_filter, % 262.32/56.73 | | | | | | | | | | | | | n2, n0) = all_74_12 & $i(all_74_12)) % 262.32/56.73 | | | | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | | | | REF_CLOSE: (30), (159), (649), (2950), (2952), (2958) are % 262.32/56.73 | | | | | | | | | | | | | inconsistent by sub-proof #4. % 262.32/56.73 | | | | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | | | End of split % 262.32/56.73 | | | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | | End of split % 262.32/56.73 | | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | Case 2: % 262.32/56.73 | | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | | (2959) all_74_15 = n3 % 262.32/56.73 | | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | | REDUCE: (2916), (2959) imply: % 262.32/56.73 | | | | | | | | | | | (2960) a_select3(id_ds1_filter, n3, n0) = all_74_13 % 262.32/56.73 | | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | | REDUCE: (2915), (2959) imply: % 262.32/56.73 | | | | | | | | | | | (2961) a_select3(id_ds1_filter, n0, n3) = all_74_12 % 262.32/56.73 | | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | | REDUCE: (684), (2959) imply: % 262.32/56.73 | | | | | | | | | | | (2962) leq(n3, n5) % 262.32/56.73 | | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | | REDUCE: (650), (2959) imply: % 262.32/56.73 | | | | | | | | | | | (2963) leq(n0, n3) % 262.32/56.73 | | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | | GROUND_INST: instantiating (82) with n0, n3, all_74_12, % 262.32/56.73 | | | | | | | | | | | simplifying with (22), (129), (2917), (2961), % 262.32/56.73 | | | | | | | | | | | (2963) gives: % 262.32/56.73 | | | | | | | | | | | (2964) ~ leq(n3, all_74_20) | ~ leq(n0, all_74_18) | % 262.32/56.73 | | | | | | | | | | | (a_select3(id_ds1_filter, n3, n0) = all_74_12 & % 262.32/56.73 | | | | | | | | | | | $i(all_74_12)) % 262.32/56.73 | | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | | BETA: splitting (2964) gives: % 262.32/56.73 | | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | | Case 1: % 262.32/56.73 | | | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | | | (2965) ~ leq(n0, all_74_18) % 262.32/56.73 | | | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | | | REDUCE: (2377), (2965) imply: % 262.32/56.73 | | | | | | | | | | | | (2966) ~ leq(n0, n4) % 262.32/56.73 | | | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | | | PRED_UNIFY: (2378), (2966) imply: % 262.32/56.73 | | | | | | | | | | | | (2967) $false % 262.32/56.73 | | | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | | | CLOSE: (2967) is inconsistent. % 262.32/56.73 | | | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | | Case 2: % 262.32/56.73 | | | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | | | (2968) ~ leq(n3, all_74_20) | (a_select3(id_ds1_filter, % 262.32/56.73 | | | | | | | | | | | | n3, n0) = all_74_12 & $i(all_74_12)) % 262.32/56.73 | | | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | | | REF_CLOSE: (30), (159), (649), (2960), (2962), (2968) are % 262.32/56.73 | | | | | | | | | | | | inconsistent by sub-proof #3. % 262.32/56.73 | | | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | | End of split % 262.32/56.73 | | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | End of split % 262.32/56.73 | | | | | | | | | | % 262.32/56.73 | | | | | | | | | Case 2: % 262.32/56.73 | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | (2969) all_74_15 = n4 % 262.32/56.73 | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | REDUCE: (2916), (2969) imply: % 262.32/56.73 | | | | | | | | | | (2970) a_select3(id_ds1_filter, n4, n0) = all_74_13 % 262.32/56.73 | | | | | | | | | | % 262.32/56.73 | | | | | | | | | | REDUCE: (2915), (2969) imply: % 262.32/56.73 | | | | | | | | | | (2971) a_select3(id_ds1_filter, n0, n4) = all_74_12 % 262.32/56.74 | | | | | | | | | | % 262.32/56.74 | | | | | | | | | | REDUCE: (684), (2969) imply: % 262.32/56.74 | | | | | | | | | | (2972) leq(n4, n5) % 262.32/56.74 | | | | | | | | | | % 262.32/56.74 | | | | | | | | | | GROUND_INST: instantiating (82) with n0, n4, all_74_12, % 262.32/56.74 | | | | | | | | | | simplifying with (22), (136), (2378), (2917), % 262.32/56.74 | | | | | | | | | | (2971) gives: % 262.32/56.74 | | | | | | | | | | (2973) ~ leq(n4, all_74_20) | ~ leq(n0, all_74_18) | % 262.32/56.74 | | | | | | | | | | (a_select3(id_ds1_filter, n4, n0) = all_74_12 & % 262.32/56.74 | | | | | | | | | | $i(all_74_12)) % 262.32/56.74 | | | | | | | | | | % 262.32/56.74 | | | | | | | | | | BETA: splitting (2973) gives: % 262.32/56.74 | | | | | | | | | | % 262.32/56.74 | | | | | | | | | | Case 1: % 262.32/56.74 | | | | | | | | | | | % 262.32/56.74 | | | | | | | | | | | (2974) ~ leq(n0, all_74_18) % 262.32/56.74 | | | | | | | | | | | % 262.32/56.74 | | | | | | | | | | | REDUCE: (2377), (2974) imply: % 262.32/56.74 | | | | | | | | | | | (2975) ~ leq(n0, n4) % 262.32/56.74 | | | | | | | | | | | % 262.32/56.74 | | | | | | | | | | | PRED_UNIFY: (2378), (2975) imply: % 262.32/56.74 | | | | | | | | | | | (2976) $false % 262.32/56.74 | | | | | | | | | | | % 262.32/56.74 | | | | | | | | | | | CLOSE: (2976) is inconsistent. % 262.32/56.74 | | | | | | | | | | | % 262.32/56.74 | | | | | | | | | | Case 2: % 262.32/56.74 | | | | | | | | | | | % 262.32/56.74 | | | | | | | | | | | (2977) ~ leq(n4, all_74_20) | (a_select3(id_ds1_filter, % 262.32/56.74 | | | | | | | | | | | n4, n0) = all_74_12 & $i(all_74_12)) % 262.32/56.74 | | | | | | | | | | | % 262.32/56.74 | | | | | | | | | | | BETA: splitting (2977) gives: % 262.32/56.74 | | | | | | | | | | | % 262.32/56.74 | | | | | | | | | | | Case 1: % 262.32/56.74 | | | | | | | | | | | | % 262.32/56.74 | | | | | | | | | | | | (2978) ~ leq(n4, all_74_20) % 262.32/56.74 | | | | | | | | | | | | % 262.32/56.74 | | | | | | | | | | | | REDUCE: (159), (2978) imply: % 262.32/56.74 | | | | | | | | | | | | (2979) ~ leq(n4, n5) % 262.32/56.74 | | | | | | | | | | | | % 262.32/56.74 | | | | | | | | | | | | PRED_UNIFY: (2972), (2979) imply: % 262.32/56.74 | | | | | | | | | | | | (2980) $false % 262.32/56.74 | | | | | | | | | | | | % 262.32/56.74 | | | | | | | | | | | | CLOSE: (2980) is inconsistent. % 262.32/56.74 | | | | | | | | | | | | % 262.32/56.74 | | | | | | | | | | | Case 2: % 262.32/56.74 | | | | | | | | | | | | % 262.32/56.74 | | | | | | | | | | | | (2981) a_select3(id_ds1_filter, n4, n0) = all_74_12 & % 262.32/56.74 | | | | | | | | | | | | $i(all_74_12) % 262.32/56.74 | | | | | | | | | | | | % 262.32/56.74 | | | | | | | | | | | | ALPHA: (2981) implies: % 262.32/56.74 | | | | | | | | | | | | (2982) a_select3(id_ds1_filter, n4, n0) = all_74_12 % 262.32/56.74 | | | | | | | | | | | | % 262.32/56.74 | | | | | | | | | | | | REF_CLOSE: (30), (649), (2970), (2982) are inconsistent by % 262.32/56.74 | | | | | | | | | | | | sub-proof #10. % 262.32/56.74 | | | | | | | | | | | | % 262.32/56.74 | | | | | | | | | | | End of split % 262.32/56.74 | | | | | | | | | | | % 262.32/56.74 | | | | | | | | | | End of split % 262.32/56.74 | | | | | | | | | | % 262.32/56.74 | | | | | | | | | End of split % 262.32/56.74 | | | | | | | | | % 262.32/56.74 | | | | | | | | End of split % 262.32/56.74 | | | | | | | | % 262.32/56.74 | | | | | | | Case 2: % 262.32/56.74 | | | | | | | | % 262.32/56.74 | | | | | | | | (2983) all_74_15 = all_74_16 % 262.32/56.74 | | | | | | | | % 262.32/56.74 | | | | | | | | COMBINE_EQS: (2375), (2983) imply: % 262.32/56.74 | | | | | | | | (2984) all_74_15 = n5 % 262.32/56.74 | | | | | | | | % 262.32/56.74 | | | | | | | | REDUCE: (2916), (2984) imply: % 262.32/56.74 | | | | | | | | (2985) a_select3(id_ds1_filter, n5, n0) = all_74_13 % 262.32/56.74 | | | | | | | | % 262.32/56.74 | | | | | | | | REDUCE: (2915), (2984) imply: % 262.32/56.74 | | | | | | | | (2986) a_select3(id_ds1_filter, n0, n5) = all_74_12 % 262.32/56.74 | | | | | | | | % 262.32/56.74 | | | | | | | | REDUCE: (684), (2984) imply: % 262.32/56.74 | | | | | | | | (2987) leq(n5, n5) % 262.32/56.74 | | | | | | | | % 262.32/56.74 | | | | | | | | REDUCE: (650), (2984) imply: % 262.32/56.74 | | | | | | | | (2988) leq(n0, n5) % 262.32/56.74 | | | | | | | | % 262.32/56.74 | | | | | | | | GROUND_INST: instantiating (82) with n0, n5, all_74_12, % 262.32/56.74 | | | | | | | | simplifying with (22), (139), (2917), (2986), % 262.32/56.74 | | | | | | | | (2988) gives: % 262.32/56.74 | | | | | | | | (2989) ~ leq(n5, all_74_20) | ~ leq(n0, all_74_18) | % 262.32/56.74 | | | | | | | | (a_select3(id_ds1_filter, n5, n0) = all_74_12 & % 262.32/56.74 | | | | | | | | $i(all_74_12)) % 262.32/56.74 | | | | | | | | % 262.32/56.74 | | | | | | | | BETA: splitting (2989) gives: % 262.32/56.74 | | | | | | | | % 262.32/56.74 | | | | | | | | Case 1: % 262.32/56.74 | | | | | | | | | % 262.32/56.74 | | | | | | | | | (2990) ~ leq(n0, all_74_18) % 262.32/56.74 | | | | | | | | | % 262.32/56.74 | | | | | | | | | REDUCE: (2377), (2990) imply: % 262.32/56.74 | | | | | | | | | (2991) ~ leq(n0, n4) % 262.32/56.74 | | | | | | | | | % 262.32/56.74 | | | | | | | | | PRED_UNIFY: (2378), (2991) imply: % 262.32/56.74 | | | | | | | | | (2992) $false % 262.32/56.74 | | | | | | | | | % 262.32/56.74 | | | | | | | | | CLOSE: (2992) is inconsistent. % 262.32/56.74 | | | | | | | | | % 262.32/56.74 | | | | | | | | Case 2: % 262.32/56.74 | | | | | | | | | % 262.32/56.74 | | | | | | | | | (2993) ~ leq(n5, all_74_20) | (a_select3(id_ds1_filter, % 262.32/56.74 | | | | | | | | | n5, n0) = all_74_12 & $i(all_74_12)) % 262.32/56.74 | | | | | | | | | % 262.32/56.74 | | | | | | | | | BETA: splitting (2993) gives: % 262.32/56.74 | | | | | | | | | % 262.32/56.74 | | | | | | | | | Case 1: % 262.32/56.74 | | | | | | | | | | % 262.32/56.74 | | | | | | | | | | (2994) ~ leq(n5, all_74_20) % 262.32/56.74 | | | | | | | | | | % 262.32/56.74 | | | | | | | | | | REDUCE: (159), (2994) imply: % 262.32/56.74 | | | | | | | | | | (2995) ~ leq(n5, n5) % 262.32/56.74 | | | | | | | | | | % 262.32/56.74 | | | | | | | | | | PRED_UNIFY: (2987), (2995) imply: % 262.32/56.74 | | | | | | | | | | (2996) $false % 262.32/56.74 | | | | | | | | | | % 262.32/56.74 | | | | | | | | | | CLOSE: (2996) is inconsistent. % 262.32/56.74 | | | | | | | | | | % 262.32/56.74 | | | | | | | | | Case 2: % 262.32/56.74 | | | | | | | | | | % 262.32/56.74 | | | | | | | | | | (2997) a_select3(id_ds1_filter, n5, n0) = all_74_12 & % 262.32/56.74 | | | | | | | | | | $i(all_74_12) % 262.32/56.74 | | | | | | | | | | % 262.32/56.74 | | | | | | | | | | ALPHA: (2997) implies: % 262.32/56.74 | | | | | | | | | | (2998) a_select3(id_ds1_filter, n5, n0) = all_74_12 % 262.32/56.74 | | | | | | | | | | % 262.32/56.74 | | | | | | | | | | GROUND_INST: instantiating (30) with all_74_12, all_74_13, n0, % 262.32/56.74 | | | | | | | | | | n5, id_ds1_filter, simplifying with (2985), (2998) % 262.32/56.74 | | | | | | | | | | gives: % 262.32/56.74 | | | | | | | | | | (2999) all_74_12 = all_74_13 % 262.32/56.74 | | | | | | | | | | % 262.32/56.74 | | | | | | | | | | REDUCE: (649), (2999) imply: % 262.32/56.74 | | | | | | | | | | (3000) $false % 262.32/56.74 | | | | | | | | | | % 262.32/56.74 | | | | | | | | | | CLOSE: (3000) is inconsistent. % 262.32/56.74 | | | | | | | | | | % 262.32/56.74 | | | | | | | | | End of split % 262.32/56.74 | | | | | | | | | % 262.32/56.74 | | | | | | | | End of split % 262.32/56.74 | | | | | | | | % 262.32/56.74 | | | | | | | End of split % 262.32/56.74 | | | | | | | % 262.32/56.74 | | | | | | Case 2: % 262.32/56.74 | | | | | | | % 262.32/56.74 | | | | | | | (3001) all_74_15 = n0 % 262.32/56.74 | | | | | | | % 262.32/56.74 | | | | | | | REF_CLOSE: (30), (649), (2915), (2916), (3001) are inconsistent by % 262.32/56.74 | | | | | | | sub-proof #2. % 262.32/56.74 | | | | | | | % 262.32/56.74 | | | | | | End of split % 262.32/56.74 | | | | | | % 262.32/56.74 | | | | | End of split % 262.32/56.74 | | | | | % 262.32/56.74 | | | | End of split % 262.32/56.74 | | | | % 262.32/56.74 | | | Case 2: % 262.32/56.74 | | | | % 262.32/56.74 | | | | (3002) pv57 = n0 % 262.32/56.74 | | | | (3003) ~ gt(pv57, n0) % 262.32/56.74 | | | | % 262.32/56.74 | | | | REDUCE: (681), (3002) imply: % 262.32/56.74 | | | | (3004) leq(all_74_15, n0) % 262.32/56.74 | | | | % 262.32/56.74 | | | | REDUCE: (3002), (3003) imply: % 262.32/56.74 | | | | (3005) ~ gt(n0, n0) % 262.32/56.74 | | | | % 262.32/56.74 | | | | BETA: splitting (141) gives: % 262.32/56.74 | | | | % 262.32/56.74 | | | | Case 1: % 262.32/56.74 | | | | | % 262.32/56.74 | | | | | % 262.32/56.74 | | | | | GROUND_INST: instantiating (transitivity_leq) with all_74_15, n0, % 262.32/56.74 | | | | | all_74_14, simplifying with (22), (66), (67), (651), % 262.32/56.74 | | | | | (3004) gives: % 262.32/56.74 | | | | | (3006) leq(all_74_15, all_74_14) % 262.32/56.74 | | | | | % 262.32/56.74 | | | | | REF_CLOSE: (1), (12), (13), (30), (66), (67), (81), (118), (129), % 262.32/56.74 | | | | | (136), (139), (145), (146), (147), (148), (159), (649), % 262.32/56.74 | | | | | (650), (655), (656), (659), (661), (665), (666), (3002), % 262.32/56.74 | | | | | (3004), (3005), (3006), (leq_gt2) are inconsistent by % 262.32/56.74 | | | | | sub-proof #1. % 262.32/56.74 | | | | | % 262.32/56.74 | | | | Case 2: % 262.32/56.74 | | | | | % 262.32/56.74 | | | | | (3007) pv5 = n0 % 262.32/56.74 | | | | | (3008) ~ gt(pv5, n0) % 262.32/56.74 | | | | | % 262.32/56.74 | | | | | GROUND_INST: instantiating (transitivity_leq) with all_74_15, n0, % 262.32/56.74 | | | | | all_74_14, simplifying with (22), (66), (67), (651), % 262.32/56.74 | | | | | (3004) gives: % 262.32/56.74 | | | | | (3009) leq(all_74_15, all_74_14) % 262.32/56.74 | | | | | % 262.32/56.74 | | | | | REF_CLOSE: (1), (12), (13), (30), (66), (67), (81), (118), (129), % 262.32/56.74 | | | | | (136), (139), (145), (146), (147), (148), (159), (649), % 262.32/56.74 | | | | | (650), (655), (656), (659), (661), (665), (666), (3002), % 262.32/56.74 | | | | | (3004), (3005), (3009), (leq_gt2) are inconsistent by % 262.32/56.74 | | | | | sub-proof #1. % 262.32/56.74 | | | | | % 262.32/56.74 | | | | End of split % 262.32/56.74 | | | | % 262.32/56.74 | | | End of split % 262.32/56.74 | | | % 262.32/56.74 | | End of split % 262.32/56.74 | | % 262.32/56.74 | End of split % 262.32/56.74 | % 262.32/56.74 End of proof % 262.32/56.74 % 262.32/56.74 Sub-proof #1 shows that the following formulas are inconsistent: % 262.32/56.74 ---------------------------------------------------------------- % 262.32/56.74 (1) $i(n3) % 262.32/56.74 (2) $i(n4) % 262.32/56.74 (3) ! [v0: $i] : (v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0, n1) | ~ % 262.32/56.74 leq(n0, v0)) % 262.32/56.74 (4) leq(all_74_15, all_74_14) % 262.32/56.74 (5) pred(n2) = n1 % 262.32/56.74 (6) a_select3(id_ds1_filter, all_74_14, all_74_15) = all_74_12 % 262.32/56.74 (7) leq(all_74_14, n5) % 262.32/56.74 (8) $i(all_74_14) % 262.32/56.74 (9) all_74_14 = n5 | all_74_14 = n4 | all_74_14 = n3 | all_74_14 = n2 | % 262.32/56.74 all_74_14 = n1 | all_74_14 = n0 % 262.32/56.74 (10) pred(n5) = n4 % 262.32/56.74 (11) ! [v0: $i] : (v0 = n0 | ~ $i(v0) | ~ leq(v0, n0) | ~ leq(n0, v0)) % 262.32/56.74 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (a_select3(id_ds1_filter, % 262.32/56.74 v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ leq(v1, all_74_20) | ~ % 262.32/56.74 leq(v0, pv57) | ~ leq(n0, v1) | ~ leq(n0, v0) | % 262.32/56.74 (a_select3(id_ds1_filter, v1, v0) = v2 & $i(v2))) % 262.32/56.74 (13) leq(all_74_15, n0) % 262.32/56.74 (14) ~ gt(n0, n0) % 262.32/56.74 (15) $i(all_74_15) % 262.32/56.74 (16) a_select3(id_ds1_filter, all_74_15, all_74_14) = all_74_13 % 262.32/56.74 (17) pred(n3) = n2 % 262.32/56.74 (18) pv57 = n0 % 262.32/56.74 (19) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 262.32/56.74 (v1 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 262.32/56.74 v0)) % 262.32/56.74 (20) pred(n4) = n3 % 262.32/56.74 (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (pred(v1) = v2) | ~ % 262.32/56.74 $i(v1) | ~ $i(v0) | ~ gt(v1, v0) | leq(v0, v2)) % 262.32/56.74 (22) all_74_14 = n5 | gt(n5, all_74_14) % 262.32/56.74 (23) ~ (all_74_12 = all_74_13) % 262.32/56.74 (24) all_74_14 = n0 | gt(all_74_14, n0) % 262.32/56.74 (25) all_74_20 = n5 % 262.32/56.74 (26) $i(n2) % 262.32/56.74 (27) $i(n5) % 262.32/56.74 (28) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ % 262.32/56.74 leq(v0, v1) | gt(v1, v0)) % 262.32/56.74 (29) leq(n0, all_74_15) % 262.32/56.74 % 262.32/56.74 Begin of proof % 262.32/56.74 | % 262.32/56.74 | GROUND_INST: instantiating (11) with all_74_15, simplifying with (13), (15), % 262.32/56.74 | (29) gives: % 262.32/56.74 | (30) all_74_15 = n0 % 262.32/56.74 | % 262.32/56.74 | REDUCE: (6), (30) imply: % 262.32/56.74 | (31) a_select3(id_ds1_filter, all_74_14, n0) = all_74_12 % 262.32/56.74 | % 262.32/56.74 | REDUCE: (16), (30) imply: % 262.32/56.75 | (32) a_select3(id_ds1_filter, n0, all_74_14) = all_74_13 % 262.32/56.75 | % 262.32/56.75 | REDUCE: (15), (30) imply: % 262.32/56.75 | (33) $i(n0) % 262.32/56.75 | % 262.32/56.75 | REDUCE: (4), (30) imply: % 262.32/56.75 | (34) leq(n0, all_74_14) % 262.32/56.75 | % 262.32/56.75 | REDUCE: (29), (30) imply: % 262.32/56.75 | (35) leq(n0, n0) % 262.32/56.75 | % 262.32/56.75 | BETA: splitting (24) gives: % 262.32/56.75 | % 262.32/56.75 | Case 1: % 262.32/56.75 | | % 262.32/56.75 | | (36) gt(all_74_14, n0) % 262.32/56.75 | | % 262.32/56.75 | | BETA: splitting (22) gives: % 262.32/56.75 | | % 262.32/56.75 | | Case 1: % 262.32/56.75 | | | % 262.32/56.75 | | | (37) gt(n5, all_74_14) % 262.32/56.75 | | | % 262.32/56.75 | | | GROUND_INST: instantiating (21) with all_74_14, n5, n4, simplifying with % 262.32/56.75 | | | (8), (10), (27), (37) gives: % 262.32/56.75 | | | (38) leq(all_74_14, n4) % 262.32/56.75 | | | % 262.32/56.75 | | | GROUND_INST: instantiating (28) with all_74_14, n4, simplifying with (2), % 262.32/56.75 | | | (8), (38) gives: % 262.32/56.75 | | | (39) all_74_14 = n4 | gt(n4, all_74_14) % 262.32/56.75 | | | % 262.32/56.75 | | | BETA: splitting (9) gives: % 262.32/56.75 | | | % 262.32/56.75 | | | Case 1: % 262.32/56.75 | | | | % 262.32/56.75 | | | | (40) all_74_14 = n0 % 262.32/56.75 | | | | % 262.32/56.75 | | | | REDUCE: (36), (40) imply: % 262.32/56.75 | | | | (41) gt(n0, n0) % 262.32/56.75 | | | | % 262.32/56.75 | | | | PRED_UNIFY: (14), (41) imply: % 262.32/56.75 | | | | (42) $false % 262.32/56.75 | | | | % 262.32/56.75 | | | | CLOSE: (42) is inconsistent. % 262.32/56.75 | | | | % 262.32/56.75 | | | Case 2: % 262.32/56.75 | | | | % 262.32/56.75 | | | | (43) ~ (all_74_14 = n0) % 262.32/56.75 | | | | % 262.32/56.75 | | | | BETA: splitting (39) gives: % 262.32/56.75 | | | | % 262.32/56.75 | | | | Case 1: % 262.32/56.75 | | | | | % 262.32/56.75 | | | | | (44) gt(n4, all_74_14) % 262.32/56.75 | | | | | % 262.32/56.75 | | | | | GROUND_INST: instantiating (21) with all_74_14, n4, n3, simplifying % 262.32/56.75 | | | | | with (2), (8), (20), (44) gives: % 262.32/56.75 | | | | | (45) leq(all_74_14, n3) % 262.32/56.75 | | | | | % 262.32/56.75 | | | | | GROUND_INST: instantiating (28) with all_74_14, n3, simplifying with % 262.32/56.75 | | | | | (1), (8), (45) gives: % 262.32/56.75 | | | | | (46) all_74_14 = n3 | gt(n3, all_74_14) % 262.32/56.75 | | | | | % 262.32/56.75 | | | | | BETA: splitting (46) gives: % 262.32/56.75 | | | | | % 262.32/56.75 | | | | | Case 1: % 262.32/56.75 | | | | | | % 262.32/56.75 | | | | | | (47) gt(n3, all_74_14) % 262.32/56.75 | | | | | | % 262.32/56.75 | | | | | | GROUND_INST: instantiating (21) with all_74_14, n3, n2, simplifying % 262.32/56.75 | | | | | | with (1), (8), (17), (47) gives: % 262.32/56.75 | | | | | | (48) leq(all_74_14, n2) % 262.32/56.75 | | | | | | % 262.32/56.75 | | | | | | GROUND_INST: instantiating (28) with all_74_14, n2, simplifying with % 262.32/56.75 | | | | | | (8), (26), (48) gives: % 262.32/56.75 | | | | | | (49) all_74_14 = n2 | gt(n2, all_74_14) % 262.32/56.75 | | | | | | % 262.32/56.75 | | | | | | BETA: splitting (49) gives: % 262.32/56.75 | | | | | | % 262.32/56.75 | | | | | | Case 1: % 262.32/56.75 | | | | | | | % 262.32/56.75 | | | | | | | (50) gt(n2, all_74_14) % 262.32/56.75 | | | | | | | % 262.32/56.75 | | | | | | | GROUND_INST: instantiating (21) with all_74_14, n2, n1, % 262.32/56.75 | | | | | | | simplifying with (5), (8), (26), (50) gives: % 262.32/56.75 | | | | | | | (51) leq(all_74_14, n1) % 262.32/56.75 | | | | | | | % 262.32/56.75 | | | | | | | GROUND_INST: instantiating (3) with all_74_14, simplifying with % 262.32/56.75 | | | | | | | (8), (34), (51) gives: % 262.32/56.75 | | | | | | | (52) all_74_14 = n1 | all_74_14 = n0 % 262.32/56.75 | | | | | | | % 262.32/56.75 | | | | | | | BETA: splitting (52) gives: % 262.32/56.75 | | | | | | | % 262.32/56.75 | | | | | | | Case 1: % 262.32/56.75 | | | | | | | | % 262.32/56.75 | | | | | | | | (53) all_74_14 = n0 % 262.32/56.75 | | | | | | | | % 262.32/56.75 | | | | | | | | REDUCE: (43), (53) imply: % 262.32/56.75 | | | | | | | | (54) $false % 262.32/56.75 | | | | | | | | % 262.32/56.75 | | | | | | | | CLOSE: (54) is inconsistent. % 262.32/56.75 | | | | | | | | % 262.32/56.75 | | | | | | | Case 2: % 262.32/56.75 | | | | | | | | % 262.32/56.75 | | | | | | | | (55) all_74_14 = n1 % 262.32/56.75 | | | | | | | | % 262.32/56.75 | | | | | | | | REDUCE: (31), (55) imply: % 262.32/56.75 | | | | | | | | (56) a_select3(id_ds1_filter, n1, n0) = all_74_12 % 262.32/56.75 | | | | | | | | % 262.32/56.75 | | | | | | | | REDUCE: (32), (55) imply: % 262.32/56.75 | | | | | | | | (57) a_select3(id_ds1_filter, n0, n1) = all_74_13 % 262.32/56.75 | | | | | | | | % 262.32/56.75 | | | | | | | | REDUCE: (8), (55) imply: % 262.32/56.75 | | | | | | | | (58) $i(n1) % 262.32/56.75 | | | | | | | | % 262.32/56.75 | | | | | | | | REDUCE: (7), (55) imply: % 262.32/56.75 | | | | | | | | (59) leq(n1, n5) % 262.32/56.75 | | | | | | | | % 262.32/56.75 | | | | | | | | REDUCE: (34), (55) imply: % 262.32/56.75 | | | | | | | | (60) leq(n0, n1) % 262.32/56.75 | | | | | | | | % 262.32/56.75 | | | | | | | | GROUND_INST: instantiating (12) with n0, n1, all_74_13, % 262.32/56.75 | | | | | | | | simplifying with (33), (35), (57), (58), (60) % 262.32/56.75 | | | | | | | | gives: % 262.32/56.75 | | | | | | | | (61) ~ leq(n1, all_74_20) | ~ leq(n0, pv57) | % 262.32/56.75 | | | | | | | | (a_select3(id_ds1_filter, n1, n0) = all_74_13 & % 262.32/56.75 | | | | | | | | $i(all_74_13)) % 262.32/56.75 | | | | | | | | % 262.32/56.75 | | | | | | | | BETA: splitting (61) gives: % 262.32/56.75 | | | | | | | | % 262.32/56.75 | | | | | | | | Case 1: % 262.32/56.75 | | | | | | | | | % 262.32/56.75 | | | | | | | | | (62) ~ leq(n0, pv57) % 262.32/56.75 | | | | | | | | | % 262.32/56.75 | | | | | | | | | REDUCE: (18), (62) imply: % 262.32/56.75 | | | | | | | | | (63) ~ leq(n0, n0) % 262.32/56.75 | | | | | | | | | % 262.32/56.75 | | | | | | | | | PRED_UNIFY: (35), (63) imply: % 262.32/56.75 | | | | | | | | | (64) $false % 262.32/56.75 | | | | | | | | | % 262.32/56.75 | | | | | | | | | CLOSE: (64) is inconsistent. % 262.32/56.75 | | | | | | | | | % 262.32/56.75 | | | | | | | | Case 2: % 262.32/56.75 | | | | | | | | | % 262.32/56.75 | | | | | | | | | (65) ~ leq(n1, all_74_20) | (a_select3(id_ds1_filter, n1, % 262.32/56.75 | | | | | | | | | n0) = all_74_13 & $i(all_74_13)) % 262.32/56.75 | | | | | | | | | % 262.32/56.75 | | | | | | | | | REF_CLOSE: (19), (23), (25), (56), (59), (65) are inconsistent % 262.32/56.75 | | | | | | | | | by sub-proof #15. % 262.32/56.75 | | | | | | | | | % 262.32/56.75 | | | | | | | | End of split % 262.32/56.75 | | | | | | | | % 262.32/56.75 | | | | | | | End of split % 262.32/56.75 | | | | | | | % 262.32/56.75 | | | | | | Case 2: % 262.32/56.75 | | | | | | | % 262.32/56.75 | | | | | | | (66) all_74_14 = n2 % 262.32/56.75 | | | | | | | % 262.32/56.75 | | | | | | | REDUCE: (31), (66) imply: % 262.32/56.75 | | | | | | | (67) a_select3(id_ds1_filter, n2, n0) = all_74_12 % 262.32/56.75 | | | | | | | % 262.32/56.75 | | | | | | | REDUCE: (32), (66) imply: % 262.32/56.75 | | | | | | | (68) a_select3(id_ds1_filter, n0, n2) = all_74_13 % 262.32/56.75 | | | | | | | % 262.32/56.75 | | | | | | | REDUCE: (7), (66) imply: % 262.32/56.75 | | | | | | | (69) leq(n2, n5) % 262.32/56.75 | | | | | | | % 262.32/56.75 | | | | | | | REDUCE: (34), (66) imply: % 262.32/56.75 | | | | | | | (70) leq(n0, n2) % 262.32/56.75 | | | | | | | % 262.32/56.75 | | | | | | | GROUND_INST: instantiating (12) with n0, n2, all_74_13, % 262.32/56.75 | | | | | | | simplifying with (26), (33), (35), (68), (70) gives: % 262.32/56.75 | | | | | | | (71) ~ leq(n2, all_74_20) | ~ leq(n0, pv57) | % 262.32/56.75 | | | | | | | (a_select3(id_ds1_filter, n2, n0) = all_74_13 & % 262.32/56.75 | | | | | | | $i(all_74_13)) % 262.32/56.75 | | | | | | | % 262.32/56.75 | | | | | | | BETA: splitting (71) gives: % 262.32/56.75 | | | | | | | % 262.32/56.75 | | | | | | | Case 1: % 262.32/56.75 | | | | | | | | % 262.32/56.75 | | | | | | | | (72) ~ leq(n0, pv57) % 262.32/56.75 | | | | | | | | % 262.32/56.75 | | | | | | | | REDUCE: (18), (72) imply: % 262.32/56.75 | | | | | | | | (73) ~ leq(n0, n0) % 262.32/56.75 | | | | | | | | % 262.32/56.75 | | | | | | | | PRED_UNIFY: (35), (73) imply: % 262.32/56.75 | | | | | | | | (74) $false % 262.32/56.75 | | | | | | | | % 262.32/56.75 | | | | | | | | CLOSE: (74) is inconsistent. % 262.32/56.75 | | | | | | | | % 262.32/56.75 | | | | | | | Case 2: % 262.32/56.75 | | | | | | | | % 262.32/56.75 | | | | | | | | (75) ~ leq(n2, all_74_20) | (a_select3(id_ds1_filter, n2, % 262.32/56.75 | | | | | | | | n0) = all_74_13 & $i(all_74_13)) % 262.32/56.75 | | | | | | | | % 262.32/56.75 | | | | | | | | REF_CLOSE: (19), (23), (25), (67), (69), (75) are inconsistent % 262.32/56.75 | | | | | | | | by sub-proof #13. % 262.32/56.75 | | | | | | | | % 262.32/56.75 | | | | | | | End of split % 262.32/56.75 | | | | | | | % 262.32/56.75 | | | | | | End of split % 262.32/56.75 | | | | | | % 262.32/56.75 | | | | | Case 2: % 262.32/56.75 | | | | | | % 262.32/56.75 | | | | | | (76) all_74_14 = n3 % 262.32/56.75 | | | | | | % 262.32/56.75 | | | | | | REDUCE: (31), (76) imply: % 262.32/56.75 | | | | | | (77) a_select3(id_ds1_filter, n3, n0) = all_74_12 % 262.32/56.75 | | | | | | % 262.32/56.75 | | | | | | REDUCE: (32), (76) imply: % 262.32/56.75 | | | | | | (78) a_select3(id_ds1_filter, n0, n3) = all_74_13 % 262.32/56.75 | | | | | | % 262.32/56.75 | | | | | | REDUCE: (7), (76) imply: % 262.32/56.75 | | | | | | (79) leq(n3, n5) % 262.32/56.75 | | | | | | % 262.32/56.75 | | | | | | REDUCE: (34), (76) imply: % 262.32/56.75 | | | | | | (80) leq(n0, n3) % 262.32/56.75 | | | | | | % 262.32/56.75 | | | | | | GROUND_INST: instantiating (12) with n0, n3, all_74_13, simplifying % 262.32/56.75 | | | | | | with (1), (33), (35), (78), (80) gives: % 262.32/56.75 | | | | | | (81) ~ leq(n3, all_74_20) | ~ leq(n0, pv57) | % 262.32/56.75 | | | | | | (a_select3(id_ds1_filter, n3, n0) = all_74_13 & % 262.32/56.75 | | | | | | $i(all_74_13)) % 262.32/56.75 | | | | | | % 262.32/56.75 | | | | | | BETA: splitting (81) gives: % 262.32/56.75 | | | | | | % 262.32/56.75 | | | | | | Case 1: % 262.32/56.75 | | | | | | | % 262.32/56.75 | | | | | | | (82) ~ leq(n0, pv57) % 262.32/56.75 | | | | | | | % 262.32/56.75 | | | | | | | REDUCE: (18), (82) imply: % 262.32/56.75 | | | | | | | (83) ~ leq(n0, n0) % 262.32/56.75 | | | | | | | % 262.32/56.75 | | | | | | | PRED_UNIFY: (35), (83) imply: % 262.32/56.75 | | | | | | | (84) $false % 262.32/56.75 | | | | | | | % 262.32/56.75 | | | | | | | CLOSE: (84) is inconsistent. % 262.32/56.75 | | | | | | | % 262.32/56.75 | | | | | | Case 2: % 262.32/56.75 | | | | | | | % 262.32/56.75 | | | | | | | (85) ~ leq(n3, all_74_20) | (a_select3(id_ds1_filter, n3, n0) % 262.32/56.75 | | | | | | | = all_74_13 & $i(all_74_13)) % 262.32/56.75 | | | | | | | % 262.32/56.75 | | | | | | | REF_CLOSE: (19), (23), (25), (77), (79), (85) are inconsistent by % 262.32/56.75 | | | | | | | sub-proof #11. % 262.32/56.75 | | | | | | | % 262.32/56.75 | | | | | | End of split % 262.32/56.75 | | | | | | % 262.32/56.75 | | | | | End of split % 262.32/56.75 | | | | | % 262.32/56.75 | | | | Case 2: % 262.32/56.75 | | | | | % 262.32/56.75 | | | | | (86) all_74_14 = n4 % 262.32/56.75 | | | | | % 262.32/56.75 | | | | | REDUCE: (31), (86) imply: % 262.32/56.75 | | | | | (87) a_select3(id_ds1_filter, n4, n0) = all_74_12 % 262.32/56.75 | | | | | % 262.32/56.75 | | | | | REDUCE: (32), (86) imply: % 262.32/56.75 | | | | | (88) a_select3(id_ds1_filter, n0, n4) = all_74_13 % 262.32/56.75 | | | | | % 262.32/56.75 | | | | | REDUCE: (7), (86) imply: % 262.32/56.75 | | | | | (89) leq(n4, n5) % 262.32/56.75 | | | | | % 262.32/56.75 | | | | | REDUCE: (34), (86) imply: % 262.32/56.75 | | | | | (90) leq(n0, n4) % 262.32/56.75 | | | | | % 262.32/56.75 | | | | | GROUND_INST: instantiating (12) with n0, n4, all_74_13, simplifying % 262.32/56.75 | | | | | with (2), (33), (35), (88), (90) gives: % 262.32/56.75 | | | | | (91) ~ leq(n4, all_74_20) | ~ leq(n0, pv57) | % 262.32/56.75 | | | | | (a_select3(id_ds1_filter, n4, n0) = all_74_13 & $i(all_74_13)) % 262.32/56.75 | | | | | % 262.32/56.75 | | | | | BETA: splitting (91) gives: % 262.32/56.75 | | | | | % 262.32/56.75 | | | | | Case 1: % 262.32/56.75 | | | | | | % 262.32/56.75 | | | | | | (92) ~ leq(n0, pv57) % 262.32/56.75 | | | | | | % 262.32/56.75 | | | | | | REDUCE: (18), (92) imply: % 262.32/56.75 | | | | | | (93) ~ leq(n0, n0) % 262.32/56.75 | | | | | | % 262.32/56.75 | | | | | | PRED_UNIFY: (35), (93) imply: % 262.32/56.75 | | | | | | (94) $false % 262.32/56.75 | | | | | | % 262.32/56.75 | | | | | | CLOSE: (94) is inconsistent. % 262.32/56.75 | | | | | | % 262.32/56.75 | | | | | Case 2: % 262.32/56.75 | | | | | | % 262.32/56.75 | | | | | | (95) ~ leq(n4, all_74_20) | (a_select3(id_ds1_filter, n4, n0) = % 262.32/56.75 | | | | | | all_74_13 & $i(all_74_13)) % 262.32/56.75 | | | | | | % 262.32/56.75 | | | | | | REF_CLOSE: (19), (23), (25), (87), (89), (95) are inconsistent by % 262.32/56.75 | | | | | | sub-proof #9. % 262.32/56.75 | | | | | | % 262.32/56.75 | | | | | End of split % 262.32/56.75 | | | | | % 262.32/56.75 | | | | End of split % 262.32/56.75 | | | | % 262.32/56.75 | | | End of split % 262.32/56.75 | | | % 262.32/56.75 | | Case 2: % 262.32/56.75 | | | % 262.32/56.75 | | | (96) all_74_14 = n5 % 262.32/56.75 | | | % 262.32/56.75 | | | REDUCE: (31), (96) imply: % 262.32/56.75 | | | (97) a_select3(id_ds1_filter, n5, n0) = all_74_12 % 262.32/56.75 | | | % 262.32/56.75 | | | REDUCE: (32), (96) imply: % 262.32/56.75 | | | (98) a_select3(id_ds1_filter, n0, n5) = all_74_13 % 262.32/56.75 | | | % 262.32/56.75 | | | REDUCE: (7), (96) imply: % 262.32/56.75 | | | (99) leq(n5, n5) % 262.32/56.75 | | | % 262.32/56.75 | | | REDUCE: (34), (96) imply: % 262.32/56.75 | | | (100) leq(n0, n5) % 262.32/56.75 | | | % 262.32/56.75 | | | GROUND_INST: instantiating (12) with n0, n5, all_74_13, simplifying with % 262.32/56.75 | | | (27), (33), (35), (98), (100) gives: % 262.32/56.75 | | | (101) ~ leq(n5, all_74_20) | ~ leq(n0, pv57) | % 262.32/56.75 | | | (a_select3(id_ds1_filter, n5, n0) = all_74_13 & $i(all_74_13)) % 262.32/56.75 | | | % 262.32/56.75 | | | BETA: splitting (101) gives: % 262.32/56.75 | | | % 262.32/56.75 | | | Case 1: % 262.32/56.75 | | | | % 262.32/56.75 | | | | (102) ~ leq(n0, pv57) % 262.32/56.75 | | | | % 262.32/56.75 | | | | REDUCE: (18), (102) imply: % 262.32/56.75 | | | | (103) ~ leq(n0, n0) % 262.32/56.75 | | | | % 262.32/56.75 | | | | PRED_UNIFY: (35), (103) imply: % 262.32/56.75 | | | | (104) $false % 262.32/56.75 | | | | % 262.32/56.75 | | | | CLOSE: (104) is inconsistent. % 262.32/56.75 | | | | % 262.32/56.75 | | | Case 2: % 262.32/56.75 | | | | % 262.32/56.75 | | | | (105) ~ leq(n5, all_74_20) | (a_select3(id_ds1_filter, n5, n0) = % 262.32/56.75 | | | | all_74_13 & $i(all_74_13)) % 262.32/56.75 | | | | % 262.32/56.75 | | | | REF_CLOSE: (19), (23), (25), (97), (99), (105) are inconsistent by % 262.32/56.75 | | | | sub-proof #7. % 262.32/56.75 | | | | % 262.32/56.75 | | | End of split % 262.32/56.75 | | | % 262.32/56.75 | | End of split % 262.32/56.75 | | % 262.32/56.75 | Case 2: % 262.32/56.75 | | % 262.32/56.75 | | (106) all_74_14 = n0 % 262.32/56.75 | | % 262.32/56.75 | | REDUCE: (31), (106) imply: % 262.32/56.75 | | (107) a_select3(id_ds1_filter, n0, n0) = all_74_12 % 262.32/56.75 | | % 262.32/56.75 | | REDUCE: (32), (106) imply: % 262.32/56.75 | | (108) a_select3(id_ds1_filter, n0, n0) = all_74_13 % 262.32/56.75 | | % 262.32/56.75 | | GROUND_INST: instantiating (19) with all_74_13, all_74_12, n0, n0, % 262.32/56.75 | | id_ds1_filter, simplifying with (107), (108) gives: % 262.32/56.75 | | (109) all_74_12 = all_74_13 % 262.32/56.75 | | % 262.32/56.75 | | REDUCE: (23), (109) imply: % 262.32/56.75 | | (110) $false % 262.32/56.75 | | % 262.32/56.75 | | CLOSE: (110) is inconsistent. % 262.32/56.75 | | % 262.32/56.75 | End of split % 262.32/56.75 | % 262.32/56.75 End of proof % 262.32/56.75 % 262.32/56.75 Sub-proof #2 shows that the following formulas are inconsistent: % 262.32/56.75 ---------------------------------------------------------------- % 262.32/56.75 (1) a_select3(id_ds1_filter, n0, all_74_15) = all_74_12 % 262.32/56.75 (2) a_select3(id_ds1_filter, all_74_15, n0) = all_74_13 % 262.32/56.75 (3) all_74_15 = n0 % 262.32/56.75 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 262.32/56.75 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 262.32/56.75 v0)) % 262.32/56.75 (5) ~ (all_74_12 = all_74_13) % 262.32/56.75 % 262.32/56.75 Begin of proof % 262.32/56.75 | % 262.32/56.75 | REDUCE: (2), (3) imply: % 262.32/56.75 | (6) a_select3(id_ds1_filter, n0, n0) = all_74_13 % 262.32/56.75 | % 262.32/56.75 | REDUCE: (1), (3) imply: % 262.32/56.75 | (7) a_select3(id_ds1_filter, n0, n0) = all_74_12 % 262.32/56.75 | % 262.32/56.75 | GROUND_INST: instantiating (4) with all_74_13, all_74_12, n0, n0, % 262.32/56.75 | id_ds1_filter, simplifying with (6), (7) gives: % 262.32/56.75 | (8) all_74_12 = all_74_13 % 262.32/56.75 | % 262.32/56.75 | REDUCE: (5), (8) imply: % 262.32/56.75 | (9) $false % 262.32/56.75 | % 262.32/56.75 | CLOSE: (9) is inconsistent. % 262.32/56.75 | % 262.32/56.75 End of proof % 262.32/56.75 % 262.32/56.75 Sub-proof #3 shows that the following formulas are inconsistent: % 262.32/56.75 ---------------------------------------------------------------- % 262.32/56.75 (1) ~ leq(n3, all_74_20) | (a_select3(id_ds1_filter, n3, n0) = all_74_12 & % 262.32/56.75 $i(all_74_12)) % 262.32/56.76 (2) leq(n3, n5) % 262.32/56.76 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 262.32/56.76 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 262.32/56.76 v0)) % 262.32/56.76 (4) ~ (all_74_12 = all_74_13) % 262.32/56.76 (5) all_74_20 = n5 % 262.32/56.76 (6) a_select3(id_ds1_filter, n3, n0) = all_74_13 % 262.32/56.76 % 262.32/56.76 Begin of proof % 262.32/56.76 | % 262.32/56.76 | BETA: splitting (1) gives: % 262.32/56.76 | % 262.32/56.76 | Case 1: % 262.32/56.76 | | % 262.32/56.76 | | (7) ~ leq(n3, all_74_20) % 262.32/56.76 | | % 262.32/56.76 | | REDUCE: (5), (7) imply: % 262.32/56.76 | | (8) ~ leq(n3, n5) % 262.32/56.76 | | % 262.32/56.76 | | PRED_UNIFY: (2), (8) imply: % 262.32/56.76 | | (9) $false % 262.32/56.76 | | % 262.32/56.76 | | CLOSE: (9) is inconsistent. % 262.32/56.76 | | % 262.32/56.76 | Case 2: % 262.32/56.76 | | % 262.32/56.76 | | (10) a_select3(id_ds1_filter, n3, n0) = all_74_12 & $i(all_74_12) % 262.32/56.76 | | % 262.32/56.76 | | ALPHA: (10) implies: % 262.32/56.76 | | (11) a_select3(id_ds1_filter, n3, n0) = all_74_12 % 262.32/56.76 | | % 262.32/56.76 | | REF_CLOSE: (3), (4), (6), (11) are inconsistent by sub-proof #12. % 262.32/56.76 | | % 262.32/56.76 | End of split % 262.32/56.76 | % 262.32/56.76 End of proof % 262.32/56.76 % 262.32/56.76 Sub-proof #4 shows that the following formulas are inconsistent: % 262.32/56.76 ---------------------------------------------------------------- % 262.32/56.76 (1) ~ leq(n2, all_74_20) | (a_select3(id_ds1_filter, n2, n0) = all_74_12 & % 262.32/56.76 $i(all_74_12)) % 262.32/56.76 (2) a_select3(id_ds1_filter, n2, n0) = all_74_13 % 262.32/56.76 (3) leq(n2, n5) % 262.32/56.76 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 262.32/56.76 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 262.32/56.76 v0)) % 262.32/56.76 (5) ~ (all_74_12 = all_74_13) % 262.32/56.76 (6) all_74_20 = n5 % 262.32/56.76 % 262.32/56.76 Begin of proof % 262.32/56.76 | % 262.32/56.76 | BETA: splitting (1) gives: % 262.32/56.76 | % 262.32/56.76 | Case 1: % 262.32/56.76 | | % 262.32/56.76 | | (7) ~ leq(n2, all_74_20) % 262.32/56.76 | | % 262.32/56.76 | | REDUCE: (6), (7) imply: % 262.32/56.76 | | (8) ~ leq(n2, n5) % 262.32/56.76 | | % 262.32/56.76 | | PRED_UNIFY: (3), (8) imply: % 262.32/56.76 | | (9) $false % 262.32/56.76 | | % 262.32/56.76 | | CLOSE: (9) is inconsistent. % 262.32/56.76 | | % 262.32/56.76 | Case 2: % 262.32/56.76 | | % 262.32/56.76 | | (10) a_select3(id_ds1_filter, n2, n0) = all_74_12 & $i(all_74_12) % 262.32/56.76 | | % 262.32/56.76 | | ALPHA: (10) implies: % 262.32/56.76 | | (11) a_select3(id_ds1_filter, n2, n0) = all_74_12 % 262.32/56.76 | | % 262.32/56.76 | | REF_CLOSE: (2), (4), (5), (11) are inconsistent by sub-proof #14. % 262.32/56.76 | | % 262.32/56.76 | End of split % 262.32/56.76 | % 262.32/56.76 End of proof % 262.32/56.76 % 262.32/56.76 Sub-proof #5 shows that the following formulas are inconsistent: % 262.32/56.76 ---------------------------------------------------------------- % 262.32/56.76 (1) a_select3(id_ds1_filter, n1, n0) = all_74_13 % 262.32/56.76 (2) leq(n1, n5) % 262.32/56.76 (3) ~ leq(n1, all_74_20) | (a_select3(id_ds1_filter, n1, n0) = all_74_12 & % 262.32/56.76 $i(all_74_12)) % 262.32/56.76 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 262.32/56.76 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 262.32/56.76 v0)) % 262.32/56.76 (5) ~ (all_74_12 = all_74_13) % 262.32/56.76 (6) all_74_20 = n5 % 262.32/56.76 % 262.32/56.76 Begin of proof % 262.32/56.76 | % 262.32/56.76 | BETA: splitting (3) gives: % 262.32/56.76 | % 262.32/56.76 | Case 1: % 262.32/56.76 | | % 262.32/56.76 | | (7) ~ leq(n1, all_74_20) % 262.32/56.76 | | % 262.32/56.76 | | REDUCE: (6), (7) imply: % 262.32/56.76 | | (8) ~ leq(n1, n5) % 262.32/56.76 | | % 262.32/56.76 | | PRED_UNIFY: (2), (8) imply: % 262.32/56.76 | | (9) $false % 262.32/56.76 | | % 262.32/56.76 | | CLOSE: (9) is inconsistent. % 262.32/56.76 | | % 262.32/56.76 | Case 2: % 262.32/56.76 | | % 262.32/56.76 | | (10) a_select3(id_ds1_filter, n1, n0) = all_74_12 & $i(all_74_12) % 262.32/56.76 | | % 262.32/56.76 | | ALPHA: (10) implies: % 262.32/56.76 | | (11) a_select3(id_ds1_filter, n1, n0) = all_74_12 % 262.32/56.76 | | % 262.32/56.76 | | REF_CLOSE: (1), (4), (5), (11) are inconsistent by sub-proof #16. % 262.32/56.76 | | % 262.32/56.76 | End of split % 262.32/56.76 | % 262.32/56.76 End of proof % 262.32/56.76 % 262.32/56.76 Sub-proof #6 shows that the following formulas are inconsistent: % 262.32/56.76 ---------------------------------------------------------------- % 262.32/56.76 (1) all_74_18 = n0 % 262.32/56.76 (2) a_select3(id_ds1_filter, n5, n0) = all_74_12 % 262.32/56.76 (3) $i(n0) % 262.32/56.76 (4) leq(n0, n5) % 262.32/56.76 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (a_select3(id_ds1_filter, % 262.32/56.76 v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ leq(v1, all_74_20) | ~ % 262.32/56.76 leq(v0, all_74_18) | ~ leq(n0, v1) | ~ leq(n0, v0) | % 262.32/56.76 (a_select3(id_ds1_filter, v1, v0) = v2 & $i(v2))) % 262.32/56.76 (6) a_select3(id_ds1_filter, n0, n5) = all_74_13 % 262.32/56.76 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 262.32/56.76 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 262.32/56.76 v0)) % 262.32/56.76 (8) ~ (all_74_12 = all_74_13) % 262.32/56.76 (9) leq(n5, n5) % 262.32/56.76 (10) all_74_20 = n5 % 262.32/56.76 (11) $i(n5) % 262.32/56.76 (12) leq(n0, n0) % 262.32/56.76 % 262.32/56.76 Begin of proof % 262.32/56.76 | % 262.32/56.76 | GROUND_INST: instantiating (5) with n0, n5, all_74_13, simplifying with (3), % 262.32/56.76 | (4), (6), (11), (12) gives: % 262.32/56.76 | (13) ~ leq(n5, all_74_20) | ~ leq(n0, all_74_18) | % 262.32/56.76 | (a_select3(id_ds1_filter, n5, n0) = all_74_13 & $i(all_74_13)) % 262.32/56.76 | % 262.32/56.76 | BETA: splitting (13) gives: % 262.32/56.76 | % 262.32/56.76 | Case 1: % 262.32/56.76 | | % 262.32/56.76 | | (14) ~ leq(n0, all_74_18) % 262.32/56.76 | | % 262.32/56.76 | | REDUCE: (1), (14) imply: % 262.32/56.76 | | (15) ~ leq(n0, n0) % 262.32/56.76 | | % 262.32/56.76 | | PRED_UNIFY: (12), (15) imply: % 262.32/56.76 | | (16) $false % 262.32/56.76 | | % 262.32/56.76 | | CLOSE: (16) is inconsistent. % 262.32/56.76 | | % 262.32/56.76 | Case 2: % 262.32/56.76 | | % 262.32/56.76 | | (17) ~ leq(n5, all_74_20) | (a_select3(id_ds1_filter, n5, n0) = % 262.32/56.76 | | all_74_13 & $i(all_74_13)) % 262.32/56.76 | | % 262.32/56.76 | | REF_CLOSE: (2), (7), (8), (9), (10), (17) are inconsistent by sub-proof #7. % 262.32/56.76 | | % 262.32/56.76 | End of split % 262.32/56.76 | % 262.32/56.76 End of proof % 262.32/56.76 % 262.32/56.76 Sub-proof #7 shows that the following formulas are inconsistent: % 262.32/56.76 ---------------------------------------------------------------- % 262.32/56.76 (1) ~ leq(n5, all_74_20) | (a_select3(id_ds1_filter, n5, n0) = all_74_13 & % 262.32/56.76 $i(all_74_13)) % 262.32/56.76 (2) a_select3(id_ds1_filter, n5, n0) = all_74_12 % 262.32/56.76 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 262.32/56.76 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 262.32/56.76 v0)) % 262.32/56.76 (4) ~ (all_74_12 = all_74_13) % 262.32/56.76 (5) leq(n5, n5) % 262.32/56.76 (6) all_74_20 = n5 % 262.32/56.76 % 262.32/56.76 Begin of proof % 262.32/56.76 | % 262.32/56.76 | BETA: splitting (1) gives: % 262.32/56.76 | % 262.32/56.76 | Case 1: % 262.32/56.76 | | % 262.32/56.76 | | (7) ~ leq(n5, all_74_20) % 262.32/56.76 | | % 262.32/56.76 | | REDUCE: (6), (7) imply: % 262.32/56.76 | | (8) ~ leq(n5, n5) % 262.32/56.76 | | % 262.32/56.76 | | PRED_UNIFY: (5), (8) imply: % 262.32/56.76 | | (9) $false % 262.32/56.76 | | % 262.32/56.76 | | CLOSE: (9) is inconsistent. % 262.32/56.76 | | % 262.32/56.76 | Case 2: % 262.32/56.76 | | % 262.32/56.76 | | (10) a_select3(id_ds1_filter, n5, n0) = all_74_13 & $i(all_74_13) % 262.32/56.76 | | % 262.32/56.76 | | ALPHA: (10) implies: % 262.32/56.76 | | (11) a_select3(id_ds1_filter, n5, n0) = all_74_13 % 262.32/56.76 | | % 262.32/56.76 | | GROUND_INST: instantiating (3) with all_74_12, all_74_13, n0, n5, % 262.32/56.76 | | id_ds1_filter, simplifying with (2), (11) gives: % 262.32/56.76 | | (12) all_74_12 = all_74_13 % 262.32/56.76 | | % 262.32/56.76 | | REDUCE: (4), (12) imply: % 262.32/56.76 | | (13) $false % 262.32/56.76 | | % 262.32/56.76 | | CLOSE: (13) is inconsistent. % 262.32/56.76 | | % 262.32/56.76 | End of split % 262.32/56.76 | % 262.32/56.76 End of proof % 262.32/56.76 % 262.32/56.76 Sub-proof #8 shows that the following formulas are inconsistent: % 262.32/56.76 ---------------------------------------------------------------- % 262.32/56.76 (1) $i(n4) % 262.32/56.76 (2) leq(n4, n5) % 262.32/56.76 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (a_select3(id_ds1_filter, % 262.32/56.76 v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ leq(v1, all_74_20) | ~ % 262.32/56.76 leq(v0, pv57) | ~ leq(n0, v1) | ~ leq(n0, v0) | % 262.32/56.76 (a_select3(id_ds1_filter, v1, v0) = v2 & $i(v2))) % 262.32/56.76 (4) pv57 = n4 % 262.32/56.76 (5) $i(n0) % 262.32/56.76 (6) a_select3(id_ds1_filter, n4, n0) = all_74_12 % 262.32/56.76 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 262.32/56.76 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 262.32/56.76 v0)) % 262.32/56.76 (8) a_select3(id_ds1_filter, n0, n4) = all_74_13 % 262.32/56.76 (9) ~ (all_74_12 = all_74_13) % 262.32/56.76 (10) all_74_20 = n5 % 262.32/56.76 (11) leq(n0, n0) % 262.32/56.76 (12) leq(n0, n4) % 262.32/56.76 % 262.32/56.76 Begin of proof % 262.32/56.76 | % 262.32/56.76 | GROUND_INST: instantiating (3) with n0, n4, all_74_13, simplifying with (1), % 262.32/56.76 | (5), (8), (11), (12) gives: % 262.32/56.76 | (13) ~ leq(n4, all_74_20) | ~ leq(n0, pv57) | (a_select3(id_ds1_filter, % 262.32/56.76 | n4, n0) = all_74_13 & $i(all_74_13)) % 262.32/56.76 | % 262.32/56.76 | BETA: splitting (13) gives: % 262.32/56.76 | % 262.32/56.76 | Case 1: % 262.32/56.76 | | % 262.32/56.76 | | (14) ~ leq(n0, pv57) % 262.32/56.76 | | % 262.32/56.76 | | REDUCE: (4), (14) imply: % 262.32/56.76 | | (15) ~ leq(n0, n4) % 262.32/56.76 | | % 262.32/56.76 | | PRED_UNIFY: (12), (15) imply: % 262.32/56.76 | | (16) $false % 262.32/56.76 | | % 262.32/56.76 | | CLOSE: (16) is inconsistent. % 262.32/56.76 | | % 262.32/56.76 | Case 2: % 262.32/56.76 | | % 262.32/56.76 | | (17) ~ leq(n4, all_74_20) | (a_select3(id_ds1_filter, n4, n0) = % 262.32/56.76 | | all_74_13 & $i(all_74_13)) % 262.32/56.76 | | % 262.32/56.76 | | REF_CLOSE: (2), (6), (7), (9), (10), (17) are inconsistent by sub-proof #9. % 262.32/56.76 | | % 262.32/56.76 | End of split % 262.32/56.76 | % 262.32/56.76 End of proof % 262.32/56.76 % 262.32/56.76 Sub-proof #9 shows that the following formulas are inconsistent: % 262.32/56.76 ---------------------------------------------------------------- % 262.32/56.76 (1) leq(n4, n5) % 262.32/56.76 (2) ~ leq(n4, all_74_20) | (a_select3(id_ds1_filter, n4, n0) = all_74_13 & % 262.32/56.76 $i(all_74_13)) % 262.32/56.76 (3) a_select3(id_ds1_filter, n4, n0) = all_74_12 % 262.32/56.76 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 262.32/56.76 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 262.32/56.76 v0)) % 262.32/56.76 (5) ~ (all_74_12 = all_74_13) % 262.32/56.76 (6) all_74_20 = n5 % 262.32/56.76 % 262.32/56.76 Begin of proof % 262.32/56.76 | % 262.32/56.76 | BETA: splitting (2) gives: % 262.32/56.76 | % 262.32/56.76 | Case 1: % 262.32/56.76 | | % 262.32/56.76 | | (7) ~ leq(n4, all_74_20) % 262.32/56.76 | | % 262.32/56.76 | | REDUCE: (6), (7) imply: % 262.32/56.76 | | (8) ~ leq(n4, n5) % 262.32/56.76 | | % 262.32/56.76 | | PRED_UNIFY: (1), (8) imply: % 262.32/56.76 | | (9) $false % 262.32/56.76 | | % 262.32/56.76 | | CLOSE: (9) is inconsistent. % 262.32/56.76 | | % 262.32/56.76 | Case 2: % 262.32/56.76 | | % 262.32/56.76 | | (10) a_select3(id_ds1_filter, n4, n0) = all_74_13 & $i(all_74_13) % 262.32/56.76 | | % 262.32/56.76 | | ALPHA: (10) implies: % 262.32/56.76 | | (11) a_select3(id_ds1_filter, n4, n0) = all_74_13 % 262.32/56.76 | | % 262.32/56.77 | | REF_CLOSE: (3), (4), (5), (11) are inconsistent by sub-proof #10. % 262.32/56.77 | | % 262.32/56.77 | End of split % 262.32/56.77 | % 262.32/56.77 End of proof % 262.32/56.77 % 262.32/56.77 Sub-proof #10 shows that the following formulas are inconsistent: % 262.32/56.77 ---------------------------------------------------------------- % 262.32/56.77 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 262.32/56.77 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 262.32/56.77 v0)) % 262.32/56.77 (2) a_select3(id_ds1_filter, n4, n0) = all_74_12 % 262.32/56.77 (3) a_select3(id_ds1_filter, n4, n0) = all_74_13 % 262.32/56.77 (4) ~ (all_74_12 = all_74_13) % 262.32/56.77 % 262.32/56.77 Begin of proof % 262.32/56.77 | % 262.32/56.77 | GROUND_INST: instantiating (1) with all_74_12, all_74_13, n0, n4, % 262.32/56.77 | id_ds1_filter, simplifying with (2), (3) gives: % 262.32/56.77 | (5) all_74_12 = all_74_13 % 262.32/56.77 | % 262.32/56.77 | REDUCE: (4), (5) imply: % 262.32/56.77 | (6) $false % 262.32/56.77 | % 262.32/56.77 | CLOSE: (6) is inconsistent. % 262.32/56.77 | % 262.32/56.77 End of proof % 262.32/56.77 % 262.32/56.77 Sub-proof #11 shows that the following formulas are inconsistent: % 262.32/56.77 ---------------------------------------------------------------- % 262.32/56.77 (1) a_select3(id_ds1_filter, n3, n0) = all_74_12 % 262.32/56.77 (2) ~ leq(n3, all_74_20) | (a_select3(id_ds1_filter, n3, n0) = all_74_13 & % 262.32/56.77 $i(all_74_13)) % 262.32/56.77 (3) leq(n3, n5) % 262.32/56.77 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 262.32/56.77 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 262.32/56.77 v0)) % 262.32/56.77 (5) ~ (all_74_12 = all_74_13) % 262.32/56.77 (6) all_74_20 = n5 % 262.32/56.77 % 262.32/56.77 Begin of proof % 262.32/56.77 | % 262.32/56.77 | BETA: splitting (2) gives: % 262.32/56.77 | % 262.32/56.77 | Case 1: % 262.32/56.77 | | % 262.32/56.77 | | (7) ~ leq(n3, all_74_20) % 262.32/56.77 | | % 262.32/56.77 | | REDUCE: (6), (7) imply: % 262.32/56.77 | | (8) ~ leq(n3, n5) % 262.32/56.77 | | % 262.32/56.77 | | PRED_UNIFY: (3), (8) imply: % 262.32/56.77 | | (9) $false % 262.32/56.77 | | % 262.32/56.77 | | CLOSE: (9) is inconsistent. % 262.32/56.77 | | % 262.32/56.77 | Case 2: % 262.32/56.77 | | % 262.32/56.77 | | (10) a_select3(id_ds1_filter, n3, n0) = all_74_13 & $i(all_74_13) % 262.32/56.77 | | % 262.32/56.77 | | ALPHA: (10) implies: % 262.32/56.77 | | (11) a_select3(id_ds1_filter, n3, n0) = all_74_13 % 262.32/56.77 | | % 262.32/56.77 | | REF_CLOSE: (1), (4), (5), (11) are inconsistent by sub-proof #12. % 262.32/56.77 | | % 262.32/56.77 | End of split % 262.32/56.77 | % 262.32/56.77 End of proof % 262.32/56.77 % 262.32/56.77 Sub-proof #12 shows that the following formulas are inconsistent: % 262.32/56.77 ---------------------------------------------------------------- % 262.32/56.77 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 262.32/56.77 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 262.32/56.77 v0)) % 262.32/56.77 (2) a_select3(id_ds1_filter, n3, n0) = all_74_12 % 262.32/56.77 (3) a_select3(id_ds1_filter, n3, n0) = all_74_13 % 262.32/56.77 (4) ~ (all_74_12 = all_74_13) % 262.32/56.77 % 262.32/56.77 Begin of proof % 262.32/56.77 | % 262.32/56.77 | GROUND_INST: instantiating (1) with all_74_12, all_74_13, n0, n3, % 262.32/56.77 | id_ds1_filter, simplifying with (2), (3) gives: % 262.32/56.77 | (5) all_74_12 = all_74_13 % 262.32/56.77 | % 262.32/56.77 | REDUCE: (4), (5) imply: % 262.32/56.77 | (6) $false % 262.32/56.77 | % 262.32/56.77 | CLOSE: (6) is inconsistent. % 262.32/56.77 | % 262.32/56.77 End of proof % 262.32/56.77 % 262.32/56.77 Sub-proof #13 shows that the following formulas are inconsistent: % 262.32/56.77 ---------------------------------------------------------------- % 262.32/56.77 (1) ~ leq(n2, all_74_20) | (a_select3(id_ds1_filter, n2, n0) = all_74_13 & % 262.32/56.77 $i(all_74_13)) % 262.32/56.77 (2) leq(n2, n5) % 262.32/56.77 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 262.32/56.77 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 262.32/56.77 v0)) % 262.32/56.77 (4) ~ (all_74_12 = all_74_13) % 262.32/56.77 (5) all_74_20 = n5 % 262.32/56.77 (6) a_select3(id_ds1_filter, n2, n0) = all_74_12 % 262.32/56.77 % 262.32/56.77 Begin of proof % 262.32/56.77 | % 262.32/56.77 | BETA: splitting (1) gives: % 262.32/56.77 | % 262.32/56.77 | Case 1: % 262.32/56.77 | | % 262.32/56.77 | | (7) ~ leq(n2, all_74_20) % 262.32/56.77 | | % 262.32/56.77 | | REDUCE: (5), (7) imply: % 262.32/56.77 | | (8) ~ leq(n2, n5) % 262.32/56.77 | | % 262.32/56.77 | | PRED_UNIFY: (2), (8) imply: % 262.32/56.77 | | (9) $false % 262.32/56.77 | | % 262.32/56.77 | | CLOSE: (9) is inconsistent. % 262.32/56.77 | | % 262.32/56.77 | Case 2: % 262.32/56.77 | | % 262.32/56.77 | | (10) a_select3(id_ds1_filter, n2, n0) = all_74_13 & $i(all_74_13) % 262.32/56.77 | | % 262.32/56.77 | | ALPHA: (10) implies: % 262.32/56.77 | | (11) a_select3(id_ds1_filter, n2, n0) = all_74_13 % 262.32/56.77 | | % 262.32/56.77 | | REF_CLOSE: (3), (4), (6), (11) are inconsistent by sub-proof #14. % 262.32/56.77 | | % 262.32/56.77 | End of split % 262.32/56.77 | % 262.32/56.77 End of proof % 262.32/56.77 % 262.32/56.77 Sub-proof #14 shows that the following formulas are inconsistent: % 262.32/56.77 ---------------------------------------------------------------- % 262.32/56.77 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 262.32/56.77 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 262.32/56.77 v0)) % 262.32/56.77 (2) a_select3(id_ds1_filter, n2, n0) = all_74_12 % 262.32/56.77 (3) a_select3(id_ds1_filter, n2, n0) = all_74_13 % 262.32/56.77 (4) ~ (all_74_12 = all_74_13) % 262.32/56.77 % 262.32/56.77 Begin of proof % 262.32/56.77 | % 262.32/56.77 | GROUND_INST: instantiating (1) with all_74_12, all_74_13, n0, n2, % 262.32/56.77 | id_ds1_filter, simplifying with (2), (3) gives: % 262.32/56.77 | (5) all_74_12 = all_74_13 % 262.32/56.77 | % 262.32/56.77 | REDUCE: (4), (5) imply: % 262.32/56.77 | (6) $false % 262.32/56.77 | % 262.32/56.77 | CLOSE: (6) is inconsistent. % 262.32/56.77 | % 262.32/56.77 End of proof % 262.32/56.77 % 262.32/56.77 Sub-proof #15 shows that the following formulas are inconsistent: % 262.32/56.77 ---------------------------------------------------------------- % 262.32/56.77 (1) leq(n1, n5) % 262.32/56.77 (2) a_select3(id_ds1_filter, n1, n0) = all_74_12 % 262.32/56.77 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 262.32/56.77 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 262.32/56.77 v0)) % 262.32/56.77 (4) ~ (all_74_12 = all_74_13) % 262.32/56.77 (5) all_74_20 = n5 % 262.32/56.77 (6) ~ leq(n1, all_74_20) | (a_select3(id_ds1_filter, n1, n0) = all_74_13 & % 262.32/56.77 $i(all_74_13)) % 262.32/56.77 % 262.32/56.77 Begin of proof % 262.32/56.77 | % 262.32/56.77 | BETA: splitting (6) gives: % 262.32/56.77 | % 262.32/56.77 | Case 1: % 262.32/56.77 | | % 262.32/56.77 | | (7) ~ leq(n1, all_74_20) % 262.32/56.77 | | % 262.32/56.77 | | REDUCE: (5), (7) imply: % 262.32/56.77 | | (8) ~ leq(n1, n5) % 262.32/56.77 | | % 262.32/56.77 | | PRED_UNIFY: (1), (8) imply: % 262.32/56.77 | | (9) $false % 262.32/56.77 | | % 262.32/56.77 | | CLOSE: (9) is inconsistent. % 262.32/56.77 | | % 262.32/56.77 | Case 2: % 262.32/56.77 | | % 262.32/56.77 | | (10) a_select3(id_ds1_filter, n1, n0) = all_74_13 & $i(all_74_13) % 262.32/56.77 | | % 262.32/56.77 | | ALPHA: (10) implies: % 262.32/56.77 | | (11) a_select3(id_ds1_filter, n1, n0) = all_74_13 % 262.32/56.77 | | % 262.32/56.77 | | REF_CLOSE: (2), (3), (4), (11) are inconsistent by sub-proof #16. % 262.32/56.77 | | % 262.32/56.77 | End of split % 262.32/56.77 | % 262.32/56.77 End of proof % 262.32/56.77 % 262.32/56.77 Sub-proof #16 shows that the following formulas are inconsistent: % 262.32/56.77 ---------------------------------------------------------------- % 262.32/56.77 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 262.32/56.77 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 262.32/56.77 v0)) % 262.32/56.77 (2) a_select3(id_ds1_filter, n1, n0) = all_74_12 % 