%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWV053+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 : n032.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 22:54:43 EDT 2023 % Result : Theorem 17.71s 2.99s % Output : Proof 140.49s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.10 % Problem : SWV053+1 : TPTP v8.1.2. Bugfixed v3.3.0. % 0.06/0.11 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.11/0.31 % Computer : n032.cluster.edu % 0.11/0.31 % Model : x86_64 x86_64 % 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.31 % Memory : 8042.1875MB % 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.31 % CPULimit : 300 % 0.11/0.31 % WCLimit : 300 % 0.11/0.31 % DateTime : Tue Aug 29 10:55:31 EDT 2023 % 0.11/0.31 % CPUTime : % 0.16/0.53 ________ _____ % 0.16/0.53 ___ __ \_________(_)________________________________ % 0.16/0.53 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.16/0.53 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.16/0.53 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.16/0.53 % 0.16/0.53 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.16/0.53 (2023-06-19) % 0.16/0.53 % 0.16/0.53 (c) Philipp Rümmer, 2009-2023 % 0.16/0.53 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.16/0.53 Amanda Stjerna. % 0.16/0.53 Free software under BSD-3-Clause. % 0.16/0.53 % 0.16/0.53 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.16/0.53 % 0.16/0.53 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.16/0.55 Running up to 7 provers in parallel. % 0.16/0.55 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.16/0.55 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.16/0.55 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.16/0.55 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.16/0.55 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.16/0.55 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.16/0.56 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.06/1.24 Prover 1: Preprocessing ... % 4.06/1.26 Prover 4: Preprocessing ... % 4.06/1.28 Prover 0: Preprocessing ... % 4.06/1.29 Prover 2: Preprocessing ... % 4.06/1.29 Prover 5: Preprocessing ... % 4.06/1.29 Prover 6: Preprocessing ... % 4.06/1.29 Prover 3: Preprocessing ... % 10.58/2.08 Prover 1: Warning: ignoring some quantifiers % 11.22/2.13 Prover 3: Warning: ignoring some quantifiers % 11.22/2.17 Prover 6: Proving ... % 11.22/2.17 Prover 3: Constructing countermodel ... % 11.72/2.18 Prover 1: Constructing countermodel ... % 11.72/2.25 Prover 4: Warning: ignoring some quantifiers % 12.85/2.35 Prover 0: Proving ... % 12.85/2.37 Prover 4: Constructing countermodel ... % 13.44/2.42 Prover 5: Proving ... % 13.44/2.42 Prover 2: Proving ... % 17.71/2.99 Prover 3: proved (2434ms) % 17.71/2.99 % 17.71/2.99 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 17.71/2.99 % 17.71/3.00 Prover 6: stopped % 17.71/3.00 Prover 2: stopped % 17.71/3.01 Prover 5: stopped % 17.71/3.01 Prover 0: stopped % 17.71/3.02 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 17.71/3.02 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 17.71/3.02 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 17.71/3.02 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 17.71/3.02 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 19.00/3.14 Prover 7: Preprocessing ... % 19.00/3.14 Prover 8: Preprocessing ... % 19.00/3.15 Prover 13: Preprocessing ... % 19.00/3.16 Prover 10: Preprocessing ... % 19.00/3.16 Prover 11: Preprocessing ... % 21.26/3.44 Prover 10: Warning: ignoring some quantifiers % 21.26/3.47 Prover 10: Constructing countermodel ... % 21.26/3.52 Prover 7: Warning: ignoring some quantifiers % 21.26/3.53 Prover 8: Warning: ignoring some quantifiers % 22.05/3.54 Prover 7: Constructing countermodel ... % 22.05/3.54 Prover 11: Warning: ignoring some quantifiers % 22.05/3.54 Prover 13: Warning: ignoring some quantifiers % 22.05/3.56 Prover 8: Constructing countermodel ... % 22.05/3.56 Prover 11: Constructing countermodel ... % 22.05/3.58 Prover 13: Constructing countermodel ... % 64.07/8.96 Prover 13: stopped % 64.07/8.96 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 64.07/9.01 Prover 16: Preprocessing ... % 65.03/9.21 Prover 16: Warning: ignoring some quantifiers % 66.04/9.22 Prover 16: Constructing countermodel ... % 109.88/14.94 Prover 16: stopped % 109.88/14.95 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 110.89/15.03 Prover 19: Preprocessing ... % 112.21/15.24 Prover 19: Warning: ignoring some quantifiers % 112.21/15.27 Prover 19: Constructing countermodel ... % 117.58/15.90 Prover 1: stopped % 136.12/18.71 Prover 19: stopped % 138.41/19.11 Prover 10: Found proof (size 1782) % 138.41/19.11 Prover 10: proved (16087ms) % 138.41/19.11 Prover 7: stopped % 138.41/19.11 Prover 4: stopped % 138.41/19.12 Prover 11: stopped % 138.41/19.12 Prover 8: stopped % 138.41/19.12 % 138.41/19.12 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 138.41/19.12 % 138.52/19.17 % SZS output start Proof for theBenchmark % 138.52/19.18 Assumptions after simplification: % 138.52/19.18 --------------------------------- % 138.52/19.18 % 138.52/19.18 (cl5_nebula_norm_0031) % 138.52/19.22 $i(pv71) & $i(x) & $i(center) & $i(q) & $i(n135300) & $i(pv12) & $i(pv10) & % 138.52/19.22 $i(n5) & $i(n1) & $i(n0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 138.52/19.22 $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : % 138.52/19.22 ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? % 138.52/19.22 [v14: $i] : ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? [v18: $i] : ? % 138.52/19.22 [v19: $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ? [v23: $i] : ? % 138.52/19.22 [v24: $i] : ? [v25: $i] : ? [v26: $i] : ? [v27: $i] : (minus(n135300, n1) = % 138.52/19.22 v0 & minus(pv12, n1) = v2 & minus(pv10, n1) = v4 & minus(n5, n1) = v1 & % 138.52/19.22 a_select2(x, pv10) = v3 & $i(v16) & $i(v15) & $i(v12) & $i(v11) & $i(v4) & % 138.52/19.22 $i(v3) & $i(v2) & $i(v1) & $i(v0) & leq(pv12, v1) & leq(pv10, v0) & leq(n0, % 138.52/19.22 pv12) & leq(n0, pv10) & ! [v28: $i] : ! [v29: $i] : ! [v30: $i] : ! % 138.52/19.22 [v31: $i] : ! [v32: $i] : ! [v33: $i] : ! [v34: $i] : ! [v35: $i] : ! % 138.52/19.22 [v36: $i] : ! [v37: $i] : ! [v38: $i] : ! [v39: $i] : ( ~ (times(v35, % 138.52/19.22 v35) = v36) | ~ (times(v31, v31) = v32) | ~ (sqrt(v36) = v37) | ~ % 138.52/19.22 (sqrt(v32) = v33) | ~ (divide(v33, v38) = v39) | ~ (minus(v34, v3) = % 138.52/19.22 v35) | ~ (minus(v30, v3) = v31) | ~ (sum(n0, v1, v37) = v38) | ~ % 138.52/19.22 (a_select3(center, v29, n0) = v34) | ~ (a_select3(center, v28, n0) = v30) % 138.52/19.22 | ~ $i(v29) | ~ $i(v28) | ~ leq(v28, v2) | ~ leq(n0, v28) | % 138.52/19.22 (a_select3(q, pv10, v28) = v39 & $i(v39))) & ! [v28: $i] : ! [v29: $i] : % 138.52/19.22 ! [v30: $i] : ( ~ (a_select3(q, v28, v29) = v30) | ~ $i(v29) | ~ $i(v28) % 138.52/19.22 | ~ leq(v28, v4) | ~ leq(n0, v28) | sum(n0, v1, v30) = n1) & (( ~ (v27 = % 138.52/19.22 v17) & times(v23, v23) = v24 & times(v19, v19) = v20 & sqrt(v24) = v25 % 138.52/19.22 & sqrt(v20) = v21 & divide(v21, v26) = v27 & minus(v22, v3) = v23 & % 138.52/19.22 minus(v18, v3) = v19 & sum(n0, v1, v25) = v26 & a_select3(center, v16, % 138.52/19.22 n0) = v22 & a_select3(center, v15, n0) = v18 & a_select3(q, pv10, v15) % 138.52/19.23 = v17 & $i(v27) & $i(v26) & $i(v25) & $i(v24) & $i(v23) & $i(v22) & % 138.52/19.23 $i(v21) & $i(v20) & $i(v19) & $i(v18) & $i(v17) & leq(v15, v2) & leq(n0, % 138.52/19.23 v15)) | ( ~ (v14 = n1) & sum(n0, v1, v13) = v14 & a_select3(q, v11, % 138.52/19.23 v12) = v13 & $i(v14) & $i(v13) & leq(v11, v4) & leq(n0, v11)) | ( ~ % 138.52/19.23 (v10 = n0) & times(v7, v7) = v8 & sqrt(v8) = v9 & minus(v6, v3) = v7 & % 138.52/19.23 minus(n0, n1) = v5 & sum(n0, v5, v9) = v10 & a_select3(center, pv71, n0) % 138.52/19.23 = v6 & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5)))) % 138.52/19.23 % 138.52/19.23 (finite_domain_1) % 138.52/19.23 $i(n1) & $i(n0) & ! [v0: $i] : (v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0, % 138.52/19.23 n1) | ~ leq(n0, v0)) % 138.52/19.23 % 138.52/19.23 (finite_domain_2) % 138.52/19.23 $i(n2) & $i(n1) & $i(n0) & ! [v0: $i] : (v0 = n2 | v0 = n1 | v0 = n0 | ~ % 138.52/19.23 $i(v0) | ~ leq(v0, n2) | ~ leq(n0, v0)) % 138.52/19.23 % 138.52/19.23 (finite_domain_3) % 138.52/19.23 $i(n3) & $i(n2) & $i(n1) & $i(n0) & ! [v0: $i] : (v0 = n3 | v0 = n2 | v0 = n1 % 138.52/19.23 | v0 = n0 | ~ $i(v0) | ~ leq(v0, n3) | ~ leq(n0, v0)) % 138.52/19.23 % 138.52/19.23 (finite_domain_4) % 138.52/19.23 $i(n4) & $i(n3) & $i(n2) & $i(n1) & $i(n0) & ! [v0: $i] : (v0 = n4 | v0 = n3 % 138.52/19.23 | v0 = n2 | v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0, n4) | ~ leq(n0, v0)) % 138.52/19.23 % 138.52/19.23 (gt_3_tptp_minus_1) % 138.52/19.23 $i(n3) & $i(tptp_minus_1) & gt(n3, tptp_minus_1) % 138.52/19.23 % 138.52/19.23 (gt_5_4) % 138.52/19.23 $i(n5) & $i(n4) & gt(n5, n4) % 138.52/19.23 % 138.52/19.23 (gt_succ) % 138.52/19.23 ! [v0: $i] : ! [v1: $i] : ( ~ (succ(v0) = v1) | ~ $i(v0) | gt(v1, v0)) % 138.52/19.23 % 138.52/19.23 (irreflexivity_gt) % 138.52/19.23 ! [v0: $i] : ( ~ $i(v0) | ~ gt(v0, v0)) % 138.52/19.23 % 138.52/19.23 (leq_gt1) % 138.52/19.23 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ gt(v1, v0) | leq(v0, % 138.52/19.23 v1)) % 138.52/19.23 % 138.52/19.23 (leq_gt2) % 138.52/19.24 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ leq(v0, v1) % 138.52/19.24 | gt(v1, v0)) % 138.52/19.24 % 138.52/19.24 (leq_gt_pred) % 138.52/19.24 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (pred(v1) = v2) | ~ $i(v1) | ~ % 138.52/19.24 $i(v0) | ~ leq(v0, v2) | gt(v1, v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 138.52/19.24 $i] : ( ~ (pred(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ gt(v1, v0) | leq(v0, % 138.52/19.24 v2)) % 138.52/19.24 % 138.52/19.24 (leq_succ_gt) % 138.52/19.24 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (succ(v0) = v2) | ~ $i(v1) | ~ % 138.52/19.24 $i(v0) | ~ leq(v2, v1) | gt(v1, v0)) % 138.52/19.24 % 138.52/19.24 (leq_succ_succ) % 138.52/19.24 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (succ(v1) = v3) | % 138.52/19.24 ~ (succ(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ leq(v2, v3) | leq(v0, v1)) & % 138.52/19.24 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (succ(v1) = v3) | % 138.52/19.24 ~ (succ(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ leq(v0, v1) | leq(v2, v3)) % 138.52/19.24 % 138.52/19.24 (pred_minus_1) % 138.52/19.24 $i(n1) & ! [v0: $i] : ! [v1: $i] : ( ~ (minus(v0, n1) = v1) | ~ $i(v0) | % 138.52/19.24 (pred(v0) = v1 & $i(v1))) % 138.52/19.24 % 138.52/19.24 (pred_succ) % 138.52/19.24 ! [v0: $i] : ! [v1: $i] : ( ~ (succ(v0) = v1) | ~ $i(v0) | pred(v1) = v0) % 138.52/19.24 % 138.52/19.24 (succ_pred) % 138.52/19.24 ! [v0: $i] : ! [v1: $i] : ( ~ (pred(v0) = v1) | ~ $i(v0) | succ(v1) = v0) % 138.52/19.24 % 138.52/19.24 (succ_tptp_minus_1) % 138.52/19.24 succ(tptp_minus_1) = n0 & $i(tptp_minus_1) & $i(n0) % 138.52/19.24 % 138.52/19.24 (successor_1) % 138.52/19.24 succ(n0) = n1 & $i(n1) & $i(n0) % 138.52/19.24 % 138.52/19.24 (successor_2) % 138.52/19.24 $i(n2) & $i(n0) & ? [v0: $i] : (succ(v0) = n2 & succ(n0) = v0 & $i(v0)) % 138.52/19.24 % 138.52/19.24 (successor_3) % 138.52/19.24 $i(n3) & $i(n0) & ? [v0: $i] : ? [v1: $i] : (succ(v1) = n3 & succ(v0) = v1 & % 138.52/19.24 succ(n0) = v0 & $i(v1) & $i(v0)) % 138.52/19.24 % 138.52/19.24 (successor_4) % 138.52/19.24 $i(n4) & $i(n0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (succ(v2) = n4 & % 138.52/19.24 succ(v1) = v2 & succ(v0) = v1 & succ(n0) = v0 & $i(v2) & $i(v1) & $i(v0)) % 138.52/19.24 % 138.52/19.24 (successor_5) % 138.52/19.24 $i(n5) & $i(n0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 138.52/19.24 (succ(v3) = n5 & succ(v2) = v3 & succ(v1) = v2 & succ(v0) = v1 & succ(n0) = v0 % 138.52/19.24 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 138.52/19.24 % 138.52/19.24 (sum_plus_base) % 138.52/19.25 $i(tptp_minus_1) & $i(n0) & ! [v0: $i] : ! [v1: $i] : (v1 = n0 | ~ (sum(n0, % 138.52/19.26 tptp_minus_1, v0) = v1) | ~ $i(v0)) % 138.52/19.26 % 138.52/19.26 (transitivity_gt) % 138.52/19.26 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 138.52/19.26 ~ gt(v1, v2) | ~ gt(v0, v1) | gt(v0, v2)) % 138.52/19.26 % 138.52/19.26 (transitivity_leq) % 138.52/19.26 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 138.52/19.26 ~ leq(v1, v2) | ~ leq(v0, v1) | leq(v0, v2)) % 138.52/19.26 % 138.52/19.26 (function-axioms) % 138.52/19.27 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 138.52/19.27 $i] : (v1 = v0 | ~ (tptp_update3(v5, v4, v3, v2) = v1) | ~ % 138.52/19.27 (tptp_update3(v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 138.52/19.27 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_update2(v4, v3, v2) = % 138.52/19.27 v1) | ~ (tptp_update2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 138.52/19.27 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (sum(v4, v3, v2) = v1) | % 138.52/19.27 ~ (sum(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 138.52/19.27 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_const_array2(v4, v3, v2) = v1) | % 138.52/19.27 ~ (tptp_const_array2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 138.52/19.27 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (a_select3(v4, v3, v2) = % 138.52/19.27 v1) | ~ (a_select3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 138.52/19.27 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (times(v3, v2) = v1) | ~ (times(v3, % 138.52/19.27 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 138.52/19.27 = v0 | ~ (divide(v3, v2) = v1) | ~ (divide(v3, v2) = v0)) & ! [v0: $i] : % 138.52/19.27 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (minus(v3, v2) = v1) | % 138.52/19.27 ~ (minus(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 138.52/19.27 $i] : (v1 = v0 | ~ (plus(v3, v2) = v1) | ~ (plus(v3, v2) = v0)) & ! [v0: % 138.52/19.27 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (tptp_mmul(v3, % 138.52/19.27 v2) = v1) | ~ (tptp_mmul(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 138.52/19.27 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (tptp_msub(v3, v2) = v1) | ~ % 138.52/19.27 (tptp_msub(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 138.52/19.27 [v3: $i] : (v1 = v0 | ~ (tptp_madd(v3, v2) = v1) | ~ (tptp_madd(v3, v2) = % 138.52/19.27 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 138.52/19.27 ~ (dim(v3, v2) = v1) | ~ (dim(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 138.52/19.27 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (tptp_const_array1(v3, v2) = v1) | ~ % 138.52/19.27 (tptp_const_array1(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 138.52/19.27 : ! [v3: $i] : (v1 = v0 | ~ (a_select2(v3, v2) = v1) | ~ (a_select2(v3, v2) % 138.52/19.27 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 % 138.52/19.27 | ~ (uniform_int_rnd(v3, v2) = v1) | ~ (uniform_int_rnd(v3, v2) = v0)) & % 138.52/19.27 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sqrt(v2) = v1) | ~ % 138.52/19.27 (sqrt(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 138.52/19.27 (inv(v2) = v1) | ~ (inv(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 138.52/19.27 $i] : (v1 = v0 | ~ (trans(v2) = v1) | ~ (trans(v2) = v0)) & ! [v0: $i] : % 138.52/19.27 ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (succ(v2) = v1) | ~ (succ(v2) = v0)) % 138.52/19.27 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (pred(v2) = v1) | ~ % 138.52/19.27 (pred(v2) = v0)) % 138.52/19.27 % 138.52/19.27 Further assumptions not needed in the proof: % 138.52/19.27 -------------------------------------------- % 138.52/19.27 const_array1_select, const_array2_select, defuse, finite_domain_0, % 138.52/19.27 finite_domain_5, gt_0_tptp_minus_1, gt_135300_0, gt_135300_1, gt_135300_2, % 138.52/19.27 gt_135300_3, gt_135300_4, gt_135300_5, gt_135300_tptp_minus_1, gt_1_0, % 138.52/19.27 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, % 138.52/19.27 gt_4_0, gt_4_1, gt_4_2, gt_4_3, gt_4_tptp_minus_1, gt_5_0, gt_5_1, gt_5_2, % 138.52/19.27 gt_5_3, gt_5_tptp_minus_1, leq_geq, leq_minus, leq_succ, leq_succ_gt_equiv, % 138.52/19.27 lt_gt, matrix_symm_aba1, matrix_symm_aba2, matrix_symm_add, matrix_symm_inv, % 138.52/19.27 matrix_symm_joseph_update, matrix_symm_sub, matrix_symm_trans, % 138.52/19.27 matrix_symm_update_diagonal, reflexivity_leq, sel2_update_1, sel2_update_2, % 138.52/19.27 sel2_update_3, sel3_update_1, sel3_update_2, sel3_update_3, succ_plus_1_l, % 138.52/19.27 succ_plus_1_r, succ_plus_2_l, succ_plus_2_r, succ_plus_3_l, succ_plus_3_r, % 138.52/19.27 succ_plus_4_l, succ_plus_4_r, succ_plus_5_l, succ_plus_5_r, sum_plus_base_float, % 138.52/19.27 totality, ttrue, uniform_int_rand_ranges_hi, uniform_int_rand_ranges_lo % 138.52/19.27 % 138.52/19.27 Those formulas are unsatisfiable: % 138.52/19.27 --------------------------------- % 138.52/19.27 % 138.52/19.27 Begin of proof % 138.52/19.28 | % 138.52/19.28 | ALPHA: (leq_gt_pred) implies: % 138.52/19.28 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (pred(v1) = v2) | ~ % 138.52/19.28 | $i(v1) | ~ $i(v0) | ~ gt(v1, v0) | leq(v0, v2)) % 138.52/19.28 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (pred(v1) = v2) | ~ % 138.52/19.28 | $i(v1) | ~ $i(v0) | ~ leq(v0, v2) | gt(v1, v0)) % 138.52/19.28 | % 138.52/19.28 | ALPHA: (sum_plus_base) implies: % 139.23/19.28 | (3) ! [v0: $i] : ! [v1: $i] : (v1 = n0 | ~ (sum(n0, tptp_minus_1, v0) = % 139.23/19.28 | v1) | ~ $i(v0)) % 139.23/19.28 | % 139.23/19.28 | ALPHA: (succ_tptp_minus_1) implies: % 139.23/19.28 | (4) succ(tptp_minus_1) = n0 % 139.23/19.28 | % 139.23/19.28 | ALPHA: (pred_minus_1) implies: % 139.23/19.28 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (minus(v0, n1) = v1) | ~ $i(v0) | % 139.23/19.28 | (pred(v0) = v1 & $i(v1))) % 139.23/19.28 | % 139.23/19.28 | ALPHA: (leq_succ_succ) implies: % 139.23/19.28 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (succ(v1) = % 139.23/19.28 | v3) | ~ (succ(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ leq(v0, v1) | % 139.23/19.28 | leq(v2, v3)) % 139.23/19.29 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (succ(v1) = % 139.23/19.29 | v3) | ~ (succ(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ leq(v2, v3) | % 139.23/19.29 | leq(v0, v1)) % 139.23/19.29 | % 139.23/19.29 | ALPHA: (gt_5_4) implies: % 139.23/19.29 | (8) gt(n5, n4) % 139.23/19.29 | % 139.23/19.29 | ALPHA: (gt_3_tptp_minus_1) implies: % 139.23/19.29 | (9) $i(tptp_minus_1) % 139.23/19.29 | % 139.23/19.29 | ALPHA: (finite_domain_4) implies: % 139.23/19.29 | (10) ! [v0: $i] : (v0 = n4 | v0 = n3 | v0 = n2 | v0 = n1 | v0 = n0 | ~ % 139.23/19.29 | $i(v0) | ~ leq(v0, n4) | ~ leq(n0, v0)) % 139.23/19.29 | % 139.23/19.29 | ALPHA: (finite_domain_1) implies: % 139.23/19.29 | (11) ! [v0: $i] : (v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0, n1) | ~ % 139.23/19.29 | leq(n0, v0)) % 139.23/19.29 | % 139.23/19.29 | ALPHA: (finite_domain_2) implies: % 139.23/19.29 | (12) ! [v0: $i] : (v0 = n2 | v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0, % 139.23/19.29 | n2) | ~ leq(n0, v0)) % 139.23/19.29 | % 139.23/19.29 | ALPHA: (finite_domain_3) implies: % 139.23/19.29 | (13) ! [v0: $i] : (v0 = n3 | v0 = n2 | v0 = n1 | v0 = n0 | ~ $i(v0) | ~ % 139.23/19.29 | leq(v0, n3) | ~ leq(n0, v0)) % 139.23/19.29 | % 139.23/19.29 | ALPHA: (successor_4) implies: % 139.23/19.29 | (14) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (succ(v2) = n4 & succ(v1) = % 139.23/19.29 | v2 & succ(v0) = v1 & succ(n0) = v0 & $i(v2) & $i(v1) & $i(v0)) % 139.23/19.29 | % 139.23/19.29 | ALPHA: (successor_5) implies: % 139.23/19.29 | (15) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (succ(v3) = n5 % 139.23/19.29 | & succ(v2) = v3 & succ(v1) = v2 & succ(v0) = v1 & succ(n0) = v0 & % 139.23/19.29 | $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 139.23/19.29 | % 139.23/19.29 | ALPHA: (successor_1) implies: % 139.23/19.29 | (16) succ(n0) = n1 % 139.23/19.29 | % 139.23/19.29 | ALPHA: (successor_2) implies: % 139.23/19.29 | (17) ? [v0: $i] : (succ(v0) = n2 & succ(n0) = v0 & $i(v0)) % 139.23/19.29 | % 139.23/19.29 | ALPHA: (successor_3) implies: % 139.23/19.29 | (18) ? [v0: $i] : ? [v1: $i] : (succ(v1) = n3 & succ(v0) = v1 & succ(n0) % 139.23/19.29 | = v0 & $i(v1) & $i(v0)) % 139.23/19.29 | % 139.23/19.29 | ALPHA: (cl5_nebula_norm_0031) implies: % 139.23/19.29 | (19) $i(n0) % 139.23/19.29 | (20) $i(n5) % 139.23/19.29 | (21) $i(pv10) % 139.23/19.29 | (22) $i(pv12) % 139.23/19.30 | (23) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 139.23/19.30 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : % 139.23/19.30 | ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: % 139.23/19.30 | $i] : ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? [v18: $i] : ? % 139.23/19.30 | [v19: $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ? [v23: $i] % 139.23/19.30 | : ? [v24: $i] : ? [v25: $i] : ? [v26: $i] : ? [v27: $i] : % 139.23/19.30 | (minus(n135300, n1) = v0 & minus(pv12, n1) = v2 & minus(pv10, n1) = v4 % 139.23/19.30 | & minus(n5, n1) = v1 & a_select2(x, pv10) = v3 & $i(v16) & $i(v15) & % 139.23/19.30 | $i(v12) & $i(v11) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & % 139.23/19.30 | leq(pv12, v1) & leq(pv10, v0) & leq(n0, pv12) & leq(n0, pv10) & ! % 139.23/19.30 | [v28: $i] : ! [v29: $i] : ! [v30: $i] : ! [v31: $i] : ! [v32: % 139.23/19.30 | $i] : ! [v33: $i] : ! [v34: $i] : ! [v35: $i] : ! [v36: $i] : % 139.23/19.30 | ! [v37: $i] : ! [v38: $i] : ! [v39: $i] : ( ~ (times(v35, v35) = % 139.23/19.30 | v36) | ~ (times(v31, v31) = v32) | ~ (sqrt(v36) = v37) | ~ % 139.23/19.30 | (sqrt(v32) = v33) | ~ (divide(v33, v38) = v39) | ~ (minus(v34, % 139.23/19.31 | v3) = v35) | ~ (minus(v30, v3) = v31) | ~ (sum(n0, v1, v37) % 139.23/19.31 | = v38) | ~ (a_select3(center, v29, n0) = v34) | ~ % 139.23/19.31 | (a_select3(center, v28, n0) = v30) | ~ $i(v29) | ~ $i(v28) | ~ % 139.23/19.31 | leq(v28, v2) | ~ leq(n0, v28) | (a_select3(q, pv10, v28) = v39 & % 139.23/19.31 | $i(v39))) & ! [v28: $i] : ! [v29: $i] : ! [v30: $i] : ( ~ % 139.23/19.31 | (a_select3(q, v28, v29) = v30) | ~ $i(v29) | ~ $i(v28) | ~ % 139.23/19.31 | leq(v28, v4) | ~ leq(n0, v28) | sum(n0, v1, v30) = n1) & (( ~ % 139.23/19.31 | (v27 = v17) & times(v23, v23) = v24 & times(v19, v19) = v20 & % 139.23/19.31 | sqrt(v24) = v25 & sqrt(v20) = v21 & divide(v21, v26) = v27 & % 139.23/19.31 | minus(v22, v3) = v23 & minus(v18, v3) = v19 & sum(n0, v1, v25) = % 139.23/19.31 | v26 & a_select3(center, v16, n0) = v22 & a_select3(center, v15, % 139.23/19.31 | n0) = v18 & a_select3(q, pv10, v15) = v17 & $i(v27) & $i(v26) % 139.23/19.31 | & $i(v25) & $i(v24) & $i(v23) & $i(v22) & $i(v21) & $i(v20) & % 139.23/19.31 | $i(v19) & $i(v18) & $i(v17) & leq(v15, v2) & leq(n0, v15)) | ( ~ % 139.23/19.31 | (v14 = n1) & sum(n0, v1, v13) = v14 & a_select3(q, v11, v12) = % 139.23/19.31 | v13 & $i(v14) & $i(v13) & leq(v11, v4) & leq(n0, v11)) | ( ~ % 139.23/19.31 | (v10 = n0) & times(v7, v7) = v8 & sqrt(v8) = v9 & minus(v6, v3) % 139.23/19.31 | = v7 & minus(n0, n1) = v5 & sum(n0, v5, v9) = v10 & % 139.23/19.31 | a_select3(center, pv71, n0) = v6 & $i(v10) & $i(v9) & $i(v8) & % 139.23/19.31 | $i(v7) & $i(v6) & $i(v5)))) % 139.23/19.31 | % 139.23/19.31 | ALPHA: (function-axioms) implies: % 139.23/19.31 | (24) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (pred(v2) = % 139.23/19.31 | v1) | ~ (pred(v2) = v0)) % 139.23/19.31 | (25) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (succ(v2) = % 139.23/19.31 | v1) | ~ (succ(v2) = v0)) % 139.23/19.31 | (26) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 139.23/19.31 | (minus(v3, v2) = v1) | ~ (minus(v3, v2) = v0)) % 139.23/19.31 | (27) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 139.23/19.31 | (v1 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) % 139.23/19.31 | = v0)) % 139.23/19.31 | (28) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 139.23/19.31 | (v1 = v0 | ~ (sum(v4, v3, v2) = v1) | ~ (sum(v4, v3, v2) = v0)) % 139.23/19.31 | % 139.23/19.31 | DELTA: instantiating (17) with fresh symbol all_54_0 gives: % 139.23/19.31 | (29) succ(all_54_0) = n2 & succ(n0) = all_54_0 & $i(all_54_0) % 139.23/19.31 | % 139.23/19.31 | ALPHA: (29) implies: % 139.23/19.31 | (30) $i(all_54_0) % 139.23/19.31 | (31) succ(n0) = all_54_0 % 139.23/19.31 | (32) succ(all_54_0) = n2 % 139.23/19.31 | % 139.23/19.31 | DELTA: instantiating (18) with fresh symbols all_56_0, all_56_1 gives: % 139.23/19.31 | (33) succ(all_56_0) = n3 & succ(all_56_1) = all_56_0 & succ(n0) = all_56_1 % 139.23/19.31 | & $i(all_56_0) & $i(all_56_1) % 139.23/19.31 | % 139.23/19.31 | ALPHA: (33) implies: % 139.23/19.31 | (34) $i(all_56_0) % 139.23/19.31 | (35) succ(n0) = all_56_1 % 139.23/19.31 | (36) succ(all_56_1) = all_56_0 % 139.23/19.31 | (37) succ(all_56_0) = n3 % 139.23/19.31 | % 139.23/19.31 | DELTA: instantiating (14) with fresh symbols all_59_0, all_59_1, all_59_2 % 139.23/19.31 | gives: % 139.23/19.31 | (38) succ(all_59_0) = n4 & succ(all_59_1) = all_59_0 & succ(all_59_2) = % 139.23/19.31 | all_59_1 & succ(n0) = all_59_2 & $i(all_59_0) & $i(all_59_1) & % 139.23/19.31 | $i(all_59_2) % 139.23/19.31 | % 139.23/19.31 | ALPHA: (38) implies: % 139.23/19.31 | (39) $i(all_59_0) % 139.23/19.31 | (40) succ(n0) = all_59_2 % 139.23/19.31 | (41) succ(all_59_2) = all_59_1 % 139.23/19.32 | (42) succ(all_59_1) = all_59_0 % 139.23/19.32 | (43) succ(all_59_0) = n4 % 139.23/19.32 | % 139.23/19.32 | DELTA: instantiating (15) with fresh symbols all_61_0, all_61_1, all_61_2, % 139.23/19.32 | all_61_3 gives: % 139.23/19.32 | (44) succ(all_61_0) = n5 & succ(all_61_1) = all_61_0 & succ(all_61_2) = % 139.23/19.32 | all_61_1 & succ(all_61_3) = all_61_2 & succ(n0) = all_61_3 & % 139.23/19.32 | $i(all_61_0) & $i(all_61_1) & $i(all_61_2) & $i(all_61_3) % 139.23/19.32 | % 139.23/19.32 | ALPHA: (44) implies: % 139.23/19.32 | (45) $i(all_61_0) % 139.23/19.32 | (46) succ(n0) = all_61_3 % 139.23/19.32 | (47) succ(all_61_3) = all_61_2 % 139.23/19.32 | (48) succ(all_61_2) = all_61_1 % 139.23/19.32 | (49) succ(all_61_1) = all_61_0 % 139.23/19.32 | (50) succ(all_61_0) = n5 % 139.23/19.32 | % 139.23/19.32 | DELTA: instantiating (23) with fresh symbols all_71_0, all_71_1, all_71_2, % 139.23/19.32 | all_71_3, all_71_4, all_71_5, all_71_6, all_71_7, all_71_8, all_71_9, % 139.23/19.32 | all_71_10, all_71_11, all_71_12, all_71_13, all_71_14, all_71_15, % 139.23/19.32 | all_71_16, all_71_17, all_71_18, all_71_19, all_71_20, all_71_21, % 139.23/19.32 | all_71_22, all_71_23, all_71_24, all_71_25, all_71_26, all_71_27 gives: % 139.23/19.33 | (51) minus(n135300, n1) = all_71_27 & minus(pv12, n1) = all_71_25 & % 139.23/19.33 | minus(pv10, n1) = all_71_23 & minus(n5, n1) = all_71_26 & a_select2(x, % 139.23/19.33 | pv10) = all_71_24 & $i(all_71_11) & $i(all_71_12) & $i(all_71_15) & % 139.23/19.33 | $i(all_71_16) & $i(all_71_23) & $i(all_71_24) & $i(all_71_25) & % 139.23/19.33 | $i(all_71_26) & $i(all_71_27) & leq(pv12, all_71_26) & leq(pv10, % 139.23/19.33 | all_71_27) & leq(n0, pv12) & leq(n0, pv10) & ! [v0: $i] : ! [v1: % 139.23/19.33 | $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! % 139.23/19.33 | [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! % 139.23/19.33 | [v11: $i] : ( ~ (times(v7, v7) = v8) | ~ (times(v3, v3) = v4) | ~ % 139.23/19.33 | (sqrt(v8) = v9) | ~ (sqrt(v4) = v5) | ~ (divide(v5, v10) = v11) | % 139.23/19.33 | ~ (minus(v6, all_71_24) = v7) | ~ (minus(v2, all_71_24) = v3) | ~ % 139.23/19.33 | (sum(n0, all_71_26, v9) = v10) | ~ (a_select3(center, v1, n0) = v6) % 139.23/19.33 | | ~ (a_select3(center, v0, n0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 139.23/19.33 | leq(v0, all_71_25) | ~ leq(n0, v0) | (a_select3(q, pv10, v0) = v11 % 139.23/19.33 | & $i(v11))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 139.23/19.33 | (a_select3(q, v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ leq(v0, % 139.23/19.33 | all_71_23) | ~ leq(n0, v0) | sum(n0, all_71_26, v2) = n1) & (( ~ % 139.23/19.33 | (all_71_0 = all_71_10) & times(all_71_4, all_71_4) = all_71_3 & % 139.23/19.33 | times(all_71_8, all_71_8) = all_71_7 & sqrt(all_71_3) = all_71_2 & % 139.23/19.33 | sqrt(all_71_7) = all_71_6 & divide(all_71_6, all_71_1) = all_71_0 % 139.23/19.33 | & minus(all_71_5, all_71_24) = all_71_4 & minus(all_71_9, % 139.23/19.33 | all_71_24) = all_71_8 & sum(n0, all_71_26, all_71_2) = all_71_1 % 139.23/19.33 | & a_select3(center, all_71_11, n0) = all_71_5 & a_select3(center, % 139.23/19.33 | all_71_12, n0) = all_71_9 & a_select3(q, pv10, all_71_12) = % 139.23/19.33 | all_71_10 & $i(all_71_0) & $i(all_71_1) & $i(all_71_2) & % 139.23/19.33 | $i(all_71_3) & $i(all_71_4) & $i(all_71_5) & $i(all_71_6) & % 139.23/19.33 | $i(all_71_7) & $i(all_71_8) & $i(all_71_9) & $i(all_71_10) & % 139.23/19.33 | leq(all_71_12, all_71_25) & leq(n0, all_71_12)) | ( ~ (all_71_13 = % 139.23/19.33 | n1) & sum(n0, all_71_26, all_71_14) = all_71_13 & a_select3(q, % 139.23/19.33 | all_71_16, all_71_15) = all_71_14 & $i(all_71_13) & % 139.23/19.33 | $i(all_71_14) & leq(all_71_16, all_71_23) & leq(n0, all_71_16)) | % 139.23/19.33 | ( ~ (all_71_17 = n0) & times(all_71_20, all_71_20) = all_71_19 & % 139.23/19.33 | sqrt(all_71_19) = all_71_18 & minus(all_71_21, all_71_24) = % 139.23/19.33 | all_71_20 & minus(n0, n1) = all_71_22 & sum(n0, all_71_22, % 139.23/19.33 | all_71_18) = all_71_17 & a_select3(center, pv71, n0) = all_71_21 % 139.23/19.33 | & $i(all_71_17) & $i(all_71_18) & $i(all_71_19) & $i(all_71_20) & % 139.23/19.33 | $i(all_71_21) & $i(all_71_22))) % 139.23/19.33 | % 139.23/19.33 | ALPHA: (51) implies: % 139.23/19.33 | (52) leq(n0, pv10) % 139.23/19.33 | (53) leq(n0, pv12) % 139.23/19.33 | (54) leq(pv12, all_71_26) % 139.23/19.33 | (55) $i(all_71_26) % 139.23/19.33 | (56) $i(all_71_16) % 139.23/19.33 | (57) $i(all_71_15) % 139.23/19.33 | (58) $i(all_71_12) % 139.23/19.33 | (59) $i(all_71_11) % 139.23/19.33 | (60) minus(n5, n1) = all_71_26 % 139.23/19.33 | (61) minus(pv10, n1) = all_71_23 % 139.23/19.33 | (62) minus(pv12, n1) = all_71_25 % 139.23/19.33 | (63) ( ~ (all_71_0 = all_71_10) & times(all_71_4, all_71_4) = all_71_3 & % 139.23/19.33 | times(all_71_8, all_71_8) = all_71_7 & sqrt(all_71_3) = all_71_2 & % 139.23/19.33 | sqrt(all_71_7) = all_71_6 & divide(all_71_6, all_71_1) = all_71_0 & % 139.23/19.33 | minus(all_71_5, all_71_24) = all_71_4 & minus(all_71_9, all_71_24) = % 139.23/19.33 | all_71_8 & sum(n0, all_71_26, all_71_2) = all_71_1 & % 139.23/19.33 | a_select3(center, all_71_11, n0) = all_71_5 & a_select3(center, % 139.23/19.33 | all_71_12, n0) = all_71_9 & a_select3(q, pv10, all_71_12) = % 139.23/19.33 | all_71_10 & $i(all_71_0) & $i(all_71_1) & $i(all_71_2) & % 139.23/19.33 | $i(all_71_3) & $i(all_71_4) & $i(all_71_5) & $i(all_71_6) & % 139.23/19.33 | $i(all_71_7) & $i(all_71_8) & $i(all_71_9) & $i(all_71_10) & % 139.23/19.33 | leq(all_71_12, all_71_25) & leq(n0, all_71_12)) | ( ~ (all_71_13 = % 139.23/19.33 | n1) & sum(n0, all_71_26, all_71_14) = all_71_13 & a_select3(q, % 139.23/19.33 | all_71_16, all_71_15) = all_71_14 & $i(all_71_13) & $i(all_71_14) % 139.23/19.33 | & leq(all_71_16, all_71_23) & leq(n0, all_71_16)) | ( ~ (all_71_17 = % 139.23/19.33 | n0) & times(all_71_20, all_71_20) = all_71_19 & sqrt(all_71_19) = % 139.23/19.33 | all_71_18 & minus(all_71_21, all_71_24) = all_71_20 & minus(n0, n1) % 139.23/19.33 | = all_71_22 & sum(n0, all_71_22, all_71_18) = all_71_17 & % 139.23/19.33 | a_select3(center, pv71, n0) = all_71_21 & $i(all_71_17) & % 139.23/19.33 | $i(all_71_18) & $i(all_71_19) & $i(all_71_20) & $i(all_71_21) & % 139.23/19.33 | $i(all_71_22)) % 139.23/19.34 | (64) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (a_select3(q, v0, v1) = % 139.23/19.34 | v2) | ~ $i(v1) | ~ $i(v0) | ~ leq(v0, all_71_23) | ~ leq(n0, % 139.23/19.34 | v0) | sum(n0, all_71_26, v2) = n1) % 139.23/19.34 | (65) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 139.23/19.34 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : % 139.23/19.34 | ! [v10: $i] : ! [v11: $i] : ( ~ (times(v7, v7) = v8) | ~ (times(v3, % 139.23/19.34 | v3) = v4) | ~ (sqrt(v8) = v9) | ~ (sqrt(v4) = v5) | ~ % 139.23/19.34 | (divide(v5, v10) = v11) | ~ (minus(v6, all_71_24) = v7) | ~ % 139.23/19.34 | (minus(v2, all_71_24) = v3) | ~ (sum(n0, all_71_26, v9) = v10) | ~ % 139.23/19.34 | (a_select3(center, v1, n0) = v6) | ~ (a_select3(center, v0, n0) = % 139.23/19.34 | v2) | ~ $i(v1) | ~ $i(v0) | ~ leq(v0, all_71_25) | ~ leq(n0, % 139.23/19.34 | v0) | (a_select3(q, pv10, v0) = v11 & $i(v11))) % 139.23/19.34 | % 139.23/19.34 | GROUND_INST: instantiating (25) with all_56_1, all_59_2, n0, simplifying with % 139.23/19.34 | (35), (40) gives: % 139.23/19.34 | (66) all_59_2 = all_56_1 % 139.23/19.34 | % 139.23/19.34 | GROUND_INST: instantiating (25) with all_54_0, all_59_2, n0, simplifying with % 139.23/19.34 | (31), (40) gives: % 139.23/19.34 | (67) all_59_2 = all_54_0 % 139.23/19.34 | % 139.23/19.34 | GROUND_INST: instantiating (25) with all_56_1, all_61_3, n0, simplifying with % 139.23/19.34 | (35), (46) gives: % 139.23/19.34 | (68) all_61_3 = all_56_1 % 139.23/19.34 | % 139.23/19.34 | GROUND_INST: instantiating (25) with n1, all_61_3, n0, simplifying with (16), % 139.23/19.34 | (46) gives: % 139.23/19.34 | (69) all_61_3 = n1 % 139.23/19.34 | % 139.23/19.34 | COMBINE_EQS: (68), (69) imply: % 139.23/19.34 | (70) all_56_1 = n1 % 139.23/19.34 | % 139.23/19.34 | SIMP: (70) implies: % 139.23/19.34 | (71) all_56_1 = n1 % 139.23/19.34 | % 139.23/19.34 | COMBINE_EQS: (66), (67) imply: % 139.23/19.34 | (72) all_56_1 = all_54_0 % 139.23/19.34 | % 139.23/19.34 | SIMP: (72) implies: % 139.23/19.34 | (73) all_56_1 = all_54_0 % 139.23/19.34 | % 139.23/19.34 | COMBINE_EQS: (71), (73) imply: % 139.23/19.34 | (74) all_54_0 = n1 % 139.23/19.34 | % 139.23/19.34 | COMBINE_EQS: (67), (74) imply: % 139.23/19.34 | (75) all_59_2 = n1 % 139.23/19.34 | % 139.23/19.34 | REDUCE: (47), (69) imply: % 139.23/19.34 | (76) succ(n1) = all_61_2 % 139.23/19.34 | % 139.23/19.34 | REDUCE: (41), (75) imply: % 139.23/19.34 | (77) succ(n1) = all_59_1 % 139.23/19.34 | % 139.23/19.34 | REDUCE: (36), (71) imply: % 139.23/19.34 | (78) succ(n1) = all_56_0 % 139.23/19.34 | % 139.23/19.34 | REDUCE: (32), (74) imply: % 139.23/19.34 | (79) succ(n1) = n2 % 139.23/19.34 | % 139.23/19.34 | REDUCE: (30), (74) imply: % 139.23/19.34 | (80) $i(n1) % 139.23/19.34 | % 139.23/19.35 | GROUND_INST: instantiating (25) with all_56_0, all_59_1, n1, simplifying with % 139.23/19.35 | (77), (78) gives: % 139.23/19.35 | (81) all_59_1 = all_56_0 % 139.23/19.35 | % 139.23/19.35 | GROUND_INST: instantiating (25) with all_59_1, all_61_2, n1, simplifying with % 139.23/19.35 | (76), (77) gives: % 139.23/19.35 | (82) all_61_2 = all_59_1 % 139.23/19.35 | % 139.23/19.35 | GROUND_INST: instantiating (25) with n2, all_61_2, n1, simplifying with (76), % 139.23/19.35 | (79) gives: % 139.23/19.35 | (83) all_61_2 = n2 % 139.23/19.35 | % 139.23/19.35 | COMBINE_EQS: (82), (83) imply: % 139.23/19.35 | (84) all_59_1 = n2 % 139.23/19.35 | % 139.23/19.35 | SIMP: (84) implies: % 139.23/19.35 | (85) all_59_1 = n2 % 139.23/19.35 | % 139.23/19.35 | COMBINE_EQS: (81), (85) imply: % 139.23/19.35 | (86) all_56_0 = n2 % 139.23/19.35 | % 139.23/19.35 | SIMP: (86) implies: % 139.23/19.35 | (87) all_56_0 = n2 % 139.23/19.35 | % 139.23/19.35 | REDUCE: (48), (83) imply: % 139.23/19.35 | (88) succ(n2) = all_61_1 % 139.23/19.35 | % 139.23/19.35 | REDUCE: (42), (85) imply: % 139.23/19.35 | (89) succ(n2) = all_59_0 % 139.23/19.35 | % 139.23/19.35 | REDUCE: (37), (87) imply: % 139.23/19.35 | (90) succ(n2) = n3 % 139.23/19.35 | % 139.23/19.35 | REDUCE: (34), (87) imply: % 139.23/19.35 | (91) $i(n2) % 139.23/19.35 | % 139.23/19.35 | GROUND_INST: instantiating (25) with all_59_0, all_61_1, n2, simplifying with % 139.23/19.35 | (88), (89) gives: % 139.23/19.35 | (92) all_61_1 = all_59_0 % 139.23/19.35 | % 139.23/19.35 | GROUND_INST: instantiating (25) with n3, all_61_1, n2, simplifying with (88), % 139.23/19.35 | (90) gives: % 139.23/19.35 | (93) all_61_1 = n3 % 139.23/19.35 | % 139.23/19.35 | COMBINE_EQS: (92), (93) imply: % 139.23/19.35 | (94) all_59_0 = n3 % 139.23/19.35 | % 139.23/19.35 | SIMP: (94) implies: % 139.23/19.35 | (95) all_59_0 = n3 % 139.23/19.35 | % 139.23/19.35 | REDUCE: (49), (93) imply: % 139.23/19.35 | (96) succ(n3) = all_61_0 % 139.23/19.35 | % 139.23/19.35 | REDUCE: (43), (95) imply: % 139.23/19.35 | (97) succ(n3) = n4 % 139.23/19.35 | % 139.23/19.35 | REDUCE: (39), (95) imply: % 139.23/19.35 | (98) $i(n3) % 139.23/19.35 | % 139.23/19.35 | GROUND_INST: instantiating (25) with n4, all_61_0, n3, simplifying with (96), % 139.23/19.35 | (97) gives: % 139.23/19.35 | (99) all_61_0 = n4 % 139.23/19.35 | % 139.23/19.35 | REDUCE: (50), (99) imply: % 139.23/19.35 | (100) succ(n4) = n5 % 139.23/19.35 | % 139.23/19.35 | REDUCE: (45), (99) imply: % 139.23/19.35 | (101) $i(n4) % 139.23/19.35 | % 139.23/19.35 | GROUND_INST: instantiating (leq_gt1) with n4, n5, simplifying with (8), (20), % 139.23/19.35 | (101) gives: % 139.23/19.35 | (102) leq(n4, n5) % 139.23/19.35 | % 139.23/19.35 | GROUND_INST: instantiating (leq_gt2) with n0, pv10, simplifying with (19), % 139.23/19.35 | (21), (52) gives: % 139.23/19.35 | (103) pv10 = n0 | gt(pv10, n0) % 139.23/19.35 | % 139.23/19.35 | GROUND_INST: instantiating (leq_gt2) with pv12, all_71_26, simplifying with % 139.23/19.35 | (22), (54), (55) gives: % 139.23/19.35 | (104) all_71_26 = pv12 | gt(all_71_26, pv12) % 139.23/19.35 | % 139.23/19.35 | GROUND_INST: instantiating (pred_succ) with n0, n1, simplifying with (16), % 139.23/19.35 | (19) gives: % 139.23/19.35 | (105) pred(n1) = n0 % 139.23/19.35 | % 139.23/19.35 | GROUND_INST: instantiating (pred_succ) with tptp_minus_1, n0, simplifying with % 139.23/19.35 | (4), (9) gives: % 139.23/19.35 | (106) pred(n0) = tptp_minus_1 % 139.23/19.35 | % 139.23/19.35 | GROUND_INST: instantiating (pred_succ) with n1, n2, simplifying with (79), % 139.23/19.35 | (80) gives: % 139.23/19.35 | (107) pred(n2) = n1 % 139.23/19.35 | % 139.23/19.35 | GROUND_INST: instantiating (pred_succ) with n2, n3, simplifying with (90), % 139.23/19.35 | (91) gives: % 139.23/19.35 | (108) pred(n3) = n2 % 139.23/19.35 | % 139.23/19.35 | GROUND_INST: instantiating (pred_succ) with n3, n4, simplifying with (97), % 139.23/19.36 | (98) gives: % 139.23/19.36 | (109) pred(n4) = n3 % 139.23/19.36 | % 139.23/19.36 | GROUND_INST: instantiating (pred_succ) with n4, n5, simplifying with (100), % 139.23/19.36 | (101) gives: % 139.23/19.36 | (110) pred(n5) = n4 % 139.23/19.36 | % 139.23/19.36 | GROUND_INST: instantiating (5) with n5, all_71_26, simplifying with (20), (60) % 139.23/19.36 | gives: % 139.23/19.36 | (111) pred(n5) = all_71_26 & $i(all_71_26) % 139.23/19.36 | % 139.23/19.36 | ALPHA: (111) implies: % 139.23/19.36 | (112) pred(n5) = all_71_26 % 139.23/19.36 | % 139.23/19.36 | GROUND_INST: instantiating (5) with pv10, all_71_23, simplifying with (21), % 139.23/19.36 | (61) gives: % 139.23/19.36 | (113) pred(pv10) = all_71_23 & $i(all_71_23) % 139.23/19.36 | % 139.23/19.36 | ALPHA: (113) implies: % 139.23/19.36 | (114) $i(all_71_23) % 139.23/19.36 | (115) pred(pv10) = all_71_23 % 139.23/19.36 | % 139.23/19.36 | GROUND_INST: instantiating (5) with pv12, all_71_25, simplifying with (22), % 139.23/19.36 | (62) gives: % 139.23/19.36 | (116) pred(pv12) = all_71_25 & $i(all_71_25) % 139.23/19.36 | % 139.23/19.36 | ALPHA: (116) implies: % 139.23/19.36 | (117) $i(all_71_25) % 139.23/19.36 | (118) pred(pv12) = all_71_25 % 139.23/19.36 | % 139.62/19.36 | GROUND_INST: instantiating (24) with n4, all_71_26, n5, simplifying with % 139.62/19.36 | (110), (112) gives: % 139.62/19.36 | (119) all_71_26 = n4 % 139.62/19.36 | % 139.62/19.36 | REDUCE: (60), (119) imply: % 139.62/19.36 | (120) minus(n5, n1) = n4 % 139.62/19.36 | % 139.62/19.36 | REDUCE: (54), (119) imply: % 139.62/19.36 | (121) leq(pv12, n4) % 139.62/19.36 | % 139.62/19.36 | GROUND_INST: instantiating (transitivity_leq) with pv12, n4, n5, simplifying % 139.62/19.36 | with (20), (22), (101), (102), (121) gives: % 139.62/19.36 | (122) leq(pv12, n5) % 139.62/19.36 | % 139.62/19.36 | GROUND_INST: instantiating (10) with pv12, simplifying with (22), (53), (121) % 139.62/19.36 | gives: % 139.62/19.36 | (123) pv12 = n4 | pv12 = n3 | pv12 = n2 | pv12 = n1 | pv12 = n0 % 139.62/19.36 | % 139.62/19.36 | GROUND_INST: instantiating (succ_pred) with pv10, all_71_23, simplifying with % 139.62/19.36 | (21), (115) gives: % 139.62/19.36 | (124) succ(all_71_23) = pv10 % 139.62/19.36 | % 139.62/19.36 | GROUND_INST: instantiating (succ_pred) with pv12, all_71_25, simplifying with % 139.62/19.36 | (22), (118) gives: % 139.62/19.36 | (125) succ(all_71_25) = pv12 % 139.62/19.36 | % 139.62/19.36 | GROUND_INST: instantiating (7) with all_71_25, n4, pv12, n5, simplifying with % 139.62/19.36 | (100), (101), (117), (122), (125) gives: % 139.62/19.36 | (126) leq(all_71_25, n4) % 139.62/19.36 | % 139.62/19.36 | GROUND_INST: instantiating (7) with all_71_25, n3, pv12, n4, simplifying with % 139.62/19.36 | (97), (98), (117), (121), (125) gives: % 139.62/19.36 | (127) leq(all_71_25, n3) % 139.62/19.36 | % 139.62/19.36 | GROUND_INST: instantiating (leq_succ_gt) with all_71_25, n4, pv12, simplifying % 139.62/19.36 | with (101), (117), (121), (125) gives: % 139.62/19.36 | (128) gt(n4, all_71_25) % 139.62/19.36 | % 139.62/19.36 | GROUND_INST: instantiating (gt_succ) with all_71_25, pv12, simplifying with % 139.62/19.36 | (117), (125) gives: % 139.62/19.36 | (129) gt(pv12, all_71_25) % 139.62/19.36 | % 139.62/19.36 | GROUND_INST: instantiating (gt_succ) with all_71_23, pv10, simplifying with % 139.62/19.36 | (114), (124) gives: % 139.62/19.36 | (130) gt(pv10, all_71_23) % 139.62/19.36 | % 139.62/19.36 | GROUND_INST: instantiating (leq_gt1) with all_71_23, pv10, simplifying with % 139.62/19.36 | (21), (114), (130) gives: % 139.62/19.36 | (131) leq(all_71_23, pv10) % 139.62/19.36 | % 139.62/19.36 | GROUND_INST: instantiating (leq_gt1) with all_71_25, pv12, simplifying with % 139.62/19.36 | (22), (117), (129) gives: % 139.62/19.36 | (132) leq(all_71_25, pv12) % 139.62/19.36 | % 139.62/19.36 | BETA: splitting (63) gives: % 139.62/19.36 | % 139.62/19.36 | Case 1: % 139.62/19.36 | | % 139.62/19.37 | | (133) ~ (all_71_0 = all_71_10) & times(all_71_4, all_71_4) = all_71_3 & % 139.62/19.37 | | times(all_71_8, all_71_8) = all_71_7 & sqrt(all_71_3) = all_71_2 & % 139.62/19.37 | | sqrt(all_71_7) = all_71_6 & divide(all_71_6, all_71_1) = all_71_0 & % 139.62/19.37 | | minus(all_71_5, all_71_24) = all_71_4 & minus(all_71_9, all_71_24) % 139.62/19.37 | | = all_71_8 & sum(n0, all_71_26, all_71_2) = all_71_1 & % 139.62/19.37 | | a_select3(center, all_71_11, n0) = all_71_5 & a_select3(center, % 139.62/19.37 | | all_71_12, n0) = all_71_9 & a_select3(q, pv10, all_71_12) = % 139.62/19.37 | | all_71_10 & $i(all_71_0) & $i(all_71_1) & $i(all_71_2) & % 139.62/19.37 | | $i(all_71_3) & $i(all_71_4) & $i(all_71_5) & $i(all_71_6) & % 139.62/19.37 | | $i(all_71_7) & $i(all_71_8) & $i(all_71_9) & $i(all_71_10) & % 139.62/19.37 | | leq(all_71_12, all_71_25) & leq(n0, all_71_12) % 139.62/19.37 | | % 139.62/19.37 | | ALPHA: (133) implies: % 139.62/19.37 | | (134) ~ (all_71_0 = all_71_10) % 139.62/19.37 | | (135) leq(n0, all_71_12) % 139.62/19.37 | | (136) leq(all_71_12, all_71_25) % 139.62/19.37 | | (137) a_select3(q, pv10, all_71_12) = all_71_10 % 139.62/19.37 | | (138) a_select3(center, all_71_12, n0) = all_71_9 % 139.62/19.37 | | (139) a_select3(center, all_71_11, n0) = all_71_5 % 139.62/19.37 | | (140) sum(n0, all_71_26, all_71_2) = all_71_1 % 139.62/19.37 | | (141) minus(all_71_9, all_71_24) = all_71_8 % 139.62/19.37 | | (142) minus(all_71_5, all_71_24) = all_71_4 % 139.62/19.37 | | (143) divide(all_71_6, all_71_1) = all_71_0 % 139.62/19.37 | | (144) sqrt(all_71_7) = all_71_6 % 139.62/19.37 | | (145) sqrt(all_71_3) = all_71_2 % 139.62/19.37 | | (146) times(all_71_8, all_71_8) = all_71_7 % 139.62/19.37 | | (147) times(all_71_4, all_71_4) = all_71_3 % 139.62/19.37 | | % 139.62/19.37 | | REDUCE: (119), (140) imply: % 139.62/19.37 | | (148) sum(n0, n4, all_71_2) = all_71_1 % 139.62/19.37 | | % 139.62/19.37 | | GROUND_INST: instantiating (leq_gt2) with n0, all_71_12, simplifying with % 139.62/19.37 | | (19), (58), (135) gives: % 139.62/19.37 | | (149) all_71_12 = n0 | gt(all_71_12, n0) % 139.62/19.37 | | % 139.62/19.37 | | GROUND_INST: instantiating (transitivity_leq) with all_71_12, all_71_25, % 139.62/19.37 | | pv12, simplifying with (22), (58), (117), (132), (136) gives: % 139.62/19.37 | | (150) leq(all_71_12, pv12) % 139.62/19.37 | | % 139.62/19.37 | | GROUND_INST: instantiating (transitivity_leq) with all_71_12, all_71_25, n4, % 139.62/19.37 | | simplifying with (58), (101), (117), (126), (136) gives: % 139.62/19.37 | | (151) leq(all_71_12, n4) % 139.62/19.37 | | % 139.62/19.37 | | GROUND_INST: instantiating (transitivity_leq) with all_71_12, all_71_25, n3, % 139.62/19.37 | | simplifying with (58), (98), (117), (127), (136) gives: % 139.62/19.37 | | (152) leq(all_71_12, n3) % 139.62/19.37 | | % 139.62/19.37 | | GROUND_INST: instantiating (transitivity_leq) with n0, all_71_12, all_71_25, % 139.62/19.37 | | simplifying with (19), (58), (117), (135), (136) gives: % 139.62/19.37 | | (153) leq(n0, all_71_25) % 139.62/19.37 | | % 139.62/19.37 | | GROUND_INST: instantiating (leq_gt2) with all_71_12, all_71_25, simplifying % 139.62/19.37 | | with (58), (117), (136) gives: % 139.62/19.37 | | (154) all_71_12 = all_71_25 | gt(all_71_25, all_71_12) % 139.62/19.37 | | % 139.62/19.37 | | GROUND_INST: instantiating (6) with n0, all_71_25, n1, pv12, simplifying % 139.62/19.37 | | with (16), (19), (117), (125), (153) gives: % 139.62/19.37 | | (155) leq(n1, pv12) % 139.62/19.37 | | % 139.62/19.37 | | GROUND_INST: instantiating (2) with n0, pv12, all_71_25, simplifying with % 139.62/19.37 | | (19), (22), (118), (153) gives: % 139.62/19.37 | | (156) gt(pv12, n0) % 139.62/19.37 | | % 139.62/19.37 | | GROUND_INST: instantiating (13) with all_71_25, simplifying with (117), % 139.62/19.37 | | (127), (153) gives: % 139.62/19.37 | | (157) all_71_25 = n3 | all_71_25 = n2 | all_71_25 = n1 | all_71_25 = n0 % 139.62/19.37 | | % 139.62/19.37 | | GROUND_INST: instantiating (leq_gt2) with n0, all_71_25, simplifying with % 139.62/19.37 | | (19), (117), (153) gives: % 139.62/19.37 | | (158) all_71_25 = n0 | gt(all_71_25, n0) % 139.62/19.37 | | % 139.62/19.37 | | GROUND_INST: instantiating (13) with all_71_12, simplifying with (58), % 139.62/19.37 | | (135), (152) gives: % 139.62/19.37 | | (159) all_71_12 = n3 | all_71_12 = n2 | all_71_12 = n1 | all_71_12 = n0 % 139.62/19.37 | | % 139.62/19.37 | | GROUND_INST: instantiating (10) with all_71_12, simplifying with (58), % 139.62/19.37 | | (135), (151) gives: % 139.62/19.37 | | (160) all_71_12 = n4 | all_71_12 = n3 | all_71_12 = n2 | all_71_12 = n1 | % 139.62/19.37 | | all_71_12 = n0 % 139.62/19.37 | | % 139.62/19.37 | | GROUND_INST: instantiating (leq_gt2) with n1, pv12, simplifying with (22), % 139.62/19.37 | | (80), (155) gives: % 139.62/19.37 | | (161) pv12 = n1 | gt(pv12, n1) % 139.62/19.37 | | % 139.62/19.37 | | BETA: splitting (103) gives: % 139.62/19.37 | | % 139.62/19.37 | | Case 1: % 139.62/19.37 | | | % 139.62/19.37 | | | (162) gt(pv10, n0) % 139.62/19.37 | | | % 139.62/19.37 | | | GROUND_INST: instantiating (1) with n0, pv10, all_71_23, simplifying with % 139.62/19.37 | | | (19), (21), (115), (162) gives: % 139.62/19.37 | | | (163) leq(n0, all_71_23) % 139.62/19.37 | | | % 139.62/19.37 | | | GROUND_INST: instantiating (6) with n0, all_71_23, n1, pv10, simplifying % 139.62/19.37 | | | with (16), (19), (114), (124), (163) gives: % 139.62/19.37 | | | (164) leq(n1, pv10) % 139.62/19.37 | | | % 139.62/19.37 | | | GROUND_INST: instantiating (leq_gt2) with n0, all_71_23, simplifying with % 139.62/19.37 | | | (19), (114), (163) gives: % 139.62/19.37 | | | (165) all_71_23 = n0 | gt(all_71_23, n0) % 139.62/19.37 | | | % 139.62/19.37 | | | GROUND_INST: instantiating (leq_gt2) with n1, pv10, simplifying with (21), % 139.62/19.37 | | | (80), (164) gives: % 139.62/19.38 | | | (166) pv10 = n1 | gt(pv10, n1) % 139.62/19.38 | | | % 139.62/19.38 | | | BETA: splitting (104) gives: % 139.62/19.38 | | | % 139.62/19.38 | | | Case 1: % 139.62/19.38 | | | | % 139.62/19.38 | | | | (167) gt(all_71_26, pv12) % 139.62/19.38 | | | | % 139.62/19.38 | | | | REDUCE: (119), (167) imply: % 139.62/19.38 | | | | (168) gt(n4, pv12) % 139.62/19.38 | | | | % 139.62/19.38 | | | | GROUND_INST: instantiating (1) with pv12, n4, n3, simplifying with (22), % 139.62/19.38 | | | | (101), (109), (168) gives: % 139.62/19.38 | | | | (169) leq(pv12, n3) % 139.62/19.38 | | | | % 139.62/19.38 | | | | GROUND_INST: instantiating (7) with all_71_25, n2, pv12, n3, simplifying % 139.62/19.38 | | | | with (90), (91), (117), (125), (169) gives: % 139.62/19.38 | | | | (170) leq(all_71_25, n2) % 139.62/19.38 | | | | % 139.62/19.38 | | | | GROUND_INST: instantiating (leq_gt2) with pv12, n3, simplifying with % 139.62/19.38 | | | | (22), (98), (169) gives: % 139.62/19.38 | | | | (171) pv12 = n3 | gt(n3, pv12) % 139.62/19.38 | | | | % 139.62/19.38 | | | | BETA: splitting (123) gives: % 139.62/19.38 | | | | % 139.62/19.38 | | | | Case 1: % 139.62/19.38 | | | | | % 139.62/19.38 | | | | | (172) pv12 = n0 % 139.62/19.38 | | | | | % 139.62/19.38 | | | | | REDUCE: (156), (172) imply: % 139.62/19.38 | | | | | (173) gt(n0, n0) % 139.62/19.38 | | | | | % 139.62/19.38 | | | | | GROUND_INST: instantiating (irreflexivity_gt) with n0, simplifying % 139.62/19.38 | | | | | with (19), (173) gives: % 139.62/19.38 | | | | | (174) $false % 139.62/19.38 | | | | | % 139.62/19.38 | | | | | CLOSE: (174) is inconsistent. % 139.62/19.38 | | | | | % 139.62/19.38 | | | | Case 2: % 139.62/19.38 | | | | | % 139.62/19.38 | | | | | (175) ~ (pv12 = n0) % 139.62/19.38 | | | | | (176) pv12 = n4 | pv12 = n3 | pv12 = n2 | pv12 = n1 % 139.62/19.38 | | | | | % 139.62/19.38 | | | | | GROUND_INST: instantiating (transitivity_leq) with all_71_12, % 139.62/19.38 | | | | | all_71_25, n2, simplifying with (58), (91), (117), (136), % 139.62/19.38 | | | | | (170) gives: % 139.62/19.38 | | | | | (177) leq(all_71_12, n2) % 139.62/19.38 | | | | | % 139.62/19.38 | | | | | GROUND_INST: instantiating (12) with all_71_25, simplifying with % 139.62/19.38 | | | | | (117), (153), (170) gives: % 139.62/19.38 | | | | | (178) all_71_25 = n2 | all_71_25 = n1 | all_71_25 = n0 % 139.62/19.38 | | | | | % 139.62/19.38 | | | | | GROUND_INST: instantiating (leq_gt2) with all_71_25, n2, simplifying % 139.62/19.38 | | | | | with (91), (117), (170) gives: % 139.62/19.38 | | | | | (179) all_71_25 = n2 | gt(n2, all_71_25) % 139.62/19.38 | | | | | % 139.62/19.38 | | | | | GROUND_INST: instantiating (12) with all_71_12, simplifying with (58), % 139.62/19.38 | | | | | (135), (177) gives: % 139.62/19.38 | | | | | (180) all_71_12 = n2 | all_71_12 = n1 | all_71_12 = n0 % 139.62/19.38 | | | | | % 139.62/19.38 | | | | | GROUND_INST: instantiating (leq_gt2) with all_71_12, n2, simplifying % 139.62/19.38 | | | | | with (58), (91), (177) gives: % 139.62/19.38 | | | | | (181) all_71_12 = n2 | gt(n2, all_71_12) % 139.62/19.38 | | | | | % 139.62/19.38 | | | | | BETA: splitting (149) gives: % 139.62/19.38 | | | | | % 139.62/19.38 | | | | | Case 1: % 139.62/19.38 | | | | | | % 139.62/19.38 | | | | | | (182) gt(all_71_12, n0) % 139.62/19.38 | | | | | | % 139.62/19.38 | | | | | | BETA: splitting (154) gives: % 139.62/19.38 | | | | | | % 139.62/19.38 | | | | | | Case 1: % 139.62/19.38 | | | | | | | % 139.62/19.38 | | | | | | | (183) gt(all_71_25, all_71_12) % 139.62/19.38 | | | | | | | % 139.62/19.38 | | | | | | | BETA: splitting (158) gives: % 139.62/19.38 | | | | | | | % 139.62/19.38 | | | | | | | Case 1: % 139.62/19.38 | | | | | | | | % 139.62/19.38 | | | | | | | | (184) gt(all_71_25, n0) % 139.62/19.38 | | | | | | | | % 139.62/19.38 | | | | | | | | BETA: splitting (159) gives: % 139.62/19.38 | | | | | | | | % 139.62/19.38 | | | | | | | | Case 1: % 139.62/19.38 | | | | | | | | | % 139.62/19.38 | | | | | | | | | (185) all_71_12 = n0 % 139.62/19.38 | | | | | | | | | % 139.62/19.38 | | | | | | | | | REF_CLOSE: (58), (182), (185), (irreflexivity_gt) are % 139.62/19.38 | | | | | | | | | inconsistent by sub-proof #25. % 139.62/19.38 | | | | | | | | | % 139.62/19.38 | | | | | | | | Case 2: % 139.62/19.38 | | | | | | | | | % 139.62/19.38 | | | | | | | | | (186) ~ (all_71_12 = n0) % 139.62/19.38 | | | | | | | | | % 139.62/19.38 | | | | | | | | | BETA: splitting (157) gives: % 139.62/19.38 | | | | | | | | | % 139.62/19.38 | | | | | | | | | Case 1: % 139.62/19.38 | | | | | | | | | | % 139.62/19.38 | | | | | | | | | | (187) all_71_25 = n0 % 139.62/19.38 | | | | | | | | | | % 139.62/19.38 | | | | | | | | | | REDUCE: (184), (187) imply: % 139.62/19.38 | | | | | | | | | | (188) gt(n0, n0) % 139.62/19.38 | | | | | | | | | | % 139.62/19.38 | | | | | | | | | | GROUND_INST: instantiating (irreflexivity_gt) with n0, % 139.62/19.38 | | | | | | | | | | simplifying with (19), (188) gives: % 139.62/19.38 | | | | | | | | | | (189) $false % 139.62/19.38 | | | | | | | | | | % 139.62/19.38 | | | | | | | | | | CLOSE: (189) is inconsistent. % 139.62/19.38 | | | | | | | | | | % 139.62/19.38 | | | | | | | | | Case 2: % 139.62/19.38 | | | | | | | | | | % 139.62/19.38 | | | | | | | | | | (190) ~ (all_71_25 = n0) % 139.62/19.38 | | | | | | | | | | % 139.62/19.38 | | | | | | | | | | BETA: splitting (160) gives: % 139.62/19.38 | | | | | | | | | | % 139.62/19.38 | | | | | | | | | | Case 1: % 139.62/19.38 | | | | | | | | | | | % 139.62/19.38 | | | | | | | | | | | (191) all_71_12 = n0 % 139.62/19.38 | | | | | | | | | | | % 139.62/19.38 | | | | | | | | | | | REDUCE: (186), (191) imply: % 139.62/19.38 | | | | | | | | | | | (192) $false % 139.62/19.38 | | | | | | | | | | | % 139.62/19.38 | | | | | | | | | | | CLOSE: (192) is inconsistent. % 139.62/19.38 | | | | | | | | | | | % 139.62/19.38 | | | | | | | | | | Case 2: % 139.62/19.38 | | | | | | | | | | | % 139.62/19.38 | | | | | | | | | | | (193) all_71_12 = n4 | all_71_12 = n3 | all_71_12 = n2 | % 139.62/19.38 | | | | | | | | | | | all_71_12 = n1 % 139.62/19.38 | | | | | | | | | | | % 139.62/19.38 | | | | | | | | | | | BETA: splitting (165) gives: % 139.62/19.38 | | | | | | | | | | | % 139.62/19.38 | | | | | | | | | | | Case 1: % 139.62/19.38 | | | | | | | | | | | | % 139.62/19.38 | | | | | | | | | | | | (194) gt(all_71_23, n0) % 139.62/19.38 | | | | | | | | | | | | % 139.62/19.38 | | | | | | | | | | | | BETA: splitting (166) gives: % 139.62/19.38 | | | | | | | | | | | | % 139.62/19.38 | | | | | | | | | | | | Case 1: % 139.62/19.38 | | | | | | | | | | | | | % 139.62/19.38 | | | | | | | | | | | | | (195) gt(pv10, n1) % 139.62/19.38 | | | | | | | | | | | | | % 139.62/19.38 | | | | | | | | | | | | | GROUND_INST: instantiating (1) with n1, pv10, all_71_23, % 139.62/19.38 | | | | | | | | | | | | | simplifying with (21), (80), (115), (195) gives: % 139.62/19.38 | | | | | | | | | | | | | (196) leq(n1, all_71_23) % 139.62/19.38 | | | | | | | | | | | | | % 139.62/19.38 | | | | | | | | | | | | | BETA: splitting (171) gives: % 139.62/19.38 | | | | | | | | | | | | | % 139.62/19.38 | | | | | | | | | | | | | Case 1: % 139.62/19.38 | | | | | | | | | | | | | | % 139.62/19.38 | | | | | | | | | | | | | | (197) gt(n3, pv12) % 139.62/19.38 | | | | | | | | | | | | | | % 139.62/19.38 | | | | | | | | | | | | | | BETA: splitting (179) gives: % 139.62/19.38 | | | | | | | | | | | | | | % 139.62/19.38 | | | | | | | | | | | | | | Case 1: % 139.62/19.38 | | | | | | | | | | | | | | | % 139.62/19.39 | | | | | | | | | | | | | | | (198) gt(n2, all_71_25) % 139.62/19.39 | | | | | | | | | | | | | | | % 139.62/19.39 | | | | | | | | | | | | | | | BETA: splitting (178) gives: % 139.62/19.39 | | | | | | | | | | | | | | | % 139.62/19.39 | | | | | | | | | | | | | | | Case 1: % 139.62/19.39 | | | | | | | | | | | | | | | | % 139.62/19.39 | | | | | | | | | | | | | | | | (199) all_71_25 = n0 % 139.62/19.39 | | | | | | | | | | | | | | | | % 139.62/19.39 | | | | | | | | | | | | | | | | REDUCE: (190), (199) imply: % 139.62/19.39 | | | | | | | | | | | | | | | | (200) $false % 139.62/19.39 | | | | | | | | | | | | | | | | % 139.62/19.39 | | | | | | | | | | | | | | | | CLOSE: (200) is inconsistent. % 139.62/19.39 | | | | | | | | | | | | | | | | % 139.62/19.39 | | | | | | | | | | | | | | | Case 2: % 139.62/19.39 | | | | | | | | | | | | | | | | % 139.62/19.39 | | | | | | | | | | | | | | | | % 139.62/19.39 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_71_25, n2, n1, % 139.62/19.39 | | | | | | | | | | | | | | | | simplifying with (91), (107), (117), (198) gives: % 139.62/19.39 | | | | | | | | | | | | | | | | (201) leq(all_71_25, n1) % 139.62/19.39 | | | | | | | | | | | | | | | | % 139.62/19.39 | | | | | | | | | | | | | | | | BETA: splitting (180) gives: % 139.62/19.39 | | | | | | | | | | | | | | | | % 139.62/19.39 | | | | | | | | | | | | | | | | Case 1: % 139.62/19.39 | | | | | | | | | | | | | | | | | % 139.62/19.39 | | | | | | | | | | | | | | | | | (202) all_71_12 = n0 % 139.62/19.39 | | | | | | | | | | | | | | | | | % 139.62/19.39 | | | | | | | | | | | | | | | | | REDUCE: (186), (202) imply: % 139.62/19.39 | | | | | | | | | | | | | | | | | (203) $false % 139.62/19.39 | | | | | | | | | | | | | | | | | % 139.62/19.39 | | | | | | | | | | | | | | | | | CLOSE: (203) is inconsistent. % 139.62/19.39 | | | | | | | | | | | | | | | | | % 139.62/19.39 | | | | | | | | | | | | | | | | Case 2: % 139.62/19.39 | | | | | | | | | | | | | | | | | % 139.62/19.39 | | | | | | | | | | | | | | | | | % 139.62/19.39 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_71_25, simplifying % 139.62/19.39 | | | | | | | | | | | | | | | | | with (117), (153), (201) gives: % 139.62/19.39 | | | | | | | | | | | | | | | | | (204) all_71_25 = n1 | all_71_25 = n0 % 139.62/19.39 | | | | | | | | | | | | | | | | | % 139.62/19.39 | | | | | | | | | | | | | | | | | BETA: splitting (204) gives: % 139.62/19.39 | | | | | | | | | | | | | | | | | % 139.62/19.39 | | | | | | | | | | | | | | | | | Case 1: % 139.62/19.39 | | | | | | | | | | | | | | | | | | % 139.62/19.39 | | | | | | | | | | | | | | | | | | (205) all_71_25 = n0 % 139.62/19.39 | | | | | | | | | | | | | | | | | | % 139.62/19.39 | | | | | | | | | | | | | | | | | | REDUCE: (190), (205) imply: % 139.62/19.39 | | | | | | | | | | | | | | | | | | (206) $false % 139.62/19.39 | | | | | | | | | | | | | | | | | | % 139.62/19.39 | | | | | | | | | | | | | | | | | | CLOSE: (206) is inconsistent. % 139.62/19.39 | | | | | | | | | | | | | | | | | | % 139.62/19.39 | | | | | | | | | | | | | | | | | Case 2: % 139.62/19.39 | | | | | | | | | | | | | | | | | | % 139.62/19.39 | | | | | | | | | | | | | | | | | | (207) all_71_25 = n1 % 139.62/19.39 | | | | | | | | | | | | | | | | | | % 139.62/19.39 | | | | | | | | | | | | | | | | | | REDUCE: (136), (207) imply: % 139.62/19.39 | | | | | | | | | | | | | | | | | | (208) leq(all_71_12, n1) % 139.62/19.39 | | | | | | | | | | | | | | | | | | % 139.62/19.39 | | | | | | | | | | | | | | | | | | REDUCE: (183), (207) imply: % 139.62/19.39 | | | | | | | | | | | | | | | | | | (209) gt(n1, all_71_12) % 139.62/19.39 | | | | | | | | | | | | | | | | | | % 139.62/19.39 | | | | | | | | | | | | | | | | | | REDUCE: (128), (207) imply: % 139.62/19.39 | | | | | | | | | | | | | | | | | | (210) gt(n4, n1) % 139.62/19.39 | | | | | | | | | | | | | | | | | | % 139.62/19.39 | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives: % 139.62/19.39 | | | | | | | | | | | | | | | | | | % 139.62/19.39 | | | | | | | | | | | | | | | | | | Case 1: % 139.62/19.39 | | | | | | | | | | | | | | | | | | | % 139.62/19.39 | | | | | | | | | | | | | | | | | | | (211) all_71_12 = n4 % 139.62/19.39 | | | | | | | | | | | | | | | | | | | % 139.62/19.39 | | | | | | | | | | | | | | | | | | | REDUCE: (209), (211) imply: % 139.62/19.39 | | | | | | | | | | | | | | | | | | | (212) gt(n1, n4) % 139.62/19.39 | | | | | | | | | | | | | | | | | | | % 139.62/19.39 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (transitivity_gt) with n1, n4, n1, % 139.62/19.39 | | | | | | | | | | | | | | | | | | | simplifying with (80), (101), (210), (212) gives: % 139.62/19.39 | | | | | | | | | | | | | | | | | | | (213) gt(n1, n1) % 139.62/19.39 | | | | | | | | | | | | | | | | | | | % 139.62/19.39 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (irreflexivity_gt) with n1, % 139.62/19.39 | | | | | | | | | | | | | | | | | | | simplifying with (80), (213) gives: % 139.62/19.39 | | | | | | | | | | | | | | | | | | | (214) $false % 139.62/19.39 | | | | | | | | | | | | | | | | | | | % 139.62/19.39 | | | | | | | | | | | | | | | | | | | CLOSE: (214) is inconsistent. % 139.62/19.39 | | | | | | | | | | | | | | | | | | | % 139.62/19.39 | | | | | | | | | | | | | | | | | | Case 2: % 139.62/19.39 | | | | | | | | | | | | | | | | | | | % 139.62/19.39 | | | | | | | | | | | | | | | | | | | % 139.62/19.39 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_71_12, simplifying % 139.62/19.39 | | | | | | | | | | | | | | | | | | | with (58), (135), (208) gives: % 139.62/19.39 | | | | | | | | | | | | | | | | | | | (215) all_71_12 = n1 | all_71_12 = n0 % 139.62/19.39 | | | | | | | | | | | | | | | | | | | % 139.62/19.39 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (117), (183), (186), (190), (204), (215), % 139.62/19.39 | | | | | | | | | | | | | | | | | | | (irreflexivity_gt) are inconsistent by sub-proof % 139.62/19.39 | | | | | | | | | | | | | | | | | | | #24. % 139.62/19.39 | | | | | | | | | | | | | | | | | | | % 139.62/19.39 | | | | | | | | | | | | | | | | | | End of split % 139.62/19.39 | | | | | | | | | | | | | | | | | | % 139.62/19.39 | | | | | | | | | | | | | | | | | End of split % 139.62/19.39 | | | | | | | | | | | | | | | | | % 139.62/19.39 | | | | | | | | | | | | | | | | End of split % 139.62/19.39 | | | | | | | | | | | | | | | | % 139.62/19.39 | | | | | | | | | | | | | | | End of split % 139.62/19.39 | | | | | | | | | | | | | | | % 139.62/19.39 | | | | | | | | | | | | | | Case 2: % 139.62/19.39 | | | | | | | | | | | | | | | % 139.62/19.39 | | | | | | | | | | | | | | | (216) all_71_25 = n2 % 139.62/19.39 | | | | | | | | | | | | | | | % 139.62/19.39 | | | | | | | | | | | | | | | REDUCE: (125), (216) imply: % 139.62/19.39 | | | | | | | | | | | | | | | (217) succ(n2) = pv12 % 139.62/19.39 | | | | | | | | | | | | | | | % 139.62/19.39 | | | | | | | | | | | | | | | REF_CLOSE: (22), (25), (90), (197), (217), (irreflexivity_gt) % 139.62/19.39 | | | | | | | | | | | | | | | are inconsistent by sub-proof #23. % 139.62/19.39 | | | | | | | | | | | | | | | % 139.62/19.39 | | | | | | | | | | | | | | End of split % 139.62/19.39 | | | | | | | | | | | | | | % 139.62/19.39 | | | | | | | | | | | | | Case 2: % 139.62/19.39 | | | | | | | | | | | | | | % 139.62/19.39 | | | | | | | | | | | | | | (218) pv12 = n3 % 139.62/19.39 | | | | | | | | | | | | | | % 139.62/19.39 | | | | | | | | | | | | | | REDUCE: (62), (218) imply: % 139.62/19.39 | | | | | | | | | | | | | | (219) minus(n3, n1) = all_71_25 % 139.62/19.39 | | | | | | | | | | | | | | % 139.62/19.39 | | | | | | | | | | | | | | REDUCE: (125), (218) imply: % 139.62/19.39 | | | | | | | | | | | | | | (220) succ(all_71_25) = n3 % 139.62/19.39 | | | | | | | | | | | | | | % 139.62/19.39 | | | | | | | | | | | | | | REDUCE: (118), (218) imply: % 139.62/19.39 | | | | | | | | | | | | | | (221) pred(n3) = all_71_25 % 139.62/19.39 | | | | | | | | | | | | | | % 139.62/19.39 | | | | | | | | | | | | | | GROUND_INST: instantiating (24) with n2, all_71_25, n3, % 139.62/19.39 | | | | | | | | | | | | | | simplifying with (108), (221) gives: % 139.62/19.39 | | | | | | | | | | | | | | (222) all_71_25 = n2 % 139.62/19.39 | | | | | | | | | | | | | | % 139.62/19.39 | | | | | | | | | | | | | | REDUCE: (219), (222) imply: % 139.62/19.39 | | | | | | | | | | | | | | (223) minus(n3, n1) = n2 % 139.62/19.39 | | | | | | | | | | | | | | % 139.62/19.39 | | | | | | | | | | | | | | REDUCE: (183), (222) imply: % 139.62/19.39 | | | | | | | | | | | | | | (224) gt(n2, all_71_12) % 139.62/19.39 | | | | | | | | | | | | | | % 139.62/19.39 | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_71_12, n2, n1, % 139.62/19.39 | | | | | | | | | | | | | | simplifying with (58), (91), (107), (224) gives: % 139.62/19.39 | | | | | | | | | | | | | | (225) leq(all_71_12, n1) % 139.62/19.39 | | | | | | | | | | | | | | % 139.62/19.39 | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with n1, all_71_23, n2, pv10, % 139.62/19.39 | | | | | | | | | | | | | | simplifying with (79), (80), (114), (124), (196) % 139.62/19.39 | | | | | | | | | | | | | | gives: % 139.62/19.39 | | | | | | | | | | | | | | (226) leq(n2, pv10) % 139.62/19.39 | | | | | | | | | | | | | | % 139.62/19.39 | | | | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with n1, all_71_23, % 139.62/19.39 | | | | | | | | | | | | | | simplifying with (80), (114), (196) gives: % 139.62/19.39 | | | | | | | | | | | | | | (227) all_71_23 = n1 | gt(all_71_23, n1) % 139.62/19.39 | | | | | | | | | | | | | | % 139.62/19.39 | | | | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with n2, pv10, simplifying % 139.62/19.39 | | | | | | | | | | | | | | with (21), (91), (226) gives: % 139.62/19.39 | | | | | | | | | | | | | | (228) pv10 = n2 | gt(pv10, n2) % 139.62/19.39 | | | | | | | | | | | | | | % 139.62/19.39 | | | | | | | | | | | | | | GROUND_INST: instantiating (transitivity_leq) with all_71_12, % 139.62/19.39 | | | | | | | | | | | | | | n1, all_71_23, simplifying with (58), (80), (114), % 139.62/19.39 | | | | | | | | | | | | | | (196), (225) gives: % 139.62/19.39 | | | | | | | | | | | | | | (229) leq(all_71_12, all_71_23) % 139.62/19.39 | | | | | | | | | | | | | | % 139.62/19.39 | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_71_12, simplifying % 139.62/19.39 | | | | | | | | | | | | | | with (58), (135), (225) gives: % 139.62/19.39 | | | | | | | | | | | | | | (230) all_71_12 = n1 | all_71_12 = n0 % 139.62/19.39 | | | | | | | | | | | | | | % 139.62/19.39 | | | | | | | | | | | | | | BETA: splitting (230) gives: % 139.62/19.39 | | | | | | | | | | | | | | % 139.62/19.39 | | | | | | | | | | | | | | Case 1: % 139.62/19.39 | | | | | | | | | | | | | | | % 139.62/19.39 | | | | | | | | | | | | | | | (231) all_71_12 = n0 % 139.62/19.39 | | | | | | | | | | | | | | | % 139.62/19.39 | | | | | | | | | | | | | | | REDUCE: (186), (231) imply: % 139.62/19.39 | | | | | | | | | | | | | | | (232) $false % 139.62/19.39 | | | | | | | | | | | | | | | % 139.62/19.39 | | | | | | | | | | | | | | | CLOSE: (232) is inconsistent. % 139.62/19.39 | | | | | | | | | | | | | | | % 139.62/19.39 | | | | | | | | | | | | | | Case 2: % 139.62/19.39 | | | | | | | | | | | | | | | % 139.62/19.39 | | | | | | | | | | | | | | | (233) all_71_12 = n1 % 139.62/19.39 | | | | | | | | | | | | | | | % 139.62/19.39 | | | | | | | | | | | | | | | REDUCE: (138), (233) imply: % 139.62/19.39 | | | | | | | | | | | | | | | (234) a_select3(center, n1, n0) = all_71_9 % 139.62/19.39 | | | | | | | | | | | | | | | % 139.62/19.39 | | | | | | | | | | | | | | | REDUCE: (137), (233) imply: % 139.62/19.39 | | | | | | | | | | | | | | | (235) a_select3(q, pv10, n1) = all_71_10 % 139.62/19.39 | | | | | | | | | | | | | | | % 139.62/19.39 | | | | | | | | | | | | | | | REDUCE: (177), (233) imply: % 139.62/19.39 | | | | | | | | | | | | | | | (236) leq(n1, n2) % 139.62/19.39 | | | | | | | | | | | | | | | % 139.62/19.39 | | | | | | | | | | | | | | | REDUCE: (135), (233) imply: % 139.62/19.39 | | | | | | | | | | | | | | | (237) leq(n0, n1) % 139.62/19.39 | | | | | | | | | | | | | | | % 139.62/19.39 | | | | | | | | | | | | | | | BETA: splitting (227) gives: % 139.62/19.39 | | | | | | | | | | | | | | | % 139.62/19.39 | | | | | | | | | | | | | | | Case 1: % 139.62/19.39 | | | | | | | | | | | | | | | | % 139.62/19.39 | | | | | | | | | | | | | | | | (238) gt(all_71_23, n1) % 139.62/19.39 | | | | | | | | | | | | | | | | % 139.62/19.39 | | | | | | | | | | | | | | | | BETA: splitting (228) gives: % 139.62/19.39 | | | | | | | | | | | | | | | | % 139.62/19.39 | | | | | | | | | | | | | | | | Case 1: % 139.62/19.39 | | | | | | | | | | | | | | | | | % 139.62/19.39 | | | | | | | | | | | | | | | | | (239) gt(pv10, n2) % 