262.32/56.77 (3) a_select3(id_ds1_filter, n1, n0) = all_74_13 % 262.32/56.77 (4) ~ (all_74_12 = all_74_13) % 262.32/56.77 % 262.32/56.77 Begin of proof % 262.32/56.77 | % 262.32/56.77 | GROUND_INST: instantiating (1) with all_74_12, all_74_13, n0, n1, % 262.32/56.77 | id_ds1_filter, simplifying with (2), (3) gives: % 262.32/56.77 | (5) all_74_12 = all_74_13 % 262.32/56.77 | % 262.32/56.77 | REDUCE: (4), (5) imply: % 262.32/56.77 | (6) $false % 262.32/56.77 | % 262.32/56.77 | CLOSE: (6) is inconsistent. % 262.32/56.77 | % 262.32/56.77 End of proof % 262.32/56.77 % 262.32/56.77 Sub-proof #17 shows that the following formulas are inconsistent: % 262.32/56.77 ---------------------------------------------------------------- % 262.32/56.77 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 262.32/56.77 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 262.32/56.77 v0)) % 262.32/56.77 (2) a_select3(id_ds1_filter, n5, n4) = all_74_12 % 262.32/56.77 (3) a_select3(id_ds1_filter, n5, n4) = all_74_13 % 262.32/56.77 (4) ~ (all_74_12 = all_74_13) % 262.32/56.77 % 262.32/56.77 Begin of proof % 262.32/56.77 | % 262.32/56.77 | GROUND_INST: instantiating (1) with all_74_12, all_74_13, n4, n5, % 262.32/56.77 | id_ds1_filter, simplifying with (2), (3) gives: % 262.32/56.77 | (5) all_74_12 = all_74_13 % 262.32/56.77 | % 262.32/56.77 | REDUCE: (4), (5) imply: % 262.32/56.77 | (6) $false % 262.32/56.77 | % 262.32/56.77 | CLOSE: (6) is inconsistent. % 262.32/56.77 | % 262.32/56.77 End of proof % 262.32/56.77 % 262.32/56.77 Sub-proof #18 shows that the following formulas are inconsistent: % 262.32/56.77 ---------------------------------------------------------------- % 262.32/56.77 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 262.32/56.77 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 262.32/56.77 v0)) % 262.32/56.77 (2) a_select3(id_ds1_filter, n5, n3) = all_74_12 % 262.32/56.77 (3) a_select3(id_ds1_filter, n5, n3) = all_74_13 % 262.32/56.77 (4) ~ (all_74_12 = all_74_13) % 262.32/56.77 % 262.32/56.77 Begin of proof % 262.32/56.77 | % 262.32/56.77 | GROUND_INST: instantiating (1) with all_74_12, all_74_13, n3, n5, % 262.32/56.77 | id_ds1_filter, simplifying with (2), (3) gives: % 262.32/56.77 | (5) all_74_12 = all_74_13 % 262.32/56.77 | % 262.32/56.77 | REDUCE: (4), (5) imply: % 262.32/56.77 | (6) $false % 262.32/56.77 | % 262.32/56.77 | CLOSE: (6) is inconsistent. % 262.32/56.77 | % 262.32/56.77 End of proof % 262.32/56.77 % 262.32/56.77 Sub-proof #19 shows that the following formulas are inconsistent: % 262.32/56.77 ---------------------------------------------------------------- % 262.32/56.77 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 262.32/56.77 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 262.32/56.77 v0)) % 262.32/56.77 (2) a_select3(id_ds1_filter, n3, n3) = all_74_12 % 262.32/56.77 (3) a_select3(id_ds1_filter, n3, n3) = all_74_13 % 262.32/56.77 (4) ~ (all_74_12 = all_74_13) % 262.32/56.77 % 262.32/56.77 Begin of proof % 262.32/56.77 | % 262.32/56.77 | GROUND_INST: instantiating (1) with all_74_13, all_74_12, n3, n3, % 262.32/56.77 | id_ds1_filter, simplifying with (2), (3) gives: % 262.32/56.77 | (5) all_74_12 = all_74_13 % 262.32/56.77 | % 262.32/56.77 | REDUCE: (4), (5) imply: % 262.32/56.77 | (6) $false % 262.32/56.77 | % 262.32/56.77 | CLOSE: (6) is inconsistent. % 262.32/56.77 | % 262.32/56.77 End of proof % 262.32/56.77 % 262.32/56.77 Sub-proof #20 shows that the following formulas are inconsistent: % 262.32/56.77 ---------------------------------------------------------------- % 262.32/56.77 (1) gt(pv57, n1) % 262.32/56.77 (2) pv57 = n1 % 262.32/56.77 (3) ~ gt(pv57, pv57) % 262.32/56.77 % 262.32/56.77 Begin of proof % 262.32/56.77 | % 262.32/56.77 | REDUCE: (1), (2) imply: % 262.32/56.77 | (4) gt(n1, n1) % 262.32/56.77 | % 262.32/56.77 | REDUCE: (2), (3) imply: % 262.32/56.77 | (5) ~ gt(n1, n1) % 262.32/56.77 | % 262.32/56.77 | PRED_UNIFY: (4), (5) imply: % 262.32/56.77 | (6) $false % 262.32/56.77 | % 262.32/56.77 | CLOSE: (6) is inconsistent. % 262.32/56.77 | % 262.32/56.77 End of proof % 262.32/56.77 % 262.32/56.77 Sub-proof #21 shows that the following formulas are inconsistent: % 262.32/56.77 ---------------------------------------------------------------- % 262.32/56.77 (1) pv57 = n1 % 262.32/56.77 (2) ! [v0: $i] : (v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0, n1) | ~ % 262.32/56.77 leq(n0, v0)) % 262.32/56.77 (3) gt(pv57, all_74_15) % 262.32/56.77 (4) leq(all_74_15, pv57) % 262.32/56.77 (5) $i(all_74_15) % 262.32/56.77 (6) ~ (all_74_15 = n0) % 262.32/56.77 (7) ~ gt(pv57, n1) % 262.32/56.77 (8) leq(n0, all_74_15) % 262.32/56.77 % 262.32/56.77 Begin of proof % 262.32/56.77 | % 262.32/56.77 | REDUCE: (1), (4) imply: % 262.32/56.77 | (9) leq(all_74_15, n1) % 262.32/56.77 | % 262.32/56.77 | REDUCE: (1), (3) imply: % 262.32/56.77 | (10) gt(n1, all_74_15) % 262.32/56.77 | % 262.32/56.77 | REDUCE: (1), (7) imply: % 262.32/56.77 | (11) ~ gt(n1, n1) % 262.32/56.77 | % 262.32/56.77 | REF_CLOSE: (2), (5), (6), (8), (9), (10), (11) are inconsistent by sub-proof % 262.32/56.77 | #32. % 262.32/56.77 | % 262.32/56.77 End of proof % 262.32/56.77 % 262.32/56.77 Sub-proof #22 shows that the following formulas are inconsistent: % 262.32/56.77 ---------------------------------------------------------------- % 262.32/56.77 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 262.32/56.77 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 262.32/56.78 v0)) % 262.32/56.78 (2) a_select3(id_ds1_filter, n5, n2) = all_74_12 % 262.32/56.78 (3) a_select3(id_ds1_filter, n5, n2) = all_74_13 % 262.32/56.78 (4) ~ (all_74_12 = all_74_13) % 262.32/56.78 % 262.32/56.78 Begin of proof % 262.32/56.78 | % 262.32/56.78 | GROUND_INST: instantiating (1) with all_74_12, all_74_13, n2, n5, % 262.32/56.78 | id_ds1_filter, simplifying with (2), (3) gives: % 262.32/56.78 | (5) all_74_12 = all_74_13 % 262.32/56.78 | % 262.32/56.78 | REDUCE: (4), (5) imply: % 262.32/56.78 | (6) $false % 262.32/56.78 | % 262.32/56.78 | CLOSE: (6) is inconsistent. % 262.32/56.78 | % 262.32/56.78 End of proof % 262.32/56.78 % 262.32/56.78 Sub-proof #23 shows that the following formulas are inconsistent: % 262.32/56.78 ---------------------------------------------------------------- % 262.32/56.78 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 262.32/56.78 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 262.32/56.78 v0)) % 262.32/56.78 (2) a_select3(id_ds1_filter, n5, n1) = all_74_12 % 262.32/56.78 (3) a_select3(id_ds1_filter, n5, n1) = all_74_13 % 262.32/56.78 (4) ~ (all_74_12 = all_74_13) % 262.32/56.78 % 262.32/56.78 Begin of proof % 262.32/56.78 | % 262.32/56.78 | GROUND_INST: instantiating (1) with all_74_12, all_74_13, n1, n5, % 262.32/56.78 | id_ds1_filter, simplifying with (2), (3) gives: % 262.32/56.78 | (5) all_74_12 = all_74_13 % 262.32/56.78 | % 262.32/56.78 | REDUCE: (4), (5) imply: % 262.32/56.78 | (6) $false % 262.32/56.78 | % 262.32/56.78 | CLOSE: (6) is inconsistent. % 262.32/56.78 | % 262.32/56.78 End of proof % 262.32/56.78 % 262.32/56.78 Sub-proof #24 shows that the following formulas are inconsistent: % 262.32/56.78 ---------------------------------------------------------------- % 262.32/56.78 (1) all_74_15 = all_74_18 | gt(all_74_18, all_74_15) % 262.32/56.78 (2) all_74_18 = n0 % 262.32/56.78 (3) ~ gt(n0, n0) % 262.32/56.78 (4) $i(all_74_15) % 262.32/56.78 (5) $i(n0) % 262.32/56.78 (6) ~ (all_74_15 = n0) % 262.32/56.78 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 262.32/56.78 $i(v0) | ~ gt(v1, v2) | ~ gt(v0, v1) | gt(v0, v2)) % 262.32/56.78 (8) gt(all_74_15, n0) % 262.32/56.78 % 262.32/56.78 Begin of proof % 262.32/56.78 | % 262.32/56.78 | BETA: splitting (1) gives: % 262.32/56.78 | % 262.32/56.78 | Case 1: % 262.32/56.78 | | % 262.32/56.78 | | (9) gt(all_74_18, all_74_15) % 262.32/56.78 | | % 262.32/56.78 | | REDUCE: (2), (9) imply: % 262.32/56.78 | | (10) gt(n0, all_74_15) % 262.32/56.78 | | % 262.32/56.78 | | GROUND_INST: instantiating (7) with n0, all_74_15, n0, simplifying with (3), % 262.32/56.78 | | (4), (5), (8), (10) gives: % 262.32/56.78 | | (11) $false % 262.32/56.78 | | % 262.32/56.78 | | CLOSE: (11) is inconsistent. % 262.32/56.78 | | % 262.32/56.78 | Case 2: % 262.32/56.78 | | % 262.32/56.78 | | (12) all_74_15 = all_74_18 % 262.32/56.78 | | % 262.32/56.78 | | COMBINE_EQS: (2), (12) imply: % 262.32/56.78 | | (13) all_74_15 = n0 % 262.32/56.78 | | % 262.32/56.78 | | REDUCE: (6), (13) imply: % 262.32/56.78 | | (14) $false % 262.32/56.78 | | % 262.32/56.78 | | CLOSE: (14) is inconsistent. % 262.32/56.78 | | % 262.32/56.78 | End of split % 262.32/56.78 | % 262.32/56.78 End of proof % 262.32/56.78 % 262.32/56.78 Sub-proof #25 shows that the following formulas are inconsistent: % 262.32/56.78 ---------------------------------------------------------------- % 262.32/56.78 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 262.32/56.78 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 262.32/56.78 v0)) % 262.32/56.78 (2) a_select3(id_ds1_filter, n4, n3) = all_74_12 % 262.32/56.78 (3) a_select3(id_ds1_filter, n4, n3) = all_74_13 % 262.32/56.78 (4) ~ (all_74_12 = all_74_13) % 262.32/56.78 % 262.32/56.78 Begin of proof % 262.32/56.78 | % 262.32/56.78 | GROUND_INST: instantiating (1) with all_74_12, all_74_13, n3, n4, % 262.32/56.78 | id_ds1_filter, simplifying with (2), (3) gives: % 262.32/56.78 | (5) all_74_12 = all_74_13 % 262.32/56.78 | % 262.32/56.78 | REDUCE: (4), (5) imply: % 262.32/56.78 | (6) $false % 262.32/56.78 | % 262.32/56.78 | CLOSE: (6) is inconsistent. % 262.32/56.78 | % 262.32/56.78 End of proof % 262.32/56.78 % 262.32/56.78 Sub-proof #26 shows that the following formulas are inconsistent: % 262.32/56.78 ---------------------------------------------------------------- % 262.32/56.78 (1) succ(all_74_18) = pv57 % 262.32/56.78 (2) gt(n4, pv57) % 262.32/56.78 (3) succ(n3) = n4 % 262.32/56.78 (4) all_74_18 = n3 % 262.32/56.78 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (succ(v2) = v1) | % 262.32/56.78 ~ (succ(v2) = v0)) % 262.32/56.78 (6) ! [v0: $i] : ( ~ $i(v0) | ~ gt(v0, v0)) % 262.32/56.78 (7) $i(pv57) % 262.32/56.78 % 262.32/56.78 Begin of proof % 262.32/56.78 | % 262.32/56.78 | REDUCE: (1), (4) imply: % 262.32/56.78 | (8) succ(n3) = pv57 % 262.32/56.78 | % 262.32/56.78 | GROUND_INST: instantiating (5) with n4, pv57, n3, simplifying with (3), (8) % 262.32/56.78 | gives: % 262.32/56.78 | (9) pv57 = n4 % 262.32/56.78 | % 262.32/56.78 | REDUCE: (7), (9) imply: % 262.32/56.78 | (10) $i(n4) % 262.32/56.78 | % 262.32/56.78 | REDUCE: (2), (9) imply: % 262.32/56.78 | (11) gt(n4, n4) % 262.32/56.78 | % 262.32/56.78 | GROUND_INST: instantiating (6) with n4, simplifying with (10), (11) gives: % 262.32/56.78 | (12) $false % 262.32/56.78 | % 262.32/56.78 | CLOSE: (12) is inconsistent. % 262.32/56.78 | % 262.32/56.78 End of proof % 262.32/56.78 % 262.32/56.78 Sub-proof #27 shows that the following formulas are inconsistent: % 262.32/56.78 ---------------------------------------------------------------- % 262.32/56.78 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 262.32/56.78 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 262.32/56.78 v0)) % 262.32/56.78 (2) a_select3(id_ds1_filter, n4, n2) = all_74_12 % 262.32/56.78 (3) a_select3(id_ds1_filter, n4, n2) = all_74_13 % 262.32/56.78 (4) ~ (all_74_12 = all_74_13) % 262.32/56.78 % 262.32/56.78 Begin of proof % 262.32/56.78 | % 262.32/56.78 | GROUND_INST: instantiating (1) with all_74_12, all_74_13, n2, n4, % 262.32/56.78 | id_ds1_filter, simplifying with (2), (3) gives: % 262.32/56.78 | (5) all_74_12 = all_74_13 % 262.32/56.78 | % 262.32/56.78 | REDUCE: (4), (5) imply: % 262.32/56.78 | (6) $false % 262.32/56.78 | % 262.32/56.78 | CLOSE: (6) is inconsistent. % 262.32/56.78 | % 262.32/56.78 End of proof % 262.32/56.78 % 262.32/56.78 Sub-proof #28 shows that the following formulas are inconsistent: % 262.32/56.78 ---------------------------------------------------------------- % 262.32/56.78 (1) ~ gt(all_74_18, n1) % 262.32/56.78 (2) ! [v0: $i] : (v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0, n1) | ~ % 262.32/56.78 leq(n0, v0)) % 262.32/56.78 (3) leq(all_74_15, all_74_18) % 262.32/56.78 (4) all_74_18 = n1 % 262.32/56.78 (5) gt(all_74_18, all_74_15) % 262.32/56.78 (6) $i(all_74_15) % 262.32/56.78 (7) ~ (all_74_15 = n0) % 262.32/56.78 (8) leq(n0, all_74_15) % 262.32/56.78 % 262.32/56.78 Begin of proof % 262.32/56.78 | % 262.32/56.78 | REDUCE: (3), (4) imply: % 262.32/56.78 | (9) leq(all_74_15, n1) % 262.32/56.78 | % 262.32/56.78 | REDUCE: (4), (5) imply: % 262.32/56.78 | (10) gt(n1, all_74_15) % 262.32/56.78 | % 262.32/56.78 | REDUCE: (1), (4) imply: % 262.32/56.78 | (11) ~ gt(n1, n1) % 262.32/56.78 | % 262.32/56.78 | REF_CLOSE: (2), (6), (7), (8), (9), (10), (11) are inconsistent by sub-proof % 262.32/56.78 | #32. % 262.32/56.78 | % 262.32/56.78 End of proof % 262.32/56.78 % 262.32/56.78 Sub-proof #29 shows that the following formulas are inconsistent: % 262.32/56.78 ---------------------------------------------------------------- % 262.32/56.78 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 262.32/56.78 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 262.32/56.78 v0)) % 262.32/56.78 (2) a_select3(id_ds1_filter, n4, n1) = all_74_12 % 262.32/56.78 (3) a_select3(id_ds1_filter, n4, n1) = all_74_13 % 262.32/56.78 (4) ~ (all_74_12 = all_74_13) % 262.32/56.78 % 262.32/56.78 Begin of proof % 262.32/56.78 | % 262.32/56.78 | GROUND_INST: instantiating (1) with all_74_12, all_74_13, n1, n4, % 262.32/56.78 | id_ds1_filter, simplifying with (2), (3) gives: % 262.32/56.78 | (5) all_74_12 = all_74_13 % 262.32/56.78 | % 262.32/56.78 | REDUCE: (4), (5) imply: % 262.32/56.78 | (6) $false % 262.32/56.78 | % 262.32/56.78 | CLOSE: (6) is inconsistent. % 262.32/56.78 | % 262.32/56.78 End of proof % 262.32/56.78 % 262.32/56.78 Sub-proof #30 shows that the following formulas are inconsistent: % 262.32/56.78 ---------------------------------------------------------------- % 262.32/56.78 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 262.32/56.78 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 262.32/56.78 v0)) % 262.32/56.78 (2) a_select3(id_ds1_filter, n3, n2) = all_74_12 % 262.32/56.78 (3) a_select3(id_ds1_filter, n3, n2) = all_74_13 % 262.32/56.78 (4) ~ (all_74_12 = all_74_13) % 262.32/56.78 % 262.32/56.78 Begin of proof % 262.32/56.78 | % 262.32/56.78 | GROUND_INST: instantiating (1) with all_74_13, all_74_12, n2, n3, % 262.32/56.78 | id_ds1_filter, simplifying with (2), (3) gives: % 262.32/56.78 | (5) all_74_12 = all_74_13 % 262.32/56.78 | % 262.32/56.78 | REDUCE: (4), (5) imply: % 262.32/56.78 | (6) $false % 262.32/56.78 | % 262.32/56.78 | CLOSE: (6) is inconsistent. % 262.32/56.78 | % 262.32/56.78 End of proof % 262.32/56.78 % 262.32/56.78 Sub-proof #31 shows that the following formulas are inconsistent: % 262.32/56.78 ---------------------------------------------------------------- % 262.32/56.78 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 262.32/56.78 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 262.32/56.78 v0)) % 262.32/56.78 (2) a_select3(id_ds1_filter, n2, n2) = all_74_12 % 262.32/56.78 (3) a_select3(id_ds1_filter, n2, n2) = all_74_13 % 262.32/56.78 (4) ~ (all_74_12 = all_74_13) % 262.32/56.78 % 262.32/56.78 Begin of proof % 262.32/56.78 | % 262.32/56.78 | GROUND_INST: instantiating (1) with all_74_13, all_74_12, n2, n2, % 262.32/56.78 | id_ds1_filter, simplifying with (2), (3) gives: % 262.32/56.78 | (5) all_74_12 = all_74_13 % 262.32/56.78 | % 262.32/56.78 | REDUCE: (4), (5) imply: % 262.32/56.78 | (6) $false % 262.32/56.78 | % 262.32/56.78 | CLOSE: (6) is inconsistent. % 262.32/56.78 | % 262.32/56.78 End of proof % 262.32/56.78 % 262.32/56.78 Sub-proof #32 shows that the following formulas are inconsistent: % 262.32/56.78 ---------------------------------------------------------------- % 262.32/56.78 (1) leq(all_74_15, n1) % 262.32/56.78 (2) ! [v0: $i] : (v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0, n1) | ~ % 262.32/56.78 leq(n0, v0)) % 262.32/56.78 (3) $i(all_74_15) % 262.32/56.78 (4) gt(n1, all_74_15) % 262.32/56.78 (5) ~ (all_74_15 = n0) % 262.32/56.78 (6) ~ gt(n1, n1) % 262.32/56.78 (7) leq(n0, all_74_15) % 262.32/56.78 % 262.32/56.78 Begin of proof % 262.32/56.78 | % 262.32/56.78 | GROUND_INST: instantiating (2) with all_74_15, simplifying with (1), (3), (7) % 262.32/56.78 | gives: % 262.32/56.78 | (8) all_74_15 = n1 | all_74_15 = n0 % 262.32/56.78 | % 262.32/56.78 | BETA: splitting (8) gives: % 262.32/56.78 | % 262.32/56.78 | Case 1: % 262.32/56.78 | | % 262.32/56.78 | | (9) all_74_15 = n0 % 262.32/56.78 | | % 262.32/56.78 | | REDUCE: (5), (9) imply: % 262.32/56.78 | | (10) $false % 262.32/56.78 | | % 262.32/56.78 | | CLOSE: (10) is inconsistent. % 262.32/56.78 | | % 262.32/56.78 | Case 2: % 262.32/56.78 | | % 262.32/56.78 | | (11) all_74_15 = n1 % 262.32/56.78 | | % 262.32/56.78 | | REDUCE: (4), (11) imply: % 262.32/56.78 | | (12) gt(n1, n1) % 262.32/56.78 | | % 262.32/56.78 | | PRED_UNIFY: (6), (12) imply: % 262.32/56.78 | | (13) $false % 262.32/56.78 | | % 262.32/56.78 | | CLOSE: (13) is inconsistent. % 262.32/56.78 | | % 262.32/56.78 | End of split % 262.32/56.78 | % 262.32/56.78 End of proof % 262.32/56.78 % 262.32/56.78 Sub-proof #33 shows that the following formulas are inconsistent: % 262.32/56.78 ---------------------------------------------------------------- % 262.32/56.78 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (pred(v2) = v1) | % 262.32/56.78 ~ (pred(v2) = v0)) % 262.32/56.78 (2) ~ (pv57 = n1) % 262.32/56.78 (3) pred(n2) = n1 % 262.32/56.78 (4) gt(all_74_18, n1) % 262.32/56.78 (5) pv57 = n3 | pv57 = n2 | pv57 = n1 | pv57 = n0 % 262.32/56.78 (6) $i(all_74_18) % 262.32/56.78 (7) ~ (pv57 = n3) % 262.32/56.78 (8) pv57 = n5 | pv57 = n4 | pv57 = n3 | pv57 = n2 % 262.32/56.78 (9) pv57 = n3 | gt(n3, pv57) % 262.32/56.78 (10) ~ (pv57 = n0) % 262.32/56.78 (11) ! [v0: $i] : ( ~ $i(v0) | ~ gt(v0, v0)) % 262.32/56.78 (12) pred(pv57) = all_74_18 % 262.32/56.78 (13) $i(pv57) % 262.32/56.78 % 262.32/56.78 Begin of proof % 262.32/56.78 | % 262.32/56.78 | BETA: splitting (9) gives: % 262.32/56.78 | % 262.32/56.78 | Case 1: % 262.32/56.78 | | % 262.32/56.78 | | (14) gt(n3, pv57) % 262.32/56.78 | | % 262.32/56.78 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (10), (11), (12), (13), (14) % 262.32/56.78 | | are inconsistent by sub-proof #34. % 262.32/56.78 | | % 262.32/56.78 | Case 2: % 262.32/56.78 | | % 262.32/56.78 | | (15) pv57 = n3 % 262.32/56.79 | | % 262.32/56.79 | | REDUCE: (7), (15) imply: % 262.32/56.79 | | (16) $false % 262.32/56.79 | | % 262.32/56.79 | | CLOSE: (16) is inconsistent. % 262.32/56.79 | | % 262.32/56.79 | End of split % 262.32/56.79 | % 262.32/56.79 End of proof % 262.32/56.79 % 262.32/56.79 Sub-proof #34 shows that the following formulas are inconsistent: % 262.32/56.79 ---------------------------------------------------------------- % 262.32/56.79 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (pred(v2) = v1) | % 262.32/56.79 ~ (pred(v2) = v0)) % 262.32/56.79 (2) ~ (pv57 = n1) % 262.32/56.79 (3) gt(n3, pv57) % 262.32/56.79 (4) pred(n2) = n1 % 262.32/56.79 (5) gt(all_74_18, n1) % 262.32/56.79 (6) pv57 = n3 | pv57 = n2 | pv57 = n1 | pv57 = n0 % 262.32/56.79 (7) $i(all_74_18) % 262.32/56.79 (8) pv57 = n5 | pv57 = n4 | pv57 = n3 | pv57 = n2 % 262.32/56.79 (9) ~ (pv57 = n0) % 262.32/56.79 (10) ! [v0: $i] : ( ~ $i(v0) | ~ gt(v0, v0)) % 262.32/56.79 (11) pred(pv57) = all_74_18 % 262.32/56.79 (12) $i(pv57) % 262.32/56.79 % 262.32/56.79 Begin of proof % 262.32/56.79 | % 262.32/56.79 | BETA: splitting (6) gives: % 262.32/56.79 | % 262.32/56.79 | Case 1: % 262.32/56.79 | | % 262.32/56.79 | | (13) pv57 = n0 % 262.32/56.79 | | % 262.32/56.79 | | REDUCE: (9), (13) imply: % 262.32/56.79 | | (14) $false % 262.32/56.79 | | % 262.32/56.79 | | CLOSE: (14) is inconsistent. % 262.32/56.79 | | % 262.32/56.79 | Case 2: % 262.32/56.79 | | % 262.32/56.79 | | (15) pv57 = n3 | pv57 = n2 | pv57 = n1 % 262.32/56.79 | | % 262.32/56.79 | | BETA: splitting (8) gives: % 262.32/56.79 | | % 262.32/56.79 | | Case 1: % 262.32/56.79 | | | % 262.32/56.79 | | | (16) pv57 = n3 % 262.32/56.79 | | | % 262.32/56.79 | | | REDUCE: (12), (16) imply: % 262.32/56.79 | | | (17) $i(n3) % 262.32/56.79 | | | % 262.32/56.79 | | | REDUCE: (3), (16) imply: % 262.32/56.79 | | | (18) gt(n3, n3) % 262.32/56.79 | | | % 262.32/56.79 | | | GROUND_INST: instantiating (10) with n3, simplifying with (17), (18) % 262.32/56.79 | | | gives: % 262.32/56.79 | | | (19) $false % 262.32/56.79 | | | % 262.32/56.79 | | | CLOSE: (19) is inconsistent. % 262.32/56.79 | | | % 262.32/56.79 | | Case 2: % 262.32/56.79 | | | % 262.32/56.79 | | | (20) ~ (pv57 = n3) % 262.32/56.79 | | | % 262.32/56.79 | | | BETA: splitting (15) gives: % 262.32/56.79 | | | % 262.32/56.79 | | | Case 1: % 262.32/56.79 | | | | % 262.32/56.79 | | | | (21) pv57 = n1 % 262.32/56.79 | | | | % 262.32/56.79 | | | | REDUCE: (2), (21) imply: % 262.32/56.79 | | | | (22) $false % 262.32/56.79 | | | | % 262.32/56.79 | | | | CLOSE: (22) is inconsistent. % 262.32/56.79 | | | | % 262.32/56.79 | | | Case 2: % 262.32/56.79 | | | | % 262.32/56.79 | | | | (23) pv57 = n3 | pv57 = n2 % 262.32/56.79 | | | | % 262.32/56.79 | | | | BETA: splitting (23) gives: % 262.32/56.79 | | | | % 262.32/56.79 | | | | Case 1: % 262.32/56.79 | | | | | % 262.32/56.79 | | | | | (24) pv57 = n3 % 262.32/56.79 | | | | | % 262.32/56.79 | | | | | REDUCE: (20), (24) imply: % 262.32/56.79 | | | | | (25) $false % 262.32/56.79 | | | | | % 262.32/56.79 | | | | | CLOSE: (25) is inconsistent. % 262.32/56.79 | | | | | % 262.32/56.79 | | | | Case 2: % 262.32/56.79 | | | | | % 262.32/56.79 | | | | | (26) pv57 = n2 % 262.32/56.79 | | | | | % 262.32/56.79 | | | | | REDUCE: (11), (26) imply: % 262.32/56.79 | | | | | (27) pred(n2) = all_74_18 % 262.32/56.79 | | | | | % 262.32/56.79 | | | | | GROUND_INST: instantiating (1) with n1, all_74_18, n2, simplifying % 262.32/56.79 | | | | | with (4), (27) gives: % 262.32/56.79 | | | | | (28) all_74_18 = n1 % 262.32/56.79 | | | | | % 262.32/56.79 | | | | | REDUCE: (7), (28) imply: % 262.32/56.79 | | | | | (29) $i(n1) % 262.32/56.79 | | | | | % 262.32/56.79 | | | | | REDUCE: (5), (28) imply: % 262.32/56.79 | | | | | (30) gt(n1, n1) % 262.32/56.79 | | | | | % 262.32/56.79 | | | | | GROUND_INST: instantiating (10) with n1, simplifying with (29), (30) % 262.32/56.79 | | | | | gives: % 262.32/56.79 | | | | | (31) $false % 262.32/56.79 | | | | | % 262.32/56.79 | | | | | CLOSE: (31) is inconsistent. % 262.32/56.79 | | | | | % 262.32/56.79 | | | | End of split % 262.32/56.79 | | | | % 262.32/56.79 | | | End of split % 262.32/56.79 | | | % 262.32/56.79 | | End of split % 262.32/56.79 | | % 262.32/56.79 | End of split % 262.32/56.79 | % 262.32/56.79 End of proof % 262.32/56.79 % 262.32/56.79 Sub-proof #35 shows that the following formulas are inconsistent: % 262.32/56.79 ---------------------------------------------------------------- % 262.32/56.79 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 262.32/56.79 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 262.32/56.79 v0)) % 262.32/56.79 (2) a_select3(id_ds1_filter, n3, n1) = all_74_12 % 262.32/56.79 (3) a_select3(id_ds1_filter, n3, n1) = all_74_13 % 262.32/56.79 (4) ~ (all_74_12 = all_74_13) % 262.32/56.79 % 262.32/56.79 Begin of proof % 262.32/56.79 | % 262.32/56.79 | GROUND_INST: instantiating (1) with all_74_13, all_74_12, n1, n3, % 262.32/56.79 | id_ds1_filter, simplifying with (2), (3) gives: % 262.32/56.79 | (5) all_74_12 = all_74_13 % 262.32/56.79 | % 262.32/56.79 | REDUCE: (4), (5) imply: % 262.32/56.79 | (6) $false % 262.32/56.79 | % 262.32/56.79 | CLOSE: (6) is inconsistent. % 262.32/56.79 | % 262.32/56.79 End of proof % 262.32/56.79 % 262.32/56.79 Sub-proof #36 shows that the following formulas are inconsistent: % 262.32/56.79 ---------------------------------------------------------------- % 262.32/56.79 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 262.32/56.79 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 262.32/56.79 v0)) % 262.32/56.79 (2) a_select3(id_ds1_filter, n2, n1) = all_74_12 % 262.32/56.79 (3) a_select3(id_ds1_filter, n2, n1) = all_74_13 % 262.32/56.79 (4) ~ (all_74_12 = all_74_13) % 262.32/56.79 % 262.32/56.79 Begin of proof % 262.32/56.79 | % 262.32/56.79 | GROUND_INST: instantiating (1) with all_74_12, all_74_13, n1, n2, % 262.32/56.79 | id_ds1_filter, simplifying with (2), (3) gives: % 262.32/56.79 | (5) all_74_12 = all_74_13 % 262.32/56.79 | % 262.32/56.79 | REDUCE: (4), (5) imply: % 262.32/56.79 | (6) $false % 262.32/56.79 | % 262.32/56.79 | CLOSE: (6) is inconsistent. % 262.32/56.79 | % 262.32/56.79 End of proof % 262.32/56.79 % 262.32/56.79 Sub-proof #37 shows that the following formulas are inconsistent: % 262.32/56.79 ---------------------------------------------------------------- % 262.32/56.79 (1) ~ (all_74_14 = n0) % 262.32/56.79 (2) ! [v0: $i] : (v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0, n1) | ~ % 262.32/56.79 leq(n0, v0)) % 262.32/56.79 (3) a_select3(id_ds1_filter, all_74_14, n1) = all_74_12 % 262.32/56.79 (4) $i(all_74_14) % 262.32/56.79 (5) leq(n0, all_74_14) % 262.32/56.79 (6) a_select3(id_ds1_filter, n1, all_74_14) = all_74_13 % 262.32/56.79 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 262.32/56.79 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 262.32/56.79 v0)) % 262.32/56.79 (8) ~ (all_74_12 = all_74_13) % 262.32/56.79 (9) leq(all_74_14, n1) % 262.32/56.79 % 262.32/56.79 Begin of proof % 262.32/56.79 | % 262.32/56.79 | GROUND_INST: instantiating (2) with all_74_14, simplifying with (4), (5), (9) % 262.32/56.79 | gives: % 262.32/56.79 | (10) all_74_14 = n1 | all_74_14 = n0 % 262.32/56.79 | % 262.32/56.79 | BETA: splitting (10) gives: % 262.32/56.79 | % 262.32/56.79 | Case 1: % 262.32/56.79 | | % 262.32/56.79 | | (11) all_74_14 = n0 % 262.32/56.79 | | % 262.32/56.79 | | REDUCE: (1), (11) imply: % 262.32/56.79 | | (12) $false % 262.32/56.79 | | % 262.32/56.79 | | CLOSE: (12) is inconsistent. % 262.32/56.79 | | % 262.32/56.79 | Case 2: % 262.32/56.79 | | % 262.32/56.79 | | (13) all_74_14 = n1 % 262.32/56.79 | | % 262.32/56.79 | | REDUCE: (3), (13) imply: % 262.32/56.79 | | (14) a_select3(id_ds1_filter, n1, n1) = all_74_12 % 262.32/56.79 | | % 262.32/56.79 | | REDUCE: (6), (13) imply: % 262.32/56.79 | | (15) a_select3(id_ds1_filter, n1, n1) = all_74_13 % 262.32/56.79 | | % 262.32/56.79 | | GROUND_INST: instantiating (7) with all_74_13, all_74_12, n1, n1, % 262.32/56.79 | | id_ds1_filter, simplifying with (14), (15) gives: % 262.32/56.79 | | (16) all_74_12 = all_74_13 % 262.32/56.79 | | % 262.32/56.79 | | REDUCE: (8), (16) imply: % 262.32/56.79 | | (17) $false % 262.32/56.79 | | % 262.32/56.79 | | CLOSE: (17) is inconsistent. % 262.32/56.79 | | % 262.32/56.79 | End of split % 262.32/56.79 | % 262.32/56.79 End of proof % 262.32/56.79 % 262.32/56.79 Sub-proof #38 shows that the following formulas are inconsistent: % 262.32/56.79 ---------------------------------------------------------------- % 262.32/56.79 (1) pred(n1) = n0 % 262.32/56.79 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (pred(v2) = v1) | % 262.32/56.79 ~ (pred(v2) = v0)) % 262.32/56.79 (3) pv57 = n1 % 262.32/56.79 (4) ~ (all_74_18 = n0) % 262.32/56.79 (5) pred(pv57) = all_74_18 % 262.32/56.79 % 262.32/56.79 Begin of proof % 262.32/56.79 | % 262.32/56.79 | REDUCE: (3), (5) imply: % 262.32/56.79 | (6) pred(n1) = all_74_18 % 262.32/56.79 | % 262.32/56.79 | GROUND_INST: instantiating (2) with n0, all_74_18, n1, simplifying with (1), % 262.32/56.79 | (6) gives: % 262.32/56.79 | (7) all_74_18 = n0 % 262.32/56.79 | % 262.32/56.79 | REDUCE: (4), (7) imply: % 262.32/56.79 | (8) $false % 262.32/56.79 | % 262.32/56.79 | CLOSE: (8) is inconsistent. % 262.32/56.79 | % 262.32/56.79 End of proof % 262.32/56.79 % 262.32/56.79 Sub-proof #39 shows that the following formulas are inconsistent: % 262.32/56.79 ---------------------------------------------------------------- % 262.32/56.79 (1) $i(all_74_18) % 262.32/56.79 (2) all_74_18 = n0 % 262.32/56.79 (3) gt(all_74_18, n0) % 262.32/56.79 (4) ! [v0: $i] : ( ~ $i(v0) | ~ gt(v0, v0)) % 262.32/56.79 % 262.32/56.79 Begin of proof % 262.32/56.79 | % 262.32/56.79 | REDUCE: (1), (2) imply: % 262.32/56.79 | (5) $i(n0) % 262.32/56.79 | % 262.32/56.79 | REDUCE: (2), (3) imply: % 262.32/56.79 | (6) gt(n0, n0) % 262.32/56.79 | % 262.32/56.79 | GROUND_INST: instantiating (4) with n0, simplifying with (5), (6) gives: % 262.32/56.79 | (7) $false % 262.32/56.79 | % 262.32/56.79 | CLOSE: (7) is inconsistent. % 262.32/56.79 | % 262.32/56.79 End of proof % 262.32/56.79 % 262.32/56.79 Sub-proof #40 shows that the following formulas are inconsistent: % 262.32/56.79 ---------------------------------------------------------------- % 262.32/56.79 (1) $i(all_74_15) % 262.32/56.79 (2) all_74_15 = n0 % 262.32/56.79 (3) gt(all_74_15, n0) % 262.32/56.79 (4) ! [v0: $i] : ( ~ $i(v0) | ~ gt(v0, v0)) % 262.32/56.79 % 262.32/56.79 Begin of proof % 262.32/56.79 | % 262.32/56.79 | REDUCE: (1), (2) imply: % 262.32/56.79 | (5) $i(n0) % 262.32/56.79 | % 262.32/56.79 | REDUCE: (2), (3) imply: % 262.32/56.79 | (6) gt(n0, n0) % 262.32/56.79 | % 262.32/56.79 | GROUND_INST: instantiating (4) with n0, simplifying with (5), (6) gives: % 262.32/56.79 | (7) $false % 262.32/56.79 | % 262.32/56.79 | CLOSE: (7) is inconsistent. % 262.32/56.79 | % 262.32/56.79 End of proof % 262.32/56.79 % 262.32/56.79 Sub-proof #41 shows that the following formulas are inconsistent: % 262.32/56.79 ---------------------------------------------------------------- % 262.32/56.79 (1) $i(all_74_14) % 262.32/56.79 (2) all_74_14 = n0 % 262.32/56.79 (3) gt(all_74_14, n0) % 262.32/56.79 (4) ! [v0: $i] : ( ~ $i(v0) | ~ gt(v0, v0)) % 262.32/56.79 % 262.32/56.79 Begin of proof % 262.32/56.79 | % 262.32/56.79 | REDUCE: (1), (2) imply: % 262.32/56.79 | (5) $i(n0) % 262.32/56.79 | % 262.32/56.79 | REDUCE: (2), (3) imply: % 262.32/56.79 | (6) gt(n0, n0) % 262.32/56.79 | % 262.32/56.79 | GROUND_INST: instantiating (4) with n0, simplifying with (5), (6) gives: % 262.32/56.79 | (7) $false % 262.32/56.79 | % 262.32/56.79 | CLOSE: (7) is inconsistent. % 262.32/56.79 | % 262.32/56.79 End of proof % 262.32/56.79 % 262.32/56.79 Sub-proof #42 shows that the following formulas are inconsistent: % 262.32/56.79 ---------------------------------------------------------------- % 262.32/56.79 (1) ~ (all_74_8 = all_74_9) % 262.32/56.79 (2) a_select3(pminus_ds1_filter, n5, n0) = all_74_9 % 262.32/56.79 (3) ~ leq(n5, all_74_20) | ~ leq(n0, all_74_20) | % 262.32/56.79 (a_select3(pminus_ds1_filter, n5, n0) = all_74_8 & $i(all_74_8)) % 262.32/56.79 (4) leq(n0, n5) % 262.32/56.79 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 262.32/56.79 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 262.32/56.79 v0)) % 262.32/56.79 (6) leq(n5, n5) % 262.32/56.79 (7) all_74_20 = n5 % 262.32/56.79 % 262.32/56.79 Begin of proof % 262.32/56.79 | % 262.32/56.79 | BETA: splitting (3) gives: % 262.32/56.79 | % 262.32/56.79 | Case 1: % 262.32/56.79 | | % 262.32/56.79 | | (8) ~ leq(n0, all_74_20) % 262.32/56.79 | | % 262.32/56.79 | | REDUCE: (7), (8) imply: % 262.32/56.79 | | (9) ~ leq(n0, n5) % 262.32/56.79 | | % 262.32/56.79 | | PRED_UNIFY: (4), (9) imply: % 262.32/56.79 | | (10) $false % 262.32/56.79 | | % 262.32/56.79 | | CLOSE: (10) is inconsistent. % 262.32/56.79 | | % 262.32/56.79 | Case 2: % 262.32/56.79 | | % 262.32/56.79 | | (11) ~ leq(n5, all_74_20) | (a_select3(pminus_ds1_filter, n5, n0) = % 262.32/56.79 | | all_74_8 & $i(all_74_8)) % 262.32/56.79 | | % 262.32/56.79 | | BETA: splitting (11) gives: % 262.32/56.79 | | % 262.32/56.79 | | Case 1: % 262.32/56.79 | | | % 262.32/56.79 | | | (12) ~ leq(n5, all_74_20) % 262.32/56.79 | | | % 262.32/56.79 | | | REDUCE: (7), (12) imply: % 262.32/56.79 | | | (13) ~ leq(n5, n5) % 262.32/56.79 | | | % 262.32/56.79 | | | PRED_UNIFY: (6), (13) imply: % 262.32/56.79 | | | (14) $false % 262.32/56.79 | | | % 262.32/56.79 | | | CLOSE: (14) is inconsistent. % 262.32/56.79 | | | % 262.32/56.79 | | Case 2: % 262.32/56.79 | | | % 262.32/56.79 | | | (15) a_select3(pminus_ds1_filter, n5, n0) = all_74_8 & $i(all_74_8) % 262.32/56.79 | | | % 262.32/56.79 | | | ALPHA: (15) implies: % 262.32/56.79 | | | (16) a_select3(pminus_ds1_filter, n5, n0) = all_74_8 % 262.32/56.79 | | | % 262.32/56.79 | | | REF_CLOSE: (1), (2), (5), (16) are inconsistent by sub-proof #46. % 262.32/56.79 | | | % 262.32/56.79 | | End of split % 262.32/56.79 | | % 262.32/56.79 | End of split % 262.32/56.79 | % 262.32/56.79 End of proof % 262.32/56.79 % 262.32/56.79 Sub-proof #43 shows that the following formulas are inconsistent: % 262.32/56.79 ---------------------------------------------------------------- % 262.32/56.79 (1) leq(all_74_11, n5) % 262.32/56.79 (2) $i(n3) % 262.32/56.79 (3) ~ (all_74_8 = all_74_9) % 262.32/56.79 (4) $i(n4) % 262.32/56.80 (5) ! [v0: $i] : (v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0, n1) | ~ % 262.32/56.80 leq(n0, v0)) % 262.32/56.80 (6) pred(n2) = n1 % 262.32/56.80 (7) all_74_11 = n5 | all_74_11 = n4 | all_74_11 = n3 | all_74_11 = n2 | % 262.32/56.80 all_74_11 = n1 | all_74_11 = n0 % 262.32/56.80 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 262.32/56.80 (a_select3(pminus_ds1_filter, v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 262.32/56.80 ~ leq(v1, all_74_20) | ~ leq(v0, all_74_20) | ~ leq(n0, v1) | ~ % 262.32/56.80 leq(n0, v0) | (a_select3(pminus_ds1_filter, v1, v0) = v2 & $i(v2))) % 262.32/56.80 (9) gt(all_74_11, n0) % 262.32/56.80 (10) leq(n0, all_74_11) % 262.32/56.80 (11) leq(all_74_11, n4) % 262.32/56.80 (12) ~ gt(n0, n0) % 262.32/56.80 (13) $i(n0) % 262.32/56.80 (14) $i(all_74_11) % 262.32/56.80 (15) pred(n3) = n2 % 262.32/56.80 (16) leq(n0, n5) % 262.32/56.80 (17) a_select3(pminus_ds1_filter, all_74_11, n0) = all_74_9 % 262.32/56.80 (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 262.32/56.80 (v1 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 262.32/56.80 v0)) % 262.32/56.80 (19) pred(n4) = n3 % 262.32/56.80 (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (pred(v1) = v2) | ~ % 262.32/56.80 $i(v1) | ~ $i(v0) | ~ gt(v1, v0) | leq(v0, v2)) % 262.32/56.80 (21) a_select3(pminus_ds1_filter, n0, all_74_11) = all_74_8 % 262.32/56.80 (22) all_74_20 = n5 % 262.32/56.80 (23) $i(n2) % 262.32/56.80 (24) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ % 262.32/56.80 leq(v0, v1) | gt(v1, v0)) % 262.32/56.80 (25) leq(n0, n0) % 262.32/56.80 % 262.32/56.80 Begin of proof % 262.32/56.80 | % 262.32/56.80 | GROUND_INST: instantiating (24) with all_74_11, n4, simplifying with (4), % 262.32/56.80 | (11), (14) gives: % 262.32/56.80 | (26) all_74_11 = n4 | gt(n4, all_74_11) % 262.32/56.80 | % 262.32/56.80 | BETA: splitting (7) gives: % 262.32/56.80 | % 262.32/56.80 | Case 1: % 262.32/56.80 | | % 262.32/56.80 | | (27) all_74_11 = n0 % 262.32/56.80 | | % 262.32/56.80 | | REDUCE: (9), (27) imply: % 262.32/56.80 | | (28) gt(n0, n0) % 262.32/56.80 | | % 262.32/56.80 | | PRED_UNIFY: (12), (28) imply: % 262.32/56.80 | | (29) $false % 262.32/56.80 | | % 262.32/56.80 | | CLOSE: (29) is inconsistent. % 262.32/56.80 | | % 262.32/56.80 | Case 2: % 262.32/56.80 | | % 262.32/56.80 | | (30) ~ (all_74_11 = n0) % 262.32/56.80 | | % 262.32/56.80 | | BETA: splitting (26) gives: % 262.32/56.80 | | % 262.32/56.80 | | Case 1: % 262.32/56.80 | | | % 262.32/56.80 | | | (31) gt(n4, all_74_11) % 262.32/56.80 | | | % 262.32/56.80 | | | GROUND_INST: instantiating (20) with all_74_11, n4, n3, simplifying with % 262.32/56.80 | | | (4), (14), (19), (31) gives: % 262.32/56.80 | | | (32) leq(all_74_11, n3) % 262.32/56.80 | | | % 262.32/56.80 | | | GROUND_INST: instantiating (24) with all_74_11, n3, simplifying with (2), % 262.32/56.80 | | | (14), (32) gives: % 262.32/56.80 | | | (33) all_74_11 = n3 | gt(n3, all_74_11) % 262.32/56.80 | | | % 262.32/56.80 | | | BETA: splitting (33) gives: % 262.32/56.80 | | | % 262.32/56.80 | | | Case 1: % 262.32/56.80 | | | | % 262.32/56.80 | | | | (34) gt(n3, all_74_11) % 262.32/56.80 | | | | % 262.32/56.80 | | | | GROUND_INST: instantiating (20) with all_74_11, n3, n2, simplifying with % 262.32/56.80 | | | | (2), (14), (15), (34) gives: % 262.32/56.80 | | | | (35) leq(all_74_11, n2) % 262.32/56.80 | | | | % 262.32/56.80 | | | | GROUND_INST: instantiating (24) with all_74_11, n2, simplifying with % 262.32/56.80 | | | | (14), (23), (35) gives: % 262.32/56.80 | | | | (36) all_74_11 = n2 | gt(n2, all_74_11) % 262.32/56.80 | | | | % 262.32/56.80 | | | | BETA: splitting (36) gives: % 262.32/56.80 | | | | % 262.32/56.80 | | | | Case 1: % 262.32/56.80 | | | | | % 262.32/56.80 | | | | | (37) gt(n2, all_74_11) % 262.32/56.80 | | | | | % 262.32/56.80 | | | | | GROUND_INST: instantiating (20) with all_74_11, n2, n1, simplifying % 262.32/56.80 | | | | | with (6), (14), (23), (37) gives: % 262.32/56.80 | | | | | (38) leq(all_74_11, n1) % 262.32/56.80 | | | | | % 262.32/56.80 | | | | | GROUND_INST: instantiating (5) with all_74_11, simplifying with (10), % 262.32/56.80 | | | | | (14), (38) gives: % 262.32/56.80 | | | | | (39) all_74_11 = n1 | all_74_11 = n0 % 262.32/56.80 | | | | | % 262.32/56.80 | | | | | BETA: splitting (39) gives: % 262.32/56.80 | | | | | % 262.32/56.80 | | | | | Case 1: % 262.32/56.80 | | | | | | % 262.32/56.80 | | | | | | (40) all_74_11 = n0 % 262.32/56.80 | | | | | | % 262.32/56.80 | | | | | | REDUCE: (30), (40) imply: % 262.32/56.80 | | | | | | (41) $false % 262.32/56.80 | | | | | | % 262.32/56.80 | | | | | | CLOSE: (41) is inconsistent. % 262.32/56.80 | | | | | | % 262.32/56.80 | | | | | Case 2: % 262.32/56.80 | | | | | | % 262.32/56.80 | | | | | | (42) all_74_11 = n1 % 262.32/56.80 | | | | | | % 262.32/56.80 | | | | | | REDUCE: (17), (42) imply: % 262.32/56.80 | | | | | | (43) a_select3(pminus_ds1_filter, n1, n0) = all_74_9 % 262.32/56.80 | | | | | | % 262.32/56.80 | | | | | | REDUCE: (21), (42) imply: % 262.32/56.80 | | | | | | (44) a_select3(pminus_ds1_filter, n0, n1) = all_74_8 % 262.32/56.80 | | | | | | % 262.32/56.80 | | | | | | REDUCE: (14), (42) imply: % 262.32/56.80 | | | | | | (45) $i(n1) % 262.32/56.80 | | | | | | % 262.32/56.80 | | | | | | REDUCE: (1), (42) imply: % 262.32/56.80 | | | | | | (46) leq(n1, n5) % 262.32/56.80 | | | | | | % 262.32/56.80 | | | | | | REDUCE: (10), (42) imply: % 262.32/56.80 | | | | | | (47) leq(n0, n1) % 262.32/56.80 | | | | | | % 262.32/56.80 | | | | | | GROUND_INST: instantiating (8) with n0, n1, all_74_8, simplifying % 262.32/56.80 | | | | | | with (13), (25), (44), (45), (47) gives: % 262.32/56.80 | | | | | | (48) ~ leq(n1, all_74_20) | ~ leq(n0, all_74_20) | % 262.32/56.80 | | | | | | (a_select3(pminus_ds1_filter, n1, n0) = all_74_8 & % 262.32/56.80 | | | | | | $i(all_74_8)) % 262.32/56.80 | | | | | | % 262.32/56.80 | | | | | | BETA: splitting (48) gives: % 262.32/56.80 | | | | | | % 262.32/56.80 | | | | | | Case 1: % 262.32/56.80 | | | | | | | % 262.32/56.80 | | | | | | | (49) ~ leq(n0, all_74_20) % 262.32/56.80 | | | | | | | % 262.32/56.80 | | | | | | | REDUCE: (22), (49) imply: % 262.32/56.80 | | | | | | | (50) ~ leq(n0, n5) % 262.32/56.80 | | | | | | | % 262.32/56.80 | | | | | | | PRED_UNIFY: (16), (50) imply: % 262.32/56.80 | | | | | | | (51) $false % 262.32/56.80 | | | | | | | % 262.32/56.80 | | | | | | | CLOSE: (51) is inconsistent. % 262.32/56.80 | | | | | | | % 262.32/56.80 | | | | | | Case 2: % 262.32/56.80 | | | | | | | % 262.32/56.80 | | | | | | | (52) ~ leq(n1, all_74_20) | (a_select3(pminus_ds1_filter, n1, % 262.32/56.80 | | | | | | | n0) = all_74_8 & $i(all_74_8)) % 262.32/56.80 | | | | | | | % 262.32/56.80 | | | | | | | BETA: splitting (52) gives: % 262.32/56.80 | | | | | | | % 262.32/56.80 | | | | | | | Case 1: % 262.32/56.80 | | | | | | | | % 262.32/56.80 | | | | | | | | (53) ~ leq(n1, all_74_20) % 262.32/56.80 | | | | | | | | % 262.32/56.80 | | | | | | | | REDUCE: (22), (53) imply: % 262.32/56.80 | | | | | | | | (54) ~ leq(n1, n5) % 262.32/56.80 | | | | | | | | % 262.32/56.80 | | | | | | | | PRED_UNIFY: (46), (54) imply: % 262.32/56.80 | | | | | | | | (55) $false % 262.32/56.80 | | | | | | | | % 262.32/56.80 | | | | | | | | CLOSE: (55) is inconsistent. % 262.32/56.80 | | | | | | | | % 262.32/56.80 | | | | | | | Case 2: % 262.32/56.80 | | | | | | | | % 262.32/56.80 | | | | | | | | (56) a_select3(pminus_ds1_filter, n1, n0) = all_74_8 & % 262.32/56.80 | | | | | | | | $i(all_74_8) % 262.32/56.80 | | | | | | | | % 262.32/56.80 | | | | | | | | ALPHA: (56) implies: % 262.32/56.80 | | | | | | | | (57) a_select3(pminus_ds1_filter, n1, n0) = all_74_8 % 262.32/56.80 | | | | | | | | % 262.32/56.80 | | | | | | | | REF_CLOSE: (3), (18), (43), (57) are inconsistent by sub-proof % 262.32/56.80 | | | | | | | | #51. % 262.32/56.80 | | | | | | | | % 262.32/56.80 | | | | | | | End of split % 262.32/56.80 | | | | | | | % 262.32/56.80 | | | | | | End of split % 262.32/56.80 | | | | | | % 262.32/56.80 | | | | | End of split % 262.32/56.80 | | | | | % 262.32/56.80 | | | | Case 2: % 262.32/56.80 | | | | | % 262.32/56.80 | | | | | (58) all_74_11 = n2 % 262.32/56.80 | | | | | % 262.32/56.80 | | | | | REDUCE: (17), (58) imply: % 262.32/56.80 | | | | | (59) a_select3(pminus_ds1_filter, n2, n0) = all_74_9 % 262.32/56.80 | | | | | % 262.32/56.80 | | | | | REDUCE: (21), (58) imply: % 262.32/56.80 | | | | | (60) a_select3(pminus_ds1_filter, n0, n2) = all_74_8 % 262.32/56.80 | | | | | % 262.32/56.80 | | | | | REDUCE: (1), (58) imply: % 262.32/56.80 | | | | | (61) leq(n2, n5) % 262.32/56.80 | | | | | % 262.32/56.80 | | | | | REDUCE: (10), (58) imply: % 262.32/56.80 | | | | | (62) leq(n0, n2) % 262.32/56.80 | | | | | % 262.32/56.80 | | | | | GROUND_INST: instantiating (8) with n0, n2, all_74_8, simplifying with % 262.32/56.80 | | | | | (13), (23), (25), (60), (62) gives: % 262.32/56.80 | | | | | (63) ~ leq(n2, all_74_20) | ~ leq(n0, all_74_20) | % 262.32/56.80 | | | | | (a_select3(pminus_ds1_filter, n2, n0) = all_74_8 & % 262.32/56.80 | | | | | $i(all_74_8)) % 262.32/56.80 | | | | | % 262.32/56.80 | | | | | BETA: splitting (63) gives: % 262.32/56.80 | | | | | % 262.32/56.80 | | | | | Case 1: % 262.32/56.80 | | | | | | % 262.32/56.80 | | | | | | (64) ~ leq(n0, all_74_20) % 262.32/56.80 | | | | | | % 262.32/56.80 | | | | | | REDUCE: (22), (64) imply: % 262.32/56.80 | | | | | | (65) ~ leq(n0, n5) % 262.32/56.80 | | | | | | % 262.32/56.80 | | | | | | PRED_UNIFY: (16), (65) imply: % 262.32/56.80 | | | | | | (66) $false % 262.32/56.80 | | | | | | % 262.32/56.80 | | | | | | CLOSE: (66) is inconsistent. % 262.32/56.80 | | | | | | % 262.32/56.80 | | | | | Case 2: % 262.32/56.80 | | | | | | % 262.32/56.80 | | | | | | (67) ~ leq(n2, all_74_20) | (a_select3(pminus_ds1_filter, n2, % 262.32/56.80 | | | | | | n0) = all_74_8 & $i(all_74_8)) % 262.32/56.80 | | | | | | % 262.32/56.80 | | | | | | BETA: splitting (67) gives: % 262.32/56.80 | | | | | | % 262.32/56.80 | | | | | | Case 1: % 262.32/56.80 | | | | | | | % 262.32/56.80 | | | | | | | (68) ~ leq(n2, all_74_20) % 262.32/56.80 | | | | | | | % 262.32/56.80 | | | | | | | REDUCE: (22), (68) imply: % 262.32/56.80 | | | | | | | (69) ~ leq(n2, n5) % 262.32/56.80 | | | | | | | % 262.32/56.80 | | | | | | | PRED_UNIFY: (61), (69) imply: % 262.32/56.80 | | | | | | | (70) $false % 262.32/56.80 | | | | | | | % 262.32/56.80 | | | | | | | CLOSE: (70) is inconsistent. % 262.32/56.80 | | | | | | | % 262.32/56.80 | | | | | | Case 2: % 262.32/56.80 | | | | | | | % 262.32/56.80 | | | | | | | (71) a_select3(pminus_ds1_filter, n2, n0) = all_74_8 & % 262.32/56.80 | | | | | | | $i(all_74_8) % 262.32/56.80 | | | | | | | % 262.32/56.80 | | | | | | | ALPHA: (71) implies: % 262.32/56.80 | | | | | | | (72) a_select3(pminus_ds1_filter, n2, n0) = all_74_8 % 262.32/56.80 | | | | | | | % 262.32/56.80 | | | | | | | REF_CLOSE: (3), (18), (59), (72) are inconsistent by sub-proof % 262.32/56.80 | | | | | | | #50. % 262.32/56.80 | | | | | | | % 262.32/56.80 | | | | | | End of split % 262.32/56.80 | | | | | | % 262.32/56.80 | | | | | End of split % 262.32/56.80 | | | | | % 262.32/56.80 | | | | End of split % 262.32/56.80 | | | | % 262.32/56.80 | | | Case 2: % 262.32/56.80 | | | | % 262.32/56.80 | | | | (73) all_74_11 = n3 % 262.32/56.80 | | | | % 262.32/56.80 | | | | REDUCE: (17), (73) imply: % 262.32/56.80 | | | | (74) a_select3(pminus_ds1_filter, n3, n0) = all_74_9 % 262.32/56.80 | | | | % 262.32/56.80 | | | | REDUCE: (21), (73) imply: % 262.32/56.80 | | | | (75) a_select3(pminus_ds1_filter, n0, n3) = all_74_8 % 262.32/56.80 | | | | % 262.32/56.80 | | | | REDUCE: (1), (73) imply: % 262.32/56.80 | | | | (76) leq(n3, n5) % 262.32/56.80 | | | | % 262.32/56.80 | | | | REDUCE: (10), (73) imply: % 262.32/56.80 | | | | (77) leq(n0, n3) % 262.32/56.80 | | | | % 262.32/56.80 | | | | GROUND_INST: instantiating (8) with n0, n3, all_74_8, simplifying with % 262.32/56.80 | | | | (2), (13), (25), (75), (77) gives: % 262.32/56.80 | | | | (78) ~ leq(n3, all_74_20) | ~ leq(n0, all_74_20) | % 262.32/56.80 | | | | (a_select3(pminus_ds1_filter, n3, n0) = all_74_8 & $i(all_74_8)) % 262.32/56.80 | | | | % 262.32/56.80 | | | | BETA: splitting (78) gives: % 262.32/56.80 | | | | % 262.32/56.80 | | | | Case 1: % 262.32/56.80 | | | | | % 262.32/56.80 | | | | | (79) ~ leq(n0, all_74_20) % 262.32/56.80 | | | | | % 262.32/56.80 | | | | | REDUCE: (22), (79) imply: % 262.32/56.80 | | | | | (80) ~ leq(n0, n5) % 262.32/56.80 | | | | | % 262.32/56.80 | | | | | PRED_UNIFY: (16), (80) imply: % 262.32/56.80 | | | | | (81) $false % 262.32/56.80 | | | | | % 262.32/56.80 | | | | | CLOSE: (81) is inconsistent. % 262.32/56.80 | | | | | % 262.32/56.80 | | | | Case 2: % 262.32/56.80 | | | | | % 262.32/56.80 | | | | | (82) ~ leq(n3, all_74_20) | (a_select3(pminus_ds1_filter, n3, n0) % 262.32/56.80 | | | | | = all_74_8 & $i(all_74_8)) % 262.32/56.80 | | | | | % 262.32/56.80 | | | | | BETA: splitting (82) gives: % 262.32/56.80 | | | | | % 262.32/56.80 | | | | | Case 1: % 262.32/56.80 | | | | | | % 262.32/56.80 | | | | | | (83) ~ leq(n3, all_74_20) % 262.32/56.80 | | | | | | % 262.32/56.80 | | | | | | REDUCE: (22), (83) imply: % 262.32/56.80 | | | | | | (84) ~ leq(n3, n5) % 262.32/56.80 | | | | | | % 262.32/56.80 | | | | | | PRED_UNIFY: (76), (84) imply: % 262.32/56.80 | | | | | | (85) $false % 262.32/56.80 | | | | | | % 262.32/56.80 | | | | | | CLOSE: (85) is inconsistent. % 262.32/56.80 | | | | | | % 262.32/56.80 | | | | | Case 2: % 262.32/56.80 | | | | | | % 262.32/56.80 | | | | | | (86) a_select3(pminus_ds1_filter, n3, n0) = all_74_8 & % 262.32/56.80 | | | | | | $i(all_74_8) % 262.32/56.80 | | | | | | % 262.32/56.80 | | | | | | ALPHA: (86) implies: % 262.32/56.80 | | | | | | (87) a_select3(pminus_ds1_filter, n3, n0) = all_74_8 % 262.32/56.80 | | | | | | % 262.32/56.80 | | | | | | REF_CLOSE: (3), (18), (74), (87) are inconsistent by sub-proof #49. % 262.32/56.80 | | | | | | % 262.32/56.80 | | | | | End of split % 262.32/56.80 | | | | | % 262.32/56.80 | | | | End of split % 262.32/56.80 | | | | % 262.32/56.80 | | | End of split % 262.32/56.80 | | | % 262.32/56.80 | | Case 2: % 262.32/56.80 | | | % 262.32/56.80 | | | (88) all_74_11 = n4 % 262.32/56.80 | | | % 262.32/56.80 | | | REDUCE: (17), (88) imply: % 262.32/56.80 | | | (89) a_select3(pminus_ds1_filter, n4, n0) = all_74_9 % 262.32/56.80 | | | % 262.32/56.80 | | | REDUCE: (21), (88) imply: % 262.32/56.80 | | | (90) a_select3(pminus_ds1_filter, n0, n4) = all_74_8 % 262.32/56.80 | | | % 262.32/56.80 | | | REDUCE: (1), (88) imply: % 262.32/56.80 | | | (91) leq(n4, n5) % 262.32/56.80 | | | % 262.32/56.80 | | | REDUCE: (10), (88) imply: % 262.32/56.80 | | | (92) leq(n0, n4) % 262.32/56.80 | | | % 262.32/56.80 | | | GROUND_INST: instantiating (8) with n0, n4, all_74_8, simplifying with % 262.32/56.80 | | | (4), (13), (25), (90), (92) gives: % 262.32/56.80 | | | (93) ~ leq(n4, all_74_20) | ~ leq(n0, all_74_20) | % 262.32/56.80 | | | (a_select3(pminus_ds1_filter, n4, n0) = all_74_8 & $i(all_74_8)) % 262.32/56.80 | | | % 262.32/56.80 | | | BETA: splitting (93) gives: % 262.32/56.80 | | | % 262.32/56.80 | | | Case 1: % 262.32/56.80 | | | | % 262.32/56.80 | | | | (94) ~ leq(n0, all_74_20) % 262.32/56.80 | | | | % 262.32/56.80 | | | | REDUCE: (22), (94) imply: % 262.32/56.80 | | | | (95) ~ leq(n0, n5) % 262.32/56.80 | | | | % 262.32/56.80 | | | | PRED_UNIFY: (16), (95) imply: % 262.32/56.80 | | | | (96) $false % 262.32/56.80 | | | | % 262.32/56.80 | | | | CLOSE: (96) is inconsistent. % 262.32/56.80 | | | | % 262.32/56.80 | | | Case 2: % 262.32/56.80 | | | | % 262.32/56.80 | | | | (97) ~ leq(n4, all_74_20) | (a_select3(pminus_ds1_filter, n4, n0) = % 262.32/56.80 | | | | all_74_8 & $i(all_74_8)) % 262.32/56.80 | | | | % 262.32/56.80 | | | | BETA: splitting (97) gives: % 262.32/56.80 | | | | % 262.32/56.80 | | | | Case 1: % 262.32/56.80 | | | | | % 262.32/56.81 | | | | | (98) ~ leq(n4, all_74_20) % 262.32/56.81 | | | | | % 262.32/56.81 | | | | | REDUCE: (22), (98) imply: % 262.32/56.81 | | | | | (99) ~ leq(n4, n5) % 262.32/56.81 | | | | | % 262.32/56.81 | | | | | PRED_UNIFY: (91), (99) imply: % 262.32/56.81 | | | | | (100) $false % 262.32/56.81 | | | | | % 262.32/56.81 | | | | | CLOSE: (100) is inconsistent. % 262.32/56.81 | | | | | % 262.32/56.81 | | | | Case 2: % 262.32/56.81 | | | | | % 262.32/56.81 | | | | | (101) a_select3(pminus_ds1_filter, n4, n0) = all_74_8 & % 262.32/56.81 | | | | | $i(all_74_8) % 262.32/56.81 | | | | | % 262.32/56.81 | | | | | ALPHA: (101) implies: % 262.32/56.81 | | | | | (102) a_select3(pminus_ds1_filter, n4, n0) = all_74_8 % 262.32/56.81 | | | | | % 262.32/56.81 | | | | | REF_CLOSE: (3), (18), (89), (102) are inconsistent by sub-proof #48. % 262.32/56.81 | | | | | % 262.32/56.81 | | | | End of split % 262.32/56.81 | | | | % 262.32/56.81 | | | End of split % 262.32/56.81 | | | % 262.32/56.81 | | End of split % 262.32/56.81 | | % 262.32/56.81 | End of split % 262.32/56.81 | % 262.32/56.81 End of proof % 262.32/56.81 % 262.32/56.81 Sub-proof #44 shows that the following formulas are inconsistent: % 262.32/56.81 ---------------------------------------------------------------- % 262.32/56.81 (1) leq(all_74_11, n5) % 262.32/56.81 (2) $i(n3) % 262.32/56.81 (3) leq(all_74_18, n5) % 262.32/56.81 (4) ~ (all_74_8 = all_74_9) % 262.32/56.81 (5) all_74_11 = n5 | gt(n5, all_74_11) % 262.32/56.81 (6) $i(n4) % 262.32/56.81 (7) ! [v0: $i] : (v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0, n1) | ~ % 262.32/56.81 leq(n0, v0)) % 262.32/56.81 (8) pred(n2) = n1 % 262.32/56.81 (9) all_74_11 = n5 | all_74_11 = n4 | all_74_11 = n3 | all_74_11 = n2 | % 262.32/56.81 all_74_11 = n1 | all_74_11 = n0 % 262.32/56.81 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 262.32/56.81 (a_select3(pminus_ds1_filter, v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 262.32/56.81 ~ leq(v1, all_74_20) | ~ leq(v0, all_74_20) | ~ leq(n0, v1) | ~ % 262.32/56.81 leq(n0, v0) | (a_select3(pminus_ds1_filter, v1, v0) = v2 & $i(v2))) % 262.32/56.81 (11) all_74_18 = n6 | all_74_18 = n5 | all_74_18 = n4 | all_74_18 = n3 | % 262.32/56.81 all_74_18 = n2 | all_74_18 = n1 | all_74_18 = n0 % 262.32/56.81 (12) pred(n5) = n4 % 262.32/56.81 (13) leq(n0, all_74_18) % 262.32/56.81 (14) leq(n0, all_74_11) % 262.32/56.81 (15) $i(all_74_18) % 262.32/56.81 (16) a_select3(pminus_ds1_filter, all_74_10, all_74_11) = all_74_8 % 262.32/56.81 (17) ~ gt(n0, n0) % 262.32/56.81 (18) leq(all_74_10, n5) % 262.32/56.81 (19) $i(all_74_10) % 262.32/56.81 (20) $i(all_74_11) % 262.32/56.81 (21) pred(n3) = n2 % 262.32/56.81 (22) ! [v0: $i] : (v0 = n4 | v0 = n3 | v0 = n2 | v0 = n1 | v0 = n0 | ~ % 262.32/56.81 $i(v0) | ~ leq(v0, n4) | ~ leq(n0, v0)) % 262.32/56.81 (23) all_74_10 = n5 | all_74_10 = n4 | all_74_10 = n3 | all_74_10 = n2 | % 262.32/56.81 all_74_10 = n1 | all_74_10 = n0 % 262.32/56.81 (24) all_74_18 = n0 | gt(all_74_18, n0) % 262.32/56.81 (25) a_select3(pminus_ds1_filter, all_74_11, all_74_10) = all_74_9 % 262.32/56.81 (26) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 262.32/56.81 (v1 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 262.32/56.81 v0)) % 262.32/56.81 (27) pred(n4) = n3 % 262.32/56.81 (28) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (pred(v1) = v2) | ~ % 262.32/56.81 $i(v1) | ~ $i(v0) | ~ gt(v1, v0) | leq(v0, v2)) % 262.32/56.81 (29) all_74_10 = n5 | gt(n5, all_74_10) % 262.32/56.81 (30) all_74_20 = n5 % 262.32/56.81 (31) all_74_18 = n4 | all_74_18 = n3 | all_74_18 = n2 | all_74_18 = n1 | % 262.32/56.81 all_74_18 = n0 % 262.32/56.81 (32) $i(n2) % 262.32/56.81 (33) $i(n5) % 262.32/56.81 (34) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ % 262.32/56.81 leq(v0, v1) | gt(v1, v0)) % 262.32/56.81 (35) gt(all_74_10, n0) % 262.32/56.81 (36) leq(n0, all_74_10) % 262.32/56.81 (37) all_74_11 = n0 | gt(all_74_11, n0) % 262.32/56.81 % 262.32/56.81 Begin of proof % 262.32/56.81 | % 262.32/56.81 | BETA: splitting (37) gives: % 262.32/56.81 | % 262.32/56.81 | Case 1: % 262.32/56.81 | | % 262.32/56.81 | | (38) gt(all_74_11, n0) % 262.32/56.81 | | % 262.32/56.81 | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (12), (14), (16), % 262.32/56.81 | | (17), (18), (19), (20), (21), (22), (23), (25), (26), (27), (28), % 262.32/56.81 | | (29), (30), (32), (33), (34), (35), (36), (38) are inconsistent % 262.32/56.81 | | by sub-proof #52. % 262.32/56.81 | | % 262.32/56.81 | Case 2: % 262.32/56.81 | | % 262.32/56.81 | | (39) all_74_11 = n0 % 262.32/56.81 | | (40) ~ gt(all_74_11, n0) % 262.32/56.81 | | % 262.32/56.81 | | REDUCE: (16), (39) imply: % 262.32/56.81 | | (41) a_select3(pminus_ds1_filter, all_74_10, n0) = all_74_8 % 262.32/56.81 | | % 262.32/56.81 | | REDUCE: (25), (39) imply: % 262.32/56.81 | | (42) a_select3(pminus_ds1_filter, n0, all_74_10) = all_74_9 % 262.32/56.81 | | % 262.32/56.81 | | REDUCE: (20), (39) imply: % 262.32/56.81 | | (43) $i(n0) % 262.32/56.81 | | % 262.32/56.81 | | REDUCE: (1), (39) imply: % 262.32/56.81 | | (44) leq(n0, n5) % 262.32/56.81 | | % 262.32/56.81 | | REDUCE: (14), (39) imply: % 262.32/56.81 | | (45) leq(n0, n0) % 262.32/56.81 | | % 262.32/56.81 | | BETA: splitting (29) gives: % 262.32/56.81 | | % 262.32/56.81 | | Case 1: % 262.32/56.81 | | | % 262.32/56.81 | | | (46) gt(n5, all_74_10) % 262.32/56.81 | | | % 262.32/56.81 | | | GROUND_INST: instantiating (28) with all_74_10, n5, n4, simplifying with % 262.32/56.81 | | | (12), (19), (33), (46) gives: % 262.32/56.81 | | | (47) leq(all_74_10, n4) % 262.32/56.81 | | | % 262.32/56.81 | | | REF_CLOSE: (2), (4), (6), (7), (8), (10), (17), (18), (19), (21), (23), % 262.32/56.81 | | | (26), (27), (28), (30), (32), (34), (35), (36), (41), (42), % 262.32/56.81 | | | (43), (44), (45), (47) are inconsistent by sub-proof #47. % 262.32/56.81 | | | % 262.32/56.81 | | Case 2: % 262.32/56.81 | | | % 262.32/56.81 | | | (48) all_74_10 = n5 % 262.32/56.81 | | | % 262.32/56.81 | | | REDUCE: (41), (48) imply: % 262.32/56.81 | | | (49) a_select3(pminus_ds1_filter, n5, n0) = all_74_8 % 262.32/56.81 | | | % 262.32/56.81 | | | REDUCE: (42), (48) imply: % 262.32/56.81 | | | (50) a_select3(pminus_ds1_filter, n0, n5) = all_74_9 % 262.32/56.81 | | | % 262.32/56.81 | | | REDUCE: (18), (48) imply: % 262.32/56.81 | | | (51) leq(n5, n5) % 262.32/56.81 | | | % 262.32/56.81 | | | BETA: splitting (24) gives: % 262.32/56.81 | | | % 262.32/56.81 | | | Case 1: % 262.32/56.81 | | | | % 262.32/56.81 | | | | (52) gt(all_74_18, n0) % 262.32/56.81 | | | | % 262.32/56.81 | | | | BETA: splitting (31) gives: % 262.32/56.81 | | | | % 262.32/56.81 | | | | Case 1: % 262.32/56.81 | | | | | % 262.32/56.81 | | | | | (53) all_74_18 = n0 % 262.32/56.81 | | | | | % 262.32/56.81 | | | | | REDUCE: (52), (53) imply: % 262.32/56.81 | | | | | (54) gt(n0, n0) % 262.32/56.81 | | | | | % 262.32/56.81 | | | | | PRED_UNIFY: (17), (54) imply: % 262.32/56.81 | | | | | (55) $false % 262.32/56.81 | | | | | % 262.32/56.81 | | | | | CLOSE: (55) is inconsistent. % 262.32/56.81 | | | | | % 262.32/56.81 | | | | Case 2: % 262.32/56.81 | | | | | % 262.32/56.81 | | | | | (56) ~ (all_74_18 = n0) % 262.32/56.81 | | | | | % 262.32/56.81 | | | | | BETA: splitting (11) gives: % 262.32/56.81 | | | | | % 262.32/56.81 | | | | | Case 1: % 262.32/56.81 | | | | | | % 262.32/56.81 | | | | | | (57) all_74_18 = n0 % 262.32/56.81 | | | | | | % 262.32/56.81 | | | | | | REDUCE: (56), (57) imply: % 262.32/56.81 | | | | | | (58) $false % 262.32/56.81 | | | | | | % 262.32/56.81 | | | | | | CLOSE: (58) is inconsistent. % 262.32/56.81 | | | | | | % 262.32/56.81 | | | | | Case 2: % 262.32/56.81 | | | | | | % 262.32/56.81 | | | | | | % 262.32/56.81 | | | | | | GROUND_INST: instantiating (10) with n0, n5, all_74_9, simplifying % 262.32/56.81 | | | | | | with (33), (43), (44), (45), (50) gives: % 262.32/56.81 | | | | | | (59) ~ leq(n5, all_74_20) | ~ leq(n0, all_74_20) | % 262.32/56.81 | | | | | | (a_select3(pminus_ds1_filter, n5, n0) = all_74_9 & % 262.32/56.81 | | | | | | $i(all_74_9)) % 262.32/56.81 | | | | | | % 262.32/56.81 | | | | | | REF_CLOSE: (4), (26), (30), (44), (49), (51), (59) are inconsistent % 262.32/56.81 | | | | | | by sub-proof #45. % 262.32/56.81 | | | | | | % 262.32/56.81 | | | | | End of split % 262.32/56.81 | | | | | % 262.32/56.81 | | | | End of split % 262.32/56.81 | | | | % 262.32/56.81 | | | Case 2: % 262.32/56.81 | | | | % 262.32/56.81 | | | | (60) all_74_18 = n0 % 262.32/56.81 | | | | % 262.32/56.81 | | | | GROUND_INST: instantiating (10) with n0, n5, all_74_9, simplifying with % 262.32/56.81 | | | | (33), (43), (44), (45), (50) gives: % 262.32/56.81 | | | | (61) ~ leq(n5, all_74_20) | ~ leq(n0, all_74_20) | % 262.32/56.81 | | | | (a_select3(pminus_ds1_filter, n5, n0) = all_74_9 & $i(all_74_9)) % 262.32/56.81 | | | | % 262.32/56.81 | | | | REF_CLOSE: (4), (26), (30), (44), (49), (51), (61) are inconsistent by % 262.32/56.81 | | | | sub-proof #45. % 262.32/56.81 | | | | % 262.32/56.81 | | | End of split % 262.32/56.81 | | | % 262.32/56.81 | | End of split % 262.32/56.81 | | % 262.32/56.81 | End of split % 262.32/56.81 | % 262.32/56.81 End of proof % 262.32/56.81 % 262.32/56.81 Sub-proof #45 shows that the following formulas are inconsistent: % 262.32/56.81 ---------------------------------------------------------------- % 262.32/56.81 (1) a_select3(pminus_ds1_filter, n5, n0) = all_74_8 % 262.32/56.81 (2) ~ (all_74_8 = all_74_9) % 262.32/56.81 (3) leq(n0, n5) % 262.32/56.81 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 262.32/56.81 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 262.32/56.81 v0)) % 262.32/56.81 (5) leq(n5, n5) % 262.32/56.81 (6) all_74_20 = n5 % 262.32/56.81 (7) ~ leq(n5, all_74_20) | ~ leq(n0, all_74_20) | % 262.32/56.81 (a_select3(pminus_ds1_filter, n5, n0) = all_74_9 & $i(all_74_9)) % 262.32/56.81 % 262.32/56.81 Begin of proof % 262.32/56.81 | % 262.32/56.81 | BETA: splitting (7) gives: % 262.32/56.81 | % 262.32/56.81 | Case 1: % 262.32/56.81 | | % 262.32/56.81 | | (8) ~ leq(n0, all_74_20) % 262.32/56.81 | | % 262.32/56.81 | | REDUCE: (6), (8) imply: % 262.32/56.81 | | (9) ~ leq(n0, n5) % 262.32/56.81 | | % 262.32/56.81 | | PRED_UNIFY: (3), (9) imply: % 262.32/56.81 | | (10) $false % 262.32/56.81 | | % 262.32/56.81 | | CLOSE: (10) is inconsistent. % 262.32/56.81 | | % 262.32/56.81 | Case 2: % 262.32/56.81 | | % 262.32/56.81 | | (11) ~ leq(n5, all_74_20) | (a_select3(pminus_ds1_filter, n5, n0) = % 262.32/56.81 | | all_74_9 & $i(all_74_9)) % 262.32/56.81 | | % 262.32/56.81 | | BETA: splitting (11) gives: % 262.32/56.81 | | % 262.32/56.81 | | Case 1: % 262.32/56.81 | | | % 262.32/56.81 | | | (12) ~ leq(n5, all_74_20) % 262.32/56.81 | | | % 262.32/56.81 | | | REDUCE: (6), (12) imply: % 262.32/56.81 | | | (13) ~ leq(n5, n5) % 262.32/56.81 | | | % 262.32/56.81 | | | PRED_UNIFY: (5), (13) imply: % 262.32/56.81 | | | (14) $false % 262.32/56.81 | | | % 262.32/56.81 | | | CLOSE: (14) is inconsistent. % 262.32/56.81 | | | % 262.32/56.81 | | Case 2: % 262.32/56.81 | | | % 262.32/56.81 | | | (15) a_select3(pminus_ds1_filter, n5, n0) = all_74_9 & $i(all_74_9) % 262.32/56.81 | | | % 262.32/56.81 | | | ALPHA: (15) implies: % 262.32/56.81 | | | (16) a_select3(pminus_ds1_filter, n5, n0) = all_74_9 % 262.32/56.81 | | | % 262.32/56.81 | | | REF_CLOSE: (1), (2), (4), (16) are inconsistent by sub-proof #46. % 262.32/56.81 | | | % 262.32/56.81 | | End of split % 262.32/56.81 | | % 262.32/56.81 | End of split % 262.32/56.81 | % 262.32/56.81 End of proof % 262.32/56.81 % 262.32/56.81 Sub-proof #46 shows that the following formulas are inconsistent: % 262.32/56.81 ---------------------------------------------------------------- % 262.32/56.81 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 262.32/56.81 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 262.32/56.81 v0)) % 262.32/56.81 (2) a_select3(pminus_ds1_filter, n5, n0) = all_74_8 % 262.32/56.81 (3) a_select3(pminus_ds1_filter, n5, n0) = all_74_9 % 262.32/56.81 (4) ~ (all_74_8 = all_74_9) % 262.32/56.81 % 262.32/56.81 Begin of proof % 262.32/56.81 | % 262.32/56.81 | GROUND_INST: instantiating (1) with all_74_8, all_74_9, n0, n5, % 262.32/56.81 | pminus_ds1_filter, simplifying with (2), (3) gives: % 262.32/56.81 | (5) all_74_8 = all_74_9 % 262.32/56.81 | % 262.32/56.81 | REDUCE: (4), (5) imply: % 262.32/56.81 | (6) $false % 262.32/56.81 | % 262.32/56.81 | CLOSE: (6) is inconsistent. % 262.32/56.81 | % 262.32/56.81 End of proof % 262.32/56.81 % 262.32/56.81 Sub-proof #47 shows that the following formulas are inconsistent: % 262.32/56.81 ---------------------------------------------------------------- % 262.32/56.81 (1) a_select3(pminus_ds1_filter, all_74_10, n0) = all_74_8 % 262.32/56.82 (2) $i(n3) % 262.32/56.82 (3) ~ (all_74_8 = all_74_9) % 262.32/56.82 (4) $i(n4) % 262.32/56.82 (5) ! [v0: $i] : (v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0, n1) | ~ % 262.32/56.82 leq(n0, v0)) % 262.32/56.82 (6) pred(n2) = n1 % 262.32/56.82 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 262.32/56.82 (a_select3(pminus_ds1_filter, v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 262.32/56.82 ~ leq(v1, all_74_20) | ~ leq(v0, all_74_20) | ~ leq(n0, v1) | ~ % 262.32/56.82 leq(n0, v0) | (a_select3(pminus_ds1_filter, v1, v0) = v2 & $i(v2))) % 262.32/56.82 (8) leq(all_74_10, n4) % 262.32/56.82 (9) a_select3(pminus_ds1_filter, n0, all_74_10) = all_74_9 % 262.32/56.82 (10) ~ gt(n0, n0) % 262.32/56.82 (11) leq(all_74_10, n5) % 262.32/56.82 (12) $i(n0) % 262.32/56.82 (13) $i(all_74_10) % 262.32/56.82 (14) pred(n3) = n2 % 262.32/56.82 (15) leq(n0, n5) % 262.32/56.82 (16) all_74_10 = n5 | all_74_10 = n4 | all_74_10 = n3 | all_74_10 = n2 | % 262.32/56.82 all_74_10 = n1 | all_74_10 = n0 % 262.32/56.82 (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 262.32/56.82 (v1 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 262.32/56.82 v0)) % 262.32/56.82 (18) pred(n4) = n3 % 262.32/56.82 (19) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (pred(v1) = v2) | ~ % 262.32/56.82 $i(v1) | ~ $i(v0) | ~ gt(v1, v0) | leq(v0, v2)) % 262.32/56.82 (20) all_74_20 = n5 % 262.32/56.82 (21) $i(n2) % 262.32/56.82 (22) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ % 262.32/56.82 leq(v0, v1) | gt(v1, v0)) % 262.32/56.82 (23) leq(n0, n0) % 262.32/56.82 (24) gt(all_74_10, n0) % 262.32/56.82 (25) leq(n0, all_74_10) % 262.32/56.82 % 262.32/56.82 Begin of proof % 262.32/56.82 | % 262.32/56.82 | GROUND_INST: instantiating (22) with all_74_10, n4, simplifying with (4), (8), % 262.32/56.82 | (13) gives: % 262.32/56.82 | (26) all_74_10 = n4 | gt(n4, all_74_10) % 262.32/56.82 | % 262.32/56.82 | BETA: splitting (16) gives: % 262.32/56.82 | % 262.32/56.82 | Case 1: % 262.32/56.82 | | % 262.32/56.82 | | (27) all_74_10 = n0 % 262.32/56.82 | | % 262.32/56.82 | | REDUCE: (24), (27) imply: % 262.32/56.82 | | (28) gt(n0, n0) % 262.32/56.82 | | % 262.32/56.82 | | PRED_UNIFY: (10), (28) imply: % 262.32/56.82 | | (29) $false % 262.32/56.82 | | % 262.32/56.82 | | CLOSE: (29) is inconsistent. % 262.32/56.82 | | % 262.32/56.82 | Case 2: % 262.32/56.82 | | % 262.32/56.82 | | (30) ~ (all_74_10 = n0) % 262.32/56.82 | | % 262.32/56.82 | | BETA: splitting (26) gives: % 262.32/56.82 | | % 262.32/56.82 | | Case 1: % 262.32/56.82 | | | % 262.32/56.82 | | | (31) gt(n4, all_74_10) % 262.32/56.82 | | | % 262.32/56.82 | | | GROUND_INST: instantiating (19) with all_74_10, n4, n3, simplifying with % 262.32/56.82 | | | (4), (13), (18), (31) gives: % 262.32/56.82 | | | (32) leq(all_74_10, n3) % 262.32/56.82 | | | % 262.32/56.82 | | | GROUND_INST: instantiating (22) with all_74_10, n3, simplifying with (2), % 262.32/56.82 | | | (13), (32) gives: % 262.32/56.82 | | | (33) all_74_10 = n3 | gt(n3, all_74_10) % 262.32/56.82 | | | % 262.32/56.82 | | | BETA: splitting (33) gives: % 262.32/56.82 | | | % 262.32/56.82 | | | Case 1: % 262.32/56.82 | | | | % 262.32/56.82 | | | | (34) gt(n3, all_74_10) % 262.32/56.82 | | | | % 262.32/56.82 | | | | GROUND_INST: instantiating (19) with all_74_10, n3, n2, simplifying with % 262.32/56.82 | | | | (2), (13), (14), (34) gives: % 262.32/56.82 | | | | (35) leq(all_74_10, n2) % 262.32/56.82 | | | | % 262.32/56.82 | | | | GROUND_INST: instantiating (22) with all_74_10, n2, simplifying with % 262.32/56.82 | | | | (13), (21), (35) gives: % 262.32/56.82 | | | | (36) all_74_10 = n2 | gt(n2, all_74_10) % 262.32/56.82 | | | | % 262.32/56.82 | | | | BETA: splitting (36) gives: % 262.32/56.82 | | | | % 262.32/56.82 | | | | Case 1: % 262.32/56.82 | | | | | % 262.32/56.82 | | | | | (37) gt(n2, all_74_10) % 262.32/56.82 | | | | | % 262.32/56.82 | | | | | GROUND_INST: instantiating (19) with all_74_10, n2, n1, simplifying % 262.32/56.82 | | | | | with (6), (13), (21), (37) gives: % 262.32/56.82 | | | | | (38) leq(all_74_10, n1) % 262.32/56.82 | | | | | % 262.32/56.82 | | | | | GROUND_INST: instantiating (5) with all_74_10, simplifying with (13), % 262.32/56.82 | | | | | (25), (38) gives: % 262.32/56.82 | | | | | (39) all_74_10 = n1 | all_74_10 = n0 % 262.32/56.82 | | | | | % 262.32/56.82 | | | | | BETA: splitting (39) gives: % 262.32/56.82 | | | | | % 262.32/56.82 | | | | | Case 1: % 262.32/56.82 | | | | | | % 262.32/56.82 | | | | | | (40) all_74_10 = n0 % 262.32/56.82 | | | | | | % 262.32/56.82 | | | | | | REDUCE: (30), (40) imply: % 262.32/56.82 | | | | | | (41) $false % 262.32/56.82 | | | | | | % 262.32/56.82 | | | | | | CLOSE: (41) is inconsistent. % 262.32/56.82 | | | | | | % 262.32/56.82 | | | | | Case 2: % 262.32/56.82 | | | | | | % 262.32/56.82 | | | | | | (42) all_74_10 = n1 % 262.32/56.82 | | | | | | % 262.32/56.82 | | | | | | REDUCE: (1), (42) imply: % 262.32/56.82 | | | | | | (43) a_select3(pminus_ds1_filter, n1, n0) = all_74_8 % 262.32/56.82 | | | | | | % 262.32/56.82 | | | | | | REDUCE: (9), (42) imply: % 262.32/56.82 | | | | | | (44) a_select3(pminus_ds1_filter, n0, n1) = all_74_9 % 262.32/56.82 | | | | | | % 262.32/56.82 | | | | | | REDUCE: (13), (42) imply: % 262.32/56.82 | | | | | | (45) $i(n1) % 262.32/56.82 | | | | | | % 262.32/56.82 | | | | | | REDUCE: (11), (42) imply: % 262.32/56.82 | | | | | | (46) leq(n1, n5) % 262.32/56.82 | | | | | | % 262.32/56.82 | | | | | | REDUCE: (25), (42) imply: % 262.32/56.82 | | | | | | (47) leq(n0, n1) % 262.32/56.82 | | | | | | % 262.32/56.82 | | | | | | GROUND_INST: instantiating (7) with n0, n1, all_74_9, simplifying % 262.32/56.82 | | | | | | with (12), (23), (44), (45), (47) gives: % 262.32/56.82 | | | | | | (48) ~ leq(n1, all_74_20) | ~ leq(n0, all_74_20) | % 262.32/56.82 | | | | | | (a_select3(pminus_ds1_filter, n1, n0) = all_74_9 & % 262.32/56.82 | | | | | | $i(all_74_9)) % 262.32/56.82 | | | | | | % 262.32/56.82 | | | | | | BETA: splitting (48) gives: % 262.32/56.82 | | | | | | % 262.32/56.82 | | | | | | Case 1: % 262.32/56.82 | | | | | | | % 262.32/56.82 | | | | | | | (49) ~ leq(n0, all_74_20) % 262.32/56.82 | | | | | | | % 262.32/56.82 | | | | | | | REDUCE: (20), (49) imply: % 262.32/56.82 | | | | | | | (50) ~ leq(n0, n5) % 262.32/56.82 | | | | | | | % 262.32/56.82 | | | | | | | PRED_UNIFY: (15), (50) imply: % 262.32/56.82 | | | | | | | (51) $false % 262.32/56.82 | | | | | | | % 262.32/56.82 | | | | | | | CLOSE: (51) is inconsistent. % 262.32/56.82 | | | | | | | % 262.32/56.82 | | | | | | Case 2: % 262.32/56.82 | | | | | | | % 262.32/56.82 | | | | | | | (52) ~ leq(n1, all_74_20) | (a_select3(pminus_ds1_filter, n1, % 262.32/56.82 | | | | | | | n0) = all_74_9 & $i(all_74_9)) % 262.32/56.82 | | | | | | | % 262.32/56.82 | | | | | | | BETA: splitting (52) gives: % 262.32/56.82 | | | | | | | % 262.32/56.82 | | | | | | | Case 1: % 262.32/56.82 | | | | | | | | % 262.32/56.82 | | | | | | | | (53) ~ leq(n1, all_74_20) % 262.32/56.82 | | | | | | | | % 262.32/56.82 | | | | | | | | REDUCE: (20), (53) imply: % 262.32/56.82 | | | | | | | | (54) ~ leq(n1, n5) % 262.32/56.82 | | | | | | | | % 262.32/56.82 | | | | | | | | PRED_UNIFY: (46), (54) imply: % 262.32/56.82 | | | | | | | | (55) $false % 262.32/56.82 | | | | | | | | % 262.32/56.82 | | | | | | | | CLOSE: (55) is inconsistent. % 262.32/56.82 | | | | | | | | % 262.32/56.82 | | | | | | | Case 2: % 262.32/56.82 | | | | | | | | % 262.32/56.82 | | | | | | | | (56) a_select3(pminus_ds1_filter, n1, n0) = all_74_9 & % 262.32/56.82 | | | | | | | | $i(all_74_9) % 262.32/56.82 | | | | | | | | % 262.32/56.82 | | | | | | | | ALPHA: (56) implies: % 262.32/56.82 | | | | | | | | (57) a_select3(pminus_ds1_filter, n1, n0) = all_74_9 % 262.32/56.82 | | | | | | | | % 262.32/56.82 | | | | | | | | REF_CLOSE: (3), (17), (43), (57) are inconsistent by sub-proof % 262.32/56.82 | | | | | | | | #51. % 262.32/56.82 | | | | | | | | % 262.32/56.82 | | | | | | | End of split % 262.32/56.82 | | | | | | | % 262.32/56.82 | | | | | | End of split % 262.32/56.82 | | | | | | % 262.32/56.82 | | | | | End of split % 262.32/56.82 | | | | | % 262.32/56.82 | | | | Case 2: % 262.32/56.82 | | | | | % 262.32/56.82 | | | | | (58) all_74_10 = n2 % 262.32/56.82 | | | | | % 262.32/56.82 | | | | | REDUCE: (1), (58) imply: % 262.32/56.82 | | | | | (59) a_select3(pminus_ds1_filter, n2, n0) = all_74_8 % 262.32/56.82 | | | | | % 262.32/56.82 | | | | | REDUCE: (9), (58) imply: % 262.32/56.82 | | | | | (60) a_select3(pminus_ds1_filter, n0, n2) = all_74_9 % 262.32/56.82 | | | | | % 262.32/56.82 | | | | | REDUCE: (11), (58) imply: % 262.32/56.82 | | | | | (61) leq(n2, n5) % 262.32/56.82 | | | | | % 262.32/56.82 | | | | | REDUCE: (25), (58) imply: % 262.32/56.82 | | | | | (62) leq(n0, n2) % 262.32/56.82 | | | | | % 262.32/56.82 | | | | | GROUND_INST: instantiating (7) with n0, n2, all_74_9, simplifying with % 262.32/56.82 | | | | | (12), (21), (23), (60), (62) gives: % 262.32/56.82 | | | | | (63) ~ leq(n2, all_74_20) | ~ leq(n0, all_74_20) | % 262.32/56.82 | | | | | (a_select3(pminus_ds1_filter, n2, n0) = all_74_9 & % 262.32/56.82 | | | | | $i(all_74_9)) % 262.32/56.82 | | | | | % 262.32/56.82 | | | | | BETA: splitting (63) gives: % 262.32/56.82 | | | | | % 262.32/56.82 | | | | | Case 1: % 262.32/56.82 | | | | | | % 262.32/56.82 | | | | | | (64) ~ leq(n0, all_74_20) % 262.32/56.82 | | | | | | % 262.32/56.82 | | | | | | REDUCE: (20), (64) imply: % 262.32/56.82 | | | | | | (65) ~ leq(n0, n5) % 262.32/56.82 | | | | | | % 262.32/56.82 | | | | | | PRED_UNIFY: (15), (65) imply: % 262.32/56.82 | | | | | | (66) $false % 262.32/56.82 | | | | | | % 262.32/56.82 | | | | | | CLOSE: (66) is inconsistent. % 262.32/56.82 | | | | | | % 262.32/56.82 | | | | | Case 2: % 262.32/56.82 | | | | | | % 262.32/56.82 | | | | | | (67) ~ leq(n2, all_74_20) | (a_select3(pminus_ds1_filter, n2, % 262.32/56.82 | | | | | | n0) = all_74_9 & $i(all_74_9)) % 262.32/56.82 | | | | | | % 262.32/56.82 | | | | | | BETA: splitting (67) gives: % 262.32/56.82 | | | | | | % 262.32/56.82 | | | | | | Case 1: % 262.32/56.82 | | | | | | | % 262.32/56.82 | | | | | | | (68) ~ leq(n2, all_74_20) % 262.32/56.82 | | | | | | | % 262.32/56.82 | | | | | | | REDUCE: (20), (68) imply: % 262.32/56.82 | | | | | | | (69) ~ leq(n2, n5) % 262.32/56.82 | | | | | | | % 262.32/56.82 | | | | | | | PRED_UNIFY: (61), (69) imply: % 262.32/56.82 | | | | | | | (70) $false % 262.32/56.82 | | | | | | | % 262.32/56.82 | | | | | | | CLOSE: (70) is inconsistent. % 262.32/56.82 | | | | | | | % 262.32/56.82 | | | | | | Case 2: % 262.32/56.82 | | | | | | | % 262.32/56.82 | | | | | | | (71) a_select3(pminus_ds1_filter, n2, n0) = all_74_9 & % 262.32/56.82 | | | | | | | $i(all_74_9) % 262.32/56.82 | | | | | | | % 262.32/56.82 | | | | | | | ALPHA: (71) implies: % 262.32/56.82 | | | | | | | (72) a_select3(pminus_ds1_filter, n2, n0) = all_74_9 % 262.32/56.82 | | | | | | | % 262.32/56.82 | | | | | | | REF_CLOSE: (3), (17), (59), (72) are inconsistent by sub-proof % 262.32/56.82 | | | | | | | #50. % 262.32/56.82 | | | | | | | % 262.32/56.82 | | | | | | End of split % 262.32/56.82 | | | | | | % 262.32/56.82 | | | | | End of split % 262.32/56.82 | | | | | % 262.32/56.82 | | | | End of split % 262.32/56.82 | | | | % 262.32/56.82 | | | Case 2: % 262.32/56.82 | | | | % 262.32/56.82 | | | | (73) all_74_10 = n3 % 262.32/56.82 | | | | % 262.32/56.82 | | | | REDUCE: (1), (73) imply: % 262.32/56.82 | | | | (74) a_select3(pminus_ds1_filter, n3, n0) = all_74_8 % 262.32/56.82 | | | | % 262.32/56.82 | | | | REDUCE: (9), (73) imply: % 262.32/56.82 | | | | (75) a_select3(pminus_ds1_filter, n0, n3) = all_74_9 % 262.32/56.82 | | | | % 262.32/56.82 | | | | REDUCE: (11), (73) imply: % 262.32/56.82 | | | | (76) leq(n3, n5) % 262.32/56.82 | | | | % 262.32/56.82 | | | | REDUCE: (25), (73) imply: % 262.32/56.82 | | | | (77) leq(n0, n3) % 262.32/56.82 | | | | % 262.32/56.82 | | | | GROUND_INST: instantiating (7) with n0, n3, all_74_9, simplifying with % 262.32/56.82 | | | | (2), (12), (23), (75), (77) gives: % 262.32/56.82 | | | | (78) ~ leq(n3, all_74_20) | ~ leq(n0, all_74_20) | % 262.32/56.82 | | | | (a_select3(pminus_ds1_filter, n3, n0) = all_74_9 & $i(all_74_9)) % 262.32/56.82 | | | | % 262.32/56.82 | | | | BETA: splitting (78) gives: % 262.32/56.82 | | | | % 262.32/56.82 | | | | Case 1: % 262.32/56.82 | | | | | % 262.32/56.82 | | | | | (79) ~ leq(n0, all_74_20) % 262.32/56.82 | | | | | % 262.32/56.82 | | | | | REDUCE: (20), (79) imply: % 262.32/56.82 | | | | | (80) ~ leq(n0, n5) % 262.32/56.82 | | | | | % 262.32/56.82 | | | | | PRED_UNIFY: (15), (80) imply: % 262.32/56.82 | | | | | (81) $false % 262.32/56.82 | | | | | % 262.32/56.82 | | | | | CLOSE: (81) is inconsistent. % 262.32/56.82 | | | | | % 262.32/56.82 | | | | Case 2: % 262.32/56.82 | | | | | % 262.32/56.82 | | | | | (82) ~ leq(n3, all_74_20) | (a_select3(pminus_ds1_filter, n3, n0) % 262.32/56.82 | | | | | = all_74_9 & $i(all_74_9)) % 262.32/56.82 | | | | | % 262.32/56.82 | | | | | BETA: splitting (82) gives: % 262.32/56.82 | | | | | % 262.32/56.82 | | | | | Case 1: % 262.32/56.82 | | | | | | % 262.32/56.82 | | | | | | (83) ~ leq(n3, all_74_20) % 262.32/56.82 | | | | | | % 262.32/56.82 | | | | | | REDUCE: (20), (83) imply: % 262.32/56.82 | | | | | | (84) ~ leq(n3, n5) % 262.32/56.82 | | | | | | % 262.32/56.82 | | | | | | PRED_UNIFY: (76), (84) imply: % 262.32/56.82 | | | | | | (85) $false % 262.32/56.82 | | | | | | % 262.32/56.82 | | | | | | CLOSE: (85) is inconsistent. % 262.32/56.82 | | | | | | % 262.32/56.82 | | | | | Case 2: % 262.32/56.82 | | | | | | % 262.32/56.82 | | | | | | (86) a_select3(pminus_ds1_filter, n3, n0) = all_74_9 & % 262.32/56.82 | | | | | | $i(all_74_9) % 262.32/56.82 | | | | | | % 262.32/56.82 | | | | | | ALPHA: (86) implies: % 262.32/56.82 | | | | | | (87) a_select3(pminus_ds1_filter, n3, n0) = all_74_9 % 262.32/56.82 | | | | | | % 262.32/56.82 | | | | | | REF_CLOSE: (3), (17), (74), (87) are inconsistent by sub-proof #49. % 262.32/56.82 | | | | | | % 262.32/56.82 | | | | | End of split % 262.32/56.82 | | | | | % 262.32/56.82 | | | | End of split % 262.32/56.82 | | | | % 262.32/56.82 | | | End of split % 262.32/56.82 | | | % 262.32/56.82 | | Case 2: % 262.32/56.82 | | | % 262.32/56.82 | | | (88) all_74_10 = n4 % 262.32/56.82 | | | % 262.32/56.82 | | | REDUCE: (1), (88) imply: % 262.32/56.82 | | | (89) a_select3(pminus_ds1_filter, n4, n0) = all_74_8 % 262.32/56.82 | | | % 262.32/56.82 | | | REDUCE: (9), (88) imply: % 262.32/56.82 | | | (90) a_select3(pminus_ds1_filter, n0, n4) = all_74_9 % 262.32/56.82 | | | % 262.32/56.82 | | | REDUCE: (11), (88) imply: % 262.32/56.82 | | | (91) leq(n4, n5) % 262.32/56.82 | | | % 262.32/56.82 | | | REDUCE: (25), (88) imply: % 262.32/56.82 | | | (92) leq(n0, n4) % 262.32/56.82 | | | % 262.32/56.82 | | | GROUND_INST: instantiating (7) with n0, n4, all_74_9, simplifying with % 262.32/56.82 | | | (4), (12), (23), (90), (92) gives: % 262.32/56.82 | | | (93) ~ leq(n4, all_74_20) | ~ leq(n0, all_74_20) | % 262.32/56.82 | | | (a_select3(pminus_ds1_filter, n4, n0) = all_74_9 & $i(all_74_9)) % 262.32/56.82 | | | % 262.32/56.82 | | | BETA: splitting (93) gives: % 262.32/56.82 | | | % 262.32/56.82 | | | Case 1: % 262.32/56.82 | | | | % 262.32/56.82 | | | | (94) ~ leq(n0, all_74_20) % 262.32/56.82 | | | | % 262.32/56.82 | | | | REDUCE: (20), (94) imply: % 262.32/56.82 | | | | (95) ~ leq(n0, n5) % 262.32/56.82 | | | | % 262.32/56.82 | | | | PRED_UNIFY: (15), (95) imply: % 262.32/56.82 | | | | (96) $false % 262.32/56.82 | | | | % 262.32/56.82 | | | | CLOSE: (96) is inconsistent. % 262.32/56.82 | | | | % 262.32/56.82 | | | Case 2: % 262.32/56.82 | | | | % 262.32/56.82 | | | | (97) ~ leq(n4, all_74_20) | (a_select3(pminus_ds1_filter, n4, n0) = % 262.32/56.82 | | | | all_74_9 & $i(all_74_9)) % 262.32/56.82 | | | | % 262.32/56.82 | | | | BETA: splitting (97) gives: % 262.32/56.82 | | | | % 262.32/56.82 | | | | Case 1: % 262.32/56.82 | | | | | % 262.32/56.82 | | | | | (98) ~ leq(n4, all_74_20) % 262.32/56.82 | | | | | % 262.32/56.82 | | | | | REDUCE: (20), (98) imply: % 262.32/56.82 | | | | | (99) ~ leq(n4, n5) % 262.32/56.82 | | | | | % 262.32/56.82 | | | | | PRED_UNIFY: (91), (99) imply: % 262.32/56.82 | | | | | (100) $false % 262.32/56.82 | | | | | % 262.32/56.82 | | | | | CLOSE: (100) is inconsistent. % 262.32/56.82 | | | | | % 262.32/56.82 | | | | Case 2: % 262.32/56.82 | | | | | % 262.32/56.83 | | | | | (101) a_select3(pminus_ds1_filter, n4, n0) = all_74_9 & % 262.32/56.83 | | | | | $i(all_74_9) % 262.32/56.83 | | | | | % 262.32/56.83 | | | | | ALPHA: (101) implies: % 262.32/56.83 | | | | | (102) a_select3(pminus_ds1_filter, n4, n0) = all_74_9 % 262.32/56.83 | | | | | % 262.32/56.83 | | | | | REF_CLOSE: (3), (17), (89), (102) are inconsistent by sub-proof #48. % 262.32/56.83 | | | | | % 262.32/56.83 | | | | End of split % 262.32/56.83 | | | | % 262.32/56.83 | | | End of split % 262.32/56.83 | | | % 262.32/56.83 | | End of split % 262.32/56.83 | | % 262.32/56.83 | End of split % 262.32/56.83 | % 262.32/56.83 End of proof % 262.32/56.83 % 262.32/56.83 Sub-proof #48 shows that the following formulas are inconsistent: % 262.32/56.83 ---------------------------------------------------------------- % 262.32/56.83 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 262.32/56.83 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 262.32/56.83 v0)) % 262.32/56.83 (2) a_select3(pminus_ds1_filter, n4, n0) = all_74_8 % 262.32/56.83 (3) a_select3(pminus_ds1_filter, n4, n0) = all_74_9 % 262.32/56.83 (4) ~ (all_74_8 = all_74_9) % 262.32/56.83 % 262.32/56.83 Begin of proof % 262.32/56.83 | % 262.32/56.83 | GROUND_INST: instantiating (1) with all_74_8, all_74_9, n0, n4, % 262.32/56.83 | pminus_ds1_filter, simplifying with (2), (3) gives: % 262.32/56.83 | (5) all_74_8 = all_74_9 % 262.32/56.83 | % 262.32/56.83 | REDUCE: (4), (5) imply: % 262.32/56.83 | (6) $false % 262.32/56.83 | % 262.32/56.83 | CLOSE: (6) is inconsistent. % 262.32/56.83 | % 262.32/56.83 End of proof % 262.32/56.83 % 262.32/56.83 Sub-proof #49 shows that the following formulas are inconsistent: % 262.32/56.83 ---------------------------------------------------------------- % 262.32/56.83 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 262.32/56.83 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 262.32/56.83 v0)) % 262.32/56.83 (2) a_select3(pminus_ds1_filter, n3, n0) = all_74_8 % 262.32/56.83 (3) a_select3(pminus_ds1_filter, n3, n0) = all_74_9 % 262.32/56.83 (4) ~ (all_74_8 = all_74_9) % 262.32/56.83 % 262.32/56.83 Begin of proof % 262.32/56.83 | % 262.32/56.83 | GROUND_INST: instantiating (1) with all_74_8, all_74_9, n0, n3, % 262.32/56.83 | pminus_ds1_filter, simplifying with (2), (3) gives: % 262.32/56.83 | (5) all_74_8 = all_74_9 % 262.32/56.83 | % 262.32/56.83 | REDUCE: (4), (5) imply: % 262.32/56.83 | (6) $false % 262.32/56.83 | % 262.32/56.83 | CLOSE: (6) is inconsistent. % 262.32/56.83 | % 262.32/56.83 End of proof % 262.32/56.83 % 262.32/56.83 Sub-proof #50 shows that the following formulas are inconsistent: % 262.32/56.83 ---------------------------------------------------------------- % 262.32/56.83 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 262.32/56.83 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 262.32/56.83 v0)) % 262.32/56.83 (2) a_select3(pminus_ds1_filter, n2, n0) = all_74_8 % 262.32/56.83 (3) a_select3(pminus_ds1_filter, n2, n0) = all_74_9 % 262.32/56.83 (4) ~ (all_74_8 = all_74_9) % 262.32/56.83 % 262.32/56.83 Begin of proof % 262.32/56.83 | % 262.32/56.83 | GROUND_INST: instantiating (1) with all_74_8, all_74_9, n0, n2, % 262.32/56.83 | pminus_ds1_filter, simplifying with (2), (3) gives: % 262.32/56.83 | (5) all_74_8 = all_74_9 % 262.32/56.83 | % 262.32/56.83 | REDUCE: (4), (5) imply: % 262.32/56.83 | (6) $false % 262.32/56.83 | % 262.32/56.83 | CLOSE: (6) is inconsistent. % 262.32/56.83 | % 262.32/56.83 End of proof % 262.32/56.83 % 262.32/56.83 Sub-proof #51 shows that the following formulas are inconsistent: % 262.32/56.83 ---------------------------------------------------------------- % 262.32/56.83 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 262.32/56.83 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 262.32/56.83 v0)) % 262.32/56.83 (2) a_select3(pminus_ds1_filter, n1, n0) = all_74_8 % 262.32/56.83 (3) a_select3(pminus_ds1_filter, n1, n0) = all_74_9 % 262.32/56.83 (4) ~ (all_74_8 = all_74_9) % 262.32/56.83 % 262.32/56.83 Begin of proof % 262.32/56.83 | % 262.32/56.83 | GROUND_INST: instantiating (1) with all_74_8, all_74_9, n0, n1, % 262.32/56.83 | pminus_ds1_filter, simplifying with (2), (3) gives: % 262.32/56.83 | (5) all_74_8 = all_74_9 % 262.32/56.83 | % 262.32/56.83 | REDUCE: (4), (5) imply: % 262.32/56.83 | (6) $false % 262.32/56.83 | % 262.32/56.83 | CLOSE: (6) is inconsistent. % 262.32/56.83 | % 262.32/56.83 End of proof % 262.32/56.83 % 262.32/56.83 Sub-proof #52 shows that the following formulas are inconsistent: % 262.32/56.83 ---------------------------------------------------------------- % 262.32/56.83 (1) leq(all_74_11, n5) % 262.32/56.83 (2) $i(n3) % 262.32/56.83 (3) ~ (all_74_8 = all_74_9) % 262.32/56.83 (4) all_74_11 = n5 | gt(n5, all_74_11) % 262.32/56.83 (5) $i(n4) % 262.32/56.83 (6) ! [v0: $i] : (v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0, n1) | ~ % 262.32/56.83 leq(n0, v0)) % 262.32/56.83 (7) pred(n2) = n1 % 262.32/56.83 (8) all_74_11 = n5 | all_74_11 = n4 | all_74_11 = n3 | all_74_11 = n2 | % 262.32/56.83 all_74_11 = n1 | all_74_11 = n0 % 262.32/56.83 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 262.32/56.83 (a_select3(pminus_ds1_filter, v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 262.32/56.83 ~ leq(v1, all_74_20) | ~ leq(v0, all_74_20) | ~ leq(n0, v1) | ~ % 262.32/56.83 leq(n0, v0) | (a_select3(pminus_ds1_filter, v1, v0) = v2 & $i(v2))) % 262.32/56.83 (10) pred(n5) = n4 % 262.32/56.83 (11) gt(all_74_11, n0) % 262.32/56.83 (12) leq(n0, all_74_11) % 262.32/56.83 (13) a_select3(pminus_ds1_filter, all_74_10, all_74_11) = all_74_8 % 262.32/56.83 (14) ~ gt(n0, n0) % 262.32/56.83 (15) leq(all_74_10, n5) % 262.32/56.83 (16) $i(all_74_10) % 262.32/56.83 (17) $i(all_74_11) % 262.32/56.83 (18) pred(n3) = n2 % 262.32/56.83 (19) ! [v0: $i] : (v0 = n4 | v0 = n3 | v0 = n2 | v0 = n1 | v0 = n0 | ~ % 262.32/56.83 $i(v0) | ~ leq(v0, n4) | ~ leq(n0, v0)) % 262.32/56.83 (20) all_74_10 = n5 | all_74_10 = n4 | all_74_10 = n3 | all_74_10 = n2 | % 262.32/56.83 all_74_10 = n1 | all_74_10 = n0 % 262.32/56.83 (21) a_select3(pminus_ds1_filter, all_74_11, all_74_10) = all_74_9 % 262.32/56.83 (22) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 262.32/56.83 (v1 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 262.32/56.83 v0)) % 262.32/56.83 (23) pred(n4) = n3 % 262.32/56.83 (24) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (pred(v1) = v2) | ~ % 262.32/56.83 $i(v1) | ~ $i(v0) | ~ gt(v1, v0) | leq(v0, v2)) % 262.32/56.83 (25) all_74_10 = n5 | gt(n5, all_74_10) % 262.32/56.83 (26) all_74_20 = n5 % 262.32/56.83 (27) $i(n2) % 262.32/56.83 (28) $i(n5) % 262.32/56.83 (29) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ % 262.32/56.83 leq(v0, v1) | gt(v1, v0)) % 262.32/56.83 (30) gt(all_74_10, n0) % 262.32/56.83 (31) leq(n0, all_74_10) % 262.32/56.83 % 262.32/56.83 Begin of proof % 262.32/56.83 | % 262.32/56.83 | BETA: splitting (4) gives: % 262.32/56.83 | % 262.32/56.83 | Case 1: % 262.32/56.83 | | % 262.32/56.83 | | (32) gt(n5, all_74_11) % 262.32/56.83 | | % 262.32/56.83 | | GROUND_INST: instantiating (24) with all_74_11, n5, n4, simplifying with % 262.32/56.83 | | (10), (17), (28), (32) gives: % 262.32/56.83 | | (33) leq(all_74_11, n4) % 262.32/56.83 | | % 262.32/56.83 | | BETA: splitting (25) gives: % 262.32/56.83 | | % 262.32/56.83 | | Case 1: % 262.32/56.83 | | | % 262.32/56.83 | | | (34) gt(n5, all_74_10) % 262.32/56.83 | | | % 262.32/56.83 | | | GROUND_INST: instantiating (24) with all_74_10, n5, n4, simplifying with % 262.32/56.83 | | | (10), (16), (28), (34) gives: % 262.32/56.83 | | | (35) leq(all_74_10, n4) % 262.32/56.83 | | | % 262.32/56.83 | | | GROUND_INST: instantiating (29) with all_74_11, n4, simplifying with (5), % 262.32/56.83 | | | (17), (33) gives: % 262.32/56.83 | | | (36) all_74_11 = n4 | gt(n4, all_74_11) % 262.32/56.83 | | | % 262.32/56.83 | | | BETA: splitting (8) gives: % 262.32/56.83 | | | % 262.32/56.83 | | | Case 1: % 262.32/56.83 | | | | % 262.32/56.83 | | | | (37) all_74_11 = n0 % 262.32/56.83 | | | | % 262.32/56.83 | | | | REDUCE: (11), (37) imply: % 262.32/56.83 | | | | (38) gt(n0, n0) % 262.32/56.83 | | | | % 262.32/56.83 | | | | PRED_UNIFY: (14), (38) imply: % 262.32/56.83 | | | | (39) $false % 262.32/56.83 | | | | % 262.32/56.83 | | | | CLOSE: (39) is inconsistent. % 262.32/56.83 | | | | % 262.32/56.83 | | | Case 2: % 262.32/56.83 | | | | % 262.32/56.83 | | | | (40) ~ (all_74_11 = n0) % 262.32/56.83 | | | | % 262.32/56.83 | | | | BETA: splitting (20) gives: % 262.32/56.83 | | | | % 262.32/56.83 | | | | Case 1: % 262.32/56.83 | | | | | % 262.32/56.83 | | | | | (41) all_74_10 = n0 % 262.32/56.83 | | | | | % 262.32/56.83 | | | | | REDUCE: (30), (41) imply: % 262.32/56.83 | | | | | (42) gt(n0, n0) % 262.32/56.83 | | | | | % 262.32/56.83 | | | | | PRED_UNIFY: (14), (42) imply: % 262.32/56.83 | | | | | (43) $false % 262.32/56.83 | | | | | % 262.32/56.83 | | | | | CLOSE: (43) is inconsistent. % 262.32/56.83 | | | | | % 262.32/56.83 | | | | Case 2: % 262.32/56.83 | | | | | % 262.32/56.83 | | | | | (44) ~ (all_74_10 = n0) % 262.32/56.83 | | | | | % 262.32/56.83 | | | | | GROUND_INST: instantiating (29) with all_74_10, n4, simplifying with % 262.32/56.83 | | | | | (5), (16), (35) gives: % 262.32/56.83 | | | | | (45) all_74_10 = n4 | gt(n4, all_74_10) % 262.32/56.83 | | | | | % 262.32/56.83 | | | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (9), (12), (13), (15), (16), % 262.32/56.83 | | | | | (17), (18), (21), (22), (23), (24), (26), (27), (29), (31), % 262.32/56.83 | | | | | (36), (40), (44), (45) are inconsistent by sub-proof #58. % 262.32/56.83 | | | | | % 262.32/56.83 | | | | End of split % 262.32/56.83 | | | | % 262.32/56.83 | | | End of split % 262.32/56.83 | | | % 262.32/56.83 | | Case 2: % 262.32/56.83 | | | % 262.32/56.83 | | | (46) all_74_10 = n5 % 262.32/56.83 | | | % 262.32/56.83 | | | REDUCE: (13), (46) imply: % 262.32/56.83 | | | (47) a_select3(pminus_ds1_filter, n5, all_74_11) = all_74_8 % 262.32/56.83 | | | % 262.32/56.83 | | | REDUCE: (21), (46) imply: % 262.32/56.83 | | | (48) a_select3(pminus_ds1_filter, all_74_11, n5) = all_74_9 % 262.32/56.83 | | | % 262.32/56.83 | | | REDUCE: (15), (46) imply: % 262.32/56.83 | | | (49) leq(n5, n5) % 262.32/56.83 | | | % 262.32/56.83 | | | REDUCE: (31), (46) imply: % 262.32/56.83 | | | (50) leq(n0, n5) % 262.32/56.83 | | | % 262.32/56.83 | | | GROUND_INST: instantiating (29) with all_74_11, n4, simplifying with (5), % 262.32/56.83 | | | (17), (33) gives: % 262.32/56.83 | | | (51) all_74_11 = n4 | gt(n4, all_74_11) % 262.32/56.83 | | | % 262.32/56.83 | | | BETA: splitting (8) gives: % 262.32/56.83 | | | % 262.32/56.83 | | | Case 1: % 262.32/56.83 | | | | % 262.32/56.83 | | | | (52) all_74_11 = n0 % 262.32/56.83 | | | | % 262.32/56.83 | | | | REDUCE: (11), (52) imply: % 262.32/56.83 | | | | (53) gt(n0, n0) % 262.32/56.83 | | | | % 262.32/56.83 | | | | PRED_UNIFY: (14), (53) imply: % 262.32/56.83 | | | | (54) $false % 262.32/56.83 | | | | % 262.32/56.83 | | | | CLOSE: (54) is inconsistent. % 262.32/56.83 | | | | % 262.32/56.83 | | | Case 2: % 262.32/56.83 | | | | % 262.32/56.83 | | | | (55) ~ (all_74_11 = n0) % 262.32/56.83 | | | | % 262.32/56.83 | | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (9), (12), (17), (18), (22), % 262.32/56.83 | | | | (23), (24), (26), (27), (28), (29), (47), (48), (49), (50), % 262.32/56.83 | | | | (51), (55) are inconsistent by sub-proof #54. % 262.32/56.83 | | | | % 262.32/56.83 | | | End of split % 262.32/56.83 | | | % 262.32/56.83 | | End of split % 262.32/56.83 | | % 262.32/56.83 | Case 2: % 262.32/56.83 | | % 262.32/56.83 | | (56) all_74_11 = n5 % 262.32/56.83 | | % 262.32/56.83 | | REDUCE: (13), (56) imply: % 262.32/56.83 | | (57) a_select3(pminus_ds1_filter, all_74_10, n5) = all_74_8 % 262.32/56.83 | | % 262.32/56.83 | | REDUCE: (21), (56) imply: % 262.32/56.83 | | (58) a_select3(pminus_ds1_filter, n5, all_74_10) = all_74_9 % 262.32/56.83 | | % 262.32/56.83 | | REDUCE: (1), (56) imply: % 262.32/56.83 | | (59) leq(n5, n5) % 262.32/56.83 | | % 262.32/56.83 | | REDUCE: (12), (56) imply: % 262.32/56.83 | | (60) leq(n0, n5) % 262.32/56.83 | | % 262.32/56.83 | | BETA: splitting (25) gives: % 262.32/56.83 | | % 262.32/56.83 | | Case 1: % 262.32/56.83 | | | % 262.32/56.83 | | | (61) gt(n5, all_74_10) % 262.32/56.83 | | | % 262.32/56.83 | | | GROUND_INST: instantiating (24) with all_74_10, n5, n4, simplifying with % 262.32/56.83 | | | (10), (16), (28), (61) gives: % 262.32/56.83 | | | (62) leq(all_74_10, n4) % 262.32/56.83 | | | % 262.32/56.83 | | | BETA: splitting (20) gives: % 262.32/56.83 | | | % 262.32/56.83 | | | Case 1: % 262.32/56.83 | | | | % 262.32/56.83 | | | | (63) all_74_10 = n0 % 262.32/56.83 | | | | % 262.32/56.83 | | | | REDUCE: (30), (63) imply: % 262.32/56.83 | | | | (64) gt(n0, n0) % 262.32/56.83 | | | | % 262.32/56.83 | | | | PRED_UNIFY: (14), (64) imply: % 262.32/56.83 | | | | (65) $false % 262.32/56.83 | | | | % 262.32/56.83 | | | | CLOSE: (65) is inconsistent. % 262.32/56.83 | | | | % 262.32/56.83 | | | Case 2: % 262.32/56.83 | | | | % 262.32/56.83 | | | | (66) ~ (all_74_10 = n0) % 262.32/56.83 | | | | % 262.32/56.83 | | | | REF_CLOSE: (2), (3), (5), (6), (7), (9), (15), (16), (18), (19), (22), % 262.32/56.83 | | | | (23), (24), (26), (27), (28), (29), (31), (57), (58), (59), % 262.32/56.83 | | | | (60), (62), (66) are inconsistent by sub-proof #53. % 262.32/56.83 | | | | % 262.32/56.83 | | | End of split % 262.32/56.83 | | | % 262.32/56.83 | | Case 2: % 262.32/56.83 | | | % 262.32/56.83 | | | (67) all_74_10 = n5 % 262.32/56.83 | | | % 262.32/56.83 | | | REDUCE: (57), (67) imply: % 262.32/56.83 | | | (68) a_select3(pminus_ds1_filter, n5, n5) = all_74_8 % 262.32/56.83 | | | % 262.32/56.83 | | | REDUCE: (58), (67) imply: % 262.32/56.83 | | | (69) a_select3(pminus_ds1_filter, n5, n5) = all_74_9 % 262.32/56.83 | | | % 262.32/56.83 | | | GROUND_INST: instantiating (22) with all_74_9, all_74_8, n5, n5, % 262.32/56.83 | | | pminus_ds1_filter, simplifying with (68), (69) gives: % 262.32/56.83 | | | (70) all_74_8 = all_74_9 % 262.32/56.83 | | | % 262.32/56.83 | | | REDUCE: (3), (70) imply: % 262.32/56.83 | | | (71) $false % 262.32/56.83 | | | % 262.32/56.84 | | | CLOSE: (71) is inconsistent. % 262.32/56.84 | | | % 262.32/56.84 | | End of split % 262.32/56.84 | | % 262.32/56.84 | End of split % 262.32/56.84 | % 262.32/56.84 End of proof % 262.32/56.84 % 262.32/56.84 Sub-proof #53 shows that the following formulas are inconsistent: % 262.32/56.84 ---------------------------------------------------------------- % 262.32/56.84 (1) $i(n3) % 262.32/56.84 (2) ~ (all_74_8 = all_74_9) % 262.32/56.84 (3) $i(n4) % 262.32/56.84 (4) ! [v0: $i] : (v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0, n1) | ~ % 262.32/56.84 leq(n0, v0)) % 262.32/56.84 (5) pred(n2) = n1 % 262.32/56.84 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 262.32/56.84 (a_select3(pminus_ds1_filter, v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 262.32/56.84 ~ leq(v1, all_74_20) | ~ leq(v0, all_74_20) | ~ leq(n0, v1) | ~ % 262.32/56.84 leq(n0, v0) | (a_select3(pminus_ds1_filter, v1, v0) = v2 & $i(v2))) % 262.32/56.84 (7) leq(all_74_10, n4) % 262.32/56.84 (8) a_select3(pminus_ds1_filter, n5, all_74_10) = all_74_9 % 262.32/56.84 (9) leq(all_74_10, n5) % 262.32/56.84 (10) $i(all_74_10) % 262.32/56.84 (11) pred(n3) = n2 % 262.32/56.84 (12) leq(n0, n5) % 262.65/56.84 (13) ! [v0: $i] : (v0 = n4 | v0 = n3 | v0 = n2 | v0 = n1 | v0 = n0 | ~ % 262.65/56.84 $i(v0) | ~ leq(v0, n4) | ~ leq(n0, v0)) % 262.65/56.84 (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 262.65/56.84 (v1 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 262.65/56.84 v0)) % 262.65/56.84 (15) pred(n4) = n3 % 262.65/56.84 (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (pred(v1) = v2) | ~ % 262.65/56.84 $i(v1) | ~ $i(v0) | ~ gt(v1, v0) | leq(v0, v2)) % 262.65/56.84 (17) ~ (all_74_10 = n0) % 262.65/56.84 (18) leq(n5, n5) % 262.65/56.84 (19) all_74_20 = n5 % 262.65/56.84 (20) $i(n2) % 262.65/56.84 (21) $i(n5) % 262.65/56.84 (22) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ % 262.65/56.84 leq(v0, v1) | gt(v1, v0)) % 262.65/56.84 (23) a_select3(pminus_ds1_filter, all_74_10, n5) = all_74_8 % 262.65/56.84 (24) leq(n0, all_74_10) % 262.65/56.84 % 262.65/56.84 Begin of proof % 262.65/56.84 | % 262.65/56.84 | GROUND_INST: instantiating (13) with all_74_10, simplifying with (7), (10), % 262.65/56.84 | (24) gives: % 262.65/56.84 | (25) all_74_10 = n4 | all_74_10 = n3 | all_74_10 = n2 | all_74_10 = n1 | % 262.65/56.84 | all_74_10 = n0 % 262.65/56.84 | % 262.65/56.84 | GROUND_INST: instantiating (22) with all_74_10, n4, simplifying with (3), (7), % 262.65/56.84 | (10) gives: % 262.65/56.84 | (26) all_74_10 = n4 | gt(n4, all_74_10) % 262.65/56.84 | % 262.65/56.84 | BETA: splitting (26) gives: % 262.65/56.84 | % 262.65/56.84 | Case 1: % 262.65/56.84 | | % 262.65/56.84 | | (27) gt(n4, all_74_10) % 262.65/56.84 | | % 262.65/56.84 | | GROUND_INST: instantiating (16) with all_74_10, n4, n3, simplifying with % 262.65/56.84 | | (3), (10), (15), (27) gives: % 262.65/56.84 | | (28) leq(all_74_10, n3) % 262.65/56.84 | | % 262.65/56.84 | | BETA: splitting (25) gives: % 262.65/56.84 | | % 262.65/56.84 | | Case 1: % 262.65/56.84 | | | % 262.65/56.84 | | | (29) all_74_10 = n0 % 262.65/56.84 | | | % 262.65/56.84 | | | REDUCE: (17), (29) imply: % 262.65/56.84 | | | (30) $false % 262.65/56.84 | | | % 262.65/56.84 | | | CLOSE: (30) is inconsistent. % 262.65/56.84 | | | % 262.65/56.84 | | Case 2: % 262.65/56.84 | | | % 262.65/56.84 | | | % 262.65/56.84 | | | GROUND_INST: instantiating (22) with all_74_10, n3, simplifying with (1), % 262.65/56.84 | | | (10), (28) gives: % 262.65/56.84 | | | (31) all_74_10 = n3 | gt(n3, all_74_10) % 262.65/56.84 | | | % 262.65/56.84 | | | BETA: splitting (31) gives: % 262.65/56.84 | | | % 262.65/56.84 | | | Case 1: % 262.65/56.84 | | | | % 262.65/56.84 | | | | (32) gt(n3, all_74_10) % 262.65/56.84 | | | | % 262.65/56.84 | | | | GROUND_INST: instantiating (16) with all_74_10, n3, n2, simplifying with % 262.65/56.84 | | | | (1), (10), (11), (32) gives: % 262.65/56.84 | | | | (33) leq(all_74_10, n2) % 262.65/56.84 | | | | % 262.65/56.84 | | | | GROUND_INST: instantiating (22) with all_74_10, n2, simplifying with % 262.65/56.84 | | | | (10), (20), (33) gives: % 262.65/56.84 | | | | (34) all_74_10 = n2 | gt(n2, all_74_10) % 262.65/56.84 | | | | % 262.65/56.84 | | | | BETA: splitting (34) gives: % 262.65/56.84 | | | | % 262.65/56.84 | | | | Case 1: % 262.65/56.84 | | | | | % 262.65/56.84 | | | | | (35) gt(n2, all_74_10) % 262.65/56.84 | | | | | % 262.65/56.84 | | | | | GROUND_INST: instantiating (16) with all_74_10, n2, n1, simplifying % 262.65/56.84 | | | | | with (5), (10), (20), (35) gives: % 262.65/56.84 | | | | | (36) leq(all_74_10, n1) % 262.65/56.84 | | | | | % 262.65/56.84 | | | | | GROUND_INST: instantiating (4) with all_74_10, simplifying with (10), % 262.65/56.84 | | | | | (24), (36) gives: % 262.65/56.84 | | | | | (37) all_74_10 = n1 | all_74_10 = n0 % 262.65/56.84 | | | | | % 262.65/56.84 | | | | | BETA: splitting (37) gives: % 262.65/56.84 | | | | | % 262.65/56.84 | | | | | Case 1: % 262.65/56.84 | | | | | | % 262.65/56.84 | | | | | | (38) all_74_10 = n0 % 262.65/56.84 | | | | | | % 262.65/56.84 | | | | | | REDUCE: (17), (38) imply: % 262.65/56.84 | | | | | | (39) $false % 262.65/56.84 | | | | | | % 262.65/56.84 | | | | | | CLOSE: (39) is inconsistent. % 262.65/56.84 | | | | | | % 262.65/56.84 | | | | | Case 2: % 262.65/56.84 | | | | | | % 262.65/56.84 | | | | | | (40) all_74_10 = n1 % 262.65/56.84 | | | | | | % 262.65/56.84 | | | | | | REDUCE: (23), (40) imply: % 262.65/56.84 | | | | | | (41) a_select3(pminus_ds1_filter, n1, n5) = all_74_8 % 262.65/56.84 | | | | | | % 262.65/56.84 | | | | | | REDUCE: (8), (40) imply: % 262.65/56.84 | | | | | | (42) a_select3(pminus_ds1_filter, n5, n1) = all_74_9 % 262.65/56.84 | | | | | | % 262.65/56.84 | | | | | | REDUCE: (10), (40) imply: % 262.65/56.84 | | | | | | (43) $i(n1) % 262.65/56.84 | | | | | | % 262.65/56.84 | | | | | | REDUCE: (9), (40) imply: % 262.65/56.84 | | | | | | (44) leq(n1, n5) % 262.65/56.84 | | | | | | % 262.65/56.84 | | | | | | REDUCE: (24), (40) imply: % 262.65/56.84 | | | | | | (45) leq(n0, n1) % 262.65/56.84 | | | | | | % 262.65/56.84 | | | | | | GROUND_INST: instantiating (6) with n1, n5, all_74_8, simplifying % 262.65/56.84 | | | | | | with (12), (21), (41), (43), (45) gives: % 262.65/56.84 | | | | | | (46) ~ leq(n5, all_74_20) | ~ leq(n1, all_74_20) | % 262.65/56.84 | | | | | | (a_select3(pminus_ds1_filter, n5, n1) = all_74_8 & % 262.65/56.84 | | | | | | $i(all_74_8)) % 262.65/56.84 | | | | | | % 262.65/56.84 | | | | | | BETA: splitting (46) gives: % 262.65/56.84 | | | | | | % 262.65/56.84 | | | | | | Case 1: % 262.65/56.84 | | | | | | | % 262.65/56.84 | | | | | | | (47) ~ leq(n5, all_74_20) % 262.65/56.84 | | | | | | | % 262.65/56.84 | | | | | | | REDUCE: (19), (47) imply: % 262.65/56.84 | | | | | | | (48) ~ leq(n5, n5) % 262.65/56.84 | | | | | | | % 262.65/56.84 | | | | | | | PRED_UNIFY: (18), (48) imply: % 262.65/56.84 | | | | | | | (49) $false % 262.65/56.84 | | | | | | | % 262.65/56.84 | | | | | | | CLOSE: (49) is inconsistent. % 262.65/56.84 | | | | | | | % 262.65/56.84 | | | | | | Case 2: % 262.65/56.84 | | | | | | | % 262.65/56.84 | | | | | | | (50) ~ leq(n1, all_74_20) | (a_select3(pminus_ds1_filter, n5, % 262.65/56.84 | | | | | | | n1) = all_74_8 & $i(all_74_8)) % 262.65/56.84 | | | | | | | % 262.65/56.84 | | | | | | | BETA: splitting (50) gives: % 262.65/56.84 | | | | | | | % 262.65/56.84 | | | | | | | Case 1: % 262.65/56.84 | | | | | | | | % 262.65/56.84 | | | | | | | | (51) ~ leq(n1, all_74_20) % 262.65/56.84 | | | | | | | | % 262.65/56.84 | | | | | | | | REDUCE: (19), (51) imply: % 262.65/56.84 | | | | | | | | (52) ~ leq(n1, n5) % 262.65/56.84 | | | | | | | | % 262.65/56.84 | | | | | | | | PRED_UNIFY: (44), (52) imply: % 262.65/56.84 | | | | | | | | (53) $false % 262.65/56.84 | | | | | | | | % 262.65/56.84 | | | | | | | | CLOSE: (53) is inconsistent. % 262.65/56.84 | | | | | | | | % 262.65/56.84 | | | | | | | Case 2: % 262.65/56.84 | | | | | | | | % 262.65/56.84 | | | | | | | | (54) a_select3(pminus_ds1_filter, n5, n1) = all_74_8 & % 262.65/56.84 | | | | | | | | $i(all_74_8) % 262.65/56.84 | | | | | | | | % 262.65/56.84 | | | | | | | | ALPHA: (54) implies: % 262.65/56.84 | | | | | | | | (55) a_select3(pminus_ds1_filter, n5, n1) = all_74_8 % 262.65/56.84 | | | | | | | | % 262.65/56.84 | | | | | | | | REF_CLOSE: (2), (14), (42), (55) are inconsistent by sub-proof % 262.65/56.84 | | | | | | | | #57. % 262.65/56.84 | | | | | | | | % 262.65/56.84 | | | | | | | End of split % 262.65/56.84 | | | | | | | % 262.65/56.84 | | | | | | End of split % 262.65/56.84 | | | | | | % 262.65/56.84 | | | | | End of split % 262.65/56.84 | | | | | % 262.65/56.84 | | | | Case 2: % 262.65/56.84 | | | | | % 262.65/56.84 | | | | | (56) all_74_10 = n2 % 262.65/56.84 | | | | | % 262.65/56.84 | | | | | REDUCE: (23), (56) imply: % 262.65/56.84 | | | | | (57) a_select3(pminus_ds1_filter, n2, n5) = all_74_8 % 262.65/56.84 | | | | | % 262.65/56.84 | | | | | REDUCE: (8), (56) imply: % 262.65/56.84 | | | | | (58) a_select3(pminus_ds1_filter, n5, n2) = all_74_9 % 262.65/56.84 | | | | | % 262.65/56.84 | | | | | REDUCE: (9), (56) imply: % 262.65/56.84 | | | | | (59) leq(n2, n5) % 262.65/56.84 | | | | | % 262.65/56.84 | | | | | REDUCE: (24), (56) imply: % 262.65/56.84 | | | | | (60) leq(n0, n2) % 262.65/56.84 | | | | | % 262.65/56.84 | | | | | GROUND_INST: instantiating (6) with n2, n5, all_74_8, simplifying with % 262.65/56.84 | | | | | (12), (20), (21), (57), (60) gives: % 262.65/56.84 | | | | | (61) ~ leq(n5, all_74_20) | ~ leq(n2, all_74_20) | % 262.65/56.84 | | | | | (a_select3(pminus_ds1_filter, n5, n2) = all_74_8 & % 262.65/56.84 | | | | | $i(all_74_8)) % 262.65/56.84 | | | | | % 262.65/56.84 | | | | | BETA: splitting (61) gives: % 262.65/56.84 | | | | | % 262.65/56.84 | | | | | Case 1: % 262.65/56.84 | | | | | | % 262.65/56.84 | | | | | | (62) ~ leq(n5, all_74_20) % 262.65/56.84 | | | | | | % 262.65/56.84 | | | | | | REDUCE: (19), (62) imply: % 262.65/56.84 | | | | | | (63) ~ leq(n5, n5) % 262.65/56.84 | | | | | | % 262.65/56.84 | | | | | | PRED_UNIFY: (18), (63) imply: % 262.65/56.84 | | | | | | (64) $false % 262.65/56.84 | | | | | | % 262.65/56.84 | | | | | | CLOSE: (64) is inconsistent. % 262.65/56.84 | | | | | | % 262.65/56.84 | | | | | Case 2: % 262.65/56.84 | | | | | | % 262.65/56.84 | | | | | | (65) ~ leq(n2, all_74_20) | (a_select3(pminus_ds1_filter, n5, % 262.65/56.84 | | | | | | n2) = all_74_8 & $i(all_74_8)) % 262.65/56.84 | | | | | | % 262.65/56.84 | | | | | | BETA: splitting (65) gives: % 262.65/56.84 | | | | | | % 262.65/56.84 | | | | | | Case 1: % 262.65/56.84 | | | | | | | % 262.65/56.84 | | | | | | | (66) ~ leq(n2, all_74_20) % 262.65/56.84 | | | | | | | % 262.65/56.84 | | | | | | | REDUCE: (19), (66) imply: % 262.65/56.84 | | | | | | | (67) ~ leq(n2, n5) % 262.65/56.84 | | | | | | | % 262.65/56.84 | | | | | | | PRED_UNIFY: (59), (67) imply: % 262.65/56.84 | | | | | | | (68) $false % 262.65/56.84 | | | | | | | % 262.65/56.84 | | | | | | | CLOSE: (68) is inconsistent. % 262.65/56.84 | | | | | | | % 262.65/56.84 | | | | | | Case 2: % 262.65/56.84 | | | | | | | % 262.65/56.84 | | | | | | | (69) a_select3(pminus_ds1_filter, n5, n2) = all_74_8 & % 262.65/56.84 | | | | | | | $i(all_74_8) % 262.65/56.84 | | | | | | | % 262.65/56.84 | | | | | | | ALPHA: (69) implies: % 262.65/56.84 | | | | | | | (70) a_select3(pminus_ds1_filter, n5, n2) = all_74_8 % 262.65/56.84 | | | | | | | % 262.65/56.84 | | | | | | | REF_CLOSE: (2), (14), (58), (70) are inconsistent by sub-proof % 262.65/56.84 | | | | | | | #56. % 262.65/56.84 | | | | | | | % 262.65/56.84 | | | | | | End of split % 262.65/56.84 | | | | | | % 262.65/56.84 | | | | | End of split % 262.65/56.84 | | | | | % 262.65/56.84 | | | | End of split % 262.65/56.84 | | | | % 262.65/56.84 | | | Case 2: % 262.65/56.84 | | | | % 262.65/56.84 | | | | (71) all_74_10 = n3 % 262.65/56.84 | | | | % 262.65/56.84 | | | | REDUCE: (23), (71) imply: % 262.65/56.84 | | | | (72) a_select3(pminus_ds1_filter, n3, n5) = all_74_8 % 262.65/56.84 | | | | % 262.65/56.84 | | | | REDUCE: (8), (71) imply: % 262.65/56.84 | | | | (73) a_select3(pminus_ds1_filter, n5, n3) = all_74_9 % 262.65/56.84 | | | | % 262.65/56.84 | | | | REDUCE: (9), (71) imply: % 262.65/56.84 | | | | (74) leq(n3, n5) % 262.65/56.84 | | | | % 262.65/56.84 | | | | REDUCE: (24), (71) imply: % 262.65/56.84 | | | | (75) leq(n0, n3) % 262.65/56.84 | | | | % 262.65/56.84 | | | | GROUND_INST: instantiating (6) with n3, n5, all_74_8, simplifying with % 262.65/56.84 | | | | (1), (12), (21), (72), (75) gives: % 262.65/56.84 | | | | (76) ~ leq(n5, all_74_20) | ~ leq(n3, all_74_20) | % 262.65/56.84 | | | | (a_select3(pminus_ds1_filter, n5, n3) = all_74_8 & $i(all_74_8)) % 262.65/56.84 | | | | % 262.65/56.84 | | | | BETA: splitting (76) gives: % 262.65/56.84 | | | | % 262.65/56.84 | | | | Case 1: % 262.65/56.84 | | | | | % 262.65/56.84 | | | | | (77) ~ leq(n5, all_74_20) % 262.65/56.84 | | | | | % 262.65/56.84 | | | | | REDUCE: (19), (77) imply: % 262.65/56.84 | | | | | (78) ~ leq(n5, n5) % 262.65/56.84 | | | | | % 262.65/56.84 | | | | | PRED_UNIFY: (18), (78) imply: % 262.65/56.84 | | | | | (79) $false % 262.65/56.84 | | | | | % 262.65/56.84 | | | | | CLOSE: (79) is inconsistent. % 262.65/56.84 | | | | | % 262.65/56.84 | | | | Case 2: % 262.65/56.84 | | | | | % 262.65/56.84 | | | | | (80) ~ leq(n3, all_74_20) | (a_select3(pminus_ds1_filter, n5, n3) % 262.65/56.84 | | | | | = all_74_8 & $i(all_74_8)) % 262.65/56.84 | | | | | % 262.65/56.84 | | | | | BETA: splitting (80) gives: % 262.65/56.84 | | | | | % 262.65/56.84 | | | | | Case 1: % 262.65/56.84 | | | | | | % 262.65/56.84 | | | | | | (81) ~ leq(n3, all_74_20) % 262.65/56.84 | | | | | | % 262.65/56.84 | | | | | | REDUCE: (19), (81) imply: % 262.65/56.84 | | | | | | (82) ~ leq(n3, n5) % 262.65/56.84 | | | | | | % 262.65/56.84 | | | | | | PRED_UNIFY: (74), (82) imply: % 262.65/56.84 | | | | | | (83) $false % 262.65/56.84 | | | | | | % 262.65/56.84 | | | | | | CLOSE: (83) is inconsistent. % 262.65/56.84 | | | | | | % 262.65/56.84 | | | | | Case 2: % 262.65/56.84 | | | | | | % 262.65/56.84 | | | | | | (84) a_select3(pminus_ds1_filter, n5, n3) = all_74_8 & % 262.65/56.84 | | | | | | $i(all_74_8) % 262.65/56.84 | | | | | | % 262.65/56.84 | | | | | | ALPHA: (84) implies: % 262.65/56.84 | | | | | | (85) a_select3(pminus_ds1_filter, n5, n3) = all_74_8 % 262.65/56.84 | | | | | | % 262.65/56.84 | | | | | | GROUND_INST: instantiating (14) with all_74_9, all_74_8, n3, n5, % 262.65/56.84 | | | | | | pminus_ds1_filter, simplifying with (73), (85) gives: % 262.65/56.84 | | | | | | (86) all_74_8 = all_74_9 % 262.65/56.84 | | | | | | % 262.65/56.84 | | | | | | REDUCE: (2), (86) imply: % 262.65/56.84 | | | | | | (87) $false % 262.65/56.84 | | | | | | % 262.65/56.84 | | | | | | CLOSE: (87) is inconsistent. % 262.65/56.84 | | | | | | % 262.65/56.84 | | | | | End of split % 262.65/56.84 | | | | | % 262.65/56.84 | | | | End of split % 262.65/56.84 | | | | % 262.65/56.84 | | | End of split % 262.65/56.84 | | | % 262.65/56.84 | | End of split % 262.65/56.84 | | % 262.65/56.84 | Case 2: % 262.65/56.84 | | % 262.65/56.84 | | (88) all_74_10 = n4 % 262.65/56.84 | | % 262.65/56.84 | | REDUCE: (23), (88) imply: % 262.65/56.84 | | (89) a_select3(pminus_ds1_filter, n4, n5) = all_74_8 % 262.65/56.84 | | % 262.65/56.84 | | REDUCE: (8), (88) imply: % 262.65/56.84 | | (90) a_select3(pminus_ds1_filter, n5, n4) = all_74_9 % 262.65/56.84 | | % 262.65/56.84 | | REDUCE: (9), (88) imply: % 262.65/56.84 | | (91) leq(n4, n5) % 262.65/56.84 | | % 262.65/56.84 | | REDUCE: (24), (88) imply: % 262.65/56.84 | | (92) leq(n0, n4) % 262.65/56.84 | | % 262.65/56.84 | | GROUND_INST: instantiating (6) with n4, n5, all_74_8, simplifying with (3), % 262.65/56.84 | | (12), (21), (89), (92) gives: % 262.65/56.84 | | (93) ~ leq(n5, all_74_20) | ~ leq(n4, all_74_20) | % 262.65/56.84 | | (a_select3(pminus_ds1_filter, n5, n4) = all_74_8 & $i(all_74_8)) % 262.65/56.84 | | % 262.65/56.84 | | BETA: splitting (93) gives: % 262.65/56.84 | | % 262.65/56.84 | | Case 1: % 262.65/56.84 | | | % 262.65/56.84 | | | (94) ~ leq(n5, all_74_20) % 262.65/56.84 | | | % 262.65/56.84 | | | REDUCE: (19), (94) imply: % 262.65/56.84 | | | (95) ~ leq(n5, n5) % 262.65/56.84 | | | % 262.65/56.84 | | | PRED_UNIFY: (18), (95) imply: % 262.65/56.84 | | | (96) $false % 262.65/56.84 | | | % 262.65/56.84 | | | CLOSE: (96) is inconsistent. % 262.65/56.84 | | | % 262.65/56.84 | | Case 2: % 262.65/56.84 | | | % 262.65/56.84 | | | (97) ~ leq(n4, all_74_20) | (a_select3(pminus_ds1_filter, n5, n4) = % 262.65/56.85 | | | all_74_8 & $i(all_74_8)) % 262.65/56.85 | | | % 262.65/56.85 | | | BETA: splitting (97) gives: % 262.65/56.85 | | | % 262.65/56.85 | | | Case 1: % 262.65/56.85 | | | | % 262.65/56.85 | | | | (98) ~ leq(n4, all_74_20) % 262.65/56.85 | | | | % 262.65/56.85 | | | | REDUCE: (19), (98) imply: % 262.65/56.85 | | | | (99) ~ leq(n4, n5) % 262.65/56.85 | | | | % 262.65/56.85 | | | | PRED_UNIFY: (91), (99) imply: % 262.65/56.85 | | | | (100) $false % 262.65/56.85 | | | | % 262.65/56.85 | | | | CLOSE: (100) is inconsistent. % 262.65/56.85 | | | | % 262.65/56.85 | | | Case 2: % 262.65/56.85 | | | | % 262.65/56.85 | | | | (101) a_select3(pminus_ds1_filter, n5, n4) = all_74_8 & $i(all_74_8) % 262.65/56.85 | | | | % 262.65/56.85 | | | | ALPHA: (101) implies: % 262.65/56.85 | | | | (102) a_select3(pminus_ds1_filter, n5, n4) = all_74_8 % 262.65/56.85 | | | | % 262.65/56.85 | | | | REF_CLOSE: (2), (14), (90), (102) are inconsistent by sub-proof #55. % 262.65/56.85 | | | | % 262.65/56.85 | | | End of split % 262.65/56.85 | | | % 262.65/56.85 | | End of split % 262.65/56.85 | | % 262.65/56.85 | End of split % 262.65/56.85 | % 262.65/56.85 End of proof % 262.65/56.85 % 262.65/56.85 Sub-proof #54 shows that the following formulas are inconsistent: % 262.65/56.85 ---------------------------------------------------------------- % 262.65/56.85 (1) leq(all_74_11, n5) % 262.65/56.85 (2) $i(n3) % 262.65/56.85 (3) ~ (all_74_8 = all_74_9) % 262.65/56.85 (4) $i(n4) % 262.65/56.85 (5) ! [v0: $i] : (v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0, n1) | ~ % 262.65/56.85 leq(n0, v0)) % 262.65/56.85 (6) pred(n2) = n1 % 262.65/56.85 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 262.65/56.85 (a_select3(pminus_ds1_filter, v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 262.65/56.85 ~ leq(v1, all_74_20) | ~ leq(v0, all_74_20) | ~ leq(n0, v1) | ~ % 262.65/56.85 leq(n0, v0) | (a_select3(pminus_ds1_filter, v1, v0) = v2 & $i(v2))) % 262.65/56.85 (8) ~ (all_74_11 = n0) % 262.65/56.85 (9) leq(n0, all_74_11) % 262.65/56.85 (10) $i(all_74_11) % 262.65/56.85 (11) pred(n3) = n2 % 262.65/56.85 (12) a_select3(pminus_ds1_filter, all_74_11, n5) = all_74_9 % 262.65/56.85 (13) leq(n0, n5) % 262.65/56.85 (14) all_74_11 = n4 | gt(n4, all_74_11) % 262.65/56.85 (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 262.65/56.85 (v1 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 262.65/56.85 v0)) % 262.65/56.85 (16) pred(n4) = n3 % 262.65/56.85 (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (pred(v1) = v2) | ~ % 262.65/56.85 $i(v1) | ~ $i(v0) | ~ gt(v1, v0) | leq(v0, v2)) % 262.65/56.85 (18) leq(n5, n5) % 262.65/56.85 (19) all_74_20 = n5 % 262.65/56.85 (20) a_select3(pminus_ds1_filter, n5, all_74_11) = all_74_8 % 262.65/56.85 (21) $i(n2) % 262.65/56.85 (22) $i(n5) % 262.65/56.85 (23) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ % 262.65/56.85 leq(v0, v1) | gt(v1, v0)) % 262.65/56.85 % 262.65/56.85 Begin of proof % 262.65/56.85 | % 262.65/56.85 | BETA: splitting (14) gives: % 262.65/56.85 | % 262.65/56.85 | Case 1: % 262.65/56.85 | | % 262.65/56.85 | | (24) gt(n4, all_74_11) % 262.65/56.85 | | % 262.65/56.85 | | GROUND_INST: instantiating (17) with all_74_11, n4, n3, simplifying with % 262.65/56.85 | | (4), (10), (16), (24) gives: % 262.65/56.85 | | (25) leq(all_74_11, n3) % 262.65/56.85 | | % 262.65/56.85 | | GROUND_INST: instantiating (23) with all_74_11, n3, simplifying with (2), % 262.65/56.85 | | (10), (25) gives: % 262.65/56.85 | | (26) all_74_11 = n3 | gt(n3, all_74_11) % 262.65/56.85 | | % 262.65/56.85 | | BETA: splitting (26) gives: % 262.65/56.85 | | % 262.65/56.85 | | Case 1: % 262.65/56.85 | | | % 262.65/56.85 | | | (27) gt(n3, all_74_11) % 262.65/56.85 | | | % 262.65/56.85 | | | GROUND_INST: instantiating (17) with all_74_11, n3, n2, simplifying with % 262.65/56.85 | | | (2), (10), (11), (27) gives: % 262.65/56.85 | | | (28) leq(all_74_11, n2) % 262.65/56.85 | | | % 262.65/56.85 | | | GROUND_INST: instantiating (23) with all_74_11, n2, simplifying with (10), % 262.65/56.85 | | | (21), (28) gives: % 262.65/56.85 | | | (29) all_74_11 = n2 | gt(n2, all_74_11) % 262.65/56.85 | | | % 262.65/56.85 | | | BETA: splitting (29) gives: % 262.65/56.85 | | | % 262.65/56.85 | | | Case 1: % 262.65/56.85 | | | | % 262.65/56.85 | | | | (30) gt(n2, all_74_11) % 262.65/56.85 | | | | % 262.65/56.85 | | | | GROUND_INST: instantiating (17) with all_74_11, n2, n1, simplifying with % 262.65/56.85 | | | | (6), (10), (21), (30) gives: % 262.65/56.85 | | | | (31) leq(all_74_11, n1) % 262.65/56.85 | | | | % 262.65/56.85 | | | | GROUND_INST: instantiating (5) with all_74_11, simplifying with (9), % 262.65/56.85 | | | | (10), (31) gives: % 262.65/56.85 | | | | (32) all_74_11 = n1 | all_74_11 = n0 % 262.65/56.85 | | | | % 262.65/56.85 | | | | BETA: splitting (32) gives: % 262.65/56.85 | | | | % 262.65/56.85 | | | | Case 1: % 262.65/56.85 | | | | | % 262.65/56.85 | | | | | (33) all_74_11 = n0 % 262.65/56.85 | | | | | % 262.65/56.85 | | | | | REDUCE: (8), (33) imply: % 262.65/56.85 | | | | | (34) $false % 262.65/56.85 | | | | | % 262.65/56.85 | | | | | CLOSE: (34) is inconsistent. % 262.65/56.85 | | | | | % 262.65/56.85 | | | | Case 2: % 262.65/56.85 | | | | | % 262.65/56.85 | | | | | (35) all_74_11 = n1 % 262.65/56.85 | | | | | % 262.65/56.85 | | | | | REDUCE: (12), (35) imply: % 262.65/56.85 | | | | | (36) a_select3(pminus_ds1_filter, n1, n5) = all_74_9 % 262.65/56.85 | | | | | % 262.65/56.85 | | | | | REDUCE: (20), (35) imply: % 262.65/56.85 | | | | | (37) a_select3(pminus_ds1_filter, n5, n1) = all_74_8 % 262.65/56.85 | | | | | % 262.65/56.85 | | | | | REDUCE: (10), (35) imply: % 262.65/56.85 | | | | | (38) $i(n1) % 262.65/56.85 | | | | | % 262.65/56.85 | | | | | REDUCE: (1), (35) imply: % 262.65/56.85 | | | | | (39) leq(n1, n5) % 262.65/56.85 | | | | | % 262.65/56.85 | | | | | REDUCE: (9), (35) imply: % 262.65/56.85 | | | | | (40) leq(n0, n1) % 262.65/56.85 | | | | | % 262.65/56.85 | | | | | GROUND_INST: instantiating (7) with n1, n5, all_74_9, simplifying with % 262.65/56.85 | | | | | (13), (22), (36), (38), (40) gives: % 262.65/56.85 | | | | | (41) ~ leq(n5, all_74_20) | ~ leq(n1, all_74_20) | % 262.65/56.85 | | | | | (a_select3(pminus_ds1_filter, n5, n1) = all_74_9 & % 262.65/56.85 | | | | | $i(all_74_9)) % 262.65/56.85 | | | | | % 262.65/56.85 | | | | | BETA: splitting (41) gives: % 262.65/56.85 | | | | | % 262.65/56.85 | | | | | Case 1: % 262.65/56.85 | | | | | | % 262.65/56.85 | | | | | | (42) ~ leq(n5, all_74_20) % 262.65/56.85 | | | | | | % 262.65/56.85 | | | | | | REDUCE: (19), (42) imply: % 262.65/56.85 | | | | | | (43) ~ leq(n5, n5) % 262.65/56.85 | | | | | | % 262.65/56.85 | | | | | | PRED_UNIFY: (18), (43) imply: % 262.65/56.85 | | | | | | (44) $false % 262.65/56.85 | | | | | | % 262.65/56.85 | | | | | | CLOSE: (44) is inconsistent. % 262.65/56.85 | | | | | | % 262.65/56.85 | | | | | Case 2: % 262.65/56.85 | | | | | | % 262.65/56.85 | | | | | | (45) ~ leq(n1, all_74_20) | (a_select3(pminus_ds1_filter, n5, % 262.65/56.85 | | | | | | n1) = all_74_9 & $i(all_74_9)) % 262.65/56.85 | | | | | | % 262.65/56.85 | | | | | | BETA: splitting (45) gives: % 262.65/56.85 | | | | | | % 262.65/56.85 | | | | | | Case 1: % 262.65/56.85 | | | | | | | % 262.65/56.85 | | | | | | | (46) ~ leq(n1, all_74_20) % 262.65/56.85 | | | | | | | % 262.65/56.85 | | | | | | | REDUCE: (19), (46) imply: % 262.65/56.85 | | | | | | | (47) ~ leq(n1, n5) % 262.65/56.85 | | | | | | | % 262.65/56.85 | | | | | | | PRED_UNIFY: (39), (47) imply: % 262.65/56.85 | | | | | | | (48) $false % 262.65/56.85 | | | | | | | % 262.65/56.85 | | | | | | | CLOSE: (48) is inconsistent. % 262.65/56.85 | | | | | | | % 262.65/56.85 | | | | | | Case 2: % 262.65/56.85 | | | | | | | % 262.65/56.85 | | | | | | | (49) a_select3(pminus_ds1_filter, n5, n1) = all_74_9 & % 262.65/56.85 | | | | | | | $i(all_74_9) % 262.65/56.85 | | | | | | | % 262.65/56.85 | | | | | | | ALPHA: (49) implies: % 262.65/56.85 | | | | | | | (50) a_select3(pminus_ds1_filter, n5, n1) = all_74_9 % 262.65/56.85 | | | | | | | % 262.65/56.85 | | | | | | | REF_CLOSE: (3), (15), (37), (50) are inconsistent by sub-proof % 262.65/56.85 | | | | | | | #57. % 262.65/56.85 | | | | | | | % 262.65/56.85 | | | | | | End of split % 262.65/56.85 | | | | | | % 262.65/56.85 | | | | | End of split % 262.65/56.85 | | | | | % 262.65/56.85 | | | | End of split % 262.65/56.85 | | | | % 262.65/56.85 | | | Case 2: % 262.65/56.85 | | | | % 262.65/56.85 | | | | (51) all_74_11 = n2 % 262.65/56.85 | | | | % 262.65/56.85 | | | | REDUCE: (12), (51) imply: % 262.65/56.85 | | | | (52) a_select3(pminus_ds1_filter, n2, n5) = all_74_9 % 262.65/56.85 | | | | % 262.65/56.85 | | | | REDUCE: (20), (51) imply: % 262.65/56.85 | | | | (53) a_select3(pminus_ds1_filter, n5, n2) = all_74_8 % 262.65/56.85 | | | | % 262.65/56.85 | | | | REDUCE: (1), (51) imply: % 262.65/56.85 | | | | (54) leq(n2, n5) % 262.65/56.85 | | | | % 263.01/56.85 | | | | REDUCE: (9), (51) imply: % 263.01/56.85 | | | | (55) leq(n0, n2) % 263.01/56.85 | | | | % 263.01/56.85 | | | | GROUND_INST: instantiating (7) with n2, n5, all_74_9, simplifying with % 263.01/56.85 | | | | (13), (21), (22), (52), (55) gives: % 263.01/56.85 | | | | (56) ~ leq(n5, all_74_20) | ~ leq(n2, all_74_20) | % 263.01/56.85 | | | | (a_select3(pminus_ds1_filter, n5, n2) = all_74_9 & $i(all_74_9)) % 263.01/56.85 | | | | % 263.01/56.85 | | | | BETA: splitting (56) gives: % 263.01/56.85 | | | | % 263.01/56.85 | | | | Case 1: % 263.01/56.85 | | | | | % 263.01/56.85 | | | | | (57) ~ leq(n5, all_74_20) % 263.01/56.85 | | | | | % 263.01/56.85 | | | | | REDUCE: (19), (57) imply: % 263.01/56.85 | | | | | (58) ~ leq(n5, n5) % 263.01/56.85 | | | | | % 263.01/56.85 | | | | | PRED_UNIFY: (18), (58) imply: % 263.01/56.85 | | | | | (59) $false % 263.01/56.85 | | | | | % 263.01/56.85 | | | | | CLOSE: (59) is inconsistent. % 263.01/56.85 | | | | | % 263.01/56.85 | | | | Case 2: % 263.01/56.85 | | | | | % 263.01/56.85 | | | | | (60) ~ leq(n2, all_74_20) | (a_select3(pminus_ds1_filter, n5, n2) % 263.01/56.85 | | | | | = all_74_9 & $i(all_74_9)) % 263.01/56.85 | | | | | % 263.01/56.85 | | | | | BETA: splitting (60) gives: % 263.01/56.85 | | | | | % 263.01/56.85 | | | | | Case 1: % 263.01/56.85 | | | | | | % 263.01/56.85 | | | | | | (61) ~ leq(n2, all_74_20) % 263.01/56.85 | | | | | | % 263.01/56.85 | | | | | | REDUCE: (19), (61) imply: % 263.01/56.85 | | | | | | (62) ~ leq(n2, n5) % 263.01/56.85 | | | | | | % 263.01/56.85 | | | | | | PRED_UNIFY: (54), (62) imply: % 263.01/56.85 | | | | | | (63) $false % 263.01/56.85 | | | | | | % 263.01/56.85 | | | | | | CLOSE: (63) is inconsistent. % 263.01/56.85 | | | | | | % 263.01/56.85 | | | | | Case 2: % 263.01/56.85 | | | | | | % 263.01/56.85 | | | | | | (64) a_select3(pminus_ds1_filter, n5, n2) = all_74_9 & % 263.01/56.85 | | | | | | $i(all_74_9) % 263.01/56.85 | | | | | | % 263.01/56.85 | | | | | | ALPHA: (64) implies: % 263.01/56.85 | | | | | | (65) a_select3(pminus_ds1_filter, n5, n2) = all_74_9 % 263.01/56.85 | | | | | | % 263.01/56.85 | | | | | | REF_CLOSE: (3), (15), (53), (65) are inconsistent by sub-proof #56. % 263.01/56.85 | | | | | | % 263.01/56.85 | | | | | End of split % 263.01/56.85 | | | | | % 263.01/56.85 | | | | End of split % 263.01/56.85 | | | | % 263.01/56.85 | | | End of split % 263.01/56.85 | | | % 263.01/56.85 | | Case 2: % 263.01/56.85 | | | % 263.01/56.85 | | | (66) all_74_11 = n3 % 263.01/56.85 | | | % 263.01/56.85 | | | REDUCE: (12), (66) imply: % 263.01/56.85 | | | (67) a_select3(pminus_ds1_filter, n3, n5) = all_74_9 % 263.01/56.85 | | | % 263.01/56.85 | | | REDUCE: (20), (66) imply: % 263.01/56.85 | | | (68) a_select3(pminus_ds1_filter, n5, n3) = all_74_8 % 263.01/56.85 | | | % 263.01/56.85 | | | REDUCE: (1), (66) imply: % 263.01/56.85 | | | (69) leq(n3, n5) % 263.01/56.85 | | | % 263.01/56.85 | | | REDUCE: (9), (66) imply: % 263.01/56.85 | | | (70) leq(n0, n3) % 263.01/56.85 | | | % 263.01/56.85 | | | GROUND_INST: instantiating (7) with n3, n5, all_74_9, simplifying with % 263.01/56.85 | | | (2), (13), (22), (67), (70) gives: % 263.01/56.85 | | | (71) ~ leq(n5, all_74_20) | ~ leq(n3, all_74_20) | % 263.01/56.85 | | | (a_select3(pminus_ds1_filter, n5, n3) = all_74_9 & $i(all_74_9)) % 263.01/56.85 | | | % 263.01/56.85 | | | BETA: splitting (71) gives: % 263.01/56.85 | | | % 263.01/56.85 | | | Case 1: % 263.01/56.85 | | | | % 263.01/56.85 | | | | (72) ~ leq(n5, all_74_20) % 263.01/56.85 | | | | % 263.01/56.85 | | | | REDUCE: (19), (72) imply: % 263.01/56.85 | | | | (73) ~ leq(n5, n5) % 263.01/56.85 | | | | % 263.01/56.85 | | | | PRED_UNIFY: (18), (73) imply: % 263.01/56.85 | | | | (74) $false % 263.01/56.85 | | | | % 263.01/56.85 | | | | CLOSE: (74) is inconsistent. % 263.01/56.85 | | | | % 263.01/56.85 | | | Case 2: % 263.01/56.85 | | | | % 263.01/56.85 | | | | (75) ~ leq(n3, all_74_20) | (a_select3(pminus_ds1_filter, n5, n3) = % 263.01/56.85 | | | | all_74_9 & $i(all_74_9)) % 263.01/56.85 | | | | % 263.01/56.85 | | | | BETA: splitting (75) gives: % 263.01/56.85 | | | | % 263.01/56.85 | | | | Case 1: % 263.01/56.85 | | | | | % 263.01/56.85 | | | | | (76) ~ leq(n3, all_74_20) % 263.01/56.85 | | | | | % 263.01/56.85 | | | | | REDUCE: (19), (76) imply: % 263.01/56.85 | | | | | (77) ~ leq(n3, n5) % 263.01/56.85 | | | | | % 263.01/56.85 | | | | | PRED_UNIFY: (69), (77) imply: % 263.01/56.85 | | | | | (78) $false % 263.01/56.85 | | | | | % 263.01/56.85 | | | | | CLOSE: (78) is inconsistent. % 263.01/56.85 | | | | | % 263.01/56.85 | | | | Case 2: % 263.01/56.85 | | | | | % 263.01/56.85 | | | | | (79) a_select3(pminus_ds1_filter, n5, n3) = all_74_9 & $i(all_74_9) % 263.01/56.85 | | | | | % 263.01/56.85 | | | | | ALPHA: (79) implies: % 263.01/56.85 | | | | | (80) a_select3(pminus_ds1_filter, n5, n3) = all_74_9 % 263.01/56.85 | | | | | % 263.01/56.85 | | | | | GROUND_INST: instantiating (15) with all_74_9, all_74_8, n3, n5, % 263.01/56.85 | | | | | pminus_ds1_filter, simplifying with (68), (80) gives: % 263.01/56.85 | | | | | (81) all_74_8 = all_74_9 % 263.01/56.85 | | | | | % 263.01/56.85 | | | | | REDUCE: (3), (81) imply: % 263.01/56.85 | | | | | (82) $false % 263.01/56.85 | | | | | % 263.01/56.85 | | | | | CLOSE: (82) is inconsistent. % 263.01/56.85 | | | | | % 263.01/56.85 | | | | End of split % 263.01/56.85 | | | | % 263.01/56.85 | | | End of split % 263.01/56.85 | | | % 263.01/56.85 | | End of split % 263.01/56.85 | | % 263.01/56.85 | Case 2: % 263.01/56.85 | | % 263.01/56.85 | | (83) all_74_11 = n4 % 263.01/56.85 | | % 263.01/56.85 | | REDUCE: (12), (83) imply: % 263.01/56.85 | | (84) a_select3(pminus_ds1_filter, n4, n5) = all_74_9 % 263.01/56.85 | | % 263.01/56.85 | | REDUCE: (20), (83) imply: % 263.01/56.85 | | (85) a_select3(pminus_ds1_filter, n5, n4) = all_74_8 % 263.01/56.85 | | % 263.01/56.85 | | REDUCE: (1), (83) imply: % 263.01/56.85 | | (86) leq(n4, n5) % 263.01/56.85 | | % 263.01/56.85 | | REDUCE: (9), (83) imply: % 263.01/56.85 | | (87) leq(n0, n4) % 263.01/56.85 | | % 263.01/56.85 | | GROUND_INST: instantiating (7) with n4, n5, all_74_9, simplifying with (4), % 263.01/56.85 | | (13), (22), (84), (87) gives: % 263.01/56.85 | | (88) ~ leq(n5, all_74_20) | ~ leq(n4, all_74_20) | % 263.01/56.85 | | (a_select3(pminus_ds1_filter, n5, n4) = all_74_9 & $i(all_74_9)) % 263.01/56.85 | | % 263.01/56.85 | | BETA: splitting (88) gives: % 263.01/56.85 | | % 263.01/56.85 | | Case 1: % 263.01/56.85 | | | % 263.01/56.85 | | | (89) ~ leq(n5, all_74_20) % 263.01/56.85 | | | % 263.01/56.85 | | | REDUCE: (19), (89) imply: % 263.01/56.85 | | | (90) ~ leq(n5, n5) % 263.01/56.85 | | | % 263.01/56.85 | | | PRED_UNIFY: (18), (90) imply: % 263.01/56.85 | | | (91) $false % 263.01/56.85 | | | % 263.01/56.85 | | | CLOSE: (91) is inconsistent. % 263.01/56.85 | | | % 263.01/56.85 | | Case 2: % 263.01/56.85 | | | % 263.01/56.85 | | | (92) ~ leq(n4, all_74_20) | (a_select3(pminus_ds1_filter, n5, n4) = % 263.01/56.85 | | | all_74_9 & $i(all_74_9)) % 263.01/56.85 | | | % 263.01/56.85 | | | BETA: splitting (92) gives: % 263.01/56.85 | | | % 263.01/56.85 | | | Case 1: % 263.01/56.85 | | | | % 263.01/56.85 | | | | (93) ~ leq(n4, all_74_20) % 263.01/56.86 | | | | % 263.01/56.86 | | | | REDUCE: (19), (93) imply: % 263.01/56.86 | | | | (94) ~ leq(n4, n5) % 263.01/56.86 | | | | % 263.01/56.86 | | | | PRED_UNIFY: (86), (94) imply: % 263.01/56.86 | | | | (95) $false % 263.01/56.86 | | | | % 263.01/56.86 | | | | CLOSE: (95) is inconsistent. % 263.01/56.86 | | | | % 263.01/56.86 | | | Case 2: % 263.01/56.86 | | | | % 263.01/56.86 | | | | (96) a_select3(pminus_ds1_filter, n5, n4) = all_74_9 & $i(all_74_9) % 263.01/56.86 | | | | % 263.01/56.86 | | | | ALPHA: (96) implies: % 263.01/56.86 | | | | (97) a_select3(pminus_ds1_filter, n5, n4) = all_74_9 % 263.01/56.86 | | | | % 263.01/56.86 | | | | REF_CLOSE: (3), (15), (85), (97) are inconsistent by sub-proof #55. % 263.01/56.86 | | | | % 263.01/56.86 | | | End of split % 263.01/56.86 | | | % 263.01/56.86 | | End of split % 263.01/56.86 | | % 263.01/56.86 | End of split % 263.01/56.86 | % 263.01/56.86 End of proof % 263.01/56.86 % 263.01/56.86 Sub-proof #55 shows that the following formulas are inconsistent: % 263.01/56.86 ---------------------------------------------------------------- % 263.01/56.86 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 263.01/56.86 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 263.01/56.86 v0)) % 263.01/56.86 (2) a_select3(pminus_ds1_filter, n5, n4) = all_74_8 % 263.01/56.86 (3) a_select3(pminus_ds1_filter, n5, n4) = all_74_9 % 263.01/56.86 (4) ~ (all_74_8 = all_74_9) % 263.01/56.86 % 263.01/56.86 Begin of proof % 263.01/56.86 | % 263.01/56.86 | GROUND_INST: instantiating (1) with all_74_9, all_74_8, n4, n5, % 263.01/56.86 | pminus_ds1_filter, simplifying with (2), (3) gives: % 263.01/56.86 | (5) all_74_8 = all_74_9 % 263.01/56.86 | % 263.01/56.86 | REDUCE: (4), (5) imply: % 263.01/56.86 | (6) $false % 263.01/56.86 | % 263.01/56.86 | CLOSE: (6) is inconsistent. % 263.01/56.86 | % 263.01/56.86 End of proof % 263.01/56.86 % 263.01/56.86 Sub-proof #56 shows that the following formulas are inconsistent: % 263.01/56.86 ---------------------------------------------------------------- % 263.01/56.86 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 263.01/56.86 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 263.01/56.86 v0)) % 263.01/56.86 (2) a_select3(pminus_ds1_filter, n5, n2) = all_74_8 % 263.01/56.86 (3) a_select3(pminus_ds1_filter, n5, n2) = all_74_9 % 263.01/56.86 (4) ~ (all_74_8 = all_74_9) % 263.01/56.86 % 263.01/56.86 Begin of proof % 263.01/56.86 | % 263.01/56.86 | GROUND_INST: instantiating (1) with all_74_9, all_74_8, n2, n5, % 263.01/56.86 | pminus_ds1_filter, simplifying with (2), (3) gives: % 263.01/56.86 | (5) all_74_8 = all_74_9 % 263.01/56.86 | % 263.01/56.86 | REDUCE: (4), (5) imply: % 263.01/56.86 | (6) $false % 263.01/56.86 | % 263.01/56.86 | CLOSE: (6) is inconsistent. % 263.01/56.86 | % 263.01/56.86 End of proof % 263.01/56.86 % 263.01/56.86 Sub-proof #57 shows that the following formulas are inconsistent: % 263.01/56.86 ---------------------------------------------------------------- % 263.01/56.86 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 263.01/56.86 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 263.01/56.86 v0)) % 263.01/56.86 (2) a_select3(pminus_ds1_filter, n5, n1) = all_74_8 % 263.01/56.86 (3) a_select3(pminus_ds1_filter, n5, n1) = all_74_9 % 263.01/56.86 (4) ~ (all_74_8 = all_74_9) % 263.01/56.86 % 263.01/56.86 Begin of proof % 263.01/56.86 | % 263.01/56.86 | GROUND_INST: instantiating (1) with all_74_9, all_74_8, n1, n5, % 263.01/56.86 | pminus_ds1_filter, simplifying with (2), (3) gives: % 263.01/56.86 | (5) all_74_8 = all_74_9 % 263.01/56.86 | % 263.01/56.86 | REDUCE: (4), (5) imply: % 263.01/56.86 | (6) $false % 263.01/56.86 | % 263.01/56.86 | CLOSE: (6) is inconsistent. % 263.01/56.86 | % 263.01/56.86 End of proof % 263.01/56.86 % 263.01/56.86 Sub-proof #58 shows that the following formulas are inconsistent: % 263.01/56.86 ---------------------------------------------------------------- % 263.01/56.86 (1) leq(all_74_11, n5) % 263.01/56.86 (2) $i(n3) % 263.01/56.86 (3) ~ (all_74_8 = all_74_9) % 263.01/56.86 (4) $i(n4) % 263.01/56.86 (5) ! [v0: $i] : (v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0, n1) | ~ % 263.01/56.86 leq(n0, v0)) % 263.01/56.86 (6) pred(n2) = n1 % 263.01/56.86 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 263.01/56.86 (a_select3(pminus_ds1_filter, v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 263.01/56.86 ~ leq(v1, all_74_20) | ~ leq(v0, all_74_20) | ~ leq(n0, v1) | ~ % 263.01/56.86 leq(n0, v0) | (a_select3(pminus_ds1_filter, v1, v0) = v2 & $i(v2))) % 263.01/56.86 (8) ~ (all_74_11 = n0) % 263.01/56.86 (9) leq(n0, all_74_11) % 263.01/56.86 (10) a_select3(pminus_ds1_filter, all_74_10, all_74_11) = all_74_8 % 263.01/56.86 (11) leq(all_74_10, n5) % 263.01/56.86 (12) $i(all_74_10) % 263.01/56.86 (13) $i(all_74_11) % 263.01/56.86 (14) pred(n3) = n2 % 263.01/56.86 (15) all_74_11 = n4 | gt(n4, all_74_11) % 263.01/56.86 (16) all_74_10 = n4 | gt(n4, all_74_10) % 263.01/56.86 (17) a_select3(pminus_ds1_filter, all_74_11, all_74_10) = all_74_9 % 263.01/56.86 (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 263.01/56.86 (v1 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 263.01/56.86 v0)) % 263.01/56.86 (19) pred(n4) = n3 % 263.01/56.86 (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (pred(v1) = v2) | ~ % 263.01/56.86 $i(v1) | ~ $i(v0) | ~ gt(v1, v0) | leq(v0, v2)) % 263.01/56.86 (21) ~ (all_74_10 = n0) % 263.01/56.86 (22) all_74_20 = n5 % 263.01/56.86 (23) $i(n2) % 263.01/56.86 (24) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ % 263.01/56.86 leq(v0, v1) | gt(v1, v0)) % 263.01/56.86 (25) leq(n0, all_74_10) % 263.01/56.86 % 263.01/56.86 Begin of proof % 263.01/56.86 | % 263.01/56.86 | BETA: splitting (15) gives: % 263.01/56.86 | % 263.01/56.86 | Case 1: % 263.01/56.86 | | % 263.01/56.86 | | (26) gt(n4, all_74_11) % 263.01/56.86 | | % 263.01/56.86 | | GROUND_INST: instantiating (20) with all_74_11, n4, n3, simplifying with % 263.01/56.86 | | (4), (13), (19), (26) gives: % 263.01/56.86 | | (27) leq(all_74_11, n3) % 263.01/56.86 | | % 263.01/56.86 | | GROUND_INST: instantiating (24) with all_74_11, n3, simplifying with (2), % 263.01/56.86 | | (13), (27) gives: % 263.01/56.86 | | (28) all_74_11 = n3 | gt(n3, all_74_11) % 263.01/56.86 | | % 263.01/56.86 | | BETA: splitting (16) gives: % 263.01/56.86 | | % 263.01/56.86 | | Case 1: % 263.01/56.86 | | | % 263.01/56.86 | | | (29) gt(n4, all_74_10) % 263.01/56.86 | | | % 263.01/56.86 | | | GROUND_INST: instantiating (20) with all_74_10, n4, n3, simplifying with % 263.01/56.86 | | | (4), (12), (19), (29) gives: % 263.01/56.86 | | | (30) leq(all_74_10, n3) % 263.01/56.86 | | | % 263.01/56.86 | | | GROUND_INST: instantiating (24) with all_74_10, n3, simplifying with (2), % 263.01/56.86 | | | (12), (30) gives: % 263.01/56.86 | | | (31) all_74_10 = n3 | gt(n3, all_74_10) % 263.01/56.86 | | | % 263.01/56.86 | | | BETA: splitting (28) gives: % 263.01/56.86 | | | % 263.01/56.86 | | | Case 1: % 263.01/56.86 | | | | % 263.01/56.86 | | | | (32) gt(n3, all_74_11) % 263.01/56.86 | | | | % 263.01/56.86 | | | | GROUND_INST: instantiating (20) with all_74_11, n3, n2, simplifying with % 263.01/56.86 | | | | (2), (13), (14), (32) gives: % 263.01/56.86 | | | | (33) leq(all_74_11, n2) % 263.01/56.86 | | | | % 263.01/56.86 | | | | GROUND_INST: instantiating (24) with all_74_11, n2, simplifying with % 263.01/56.86 | | | | (13), (23), (33) gives: % 263.01/56.86 | | | | (34) all_74_11 = n2 | gt(n2, all_74_11) % 263.01/56.86 | | | | % 263.01/56.86 | | | | BETA: splitting (31) gives: % 263.01/56.86 | | | | % 263.01/56.86 | | | | Case 1: % 263.01/56.86 | | | | | % 263.01/56.86 | | | | | (35) gt(n3, all_74_10) % 263.01/56.86 | | | | | % 263.01/56.86 | | | | | GROUND_INST: instantiating (20) with all_74_10, n3, n2, simplifying % 263.01/56.86 | | | | | with (2), (12), (14), (35) gives: % 263.01/56.86 | | | | | (36) leq(all_74_10, n2) % 263.01/56.86 | | | | | % 263.01/56.86 | | | | | GROUND_INST: instantiating (24) with all_74_10, n2, simplifying with % 263.01/56.86 | | | | | (12), (23), (36) gives: % 263.01/56.86 | | | | | (37) all_74_10 = n2 | gt(n2, all_74_10) % 263.01/56.86 | | | | | % 263.01/56.86 | | | | | BETA: splitting (34) gives: % 263.01/56.86 | | | | | % 263.01/56.86 | | | | | Case 1: % 263.01/56.86 | | | | | | % 263.01/56.86 | | | | | | (38) gt(n2, all_74_11) % 263.01/56.86 | | | | | | % 263.01/56.86 | | | | | | GROUND_INST: instantiating (20) with all_74_11, n2, n1, simplifying % 263.01/56.86 | | | | | | with (6), (13), (23), (38) gives: % 263.01/56.86 | | | | | | (39) leq(all_74_11, n1) % 263.01/56.86 | | | | | | % 263.01/56.86 | | | | | | GROUND_INST: instantiating (5) with all_74_11, simplifying with (9), % 263.01/56.86 | | | | | | (13), (39) gives: % 263.01/56.86 | | | | | | (40) all_74_11 = n1 | all_74_11 = n0 % 263.01/56.86 | | | | | | % 263.01/56.86 | | | | | | BETA: splitting (40) gives: % 263.01/56.86 | | | | | | % 263.01/56.86 | | | | | | Case 1: % 263.01/56.86 | | | | | | | % 263.01/56.86 | | | | | | | (41) all_74_11 = n0 % 263.01/56.86 | | | | | | | % 263.01/56.86 | | | | | | | REDUCE: (8), (41) imply: % 263.01/56.86 | | | | | | | (42) $false % 263.01/56.86 | | | | | | | % 263.01/56.86 | | | | | | | CLOSE: (42) is inconsistent. % 263.01/56.86 | | | | | | | % 263.01/56.86 | | | | | | Case 2: % 263.01/56.86 | | | | | | | % 263.01/56.86 | | | | | | | (43) all_74_11 = n1 % 263.01/56.86 | | | | | | | % 263.01/56.86 | | | | | | | REDUCE: (10), (43) imply: % 263.01/56.86 | | | | | | | (44) a_select3(pminus_ds1_filter, all_74_10, n1) = all_74_8 % 263.01/56.86 | | | | | | | % 263.01/56.86 | | | | | | | REDUCE: (17), (43) imply: % 263.01/56.86 | | | | | | | (45) a_select3(pminus_ds1_filter, n1, all_74_10) = all_74_9 % 263.01/56.86 | | | | | | | % 263.01/56.86 | | | | | | | REDUCE: (13), (43) imply: % 263.01/56.86 | | | | | | | (46) $i(n1) % 263.01/56.86 | | | | | | | % 263.01/56.86 | | | | | | | REDUCE: (1), (43) imply: % 263.01/56.86 | | | | | | | (47) leq(n1, n5) % 263.01/56.86 | | | | | | | % 263.01/56.86 | | | | | | | REDUCE: (9), (43) imply: % 263.01/56.86 | | | | | | | (48) leq(n0, n1) % 263.01/56.86 | | | | | | | % 263.01/56.86 | | | | | | | BETA: splitting (37) gives: % 263.01/56.86 | | | | | | | % 263.01/56.86 | | | | | | | Case 1: % 263.01/56.86 | | | | | | | | % 263.01/56.86 | | | | | | | | (49) gt(n2, all_74_10) % 263.01/56.86 | | | | | | | | % 263.01/56.86 | | | | | | | | GROUND_INST: instantiating (20) with all_74_10, n2, n1, % 263.01/56.86 | | | | | | | | simplifying with (6), (12), (23), (49) gives: % 263.01/56.86 | | | | | | | | (50) leq(all_74_10, n1) % 263.01/56.86 | | | | | | | | % 263.01/56.86 | | | | | | | | GROUND_INST: instantiating (5) with all_74_10, simplifying with % 263.01/56.86 | | | | | | | | (12), (25), (50) gives: % 263.01/56.86 | | | | | | | | (51) all_74_10 = n1 | all_74_10 = n0 % 263.01/56.86 | | | | | | | | % 263.01/56.86 | | | | | | | | BETA: splitting (51) gives: % 263.01/56.86 | | | | | | | | % 263.01/56.86 | | | | | | | | Case 1: % 263.01/56.86 | | | | | | | | | % 263.01/56.86 | | | | | | | | | (52) all_74_10 = n0 % 263.01/56.86 | | | | | | | | | % 263.01/56.86 | | | | | | | | | REDUCE: (21), (52) imply: % 263.01/56.86 | | | | | | | | | (53) $false % 263.01/56.86 | | | | | | | | | % 263.01/56.86 | | | | | | | | | CLOSE: (53) is inconsistent. % 263.01/56.86 | | | | | | | | | % 263.01/56.86 | | | | | | | | Case 2: % 263.01/56.86 | | | | | | | | | % 263.01/56.86 | | | | | | | | | (54) all_74_10 = n1 % 263.01/56.86 | | | | | | | | | % 263.01/56.86 | | | | | | | | | REDUCE: (44), (54) imply: % 263.01/56.86 | | | | | | | | | (55) a_select3(pminus_ds1_filter, n1, n1) = all_74_8 % 263.01/56.86 | | | | | | | | | % 263.01/56.86 | | | | | | | | | REDUCE: (45), (54) imply: % 263.01/56.86 | | | | | | | | | (56) a_select3(pminus_ds1_filter, n1, n1) = all_74_9 % 263.01/56.86 | | | | | | | | | % 263.01/56.86 | | | | | | | | | GROUND_INST: instantiating (18) with all_74_9, all_74_8, n1, % 263.01/56.86 | | | | | | | | | n1, pminus_ds1_filter, simplifying with (55), (56) % 263.01/56.86 | | | | | | | | | gives: % 263.01/56.86 | | | | | | | | | (57) all_74_8 = all_74_9 % 263.01/56.86 | | | | | | | | | % 263.01/56.86 | | | | | | | | | REDUCE: (3), (57) imply: % 263.01/56.86 | | | | | | | | | (58) $false % 263.01/56.86 | | | | | | | | | % 263.01/56.86 | | | | | | | | | CLOSE: (58) is inconsistent. % 263.01/56.86 | | | | | | | | | % 263.01/56.86 | | | | | | | | End of split % 263.01/56.86 | | | | | | | | % 263.01/56.86 | | | | | | | Case 2: % 263.01/56.86 | | | | | | | | % 263.01/56.86 | | | | | | | | (59) all_74_10 = n2 % 263.01/56.86 | | | | | | | | % 263.01/56.86 | | | | | | | | REDUCE: (44), (59) imply: % 263.01/56.86 | | | | | | | | (60) a_select3(pminus_ds1_filter, n2, n1) = all_74_8 % 263.01/56.86 | | | | | | | | % 263.01/56.86 | | | | | | | | REDUCE: (45), (59) imply: % 263.01/56.86 | | | | | | | | (61) a_select3(pminus_ds1_filter, n1, n2) = all_74_9 % 263.01/56.86 | | | | | | | | % 263.01/56.86 | | | | | | | | REDUCE: (11), (59) imply: % 263.01/56.86 | | | | | | | | (62) leq(n2, n5) % 263.01/56.86 | | | | | | | | % 263.01/56.86 | | | | | | | | REDUCE: (25), (59) imply: % 263.01/56.86 | | | | | | | | (63) leq(n0, n2) % 263.01/56.86 | | | | | | | | % 263.01/56.86 | | | | | | | | GROUND_INST: instantiating (7) with n1, n2, all_74_9, % 263.01/56.86 | | | | | | | | simplifying with (23), (46), (48), (61), (63) % 263.01/56.86 | | | | | | | | gives: % 263.01/56.86 | | | | | | | | (64) ~ leq(n2, all_74_20) | ~ leq(n1, all_74_20) | % 263.01/56.86 | | | | | | | | (a_select3(pminus_ds1_filter, n2, n1) = all_74_9 & % 263.01/56.86 | | | | | | | | $i(all_74_9)) % 263.01/56.86 | | | | | | | | % 263.01/56.86 | | | | | | | | BETA: splitting (64) gives: % 263.01/56.86 | | | | | | | | % 263.01/56.86 | | | | | | | | Case 1: % 263.01/56.86 | | | | | | | | | % 263.01/56.86 | | | | | | | | | (65) ~ leq(n2, all_74_20) % 263.01/56.86 | | | | | | | | | % 263.01/56.86 | | | | | | | | | REDUCE: (22), (65) imply: % 263.01/56.86 | | | | | | | | | (66) ~ leq(n2, n5) % 263.01/56.86 | | | | | | | | | % 263.01/56.86 | | | | | | | | | PRED_UNIFY: (62), (66) imply: % 263.01/56.86 | | | | | | | | | (67) $false % 263.01/56.86 | | | | | | | | | % 263.01/56.86 | | | | | | | | | CLOSE: (67) is inconsistent. % 263.01/56.86 | | | | | | | | | % 263.01/56.86 | | | | | | | | Case 2: % 263.01/56.86 | | | | | | | | | % 263.01/56.86 | | | | | | | | | (68) ~ leq(n1, all_74_20) | (a_select3(pminus_ds1_filter, % 263.01/56.86 | | | | | | | | | n2, n1) = all_74_9 & $i(all_74_9)) % 263.01/56.86 | | | | | | | | | % 263.01/56.86 | | | | | | | | | BETA: splitting (68) gives: % 263.01/56.86 | | | | | | | | | % 263.01/56.86 | | | | | | | | | Case 1: % 263.01/56.86 | | | | | | | | | | % 263.01/56.86 | | | | | | | | | | (69) ~ leq(n1, all_74_20) % 263.01/56.86 | | | | | | | | | | % 263.01/56.86 | | | | | | | | | | REDUCE: (22), (69) imply: % 263.01/56.86 | | | | | | | | | | (70) ~ leq(n1, n5) % 263.01/56.86 | | | | | | | | | | % 263.01/56.86 | | | | | | | | | | PRED_UNIFY: (47), (70) imply: % 263.01/56.86 | | | | | | | | | | (71) $false % 263.01/56.86 | | | | | | | | | | % 263.01/56.86 | | | | | | | | | | CLOSE: (71) is inconsistent. % 263.01/56.86 | | | | | | | | | | % 263.01/56.86 | | | | | | | | | Case 2: % 263.01/56.86 | | | | | | | | | | % 263.01/56.86 | | | | | | | | | | (72) a_select3(pminus_ds1_filter, n2, n1) = all_74_9 & % 263.01/56.86 | | | | | | | | | | $i(all_74_9) % 263.01/56.86 | | | | | | | | | | % 263.01/56.86 | | | | | | | | | | ALPHA: (72) implies: % 263.01/56.86 | | | | | | | | | | (73) a_select3(pminus_ds1_filter, n2, n1) = all_74_9 % 263.01/56.86 | | | | | | | | | | % 263.01/56.86 | | | | | | | | | | REF_CLOSE: (3), (18), (60), (73) are inconsistent by % 263.01/56.86 | | | | | | | | | | sub-proof #62. % 263.01/56.86 | | | | | | | | | | % 263.01/56.86 | | | | | | | | | End of split % 263.01/56.86 | | | | | | | | | % 263.01/56.86 | | | | | | | | End of split % 263.01/56.86 | | | | | | | | % 263.01/56.86 | | | | | | | End of split % 263.01/56.86 | | | | | | | % 263.01/56.86 | | | | | | End of split % 263.01/56.86 | | | | | | % 263.01/56.86 | | | | | Case 2: % 263.01/56.86 | | | | | | % 263.01/56.86 | | | | | | (74) all_74_11 = n2 % 263.01/56.86 | | | | | | % 263.01/56.86 | | | | | | REDUCE: (10), (74) imply: % 263.01/56.86 | | | | | | (75) a_select3(pminus_ds1_filter, all_74_10, n2) = all_74_8 % 263.01/56.86 | | | | | | % 263.01/56.86 | | | | | | REDUCE: (17), (74) imply: % 263.01/56.86 | | | | | | (76) a_select3(pminus_ds1_filter, n2, all_74_10) = all_74_9 % 263.01/56.86 | | | | | | % 263.01/56.86 | | | | | | REDUCE: (1), (74) imply: % 263.01/56.86 | | | | | | (77) leq(n2, n5) % 263.01/56.86 | | | | | | % 263.01/56.86 | | | | | | REDUCE: (9), (74) imply: % 263.01/56.86 | | | | | | (78) leq(n0, n2) % 263.01/56.86 | | | | | | % 263.01/56.86 | | | | | | BETA: splitting (37) gives: % 263.01/56.86 | | | | | | % 263.01/56.86 | | | | | | Case 1: % 263.01/56.86 | | | | | | | % 263.01/56.86 | | | | | | | (79) gt(n2, all_74_10) % 263.01/56.86 | | | | | | | % 263.01/56.86 | | | | | | | GROUND_INST: instantiating (20) with all_74_10, n2, n1, % 263.01/56.86 | | | | | | | simplifying with (6), (12), (23), (79) gives: % 263.01/56.86 | | | | | | | (80) leq(all_74_10, n1) % 263.01/56.86 | | | | | | | % 263.01/56.87 | | | | | | | GROUND_INST: instantiating (5) with all_74_10, simplifying with % 263.01/56.87 | | | | | | | (12), (25), (80) gives: % 263.01/56.87 | | | | | | | (81) all_74_10 = n1 | all_74_10 = n0 % 263.01/56.87 | | | | | | | % 263.01/56.87 | | | | | | | BETA: splitting (81) gives: % 263.01/56.87 | | | | | | | % 263.01/56.87 | | | | | | | Case 1: % 263.01/56.87 | | | | | | | | % 263.01/56.87 | | | | | | | | (82) all_74_10 = n0 % 263.01/56.87 | | | | | | | | % 263.01/56.87 | | | | | | | | REDUCE: (21), (82) imply: % 263.01/56.87 | | | | | | | | (83) $false % 263.01/56.87 | | | | | | | | % 263.01/56.87 | | | | | | | | CLOSE: (83) is inconsistent. % 263.01/56.87 | | | | | | | | % 263.01/56.87 | | | | | | | Case 2: % 263.01/56.87 | | | | | | | | % 263.01/56.87 | | | | | | | | (84) all_74_10 = n1 % 263.01/56.87 | | | | | | | | % 263.01/56.87 | | | | | | | | REDUCE: (75), (84) imply: % 263.01/56.87 | | | | | | | | (85) a_select3(pminus_ds1_filter, n1, n2) = all_74_8 % 263.01/56.87 | | | | | | | | % 263.01/56.87 | | | | | | | | REDUCE: (76), (84) imply: % 263.01/56.87 | | | | | | | | (86) a_select3(pminus_ds1_filter, n2, n1) = all_74_9 % 263.01/56.87 | | | | | | | | % 263.01/56.87 | | | | | | | | REDUCE: (12), (84) imply: % 263.01/56.87 | | | | | | | | (87) $i(n1) % 263.01/56.87 | | | | | | | | % 263.01/56.87 | | | | | | | | REDUCE: (11), (84) imply: % 263.01/56.87 | | | | | | | | (88) leq(n1, n5) % 263.01/56.87 | | | | | | | | % 263.01/56.87 | | | | | | | | REDUCE: (25), (84) imply: % 263.01/56.87 | | | | | | | | (89) leq(n0, n1) % 263.01/56.87 | | | | | | | | % 263.01/56.87 | | | | | | | | GROUND_INST: instantiating (7) with n1, n2, all_74_8, % 263.01/56.87 | | | | | | | | simplifying with (23), (78), (85), (87), (89) % 263.01/56.87 | | | | | | | | gives: % 263.01/56.87 | | | | | | | | (90) ~ leq(n2, all_74_20) | ~ leq(n1, all_74_20) | % 263.01/56.87 | | | | | | | | (a_select3(pminus_ds1_filter, n2, n1) = all_74_8 & % 263.01/56.87 | | | | | | | | $i(all_74_8)) % 263.01/56.87 | | | | | | | | % 263.01/56.87 | | | | | | | | BETA: splitting (90) gives: % 263.01/56.87 | | | | | | | | % 263.01/56.87 | | | | | | | | Case 1: % 263.01/56.87 | | | | | | | | | % 263.01/56.87 | | | | | | | | | (91) ~ leq(n2, all_74_20) % 263.01/56.87 | | | | | | | | | % 263.01/56.87 | | | | | | | | | REDUCE: (22), (91) imply: % 263.01/56.87 | | | | | | | | | (92) ~ leq(n2, n5) % 263.01/56.87 | | | | | | | | | % 263.01/56.87 | | | | | | | | | PRED_UNIFY: (77), (92) imply: % 263.01/56.87 | | | | | | | | | (93) $false % 263.01/56.87 | | | | | | | | | % 263.01/56.87 | | | | | | | | | CLOSE: (93) is inconsistent. % 263.01/56.87 | | | | | | | | | % 263.01/56.87 | | | | | | | | Case 2: % 263.01/56.87 | | | | | | | | | % 263.01/56.87 | | | | | | | | | (94) ~ leq(n1, all_74_20) | (a_select3(pminus_ds1_filter, % 263.01/56.87 | | | | | | | | | n2, n1) = all_74_8 & $i(all_74_8)) % 263.01/56.87 | | | | | | | | | % 263.01/56.87 | | | | | | | | | BETA: splitting (94) gives: % 263.01/56.87 | | | | | | | | | % 263.01/56.87 | | | | | | | | | Case 1: % 263.01/56.87 | | | | | | | | | | % 263.01/56.87 | | | | | | | | | | (95) ~ leq(n1, all_74_20) % 263.01/56.87 | | | | | | | | | | % 263.01/56.87 | | | | | | | | | | REDUCE: (22), (95) imply: % 263.01/56.87 | | | | | | | | | | (96) ~ leq(n1, n5) % 263.01/56.87 | | | | | | | | | | % 263.01/56.87 | | | | | | | | | | PRED_UNIFY: (88), (96) imply: % 263.01/56.87 | | | | | | | | | | (97) $false % 263.01/56.87 | | | | | | | | | | % 263.01/56.87 | | | | | | | | | | CLOSE: (97) is inconsistent. % 263.01/56.87 | | | | | | | | | | % 263.01/56.87 | | | | | | | | | Case 2: % 263.01/56.87 | | | | | | | | | | % 263.01/56.87 | | | | | | | | | | (98) a_select3(pminus_ds1_filter, n2, n1) = all_74_8 & % 263.01/56.87 | | | | | | | | | | $i(all_74_8) % 263.01/56.87 | | | | | | | | | | % 263.01/56.87 | | | | | | | | | | ALPHA: (98) implies: % 263.01/56.87 | | | | | | | | | | (99) a_select3(pminus_ds1_filter, n2, n1) = all_74_8 % 263.01/56.87 | | | | | | | | | | % 263.01/56.87 | | | | | | | | | | REF_CLOSE: (3), (18), (86), (99) are inconsistent by % 263.01/56.87 | | | | | | | | | | sub-proof #62. % 263.01/56.87 | | | | | | | | | | % 263.01/56.87 | | | | | | | | | End of split % 263.01/56.87 | | | | | | | | | % 263.01/56.87 | | | | | | | | End of split % 263.01/56.87 | | | | | | | | % 263.01/56.87 | | | | | | | End of split % 263.01/56.87 | | | | | | | % 263.01/56.87 | | | | | | Case 2: % 263.01/56.87 | | | | | | | % 263.01/56.87 | | | | | | | (100) all_74_10 = n2 % 263.01/56.87 | | | | | | | % 263.01/56.87 | | | | | | | REDUCE: (75), (100) imply: % 263.01/56.87 | | | | | | | (101) a_select3(pminus_ds1_filter, n2, n2) = all_74_8 % 263.01/56.87 | | | | | | | % 263.01/56.87 | | | | | | | REDUCE: (76), (100) imply: % 263.01/56.87 | | | | | | | (102) a_select3(pminus_ds1_filter, n2, n2) = all_74_9 % 263.01/56.87 | | | | | | | % 263.01/56.87 | | | | | | | GROUND_INST: instantiating (18) with all_74_9, all_74_8, n2, n2, % 263.01/56.87 | | | | | | | pminus_ds1_filter, simplifying with (101), (102) % 263.01/56.87 | | | | | | | gives: % 263.01/56.87 | | | | | | | (103) all_74_8 = all_74_9 % 263.01/56.87 | | | | | | | % 263.01/56.87 | | | | | | | REDUCE: (3), (103) imply: % 263.01/56.87 | | | | | | | (104) $false % 263.01/56.87 | | | | | | | % 263.01/56.87 | | | | | | | CLOSE: (104) is inconsistent. % 263.01/56.87 | | | | | | | % 263.01/56.87 | | | | | | End of split % 263.01/56.87 | | | | | | % 263.01/56.87 | | | | | End of split % 263.01/56.87 | | | | | % 263.01/56.87 | | | | Case 2: % 263.01/56.87 | | | | | % 263.01/56.87 | | | | | (105) all_74_10 = n3 % 263.01/56.87 | | | | | % 263.01/56.87 | | | | | REDUCE: (10), (105) imply: % 263.01/56.87 | | | | | (106) a_select3(pminus_ds1_filter, n3, all_74_11) = all_74_8 % 263.01/56.87 | | | | | % 263.01/56.87 | | | | | REDUCE: (17), (105) imply: % 263.01/56.87 | | | | | (107) a_select3(pminus_ds1_filter, all_74_11, n3) = all_74_9 % 263.01/56.87 | | | | | % 263.01/56.87 | | | | | REDUCE: (11), (105) imply: % 263.01/56.87 | | | | | (108) leq(n3, n5) % 263.01/56.87 | | | | | % 263.01/56.87 | | | | | REDUCE: (25), (105) imply: % 263.01/56.87 | | | | | (109) leq(n0, n3) % 263.01/56.87 | | | | | % 263.01/56.87 | | | | | BETA: splitting (34) gives: % 263.01/56.87 | | | | | % 263.01/56.87 | | | | | Case 1: % 263.01/56.87 | | | | | | % 263.01/56.87 | | | | | | (110) gt(n2, all_74_11) % 263.01/56.87 | | | | | | % 263.01/56.87 | | | | | | GROUND_INST: instantiating (20) with all_74_11, n2, n1, simplifying % 263.01/56.87 | | | | | | with (6), (13), (23), (110) gives: % 263.01/56.87 | | | | | | (111) leq(all_74_11, n1) % 263.01/56.87 | | | | | | % 263.01/56.87 | | | | | | GROUND_INST: instantiating (5) with all_74_11, simplifying with (9), % 263.01/56.87 | | | | | | (13), (111) gives: % 263.01/56.87 | | | | | | (112) all_74_11 = n1 | all_74_11 = n0 % 263.01/56.87 | | | | | | % 263.01/56.87 | | | | | | BETA: splitting (112) gives: % 263.01/56.87 | | | | | | % 263.01/56.87 | | | | | | Case 1: % 263.01/56.87 | | | | | | | % 263.01/56.87 | | | | | | | (113) all_74_11 = n0 % 263.01/56.87 | | | | | | | % 263.01/56.87 | | | | | | | REDUCE: (8), (113) imply: % 263.01/56.87 | | | | | | | (114) $false % 263.01/56.87 | | | | | | | % 263.01/56.87 | | | | | | | CLOSE: (114) is inconsistent. % 263.01/56.87 | | | | | | | % 263.01/56.87 | | | | | | Case 2: % 263.01/56.87 | | | | | | | % 263.01/56.87 | | | | | | | (115) all_74_11 = n1 % 263.01/56.87 | | | | | | | % 263.01/56.87 | | | | | | | REDUCE: (107), (115) imply: % 263.01/56.87 | | | | | | | (116) a_select3(pminus_ds1_filter, n1, n3) = all_74_9 % 263.01/56.87 | | | | | | | % 263.01/56.87 | | | | | | | REDUCE: (106), (115) imply: % 263.01/56.87 | | | | | | | (117) a_select3(pminus_ds1_filter, n3, n1) = all_74_8 % 263.01/56.87 | | | | | | | % 263.01/56.87 | | | | | | | REDUCE: (13), (115) imply: % 263.01/56.87 | | | | | | | (118) $i(n1) % 263.01/56.87 | | | | | | | % 263.01/56.87 | | | | | | | REDUCE: (1), (115) imply: % 263.01/56.87 | | | | | | | (119) leq(n1, n5) % 263.01/56.87 | | | | | | | % 263.01/56.87 | | | | | | | REDUCE: (9), (115) imply: % 263.01/56.87 | | | | | | | (120) leq(n0, n1) % 263.01/56.87 | | | | | | | % 263.01/56.87 | | | | | | | GROUND_INST: instantiating (7) with n1, n3, all_74_9, simplifying % 263.01/56.87 | | | | | | | with (2), (109), (116), (118), (120) gives: % 263.01/56.87 | | | | | | | (121) ~ leq(n3, all_74_20) | ~ leq(n1, all_74_20) | % 263.01/56.87 | | | | | | | (a_select3(pminus_ds1_filter, n3, n1) = all_74_9 & % 263.01/56.87 | | | | | | | $i(all_74_9)) % 263.01/56.87 | | | | | | | % 263.01/56.87 | | | | | | | BETA: splitting (121) gives: % 263.01/56.87 | | | | | | | % 263.01/56.87 | | | | | | | Case 1: % 263.01/56.87 | | | | | | | | % 263.01/56.87 | | | | | | | | (122) ~ leq(n3, all_74_20) % 263.01/56.87 | | | | | | | | % 263.01/56.87 | | | | | | | | REDUCE: (22), (122) imply: % 263.01/56.87 | | | | | | | | (123) ~ leq(n3, n5) % 263.01/56.87 | | | | | | | | % 263.01/56.87 | | | | | | | | PRED_UNIFY: (108), (123) imply: % 263.01/56.87 | | | | | | | | (124) $false % 263.01/56.87 | | | | | | | | % 263.01/56.87 | | | | | | | | CLOSE: (124) is inconsistent. % 263.01/56.87 | | | | | | | | % 263.01/56.87 | | | | | | | Case 2: % 263.01/56.87 | | | | | | | | % 263.01/56.87 | | | | | | | | (125) ~ leq(n1, all_74_20) | (a_select3(pminus_ds1_filter, % 263.01/56.87 | | | | | | | | n3, n1) = all_74_9 & $i(all_74_9)) % 263.01/56.87 | | | | | | | | % 263.01/56.87 | | | | | | | | BETA: splitting (125) gives: % 263.01/56.87 | | | | | | | | % 263.01/56.87 | | | | | | | | Case 1: % 263.01/56.87 | | | | | | | | | % 263.01/56.87 | | | | | | | | | (126) ~ leq(n1, all_74_20) % 263.01/56.87 | | | | | | | | | % 263.01/56.87 | | | | | | | | | REDUCE: (22), (126) imply: % 263.01/56.87 | | | | | | | | | (127) ~ leq(n1, n5) % 263.01/56.87 | | | | | | | | | % 263.01/56.87 | | | | | | | | | PRED_UNIFY: (119), (127) imply: % 263.01/56.87 | | | | | | | | | (128) $false % 263.01/56.87 | | | | | | | | | % 263.01/56.87 | | | | | | | | | CLOSE: (128) is inconsistent. % 263.01/56.87 | | | | | | | | | % 263.01/56.87 | | | | | | | | Case 2: % 263.01/56.87 | | | | | | | | | % 263.01/56.87 | | | | | | | | | (129) a_select3(pminus_ds1_filter, n3, n1) = all_74_9 & % 263.01/56.87 | | | | | | | | | $i(all_74_9) % 263.01/56.87 | | | | | | | | | % 263.01/56.87 | | | | | | | | | ALPHA: (129) implies: % 263.01/56.87 | | | | | | | | | (130) a_select3(pminus_ds1_filter, n3, n1) = all_74_9 % 263.01/56.87 | | | | | | | | | % 263.01/56.87 | | | | | | | | | GROUND_INST: instantiating (18) with all_74_8, all_74_9, n1, % 263.01/56.87 | | | | | | | | | n3, pminus_ds1_filter, simplifying with (117), % 263.01/56.87 | | | | | | | | | (130) gives: % 263.01/56.87 | | | | | | | | | (131) all_74_8 = all_74_9 % 263.01/56.87 | | | | | | | | | % 263.01/56.87 | | | | | | | | | REDUCE: (3), (131) imply: % 263.01/56.87 | | | | | | | | | (132) $false % 263.01/56.87 | | | | | | | | | % 263.01/56.87 | | | | | | | | | CLOSE: (132) is inconsistent. % 263.01/56.87 | | | | | | | | | % 263.01/56.87 | | | | | | | | End of split % 263.01/56.87 | | | | | | | | % 263.01/56.87 | | | | | | | End of split % 263.01/56.87 | | | | | | | % 263.01/56.87 | | | | | | End of split % 263.01/56.87 | | | | | | % 263.01/56.87 | | | | | Case 2: % 263.01/56.87 | | | | | | % 263.01/56.87 | | | | | | (133) all_74_11 = n2 % 263.01/56.87 | | | | | | % 263.01/56.87 | | | | | | REDUCE: (107), (133) imply: % 263.01/56.87 | | | | | | (134) a_select3(pminus_ds1_filter, n2, n3) = all_74_9 % 263.01/56.87 | | | | | | % 263.01/56.87 | | | | | | REDUCE: (106), (133) imply: % 263.01/56.87 | | | | | | (135) a_select3(pminus_ds1_filter, n3, n2) = all_74_8 % 263.01/56.87 | | | | | | % 263.01/56.87 | | | | | | REDUCE: (1), (133) imply: % 263.01/56.87 | | | | | | (136) leq(n2, n5) % 263.01/56.87 | | | | | | % 263.01/56.87 | | | | | | REDUCE: (9), (133) imply: % 263.01/56.87 | | | | | | (137) leq(n0, n2) % 263.01/56.87 | | | | | | % 263.01/56.87 | | | | | | GROUND_INST: instantiating (7) with n2, n3, all_74_9, simplifying % 263.01/56.87 | | | | | | with (2), (23), (109), (134), (137) gives: % 263.01/56.87 | | | | | | (138) ~ leq(n3, all_74_20) | ~ leq(n2, all_74_20) | % 263.01/56.87 | | | | | | (a_select3(pminus_ds1_filter, n3, n2) = all_74_9 & % 263.01/56.87 | | | | | | $i(all_74_9)) % 263.01/56.87 | | | | | | % 263.01/56.87 | | | | | | BETA: splitting (138) gives: % 263.01/56.87 | | | | | | % 263.01/56.87 | | | | | | Case 1: % 263.01/56.87 | | | | | | | % 263.01/56.87 | | | | | | | (139) ~ leq(n3, all_74_20) % 263.01/56.87 | | | | | | | % 263.01/56.87 | | | | | | | REDUCE: (22), (139) imply: % 263.01/56.87 | | | | | | | (140) ~ leq(n3, n5) % 263.01/56.87 | | | | | | | % 263.01/56.87 | | | | | | | PRED_UNIFY: (108), (140) imply: % 263.01/56.87 | | | | | | | (141) $false % 263.01/56.87 | | | | | | | % 263.01/56.87 | | | | | | | CLOSE: (141) is inconsistent. % 263.01/56.87 | | | | | | | % 263.01/56.87 | | | | | | Case 2: % 263.01/56.87 | | | | | | | % 263.01/56.87 | | | | | | | (142) ~ leq(n2, all_74_20) | (a_select3(pminus_ds1_filter, n3, % 263.01/56.87 | | | | | | | n2) = all_74_9 & $i(all_74_9)) % 263.01/56.87 | | | | | | | % 263.01/56.87 | | | | | | | BETA: splitting (142) gives: % 263.01/56.87 | | | | | | | % 263.01/56.87 | | | | | | | Case 1: % 263.01/56.87 | | | | | | | | % 263.01/56.87 | | | | | | | | (143) ~ leq(n2, all_74_20) % 263.01/56.87 | | | | | | | | % 263.01/56.87 | | | | | | | | REDUCE: (22), (143) imply: % 263.01/56.87 | | | | | | | | (144) ~ leq(n2, n5) % 263.01/56.87 | | | | | | | | % 263.01/56.87 | | | | | | | | PRED_UNIFY: (136), (144) imply: % 263.01/56.87 | | | | | | | | (145) $false % 263.01/56.87 | | | | | | | | % 263.01/56.87 | | | | | | | | CLOSE: (145) is inconsistent. % 263.01/56.87 | | | | | | | | % 263.01/56.87 | | | | | | | Case 2: % 263.01/56.87 | | | | | | | | % 263.01/56.87 | | | | | | | | (146) a_select3(pminus_ds1_filter, n3, n2) = all_74_9 & % 263.01/56.87 | | | | | | | | $i(all_74_9) % 263.01/56.87 | | | | | | | | % 263.01/56.87 | | | | | | | | ALPHA: (146) implies: % 263.01/56.87 | | | | | | | | (147) a_select3(pminus_ds1_filter, n3, n2) = all_74_9 % 263.01/56.87 | | | | | | | | % 263.01/56.87 | | | | | | | | REF_CLOSE: (3), (18), (135), (147) are inconsistent by sub-proof % 263.01/56.87 | | | | | | | | #61. % 263.01/56.87 | | | | | | | | % 263.01/56.87 | | | | | | | End of split % 263.01/56.87 | | | | | | | % 263.01/56.87 | | | | | | End of split % 263.01/56.87 | | | | | | % 263.01/56.87 | | | | | End of split % 263.01/56.87 | | | | | % 263.01/56.87 | | | | End of split % 263.01/56.87 | | | | % 263.01/56.87 | | | Case 2: % 263.01/56.87 | | | | % 263.01/56.87 | | | | (148) all_74_11 = n3 % 263.01/56.87 | | | | % 263.01/56.87 | | | | REDUCE: (10), (148) imply: % 263.01/56.87 | | | | (149) a_select3(pminus_ds1_filter, all_74_10, n3) = all_74_8 % 263.01/56.87 | | | | % 263.01/56.87 | | | | REDUCE: (17), (148) imply: % 263.01/56.87 | | | | (150) a_select3(pminus_ds1_filter, n3, all_74_10) = all_74_9 % 263.01/56.87 | | | | % 263.01/56.87 | | | | REDUCE: (1), (148) imply: % 263.01/56.87 | | | | (151) leq(n3, n5) % 263.01/56.87 | | | | % 263.01/56.87 | | | | REDUCE: (9), (148) imply: % 263.01/56.87 | | | | (152) leq(n0, n3) % 263.01/56.87 | | | | % 263.01/56.87 | | | | BETA: splitting (31) gives: % 263.01/56.87 | | | | % 263.01/56.87 | | | | Case 1: % 263.01/56.87 | | | | | % 263.01/56.87 | | | | | (153) gt(n3, all_74_10) % 263.01/56.87 | | | | | % 263.01/56.87 | | | | | GROUND_INST: instantiating (20) with all_74_10, n3, n2, simplifying % 263.01/56.87 | | | | | with (2), (12), (14), (153) gives: % 263.01/56.87 | | | | | (154) leq(all_74_10, n2) % 263.01/56.87 | | | | | % 263.01/56.87 | | | | | GROUND_INST: instantiating (24) with all_74_10, n2, simplifying with % 263.01/56.87 | | | | | (12), (23), (154) gives: % 263.01/56.87 | | | | | (155) all_74_10 = n2 | gt(n2, all_74_10) % 263.01/56.87 | | | | | % 263.01/56.87 | | | | | BETA: splitting (155) gives: % 263.01/56.87 | | | | | % 263.01/56.87 | | | | | Case 1: % 263.01/56.87 | | | | | | % 263.01/56.87 | | | | | | (156) gt(n2, all_74_10) % 263.01/56.87 | | | | | | % 263.01/56.87 | | | | | | GROUND_INST: instantiating (20) with all_74_10, n2, n1, simplifying % 263.01/56.87 | | | | | | with (6), (12), (23), (156) gives: % 263.01/56.87 | | | | | | (157) leq(all_74_10, n1) % 263.01/56.87 | | | | | | % 263.01/56.87 | | | | | | GROUND_INST: instantiating (5) with all_74_10, simplifying with % 263.01/56.87 | | | | | | (12), (25), (157) gives: % 263.01/56.87 | | | | | | (158) all_74_10 = n1 | all_74_10 = n0 % 263.01/56.87 | | | | | | % 263.01/56.87 | | | | | | BETA: splitting (158) gives: % 263.01/56.87 | | | | | | % 263.01/56.87 | | | | | | Case 1: % 263.01/56.87 | | | | | | | % 263.01/56.87 | | | | | | | (159) all_74_10 = n0 % 263.01/56.87 | | | | | | | % 263.01/56.87 | | | | | | | REDUCE: (21), (159) imply: % 263.01/56.87 | | | | | | | (160) $false % 263.01/56.87 | | | | | | | % 263.01/56.87 | | | | | | | CLOSE: (160) is inconsistent. % 263.01/56.87 | | | | | | | % 263.01/56.87 | | | | | | Case 2: % 263.01/56.87 | | | | | | | % 263.01/56.87 | | | | | | | (161) all_74_10 = n1 % 263.01/56.87 | | | | | | | % 263.01/56.87 | | | | | | | REDUCE: (149), (161) imply: % 263.01/56.87 | | | | | | | (162) a_select3(pminus_ds1_filter, n1, n3) = all_74_8 % 263.01/56.87 | | | | | | | % 263.01/56.87 | | | | | | | REDUCE: (150), (161) imply: % 263.01/56.87 | | | | | | | (163) a_select3(pminus_ds1_filter, n3, n1) = all_74_9 % 263.01/56.87 | | | | | | | % 263.01/56.87 | | | | | | | REDUCE: (12), (161) imply: % 263.01/56.87 | | | | | | | (164) $i(n1) % 263.01/56.87 | | | | | | | % 263.01/56.87 | | | | | | | REDUCE: (11), (161) imply: % 263.01/56.87 | | | | | | | (165) leq(n1, n5) % 263.01/56.87 | | | | | | | % 263.01/56.87 | | | | | | | REDUCE: (25), (161) imply: % 263.01/56.87 | | | | | | | (166) leq(n0, n1) % 263.01/56.87 | | | | | | | % 263.01/56.87 | | | | | | | GROUND_INST: instantiating (7) with n1, n3, all_74_8, simplifying % 263.01/56.87 | | | | | | | with (2), (152), (162), (164), (166) gives: % 263.01/56.87 | | | | | | | (167) ~ leq(n3, all_74_20) | ~ leq(n1, all_74_20) | % 263.01/56.87 | | | | | | | (a_select3(pminus_ds1_filter, n3, n1) = all_74_8 & % 263.01/56.87 | | | | | | | $i(all_74_8)) % 263.01/56.87 | | | | | | | % 263.01/56.87 | | | | | | | BETA: splitting (167) gives: % 263.01/56.87 | | | | | | | % 263.01/56.87 | | | | | | | Case 1: % 263.01/56.87 | | | | | | | | % 263.01/56.87 | | | | | | | | (168) ~ leq(n3, all_74_20) % 263.01/56.87 | | | | | | | | % 263.01/56.87 | | | | | | | | REDUCE: (22), (168) imply: % 263.01/56.87 | | | | | | | | (169) ~ leq(n3, n5) % 263.01/56.87 | | | | | | | | % 263.01/56.87 | | | | | | | | PRED_UNIFY: (151), (169) imply: % 263.01/56.87 | | | | | | | | (170) $false % 263.01/56.87 | | | | | | | | % 263.01/56.87 | | | | | | | | CLOSE: (170) is inconsistent. % 263.01/56.87 | | | | | | | | % 263.01/56.87 | | | | | | | Case 2: % 263.01/56.87 | | | | | | | | % 263.01/56.87 | | | | | | | | (171) ~ leq(n1, all_74_20) | (a_select3(pminus_ds1_filter, % 263.01/56.87 | | | | | | | | n3, n1) = all_74_8 & $i(all_74_8)) % 263.01/56.87 | | | | | | | | % 263.01/56.87 | | | | | | | | BETA: splitting (171) gives: % 263.01/56.87 | | | | | | | | % 263.01/56.87 | | | | | | | | Case 1: % 263.01/56.87 | | | | | | | | | % 263.01/56.87 | | | | | | | | | (172) ~ leq(n1, all_74_20) % 263.01/56.87 | | | | | | | | | % 263.01/56.87 | | | | | | | | | REDUCE: (22), (172) imply: % 263.01/56.87 | | | | | | | | | (173) ~ leq(n1, n5) % 263.01/56.87 | | | | | | | | | % 263.01/56.87 | | | | | | | | | PRED_UNIFY: (165), (173) imply: % 263.01/56.87 | | | | | | | | | (174) $false % 263.01/56.87 | | | | | | | | | % 263.01/56.87 | | | | | | | | | CLOSE: (174) is inconsistent. % 263.01/56.87 | | | | | | | | | % 263.01/56.87 | | | | | | | | Case 2: % 263.01/56.87 | | | | | | | | | % 263.01/56.87 | | | | | | | | | (175) a_select3(pminus_ds1_filter, n3, n1) = all_74_8 & % 263.01/56.87 | | | | | | | | | $i(all_74_8) % 263.01/56.87 | | | | | | | | | % 263.01/56.87 | | | | | | | | | ALPHA: (175) implies: % 263.01/56.87 | | | | | | | | | (176) a_select3(pminus_ds1_filter, n3, n1) = all_74_8 % 263.01/56.87 | | | | | | | | | % 263.01/56.87 | | | | | | | | | GROUND_INST: instantiating (18) with all_74_8, all_74_9, n1, % 263.01/56.87 | | | | | | | | | n3, pminus_ds1_filter, simplifying with (163), % 263.01/56.87 | | | | | | | | | (176) gives: % 263.01/56.87 | | | | | | | | | (177) all_74_8 = all_74_9 % 263.01/56.87 | | | | | | | | | % 263.01/56.87 | | | | | | | | | REDUCE: (3), (177) imply: % 263.01/56.87 | | | | | | | | | (178) $false % 263.01/56.87 | | | | | | | | | % 263.01/56.87 | | | | | | | | | CLOSE: (178) is inconsistent. % 263.01/56.87 | | | | | | | | | % 263.01/56.87 | | | | | | | | End of split % 263.01/56.87 | | | | | | | | % 263.01/56.87 | | | | | | | End of split % 263.01/56.87 | | | | | | | % 263.01/56.87 | | | | | | End of split % 263.01/56.87 | | | | | | % 263.01/56.87 | | | | | Case 2: % 263.01/56.87 | | | | | | % 263.01/56.87 | | | | | | (179) all_74_10 = n2 % 263.01/56.87 | | | | | | % 263.01/56.87 | | | | | | REDUCE: (149), (179) imply: % 263.01/56.87 | | | | | | (180) a_select3(pminus_ds1_filter, n2, n3) = all_74_8 % 263.01/56.87 | | | | | | % 263.01/56.87 | | | | | | REDUCE: (150), (179) imply: % 263.01/56.87 | | | | | | (181) a_select3(pminus_ds1_filter, n3, n2) = all_74_9 % 263.01/56.87 | | | | | | % 263.01/56.87 | | | | | | REDUCE: (11), (179) imply: % 263.01/56.87 | | | | | | (182) leq(n2, n5) % 263.01/56.87 | | | | | | % 263.01/56.87 | | | | | | REDUCE: (25), (179) imply: % 263.01/56.87 | | | | | | (183) leq(n0, n2) % 263.01/56.87 | | | | | | % 263.01/56.87 | | | | | | GROUND_INST: instantiating (7) with n2, n3, all_74_8, simplifying % 263.01/56.87 | | | | | | with (2), (23), (152), (180), (183) gives: % 263.01/56.87 | | | | | | (184) ~ leq(n3, all_74_20) | ~ leq(n2, all_74_20) | % 263.01/56.87 | | | | | | (a_select3(pminus_ds1_filter, n3, n2) = all_74_8 & % 263.01/56.87 | | | | | | $i(all_74_8)) % 263.01/56.87 | | | | | | % 263.01/56.87 | | | | | | BETA: splitting (184) gives: % 263.01/56.87 | | | | | | % 263.01/56.87 | | | | | | Case 1: % 263.01/56.87 | | | | | | | % 263.01/56.87 | | | | | | | (185) ~ leq(n3, all_74_20) % 263.01/56.87 | | | | | | | % 263.01/56.87 | | | | | | | REDUCE: (22), (185) imply: % 263.01/56.87 | | | | | | | (186) ~ leq(n3, n5) % 263.01/56.87 | | | | | | | % 263.01/56.87 | | | | | | | PRED_UNIFY: (151), (186) imply: % 263.01/56.88 | | | | | | | (187) $false % 263.01/56.88 | | | | | | | % 263.01/56.88 | | | | | | | CLOSE: (187) is inconsistent. % 263.01/56.88 | | | | | | | % 263.01/56.88 | | | | | | Case 2: % 263.01/56.88 | | | | | | | % 263.01/56.88 | | | | | | | (188) ~ leq(n2, all_74_20) | (a_select3(pminus_ds1_filter, n3, % 263.01/56.88 | | | | | | | n2) = all_74_8 & $i(all_74_8)) % 263.01/56.88 | | | | | | | % 263.01/56.88 | | | | | | | BETA: splitting (188) gives: % 263.01/56.88 | | | | | | | % 263.01/56.88 | | | | | | | Case 1: % 263.01/56.88 | | | | | | | | % 263.01/56.88 | | | | | | | | (189) ~ leq(n2, all_74_20) % 263.01/56.88 | | | | | | | | % 263.01/56.88 | | | | | | | | REDUCE: (22), (189) imply: % 263.01/56.88 | | | | | | | | (190) ~ leq(n2, n5) % 263.01/56.88 | | | | | | | | % 263.01/56.88 | | | | | | | | PRED_UNIFY: (182), (190) imply: % 263.01/56.88 | | | | | | | | (191) $false % 263.01/56.88 | | | | | | | | % 263.01/56.88 | | | | | | | | CLOSE: (191) is inconsistent. % 263.01/56.88 | | | | | | | | % 263.01/56.88 | | | | | | | Case 2: % 263.01/56.88 | | | | | | | | % 263.01/56.88 | | | | | | | | (192) a_select3(pminus_ds1_filter, n3, n2) = all_74_8 & % 263.01/56.88 | | | | | | | | $i(all_74_8) % 263.01/56.88 | | | | | | | | % 263.01/56.88 | | | | | | | | ALPHA: (192) implies: % 263.01/56.88 | | | | | | | | (193) a_select3(pminus_ds1_filter, n3, n2) = all_74_8 % 263.01/56.88 | | | | | | | | % 263.01/56.88 | | | | | | | | REF_CLOSE: (3), (18), (181), (193) are inconsistent by sub-proof % 263.01/56.88 | | | | | | | | #61. % 263.01/56.88 | | | | | | | | % 263.01/56.88 | | | | | | | End of split % 263.01/56.88 | | | | | | | % 263.01/56.88 | | | | | | End of split % 263.01/56.88 | | | | | | % 263.01/56.88 | | | | | End of split % 263.01/56.88 | | | | | % 263.01/56.88 | | | | Case 2: % 263.01/56.88 | | | | | % 263.01/56.88 | | | | | (194) all_74_10 = n3 % 263.01/56.88 | | | | | % 263.01/56.88 | | | | | REDUCE: (149), (194) imply: % 263.01/56.88 | | | | | (195) a_select3(pminus_ds1_filter, n3, n3) = all_74_8 % 263.01/56.88 | | | | | % 263.01/56.88 | | | | | REDUCE: (150), (194) imply: % 263.01/56.88 | | | | | (196) a_select3(pminus_ds1_filter, n3, n3) = all_74_9 % 263.01/56.88 | | | | | % 263.01/56.88 | | | | | GROUND_INST: instantiating (18) with all_74_9, all_74_8, n3, n3, % 263.01/56.88 | | | | | pminus_ds1_filter, simplifying with (195), (196) gives: % 263.01/56.88 | | | | | (197) all_74_8 = all_74_9 % 263.01/56.88 | | | | | % 263.01/56.88 | | | | | REDUCE: (3), (197) imply: % 263.01/56.88 | | | | | (198) $false % 263.01/56.88 | | | | | % 263.01/56.88 | | | | | CLOSE: (198) is inconsistent. % 263.01/56.88 | | | | | % 263.01/56.88 | | | | End of split % 263.01/56.88 | | | | % 263.01/56.88 | | | End of split % 263.01/56.88 | | | % 263.01/56.88 | | Case 2: % 263.01/56.88 | | | % 263.01/56.88 | | | (199) all_74_10 = n4 % 263.01/56.88 | | | % 263.01/56.88 | | | REDUCE: (10), (199) imply: % 263.01/56.88 | | | (200) a_select3(pminus_ds1_filter, n4, all_74_11) = all_74_8 % 263.01/56.88 | | | % 263.01/56.88 | | | REDUCE: (17), (199) imply: % 263.01/56.88 | | | (201) a_select3(pminus_ds1_filter, all_74_11, n4) = all_74_9 % 263.01/56.88 | | | % 263.01/56.88 | | | REDUCE: (11), (199) imply: % 263.01/56.88 | | | (202) leq(n4, n5) % 263.01/56.88 | | | % 263.01/56.88 | | | REDUCE: (25), (199) imply: % 263.01/56.88 | | | (203) leq(n0, n4) % 263.01/56.88 | | | % 263.01/56.88 | | | BETA: splitting (28) gives: % 263.01/56.88 | | | % 263.01/56.88 | | | Case 1: % 263.01/56.88 | | | | % 263.01/56.88 | | | | (204) gt(n3, all_74_11) % 263.01/56.88 | | | | % 263.01/56.88 | | | | GROUND_INST: instantiating (20) with all_74_11, n3, n2, simplifying with % 263.01/56.88 | | | | (2), (13), (14), (204) gives: % 263.01/56.88 | | | | (205) leq(all_74_11, n2) % 263.01/56.88 | | | | % 263.01/56.88 | | | | GROUND_INST: instantiating (24) with all_74_11, n2, simplifying with % 263.01/56.88 | | | | (13), (23), (205) gives: % 263.01/56.88 | | | | (206) all_74_11 = n2 | gt(n2, all_74_11) % 263.01/56.88 | | | | % 263.01/56.88 | | | | BETA: splitting (206) gives: % 263.01/56.88 | | | | % 263.01/56.88 | | | | Case 1: % 263.01/56.88 | | | | | % 263.01/56.88 | | | | | (207) gt(n2, all_74_11) % 263.01/56.88 | | | | | % 263.01/56.88 | | | | | GROUND_INST: instantiating (20) with all_74_11, n2, n1, simplifying % 263.01/56.88 | | | | | with (6), (13), (23), (207) gives: % 263.01/56.88 | | | | | (208) leq(all_74_11, n1) % 263.01/56.88 | | | | | % 263.01/56.88 | | | | | GROUND_INST: instantiating (5) with all_74_11, simplifying with (9), % 263.01/56.88 | | | | | (13), (208) gives: % 263.01/56.88 | | | | | (209) all_74_11 = n1 | all_74_11 = n0 % 263.01/56.88 | | | | | % 263.01/56.88 | | | | | BETA: splitting (209) gives: % 263.01/56.88 | | | | | % 263.01/56.88 | | | | | Case 1: % 263.01/56.88 | | | | | | % 263.01/56.88 | | | | | | (210) all_74_11 = n0 % 263.01/56.88 | | | | | | % 263.01/56.88 | | | | | | REDUCE: (8), (210) imply: % 263.01/56.88 | | | | | | (211) $false % 263.01/56.88 | | | | | | % 263.01/56.88 | | | | | | CLOSE: (211) is inconsistent. % 263.01/56.88 | | | | | | % 263.01/56.88 | | | | | Case 2: % 263.01/56.88 | | | | | | % 263.01/56.88 | | | | | | (212) all_74_11 = n1 % 263.01/56.88 | | | | | | % 263.01/56.88 | | | | | | REDUCE: (201), (212) imply: % 263.01/56.88 | | | | | | (213) a_select3(pminus_ds1_filter, n1, n4) = all_74_9 % 263.01/56.88 | | | | | | % 263.01/56.88 | | | | | | REDUCE: (200), (212) imply: % 263.01/56.88 | | | | | | (214) a_select3(pminus_ds1_filter, n4, n1) = all_74_8 % 263.01/56.88 | | | | | | % 263.01/56.88 | | | | | | REDUCE: (13), (212) imply: % 263.01/56.88 | | | | | | (215) $i(n1) % 263.01/56.88 | | | | | | % 263.01/56.88 | | | | | | REDUCE: (1), (212) imply: % 263.01/56.88 | | | | | | (216) leq(n1, n5) % 263.01/56.88 | | | | | | % 263.01/56.88 | | | | | | REDUCE: (9), (212) imply: % 263.01/56.88 | | | | | | (217) leq(n0, n1) % 263.01/56.88 | | | | | | % 263.01/56.88 | | | | | | GROUND_INST: instantiating (7) with n1, n4, all_74_9, simplifying % 263.01/56.88 | | | | | | with (4), (203), (213), (215), (217) gives: % 263.01/56.88 | | | | | | (218) ~ leq(n4, all_74_20) | ~ leq(n1, all_74_20) | % 263.01/56.88 | | | | | | (a_select3(pminus_ds1_filter, n4, n1) = all_74_9 & % 263.01/56.88 | | | | | | $i(all_74_9)) % 263.01/56.88 | | | | | | % 263.01/56.88 | | | | | | BETA: splitting (218) gives: % 263.01/56.88 | | | | | | % 263.01/56.88 | | | | | | Case 1: % 263.01/56.88 | | | | | | | % 263.01/56.88 | | | | | | | (219) ~ leq(n4, all_74_20) % 263.01/56.88 | | | | | | | % 263.01/56.88 | | | | | | | REDUCE: (22), (219) imply: % 263.01/56.88 | | | | | | | (220) ~ leq(n4, n5) % 263.01/56.88 | | | | | | | % 263.01/56.88 | | | | | | | PRED_UNIFY: (202), (220) imply: % 263.01/56.88 | | | | | | | (221) $false % 263.01/56.88 | | | | | | | % 263.01/56.88 | | | | | | | CLOSE: (221) is inconsistent. % 263.01/56.88 | | | | | | | % 263.01/56.88 | | | | | | Case 2: % 263.01/56.88 | | | | | | | % 263.01/56.88 | | | | | | | (222) ~ leq(n1, all_74_20) | (a_select3(pminus_ds1_filter, n4, % 263.01/56.88 | | | | | | | n1) = all_74_9 & $i(all_74_9)) % 263.01/56.88 | | | | | | | % 263.01/56.88 | | | | | | | BETA: splitting (222) gives: % 263.01/56.88 | | | | | | | % 263.01/56.88 | | | | | | | Case 1: % 263.01/56.88 | | | | | | | | % 263.01/56.88 | | | | | | | | (223) ~ leq(n1, all_74_20) % 263.01/56.88 | | | | | | | | % 263.01/56.88 | | | | | | | | REDUCE: (22), (223) imply: % 263.01/56.88 | | | | | | | | (224) ~ leq(n1, n5) % 263.01/56.88 | | | | | | | | % 263.01/56.88 | | | | | | | | PRED_UNIFY: (216), (224) imply: % 263.01/56.88 | | | | | | | | (225) $false % 263.01/56.88 | | | | | | | | % 263.01/56.88 | | | | | | | | CLOSE: (225) is inconsistent. % 263.01/56.88 | | | | | | | | % 263.01/56.88 | | | | | | | Case 2: % 263.01/56.88 | | | | | | | | % 263.01/56.88 | | | | | | | | (226) a_select3(pminus_ds1_filter, n4, n1) = all_74_9 & % 263.01/56.88 | | | | | | | | $i(all_74_9) % 263.01/56.88 | | | | | | | | % 263.01/56.88 | | | | | | | | ALPHA: (226) implies: % 263.01/56.88 | | | | | | | | (227) a_select3(pminus_ds1_filter, n4, n1) = all_74_9 % 263.01/56.88 | | | | | | | | % 263.01/56.88 | | | | | | | | GROUND_INST: instantiating (18) with all_74_8, all_74_9, n1, n4, % 263.01/56.88 | | | | | | | | pminus_ds1_filter, simplifying with (214), (227) % 263.01/56.88 | | | | | | | | gives: % 263.01/56.88 | | | | | | | | (228) all_74_8 = all_74_9 % 263.01/56.88 | | | | | | | | % 263.01/56.88 | | | | | | | | REDUCE: (3), (228) imply: % 263.01/56.88 | | | | | | | | (229) $false % 263.01/56.88 | | | | | | | | % 263.01/56.88 | | | | | | | | CLOSE: (229) is inconsistent. % 263.01/56.88 | | | | | | | | % 263.01/56.88 | | | | | | | End of split % 263.01/56.88 | | | | | | | % 263.01/56.88 | | | | | | End of split % 263.01/56.88 | | | | | | % 263.01/56.88 | | | | | End of split % 263.01/56.88 | | | | | % 263.01/56.88 | | | | Case 2: % 263.01/56.88 | | | | | % 263.01/56.88 | | | | | (230) all_74_11 = n2 % 263.01/56.88 | | | | | % 263.01/56.88 | | | | | REDUCE: (201), (230) imply: % 263.01/56.88 | | | | | (231) a_select3(pminus_ds1_filter, n2, n4) = all_74_9 % 263.01/56.88 | | | | | % 263.01/56.88 | | | | | REDUCE: (200), (230) imply: % 263.01/56.88 | | | | | (232) a_select3(pminus_ds1_filter, n4, n2) = all_74_8 % 263.01/56.88 | | | | | % 263.01/56.88 | | | | | REDUCE: (1), (230) imply: % 263.01/56.88 | | | | | (233) leq(n2, n5) % 263.01/56.88 | | | | | % 263.01/56.88 | | | | | REDUCE: (9), (230) imply: % 263.01/56.88 | | | | | (234) leq(n0, n2) % 263.01/56.88 | | | | | % 263.01/56.88 | | | | | GROUND_INST: instantiating (7) with n2, n4, all_74_9, simplifying with % 263.01/56.88 | | | | | (4), (23), (203), (231), (234) gives: % 263.01/56.88 | | | | | (235) ~ leq(n4, all_74_20) | ~ leq(n2, all_74_20) | % 263.01/56.88 | | | | | (a_select3(pminus_ds1_filter, n4, n2) = all_74_9 & % 263.01/56.88 | | | | | $i(all_74_9)) % 263.01/56.88 | | | | | % 263.01/56.88 | | | | | BETA: splitting (235) gives: % 263.01/56.88 | | | | | % 263.01/56.88 | | | | | Case 1: % 263.01/56.88 | | | | | | % 263.01/56.88 | | | | | | (236) ~ leq(n4, all_74_20) % 263.01/56.88 | | | | | | % 263.01/56.88 | | | | | | REDUCE: (22), (236) imply: % 263.01/56.88 | | | | | | (237) ~ leq(n4, n5) % 263.01/56.88 | | | | | | % 263.01/56.88 | | | | | | PRED_UNIFY: (202), (237) imply: % 263.01/56.88 | | | | | | (238) $false % 263.01/56.88 | | | | | | % 263.01/56.88 | | | | | | CLOSE: (238) is inconsistent. % 263.01/56.88 | | | | | | % 263.01/56.88 | | | | | Case 2: % 263.01/56.88 | | | | | | % 263.01/56.88 | | | | | | (239) ~ leq(n2, all_74_20) | (a_select3(pminus_ds1_filter, n4, % 263.01/56.88 | | | | | | n2) = all_74_9 & $i(all_74_9)) % 263.01/56.88 | | | | | | % 263.01/56.88 | | | | | | BETA: splitting (239) gives: % 263.01/56.88 | | | | | | % 263.01/56.88 | | | | | | Case 1: % 263.01/56.88 | | | | | | | % 263.01/56.88 | | | | | | | (240) ~ leq(n2, all_74_20) % 263.01/56.88 | | | | | | | % 263.01/56.88 | | | | | | | REDUCE: (22), (240) imply: % 263.01/56.88 | | | | | | | (241) ~ leq(n2, n5) % 263.01/56.88 | | | | | | | % 263.01/56.88 | | | | | | | PRED_UNIFY: (233), (241) imply: % 263.01/56.88 | | | | | | | (242) $false % 263.01/56.88 | | | | | | | % 263.01/56.88 | | | | | | | CLOSE: (242) is inconsistent. % 263.01/56.88 | | | | | | | % 263.01/56.88 | | | | | | Case 2: % 263.01/56.88 | | | | | | | % 263.01/56.88 | | | | | | | (243) a_select3(pminus_ds1_filter, n4, n2) = all_74_9 & % 263.01/56.88 | | | | | | | $i(all_74_9) % 263.01/56.88 | | | | | | | % 263.01/56.88 | | | | | | | ALPHA: (243) implies: % 263.01/56.88 | | | | | | | (244) a_select3(pminus_ds1_filter, n4, n2) = all_74_9 % 263.01/56.88 | | | | | | | % 263.01/56.88 | | | | | | | REF_CLOSE: (3), (18), (232), (244) are inconsistent by sub-proof % 263.01/56.88 | | | | | | | #60. % 263.01/56.88 | | | | | | | % 263.01/56.88 | | | | | | End of split % 263.01/56.88 | | | | | | % 263.01/56.88 | | | | | End of split % 263.01/56.88 | | | | | % 263.01/56.88 | | | | End of split % 263.01/56.88 | | | | % 263.01/56.88 | | | Case 2: % 263.01/56.88 | | | | % 263.01/56.88 | | | | (245) all_74_11 = n3 % 263.01/56.88 | | | | % 263.01/56.88 | | | | REDUCE: (201), (245) imply: % 263.01/56.88 | | | | (246) a_select3(pminus_ds1_filter, n3, n4) = all_74_9 % 263.01/56.88 | | | | % 263.01/56.88 | | | | REDUCE: (200), (245) imply: % 263.01/56.88 | | | | (247) a_select3(pminus_ds1_filter, n4, n3) = all_74_8 % 263.01/56.88 | | | | % 263.01/56.88 | | | | REDUCE: (1), (245) imply: % 263.01/56.88 | | | | (248) leq(n3, n5) % 263.01/56.88 | | | | % 263.01/56.88 | | | | REDUCE: (9), (245) imply: % 263.01/56.88 | | | | (249) leq(n0, n3) % 263.01/56.88 | | | | % 263.01/56.88 | | | | GROUND_INST: instantiating (7) with n3, n4, all_74_9, simplifying with % 263.01/56.88 | | | | (2), (4), (203), (246), (249) gives: % 263.01/56.88 | | | | (250) ~ leq(n4, all_74_20) | ~ leq(n3, all_74_20) | % 263.01/56.88 | | | | (a_select3(pminus_ds1_filter, n4, n3) = all_74_9 & % 263.01/56.88 | | | | $i(all_74_9)) % 263.01/56.88 | | | | % 263.01/56.88 | | | | BETA: splitting (250) gives: % 263.01/56.88 | | | | % 263.01/56.88 | | | | Case 1: % 263.01/56.88 | | | | | % 263.01/56.88 | | | | | (251) ~ leq(n4, all_74_20) % 263.01/56.88 | | | | | % 263.01/56.88 | | | | | REDUCE: (22), (251) imply: % 263.01/56.88 | | | | | (252) ~ leq(n4, n5) % 263.01/56.88 | | | | | % 263.01/56.88 | | | | | PRED_UNIFY: (202), (252) imply: % 263.01/56.88 | | | | | (253) $false % 263.01/56.88 | | | | | % 263.01/56.88 | | | | | CLOSE: (253) is inconsistent. % 263.01/56.88 | | | | | % 263.01/56.88 | | | | Case 2: % 263.01/56.88 | | | | | % 263.01/56.88 | | | | | (254) ~ leq(n3, all_74_20) | (a_select3(pminus_ds1_filter, n4, n3) % 263.01/56.88 | | | | | = all_74_9 & $i(all_74_9)) % 263.01/56.88 | | | | | % 263.01/56.88 | | | | | BETA: splitting (254) gives: % 263.01/56.88 | | | | | % 263.01/56.88 | | | | | Case 1: % 263.01/56.88 | | | | | | % 263.01/56.88 | | | | | | (255) ~ leq(n3, all_74_20) % 263.01/56.88 | | | | | | % 263.01/56.88 | | | | | | REDUCE: (22), (255) imply: % 263.01/56.88 | | | | | | (256) ~ leq(n3, n5) % 263.01/56.88 | | | | | | % 263.01/56.88 | | | | | | PRED_UNIFY: (248), (256) imply: % 263.01/56.88 | | | | | | (257) $false % 263.01/56.88 | | | | | | % 263.01/56.88 | | | | | | CLOSE: (257) is inconsistent. % 263.01/56.88 | | | | | | % 263.01/56.88 | | | | | Case 2: % 263.01/56.88 | | | | | | % 263.01/56.88 | | | | | | (258) a_select3(pminus_ds1_filter, n4, n3) = all_74_9 & % 263.01/56.88 | | | | | | $i(all_74_9) % 263.01/56.88 | | | | | | % 263.01/56.88 | | | | | | ALPHA: (258) implies: % 263.01/56.88 | | | | | | (259) a_select3(pminus_ds1_filter, n4, n3) = all_74_9 % 263.01/56.88 | | | | | | % 263.01/56.88 | | | | | | REF_CLOSE: (3), (18), (247), (259) are inconsistent by sub-proof % 263.01/56.88 | | | | | | #59. % 263.01/56.88 | | | | | | % 263.01/56.88 | | | | | End of split % 263.01/56.88 | | | | | % 263.01/56.88 | | | | End of split % 263.01/56.88 | | | | % 263.01/56.88 | | | End of split % 263.01/56.88 | | | % 263.01/56.88 | | End of split % 263.01/56.88 | | % 263.01/56.88 | Case 2: % 263.01/56.88 | | % 263.01/56.88 | | (260) all_74_11 = n4 % 263.01/56.88 | | % 263.01/56.88 | | REDUCE: (10), (260) imply: % 263.01/56.88 | | (261) a_select3(pminus_ds1_filter, all_74_10, n4) = all_74_8 % 263.01/56.88 | | % 263.01/56.88 | | REDUCE: (17), (260) imply: % 263.01/56.88 | | (262) a_select3(pminus_ds1_filter, n4, all_74_10) = all_74_9 % 263.01/56.88 | | % 263.01/56.88 | | REDUCE: (1), (260) imply: % 263.01/56.88 | | (263) leq(n4, n5) % 263.01/56.88 | | % 263.01/56.88 | | REDUCE: (9), (260) imply: % 263.01/56.88 | | (264) leq(n0, n4) % 263.01/56.88 | | % 263.01/56.88 | | BETA: splitting (16) gives: % 263.01/56.88 | | % 263.01/56.88 | | Case 1: % 263.01/56.88 | | | % 263.01/56.88 | | | (265) gt(n4, all_74_10) % 263.01/56.88 | | | % 263.01/56.88 | | | GROUND_INST: instantiating (20) with all_74_10, n4, n3, simplifying with % 263.01/56.88 | | | (4), (12), (19), (265) gives: % 263.01/56.88 | | | (266) leq(all_74_10, n3) % 263.01/56.88 | | | % 263.01/56.88 | | | GROUND_INST: instantiating (24) with all_74_10, n3, simplifying with (2), % 263.01/56.88 | | | (12), (266) gives: % 263.01/56.88 | | | (267) all_74_10 = n3 | gt(n3, all_74_10) % 263.01/56.88 | | | % 263.01/56.88 | | | BETA: splitting (267) gives: % 263.01/56.88 | | | % 263.01/56.88 | | | Case 1: % 263.01/56.88 | | | | % 263.01/56.88 | | | | (268) gt(n3, all_74_10) % 263.01/56.88 | | | | % 263.01/56.88 | | | | GROUND_INST: instantiating (20) with all_74_10, n3, n2, simplifying with % 263.01/56.88 | | | | (2), (12), (14), (268) gives: % 263.01/56.88 | | | | (269) leq(all_74_10, n2) % 263.01/56.88 | | | | % 263.01/56.88 | | | | GROUND_INST: instantiating (24) with all_74_10, n2, simplifying with % 263.01/56.88 | | | | (12), (23), (269) gives: % 263.01/56.88 | | | | (270) all_74_10 = n2 | gt(n2, all_74_10) % 263.01/56.88 | | | | % 263.01/56.88 | | | | BETA: splitting (270) gives: % 263.01/56.88 | | | | % 263.01/56.88 | | | | Case 1: % 263.01/56.88 | | | | | % 263.01/56.88 | | | | | (271) gt(n2, all_74_10) % 263.01/56.88 | | | | | % 263.01/56.88 | | | | | GROUND_INST: instantiating (20) with all_74_10, n2, n1, simplifying % 263.01/56.88 | | | | | with (6), (12), (23), (271) gives: % 263.01/56.88 | | | | | (272) leq(all_74_10, n1) % 263.01/56.88 | | | | | % 263.01/56.88 | | | | | GROUND_INST: instantiating (5) with all_74_10, simplifying with (12), % 263.01/56.88 | | | | | (25), (272) gives: % 263.01/56.88 | | | | | (273) all_74_10 = n1 | all_74_10 = n0 % 263.01/56.88 | | | | | % 263.01/56.88 | | | | | BETA: splitting (273) gives: % 263.01/56.88 | | | | | % 263.01/56.88 | | | | | Case 1: % 263.01/56.88 | | | | | | % 263.01/56.88 | | | | | | (274) all_74_10 = n0 % 263.01/56.88 | | | | | | % 263.01/56.88 | | | | | | REDUCE: (21), (274) imply: % 263.01/56.88 | | | | | | (275) $false % 263.01/56.88 | | | | | | % 263.01/56.88 | | | | | | CLOSE: (275) is inconsistent. % 263.01/56.88 | | | | | | % 263.01/56.88 | | | | | Case 2: % 263.01/56.88 | | | | | | % 263.01/56.88 | | | | | | (276) all_74_10 = n1 % 263.01/56.88 | | | | | | % 263.01/56.88 | | | | | | REDUCE: (261), (276) imply: % 263.01/56.88 | | | | | | (277) a_select3(pminus_ds1_filter, n1, n4) = all_74_8 % 263.01/56.88 | | | | | | % 263.01/56.88 | | | | | | REDUCE: (262), (276) imply: % 263.01/56.88 | | | | | | (278) a_select3(pminus_ds1_filter, n4, n1) = all_74_9 % 263.01/56.88 | | | | | | % 263.01/56.88 | | | | | | REDUCE: (12), (276) imply: % 263.01/56.88 | | | | | | (279) $i(n1) % 263.01/56.88 | | | | | | % 263.01/56.88 | | | | | | REDUCE: (11), (276) imply: % 263.01/56.88 | | | | | | (280) leq(n1, n5) % 263.01/56.88 | | | | | | % 263.01/56.88 | | | | | | REDUCE: (25), (276) imply: % 263.01/56.88 | | | | | | (281) leq(n0, n1) % 263.01/56.88 | | | | | | % 263.01/56.88 | | | | | | GROUND_INST: instantiating (7) with n1, n4, all_74_8, simplifying % 263.01/56.88 | | | | | | with (4), (264), (277), (279), (281) gives: % 263.01/56.88 | | | | | | (282) ~ leq(n4, all_74_20) | ~ leq(n1, all_74_20) | % 263.01/56.88 | | | | | | (a_select3(pminus_ds1_filter, n4, n1) = all_74_8 & % 263.01/56.88 | | | | | | $i(all_74_8)) % 263.01/56.88 | | | | | | % 263.01/56.88 | | | | | | BETA: splitting (282) gives: % 263.01/56.88 | | | | | | % 263.01/56.88 | | | | | | Case 1: % 263.01/56.88 | | | | | | | % 263.01/56.88 | | | | | | | (283) ~ leq(n4, all_74_20) % 263.01/56.88 | | | | | | | % 263.01/56.88 | | | | | | | REDUCE: (22), (283) imply: % 263.01/56.88 | | | | | | | (284) ~ leq(n4, n5) % 263.01/56.88 | | | | | | | % 263.01/56.88 | | | | | | | PRED_UNIFY: (263), (284) imply: % 263.01/56.88 | | | | | | | (285) $false % 263.01/56.88 | | | | | | | % 263.01/56.88 | | | | | | | CLOSE: (285) is inconsistent. % 263.01/56.88 | | | | | | | % 263.01/56.88 | | | | | | Case 2: % 263.01/56.88 | | | | | | | % 263.01/56.88 | | | | | | | (286) ~ leq(n1, all_74_20) | (a_select3(pminus_ds1_filter, n4, % 263.01/56.88 | | | | | | | n1) = all_74_8 & $i(all_74_8)) % 263.01/56.88 | | | | | | | % 263.01/56.88 | | | | | | | BETA: splitting (286) gives: % 263.01/56.88 | | | | | | | % 263.01/56.88 | | | | | | | Case 1: % 263.01/56.88 | | | | | | | | % 263.01/56.88 | | | | | | | | (287) ~ leq(n1, all_74_20) % 263.01/56.88 | | | | | | | | % 263.01/56.88 | | | | | | | | REDUCE: (22), (287) imply: % 263.01/56.88 | | | | | | | | (288) ~ leq(n1, n5) % 263.01/56.88 | | | | | | | | % 263.01/56.88 | | | | | | | | PRED_UNIFY: (280), (288) imply: % 263.01/56.89 | | | | | | | | (289) $false % 263.01/56.89 | | | | | | | | % 263.01/56.89 | | | | | | | | CLOSE: (289) is inconsistent. % 263.01/56.89 | | | | | | | | % 263.01/56.89 | | | | | | | Case 2: % 263.01/56.89 | | | | | | | | % 263.01/56.89 | | | | | | | | (290) a_select3(pminus_ds1_filter, n4, n1) = all_74_8 & % 263.01/56.89 | | | | | | | | $i(all_74_8) % 263.01/56.89 | | | | | | | | % 263.01/56.89 | | | | | | | | ALPHA: (290) implies: % 263.01/56.89 | | | | | | | | (291) a_select3(pminus_ds1_filter, n4, n1) = all_74_8 % 263.01/56.89 | | | | | | | | % 263.01/56.89 | | | | | | | | GROUND_INST: instantiating (18) with all_74_8, all_74_9, n1, n4, % 263.01/56.89 | | | | | | | | pminus_ds1_filter, simplifying with (278), (291) % 263.01/56.89 | | | | | | | | gives: % 263.01/56.89 | | | | | | | | (292) all_74_8 = all_74_9 % 263.01/56.89 | | | | | | | | % 263.01/56.89 | | | | | | | | REDUCE: (3), (292) imply: % 263.01/56.89 | | | | | | | | (293) $false % 263.01/56.89 | | | | | | | | % 263.01/56.89 | | | | | | | | CLOSE: (293) is inconsistent. % 263.01/56.89 | | | | | | | | % 263.01/56.89 | | | | | | | End of split % 263.01/56.89 | | | | | | | % 263.01/56.89 | | | | | | End of split % 263.01/56.89 | | | | | | % 263.01/56.89 | | | | | End of split % 263.01/56.89 | | | | | % 263.01/56.89 | | | | Case 2: % 263.01/56.89 | | | | | % 263.01/56.89 | | | | | (294) all_74_10 = n2 % 263.01/56.89 | | | | | % 263.01/56.89 | | | | | REDUCE: (261), (294) imply: % 263.01/56.89 | | | | | (295) a_select3(pminus_ds1_filter, n2, n4) = all_74_8 % 263.01/56.89 | | | | | % 263.01/56.89 | | | | | REDUCE: (262), (294) imply: % 263.01/56.89 | | | | | (296) a_select3(pminus_ds1_filter, n4, n2) = all_74_9 % 263.01/56.89 | | | | | % 263.01/56.89 | | | | | REDUCE: (11), (294) imply: % 263.01/56.89 | | | | | (297) leq(n2, n5) % 263.01/56.89 | | | | | % 263.01/56.89 | | | | | REDUCE: (25), (294) imply: % 263.01/56.89 | | | | | (298) leq(n0, n2) % 263.01/56.89 | | | | | % 263.01/56.89 | | | | | GROUND_INST: instantiating (7) with n2, n4, all_74_8, simplifying with % 263.01/56.89 | | | | | (4), (23), (264), (295), (298) gives: % 263.01/56.89 | | | | | (299) ~ leq(n4, all_74_20) | ~ leq(n2, all_74_20) | % 263.01/56.89 | | | | | (a_select3(pminus_ds1_filter, n4, n2) = all_74_8 & % 263.01/56.89 | | | | | $i(all_74_8)) % 263.01/56.89 | | | | | % 263.01/56.89 | | | | | BETA: splitting (299) gives: % 263.01/56.89 | | | | | % 263.01/56.89 | | | | | Case 1: % 263.01/56.89 | | | | | | % 263.01/56.89 | | | | | | (300) ~ leq(n4, all_74_20) % 263.01/56.89 | | | | | | % 263.01/56.89 | | | | | | REDUCE: (22), (300) imply: % 263.01/56.89 | | | | | | (301) ~ leq(n4, n5) % 263.01/56.89 | | | | | | % 263.01/56.89 | | | | | | PRED_UNIFY: (263), (301) imply: % 263.01/56.89 | | | | | | (302) $false % 263.01/56.89 | | | | | | % 263.01/56.89 | | | | | | CLOSE: (302) is inconsistent. % 263.01/56.89 | | | | | | % 263.01/56.89 | | | | | Case 2: % 263.01/56.89 | | | | | | % 263.01/56.89 | | | | | | (303) ~ leq(n2, all_74_20) | (a_select3(pminus_ds1_filter, n4, % 263.01/56.89 | | | | | | n2) = all_74_8 & $i(all_74_8)) % 263.01/56.89 | | | | | | % 263.01/56.89 | | | | | | BETA: splitting (303) gives: % 263.01/56.89 | | | | | | % 263.01/56.89 | | | | | | Case 1: % 263.01/56.89 | | | | | | | % 263.01/56.89 | | | | | | | (304) ~ leq(n2, all_74_20) % 263.01/56.89 | | | | | | | % 263.01/56.89 | | | | | | | REDUCE: (22), (304) imply: % 263.01/56.89 | | | | | | | (305) ~ leq(n2, n5) % 263.01/56.89 | | | | | | | % 263.01/56.89 | | | | | | | PRED_UNIFY: (297), (305) imply: % 263.01/56.89 | | | | | | | (306) $false % 263.01/56.89 | | | | | | | % 263.01/56.89 | | | | | | | CLOSE: (306) is inconsistent. % 263.01/56.89 | | | | | | | % 263.01/56.89 | | | | | | Case 2: % 263.01/56.89 | | | | | | | % 263.01/56.89 | | | | | | | (307) a_select3(pminus_ds1_filter, n4, n2) = all_74_8 & % 263.01/56.89 | | | | | | | $i(all_74_8) % 263.01/56.89 | | | | | | | % 263.01/56.89 | | | | | | | ALPHA: (307) implies: % 263.01/56.89 | | | | | | | (308) a_select3(pminus_ds1_filter, n4, n2) = all_74_8 % 263.01/56.89 | | | | | | | % 263.01/56.89 | | | | | | | REF_CLOSE: (3), (18), (296), (308) are inconsistent by sub-proof % 263.01/56.89 | | | | | | | #60. % 263.01/56.89 | | | | | | | % 263.01/56.89 | | | | | | End of split % 263.01/56.89 | | | | | | % 263.01/56.89 | | | | | End of split % 263.01/56.89 | | | | | % 263.01/56.89 | | | | End of split % 263.01/56.89 | | | | % 263.01/56.89 | | | Case 2: % 263.01/56.89 | | | | % 263.01/56.89 | | | | (309) all_74_10 = n3 % 263.01/56.89 | | | | % 263.01/56.89 | | | | REDUCE: (261), (309) imply: % 263.01/56.89 | | | | (310) a_select3(pminus_ds1_filter, n3, n4) = all_74_8 % 263.01/56.89 | | | | % 263.01/56.89 | | | | REDUCE: (262), (309) imply: % 263.01/56.89 | | | | (311) a_select3(pminus_ds1_filter, n4, n3) = all_74_9 % 263.01/56.89 | | | | % 263.01/56.89 | | | | REDUCE: (11), (309) imply: % 263.01/56.89 | | | | (312) leq(n3, n5) % 263.01/56.89 | | | | % 263.01/56.89 | | | | REDUCE: (25), (309) imply: % 263.01/56.89 | | | | (313) leq(n0, n3) % 263.01/56.89 | | | | % 263.01/56.89 | | | | GROUND_INST: instantiating (7) with n3, n4, all_74_8, simplifying with % 263.01/56.89 | | | | (2), (4), (264), (310), (313) gives: % 263.01/56.89 | | | | (314) ~ leq(n4, all_74_20) | ~ leq(n3, all_74_20) | % 263.01/56.89 | | | | (a_select3(pminus_ds1_filter, n4, n3) = all_74_8 & % 263.01/56.89 | | | | $i(all_74_8)) % 263.01/56.89 | | | | % 263.01/56.89 | | | | BETA: splitting (314) gives: % 263.01/56.89 | | | | % 263.01/56.89 | | | | Case 1: % 263.01/56.89 | | | | | % 263.01/56.89 | | | | | (315) ~ leq(n4, all_74_20) % 263.01/56.89 | | | | | % 263.01/56.89 | | | | | REDUCE: (22), (315) imply: % 263.01/56.89 | | | | | (316) ~ leq(n4, n5) % 263.01/56.89 | | | | | % 263.01/56.89 | | | | | PRED_UNIFY: (263), (316) imply: % 263.01/56.89 | | | | | (317) $false % 263.01/56.89 | | | | | % 263.01/56.89 | | | | | CLOSE: (317) is inconsistent. % 263.01/56.89 | | | | | % 263.01/56.89 | | | | Case 2: % 263.01/56.89 | | | | | % 263.01/56.89 | | | | | (318) ~ leq(n3, all_74_20) | (a_select3(pminus_ds1_filter, n4, n3) % 263.01/56.89 | | | | | = all_74_8 & $i(all_74_8)) % 263.01/56.89 | | | | | % 263.01/56.89 | | | | | BETA: splitting (318) gives: % 263.01/56.89 | | | | | % 263.01/56.89 | | | | | Case 1: % 263.01/56.89 | | | | | | % 263.01/56.89 | | | | | | (319) ~ leq(n3, all_74_20) % 263.01/56.89 | | | | | | % 263.01/56.89 | | | | | | REDUCE: (22), (319) imply: % 263.01/56.89 | | | | | | (320) ~ leq(n3, n5) % 263.01/56.89 | | | | | | % 263.01/56.89 | | | | | | PRED_UNIFY: (312), (320) imply: % 263.01/56.89 | | | | | | (321) $false % 263.01/56.89 | | | | | | % 263.01/56.89 | | | | | | CLOSE: (321) is inconsistent. % 263.01/56.89 | | | | | | % 263.01/56.89 | | | | | Case 2: % 263.01/56.89 | | | | | | % 263.01/56.89 | | | | | | (322) a_select3(pminus_ds1_filter, n4, n3) = all_74_8 & % 263.01/56.89 | | | | | | $i(all_74_8) % 263.01/56.89 | | | | | | % 263.01/56.89 | | | | | | ALPHA: (322) implies: % 263.01/56.89 | | | | | | (323) a_select3(pminus_ds1_filter, n4, n3) = all_74_8 % 263.01/56.89 | | | | | | % 263.01/56.89 | | | | | | REF_CLOSE: (3), (18), (311), (323) are inconsistent by sub-proof % 263.01/56.89 | | | | | | #59. % 263.01/56.89 | | | | | | % 263.01/56.89 | | | | | End of split % 263.01/56.89 | | | | | % 263.01/56.89 | | | | End of split % 263.01/56.89 | | | | % 263.01/56.89 | | | End of split % 263.01/56.89 | | | % 263.01/56.89 | | Case 2: % 263.01/56.89 | | | % 263.01/56.89 | | | (324) all_74_10 = n4 % 263.01/56.89 | | | % 263.01/56.89 | | | REDUCE: (261), (324) imply: % 263.01/56.89 | | | (325) a_select3(pminus_ds1_filter, n4, n4) = all_74_8 % 263.01/56.89 | | | % 263.01/56.89 | | | REDUCE: (262), (324) imply: % 263.01/56.89 | | | (326) a_select3(pminus_ds1_filter, n4, n4) = all_74_9 % 263.01/56.89 | | | % 263.01/56.89 | | | GROUND_INST: instantiating (18) with all_74_9, all_74_8, n4, n4, % 263.01/56.89 | | | pminus_ds1_filter, simplifying with (325), (326) gives: % 263.01/56.89 | | | (327) all_74_8 = all_74_9 % 263.01/56.89 | | | % 263.01/56.89 | | | REDUCE: (3), (327) imply: % 263.01/56.89 | | | (328) $false % 263.01/56.89 | | | % 263.01/56.89 | | | CLOSE: (328) is inconsistent. % 263.01/56.89 | | | % 263.01/56.89 | | End of split % 263.01/56.89 | | % 263.01/56.89 | End of split % 263.01/56.89 | % 263.01/56.89 End of proof % 263.01/56.89 % 263.01/56.89 Sub-proof #59 shows that the following formulas are inconsistent: % 263.01/56.89 ---------------------------------------------------------------- % 263.01/56.89 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 263.01/56.89 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 263.01/56.89 v0)) % 263.01/56.89 (2) a_select3(pminus_ds1_filter, n4, n3) = all_74_8 % 263.01/56.89 (3) a_select3(pminus_ds1_filter, n4, n3) = all_74_9 % 263.01/56.89 (4) ~ (all_74_8 = all_74_9) % 263.01/56.89 % 263.01/56.89 Begin of proof % 263.01/56.89 | % 263.01/56.89 | GROUND_INST: instantiating (1) with all_74_8, all_74_9, n3, n4, % 263.01/56.89 | pminus_ds1_filter, simplifying with (2), (3) gives: % 263.01/56.89 | (5) all_74_8 = all_74_9 % 263.01/56.89 | % 263.01/56.89 | REDUCE: (4), (5) imply: % 263.01/56.89 | (6) $false % 263.01/56.89 | % 263.01/56.89 | CLOSE: (6) is inconsistent. % 263.01/56.89 | % 263.01/56.89 End of proof % 263.01/56.89 % 263.01/56.89 Sub-proof #60 shows that the following formulas are inconsistent: % 263.01/56.89 ---------------------------------------------------------------- % 263.01/56.89 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 263.01/56.89 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 263.01/56.89 v0)) % 263.01/56.89 (2) a_select3(pminus_ds1_filter, n4, n2) = all_74_8 % 263.01/56.89 (3) a_select3(pminus_ds1_filter, n4, n2) = all_74_9 % 263.01/56.89 (4) ~ (all_74_8 = all_74_9) % 263.01/56.89 % 263.01/56.89 Begin of proof % 263.01/56.89 | % 263.01/56.89 | GROUND_INST: instantiating (1) with all_74_8, all_74_9, n2, n4, % 263.01/56.89 | pminus_ds1_filter, simplifying with (2), (3) gives: % 263.01/56.89 | (5) all_74_8 = all_74_9 % 263.01/56.89 | % 263.01/56.89 | REDUCE: (4), (5) imply: % 263.01/56.89 | (6) $false % 263.01/56.89 | % 263.01/56.89 | CLOSE: (6) is inconsistent. % 263.01/56.89 | % 263.01/56.89 End of proof % 263.01/56.89 % 263.01/56.89 Sub-proof #61 shows that the following formulas are inconsistent: % 263.01/56.89 ---------------------------------------------------------------- % 263.01/56.89 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 263.01/56.89 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 263.01/56.89 v0)) % 263.01/56.89 (2) a_select3(pminus_ds1_filter, n3, n2) = all_74_8 % 263.01/56.89 (3) a_select3(pminus_ds1_filter, n3, n2) = all_74_9 % 263.01/56.89 (4) ~ (all_74_8 = all_74_9) % 263.01/56.89 % 263.01/56.89 Begin of proof % 263.01/56.89 | % 263.01/56.89 | GROUND_INST: instantiating (1) with all_74_8, all_74_9, n2, n3, % 263.01/56.89 | pminus_ds1_filter, simplifying with (2), (3) gives: % 263.01/56.89 | (5) all_74_8 = all_74_9 % 263.01/56.89 | % 263.01/56.89 | REDUCE: (4), (5) imply: % 263.01/56.89 | (6) $false % 263.01/56.89 | % 263.01/56.89 | CLOSE: (6) is inconsistent. % 263.01/56.89 | % 263.01/56.89 End of proof % 263.01/56.89 % 263.01/56.89 Sub-proof #62 shows that the following formulas are inconsistent: % 263.01/56.89 ---------------------------------------------------------------- % 263.01/56.89 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 263.01/56.89 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 263.01/56.89 v0)) % 263.01/56.89 (2) a_select3(pminus_ds1_filter, n2, n1) = all_74_8 % 263.01/56.89 (3) a_select3(pminus_ds1_filter, n2, n1) = all_74_9 % 263.01/56.89 (4) ~ (all_74_8 = all_74_9) % 263.01/56.89 % 263.01/56.89 Begin of proof % 263.01/56.89 | % 263.01/56.89 | GROUND_INST: instantiating (1) with all_74_9, all_74_8, n1, n2, % 263.01/56.89 | pminus_ds1_filter, simplifying with (2), (3) gives: % 263.01/56.89 | (5) all_74_8 = all_74_9 % 263.01/56.89 | % 263.01/56.89 | REDUCE: (4), (5) imply: % 263.01/56.89 | (6) $false % 263.01/56.89 | % 263.01/56.89 | CLOSE: (6) is inconsistent. % 263.01/56.89 | % 263.01/56.89 End of proof % 263.01/56.89 % 263.01/56.89 Sub-proof #63 shows that the following formulas are inconsistent: % 263.01/56.89 ---------------------------------------------------------------- % 263.01/56.89 (1) $i(all_74_11) % 263.01/56.89 (2) all_74_11 = n0 % 263.01/56.89 (3) gt(all_74_11, n0) % 263.01/56.89 (4) ! [v0: $i] : ( ~ $i(v0) | ~ gt(v0, v0)) % 263.01/56.89 % 263.01/56.89 Begin of proof % 263.01/56.89 | % 263.01/56.89 | REDUCE: (1), (2) imply: % 263.01/56.89 | (5) $i(n0) % 263.01/56.89 | % 263.01/56.89 | REDUCE: (2), (3) imply: % 263.01/56.89 | (6) gt(n0, n0) % 263.01/56.89 | % 263.01/56.89 | GROUND_INST: instantiating (4) with n0, simplifying with (5), (6) gives: % 263.01/56.89 | (7) $false % 263.01/56.89 | % 263.01/56.89 | CLOSE: (7) is inconsistent. % 263.01/56.89 | % 263.01/56.89 End of proof % 263.01/56.89 % 263.01/56.89 Sub-proof #64 shows that the following formulas are inconsistent: % 263.01/56.89 ---------------------------------------------------------------- % 263.01/56.89 (1) $i(all_74_10) % 263.01/56.89 (2) all_74_10 = n0 % 263.01/56.89 (3) gt(all_74_10, n0) % 263.01/56.89 (4) ! [v0: $i] : ( ~ $i(v0) | ~ gt(v0, v0)) % 263.01/56.89 % 263.01/56.89 Begin of proof % 263.01/56.89 | % 263.01/56.89 | REDUCE: (1), (2) imply: % 263.01/56.89 | (5) $i(n0) % 263.01/56.89 | % 263.01/56.89 | REDUCE: (2), (3) imply: % 263.01/56.89 | (6) gt(n0, n0) % 263.01/56.89 | % 263.01/56.89 | GROUND_INST: instantiating (4) with n0, simplifying with (5), (6) gives: % 263.01/56.89 | (7) $false % 263.01/56.89 | % 263.01/56.89 | CLOSE: (7) is inconsistent. % 263.01/56.89 | % 263.01/56.89 End of proof % 263.01/56.89 % 263.01/56.89 Sub-proof #65 shows that the following formulas are inconsistent: % 263.01/56.89 ---------------------------------------------------------------- % 263.01/56.89 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 263.01/56.89 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 263.01/56.89 v0)) % 263.01/56.89 (2) a_select3(r_ds1_filter, n1, n0) = all_74_4 % 263.01/56.89 (3) a_select3(r_ds1_filter, n1, n0) = all_74_5 % 263.01/56.89 (4) ~ (all_74_4 = all_74_5) % 263.01/56.89 % 263.01/56.89 Begin of proof % 263.01/56.89 | % 263.01/56.89 | GROUND_INST: instantiating (1) with all_74_5, all_74_4, n0, n1, r_ds1_filter, % 263.01/56.89 | simplifying with (2), (3) gives: % 263.01/56.89 | (5) all_74_4 = all_74_5 % 263.01/56.89 | % 263.01/56.89 | REDUCE: (4), (5) imply: % 263.01/56.89 | (6) $false % 263.01/56.89 | % 263.01/56.89 | CLOSE: (6) is inconsistent. % 263.01/56.89 | % 263.01/56.89 End of proof % 263.01/56.89 % 263.01/56.89 Sub-proof #66 shows that the following formulas are inconsistent: % 263.01/56.89 ---------------------------------------------------------------- % 263.01/56.89 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 263.01/56.89 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 263.01/56.89 v0)) % 263.01/56.89 (2) a_select3(r_ds1_filter, n2, n1) = all_74_4 % 263.01/56.89 (3) a_select3(r_ds1_filter, n2, n1) = all_74_5 % 263.01/56.89 (4) ~ (all_74_4 = all_74_5) % 263.01/56.89 % 263.01/56.89 Begin of proof % 263.01/56.89 | % 263.01/56.89 | GROUND_INST: instantiating (1) with all_74_4, all_74_5, n1, n2, r_ds1_filter, % 263.01/56.89 | simplifying with (2), (3) gives: % 263.01/56.89 | (5) all_74_4 = all_74_5 % 263.01/56.89 | % 263.01/56.89 | REDUCE: (4), (5) imply: % 263.01/56.89 | (6) $false % 263.01/56.89 | % 263.01/56.89 | CLOSE: (6) is inconsistent. % 263.01/56.89 | % 263.01/56.89 End of proof % 263.01/56.89 % 263.01/56.89 Sub-proof #67 shows that the following formulas are inconsistent: % 263.01/56.89 ---------------------------------------------------------------- % 263.01/56.89 (1) $i(all_74_7) % 263.01/56.89 (2) all_74_7 = n0 % 263.01/56.89 (3) gt(all_74_7, n0) % 263.01/56.89 (4) ! [v0: $i] : ( ~ $i(v0) | ~ gt(v0, v0)) % 263.01/56.89 % 263.01/56.89 Begin of proof % 263.01/56.89 | % 263.01/56.89 | REDUCE: (1), (2) imply: % 263.01/56.89 | (5) $i(n0) % 263.01/56.89 | % 263.01/56.89 | REDUCE: (2), (3) imply: % 263.01/56.89 | (6) gt(n0, n0) % 263.01/56.89 | % 263.01/56.89 | GROUND_INST: instantiating (4) with n0, simplifying with (5), (6) gives: % 263.01/56.89 | (7) $false % 263.01/56.89 | % 263.01/56.89 | CLOSE: (7) is inconsistent. % 263.01/56.89 | % 263.01/56.89 End of proof % 263.01/56.89 % 263.01/56.89 Sub-proof #68 shows that the following formulas are inconsistent: % 263.01/56.89 ---------------------------------------------------------------- % 263.01/56.89 (1) $i(all_74_6) % 263.01/56.89 (2) all_74_6 = n0 % 263.01/56.89 (3) gt(all_74_6, n0) % 263.01/56.89 (4) ! [v0: $i] : ( ~ $i(v0) | ~ gt(v0, v0)) % 263.01/56.89 % 263.01/56.89 Begin of proof % 263.01/56.89 | % 263.01/56.89 | REDUCE: (1), (2) imply: % 263.01/56.89 | (5) $i(n0) % 263.01/56.89 | % 263.01/56.89 | REDUCE: (2), (3) imply: % 263.01/56.89 | (6) gt(n0, n0) % 263.01/56.89 | % 263.01/56.89 | GROUND_INST: instantiating (4) with n0, simplifying with (5), (6) gives: % 263.01/56.89 | (7) $false % 263.01/56.89 | % 263.01/56.89 | CLOSE: (7) is inconsistent. % 263.01/56.89 | % 263.01/56.89 End of proof % 263.01/56.89 % 263.01/56.89 Sub-proof #69 shows that the following formulas are inconsistent: % 263.01/56.89 ---------------------------------------------------------------- % 263.01/56.89 (1) leq(all_74_3, n4) % 263.01/56.89 (2) a_select3(q_ds1_filter, n0, all_74_3) = all_74_0 % 263.01/56.89 (3) $i(n3) % 263.01/56.89 (4) $i(n4) % 263.01/56.90 (5) ! [v0: $i] : (v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0, n1) | ~ % 263.01/56.90 leq(n0, v0)) % 263.01/56.90 (6) pred(n2) = n1 % 263.01/56.90 (7) leq(n0, all_74_3) % 263.01/56.90 (8) ~ (all_74_0 = all_74_1) % 263.01/56.90 (9) gt(all_74_3, n0) % 263.01/56.90 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (a_select3(q_ds1_filter, % 263.01/56.90 v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ leq(v1, all_74_20) | ~ % 263.01/56.90 leq(v0, all_74_20) | ~ leq(n0, v1) | ~ leq(n0, v0) | % 263.01/56.90 (a_select3(q_ds1_filter, v1, v0) = v2 & $i(v2))) % 263.01/56.90 (11) a_select3(q_ds1_filter, all_74_3, n0) = all_74_1 % 263.01/56.90 (12) $i(all_74_3) % 263.01/56.90 (13) all_74_3 = n5 | all_74_3 = n4 | all_74_3 = n3 | all_74_3 = n2 | all_74_3 % 263.01/56.90 = n1 | all_74_3 = n0 % 263.01/56.90 (14) ~ gt(n0, n0) % 263.01/56.90 (15) $i(n0) % 263.01/56.90 (16) pred(n3) = n2 % 263.01/56.90 (17) leq(n0, n5) % 263.01/56.90 (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 263.01/56.90 (v1 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 263.01/56.90 v0)) % 263.01/56.90 (19) pred(n4) = n3 % 263.01/56.90 (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (pred(v1) = v2) | ~ % 263.01/56.90 $i(v1) | ~ $i(v0) | ~ gt(v1, v0) | leq(v0, v2)) % 263.01/56.90 (21) all_74_20 = n5 % 263.01/56.90 (22) $i(n2) % 263.01/56.90 (23) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ % 263.01/56.90 leq(v0, v1) | gt(v1, v0)) % 263.01/56.90 (24) leq(n0, n0) % 263.01/56.90 (25) leq(all_74_3, n5) % 263.01/56.90 % 263.01/56.90 Begin of proof % 263.01/56.90 | % 263.01/56.90 | GROUND_INST: instantiating (23) with all_74_3, n4, simplifying with (1), (4), % 263.01/56.90 | (12) gives: % 263.01/56.90 | (26) all_74_3 = n4 | gt(n4, all_74_3) % 263.01/56.90 | % 263.01/56.90 | BETA: splitting (13) gives: % 263.01/56.90 | % 263.01/56.90 | Case 1: % 263.01/56.90 | | % 263.01/56.90 | | (27) all_74_3 = n0 % 263.01/56.90 | | % 263.01/56.90 | | REDUCE: (9), (27) imply: % 263.01/56.90 | | (28) gt(n0, n0) % 263.01/56.90 | | % 263.01/56.90 | | PRED_UNIFY: (14), (28) imply: % 263.01/56.90 | | (29) $false % 263.01/56.90 | | % 263.01/56.90 | | CLOSE: (29) is inconsistent. % 263.01/56.90 | | % 263.01/56.90 | Case 2: % 263.01/56.90 | | % 263.01/56.90 | | (30) ~ (all_74_3 = n0) % 263.01/56.90 | | % 263.01/56.90 | | BETA: splitting (26) gives: % 263.01/56.90 | | % 263.01/56.90 | | Case 1: % 263.01/56.90 | | | % 263.01/56.90 | | | (31) gt(n4, all_74_3) % 263.01/56.90 | | | % 263.01/56.90 | | | GROUND_INST: instantiating (20) with all_74_3, n4, n3, simplifying with % 263.01/56.90 | | | (4), (12), (19), (31) gives: % 263.01/56.90 | | | (32) leq(all_74_3, n3) % 263.01/56.90 | | | % 263.01/56.90 | | | GROUND_INST: instantiating (23) with all_74_3, n3, simplifying with (3), % 263.01/56.90 | | | (12), (32) gives: % 263.01/56.90 | | | (33) all_74_3 = n3 | gt(n3, all_74_3) % 263.01/56.90 | | | % 263.01/56.90 | | | BETA: splitting (33) gives: % 263.01/56.90 | | | % 263.01/56.90 | | | Case 1: % 263.01/56.90 | | | | % 263.01/56.90 | | | | (34) gt(n3, all_74_3) % 263.01/56.90 | | | | % 263.01/56.90 | | | | GROUND_INST: instantiating (20) with all_74_3, n3, n2, simplifying with % 263.01/56.90 | | | | (3), (12), (16), (34) gives: % 263.01/56.90 | | | | (35) leq(all_74_3, n2) % 263.01/56.90 | | | | % 263.01/56.90 | | | | GROUND_INST: instantiating (23) with all_74_3, n2, simplifying with % 263.01/56.90 | | | | (12), (22), (35) gives: % 263.01/56.90 | | | | (36) all_74_3 = n2 | gt(n2, all_74_3) % 263.01/56.90 | | | | % 263.01/56.90 | | | | BETA: splitting (36) gives: % 263.01/56.90 | | | | % 263.01/56.90 | | | | Case 1: % 263.01/56.90 | | | | | % 263.01/56.90 | | | | | (37) gt(n2, all_74_3) % 263.01/56.90 | | | | | % 263.01/56.90 | | | | | GROUND_INST: instantiating (20) with all_74_3, n2, n1, simplifying % 263.01/56.90 | | | | | with (6), (12), (22), (37) gives: % 263.01/56.90 | | | | | (38) leq(all_74_3, n1) % 263.01/56.90 | | | | | % 263.01/56.90 | | | | | GROUND_INST: instantiating (5) with all_74_3, simplifying with (7), % 263.01/56.90 | | | | | (12), (38) gives: % 263.01/56.90 | | | | | (39) all_74_3 = n1 | all_74_3 = n0 % 263.01/56.90 | | | | | % 263.01/56.90 | | | | | BETA: splitting (39) gives: % 263.01/56.90 | | | | | % 263.01/56.90 | | | | | Case 1: % 263.01/56.90 | | | | | | % 263.01/56.90 | | | | | | (40) all_74_3 = n0 % 263.01/56.90 | | | | | | % 263.01/56.90 | | | | | | REDUCE: (30), (40) imply: % 263.01/56.90 | | | | | | (41) $false % 263.01/56.90 | | | | | | % 263.01/56.90 | | | | | | CLOSE: (41) is inconsistent. % 263.01/56.90 | | | | | | % 263.01/56.90 | | | | | Case 2: % 263.01/56.90 | | | | | | % 263.01/56.90 | | | | | | (42) all_74_3 = n1 % 263.01/56.90 | | | | | | % 263.01/56.90 | | | | | | REDUCE: (11), (42) imply: % 263.01/56.90 | | | | | | (43) a_select3(q_ds1_filter, n1, n0) = all_74_1 % 263.01/56.90 | | | | | | % 263.01/56.90 | | | | | | REDUCE: (2), (42) imply: % 263.01/56.90 | | | | | | (44) a_select3(q_ds1_filter, n0, n1) = all_74_0 % 263.01/56.90 | | | | | | % 263.01/56.90 | | | | | | REDUCE: (12), (42) imply: % 263.01/56.90 | | | | | | (45) $i(n1) % 263.01/56.90 | | | | | | % 263.01/56.90 | | | | | | REDUCE: (25), (42) imply: % 263.01/56.90 | | | | | | (46) leq(n1, n5) % 263.01/56.90 | | | | | | % 263.01/56.90 | | | | | | REDUCE: (7), (42) imply: % 263.01/56.90 | | | | | | (47) leq(n0, n1) % 263.01/56.90 | | | | | | % 263.01/56.90 | | | | | | GROUND_INST: instantiating (10) with n0, n1, all_74_0, simplifying % 263.01/56.90 | | | | | | with (15), (24), (44), (45), (47) gives: % 263.01/56.90 | | | | | | (48) ~ leq(n1, all_74_20) | ~ leq(n0, all_74_20) | % 263.01/56.90 | | | | | | (a_select3(q_ds1_filter, n1, n0) = all_74_0 & $i(all_74_0)) % 263.01/56.90 | | | | | | % 263.01/56.90 | | | | | | BETA: splitting (48) gives: % 263.01/56.90 | | | | | | % 263.01/56.90 | | | | | | Case 1: % 263.01/56.90 | | | | | | | % 263.01/56.90 | | | | | | | (49) ~ leq(n0, all_74_20) % 263.01/56.90 | | | | | | | % 263.01/56.90 | | | | | | | REDUCE: (21), (49) imply: % 263.01/56.90 | | | | | | | (50) ~ leq(n0, n5) % 263.01/56.90 | | | | | | | % 263.01/56.90 | | | | | | | PRED_UNIFY: (17), (50) imply: % 263.01/56.90 | | | | | | | (51) $false % 263.01/56.90 | | | | | | | % 263.01/56.90 | | | | | | | CLOSE: (51) is inconsistent. % 263.01/56.90 | | | | | | | % 263.01/56.90 | | | | | | Case 2: % 263.01/56.90 | | | | | | | % 263.01/56.90 | | | | | | | (52) ~ leq(n1, all_74_20) | (a_select3(q_ds1_filter, n1, n0) = % 263.01/56.90 | | | | | | | all_74_0 & $i(all_74_0)) % 263.01/56.90 | | | | | | | % 263.01/56.90 | | | | | | | BETA: splitting (52) gives: % 263.01/56.90 | | | | | | | % 263.01/56.90 | | | | | | | Case 1: % 263.01/56.90 | | | | | | | | % 263.01/56.90 | | | | | | | | (53) ~ leq(n1, all_74_20) % 263.01/56.90 | | | | | | | | % 263.01/56.90 | | | | | | | | REDUCE: (21), (53) imply: % 263.01/56.90 | | | | | | | | (54) ~ leq(n1, n5) % 263.01/56.90 | | | | | | | | % 263.01/56.90 | | | | | | | | PRED_UNIFY: (46), (54) imply: % 263.01/56.90 | | | | | | | | (55) $false % 263.01/56.90 | | | | | | | | % 263.01/56.90 | | | | | | | | CLOSE: (55) is inconsistent. % 263.01/56.90 | | | | | | | | % 263.01/56.90 | | | | | | | Case 2: % 263.01/56.90 | | | | | | | | % 263.01/56.90 | | | | | | | | (56) a_select3(q_ds1_filter, n1, n0) = all_74_0 & % 263.01/56.90 | | | | | | | | $i(all_74_0) % 263.01/56.90 | | | | | | | | % 263.01/56.90 | | | | | | | | ALPHA: (56) implies: % 263.01/56.90 | | | | | | | | (57) a_select3(q_ds1_filter, n1, n0) = all_74_0 % 263.01/56.90 | | | | | | | | % 263.01/56.90 | | | | | | | | REF_CLOSE: (8), (18), (43), (57) are inconsistent by sub-proof % 263.01/56.90 | | | | | | | | #80. % 263.01/56.90 | | | | | | | | % 263.01/56.90 | | | | | | | End of split % 263.01/56.90 | | | | | | | % 263.01/56.90 | | | | | | End of split % 263.01/56.90 | | | | | | % 263.01/56.90 | | | | | End of split % 263.01/56.90 | | | | | % 263.01/56.90 | | | | Case 2: % 263.01/56.90 | | | | | % 263.01/56.90 | | | | | (58) all_74_3 = n2 % 263.01/56.90 | | | | | % 263.01/56.90 | | | | | REDUCE: (11), (58) imply: % 263.01/56.90 | | | | | (59) a_select3(q_ds1_filter, n2, n0) = all_74_1 % 263.01/56.90 | | | | | % 263.01/56.90 | | | | | REDUCE: (2), (58) imply: % 263.01/56.90 | | | | | (60) a_select3(q_ds1_filter, n0, n2) = all_74_0 % 263.01/56.90 | | | | | % 263.01/56.90 | | | | | REDUCE: (25), (58) imply: % 263.01/56.90 | | | | | (61) leq(n2, n5) % 263.01/56.90 | | | | | % 263.01/56.90 | | | | | REDUCE: (7), (58) imply: % 263.01/56.90 | | | | | (62) leq(n0, n2) % 263.01/56.90 | | | | | % 263.01/56.90 | | | | | GROUND_INST: instantiating (10) with n0, n2, all_74_0, simplifying % 263.01/56.90 | | | | | with (15), (22), (24), (60), (62) gives: % 263.01/56.90 | | | | | (63) ~ leq(n2, all_74_20) | ~ leq(n0, all_74_20) | % 263.01/56.90 | | | | | (a_select3(q_ds1_filter, n2, n0) = all_74_0 & $i(all_74_0)) % 263.01/56.90 | | | | | % 263.01/56.90 | | | | | BETA: splitting (63) gives: % 263.01/56.90 | | | | | % 263.01/56.90 | | | | | Case 1: % 263.01/56.90 | | | | | | % 263.01/56.90 | | | | | | (64) ~ leq(n0, all_74_20) % 263.01/56.90 | | | | | | % 263.01/56.90 | | | | | | REDUCE: (21), (64) imply: % 263.01/56.90 | | | | | | (65) ~ leq(n0, n5) % 263.01/56.90 | | | | | | % 263.01/56.90 | | | | | | PRED_UNIFY: (17), (65) imply: % 263.01/56.90 | | | | | | (66) $false % 263.01/56.90 | | | | | | % 263.01/56.90 | | | | | | CLOSE: (66) is inconsistent. % 263.01/56.90 | | | | | | % 263.01/56.90 | | | | | Case 2: % 263.01/56.90 | | | | | | % 263.01/56.90 | | | | | | (67) ~ leq(n2, all_74_20) | (a_select3(q_ds1_filter, n2, n0) = % 263.01/56.90 | | | | | | all_74_0 & $i(all_74_0)) % 263.01/56.90 | | | | | | % 263.01/56.90 | | | | | | BETA: splitting (67) gives: % 263.01/56.90 | | | | | | % 263.01/56.90 | | | | | | Case 1: % 263.01/56.90 | | | | | | | % 263.01/56.90 | | | | | | | (68) ~ leq(n2, all_74_20) % 263.01/56.90 | | | | | | | % 263.01/56.90 | | | | | | | REDUCE: (21), (68) imply: % 263.01/56.90 | | | | | | | (69) ~ leq(n2, n5) % 263.01/56.90 | | | | | | | % 263.01/56.90 | | | | | | | PRED_UNIFY: (61), (69) imply: % 263.01/56.90 | | | | | | | (70) $false % 263.01/56.90 | | | | | | | % 263.01/56.90 | | | | | | | CLOSE: (70) is inconsistent. % 263.01/56.90 | | | | | | | % 263.01/56.90 | | | | | | Case 2: % 263.01/56.90 | | | | | | | % 263.01/56.90 | | | | | | | (71) a_select3(q_ds1_filter, n2, n0) = all_74_0 & $i(all_74_0) % 263.01/56.90 | | | | | | | % 263.01/56.90 | | | | | | | ALPHA: (71) implies: % 263.01/56.90 | | | | | | | (72) a_select3(q_ds1_filter, n2, n0) = all_74_0 % 263.01/56.90 | | | | | | | % 263.01/56.90 | | | | | | | REF_CLOSE: (8), (18), (59), (72) are inconsistent by sub-proof % 263.01/56.90 | | | | | | | #79. % 263.01/56.90 | | | | | | | % 263.01/56.90 | | | | | | End of split % 263.01/56.90 | | | | | | % 263.01/56.90 | | | | | End of split % 263.01/56.90 | | | | | % 263.01/56.90 | | | | End of split % 263.01/56.90 | | | | % 263.01/56.90 | | | Case 2: % 263.01/56.90 | | | | % 263.01/56.90 | | | | (73) all_74_3 = n3 % 263.01/56.90 | | | | % 263.01/56.90 | | | | REDUCE: (11), (73) imply: % 263.01/56.90 | | | | (74) a_select3(q_ds1_filter, n3, n0) = all_74_1 % 263.01/56.90 | | | | % 263.01/56.90 | | | | REDUCE: (2), (73) imply: % 263.01/56.90 | | | | (75) a_select3(q_ds1_filter, n0, n3) = all_74_0 % 263.01/56.90 | | | | % 263.01/56.90 | | | | REDUCE: (25), (73) imply: % 263.01/56.90 | | | | (76) leq(n3, n5) % 263.01/56.90 | | | | % 263.01/56.90 | | | | REDUCE: (7), (73) imply: % 263.01/56.90 | | | | (77) leq(n0, n3) % 263.01/56.90 | | | | % 263.01/56.90 | | | | GROUND_INST: instantiating (10) with n0, n3, all_74_0, simplifying with % 263.01/56.90 | | | | (3), (15), (24), (75), (77) gives: % 263.01/56.90 | | | | (78) ~ leq(n3, all_74_20) | ~ leq(n0, all_74_20) | % 263.01/56.90 | | | | (a_select3(q_ds1_filter, n3, n0) = all_74_0 & $i(all_74_0)) % 263.01/56.90 | | | | % 263.01/56.90 | | | | BETA: splitting (78) gives: % 263.01/56.90 | | | | % 263.01/56.90 | | | | Case 1: % 263.01/56.90 | | | | | % 263.01/56.90 | | | | | (79) ~ leq(n0, all_74_20) % 263.01/56.90 | | | | | % 263.01/56.90 | | | | | REDUCE: (21), (79) imply: % 263.01/56.90 | | | | | (80) ~ leq(n0, n5) % 263.01/56.90 | | | | | % 263.01/56.90 | | | | | PRED_UNIFY: (17), (80) imply: % 263.01/56.90 | | | | | (81) $false % 263.01/56.90 | | | | | % 263.01/56.90 | | | | | CLOSE: (81) is inconsistent. % 263.01/56.90 | | | | | % 263.01/56.90 | | | | Case 2: % 263.01/56.90 | | | | | % 263.01/56.90 | | | | | (82) ~ leq(n3, all_74_20) | (a_select3(q_ds1_filter, n3, n0) = % 263.01/56.90 | | | | | all_74_0 & $i(all_74_0)) % 263.01/56.90 | | | | | % 263.01/56.90 | | | | | BETA: splitting (82) gives: % 263.01/56.90 | | | | | % 263.01/56.90 | | | | | Case 1: % 263.01/56.90 | | | | | | % 263.01/56.90 | | | | | | (83) ~ leq(n3, all_74_20) % 263.01/56.90 | | | | | | % 263.01/56.90 | | | | | | REDUCE: (21), (83) imply: % 263.01/56.90 | | | | | | (84) ~ leq(n3, n5) % 263.01/56.90 | | | | | | % 263.01/56.90 | | | | | | PRED_UNIFY: (76), (84) imply: % 263.01/56.90 | | | | | | (85) $false % 263.01/56.90 | | | | | | % 263.01/56.90 | | | | | | CLOSE: (85) is inconsistent. % 263.01/56.90 | | | | | | % 263.01/56.90 | | | | | Case 2: % 263.01/56.90 | | | | | | % 263.01/56.90 | | | | | | (86) a_select3(q_ds1_filter, n3, n0) = all_74_0 & $i(all_74_0) % 263.01/56.90 | | | | | | % 263.01/56.90 | | | | | | ALPHA: (86) implies: % 263.01/56.90 | | | | | | (87) a_select3(q_ds1_filter, n3, n0) = all_74_0 % 263.01/56.90 | | | | | | % 263.01/56.90 | | | | | | REF_CLOSE: (8), (18), (74), (87) are inconsistent by sub-proof #78. % 263.01/56.90 | | | | | | % 263.01/56.90 | | | | | End of split % 263.01/56.90 | | | | | % 263.01/56.90 | | | | End of split % 263.01/56.90 | | | | % 263.01/56.90 | | | End of split % 263.01/56.90 | | | % 263.01/56.90 | | Case 2: % 263.01/56.90 | | | % 263.01/56.90 | | | (88) all_74_3 = n4 % 263.01/56.90 | | | % 263.01/56.90 | | | REDUCE: (11), (88) imply: % 263.01/56.90 | | | (89) a_select3(q_ds1_filter, n4, n0) = all_74_1 % 263.01/56.90 | | | % 263.01/56.90 | | | REDUCE: (2), (88) imply: % 263.01/56.90 | | | (90) a_select3(q_ds1_filter, n0, n4) = all_74_0 % 263.01/56.90 | | | % 263.01/56.90 | | | REDUCE: (25), (88) imply: % 263.01/56.90 | | | (91) leq(n4, n5) % 263.01/56.90 | | | % 263.01/56.90 | | | REDUCE: (7), (88) imply: % 263.01/56.90 | | | (92) leq(n0, n4) % 263.01/56.90 | | | % 263.01/56.90 | | | GROUND_INST: instantiating (10) with n0, n4, all_74_0, simplifying with % 263.01/56.90 | | | (4), (15), (24), (90), (92) gives: % 263.01/56.90 | | | (93) ~ leq(n4, all_74_20) | ~ leq(n0, all_74_20) | % 263.01/56.90 | | | (a_select3(q_ds1_filter, n4, n0) = all_74_0 & $i(all_74_0)) % 263.01/56.90 | | | % 263.01/56.90 | | | BETA: splitting (93) gives: % 263.01/56.90 | | | % 263.01/56.90 | | | Case 1: % 263.01/56.90 | | | | % 263.01/56.90 | | | | (94) ~ leq(n0, all_74_20) % 263.01/56.90 | | | | % 263.01/56.90 | | | | REDUCE: (21), (94) imply: % 263.01/56.90 | | | | (95) ~ leq(n0, n5) % 263.01/56.90 | | | | % 263.01/56.90 | | | | PRED_UNIFY: (17), (95) imply: % 263.01/56.90 | | | | (96) $false % 263.01/56.90 | | | | % 263.01/56.90 | | | | CLOSE: (96) is inconsistent. % 263.01/56.90 | | | | % 263.01/56.90 | | | Case 2: % 263.01/56.90 | | | | % 263.01/56.90 | | | | (97) ~ leq(n4, all_74_20) | (a_select3(q_ds1_filter, n4, n0) = % 263.01/56.90 | | | | all_74_0 & $i(all_74_0)) % 263.01/56.90 | | | | % 263.01/56.90 | | | | BETA: splitting (97) gives: % 263.01/56.90 | | | | % 263.01/56.90 | | | | Case 1: % 263.01/56.90 | | | | | % 263.01/56.90 | | | | | (98) ~ leq(n4, all_74_20) % 263.01/56.90 | | | | | % 263.01/56.90 | | | | | REDUCE: (21), (98) imply: % 263.01/56.90 | | | | | (99) ~ leq(n4, n5) % 263.01/56.90 | | | | | % 263.01/56.90 | | | | | PRED_UNIFY: (91), (99) imply: % 263.01/56.90 | | | | | (100) $false % 263.01/56.90 | | | | | % 263.01/56.90 | | | | | CLOSE: (100) is inconsistent. % 263.01/56.90 | | | | | % 263.01/56.90 | | | | Case 2: % 263.01/56.90 | | | | | % 263.01/56.91 | | | | | (101) a_select3(q_ds1_filter, n4, n0) = all_74_0 & $i(all_74_0) % 263.01/56.91 | | | | | % 263.01/56.91 | | | | | ALPHA: (101) implies: % 263.01/56.91 | | | | | (102) a_select3(q_ds1_filter, n4, n0) = all_74_0 % 263.01/56.91 | | | | | % 263.01/56.91 | | | | | REF_CLOSE: (8), (18), (89), (102) are inconsistent by sub-proof #77. % 263.01/56.91 | | | | | % 263.01/56.91 | | | | End of split % 263.01/56.91 | | | | % 263.01/56.91 | | | End of split % 263.01/56.91 | | | % 263.01/56.91 | | End of split % 263.01/56.91 | | % 263.01/56.91 | End of split % 263.01/56.91 | % 263.01/56.91 End of proof % 263.01/56.91 % 263.01/56.91 Sub-proof #70 shows that the following formulas are inconsistent: % 263.01/56.91 ---------------------------------------------------------------- % 263.01/56.91 (1) pred(n1) = n0 % 263.01/56.91 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (pred(v2) = v1) | % 263.01/56.91 ~ (pred(v2) = v0)) % 263.01/56.91 (3) succ(all_74_18) = pv57 % 263.01/56.91 (4) succ(n0) = n1 % 263.01/56.91 (5) gt(all_74_2, n0) % 263.01/56.91 (6) $i(n3) % 263.01/56.91 (7) leq(all_74_18, n5) % 263.01/56.91 (8) pv57 = n5 | pv57 = n4 | pv57 = n3 | pv57 = n2 | pv57 = n1 % 263.01/56.91 (9) all_74_3 = n6 | all_74_3 = n5 | all_74_3 = n4 | all_74_3 = n3 | all_74_3 % 263.01/56.91 = n2 | all_74_3 = n1 | all_74_3 = n0 % 263.01/56.91 (10) $i(n4) % 263.01/56.91 (11) ! [v0: $i] : (v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0, n1) | ~ % 263.01/56.91 leq(n0, v0)) % 263.01/56.91 (12) a_select3(q_ds1_filter, all_74_2, all_74_3) = all_74_0 % 263.01/56.91 (13) a_select3(q_ds1_filter, all_74_3, all_74_2) = all_74_1 % 263.01/56.91 (14) pred(n2) = n1 % 263.01/56.91 (15) leq(n0, all_74_3) % 263.01/56.91 (16) all_74_3 = n0 | gt(all_74_3, n0) % 263.01/56.91 (17) all_74_2 = n5 | all_74_2 = n4 | all_74_2 = n3 | all_74_2 = n2 | all_74_2 % 263.01/56.91 = n1 | all_74_2 = n0 % 263.01/56.91 (18) ~ (all_74_0 = all_74_1) % 263.01/56.91 (19) pred(n5) = n4 % 263.01/56.91 (20) leq(n0, all_74_2) % 263.01/56.91 (21) leq(n0, all_74_18) % 263.01/56.91 (22) leq(all_74_2, n5) % 263.01/56.91 (23) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (a_select3(q_ds1_filter, % 263.01/56.91 v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ leq(v1, all_74_20) | ~ % 263.01/56.91 leq(v0, all_74_20) | ~ leq(n0, v1) | ~ leq(n0, v0) | % 263.01/56.91 (a_select3(q_ds1_filter, v1, v0) = v2 & $i(v2))) % 263.01/56.91 (24) n6 = pv57 | pv57 = n5 | pv57 = n4 | pv57 = n3 | pv57 = n2 | pv57 = n1 % 263.01/56.91 (25) $i(all_74_3) % 263.01/56.91 (26) all_74_3 = n5 | all_74_3 = n4 | all_74_3 = n3 | all_74_3 = n2 | all_74_3 % 263.01/56.91 = n1 | all_74_3 = n0 % 263.01/56.91 (27) $i(all_74_18) % 263.01/56.91 (28) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (succ(v2) = v1) % 263.01/56.91 | ~ (succ(v2) = v0)) % 263.01/56.91 (29) ~ gt(n0, n0) % 263.01/56.91 (30) pred(n3) = n2 % 263.01/56.91 (31) all_74_3 = n5 | gt(n5, all_74_3) % 263.01/56.91 (32) ! [v0: $i] : (v0 = n4 | v0 = n3 | v0 = n2 | v0 = n1 | v0 = n0 | ~ % 263.01/56.91 $i(v0) | ~ leq(v0, n4) | ~ leq(n0, v0)) % 263.01/56.91 (33) $i(all_74_2) % 263.01/56.91 (34) all_74_18 = n0 | gt(all_74_18, n0) % 263.01/56.91 (35) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 263.01/56.91 (v1 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 263.01/56.91 v0)) % 263.01/56.91 (36) pred(n4) = n3 % 263.01/56.91 (37) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (pred(v1) = v2) | ~ % 263.01/56.91 $i(v1) | ~ $i(v0) | ~ gt(v1, v0) | leq(v0, v2)) % 263.01/56.91 (38) all_74_2 = n5 | gt(n5, all_74_2) % 263.01/56.91 (39) pred(pv57) = all_74_18 % 263.01/56.91 (40) all_74_20 = n5 % 263.01/56.91 (41) $i(n2) % 263.01/56.91 (42) $i(n5) % 263.01/56.91 (43) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ % 263.01/56.91 leq(v0, v1) | gt(v1, v0)) % 263.01/56.91 (44) leq(all_74_3, n5) % 263.01/56.91 % 263.01/56.91 Begin of proof % 263.25/56.91 | % 263.25/56.91 | BETA: splitting (16) gives: % 263.25/56.91 | % 263.25/56.91 | Case 1: % 263.25/56.91 | | % 263.25/56.91 | | (45) gt(all_74_3, n0) % 263.25/56.91 | | % 263.25/56.91 | | REF_CLOSE: (5), (6), (9), (10), (11), (12), (13), (14), (15), (17), (18), % 263.25/56.91 | | (19), (20), (22), (23), (25), (26), (29), (30), (31), (32), (33), % 263.25/56.91 | | (35), (36), (37), (38), (40), (41), (42), (43), (44), (45) are % 263.25/56.91 | | inconsistent by sub-proof #81. % 263.25/56.91 | | % 263.25/56.91 | Case 2: % 263.25/56.91 | | % 263.25/56.91 | | (46) all_74_3 = n0 % 263.25/56.91 | | (47) ~ gt(all_74_3, n0) % 263.25/56.91 | | % 263.25/56.91 | | REDUCE: (12), (46) imply: % 263.25/56.91 | | (48) a_select3(q_ds1_filter, all_74_2, n0) = all_74_0 % 263.25/56.91 | | % 263.25/56.91 | | REDUCE: (13), (46) imply: % 263.25/56.91 | | (49) a_select3(q_ds1_filter, n0, all_74_2) = all_74_1 % 263.25/56.91 | | % 263.25/56.91 | | REDUCE: (25), (46) imply: % 263.25/56.91 | | (50) $i(n0) % 263.25/56.91 | | % 263.25/56.91 | | REDUCE: (44), (46) imply: % 263.25/56.91 | | (51) leq(n0, n5) % 263.25/56.91 | | % 263.25/56.91 | | REDUCE: (15), (46) imply: % 263.25/56.91 | | (52) leq(n0, n0) % 263.25/56.91 | | % 263.25/56.91 | | BETA: splitting (38) gives: % 263.25/56.91 | | % 263.25/56.91 | | Case 1: % 263.25/56.91 | | | % 263.25/56.91 | | | (53) gt(n5, all_74_2) % 263.25/56.91 | | | % 263.25/56.91 | | | GROUND_INST: instantiating (37) with all_74_2, n5, n4, simplifying with % 263.25/56.91 | | | (19), (33), (42), (53) gives: % 263.25/56.91 | | | (54) leq(all_74_2, n4) % 263.25/56.91 | | | % 263.25/56.91 | | | REF_CLOSE: (5), (6), (10), (11), (14), (17), (18), (20), (22), (23), (29), % 263.25/56.91 | | | (30), (32), (33), (35), (36), (37), (40), (41), (43), (48), % 263.25/56.91 | | | (49), (50), (51), (52), (54) are inconsistent by sub-proof #76. % 263.25/56.91 | | | % 263.25/56.91 | | Case 2: % 263.25/56.91 | | | % 263.25/56.91 | | | (55) all_74_2 = n5 % 263.25/56.91 | | | % 263.25/56.91 | | | REDUCE: (48), (55) imply: % 263.25/56.91 | | | (56) a_select3(q_ds1_filter, n5, n0) = all_74_0 % 263.25/56.91 | | | % 263.25/56.91 | | | REDUCE: (49), (55) imply: % 263.25/56.91 | | | (57) a_select3(q_ds1_filter, n0, n5) = all_74_1 % 263.25/56.91 | | | % 263.25/56.91 | | | REDUCE: (22), (55) imply: % 263.25/56.91 | | | (58) leq(n5, n5) % 263.25/56.91 | | | % 263.25/56.91 | | | BETA: splitting (34) gives: % 263.25/56.91 | | | % 263.25/56.91 | | | Case 1: % 263.25/56.91 | | | | % 263.25/56.91 | | | | (59) gt(all_74_18, n0) % 263.25/56.91 | | | | % 263.25/56.91 | | | | BETA: splitting (8) gives: % 263.25/56.91 | | | | % 263.25/56.91 | | | | Case 1: % 263.25/56.91 | | | | | % 263.25/56.91 | | | | | (60) pv57 = n1 % 263.25/56.91 | | | | | % 263.25/56.91 | | | | | REF_CLOSE: (1), (2), (29), (39), (59), (60) are inconsistent by % 263.25/56.91 | | | | | sub-proof #75. % 263.25/56.91 | | | | | % 263.25/56.91 | | | | Case 2: % 263.25/56.91 | | | | | % 263.25/56.91 | | | | | (61) ~ (pv57 = n1) % 263.25/56.91 | | | | | % 263.25/56.91 | | | | | BETA: splitting (24) gives: % 263.25/56.91 | | | | | % 263.25/56.91 | | | | | Case 1: % 263.25/56.91 | | | | | | % 263.25/56.91 | | | | | | (62) pv57 = n1 % 263.25/56.91 | | | | | | % 263.25/56.91 | | | | | | REDUCE: (61), (62) imply: % 263.25/56.91 | | | | | | (63) $false % 263.25/56.91 | | | | | | % 263.25/56.91 | | | | | | CLOSE: (63) is inconsistent. % 263.25/56.91 | | | | | | % 263.25/56.91 | | | | | Case 2: % 263.25/56.91 | | | | | | % 263.25/56.91 | | | | | | % 263.25/56.91 | | | | | | GROUND_INST: instantiating (23) with n0, n5, all_74_1, simplifying % 263.25/56.91 | | | | | | with (42), (50), (51), (52), (57) gives: % 263.25/56.91 | | | | | | (64) ~ leq(n5, all_74_20) | ~ leq(n0, all_74_20) | % 263.25/56.91 | | | | | | (a_select3(q_ds1_filter, n5, n0) = all_74_1 & $i(all_74_1)) % 263.25/56.91 | | | | | | % 263.25/56.91 | | | | | | REF_CLOSE: (1), (2), (7), (8), (18), (21), (23), (24), (27), (29), % 263.25/56.91 | | | | | | (34), (35), (39), (40), (42), (50), (51), (52), (56), % 263.25/56.91 | | | | | | (58), (64) are inconsistent by sub-proof #71. % 263.25/56.91 | | | | | | % 263.25/56.91 | | | | | End of split % 263.25/56.91 | | | | | % 263.25/56.91 | | | | End of split % 263.25/56.91 | | | | % 263.25/56.91 | | | Case 2: % 263.25/56.91 | | | | % 263.25/56.91 | | | | (65) all_74_18 = n0 % 263.25/56.91 | | | | (66) ~ gt(all_74_18, n0) % 263.25/56.91 | | | | % 263.25/56.91 | | | | REDUCE: (3), (65) imply: % 263.25/56.91 | | | | (67) succ(n0) = pv57 % 263.25/56.91 | | | | % 263.25/56.91 | | | | REDUCE: (39), (65) imply: % 263.25/56.91 | | | | (68) pred(pv57) = n0 % 263.25/56.91 | | | | % 263.25/56.91 | | | | GROUND_INST: instantiating (28) with n1, pv57, n0, simplifying with (4), % 263.25/56.91 | | | | (67) gives: % 263.25/56.91 | | | | (69) pv57 = n1 % 263.25/56.91 | | | | % 263.25/56.91 | | | | GROUND_INST: instantiating (23) with n0, n5, all_74_1, simplifying with % 263.25/56.91 | | | | (42), (50), (51), (52), (57) gives: % 263.25/56.91 | | | | (70) ~ leq(n5, all_74_20) | ~ leq(n0, all_74_20) | % 263.25/56.91 | | | | (a_select3(q_ds1_filter, n5, n0) = all_74_1 & $i(all_74_1)) % 263.25/56.91 | | | | % 263.25/56.91 | | | | REF_CLOSE: (1), (2), (7), (8), (18), (21), (23), (24), (27), (29), (34), % 263.25/56.91 | | | | (35), (39), (40), (42), (50), (51), (52), (56), (58), (70) % 263.25/56.91 | | | | are inconsistent by sub-proof #71. % 263.25/56.91 | | | | % 263.25/56.91 | | | End of split % 263.25/56.91 | | | % 263.25/56.91 | | End of split % 263.25/56.91 | | % 263.25/56.91 | End of split % 263.25/56.91 | % 263.25/56.91 End of proof % 263.25/56.91 % 263.25/56.91 Sub-proof #71 shows that the following formulas are inconsistent: % 263.25/56.91 ---------------------------------------------------------------- % 263.25/56.91 (1) pred(n1) = n0 % 263.25/56.91 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (pred(v2) = v1) | % 263.25/56.91 ~ (pred(v2) = v0)) % 263.25/56.91 (3) leq(all_74_18, n5) % 263.25/56.91 (4) pv57 = n5 | pv57 = n4 | pv57 = n3 | pv57 = n2 | pv57 = n1 % 263.25/56.91 (5) ~ leq(n5, all_74_20) | ~ leq(n0, all_74_20) | (a_select3(q_ds1_filter, % 263.25/56.91 n5, n0) = all_74_1 & $i(all_74_1)) % 263.25/56.91 (6) ~ (all_74_0 = all_74_1) % 263.25/56.91 (7) leq(n0, all_74_18) % 263.25/56.91 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (a_select3(q_ds1_filter, % 263.25/56.91 v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ leq(v1, all_74_20) | ~ % 263.25/56.91 leq(v0, all_74_20) | ~ leq(n0, v1) | ~ leq(n0, v0) | % 263.25/56.91 (a_select3(q_ds1_filter, v1, v0) = v2 & $i(v2))) % 263.25/56.91 (9) n6 = pv57 | pv57 = n5 | pv57 = n4 | pv57 = n3 | pv57 = n2 | pv57 = n1 % 263.25/56.91 (10) a_select3(q_ds1_filter, n5, n0) = all_74_0 % 263.25/56.91 (11) $i(all_74_18) % 263.25/56.91 (12) ~ gt(n0, n0) % 263.25/56.92 (13) $i(n0) % 263.25/56.92 (14) leq(n0, n5) % 263.25/56.92 (15) all_74_18 = n0 | gt(all_74_18, n0) % 263.25/56.92 (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 263.25/56.92 (v1 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 263.25/56.92 v0)) % 263.25/56.92 (17) leq(n5, n5) % 263.25/56.92 (18) pred(pv57) = all_74_18 % 263.25/56.92 (19) all_74_20 = n5 % 263.25/56.92 (20) $i(n5) % 263.25/56.92 (21) leq(n0, n0) % 263.25/56.92 % 263.25/56.92 Begin of proof % 263.25/56.92 | % 263.25/56.92 | GROUND_INST: instantiating (8) with n5, n0, all_74_0, simplifying with (10), % 263.25/56.92 | (13), (14), (20), (21) gives: % 263.25/56.92 | (22) ~ leq(n5, all_74_20) | ~ leq(n0, all_74_20) | % 263.25/56.92 | (a_select3(q_ds1_filter, n0, n5) = all_74_0 & $i(all_74_0)) % 263.25/56.92 | % 263.25/56.92 | BETA: splitting (22) gives: % 263.25/56.92 | % 263.25/56.92 | Case 1: % 263.25/56.92 | | % 263.25/56.92 | | (23) ~ leq(n0, all_74_20) % 263.25/56.92 | | % 263.25/56.92 | | REDUCE: (19), (23) imply: % 263.25/56.92 | | (24) ~ leq(n0, n5) % 263.25/56.92 | | % 263.25/56.92 | | PRED_UNIFY: (14), (24) imply: % 263.25/56.92 | | (25) $false % 263.25/56.92 | | % 263.25/56.92 | | CLOSE: (25) is inconsistent. % 263.25/56.92 | | % 263.25/56.92 | Case 2: % 263.25/56.92 | | % 263.25/56.92 | | (26) leq(n0, all_74_20) % 263.25/56.92 | | (27) ~ leq(n5, all_74_20) | (a_select3(q_ds1_filter, n0, n5) = all_74_0 % 263.25/56.92 | | & $i(all_74_0)) % 263.25/56.92 | | % 263.25/56.92 | | BETA: splitting (27) gives: % 263.25/56.92 | | % 263.25/56.92 | | Case 1: % 263.25/56.92 | | | % 263.25/56.92 | | | (28) ~ leq(n5, all_74_20) % 263.25/56.92 | | | % 263.25/56.92 | | | REDUCE: (19), (28) imply: % 263.25/56.92 | | | (29) ~ leq(n5, n5) % 263.25/56.92 | | | % 263.25/56.92 | | | PRED_UNIFY: (17), (29) imply: % 263.25/56.92 | | | (30) $false % 263.25/56.92 | | | % 263.25/56.92 | | | CLOSE: (30) is inconsistent. % 263.25/56.92 | | | % 263.25/56.92 | | Case 2: % 263.25/56.92 | | | % 263.25/56.92 | | | (31) leq(n5, all_74_20) % 263.25/56.92 | | | (32) a_select3(q_ds1_filter, n0, n5) = all_74_0 & $i(all_74_0) % 263.25/56.92 | | | % 263.25/56.92 | | | ALPHA: (32) implies: % 263.25/56.92 | | | (33) a_select3(q_ds1_filter, n0, n5) = all_74_0 % 263.25/56.92 | | | % 263.25/56.92 | | | BETA: splitting (5) gives: % 263.25/56.92 | | | % 263.25/56.92 | | | Case 1: % 263.25/56.92 | | | | % 263.25/56.92 | | | | (34) ~ leq(n0, all_74_20) % 263.25/56.92 | | | | % 263.25/56.92 | | | | REDUCE: (19), (34) imply: % 263.25/56.92 | | | | (35) ~ leq(n0, n5) % 263.25/56.92 | | | | % 263.25/56.92 | | | | PRED_UNIFY: (14), (35) imply: % 263.25/56.92 | | | | (36) $false % 263.25/56.92 | | | | % 263.25/56.92 | | | | CLOSE: (36) is inconsistent. % 263.25/56.92 | | | | % 263.25/56.92 | | | Case 2: % 263.25/56.92 | | | | % 263.25/56.92 | | | | (37) ~ leq(n5, all_74_20) | (a_select3(q_ds1_filter, n5, n0) = % 263.25/56.92 | | | | all_74_1 & $i(all_74_1)) % 263.25/56.92 | | | | % 263.25/56.92 | | | | BETA: splitting (37) gives: % 263.25/56.92 | | | | % 263.25/56.92 | | | | Case 1: % 263.25/56.92 | | | | | % 263.25/56.92 | | | | | (38) ~ leq(n5, all_74_20) % 263.25/56.92 | | | | | % 263.25/56.92 | | | | | REDUCE: (19), (38) imply: % 263.25/56.92 | | | | | (39) ~ leq(n5, n5) % 263.25/56.92 | | | | | % 263.25/56.92 | | | | | PRED_UNIFY: (17), (39) imply: % 263.25/56.92 | | | | | (40) $false % 263.25/56.92 | | | | | % 263.25/56.92 | | | | | CLOSE: (40) is inconsistent. % 263.25/56.92 | | | | | % 263.25/56.92 | | | | Case 2: % 263.25/56.92 | | | | | % 263.25/56.92 | | | | | (41) a_select3(q_ds1_filter, n5, n0) = all_74_1 & $i(all_74_1) % 263.25/56.92 | | | | | % 263.25/56.92 | | | | | ALPHA: (41) implies: % 263.25/56.92 | | | | | (42) a_select3(q_ds1_filter, n5, n0) = all_74_1 % 263.25/56.92 | | | | | % 263.25/56.92 | | | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (11), (12), (13), % 263.25/56.92 | | | | | (14), (15), (16), (17), (18), (19), (20), (21), (33), (42) % 263.25/56.92 | | | | | are inconsistent by sub-proof #72. % 263.25/56.92 | | | | | % 263.25/56.92 | | | | End of split % 263.25/56.92 | | | | % 263.25/56.92 | | | End of split % 263.25/56.92 | | | % 263.25/56.92 | | End of split % 263.25/56.92 | | % 263.25/56.92 | End of split % 263.25/56.92 | % 263.25/56.92 End of proof % 263.25/56.92 % 263.25/56.92 Sub-proof #72 shows that the following formulas are inconsistent: % 263.25/56.92 ---------------------------------------------------------------- % 263.25/56.92 (1) pred(n1) = n0 % 263.25/56.92 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (pred(v2) = v1) | % 263.25/56.92 ~ (pred(v2) = v0)) % 263.25/56.92 (3) a_select3(q_ds1_filter, n0, n5) = all_74_0 % 263.25/56.92 (4) leq(all_74_18, n5) % 263.25/56.92 (5) pv57 = n5 | pv57 = n4 | pv57 = n3 | pv57 = n2 | pv57 = n1 % 263.25/56.92 (6) ~ (all_74_0 = all_74_1) % 263.25/56.92 (7) a_select3(q_ds1_filter, n5, n0) = all_74_1 % 263.25/56.92 (8) leq(n0, all_74_18) % 263.25/56.92 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (a_select3(q_ds1_filter, % 263.25/56.92 v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ leq(v1, all_74_20) | ~ % 263.25/56.92 leq(v0, all_74_20) | ~ leq(n0, v1) | ~ leq(n0, v0) | % 263.25/56.92 (a_select3(q_ds1_filter, v1, v0) = v2 & $i(v2))) % 263.25/56.92 (10) n6 = pv57 | pv57 = n5 | pv57 = n4 | pv57 = n3 | pv57 = n2 | pv57 = n1 % 263.25/56.92 (11) $i(all_74_18) % 263.25/56.92 (12) ~ gt(n0, n0) % 263.25/56.92 (13) $i(n0) % 263.25/56.92 (14) leq(n0, n5) % 263.25/56.92 (15) all_74_18 = n0 | gt(all_74_18, n0) % 263.25/56.92 (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 263.25/56.92 (v1 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 263.25/56.92 v0)) % 263.25/56.92 (17) leq(n5, n5) % 263.25/56.92 (18) pred(pv57) = all_74_18 % 263.25/56.92 (19) all_74_20 = n5 % 263.25/56.92 (20) $i(n5) % 263.25/56.92 (21) leq(n0, n0) % 263.25/56.92 % 263.25/56.92 Begin of proof % 263.25/56.92 | % 263.25/56.92 | BETA: splitting (15) gives: % 263.25/56.92 | % 263.25/56.92 | Case 1: % 263.25/56.92 | | % 263.25/56.92 | | (22) gt(all_74_18, n0) % 263.25/56.92 | | % 263.25/56.92 | | BETA: splitting (5) gives: % 263.25/56.92 | | % 263.25/56.92 | | Case 1: % 263.25/56.92 | | | % 263.25/56.92 | | | (23) pv57 = n1 % 263.25/56.92 | | | % 263.25/56.92 | | | REF_CLOSE: (1), (2), (12), (18), (22), (23) are inconsistent by sub-proof % 263.25/56.92 | | | #75. % 263.25/56.92 | | | % 263.25/56.92 | | Case 2: % 263.25/56.92 | | | % 263.25/56.92 | | | (24) ~ (pv57 = n1) % 263.25/56.92 | | | % 263.25/56.92 | | | BETA: splitting (10) gives: % 263.25/56.92 | | | % 263.25/56.92 | | | Case 1: % 263.25/56.92 | | | | % 263.25/56.92 | | | | (25) pv57 = n1 % 263.25/56.92 | | | | % 263.25/56.92 | | | | REDUCE: (24), (25) imply: % 263.25/56.92 | | | | (26) $false % 263.25/56.92 | | | | % 263.25/56.92 | | | | CLOSE: (26) is inconsistent. % 263.25/56.92 | | | | % 263.25/56.92 | | | Case 2: % 263.25/56.92 | | | | % 263.25/56.92 | | | | % 263.25/56.92 | | | | GROUND_INST: instantiating (9) with n0, n5, all_74_0, simplifying with % 263.25/56.92 | | | | (3), (13), (14), (20), (21) gives: % 263.25/56.92 | | | | (27) ~ leq(n5, all_74_20) | ~ leq(n0, all_74_20) | % 263.25/56.92 | | | | (a_select3(q_ds1_filter, n5, n0) = all_74_0 & $i(all_74_0)) % 263.25/56.92 | | | | % 263.25/56.92 | | | | REF_CLOSE: (6), (7), (14), (16), (17), (19), (27) are inconsistent by % 263.25/56.92 | | | | sub-proof #73. % 263.25/56.92 | | | | % 263.25/56.92 | | | End of split % 263.25/56.92 | | | % 263.25/56.92 | | End of split % 263.25/56.92 | | % 263.25/56.92 | Case 2: % 263.25/56.92 | | % 263.25/56.92 | | (28) all_74_18 = n0 % 263.25/56.92 | | % 263.25/56.92 | | GROUND_INST: instantiating (9) with n0, n5, all_74_0, simplifying with (3), % 263.25/56.92 | | (13), (14), (20), (21) gives: % 263.25/56.92 | | (29) ~ leq(n5, all_74_20) | ~ leq(n0, all_74_20) | % 263.25/56.92 | | (a_select3(q_ds1_filter, n5, n0) = all_74_0 & $i(all_74_0)) % 263.25/56.92 | | % 263.25/56.92 | | REF_CLOSE: (6), (7), (14), (16), (17), (19), (29) are inconsistent by % 263.25/56.92 | | sub-proof #73. % 263.25/56.92 | | % 263.25/56.92 | End of split % 263.25/56.92 | % 263.25/56.92 End of proof % 263.25/56.92 % 263.25/56.92 Sub-proof #73 shows that the following formulas are inconsistent: % 263.25/56.92 ---------------------------------------------------------------- % 263.25/56.92 (1) ~ (all_74_0 = all_74_1) % 263.25/56.92 (2) ~ leq(n5, all_74_20) | ~ leq(n0, all_74_20) | (a_select3(q_ds1_filter, % 263.25/56.92 n5, n0) = all_74_0 & $i(all_74_0)) % 263.25/56.92 (3) a_select3(q_ds1_filter, n5, n0) = all_74_1 % 263.25/56.92 (4) leq(n0, n5) % 263.25/56.92 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 263.25/56.92 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 263.25/56.92 v0)) % 263.25/56.92 (6) leq(n5, n5) % 263.25/56.92 (7) all_74_20 = n5 % 263.25/56.92 % 263.25/56.92 Begin of proof % 263.25/56.92 | % 263.25/56.92 | BETA: splitting (2) gives: % 263.25/56.92 | % 263.25/56.92 | Case 1: % 263.25/56.92 | | % 263.25/56.92 | | (8) ~ leq(n0, all_74_20) % 263.25/56.92 | | % 263.25/56.92 | | REDUCE: (7), (8) imply: % 263.25/56.92 | | (9) ~ leq(n0, n5) % 263.25/56.92 | | % 263.25/56.92 | | PRED_UNIFY: (4), (9) imply: % 263.25/56.92 | | (10) $false % 263.25/56.92 | | % 263.25/56.92 | | CLOSE: (10) is inconsistent. % 263.25/56.92 | | % 263.25/56.92 | Case 2: % 263.25/56.92 | | % 263.25/56.92 | | (11) ~ leq(n5, all_74_20) | (a_select3(q_ds1_filter, n5, n0) = all_74_0 % 263.25/56.92 | | & $i(all_74_0)) % 263.25/56.92 | | % 263.25/56.92 | | BETA: splitting (11) gives: % 263.25/56.92 | | % 263.25/56.92 | | Case 1: % 263.25/56.92 | | | % 263.25/56.92 | | | (12) ~ leq(n5, all_74_20) % 263.25/56.92 | | | % 263.25/56.92 | | | REDUCE: (7), (12) imply: % 263.25/56.92 | | | (13) ~ leq(n5, n5) % 263.25/56.92 | | | % 263.25/56.92 | | | PRED_UNIFY: (6), (13) imply: % 263.25/56.92 | | | (14) $false % 263.25/56.92 | | | % 263.25/56.92 | | | CLOSE: (14) is inconsistent. % 263.25/56.92 | | | % 263.25/56.92 | | Case 2: % 263.25/56.92 | | | % 263.25/56.92 | | | (15) a_select3(q_ds1_filter, n5, n0) = all_74_0 & $i(all_74_0) % 263.25/56.92 | | | % 263.25/56.92 | | | ALPHA: (15) implies: % 263.25/56.92 | | | (16) a_select3(q_ds1_filter, n5, n0) = all_74_0 % 263.25/56.92 | | | % 263.25/56.92 | | | REF_CLOSE: (1), (3), (5), (16) are inconsistent by sub-proof #74. % 263.25/56.92 | | | % 263.25/56.92 | | End of split % 263.25/56.92 | | % 263.25/56.92 | End of split % 263.25/56.92 | % 263.25/56.92 End of proof % 263.25/56.92 % 263.25/56.92 Sub-proof #74 shows that the following formulas are inconsistent: % 263.25/56.92 ---------------------------------------------------------------- % 263.25/56.92 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 263.25/56.92 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 263.25/56.92 v0)) % 263.25/56.92 (2) a_select3(q_ds1_filter, n5, n0) = all_74_0 % 263.25/56.92 (3) a_select3(q_ds1_filter, n5, n0) = all_74_1 % 263.25/56.92 (4) ~ (all_74_0 = all_74_1) % 263.25/56.92 % 263.25/56.92 Begin of proof % 263.25/56.92 | % 263.25/56.92 | GROUND_INST: instantiating (1) with all_74_1, all_74_0, n0, n5, q_ds1_filter, % 263.25/56.92 | simplifying with (2), (3) gives: % 263.25/56.92 | (5) all_74_0 = all_74_1 % 263.25/56.92 | % 263.25/56.92 | REDUCE: (4), (5) imply: % 263.25/56.92 | (6) $false % 263.25/56.92 | % 263.25/56.92 | CLOSE: (6) is inconsistent. % 263.25/56.92 | % 263.25/56.92 End of proof % 263.25/56.92 % 263.25/56.92 Sub-proof #75 shows that the following formulas are inconsistent: % 263.25/56.92 ---------------------------------------------------------------- % 263.25/56.92 (1) pred(n1) = n0 % 263.25/56.92 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (pred(v2) = v1) | % 263.25/56.92 ~ (pred(v2) = v0)) % 263.25/56.92 (3) pv57 = n1 % 263.25/56.92 (4) gt(all_74_18, n0) % 263.25/56.92 (5) ~ gt(n0, n0) % 263.25/56.92 (6) pred(pv57) = all_74_18 % 263.25/56.92 % 263.25/56.92 Begin of proof % 263.25/56.92 | % 263.25/56.92 | REDUCE: (3), (6) imply: % 263.25/56.92 | (7) pred(n1) = all_74_18 % 263.25/56.92 | % 263.25/56.92 | GROUND_INST: instantiating (2) with n0, all_74_18, n1, simplifying with (1), % 263.25/56.92 | (7) gives: % 263.25/56.92 | (8) all_74_18 = n0 % 263.25/56.92 | % 263.25/56.92 | REDUCE: (4), (8) imply: % 263.25/56.92 | (9) gt(n0, n0) % 263.25/56.92 | % 263.25/56.92 | PRED_UNIFY: (5), (9) imply: % 263.25/56.92 | (10) $false % 263.25/56.92 | % 263.25/56.92 | CLOSE: (10) is inconsistent. % 263.25/56.92 | % 263.25/56.92 End of proof % 263.25/56.92 % 263.25/56.92 Sub-proof #76 shows that the following formulas are inconsistent: % 263.25/56.92 ---------------------------------------------------------------- % 263.25/56.92 (1) gt(all_74_2, n0) % 263.25/56.92 (2) $i(n3) % 263.25/56.92 (3) $i(n4) % 263.25/56.92 (4) ! [v0: $i] : (v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0, n1) | ~ % 263.25/56.92 leq(n0, v0)) % 263.25/56.92 (5) pred(n2) = n1 % 263.25/56.93 (6) all_74_2 = n5 | all_74_2 = n4 | all_74_2 = n3 | all_74_2 = n2 | all_74_2 % 263.25/56.93 = n1 | all_74_2 = n0 % 263.25/56.93 (7) ~ (all_74_0 = all_74_1) % 263.25/56.93 (8) leq(n0, all_74_2) % 263.25/56.93 (9) leq(all_74_2, n5) % 263.25/56.93 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (a_select3(q_ds1_filter, % 263.25/56.93 v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ leq(v1, all_74_20) | ~ % 263.25/56.93 leq(v0, all_74_20) | ~ leq(n0, v1) | ~ leq(n0, v0) | % 263.25/56.93 (a_select3(q_ds1_filter, v1, v0) = v2 & $i(v2))) % 263.25/56.93 (11) leq(all_74_2, n4) % 263.25/56.93 (12) a_select3(q_ds1_filter, n0, all_74_2) = all_74_1 % 263.25/56.93 (13) ~ gt(n0, n0) % 263.25/56.93 (14) $i(n0) % 263.25/56.93 (15) pred(n3) = n2 % 263.25/56.93 (16) leq(n0, n5) % 263.25/56.93 (17) ! [v0: $i] : (v0 = n4 | v0 = n3 | v0 = n2 | v0 = n1 | v0 = n0 | ~ % 263.25/56.93 $i(v0) | ~ leq(v0, n4) | ~ leq(n0, v0)) % 263.25/56.93 (18) $i(all_74_2) % 263.25/56.93 (19) a_select3(q_ds1_filter, all_74_2, n0) = all_74_0 % 263.25/56.93 (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 263.25/56.93 (v1 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 263.25/56.93 v0)) % 263.25/56.93 (21) pred(n4) = n3 % 263.25/56.93 (22) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (pred(v1) = v2) | ~ % 263.25/56.93 $i(v1) | ~ $i(v0) | ~ gt(v1, v0) | leq(v0, v2)) % 263.25/56.93 (23) all_74_20 = n5 % 263.25/56.93 (24) $i(n2) % 263.25/56.93 (25) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ % 263.25/56.93 leq(v0, v1) | gt(v1, v0)) % 263.25/56.93 (26) leq(n0, n0) % 263.25/56.93 % 263.25/56.93 Begin of proof % 263.25/56.93 | % 263.25/56.93 | GROUND_INST: instantiating (17) with all_74_2, simplifying with (8), (11), % 263.25/56.93 | (18) gives: % 263.25/56.93 | (27) all_74_2 = n4 | all_74_2 = n3 | all_74_2 = n2 | all_74_2 = n1 | % 263.25/56.93 | all_74_2 = n0 % 263.25/56.93 | % 263.25/56.93 | GROUND_INST: instantiating (25) with all_74_2, n4, simplifying with (3), (11), % 263.25/56.93 | (18) gives: % 263.25/56.93 | (28) all_74_2 = n4 | gt(n4, all_74_2) % 263.25/56.93 | % 263.25/56.93 | BETA: splitting (6) gives: % 263.25/56.93 | % 263.25/56.93 | Case 1: % 263.25/56.93 | | % 263.25/56.93 | | (29) all_74_2 = n0 % 263.25/56.93 | | % 263.25/56.93 | | REDUCE: (1), (29) imply: % 263.25/56.93 | | (30) gt(n0, n0) % 263.25/56.93 | | % 263.25/56.93 | | PRED_UNIFY: (13), (30) imply: % 263.25/56.93 | | (31) $false % 263.25/56.93 | | % 263.25/56.93 | | CLOSE: (31) is inconsistent. % 263.25/56.93 | | % 263.25/56.93 | Case 2: % 263.25/56.93 | | % 263.25/56.93 | | (32) ~ (all_74_2 = n0) % 263.25/56.93 | | % 263.25/56.93 | | BETA: splitting (28) gives: % 263.25/56.93 | | % 263.25/56.93 | | Case 1: % 263.25/56.93 | | | % 263.25/56.93 | | | (33) gt(n4, all_74_2) % 263.25/56.93 | | | % 263.25/56.93 | | | GROUND_INST: instantiating (22) with all_74_2, n4, n3, simplifying with % 263.25/56.93 | | | (3), (18), (21), (33) gives: % 263.25/56.93 | | | (34) leq(all_74_2, n3) % 263.25/56.93 | | | % 263.25/56.93 | | | BETA: splitting (27) gives: % 263.25/56.93 | | | % 263.25/56.93 | | | Case 1: % 263.25/56.93 | | | | % 263.25/56.93 | | | | (35) all_74_2 = n0 % 263.25/56.93 | | | | % 263.25/56.93 | | | | REDUCE: (32), (35) imply: % 263.25/56.93 | | | | (36) $false % 263.25/56.93 | | | | % 263.25/56.93 | | | | CLOSE: (36) is inconsistent. % 263.25/56.93 | | | | % 263.25/56.93 | | | Case 2: % 263.25/56.93 | | | | % 263.25/56.93 | | | | % 263.25/56.93 | | | | GROUND_INST: instantiating (25) with all_74_2, n3, simplifying with (2), % 263.25/56.93 | | | | (18), (34) gives: % 263.25/56.93 | | | | (37) all_74_2 = n3 | gt(n3, all_74_2) % 263.25/56.93 | | | | % 263.25/56.93 | | | | BETA: splitting (37) gives: % 263.25/56.93 | | | | % 263.25/56.93 | | | | Case 1: % 263.25/56.93 | | | | | % 263.25/56.93 | | | | | (38) gt(n3, all_74_2) % 263.25/56.93 | | | | | % 263.25/56.93 | | | | | GROUND_INST: instantiating (22) with all_74_2, n3, n2, simplifying % 263.25/56.93 | | | | | with (2), (15), (18), (38) gives: % 263.25/56.93 | | | | | (39) leq(all_74_2, n2) % 263.25/56.93 | | | | | % 263.25/56.93 | | | | | GROUND_INST: instantiating (25) with all_74_2, n2, simplifying with % 263.25/56.93 | | | | | (18), (24), (39) gives: % 263.25/56.93 | | | | | (40) all_74_2 = n2 | gt(n2, all_74_2) % 263.25/56.93 | | | | | % 263.25/56.93 | | | | | BETA: splitting (40) gives: % 263.25/56.93 | | | | | % 263.25/56.93 | | | | | Case 1: % 263.25/56.93 | | | | | | % 263.25/56.93 | | | | | | (41) gt(n2, all_74_2) % 263.25/56.93 | | | | | | % 263.25/56.93 | | | | | | GROUND_INST: instantiating (22) with all_74_2, n2, n1, simplifying % 263.25/56.93 | | | | | | with (5), (18), (24), (41) gives: % 263.25/56.93 | | | | | | (42) leq(all_74_2, n1) % 263.25/56.93 | | | | | | % 263.25/56.93 | | | | | | GROUND_INST: instantiating (4) with all_74_2, simplifying with (8), % 263.25/56.93 | | | | | | (18), (42) gives: % 263.25/56.93 | | | | | | (43) all_74_2 = n1 | all_74_2 = n0 % 263.25/56.93 | | | | | | % 263.25/56.93 | | | | | | BETA: splitting (43) gives: % 263.25/56.93 | | | | | | % 263.25/56.93 | | | | | | Case 1: % 263.25/56.93 | | | | | | | % 263.25/56.93 | | | | | | | (44) all_74_2 = n0 % 263.25/56.93 | | | | | | | % 263.25/56.93 | | | | | | | REDUCE: (32), (44) imply: % 263.25/56.93 | | | | | | | (45) $false % 263.25/56.93 | | | | | | | % 263.25/56.93 | | | | | | | CLOSE: (45) is inconsistent. % 263.25/56.93 | | | | | | | % 263.25/56.93 | | | | | | Case 2: % 263.25/56.93 | | | | | | | % 263.25/56.93 | | | | | | | (46) all_74_2 = n1 % 263.25/56.93 | | | | | | | % 263.25/56.93 | | | | | | | REDUCE: (19), (46) imply: % 263.25/56.93 | | | | | | | (47) a_select3(q_ds1_filter, n1, n0) = all_74_0 % 263.25/56.93 | | | | | | | % 263.25/56.93 | | | | | | | REDUCE: (12), (46) imply: % 263.25/56.93 | | | | | | | (48) a_select3(q_ds1_filter, n0, n1) = all_74_1 % 263.25/56.93 | | | | | | | % 263.25/56.93 | | | | | | | REDUCE: (18), (46) imply: % 263.25/56.93 | | | | | | | (49) $i(n1) % 263.25/56.93 | | | | | | | % 263.25/56.93 | | | | | | | REDUCE: (9), (46) imply: % 263.25/56.93 | | | | | | | (50) leq(n1, n5) % 263.25/56.93 | | | | | | | % 263.25/56.93 | | | | | | | REDUCE: (8), (46) imply: % 263.25/56.93 | | | | | | | (51) leq(n0, n1) % 263.25/56.93 | | | | | | | % 263.25/56.93 | | | | | | | GROUND_INST: instantiating (10) with n0, n1, all_74_1, simplifying % 263.25/56.93 | | | | | | | with (14), (26), (48), (49), (51) gives: % 263.25/56.93 | | | | | | | (52) ~ leq(n1, all_74_20) | ~ leq(n0, all_74_20) | % 263.25/56.93 | | | | | | | (a_select3(q_ds1_filter, n1, n0) = all_74_1 & % 263.25/56.93 | | | | | | | $i(all_74_1)) % 263.25/56.93 | | | | | | | % 263.25/56.93 | | | | | | | BETA: splitting (52) gives: % 263.25/56.93 | | | | | | | % 263.25/56.93 | | | | | | | Case 1: % 263.25/56.93 | | | | | | | | % 263.25/56.93 | | | | | | | | (53) ~ leq(n0, all_74_20) % 263.25/56.93 | | | | | | | | % 263.25/56.93 | | | | | | | | REDUCE: (23), (53) imply: % 263.25/56.93 | | | | | | | | (54) ~ leq(n0, n5) % 263.25/56.93 | | | | | | | | % 263.25/56.93 | | | | | | | | PRED_UNIFY: (16), (54) imply: % 263.25/56.93 | | | | | | | | (55) $false % 263.25/56.93 | | | | | | | | % 263.25/56.93 | | | | | | | | CLOSE: (55) is inconsistent. % 263.25/56.93 | | | | | | | | % 263.25/56.93 | | | | | | | Case 2: % 263.25/56.93 | | | | | | | | % 263.25/56.93 | | | | | | | | (56) ~ leq(n1, all_74_20) | (a_select3(q_ds1_filter, n1, n0) % 263.25/56.93 | | | | | | | | = all_74_1 & $i(all_74_1)) % 263.25/56.93 | | | | | | | | % 263.25/56.93 | | | | | | | | BETA: splitting (56) gives: % 263.25/56.93 | | | | | | | | % 263.25/56.93 | | | | | | | | Case 1: % 263.25/56.93 | | | | | | | | | % 263.25/56.93 | | | | | | | | | (57) ~ leq(n1, all_74_20) % 263.25/56.93 | | | | | | | | | % 263.25/56.93 | | | | | | | | | REDUCE: (23), (57) imply: % 263.25/56.93 | | | | | | | | | (58) ~ leq(n1, n5) % 263.25/56.93 | | | | | | | | | % 263.25/56.93 | | | | | | | | | PRED_UNIFY: (50), (58) imply: % 263.25/56.93 | | | | | | | | | (59) $false % 263.25/56.93 | | | | | | | | | % 263.25/56.93 | | | | | | | | | CLOSE: (59) is inconsistent. % 263.25/56.93 | | | | | | | | | % 263.25/56.93 | | | | | | | | Case 2: % 263.25/56.93 | | | | | | | | | % 263.25/56.93 | | | | | | | | | (60) a_select3(q_ds1_filter, n1, n0) = all_74_1 & % 263.25/56.93 | | | | | | | | | $i(all_74_1) % 263.25/56.93 | | | | | | | | | % 263.25/56.93 | | | | | | | | | ALPHA: (60) implies: % 263.25/56.93 | | | | | | | | | (61) a_select3(q_ds1_filter, n1, n0) = all_74_1 % 263.25/56.93 | | | | | | | | | % 263.25/56.93 | | | | | | | | | REF_CLOSE: (7), (20), (47), (61) are inconsistent by sub-proof % 263.25/56.93 | | | | | | | | | #80. % 263.25/56.93 | | | | | | | | | % 263.25/56.93 | | | | | | | | End of split % 263.25/56.93 | | | | | | | | % 263.25/56.93 | | | | | | | End of split % 263.25/56.93 | | | | | | | % 263.25/56.93 | | | | | | End of split % 263.25/56.93 | | | | | | % 263.25/56.93 | | | | | Case 2: % 263.25/56.93 | | | | | | % 263.25/56.93 | | | | | | (62) all_74_2 = n2 % 263.25/56.93 | | | | | | % 263.25/56.93 | | | | | | REDUCE: (19), (62) imply: % 263.25/56.93 | | | | | | (63) a_select3(q_ds1_filter, n2, n0) = all_74_0 % 263.25/56.93 | | | | | | % 263.25/56.93 | | | | | | REDUCE: (12), (62) imply: % 263.25/56.93 | | | | | | (64) a_select3(q_ds1_filter, n0, n2) = all_74_1 % 263.25/56.93 | | | | | | % 263.25/56.93 | | | | | | REDUCE: (9), (62) imply: % 263.25/56.93 | | | | | | (65) leq(n2, n5) % 263.25/56.93 | | | | | | % 263.25/56.93 | | | | | | REDUCE: (8), (62) imply: % 263.25/56.93 | | | | | | (66) leq(n0, n2) % 263.25/56.93 | | | | | | % 263.25/56.93 | | | | | | GROUND_INST: instantiating (10) with n0, n2, all_74_1, simplifying % 263.25/56.93 | | | | | | with (14), (24), (26), (64), (66) gives: % 263.25/56.93 | | | | | | (67) ~ leq(n2, all_74_20) | ~ leq(n0, all_74_20) | % 263.25/56.93 | | | | | | (a_select3(q_ds1_filter, n2, n0) = all_74_1 & $i(all_74_1)) % 263.25/56.93 | | | | | | % 263.25/56.93 | | | | | | BETA: splitting (67) gives: % 263.25/56.93 | | | | | | % 263.25/56.93 | | | | | | Case 1: % 263.25/56.93 | | | | | | | % 263.25/56.93 | | | | | | | (68) ~ leq(n0, all_74_20) % 263.25/56.93 | | | | | | | % 263.25/56.93 | | | | | | | REDUCE: (23), (68) imply: % 263.25/56.93 | | | | | | | (69) ~ leq(n0, n5) % 263.25/56.93 | | | | | | | % 263.25/56.93 | | | | | | | PRED_UNIFY: (16), (69) imply: % 263.25/56.93 | | | | | | | (70) $false % 263.25/56.93 | | | | | | | % 263.25/56.93 | | | | | | | CLOSE: (70) is inconsistent. % 263.25/56.93 | | | | | | | % 263.25/56.93 | | | | | | Case 2: % 263.25/56.93 | | | | | | | % 263.25/56.93 | | | | | | | (71) ~ leq(n2, all_74_20) | (a_select3(q_ds1_filter, n2, n0) = % 263.25/56.93 | | | | | | | all_74_1 & $i(all_74_1)) % 263.25/56.93 | | | | | | | % 263.25/56.93 | | | | | | | BETA: splitting (71) gives: % 263.25/56.93 | | | | | | | % 263.25/56.93 | | | | | | | Case 1: % 263.25/56.93 | | | | | | | | % 263.25/56.93 | | | | | | | | (72) ~ leq(n2, all_74_20) % 263.25/56.93 | | | | | | | | % 263.25/56.93 | | | | | | | | REDUCE: (23), (72) imply: % 263.25/56.93 | | | | | | | | (73) ~ leq(n2, n5) % 263.25/56.93 | | | | | | | | % 263.25/56.93 | | | | | | | | PRED_UNIFY: (65), (73) imply: % 263.25/56.93 | | | | | | | | (74) $false % 263.25/56.93 | | | | | | | | % 263.25/56.93 | | | | | | | | CLOSE: (74) is inconsistent. % 263.25/56.93 | | | | | | | | % 263.25/56.93 | | | | | | | Case 2: % 263.25/56.93 | | | | | | | | % 263.25/56.93 | | | | | | | | (75) a_select3(q_ds1_filter, n2, n0) = all_74_1 & % 263.25/56.93 | | | | | | | | $i(all_74_1) % 263.25/56.93 | | | | | | | | % 263.25/56.93 | | | | | | | | ALPHA: (75) implies: % 263.25/56.93 | | | | | | | | (76) a_select3(q_ds1_filter, n2, n0) = all_74_1 % 263.25/56.93 | | | | | | | | % 263.25/56.93 | | | | | | | | REF_CLOSE: (7), (20), (63), (76) are inconsistent by sub-proof % 263.25/56.93 | | | | | | | | #79. % 263.25/56.93 | | | | | | | | % 263.25/56.93 | | | | | | | End of split % 263.25/56.93 | | | | | | | % 263.25/56.93 | | | | | | End of split % 263.25/56.93 | | | | | | % 263.25/56.93 | | | | | End of split % 263.25/56.93 | | | | | % 263.25/56.93 | | | | Case 2: % 263.25/56.93 | | | | | % 263.25/56.93 | | | | | (77) all_74_2 = n3 % 263.25/56.93 | | | | | % 263.25/56.93 | | | | | REDUCE: (19), (77) imply: % 263.25/56.93 | | | | | (78) a_select3(q_ds1_filter, n3, n0) = all_74_0 % 263.25/56.93 | | | | | % 263.25/56.93 | | | | | REDUCE: (12), (77) imply: % 263.25/56.93 | | | | | (79) a_select3(q_ds1_filter, n0, n3) = all_74_1 % 263.25/56.93 | | | | | % 263.25/56.93 | | | | | REDUCE: (9), (77) imply: % 263.25/56.93 | | | | | (80) leq(n3, n5) % 263.25/56.93 | | | | | % 263.25/56.93 | | | | | REDUCE: (8), (77) imply: % 263.25/56.93 | | | | | (81) leq(n0, n3) % 263.25/56.93 | | | | | % 263.25/56.93 | | | | | GROUND_INST: instantiating (10) with n0, n3, all_74_1, simplifying % 263.25/56.93 | | | | | with (2), (14), (26), (79), (81) gives: % 263.25/56.93 | | | | | (82) ~ leq(n3, all_74_20) | ~ leq(n0, all_74_20) | % 263.25/56.93 | | | | | (a_select3(q_ds1_filter, n3, n0) = all_74_1 & $i(all_74_1)) % 263.25/56.93 | | | | | % 263.25/56.93 | | | | | BETA: splitting (82) gives: % 263.25/56.93 | | | | | % 263.25/56.93 | | | | | Case 1: % 263.25/56.93 | | | | | | % 263.25/56.93 | | | | | | (83) ~ leq(n0, all_74_20) % 263.25/56.93 | | | | | | % 263.25/56.93 | | | | | | REDUCE: (23), (83) imply: % 263.25/56.93 | | | | | | (84) ~ leq(n0, n5) % 263.25/56.93 | | | | | | % 263.25/56.93 | | | | | | PRED_UNIFY: (16), (84) imply: % 263.25/56.93 | | | | | | (85) $false % 263.25/56.93 | | | | | | % 263.25/56.93 | | | | | | CLOSE: (85) is inconsistent. % 263.25/56.93 | | | | | | % 263.25/56.93 | | | | | Case 2: % 263.25/56.93 | | | | | | % 263.25/56.93 | | | | | | (86) ~ leq(n3, all_74_20) | (a_select3(q_ds1_filter, n3, n0) = % 263.25/56.93 | | | | | | all_74_1 & $i(all_74_1)) % 263.25/56.93 | | | | | | % 263.25/56.93 | | | | | | BETA: splitting (86) gives: % 263.25/56.93 | | | | | | % 263.25/56.93 | | | | | | Case 1: % 263.25/56.93 | | | | | | | % 263.25/56.93 | | | | | | | (87) ~ leq(n3, all_74_20) % 263.25/56.93 | | | | | | | % 263.25/56.93 | | | | | | | REDUCE: (23), (87) imply: % 263.25/56.93 | | | | | | | (88) ~ leq(n3, n5) % 263.25/56.93 | | | | | | | % 263.25/56.93 | | | | | | | PRED_UNIFY: (80), (88) imply: % 263.25/56.93 | | | | | | | (89) $false % 263.25/56.93 | | | | | | | % 263.25/56.93 | | | | | | | CLOSE: (89) is inconsistent. % 263.25/56.93 | | | | | | | % 263.25/56.93 | | | | | | Case 2: % 263.25/56.93 | | | | | | | % 263.25/56.93 | | | | | | | (90) a_select3(q_ds1_filter, n3, n0) = all_74_1 & $i(all_74_1) % 263.25/56.93 | | | | | | | % 263.25/56.93 | | | | | | | ALPHA: (90) implies: % 263.25/56.93 | | | | | | | (91) a_select3(q_ds1_filter, n3, n0) = all_74_1 % 263.25/56.93 | | | | | | | % 263.25/56.93 | | | | | | | REF_CLOSE: (7), (20), (78), (91) are inconsistent by sub-proof % 263.25/56.93 | | | | | | | #78. % 263.25/56.93 | | | | | | | % 263.25/56.93 | | | | | | End of split % 263.25/56.93 | | | | | | % 263.25/56.93 | | | | | End of split % 263.25/56.93 | | | | | % 263.25/56.93 | | | | End of split % 263.25/56.93 | | | | % 263.25/56.93 | | | End of split % 263.25/56.93 | | | % 263.25/56.93 | | Case 2: % 263.25/56.93 | | | % 263.25/56.93 | | | (92) all_74_2 = n4 % 263.25/56.93 | | | % 263.25/56.93 | | | REDUCE: (19), (92) imply: % 263.25/56.93 | | | (93) a_select3(q_ds1_filter, n4, n0) = all_74_0 % 263.25/56.93 | | | % 263.25/56.93 | | | REDUCE: (12), (92) imply: % 263.25/56.93 | | | (94) a_select3(q_ds1_filter, n0, n4) = all_74_1 % 263.25/56.93 | | | % 263.25/56.93 | | | REDUCE: (9), (92) imply: % 263.25/56.93 | | | (95) leq(n4, n5) % 263.25/56.93 | | | % 263.25/56.93 | | | REDUCE: (8), (92) imply: % 263.25/56.93 | | | (96) leq(n0, n4) % 263.25/56.93 | | | % 263.25/56.93 | | | GROUND_INST: instantiating (10) with n0, n4, all_74_1, simplifying with % 263.25/56.93 | | | (3), (14), (26), (94), (96) gives: % 263.25/56.93 | | | (97) ~ leq(n4, all_74_20) | ~ leq(n0, all_74_20) | % 263.25/56.93 | | | (a_select3(q_ds1_filter, n4, n0) = all_74_1 & $i(all_74_1)) % 263.25/56.93 | | | % 263.25/56.93 | | | BETA: splitting (97) gives: % 263.25/56.93 | | | % 263.25/56.93 | | | Case 1: % 263.25/56.93 | | | | % 263.25/56.93 | | | | (98) ~ leq(n0, all_74_20) % 263.25/56.93 | | | | % 263.25/56.93 | | | | REDUCE: (23), (98) imply: % 263.25/56.93 | | | | (99) ~ leq(n0, n5) % 263.25/56.93 | | | | % 263.25/56.93 | | | | PRED_UNIFY: (16), (99) imply: % 263.25/56.93 | | | | (100) $false % 263.25/56.93 | | | | % 263.25/56.93 | | | | CLOSE: (100) is inconsistent. % 263.25/56.93 | | | | % 263.25/56.93 | | | Case 2: % 263.25/56.93 | | | | % 263.25/56.93 | | | | (101) ~ leq(n4, all_74_20) | (a_select3(q_ds1_filter, n4, n0) = % 263.25/56.93 | | | | all_74_1 & $i(all_74_1)) % 263.25/56.93 | | | | % 263.25/56.93 | | | | BETA: splitting (101) gives: % 263.25/56.93 | | | | % 263.25/56.93 | | | | Case 1: % 263.25/56.93 | | | | | % 263.25/56.93 | | | | | (102) ~ leq(n4, all_74_20) % 263.25/56.93 | | | | | % 263.25/56.93 | | | | | REDUCE: (23), (102) imply: % 263.25/56.94 | | | | | (103) ~ leq(n4, n5) % 263.25/56.94 | | | | | % 263.25/56.94 | | | | | PRED_UNIFY: (95), (103) imply: % 263.25/56.94 | | | | | (104) $false % 263.25/56.94 | | | | | % 263.25/56.94 | | | | | CLOSE: (104) is inconsistent. % 263.25/56.94 | | | | | % 263.25/56.94 | | | | Case 2: % 263.25/56.94 | | | | | % 263.25/56.94 | | | | | (105) a_select3(q_ds1_filter, n4, n0) = all_74_1 & $i(all_74_1) % 263.25/56.94 | | | | | % 263.25/56.94 | | | | | ALPHA: (105) implies: % 263.25/56.94 | | | | | (106) a_select3(q_ds1_filter, n4, n0) = all_74_1 % 263.25/56.94 | | | | | % 263.25/56.94 | | | | | REF_CLOSE: (7), (20), (93), (106) are inconsistent by sub-proof #77. % 263.25/56.94 | | | | | % 263.25/56.94 | | | | End of split % 263.25/56.94 | | | | % 263.25/56.94 | | | End of split % 263.25/56.94 | | | % 263.25/56.94 | | End of split % 263.25/56.94 | | % 263.25/56.94 | End of split % 263.25/56.94 | % 263.25/56.94 End of proof % 263.25/56.94 % 263.25/56.94 Sub-proof #77 shows that the following formulas are inconsistent: % 263.25/56.94 ---------------------------------------------------------------- % 263.25/56.94 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 263.25/56.94 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 263.25/56.94 v0)) % 263.25/56.94 (2) a_select3(q_ds1_filter, n4, n0) = all_74_0 % 263.25/56.94 (3) a_select3(q_ds1_filter, n4, n0) = all_74_1 % 263.25/56.94 (4) ~ (all_74_0 = all_74_1) % 263.25/56.94 % 263.25/56.94 Begin of proof % 263.25/56.94 | % 263.25/56.94 | GROUND_INST: instantiating (1) with all_74_1, all_74_0, n0, n4, q_ds1_filter, % 263.25/56.94 | simplifying with (2), (3) gives: % 263.25/56.94 | (5) all_74_0 = all_74_1 % 263.25/56.94 | % 263.25/56.94 | REDUCE: (4), (5) imply: % 263.25/56.94 | (6) $false % 263.25/56.94 | % 263.25/56.94 | CLOSE: (6) is inconsistent. % 263.25/56.94 | % 263.25/56.94 End of proof % 263.25/56.94 % 263.25/56.94 Sub-proof #78 shows that the following formulas are inconsistent: % 263.25/56.94 ---------------------------------------------------------------- % 263.25/56.94 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 263.25/56.94 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 263.25/56.94 v0)) % 263.25/56.94 (2) a_select3(q_ds1_filter, n3, n0) = all_74_0 % 263.25/56.94 (3) a_select3(q_ds1_filter, n3, n0) = all_74_1 % 263.25/56.94 (4) ~ (all_74_0 = all_74_1) % 263.25/56.94 % 263.25/56.94 Begin of proof % 263.25/56.94 | % 263.25/56.94 | GROUND_INST: instantiating (1) with all_74_1, all_74_0, n0, n3, q_ds1_filter, % 263.25/56.94 | simplifying with (2), (3) gives: % 263.25/56.94 | (5) all_74_0 = all_74_1 % 263.25/56.94 | % 263.25/56.94 | REDUCE: (4), (5) imply: % 263.25/56.94 | (6) $false % 263.25/56.94 | % 263.25/56.94 | CLOSE: (6) is inconsistent. % 263.25/56.94 | % 263.25/56.94 End of proof % 263.25/56.94 % 263.25/56.94 Sub-proof #79 shows that the following formulas are inconsistent: % 263.25/56.94 ---------------------------------------------------------------- % 263.25/56.94 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 263.25/56.94 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 263.25/56.94 v0)) % 263.25/56.94 (2) a_select3(q_ds1_filter, n2, n0) = all_74_0 % 263.25/56.94 (3) a_select3(q_ds1_filter, n2, n0) = all_74_1 % 263.25/56.94 (4) ~ (all_74_0 = all_74_1) % 263.25/56.94 % 263.25/56.94 Begin of proof % 263.25/56.94 | % 263.25/56.94 | GROUND_INST: instantiating (1) with all_74_1, all_74_0, n0, n2, q_ds1_filter, % 263.25/56.94 | simplifying with (2), (3) gives: % 263.25/56.94 | (5) all_74_0 = all_74_1 % 263.25/56.94 | % 263.25/56.94 | REDUCE: (4), (5) imply: % 263.25/56.94 | (6) $false % 263.25/56.94 | % 263.25/56.94 | CLOSE: (6) is inconsistent. % 263.25/56.94 | % 263.25/56.94 End of proof % 263.25/56.94 % 263.25/56.94 Sub-proof #80 shows that the following formulas are inconsistent: % 263.25/56.94 ---------------------------------------------------------------- % 263.25/56.94 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 263.25/56.94 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 263.25/56.94 v0)) % 263.25/56.94 (2) a_select3(q_ds1_filter, n1, n0) = all_74_0 % 263.25/56.94 (3) a_select3(q_ds1_filter, n1, n0) = all_74_1 % 263.25/56.94 (4) ~ (all_74_0 = all_74_1) % 263.25/56.94 % 263.25/56.94 Begin of proof % 263.25/56.94 | % 263.25/56.94 | GROUND_INST: instantiating (1) with all_74_1, all_74_0, n0, n1, q_ds1_filter, % 263.25/56.94 | simplifying with (2), (3) gives: % 263.25/56.94 | (5) all_74_0 = all_74_1 % 263.25/56.94 | % 263.25/56.94 | REDUCE: (4), (5) imply: % 263.25/56.94 | (6) $false % 263.25/56.94 | % 263.25/56.94 | CLOSE: (6) is inconsistent. % 263.25/56.94 | % 263.25/56.94 End of proof % 263.25/56.94 % 263.25/56.94 Sub-proof #81 shows that the following formulas are inconsistent: % 263.25/56.94 ---------------------------------------------------------------- % 263.25/56.94 (1) gt(all_74_2, n0) % 263.25/56.94 (2) $i(n3) % 263.25/56.94 (3) all_74_3 = n6 | all_74_3 = n5 | all_74_3 = n4 | all_74_3 = n3 | all_74_3 % 263.25/56.94 = n2 | all_74_3 = n1 | all_74_3 = n0 % 263.25/56.94 (4) $i(n4) % 263.25/56.94 (5) ! [v0: $i] : (v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0, n1) | ~ % 263.25/56.94 leq(n0, v0)) % 263.25/56.94 (6) a_select3(q_ds1_filter, all_74_2, all_74_3) = all_74_0 % 263.25/56.94 (7) a_select3(q_ds1_filter, all_74_3, all_74_2) = all_74_1 % 263.25/56.94 (8) pred(n2) = n1 % 263.25/56.94 (9) leq(n0, all_74_3) % 263.25/56.94 (10) all_74_2 = n5 | all_74_2 = n4 | all_74_2 = n3 | all_74_2 = n2 | all_74_2 % 263.25/56.94 = n1 | all_74_2 = n0 % 263.25/56.94 (11) ~ (all_74_0 = all_74_1) % 263.25/56.94 (12) gt(all_74_3, n0) % 263.25/56.94 (13) pred(n5) = n4 % 263.25/56.94 (14) leq(n0, all_74_2) % 263.25/56.94 (15) leq(all_74_2, n5) % 263.25/56.94 (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (a_select3(q_ds1_filter, % 263.25/56.94 v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ leq(v1, all_74_20) | ~ % 263.25/56.94 leq(v0, all_74_20) | ~ leq(n0, v1) | ~ leq(n0, v0) | % 263.25/56.94 (a_select3(q_ds1_filter, v1, v0) = v2 & $i(v2))) % 263.25/56.94 (17) $i(all_74_3) % 263.25/56.94 (18) all_74_3 = n5 | all_74_3 = n4 | all_74_3 = n3 | all_74_3 = n2 | all_74_3 % 263.25/56.94 = n1 | all_74_3 = n0 % 263.25/56.94 (19) ~ gt(n0, n0) % 263.25/56.94 (20) pred(n3) = n2 % 263.25/56.94 (21) all_74_3 = n5 | gt(n5, all_74_3) % 263.25/56.94 (22) ! [v0: $i] : (v0 = n4 | v0 = n3 | v0 = n2 | v0 = n1 | v0 = n0 | ~ % 263.25/56.94 $i(v0) | ~ leq(v0, n4) | ~ leq(n0, v0)) % 263.25/56.94 (23) $i(all_74_2) % 263.25/56.94 (24) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 263.25/56.94 (v1 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 263.25/56.94 v0)) % 263.25/56.94 (25) pred(n4) = n3 % 263.25/56.94 (26) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (pred(v1) = v2) | ~ % 263.25/56.94 $i(v1) | ~ $i(v0) | ~ gt(v1, v0) | leq(v0, v2)) % 263.25/56.94 (27) all_74_2 = n5 | gt(n5, all_74_2) % 263.25/56.94 (28) all_74_20 = n5 % 263.25/56.94 (29) $i(n2) % 263.25/56.94 (30) $i(n5) % 263.25/56.94 (31) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ % 263.25/56.94 leq(v0, v1) | gt(v1, v0)) % 263.25/56.94 (32) leq(all_74_3, n5) % 263.25/56.94 % 263.25/56.94 Begin of proof % 263.25/56.94 | % 263.25/56.94 | BETA: splitting (27) gives: % 263.25/56.94 | % 263.25/56.94 | Case 1: % 263.25/56.94 | | % 263.25/56.94 | | (33) gt(n5, all_74_2) % 263.25/56.94 | | % 263.25/56.94 | | GROUND_INST: instantiating (26) with all_74_2, n5, n4, simplifying with % 263.25/56.94 | | (13), (23), (30), (33) gives: % 263.25/56.94 | | (34) leq(all_74_2, n4) % 263.25/56.94 | | % 263.25/56.94 | | BETA: splitting (21) gives: % 263.25/56.94 | | % 263.25/56.94 | | Case 1: % 263.25/56.94 | | | % 263.25/56.94 | | | (35) gt(n5, all_74_3) % 263.25/56.94 | | | % 263.25/56.94 | | | GROUND_INST: instantiating (26) with all_74_3, n5, n4, simplifying with % 263.25/56.94 | | | (13), (17), (30), (35) gives: % 263.25/56.94 | | | (36) leq(all_74_3, n4) % 263.25/56.94 | | | % 263.25/56.94 | | | GROUND_INST: instantiating (31) with all_74_2, n4, simplifying with (4), % 263.25/56.94 | | | (23), (34) gives: % 263.25/56.94 | | | (37) all_74_2 = n4 | gt(n4, all_74_2) % 263.25/56.94 | | | % 263.25/56.94 | | | BETA: splitting (10) gives: % 263.25/56.94 | | | % 263.25/56.94 | | | Case 1: % 263.25/56.94 | | | | % 263.25/56.94 | | | | (38) all_74_2 = n0 % 263.25/56.94 | | | | % 263.25/56.94 | | | | REDUCE: (1), (38) imply: % 263.25/56.94 | | | | (39) gt(n0, n0) % 263.25/56.94 | | | | % 263.25/56.94 | | | | PRED_UNIFY: (19), (39) imply: % 263.25/56.94 | | | | (40) $false % 263.25/56.94 | | | | % 263.25/56.94 | | | | CLOSE: (40) is inconsistent. % 263.25/56.94 | | | | % 263.25/56.94 | | | Case 2: % 263.25/56.94 | | | | % 263.25/56.94 | | | | (41) ~ (all_74_2 = n0) % 263.25/56.94 | | | | % 263.25/56.94 | | | | BETA: splitting (18) gives: % 263.25/56.94 | | | | % 263.25/56.94 | | | | Case 1: % 263.25/56.94 | | | | | % 263.25/56.94 | | | | | (42) all_74_3 = n0 % 263.25/56.94 | | | | | % 263.25/56.94 | | | | | REDUCE: (12), (42) imply: % 263.25/56.94 | | | | | (43) gt(n0, n0) % 263.25/56.94 | | | | | % 263.25/56.94 | | | | | PRED_UNIFY: (19), (43) imply: % 263.25/56.94 | | | | | (44) $false % 263.25/56.94 | | | | | % 263.25/56.94 | | | | | CLOSE: (44) is inconsistent. % 263.25/56.94 | | | | | % 263.25/56.94 | | | | Case 2: % 263.25/56.94 | | | | | % 263.25/56.94 | | | | | (45) ~ (all_74_3 = n0) % 263.25/56.94 | | | | | % 263.25/56.94 | | | | | GROUND_INST: instantiating (31) with all_74_3, n4, simplifying with % 263.25/56.94 | | | | | (4), (17), (36) gives: % 263.25/56.94 | | | | | (46) all_74_3 = n4 | gt(n4, all_74_3) % 263.25/56.94 | | | | | % 263.25/56.94 | | | | | REF_CLOSE: (2), (4), (5), (6), (7), (8), (9), (11), (14), (15), (16), % 263.25/56.94 | | | | | (17), (20), (23), (24), (25), (26), (28), (29), (31), (32), % 263.25/56.94 | | | | | (37), (41), (45), (46) are inconsistent by sub-proof #87. % 263.25/56.94 | | | | | % 263.25/56.94 | | | | End of split % 263.25/56.94 | | | | % 263.25/56.94 | | | End of split % 263.25/56.94 | | | % 263.25/56.94 | | Case 2: % 263.25/56.94 | | | % 263.25/56.94 | | | (47) all_74_3 = n5 % 263.25/56.94 | | | % 263.25/56.94 | | | REDUCE: (6), (47) imply: % 263.25/56.94 | | | (48) a_select3(q_ds1_filter, all_74_2, n5) = all_74_0 % 263.25/56.94 | | | % 263.25/56.94 | | | REDUCE: (7), (47) imply: % 263.25/56.94 | | | (49) a_select3(q_ds1_filter, n5, all_74_2) = all_74_1 % 263.25/56.94 | | | % 263.25/56.94 | | | REDUCE: (32), (47) imply: % 263.25/56.94 | | | (50) leq(n5, n5) % 263.25/56.94 | | | % 263.25/56.94 | | | REDUCE: (9), (47) imply: % 263.25/56.94 | | | (51) leq(n0, n5) % 263.25/56.94 | | | % 263.25/56.94 | | | GROUND_INST: instantiating (22) with all_74_2, simplifying with (14), % 263.25/56.94 | | | (23), (34) gives: % 263.25/56.94 | | | (52) all_74_2 = n4 | all_74_2 = n3 | all_74_2 = n2 | all_74_2 = n1 | % 263.25/56.94 | | | all_74_2 = n0 % 263.25/56.94 | | | % 263.25/56.94 | | | GROUND_INST: instantiating (31) with all_74_2, n4, simplifying with (4), % 263.25/56.94 | | | (23), (34) gives: % 263.25/56.94 | | | (53) all_74_2 = n4 | gt(n4, all_74_2) % 263.25/56.94 | | | % 263.25/56.94 | | | BETA: splitting (10) gives: % 263.25/56.94 | | | % 263.25/56.94 | | | Case 1: % 263.25/56.94 | | | | % 263.25/56.94 | | | | (54) all_74_2 = n0 % 263.25/56.94 | | | | % 263.25/56.94 | | | | REDUCE: (1), (54) imply: % 263.25/56.94 | | | | (55) gt(n0, n0) % 263.25/56.94 | | | | % 263.25/56.94 | | | | PRED_UNIFY: (19), (55) imply: % 263.25/56.94 | | | | (56) $false % 263.25/56.94 | | | | % 263.25/56.94 | | | | CLOSE: (56) is inconsistent. % 263.25/56.94 | | | | % 263.25/56.94 | | | Case 2: % 263.25/56.94 | | | | % 263.25/56.94 | | | | (57) ~ (all_74_2 = n0) % 263.25/56.94 | | | | % 263.25/56.94 | | | | REF_CLOSE: (2), (4), (5), (8), (11), (14), (15), (16), (20), (23), (24), % 263.25/56.94 | | | | (25), (26), (28), (29), (30), (31), (48), (49), (50), (51), % 263.25/56.94 | | | | (52), (53), (57) are inconsistent by sub-proof #83. % 263.25/56.94 | | | | % 263.25/56.94 | | | End of split % 263.25/56.94 | | | % 263.25/56.94 | | End of split % 263.25/56.94 | | % 263.25/56.94 | Case 2: % 263.25/56.94 | | % 263.25/56.94 | | (58) all_74_2 = n5 % 263.25/56.94 | | % 263.25/56.94 | | REDUCE: (6), (58) imply: % 263.25/56.94 | | (59) a_select3(q_ds1_filter, n5, all_74_3) = all_74_0 % 263.25/56.94 | | % 263.25/56.94 | | REDUCE: (7), (58) imply: % 263.25/56.94 | | (60) a_select3(q_ds1_filter, all_74_3, n5) = all_74_1 % 263.25/56.94 | | % 263.25/56.94 | | REDUCE: (15), (58) imply: % 263.25/56.94 | | (61) leq(n5, n5) % 263.25/56.94 | | % 263.25/56.94 | | REDUCE: (14), (58) imply: % 263.25/56.94 | | (62) leq(n0, n5) % 263.25/56.94 | | % 263.25/56.94 | | BETA: splitting (21) gives: % 263.25/56.94 | | % 263.25/56.94 | | Case 1: % 263.25/56.94 | | | % 263.25/56.94 | | | (63) gt(n5, all_74_3) % 263.25/56.94 | | | % 263.25/56.94 | | | GROUND_INST: instantiating (26) with all_74_3, n5, n4, simplifying with % 263.25/56.94 | | | (13), (17), (30), (63) gives: % 263.25/56.94 | | | (64) leq(all_74_3, n4) % 263.25/56.94 | | | % 263.25/56.94 | | | BETA: splitting (18) gives: % 263.25/56.94 | | | % 263.25/56.94 | | | Case 1: % 263.25/56.94 | | | | % 263.25/56.94 | | | | (65) all_74_3 = n0 % 263.25/56.94 | | | | % 263.25/56.94 | | | | REDUCE: (12), (65) imply: % 263.25/56.94 | | | | (66) gt(n0, n0) % 263.25/56.94 | | | | % 263.25/56.94 | | | | PRED_UNIFY: (19), (66) imply: % 263.25/56.94 | | | | (67) $false % 263.25/56.94 | | | | % 263.25/56.94 | | | | CLOSE: (67) is inconsistent. % 263.25/56.94 | | | | % 263.25/56.94 | | | Case 2: % 263.25/56.94 | | | | % 263.25/56.94 | | | | (68) ~ (all_74_3 = n0) % 263.25/56.94 | | | | % 263.25/56.94 | | | | REF_CLOSE: (2), (3), (4), (5), (8), (9), (11), (16), (17), (20), (24), % 263.25/56.94 | | | | (25), (26), (28), (29), (30), (31), (32), (59), (60), (61), % 263.25/56.95 | | | | (62), (64), (68) are inconsistent by sub-proof #82. % 263.25/56.95 | | | | % 263.25/56.95 | | | End of split % 263.25/56.95 | | | % 263.25/56.95 | | Case 2: % 263.25/56.95 | | | % 263.25/56.95 | | | (69) all_74_3 = n5 % 263.25/56.95 | | | % 263.25/56.95 | | | REDUCE: (60), (69) imply: % 263.25/56.95 | | | (70) a_select3(q_ds1_filter, n5, n5) = all_74_1 % 263.25/56.95 | | | % 263.25/56.95 | | | REDUCE: (59), (69) imply: % 263.25/56.95 | | | (71) a_select3(q_ds1_filter, n5, n5) = all_74_0 % 263.25/56.95 | | | % 263.25/56.95 | | | GROUND_INST: instantiating (24) with all_74_1, all_74_0, n5, n5, % 263.25/56.95 | | | q_ds1_filter, simplifying with (70), (71) gives: % 263.25/56.95 | | | (72) all_74_0 = all_74_1 % 263.25/56.95 | | | % 263.25/56.95 | | | REDUCE: (11), (72) imply: % 263.25/56.95 | | | (73) $false % 263.25/56.95 | | | % 263.25/56.95 | | | CLOSE: (73) is inconsistent. % 263.25/56.95 | | | % 263.25/56.95 | | End of split % 263.25/56.95 | | % 263.25/56.95 | End of split % 263.25/56.95 | % 263.25/56.95 End of proof % 263.25/56.95 % 263.25/56.95 Sub-proof #82 shows that the following formulas are inconsistent: % 263.25/56.95 ---------------------------------------------------------------- % 263.25/56.95 (1) leq(all_74_3, n4) % 263.25/56.95 (2) $i(n3) % 263.25/56.95 (3) all_74_3 = n6 | all_74_3 = n5 | all_74_3 = n4 | all_74_3 = n3 | all_74_3 % 263.25/56.95 = n2 | all_74_3 = n1 | all_74_3 = n0 % 263.25/56.95 (4) $i(n4) % 263.25/56.95 (5) ! [v0: $i] : (v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0, n1) | ~ % 263.25/56.95 leq(n0, v0)) % 263.25/56.95 (6) pred(n2) = n1 % 263.25/56.95 (7) leq(n0, all_74_3) % 263.25/56.95 (8) ~ (all_74_0 = all_74_1) % 263.25/56.95 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (a_select3(q_ds1_filter, % 263.25/56.95 v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ leq(v1, all_74_20) | ~ % 263.25/56.95 leq(v0, all_74_20) | ~ leq(n0, v1) | ~ leq(n0, v0) | % 263.25/56.95 (a_select3(q_ds1_filter, v1, v0) = v2 & $i(v2))) % 263.25/56.95 (10) $i(all_74_3) % 263.25/56.95 (11) a_select3(q_ds1_filter, n5, all_74_3) = all_74_0 % 263.25/56.95 (12) pred(n3) = n2 % 263.25/56.95 (13) leq(n0, n5) % 263.25/56.95 (14) a_select3(q_ds1_filter, all_74_3, n5) = all_74_1 % 263.25/56.95 (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 263.25/56.95 (v1 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 263.25/56.95 v0)) % 263.25/56.95 (16) pred(n4) = n3 % 263.25/56.95 (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (pred(v1) = v2) | ~ % 263.25/56.95 $i(v1) | ~ $i(v0) | ~ gt(v1, v0) | leq(v0, v2)) % 263.25/56.95 (18) leq(n5, n5) % 263.25/56.95 (19) all_74_20 = n5 % 263.25/56.95 (20) ~ (all_74_3 = n0) % 263.25/56.95 (21) $i(n2) % 263.25/56.95 (22) $i(n5) % 263.25/56.95 (23) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ % 263.25/56.95 leq(v0, v1) | gt(v1, v0)) % 263.25/56.95 (24) leq(all_74_3, n5) % 263.25/56.95 % 263.25/56.95 Begin of proof % 263.25/56.95 | % 263.25/56.95 | BETA: splitting (3) gives: % 263.25/56.95 | % 263.25/56.95 | Case 1: % 263.25/56.95 | | % 263.25/56.95 | | (25) all_74_3 = n0 % 263.25/56.95 | | % 263.25/56.95 | | REDUCE: (20), (25) imply: % 263.25/56.95 | | (26) $false % 263.25/56.95 | | % 263.25/56.95 | | CLOSE: (26) is inconsistent. % 263.25/56.95 | | % 263.25/56.95 | Case 2: % 263.25/56.95 | | % 263.25/56.95 | | % 263.25/56.95 | | GROUND_INST: instantiating (23) with all_74_3, n4, simplifying with (1), % 263.25/56.95 | | (4), (10) gives: % 263.25/56.95 | | (27) all_74_3 = n4 | gt(n4, all_74_3) % 263.25/56.95 | | % 263.25/56.95 | | BETA: splitting (27) gives: % 263.25/56.95 | | % 263.25/56.95 | | Case 1: % 263.25/56.95 | | | % 263.25/56.95 | | | (28) gt(n4, all_74_3) % 263.25/56.95 | | | % 263.25/56.95 | | | GROUND_INST: instantiating (17) with all_74_3, n4, n3, simplifying with % 263.25/56.95 | | | (4), (10), (16), (28) gives: % 263.25/56.95 | | | (29) leq(all_74_3, n3) % 263.25/56.95 | | | % 263.25/56.95 | | | GROUND_INST: instantiating (23) with all_74_3, n3, simplifying with (2), % 263.25/56.95 | | | (10), (29) gives: % 263.25/56.95 | | | (30) all_74_3 = n3 | gt(n3, all_74_3) % 263.25/56.95 | | | % 263.25/56.95 | | | BETA: splitting (30) gives: % 263.25/56.95 | | | % 263.25/56.95 | | | Case 1: % 263.25/56.95 | | | | % 263.25/56.95 | | | | (31) gt(n3, all_74_3) % 263.25/56.95 | | | | % 263.25/56.95 | | | | GROUND_INST: instantiating (17) with all_74_3, n3, n2, simplifying with % 263.25/56.95 | | | | (2), (10), (12), (31) gives: % 263.25/56.95 | | | | (32) leq(all_74_3, n2) % 263.25/56.95 | | | | % 263.25/56.95 | | | | GROUND_INST: instantiating (23) with all_74_3, n2, simplifying with % 263.25/56.95 | | | | (10), (21), (32) gives: % 263.25/56.95 | | | | (33) all_74_3 = n2 | gt(n2, all_74_3) % 263.25/56.95 | | | | % 263.25/56.95 | | | | BETA: splitting (33) gives: % 263.25/56.95 | | | | % 263.25/56.95 | | | | Case 1: % 263.25/56.95 | | | | | % 263.25/56.95 | | | | | (34) gt(n2, all_74_3) % 263.25/56.95 | | | | | % 263.25/56.95 | | | | | GROUND_INST: instantiating (17) with all_74_3, n2, n1, simplifying % 263.25/56.95 | | | | | with (6), (10), (21), (34) gives: % 263.25/56.95 | | | | | (35) leq(all_74_3, n1) % 263.25/56.95 | | | | | % 263.25/56.95 | | | | | GROUND_INST: instantiating (5) with all_74_3, simplifying with (7), % 263.25/56.95 | | | | | (10), (35) gives: % 263.25/56.95 | | | | | (36) all_74_3 = n1 | all_74_3 = n0 % 263.25/56.95 | | | | | % 263.25/56.95 | | | | | BETA: splitting (36) gives: % 263.25/56.95 | | | | | % 263.25/56.95 | | | | | Case 1: % 263.25/56.95 | | | | | | % 263.25/56.95 | | | | | | (37) all_74_3 = n0 % 263.25/56.95 | | | | | | % 263.25/56.95 | | | | | | REDUCE: (20), (37) imply: % 263.25/56.95 | | | | | | (38) $false % 263.25/56.95 | | | | | | % 263.25/56.95 | | | | | | CLOSE: (38) is inconsistent. % 263.25/56.95 | | | | | | % 263.25/56.95 | | | | | Case 2: % 263.25/56.95 | | | | | | % 263.25/56.95 | | | | | | (39) all_74_3 = n1 % 263.25/56.95 | | | | | | % 263.25/56.95 | | | | | | REDUCE: (14), (39) imply: % 263.25/56.95 | | | | | | (40) a_select3(q_ds1_filter, n1, n5) = all_74_1 % 263.25/56.95 | | | | | | % 263.25/56.95 | | | | | | REDUCE: (11), (39) imply: % 263.25/56.95 | | | | | | (41) a_select3(q_ds1_filter, n5, n1) = all_74_0 % 263.25/56.95 | | | | | | % 263.25/56.95 | | | | | | REDUCE: (10), (39) imply: % 263.25/56.95 | | | | | | (42) $i(n1) % 263.25/56.95 | | | | | | % 263.25/56.95 | | | | | | REDUCE: (24), (39) imply: % 263.25/56.95 | | | | | | (43) leq(n1, n5) % 263.25/56.95 | | | | | | % 263.25/56.95 | | | | | | REDUCE: (7), (39) imply: % 263.25/56.95 | | | | | | (44) leq(n0, n1) % 263.25/56.95 | | | | | | % 263.25/56.95 | | | | | | GROUND_INST: instantiating (9) with n1, n5, all_74_1, simplifying % 263.25/56.95 | | | | | | with (13), (22), (40), (42), (44) gives: % 263.25/56.95 | | | | | | (45) ~ leq(n5, all_74_20) | ~ leq(n1, all_74_20) | % 263.25/56.95 | | | | | | (a_select3(q_ds1_filter, n5, n1) = all_74_1 & $i(all_74_1)) % 263.25/56.95 | | | | | | % 263.25/56.95 | | | | | | BETA: splitting (45) gives: % 263.25/56.95 | | | | | | % 263.25/56.95 | | | | | | Case 1: % 263.25/56.95 | | | | | | | % 263.25/56.95 | | | | | | | (46) ~ leq(n5, all_74_20) % 263.25/56.95 | | | | | | | % 263.25/56.95 | | | | | | | REDUCE: (19), (46) imply: % 263.25/56.95 | | | | | | | (47) ~ leq(n5, n5) % 263.25/56.95 | | | | | | | % 263.25/56.95 | | | | | | | PRED_UNIFY: (18), (47) imply: % 263.25/56.95 | | | | | | | (48) $false % 263.25/56.95 | | | | | | | % 263.25/56.95 | | | | | | | CLOSE: (48) is inconsistent. % 263.25/56.95 | | | | | | | % 263.25/56.95 | | | | | | Case 2: % 263.25/56.95 | | | | | | | % 263.25/56.95 | | | | | | | (49) ~ leq(n1, all_74_20) | (a_select3(q_ds1_filter, n5, n1) = % 263.25/56.95 | | | | | | | all_74_1 & $i(all_74_1)) % 263.25/56.95 | | | | | | | % 263.25/56.95 | | | | | | | BETA: splitting (49) gives: % 263.25/56.95 | | | | | | | % 263.25/56.95 | | | | | | | Case 1: % 263.25/56.95 | | | | | | | | % 263.25/56.95 | | | | | | | | (50) ~ leq(n1, all_74_20) % 263.25/56.95 | | | | | | | | % 263.25/56.95 | | | | | | | | REDUCE: (19), (50) imply: % 263.25/56.95 | | | | | | | | (51) ~ leq(n1, n5) % 263.25/56.95 | | | | | | | | % 263.25/56.95 | | | | | | | | PRED_UNIFY: (43), (51) imply: % 263.25/56.95 | | | | | | | | (52) $false % 263.25/56.95 | | | | | | | | % 263.25/56.95 | | | | | | | | CLOSE: (52) is inconsistent. % 263.25/56.95 | | | | | | | | % 263.25/56.95 | | | | | | | Case 2: % 263.25/56.95 | | | | | | | | % 263.25/56.95 | | | | | | | | (53) a_select3(q_ds1_filter, n5, n1) = all_74_1 & % 263.25/56.95 | | | | | | | | $i(all_74_1) % 263.25/56.95 | | | | | | | | % 263.25/56.95 | | | | | | | | ALPHA: (53) implies: % 263.25/56.95 | | | | | | | | (54) a_select3(q_ds1_filter, n5, n1) = all_74_1 % 263.25/56.95 | | | | | | | | % 263.25/56.95 | | | | | | | | REF_CLOSE: (8), (15), (41), (54) are inconsistent by sub-proof % 263.25/56.95 | | | | | | | | #86. % 263.25/56.95 | | | | | | | | % 263.25/56.95 | | | | | | | End of split % 263.25/56.95 | | | | | | | % 263.25/56.95 | | | | | | End of split % 263.25/56.95 | | | | | | % 263.25/56.95 | | | | | End of split % 263.25/56.95 | | | | | % 263.25/56.95 | | | | Case 2: % 263.25/56.95 | | | | | % 263.25/56.95 | | | | | (55) all_74_3 = n2 % 263.25/56.95 | | | | | % 263.25/56.95 | | | | | REDUCE: (14), (55) imply: % 263.25/56.95 | | | | | (56) a_select3(q_ds1_filter, n2, n5) = all_74_1 % 263.25/56.95 | | | | | % 263.25/56.95 | | | | | REDUCE: (11), (55) imply: % 263.25/56.95 | | | | | (57) a_select3(q_ds1_filter, n5, n2) = all_74_0 % 263.25/56.95 | | | | | % 263.25/56.95 | | | | | REDUCE: (24), (55) imply: % 263.25/56.95 | | | | | (58) leq(n2, n5) % 263.25/56.95 | | | | | % 263.25/56.95 | | | | | REDUCE: (7), (55) imply: % 263.25/56.95 | | | | | (59) leq(n0, n2) % 263.25/56.95 | | | | | % 263.25/56.95 | | | | | GROUND_INST: instantiating (9) with n2, n5, all_74_1, simplifying with % 263.25/56.95 | | | | | (13), (21), (22), (56), (59) gives: % 263.25/56.95 | | | | | (60) ~ leq(n5, all_74_20) | ~ leq(n2, all_74_20) | % 263.25/56.95 | | | | | (a_select3(q_ds1_filter, n5, n2) = all_74_1 & $i(all_74_1)) % 263.25/56.95 | | | | | % 263.25/56.95 | | | | | BETA: splitting (60) gives: % 263.25/56.95 | | | | | % 263.25/56.95 | | | | | Case 1: % 263.25/56.95 | | | | | | % 263.25/56.95 | | | | | | (61) ~ leq(n5, all_74_20) % 263.25/56.95 | | | | | | % 263.25/56.95 | | | | | | REDUCE: (19), (61) imply: % 263.25/56.95 | | | | | | (62) ~ leq(n5, n5) % 263.25/56.95 | | | | | | % 263.25/56.95 | | | | | | PRED_UNIFY: (18), (62) imply: % 263.25/56.95 | | | | | | (63) $false % 263.25/56.95 | | | | | | % 263.25/56.95 | | | | | | CLOSE: (63) is inconsistent. % 263.25/56.95 | | | | | | % 263.25/56.95 | | | | | Case 2: % 263.25/56.95 | | | | | | % 263.25/56.95 | | | | | | (64) ~ leq(n2, all_74_20) | (a_select3(q_ds1_filter, n5, n2) = % 263.25/56.95 | | | | | | all_74_1 & $i(all_74_1)) % 263.25/56.95 | | | | | | % 263.25/56.95 | | | | | | BETA: splitting (64) gives: % 263.25/56.95 | | | | | | % 263.25/56.95 | | | | | | Case 1: % 263.25/56.95 | | | | | | | % 263.25/56.95 | | | | | | | (65) ~ leq(n2, all_74_20) % 263.25/56.95 | | | | | | | % 263.25/56.95 | | | | | | | REDUCE: (19), (65) imply: % 263.25/56.95 | | | | | | | (66) ~ leq(n2, n5) % 263.25/56.95 | | | | | | | % 263.25/56.95 | | | | | | | PRED_UNIFY: (58), (66) imply: % 263.25/56.95 | | | | | | | (67) $false % 263.25/56.95 | | | | | | | % 263.25/56.95 | | | | | | | CLOSE: (67) is inconsistent. % 263.25/56.95 | | | | | | | % 263.25/56.95 | | | | | | Case 2: % 263.25/56.95 | | | | | | | % 263.25/56.95 | | | | | | | (68) a_select3(q_ds1_filter, n5, n2) = all_74_1 & $i(all_74_1) % 263.25/56.95 | | | | | | | % 263.25/56.95 | | | | | | | ALPHA: (68) implies: % 263.25/56.95 | | | | | | | (69) a_select3(q_ds1_filter, n5, n2) = all_74_1 % 263.25/56.95 | | | | | | | % 263.25/56.95 | | | | | | | REF_CLOSE: (8), (15), (57), (69) are inconsistent by sub-proof % 263.25/56.95 | | | | | | | #85. % 263.25/56.95 | | | | | | | % 263.25/56.95 | | | | | | End of split % 263.25/56.95 | | | | | | % 263.25/56.95 | | | | | End of split % 263.25/56.95 | | | | | % 263.25/56.95 | | | | End of split % 263.25/56.95 | | | | % 263.25/56.95 | | | Case 2: % 263.25/56.95 | | | | % 263.25/56.95 | | | | (70) all_74_3 = n3 % 263.25/56.95 | | | | % 263.25/56.95 | | | | REDUCE: (14), (70) imply: % 263.25/56.95 | | | | (71) a_select3(q_ds1_filter, n3, n5) = all_74_1 % 263.25/56.95 | | | | % 263.25/56.95 | | | | REDUCE: (11), (70) imply: % 263.25/56.95 | | | | (72) a_select3(q_ds1_filter, n5, n3) = all_74_0 % 263.25/56.95 | | | | % 263.25/56.95 | | | | REDUCE: (24), (70) imply: % 263.25/56.95 | | | | (73) leq(n3, n5) % 263.25/56.95 | | | | % 263.25/56.95 | | | | REDUCE: (7), (70) imply: % 263.25/56.95 | | | | (74) leq(n0, n3) % 263.25/56.95 | | | | % 263.25/56.95 | | | | GROUND_INST: instantiating (9) with n3, n5, all_74_1, simplifying with % 263.25/56.95 | | | | (2), (13), (22), (71), (74) gives: % 263.25/56.95 | | | | (75) ~ leq(n5, all_74_20) | ~ leq(n3, all_74_20) | % 263.25/56.95 | | | | (a_select3(q_ds1_filter, n5, n3) = all_74_1 & $i(all_74_1)) % 263.25/56.95 | | | | % 263.25/56.95 | | | | BETA: splitting (75) gives: % 263.25/56.95 | | | | % 263.25/56.95 | | | | Case 1: % 263.25/56.95 | | | | | % 263.25/56.95 | | | | | (76) ~ leq(n5, all_74_20) % 263.25/56.95 | | | | | % 263.25/56.95 | | | | | REDUCE: (19), (76) imply: % 263.25/56.95 | | | | | (77) ~ leq(n5, n5) % 263.25/56.95 | | | | | % 263.25/56.95 | | | | | PRED_UNIFY: (18), (77) imply: % 263.25/56.95 | | | | | (78) $false % 263.25/56.95 | | | | | % 263.25/56.95 | | | | | CLOSE: (78) is inconsistent. % 263.25/56.95 | | | | | % 263.25/56.95 | | | | Case 2: % 263.25/56.95 | | | | | % 263.25/56.95 | | | | | (79) ~ leq(n3, all_74_20) | (a_select3(q_ds1_filter, n5, n3) = % 263.25/56.95 | | | | | all_74_1 & $i(all_74_1)) % 263.25/56.95 | | | | | % 263.25/56.95 | | | | | BETA: splitting (79) gives: % 263.25/56.95 | | | | | % 263.25/56.95 | | | | | Case 1: % 263.25/56.95 | | | | | | % 263.25/56.95 | | | | | | (80) ~ leq(n3, all_74_20) % 263.25/56.95 | | | | | | % 263.25/56.95 | | | | | | REDUCE: (19), (80) imply: % 263.25/56.95 | | | | | | (81) ~ leq(n3, n5) % 263.25/56.95 | | | | | | % 263.25/56.95 | | | | | | PRED_UNIFY: (73), (81) imply: % 263.25/56.95 | | | | | | (82) $false % 263.25/56.95 | | | | | | % 263.25/56.95 | | | | | | CLOSE: (82) is inconsistent. % 263.25/56.95 | | | | | | % 263.25/56.95 | | | | | Case 2: % 263.25/56.95 | | | | | | % 263.25/56.95 | | | | | | (83) a_select3(q_ds1_filter, n5, n3) = all_74_1 & $i(all_74_1) % 263.25/56.95 | | | | | | % 263.25/56.95 | | | | | | ALPHA: (83) implies: % 263.25/56.95 | | | | | | (84) a_select3(q_ds1_filter, n5, n3) = all_74_1 % 263.25/56.95 | | | | | | % 263.25/56.95 | | | | | | REF_CLOSE: (8), (15), (72), (84) are inconsistent by sub-proof #84. % 263.25/56.95 | | | | | | % 263.25/56.95 | | | | | End of split % 263.25/56.95 | | | | | % 263.25/56.95 | | | | End of split % 263.25/56.95 | | | | % 263.25/56.95 | | | End of split % 263.25/56.95 | | | % 263.25/56.95 | | Case 2: % 263.25/56.95 | | | % 263.25/56.95 | | | (85) all_74_3 = n4 % 263.25/56.95 | | | % 263.25/56.95 | | | REDUCE: (14), (85) imply: % 263.25/56.95 | | | (86) a_select3(q_ds1_filter, n4, n5) = all_74_1 % 263.25/56.95 | | | % 263.25/56.95 | | | REDUCE: (11), (85) imply: % 263.25/56.95 | | | (87) a_select3(q_ds1_filter, n5, n4) = all_74_0 % 263.25/56.95 | | | % 263.25/56.95 | | | REDUCE: (24), (85) imply: % 263.25/56.95 | | | (88) leq(n4, n5) % 263.25/56.95 | | | % 263.25/56.95 | | | REDUCE: (7), (85) imply: % 263.25/56.95 | | | (89) leq(n0, n4) % 263.25/56.95 | | | % 263.25/56.95 | | | GROUND_INST: instantiating (9) with n4, n5, all_74_1, simplifying with % 263.25/56.95 | | | (4), (13), (22), (86), (89) gives: % 263.25/56.95 | | | (90) ~ leq(n5, all_74_20) | ~ leq(n4, all_74_20) | % 263.25/56.95 | | | (a_select3(q_ds1_filter, n5, n4) = all_74_1 & $i(all_74_1)) % 263.25/56.95 | | | % 263.25/56.95 | | | BETA: splitting (90) gives: % 263.25/56.95 | | | % 263.25/56.95 | | | Case 1: % 263.25/56.95 | | | | % 263.25/56.95 | | | | (91) ~ leq(n5, all_74_20) % 263.25/56.95 | | | | % 263.25/56.95 | | | | REDUCE: (19), (91) imply: % 263.25/56.95 | | | | (92) ~ leq(n5, n5) % 263.25/56.95 | | | | % 263.25/56.95 | | | | PRED_UNIFY: (18), (92) imply: % 263.25/56.95 | | | | (93) $false % 263.25/56.95 | | | | % 263.25/56.95 | | | | CLOSE: (93) is inconsistent. % 263.25/56.95 | | | | % 263.25/56.95 | | | Case 2: % 263.25/56.95 | | | | % 263.25/56.95 | | | | (94) ~ leq(n4, all_74_20) | (a_select3(q_ds1_filter, n5, n4) = % 263.25/56.95 | | | | all_74_1 & $i(all_74_1)) % 263.25/56.95 | | | | % 263.25/56.95 | | | | BETA: splitting (94) gives: % 263.25/56.95 | | | | % 263.25/56.95 | | | | Case 1: % 263.25/56.95 | | | | | % 263.25/56.95 | | | | | (95) ~ leq(n4, all_74_20) % 263.25/56.95 | | | | | % 263.25/56.95 | | | | | REDUCE: (19), (95) imply: % 263.25/56.95 | | | | | (96) ~ leq(n4, n5) % 263.25/56.95 | | | | | % 263.25/56.95 | | | | | PRED_UNIFY: (88), (96) imply: % 263.25/56.95 | | | | | (97) $false % 263.25/56.95 | | | | | % 263.25/56.95 | | | | | CLOSE: (97) is inconsistent. % 263.25/56.95 | | | | | % 263.25/56.95 | | | | Case 2: % 263.25/56.95 | | | | | % 263.25/56.96 | | | | | (98) a_select3(q_ds1_filter, n5, n4) = all_74_1 & $i(all_74_1) % 263.25/56.96 | | | | | % 263.25/56.96 | | | | | ALPHA: (98) implies: % 263.25/56.96 | | | | | (99) a_select3(q_ds1_filter, n5, n4) = all_74_1 % 263.25/56.96 | | | | | % 263.25/56.96 | | | | | GROUND_INST: instantiating (15) with all_74_0, all_74_1, n4, n5, % 263.25/56.96 | | | | | q_ds1_filter, simplifying with (87), (99) gives: % 263.42/56.96 | | | | | (100) all_74_0 = all_74_1 % 263.42/56.96 | | | | | % 263.42/56.96 | | | | | REDUCE: (8), (100) imply: % 263.42/56.96 | | | | | (101) $false % 263.42/56.96 | | | | | % 263.42/56.96 | | | | | CLOSE: (101) is inconsistent. % 263.42/56.96 | | | | | % 263.42/56.96 | | | | End of split % 263.42/56.96 | | | | % 263.42/56.96 | | | End of split % 263.42/56.96 | | | % 263.42/56.96 | | End of split % 263.42/56.96 | | % 263.42/56.96 | End of split % 263.42/56.96 | % 263.42/56.96 End of proof % 263.42/56.96 % 263.42/56.96 Sub-proof #83 shows that the following formulas are inconsistent: % 263.42/56.96 ---------------------------------------------------------------- % 263.42/56.96 (1) $i(n3) % 263.42/56.96 (2) $i(n4) % 263.42/56.96 (3) ! [v0: $i] : (v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0, n1) | ~ % 263.42/56.96 leq(n0, v0)) % 263.42/56.96 (4) a_select3(q_ds1_filter, all_74_2, n5) = all_74_0 % 263.42/56.96 (5) pred(n2) = n1 % 263.42/56.96 (6) ~ (all_74_2 = n0) % 263.42/56.96 (7) ~ (all_74_0 = all_74_1) % 263.42/56.96 (8) leq(n0, all_74_2) % 263.42/56.96 (9) leq(all_74_2, n5) % 263.42/56.96 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (a_select3(q_ds1_filter, % 263.42/56.96 v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ leq(v1, all_74_20) | ~ % 263.42/56.96 leq(v0, all_74_20) | ~ leq(n0, v1) | ~ leq(n0, v0) | % 263.42/56.96 (a_select3(q_ds1_filter, v1, v0) = v2 & $i(v2))) % 263.42/56.96 (11) all_74_2 = n4 | gt(n4, all_74_2) % 263.42/56.96 (12) a_select3(q_ds1_filter, n5, all_74_2) = all_74_1 % 263.42/56.96 (13) pred(n3) = n2 % 263.42/56.96 (14) leq(n0, n5) % 263.42/56.96 (15) $i(all_74_2) % 263.42/56.96 (16) all_74_2 = n4 | all_74_2 = n3 | all_74_2 = n2 | all_74_2 = n1 | all_74_2 % 263.42/56.96 = n0 % 263.42/56.96 (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 263.42/56.96 (v1 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 263.42/56.96 v0)) % 263.42/56.96 (18) pred(n4) = n3 % 263.42/56.96 (19) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (pred(v1) = v2) | ~ % 263.42/56.96 $i(v1) | ~ $i(v0) | ~ gt(v1, v0) | leq(v0, v2)) % 263.42/56.96 (20) leq(n5, n5) % 263.42/56.96 (21) all_74_20 = n5 % 263.42/56.96 (22) $i(n2) % 263.42/56.96 (23) $i(n5) % 263.42/56.96 (24) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ % 263.42/56.96 leq(v0, v1) | gt(v1, v0)) % 263.42/56.96 % 263.42/56.96 Begin of proof % 263.42/56.96 | % 263.42/56.96 | BETA: splitting (11) gives: % 263.42/56.96 | % 263.42/56.96 | Case 1: % 263.42/56.96 | | % 263.42/56.96 | | (25) gt(n4, all_74_2) % 263.42/56.96 | | % 263.42/56.96 | | GROUND_INST: instantiating (19) with all_74_2, n4, n3, simplifying with (2), % 263.42/56.96 | | (15), (18), (25) gives: % 263.42/56.96 | | (26) leq(all_74_2, n3) % 263.42/56.96 | | % 263.42/56.96 | | BETA: splitting (16) gives: % 263.42/56.96 | | % 263.42/56.96 | | Case 1: % 263.42/56.96 | | | % 263.42/56.96 | | | (27) all_74_2 = n0 % 263.42/56.96 | | | % 263.42/56.96 | | | REDUCE: (6), (27) imply: % 263.42/56.96 | | | (28) $false % 263.42/56.96 | | | % 263.42/56.96 | | | CLOSE: (28) is inconsistent. % 263.42/56.96 | | | % 263.42/56.96 | | Case 2: % 263.42/56.96 | | | % 263.42/56.96 | | | % 263.42/56.96 | | | GROUND_INST: instantiating (24) with all_74_2, n3, simplifying with (1), % 263.42/56.96 | | | (15), (26) gives: % 263.42/56.96 | | | (29) all_74_2 = n3 | gt(n3, all_74_2) % 263.42/56.96 | | | % 263.42/56.96 | | | BETA: splitting (29) gives: % 263.42/56.96 | | | % 263.42/56.96 | | | Case 1: % 263.42/56.96 | | | | % 263.42/56.96 | | | | (30) gt(n3, all_74_2) % 263.42/56.96 | | | | % 263.42/56.96 | | | | GROUND_INST: instantiating (19) with all_74_2, n3, n2, simplifying with % 263.42/56.96 | | | | (1), (13), (15), (30) gives: % 263.42/56.96 | | | | (31) leq(all_74_2, n2) % 263.42/56.96 | | | | % 263.42/56.96 | | | | GROUND_INST: instantiating (24) with all_74_2, n2, simplifying with % 263.42/56.96 | | | | (15), (22), (31) gives: % 263.42/56.96 | | | | (32) all_74_2 = n2 | gt(n2, all_74_2) % 263.42/56.96 | | | | % 263.42/56.96 | | | | BETA: splitting (32) gives: % 263.42/56.96 | | | | % 263.42/56.96 | | | | Case 1: % 263.42/56.96 | | | | | % 263.42/56.96 | | | | | (33) gt(n2, all_74_2) % 263.42/56.96 | | | | | % 263.42/56.96 | | | | | GROUND_INST: instantiating (19) with all_74_2, n2, n1, simplifying % 263.42/56.96 | | | | | with (5), (15), (22), (33) gives: % 263.42/56.96 | | | | | (34) leq(all_74_2, n1) % 263.42/56.96 | | | | | % 263.42/56.96 | | | | | GROUND_INST: instantiating (3) with all_74_2, simplifying with (8), % 263.42/56.96 | | | | | (15), (34) gives: % 263.42/56.96 | | | | | (35) all_74_2 = n1 | all_74_2 = n0 % 263.42/56.96 | | | | | % 263.42/56.96 | | | | | BETA: splitting (35) gives: % 263.42/56.96 | | | | | % 263.42/56.96 | | | | | Case 1: % 263.42/56.96 | | | | | | % 263.42/56.96 | | | | | | (36) all_74_2 = n0 % 263.42/56.96 | | | | | | % 263.42/56.96 | | | | | | REDUCE: (6), (36) imply: % 263.42/56.96 | | | | | | (37) $false % 263.42/56.96 | | | | | | % 263.42/56.96 | | | | | | CLOSE: (37) is inconsistent. % 263.42/56.96 | | | | | | % 263.42/56.96 | | | | | Case 2: % 263.42/56.96 | | | | | | % 263.42/56.96 | | | | | | (38) all_74_2 = n1 % 263.42/56.96 | | | | | | % 263.42/56.96 | | | | | | REDUCE: (4), (38) imply: % 263.42/56.96 | | | | | | (39) a_select3(q_ds1_filter, n1, n5) = all_74_0 % 263.42/56.96 | | | | | | % 263.42/56.96 | | | | | | REDUCE: (12), (38) imply: % 263.42/56.96 | | | | | | (40) a_select3(q_ds1_filter, n5, n1) = all_74_1 % 263.42/56.96 | | | | | | % 263.42/56.96 | | | | | | REDUCE: (15), (38) imply: % 263.42/56.96 | | | | | | (41) $i(n1) % 263.42/56.96 | | | | | | % 263.42/56.96 | | | | | | REDUCE: (9), (38) imply: % 263.42/56.96 | | | | | | (42) leq(n1, n5) % 263.42/56.96 | | | | | | % 263.42/56.96 | | | | | | REDUCE: (8), (38) imply: % 263.42/56.96 | | | | | | (43) leq(n0, n1) % 263.42/56.96 | | | | | | % 263.42/56.96 | | | | | | GROUND_INST: instantiating (10) with n1, n5, all_74_0, simplifying % 263.42/56.96 | | | | | | with (14), (23), (39), (41), (43) gives: % 263.42/56.96 | | | | | | (44) ~ leq(n5, all_74_20) | ~ leq(n1, all_74_20) | % 263.42/56.96 | | | | | | (a_select3(q_ds1_filter, n5, n1) = all_74_0 & $i(all_74_0)) % 263.42/56.96 | | | | | | % 263.42/56.96 | | | | | | BETA: splitting (44) gives: % 263.42/56.96 | | | | | | % 263.42/56.96 | | | | | | Case 1: % 263.42/56.96 | | | | | | | % 263.42/56.96 | | | | | | | (45) ~ leq(n5, all_74_20) % 263.42/56.96 | | | | | | | % 263.42/56.96 | | | | | | | REDUCE: (21), (45) imply: % 263.42/56.96 | | | | | | | (46) ~ leq(n5, n5) % 263.42/56.96 | | | | | | | % 263.42/56.96 | | | | | | | PRED_UNIFY: (20), (46) imply: % 263.42/56.96 | | | | | | | (47) $false % 263.42/56.96 | | | | | | | % 263.42/56.96 | | | | | | | CLOSE: (47) is inconsistent. % 263.42/56.96 | | | | | | | % 263.42/56.96 | | | | | | Case 2: % 263.42/56.96 | | | | | | | % 263.42/56.96 | | | | | | | (48) ~ leq(n1, all_74_20) | (a_select3(q_ds1_filter, n5, n1) = % 263.42/56.96 | | | | | | | all_74_0 & $i(all_74_0)) % 263.42/56.96 | | | | | | | % 263.42/56.96 | | | | | | | BETA: splitting (48) gives: % 263.42/56.96 | | | | | | | % 263.42/56.96 | | | | | | | Case 1: % 263.42/56.96 | | | | | | | | % 263.42/56.96 | | | | | | | | (49) ~ leq(n1, all_74_20) % 263.42/56.96 | | | | | | | | % 263.42/56.96 | | | | | | | | REDUCE: (21), (49) imply: % 263.42/56.96 | | | | | | | | (50) ~ leq(n1, n5) % 263.42/56.96 | | | | | | | | % 263.42/56.96 | | | | | | | | PRED_UNIFY: (42), (50) imply: % 263.42/56.96 | | | | | | | | (51) $false % 263.42/56.96 | | | | | | | | % 263.42/56.96 | | | | | | | | CLOSE: (51) is inconsistent. % 263.42/56.96 | | | | | | | | % 263.42/56.96 | | | | | | | Case 2: % 263.42/56.96 | | | | | | | | % 263.42/56.96 | | | | | | | | (52) a_select3(q_ds1_filter, n5, n1) = all_74_0 & % 263.42/56.96 | | | | | | | | $i(all_74_0) % 263.42/56.96 | | | | | | | | % 263.42/56.96 | | | | | | | | ALPHA: (52) implies: % 263.42/56.96 | | | | | | | | (53) a_select3(q_ds1_filter, n5, n1) = all_74_0 % 263.42/56.96 | | | | | | | | % 263.42/56.96 | | | | | | | | REF_CLOSE: (7), (17), (40), (53) are inconsistent by sub-proof % 263.42/56.96 | | | | | | | | #86. % 263.42/56.96 | | | | | | | | % 263.42/56.96 | | | | | | | End of split % 263.42/56.96 | | | | | | | % 263.42/56.96 | | | | | | End of split % 263.42/56.96 | | | | | | % 263.42/56.96 | | | | | End of split % 263.42/56.96 | | | | | % 263.42/56.96 | | | | Case 2: % 263.42/56.96 | | | | | % 263.42/56.96 | | | | | (54) all_74_2 = n2 % 263.42/56.96 | | | | | % 263.42/56.96 | | | | | REDUCE: (4), (54) imply: % 263.42/56.96 | | | | | (55) a_select3(q_ds1_filter, n2, n5) = all_74_0 % 263.42/56.96 | | | | | % 263.42/56.96 | | | | | REDUCE: (12), (54) imply: % 263.42/56.96 | | | | | (56) a_select3(q_ds1_filter, n5, n2) = all_74_1 % 263.42/56.96 | | | | | % 263.42/56.96 | | | | | REDUCE: (9), (54) imply: % 263.42/56.96 | | | | | (57) leq(n2, n5) % 263.42/56.96 | | | | | % 263.42/56.96 | | | | | REDUCE: (8), (54) imply: % 263.42/56.96 | | | | | (58) leq(n0, n2) % 263.42/56.96 | | | | | % 263.42/56.96 | | | | | GROUND_INST: instantiating (10) with n2, n5, all_74_0, simplifying % 263.42/56.96 | | | | | with (14), (22), (23), (55), (58) gives: % 263.42/56.96 | | | | | (59) ~ leq(n5, all_74_20) | ~ leq(n2, all_74_20) | % 263.42/56.96 | | | | | (a_select3(q_ds1_filter, n5, n2) = all_74_0 & $i(all_74_0)) % 263.42/56.96 | | | | | % 263.42/56.96 | | | | | BETA: splitting (59) gives: % 263.42/56.96 | | | | | % 263.42/56.96 | | | | | Case 1: % 263.42/56.96 | | | | | | % 263.42/56.96 | | | | | | (60) ~ leq(n5, all_74_20) % 263.42/56.96 | | | | | | % 263.42/56.96 | | | | | | REDUCE: (21), (60) imply: % 263.42/56.96 | | | | | | (61) ~ leq(n5, n5) % 263.42/56.96 | | | | | | % 263.42/56.96 | | | | | | PRED_UNIFY: (20), (61) imply: % 263.42/56.96 | | | | | | (62) $false % 263.42/56.96 | | | | | | % 263.42/56.96 | | | | | | CLOSE: (62) is inconsistent. % 263.42/56.96 | | | | | | % 263.42/56.96 | | | | | Case 2: % 263.42/56.96 | | | | | | % 263.42/56.96 | | | | | | (63) ~ leq(n2, all_74_20) | (a_select3(q_ds1_filter, n5, n2) = % 263.42/56.96 | | | | | | all_74_0 & $i(all_74_0)) % 263.42/56.96 | | | | | | % 263.42/56.96 | | | | | | BETA: splitting (63) gives: % 263.42/56.96 | | | | | | % 263.42/56.96 | | | | | | Case 1: % 263.42/56.96 | | | | | | | % 263.42/56.96 | | | | | | | (64) ~ leq(n2, all_74_20) % 263.42/56.96 | | | | | | | % 263.42/56.96 | | | | | | | REDUCE: (21), (64) imply: % 263.42/56.96 | | | | | | | (65) ~ leq(n2, n5) % 263.42/56.96 | | | | | | | % 263.42/56.96 | | | | | | | PRED_UNIFY: (57), (65) imply: % 263.42/56.96 | | | | | | | (66) $false % 263.42/56.96 | | | | | | | % 263.42/56.96 | | | | | | | CLOSE: (66) is inconsistent. % 263.42/56.96 | | | | | | | % 263.42/56.96 | | | | | | Case 2: % 263.42/56.96 | | | | | | | % 263.42/56.96 | | | | | | | (67) a_select3(q_ds1_filter, n5, n2) = all_74_0 & $i(all_74_0) % 263.42/56.96 | | | | | | | % 263.42/56.96 | | | | | | | ALPHA: (67) implies: % 263.42/56.96 | | | | | | | (68) a_select3(q_ds1_filter, n5, n2) = all_74_0 % 263.42/56.96 | | | | | | | % 263.42/56.96 | | | | | | | REF_CLOSE: (7), (17), (56), (68) are inconsistent by sub-proof % 263.42/56.96 | | | | | | | #85. % 263.42/56.96 | | | | | | | % 263.42/56.96 | | | | | | End of split % 263.42/56.96 | | | | | | % 263.42/56.96 | | | | | End of split % 263.42/56.96 | | | | | % 263.42/56.96 | | | | End of split % 263.42/56.96 | | | | % 263.42/56.96 | | | Case 2: % 263.42/56.96 | | | | % 263.42/56.96 | | | | (69) all_74_2 = n3 % 263.42/56.96 | | | | % 263.42/56.96 | | | | REDUCE: (4), (69) imply: % 263.42/56.96 | | | | (70) a_select3(q_ds1_filter, n3, n5) = all_74_0 % 263.42/56.96 | | | | % 263.42/56.96 | | | | REDUCE: (12), (69) imply: % 263.42/56.96 | | | | (71) a_select3(q_ds1_filter, n5, n3) = all_74_1 % 263.42/56.96 | | | | % 263.42/56.96 | | | | REDUCE: (9), (69) imply: % 263.42/56.96 | | | | (72) leq(n3, n5) % 263.42/56.96 | | | | % 263.42/56.96 | | | | REDUCE: (8), (69) imply: % 263.42/56.96 | | | | (73) leq(n0, n3) % 263.42/56.96 | | | | % 263.42/56.96 | | | | GROUND_INST: instantiating (10) with n3, n5, all_74_0, simplifying with % 263.42/56.96 | | | | (1), (14), (23), (70), (73) gives: % 263.42/56.96 | | | | (74) ~ leq(n5, all_74_20) | ~ leq(n3, all_74_20) | % 263.42/56.96 | | | | (a_select3(q_ds1_filter, n5, n3) = all_74_0 & $i(all_74_0)) % 263.42/56.96 | | | | % 263.42/56.96 | | | | BETA: splitting (74) gives: % 263.42/56.96 | | | | % 263.42/56.96 | | | | Case 1: % 263.42/56.96 | | | | | % 263.42/56.96 | | | | | (75) ~ leq(n5, all_74_20) % 263.42/56.96 | | | | | % 263.42/56.96 | | | | | REDUCE: (21), (75) imply: % 263.42/56.96 | | | | | (76) ~ leq(n5, n5) % 263.42/56.96 | | | | | % 263.42/56.96 | | | | | PRED_UNIFY: (20), (76) imply: % 263.42/56.96 | | | | | (77) $false % 263.42/56.96 | | | | | % 263.42/56.96 | | | | | CLOSE: (77) is inconsistent. % 263.42/56.96 | | | | | % 263.42/56.96 | | | | Case 2: % 263.42/56.96 | | | | | % 263.42/56.96 | | | | | (78) ~ leq(n3, all_74_20) | (a_select3(q_ds1_filter, n5, n3) = % 263.42/56.96 | | | | | all_74_0 & $i(all_74_0)) % 263.42/56.96 | | | | | % 263.42/56.96 | | | | | BETA: splitting (78) gives: % 263.42/56.96 | | | | | % 263.42/56.96 | | | | | Case 1: % 263.42/56.96 | | | | | | % 263.42/56.96 | | | | | | (79) ~ leq(n3, all_74_20) % 263.42/56.96 | | | | | | % 263.42/56.96 | | | | | | REDUCE: (21), (79) imply: % 263.42/56.96 | | | | | | (80) ~ leq(n3, n5) % 263.42/56.96 | | | | | | % 263.42/56.96 | | | | | | PRED_UNIFY: (72), (80) imply: % 263.42/56.96 | | | | | | (81) $false % 263.42/56.96 | | | | | | % 263.42/56.96 | | | | | | CLOSE: (81) is inconsistent. % 263.42/56.96 | | | | | | % 263.42/56.96 | | | | | Case 2: % 263.42/56.96 | | | | | | % 263.42/56.96 | | | | | | (82) a_select3(q_ds1_filter, n5, n3) = all_74_0 & $i(all_74_0) % 263.42/56.96 | | | | | | % 263.42/56.96 | | | | | | ALPHA: (82) implies: % 263.42/56.96 | | | | | | (83) a_select3(q_ds1_filter, n5, n3) = all_74_0 % 263.42/56.96 | | | | | | % 263.42/56.96 | | | | | | REF_CLOSE: (7), (17), (71), (83) are inconsistent by sub-proof #84. % 263.42/56.96 | | | | | | % 263.42/56.96 | | | | | End of split % 263.42/56.96 | | | | | % 263.42/56.96 | | | | End of split % 263.42/56.96 | | | | % 263.42/56.96 | | | End of split % 263.42/56.96 | | | % 263.42/56.96 | | End of split % 263.42/56.96 | | % 263.42/56.96 | Case 2: % 263.42/56.96 | | % 263.42/56.96 | | (84) all_74_2 = n4 % 263.42/56.96 | | % 263.42/56.96 | | REDUCE: (4), (84) imply: % 263.42/56.96 | | (85) a_select3(q_ds1_filter, n4, n5) = all_74_0 % 263.42/56.96 | | % 263.42/56.96 | | REDUCE: (12), (84) imply: % 263.42/56.96 | | (86) a_select3(q_ds1_filter, n5, n4) = all_74_1 % 263.42/56.96 | | % 263.42/56.96 | | REDUCE: (9), (84) imply: % 263.42/56.96 | | (87) leq(n4, n5) % 263.42/56.96 | | % 263.42/56.96 | | REDUCE: (8), (84) imply: % 263.42/56.96 | | (88) leq(n0, n4) % 263.42/56.96 | | % 263.42/56.96 | | GROUND_INST: instantiating (10) with n4, n5, all_74_0, simplifying with (2), % 263.42/56.96 | | (14), (23), (85), (88) gives: % 263.42/56.96 | | (89) ~ leq(n5, all_74_20) | ~ leq(n4, all_74_20) | % 263.42/56.96 | | (a_select3(q_ds1_filter, n5, n4) = all_74_0 & $i(all_74_0)) % 263.42/56.96 | | % 263.42/56.96 | | BETA: splitting (89) gives: % 263.42/56.96 | | % 263.42/56.96 | | Case 1: % 263.42/56.96 | | | % 263.42/56.96 | | | (90) ~ leq(n5, all_74_20) % 263.42/56.96 | | | % 263.42/56.96 | | | REDUCE: (21), (90) imply: % 263.42/56.96 | | | (91) ~ leq(n5, n5) % 263.42/56.96 | | | % 263.42/56.96 | | | PRED_UNIFY: (20), (91) imply: % 263.42/56.96 | | | (92) $false % 263.42/56.96 | | | % 263.42/56.96 | | | CLOSE: (92) is inconsistent. % 263.42/56.96 | | | % 263.42/56.96 | | Case 2: % 263.42/56.96 | | | % 263.42/56.97 | | | (93) ~ leq(n4, all_74_20) | (a_select3(q_ds1_filter, n5, n4) = % 263.42/56.97 | | | all_74_0 & $i(all_74_0)) % 263.42/56.97 | | | % 263.42/56.97 | | | BETA: splitting (93) gives: % 263.42/56.97 | | | % 263.42/56.97 | | | Case 1: % 263.42/56.97 | | | | % 263.42/56.97 | | | | (94) ~ leq(n4, all_74_20) % 263.42/56.97 | | | | % 263.42/56.97 | | | | REDUCE: (21), (94) imply: % 263.42/56.97 | | | | (95) ~ leq(n4, n5) % 263.42/56.97 | | | | % 263.42/56.97 | | | | PRED_UNIFY: (87), (95) imply: % 263.42/56.97 | | | | (96) $false % 263.42/56.97 | | | | % 263.42/56.97 | | | | CLOSE: (96) is inconsistent. % 263.42/56.97 | | | | % 263.42/56.97 | | | Case 2: % 263.42/56.97 | | | | % 263.42/56.97 | | | | (97) a_select3(q_ds1_filter, n5, n4) = all_74_0 & $i(all_74_0) % 263.42/56.97 | | | | % 263.42/56.97 | | | | ALPHA: (97) implies: % 263.42/56.97 | | | | (98) a_select3(q_ds1_filter, n5, n4) = all_74_0 % 263.42/56.97 | | | | % 263.42/56.97 | | | | GROUND_INST: instantiating (17) with all_74_0, all_74_1, n4, n5, % 263.42/56.97 | | | | q_ds1_filter, simplifying with (86), (98) gives: % 263.42/56.97 | | | | (99) all_74_0 = all_74_1 % 263.42/56.97 | | | | % 263.42/56.97 | | | | REDUCE: (7), (99) imply: % 263.42/56.97 | | | | (100) $false % 263.42/56.97 | | | | % 263.42/56.97 | | | | CLOSE: (100) is inconsistent. % 263.42/56.97 | | | | % 263.42/56.97 | | | End of split % 263.42/56.97 | | | % 263.42/56.97 | | End of split % 263.42/56.97 | | % 263.42/56.97 | End of split % 263.42/56.97 | % 263.42/56.97 End of proof % 263.42/56.97 % 263.42/56.97 Sub-proof #84 shows that the following formulas are inconsistent: % 263.42/56.97 ---------------------------------------------------------------- % 263.42/56.97 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 263.42/56.97 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 263.42/56.97 v0)) % 263.42/56.97 (2) a_select3(q_ds1_filter, n5, n3) = all_74_0 % 263.42/56.97 (3) a_select3(q_ds1_filter, n5, n3) = all_74_1 % 263.42/56.97 (4) ~ (all_74_0 = all_74_1) % 263.42/56.97 % 263.42/56.97 Begin of proof % 263.42/56.97 | % 263.42/56.97 | GROUND_INST: instantiating (1) with all_74_0, all_74_1, n3, n5, q_ds1_filter, % 263.42/56.97 | simplifying with (2), (3) gives: % 263.42/56.97 | (5) all_74_0 = all_74_1 % 263.42/56.97 | % 263.42/56.97 | REDUCE: (4), (5) imply: % 263.42/56.97 | (6) $false % 263.42/56.97 | % 263.42/56.97 | CLOSE: (6) is inconsistent. % 263.42/56.97 | % 263.42/56.97 End of proof % 263.42/56.97 % 263.42/56.97 Sub-proof #85 shows that the following formulas are inconsistent: % 263.42/56.97 ---------------------------------------------------------------- % 263.42/56.97 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 263.42/56.97 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 263.42/56.97 v0)) % 263.42/56.97 (2) a_select3(q_ds1_filter, n5, n2) = all_74_0 % 263.42/56.97 (3) a_select3(q_ds1_filter, n5, n2) = all_74_1 % 263.42/56.97 (4) ~ (all_74_0 = all_74_1) % 263.42/56.97 % 263.42/56.97 Begin of proof % 263.42/56.97 | % 263.42/56.97 | GROUND_INST: instantiating (1) with all_74_0, all_74_1, n2, n5, q_ds1_filter, % 263.42/56.97 | simplifying with (2), (3) gives: % 263.42/56.97 | (5) all_74_0 = all_74_1 % 263.42/56.97 | % 263.42/56.97 | REDUCE: (4), (5) imply: % 263.42/56.97 | (6) $false % 263.42/56.97 | % 263.42/56.97 | CLOSE: (6) is inconsistent. % 263.42/56.97 | % 263.42/56.97 End of proof % 263.42/56.97 % 263.42/56.97 Sub-proof #86 shows that the following formulas are inconsistent: % 263.42/56.97 ---------------------------------------------------------------- % 263.42/56.97 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 263.42/56.97 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 263.42/56.97 v0)) % 263.42/56.97 (2) a_select3(q_ds1_filter, n5, n1) = all_74_0 % 263.42/56.97 (3) a_select3(q_ds1_filter, n5, n1) = all_74_1 % 263.42/56.97 (4) ~ (all_74_0 = all_74_1) % 263.42/56.97 % 263.42/56.97 Begin of proof % 263.42/56.97 | % 263.42/56.97 | GROUND_INST: instantiating (1) with all_74_0, all_74_1, n1, n5, q_ds1_filter, % 263.42/56.97 | simplifying with (2), (3) gives: % 263.42/56.97 | (5) all_74_0 = all_74_1 % 263.42/56.97 | % 263.42/56.97 | REDUCE: (4), (5) imply: % 263.42/56.97 | (6) $false % 263.42/56.97 | % 263.42/56.97 | CLOSE: (6) is inconsistent. % 263.42/56.97 | % 263.42/56.97 End of proof % 263.42/56.97 % 263.42/56.97 Sub-proof #87 shows that the following formulas are inconsistent: % 263.42/56.97 ---------------------------------------------------------------- % 263.42/56.97 (1) $i(n3) % 263.42/56.97 (2) all_74_3 = n4 | gt(n4, all_74_3) % 263.42/56.97 (3) $i(n4) % 263.42/56.97 (4) ! [v0: $i] : (v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0, n1) | ~ % 263.42/56.97 leq(n0, v0)) % 263.42/56.97 (5) a_select3(q_ds1_filter, all_74_2, all_74_3) = all_74_0 % 263.42/56.97 (6) a_select3(q_ds1_filter, all_74_3, all_74_2) = all_74_1 % 263.42/56.97 (7) pred(n2) = n1 % 263.42/56.97 (8) leq(n0, all_74_3) % 263.42/56.97 (9) ~ (all_74_2 = n0) % 263.42/56.97 (10) ~ (all_74_0 = all_74_1) % 263.42/56.97 (11) leq(n0, all_74_2) % 263.42/56.97 (12) leq(all_74_2, n5) % 263.42/56.97 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (a_select3(q_ds1_filter, % 263.42/56.97 v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ leq(v1, all_74_20) | ~ % 263.42/56.97 leq(v0, all_74_20) | ~ leq(n0, v1) | ~ leq(n0, v0) | % 263.42/56.97 (a_select3(q_ds1_filter, v1, v0) = v2 & $i(v2))) % 263.42/56.97 (14) $i(all_74_3) % 263.42/56.97 (15) all_74_2 = n4 | gt(n4, all_74_2) % 263.42/56.97 (16) pred(n3) = n2 % 263.42/56.97 (17) $i(all_74_2) % 263.42/56.97 (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 263.42/56.97 (v1 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 263.42/56.97 v0)) % 263.42/56.97 (19) pred(n4) = n3 % 263.42/56.97 (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (pred(v1) = v2) | ~ % 263.42/56.97 $i(v1) | ~ $i(v0) | ~ gt(v1, v0) | leq(v0, v2)) % 263.42/56.97 (21) all_74_20 = n5 % 263.42/56.97 (22) ~ (all_74_3 = n0) % 263.42/56.97 (23) $i(n2) % 263.42/56.97 (24) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ % 263.42/56.97 leq(v0, v1) | gt(v1, v0)) % 263.42/56.97 (25) leq(all_74_3, n5) % 263.42/56.97 % 263.42/56.97 Begin of proof % 263.42/56.97 | % 263.42/56.97 | BETA: splitting (15) gives: % 263.42/56.97 | % 263.42/56.97 | Case 1: % 263.42/56.97 | | % 263.42/56.97 | | (26) gt(n4, all_74_2) % 263.42/56.97 | | % 263.42/56.97 | | GROUND_INST: instantiating (20) with all_74_2, n4, n3, simplifying with (3), % 263.42/56.97 | | (17), (19), (26) gives: % 263.42/56.97 | | (27) leq(all_74_2, n3) % 263.42/56.97 | | % 263.42/56.97 | | GROUND_INST: instantiating (24) with all_74_2, n3, simplifying with (1), % 263.42/56.97 | | (17), (27) gives: % 263.42/56.97 | | (28) all_74_2 = n3 | gt(n3, all_74_2) % 263.42/56.97 | | % 263.42/56.97 | | BETA: splitting (2) gives: % 263.42/56.97 | | % 263.42/56.97 | | Case 1: % 263.42/56.97 | | | % 263.42/56.97 | | | (29) gt(n4, all_74_3) % 263.42/56.97 | | | % 263.42/56.97 | | | GROUND_INST: instantiating (20) with all_74_3, n4, n3, simplifying with % 263.42/56.97 | | | (3), (14), (19), (29) gives: % 263.42/56.97 | | | (30) leq(all_74_3, n3) % 263.42/56.97 | | | % 263.42/56.97 | | | GROUND_INST: instantiating (24) with all_74_3, n3, simplifying with (1), % 263.42/56.97 | | | (14), (30) gives: % 263.42/56.97 | | | (31) all_74_3 = n3 | gt(n3, all_74_3) % 263.42/56.97 | | | % 263.42/56.97 | | | BETA: splitting (28) gives: % 263.42/56.97 | | | % 263.42/56.97 | | | Case 1: % 263.42/56.97 | | | | % 263.42/56.97 | | | | (32) gt(n3, all_74_2) % 263.42/56.97 | | | | % 263.42/56.97 | | | | GROUND_INST: instantiating (20) with all_74_2, n3, n2, simplifying with % 263.42/56.97 | | | | (1), (16), (17), (32) gives: % 263.42/56.97 | | | | (33) leq(all_74_2, n2) % 263.42/56.97 | | | | % 263.42/56.97 | | | | GROUND_INST: instantiating (24) with all_74_2, n2, simplifying with % 263.42/56.97 | | | | (17), (23), (33) gives: % 263.42/56.97 | | | | (34) all_74_2 = n2 | gt(n2, all_74_2) % 263.42/56.97 | | | | % 263.42/56.97 | | | | BETA: splitting (31) gives: % 263.42/56.97 | | | | % 263.42/56.97 | | | | Case 1: % 263.42/56.97 | | | | | % 263.42/56.97 | | | | | (35) gt(n3, all_74_3) % 263.42/56.97 | | | | | % 263.42/56.97 | | | | | GROUND_INST: instantiating (20) with all_74_3, n3, n2, simplifying % 263.42/56.97 | | | | | with (1), (14), (16), (35) gives: % 263.42/56.97 | | | | | (36) leq(all_74_3, n2) % 263.42/56.97 | | | | | % 263.42/56.97 | | | | | GROUND_INST: instantiating (24) with all_74_3, n2, simplifying with % 263.42/56.97 | | | | | (14), (23), (36) gives: % 263.42/56.97 | | | | | (37) all_74_3 = n2 | gt(n2, all_74_3) % 263.42/56.97 | | | | | % 263.42/56.97 | | | | | BETA: splitting (34) gives: % 263.42/56.97 | | | | | % 263.42/56.97 | | | | | Case 1: % 263.42/56.97 | | | | | | % 263.42/56.97 | | | | | | (38) gt(n2, all_74_2) % 263.42/56.97 | | | | | | % 263.42/56.97 | | | | | | GROUND_INST: instantiating (20) with all_74_2, n2, n1, simplifying % 263.42/56.97 | | | | | | with (7), (17), (23), (38) gives: % 263.42/56.97 | | | | | | (39) leq(all_74_2, n1) % 263.42/56.97 | | | | | | % 263.42/56.97 | | | | | | GROUND_INST: instantiating (4) with all_74_2, simplifying with (11), % 263.42/56.97 | | | | | | (17), (39) gives: % 263.42/56.97 | | | | | | (40) all_74_2 = n1 | all_74_2 = n0 % 263.42/56.97 | | | | | | % 263.42/56.97 | | | | | | BETA: splitting (40) gives: % 263.42/56.97 | | | | | | % 263.42/56.97 | | | | | | Case 1: % 263.42/56.97 | | | | | | | % 263.42/56.97 | | | | | | | (41) all_74_2 = n0 % 263.42/56.97 | | | | | | | % 263.42/56.97 | | | | | | | REDUCE: (9), (41) imply: % 263.42/56.97 | | | | | | | (42) $false % 263.42/56.97 | | | | | | | % 263.42/56.97 | | | | | | | CLOSE: (42) is inconsistent. % 263.42/56.97 | | | | | | | % 263.42/56.97 | | | | | | Case 2: % 263.42/56.97 | | | | | | | % 263.42/56.97 | | | | | | | (43) all_74_2 = n1 % 263.42/56.97 | | | | | | | % 263.42/56.97 | | | | | | | REDUCE: (5), (43) imply: % 263.42/56.97 | | | | | | | (44) a_select3(q_ds1_filter, n1, all_74_3) = all_74_0 % 263.42/56.97 | | | | | | | % 263.42/56.97 | | | | | | | REDUCE: (6), (43) imply: % 263.42/56.97 | | | | | | | (45) a_select3(q_ds1_filter, all_74_3, n1) = all_74_1 % 263.42/56.97 | | | | | | | % 263.42/56.97 | | | | | | | REDUCE: (17), (43) imply: % 263.42/56.97 | | | | | | | (46) $i(n1) % 263.42/56.97 | | | | | | | % 263.42/56.97 | | | | | | | REDUCE: (12), (43) imply: % 263.42/56.97 | | | | | | | (47) leq(n1, n5) % 263.42/56.97 | | | | | | | % 263.42/56.97 | | | | | | | REDUCE: (11), (43) imply: % 263.42/56.97 | | | | | | | (48) leq(n0, n1) % 263.42/56.97 | | | | | | | % 263.42/56.97 | | | | | | | BETA: splitting (37) gives: % 263.42/56.97 | | | | | | | % 263.42/56.97 | | | | | | | Case 1: % 263.42/56.97 | | | | | | | | % 263.42/56.97 | | | | | | | | (49) gt(n2, all_74_3) % 263.42/56.97 | | | | | | | | % 263.42/56.97 | | | | | | | | GROUND_INST: instantiating (20) with all_74_3, n2, n1, % 263.42/56.97 | | | | | | | | simplifying with (7), (14), (23), (49) gives: % 263.42/56.97 | | | | | | | | (50) leq(all_74_3, n1) % 263.42/56.97 | | | | | | | | % 263.42/56.97 | | | | | | | | GROUND_INST: instantiating (4) with all_74_3, simplifying with % 263.42/56.97 | | | | | | | | (8), (14), (50) gives: % 263.42/56.97 | | | | | | | | (51) all_74_3 = n1 | all_74_3 = n0 % 263.42/56.97 | | | | | | | | % 263.42/56.97 | | | | | | | | BETA: splitting (51) gives: % 263.42/56.97 | | | | | | | | % 263.42/56.97 | | | | | | | | Case 1: % 263.42/56.97 | | | | | | | | | % 263.42/56.97 | | | | | | | | | (52) all_74_3 = n0 % 263.42/56.97 | | | | | | | | | % 263.42/56.97 | | | | | | | | | REDUCE: (22), (52) imply: % 263.42/56.97 | | | | | | | | | (53) $false % 263.42/56.97 | | | | | | | | | % 263.42/56.97 | | | | | | | | | CLOSE: (53) is inconsistent. % 263.42/56.97 | | | | | | | | | % 263.42/56.97 | | | | | | | | Case 2: % 263.42/56.97 | | | | | | | | | % 263.42/56.97 | | | | | | | | | (54) all_74_3 = n1 % 263.42/56.97 | | | | | | | | | % 263.42/56.97 | | | | | | | | | REDUCE: (45), (54) imply: % 263.42/56.97 | | | | | | | | | (55) a_select3(q_ds1_filter, n1, n1) = all_74_1 % 263.42/56.97 | | | | | | | | | % 263.42/56.97 | | | | | | | | | REDUCE: (44), (54) imply: % 263.42/56.97 | | | | | | | | | (56) a_select3(q_ds1_filter, n1, n1) = all_74_0 % 263.42/56.97 | | | | | | | | | % 263.42/56.97 | | | | | | | | | GROUND_INST: instantiating (18) with all_74_1, all_74_0, n1, % 263.42/56.97 | | | | | | | | | n1, q_ds1_filter, simplifying with (55), (56) % 263.42/56.97 | | | | | | | | | gives: % 263.42/56.97 | | | | | | | | | (57) all_74_0 = all_74_1 % 263.42/56.97 | | | | | | | | | % 263.42/56.97 | | | | | | | | | REDUCE: (10), (57) imply: % 263.42/56.97 | | | | | | | | | (58) $false % 263.42/56.97 | | | | | | | | | % 263.42/56.97 | | | | | | | | | CLOSE: (58) is inconsistent. % 263.42/56.97 | | | | | | | | | % 263.42/56.97 | | | | | | | | End of split % 263.42/56.97 | | | | | | | | % 263.42/56.97 | | | | | | | Case 2: % 263.42/56.97 | | | | | | | | % 263.42/56.97 | | | | | | | | (59) all_74_3 = n2 % 263.42/56.97 | | | | | | | | % 263.42/56.97 | | | | | | | | REDUCE: (45), (59) imply: % 263.42/56.97 | | | | | | | | (60) a_select3(q_ds1_filter, n2, n1) = all_74_1 % 263.42/56.97 | | | | | | | | % 263.42/56.97 | | | | | | | | REDUCE: (44), (59) imply: % 263.42/56.97 | | | | | | | | (61) a_select3(q_ds1_filter, n1, n2) = all_74_0 % 263.42/56.97 | | | | | | | | % 263.42/56.97 | | | | | | | | REDUCE: (25), (59) imply: % 263.42/56.97 | | | | | | | | (62) leq(n2, n5) % 263.42/56.97 | | | | | | | | % 263.42/56.97 | | | | | | | | REDUCE: (8), (59) imply: % 263.42/56.97 | | | | | | | | (63) leq(n0, n2) % 263.42/56.97 | | | | | | | | % 263.42/56.97 | | | | | | | | GROUND_INST: instantiating (13) with n1, n2, all_74_0, % 263.42/56.97 | | | | | | | | simplifying with (23), (46), (48), (61), (63) % 263.42/56.97 | | | | | | | | gives: % 263.42/56.97 | | | | | | | | (64) ~ leq(n2, all_74_20) | ~ leq(n1, all_74_20) | % 263.42/56.97 | | | | | | | | (a_select3(q_ds1_filter, n2, n1) = all_74_0 & % 263.42/56.97 | | | | | | | | $i(all_74_0)) % 263.42/56.97 | | | | | | | | % 263.42/56.97 | | | | | | | | BETA: splitting (64) gives: % 263.42/56.97 | | | | | | | | % 263.42/56.97 | | | | | | | | Case 1: % 263.42/56.97 | | | | | | | | | % 263.42/56.97 | | | | | | | | | (65) ~ leq(n2, all_74_20) % 263.42/56.97 | | | | | | | | | % 263.42/56.97 | | | | | | | | | REDUCE: (21), (65) imply: % 263.42/56.97 | | | | | | | | | (66) ~ leq(n2, n5) % 263.42/56.97 | | | | | | | | | % 263.42/56.97 | | | | | | | | | PRED_UNIFY: (62), (66) imply: % 263.42/56.97 | | | | | | | | | (67) $false % 263.42/56.97 | | | | | | | | | % 263.42/56.97 | | | | | | | | | CLOSE: (67) is inconsistent. % 263.42/56.97 | | | | | | | | | % 263.42/56.97 | | | | | | | | Case 2: % 263.42/56.97 | | | | | | | | | % 263.42/56.97 | | | | | | | | | (68) ~ leq(n1, all_74_20) | (a_select3(q_ds1_filter, n2, % 263.42/56.97 | | | | | | | | | n1) = all_74_0 & $i(all_74_0)) % 263.42/56.97 | | | | | | | | | % 263.42/56.97 | | | | | | | | | BETA: splitting (68) gives: % 263.42/56.97 | | | | | | | | | % 263.42/56.97 | | | | | | | | | Case 1: % 263.42/56.97 | | | | | | | | | | % 263.42/56.97 | | | | | | | | | | (69) ~ leq(n1, all_74_20) % 263.42/56.97 | | | | | | | | | | % 263.42/56.97 | | | | | | | | | | REDUCE: (21), (69) imply: % 263.42/56.97 | | | | | | | | | | (70) ~ leq(n1, n5) % 263.42/56.97 | | | | | | | | | | % 263.42/56.97 | | | | | | | | | | PRED_UNIFY: (47), (70) imply: % 263.42/56.97 | | | | | | | | | | (71) $false % 263.42/56.97 | | | | | | | | | | % 263.42/56.97 | | | | | | | | | | CLOSE: (71) is inconsistent. % 263.42/56.97 | | | | | | | | | | % 263.42/56.97 | | | | | | | | | Case 2: % 263.42/56.97 | | | | | | | | | | % 263.42/56.97 | | | | | | | | | | (72) a_select3(q_ds1_filter, n2, n1) = all_74_0 & % 263.42/56.97 | | | | | | | | | | $i(all_74_0) % 263.42/56.97 | | | | | | | | | | % 263.42/56.97 | | | | | | | | | | ALPHA: (72) implies: % 263.42/56.97 | | | | | | | | | | (73) a_select3(q_ds1_filter, n2, n1) = all_74_0 % 263.42/56.97 | | | | | | | | | | % 263.42/56.97 | | | | | | | | | | REF_CLOSE: (10), (18), (60), (73) are inconsistent by % 263.42/56.97 | | | | | | | | | | sub-proof #92. % 263.42/56.97 | | | | | | | | | | % 263.42/56.97 | | | | | | | | | End of split % 263.42/56.97 | | | | | | | | | % 263.42/56.97 | | | | | | | | End of split % 263.42/56.97 | | | | | | | | % 263.42/56.97 | | | | | | | End of split % 263.42/56.97 | | | | | | | % 263.42/56.97 | | | | | | End of split % 263.42/56.97 | | | | | | % 263.42/56.97 | | | | | Case 2: % 263.42/56.97 | | | | | | % 263.42/56.97 | | | | | | (74) all_74_2 = n2 % 263.42/56.98 | | | | | | % 263.42/56.98 | | | | | | REDUCE: (5), (74) imply: % 263.42/56.98 | | | | | | (75) a_select3(q_ds1_filter, n2, all_74_3) = all_74_0 % 263.42/56.98 | | | | | | % 263.42/56.98 | | | | | | REDUCE: (6), (74) imply: % 263.42/56.98 | | | | | | (76) a_select3(q_ds1_filter, all_74_3, n2) = all_74_1 % 263.42/56.98 | | | | | | % 263.42/56.98 | | | | | | REDUCE: (12), (74) imply: % 263.42/56.98 | | | | | | (77) leq(n2, n5) % 263.42/56.98 | | | | | | % 263.42/56.98 | | | | | | REDUCE: (11), (74) imply: % 263.42/56.98 | | | | | | (78) leq(n0, n2) % 263.42/56.98 | | | | | | % 263.42/56.98 | | | | | | BETA: splitting (37) gives: % 263.42/56.98 | | | | | | % 263.42/56.98 | | | | | | Case 1: % 263.42/56.98 | | | | | | | % 263.42/56.98 | | | | | | | (79) gt(n2, all_74_3) % 263.42/56.98 | | | | | | | % 263.42/56.98 | | | | | | | GROUND_INST: instantiating (20) with all_74_3, n2, n1, simplifying % 263.42/56.98 | | | | | | | with (7), (14), (23), (79) gives: % 263.42/56.98 | | | | | | | (80) leq(all_74_3, n1) % 263.42/56.98 | | | | | | | % 263.42/56.98 | | | | | | | GROUND_INST: instantiating (4) with all_74_3, simplifying with % 263.42/56.98 | | | | | | | (8), (14), (80) gives: % 263.42/56.98 | | | | | | | (81) all_74_3 = n1 | all_74_3 = n0 % 263.42/56.98 | | | | | | | % 263.42/56.98 | | | | | | | BETA: splitting (81) gives: % 263.42/56.98 | | | | | | | % 263.42/56.98 | | | | | | | Case 1: % 263.42/56.98 | | | | | | | | % 263.42/56.98 | | | | | | | | (82) all_74_3 = n0 % 263.42/56.98 | | | | | | | | % 263.42/56.98 | | | | | | | | REDUCE: (22), (82) imply: % 263.42/56.98 | | | | | | | | (83) $false % 263.42/56.98 | | | | | | | | % 263.42/56.98 | | | | | | | | CLOSE: (83) is inconsistent. % 263.42/56.98 | | | | | | | | % 263.42/56.98 | | | | | | | Case 2: % 263.42/56.98 | | | | | | | | % 263.42/56.98 | | | | | | | | (84) all_74_3 = n1 % 263.42/56.98 | | | | | | | | % 263.42/56.98 | | | | | | | | REDUCE: (76), (84) imply: % 263.42/56.98 | | | | | | | | (85) a_select3(q_ds1_filter, n1, n2) = all_74_1 % 263.42/56.98 | | | | | | | | % 263.42/56.98 | | | | | | | | REDUCE: (75), (84) imply: % 263.42/56.98 | | | | | | | | (86) a_select3(q_ds1_filter, n2, n1) = all_74_0 % 263.42/56.98 | | | | | | | | % 263.42/56.98 | | | | | | | | REDUCE: (14), (84) imply: % 263.42/56.98 | | | | | | | | (87) $i(n1) % 263.42/56.98 | | | | | | | | % 263.42/56.98 | | | | | | | | REDUCE: (25), (84) imply: % 263.42/56.98 | | | | | | | | (88) leq(n1, n5) % 263.42/56.98 | | | | | | | | % 263.42/56.98 | | | | | | | | REDUCE: (8), (84) imply: % 263.42/56.98 | | | | | | | | (89) leq(n0, n1) % 263.42/56.98 | | | | | | | | % 263.42/56.98 | | | | | | | | GROUND_INST: instantiating (13) with n1, n2, all_74_1, % 263.42/56.98 | | | | | | | | simplifying with (23), (78), (85), (87), (89) % 263.42/56.98 | | | | | | | | gives: % 263.42/56.98 | | | | | | | | (90) ~ leq(n2, all_74_20) | ~ leq(n1, all_74_20) | % 263.42/56.98 | | | | | | | | (a_select3(q_ds1_filter, n2, n1) = all_74_1 & % 263.42/56.98 | | | | | | | | $i(all_74_1)) % 263.42/56.98 | | | | | | | | % 263.42/56.98 | | | | | | | | BETA: splitting (90) gives: % 263.42/56.98 | | | | | | | | % 263.42/56.98 | | | | | | | | Case 1: % 263.42/56.98 | | | | | | | | | % 263.42/56.98 | | | | | | | | | (91) ~ leq(n2, all_74_20) % 263.42/56.98 | | | | | | | | | % 263.42/56.98 | | | | | | | | | REDUCE: (21), (91) imply: % 263.42/56.98 | | | | | | | | | (92) ~ leq(n2, n5) % 263.42/56.98 | | | | | | | | | % 263.42/56.98 | | | | | | | | | PRED_UNIFY: (77), (92) imply: % 263.42/56.98 | | | | | | | | | (93) $false % 263.42/56.98 | | | | | | | | | % 263.42/56.98 | | | | | | | | | CLOSE: (93) is inconsistent. % 263.42/56.98 | | | | | | | | | % 263.42/56.98 | | | | | | | | Case 2: % 263.42/56.98 | | | | | | | | | % 263.42/56.98 | | | | | | | | | (94) ~ leq(n1, all_74_20) | (a_select3(q_ds1_filter, n2, % 263.42/56.98 | | | | | | | | | n1) = all_74_1 & $i(all_74_1)) % 263.42/56.98 | | | | | | | | | % 263.42/56.98 | | | | | | | | | BETA: splitting (94) gives: % 263.42/56.98 | | | | | | | | | % 263.42/56.98 | | | | | | | | | Case 1: % 263.42/56.98 | | | | | | | | | | % 263.42/56.98 | | | | | | | | | | (95) ~ leq(n1, all_74_20) % 263.42/56.98 | | | | | | | | | | % 263.42/56.98 | | | | | | | | | | REDUCE: (21), (95) imply: % 263.42/56.98 | | | | | | | | | | (96) ~ leq(n1, n5) % 263.42/56.98 | | | | | | | | | | % 263.42/56.98 | | | | | | | | | | PRED_UNIFY: (88), (96) imply: % 263.42/56.98 | | | | | | | | | | (97) $false % 263.42/56.98 | | | | | | | | | | % 263.42/56.98 | | | | | | | | | | CLOSE: (97) is inconsistent. % 263.42/56.98 | | | | | | | | | | % 263.42/56.98 | | | | | | | | | Case 2: % 263.42/56.98 | | | | | | | | | | % 263.42/56.98 | | | | | | | | | | (98) a_select3(q_ds1_filter, n2, n1) = all_74_1 & % 263.42/56.98 | | | | | | | | | | $i(all_74_1) % 263.42/56.98 | | | | | | | | | | % 263.42/56.98 | | | | | | | | | | ALPHA: (98) implies: % 263.42/56.98 | | | | | | | | | | (99) a_select3(q_ds1_filter, n2, n1) = all_74_1 % 263.42/56.98 | | | | | | | | | | % 263.42/56.98 | | | | | | | | | | REF_CLOSE: (10), (18), (86), (99) are inconsistent by % 263.42/56.98 | | | | | | | | | | sub-proof #92. % 263.42/56.98 | | | | | | | | | | % 263.42/56.98 | | | | | | | | | End of split % 263.42/56.98 | | | | | | | | | % 263.42/56.98 | | | | | | | | End of split % 263.42/56.98 | | | | | | | | % 263.42/56.98 | | | | | | | End of split % 263.42/56.98 | | | | | | | % 263.42/56.98 | | | | | | Case 2: % 263.42/56.98 | | | | | | | % 263.42/56.98 | | | | | | | (100) all_74_3 = n2 % 263.42/56.98 | | | | | | | % 263.42/56.98 | | | | | | | REDUCE: (76), (100) imply: % 263.42/56.98 | | | | | | | (101) a_select3(q_ds1_filter, n2, n2) = all_74_1 % 263.42/56.98 | | | | | | | % 263.42/56.98 | | | | | | | REDUCE: (75), (100) imply: % 263.42/56.98 | | | | | | | (102) a_select3(q_ds1_filter, n2, n2) = all_74_0 % 263.42/56.98 | | | | | | | % 263.42/56.98 | | | | | | | GROUND_INST: instantiating (18) with all_74_1, all_74_0, n2, n2, % 263.42/56.98 | | | | | | | q_ds1_filter, simplifying with (101), (102) gives: % 263.42/56.98 | | | | | | | (103) all_74_0 = all_74_1 % 263.42/56.98 | | | | | | | % 263.42/56.98 | | | | | | | REDUCE: (10), (103) imply: % 263.42/56.98 | | | | | | | (104) $false % 263.42/56.98 | | | | | | | % 263.42/56.98 | | | | | | | CLOSE: (104) is inconsistent. % 263.42/56.98 | | | | | | | % 263.42/56.98 | | | | | | End of split % 263.42/56.98 | | | | | | % 263.42/56.98 | | | | | End of split % 263.42/56.98 | | | | | % 263.42/56.98 | | | | Case 2: % 263.42/56.98 | | | | | % 263.42/56.98 | | | | | (105) all_74_3 = n3 % 263.42/56.98 | | | | | % 263.42/56.98 | | | | | REDUCE: (5), (105) imply: % 263.42/56.98 | | | | | (106) a_select3(q_ds1_filter, all_74_2, n3) = all_74_0 % 263.42/56.98 | | | | | % 263.42/56.98 | | | | | REDUCE: (6), (105) imply: % 263.42/56.98 | | | | | (107) a_select3(q_ds1_filter, n3, all_74_2) = all_74_1 % 263.42/56.98 | | | | | % 263.42/56.98 | | | | | REDUCE: (25), (105) imply: % 263.42/56.98 | | | | | (108) leq(n3, n5) % 263.42/56.98 | | | | | % 263.42/56.98 | | | | | REDUCE: (8), (105) imply: % 263.42/56.98 | | | | | (109) leq(n0, n3) % 263.42/56.98 | | | | | % 263.42/56.98 | | | | | BETA: splitting (34) gives: % 263.42/56.98 | | | | | % 263.42/56.98 | | | | | Case 1: % 263.42/56.98 | | | | | | % 263.42/56.98 | | | | | | (110) gt(n2, all_74_2) % 263.42/56.98 | | | | | | % 263.42/56.98 | | | | | | GROUND_INST: instantiating (20) with all_74_2, n2, n1, simplifying % 263.42/56.98 | | | | | | with (7), (17), (23), (110) gives: % 263.42/56.98 | | | | | | (111) leq(all_74_2, n1) % 263.42/56.98 | | | | | | % 263.42/56.98 | | | | | | GROUND_INST: instantiating (4) with all_74_2, simplifying with (11), % 263.42/56.98 | | | | | | (17), (111) gives: % 263.42/56.98 | | | | | | (112) all_74_2 = n1 | all_74_2 = n0 % 263.42/56.98 | | | | | | % 263.42/56.98 | | | | | | BETA: splitting (112) gives: % 263.42/56.98 | | | | | | % 263.42/56.98 | | | | | | Case 1: % 263.42/56.98 | | | | | | | % 263.42/56.98 | | | | | | | (113) all_74_2 = n0 % 263.42/56.98 | | | | | | | % 263.42/56.98 | | | | | | | REDUCE: (9), (113) imply: % 263.42/56.98 | | | | | | | (114) $false % 263.42/56.98 | | | | | | | % 263.42/56.98 | | | | | | | CLOSE: (114) is inconsistent. % 263.42/56.98 | | | | | | | % 263.42/56.98 | | | | | | Case 2: % 263.42/56.98 | | | | | | | % 263.42/56.98 | | | | | | | (115) all_74_2 = n1 % 263.42/56.98 | | | | | | | % 263.42/56.98 | | | | | | | REDUCE: (106), (115) imply: % 263.42/56.98 | | | | | | | (116) a_select3(q_ds1_filter, n1, n3) = all_74_0 % 263.42/56.98 | | | | | | | % 263.42/56.98 | | | | | | | REDUCE: (107), (115) imply: % 263.42/56.98 | | | | | | | (117) a_select3(q_ds1_filter, n3, n1) = all_74_1 % 263.42/56.98 | | | | | | | % 263.42/56.98 | | | | | | | REDUCE: (17), (115) imply: % 263.42/56.98 | | | | | | | (118) $i(n1) % 263.42/56.98 | | | | | | | % 263.42/56.98 | | | | | | | REDUCE: (12), (115) imply: % 263.42/56.98 | | | | | | | (119) leq(n1, n5) % 263.42/56.98 | | | | | | | % 263.42/56.98 | | | | | | | REDUCE: (11), (115) imply: % 263.42/56.98 | | | | | | | (120) leq(n0, n1) % 263.42/56.98 | | | | | | | % 263.42/56.98 | | | | | | | GROUND_INST: instantiating (13) with n1, n3, all_74_0, simplifying % 263.42/56.98 | | | | | | | with (1), (109), (116), (118), (120) gives: % 263.42/56.98 | | | | | | | (121) ~ leq(n3, all_74_20) | ~ leq(n1, all_74_20) | % 263.42/56.98 | | | | | | | (a_select3(q_ds1_filter, n3, n1) = all_74_0 & % 263.42/56.98 | | | | | | | $i(all_74_0)) % 263.42/56.98 | | | | | | | % 263.42/56.98 | | | | | | | BETA: splitting (121) gives: % 263.42/56.98 | | | | | | | % 263.42/56.98 | | | | | | | Case 1: % 263.42/56.98 | | | | | | | | % 263.42/56.98 | | | | | | | | (122) ~ leq(n3, all_74_20) % 263.42/56.98 | | | | | | | | % 263.42/56.98 | | | | | | | | REDUCE: (21), (122) imply: % 263.42/56.98 | | | | | | | | (123) ~ leq(n3, n5) % 263.42/56.98 | | | | | | | | % 263.42/56.98 | | | | | | | | PRED_UNIFY: (108), (123) imply: % 263.42/56.98 | | | | | | | | (124) $false % 263.42/56.98 | | | | | | | | % 263.42/56.98 | | | | | | | | CLOSE: (124) is inconsistent. % 263.42/56.98 | | | | | | | | % 263.42/56.98 | | | | | | | Case 2: % 263.42/56.98 | | | | | | | | % 263.42/56.98 | | | | | | | | (125) ~ leq(n1, all_74_20) | (a_select3(q_ds1_filter, n3, % 263.42/56.98 | | | | | | | | n1) = all_74_0 & $i(all_74_0)) % 263.42/56.98 | | | | | | | | % 263.42/56.98 | | | | | | | | BETA: splitting (125) gives: % 263.42/56.98 | | | | | | | | % 263.42/56.98 | | | | | | | | Case 1: % 263.42/56.98 | | | | | | | | | % 263.42/56.98 | | | | | | | | | (126) ~ leq(n1, all_74_20) % 263.42/56.98 | | | | | | | | | % 263.42/56.98 | | | | | | | | | REDUCE: (21), (126) imply: % 263.42/56.98 | | | | | | | | | (127) ~ leq(n1, n5) % 263.42/56.98 | | | | | | | | | % 263.42/56.98 | | | | | | | | | PRED_UNIFY: (119), (127) imply: % 263.42/56.98 | | | | | | | | | (128) $false % 263.42/56.98 | | | | | | | | | % 263.42/56.98 | | | | | | | | | CLOSE: (128) is inconsistent. % 263.42/56.98 | | | | | | | | | % 263.42/56.98 | | | | | | | | Case 2: % 263.42/56.98 | | | | | | | | | % 263.42/56.98 | | | | | | | | | (129) a_select3(q_ds1_filter, n3, n1) = all_74_0 & % 263.42/56.98 | | | | | | | | | $i(all_74_0) % 263.42/56.98 | | | | | | | | | % 263.42/56.98 | | | | | | | | | ALPHA: (129) implies: % 263.42/56.98 | | | | | | | | | (130) a_select3(q_ds1_filter, n3, n1) = all_74_0 % 263.42/56.98 | | | | | | | | | % 263.42/56.98 | | | | | | | | | REF_CLOSE: (10), (18), (117), (130) are inconsistent by % 263.42/56.98 | | | | | | | | | sub-proof #91. % 263.42/56.98 | | | | | | | | | % 263.42/56.98 | | | | | | | | End of split % 263.42/56.98 | | | | | | | | % 263.42/56.98 | | | | | | | End of split % 263.42/56.98 | | | | | | | % 263.42/56.98 | | | | | | End of split % 263.42/56.98 | | | | | | % 263.42/56.98 | | | | | Case 2: % 263.42/56.98 | | | | | | % 263.42/56.98 | | | | | | (131) all_74_2 = n2 % 263.42/56.98 | | | | | | % 263.42/56.98 | | | | | | REDUCE: (106), (131) imply: % 263.42/56.98 | | | | | | (132) a_select3(q_ds1_filter, n2, n3) = all_74_0 % 263.42/56.98 | | | | | | % 263.42/56.98 | | | | | | REDUCE: (107), (131) imply: % 263.42/56.98 | | | | | | (133) a_select3(q_ds1_filter, n3, n2) = all_74_1 % 263.42/56.98 | | | | | | % 263.42/56.98 | | | | | | REDUCE: (12), (131) imply: % 263.42/56.98 | | | | | | (134) leq(n2, n5) % 263.42/56.98 | | | | | | % 263.42/56.98 | | | | | | REDUCE: (11), (131) imply: % 263.42/56.98 | | | | | | (135) leq(n0, n2) % 263.42/56.98 | | | | | | % 263.42/56.98 | | | | | | GROUND_INST: instantiating (13) with n2, n3, all_74_0, simplifying % 263.42/56.98 | | | | | | with (1), (23), (109), (132), (135) gives: % 263.42/56.98 | | | | | | (136) ~ leq(n3, all_74_20) | ~ leq(n2, all_74_20) | % 263.42/56.98 | | | | | | (a_select3(q_ds1_filter, n3, n2) = all_74_0 & $i(all_74_0)) % 263.42/56.98 | | | | | | % 263.42/56.98 | | | | | | BETA: splitting (136) gives: % 263.42/56.98 | | | | | | % 263.42/56.98 | | | | | | Case 1: % 263.42/56.98 | | | | | | | % 263.42/56.98 | | | | | | | (137) ~ leq(n3, all_74_20) % 263.42/56.98 | | | | | | | % 263.42/56.98 | | | | | | | REDUCE: (21), (137) imply: % 263.42/56.98 | | | | | | | (138) ~ leq(n3, n5) % 263.42/56.98 | | | | | | | % 263.42/56.98 | | | | | | | PRED_UNIFY: (108), (138) imply: % 263.42/56.98 | | | | | | | (139) $false % 263.42/56.98 | | | | | | | % 263.42/56.98 | | | | | | | CLOSE: (139) is inconsistent. % 263.42/56.98 | | | | | | | % 263.42/56.98 | | | | | | Case 2: % 263.42/56.98 | | | | | | | % 263.42/56.98 | | | | | | | (140) ~ leq(n2, all_74_20) | (a_select3(q_ds1_filter, n3, n2) % 263.42/56.98 | | | | | | | = all_74_0 & $i(all_74_0)) % 263.42/56.98 | | | | | | | % 263.42/56.98 | | | | | | | BETA: splitting (140) gives: % 263.42/56.98 | | | | | | | % 263.42/56.98 | | | | | | | Case 1: % 263.42/56.98 | | | | | | | | % 263.42/56.98 | | | | | | | | (141) ~ leq(n2, all_74_20) % 263.42/56.98 | | | | | | | | % 263.42/56.98 | | | | | | | | REDUCE: (21), (141) imply: % 263.42/56.98 | | | | | | | | (142) ~ leq(n2, n5) % 263.42/56.98 | | | | | | | | % 263.42/56.98 | | | | | | | | PRED_UNIFY: (134), (142) imply: % 263.42/56.98 | | | | | | | | (143) $false % 263.42/56.98 | | | | | | | | % 263.42/56.98 | | | | | | | | CLOSE: (143) is inconsistent. % 263.42/56.98 | | | | | | | | % 263.42/56.98 | | | | | | | Case 2: % 263.42/56.98 | | | | | | | | % 263.42/56.98 | | | | | | | | (144) a_select3(q_ds1_filter, n3, n2) = all_74_0 & % 263.42/56.98 | | | | | | | | $i(all_74_0) % 263.42/56.98 | | | | | | | | % 263.42/56.98 | | | | | | | | ALPHA: (144) implies: % 263.42/56.98 | | | | | | | | (145) a_select3(q_ds1_filter, n3, n2) = all_74_0 % 263.42/56.98 | | | | | | | | % 263.42/56.98 | | | | | | | | REF_CLOSE: (10), (18), (133), (145) are inconsistent by % 263.42/56.98 | | | | | | | | sub-proof #90. % 263.42/56.98 | | | | | | | | % 263.42/56.98 | | | | | | | End of split % 263.42/56.98 | | | | | | | % 263.42/56.98 | | | | | | End of split % 263.42/56.98 | | | | | | % 263.42/56.98 | | | | | End of split % 263.42/56.98 | | | | | % 263.42/56.98 | | | | End of split % 263.42/56.98 | | | | % 263.42/56.98 | | | Case 2: % 263.42/56.98 | | | | % 263.42/56.98 | | | | (146) all_74_2 = n3 % 263.42/56.98 | | | | % 263.42/56.98 | | | | REDUCE: (5), (146) imply: % 263.42/56.98 | | | | (147) a_select3(q_ds1_filter, n3, all_74_3) = all_74_0 % 263.42/56.98 | | | | % 263.42/56.98 | | | | REDUCE: (6), (146) imply: % 263.42/56.98 | | | | (148) a_select3(q_ds1_filter, all_74_3, n3) = all_74_1 % 263.42/56.98 | | | | % 263.42/56.98 | | | | REDUCE: (12), (146) imply: % 263.42/56.98 | | | | (149) leq(n3, n5) % 263.42/56.98 | | | | % 263.42/56.98 | | | | REDUCE: (11), (146) imply: % 263.42/56.98 | | | | (150) leq(n0, n3) % 263.42/56.98 | | | | % 263.42/56.98 | | | | BETA: splitting (31) gives: % 263.42/56.98 | | | | % 263.42/56.98 | | | | Case 1: % 263.42/56.98 | | | | | % 263.42/56.98 | | | | | (151) gt(n3, all_74_3) % 263.42/56.98 | | | | | % 263.42/56.98 | | | | | GROUND_INST: instantiating (20) with all_74_3, n3, n2, simplifying % 263.42/56.98 | | | | | with (1), (14), (16), (151) gives: % 263.42/56.98 | | | | | (152) leq(all_74_3, n2) % 263.42/56.98 | | | | | % 263.42/56.98 | | | | | GROUND_INST: instantiating (24) with all_74_3, n2, simplifying with % 263.42/56.98 | | | | | (14), (23), (152) gives: % 263.42/56.98 | | | | | (153) all_74_3 = n2 | gt(n2, all_74_3) % 263.42/56.98 | | | | | % 263.42/56.98 | | | | | BETA: splitting (153) gives: % 263.42/56.98 | | | | | % 263.42/56.98 | | | | | Case 1: % 263.42/56.98 | | | | | | % 263.42/56.98 | | | | | | (154) gt(n2, all_74_3) % 263.42/56.98 | | | | | | % 263.42/56.98 | | | | | | GROUND_INST: instantiating (20) with all_74_3, n2, n1, simplifying % 263.42/56.98 | | | | | | with (7), (14), (23), (154) gives: % 263.42/56.98 | | | | | | (155) leq(all_74_3, n1) % 263.42/56.98 | | | | | | % 263.42/56.98 | | | | | | GROUND_INST: instantiating (4) with all_74_3, simplifying with (8), % 263.42/56.98 | | | | | | (14), (155) gives: % 263.42/56.98 | | | | | | (156) all_74_3 = n1 | all_74_3 = n0 % 263.42/56.98 | | | | | | % 263.42/56.98 | | | | | | BETA: splitting (156) gives: % 263.42/56.98 | | | | | | % 263.42/56.98 | | | | | | Case 1: % 263.42/56.98 | | | | | | | % 263.42/56.98 | | | | | | | (157) all_74_3 = n0 % 263.42/56.98 | | | | | | | % 263.42/56.98 | | | | | | | REDUCE: (22), (157) imply: % 263.42/56.98 | | | | | | | (158) $false % 263.42/56.98 | | | | | | | % 263.42/56.98 | | | | | | | CLOSE: (158) is inconsistent. % 263.42/56.98 | | | | | | | % 263.42/56.98 | | | | | | Case 2: % 263.42/56.98 | | | | | | | % 263.42/56.98 | | | | | | | (159) all_74_3 = n1 % 263.42/56.98 | | | | | | | % 263.42/56.98 | | | | | | | REDUCE: (148), (159) imply: % 263.42/56.98 | | | | | | | (160) a_select3(q_ds1_filter, n1, n3) = all_74_1 % 263.42/56.98 | | | | | | | % 263.42/56.98 | | | | | | | REDUCE: (147), (159) imply: % 263.42/56.98 | | | | | | | (161) a_select3(q_ds1_filter, n3, n1) = all_74_0 % 263.42/56.98 | | | | | | | % 263.42/56.98 | | | | | | | REDUCE: (14), (159) imply: % 263.42/56.98 | | | | | | | (162) $i(n1) % 263.42/56.98 | | | | | | | % 263.42/56.98 | | | | | | | REDUCE: (25), (159) imply: % 263.42/56.98 | | | | | | | (163) leq(n1, n5) % 263.42/56.98 | | | | | | | % 263.42/56.98 | | | | | | | REDUCE: (8), (159) imply: % 263.42/56.98 | | | | | | | (164) leq(n0, n1) % 263.42/56.98 | | | | | | | % 263.42/56.98 | | | | | | | GROUND_INST: instantiating (13) with n1, n3, all_74_1, simplifying % 263.42/56.98 | | | | | | | with (1), (150), (160), (162), (164) gives: % 263.42/56.98 | | | | | | | (165) ~ leq(n3, all_74_20) | ~ leq(n1, all_74_20) | % 263.42/56.98 | | | | | | | (a_select3(q_ds1_filter, n3, n1) = all_74_1 & % 263.42/56.98 | | | | | | | $i(all_74_1)) % 263.42/56.98 | | | | | | | % 263.42/56.98 | | | | | | | BETA: splitting (165) gives: % 263.42/56.98 | | | | | | | % 263.42/56.98 | | | | | | | Case 1: % 263.42/56.98 | | | | | | | | % 263.42/56.98 | | | | | | | | (166) ~ leq(n3, all_74_20) % 263.42/56.98 | | | | | | | | % 263.42/56.98 | | | | | | | | REDUCE: (21), (166) imply: % 263.42/56.98 | | | | | | | | (167) ~ leq(n3, n5) % 263.42/56.98 | | | | | | | | % 263.42/56.98 | | | | | | | | PRED_UNIFY: (149), (167) imply: % 263.42/56.98 | | | | | | | | (168) $false % 263.42/56.98 | | | | | | | | % 263.42/56.98 | | | | | | | | CLOSE: (168) is inconsistent. % 263.42/56.98 | | | | | | | | % 263.42/56.98 | | | | | | | Case 2: % 263.42/56.98 | | | | | | | | % 263.42/56.98 | | | | | | | | (169) ~ leq(n1, all_74_20) | (a_select3(q_ds1_filter, n3, % 263.42/56.98 | | | | | | | | n1) = all_74_1 & $i(all_74_1)) % 263.42/56.98 | | | | | | | | % 263.42/56.98 | | | | | | | | BETA: splitting (169) gives: % 263.42/56.98 | | | | | | | | % 263.42/56.98 | | | | | | | | Case 1: % 263.42/56.98 | | | | | | | | | % 263.42/56.98 | | | | | | | | | (170) ~ leq(n1, all_74_20) % 263.42/56.98 | | | | | | | | | % 263.42/56.98 | | | | | | | | | REDUCE: (21), (170) imply: % 263.42/56.98 | | | | | | | | | (171) ~ leq(n1, n5) % 263.42/56.98 | | | | | | | | | % 263.42/56.98 | | | | | | | | | PRED_UNIFY: (163), (171) imply: % 263.42/56.98 | | | | | | | | | (172) $false % 263.42/56.98 | | | | | | | | | % 263.42/56.98 | | | | | | | | | CLOSE: (172) is inconsistent. % 263.42/56.98 | | | | | | | | | % 263.42/56.98 | | | | | | | | Case 2: % 263.42/56.98 | | | | | | | | | % 263.42/56.98 | | | | | | | | | (173) a_select3(q_ds1_filter, n3, n1) = all_74_1 & % 263.42/56.98 | | | | | | | | | $i(all_74_1) % 263.42/56.98 | | | | | | | | | % 263.42/56.98 | | | | | | | | | ALPHA: (173) implies: % 263.42/56.98 | | | | | | | | | (174) a_select3(q_ds1_filter, n3, n1) = all_74_1 % 263.42/56.98 | | | | | | | | | % 263.42/56.98 | | | | | | | | | REF_CLOSE: (10), (18), (161), (174) are inconsistent by % 263.42/56.98 | | | | | | | | | sub-proof #91. % 263.42/56.98 | | | | | | | | | % 263.42/56.98 | | | | | | | | End of split % 263.42/56.98 | | | | | | | | % 263.42/56.98 | | | | | | | End of split % 263.42/56.98 | | | | | | | % 263.42/56.98 | | | | | | End of split % 263.42/56.98 | | | | | | % 263.42/56.98 | | | | | Case 2: % 263.42/56.98 | | | | | | % 263.42/56.98 | | | | | | (175) all_74_3 = n2 % 263.42/56.98 | | | | | | % 263.42/56.98 | | | | | | REDUCE: (148), (175) imply: % 263.42/56.98 | | | | | | (176) a_select3(q_ds1_filter, n2, n3) = all_74_1 % 263.42/56.98 | | | | | | % 263.42/56.98 | | | | | | REDUCE: (147), (175) imply: % 263.42/56.98 | | | | | | (177) a_select3(q_ds1_filter, n3, n2) = all_74_0 % 263.42/56.98 | | | | | | % 263.42/56.98 | | | | | | REDUCE: (25), (175) imply: % 263.42/56.98 | | | | | | (178) leq(n2, n5) % 263.42/56.98 | | | | | | % 263.42/56.98 | | | | | | REDUCE: (8), (175) imply: % 263.42/56.99 | | | | | | (179) leq(n0, n2) % 263.42/56.99 | | | | | | % 263.42/56.99 | | | | | | GROUND_INST: instantiating (13) with n2, n3, all_74_1, simplifying % 263.42/56.99 | | | | | | with (1), (23), (150), (176), (179) gives: % 263.42/56.99 | | | | | | (180) ~ leq(n3, all_74_20) | ~ leq(n2, all_74_20) | % 263.42/56.99 | | | | | | (a_select3(q_ds1_filter, n3, n2) = all_74_1 & $i(all_74_1)) % 263.42/56.99 | | | | | | % 263.42/56.99 | | | | | | BETA: splitting (180) gives: % 263.42/56.99 | | | | | | % 263.42/56.99 | | | | | | Case 1: % 263.42/56.99 | | | | | | | % 263.42/56.99 | | | | | | | (181) ~ leq(n3, all_74_20) % 263.42/56.99 | | | | | | | % 263.42/56.99 | | | | | | | REDUCE: (21), (181) imply: % 263.42/56.99 | | | | | | | (182) ~ leq(n3, n5) % 263.42/56.99 | | | | | | | % 263.42/56.99 | | | | | | | PRED_UNIFY: (149), (182) imply: % 263.42/56.99 | | | | | | | (183) $false % 263.42/56.99 | | | | | | | % 263.42/56.99 | | | | | | | CLOSE: (183) is inconsistent. % 263.42/56.99 | | | | | | | % 263.42/56.99 | | | | | | Case 2: % 263.42/56.99 | | | | | | | % 263.42/56.99 | | | | | | | (184) ~ leq(n2, all_74_20) | (a_select3(q_ds1_filter, n3, n2) % 263.42/56.99 | | | | | | | = all_74_1 & $i(all_74_1)) % 263.42/56.99 | | | | | | | % 263.42/56.99 | | | | | | | BETA: splitting (184) gives: % 263.42/56.99 | | | | | | | % 263.42/56.99 | | | | | | | Case 1: % 263.42/56.99 | | | | | | | | % 263.42/56.99 | | | | | | | | (185) ~ leq(n2, all_74_20) % 263.42/56.99 | | | | | | | | % 263.42/56.99 | | | | | | | | REDUCE: (21), (185) imply: % 263.42/56.99 | | | | | | | | (186) ~ leq(n2, n5) % 263.42/56.99 | | | | | | | | % 263.42/56.99 | | | | | | | | PRED_UNIFY: (178), (186) imply: % 263.42/56.99 | | | | | | | | (187) $false % 263.42/56.99 | | | | | | | | % 263.42/56.99 | | | | | | | | CLOSE: (187) is inconsistent. % 263.42/56.99 | | | | | | | | % 263.42/56.99 | | | | | | | Case 2: % 263.42/56.99 | | | | | | | | % 263.42/56.99 | | | | | | | | (188) a_select3(q_ds1_filter, n3, n2) = all_74_1 & % 263.42/56.99 | | | | | | | | $i(all_74_1) % 263.42/56.99 | | | | | | | | % 263.42/56.99 | | | | | | | | ALPHA: (188) implies: % 263.42/56.99 | | | | | | | | (189) a_select3(q_ds1_filter, n3, n2) = all_74_1 % 263.42/56.99 | | | | | | | | % 263.42/56.99 | | | | | | | | REF_CLOSE: (10), (18), (177), (189) are inconsistent by % 263.42/56.99 | | | | | | | | sub-proof #90. % 263.42/56.99 | | | | | | | | % 263.42/56.99 | | | | | | | End of split % 263.42/56.99 | | | | | | | % 263.42/56.99 | | | | | | End of split % 263.42/56.99 | | | | | | % 263.42/56.99 | | | | | End of split % 263.42/56.99 | | | | | % 263.42/56.99 | | | | Case 2: % 263.42/56.99 | | | | | % 263.42/56.99 | | | | | (190) all_74_3 = n3 % 263.42/56.99 | | | | | % 263.42/56.99 | | | | | REDUCE: (148), (190) imply: % 263.42/56.99 | | | | | (191) a_select3(q_ds1_filter, n3, n3) = all_74_1 % 263.42/56.99 | | | | | % 263.42/56.99 | | | | | REDUCE: (147), (190) imply: % 263.42/56.99 | | | | | (192) a_select3(q_ds1_filter, n3, n3) = all_74_0 % 263.42/56.99 | | | | | % 263.42/56.99 | | | | | GROUND_INST: instantiating (18) with all_74_1, all_74_0, n3, n3, % 263.42/56.99 | | | | | q_ds1_filter, simplifying with (191), (192) gives: % 263.42/56.99 | | | | | (193) all_74_0 = all_74_1 % 263.42/56.99 | | | | | % 263.42/56.99 | | | | | REDUCE: (10), (193) imply: % 263.42/56.99 | | | | | (194) $false % 263.42/56.99 | | | | | % 263.42/56.99 | | | | | CLOSE: (194) is inconsistent. % 263.42/56.99 | | | | | % 263.42/56.99 | | | | End of split % 263.42/56.99 | | | | % 263.42/56.99 | | | End of split % 263.42/56.99 | | | % 263.42/56.99 | | Case 2: % 263.42/56.99 | | | % 263.42/56.99 | | | (195) all_74_3 = n4 % 263.42/56.99 | | | % 263.42/56.99 | | | REDUCE: (5), (195) imply: % 263.42/56.99 | | | (196) a_select3(q_ds1_filter, all_74_2, n4) = all_74_0 % 263.42/56.99 | | | % 263.42/56.99 | | | REDUCE: (6), (195) imply: % 263.42/56.99 | | | (197) a_select3(q_ds1_filter, n4, all_74_2) = all_74_1 % 263.42/56.99 | | | % 263.42/56.99 | | | REDUCE: (25), (195) imply: % 263.42/56.99 | | | (198) leq(n4, n5) % 263.42/56.99 | | | % 263.42/56.99 | | | REDUCE: (8), (195) imply: % 263.42/56.99 | | | (199) leq(n0, n4) % 263.42/56.99 | | | % 263.42/56.99 | | | BETA: splitting (28) gives: % 263.42/56.99 | | | % 263.42/56.99 | | | Case 1: % 263.42/56.99 | | | | % 263.42/56.99 | | | | (200) gt(n3, all_74_2) % 263.42/56.99 | | | | % 263.42/56.99 | | | | GROUND_INST: instantiating (20) with all_74_2, n3, n2, simplifying with % 263.42/56.99 | | | | (1), (16), (17), (200) gives: % 263.42/56.99 | | | | (201) leq(all_74_2, n2) % 263.42/56.99 | | | | % 263.42/56.99 | | | | GROUND_INST: instantiating (24) with all_74_2, n2, simplifying with % 263.42/56.99 | | | | (17), (23), (201) gives: % 263.42/56.99 | | | | (202) all_74_2 = n2 | gt(n2, all_74_2) % 263.42/56.99 | | | | % 263.42/56.99 | | | | BETA: splitting (202) gives: % 263.42/56.99 | | | | % 263.42/56.99 | | | | Case 1: % 263.42/56.99 | | | | | % 263.42/56.99 | | | | | (203) gt(n2, all_74_2) % 263.42/56.99 | | | | | % 263.42/56.99 | | | | | GROUND_INST: instantiating (20) with all_74_2, n2, n1, simplifying % 263.42/56.99 | | | | | with (7), (17), (23), (203) gives: % 263.42/56.99 | | | | | (204) leq(all_74_2, n1) % 263.42/56.99 | | | | | % 263.42/56.99 | | | | | GROUND_INST: instantiating (4) with all_74_2, simplifying with (11), % 263.42/56.99 | | | | | (17), (204) gives: % 263.42/56.99 | | | | | (205) all_74_2 = n1 | all_74_2 = n0 % 263.42/56.99 | | | | | % 263.42/56.99 | | | | | BETA: splitting (205) gives: % 263.42/56.99 | | | | | % 263.42/56.99 | | | | | Case 1: % 263.42/56.99 | | | | | | % 263.42/56.99 | | | | | | (206) all_74_2 = n0 % 263.42/56.99 | | | | | | % 263.42/56.99 | | | | | | REDUCE: (9), (206) imply: % 263.42/56.99 | | | | | | (207) $false % 263.42/56.99 | | | | | | % 263.42/56.99 | | | | | | CLOSE: (207) is inconsistent. % 263.42/56.99 | | | | | | % 263.42/56.99 | | | | | Case 2: % 263.42/56.99 | | | | | | % 263.42/56.99 | | | | | | (208) all_74_2 = n1 % 263.42/56.99 | | | | | | % 263.42/56.99 | | | | | | REDUCE: (196), (208) imply: % 263.42/56.99 | | | | | | (209) a_select3(q_ds1_filter, n1, n4) = all_74_0 % 263.42/56.99 | | | | | | % 263.42/56.99 | | | | | | REDUCE: (197), (208) imply: % 263.42/56.99 | | | | | | (210) a_select3(q_ds1_filter, n4, n1) = all_74_1 % 263.42/56.99 | | | | | | % 263.42/56.99 | | | | | | REDUCE: (17), (208) imply: % 263.42/56.99 | | | | | | (211) $i(n1) % 263.42/56.99 | | | | | | % 263.42/56.99 | | | | | | REDUCE: (12), (208) imply: % 263.42/56.99 | | | | | | (212) leq(n1, n5) % 263.42/56.99 | | | | | | % 263.42/56.99 | | | | | | REDUCE: (11), (208) imply: % 263.42/56.99 | | | | | | (213) leq(n0, n1) % 263.42/56.99 | | | | | | % 263.42/56.99 | | | | | | GROUND_INST: instantiating (13) with n1, n4, all_74_0, simplifying % 263.42/56.99 | | | | | | with (3), (199), (209), (211), (213) gives: % 263.42/56.99 | | | | | | (214) ~ leq(n4, all_74_20) | ~ leq(n1, all_74_20) | % 263.42/56.99 | | | | | | (a_select3(q_ds1_filter, n4, n1) = all_74_0 & $i(all_74_0)) % 263.42/56.99 | | | | | | % 263.42/56.99 | | | | | | BETA: splitting (214) gives: % 263.42/56.99 | | | | | | % 263.42/56.99 | | | | | | Case 1: % 263.42/56.99 | | | | | | | % 263.42/56.99 | | | | | | | (215) ~ leq(n4, all_74_20) % 263.42/56.99 | | | | | | | % 263.42/56.99 | | | | | | | REDUCE: (21), (215) imply: % 263.42/56.99 | | | | | | | (216) ~ leq(n4, n5) % 263.42/56.99 | | | | | | | % 263.42/56.99 | | | | | | | PRED_UNIFY: (198), (216) imply: % 263.42/56.99 | | | | | | | (217) $false % 263.42/56.99 | | | | | | | % 263.42/56.99 | | | | | | | CLOSE: (217) is inconsistent. % 263.42/56.99 | | | | | | | % 263.42/56.99 | | | | | | Case 2: % 263.42/56.99 | | | | | | | % 263.42/56.99 | | | | | | | (218) ~ leq(n1, all_74_20) | (a_select3(q_ds1_filter, n4, n1) % 263.42/56.99 | | | | | | | = all_74_0 & $i(all_74_0)) % 263.42/56.99 | | | | | | | % 263.42/56.99 | | | | | | | BETA: splitting (218) gives: % 263.42/56.99 | | | | | | | % 263.42/56.99 | | | | | | | Case 1: % 263.42/56.99 | | | | | | | | % 263.42/56.99 | | | | | | | | (219) ~ leq(n1, all_74_20) % 263.42/56.99 | | | | | | | | % 263.42/56.99 | | | | | | | | REDUCE: (21), (219) imply: % 263.42/56.99 | | | | | | | | (220) ~ leq(n1, n5) % 263.42/56.99 | | | | | | | | % 263.42/56.99 | | | | | | | | PRED_UNIFY: (212), (220) imply: % 263.42/56.99 | | | | | | | | (221) $false % 263.42/56.99 | | | | | | | | % 263.42/56.99 | | | | | | | | CLOSE: (221) is inconsistent. % 263.42/56.99 | | | | | | | | % 263.42/56.99 | | | | | | | Case 2: % 263.42/56.99 | | | | | | | | % 263.42/56.99 | | | | | | | | (222) a_select3(q_ds1_filter, n4, n1) = all_74_0 & % 263.42/56.99 | | | | | | | | $i(all_74_0) % 263.42/56.99 | | | | | | | | % 263.42/56.99 | | | | | | | | ALPHA: (222) implies: % 263.42/56.99 | | | | | | | | (223) a_select3(q_ds1_filter, n4, n1) = all_74_0 % 263.42/56.99 | | | | | | | | % 263.42/56.99 | | | | | | | | REF_CLOSE: (10), (18), (210), (223) are inconsistent by % 263.42/56.99 | | | | | | | | sub-proof #89. % 263.42/56.99 | | | | | | | | % 263.42/56.99 | | | | | | | End of split % 263.42/56.99 | | | | | | | % 263.42/56.99 | | | | | | End of split % 263.42/56.99 | | | | | | % 263.42/56.99 | | | | | End of split % 263.42/56.99 | | | | | % 263.42/56.99 | | | | Case 2: % 263.42/56.99 | | | | | % 263.42/56.99 | | | | | (224) all_74_2 = n2 % 263.42/56.99 | | | | | % 263.42/56.99 | | | | | REDUCE: (196), (224) imply: % 263.42/56.99 | | | | | (225) a_select3(q_ds1_filter, n2, n4) = all_74_0 % 263.42/56.99 | | | | | % 263.42/56.99 | | | | | REDUCE: (197), (224) imply: % 263.42/56.99 | | | | | (226) a_select3(q_ds1_filter, n4, n2) = all_74_1 % 263.42/56.99 | | | | | % 263.42/56.99 | | | | | REDUCE: (12), (224) imply: % 263.42/56.99 | | | | | (227) leq(n2, n5) % 263.42/56.99 | | | | | % 263.42/56.99 | | | | | REDUCE: (11), (224) imply: % 263.42/56.99 | | | | | (228) leq(n0, n2) % 263.42/56.99 | | | | | % 263.42/56.99 | | | | | GROUND_INST: instantiating (13) with n2, n4, all_74_0, simplifying % 263.42/56.99 | | | | | with (3), (23), (199), (225), (228) gives: % 263.42/56.99 | | | | | (229) ~ leq(n4, all_74_20) | ~ leq(n2, all_74_20) | % 263.42/56.99 | | | | | (a_select3(q_ds1_filter, n4, n2) = all_74_0 & $i(all_74_0)) % 263.42/56.99 | | | | | % 263.42/56.99 | | | | | BETA: splitting (229) gives: % 263.42/56.99 | | | | | % 263.42/56.99 | | | | | Case 1: % 263.42/56.99 | | | | | | % 263.42/56.99 | | | | | | (230) ~ leq(n4, all_74_20) % 263.42/56.99 | | | | | | % 263.42/56.99 | | | | | | REDUCE: (21), (230) imply: % 263.42/56.99 | | | | | | (231) ~ leq(n4, n5) % 263.42/56.99 | | | | | | % 263.42/56.99 | | | | | | PRED_UNIFY: (198), (231) imply: % 263.42/56.99 | | | | | | (232) $false % 263.42/56.99 | | | | | | % 263.42/56.99 | | | | | | CLOSE: (232) is inconsistent. % 263.42/56.99 | | | | | | % 263.42/56.99 | | | | | Case 2: % 263.42/56.99 | | | | | | % 263.42/56.99 | | | | | | (233) ~ leq(n2, all_74_20) | (a_select3(q_ds1_filter, n4, n2) = % 263.42/56.99 | | | | | | all_74_0 & $i(all_74_0)) % 263.42/56.99 | | | | | | % 263.42/56.99 | | | | | | BETA: splitting (233) gives: % 263.42/56.99 | | | | | | % 263.42/56.99 | | | | | | Case 1: % 263.42/56.99 | | | | | | | % 263.42/56.99 | | | | | | | (234) ~ leq(n2, all_74_20) % 263.42/56.99 | | | | | | | % 263.42/56.99 | | | | | | | REDUCE: (21), (234) imply: % 263.42/56.99 | | | | | | | (235) ~ leq(n2, n5) % 263.42/56.99 | | | | | | | % 263.42/56.99 | | | | | | | PRED_UNIFY: (227), (235) imply: % 263.42/56.99 | | | | | | | (236) $false % 263.42/56.99 | | | | | | | % 263.42/56.99 | | | | | | | CLOSE: (236) is inconsistent. % 263.42/56.99 | | | | | | | % 263.42/56.99 | | | | | | Case 2: % 263.42/56.99 | | | | | | | % 263.42/56.99 | | | | | | | (237) a_select3(q_ds1_filter, n4, n2) = all_74_0 & $i(all_74_0) % 263.42/56.99 | | | | | | | % 263.42/56.99 | | | | | | | ALPHA: (237) implies: % 263.42/56.99 | | | | | | | (238) a_select3(q_ds1_filter, n4, n2) = all_74_0 % 263.42/56.99 | | | | | | | % 263.42/56.99 | | | | | | | REF_CLOSE: (10), (18), (226), (238) are inconsistent by sub-proof % 263.42/56.99 | | | | | | | #88. % 263.42/56.99 | | | | | | | % 263.42/56.99 | | | | | | End of split % 263.42/56.99 | | | | | | % 263.42/56.99 | | | | | End of split % 263.42/56.99 | | | | | % 263.42/56.99 | | | | End of split % 263.42/56.99 | | | | % 263.42/56.99 | | | Case 2: % 263.42/56.99 | | | | % 263.42/56.99 | | | | (239) all_74_2 = n3 % 263.42/56.99 | | | | % 263.42/56.99 | | | | REDUCE: (196), (239) imply: % 263.42/56.99 | | | | (240) a_select3(q_ds1_filter, n3, n4) = all_74_0 % 263.42/56.99 | | | | % 263.42/56.99 | | | | REDUCE: (197), (239) imply: % 263.42/56.99 | | | | (241) a_select3(q_ds1_filter, n4, n3) = all_74_1 % 263.42/56.99 | | | | % 263.42/56.99 | | | | REDUCE: (12), (239) imply: % 263.42/56.99 | | | | (242) leq(n3, n5) % 263.42/56.99 | | | | % 263.42/56.99 | | | | REDUCE: (11), (239) imply: % 263.42/56.99 | | | | (243) leq(n0, n3) % 263.42/56.99 | | | | % 263.42/56.99 | | | | GROUND_INST: instantiating (13) with n3, n4, all_74_0, simplifying with % 263.42/56.99 | | | | (1), (3), (199), (240), (243) gives: % 263.42/56.99 | | | | (244) ~ leq(n4, all_74_20) | ~ leq(n3, all_74_20) | % 263.42/56.99 | | | | (a_select3(q_ds1_filter, n4, n3) = all_74_0 & $i(all_74_0)) % 263.42/56.99 | | | | % 263.42/56.99 | | | | BETA: splitting (244) gives: % 263.42/56.99 | | | | % 263.42/56.99 | | | | Case 1: % 263.42/56.99 | | | | | % 263.42/56.99 | | | | | (245) ~ leq(n4, all_74_20) % 263.42/56.99 | | | | | % 263.42/56.99 | | | | | REDUCE: (21), (245) imply: % 263.42/56.99 | | | | | (246) ~ leq(n4, n5) % 263.42/56.99 | | | | | % 263.42/56.99 | | | | | PRED_UNIFY: (198), (246) imply: % 263.42/56.99 | | | | | (247) $false % 263.42/56.99 | | | | | % 263.42/56.99 | | | | | CLOSE: (247) is inconsistent. % 263.42/56.99 | | | | | % 263.42/56.99 | | | | Case 2: % 263.42/56.99 | | | | | % 263.42/56.99 | | | | | (248) ~ leq(n3, all_74_20) | (a_select3(q_ds1_filter, n4, n3) = % 263.42/56.99 | | | | | all_74_0 & $i(all_74_0)) % 263.42/56.99 | | | | | % 263.42/56.99 | | | | | BETA: splitting (248) gives: % 263.42/56.99 | | | | | % 263.42/56.99 | | | | | Case 1: % 263.42/56.99 | | | | | | % 263.42/56.99 | | | | | | (249) ~ leq(n3, all_74_20) % 263.42/56.99 | | | | | | % 263.42/56.99 | | | | | | REDUCE: (21), (249) imply: % 263.42/56.99 | | | | | | (250) ~ leq(n3, n5) % 263.42/56.99 | | | | | | % 263.42/56.99 | | | | | | PRED_UNIFY: (242), (250) imply: % 263.42/56.99 | | | | | | (251) $false % 263.42/56.99 | | | | | | % 263.42/56.99 | | | | | | CLOSE: (251) is inconsistent. % 263.42/56.99 | | | | | | % 263.42/56.99 | | | | | Case 2: % 263.42/56.99 | | | | | | % 263.42/56.99 | | | | | | (252) a_select3(q_ds1_filter, n4, n3) = all_74_0 & $i(all_74_0) % 263.42/56.99 | | | | | | % 263.42/56.99 | | | | | | ALPHA: (252) implies: % 263.42/56.99 | | | | | | (253) a_select3(q_ds1_filter, n4, n3) = all_74_0 % 263.42/56.99 | | | | | | % 263.42/56.99 | | | | | | GROUND_INST: instantiating (18) with all_74_0, all_74_1, n3, n4, % 263.42/56.99 | | | | | | q_ds1_filter, simplifying with (241), (253) gives: % 263.42/56.99 | | | | | | (254) all_74_0 = all_74_1 % 263.42/56.99 | | | | | | % 263.42/56.99 | | | | | | REDUCE: (10), (254) imply: % 263.42/56.99 | | | | | | (255) $false % 263.42/56.99 | | | | | | % 263.42/56.99 | | | | | | CLOSE: (255) is inconsistent. % 263.42/56.99 | | | | | | % 263.42/56.99 | | | | | End of split % 263.42/56.99 | | | | | % 263.42/56.99 | | | | End of split % 263.42/56.99 | | | | % 263.42/56.99 | | | End of split % 263.42/56.99 | | | % 263.42/56.99 | | End of split % 263.42/56.99 | | % 263.42/56.99 | Case 2: % 263.42/56.99 | | % 263.42/56.99 | | (256) all_74_2 = n4 % 263.42/56.99 | | % 263.42/56.99 | | REDUCE: (5), (256) imply: % 263.42/56.99 | | (257) a_select3(q_ds1_filter, n4, all_74_3) = all_74_0 % 263.42/56.99 | | % 263.42/56.99 | | REDUCE: (6), (256) imply: % 263.42/56.99 | | (258) a_select3(q_ds1_filter, all_74_3, n4) = all_74_1 % 263.42/56.99 | | % 263.42/56.99 | | REDUCE: (12), (256) imply: % 263.42/56.99 | | (259) leq(n4, n5) % 263.42/56.99 | | % 263.42/56.99 | | REDUCE: (11), (256) imply: % 263.42/56.99 | | (260) leq(n0, n4) % 263.42/56.99 | | % 263.42/56.99 | | BETA: splitting (2) gives: % 263.42/56.99 | | % 263.42/56.99 | | Case 1: % 263.42/56.99 | | | % 263.42/56.99 | | | (261) gt(n4, all_74_3) % 263.42/56.99 | | | % 263.42/56.99 | | | GROUND_INST: instantiating (20) with all_74_3, n4, n3, simplifying with % 263.42/56.99 | | | (3), (14), (19), (261) gives: % 263.42/56.99 | | | (262) leq(all_74_3, n3) % 263.42/56.99 | | | % 263.42/56.99 | | | GROUND_INST: instantiating (24) with all_74_3, n3, simplifying with (1), % 263.42/56.99 | | | (14), (262) gives: % 263.42/56.99 | | | (263) all_74_3 = n3 | gt(n3, all_74_3) % 263.42/56.99 | | | % 263.42/56.99 | | | BETA: splitting (263) gives: % 263.42/56.99 | | | % 263.42/56.99 | | | Case 1: % 263.42/56.99 | | | | % 263.42/56.99 | | | | (264) gt(n3, all_74_3) % 263.42/56.99 | | | | % 263.42/56.99 | | | | GROUND_INST: instantiating (20) with all_74_3, n3, n2, simplifying with % 263.42/56.99 | | | | (1), (14), (16), (264) gives: % 263.42/56.99 | | | | (265) leq(all_74_3, n2) % 263.42/56.99 | | | | % 263.42/56.99 | | | | GROUND_INST: instantiating (24) with all_74_3, n2, simplifying with % 263.42/56.99 | | | | (14), (23), (265) gives: % 263.42/56.99 | | | | (266) all_74_3 = n2 | gt(n2, all_74_3) % 263.42/56.99 | | | | % 263.42/56.99 | | | | BETA: splitting (266) gives: % 263.42/56.99 | | | | % 263.42/56.99 | | | | Case 1: % 263.42/56.99 | | | | | % 263.42/56.99 | | | | | (267) gt(n2, all_74_3) % 263.42/56.99 | | | | | % 263.42/56.99 | | | | | GROUND_INST: instantiating (20) with all_74_3, n2, n1, simplifying % 263.42/56.99 | | | | | with (7), (14), (23), (267) gives: % 263.42/56.99 | | | | | (268) leq(all_74_3, n1) % 263.42/56.99 | | | | | % 263.42/56.99 | | | | | GROUND_INST: instantiating (4) with all_74_3, simplifying with (8), % 263.42/56.99 | | | | | (14), (268) gives: % 263.42/56.99 | | | | | (269) all_74_3 = n1 | all_74_3 = n0 % 263.42/56.99 | | | | | % 263.42/56.99 | | | | | BETA: splitting (269) gives: % 263.42/56.99 | | | | | % 263.42/56.99 | | | | | Case 1: % 263.42/56.99 | | | | | | % 263.42/56.99 | | | | | | (270) all_74_3 = n0 % 263.42/56.99 | | | | | | % 263.42/56.99 | | | | | | REDUCE: (22), (270) imply: % 263.42/56.99 | | | | | | (271) $false % 263.42/56.99 | | | | | | % 263.42/56.99 | | | | | | CLOSE: (271) is inconsistent. % 263.42/56.99 | | | | | | % 263.42/56.99 | | | | | Case 2: % 263.42/56.99 | | | | | | % 263.42/56.99 | | | | | | (272) all_74_3 = n1 % 263.42/56.99 | | | | | | % 263.42/56.99 | | | | | | REDUCE: (258), (272) imply: % 263.42/56.99 | | | | | | (273) a_select3(q_ds1_filter, n1, n4) = all_74_1 % 263.42/56.99 | | | | | | % 263.42/56.99 | | | | | | REDUCE: (257), (272) imply: % 263.42/56.99 | | | | | | (274) a_select3(q_ds1_filter, n4, n1) = all_74_0 % 263.42/56.99 | | | | | | % 263.42/56.99 | | | | | | REDUCE: (14), (272) imply: % 263.42/56.99 | | | | | | (275) $i(n1) % 263.42/56.99 | | | | | | % 263.42/56.99 | | | | | | REDUCE: (25), (272) imply: % 263.42/56.99 | | | | | | (276) leq(n1, n5) % 263.42/56.99 | | | | | | % 263.42/56.99 | | | | | | REDUCE: (8), (272) imply: % 263.42/56.99 | | | | | | (277) leq(n0, n1) % 263.42/56.99 | | | | | | % 263.42/56.99 | | | | | | GROUND_INST: instantiating (13) with n1, n4, all_74_1, simplifying % 263.42/56.99 | | | | | | with (3), (260), (273), (275), (277) gives: % 263.42/56.99 | | | | | | (278) ~ leq(n4, all_74_20) | ~ leq(n1, all_74_20) | % 263.42/56.99 | | | | | | (a_select3(q_ds1_filter, n4, n1) = all_74_1 & $i(all_74_1)) % 263.42/56.99 | | | | | | % 263.42/56.99 | | | | | | BETA: splitting (278) gives: % 263.42/56.99 | | | | | | % 263.42/56.99 | | | | | | Case 1: % 263.42/56.99 | | | | | | | % 263.42/56.99 | | | | | | | (279) ~ leq(n4, all_74_20) % 263.42/56.99 | | | | | | | % 263.42/56.99 | | | | | | | REDUCE: (21), (279) imply: % 263.42/56.99 | | | | | | | (280) ~ leq(n4, n5) % 263.42/56.99 | | | | | | | % 263.42/56.99 | | | | | | | PRED_UNIFY: (259), (280) imply: % 263.42/56.99 | | | | | | | (281) $false % 263.42/56.99 | | | | | | | % 263.42/56.99 | | | | | | | CLOSE: (281) is inconsistent. % 263.42/56.99 | | | | | | | % 263.42/56.99 | | | | | | Case 2: % 263.42/56.99 | | | | | | | % 263.42/56.99 | | | | | | | (282) ~ leq(n1, all_74_20) | (a_select3(q_ds1_filter, n4, n1) % 263.42/56.99 | | | | | | | = all_74_1 & $i(all_74_1)) % 263.42/56.99 | | | | | | | % 263.42/56.99 | | | | | | | BETA: splitting (282) gives: % 263.42/56.99 | | | | | | | % 263.42/56.99 | | | | | | | Case 1: % 263.42/56.99 | | | | | | | | % 263.42/56.99 | | | | | | | | (283) ~ leq(n1, all_74_20) % 263.42/56.99 | | | | | | | | % 263.42/56.99 | | | | | | | | REDUCE: (21), (283) imply: % 263.42/57.00 | | | | | | | | (284) ~ leq(n1, n5) % 263.42/57.00 | | | | | | | | % 263.42/57.00 | | | | | | | | PRED_UNIFY: (276), (284) imply: % 263.42/57.00 | | | | | | | | (285) $false % 263.42/57.00 | | | | | | | | % 263.42/57.00 | | | | | | | | CLOSE: (285) is inconsistent. % 263.42/57.00 | | | | | | | | % 263.42/57.00 | | | | | | | Case 2: % 263.42/57.00 | | | | | | | | % 263.42/57.00 | | | | | | | | (286) a_select3(q_ds1_filter, n4, n1) = all_74_1 & % 263.42/57.00 | | | | | | | | $i(all_74_1) % 263.42/57.00 | | | | | | | | % 263.42/57.00 | | | | | | | | ALPHA: (286) implies: % 263.42/57.00 | | | | | | | | (287) a_select3(q_ds1_filter, n4, n1) = all_74_1 % 263.42/57.00 | | | | | | | | % 263.42/57.00 | | | | | | | | REF_CLOSE: (10), (18), (274), (287) are inconsistent by % 263.42/57.00 | | | | | | | | sub-proof #89. % 263.42/57.00 | | | | | | | | % 263.42/57.00 | | | | | | | End of split % 263.42/57.00 | | | | | | | % 263.42/57.00 | | | | | | End of split % 263.42/57.00 | | | | | | % 263.42/57.00 | | | | | End of split % 263.42/57.00 | | | | | % 263.42/57.00 | | | | Case 2: % 263.42/57.00 | | | | | % 263.42/57.00 | | | | | (288) all_74_3 = n2 % 263.42/57.00 | | | | | % 263.42/57.00 | | | | | REDUCE: (258), (288) imply: % 263.42/57.00 | | | | | (289) a_select3(q_ds1_filter, n2, n4) = all_74_1 % 263.42/57.00 | | | | | % 263.42/57.00 | | | | | REDUCE: (257), (288) imply: % 263.42/57.00 | | | | | (290) a_select3(q_ds1_filter, n4, n2) = all_74_0 % 263.42/57.00 | | | | | % 263.42/57.00 | | | | | REDUCE: (25), (288) imply: % 263.42/57.00 | | | | | (291) leq(n2, n5) % 263.42/57.00 | | | | | % 263.42/57.00 | | | | | REDUCE: (8), (288) imply: % 263.42/57.00 | | | | | (292) leq(n0, n2) % 263.42/57.00 | | | | | % 263.42/57.00 | | | | | GROUND_INST: instantiating (13) with n2, n4, all_74_1, simplifying % 263.42/57.00 | | | | | with (3), (23), (260), (289), (292) gives: % 263.42/57.00 | | | | | (293) ~ leq(n4, all_74_20) | ~ leq(n2, all_74_20) | % 263.42/57.00 | | | | | (a_select3(q_ds1_filter, n4, n2) = all_74_1 & $i(all_74_1)) % 263.42/57.00 | | | | | % 263.42/57.00 | | | | | BETA: splitting (293) gives: % 263.42/57.00 | | | | | % 263.42/57.00 | | | | | Case 1: % 263.42/57.00 | | | | | | % 263.42/57.00 | | | | | | (294) ~ leq(n4, all_74_20) % 263.42/57.00 | | | | | | % 263.42/57.00 | | | | | | REDUCE: (21), (294) imply: % 263.42/57.00 | | | | | | (295) ~ leq(n4, n5) % 263.42/57.00 | | | | | | % 263.42/57.00 | | | | | | PRED_UNIFY: (259), (295) imply: % 263.42/57.00 | | | | | | (296) $false % 263.42/57.00 | | | | | | % 263.42/57.00 | | | | | | CLOSE: (296) is inconsistent. % 263.42/57.00 | | | | | | % 263.42/57.00 | | | | | Case 2: % 263.42/57.00 | | | | | | % 263.42/57.00 | | | | | | (297) ~ leq(n2, all_74_20) | (a_select3(q_ds1_filter, n4, n2) = % 263.42/57.00 | | | | | | all_74_1 & $i(all_74_1)) % 263.42/57.00 | | | | | | % 263.42/57.00 | | | | | | BETA: splitting (297) gives: % 263.42/57.00 | | | | | | % 263.42/57.00 | | | | | | Case 1: % 263.42/57.00 | | | | | | | % 263.42/57.00 | | | | | | | (298) ~ leq(n2, all_74_20) % 263.42/57.00 | | | | | | | % 263.42/57.00 | | | | | | | REDUCE: (21), (298) imply: % 263.42/57.00 | | | | | | | (299) ~ leq(n2, n5) % 263.42/57.00 | | | | | | | % 263.42/57.00 | | | | | | | PRED_UNIFY: (291), (299) imply: % 263.42/57.00 | | | | | | | (300) $false % 263.42/57.00 | | | | | | | % 263.42/57.00 | | | | | | | CLOSE: (300) is inconsistent. % 263.42/57.00 | | | | | | | % 263.42/57.00 | | | | | | Case 2: % 263.42/57.00 | | | | | | | % 263.42/57.00 | | | | | | | (301) a_select3(q_ds1_filter, n4, n2) = all_74_1 & $i(all_74_1) % 263.42/57.00 | | | | | | | % 263.42/57.00 | | | | | | | ALPHA: (301) implies: % 263.42/57.00 | | | | | | | (302) a_select3(q_ds1_filter, n4, n2) = all_74_1 % 263.42/57.00 | | | | | | | % 263.42/57.00 | | | | | | | REF_CLOSE: (10), (18), (290), (302) are inconsistent by sub-proof % 263.42/57.00 | | | | | | | #88. % 263.42/57.00 | | | | | | | % 263.42/57.00 | | | | | | End of split % 263.42/57.00 | | | | | | % 263.42/57.00 | | | | | End of split % 263.42/57.00 | | | | | % 263.42/57.00 | | | | End of split % 263.42/57.00 | | | | % 263.42/57.00 | | | Case 2: % 263.42/57.00 | | | | % 263.42/57.00 | | | | (303) all_74_3 = n3 % 263.42/57.00 | | | | % 263.42/57.00 | | | | REDUCE: (258), (303) imply: % 263.42/57.00 | | | | (304) a_select3(q_ds1_filter, n3, n4) = all_74_1 % 263.42/57.00 | | | | % 263.42/57.00 | | | | REDUCE: (257), (303) imply: % 263.42/57.00 | | | | (305) a_select3(q_ds1_filter, n4, n3) = all_74_0 % 263.42/57.00 | | | | % 263.42/57.00 | | | | REDUCE: (25), (303) imply: % 263.42/57.00 | | | | (306) leq(n3, n5) % 263.42/57.00 | | | | % 263.42/57.00 | | | | REDUCE: (8), (303) imply: % 263.42/57.00 | | | | (307) leq(n0, n3) % 263.42/57.00 | | | | % 263.42/57.00 | | | | GROUND_INST: instantiating (13) with n3, n4, all_74_1, simplifying with % 263.42/57.00 | | | | (1), (3), (260), (304), (307) gives: % 263.42/57.00 | | | | (308) ~ leq(n4, all_74_20) | ~ leq(n3, all_74_20) | % 263.42/57.00 | | | | (a_select3(q_ds1_filter, n4, n3) = all_74_1 & $i(all_74_1)) % 263.42/57.00 | | | | % 263.42/57.00 | | | | BETA: splitting (308) gives: % 263.42/57.00 | | | | % 263.42/57.00 | | | | Case 1: % 263.42/57.00 | | | | | % 263.42/57.00 | | | | | (309) ~ leq(n4, all_74_20) % 263.42/57.00 | | | | | % 263.42/57.00 | | | | | REDUCE: (21), (309) imply: % 263.42/57.00 | | | | | (310) ~ leq(n4, n5) % 263.42/57.00 | | | | | % 263.42/57.00 | | | | | PRED_UNIFY: (259), (310) imply: % 263.42/57.00 | | | | | (311) $false % 263.42/57.00 | | | | | % 263.42/57.00 | | | | | CLOSE: (311) is inconsistent. % 263.42/57.00 | | | | | % 263.42/57.00 | | | | Case 2: % 263.42/57.00 | | | | | % 263.42/57.00 | | | | | (312) ~ leq(n3, all_74_20) | (a_select3(q_ds1_filter, n4, n3) = % 263.42/57.00 | | | | | all_74_1 & $i(all_74_1)) % 263.42/57.00 | | | | | % 263.42/57.00 | | | | | BETA: splitting (312) gives: % 263.42/57.00 | | | | | % 263.42/57.00 | | | | | Case 1: % 263.42/57.00 | | | | | | % 263.42/57.00 | | | | | | (313) ~ leq(n3, all_74_20) % 263.42/57.00 | | | | | | % 263.42/57.00 | | | | | | REDUCE: (21), (313) imply: % 263.42/57.00 | | | | | | (314) ~ leq(n3, n5) % 263.42/57.00 | | | | | | % 263.42/57.00 | | | | | | PRED_UNIFY: (306), (314) imply: % 263.42/57.00 | | | | | | (315) $false % 263.42/57.00 | | | | | | % 263.42/57.00 | | | | | | CLOSE: (315) is inconsistent. % 263.42/57.00 | | | | | | % 263.42/57.00 | | | | | Case 2: % 263.42/57.00 | | | | | | % 263.42/57.00 | | | | | | (316) a_select3(q_ds1_filter, n4, n3) = all_74_1 & $i(all_74_1) % 263.42/57.00 | | | | | | % 263.42/57.00 | | | | | | ALPHA: (316) implies: % 263.42/57.00 | | | | | | (317) a_select3(q_ds1_filter, n4, n3) = all_74_1 % 263.42/57.00 | | | | | | % 263.42/57.00 | | | | | | GROUND_INST: instantiating (18) with all_74_0, all_74_1, n3, n4, % 263.42/57.00 | | | | | | q_ds1_filter, simplifying with (305), (317) gives: % 263.42/57.00 | | | | | | (318) all_74_0 = all_74_1 % 263.42/57.00 | | | | | | % 263.42/57.00 | | | | | | REDUCE: (10), (318) imply: % 263.42/57.00 | | | | | | (319) $false % 263.42/57.00 | | | | | | % 263.42/57.00 | | | | | | CLOSE: (319) is inconsistent. % 263.42/57.00 | | | | | | % 263.42/57.00 | | | | | End of split % 263.42/57.00 | | | | | % 263.42/57.00 | | | | End of split % 263.42/57.00 | | | | % 263.42/57.00 | | | End of split % 263.42/57.00 | | | % 263.42/57.00 | | Case 2: % 263.42/57.00 | | | % 263.42/57.00 | | | (320) all_74_3 = n4 % 263.42/57.00 | | | % 263.42/57.00 | | | REDUCE: (258), (320) imply: % 263.42/57.00 | | | (321) a_select3(q_ds1_filter, n4, n4) = all_74_1 % 263.42/57.00 | | | % 263.42/57.00 | | | REDUCE: (257), (320) imply: % 263.42/57.00 | | | (322) a_select3(q_ds1_filter, n4, n4) = all_74_0 % 263.42/57.00 | | | % 263.42/57.00 | | | GROUND_INST: instantiating (18) with all_74_1, all_74_0, n4, n4, % 263.42/57.00 | | | q_ds1_filter, simplifying with (321), (322) gives: % 263.42/57.00 | | | (323) all_74_0 = all_74_1 % 263.42/57.00 | | | % 263.42/57.00 | | | REDUCE: (10), (323) imply: % 263.42/57.00 | | | (324) $false % 263.42/57.00 | | | % 263.42/57.00 | | | CLOSE: (324) is inconsistent. % 263.42/57.00 | | | % 263.42/57.00 | | End of split % 263.42/57.00 | | % 263.42/57.00 | End of split % 263.42/57.00 | % 263.42/57.00 End of proof % 263.42/57.00 % 263.42/57.00 Sub-proof #88 shows that the following formulas are inconsistent: % 263.42/57.00 ---------------------------------------------------------------- % 263.42/57.00 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 263.42/57.00 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 263.42/57.00 v0)) % 263.42/57.00 (2) a_select3(q_ds1_filter, n4, n2) = all_74_0 % 263.42/57.00 (3) a_select3(q_ds1_filter, n4, n2) = all_74_1 % 263.42/57.00 (4) ~ (all_74_0 = all_74_1) % 263.42/57.00 % 263.42/57.00 Begin of proof % 263.42/57.00 | % 263.42/57.00 | GROUND_INST: instantiating (1) with all_74_0, all_74_1, n2, n4, q_ds1_filter, % 263.42/57.00 | simplifying with (2), (3) gives: % 263.42/57.00 | (5) all_74_0 = all_74_1 % 263.42/57.00 | % 263.42/57.00 | REDUCE: (4), (5) imply: % 263.42/57.00 | (6) $false % 263.42/57.00 | % 263.42/57.00 | CLOSE: (6) is inconsistent. % 263.42/57.00 | % 263.42/57.00 End of proof % 263.42/57.00 % 263.42/57.00 Sub-proof #89 shows that the following formulas are inconsistent: % 263.42/57.00 ---------------------------------------------------------------- % 263.42/57.00 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 263.42/57.00 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 263.42/57.00 v0)) % 263.42/57.00 (2) a_select3(q_ds1_filter, n4, n1) = all_74_0 % 263.42/57.00 (3) a_select3(q_ds1_filter, n4, n1) = all_74_1 % 263.42/57.00 (4) ~ (all_74_0 = all_74_1) % 263.42/57.00 % 263.42/57.00 Begin of proof % 263.42/57.00 | % 263.42/57.00 | GROUND_INST: instantiating (1) with all_74_0, all_74_1, n1, n4, q_ds1_filter, % 263.42/57.00 | simplifying with (2), (3) gives: % 263.42/57.00 | (5) all_74_0 = all_74_1 % 263.42/57.00 | % 263.42/57.00 | REDUCE: (4), (5) imply: % 263.42/57.00 | (6) $false % 263.42/57.00 | % 263.42/57.00 | CLOSE: (6) is inconsistent. % 263.42/57.00 | % 263.42/57.00 End of proof % 263.42/57.00 % 263.42/57.00 Sub-proof #90 shows that the following formulas are inconsistent: % 263.42/57.00 ---------------------------------------------------------------- % 263.42/57.00 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 263.42/57.00 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 263.42/57.00 v0)) % 263.42/57.00 (2) a_select3(q_ds1_filter, n3, n2) = all_74_0 % 263.42/57.00 (3) a_select3(q_ds1_filter, n3, n2) = all_74_1 % 263.42/57.00 (4) ~ (all_74_0 = all_74_1) % 263.42/57.00 % 263.42/57.00 Begin of proof % 263.42/57.00 | % 263.42/57.00 | GROUND_INST: instantiating (1) with all_74_0, all_74_1, n2, n3, q_ds1_filter, % 263.42/57.00 | simplifying with (2), (3) gives: % 263.42/57.00 | (5) all_74_0 = all_74_1 % 263.42/57.00 | % 263.42/57.00 | REDUCE: (4), (5) imply: % 263.42/57.00 | (6) $false % 263.42/57.00 | % 263.42/57.00 | CLOSE: (6) is inconsistent. % 263.42/57.00 | % 263.42/57.00 End of proof % 263.42/57.00 % 263.42/57.00 Sub-proof #91 shows that the following formulas are inconsistent: % 263.42/57.00 ---------------------------------------------------------------- % 263.42/57.00 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 263.42/57.00 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 263.42/57.00 v0)) % 263.42/57.00 (2) a_select3(q_ds1_filter, n3, n1) = all_74_0 % 263.42/57.00 (3) a_select3(q_ds1_filter, n3, n1) = all_74_1 % 263.42/57.00 (4) ~ (all_74_0 = all_74_1) % 263.42/57.00 % 263.42/57.00 Begin of proof % 263.42/57.00 | % 263.42/57.00 | GROUND_INST: instantiating (1) with all_74_0, all_74_1, n1, n3, q_ds1_filter, % 263.42/57.00 | simplifying with (2), (3) gives: % 263.42/57.00 | (5) all_74_0 = all_74_1 % 263.42/57.00 | % 263.42/57.00 | REDUCE: (4), (5) imply: % 263.42/57.00 | (6) $false % 263.42/57.00 | % 263.42/57.00 | CLOSE: (6) is inconsistent. % 263.42/57.00 | % 263.42/57.00 End of proof % 263.42/57.00 % 263.42/57.00 Sub-proof #92 shows that the following formulas are inconsistent: % 263.42/57.00 ---------------------------------------------------------------- % 263.42/57.00 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 263.42/57.00 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 263.42/57.00 v0)) % 263.42/57.00 (2) a_select3(q_ds1_filter, n2, n1) = all_74_0 % 263.42/57.00 (3) a_select3(q_ds1_filter, n2, n1) = all_74_1 % 263.42/57.00 (4) ~ (all_74_0 = all_74_1) % 263.42/57.00 % 263.42/57.00 Begin of proof % 263.42/57.00 | % 263.42/57.00 | GROUND_INST: instantiating (1) with all_74_0, all_74_1, n1, n2, q_ds1_filter, % 263.42/57.00 | simplifying with (2), (3) gives: % 263.42/57.00 | (5) all_74_0 = all_74_1 % 263.42/57.00 | % 263.42/57.00 | REDUCE: (4), (5) imply: % 263.42/57.00 | (6) $false % 263.42/57.00 | % 263.42/57.00 | CLOSE: (6) is inconsistent. % 263.42/57.00 | % 263.42/57.00 End of proof % 263.42/57.00 % 263.42/57.00 Sub-proof #93 shows that the following formulas are inconsistent: % 263.42/57.00 ---------------------------------------------------------------- % 263.42/57.00 (1) $i(all_74_2) % 263.42/57.00 (2) all_74_2 = n0 % 263.42/57.00 (3) gt(all_74_2, n0) % 263.42/57.00 (4) ! [v0: $i] : ( ~ $i(v0) | ~ gt(v0, v0)) % 263.42/57.00 % 263.42/57.00 Begin of proof % 263.42/57.00 | % 263.42/57.00 | REDUCE: (1), (2) imply: % 263.42/57.00 | (5) $i(n0) % 263.42/57.00 | % 263.42/57.00 | REDUCE: (2), (3) imply: % 263.42/57.00 | (6) gt(n0, n0) % 263.42/57.00 | % 263.42/57.00 | GROUND_INST: instantiating (4) with n0, simplifying with (5), (6) gives: % 263.42/57.00 | (7) $false % 263.42/57.00 | % 263.42/57.00 | CLOSE: (7) is inconsistent. % 263.42/57.00 | % 263.42/57.00 End of proof % 263.42/57.00 % 263.42/57.00 Sub-proof #94 shows that the following formulas are inconsistent: % 263.42/57.00 ---------------------------------------------------------------- % 263.42/57.00 (1) $i(all_74_3) % 263.42/57.00 (2) all_74_3 = n0 % 263.42/57.00 (3) gt(all_74_3, n0) % 263.42/57.00 (4) ! [v0: $i] : ( ~ $i(v0) | ~ gt(v0, v0)) % 263.42/57.00 % 263.42/57.00 Begin of proof % 263.42/57.00 | % 263.42/57.00 | REDUCE: (1), (2) imply: % 263.42/57.00 | (5) $i(n0) % 263.42/57.00 | % 263.42/57.00 | REDUCE: (2), (3) imply: % 263.42/57.00 | (6) gt(n0, n0) % 263.42/57.00 | % 263.42/57.00 | GROUND_INST: instantiating (4) with n0, simplifying with (5), (6) gives: % 263.42/57.00 | (7) $false % 263.42/57.00 | % 263.42/57.00 | CLOSE: (7) is inconsistent. % 263.42/57.00 | % 263.42/57.00 End of proof % 263.42/57.00 % 263.42/57.00 Sub-proof #95 shows that the following formulas are inconsistent: % 263.42/57.00 ---------------------------------------------------------------- % 263.42/57.00 (1) $i(pv57) % 263.42/57.00 (2) pv57 = n0 % 263.42/57.00 (3) gt(pv57, n0) % 263.42/57.00 (4) ! [v0: $i] : ( ~ $i(v0) | ~ gt(v0, v0)) % 263.42/57.00 % 263.42/57.00 Begin of proof % 263.42/57.00 | % 263.42/57.00 | REDUCE: (1), (2) imply: % 263.42/57.00 | (5) $i(n0) % 263.42/57.00 | % 263.42/57.00 | REDUCE: (2), (3) imply: % 263.42/57.00 | (6) gt(n0, n0) % 263.42/57.00 | % 263.42/57.00 | GROUND_INST: instantiating (4) with n0, simplifying with (5), (6) gives: % 263.42/57.00 | (7) $false % 263.42/57.00 | % 263.42/57.00 | CLOSE: (7) is inconsistent. % 263.42/57.00 | % 263.42/57.00 End of proof % 263.42/57.00 % SZS output end Proof for theBenchmark % 263.42/57.00 % 263.42/57.00 56404ms %------------------------------------------------------------------------------