139.62/19.39 | | | | | | | | | | | | | | | | | % 139.62/19.39 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with n2, pv10, all_71_23, % 139.62/19.39 | | | | | | | | | | | | | | | | | simplifying with (21), (91), (115), (239) gives: % 139.62/19.39 | | | | | | | | | | | | | | | | | (240) leq(n2, all_71_23) % 139.62/19.39 | | | | | | | | | | | | | | | | | % 139.62/19.39 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with n2, all_71_23, n3, pv10, % 139.62/19.39 | | | | | | | | | | | | | | | | | simplifying with (90), (91), (114), (124), (240) % 139.62/19.39 | | | | | | | | | | | | | | | | | gives: % 139.62/19.39 | | | | | | | | | | | | | | | | | (241) leq(n3, pv10) % 139.62/19.39 | | | | | | | | | | | | | | | | | % 139.62/19.39 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with n2, all_71_23, % 139.62/19.39 | | | | | | | | | | | | | | | | | simplifying with (91), (114), (240) gives: % 139.62/19.39 | | | | | | | | | | | | | | | | | (242) all_71_23 = n2 | gt(all_71_23, n2) % 139.62/19.39 | | | | | | | | | | | | | | | | | % 139.62/19.39 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with n3, pv10, simplifying % 139.62/19.39 | | | | | | | | | | | | | | | | | with (21), (98), (241) gives: % 139.62/19.39 | | | | | | | | | | | | | | | | | (243) pv10 = n3 | gt(pv10, n3) % 139.62/19.39 | | | | | | | | | | | | | | | | | % 139.62/19.39 | | | | | | | | | | | | | | | | | BETA: splitting (242) gives: % 139.62/19.39 | | | | | | | | | | | | | | | | | % 139.62/19.39 | | | | | | | | | | | | | | | | | Case 1: % 139.62/19.39 | | | | | | | | | | | | | | | | | | % 139.62/19.39 | | | | | | | | | | | | | | | | | | (244) gt(all_71_23, n2) % 139.62/19.39 | | | | | | | | | | | | | | | | | | % 139.62/19.39 | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives: % 139.62/19.39 | | | | | | | | | | | | | | | | | | % 139.62/19.39 | | | | | | | | | | | | | | | | | | Case 1: % 139.62/19.39 | | | | | | | | | | | | | | | | | | | % 139.62/19.39 | | | | | | | | | | | | | | | | | | | % 139.62/19.40 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (65) with n1, all_71_11, all_71_9, % 139.62/19.40 | | | | | | | | | | | | | | | | | | | all_71_8, all_71_7, all_71_6, all_71_5, all_71_4, % 139.62/19.40 | | | | | | | | | | | | | | | | | | | all_71_3, all_71_2, all_71_1, all_71_0, % 139.62/19.40 | | | | | | | | | | | | | | | | | | | simplifying with (59), (80), (139), (141), (142), % 139.62/19.40 | | | | | | | | | | | | | | | | | | | (143), (144), (145), (146), (147), (234), (237) % 139.62/19.40 | | | | | | | | | | | | | | | | | | | gives: % 139.62/19.40 | | | | | | | | | | | | | | | | | | | (245) ~ (sum(n0, all_71_26, all_71_2) = all_71_1) | ~ % 139.62/19.40 | | | | | | | | | | | | | | | | | | | leq(n1, all_71_25) | (a_select3(q, pv10, n1) = % 139.62/19.40 | | | | | | | | | | | | | | | | | | | all_71_0 & $i(all_71_0)) % 139.62/19.40 | | | | | | | | | | | | | | | | | | | % 139.62/19.40 | | | | | | | | | | | | | | | | | | | BETA: splitting (245) gives: % 139.62/19.40 | | | | | | | | | | | | | | | | | | | % 139.62/19.40 | | | | | | | | | | | | | | | | | | | Case 1: % 139.62/19.40 | | | | | | | | | | | | | | | | | | | | % 139.62/19.40 | | | | | | | | | | | | | | | | | | | | (246) ~ (sum(n0, all_71_26, all_71_2) = all_71_1) % 139.62/19.40 | | | | | | | | | | | | | | | | | | | | % 139.62/19.40 | | | | | | | | | | | | | | | | | | | | REDUCE: (119), (246) imply: % 139.62/19.40 | | | | | | | | | | | | | | | | | | | | (247) ~ (sum(n0, n4, all_71_2) = all_71_1) % 139.62/19.40 | | | | | | | | | | | | | | | | | | | | % 139.62/19.40 | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (148), (247) imply: % 139.62/19.40 | | | | | | | | | | | | | | | | | | | | (248) $false % 139.62/19.40 | | | | | | | | | | | | | | | | | | | | % 139.62/19.40 | | | | | | | | | | | | | | | | | | | | CLOSE: (248) is inconsistent. % 139.62/19.40 | | | | | | | | | | | | | | | | | | | | % 139.62/19.40 | | | | | | | | | | | | | | | | | | | Case 2: % 139.62/19.40 | | | | | | | | | | | | | | | | | | | | % 139.62/19.40 | | | | | | | | | | | | | | | | | | | | (249) ~ leq(n1, all_71_25) | (a_select3(q, pv10, n1) = % 139.62/19.40 | | | | | | | | | | | | | | | | | | | | all_71_0 & $i(all_71_0)) % 139.62/19.40 | | | | | | | | | | | | | | | | | | | | % 139.62/19.40 | | | | | | | | | | | | | | | | | | | | BETA: splitting (249) gives: % 139.62/19.40 | | | | | | | | | | | | | | | | | | | | % 139.62/19.40 | | | | | | | | | | | | | | | | | | | | Case 1: % 139.62/19.40 | | | | | | | | | | | | | | | | | | | | | % 139.62/19.40 | | | | | | | | | | | | | | | | | | | | | (250) ~ leq(n1, all_71_25) % 139.62/19.40 | | | | | | | | | | | | | | | | | | | | | % 139.62/19.40 | | | | | | | | | | | | | | | | | | | | | REDUCE: (222), (250) imply: % 139.62/19.40 | | | | | | | | | | | | | | | | | | | | | (251) ~ leq(n1, n2) % 139.62/19.40 | | | | | | | | | | | | | | | | | | | | | % 139.62/19.40 | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (236), (251) imply: % 139.62/19.40 | | | | | | | | | | | | | | | | | | | | | (252) $false % 139.62/19.40 | | | | | | | | | | | | | | | | | | | | | % 139.62/19.40 | | | | | | | | | | | | | | | | | | | | | CLOSE: (252) is inconsistent. % 139.62/19.40 | | | | | | | | | | | | | | | | | | | | | % 139.62/19.40 | | | | | | | | | | | | | | | | | | | | Case 2: % 139.62/19.40 | | | | | | | | | | | | | | | | | | | | | % 139.62/19.40 | | | | | | | | | | | | | | | | | | | | | (253) a_select3(q, pv10, n1) = all_71_0 & $i(all_71_0) % 139.62/19.40 | | | | | | | | | | | | | | | | | | | | | % 139.62/19.40 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (27), (134), (235), (253) are inconsistent by % 139.62/19.40 | | | | | | | | | | | | | | | | | | | | | sub-proof #22. % 139.62/19.40 | | | | | | | | | | | | | | | | | | | | | % 139.62/19.40 | | | | | | | | | | | | | | | | | | | | End of split % 139.62/19.40 | | | | | | | | | | | | | | | | | | | | % 139.62/19.40 | | | | | | | | | | | | | | | | | | | End of split % 139.62/19.40 | | | | | | | | | | | | | | | | | | | % 139.62/19.40 | | | | | | | | | | | | | | | | | | Case 2: % 139.62/19.40 | | | | | | | | | | | | | | | | | | | % 139.62/19.40 | | | | | | | | | | | | | | | | | | | (254) pv10 = n3 % 139.62/19.40 | | | | | | | | | | | | | | | | | | | % 139.62/19.40 | | | | | | | | | | | | | | | | | | | REDUCE: (61), (254) imply: % 139.62/19.40 | | | | | | | | | | | | | | | | | | | (255) minus(n3, n1) = all_71_23 % 139.62/19.40 | | | | | | | | | | | | | | | | | | | % 139.62/19.40 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (26), (114), (223), (244), (255), % 139.62/19.40 | | | | | | | | | | | | | | | | | | | (irreflexivity_gt) are inconsistent by sub-proof % 139.62/19.40 | | | | | | | | | | | | | | | | | | | #21. % 139.62/19.40 | | | | | | | | | | | | | | | | | | | % 139.62/19.40 | | | | | | | | | | | | | | | | | | End of split % 139.62/19.40 | | | | | | | | | | | | | | | | | | % 139.62/19.40 | | | | | | | | | | | | | | | | | Case 2: % 139.62/19.40 | | | | | | | | | | | | | | | | | | % 139.62/19.40 | | | | | | | | | | | | | | | | | | (256) all_71_23 = n2 % 139.62/19.40 | | | | | | | | | | | | | | | | | | % 139.62/19.40 | | | | | | | | | | | | | | | | | | REDUCE: (124), (256) imply: % 139.62/19.40 | | | | | | | | | | | | | | | | | | (257) succ(n2) = pv10 % 139.62/19.40 | | | | | | | | | | | | | | | | | | % 139.62/19.40 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (25) with n3, pv10, n2, simplifying % 139.62/19.40 | | | | | | | | | | | | | | | | | | with (90), (257) gives: % 139.62/19.40 | | | | | | | | | | | | | | | | | | (258) pv10 = n3 % 139.62/19.40 | | | | | | | | | | | | | | | | | | % 139.62/19.40 | | | | | | | | | | | | | | | | | | REDUCE: (235), (258) imply: % 139.62/19.40 | | | | | | | | | | | | | | | | | | (259) a_select3(q, n3, n1) = all_71_10 % 139.62/19.40 | | | | | | | | | | | | | | | | | | % 139.62/19.40 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (65) with n1, all_71_11, all_71_9, % 139.62/19.40 | | | | | | | | | | | | | | | | | | all_71_8, all_71_7, all_71_6, all_71_5, all_71_4, % 139.62/19.40 | | | | | | | | | | | | | | | | | | all_71_3, all_71_2, all_71_1, all_71_0, % 139.62/19.40 | | | | | | | | | | | | | | | | | | simplifying with (59), (80), (139), (141), (142), % 139.62/19.40 | | | | | | | | | | | | | | | | | | (143), (144), (145), (146), (147), (234), (237) % 139.62/19.40 | | | | | | | | | | | | | | | | | | gives: % 139.62/19.40 | | | | | | | | | | | | | | | | | | (260) ~ (sum(n0, all_71_26, all_71_2) = all_71_1) | ~ % 139.62/19.40 | | | | | | | | | | | | | | | | | | leq(n1, all_71_25) | (a_select3(q, pv10, n1) = % 139.62/19.40 | | | | | | | | | | | | | | | | | | all_71_0 & $i(all_71_0)) % 139.62/19.40 | | | | | | | | | | | | | | | | | | % 139.62/19.40 | | | | | | | | | | | | | | | | | | BETA: splitting (260) gives: % 139.62/19.40 | | | | | | | | | | | | | | | | | | % 139.62/19.40 | | | | | | | | | | | | | | | | | | Case 1: % 139.62/19.40 | | | | | | | | | | | | | | | | | | | % 139.62/19.40 | | | | | | | | | | | | | | | | | | | (261) ~ (sum(n0, all_71_26, all_71_2) = all_71_1) % 139.62/19.40 | | | | | | | | | | | | | | | | | | | % 139.62/19.40 | | | | | | | | | | | | | | | | | | | REDUCE: (119), (261) imply: % 139.62/19.40 | | | | | | | | | | | | | | | | | | | (262) ~ (sum(n0, n4, all_71_2) = all_71_1) % 139.62/19.40 | | | | | | | | | | | | | | | | | | | % 139.62/19.40 | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (148), (262) imply: % 139.62/19.40 | | | | | | | | | | | | | | | | | | | (263) $false % 139.62/19.40 | | | | | | | | | | | | | | | | | | | % 139.62/19.40 | | | | | | | | | | | | | | | | | | | CLOSE: (263) is inconsistent. % 139.62/19.40 | | | | | | | | | | | | | | | | | | | % 139.62/19.40 | | | | | | | | | | | | | | | | | | Case 2: % 139.62/19.40 | | | | | | | | | | | | | | | | | | | % 139.62/19.40 | | | | | | | | | | | | | | | | | | | (264) ~ leq(n1, all_71_25) | (a_select3(q, pv10, n1) = % 139.62/19.40 | | | | | | | | | | | | | | | | | | | all_71_0 & $i(all_71_0)) % 139.62/19.40 | | | | | | | | | | | | | | | | | | | % 139.62/19.40 | | | | | | | | | | | | | | | | | | | BETA: splitting (264) gives: % 139.62/19.40 | | | | | | | | | | | | | | | | | | | % 139.62/19.40 | | | | | | | | | | | | | | | | | | | Case 1: % 139.62/19.40 | | | | | | | | | | | | | | | | | | | | % 139.62/19.40 | | | | | | | | | | | | | | | | | | | | (265) ~ leq(n1, all_71_25) % 139.62/19.40 | | | | | | | | | | | | | | | | | | | | % 139.62/19.40 | | | | | | | | | | | | | | | | | | | | REDUCE: (222), (265) imply: % 139.62/19.40 | | | | | | | | | | | | | | | | | | | | (266) ~ leq(n1, n2) % 139.62/19.40 | | | | | | | | | | | | | | | | | | | | % 139.62/19.40 | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (236), (266) imply: % 139.62/19.40 | | | | | | | | | | | | | | | | | | | | (267) $false % 139.62/19.40 | | | | | | | | | | | | | | | | | | | | % 139.62/19.40 | | | | | | | | | | | | | | | | | | | | CLOSE: (267) is inconsistent. % 139.62/19.40 | | | | | | | | | | | | | | | | | | | | % 139.62/19.40 | | | | | | | | | | | | | | | | | | | Case 2: % 139.62/19.40 | | | | | | | | | | | | | | | | | | | | % 139.62/19.40 | | | | | | | | | | | | | | | | | | | | (268) a_select3(q, pv10, n1) = all_71_0 & $i(all_71_0) % 139.62/19.40 | | | | | | | | | | | | | | | | | | | | % 139.62/19.40 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (27), (134), (258), (259), (268) are inconsistent % 139.62/19.40 | | | | | | | | | | | | | | | | | | | | by sub-proof #20. % 139.62/19.40 | | | | | | | | | | | | | | | | | | | | % 139.62/19.40 | | | | | | | | | | | | | | | | | | | End of split % 139.62/19.40 | | | | | | | | | | | | | | | | | | | % 139.62/19.40 | | | | | | | | | | | | | | | | | | End of split % 139.62/19.40 | | | | | | | | | | | | | | | | | | % 139.62/19.40 | | | | | | | | | | | | | | | | | End of split % 139.62/19.40 | | | | | | | | | | | | | | | | | % 139.62/19.40 | | | | | | | | | | | | | | | | Case 2: % 139.62/19.40 | | | | | | | | | | | | | | | | | % 139.62/19.40 | | | | | | | | | | | | | | | | | (269) pv10 = n2 % 139.62/19.40 | | | | | | | | | | | | | | | | | % 139.62/19.40 | | | | | | | | | | | | | | | | | REDUCE: (115), (269) imply: % 139.62/19.40 | | | | | | | | | | | | | | | | | (270) pred(n2) = all_71_23 % 139.62/19.40 | | | | | | | | | | | | | | | | | % 139.62/19.40 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (24) with n1, all_71_23, n2, % 139.62/19.40 | | | | | | | | | | | | | | | | | simplifying with (107), (270) gives: % 139.62/19.40 | | | | | | | | | | | | | | | | | (271) all_71_23 = n1 % 139.62/19.40 | | | | | | | | | | | | | | | | | % 139.62/19.40 | | | | | | | | | | | | | | | | | REF_CLOSE: (114), (238), (271), (irreflexivity_gt) are % 139.62/19.40 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #19. % 139.62/19.40 | | | | | | | | | | | | | | | | | % 139.62/19.40 | | | | | | | | | | | | | | | | End of split % 139.62/19.40 | | | | | | | | | | | | | | | | % 139.62/19.40 | | | | | | | | | | | | | | | Case 2: % 139.62/19.40 | | | | | | | | | | | | | | | | % 139.62/19.40 | | | | | | | | | | | | | | | | (272) all_71_23 = n1 % 139.62/19.40 | | | | | | | | | | | | | | | | % 139.62/19.40 | | | | | | | | | | | | | | | | REDUCE: (124), (272) imply: % 139.62/19.40 | | | | | | | | | | | | | | | | (273) succ(n1) = pv10 % 139.62/19.40 | | | | | | | | | | | | | | | | % 139.62/19.40 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (25) with n2, pv10, n1, simplifying % 139.62/19.40 | | | | | | | | | | | | | | | | with (79), (273) gives: % 139.62/19.40 | | | | | | | | | | | | | | | | (274) pv10 = n2 % 139.62/19.40 | | | | | | | | | | | | | | | | % 139.62/19.40 | | | | | | | | | | | | | | | | REDUCE: (235), (274) imply: % 139.62/19.40 | | | | | | | | | | | | | | | | (275) a_select3(q, n2, n1) = all_71_10 % 139.62/19.40 | | | | | | | | | | | | | | | | % 139.62/19.40 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (65) with n1, all_71_11, all_71_9, % 139.62/19.40 | | | | | | | | | | | | | | | | all_71_8, all_71_7, all_71_6, all_71_5, all_71_4, % 139.62/19.40 | | | | | | | | | | | | | | | | all_71_3, all_71_2, all_71_1, all_71_0, % 139.62/19.40 | | | | | | | | | | | | | | | | simplifying with (59), (80), (139), (141), (142), % 139.62/19.40 | | | | | | | | | | | | | | | | (143), (144), (145), (146), (147), (234), (237) % 139.62/19.40 | | | | | | | | | | | | | | | | gives: % 139.62/19.40 | | | | | | | | | | | | | | | | (276) ~ (sum(n0, all_71_26, all_71_2) = all_71_1) | ~ % 139.62/19.40 | | | | | | | | | | | | | | | | leq(n1, all_71_25) | (a_select3(q, pv10, n1) = % 139.62/19.40 | | | | | | | | | | | | | | | | all_71_0 & $i(all_71_0)) % 139.62/19.40 | | | | | | | | | | | | | | | | % 139.62/19.40 | | | | | | | | | | | | | | | | BETA: splitting (276) gives: % 139.62/19.40 | | | | | | | | | | | | | | | | % 139.62/19.40 | | | | | | | | | | | | | | | | Case 1: % 139.62/19.40 | | | | | | | | | | | | | | | | | % 139.62/19.40 | | | | | | | | | | | | | | | | | (277) ~ (sum(n0, all_71_26, all_71_2) = all_71_1) % 139.62/19.40 | | | | | | | | | | | | | | | | | % 139.62/19.40 | | | | | | | | | | | | | | | | | REDUCE: (119), (277) imply: % 139.62/19.40 | | | | | | | | | | | | | | | | | (278) ~ (sum(n0, n4, all_71_2) = all_71_1) % 139.62/19.40 | | | | | | | | | | | | | | | | | % 139.62/19.40 | | | | | | | | | | | | | | | | | PRED_UNIFY: (148), (278) imply: % 139.62/19.40 | | | | | | | | | | | | | | | | | (279) $false % 139.62/19.40 | | | | | | | | | | | | | | | | | % 139.62/19.40 | | | | | | | | | | | | | | | | | CLOSE: (279) is inconsistent. % 139.62/19.40 | | | | | | | | | | | | | | | | | % 139.62/19.40 | | | | | | | | | | | | | | | | Case 2: % 139.62/19.40 | | | | | | | | | | | | | | | | | % 139.62/19.40 | | | | | | | | | | | | | | | | | (280) ~ leq(n1, all_71_25) | (a_select3(q, pv10, n1) = % 139.62/19.40 | | | | | | | | | | | | | | | | | all_71_0 & $i(all_71_0)) % 139.62/19.40 | | | | | | | | | | | | | | | | | % 139.62/19.40 | | | | | | | | | | | | | | | | | BETA: splitting (280) gives: % 139.62/19.40 | | | | | | | | | | | | | | | | | % 139.62/19.40 | | | | | | | | | | | | | | | | | Case 1: % 139.62/19.40 | | | | | | | | | | | | | | | | | | % 139.62/19.40 | | | | | | | | | | | | | | | | | | (281) ~ leq(n1, all_71_25) % 139.62/19.40 | | | | | | | | | | | | | | | | | | % 139.62/19.40 | | | | | | | | | | | | | | | | | | REDUCE: (222), (281) imply: % 139.62/19.40 | | | | | | | | | | | | | | | | | | (282) ~ leq(n1, n2) % 139.62/19.40 | | | | | | | | | | | | | | | | | | % 139.62/19.40 | | | | | | | | | | | | | | | | | | PRED_UNIFY: (236), (282) imply: % 139.62/19.40 | | | | | | | | | | | | | | | | | | (283) $false % 139.62/19.40 | | | | | | | | | | | | | | | | | | % 139.62/19.40 | | | | | | | | | | | | | | | | | | CLOSE: (283) is inconsistent. % 139.62/19.40 | | | | | | | | | | | | | | | | | | % 139.62/19.40 | | | | | | | | | | | | | | | | | Case 2: % 139.62/19.40 | | | | | | | | | | | | | | | | | | % 139.62/19.40 | | | | | | | | | | | | | | | | | | (284) a_select3(q, pv10, n1) = all_71_0 & $i(all_71_0) % 139.62/19.40 | | | | | | | | | | | | | | | | | | % 139.62/19.40 | | | | | | | | | | | | | | | | | | REF_CLOSE: (27), (134), (274), (275), (284) are inconsistent % 139.62/19.40 | | | | | | | | | | | | | | | | | | by sub-proof #18. % 139.62/19.40 | | | | | | | | | | | | | | | | | | % 139.62/19.40 | | | | | | | | | | | | | | | | | End of split % 139.62/19.40 | | | | | | | | | | | | | | | | | % 139.62/19.40 | | | | | | | | | | | | | | | | End of split % 139.62/19.40 | | | | | | | | | | | | | | | | % 139.62/19.40 | | | | | | | | | | | | | | | End of split % 139.62/19.40 | | | | | | | | | | | | | | | % 139.62/19.40 | | | | | | | | | | | | | | End of split % 139.62/19.40 | | | | | | | | | | | | | | % 139.62/19.40 | | | | | | | | | | | | | End of split % 139.62/19.40 | | | | | | | | | | | | | % 139.62/19.40 | | | | | | | | | | | | Case 2: % 139.62/19.40 | | | | | | | | | | | | | % 139.62/19.40 | | | | | | | | | | | | | (285) pv10 = n1 % 139.62/19.40 | | | | | | | | | | | | | % 139.62/19.40 | | | | | | | | | | | | | REF_CLOSE: (24), (105), (114), (115), (194), (285), % 139.62/19.40 | | | | | | | | | | | | | (irreflexivity_gt) are inconsistent by sub-proof % 139.62/19.40 | | | | | | | | | | | | | #17. % 139.62/19.40 | | | | | | | | | | | | | % 139.62/19.40 | | | | | | | | | | | | End of split % 139.62/19.40 | | | | | | | | | | | | % 139.62/19.40 | | | | | | | | | | | Case 2: % 139.62/19.40 | | | | | | | | | | | | % 139.62/19.41 | | | | | | | | | | | | (286) all_71_23 = n0 % 139.62/19.41 | | | | | | | | | | | | (287) ~ gt(all_71_23, n0) % 139.62/19.41 | | | | | | | | | | | | % 139.62/19.41 | | | | | | | | | | | | REDUCE: (124), (286) imply: % 139.62/19.41 | | | | | | | | | | | | (288) succ(n0) = pv10 % 139.62/19.41 | | | | | | | | | | | | % 139.62/19.41 | | | | | | | | | | | | REDUCE: (115), (286) imply: % 139.62/19.41 | | | | | | | | | | | | (289) pred(pv10) = n0 % 139.62/19.41 | | | | | | | | | | | | % 139.62/19.41 | | | | | | | | | | | | REDUCE: (286), (287) imply: % 139.62/19.41 | | | | | | | | | | | | (290) ~ gt(n0, n0) % 139.62/19.41 | | | | | | | | | | | | % 139.62/19.41 | | | | | | | | | | | | GROUND_INST: instantiating (25) with n1, pv10, n0, simplifying % 139.62/19.41 | | | | | | | | | | | | with (16), (288) gives: % 139.62/19.41 | | | | | | | | | | | | (291) pv10 = n1 % 139.62/19.41 | | | | | | | | | | | | % 139.62/19.41 | | | | | | | | | | | | REDUCE: (137), (291) imply: % 139.62/19.41 | | | | | | | | | | | | (292) a_select3(q, n1, all_71_12) = all_71_10 % 139.62/19.41 | | | | | | | | | | | | % 139.62/19.41 | | | | | | | | | | | | BETA: splitting (171) gives: % 139.62/19.41 | | | | | | | | | | | | % 139.62/19.41 | | | | | | | | | | | | Case 1: % 139.62/19.41 | | | | | | | | | | | | | % 139.62/19.41 | | | | | | | | | | | | | (293) gt(n3, pv12) % 139.62/19.41 | | | | | | | | | | | | | % 139.62/19.41 | | | | | | | | | | | | | REF_CLOSE: (1), (11), (22), (24), (25), (58), (90), (91), % 139.62/19.41 | | | | | | | | | | | | | (105), (107), (117), (118), (125), (135), (153), % 139.62/19.41 | | | | | | | | | | | | | (176), (179), (181), (183), (184), (186), (190), % 139.62/19.41 | | | | | | | | | | | | | (290), (293), (irreflexivity_gt), % 139.62/19.41 | | | | | | | | | | | | | (transitivity_gt) are inconsistent by sub-proof % 139.62/19.41 | | | | | | | | | | | | | #15. % 139.62/19.41 | | | | | | | | | | | | | % 139.62/19.41 | | | | | | | | | | | | Case 2: % 139.62/19.41 | | | | | | | | | | | | | % 139.62/19.41 | | | | | | | | | | | | | (294) pv12 = n3 % 139.62/19.41 | | | | | | | | | | | | | % 139.62/19.41 | | | | | | | | | | | | | REDUCE: (118), (294) imply: % 139.62/19.41 | | | | | | | | | | | | | (295) pred(n3) = all_71_25 % 139.62/19.41 | | | | | | | | | | | | | % 139.62/19.41 | | | | | | | | | | | | | GROUND_INST: instantiating (24) with n2, all_71_25, n3, % 139.62/19.41 | | | | | | | | | | | | | simplifying with (108), (295) gives: % 139.62/19.41 | | | | | | | | | | | | | (296) all_71_25 = n2 % 139.62/19.41 | | | | | | | | | | | | | % 139.62/19.41 | | | | | | | | | | | | | REDUCE: (183), (296) imply: % 139.62/19.41 | | | | | | | | | | | | | (297) gt(n2, all_71_12) % 139.62/19.41 | | | | | | | | | | | | | % 139.62/19.41 | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_71_12, n2, n1, % 139.62/19.41 | | | | | | | | | | | | | simplifying with (58), (91), (107), (297) gives: % 139.62/19.41 | | | | | | | | | | | | | (298) leq(all_71_12, n1) % 139.62/19.41 | | | | | | | | | | | | | % 139.62/19.41 | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_71_12, simplifying % 139.62/19.41 | | | | | | | | | | | | | with (58), (135), (298) gives: % 139.62/19.41 | | | | | | | | | | | | | (299) all_71_12 = n1 | all_71_12 = n0 % 139.62/19.41 | | | | | | | | | | | | | % 139.62/19.41 | | | | | | | | | | | | | BETA: splitting (299) gives: % 139.62/19.41 | | | | | | | | | | | | | % 139.62/19.41 | | | | | | | | | | | | | Case 1: % 139.62/19.41 | | | | | | | | | | | | | | % 139.62/19.41 | | | | | | | | | | | | | | (300) all_71_12 = n0 % 139.62/19.41 | | | | | | | | | | | | | | % 139.62/19.41 | | | | | | | | | | | | | | REDUCE: (186), (300) imply: % 139.62/19.41 | | | | | | | | | | | | | | (301) $false % 139.62/19.41 | | | | | | | | | | | | | | % 139.62/19.41 | | | | | | | | | | | | | | CLOSE: (301) is inconsistent. % 139.62/19.41 | | | | | | | | | | | | | | % 139.62/19.41 | | | | | | | | | | | | | Case 2: % 139.62/19.41 | | | | | | | | | | | | | | % 139.62/19.41 | | | | | | | | | | | | | | (302) all_71_12 = n1 % 139.62/19.41 | | | | | | | | | | | | | | % 139.62/19.41 | | | | | | | | | | | | | | REDUCE: (138), (302) imply: % 139.62/19.41 | | | | | | | | | | | | | | (303) a_select3(center, n1, n0) = all_71_9 % 139.62/19.41 | | | | | | | | | | | | | | % 139.62/19.41 | | | | | | | | | | | | | | REDUCE: (292), (302) imply: % 139.62/19.41 | | | | | | | | | | | | | | (304) a_select3(q, n1, n1) = all_71_10 % 139.62/19.41 | | | | | | | | | | | | | | % 139.62/19.41 | | | | | | | | | | | | | | REDUCE: (177), (302) imply: % 139.62/19.41 | | | | | | | | | | | | | | (305) leq(n1, n2) % 139.62/19.41 | | | | | | | | | | | | | | % 139.62/19.41 | | | | | | | | | | | | | | REDUCE: (135), (302) imply: % 139.62/19.41 | | | | | | | | | | | | | | (306) leq(n0, n1) % 139.62/19.41 | | | | | | | | | | | | | | % 139.62/19.41 | | | | | | | | | | | | | | GROUND_INST: instantiating (65) with n1, all_71_11, all_71_9, % 139.62/19.41 | | | | | | | | | | | | | | all_71_8, all_71_7, all_71_6, all_71_5, all_71_4, % 139.62/19.41 | | | | | | | | | | | | | | all_71_3, all_71_2, all_71_1, all_71_0, % 139.62/19.41 | | | | | | | | | | | | | | simplifying with (59), (80), (139), (141), (142), % 139.62/19.41 | | | | | | | | | | | | | | (143), (144), (145), (146), (147), (303), (306) % 139.62/19.41 | | | | | | | | | | | | | | gives: % 139.62/19.41 | | | | | | | | | | | | | | (307) ~ (sum(n0, all_71_26, all_71_2) = all_71_1) | ~ % 139.62/19.41 | | | | | | | | | | | | | | leq(n1, all_71_25) | (a_select3(q, pv10, n1) = % 139.62/19.41 | | | | | | | | | | | | | | all_71_0 & $i(all_71_0)) % 139.62/19.41 | | | | | | | | | | | | | | % 139.62/19.41 | | | | | | | | | | | | | | BETA: splitting (307) gives: % 139.62/19.41 | | | | | | | | | | | | | | % 139.62/19.41 | | | | | | | | | | | | | | Case 1: % 139.62/19.41 | | | | | | | | | | | | | | | % 139.62/19.41 | | | | | | | | | | | | | | | (308) ~ (sum(n0, all_71_26, all_71_2) = all_71_1) % 139.62/19.41 | | | | | | | | | | | | | | | % 139.62/19.41 | | | | | | | | | | | | | | | REDUCE: (119), (308) imply: % 139.62/19.41 | | | | | | | | | | | | | | | (309) ~ (sum(n0, n4, all_71_2) = all_71_1) % 139.62/19.41 | | | | | | | | | | | | | | | % 139.62/19.41 | | | | | | | | | | | | | | | PRED_UNIFY: (148), (309) imply: % 139.62/19.41 | | | | | | | | | | | | | | | (310) $false % 139.62/19.41 | | | | | | | | | | | | | | | % 139.62/19.41 | | | | | | | | | | | | | | | CLOSE: (310) is inconsistent. % 139.62/19.41 | | | | | | | | | | | | | | | % 139.62/19.41 | | | | | | | | | | | | | | Case 2: % 139.62/19.41 | | | | | | | | | | | | | | | % 139.62/19.41 | | | | | | | | | | | | | | | (311) ~ leq(n1, all_71_25) | (a_select3(q, pv10, n1) = % 139.62/19.41 | | | | | | | | | | | | | | | all_71_0 & $i(all_71_0)) % 139.62/19.41 | | | | | | | | | | | | | | | % 139.62/19.41 | | | | | | | | | | | | | | | BETA: splitting (311) gives: % 139.62/19.41 | | | | | | | | | | | | | | | % 139.62/19.41 | | | | | | | | | | | | | | | Case 1: % 139.62/19.41 | | | | | | | | | | | | | | | | % 139.62/19.41 | | | | | | | | | | | | | | | | (312) ~ leq(n1, all_71_25) % 139.62/19.41 | | | | | | | | | | | | | | | | % 139.62/19.41 | | | | | | | | | | | | | | | | REDUCE: (296), (312) imply: % 139.62/19.41 | | | | | | | | | | | | | | | | (313) ~ leq(n1, n2) % 139.62/19.41 | | | | | | | | | | | | | | | | % 139.62/19.41 | | | | | | | | | | | | | | | | PRED_UNIFY: (305), (313) imply: % 139.62/19.41 | | | | | | | | | | | | | | | | (314) $false % 139.62/19.41 | | | | | | | | | | | | | | | | % 139.62/19.41 | | | | | | | | | | | | | | | | CLOSE: (314) is inconsistent. % 139.62/19.41 | | | | | | | | | | | | | | | | % 139.62/19.41 | | | | | | | | | | | | | | | Case 2: % 139.62/19.41 | | | | | | | | | | | | | | | | % 139.62/19.41 | | | | | | | | | | | | | | | | (315) a_select3(q, pv10, n1) = all_71_0 & $i(all_71_0) % 139.62/19.41 | | | | | | | | | | | | | | | | % 139.62/19.41 | | | | | | | | | | | | | | | | ALPHA: (315) implies: % 139.62/19.41 | | | | | | | | | | | | | | | | (316) a_select3(q, pv10, n1) = all_71_0 % 139.62/19.41 | | | | | | | | | | | | | | | | % 139.62/19.41 | | | | | | | | | | | | | | | | REDUCE: (291), (316) imply: % 139.62/19.41 | | | | | | | | | | | | | | | | (317) a_select3(q, n1, n1) = all_71_0 % 139.62/19.41 | | | | | | | | | | | | | | | | % 139.62/19.41 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (27) with all_71_10, all_71_0, n1, % 139.62/19.41 | | | | | | | | | | | | | | | | n1, q, simplifying with (304), (317) gives: % 139.62/19.41 | | | | | | | | | | | | | | | | (318) all_71_0 = all_71_10 % 139.62/19.41 | | | | | | | | | | | | | | | | % 139.62/19.41 | | | | | | | | | | | | | | | | REDUCE: (134), (318) imply: % 139.62/19.41 | | | | | | | | | | | | | | | | (319) $false % 139.62/19.41 | | | | | | | | | | | | | | | | % 139.62/19.41 | | | | | | | | | | | | | | | | CLOSE: (319) is inconsistent. % 139.62/19.41 | | | | | | | | | | | | | | | | % 139.62/19.41 | | | | | | | | | | | | | | | End of split % 139.62/19.41 | | | | | | | | | | | | | | | % 139.62/19.41 | | | | | | | | | | | | | | End of split % 139.62/19.41 | | | | | | | | | | | | | | % 139.62/19.41 | | | | | | | | | | | | | End of split % 139.62/19.41 | | | | | | | | | | | | | % 139.62/19.41 | | | | | | | | | | | | End of split % 139.62/19.41 | | | | | | | | | | | | % 139.62/19.41 | | | | | | | | | | | End of split % 139.62/19.41 | | | | | | | | | | | % 139.62/19.41 | | | | | | | | | | End of split % 139.62/19.41 | | | | | | | | | | % 139.62/19.41 | | | | | | | | | End of split % 139.62/19.41 | | | | | | | | | % 139.62/19.41 | | | | | | | | End of split % 139.62/19.41 | | | | | | | | % 139.62/19.41 | | | | | | | Case 2: % 139.62/19.41 | | | | | | | | % 139.62/19.41 | | | | | | | | (320) all_71_25 = n0 % 139.62/19.41 | | | | | | | | (321) ~ gt(all_71_25, n0) % 139.62/19.41 | | | | | | | | % 139.62/19.41 | | | | | | | | REDUCE: (183), (320) imply: % 139.62/19.41 | | | | | | | | (322) gt(n0, all_71_12) % 139.62/19.41 | | | | | | | | % 139.62/19.41 | | | | | | | | REDUCE: (320), (321) imply: % 139.62/19.41 | | | | | | | | (323) ~ gt(n0, n0) % 139.62/19.41 | | | | | | | | % 139.62/19.41 | | | | | | | | GROUND_INST: instantiating (transitivity_gt) with n0, all_71_12, % 139.62/19.41 | | | | | | | | n0, simplifying with (19), (58), (182), (322), % 139.62/19.41 | | | | | | | | (323) gives: % 139.62/19.41 | | | | | | | | (324) $false % 139.62/19.41 | | | | | | | | % 139.62/19.41 | | | | | | | | CLOSE: (324) is inconsistent. % 139.62/19.41 | | | | | | | | % 139.62/19.41 | | | | | | | End of split % 139.62/19.41 | | | | | | | % 139.62/19.41 | | | | | | Case 2: % 139.62/19.41 | | | | | | | % 139.62/19.41 | | | | | | | (325) all_71_12 = all_71_25 % 139.62/19.41 | | | | | | | (326) ~ gt(all_71_25, all_71_12) % 139.62/19.41 | | | | | | | % 139.62/19.41 | | | | | | | REDUCE: (138), (325) imply: % 139.62/19.41 | | | | | | | (327) a_select3(center, all_71_25, n0) = all_71_9 % 139.62/19.41 | | | | | | | % 139.62/19.41 | | | | | | | REDUCE: (137), (325) imply: % 139.62/19.41 | | | | | | | (328) a_select3(q, pv10, all_71_25) = all_71_10 % 139.62/19.41 | | | | | | | % 139.62/19.41 | | | | | | | REDUCE: (182), (325) imply: % 139.62/19.41 | | | | | | | (329) gt(all_71_25, n0) % 139.62/19.41 | | | | | | | % 139.62/19.41 | | | | | | | REDUCE: (325), (326) imply: % 139.62/19.41 | | | | | | | (330) ~ gt(all_71_25, all_71_25) % 139.62/19.41 | | | | | | | % 139.62/19.41 | | | | | | | BETA: splitting (161) gives: % 139.62/19.41 | | | | | | | % 139.62/19.41 | | | | | | | Case 1: % 139.62/19.41 | | | | | | | | % 139.62/19.41 | | | | | | | | (331) gt(pv12, n1) % 139.62/19.41 | | | | | | | | % 139.62/19.41 | | | | | | | | BETA: splitting (159) gives: % 139.62/19.41 | | | | | | | | % 139.62/19.41 | | | | | | | | Case 1: % 139.62/19.41 | | | | | | | | | % 139.62/19.41 | | | | | | | | | (332) all_71_12 = n0 % 139.62/19.41 | | | | | | | | | % 139.62/19.41 | | | | | | | | | COMBINE_EQS: (325), (332) imply: % 139.62/19.41 | | | | | | | | | (333) all_71_25 = n0 % 139.62/19.41 | | | | | | | | | % 139.62/19.41 | | | | | | | | | REF_CLOSE: (329), (330), (333) are inconsistent by sub-proof % 139.62/19.41 | | | | | | | | | #14. % 139.62/19.41 | | | | | | | | | % 139.62/19.41 | | | | | | | | Case 2: % 139.62/19.41 | | | | | | | | | % 139.62/19.41 | | | | | | | | | (334) ~ (all_71_12 = n0) % 139.62/19.41 | | | | | | | | | % 139.62/19.41 | | | | | | | | | REDUCE: (325), (334) imply: % 139.62/19.41 | | | | | | | | | (335) ~ (all_71_25 = n0) % 139.62/19.41 | | | | | | | | | % 139.62/19.41 | | | | | | | | | BETA: splitting (160) gives: % 139.62/19.41 | | | | | | | | | % 139.62/19.41 | | | | | | | | | Case 1: % 139.62/19.41 | | | | | | | | | | % 139.62/19.41 | | | | | | | | | | (336) all_71_12 = n0 % 139.62/19.41 | | | | | | | | | | % 139.62/19.41 | | | | | | | | | | COMBINE_EQS: (325), (336) imply: % 139.62/19.41 | | | | | | | | | | (337) all_71_25 = n0 % 139.62/19.41 | | | | | | | | | | % 139.62/19.41 | | | | | | | | | | REDUCE: (335), (337) imply: % 139.62/19.41 | | | | | | | | | | (338) $false % 139.62/19.41 | | | | | | | | | | % 139.62/19.41 | | | | | | | | | | CLOSE: (338) is inconsistent. % 139.62/19.41 | | | | | | | | | | % 139.62/19.41 | | | | | | | | | Case 2: % 139.62/19.41 | | | | | | | | | | % 139.62/19.41 | | | | | | | | | | % 139.62/19.41 | | | | | | | | | | GROUND_INST: instantiating (1) with n1, pv12, all_71_25, % 139.62/19.41 | | | | | | | | | | simplifying with (22), (80), (118), (331) gives: % 139.62/19.41 | | | | | | | | | | (339) leq(n1, all_71_25) % 139.62/19.41 | | | | | | | | | | % 139.62/19.41 | | | | | | | | | | BETA: splitting (165) gives: % 139.62/19.41 | | | | | | | | | | % 139.62/19.41 | | | | | | | | | | Case 1: % 139.62/19.41 | | | | | | | | | | | % 139.62/19.41 | | | | | | | | | | | (340) gt(all_71_23, n0) % 139.62/19.41 | | | | | | | | | | | % 139.62/19.41 | | | | | | | | | | | BETA: splitting (166) gives: % 139.62/19.41 | | | | | | | | | | | % 139.62/19.41 | | | | | | | | | | | Case 1: % 139.62/19.41 | | | | | | | | | | | | % 139.62/19.41 | | | | | | | | | | | | (341) gt(pv10, n1) % 139.62/19.41 | | | | | | | | | | | | % 139.62/19.41 | | | | | | | | | | | | GROUND_INST: instantiating (1) with n1, pv10, all_71_23, % 139.62/19.41 | | | | | | | | | | | | simplifying with (21), (80), (115), (341) gives: % 139.62/19.41 | | | | | | | | | | | | (342) leq(n1, all_71_23) % 139.62/19.41 | | | | | | | | | | | | % 139.62/19.41 | | | | | | | | | | | | BETA: splitting (171) gives: % 139.62/19.41 | | | | | | | | | | | | % 139.62/19.41 | | | | | | | | | | | | Case 1: % 139.62/19.41 | | | | | | | | | | | | | % 139.62/19.42 | | | | | | | | | | | | | (343) gt(n3, pv12) % 139.62/19.42 | | | | | | | | | | | | | % 139.62/19.42 | | | | | | | | | | | | | GROUND_INST: instantiating (1) with pv12, n3, n2, simplifying % 139.62/19.42 | | | | | | | | | | | | | with (22), (98), (108), (343) gives: % 139.62/19.42 | | | | | | | | | | | | | (344) leq(pv12, n2) % 139.62/19.42 | | | | | | | | | | | | | % 139.62/19.42 | | | | | | | | | | | | | GROUND_INST: instantiating (6) with n1, all_71_23, n2, pv10, % 139.62/19.42 | | | | | | | | | | | | | simplifying with (79), (80), (114), (124), (342) % 139.62/19.42 | | | | | | | | | | | | | gives: % 139.62/19.42 | | | | | | | | | | | | | (345) leq(n2, pv10) % 139.62/19.42 | | | | | | | | | | | | | % 139.62/19.42 | | | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with n1, all_71_23, % 139.62/19.42 | | | | | | | | | | | | | simplifying with (80), (114), (342) gives: % 139.62/19.42 | | | | | | | | | | | | | (346) all_71_23 = n1 | gt(all_71_23, n1) % 139.62/19.42 | | | | | | | | | | | | | % 139.62/19.42 | | | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with n2, pv10, simplifying % 139.62/19.42 | | | | | | | | | | | | | with (21), (91), (345) gives: % 139.62/19.42 | | | | | | | | | | | | | (347) pv10 = n2 | gt(pv10, n2) % 139.62/19.42 | | | | | | | | | | | | | % 139.62/19.42 | | | | | | | | | | | | | GROUND_INST: instantiating (12) with pv12, simplifying with % 139.62/19.42 | | | | | | | | | | | | | (22), (53), (344) gives: % 139.62/19.42 | | | | | | | | | | | | | (348) pv12 = n2 | pv12 = n1 | pv12 = n0 % 139.62/19.42 | | | | | | | | | | | | | % 139.62/19.42 | | | | | | | | | | | | | BETA: splitting (176) gives: % 139.62/19.42 | | | | | | | | | | | | | % 139.62/19.42 | | | | | | | | | | | | | Case 1: % 139.62/19.42 | | | | | | | | | | | | | | % 139.62/19.42 | | | | | | | | | | | | | | (349) pv12 = n1 % 139.62/19.42 | | | | | | | | | | | | | | % 139.62/19.42 | | | | | | | | | | | | | | REF_CLOSE: (22), (331), (349), (irreflexivity_gt) are % 139.62/19.42 | | | | | | | | | | | | | | inconsistent by sub-proof #13. % 139.62/19.42 | | | | | | | | | | | | | | % 139.62/19.42 | | | | | | | | | | | | | Case 2: % 139.62/19.42 | | | | | | | | | | | | | | % 139.62/19.42 | | | | | | | | | | | | | | (350) ~ (pv12 = n1) % 139.62/19.42 | | | | | | | | | | | | | | % 139.62/19.42 | | | | | | | | | | | | | | BETA: splitting (348) gives: % 139.62/19.42 | | | | | | | | | | | | | | % 139.62/19.42 | | | | | | | | | | | | | | Case 1: % 139.62/19.42 | | | | | | | | | | | | | | | % 139.62/19.42 | | | | | | | | | | | | | | | (351) pv12 = n0 % 139.62/19.42 | | | | | | | | | | | | | | | % 139.62/19.42 | | | | | | | | | | | | | | | REDUCE: (175), (351) imply: % 139.62/19.42 | | | | | | | | | | | | | | | (352) $false % 139.62/19.42 | | | | | | | | | | | | | | | % 139.62/19.42 | | | | | | | | | | | | | | | CLOSE: (352) is inconsistent. % 139.62/19.42 | | | | | | | | | | | | | | | % 139.62/19.42 | | | | | | | | | | | | | | Case 2: % 139.62/19.42 | | | | | | | | | | | | | | | % 139.62/19.42 | | | | | | | | | | | | | | | (353) pv12 = n2 | pv12 = n1 % 139.62/19.42 | | | | | | | | | | | | | | | % 139.62/19.42 | | | | | | | | | | | | | | | BETA: splitting (353) gives: % 139.62/19.42 | | | | | | | | | | | | | | | % 139.62/19.42 | | | | | | | | | | | | | | | Case 1: % 139.62/19.42 | | | | | | | | | | | | | | | | % 139.62/19.42 | | | | | | | | | | | | | | | | (354) pv12 = n1 % 139.62/19.42 | | | | | | | | | | | | | | | | % 139.62/19.42 | | | | | | | | | | | | | | | | REDUCE: (350), (354) imply: % 139.62/19.42 | | | | | | | | | | | | | | | | (355) $false % 139.62/19.42 | | | | | | | | | | | | | | | | % 139.62/19.42 | | | | | | | | | | | | | | | | CLOSE: (355) is inconsistent. % 139.62/19.42 | | | | | | | | | | | | | | | | % 139.62/19.42 | | | | | | | | | | | | | | | Case 2: % 139.62/19.42 | | | | | | | | | | | | | | | | % 139.62/19.42 | | | | | | | | | | | | | | | | (356) pv12 = n2 % 139.62/19.42 | | | | | | | | | | | | | | | | % 139.62/19.42 | | | | | | | | | | | | | | | | REDUCE: (62), (356) imply: % 139.62/19.42 | | | | | | | | | | | | | | | | (357) minus(n2, n1) = all_71_25 % 139.62/19.42 | | | | | | | | | | | | | | | | % 139.62/19.42 | | | | | | | | | | | | | | | | REDUCE: (125), (356) imply: % 139.62/19.42 | | | | | | | | | | | | | | | | (358) succ(all_71_25) = n2 % 139.62/19.42 | | | | | | | | | | | | | | | | % 139.62/19.42 | | | | | | | | | | | | | | | | REDUCE: (118), (356) imply: % 139.62/19.42 | | | | | | | | | | | | | | | | (359) pred(n2) = all_71_25 % 139.62/19.42 | | | | | | | | | | | | | | | | % 139.62/19.42 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (24) with n1, all_71_25, n2, % 139.62/19.42 | | | | | | | | | | | | | | | | simplifying with (107), (359) gives: % 139.62/19.42 | | | | | | | | | | | | | | | | (360) all_71_25 = n1 % 139.62/19.42 | | | | | | | | | | | | | | | | % 139.62/19.42 | | | | | | | | | | | | | | | | REDUCE: (357), (360) imply: % 139.62/19.42 | | | | | | | | | | | | | | | | (361) minus(n2, n1) = n1 % 139.62/19.42 | | | | | | | | | | | | | | | | % 139.62/19.42 | | | | | | | | | | | | | | | | REDUCE: (327), (360) imply: % 139.62/19.42 | | | | | | | | | | | | | | | | (362) a_select3(center, n1, n0) = all_71_9 % 139.62/19.42 | | | | | | | | | | | | | | | | % 139.62/19.42 | | | | | | | | | | | | | | | | REDUCE: (328), (360) imply: % 139.62/19.42 | | | | | | | | | | | | | | | | (363) a_select3(q, pv10, n1) = all_71_10 % 139.62/19.42 | | | | | | | | | | | | | | | | % 139.62/19.42 | | | | | | | | | | | | | | | | REDUCE: (339), (360) imply: % 139.62/19.42 | | | | | | | | | | | | | | | | (364) leq(n1, n1) % 139.62/19.42 | | | | | | | | | | | | | | | | % 139.62/19.42 | | | | | | | | | | | | | | | | REDUCE: (153), (360) imply: % 139.62/19.42 | | | | | | | | | | | | | | | | (365) leq(n0, n1) % 139.62/19.42 | | | | | | | | | | | | | | | | % 139.62/19.42 | | | | | | | | | | | | | | | | REDUCE: (330), (360) imply: % 139.62/19.42 | | | | | | | | | | | | | | | | (366) ~ gt(n1, n1) % 139.62/19.42 | | | | | | | | | | | | | | | | % 139.62/19.42 | | | | | | | | | | | | | | | | BETA: splitting (346) gives: % 139.62/19.42 | | | | | | | | | | | | | | | | % 139.62/19.42 | | | | | | | | | | | | | | | | Case 1: % 139.62/19.42 | | | | | | | | | | | | | | | | | % 139.62/19.42 | | | | | | | | | | | | | | | | | (367) gt(all_71_23, n1) % 139.62/19.42 | | | | | | | | | | | | | | | | | % 139.62/19.42 | | | | | | | | | | | | | | | | | BETA: splitting (347) gives: % 139.62/19.42 | | | | | | | | | | | | | | | | | % 139.62/19.42 | | | | | | | | | | | | | | | | | Case 1: % 139.62/19.42 | | | | | | | | | | | | | | | | | | % 139.62/19.42 | | | | | | | | | | | | | | | | | | (368) gt(pv10, n2) % 139.62/19.42 | | | | | | | | | | | | | | | | | | % 139.62/19.42 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with n2, pv10, all_71_23, % 139.62/19.42 | | | | | | | | | | | | | | | | | | simplifying with (21), (91), (115), (368) gives: % 139.62/19.42 | | | | | | | | | | | | | | | | | | (369) leq(n2, all_71_23) % 139.62/19.42 | | | | | | | | | | | | | | | | | | % 139.62/19.42 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with n2, all_71_23, n3, pv10, % 139.62/19.42 | | | | | | | | | | | | | | | | | | simplifying with (90), (91), (114), (124), (369) % 139.62/19.42 | | | | | | | | | | | | | | | | | | gives: % 139.62/19.42 | | | | | | | | | | | | | | | | | | (370) leq(n3, pv10) % 139.62/19.42 | | | | | | | | | | | | | | | | | | % 139.62/19.42 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with n2, all_71_23, % 139.62/19.42 | | | | | | | | | | | | | | | | | | simplifying with (91), (114), (369) gives: % 139.62/19.42 | | | | | | | | | | | | | | | | | | (371) all_71_23 = n2 | gt(all_71_23, n2) % 139.62/19.42 | | | | | | | | | | | | | | | | | | % 139.62/19.42 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with n3, pv10, simplifying % 139.62/19.42 | | | | | | | | | | | | | | | | | | with (21), (98), (370) gives: % 139.62/19.42 | | | | | | | | | | | | | | | | | | (372) pv10 = n3 | gt(pv10, n3) % 139.62/19.42 | | | | | | | | | | | | | | | | | | % 139.62/19.42 | | | | | | | | | | | | | | | | | | BETA: splitting (371) gives: % 139.62/19.42 | | | | | | | | | | | | | | | | | | % 139.62/19.42 | | | | | | | | | | | | | | | | | | Case 1: % 139.62/19.42 | | | | | | | | | | | | | | | | | | | % 139.62/19.42 | | | | | | | | | | | | | | | | | | | (373) gt(all_71_23, n2) % 139.62/19.42 | | | | | | | | | | | | | | | | | | | % 139.62/19.42 | | | | | | | | | | | | | | | | | | | BETA: splitting (372) gives: % 139.62/19.42 | | | | | | | | | | | | | | | | | | | % 139.62/19.42 | | | | | | | | | | | | | | | | | | | Case 1: % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | (374) gt(pv10, n3) % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with n3, pv10, all_71_23, % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | simplifying with (21), (98), (115), (374) gives: % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | (375) leq(n3, all_71_23) % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with n3, all_71_23, n4, pv10, % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | simplifying with (97), (98), (114), (124), (375) % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | gives: % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | (376) leq(n4, pv10) % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with n3, all_71_23, % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | simplifying with (98), (114), (375) gives: % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | (377) all_71_23 = n3 | gt(all_71_23, n3) % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with n4, pv10, simplifying % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | with (21), (101), (376) gives: % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | (378) pv10 = n4 | gt(pv10, n4) % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | BETA: splitting (377) gives: % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | Case 1: % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | (379) gt(all_71_23, n3) % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (378) gives: % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | Case 1: % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | | % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | | (380) gt(pv10, n4) % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | | % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with n4, pv10, all_71_23, % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | | simplifying with (21), (101), (115), (380) gives: % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | | (381) leq(n4, all_71_23) % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | | % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with n4, all_71_23, n5, pv10, % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | | simplifying with (100), (101), (114), (124), (381) % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | | gives: % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | | (382) leq(n5, pv10) % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | | % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with n4, all_71_23, % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | | simplifying with (101), (114), (381) gives: % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | | (383) all_71_23 = n4 | gt(all_71_23, n4) % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | | % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with n5, pv10, simplifying % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | | with (20), (21), (382) gives: % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | | (384) pv10 = n5 | gt(pv10, n5) % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | | % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (383) gives: % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | | % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | | | % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | | | (385) gt(all_71_23, n4) % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | | | % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (384) gives: % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | | | % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | | | | % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | | | | % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (27), (59), (65), (80), (119), (134), (139), % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | | | | (141), (142), (143), (144), (145), (146), (147), % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | | | | (148), (360), (362), (363), (364), (365) are % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #12. % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | | | | % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | | | | % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | | | | (386) pv10 = n5 % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | | | | % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (26), (61), (114), (120), (385), (386), % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | | | | (irreflexivity_gt) are inconsistent by sub-proof % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | | | | #11. % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | | | | % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | | | End of split % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | | | % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | | | % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | | | % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (27), (59), (65), (80), (119), (134), (139), % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | | | (141), (142), (143), (144), (145), (146), (147), % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | | | (148), (360), (362), (363), (364), (365) are % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #12. % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | | | % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | | End of split % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | | % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | Case 2: % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | | % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | | (387) pv10 = n4 % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | | % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (115), (387) imply: % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | | (388) pred(n4) = all_71_23 % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | | % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (24), (109), (114), (379), (388), % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | | (irreflexivity_gt) are inconsistent by sub-proof % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | | #10. % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | | % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | End of split % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | Case 2: % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | (389) all_71_23 = n3 % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | REDUCE: (124), (389) imply: % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | (390) succ(n3) = pv10 % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (25) with n4, pv10, n3, simplifying % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | with (97), (390) gives: % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | (391) pv10 = n4 % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | REDUCE: (363), (391) imply: % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | (392) a_select3(q, n4, n1) = all_71_10 % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (65) with n1, all_71_11, all_71_9, % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | all_71_8, all_71_7, all_71_6, all_71_5, all_71_4, % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | all_71_3, all_71_2, all_71_1, all_71_0, % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | simplifying with (59), (80), (139), (141), (142), % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | (143), (144), (145), (146), (147), (362), (365) % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | gives: % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | (393) ~ (sum(n0, all_71_26, all_71_2) = all_71_1) | ~ % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | leq(n1, all_71_25) | (a_select3(q, pv10, n1) = % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | all_71_0 & $i(all_71_0)) % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (393) gives: % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | Case 1: % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | | % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | | (394) ~ (sum(n0, all_71_26, all_71_2) = all_71_1) % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | | % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (119), (394) imply: % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | | (395) ~ (sum(n0, n4, all_71_2) = all_71_1) % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | | % 139.62/19.42 | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (148), (395) imply: % 139.62/19.43 | | | | | | | | | | | | | | | | | | | | | | (396) $false % 139.62/19.43 | | | | | | | | | | | | | | | | | | | | | | % 139.62/19.43 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (396) is inconsistent. % 139.62/19.43 | | | | | | | | | | | | | | | | | | | | | | % 139.62/19.43 | | | | | | | | | | | | | | | | | | | | | Case 2: % 139.62/19.43 | | | | | | | | | | | | | | | | | | | | | | % 139.62/19.43 | | | | | | | | | | | | | | | | | | | | | | (397) ~ leq(n1, all_71_25) | (a_select3(q, pv10, n1) = % 139.62/19.43 | | | | | | | | | | | | | | | | | | | | | | all_71_0 & $i(all_71_0)) % 139.62/19.43 | | | | | | | | | | | | | | | | | | | | | | % 139.62/19.43 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (397) gives: % 139.62/19.43 | | | | | | | | | | | | | | | | | | | | | | % 139.62/19.43 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 139.62/19.43 | | | | | | | | | | | | | | | | | | | | | | | % 139.62/19.43 | | | | | | | | | | | | | | | | | | | | | | | (398) ~ leq(n1, all_71_25) % 139.62/19.43 | | | | | | | | | | | | | | | | | | | | | | | % 139.62/19.43 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (360), (398) imply: % 139.62/19.43 | | | | | | | | | | | | | | | | | | | | | | | (399) ~ leq(n1, n1) % 139.62/19.43 | | | | | | | | | | | | | | | | | | | | | | | % 139.62/19.43 | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (364), (399) imply: % 139.62/19.43 | | | | | | | | | | | | | | | | | | | | | | | (400) $false % 139.62/19.43 | | | | | | | | | | | | | | | | | | | | | | | % 139.62/19.43 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (400) is inconsistent. % 139.62/19.43 | | | | | | | | | | | | | | | | | | | | | | | % 139.62/19.43 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 139.62/19.43 | | | | | | | | | | | | | | | | | | | | | | | % 139.62/19.43 | | | | | | | | | | | | | | | | | | | | | | | (401) a_select3(q, pv10, n1) = all_71_0 & $i(all_71_0) % 139.62/19.43 | | | | | | | | | | | | | | | | | | | | | | | % 139.62/19.43 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (401) implies: % 139.62/19.43 | | | | | | | | | | | | | | | | | | | | | | | (402) a_select3(q, pv10, n1) = all_71_0 % 139.62/19.43 | | | | | | | | | | | | | | | | | | | | | | | % 139.62/19.43 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (391), (402) imply: % 139.62/19.43 | | | | | | | | | | | | | | | | | | | | | | | (403) a_select3(q, n4, n1) = all_71_0 % 139.62/19.43 | | | | | | | | | | | | | | | | | | | | | | | % 139.62/19.43 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (27) with all_71_10, all_71_0, n1, % 139.62/19.43 | | | | | | | | | | | | | | | | | | | | | | | n4, q, simplifying with (392), (403) gives: % 139.62/19.43 | | | | | | | | | | | | | | | | | | | | | | | (404) all_71_0 = all_71_10 % 139.62/19.43 | | | | | | | | | | | | | | | | | | | | | | | % 139.62/19.43 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (404) imply: % 139.62/19.43 | | | | | | | | | | | | | | | | | | | | | | | (405) $false % 139.62/19.43 | | | | | | | | | | | | | | | | | | | | | | | % 139.62/19.43 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (405) is inconsistent. % 139.62/19.43 | | | | | | | | | | | | | | | | | | | | | | | % 139.62/19.43 | | | | | | | | | | | | | | | | | | | | | | End of split % 139.62/19.43 | | | | | | | | | | | | | | | | | | | | | | % 139.62/19.43 | | | | | | | | | | | | | | | | | | | | | End of split % 139.62/19.43 | | | | | | | | | | | | | | | | | | | | | % 139.62/19.43 | | | | | | | | | | | | | | | | | | | | End of split % 139.62/19.43 | | | | | | | | | | | | | | | | | | | | % 139.62/19.43 | | | | | | | | | | | | | | | | | | | Case 2: % 139.62/19.43 | | | | | | | | | | | | | | | | | | | | % 139.62/19.43 | | | | | | | | | | | | | | | | | | | | (406) pv10 = n3 % 139.62/19.43 | | | | | | | | | | | | | | | | | | | | % 139.62/19.43 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (24), (26), (61), (108), (114), (115), (373), % 139.62/19.43 | | | | | | | | | | | | | | | | | | | | (406), (irreflexivity_gt) are inconsistent by % 139.62/19.43 | | | | | | | | | | | | | | | | | | | | sub-proof #9. % 139.62/19.43 | | | | | | | | | | | | | | | | | | | | % 139.62/19.43 | | | | | | | | | | | | | | | | | | | End of split % 139.62/19.43 | | | | | | | | | | | | | | | | | | | % 139.62/19.43 | | | | | | | | | | | | | | | | | | Case 2: % 139.62/19.43 | | | | | | | | | | | | | | | | | | | % 139.62/19.43 | | | | | | | | | | | | | | | | | | | (407) all_71_23 = n2 % 139.62/19.43 | | | | | | | | | | | | | | | | | | | % 139.62/19.43 | | | | | | | | | | | | | | | | | | | REDUCE: (124), (407) imply: % 139.62/19.43 | | | | | | | | | | | | | | | | | | | (408) succ(n2) = pv10 % 139.62/19.43 | | | | | | | | | | | | | | | | | | | % 139.62/19.43 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (25) with n3, pv10, n2, simplifying % 139.62/19.43 | | | | | | | | | | | | | | | | | | | with (90), (408) gives: % 139.62/19.43 | | | | | | | | | | | | | | | | | | | (409) pv10 = n3 % 139.62/19.43 | | | | | | | | | | | | | | | | | | | % 139.62/19.43 | | | | | | | | | | | | | | | | | | | REDUCE: (363), (409) imply: % 139.62/19.43 | | | | | | | | | | | | | | | | | | | (410) a_select3(q, n3, n1) = all_71_10 % 139.62/19.43 | | | | | | | | | | | | | | | | | | | % 139.62/19.43 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (65) with n1, all_71_11, all_71_9, % 139.62/19.43 | | | | | | | | | | | | | | | | | | | all_71_8, all_71_7, all_71_6, all_71_5, all_71_4, % 139.62/19.43 | | | | | | | | | | | | | | | | | | | all_71_3, all_71_2, all_71_1, all_71_0, % 139.62/19.43 | | | | | | | | | | | | | | | | | | | simplifying with (59), (80), (139), (141), (142), % 139.62/19.43 | | | | | | | | | | | | | | | | | | | (143), (144), (145), (146), (147), (362), (365) % 139.62/19.43 | | | | | | | | | | | | | | | | | | | gives: % 139.62/19.43 | | | | | | | | | | | | | | | | | | | (411) ~ (sum(n0, all_71_26, all_71_2) = all_71_1) | ~ % 139.62/19.43 | | | | | | | | | | | | | | | | | | | leq(n1, all_71_25) | (a_select3(q, pv10, n1) = % 139.62/19.43 | | | | | | | | | | | | | | | | | | | all_71_0 & $i(all_71_0)) % 139.62/19.43 | | | | | | | | | | | | | | | | | | | % 139.62/19.43 | | | | | | | | | | | | | | | | | | | BETA: splitting (411) gives: % 139.62/19.43 | | | | | | | | | | | | | | | | | | | % 139.62/19.43 | | | | | | | | | | | | | | | | | | | Case 1: % 139.62/19.43 | | | | | | | | | | | | | | | | | | | | % 139.62/19.43 | | | | | | | | | | | | | | | | | | | | (412) ~ (sum(n0, all_71_26, all_71_2) = all_71_1) % 139.62/19.43 | | | | | | | | | | | | | | | | | | | | % 139.62/19.43 | | | | | | | | | | | | | | | | | | | | REDUCE: (119), (412) imply: % 139.62/19.43 | | | | | | | | | | | | | | | | | | | | (413) ~ (sum(n0, n4, all_71_2) = all_71_1) % 139.62/19.43 | | | | | | | | | | | | | | | | | | | | % 139.62/19.43 | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (148), (413) imply: % 139.62/19.43 | | | | | | | | | | | | | | | | | | | | (414) $false % 139.62/19.43 | | | | | | | | | | | | | | | | | | | | % 139.62/19.43 | | | | | | | | | | | | | | | | | | | | CLOSE: (414) is inconsistent. % 139.62/19.43 | | | | | | | | | | | | | | | | | | | | % 139.62/19.43 | | | | | | | | | | | | | | | | | | | Case 2: % 139.62/19.43 | | | | | | | | | | | | | | | | | | | | % 139.62/19.43 | | | | | | | | | | | | | | | | | | | | (415) ~ leq(n1, all_71_25) | (a_select3(q, pv10, n1) = % 139.62/19.43 | | | | | | | | | | | | | | | | | | | | all_71_0 & $i(all_71_0)) % 139.62/19.43 | | | | | | | | | | | | | | | | | | | | % 139.62/19.43 | | | | | | | | | | | | | | | | | | | | BETA: splitting (415) gives: % 139.62/19.43 | | | | | | | | | | | | | | | | | | | | % 139.62/19.43 | | | | | | | | | | | | | | | | | | | | Case 1: % 139.62/19.43 | | | | | | | | | | | | | | | | | | | | | % 139.62/19.43 | | | | | | | | | | | | | | | | | | | | | (416) ~ leq(n1, all_71_25) % 139.62/19.43 | | | | | | | | | | | | | | | | | | | | | % 139.62/19.43 | | | | | | | | | | | | | | | | | | | | | REDUCE: (360), (416) imply: % 139.62/19.43 | | | | | | | | | | | | | | | | | | | | | (417) ~ leq(n1, n1) % 139.62/19.43 | | | | | | | | | | | | | | | | | | | | | % 139.62/19.43 | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (364), (417) imply: % 139.62/19.43 | | | | | | | | | | | | | | | | | | | | | (418) $false % 139.62/19.43 | | | | | | | | | | | | | | | | | | | | | % 139.62/19.43 | | | | | | | | | | | | | | | | | | | | | CLOSE: (418) is inconsistent. % 139.62/19.43 | | | | | | | | | | | | | | | | | | | | | % 139.62/19.43 | | | | | | | | | | | | | | | | | | | | Case 2: % 139.62/19.43 | | | | | | | | | | | | | | | | | | | | | % 139.62/19.43 | | | | | | | | | | | | | | | | | | | | | (419) a_select3(q, pv10, n1) = all_71_0 & $i(all_71_0) % 139.62/19.43 | | | | | | | | | | | | | | | | | | | | | % 139.62/19.43 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (27), (134), (409), (410), (419) are inconsistent % 139.62/19.43 | | | | | | | | | | | | | | | | | | | | | by sub-proof #20. % 139.62/19.43 | | | | | | | | | | | | | | | | | | | | | % 139.62/19.43 | | | | | | | | | | | | | | | | | | | | End of split % 139.62/19.43 | | | | | | | | | | | | | | | | | | | | % 139.62/19.43 | | | | | | | | | | | | | | | | | | | End of split % 139.62/19.43 | | | | | | | | | | | | | | | | | | | % 139.62/19.43 | | | | | | | | | | | | | | | | | | End of split % 139.62/19.43 | | | | | | | | | | | | | | | | | | % 139.62/19.43 | | | | | | | | | | | | | | | | | Case 2: % 139.62/19.43 | | | | | | | | | | | | | | | | | | % 139.62/19.43 | | | | | | | | | | | | | | | | | | (420) pv10 = n2 % 139.62/19.43 | | | | | | | | | | | | | | | | | | % 139.62/19.43 | | | | | | | | | | | | | | | | | | REDUCE: (61), (420) imply: % 139.62/19.43 | | | | | | | | | | | | | | | | | | (421) minus(n2, n1) = all_71_23 % 139.62/19.43 | | | | | | | | | | | | | | | | | | % 139.62/19.43 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (26) with n1, all_71_23, n1, n2, % 139.62/19.43 | | | | | | | | | | | | | | | | | | simplifying with (361), (421) gives: % 139.62/19.43 | | | | | | | | | | | | | | | | | | (422) all_71_23 = n1 % 139.62/19.43 | | | | | | | | | | | | | | | | | | % 139.62/19.43 | | | | | | | | | | | | | | | | | | REDUCE: (367), (422) imply: % 139.62/19.43 | | | | | | | | | | | | | | | | | | (423) gt(n1, n1) % 139.62/19.43 | | | | | | | | | | | | | | | | | | % 139.62/19.43 | | | | | | | | | | | | | | | | | | PRED_UNIFY: (366), (423) imply: % 139.62/19.43 | | | | | | | | | | | | | | | | | | (424) $false % 139.62/19.43 | | | | | | | | | | | | | | | | | | % 139.62/19.43 | | | | | | | | | | | | | | | | | | CLOSE: (424) is inconsistent. % 139.62/19.43 | | | | | | | | | | | | | | | | | | % 139.62/19.43 | | | | | | | | | | | | | | | | | End of split % 139.62/19.43 | | | | | | | | | | | | | | | | | % 139.62/19.43 | | | | | | | | | | | | | | | | Case 2: % 139.62/19.43 | | | | | | | | | | | | | | | | | % 139.62/19.43 | | | | | | | | | | | | | | | | | (425) all_71_23 = n1 % 139.62/19.43 | | | | | | | | | | | | | | | | | % 139.62/19.43 | | | | | | | | | | | | | | | | | REDUCE: (124), (425) imply: % 139.62/19.43 | | | | | | | | | | | | | | | | | (426) succ(n1) = pv10 % 139.62/19.43 | | | | | | | | | | | | | | | | | % 139.62/19.43 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (25) with n2, pv10, n1, simplifying % 139.62/19.43 | | | | | | | | | | | | | | | | | with (79), (426) gives: % 139.62/19.43 | | | | | | | | | | | | | | | | | (427) pv10 = n2 % 139.62/19.43 | | | | | | | | | | | | | | | | | % 139.62/19.43 | | | | | | | | | | | | | | | | | REDUCE: (363), (427) imply: % 139.62/19.43 | | | | | | | | | | | | | | | | | (428) a_select3(q, n2, n1) = all_71_10 % 139.62/19.43 | | | | | | | | | | | | | | | | | % 139.62/19.43 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (65) with n1, all_71_11, all_71_9, % 139.62/19.43 | | | | | | | | | | | | | | | | | all_71_8, all_71_7, all_71_6, all_71_5, all_71_4, % 139.62/19.43 | | | | | | | | | | | | | | | | | all_71_3, all_71_2, all_71_1, all_71_0, % 139.62/19.43 | | | | | | | | | | | | | | | | | simplifying with (59), (80), (139), (141), (142), % 139.62/19.43 | | | | | | | | | | | | | | | | | (143), (144), (145), (146), (147), (362), (365) % 139.62/19.43 | | | | | | | | | | | | | | | | | gives: % 139.62/19.43 | | | | | | | | | | | | | | | | | (429) ~ (sum(n0, all_71_26, all_71_2) = all_71_1) | ~ % 139.62/19.43 | | | | | | | | | | | | | | | | | leq(n1, all_71_25) | (a_select3(q, pv10, n1) = % 139.62/19.43 | | | | | | | | | | | | | | | | | all_71_0 & $i(all_71_0)) % 139.62/19.43 | | | | | | | | | | | | | | | | | % 139.62/19.43 | | | | | | | | | | | | | | | | | BETA: splitting (429) gives: % 139.62/19.43 | | | | | | | | | | | | | | | | | % 139.62/19.43 | | | | | | | | | | | | | | | | | Case 1: % 139.62/19.43 | | | | | | | | | | | | | | | | | | % 139.62/19.43 | | | | | | | | | | | | | | | | | | (430) ~ (sum(n0, all_71_26, all_71_2) = all_71_1) % 139.62/19.43 | | | | | | | | | | | | | | | | | | % 139.62/19.43 | | | | | | | | | | | | | | | | | | REDUCE: (119), (430) imply: % 139.62/19.43 | | | | | | | | | | | | | | | | | | (431) ~ (sum(n0, n4, all_71_2) = all_71_1) % 139.62/19.43 | | | | | | | | | | | | | | | | | | % 139.62/19.43 | | | | | | | | | | | | | | | | | | PRED_UNIFY: (148), (431) imply: % 139.62/19.43 | | | | | | | | | | | | | | | | | | (432) $false % 139.62/19.43 | | | | | | | | | | | | | | | | | | % 139.62/19.43 | | | | | | | | | | | | | | | | | | CLOSE: (432) is inconsistent. % 139.62/19.43 | | | | | | | | | | | | | | | | | | % 139.62/19.43 | | | | | | | | | | | | | | | | | Case 2: % 139.62/19.43 | | | | | | | | | | | | | | | | | | % 139.62/19.43 | | | | | | | | | | | | | | | | | | (433) ~ leq(n1, all_71_25) | (a_select3(q, pv10, n1) = % 139.62/19.43 | | | | | | | | | | | | | | | | | | all_71_0 & $i(all_71_0)) % 139.62/19.43 | | | | | | | | | | | | | | | | | | % 139.62/19.43 | | | | | | | | | | | | | | | | | | BETA: splitting (433) gives: % 139.62/19.43 | | | | | | | | | | | | | | | | | | % 139.62/19.43 | | | | | | | | | | | | | | | | | | Case 1: % 139.62/19.43 | | | | | | | | | | | | | | | | | | | % 139.62/19.43 | | | | | | | | | | | | | | | | | | | (434) ~ leq(n1, all_71_25) % 139.62/19.43 | | | | | | | | | | | | | | | | | | | % 139.62/19.43 | | | | | | | | | | | | | | | | | | | REDUCE: (360), (434) imply: % 139.62/19.43 | | | | | | | | | | | | | | | | | | | (435) ~ leq(n1, n1) % 139.62/19.43 | | | | | | | | | | | | | | | | | | | % 139.62/19.43 | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (364), (435) imply: % 139.62/19.43 | | | | | | | | | | | | | | | | | | | (436) $false % 139.62/19.43 | | | | | | | | | | | | | | | | | | | % 139.62/19.43 | | | | | | | | | | | | | | | | | | | CLOSE: (436) is inconsistent. % 139.62/19.43 | | | | | | | | | | | | | | | | | | | % 139.62/19.43 | | | | | | | | | | | | | | | | | | Case 2: % 139.62/19.43 | | | | | | | | | | | | | | | | | | | % 139.62/19.43 | | | | | | | | | | | | | | | | | | | (437) a_select3(q, pv10, n1) = all_71_0 & $i(all_71_0) % 139.62/19.43 | | | | | | | | | | | | | | | | | | | % 139.62/19.43 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (27), (134), (427), (428), (437) are inconsistent % 139.62/19.43 | | | | | | | | | | | | | | | | | | | by sub-proof #18. % 139.62/19.43 | | | | | | | | | | | | | | | | | | | % 139.62/19.43 | | | | | | | | | | | | | | | | | | End of split % 139.62/19.43 | | | | | | | | | | | | | | | | | | % 139.62/19.43 | | | | | | | | | | | | | | | | | End of split % 139.62/19.43 | | | | | | | | | | | | | | | | | % 139.62/19.43 | | | | | | | | | | | | | | | | End of split % 139.62/19.43 | | | | | | | | | | | | | | | | % 139.62/19.43 | | | | | | | | | | | | | | | End of split % 139.62/19.43 | | | | | | | | | | | | | | | % 139.62/19.43 | | | | | | | | | | | | | | End of split % 139.62/19.43 | | | | | | | | | | | | | | % 139.62/19.43 | | | | | | | | | | | | | End of split % 139.62/19.43 | | | | | | | | | | | | | % 139.62/19.43 | | | | | | | | | | | | Case 2: % 139.62/19.43 | | | | | | | | | | | | | % 139.62/19.43 | | | | | | | | | | | | | (438) pv12 = n3 % 139.62/19.43 | | | | | | | | | | | | | % 139.62/19.43 | | | | | | | | | | | | | REDUCE: (62), (438) imply: % 139.62/19.43 | | | | | | | | | | | | | (439) minus(n3, n1) = all_71_25 % 139.62/19.43 | | | | | | | | | | | | | % 139.62/19.43 | | | | | | | | | | | | | REDUCE: (125), (438) imply: % 139.62/19.43 | | | | | | | | | | | | | (440) succ(all_71_25) = n3 % 139.62/19.43 | | | | | | | | | | | | | % 139.62/19.43 | | | | | | | | | | | | | REDUCE: (118), (438) imply: % 139.62/19.43 | | | | | | | | | | | | | (441) pred(n3) = all_71_25 % 139.62/19.43 | | | | | | | | | | | | | % 139.62/19.43 | | | | | | | | | | | | | GROUND_INST: instantiating (24) with n2, all_71_25, n3, % 139.62/19.43 | | | | | | | | | | | | | simplifying with (108), (441) gives: % 139.62/19.43 | | | | | | | | | | | | | (442) all_71_25 = n2 % 139.62/19.43 | | | | | | | | | | | | | % 139.62/19.43 | | | | | | | | | | | | | REDUCE: (439), (442) imply: % 139.62/19.43 | | | | | | | | | | | | | (443) minus(n3, n1) = n2 % 139.62/19.43 | | | | | | | | | | | | | % 139.62/19.43 | | | | | | | | | | | | | REDUCE: (327), (442) imply: % 139.62/19.43 | | | | | | | | | | | | | (444) a_select3(center, n2, n0) = all_71_9 % 139.62/19.43 | | | | | | | | | | | | | % 139.62/19.43 | | | | | | | | | | | | | REDUCE: (328), (442) imply: % 139.62/19.43 | | | | | | | | | | | | | (445) a_select3(q, pv10, n2) = all_71_10 % 139.62/19.43 | | | | | | | | | | | | | % 139.62/19.43 | | | | | | | | | | | | | REDUCE: (170), (442) imply: % 139.62/19.43 | | | | | | | | | | | | | (446) leq(n2, n2) % 139.62/19.43 | | | | | | | | | | | | | % 139.62/19.43 | | | | | | | | | | | | | REDUCE: (153), (442) imply: % 139.62/19.43 | | | | | | | | | | | | | (447) leq(n0, n2) % 139.62/19.43 | | | | | | | | | | | | | % 139.62/19.43 | | | | | | | | | | | | | GROUND_INST: instantiating (6) with n1, all_71_23, n2, pv10, % 139.62/19.43 | | | | | | | | | | | | | simplifying with (79), (80), (114), (124), (342) % 139.62/19.43 | | | | | | | | | | | | | gives: % 139.62/19.43 | | | | | | | | | | | | | (448) leq(n2, pv10) % 139.62/19.43 | | | | | | | | | | | | | % 139.62/19.43 | | | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with n1, all_71_23, % 139.62/19.43 | | | | | | | | | | | | | simplifying with (80), (114), (342) gives: % 139.62/19.43 | | | | | | | | | | | | | (449) all_71_23 = n1 | gt(all_71_23, n1) % 139.62/19.43 | | | | | | | | | | | | | % 139.62/19.44 | | | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with n2, pv10, simplifying % 139.62/19.44 | | | | | | | | | | | | | with (21), (91), (448) gives: % 139.62/19.44 | | | | | | | | | | | | | (450) pv10 = n2 | gt(pv10, n2) % 139.62/19.44 | | | | | | | | | | | | | % 139.62/19.44 | | | | | | | | | | | | | BETA: splitting (449) gives: % 139.62/19.44 | | | | | | | | | | | | | % 139.62/19.44 | | | | | | | | | | | | | Case 1: % 139.62/19.44 | | | | | | | | | | | | | | % 139.62/19.44 | | | | | | | | | | | | | | (451) gt(all_71_23, n1) % 139.62/19.44 | | | | | | | | | | | | | | % 139.62/19.44 | | | | | | | | | | | | | | BETA: splitting (450) gives: % 139.62/19.44 | | | | | | | | | | | | | | % 139.62/19.44 | | | | | | | | | | | | | | Case 1: % 139.62/19.44 | | | | | | | | | | | | | | | % 139.62/19.44 | | | | | | | | | | | | | | | (452) gt(pv10, n2) % 139.62/19.44 | | | | | | | | | | | | | | | % 139.62/19.44 | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with n2, pv10, all_71_23, % 139.62/19.44 | | | | | | | | | | | | | | | simplifying with (21), (91), (115), (452) gives: % 139.62/19.44 | | | | | | | | | | | | | | | (453) leq(n2, all_71_23) % 139.62/19.44 | | | | | | | | | | | | | | | % 139.62/19.44 | | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with n2, all_71_23, n3, pv10, % 139.62/19.44 | | | | | | | | | | | | | | | simplifying with (90), (91), (114), (124), (453) % 139.62/19.44 | | | | | | | | | | | | | | | gives: % 139.62/19.44 | | | | | | | | | | | | | | | (454) leq(n3, pv10) % 139.62/19.44 | | | | | | | | | | | | | | | % 139.62/19.44 | | | | | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with n2, all_71_23, % 139.62/19.44 | | | | | | | | | | | | | | | simplifying with (91), (114), (453) gives: % 139.62/19.44 | | | | | | | | | | | | | | | (455) all_71_23 = n2 | gt(all_71_23, n2) % 139.62/19.44 | | | | | | | | | | | | | | | % 139.62/19.44 | | | | | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with n3, pv10, simplifying % 139.62/19.44 | | | | | | | | | | | | | | | with (21), (98), (454) gives: % 139.62/19.44 | | | | | | | | | | | | | | | (456) pv10 = n3 | gt(pv10, n3) % 139.62/19.44 | | | | | | | | | | | | | | | % 139.62/19.44 | | | | | | | | | | | | | | | BETA: splitting (455) gives: % 139.62/19.44 | | | | | | | | | | | | | | | % 139.62/19.44 | | | | | | | | | | | | | | | Case 1: % 139.62/19.44 | | | | | | | | | | | | | | | | % 139.62/19.44 | | | | | | | | | | | | | | | | (457) gt(all_71_23, n2) % 139.62/19.44 | | | | | | | | | | | | | | | | % 139.62/19.44 | | | | | | | | | | | | | | | | BETA: splitting (456) gives: % 139.62/19.44 | | | | | | | | | | | | | | | | % 139.62/19.44 | | | | | | | | | | | | | | | | Case 1: % 139.62/19.44 | | | | | | | | | | | | | | | | | % 139.62/19.44 | | | | | | | | | | | | | | | | | (458) gt(pv10, n3) % 139.62/19.44 | | | | | | | | | | | | | | | | | % 139.62/19.44 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with n3, pv10, all_71_23, % 139.62/19.44 | | | | | | | | | | | | | | | | | simplifying with (21), (98), (115), (458) gives: % 139.62/19.44 | | | | | | | | | | | | | | | | | (459) leq(n3, all_71_23) % 139.62/19.44 | | | | | | | | | | | | | | | | | % 139.62/19.44 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with n3, all_71_23, n4, pv10, % 139.62/19.44 | | | | | | | | | | | | | | | | | simplifying with (97), (98), (114), (124), (459) % 139.62/19.44 | | | | | | | | | | | | | | | | | gives: % 139.62/19.44 | | | | | | | | | | | | | | | | | (460) leq(n4, pv10) % 139.62/19.44 | | | | | | | | | | | | | | | | | % 139.62/19.44 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with n3, all_71_23, % 139.62/19.44 | | | | | | | | | | | | | | | | | simplifying with (98), (114), (459) gives: % 139.62/19.44 | | | | | | | | | | | | | | | | | (461) all_71_23 = n3 | gt(all_71_23, n3) % 139.62/19.44 | | | | | | | | | | | | | | | | | % 139.62/19.44 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with n4, pv10, simplifying % 139.62/19.44 | | | | | | | | | | | | | | | | | with (21), (101), (460) gives: % 139.62/19.44 | | | | | | | | | | | | | | | | | (462) pv10 = n4 | gt(pv10, n4) % 139.62/19.44 | | | | | | | | | | | | | | | | | % 139.62/19.44 | | | | | | | | | | | | | | | | | BETA: splitting (461) gives: % 139.62/19.44 | | | | | | | | | | | | | | | | | % 139.62/19.44 | | | | | | | | | | | | | | | | | Case 1: % 139.62/19.44 | | | | | | | | | | | | | | | | | | % 139.62/19.44 | | | | | | | | | | | | | | | | | | (463) gt(all_71_23, n3) % 139.62/19.44 | | | | | | | | | | | | | | | | | | % 139.62/19.44 | | | | | | | | | | | | | | | | | | BETA: splitting (462) gives: % 139.62/19.44 | | | | | | | | | | | | | | | | | | % 139.62/19.44 | | | | | | | | | | | | | | | | | | Case 1: % 139.62/19.44 | | | | | | | | | | | | | | | | | | | % 139.62/19.44 | | | | | | | | | | | | | | | | | | | (464) gt(pv10, n4) % 139.62/19.44 | | | | | | | | | | | | | | | | | | | % 139.62/19.44 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with n4, pv10, all_71_23, % 139.62/19.44 | | | | | | | | | | | | | | | | | | | simplifying with (21), (101), (115), (464) gives: % 139.62/19.44 | | | | | | | | | | | | | | | | | | | (465) leq(n4, all_71_23) % 139.62/19.44 | | | | | | | | | | | | | | | | | | | % 139.62/19.44 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with n4, all_71_23, n5, pv10, % 139.62/19.44 | | | | | | | | | | | | | | | | | | | simplifying with (100), (101), (114), (124), (465) % 139.62/19.44 | | | | | | | | | | | | | | | | | | | gives: % 139.62/19.44 | | | | | | | | | | | | | | | | | | | (466) leq(n5, pv10) % 139.62/19.44 | | | | | | | | | | | | | | | | | | | % 139.98/19.44 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with n4, all_71_23, % 139.98/19.44 | | | | | | | | | | | | | | | | | | | simplifying with (101), (114), (465) gives: % 139.98/19.44 | | | | | | | | | | | | | | | | | | | (467) all_71_23 = n4 | gt(all_71_23, n4) % 139.98/19.44 | | | | | | | | | | | | | | | | | | | % 139.98/19.44 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with n5, pv10, simplifying % 139.98/19.44 | | | | | | | | | | | | | | | | | | | with (20), (21), (466) gives: % 139.98/19.44 | | | | | | | | | | | | | | | | | | | (468) pv10 = n5 | gt(pv10, n5) % 139.98/19.44 | | | | | | | | | | | | | | | | | | | % 139.98/19.44 | | | | | | | | | | | | | | | | | | | BETA: splitting (467) gives: % 139.98/19.44 | | | | | | | | | | | | | | | | | | | % 139.98/19.44 | | | | | | | | | | | | | | | | | | | Case 1: % 139.98/19.44 | | | | | | | | | | | | | | | | | | | | % 139.98/19.44 | | | | | | | | | | | | | | | | | | | | (469) gt(all_71_23, n4) % 139.98/19.44 | | | | | | | | | | | | | | | | | | | | % 139.98/19.44 | | | | | | | | | | | | | | | | | | | | BETA: splitting (468) gives: % 139.98/19.44 | | | | | | | | | | | | | | | | | | | | % 139.98/19.44 | | | | | | | | | | | | | | | | | | | | Case 1: % 139.98/19.44 | | | | | | | | | | | | | | | | | | | | | % 139.98/19.44 | | | | | | | | | | | | | | | | | | | | | % 139.98/19.44 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (27), (59), (65), (91), (119), (134), (139), % 139.98/19.44 | | | | | | | | | | | | | | | | | | | | | (141), (142), (143), (144), (145), (146), (147), % 139.98/19.44 | | | | | | | | | | | | | | | | | | | | | (148), (442), (444), (445), (446), (447) are % 139.98/19.44 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #8. % 139.98/19.44 | | | | | | | | | | | | | | | | | | | | | % 139.98/19.44 | | | | | | | | | | | | | | | | | | | | Case 2: % 139.98/19.44 | | | | | | | | | | | | | | | | | | | | | % 139.98/19.44 | | | | | | | | | | | | | | | | | | | | | (470) pv10 = n5 % 139.98/19.44 | | | | | | | | | | | | | | | | | | | | | % 139.98/19.44 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (26), (61), (114), (120), (469), (470), % 139.98/19.44 | | | | | | | | | | | | | | | | | | | | | (irreflexivity_gt) are inconsistent by sub-proof % 139.98/19.44 | | | | | | | | | | | | | | | | | | | | | #11. % 139.98/19.44 | | | | | | | | | | | | | | | | | | | | | % 139.98/19.44 | | | | | | | | | | | | | | | | | | | | End of split % 139.98/19.44 | | | | | | | | | | | | | | | | | | | | % 139.98/19.44 | | | | | | | | | | | | | | | | | | | Case 2: % 139.98/19.44 | | | | | | | | | | | | | | | | | | | | % 139.98/19.44 | | | | | | | | | | | | | | | | | | | | % 139.98/19.44 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (27), (59), (65), (91), (119), (134), (139), % 139.98/19.44 | | | | | | | | | | | | | | | | | | | | (141), (142), (143), (144), (145), (146), (147), % 139.98/19.44 | | | | | | | | | | | | | | | | | | | | (148), (442), (444), (445), (446), (447) are % 139.98/19.44 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #8. % 139.98/19.44 | | | | | | | | | | | | | | | | | | | | % 139.98/19.44 | | | | | | | | | | | | | | | | | | | End of split % 139.98/19.44 | | | | | | | | | | | | | | | | | | | % 139.98/19.44 | | | | | | | | | | | | | | | | | | Case 2: % 139.98/19.44 | | | | | | | | | | | | | | | | | | | % 139.98/19.44 | | | | | | | | | | | | | | | | | | | (471) pv10 = n4 % 139.98/19.44 | | | | | | | | | | | | | | | | | | | % 139.98/19.44 | | | | | | | | | | | | | | | | | | | REDUCE: (115), (471) imply: % 139.98/19.44 | | | | | | | | | | | | | | | | | | | (472) pred(n4) = all_71_23 % 139.98/19.44 | | | | | | | | | | | | | | | | | | | % 139.98/19.44 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (24), (109), (114), (463), (472), % 139.98/19.44 | | | | | | | | | | | | | | | | | | | (irreflexivity_gt) are inconsistent by sub-proof % 139.98/19.44 | | | | | | | | | | | | | | | | | | | #10. % 139.98/19.44 | | | | | | | | | | | | | | | | | | | % 139.98/19.44 | | | | | | | | | | | | | | | | | | End of split % 139.98/19.44 | | | | | | | | | | | | | | | | | | % 139.98/19.44 | | | | | | | | | | | | | | | | | Case 2: % 139.98/19.44 | | | | | | | | | | | | | | | | | | % 139.98/19.44 | | | | | | | | | | | | | | | | | | (473) all_71_23 = n3 % 139.98/19.44 | | | | | | | | | | | | | | | | | | % 139.98/19.44 | | | | | | | | | | | | | | | | | | REDUCE: (124), (473) imply: % 139.98/19.44 | | | | | | | | | | | | | | | | | | (474) succ(n3) = pv10 % 139.98/19.44 | | | | | | | | | | | | | | | | | | % 139.98/19.44 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (25) with n4, pv10, n3, simplifying % 139.98/19.44 | | | | | | | | | | | | | | | | | | with (97), (474) gives: % 139.98/19.44 | | | | | | | | | | | | | | | | | | (475) pv10 = n4 % 139.98/19.44 | | | | | | | | | | | | | | | | | | % 139.98/19.44 | | | | | | | | | | | | | | | | | | REDUCE: (445), (475) imply: % 139.98/19.44 | | | | | | | | | | | | | | | | | | (476) a_select3(q, n4, n2) = all_71_10 % 139.98/19.44 | | | | | | | | | | | | | | | | | | % 139.98/19.44 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (65) with n2, all_71_11, all_71_9, % 139.98/19.44 | | | | | | | | | | | | | | | | | | all_71_8, all_71_7, all_71_6, all_71_5, all_71_4, % 139.98/19.44 | | | | | | | | | | | | | | | | | | all_71_3, all_71_2, all_71_1, all_71_0, % 139.98/19.44 | | | | | | | | | | | | | | | | | | simplifying with (59), (91), (139), (141), (142), % 139.98/19.44 | | | | | | | | | | | | | | | | | | (143), (144), (145), (146), (147), (444), (447) % 139.98/19.44 | | | | | | | | | | | | | | | | | | gives: % 139.98/19.44 | | | | | | | | | | | | | | | | | | (477) ~ (sum(n0, all_71_26, all_71_2) = all_71_1) | ~ % 139.98/19.44 | | | | | | | | | | | | | | | | | | leq(n2, all_71_25) | (a_select3(q, pv10, n2) = % 139.98/19.44 | | | | | | | | | | | | | | | | | | all_71_0 & $i(all_71_0)) % 139.98/19.44 | | | | | | | | | | | | | | | | | | % 139.98/19.44 | | | | | | | | | | | | | | | | | | BETA: splitting (477) gives: % 139.98/19.44 | | | | | | | | | | | | | | | | | | % 139.98/19.44 | | | | | | | | | | | | | | | | | | Case 1: % 139.98/19.44 | | | | | | | | | | | | | | | | | | | % 139.98/19.44 | | | | | | | | | | | | | | | | | | | (478) ~ (sum(n0, all_71_26, all_71_2) = all_71_1) % 139.98/19.44 | | | | | | | | | | | | | | | | | | | % 139.98/19.44 | | | | | | | | | | | | | | | | | | | REDUCE: (119), (478) imply: % 139.98/19.44 | | | | | | | | | | | | | | | | | | | (479) ~ (sum(n0, n4, all_71_2) = all_71_1) % 139.98/19.44 | | | | | | | | | | | | | | | | | | | % 139.98/19.44 | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (148), (479) imply: % 139.98/19.44 | | | | | | | | | | | | | | | | | | | (480) $false % 139.98/19.44 | | | | | | | | | | | | | | | | | | | % 139.98/19.44 | | | | | | | | | | | | | | | | | | | CLOSE: (480) is inconsistent. % 139.98/19.44 | | | | | | | | | | | | | | | | | | | % 139.98/19.44 | | | | | | | | | | | | | | | | | | Case 2: % 139.98/19.44 | | | | | | | | | | | | | | | | | | | % 139.98/19.44 | | | | | | | | | | | | | | | | | | | (481) ~ leq(n2, all_71_25) | (a_select3(q, pv10, n2) = % 139.98/19.44 | | | | | | | | | | | | | | | | | | | all_71_0 & $i(all_71_0)) % 139.98/19.44 | | | | | | | | | | | | | | | | | | | % 139.98/19.44 | | | | | | | | | | | | | | | | | | | BETA: splitting (481) gives: % 139.98/19.44 | | | | | | | | | | | | | | | | | | | % 139.98/19.44 | | | | | | | | | | | | | | | | | | | Case 1: % 139.98/19.44 | | | | | | | | | | | | | | | | | | | | % 139.98/19.44 | | | | | | | | | | | | | | | | | | | | (482) ~ leq(n2, all_71_25) % 139.98/19.44 | | | | | | | | | | | | | | | | | | | | % 139.98/19.44 | | | | | | | | | | | | | | | | | | | | REDUCE: (442), (482) imply: % 139.98/19.44 | | | | | | | | | | | | | | | | | | | | (483) ~ leq(n2, n2) % 139.98/19.44 | | | | | | | | | | | | | | | | | | | | % 139.98/19.44 | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (446), (483) imply: % 139.98/19.44 | | | | | | | | | | | | | | | | | | | | (484) $false % 139.98/19.44 | | | | | | | | | | | | | | | | | | | | % 139.98/19.44 | | | | | | | | | | | | | | | | | | | | CLOSE: (484) is inconsistent. % 139.98/19.44 | | | | | | | | | | | | | | | | | | | | % 139.98/19.44 | | | | | | | | | | | | | | | | | | | Case 2: % 139.98/19.44 | | | | | | | | | | | | | | | | | | | | % 139.98/19.44 | | | | | | | | | | | | | | | | | | | | (485) a_select3(q, pv10, n2) = all_71_0 & $i(all_71_0) % 139.98/19.44 | | | | | | | | | | | | | | | | | | | | % 139.98/19.44 | | | | | | | | | | | | | | | | | | | | ALPHA: (485) implies: % 139.98/19.44 | | | | | | | | | | | | | | | | | | | | (486) a_select3(q, pv10, n2) = all_71_0 % 139.98/19.44 | | | | | | | | | | | | | | | | | | | | % 139.98/19.44 | | | | | | | | | | | | | | | | | | | | REDUCE: (475), (486) imply: % 139.98/19.44 | | | | | | | | | | | | | | | | | | | | (487) a_select3(q, n4, n2) = all_71_0 % 139.98/19.44 | | | | | | | | | | | | | | | | | | | | % 139.98/19.44 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (27) with all_71_10, all_71_0, n2, % 139.98/19.44 | | | | | | | | | | | | | | | | | | | | n4, q, simplifying with (476), (487) gives: % 139.98/19.44 | | | | | | | | | | | | | | | | | | | | (488) all_71_0 = all_71_10 % 139.98/19.44 | | | | | | | | | | | | | | | | | | | | % 139.98/19.44 | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (488) imply: % 139.98/19.44 | | | | | | | | | | | | | | | | | | | | (489) $false % 139.98/19.44 | | | | | | | | | | | | | | | | | | | | % 139.98/19.44 | | | | | | | | | | | | | | | | | | | | CLOSE: (489) is inconsistent. % 139.98/19.44 | | | | | | | | | | | | | | | | | | | | % 139.98/19.44 | | | | | | | | | | | | | | | | | | | End of split % 139.98/19.44 | | | | | | | | | | | | | | | | | | | % 139.98/19.44 | | | | | | | | | | | | | | | | | | End of split % 139.98/19.44 | | | | | | | | | | | | | | | | | | % 139.98/19.44 | | | | | | | | | | | | | | | | | End of split % 139.98/19.44 | | | | | | | | | | | | | | | | | % 139.98/19.44 | | | | | | | | | | | | | | | | Case 2: % 139.98/19.44 | | | | | | | | | | | | | | | | | % 139.98/19.44 | | | | | | | | | | | | | | | | | (490) pv10 = n3 % 139.98/19.44 | | | | | | | | | | | | | | | | | % 139.98/19.44 | | | | | | | | | | | | | | | | | REDUCE: (61), (490) imply: % 139.98/19.44 | | | | | | | | | | | | | | | | | (491) minus(n3, n1) = all_71_23 % 139.98/19.44 | | | | | | | | | | | | | | | | | % 139.98/19.44 | | | | | | | | | | | | | | | | | REF_CLOSE: (26), (114), (443), (457), (491), % 139.98/19.44 | | | | | | | | | | | | | | | | | (irreflexivity_gt) are inconsistent by sub-proof % 139.98/19.44 | | | | | | | | | | | | | | | | | #21. % 139.98/19.44 | | | | | | | | | | | | | | | | | % 139.98/19.44 | | | | | | | | | | | | | | | | End of split % 139.98/19.44 | | | | | | | | | | | | | | | | % 139.98/19.44 | | | | | | | | | | | | | | | Case 2: % 139.98/19.44 | | | | | | | | | | | | | | | | % 139.98/19.44 | | | | | | | | | | | | | | | | (492) all_71_23 = n2 % 139.98/19.44 | | | | | | | | | | | | | | | | % 139.98/19.44 | | | | | | | | | | | | | | | | REDUCE: (124), (492) imply: % 139.98/19.44 | | | | | | | | | | | | | | | | (493) succ(n2) = pv10 % 139.98/19.44 | | | | | | | | | | | | | | | | % 139.98/19.44 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (25) with n3, pv10, n2, simplifying % 139.98/19.44 | | | | | | | | | | | | | | | | with (90), (493) gives: % 139.98/19.44 | | | | | | | | | | | | | | | | (494) pv10 = n3 % 139.98/19.44 | | | | | | | | | | | | | | | | % 139.98/19.44 | | | | | | | | | | | | | | | | REDUCE: (445), (494) imply: % 139.98/19.44 | | | | | | | | | | | | | | | | (495) a_select3(q, n3, n2) = all_71_10 % 139.98/19.44 | | | | | | | | | | | | | | | | % 139.98/19.44 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (65) with n2, all_71_11, all_71_9, % 139.98/19.44 | | | | | | | | | | | | | | | | all_71_8, all_71_7, all_71_6, all_71_5, all_71_4, % 139.98/19.44 | | | | | | | | | | | | | | | | all_71_3, all_71_2, all_71_1, all_71_0, % 139.98/19.44 | | | | | | | | | | | | | | | | simplifying with (59), (91), (139), (141), (142), % 139.98/19.44 | | | | | | | | | | | | | | | | (143), (144), (145), (146), (147), (444), (447) % 139.98/19.44 | | | | | | | | | | | | | | | | gives: % 139.98/19.44 | | | | | | | | | | | | | | | | (496) ~ (sum(n0, all_71_26, all_71_2) = all_71_1) | ~ % 139.98/19.44 | | | | | | | | | | | | | | | | leq(n2, all_71_25) | (a_select3(q, pv10, n2) = % 139.98/19.44 | | | | | | | | | | | | | | | | all_71_0 & $i(all_71_0)) % 139.98/19.44 | | | | | | | | | | | | | | | | % 139.98/19.44 | | | | | | | | | | | | | | | | BETA: splitting (496) gives: % 139.98/19.44 | | | | | | | | | | | | | | | | % 139.98/19.44 | | | | | | | | | | | | | | | | Case 1: % 139.98/19.44 | | | | | | | | | | | | | | | | | % 139.98/19.44 | | | | | | | | | | | | | | | | | (497) ~ (sum(n0, all_71_26, all_71_2) = all_71_1) % 139.98/19.44 | | | | | | | | | | | | | | | | | % 139.98/19.44 | | | | | | | | | | | | | | | | | REDUCE: (119), (497) imply: % 139.98/19.44 | | | | | | | | | | | | | | | | | (498) ~ (sum(n0, n4, all_71_2) = all_71_1) % 139.98/19.44 | | | | | | | | | | | | | | | | | % 139.98/19.44 | | | | | | | | | | | | | | | | | PRED_UNIFY: (148), (498) imply: % 139.98/19.44 | | | | | | | | | | | | | | | | | (499) $false % 139.98/19.44 | | | | | | | | | | | | | | | | | % 139.98/19.44 | | | | | | | | | | | | | | | | | CLOSE: (499) is inconsistent. % 139.98/19.44 | | | | | | | | | | | | | | | | | % 139.98/19.44 | | | | | | | | | | | | | | | | Case 2: % 139.98/19.44 | | | | | | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | | | | | | | (500) ~ leq(n2, all_71_25) | (a_select3(q, pv10, n2) = % 139.98/19.45 | | | | | | | | | | | | | | | | | all_71_0 & $i(all_71_0)) % 139.98/19.45 | | | | | | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | | | | | | | BETA: splitting (500) gives: % 139.98/19.45 | | | | | | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | | | | | | | Case 1: % 139.98/19.45 | | | | | | | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | | | | | | | | (501) ~ leq(n2, all_71_25) % 139.98/19.45 | | | | | | | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | | | | | | | | REDUCE: (442), (501) imply: % 139.98/19.45 | | | | | | | | | | | | | | | | | | (502) ~ leq(n2, n2) % 139.98/19.45 | | | | | | | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | | | | | | | | PRED_UNIFY: (446), (502) imply: % 139.98/19.45 | | | | | | | | | | | | | | | | | | (503) $false % 139.98/19.45 | | | | | | | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | | | | | | | | CLOSE: (503) is inconsistent. % 139.98/19.45 | | | | | | | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | | | | | | | Case 2: % 139.98/19.45 | | | | | | | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | | | | | | | | (504) a_select3(q, pv10, n2) = all_71_0 & $i(all_71_0) % 139.98/19.45 | | | | | | | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | | | | | | | | ALPHA: (504) implies: % 139.98/19.45 | | | | | | | | | | | | | | | | | | (505) a_select3(q, pv10, n2) = all_71_0 % 139.98/19.45 | | | | | | | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | | | | | | | | REDUCE: (494), (505) imply: % 139.98/19.45 | | | | | | | | | | | | | | | | | | (506) a_select3(q, n3, n2) = all_71_0 % 139.98/19.45 | | | | | | | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (27) with all_71_10, all_71_0, n2, % 139.98/19.45 | | | | | | | | | | | | | | | | | | n3, q, simplifying with (495), (506) gives: % 139.98/19.45 | | | | | | | | | | | | | | | | | | (507) all_71_0 = all_71_10 % 139.98/19.45 | | | | | | | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | | | | | | | | REDUCE: (134), (507) imply: % 139.98/19.45 | | | | | | | | | | | | | | | | | | (508) $false % 139.98/19.45 | | | | | | | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | | | | | | | | CLOSE: (508) is inconsistent. % 139.98/19.45 | | | | | | | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | | | | | | | End of split % 139.98/19.45 | | | | | | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | | | | | | End of split % 139.98/19.45 | | | | | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | | | | | End of split % 139.98/19.45 | | | | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | | | | Case 2: % 139.98/19.45 | | | | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | | | | | (509) pv10 = n2 % 139.98/19.45 | | | | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | | | | | REDUCE: (115), (509) imply: % 139.98/19.45 | | | | | | | | | | | | | | | (510) pred(n2) = all_71_23 % 139.98/19.45 | | | | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | | | | | GROUND_INST: instantiating (24) with n1, all_71_23, n2, % 139.98/19.45 | | | | | | | | | | | | | | | simplifying with (107), (510) gives: % 139.98/19.45 | | | | | | | | | | | | | | | (511) all_71_23 = n1 % 139.98/19.45 | | | | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | | | | | REF_CLOSE: (114), (451), (511), (irreflexivity_gt) are % 139.98/19.45 | | | | | | | | | | | | | | | inconsistent by sub-proof #19. % 139.98/19.45 | | | | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | | | | End of split % 139.98/19.45 | | | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | | | Case 2: % 139.98/19.45 | | | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | | | | (512) all_71_23 = n1 % 139.98/19.45 | | | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | | | | REDUCE: (124), (512) imply: % 139.98/19.45 | | | | | | | | | | | | | | (513) succ(n1) = pv10 % 139.98/19.45 | | | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | | | | GROUND_INST: instantiating (25) with n2, pv10, n1, simplifying % 139.98/19.45 | | | | | | | | | | | | | | with (79), (513) gives: % 139.98/19.45 | | | | | | | | | | | | | | (514) pv10 = n2 % 139.98/19.45 | | | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | | | | REDUCE: (445), (514) imply: % 139.98/19.45 | | | | | | | | | | | | | | (515) a_select3(q, n2, n2) = all_71_10 % 139.98/19.45 | | | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | | | | GROUND_INST: instantiating (65) with n2, all_71_11, all_71_9, % 139.98/19.45 | | | | | | | | | | | | | | all_71_8, all_71_7, all_71_6, all_71_5, all_71_4, % 139.98/19.45 | | | | | | | | | | | | | | all_71_3, all_71_2, all_71_1, all_71_0, % 139.98/19.45 | | | | | | | | | | | | | | simplifying with (59), (91), (139), (141), (142), % 139.98/19.45 | | | | | | | | | | | | | | (143), (144), (145), (146), (147), (444), (447) % 139.98/19.45 | | | | | | | | | | | | | | gives: % 139.98/19.45 | | | | | | | | | | | | | | (516) ~ (sum(n0, all_71_26, all_71_2) = all_71_1) | ~ % 139.98/19.45 | | | | | | | | | | | | | | leq(n2, all_71_25) | (a_select3(q, pv10, n2) = % 139.98/19.45 | | | | | | | | | | | | | | all_71_0 & $i(all_71_0)) % 139.98/19.45 | | | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | | | | BETA: splitting (516) gives: % 139.98/19.45 | | | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | | | | Case 1: % 139.98/19.45 | | | | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | | | | | (517) ~ (sum(n0, all_71_26, all_71_2) = all_71_1) % 139.98/19.45 | | | | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | | | | | REDUCE: (119), (517) imply: % 139.98/19.45 | | | | | | | | | | | | | | | (518) ~ (sum(n0, n4, all_71_2) = all_71_1) % 139.98/19.45 | | | | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | | | | | PRED_UNIFY: (148), (518) imply: % 139.98/19.45 | | | | | | | | | | | | | | | (519) $false % 139.98/19.45 | | | | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | | | | | CLOSE: (519) is inconsistent. % 139.98/19.45 | | | | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | | | | Case 2: % 139.98/19.45 | | | | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | | | | | (520) ~ leq(n2, all_71_25) | (a_select3(q, pv10, n2) = % 139.98/19.45 | | | | | | | | | | | | | | | all_71_0 & $i(all_71_0)) % 139.98/19.45 | | | | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | | | | | BETA: splitting (520) gives: % 139.98/19.45 | | | | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | | | | | Case 1: % 139.98/19.45 | | | | | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | | | | | | (521) ~ leq(n2, all_71_25) % 139.98/19.45 | | | | | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | | | | | | REDUCE: (442), (521) imply: % 139.98/19.45 | | | | | | | | | | | | | | | | (522) ~ leq(n2, n2) % 139.98/19.45 | | | | | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | | | | | | PRED_UNIFY: (446), (522) imply: % 139.98/19.45 | | | | | | | | | | | | | | | | (523) $false % 139.98/19.45 | | | | | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | | | | | | CLOSE: (523) is inconsistent. % 139.98/19.45 | | | | | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | | | | | Case 2: % 139.98/19.45 | | | | | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | | | | | | (524) a_select3(q, pv10, n2) = all_71_0 & $i(all_71_0) % 139.98/19.45 | | | | | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | | | | | | ALPHA: (524) implies: % 139.98/19.45 | | | | | | | | | | | | | | | | (525) a_select3(q, pv10, n2) = all_71_0 % 139.98/19.45 | | | | | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | | | | | | REDUCE: (514), (525) imply: % 139.98/19.45 | | | | | | | | | | | | | | | | (526) a_select3(q, n2, n2) = all_71_0 % 139.98/19.45 | | | | | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (27) with all_71_10, all_71_0, n2, % 139.98/19.45 | | | | | | | | | | | | | | | | n2, q, simplifying with (515), (526) gives: % 139.98/19.45 | | | | | | | | | | | | | | | | (527) all_71_0 = all_71_10 % 139.98/19.45 | | | | | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | | | | | | REDUCE: (134), (527) imply: % 139.98/19.45 | | | | | | | | | | | | | | | | (528) $false % 139.98/19.45 | | | | | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | | | | | | CLOSE: (528) is inconsistent. % 139.98/19.45 | | | | | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | | | | | End of split % 139.98/19.45 | | | | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | | | | End of split % 139.98/19.45 | | | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | | | End of split % 139.98/19.45 | | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | | End of split % 139.98/19.45 | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | Case 2: % 139.98/19.45 | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | | (529) pv10 = n1 % 139.98/19.45 | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | | REF_CLOSE: (24), (105), (114), (115), (340), (529), % 139.98/19.45 | | | | | | | | | | | | (irreflexivity_gt) are inconsistent by sub-proof % 139.98/19.45 | | | | | | | | | | | | #17. % 139.98/19.45 | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | End of split % 139.98/19.45 | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | Case 2: % 139.98/19.45 | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | (530) all_71_23 = n0 % 139.98/19.45 | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | REDUCE: (124), (530) imply: % 139.98/19.45 | | | | | | | | | | | (531) succ(n0) = pv10 % 139.98/19.45 | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | GROUND_INST: instantiating (25) with n1, pv10, n0, simplifying % 139.98/19.45 | | | | | | | | | | | with (16), (531) gives: % 139.98/19.45 | | | | | | | | | | | (532) pv10 = n1 % 139.98/19.45 | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | REDUCE: (328), (532) imply: % 139.98/19.45 | | | | | | | | | | | (533) a_select3(q, n1, all_71_25) = all_71_10 % 139.98/19.45 | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | BETA: splitting (171) gives: % 139.98/19.45 | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | Case 1: % 139.98/19.45 | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | | (534) gt(n3, pv12) % 139.98/19.45 | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | | GROUND_INST: instantiating (1) with pv12, n3, n2, simplifying % 139.98/19.45 | | | | | | | | | | | | with (22), (98), (108), (534) gives: % 139.98/19.45 | | | | | | | | | | | | (535) leq(pv12, n2) % 139.98/19.45 | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | | GROUND_INST: instantiating (12) with pv12, simplifying with % 139.98/19.45 | | | | | | | | | | | | (22), (53), (535) gives: % 139.98/19.45 | | | | | | | | | | | | (536) pv12 = n2 | pv12 = n1 | pv12 = n0 % 139.98/19.45 | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | | BETA: splitting (176) gives: % 139.98/19.45 | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | | Case 1: % 139.98/19.45 | | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | | | (537) pv12 = n1 % 139.98/19.45 | | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | | | REF_CLOSE: (22), (331), (537), (irreflexivity_gt) are % 139.98/19.45 | | | | | | | | | | | | | inconsistent by sub-proof #13. % 139.98/19.45 | | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | | Case 2: % 139.98/19.45 | | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | | | (538) ~ (pv12 = n1) % 139.98/19.45 | | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | | | BETA: splitting (536) gives: % 139.98/19.45 | | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | | | Case 1: % 139.98/19.45 | | | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | | | | (539) pv12 = n0 % 139.98/19.45 | | | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | | | | REDUCE: (175), (539) imply: % 139.98/19.45 | | | | | | | | | | | | | | (540) $false % 139.98/19.45 | | | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | | | | CLOSE: (540) is inconsistent. % 139.98/19.45 | | | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | | | Case 2: % 139.98/19.45 | | | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | | | | (541) pv12 = n2 | pv12 = n1 % 139.98/19.45 | | | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | | | | BETA: splitting (541) gives: % 139.98/19.45 | | | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | | | | Case 1: % 139.98/19.45 | | | | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | | | | | (542) pv12 = n1 % 139.98/19.45 | | | | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | | | | | REDUCE: (538), (542) imply: % 139.98/19.45 | | | | | | | | | | | | | | | (543) $false % 139.98/19.45 | | | | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | | | | | CLOSE: (543) is inconsistent. % 139.98/19.45 | | | | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | | | | Case 2: % 139.98/19.45 | | | | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | | | | | (544) pv12 = n2 % 139.98/19.45 | | | | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | | | | | REDUCE: (118), (544) imply: % 139.98/19.45 | | | | | | | | | | | | | | | (545) pred(n2) = all_71_25 % 139.98/19.45 | | | | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | | | | | GROUND_INST: instantiating (24) with n1, all_71_25, n2, % 139.98/19.45 | | | | | | | | | | | | | | | simplifying with (107), (545) gives: % 139.98/19.45 | | | | | | | | | | | | | | | (546) all_71_25 = n1 % 139.98/19.45 | | | | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | | | | | REDUCE: (327), (546) imply: % 139.98/19.45 | | | | | | | | | | | | | | | (547) a_select3(center, n1, n0) = all_71_9 % 139.98/19.45 | | | | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | | | | | REDUCE: (533), (546) imply: % 139.98/19.45 | | | | | | | | | | | | | | | (548) a_select3(q, n1, n1) = all_71_10 % 139.98/19.45 | | | | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | | | | | REDUCE: (339), (546) imply: % 139.98/19.45 | | | | | | | | | | | | | | | (549) leq(n1, n1) % 139.98/19.45 | | | | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | | | | | REDUCE: (153), (546) imply: % 139.98/19.45 | | | | | | | | | | | | | | | (550) leq(n0, n1) % 139.98/19.45 | | | | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | | | | | GROUND_INST: instantiating (65) with n1, all_71_11, all_71_9, % 139.98/19.45 | | | | | | | | | | | | | | | all_71_8, all_71_7, all_71_6, all_71_5, all_71_4, % 139.98/19.45 | | | | | | | | | | | | | | | all_71_3, all_71_2, all_71_1, all_71_0, % 139.98/19.45 | | | | | | | | | | | | | | | simplifying with (59), (80), (139), (141), (142), % 139.98/19.45 | | | | | | | | | | | | | | | (143), (144), (145), (146), (147), (547), (550) % 139.98/19.45 | | | | | | | | | | | | | | | gives: % 139.98/19.45 | | | | | | | | | | | | | | | (551) ~ (sum(n0, all_71_26, all_71_2) = all_71_1) | ~ % 139.98/19.45 | | | | | | | | | | | | | | | leq(n1, all_71_25) | (a_select3(q, pv10, n1) = % 139.98/19.45 | | | | | | | | | | | | | | | all_71_0 & $i(all_71_0)) % 139.98/19.45 | | | | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | | | | | BETA: splitting (551) gives: % 139.98/19.45 | | | | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | | | | | Case 1: % 139.98/19.45 | | | | | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | | | | | | (552) ~ (sum(n0, all_71_26, all_71_2) = all_71_1) % 139.98/19.45 | | | | | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | | | | | | REDUCE: (119), (552) imply: % 139.98/19.45 | | | | | | | | | | | | | | | | (553) ~ (sum(n0, n4, all_71_2) = all_71_1) % 139.98/19.45 | | | | | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | | | | | | PRED_UNIFY: (148), (553) imply: % 139.98/19.45 | | | | | | | | | | | | | | | | (554) $false % 139.98/19.45 | | | | | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | | | | | | CLOSE: (554) is inconsistent. % 139.98/19.45 | | | | | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | | | | | Case 2: % 139.98/19.45 | | | | | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | | | | | | (555) ~ leq(n1, all_71_25) | (a_select3(q, pv10, n1) = % 139.98/19.45 | | | | | | | | | | | | | | | | all_71_0 & $i(all_71_0)) % 139.98/19.45 | | | | | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | | | | | | BETA: splitting (555) gives: % 139.98/19.45 | | | | | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | | | | | | Case 1: % 139.98/19.45 | | | | | | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | | | | | | | (556) ~ leq(n1, all_71_25) % 139.98/19.45 | | | | | | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | | | | | | | REDUCE: (546), (556) imply: % 139.98/19.45 | | | | | | | | | | | | | | | | | (557) ~ leq(n1, n1) % 139.98/19.45 | | | | | | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | | | | | | | PRED_UNIFY: (549), (557) imply: % 139.98/19.45 | | | | | | | | | | | | | | | | | (558) $false % 139.98/19.45 | | | | | | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | | | | | | | CLOSE: (558) is inconsistent. % 139.98/19.45 | | | | | | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | | | | | | Case 2: % 139.98/19.45 | | | | | | | | | | | | | | | | | % 139.98/19.45 | | | | | | | | | | | | | | | | | (559) a_select3(q, pv10, n1) = all_71_0 & $i(all_71_0) % 139.98/19.45 | | | | | | | | | | | | | | | | | % 139.98/19.46 | | | | | | | | | | | | | | | | | REF_CLOSE: (27), (134), (532), (548), (559) are inconsistent % 139.98/19.46 | | | | | | | | | | | | | | | | | by sub-proof #7. % 139.98/19.46 | | | | | | | | | | | | | | | | | % 139.98/19.46 | | | | | | | | | | | | | | | | End of split % 139.98/19.46 | | | | | | | | | | | | | | | | % 139.98/19.46 | | | | | | | | | | | | | | | End of split % 139.98/19.46 | | | | | | | | | | | | | | | % 139.98/19.46 | | | | | | | | | | | | | | End of split % 139.98/19.46 | | | | | | | | | | | | | | % 139.98/19.46 | | | | | | | | | | | | | End of split % 139.98/19.46 | | | | | | | | | | | | | % 139.98/19.46 | | | | | | | | | | | | End of split % 139.98/19.46 | | | | | | | | | | | | % 139.98/19.46 | | | | | | | | | | | Case 2: % 139.98/19.46 | | | | | | | | | | | | % 139.98/19.46 | | | | | | | | | | | | (560) pv12 = n3 % 139.98/19.46 | | | | | | | | | | | | % 139.98/19.46 | | | | | | | | | | | | REDUCE: (118), (560) imply: % 139.98/19.46 | | | | | | | | | | | | (561) pred(n3) = all_71_25 % 139.98/19.46 | | | | | | | | | | | | % 139.98/19.46 | | | | | | | | | | | | GROUND_INST: instantiating (24) with n2, all_71_25, n3, % 139.98/19.46 | | | | | | | | | | | | simplifying with (108), (561) gives: % 139.98/19.46 | | | | | | | | | | | | (562) all_71_25 = n2 % 139.98/19.46 | | | | | | | | | | | | % 139.98/19.46 | | | | | | | | | | | | REDUCE: (327), (562) imply: % 139.98/19.46 | | | | | | | | | | | | (563) a_select3(center, n2, n0) = all_71_9 % 139.98/19.46 | | | | | | | | | | | | % 139.98/19.46 | | | | | | | | | | | | REDUCE: (533), (562) imply: % 139.98/19.46 | | | | | | | | | | | | (564) a_select3(q, n1, n2) = all_71_10 % 139.98/19.46 | | | | | | | | | | | | % 139.98/19.46 | | | | | | | | | | | | REDUCE: (170), (562) imply: % 139.98/19.46 | | | | | | | | | | | | (565) leq(n2, n2) % 139.98/19.46 | | | | | | | | | | | | % 139.98/19.46 | | | | | | | | | | | | REDUCE: (153), (562) imply: % 139.98/19.46 | | | | | | | | | | | | (566) leq(n0, n2) % 139.98/19.46 | | | | | | | | | | | | % 139.98/19.46 | | | | | | | | | | | | GROUND_INST: instantiating (65) with n2, all_71_11, all_71_9, % 139.98/19.46 | | | | | | | | | | | | all_71_8, all_71_7, all_71_6, all_71_5, all_71_4, % 139.98/19.46 | | | | | | | | | | | | all_71_3, all_71_2, all_71_1, all_71_0, % 139.98/19.46 | | | | | | | | | | | | simplifying with (59), (91), (139), (141), (142), % 139.98/19.46 | | | | | | | | | | | | (143), (144), (145), (146), (147), (563), (566) % 139.98/19.46 | | | | | | | | | | | | gives: % 139.98/19.46 | | | | | | | | | | | | (567) ~ (sum(n0, all_71_26, all_71_2) = all_71_1) | ~ % 139.98/19.46 | | | | | | | | | | | | leq(n2, all_71_25) | (a_select3(q, pv10, n2) = % 139.98/19.46 | | | | | | | | | | | | all_71_0 & $i(all_71_0)) % 139.98/19.46 | | | | | | | | | | | | % 139.98/19.46 | | | | | | | | | | | | BETA: splitting (567) gives: % 139.98/19.46 | | | | | | | | | | | | % 139.98/19.46 | | | | | | | | | | | | Case 1: % 139.98/19.46 | | | | | | | | | | | | | % 139.98/19.46 | | | | | | | | | | | | | (568) ~ (sum(n0, all_71_26, all_71_2) = all_71_1) % 139.98/19.46 | | | | | | | | | | | | | % 139.98/19.46 | | | | | | | | | | | | | REDUCE: (119), (568) imply: % 139.98/19.46 | | | | | | | | | | | | | (569) ~ (sum(n0, n4, all_71_2) = all_71_1) % 139.98/19.46 | | | | | | | | | | | | | % 139.98/19.46 | | | | | | | | | | | | | PRED_UNIFY: (148), (569) imply: % 139.98/19.46 | | | | | | | | | | | | | (570) $false % 139.98/19.46 | | | | | | | | | | | | | % 139.98/19.46 | | | | | | | | | | | | | CLOSE: (570) is inconsistent. % 139.98/19.46 | | | | | | | | | | | | | % 139.98/19.46 | | | | | | | | | | | | Case 2: % 139.98/19.46 | | | | | | | | | | | | | % 139.98/19.46 | | | | | | | | | | | | | (571) ~ leq(n2, all_71_25) | (a_select3(q, pv10, n2) = % 139.98/19.46 | | | | | | | | | | | | | all_71_0 & $i(all_71_0)) % 139.98/19.46 | | | | | | | | | | | | | % 139.98/19.46 | | | | | | | | | | | | | BETA: splitting (571) gives: % 139.98/19.46 | | | | | | | | | | | | | % 139.98/19.46 | | | | | | | | | | | | | Case 1: % 139.98/19.46 | | | | | | | | | | | | | | % 139.98/19.46 | | | | | | | | | | | | | | (572) ~ leq(n2, all_71_25) % 139.98/19.46 | | | | | | | | | | | | | | % 139.98/19.46 | | | | | | | | | | | | | | REDUCE: (562), (572) imply: % 139.98/19.46 | | | | | | | | | | | | | | (573) ~ leq(n2, n2) % 139.98/19.46 | | | | | | | | | | | | | | % 139.98/19.46 | | | | | | | | | | | | | | PRED_UNIFY: (565), (573) imply: % 139.98/19.46 | | | | | | | | | | | | | | (574) $false % 139.98/19.46 | | | | | | | | | | | | | | % 139.98/19.46 | | | | | | | | | | | | | | CLOSE: (574) is inconsistent. % 139.98/19.46 | | | | | | | | | | | | | | % 139.98/19.46 | | | | | | | | | | | | | Case 2: % 139.98/19.46 | | | | | | | | | | | | | | % 139.98/19.46 | | | | | | | | | | | | | | (575) a_select3(q, pv10, n2) = all_71_0 & $i(all_71_0) % 139.98/19.46 | | | | | | | | | | | | | | % 139.98/19.46 | | | | | | | | | | | | | | ALPHA: (575) implies: % 139.98/19.46 | | | | | | | | | | | | | | (576) a_select3(q, pv10, n2) = all_71_0 % 139.98/19.46 | | | | | | | | | | | | | | % 139.98/19.46 | | | | | | | | | | | | | | REDUCE: (532), (576) imply: % 139.98/19.46 | | | | | | | | | | | | | | (577) a_select3(q, n1, n2) = all_71_0 % 139.98/19.46 | | | | | | | | | | | | | | % 139.98/19.46 | | | | | | | | | | | | | | GROUND_INST: instantiating (27) with all_71_10, all_71_0, n2, % 139.98/19.46 | | | | | | | | | | | | | | n1, q, simplifying with (564), (577) gives: % 139.98/19.46 | | | | | | | | | | | | | | (578) all_71_0 = all_71_10 % 139.98/19.46 | | | | | | | | | | | | | | % 139.98/19.46 | | | | | | | | | | | | | | REDUCE: (134), (578) imply: % 139.98/19.46 | | | | | | | | | | | | | | (579) $false % 139.98/19.46 | | | | | | | | | | | | | | % 139.98/19.46 | | | | | | | | | | | | | | CLOSE: (579) is inconsistent. % 139.98/19.46 | | | | | | | | | | | | | | % 139.98/19.46 | | | | | | | | | | | | | End of split % 139.98/19.46 | | | | | | | | | | | | | % 139.98/19.46 | | | | | | | | | | | | End of split % 139.98/19.46 | | | | | | | | | | | | % 139.98/19.46 | | | | | | | | | | | End of split % 139.98/19.46 | | | | | | | | | | | % 139.98/19.46 | | | | | | | | | | End of split % 139.98/19.46 | | | | | | | | | | % 139.98/19.46 | | | | | | | | | End of split % 139.98/19.46 | | | | | | | | | % 139.98/19.46 | | | | | | | | End of split % 139.98/19.46 | | | | | | | | % 139.98/19.46 | | | | | | | Case 2: % 139.98/19.46 | | | | | | | | % 139.98/19.46 | | | | | | | | (580) pv12 = n1 % 139.98/19.46 | | | | | | | | % 139.98/19.46 | | | | | | | | REDUCE: (118), (580) imply: % 139.98/19.46 | | | | | | | | (581) pred(n1) = all_71_25 % 139.98/19.46 | | | | | | | | % 139.98/19.46 | | | | | | | | GROUND_INST: instantiating (24) with n0, all_71_25, n1, % 139.98/19.46 | | | | | | | | simplifying with (105), (581) gives: % 139.98/19.46 | | | | | | | | (582) all_71_25 = n0 % 139.98/19.46 | | | | | | | | % 139.98/19.46 | | | | | | | | REF_CLOSE: (329), (330), (582) are inconsistent by sub-proof % 139.98/19.46 | | | | | | | | #14. % 139.98/19.46 | | | | | | | | % 139.98/19.46 | | | | | | | End of split % 139.98/19.46 | | | | | | | % 139.98/19.46 | | | | | | End of split % 139.98/19.46 | | | | | | % 139.98/19.46 | | | | | Case 2: % 139.98/19.46 | | | | | | % 139.98/19.46 | | | | | | (583) all_71_12 = n0 % 139.98/19.46 | | | | | | (584) ~ gt(all_71_12, n0) % 139.98/19.46 | | | | | | % 139.98/19.46 | | | | | | REDUCE: (138), (583) imply: % 139.98/19.46 | | | | | | (585) a_select3(center, n0, n0) = all_71_9 % 139.98/19.46 | | | | | | % 139.98/19.46 | | | | | | REDUCE: (137), (583) imply: % 139.98/19.46 | | | | | | (586) a_select3(q, pv10, n0) = all_71_10 % 139.98/19.46 | | | | | | % 139.98/19.46 | | | | | | REDUCE: (135), (583) imply: % 139.98/19.46 | | | | | | (587) leq(n0, n0) % 139.98/19.46 | | | | | | % 139.98/19.46 | | | | | | REDUCE: (583), (584) imply: % 139.98/19.46 | | | | | | (588) ~ gt(n0, n0) % 139.98/19.46 | | | | | | % 139.98/19.46 | | | | | | BETA: splitting (154) gives: % 139.98/19.46 | | | | | | % 139.98/19.46 | | | | | | Case 1: % 139.98/19.46 | | | | | | | % 139.98/19.46 | | | | | | | (589) gt(all_71_25, all_71_12) % 139.98/19.46 | | | | | | | % 139.98/19.46 | | | | | | | REDUCE: (583), (589) imply: % 139.98/19.46 | | | | | | | (590) gt(all_71_25, n0) % 139.98/19.46 | | | | | | | % 139.98/19.46 | | | | | | | BETA: splitting (161) gives: % 139.98/19.46 | | | | | | | % 139.98/19.46 | | | | | | | Case 1: % 139.98/19.46 | | | | | | | | % 139.98/19.46 | | | | | | | | (591) gt(pv12, n1) % 139.98/19.46 | | | | | | | | % 139.98/19.46 | | | | | | | | BETA: splitting (165) gives: % 139.98/19.46 | | | | | | | | % 139.98/19.46 | | | | | | | | Case 1: % 139.98/19.46 | | | | | | | | | % 139.98/19.46 | | | | | | | | | (592) gt(all_71_23, n0) % 139.98/19.46 | | | | | | | | | % 139.98/19.46 | | | | | | | | | BETA: splitting (166) gives: % 139.98/19.46 | | | | | | | | | % 139.98/19.46 | | | | | | | | | Case 1: % 139.98/19.46 | | | | | | | | | | % 139.98/19.46 | | | | | | | | | | (593) gt(pv10, n1) % 139.98/19.46 | | | | | | | | | | % 139.98/19.46 | | | | | | | | | | GROUND_INST: instantiating (1) with n1, pv10, all_71_23, % 139.98/19.46 | | | | | | | | | | simplifying with (21), (80), (115), (593) gives: % 139.98/19.46 | | | | | | | | | | (594) leq(n1, all_71_23) % 139.98/19.46 | | | | | | | | | | % 139.98/19.46 | | | | | | | | | | GROUND_INST: instantiating (6) with n1, all_71_23, n2, pv10, % 139.98/19.46 | | | | | | | | | | simplifying with (79), (80), (114), (124), (594) % 139.98/19.46 | | | | | | | | | | gives: % 139.98/19.46 | | | | | | | | | | (595) leq(n2, pv10) % 139.98/19.46 | | | | | | | | | | % 139.98/19.46 | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with n1, all_71_23, % 139.98/19.46 | | | | | | | | | | simplifying with (80), (114), (594) gives: % 139.98/19.46 | | | | | | | | | | (596) all_71_23 = n1 | gt(all_71_23, n1) % 139.98/19.46 | | | | | | | | | | % 139.98/19.46 | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with n2, pv10, simplifying % 139.98/19.46 | | | | | | | | | | with (21), (91), (595) gives: % 139.98/19.46 | | | | | | | | | | (597) pv10 = n2 | gt(pv10, n2) % 139.98/19.46 | | | | | | | | | | % 139.98/19.46 | | | | | | | | | | BETA: splitting (171) gives: % 139.98/19.46 | | | | | | | | | | % 139.98/19.46 | | | | | | | | | | Case 1: % 139.98/19.46 | | | | | | | | | | | % 139.98/19.46 | | | | | | | | | | | (598) gt(n3, pv12) % 139.98/19.46 | | | | | | | | | | | % 139.98/19.46 | | | | | | | | | | | GROUND_INST: instantiating (1) with pv12, n3, n2, simplifying % 139.98/19.46 | | | | | | | | | | | with (22), (98), (108), (598) gives: % 139.98/19.46 | | | | | | | | | | | (599) leq(pv12, n2) % 139.98/19.46 | | | | | | | | | | | % 139.98/19.46 | | | | | | | | | | | GROUND_INST: instantiating (12) with pv12, simplifying with % 139.98/19.46 | | | | | | | | | | | (22), (53), (599) gives: % 139.98/19.46 | | | | | | | | | | | (600) pv12 = n2 | pv12 = n1 | pv12 = n0 % 139.98/19.46 | | | | | | | | | | | % 139.98/19.46 | | | | | | | | | | | BETA: splitting (176) gives: % 139.98/19.46 | | | | | | | | | | | % 139.98/19.46 | | | | | | | | | | | Case 1: % 139.98/19.46 | | | | | | | | | | | | % 139.98/19.46 | | | | | | | | | | | | (601) pv12 = n1 % 139.98/19.46 | | | | | | | | | | | | % 139.98/19.46 | | | | | | | | | | | | REF_CLOSE: (22), (591), (601), (irreflexivity_gt) are % 139.98/19.46 | | | | | | | | | | | | inconsistent by sub-proof #13. % 139.98/19.46 | | | | | | | | | | | | % 139.98/19.46 | | | | | | | | | | | Case 2: % 139.98/19.46 | | | | | | | | | | | | % 139.98/19.46 | | | | | | | | | | | | (602) ~ (pv12 = n1) % 139.98/19.46 | | | | | | | | | | | | % 139.98/19.46 | | | | | | | | | | | | BETA: splitting (600) gives: % 139.98/19.46 | | | | | | | | | | | | % 139.98/19.46 | | | | | | | | | | | | Case 1: % 139.98/19.46 | | | | | | | | | | | | | % 139.98/19.46 | | | | | | | | | | | | | (603) pv12 = n0 % 139.98/19.46 | | | | | | | | | | | | | % 139.98/19.46 | | | | | | | | | | | | | REDUCE: (175), (603) imply: % 139.98/19.46 | | | | | | | | | | | | | (604) $false % 139.98/19.46 | | | | | | | | | | | | | % 139.98/19.46 | | | | | | | | | | | | | CLOSE: (604) is inconsistent. % 139.98/19.46 | | | | | | | | | | | | | % 139.98/19.46 | | | | | | | | | | | | Case 2: % 139.98/19.46 | | | | | | | | | | | | | % 139.98/19.46 | | | | | | | | | | | | | (605) pv12 = n2 | pv12 = n1 % 139.98/19.46 | | | | | | | | | | | | | % 139.98/19.46 | | | | | | | | | | | | | BETA: splitting (605) gives: % 139.98/19.46 | | | | | | | | | | | | | % 139.98/19.46 | | | | | | | | | | | | | Case 1: % 139.98/19.46 | | | | | | | | | | | | | | % 139.98/19.46 | | | | | | | | | | | | | | (606) pv12 = n1 % 139.98/19.46 | | | | | | | | | | | | | | % 139.98/19.46 | | | | | | | | | | | | | | REDUCE: (602), (606) imply: % 139.98/19.46 | | | | | | | | | | | | | | (607) $false % 139.98/19.46 | | | | | | | | | | | | | | % 139.98/19.46 | | | | | | | | | | | | | | CLOSE: (607) is inconsistent. % 139.98/19.46 | | | | | | | | | | | | | | % 139.98/19.46 | | | | | | | | | | | | | Case 2: % 139.98/19.46 | | | | | | | | | | | | | | % 139.98/19.46 | | | | | | | | | | | | | | (608) pv12 = n2 % 139.98/19.46 | | | | | | | | | | | | | | % 139.98/19.46 | | | | | | | | | | | | | | REDUCE: (62), (608) imply: % 139.98/19.46 | | | | | | | | | | | | | | (609) minus(n2, n1) = all_71_25 % 139.98/19.46 | | | | | | | | | | | | | | % 139.98/19.46 | | | | | | | | | | | | | | REDUCE: (125), (608) imply: % 139.98/19.46 | | | | | | | | | | | | | | (610) succ(all_71_25) = n2 % 139.98/19.46 | | | | | | | | | | | | | | % 139.98/19.46 | | | | | | | | | | | | | | REDUCE: (118), (608) imply: % 139.98/19.46 | | | | | | | | | | | | | | (611) pred(n2) = all_71_25 % 139.98/19.46 | | | | | | | | | | | | | | % 139.98/19.46 | | | | | | | | | | | | | | GROUND_INST: instantiating (24) with n1, all_71_25, n2, % 139.98/19.46 | | | | | | | | | | | | | | simplifying with (107), (611) gives: % 139.98/19.46 | | | | | | | | | | | | | | (612) all_71_25 = n1 % 139.98/19.46 | | | | | | | | | | | | | | % 139.98/19.46 | | | | | | | | | | | | | | REDUCE: (609), (612) imply: % 139.98/19.46 | | | | | | | | | | | | | | (613) minus(n2, n1) = n1 % 139.98/19.46 | | | | | | | | | | | | | | % 139.98/19.46 | | | | | | | | | | | | | | REDUCE: (153), (612) imply: % 139.98/19.46 | | | | | | | | | | | | | | (614) leq(n0, n1) % 139.98/19.46 | | | | | | | | | | | | | | % 139.98/19.46 | | | | | | | | | | | | | | BETA: splitting (596) gives: % 139.98/19.46 | | | | | | | | | | | | | | % 139.98/19.46 | | | | | | | | | | | | | | Case 1: % 139.98/19.46 | | | | | | | | | | | | | | | % 139.98/19.46 | | | | | | | | | | | | | | | (615) gt(all_71_23, n1) % 139.98/19.46 | | | | | | | | | | | | | | | % 139.98/19.46 | | | | | | | | | | | | | | | BETA: splitting (597) gives: % 139.98/19.46 | | | | | | | | | | | | | | | % 139.98/19.46 | | | | | | | | | | | | | | | Case 1: % 139.98/19.46 | | | | | | | | | | | | | | | | % 139.98/19.46 | | | | | | | | | | | | | | | | (616) gt(pv10, n2) % 139.98/19.46 | | | | | | | | | | | | | | | | % 139.98/19.46 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with n2, pv10, all_71_23, % 139.98/19.46 | | | | | | | | | | | | | | | | simplifying with (21), (91), (115), (616) gives: % 139.98/19.46 | | | | | | | | | | | | | | | | (617) leq(n2, all_71_23) % 139.98/19.46 | | | | | | | | | | | | | | | | % 139.98/19.46 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with n2, all_71_23, n3, pv10, % 139.98/19.46 | | | | | | | | | | | | | | | | simplifying with (90), (91), (114), (124), (617) % 139.98/19.46 | | | | | | | | | | | | | | | | gives: % 139.98/19.46 | | | | | | | | | | | | | | | | (618) leq(n3, pv10) % 139.98/19.46 | | | | | | | | | | | | | | | | % 139.98/19.46 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with n2, all_71_23, % 139.98/19.46 | | | | | | | | | | | | | | | | simplifying with (91), (114), (617) gives: % 139.98/19.46 | | | | | | | | | | | | | | | | (619) all_71_23 = n2 | gt(all_71_23, n2) % 139.98/19.46 | | | | | | | | | | | | | | | | % 139.98/19.46 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with n3, pv10, simplifying % 139.98/19.46 | | | | | | | | | | | | | | | | with (21), (98), (618) gives: % 139.98/19.46 | | | | | | | | | | | | | | | | (620) pv10 = n3 | gt(pv10, n3) % 139.98/19.46 | | | | | | | | | | | | | | | | % 139.98/19.46 | | | | | | | | | | | | | | | | BETA: splitting (619) gives: % 139.98/19.46 | | | | | | | | | | | | | | | | % 139.98/19.46 | | | | | | | | | | | | | | | | Case 1: % 139.98/19.46 | | | | | | | | | | | | | | | | | % 139.98/19.46 | | | | | | | | | | | | | | | | | (621) gt(all_71_23, n2) % 139.98/19.46 | | | | | | | | | | | | | | | | | % 139.98/19.46 | | | | | | | | | | | | | | | | | BETA: splitting (620) gives: % 139.98/19.46 | | | | | | | | | | | | | | | | | % 139.98/19.46 | | | | | | | | | | | | | | | | | Case 1: % 139.98/19.46 | | | | | | | | | | | | | | | | | | % 139.98/19.46 | | | | | | | | | | | | | | | | | | (622) gt(pv10, n3) % 139.98/19.46 | | | | | | | | | | | | | | | | | | % 139.98/19.46 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with n3, pv10, all_71_23, % 139.98/19.46 | | | | | | | | | | | | | | | | | | simplifying with (21), (98), (115), (622) gives: % 139.98/19.46 | | | | | | | | | | | | | | | | | | (623) leq(n3, all_71_23) % 139.98/19.46 | | | | | | | | | | | | | | | | | | % 139.98/19.46 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with n3, all_71_23, n4, pv10, % 139.98/19.46 | | | | | | | | | | | | | | | | | | simplifying with (97), (98), (114), (124), (623) % 139.98/19.46 | | | | | | | | | | | | | | | | | | gives: % 139.98/19.46 | | | | | | | | | | | | | | | | | | (624) leq(n4, pv10) % 139.98/19.46 | | | | | | | | | | | | | | | | | | % 139.98/19.46 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with n4, pv10, simplifying % 139.98/19.46 | | | | | | | | | | | | | | | | | | with (21), (101), (624) gives: % 139.98/19.46 | | | | | | | | | | | | | | | | | | (625) pv10 = n4 | gt(pv10, n4) % 139.98/19.46 | | | | | | | | | | | | | | | | | | % 139.98/19.46 | | | | | | | | | | | | | | | | | | BETA: splitting (625) gives: % 139.98/19.46 | | | | | | | | | | | | | | | | | | % 139.98/19.46 | | | | | | | | | | | | | | | | | | Case 1: % 139.98/19.46 | | | | | | | | | | | | | | | | | | | % 139.98/19.46 | | | | | | | | | | | | | | | | | | | % 139.98/19.46 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (65) with n0, all_71_11, all_71_9, % 139.98/19.46 | | | | | | | | | | | | | | | | | | | all_71_8, all_71_7, all_71_6, all_71_5, all_71_4, % 139.98/19.47 | | | | | | | | | | | | | | | | | | | all_71_3, all_71_2, all_71_1, all_71_0, % 139.98/19.47 | | | | | | | | | | | | | | | | | | | simplifying with (19), (59), (139), (141), (142), % 139.98/19.47 | | | | | | | | | | | | | | | | | | | (143), (144), (145), (146), (147), (585), (587) % 139.98/19.47 | | | | | | | | | | | | | | | | | | | gives: % 139.98/19.47 | | | | | | | | | | | | | | | | | | | (626) ~ (sum(n0, all_71_26, all_71_2) = all_71_1) | ~ % 139.98/19.47 | | | | | | | | | | | | | | | | | | | leq(n0, all_71_25) | (a_select3(q, pv10, n0) = % 139.98/19.47 | | | | | | | | | | | | | | | | | | | all_71_0 & $i(all_71_0)) % 139.98/19.47 | | | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | | | | BETA: splitting (626) gives: % 139.98/19.47 | | | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | | | | Case 1: % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | (627) ~ (sum(n0, all_71_26, all_71_2) = all_71_1) % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | REDUCE: (119), (627) imply: % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | (628) ~ (sum(n0, n4, all_71_2) = all_71_1) % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (148), (628) imply: % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | (629) $false % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | CLOSE: (629) is inconsistent. % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | | | | Case 2: % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | (630) ~ leq(n0, all_71_25) | (a_select3(q, pv10, n0) = % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | all_71_0 & $i(all_71_0)) % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | BETA: splitting (630) gives: % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | Case 1: % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | | (631) ~ leq(n0, all_71_25) % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | | REDUCE: (612), (631) imply: % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | | (632) ~ leq(n0, n1) % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (614), (632) imply: % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | | (633) $false % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | | CLOSE: (633) is inconsistent. % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | Case 2: % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | | (634) a_select3(q, pv10, n0) = all_71_0 & $i(all_71_0) % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (27), (134), (586), (634) are inconsistent by % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | | sub-proof #6. % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | End of split % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | | | | End of split % 139.98/19.47 | | | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | | | Case 2: % 139.98/19.47 | | | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | | | | (635) pv10 = n4 % 139.98/19.47 | | | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | | | | REDUCE: (586), (635) imply: % 139.98/19.47 | | | | | | | | | | | | | | | | | | | (636) a_select3(q, n4, n0) = all_71_10 % 139.98/19.47 | | | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | | | | BETA: splitting (600) gives: % 139.98/19.47 | | | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | | | | Case 1: % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | (637) pv12 = n0 % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | REDUCE: (175), (637) imply: % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | (638) $false % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | CLOSE: (638) is inconsistent. % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | | | | Case 2: % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | BETA: splitting (605) gives: % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | Case 1: % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | | (639) pv12 = n1 % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | | REDUCE: (602), (639) imply: % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | | (640) $false % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | | CLOSE: (640) is inconsistent. % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | Case 2: % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (65) with n0, all_71_11, all_71_9, % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | | all_71_8, all_71_7, all_71_6, all_71_5, all_71_4, % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | | all_71_3, all_71_2, all_71_1, all_71_0, % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | | simplifying with (19), (59), (139), (141), (142), % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | | (143), (144), (145), (146), (147), (585), (587) % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | | gives: % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | | (641) ~ (sum(n0, all_71_26, all_71_2) = all_71_1) | ~ % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | | leq(n0, all_71_25) | (a_select3(q, pv10, n0) = % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | | all_71_0 & $i(all_71_0)) % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (641) gives: % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | | Case 1: % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | | | (642) ~ (sum(n0, all_71_26, all_71_2) = all_71_1) % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (119), (642) imply: % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | | | (643) ~ (sum(n0, n4, all_71_2) = all_71_1) % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (148), (643) imply: % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | | | (644) $false % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (644) is inconsistent. % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | | Case 2: % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | | | (645) ~ leq(n0, all_71_25) | (a_select3(q, pv10, n0) = % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | | | all_71_0 & $i(all_71_0)) % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (645) gives: % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | | | | (646) ~ leq(n0, all_71_25) % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (612), (646) imply: % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | | | | (647) ~ leq(n0, n1) % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (614), (647) imply: % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | | | | (648) $false % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (648) is inconsistent. % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | | | | (649) a_select3(q, pv10, n0) = all_71_0 & $i(all_71_0) % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (649) implies: % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | | | | (650) a_select3(q, pv10, n0) = all_71_0 % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (635), (650) imply: % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | | | | (651) a_select3(q, n4, n0) = all_71_0 % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (27) with all_71_10, all_71_0, n0, % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | | | | n4, q, simplifying with (636), (651) gives: % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | | | | (652) all_71_0 = all_71_10 % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (652) imply: % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | | | | (653) $false % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (653) is inconsistent. % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | | | End of split % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | | End of split % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | End of split % 139.98/19.47 | | | | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | | | | End of split % 139.98/19.47 | | | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | | | End of split % 139.98/19.47 | | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | | Case 2: % 139.98/19.47 | | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | | | (654) pv10 = n3 % 139.98/19.47 | | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | | | REF_CLOSE: (24), (26), (61), (108), (114), (115), (621), % 139.98/19.47 | | | | | | | | | | | | | | | | | | (654), (irreflexivity_gt) are inconsistent by % 139.98/19.47 | | | | | | | | | | | | | | | | | | sub-proof #9. % 139.98/19.47 | | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | | End of split % 139.98/19.47 | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | Case 2: % 139.98/19.47 | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | | (655) all_71_23 = n2 % 139.98/19.47 | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | | REDUCE: (124), (655) imply: % 139.98/19.47 | | | | | | | | | | | | | | | | | (656) succ(n2) = pv10 % 139.98/19.47 | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (25) with n3, pv10, n2, simplifying % 139.98/19.47 | | | | | | | | | | | | | | | | | with (90), (656) gives: % 139.98/19.47 | | | | | | | | | | | | | | | | | (657) pv10 = n3 % 139.98/19.47 | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | | REDUCE: (586), (657) imply: % 139.98/19.47 | | | | | | | | | | | | | | | | | (658) a_select3(q, n3, n0) = all_71_10 % 139.98/19.47 | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (65) with n0, all_71_11, all_71_9, % 139.98/19.47 | | | | | | | | | | | | | | | | | all_71_8, all_71_7, all_71_6, all_71_5, all_71_4, % 139.98/19.47 | | | | | | | | | | | | | | | | | all_71_3, all_71_2, all_71_1, all_71_0, % 139.98/19.47 | | | | | | | | | | | | | | | | | simplifying with (19), (59), (139), (141), (142), % 139.98/19.47 | | | | | | | | | | | | | | | | | (143), (144), (145), (146), (147), (585), (587) % 139.98/19.47 | | | | | | | | | | | | | | | | | gives: % 139.98/19.47 | | | | | | | | | | | | | | | | | (659) ~ (sum(n0, all_71_26, all_71_2) = all_71_1) | ~ % 139.98/19.47 | | | | | | | | | | | | | | | | | leq(n0, all_71_25) | (a_select3(q, pv10, n0) = % 139.98/19.47 | | | | | | | | | | | | | | | | | all_71_0 & $i(all_71_0)) % 139.98/19.47 | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | | BETA: splitting (659) gives: % 139.98/19.47 | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | | Case 1: % 139.98/19.47 | | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | | | (660) ~ (sum(n0, all_71_26, all_71_2) = all_71_1) % 139.98/19.47 | | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | | | REDUCE: (119), (660) imply: % 139.98/19.47 | | | | | | | | | | | | | | | | | | (661) ~ (sum(n0, n4, all_71_2) = all_71_1) % 139.98/19.47 | | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | | | PRED_UNIFY: (148), (661) imply: % 139.98/19.47 | | | | | | | | | | | | | | | | | | (662) $false % 139.98/19.47 | | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | | | CLOSE: (662) is inconsistent. % 139.98/19.47 | | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | | Case 2: % 139.98/19.47 | | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | | | (663) ~ leq(n0, all_71_25) | (a_select3(q, pv10, n0) = % 139.98/19.47 | | | | | | | | | | | | | | | | | | all_71_0 & $i(all_71_0)) % 139.98/19.47 | | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | | | BETA: splitting (663) gives: % 139.98/19.47 | | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | | | Case 1: % 139.98/19.47 | | | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | | | | (664) ~ leq(n0, all_71_25) % 139.98/19.47 | | | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | | | | REDUCE: (612), (664) imply: % 139.98/19.47 | | | | | | | | | | | | | | | | | | | (665) ~ leq(n0, n1) % 139.98/19.47 | | | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (614), (665) imply: % 139.98/19.47 | | | | | | | | | | | | | | | | | | | (666) $false % 139.98/19.47 | | | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | | | | CLOSE: (666) is inconsistent. % 139.98/19.47 | | | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | | | Case 2: % 139.98/19.47 | | | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | | | | (667) a_select3(q, pv10, n0) = all_71_0 & $i(all_71_0) % 139.98/19.47 | | | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | | | | ALPHA: (667) implies: % 139.98/19.47 | | | | | | | | | | | | | | | | | | | (668) a_select3(q, pv10, n0) = all_71_0 % 139.98/19.47 | | | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | | | | REDUCE: (657), (668) imply: % 139.98/19.47 | | | | | | | | | | | | | | | | | | | (669) a_select3(q, n3, n0) = all_71_0 % 139.98/19.47 | | | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (27) with all_71_10, all_71_0, n0, % 139.98/19.47 | | | | | | | | | | | | | | | | | | | n3, q, simplifying with (658), (669) gives: % 139.98/19.47 | | | | | | | | | | | | | | | | | | | (670) all_71_0 = all_71_10 % 139.98/19.47 | | | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | | | | REDUCE: (134), (670) imply: % 139.98/19.47 | | | | | | | | | | | | | | | | | | | (671) $false % 139.98/19.47 | | | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | | | | CLOSE: (671) is inconsistent. % 139.98/19.47 | | | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | | | End of split % 139.98/19.47 | | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | | End of split % 139.98/19.47 | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | End of split % 139.98/19.47 | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | Case 2: % 139.98/19.47 | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | (672) pv10 = n2 % 139.98/19.47 | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | REDUCE: (61), (672) imply: % 139.98/19.47 | | | | | | | | | | | | | | | | (673) minus(n2, n1) = all_71_23 % 139.98/19.47 | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (26) with n1, all_71_23, n1, n2, % 139.98/19.47 | | | | | | | | | | | | | | | | simplifying with (613), (673) gives: % 139.98/19.47 | | | | | | | | | | | | | | | | (674) all_71_23 = n1 % 139.98/19.47 | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | REF_CLOSE: (114), (615), (674), (irreflexivity_gt) are % 139.98/19.47 | | | | | | | | | | | | | | | | inconsistent by sub-proof #19. % 139.98/19.47 | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | End of split % 139.98/19.47 | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | Case 2: % 139.98/19.47 | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | (675) all_71_23 = n1 % 139.98/19.47 | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | REDUCE: (124), (675) imply: % 139.98/19.47 | | | | | | | | | | | | | | | (676) succ(n1) = pv10 % 139.98/19.47 | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | GROUND_INST: instantiating (25) with n2, pv10, n1, simplifying % 139.98/19.47 | | | | | | | | | | | | | | | with (79), (676) gives: % 139.98/19.47 | | | | | | | | | | | | | | | (677) pv10 = n2 % 139.98/19.47 | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | REDUCE: (586), (677) imply: % 139.98/19.47 | | | | | | | | | | | | | | | (678) a_select3(q, n2, n0) = all_71_10 % 139.98/19.47 | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | GROUND_INST: instantiating (65) with n0, all_71_11, all_71_9, % 139.98/19.47 | | | | | | | | | | | | | | | all_71_8, all_71_7, all_71_6, all_71_5, all_71_4, % 139.98/19.47 | | | | | | | | | | | | | | | all_71_3, all_71_2, all_71_1, all_71_0, % 139.98/19.47 | | | | | | | | | | | | | | | simplifying with (19), (59), (139), (141), (142), % 139.98/19.47 | | | | | | | | | | | | | | | (143), (144), (145), (146), (147), (585), (587) % 139.98/19.47 | | | | | | | | | | | | | | | gives: % 139.98/19.47 | | | | | | | | | | | | | | | (679) ~ (sum(n0, all_71_26, all_71_2) = all_71_1) | ~ % 139.98/19.47 | | | | | | | | | | | | | | | leq(n0, all_71_25) | (a_select3(q, pv10, n0) = % 139.98/19.47 | | | | | | | | | | | | | | | all_71_0 & $i(all_71_0)) % 139.98/19.47 | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | BETA: splitting (679) gives: % 139.98/19.47 | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | Case 1: % 139.98/19.47 | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | (680) ~ (sum(n0, all_71_26, all_71_2) = all_71_1) % 139.98/19.47 | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | REDUCE: (119), (680) imply: % 139.98/19.47 | | | | | | | | | | | | | | | | (681) ~ (sum(n0, n4, all_71_2) = all_71_1) % 139.98/19.47 | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | PRED_UNIFY: (148), (681) imply: % 139.98/19.47 | | | | | | | | | | | | | | | | (682) $false % 139.98/19.47 | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | CLOSE: (682) is inconsistent. % 139.98/19.47 | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | Case 2: % 139.98/19.47 | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | (683) ~ leq(n0, all_71_25) | (a_select3(q, pv10, n0) = % 139.98/19.47 | | | | | | | | | | | | | | | | all_71_0 & $i(all_71_0)) % 139.98/19.47 | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | BETA: splitting (683) gives: % 139.98/19.47 | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | Case 1: % 139.98/19.47 | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | | (684) ~ leq(n0, all_71_25) % 139.98/19.47 | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | | REDUCE: (612), (684) imply: % 139.98/19.47 | | | | | | | | | | | | | | | | | (685) ~ leq(n0, n1) % 139.98/19.47 | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | | PRED_UNIFY: (614), (685) imply: % 139.98/19.47 | | | | | | | | | | | | | | | | | (686) $false % 139.98/19.47 | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | | CLOSE: (686) is inconsistent. % 139.98/19.47 | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | Case 2: % 139.98/19.47 | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | | (687) a_select3(q, pv10, n0) = all_71_0 & $i(all_71_0) % 139.98/19.47 | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | | ALPHA: (687) implies: % 139.98/19.47 | | | | | | | | | | | | | | | | | (688) a_select3(q, pv10, n0) = all_71_0 % 139.98/19.47 | | | | | | | | | | | | | | | | | % 139.98/19.47 | | | | | | | | | | | | | | | | | REDUCE: (677), (688) imply: % 139.98/19.47 | | | | | | | | | | | | | | | | | (689) a_select3(q, n2, n0) = all_71_0 % 139.98/19.47 | | | | | | | | | | | | | | | | | % 139.98/19.48 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (27) with all_71_10, all_71_0, n0, % 139.98/19.48 | | | | | | | | | | | | | | | | | n2, q, simplifying with (678), (689) gives: % 139.98/19.48 | | | | | | | | | | | | | | | | | (690) all_71_0 = all_71_10 % 139.98/19.48 | | | | | | | | | | | | | | | | | % 139.98/19.48 | | | | | | | | | | | | | | | | | REDUCE: (134), (690) imply: % 139.98/19.48 | | | | | | | | | | | | | | | | | (691) $false % 139.98/19.48 | | | | | | | | | | | | | | | | | % 139.98/19.48 | | | | | | | | | | | | | | | | | CLOSE: (691) is inconsistent. % 139.98/19.48 | | | | | | | | | | | | | | | | | % 139.98/19.48 | | | | | | | | | | | | | | | | End of split % 139.98/19.48 | | | | | | | | | | | | | | | | % 139.98/19.48 | | | | | | | | | | | | | | | End of split % 139.98/19.48 | | | | | | | | | | | | | | | % 139.98/19.48 | | | | | | | | | | | | | | End of split % 139.98/19.48 | | | | | | | | | | | | | | % 139.98/19.48 | | | | | | | | | | | | | End of split % 139.98/19.48 | | | | | | | | | | | | | % 139.98/19.48 | | | | | | | | | | | | End of split % 139.98/19.48 | | | | | | | | | | | | % 139.98/19.48 | | | | | | | | | | | End of split % 139.98/19.48 | | | | | | | | | | | % 139.98/19.48 | | | | | | | | | | Case 2: % 139.98/19.48 | | | | | | | | | | | % 139.98/19.48 | | | | | | | | | | | (692) pv12 = n3 % 139.98/19.48 | | | | | | | | | | | % 139.98/19.48 | | | | | | | | | | | REDUCE: (118), (692) imply: % 139.98/19.48 | | | | | | | | | | | (693) pred(n3) = all_71_25 % 139.98/19.48 | | | | | | | | | | | % 139.98/19.48 | | | | | | | | | | | GROUND_INST: instantiating (24) with n2, all_71_25, n3, % 139.98/19.48 | | | | | | | | | | | simplifying with (108), (693) gives: % 139.98/19.48 | | | | | | | | | | | (694) all_71_25 = n2 % 139.98/19.48 | | | | | | | | | | | % 139.98/19.48 | | | | | | | | | | | REDUCE: (153), (694) imply: % 139.98/19.48 | | | | | | | | | | | (695) leq(n0, n2) % 139.98/19.48 | | | | | | | | | | | % 139.98/19.48 | | | | | | | | | | | GROUND_INST: instantiating (65) with n0, all_71_11, all_71_9, % 139.98/19.48 | | | | | | | | | | | all_71_8, all_71_7, all_71_6, all_71_5, all_71_4, % 139.98/19.48 | | | | | | | | | | | all_71_3, all_71_2, all_71_1, all_71_0, % 139.98/19.48 | | | | | | | | | | | simplifying with (19), (59), (139), (141), (142), % 139.98/19.48 | | | | | | | | | | | (143), (144), (145), (146), (147), (585), (587) % 139.98/19.48 | | | | | | | | | | | gives: % 139.98/19.48 | | | | | | | | | | | (696) ~ (sum(n0, all_71_26, all_71_2) = all_71_1) | ~ % 139.98/19.48 | | | | | | | | | | | leq(n0, all_71_25) | (a_select3(q, pv10, n0) = % 139.98/19.48 | | | | | | | | | | | all_71_0 & $i(all_71_0)) % 139.98/19.48 | | | | | | | | | | | % 140.16/19.48 | | | | | | | | | | | BETA: splitting (696) gives: % 140.16/19.48 | | | | | | | | | | | % 140.16/19.48 | | | | | | | | | | | Case 1: % 140.16/19.48 | | | | | | | | | | | | % 140.16/19.48 | | | | | | | | | | | | (697) ~ (sum(n0, all_71_26, all_71_2) = all_71_1) % 140.16/19.48 | | | | | | | | | | | | % 140.16/19.48 | | | | | | | | | | | | REDUCE: (119), (697) imply: % 140.16/19.48 | | | | | | | | | | | | (698) ~ (sum(n0, n4, all_71_2) = all_71_1) % 140.16/19.48 | | | | | | | | | | | | % 140.16/19.48 | | | | | | | | | | | | PRED_UNIFY: (148), (698) imply: % 140.16/19.48 | | | | | | | | | | | | (699) $false % 140.16/19.48 | | | | | | | | | | | | % 140.16/19.48 | | | | | | | | | | | | CLOSE: (699) is inconsistent. % 140.16/19.48 | | | | | | | | | | | | % 140.16/19.48 | | | | | | | | | | | Case 2: % 140.16/19.48 | | | | | | | | | | | | % 140.16/19.48 | | | | | | | | | | | | (700) ~ leq(n0, all_71_25) | (a_select3(q, pv10, n0) = % 140.16/19.48 | | | | | | | | | | | | all_71_0 & $i(all_71_0)) % 140.16/19.48 | | | | | | | | | | | | % 140.16/19.48 | | | | | | | | | | | | BETA: splitting (700) gives: % 140.16/19.48 | | | | | | | | | | | | % 140.16/19.48 | | | | | | | | | | | | Case 1: % 140.16/19.48 | | | | | | | | | | | | | % 140.16/19.48 | | | | | | | | | | | | | (701) ~ leq(n0, all_71_25) % 140.16/19.48 | | | | | | | | | | | | | % 140.16/19.48 | | | | | | | | | | | | | REDUCE: (694), (701) imply: % 140.16/19.48 | | | | | | | | | | | | | (702) ~ leq(n0, n2) % 140.16/19.48 | | | | | | | | | | | | | % 140.16/19.48 | | | | | | | | | | | | | PRED_UNIFY: (695), (702) imply: % 140.16/19.48 | | | | | | | | | | | | | (703) $false % 140.16/19.48 | | | | | | | | | | | | | % 140.16/19.48 | | | | | | | | | | | | | CLOSE: (703) is inconsistent. % 140.16/19.48 | | | | | | | | | | | | | % 140.16/19.48 | | | | | | | | | | | | Case 2: % 140.16/19.48 | | | | | | | | | | | | | % 140.16/19.48 | | | | | | | | | | | | | (704) a_select3(q, pv10, n0) = all_71_0 & $i(all_71_0) % 140.16/19.48 | | | | | | | | | | | | | % 140.16/19.48 | | | | | | | | | | | | | ALPHA: (704) implies: % 140.16/19.48 | | | | | | | | | | | | | (705) a_select3(q, pv10, n0) = all_71_0 % 140.16/19.48 | | | | | | | | | | | | | % 140.16/19.48 | | | | | | | | | | | | | GROUND_INST: instantiating (27) with all_71_10, all_71_0, n0, % 140.16/19.48 | | | | | | | | | | | | | pv10, q, simplifying with (586), (705) gives: % 140.16/19.48 | | | | | | | | | | | | | (706) all_71_0 = all_71_10 % 140.16/19.48 | | | | | | | | | | | | | % 140.16/19.48 | | | | | | | | | | | | | REDUCE: (134), (706) imply: % 140.16/19.48 | | | | | | | | | | | | | (707) $false % 140.16/19.48 | | | | | | | | | | | | | % 140.16/19.48 | | | | | | | | | | | | | CLOSE: (707) is inconsistent. % 140.16/19.48 | | | | | | | | | | | | | % 140.16/19.48 | | | | | | | | | | | | End of split % 140.16/19.48 | | | | | | | | | | | | % 140.16/19.48 | | | | | | | | | | | End of split % 140.16/19.48 | | | | | | | | | | | % 140.16/19.48 | | | | | | | | | | End of split % 140.16/19.48 | | | | | | | | | | % 140.16/19.48 | | | | | | | | | Case 2: % 140.16/19.48 | | | | | | | | | | % 140.16/19.48 | | | | | | | | | | (708) pv10 = n1 % 140.16/19.48 | | | | | | | | | | % 140.16/19.48 | | | | | | | | | | REDUCE: (115), (708) imply: % 140.16/19.48 | | | | | | | | | | (709) pred(n1) = all_71_23 % 140.16/19.48 | | | | | | | | | | % 140.16/19.48 | | | | | | | | | | GROUND_INST: instantiating (24) with n0, all_71_23, n1, % 140.16/19.48 | | | | | | | | | | simplifying with (105), (709) gives: % 140.16/19.48 | | | | | | | | | | (710) all_71_23 = n0 % 140.16/19.48 | | | | | | | | | | % 140.16/19.48 | | | | | | | | | | REDUCE: (592), (710) imply: % 140.16/19.48 | | | | | | | | | | (711) gt(n0, n0) % 140.16/19.48 | | | | | | | | | | % 140.16/19.48 | | | | | | | | | | PRED_UNIFY: (588), (711) imply: % 140.16/19.48 | | | | | | | | | | (712) $false % 140.16/19.48 | | | | | | | | | | % 140.16/19.48 | | | | | | | | | | CLOSE: (712) is inconsistent. % 140.16/19.48 | | | | | | | | | | % 140.16/19.48 | | | | | | | | | End of split % 140.16/19.48 | | | | | | | | | % 140.16/19.48 | | | | | | | | Case 2: % 140.16/19.48 | | | | | | | | | % 140.16/19.48 | | | | | | | | | (713) all_71_23 = n0 % 140.16/19.48 | | | | | | | | | % 140.16/19.48 | | | | | | | | | REDUCE: (124), (713) imply: % 140.16/19.48 | | | | | | | | | (714) succ(n0) = pv10 % 140.16/19.48 | | | | | | | | | % 140.16/19.48 | | | | | | | | | GROUND_INST: instantiating (25) with n1, pv10, n0, simplifying % 140.16/19.48 | | | | | | | | | with (16), (714) gives: % 140.16/19.48 | | | | | | | | | (715) pv10 = n1 % 140.16/19.48 | | | | | | | | | % 140.16/19.48 | | | | | | | | | REDUCE: (586), (715) imply: % 140.16/19.48 | | | | | | | | | (716) a_select3(q, n1, n0) = all_71_10 % 140.16/19.48 | | | | | | | | | % 140.16/19.48 | | | | | | | | | BETA: splitting (171) gives: % 140.16/19.48 | | | | | | | | | % 140.16/19.48 | | | | | | | | | Case 1: % 140.16/19.48 | | | | | | | | | | % 140.16/19.48 | | | | | | | | | | (717) gt(n3, pv12) % 140.16/19.48 | | | | | | | | | | % 140.16/19.48 | | | | | | | | | | GROUND_INST: instantiating (1) with pv12, n3, n2, simplifying % 140.16/19.48 | | | | | | | | | | with (22), (98), (108), (717) gives: % 140.16/19.48 | | | | | | | | | | (718) leq(pv12, n2) % 140.16/19.48 | | | | | | | | | | % 140.16/19.48 | | | | | | | | | | GROUND_INST: instantiating (7) with all_71_25, n1, pv12, n2, % 140.16/19.48 | | | | | | | | | | simplifying with (79), (80), (117), (125), (718) % 140.16/19.48 | | | | | | | | | | gives: % 140.16/19.48 | | | | | | | | | | (719) leq(all_71_25, n1) % 140.16/19.48 | | | | | | | | | | % 140.16/19.48 | | | | | | | | | | GROUND_INST: instantiating (11) with all_71_25, simplifying % 140.16/19.48 | | | | | | | | | | with (117), (153), (719) gives: % 140.16/19.48 | | | | | | | | | | (720) all_71_25 = n1 | all_71_25 = n0 % 140.16/19.48 | | | | | | | | | | % 140.16/19.48 | | | | | | | | | | BETA: splitting (720) gives: % 140.16/19.48 | | | | | | | | | | % 140.16/19.48 | | | | | | | | | | Case 1: % 140.16/19.48 | | | | | | | | | | | % 140.16/19.48 | | | | | | | | | | | (721) all_71_25 = n0 % 140.16/19.48 | | | | | | | | | | | % 140.16/19.48 | | | | | | | | | | | GROUND_INST: instantiating (65) with n0, all_71_11, all_71_9, % 140.16/19.48 | | | | | | | | | | | all_71_8, all_71_7, all_71_6, all_71_5, all_71_4, % 140.16/19.48 | | | | | | | | | | | all_71_3, all_71_2, all_71_1, all_71_0, % 140.16/19.48 | | | | | | | | | | | simplifying with (19), (59), (139), (141), (142), % 140.16/19.48 | | | | | | | | | | | (143), (144), (145), (146), (147), (585), (587) % 140.16/19.48 | | | | | | | | | | | gives: % 140.16/19.48 | | | | | | | | | | | (722) ~ (sum(n0, all_71_26, all_71_2) = all_71_1) | ~ % 140.16/19.48 | | | | | | | | | | | leq(n0, all_71_25) | (a_select3(q, pv10, n0) = % 140.16/19.48 | | | | | | | | | | | all_71_0 & $i(all_71_0)) % 140.16/19.48 | | | | | | | | | | | % 140.16/19.48 | | | | | | | | | | | BETA: splitting (722) gives: % 140.16/19.48 | | | | | | | | | | | % 140.16/19.48 | | | | | | | | | | | Case 1: % 140.16/19.48 | | | | | | | | | | | | % 140.16/19.48 | | | | | | | | | | | | (723) ~ (sum(n0, all_71_26, all_71_2) = all_71_1) % 140.16/19.48 | | | | | | | | | | | | % 140.16/19.48 | | | | | | | | | | | | REDUCE: (119), (723) imply: % 140.16/19.48 | | | | | | | | | | | | (724) ~ (sum(n0, n4, all_71_2) = all_71_1) % 140.16/19.48 | | | | | | | | | | | | % 140.16/19.48 | | | | | | | | | | | | PRED_UNIFY: (148), (724) imply: % 140.16/19.48 | | | | | | | | | | | | (725) $false % 140.16/19.48 | | | | | | | | | | | | % 140.16/19.48 | | | | | | | | | | | | CLOSE: (725) is inconsistent. % 140.16/19.48 | | | | | | | | | | | | % 140.16/19.48 | | | | | | | | | | | Case 2: % 140.16/19.48 | | | | | | | | | | | | % 140.16/19.48 | | | | | | | | | | | | (726) ~ leq(n0, all_71_25) | (a_select3(q, pv10, n0) = % 140.16/19.48 | | | | | | | | | | | | all_71_0 & $i(all_71_0)) % 140.16/19.48 | | | | | | | | | | | | % 140.16/19.48 | | | | | | | | | | | | BETA: splitting (726) gives: % 140.16/19.48 | | | | | | | | | | | | % 140.16/19.48 | | | | | | | | | | | | Case 1: % 140.16/19.48 | | | | | | | | | | | | | % 140.16/19.48 | | | | | | | | | | | | | (727) ~ leq(n0, all_71_25) % 140.16/19.48 | | | | | | | | | | | | | % 140.16/19.48 | | | | | | | | | | | | | REDUCE: (721), (727) imply: % 140.16/19.48 | | | | | | | | | | | | | (728) ~ leq(n0, n0) % 140.16/19.48 | | | | | | | | | | | | | % 140.16/19.48 | | | | | | | | | | | | | PRED_UNIFY: (587), (728) imply: % 140.16/19.48 | | | | | | | | | | | | | (729) $false % 140.16/19.48 | | | | | | | | | | | | | % 140.16/19.48 | | | | | | | | | | | | | CLOSE: (729) is inconsistent. % 140.16/19.48 | | | | | | | | | | | | | % 140.16/19.48 | | | | | | | | | | | | Case 2: % 140.16/19.48 | | | | | | | | | | | | | % 140.16/19.48 | | | | | | | | | | | | | (730) a_select3(q, pv10, n0) = all_71_0 & $i(all_71_0) % 140.16/19.48 | | | | | | | | | | | | | % 140.16/19.48 | | | | | | | | | | | | | ALPHA: (730) implies: % 140.16/19.48 | | | | | | | | | | | | | (731) a_select3(q, pv10, n0) = all_71_0 % 140.16/19.48 | | | | | | | | | | | | | % 140.16/19.48 | | | | | | | | | | | | | REDUCE: (715), (731) imply: % 140.16/19.48 | | | | | | | | | | | | | (732) a_select3(q, n1, n0) = all_71_0 % 140.16/19.48 | | | | | | | | | | | | | % 140.16/19.48 | | | | | | | | | | | | | GROUND_INST: instantiating (27) with all_71_10, all_71_0, n0, % 140.16/19.48 | | | | | | | | | | | | | n1, q, simplifying with (716), (732) gives: % 140.16/19.48 | | | | | | | | | | | | | (733) all_71_0 = all_71_10 % 140.16/19.48 | | | | | | | | | | | | | % 140.16/19.48 | | | | | | | | | | | | | REDUCE: (134), (733) imply: % 140.16/19.48 | | | | | | | | | | | | | (734) $false % 140.16/19.48 | | | | | | | | | | | | | % 140.16/19.48 | | | | | | | | | | | | | CLOSE: (734) is inconsistent. % 140.16/19.48 | | | | | | | | | | | | | % 140.16/19.48 | | | | | | | | | | | | End of split % 140.16/19.48 | | | | | | | | | | | | % 140.16/19.48 | | | | | | | | | | | End of split % 140.16/19.48 | | | | | | | | | | | % 140.16/19.48 | | | | | | | | | | Case 2: % 140.16/19.48 | | | | | | | | | | | % 140.16/19.48 | | | | | | | | | | | (735) all_71_25 = n1 % 140.16/19.48 | | | | | | | | | | | % 140.16/19.48 | | | | | | | | | | | REDUCE: (153), (735) imply: % 140.16/19.48 | | | | | | | | | | | (736) leq(n0, n1) % 140.16/19.48 | | | | | | | | | | | % 140.16/19.48 | | | | | | | | | | | GROUND_INST: instantiating (65) with n0, all_71_11, all_71_9, % 140.16/19.48 | | | | | | | | | | | all_71_8, all_71_7, all_71_6, all_71_5, all_71_4, % 140.16/19.48 | | | | | | | | | | | all_71_3, all_71_2, all_71_1, all_71_0, % 140.16/19.48 | | | | | | | | | | | simplifying with (19), (59), (139), (141), (142), % 140.16/19.48 | | | | | | | | | | | (143), (144), (145), (146), (147), (585), (587) % 140.16/19.48 | | | | | | | | | | | gives: % 140.16/19.48 | | | | | | | | | | | (737) ~ (sum(n0, all_71_26, all_71_2) = all_71_1) | ~ % 140.16/19.48 | | | | | | | | | | | leq(n0, all_71_25) | (a_select3(q, pv10, n0) = % 140.16/19.48 | | | | | | | | | | | all_71_0 & $i(all_71_0)) % 140.16/19.48 | | | | | | | | | | | % 140.16/19.48 | | | | | | | | | | | BETA: splitting (737) gives: % 140.16/19.48 | | | | | | | | | | | % 140.16/19.48 | | | | | | | | | | | Case 1: % 140.16/19.48 | | | | | | | | | | | | % 140.16/19.48 | | | | | | | | | | | | (738) ~ (sum(n0, all_71_26, all_71_2) = all_71_1) % 140.16/19.48 | | | | | | | | | | | | % 140.16/19.48 | | | | | | | | | | | | REDUCE: (119), (738) imply: % 140.16/19.48 | | | | | | | | | | | | (739) ~ (sum(n0, n4, all_71_2) = all_71_1) % 140.16/19.48 | | | | | | | | | | | | % 140.16/19.48 | | | | | | | | | | | | PRED_UNIFY: (148), (739) imply: % 140.16/19.48 | | | | | | | | | | | | (740) $false % 140.16/19.48 | | | | | | | | | | | | % 140.16/19.48 | | | | | | | | | | | | CLOSE: (740) is inconsistent. % 140.16/19.48 | | | | | | | | | | | | % 140.16/19.48 | | | | | | | | | | | Case 2: % 140.16/19.48 | | | | | | | | | | | | % 140.16/19.48 | | | | | | | | | | | | (741) ~ leq(n0, all_71_25) | (a_select3(q, pv10, n0) = % 140.16/19.48 | | | | | | | | | | | | all_71_0 & $i(all_71_0)) % 140.16/19.48 | | | | | | | | | | | | % 140.16/19.48 | | | | | | | | | | | | BETA: splitting (741) gives: % 140.16/19.48 | | | | | | | | | | | | % 140.16/19.48 | | | | | | | | | | | | Case 1: % 140.16/19.48 | | | | | | | | | | | | | % 140.16/19.48 | | | | | | | | | | | | | (742) ~ leq(n0, all_71_25) % 140.16/19.48 | | | | | | | | | | | | | % 140.16/19.48 | | | | | | | | | | | | | REDUCE: (735), (742) imply: % 140.16/19.48 | | | | | | | | | | | | | (743) ~ leq(n0, n1) % 140.16/19.48 | | | | | | | | | | | | | % 140.16/19.48 | | | | | | | | | | | | | PRED_UNIFY: (736), (743) imply: % 140.16/19.48 | | | | | | | | | | | | | (744) $false % 140.16/19.48 | | | | | | | | | | | | | % 140.16/19.48 | | | | | | | | | | | | | CLOSE: (744) is inconsistent. % 140.16/19.48 | | | | | | | | | | | | | % 140.16/19.48 | | | | | | | | | | | | Case 2: % 140.16/19.48 | | | | | | | | | | | | | % 140.16/19.48 | | | | | | | | | | | | | (745) a_select3(q, pv10, n0) = all_71_0 & $i(all_71_0) % 140.16/19.48 | | | | | | | | | | | | | % 140.16/19.48 | | | | | | | | | | | | | REF_CLOSE: (27), (134), (715), (716), (745) are inconsistent % 140.16/19.48 | | | | | | | | | | | | | by sub-proof #5. % 140.16/19.48 | | | | | | | | | | | | | % 140.16/19.48 | | | | | | | | | | | | End of split % 140.16/19.48 | | | | | | | | | | | | % 140.16/19.48 | | | | | | | | | | | End of split % 140.16/19.48 | | | | | | | | | | | % 140.16/19.48 | | | | | | | | | | End of split % 140.16/19.48 | | | | | | | | | | % 140.16/19.48 | | | | | | | | | Case 2: % 140.16/19.48 | | | | | | | | | | % 140.16/19.48 | | | | | | | | | | (746) pv12 = n3 % 140.16/19.48 | | | | | | | | | | % 140.16/19.48 | | | | | | | | | | REDUCE: (118), (746) imply: % 140.16/19.48 | | | | | | | | | | (747) pred(n3) = all_71_25 % 140.16/19.48 | | | | | | | | | | % 140.16/19.48 | | | | | | | | | | GROUND_INST: instantiating (24) with n2, all_71_25, n3, % 140.16/19.48 | | | | | | | | | | simplifying with (108), (747) gives: % 140.16/19.48 | | | | | | | | | | (748) all_71_25 = n2 % 140.16/19.48 | | | | | | | | | | % 140.16/19.48 | | | | | | | | | | REDUCE: (153), (748) imply: % 140.16/19.48 | | | | | | | | | | (749) leq(n0, n2) % 140.16/19.48 | | | | | | | | | | % 140.16/19.48 | | | | | | | | | | GROUND_INST: instantiating (65) with n0, all_71_11, all_71_9, % 140.16/19.48 | | | | | | | | | | all_71_8, all_71_7, all_71_6, all_71_5, all_71_4, % 140.16/19.48 | | | | | | | | | | all_71_3, all_71_2, all_71_1, all_71_0, % 140.16/19.48 | | | | | | | | | | simplifying with (19), (59), (139), (141), (142), % 140.16/19.48 | | | | | | | | | | (143), (144), (145), (146), (147), (585), (587) % 140.16/19.48 | | | | | | | | | | gives: % 140.16/19.48 | | | | | | | | | | (750) ~ (sum(n0, all_71_26, all_71_2) = all_71_1) | ~ % 140.16/19.48 | | | | | | | | | | leq(n0, all_71_25) | (a_select3(q, pv10, n0) = % 140.16/19.48 | | | | | | | | | | all_71_0 & $i(all_71_0)) % 140.16/19.48 | | | | | | | | | | % 140.16/19.48 | | | | | | | | | | BETA: splitting (750) gives: % 140.16/19.48 | | | | | | | | | | % 140.16/19.48 | | | | | | | | | | Case 1: % 140.16/19.48 | | | | | | | | | | | % 140.16/19.49 | | | | | | | | | | | (751) ~ (sum(n0, all_71_26, all_71_2) = all_71_1) % 140.16/19.49 | | | | | | | | | | | % 140.16/19.49 | | | | | | | | | | | REDUCE: (119), (751) imply: % 140.16/19.49 | | | | | | | | | | | (752) ~ (sum(n0, n4, all_71_2) = all_71_1) % 140.16/19.49 | | | | | | | | | | | % 140.16/19.49 | | | | | | | | | | | PRED_UNIFY: (148), (752) imply: % 140.16/19.49 | | | | | | | | | | | (753) $false % 140.16/19.49 | | | | | | | | | | | % 140.16/19.49 | | | | | | | | | | | CLOSE: (753) is inconsistent. % 140.16/19.49 | | | | | | | | | | | % 140.16/19.49 | | | | | | | | | | Case 2: % 140.16/19.49 | | | | | | | | | | | % 140.16/19.49 | | | | | | | | | | | (754) ~ leq(n0, all_71_25) | (a_select3(q, pv10, n0) = % 140.16/19.49 | | | | | | | | | | | all_71_0 & $i(all_71_0)) % 140.16/19.49 | | | | | | | | | | | % 140.16/19.49 | | | | | | | | | | | BETA: splitting (754) gives: % 140.16/19.49 | | | | | | | | | | | % 140.16/19.49 | | | | | | | | | | | Case 1: % 140.16/19.49 | | | | | | | | | | | | % 140.16/19.49 | | | | | | | | | | | | (755) ~ leq(n0, all_71_25) % 140.16/19.49 | | | | | | | | | | | | % 140.16/19.49 | | | | | | | | | | | | REDUCE: (748), (755) imply: % 140.16/19.49 | | | | | | | | | | | | (756) ~ leq(n0, n2) % 140.16/19.49 | | | | | | | | | | | | % 140.16/19.49 | | | | | | | | | | | | PRED_UNIFY: (749), (756) imply: % 140.16/19.49 | | | | | | | | | | | | (757) $false % 140.16/19.49 | | | | | | | | | | | | % 140.16/19.49 | | | | | | | | | | | | CLOSE: (757) is inconsistent. % 140.16/19.49 | | | | | | | | | | | | % 140.16/19.49 | | | | | | | | | | | Case 2: % 140.16/19.49 | | | | | | | | | | | | % 140.16/19.49 | | | | | | | | | | | | (758) a_select3(q, pv10, n0) = all_71_0 & $i(all_71_0) % 140.16/19.49 | | | | | | | | | | | | % 140.16/19.49 | | | | | | | | | | | | REF_CLOSE: (27), (134), (715), (716), (758) are inconsistent % 140.16/19.49 | | | | | | | | | | | | by sub-proof #5. % 140.16/19.49 | | | | | | | | | | | | % 140.16/19.49 | | | | | | | | | | | End of split % 140.16/19.49 | | | | | | | | | | | % 140.16/19.49 | | | | | | | | | | End of split % 140.16/19.49 | | | | | | | | | | % 140.16/19.49 | | | | | | | | | End of split % 140.16/19.49 | | | | | | | | | % 140.16/19.49 | | | | | | | | End of split % 140.16/19.49 | | | | | | | | % 140.16/19.49 | | | | | | | Case 2: % 140.16/19.49 | | | | | | | | % 140.16/19.49 | | | | | | | | (759) pv12 = n1 % 140.16/19.49 | | | | | | | | % 140.16/19.49 | | | | | | | | REF_CLOSE: (24), (105), (118), (588), (590), (759) are % 140.16/19.49 | | | | | | | | inconsistent by sub-proof #16. % 140.16/19.49 | | | | | | | | % 140.16/19.49 | | | | | | | End of split % 140.16/19.49 | | | | | | | % 140.16/19.49 | | | | | | Case 2: % 140.16/19.49 | | | | | | | % 140.16/19.49 | | | | | | | (760) all_71_12 = all_71_25 % 140.16/19.49 | | | | | | | % 140.16/19.49 | | | | | | | COMBINE_EQS: (583), (760) imply: % 140.16/19.49 | | | | | | | (761) all_71_25 = n0 % 140.16/19.49 | | | | | | | % 140.16/19.49 | | | | | | | SIMP: (761) implies: % 140.16/19.49 | | | | | | | (762) all_71_25 = n0 % 140.16/19.49 | | | | | | | % 140.16/19.49 | | | | | | | GROUND_INST: instantiating (65) with n0, all_71_11, all_71_9, % 140.16/19.49 | | | | | | | all_71_8, all_71_7, all_71_6, all_71_5, all_71_4, % 140.16/19.49 | | | | | | | all_71_3, all_71_2, all_71_1, all_71_0, simplifying % 140.16/19.49 | | | | | | | with (19), (59), (139), (141), (142), (143), (144), % 140.16/19.49 | | | | | | | (145), (146), (147), (585), (587) gives: % 140.16/19.49 | | | | | | | (763) ~ (sum(n0, all_71_26, all_71_2) = all_71_1) | ~ leq(n0, % 140.16/19.49 | | | | | | | all_71_25) | (a_select3(q, pv10, n0) = all_71_0 & % 140.16/19.49 | | | | | | | $i(all_71_0)) % 140.16/19.49 | | | | | | | % 140.16/19.49 | | | | | | | BETA: splitting (763) gives: % 140.16/19.49 | | | | | | | % 140.16/19.49 | | | | | | | Case 1: % 140.16/19.49 | | | | | | | | % 140.16/19.49 | | | | | | | | (764) ~ (sum(n0, all_71_26, all_71_2) = all_71_1) % 140.16/19.49 | | | | | | | | % 140.16/19.49 | | | | | | | | REDUCE: (119), (764) imply: % 140.16/19.49 | | | | | | | | (765) ~ (sum(n0, n4, all_71_2) = all_71_1) % 140.16/19.49 | | | | | | | | % 140.16/19.49 | | | | | | | | PRED_UNIFY: (148), (765) imply: % 140.16/19.49 | | | | | | | | (766) $false % 140.16/19.49 | | | | | | | | % 140.16/19.49 | | | | | | | | CLOSE: (766) is inconsistent. % 140.16/19.49 | | | | | | | | % 140.16/19.49 | | | | | | | Case 2: % 140.16/19.49 | | | | | | | | % 140.16/19.49 | | | | | | | | (767) ~ leq(n0, all_71_25) | (a_select3(q, pv10, n0) = % 140.16/19.49 | | | | | | | | all_71_0 & $i(all_71_0)) % 140.16/19.49 | | | | | | | | % 140.16/19.49 | | | | | | | | BETA: splitting (767) gives: % 140.16/19.49 | | | | | | | | % 140.16/19.49 | | | | | | | | Case 1: % 140.16/19.49 | | | | | | | | | % 140.16/19.49 | | | | | | | | | (768) ~ leq(n0, all_71_25) % 140.16/19.49 | | | | | | | | | % 140.16/19.49 | | | | | | | | | REDUCE: (762), (768) imply: % 140.16/19.49 | | | | | | | | | (769) ~ leq(n0, n0) % 140.16/19.49 | | | | | | | | | % 140.16/19.49 | | | | | | | | | PRED_UNIFY: (587), (769) imply: % 140.16/19.49 | | | | | | | | | (770) $false % 140.16/19.49 | | | | | | | | | % 140.16/19.49 | | | | | | | | | CLOSE: (770) is inconsistent. % 140.16/19.49 | | | | | | | | | % 140.16/19.49 | | | | | | | | Case 2: % 140.16/19.49 | | | | | | | | | % 140.16/19.49 | | | | | | | | | (771) a_select3(q, pv10, n0) = all_71_0 & $i(all_71_0) % 140.16/19.49 | | | | | | | | | % 140.16/19.49 | | | | | | | | | REF_CLOSE: (27), (134), (586), (771) are inconsistent by % 140.16/19.49 | | | | | | | | | sub-proof #6. % 140.16/19.49 | | | | | | | | | % 140.16/19.49 | | | | | | | | End of split % 140.16/19.49 | | | | | | | | % 140.16/19.49 | | | | | | | End of split % 140.16/19.49 | | | | | | | % 140.16/19.49 | | | | | | End of split % 140.16/19.49 | | | | | | % 140.16/19.49 | | | | | End of split % 140.16/19.49 | | | | | % 140.16/19.49 | | | | End of split % 140.16/19.49 | | | | % 140.16/19.49 | | | Case 2: % 140.16/19.49 | | | | % 140.16/19.49 | | | | (772) all_71_26 = pv12 % 140.16/19.49 | | | | % 140.16/19.49 | | | | COMBINE_EQS: (119), (772) imply: % 140.16/19.49 | | | | (773) pv12 = n4 % 140.16/19.49 | | | | % 140.16/19.49 | | | | SIMP: (773) implies: % 140.16/19.49 | | | | (774) pv12 = n4 % 140.16/19.49 | | | | % 140.16/19.49 | | | | REDUCE: (118), (774) imply: % 140.16/19.49 | | | | (775) pred(n4) = all_71_25 % 140.16/19.49 | | | | % 140.16/19.49 | | | | GROUND_INST: instantiating (24) with n3, all_71_25, n4, simplifying with % 140.16/19.49 | | | | (109), (775) gives: % 140.16/19.49 | | | | (776) all_71_25 = n3 % 140.16/19.49 | | | | % 140.16/19.49 | | | | BETA: splitting (149) gives: % 140.16/19.49 | | | | % 140.16/19.49 | | | | Case 1: % 140.16/19.49 | | | | | % 140.16/19.49 | | | | | (777) gt(all_71_12, n0) % 140.16/19.49 | | | | | % 140.16/19.49 | | | | | BETA: splitting (154) gives: % 140.16/19.49 | | | | | % 140.16/19.49 | | | | | Case 1: % 140.16/19.49 | | | | | | % 140.16/19.49 | | | | | | (778) gt(all_71_25, all_71_12) % 140.16/19.49 | | | | | | % 140.16/19.49 | | | | | | REDUCE: (776), (778) imply: % 140.16/19.49 | | | | | | (779) gt(n3, all_71_12) % 140.16/19.49 | | | | | | % 140.16/19.49 | | | | | | GROUND_INST: instantiating (1) with all_71_12, n3, n2, simplifying % 140.16/19.49 | | | | | | with (58), (98), (108), (779) gives: % 140.16/19.49 | | | | | | (780) leq(all_71_12, n2) % 140.16/19.49 | | | | | | % 140.16/19.49 | | | | | | GROUND_INST: instantiating (leq_gt2) with all_71_12, n2, simplifying % 140.16/19.49 | | | | | | with (58), (91), (780) gives: % 140.16/19.49 | | | | | | (781) all_71_12 = n2 | gt(n2, all_71_12) % 140.16/19.49 | | | | | | % 140.16/19.49 | | | | | | BETA: splitting (159) gives: % 140.16/19.49 | | | | | | % 140.16/19.49 | | | | | | Case 1: % 140.16/19.49 | | | | | | | % 140.16/19.49 | | | | | | | (782) all_71_12 = n0 % 140.16/19.49 | | | | | | | % 140.16/19.49 | | | | | | | REF_CLOSE: (58), (777), (782), (irreflexivity_gt) are inconsistent % 140.16/19.49 | | | | | | | by sub-proof #25. % 140.16/19.49 | | | | | | | % 140.16/19.49 | | | | | | Case 2: % 140.16/19.49 | | | | | | | % 140.16/19.49 | | | | | | | (783) ~ (all_71_12 = n0) % 140.16/19.49 | | | | | | | % 140.16/19.49 | | | | | | | BETA: splitting (165) gives: % 140.16/19.49 | | | | | | | % 140.16/19.49 | | | | | | | Case 1: % 140.16/19.49 | | | | | | | | % 140.16/19.49 | | | | | | | | (784) gt(all_71_23, n0) % 140.16/19.49 | | | | | | | | % 140.16/19.49 | | | | | | | | BETA: splitting (166) gives: % 140.16/19.49 | | | | | | | | % 140.16/19.49 | | | | | | | | Case 1: % 140.16/19.49 | | | | | | | | | % 140.16/19.49 | | | | | | | | | (785) gt(pv10, n1) % 140.16/19.49 | | | | | | | | | % 140.16/19.49 | | | | | | | | | GROUND_INST: instantiating (1) with n1, pv10, all_71_23, % 140.16/19.49 | | | | | | | | | simplifying with (21), (80), (115), (785) gives: % 140.16/19.49 | | | | | | | | | (786) leq(n1, all_71_23) % 140.16/19.49 | | | | | | | | | % 140.16/19.49 | | | | | | | | | GROUND_INST: instantiating (6) with n1, all_71_23, n2, pv10, % 140.16/19.49 | | | | | | | | | simplifying with (79), (80), (114), (124), (786) % 140.16/19.49 | | | | | | | | | gives: % 140.16/19.49 | | | | | | | | | (787) leq(n2, pv10) % 140.16/19.49 | | | | | | | | | % 140.16/19.49 | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with n1, all_71_23, % 140.16/19.49 | | | | | | | | | simplifying with (80), (114), (786) gives: % 140.16/19.49 | | | | | | | | | (788) all_71_23 = n1 | gt(all_71_23, n1) % 140.16/19.49 | | | | | | | | | % 140.16/19.49 | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with n2, pv10, simplifying % 140.16/19.49 | | | | | | | | | with (21), (91), (787) gives: % 140.16/19.49 | | | | | | | | | (789) pv10 = n2 | gt(pv10, n2) % 140.16/19.49 | | | | | | | | | % 140.16/19.49 | | | | | | | | | BETA: splitting (781) gives: % 140.16/19.49 | | | | | | | | | % 140.16/19.49 | | | | | | | | | Case 1: % 140.16/19.49 | | | | | | | | | | % 140.16/19.49 | | | | | | | | | | (790) gt(n2, all_71_12) % 140.16/19.49 | | | | | | | | | | % 140.16/19.49 | | | | | | | | | | GROUND_INST: instantiating (1) with all_71_12, n2, n1, % 140.16/19.49 | | | | | | | | | | simplifying with (58), (91), (107), (790) gives: % 140.16/19.49 | | | | | | | | | | (791) leq(all_71_12, n1) % 140.16/19.49 | | | | | | | | | | % 140.16/19.49 | | | | | | | | | | GROUND_INST: instantiating (11) with all_71_12, simplifying % 140.16/19.49 | | | | | | | | | | with (58), (135), (791) gives: % 140.16/19.49 | | | | | | | | | | (792) all_71_12 = n1 | all_71_12 = n0 % 140.16/19.49 | | | | | | | | | | % 140.16/19.49 | | | | | | | | | | BETA: splitting (792) gives: % 140.16/19.49 | | | | | | | | | | % 140.16/19.49 | | | | | | | | | | Case 1: % 140.16/19.49 | | | | | | | | | | | % 140.16/19.49 | | | | | | | | | | | (793) all_71_12 = n0 % 140.16/19.49 | | | | | | | | | | | % 140.16/19.49 | | | | | | | | | | | REDUCE: (783), (793) imply: % 140.16/19.49 | | | | | | | | | | | (794) $false % 140.16/19.49 | | | | | | | | | | | % 140.16/19.49 | | | | | | | | | | | CLOSE: (794) is inconsistent. % 140.16/19.49 | | | | | | | | | | | % 140.16/19.49 | | | | | | | | | | Case 2: % 140.16/19.49 | | | | | | | | | | | % 140.16/19.49 | | | | | | | | | | | (795) all_71_12 = n1 % 140.16/19.49 | | | | | | | | | | | % 140.16/19.49 | | | | | | | | | | | REDUCE: (138), (795) imply: % 140.16/19.49 | | | | | | | | | | | (796) a_select3(center, n1, n0) = all_71_9 % 140.16/19.49 | | | | | | | | | | | % 140.16/19.49 | | | | | | | | | | | REDUCE: (137), (795) imply: % 140.16/19.49 | | | | | | | | | | | (797) a_select3(q, pv10, n1) = all_71_10 % 140.16/19.49 | | | | | | | | | | | % 140.16/19.49 | | | | | | | | | | | REDUCE: (152), (795) imply: % 140.16/19.49 | | | | | | | | | | | (798) leq(n1, n3) % 140.16/19.49 | | | | | | | | | | | % 140.16/19.49 | | | | | | | | | | | REDUCE: (135), (795) imply: % 140.16/19.49 | | | | | | | | | | | (799) leq(n0, n1) % 140.16/19.49 | | | | | | | | | | | % 140.16/19.49 | | | | | | | | | | | BETA: splitting (788) gives: % 140.16/19.49 | | | | | | | | | | | % 140.16/19.49 | | | | | | | | | | | Case 1: % 140.16/19.49 | | | | | | | | | | | | % 140.16/19.49 | | | | | | | | | | | | (800) gt(all_71_23, n1) % 140.16/19.49 | | | | | | | | | | | | % 140.16/19.49 | | | | | | | | | | | | BETA: splitting (789) gives: % 140.16/19.49 | | | | | | | | | | | | % 140.16/19.49 | | | | | | | | | | | | Case 1: % 140.16/19.49 | | | | | | | | | | | | | % 140.16/19.49 | | | | | | | | | | | | | % 140.16/19.49 | | | | | | | | | | | | | GROUND_INST: instantiating (65) with n1, all_71_11, all_71_9, % 140.16/19.49 | | | | | | | | | | | | | all_71_8, all_71_7, all_71_6, all_71_5, all_71_4, % 140.16/19.49 | | | | | | | | | | | | | all_71_3, all_71_2, all_71_1, all_71_0, % 140.16/19.49 | | | | | | | | | | | | | simplifying with (59), (80), (139), (141), (142), % 140.16/19.49 | | | | | | | | | | | | | (143), (144), (145), (146), (147), (796), (799) % 140.16/19.49 | | | | | | | | | | | | | gives: % 140.16/19.49 | | | | | | | | | | | | | (801) ~ (sum(n0, all_71_26, all_71_2) = all_71_1) | ~ % 140.16/19.49 | | | | | | | | | | | | | leq(n1, all_71_25) | (a_select3(q, pv10, n1) = % 140.16/19.49 | | | | | | | | | | | | | all_71_0 & $i(all_71_0)) % 140.16/19.49 | | | | | | | | | | | | | % 140.16/19.49 | | | | | | | | | | | | | REF_CLOSE: (27), (119), (134), (148), (776), (797), (798), % 140.16/19.49 | | | | | | | | | | | | | (801) are inconsistent by sub-proof #4. % 140.16/19.49 | | | | | | | | | | | | | % 140.16/19.49 | | | | | | | | | | | | Case 2: % 140.16/19.49 | | | | | | | | | | | | | % 140.16/19.49 | | | | | | | | | | | | | (802) pv10 = n2 % 140.16/19.49 | | | | | | | | | | | | | % 140.16/19.49 | | | | | | | | | | | | | REDUCE: (115), (802) imply: % 140.16/19.49 | | | | | | | | | | | | | (803) pred(n2) = all_71_23 % 140.16/19.49 | | | | | | | | | | | | | % 140.16/19.49 | | | | | | | | | | | | | GROUND_INST: instantiating (24) with n1, all_71_23, n2, % 140.16/19.49 | | | | | | | | | | | | | simplifying with (107), (803) gives: % 140.16/19.49 | | | | | | | | | | | | | (804) all_71_23 = n1 % 140.16/19.49 | | | | | | | | | | | | | % 140.16/19.49 | | | | | | | | | | | | | REF_CLOSE: (114), (800), (804), (irreflexivity_gt) are % 140.16/19.49 | | | | | | | | | | | | | inconsistent by sub-proof #19. % 140.16/19.49 | | | | | | | | | | | | | % 140.16/19.49 | | | | | | | | | | | | End of split % 140.16/19.49 | | | | | | | | | | | | % 140.16/19.49 | | | | | | | | | | | Case 2: % 140.16/19.49 | | | | | | | | | | | | % 140.16/19.49 | | | | | | | | | | | | (805) all_71_23 = n1 % 140.16/19.49 | | | | | | | | | | | | % 140.16/19.49 | | | | | | | | | | | | GROUND_INST: instantiating (65) with n1, all_71_11, all_71_9, % 140.16/19.49 | | | | | | | | | | | | all_71_8, all_71_7, all_71_6, all_71_5, all_71_4, % 140.16/19.49 | | | | | | | | | | | | all_71_3, all_71_2, all_71_1, all_71_0, % 140.16/19.49 | | | | | | | | | | | | simplifying with (59), (80), (139), (141), (142), % 140.16/19.49 | | | | | | | | | | | | (143), (144), (145), (146), (147), (796), (799) % 140.16/19.49 | | | | | | | | | | | | gives: % 140.16/19.49 | | | | | | | | | | | | (806) ~ (sum(n0, all_71_26, all_71_2) = all_71_1) | ~ % 140.16/19.49 | | | | | | | | | | | | leq(n1, all_71_25) | (a_select3(q, pv10, n1) = % 140.16/19.49 | | | | | | | | | | | | all_71_0 & $i(all_71_0)) % 140.16/19.49 | | | | | | | | | | | | % 140.16/19.49 | | | | | | | | | | | | REF_CLOSE: (27), (119), (134), (148), (776), (797), (798), % 140.16/19.49 | | | | | | | | | | | | (806) are inconsistent by sub-proof #4. % 140.16/19.49 | | | | | | | | | | | | % 140.16/19.49 | | | | | | | | | | | End of split % 140.16/19.49 | | | | | | | | | | | % 140.16/19.49 | | | | | | | | | | End of split % 140.16/19.49 | | | | | | | | | | % 140.16/19.49 | | | | | | | | | Case 2: % 140.16/19.49 | | | | | | | | | | % 140.16/19.49 | | | | | | | | | | (807) all_71_12 = n2 % 140.16/19.49 | | | | | | | | | | (808) ~ gt(n2, all_71_12) % 140.16/19.49 | | | | | | | | | | % 140.16/19.49 | | | | | | | | | | REDUCE: (138), (807) imply: % 140.16/19.49 | | | | | | | | | | (809) a_select3(center, n2, n0) = all_71_9 % 140.16/19.49 | | | | | | | | | | % 140.16/19.49 | | | | | | | | | | REDUCE: (137), (807) imply: % 140.16/19.49 | | | | | | | | | | (810) a_select3(q, pv10, n2) = all_71_10 % 140.16/19.49 | | | | | | | | | | % 140.16/19.49 | | | | | | | | | | REDUCE: (152), (807) imply: % 140.16/19.49 | | | | | | | | | | (811) leq(n2, n3) % 140.16/19.49 | | | | | | | | | | % 140.16/19.49 | | | | | | | | | | REDUCE: (135), (807) imply: % 140.16/19.49 | | | | | | | | | | (812) leq(n0, n2) % 140.16/19.49 | | | | | | | | | | % 140.16/19.49 | | | | | | | | | | REDUCE: (807), (808) imply: % 140.16/19.49 | | | | | | | | | | (813) ~ gt(n2, n2) % 140.16/19.49 | | | | | | | | | | % 140.16/19.49 | | | | | | | | | | BETA: splitting (788) gives: % 140.16/19.49 | | | | | | | | | | % 140.16/19.49 | | | | | | | | | | Case 1: % 140.16/19.49 | | | | | | | | | | | % 140.16/19.49 | | | | | | | | | | | (814) gt(all_71_23, n1) % 140.16/19.49 | | | | | | | | | | | % 140.16/19.49 | | | | | | | | | | | BETA: splitting (789) gives: % 140.16/19.49 | | | | | | | | | | | % 140.16/19.49 | | | | | | | | | | | Case 1: % 140.16/19.49 | | | | | | | | | | | | % 140.16/19.49 | | | | | | | | | | | | (815) gt(pv10, n2) % 140.16/19.49 | | | | | | | | | | | | % 140.16/19.50 | | | | | | | | | | | | GROUND_INST: instantiating (1) with n2, pv10, all_71_23, % 140.16/19.50 | | | | | | | | | | | | simplifying with (21), (91), (115), (815) gives: % 140.16/19.50 | | | | | | | | | | | | (816) leq(n2, all_71_23) % 140.16/19.50 | | | | | | | | | | | | % 140.16/19.50 | | | | | | | | | | | | GROUND_INST: instantiating (6) with n2, all_71_23, n3, pv10, % 140.16/19.50 | | | | | | | | | | | | simplifying with (90), (91), (114), (124), (816) % 140.16/19.50 | | | | | | | | | | | | gives: % 140.16/19.50 | | | | | | | | | | | | (817) leq(n3, pv10) % 140.16/19.50 | | | | | | | | | | | | % 140.16/19.50 | | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with n2, all_71_23, % 140.16/19.50 | | | | | | | | | | | | simplifying with (91), (114), (816) gives: % 140.16/19.50 | | | | | | | | | | | | (818) all_71_23 = n2 | gt(all_71_23, n2) % 140.16/19.50 | | | | | | | | | | | | % 140.16/19.50 | | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with n3, pv10, simplifying % 140.16/19.50 | | | | | | | | | | | | with (21), (98), (817) gives: % 140.16/19.50 | | | | | | | | | | | | (819) pv10 = n3 | gt(pv10, n3) % 140.16/19.50 | | | | | | | | | | | | % 140.16/19.50 | | | | | | | | | | | | BETA: splitting (818) gives: % 140.16/19.50 | | | | | | | | | | | | % 140.16/19.50 | | | | | | | | | | | | Case 1: % 140.16/19.50 | | | | | | | | | | | | | % 140.16/19.50 | | | | | | | | | | | | | (820) gt(all_71_23, n2) % 140.16/19.50 | | | | | | | | | | | | | % 140.16/19.50 | | | | | | | | | | | | | BETA: splitting (819) gives: % 140.16/19.50 | | | | | | | | | | | | | % 140.16/19.50 | | | | | | | | | | | | | Case 1: % 140.16/19.50 | | | | | | | | | | | | | | % 140.16/19.50 | | | | | | | | | | | | | | (821) gt(pv10, n3) % 140.16/19.50 | | | | | | | | | | | | | | % 140.16/19.50 | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with n3, pv10, all_71_23, % 140.16/19.50 | | | | | | | | | | | | | | simplifying with (21), (98), (115), (821) gives: % 140.16/19.50 | | | | | | | | | | | | | | (822) leq(n3, all_71_23) % 140.16/19.50 | | | | | | | | | | | | | | % 140.16/19.50 | | | | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with n3, all_71_23, % 140.16/19.50 | | | | | | | | | | | | | | simplifying with (98), (114), (822) gives: % 140.16/19.50 | | | | | | | | | | | | | | (823) all_71_23 = n3 | gt(all_71_23, n3) % 140.16/19.50 | | | | | | | | | | | | | | % 140.16/19.50 | | | | | | | | | | | | | | BETA: splitting (823) gives: % 140.16/19.50 | | | | | | | | | | | | | | % 140.16/19.50 | | | | | | | | | | | | | | Case 1: % 140.16/19.50 | | | | | | | | | | | | | | | % 140.16/19.50 | | | | | | | | | | | | | | | % 140.16/19.50 | | | | | | | | | | | | | | | GROUND_INST: instantiating (65) with n2, all_71_11, all_71_9, % 140.16/19.50 | | | | | | | | | | | | | | | all_71_8, all_71_7, all_71_6, all_71_5, all_71_4, % 140.16/19.50 | | | | | | | | | | | | | | | all_71_3, all_71_2, all_71_1, all_71_0, % 140.16/19.50 | | | | | | | | | | | | | | | simplifying with (59), (91), (139), (141), (142), % 140.16/19.50 | | | | | | | | | | | | | | | (143), (144), (145), (146), (147), (809), (812) % 140.16/19.50 | | | | | | | | | | | | | | | gives: % 140.16/19.50 | | | | | | | | | | | | | | | (824) ~ (sum(n0, all_71_26, all_71_2) = all_71_1) | ~ % 140.16/19.50 | | | | | | | | | | | | | | | leq(n2, all_71_25) | (a_select3(q, pv10, n2) = % 140.16/19.50 | | | | | | | | | | | | | | | all_71_0 & $i(all_71_0)) % 140.16/19.50 | | | | | | | | | | | | | | | % 140.16/19.50 | | | | | | | | | | | | | | | REF_CLOSE: (27), (119), (134), (148), (776), (810), (811), % 140.16/19.50 | | | | | | | | | | | | | | | (824) are inconsistent by sub-proof #3. % 140.16/19.50 | | | | | | | | | | | | | | | % 140.16/19.50 | | | | | | | | | | | | | | Case 2: % 140.16/19.50 | | | | | | | | | | | | | | | % 140.16/19.50 | | | | | | | | | | | | | | | (825) all_71_23 = n3 % 140.16/19.50 | | | | | | | | | | | | | | | % 140.16/19.50 | | | | | | | | | | | | | | | GROUND_INST: instantiating (65) with n2, all_71_11, all_71_9, % 140.16/19.50 | | | | | | | | | | | | | | | all_71_8, all_71_7, all_71_6, all_71_5, all_71_4, % 140.16/19.50 | | | | | | | | | | | | | | | all_71_3, all_71_2, all_71_1, all_71_0, % 140.16/19.50 | | | | | | | | | | | | | | | simplifying with (59), (91), (139), (141), (142), % 140.16/19.50 | | | | | | | | | | | | | | | (143), (144), (145), (146), (147), (809), (812) % 140.16/19.50 | | | | | | | | | | | | | | | gives: % 140.16/19.50 | | | | | | | | | | | | | | | (826) ~ (sum(n0, all_71_26, all_71_2) = all_71_1) | ~ % 140.16/19.50 | | | | | | | | | | | | | | | leq(n2, all_71_25) | (a_select3(q, pv10, n2) = % 140.16/19.50 | | | | | | | | | | | | | | | all_71_0 & $i(all_71_0)) % 140.16/19.50 | | | | | | | | | | | | | | | % 140.16/19.50 | | | | | | | | | | | | | | | REF_CLOSE: (27), (119), (134), (148), (776), (810), (811), % 140.16/19.50 | | | | | | | | | | | | | | | (826) are inconsistent by sub-proof #3. % 140.16/19.50 | | | | | | | | | | | | | | | % 140.16/19.50 | | | | | | | | | | | | | | End of split % 140.16/19.50 | | | | | | | | | | | | | | % 140.16/19.50 | | | | | | | | | | | | | Case 2: % 140.16/19.50 | | | | | | | | | | | | | | % 140.16/19.50 | | | | | | | | | | | | | | (827) pv10 = n3 % 140.16/19.50 | | | | | | | | | | | | | | % 140.16/19.50 | | | | | | | | | | | | | | REDUCE: (115), (827) imply: % 140.16/19.50 | | | | | | | | | | | | | | (828) pred(n3) = all_71_23 % 140.16/19.50 | | | | | | | | | | | | | | % 140.16/19.50 | | | | | | | | | | | | | | GROUND_INST: instantiating (24) with n2, all_71_23, n3, % 140.16/19.50 | | | | | | | | | | | | | | simplifying with (108), (828) gives: % 140.16/19.50 | | | | | | | | | | | | | | (829) all_71_23 = n2 % 140.16/19.50 | | | | | | | | | | | | | | % 140.16/19.50 | | | | | | | | | | | | | | REDUCE: (820), (829) imply: % 140.16/19.50 | | | | | | | | | | | | | | (830) gt(n2, n2) % 140.16/19.50 | | | | | | | | | | | | | | % 140.16/19.50 | | | | | | | | | | | | | | PRED_UNIFY: (813), (830) imply: % 140.16/19.50 | | | | | | | | | | | | | | (831) $false % 140.16/19.50 | | | | | | | | | | | | | | % 140.16/19.50 | | | | | | | | | | | | | | CLOSE: (831) is inconsistent. % 140.16/19.50 | | | | | | | | | | | | | | % 140.16/19.50 | | | | | | | | | | | | | End of split % 140.16/19.50 | | | | | | | | | | | | | % 140.16/19.50 | | | | | | | | | | | | Case 2: % 140.16/19.50 | | | | | | | | | | | | | % 140.16/19.50 | | | | | | | | | | | | | (832) all_71_23 = n2 % 140.16/19.50 | | | | | | | | | | | | | % 140.16/19.50 | | | | | | | | | | | | | REDUCE: (124), (832) imply: % 140.16/19.50 | | | | | | | | | | | | | (833) succ(n2) = pv10 % 140.16/19.50 | | | | | | | | | | | | | % 140.16/19.50 | | | | | | | | | | | | | GROUND_INST: instantiating (25) with n3, pv10, n2, simplifying % 140.16/19.50 | | | | | | | | | | | | | with (90), (833) gives: % 140.16/19.50 | | | | | | | | | | | | | (834) pv10 = n3 % 140.16/19.50 | | | | | | | | | | | | | % 140.16/19.50 | | | | | | | | | | | | | GROUND_INST: instantiating (65) with n2, all_71_11, all_71_9, % 140.16/19.50 | | | | | | | | | | | | | all_71_8, all_71_7, all_71_6, all_71_5, all_71_4, % 140.16/19.50 | | | | | | | | | | | | | all_71_3, all_71_2, all_71_1, all_71_0, % 140.16/19.50 | | | | | | | | | | | | | simplifying with (59), (91), (139), (141), (142), % 140.16/19.50 | | | | | | | | | | | | | (143), (144), (145), (146), (147), (809), (812) % 140.16/19.50 | | | | | | | | | | | | | gives: % 140.16/19.50 | | | | | | | | | | | | | (835) ~ (sum(n0, all_71_26, all_71_2) = all_71_1) | ~ % 140.16/19.50 | | | | | | | | | | | | | leq(n2, all_71_25) | (a_select3(q, pv10, n2) = % 140.16/19.50 | | | | | | | | | | | | | all_71_0 & $i(all_71_0)) % 140.16/19.50 | | | | | | | | | | | | | % 140.16/19.50 | | | | | | | | | | | | | REF_CLOSE: (27), (119), (134), (148), (776), (810), (811), % 140.16/19.50 | | | | | | | | | | | | | (835) are inconsistent by sub-proof #3. % 140.16/19.50 | | | | | | | | | | | | | % 140.16/19.50 | | | | | | | | | | | | End of split % 140.16/19.50 | | | | | | | | | | | | % 140.16/19.50 | | | | | | | | | | | Case 2: % 140.16/19.50 | | | | | | | | | | | | % 140.16/19.50 | | | | | | | | | | | | (836) pv10 = n2 % 140.16/19.50 | | | | | | | | | | | | % 140.16/19.50 | | | | | | | | | | | | REDUCE: (115), (836) imply: % 140.16/19.50 | | | | | | | | | | | | (837) pred(n2) = all_71_23 % 140.16/19.50 | | | | | | | | | | | | % 140.16/19.50 | | | | | | | | | | | | GROUND_INST: instantiating (24) with n1, all_71_23, n2, % 140.16/19.50 | | | | | | | | | | | | simplifying with (107), (837) gives: % 140.16/19.50 | | | | | | | | | | | | (838) all_71_23 = n1 % 140.16/19.50 | | | | | | | | | | | | % 140.16/19.50 | | | | | | | | | | | | REF_CLOSE: (114), (814), (838), (irreflexivity_gt) are % 140.16/19.50 | | | | | | | | | | | | inconsistent by sub-proof #19. % 140.16/19.50 | | | | | | | | | | | | % 140.16/19.50 | | | | | | | | | | | End of split % 140.16/19.50 | | | | | | | | | | | % 140.16/19.50 | | | | | | | | | | Case 2: % 140.16/19.50 | | | | | | | | | | | % 140.16/19.50 | | | | | | | | | | | (839) all_71_23 = n1 % 140.16/19.50 | | | | | | | | | | | % 140.16/19.50 | | | | | | | | | | | REDUCE: (124), (839) imply: % 140.16/19.50 | | | | | | | | | | | (840) succ(n1) = pv10 % 140.16/19.50 | | | | | | | | | | | % 140.16/19.50 | | | | | | | | | | | GROUND_INST: instantiating (25) with n2, pv10, n1, simplifying % 140.16/19.50 | | | | | | | | | | | with (79), (840) gives: % 140.16/19.50 | | | | | | | | | | | (841) pv10 = n2 % 140.16/19.50 | | | | | | | | | | | % 140.16/19.50 | | | | | | | | | | | GROUND_INST: instantiating (65) with n2, all_71_11, all_71_9, % 140.16/19.50 | | | | | | | | | | | all_71_8, all_71_7, all_71_6, all_71_5, all_71_4, % 140.16/19.50 | | | | | | | | | | | all_71_3, all_71_2, all_71_1, all_71_0, % 140.16/19.50 | | | | | | | | | | | simplifying with (59), (91), (139), (141), (142), % 140.16/19.50 | | | | | | | | | | | (143), (144), (145), (146), (147), (809), (812) % 140.16/19.50 | | | | | | | | | | | gives: % 140.16/19.50 | | | | | | | | | | | (842) ~ (sum(n0, all_71_26, all_71_2) = all_71_1) | ~ % 140.16/19.50 | | | | | | | | | | | leq(n2, all_71_25) | (a_select3(q, pv10, n2) = % 140.16/19.50 | | | | | | | | | | | all_71_0 & $i(all_71_0)) % 140.16/19.50 | | | | | | | | | | | % 140.16/19.50 | | | | | | | | | | | REF_CLOSE: (27), (119), (134), (148), (776), (810), (811), % 140.16/19.50 | | | | | | | | | | | (842) are inconsistent by sub-proof #3. % 140.16/19.50 | | | | | | | | | | | % 140.16/19.50 | | | | | | | | | | End of split % 140.16/19.50 | | | | | | | | | | % 140.16/19.50 | | | | | | | | | End of split % 140.16/19.50 | | | | | | | | | % 140.16/19.50 | | | | | | | | Case 2: % 140.16/19.50 | | | | | | | | | % 140.16/19.50 | | | | | | | | | (843) pv10 = n1 % 140.16/19.50 | | | | | | | | | % 140.16/19.50 | | | | | | | | | REF_CLOSE: (24), (105), (114), (115), (784), (843), % 140.16/19.50 | | | | | | | | | (irreflexivity_gt) are inconsistent by sub-proof % 140.16/19.50 | | | | | | | | | #17. % 140.16/19.50 | | | | | | | | | % 140.16/19.50 | | | | | | | | End of split % 140.16/19.50 | | | | | | | | % 140.16/19.50 | | | | | | | Case 2: % 140.16/19.50 | | | | | | | | % 140.16/19.50 | | | | | | | | (844) all_71_23 = n0 % 140.16/19.50 | | | | | | | | % 140.16/19.50 | | | | | | | | REDUCE: (124), (844) imply: % 140.16/19.50 | | | | | | | | (845) succ(n0) = pv10 % 140.16/19.50 | | | | | | | | % 140.16/19.50 | | | | | | | | GROUND_INST: instantiating (25) with n1, pv10, n0, simplifying % 140.16/19.50 | | | | | | | | with (16), (845) gives: % 140.16/19.50 | | | | | | | | (846) pv10 = n1 % 140.16/19.50 | | | | | | | | % 140.16/19.50 | | | | | | | | REDUCE: (137), (846) imply: % 140.16/19.50 | | | | | | | | (847) a_select3(q, n1, all_71_12) = all_71_10 % 140.16/19.50 | | | | | | | | % 140.16/19.50 | | | | | | | | BETA: splitting (781) gives: % 140.16/19.50 | | | | | | | | % 140.16/19.50 | | | | | | | | Case 1: % 140.16/19.50 | | | | | | | | | % 140.16/19.50 | | | | | | | | | (848) gt(n2, all_71_12) % 140.16/19.50 | | | | | | | | | % 140.16/19.50 | | | | | | | | | GROUND_INST: instantiating (1) with all_71_12, n2, n1, % 140.16/19.50 | | | | | | | | | simplifying with (58), (91), (107), (848) gives: % 140.16/19.50 | | | | | | | | | (849) leq(all_71_12, n1) % 140.16/19.50 | | | | | | | | | % 140.16/19.50 | | | | | | | | | GROUND_INST: instantiating (11) with all_71_12, simplifying % 140.16/19.50 | | | | | | | | | with (58), (135), (849) gives: % 140.16/19.50 | | | | | | | | | (850) all_71_12 = n1 | all_71_12 = n0 % 140.16/19.50 | | | | | | | | | % 140.16/19.50 | | | | | | | | | BETA: splitting (850) gives: % 140.16/19.50 | | | | | | | | | % 140.16/19.50 | | | | | | | | | Case 1: % 140.16/19.50 | | | | | | | | | | % 140.16/19.50 | | | | | | | | | | (851) all_71_12 = n0 % 140.16/19.50 | | | | | | | | | | % 140.16/19.50 | | | | | | | | | | REDUCE: (783), (851) imply: % 140.16/19.50 | | | | | | | | | | (852) $false % 140.16/19.50 | | | | | | | | | | % 140.16/19.50 | | | | | | | | | | CLOSE: (852) is inconsistent. % 140.16/19.50 | | | | | | | | | | % 140.16/19.50 | | | | | | | | | Case 2: % 140.16/19.50 | | | | | | | | | | % 140.16/19.50 | | | | | | | | | | (853) all_71_12 = n1 % 140.16/19.50 | | | | | | | | | | % 140.16/19.50 | | | | | | | | | | REDUCE: (138), (853) imply: % 140.16/19.50 | | | | | | | | | | (854) a_select3(center, n1, n0) = all_71_9 % 140.16/19.50 | | | | | | | | | | % 140.16/19.50 | | | | | | | | | | REDUCE: (847), (853) imply: % 140.16/19.50 | | | | | | | | | | (855) a_select3(q, n1, n1) = all_71_10 % 140.16/19.50 | | | | | | | | | | % 140.16/19.50 | | | | | | | | | | REDUCE: (152), (853) imply: % 140.16/19.50 | | | | | | | | | | (856) leq(n1, n3) % 140.16/19.50 | | | | | | | | | | % 140.16/19.50 | | | | | | | | | | REDUCE: (135), (853) imply: % 140.16/19.50 | | | | | | | | | | (857) leq(n0, n1) % 140.16/19.50 | | | | | | | | | | % 140.16/19.50 | | | | | | | | | | GROUND_INST: instantiating (65) with n1, all_71_11, all_71_9, % 140.16/19.50 | | | | | | | | | | all_71_8, all_71_7, all_71_6, all_71_5, all_71_4, % 140.16/19.50 | | | | | | | | | | all_71_3, all_71_2, all_71_1, all_71_0, % 140.16/19.50 | | | | | | | | | | simplifying with (59), (80), (139), (141), (142), % 140.16/19.50 | | | | | | | | | | (143), (144), (145), (146), (147), (854), (857) % 140.16/19.50 | | | | | | | | | | gives: % 140.16/19.50 | | | | | | | | | | (858) ~ (sum(n0, all_71_26, all_71_2) = all_71_1) | ~ % 140.16/19.50 | | | | | | | | | | leq(n1, all_71_25) | (a_select3(q, pv10, n1) = % 140.16/19.50 | | | | | | | | | | all_71_0 & $i(all_71_0)) % 140.16/19.50 | | | | | | | | | | % 140.16/19.50 | | | | | | | | | | BETA: splitting (858) gives: % 140.16/19.50 | | | | | | | | | | % 140.16/19.50 | | | | | | | | | | Case 1: % 140.16/19.50 | | | | | | | | | | | % 140.16/19.50 | | | | | | | | | | | (859) ~ (sum(n0, all_71_26, all_71_2) = all_71_1) % 140.16/19.50 | | | | | | | | | | | % 140.16/19.50 | | | | | | | | | | | REDUCE: (119), (859) imply: % 140.16/19.50 | | | | | | | | | | | (860) ~ (sum(n0, n4, all_71_2) = all_71_1) % 140.16/19.50 | | | | | | | | | | | % 140.16/19.50 | | | | | | | | | | | PRED_UNIFY: (148), (860) imply: % 140.16/19.50 | | | | | | | | | | | (861) $false % 140.16/19.50 | | | | | | | | | | | % 140.16/19.50 | | | | | | | | | | | CLOSE: (861) is inconsistent. % 140.16/19.50 | | | | | | | | | | | % 140.16/19.50 | | | | | | | | | | Case 2: % 140.16/19.50 | | | | | | | | | | | % 140.16/19.50 | | | | | | | | | | | (862) ~ leq(n1, all_71_25) | (a_select3(q, pv10, n1) = % 140.16/19.50 | | | | | | | | | | | all_71_0 & $i(all_71_0)) % 140.16/19.50 | | | | | | | | | | | % 140.16/19.50 | | | | | | | | | | | BETA: splitting (862) gives: % 140.16/19.50 | | | | | | | | | | | % 140.16/19.50 | | | | | | | | | | | Case 1: % 140.16/19.50 | | | | | | | | | | | | % 140.16/19.50 | | | | | | | | | | | | (863) ~ leq(n1, all_71_25) % 140.16/19.50 | | | | | | | | | | | | % 140.16/19.50 | | | | | | | | | | | | REDUCE: (776), (863) imply: % 140.16/19.50 | | | | | | | | | | | | (864) ~ leq(n1, n3) % 140.16/19.50 | | | | | | | | | | | | % 140.16/19.50 | | | | | | | | | | | | PRED_UNIFY: (856), (864) imply: % 140.16/19.50 | | | | | | | | | | | | (865) $false % 140.16/19.50 | | | | | | | | | | | | % 140.16/19.50 | | | | | | | | | | | | CLOSE: (865) is inconsistent. % 140.16/19.50 | | | | | | | | | | | | % 140.16/19.50 | | | | | | | | | | | Case 2: % 140.16/19.50 | | | | | | | | | | | | % 140.16/19.50 | | | | | | | | | | | | (866) a_select3(q, pv10, n1) = all_71_0 & $i(all_71_0) % 140.16/19.50 | | | | | | | | | | | | % 140.16/19.50 | | | | | | | | | | | | REF_CLOSE: (27), (134), (846), (855), (866) are inconsistent % 140.16/19.50 | | | | | | | | | | | | by sub-proof #7. % 140.16/19.50 | | | | | | | | | | | | % 140.16/19.50 | | | | | | | | | | | End of split % 140.16/19.50 | | | | | | | | | | | % 140.16/19.50 | | | | | | | | | | End of split % 140.16/19.50 | | | | | | | | | | % 140.16/19.50 | | | | | | | | | End of split % 140.16/19.50 | | | | | | | | | % 140.16/19.50 | | | | | | | | Case 2: % 140.16/19.50 | | | | | | | | | % 140.16/19.50 | | | | | | | | | (867) all_71_12 = n2 % 140.16/19.50 | | | | | | | | | % 140.16/19.50 | | | | | | | | | REDUCE: (138), (867) imply: % 140.16/19.50 | | | | | | | | | (868) a_select3(center, n2, n0) = all_71_9 % 140.16/19.50 | | | | | | | | | % 140.16/19.50 | | | | | | | | | REDUCE: (847), (867) imply: % 140.16/19.50 | | | | | | | | | (869) a_select3(q, n1, n2) = all_71_10 % 140.16/19.50 | | | | | | | | | % 140.16/19.50 | | | | | | | | | REDUCE: (152), (867) imply: % 140.16/19.50 | | | | | | | | | (870) leq(n2, n3) % 140.16/19.50 | | | | | | | | | % 140.16/19.50 | | | | | | | | | REDUCE: (135), (867) imply: % 140.16/19.51 | | | | | | | | | (871) leq(n0, n2) % 140.16/19.51 | | | | | | | | | % 140.16/19.51 | | | | | | | | | GROUND_INST: instantiating (65) with n2, all_71_11, all_71_9, % 140.16/19.51 | | | | | | | | | all_71_8, all_71_7, all_71_6, all_71_5, all_71_4, % 140.16/19.51 | | | | | | | | | all_71_3, all_71_2, all_71_1, all_71_0, % 140.16/19.51 | | | | | | | | | simplifying with (59), (91), (139), (141), (142), % 140.16/19.51 | | | | | | | | | (143), (144), (145), (146), (147), (868), (871) % 140.16/19.51 | | | | | | | | | gives: % 140.16/19.51 | | | | | | | | | (872) ~ (sum(n0, all_71_26, all_71_2) = all_71_1) | ~ % 140.16/19.51 | | | | | | | | | leq(n2, all_71_25) | (a_select3(q, pv10, n2) = % 140.16/19.51 | | | | | | | | | all_71_0 & $i(all_71_0)) % 140.16/19.51 | | | | | | | | | % 140.16/19.51 | | | | | | | | | BETA: splitting (872) gives: % 140.16/19.51 | | | | | | | | | % 140.16/19.51 | | | | | | | | | Case 1: % 140.16/19.51 | | | | | | | | | | % 140.16/19.51 | | | | | | | | | | (873) ~ (sum(n0, all_71_26, all_71_2) = all_71_1) % 140.16/19.51 | | | | | | | | | | % 140.16/19.51 | | | | | | | | | | REDUCE: (119), (873) imply: % 140.16/19.51 | | | | | | | | | | (874) ~ (sum(n0, n4, all_71_2) = all_71_1) % 140.16/19.51 | | | | | | | | | | % 140.16/19.51 | | | | | | | | | | PRED_UNIFY: (148), (874) imply: % 140.16/19.51 | | | | | | | | | | (875) $false % 140.16/19.51 | | | | | | | | | | % 140.16/19.51 | | | | | | | | | | CLOSE: (875) is inconsistent. % 140.16/19.51 | | | | | | | | | | % 140.16/19.51 | | | | | | | | | Case 2: % 140.16/19.51 | | | | | | | | | | % 140.16/19.51 | | | | | | | | | | (876) ~ leq(n2, all_71_25) | (a_select3(q, pv10, n2) = % 140.16/19.51 | | | | | | | | | | all_71_0 & $i(all_71_0)) % 140.16/19.51 | | | | | | | | | | % 140.16/19.51 | | | | | | | | | | BETA: splitting (876) gives: % 140.16/19.51 | | | | | | | | | | % 140.16/19.51 | | | | | | | | | | Case 1: % 140.16/19.51 | | | | | | | | | | | % 140.16/19.51 | | | | | | | | | | | (877) ~ leq(n2, all_71_25) % 140.16/19.51 | | | | | | | | | | | % 140.16/19.51 | | | | | | | | | | | REDUCE: (776), (877) imply: % 140.16/19.51 | | | | | | | | | | | (878) ~ leq(n2, n3) % 140.16/19.51 | | | | | | | | | | | % 140.16/19.51 | | | | | | | | | | | PRED_UNIFY: (870), (878) imply: % 140.16/19.51 | | | | | | | | | | | (879) $false % 140.16/19.51 | | | | | | | | | | | % 140.16/19.51 | | | | | | | | | | | CLOSE: (879) is inconsistent. % 140.16/19.51 | | | | | | | | | | | % 140.16/19.51 | | | | | | | | | | Case 2: % 140.16/19.51 | | | | | | | | | | | % 140.16/19.51 | | | | | | | | | | | (880) a_select3(q, pv10, n2) = all_71_0 & $i(all_71_0) % 140.16/19.51 | | | | | | | | | | | % 140.16/19.51 | | | | | | | | | | | ALPHA: (880) implies: % 140.16/19.51 | | | | | | | | | | | (881) a_select3(q, pv10, n2) = all_71_0 % 140.16/19.51 | | | | | | | | | | | % 140.16/19.51 | | | | | | | | | | | REDUCE: (846), (881) imply: % 140.16/19.51 | | | | | | | | | | | (882) a_select3(q, n1, n2) = all_71_0 % 140.16/19.51 | | | | | | | | | | | % 140.16/19.51 | | | | | | | | | | | GROUND_INST: instantiating (27) with all_71_10, all_71_0, n2, % 140.16/19.51 | | | | | | | | | | | n1, q, simplifying with (869), (882) gives: % 140.16/19.51 | | | | | | | | | | | (883) all_71_0 = all_71_10 % 140.16/19.51 | | | | | | | | | | | % 140.16/19.51 | | | | | | | | | | | REDUCE: (134), (883) imply: % 140.16/19.51 | | | | | | | | | | | (884) $false % 140.16/19.51 | | | | | | | | | | | % 140.16/19.51 | | | | | | | | | | | CLOSE: (884) is inconsistent. % 140.16/19.51 | | | | | | | | | | | % 140.16/19.51 | | | | | | | | | | End of split % 140.16/19.51 | | | | | | | | | | % 140.16/19.51 | | | | | | | | | End of split % 140.16/19.51 | | | | | | | | | % 140.16/19.51 | | | | | | | | End of split % 140.16/19.51 | | | | | | | | % 140.16/19.51 | | | | | | | End of split % 140.16/19.51 | | | | | | | % 140.16/19.51 | | | | | | End of split % 140.16/19.51 | | | | | | % 140.16/19.51 | | | | | Case 2: % 140.16/19.51 | | | | | | % 140.16/19.51 | | | | | | (885) all_71_12 = all_71_25 % 140.16/19.51 | | | | | | % 140.16/19.51 | | | | | | COMBINE_EQS: (776), (885) imply: % 140.16/19.51 | | | | | | (886) all_71_12 = n3 % 140.16/19.51 | | | | | | % 140.16/19.51 | | | | | | REDUCE: (138), (886) imply: % 140.16/19.51 | | | | | | (887) a_select3(center, n3, n0) = all_71_9 % 140.16/19.51 | | | | | | % 140.16/19.51 | | | | | | REDUCE: (137), (886) imply: % 140.16/19.51 | | | | | | (888) a_select3(q, pv10, n3) = all_71_10 % 140.16/19.51 | | | | | | % 140.16/19.51 | | | | | | REDUCE: (152), (886) imply: % 140.16/19.51 | | | | | | (889) leq(n3, n3) % 140.16/19.51 | | | | | | % 140.16/19.51 | | | | | | REDUCE: (135), (886) imply: % 140.16/19.51 | | | | | | (890) leq(n0, n3) % 140.16/19.51 | | | | | | % 140.16/19.51 | | | | | | GROUND_INST: instantiating (65) with n3, all_71_11, all_71_9, % 140.16/19.51 | | | | | | all_71_8, all_71_7, all_71_6, all_71_5, all_71_4, % 140.16/19.51 | | | | | | all_71_3, all_71_2, all_71_1, all_71_0, simplifying % 140.16/19.51 | | | | | | with (59), (98), (139), (141), (142), (143), (144), % 140.16/19.51 | | | | | | (145), (146), (147), (887), (890) gives: % 140.16/19.51 | | | | | | (891) ~ (sum(n0, all_71_26, all_71_2) = all_71_1) | ~ leq(n3, % 140.16/19.51 | | | | | | all_71_25) | (a_select3(q, pv10, n3) = all_71_0 & % 140.16/19.51 | | | | | | $i(all_71_0)) % 140.16/19.51 | | | | | | % 140.16/19.51 | | | | | | BETA: splitting (891) gives: % 140.16/19.51 | | | | | | % 140.16/19.51 | | | | | | Case 1: % 140.16/19.51 | | | | | | | % 140.16/19.51 | | | | | | | (892) ~ (sum(n0, all_71_26, all_71_2) = all_71_1) % 140.16/19.51 | | | | | | | % 140.16/19.51 | | | | | | | REDUCE: (119), (892) imply: % 140.16/19.51 | | | | | | | (893) ~ (sum(n0, n4, all_71_2) = all_71_1) % 140.16/19.51 | | | | | | | % 140.16/19.51 | | | | | | | PRED_UNIFY: (148), (893) imply: % 140.16/19.51 | | | | | | | (894) $false % 140.16/19.51 | | | | | | | % 140.16/19.51 | | | | | | | CLOSE: (894) is inconsistent. % 140.16/19.51 | | | | | | | % 140.16/19.51 | | | | | | Case 2: % 140.16/19.51 | | | | | | | % 140.16/19.51 | | | | | | | (895) ~ leq(n3, all_71_25) | (a_select3(q, pv10, n3) = % 140.16/19.51 | | | | | | | all_71_0 & $i(all_71_0)) % 140.16/19.51 | | | | | | | % 140.16/19.51 | | | | | | | BETA: splitting (895) gives: % 140.16/19.51 | | | | | | | % 140.16/19.51 | | | | | | | Case 1: % 140.16/19.51 | | | | | | | | % 140.16/19.51 | | | | | | | | (896) ~ leq(n3, all_71_25) % 140.16/19.51 | | | | | | | | % 140.16/19.51 | | | | | | | | REDUCE: (776), (896) imply: % 140.16/19.51 | | | | | | | | (897) ~ leq(n3, n3) % 140.16/19.51 | | | | | | | | % 140.16/19.51 | | | | | | | | PRED_UNIFY: (889), (897) imply: % 140.16/19.51 | | | | | | | | (898) $false % 140.16/19.51 | | | | | | | | % 140.16/19.51 | | | | | | | | CLOSE: (898) is inconsistent. % 140.16/19.51 | | | | | | | | % 140.16/19.51 | | | | | | | Case 2: % 140.16/19.51 | | | | | | | | % 140.16/19.51 | | | | | | | | (899) a_select3(q, pv10, n3) = all_71_0 & $i(all_71_0) % 140.16/19.51 | | | | | | | | % 140.16/19.51 | | | | | | | | ALPHA: (899) implies: % 140.16/19.51 | | | | | | | | (900) a_select3(q, pv10, n3) = all_71_0 % 140.16/19.51 | | | | | | | | % 140.16/19.51 | | | | | | | | GROUND_INST: instantiating (27) with all_71_10, all_71_0, n3, % 140.16/19.51 | | | | | | | | pv10, q, simplifying with (888), (900) gives: % 140.16/19.51 | | | | | | | | (901) all_71_0 = all_71_10 % 140.16/19.51 | | | | | | | | % 140.16/19.51 | | | | | | | | REDUCE: (134), (901) imply: % 140.16/19.51 | | | | | | | | (902) $false % 140.16/19.51 | | | | | | | | % 140.16/19.51 | | | | | | | | CLOSE: (902) is inconsistent. % 140.16/19.51 | | | | | | | | % 140.16/19.51 | | | | | | | End of split % 140.16/19.51 | | | | | | | % 140.16/19.51 | | | | | | End of split % 140.16/19.51 | | | | | | % 140.16/19.51 | | | | | End of split % 140.16/19.51 | | | | | % 140.16/19.51 | | | | Case 2: % 140.16/19.51 | | | | | % 140.16/19.51 | | | | | (903) all_71_12 = n0 % 140.16/19.51 | | | | | % 140.16/19.51 | | | | | REDUCE: (138), (903) imply: % 140.16/19.51 | | | | | (904) a_select3(center, n0, n0) = all_71_9 % 140.16/19.51 | | | | | % 140.16/19.51 | | | | | REDUCE: (137), (903) imply: % 140.16/19.51 | | | | | (905) a_select3(q, pv10, n0) = all_71_10 % 140.16/19.51 | | | | | % 140.16/19.51 | | | | | REDUCE: (152), (903) imply: % 140.16/19.51 | | | | | (906) leq(n0, n3) % 140.16/19.51 | | | | | % 140.16/19.51 | | | | | REDUCE: (135), (903) imply: % 140.16/19.51 | | | | | (907) leq(n0, n0) % 140.16/19.51 | | | | | % 140.16/19.51 | | | | | GROUND_INST: instantiating (65) with n0, all_71_11, all_71_9, % 140.16/19.51 | | | | | all_71_8, all_71_7, all_71_6, all_71_5, all_71_4, % 140.16/19.51 | | | | | all_71_3, all_71_2, all_71_1, all_71_0, simplifying with % 140.16/19.51 | | | | | (19), (59), (139), (141), (142), (143), (144), (145), % 140.16/19.51 | | | | | (146), (147), (904), (907) gives: % 140.16/19.51 | | | | | (908) ~ (sum(n0, all_71_26, all_71_2) = all_71_1) | ~ leq(n0, % 140.16/19.51 | | | | | all_71_25) | (a_select3(q, pv10, n0) = all_71_0 & % 140.16/19.51 | | | | | $i(all_71_0)) % 140.16/19.51 | | | | | % 140.16/19.51 | | | | | BETA: splitting (908) gives: % 140.16/19.51 | | | | | % 140.16/19.51 | | | | | Case 1: % 140.16/19.51 | | | | | | % 140.16/19.51 | | | | | | (909) ~ (sum(n0, all_71_26, all_71_2) = all_71_1) % 140.16/19.51 | | | | | | % 140.16/19.51 | | | | | | REDUCE: (119), (909) imply: % 140.16/19.51 | | | | | | (910) ~ (sum(n0, n4, all_71_2) = all_71_1) % 140.16/19.51 | | | | | | % 140.16/19.51 | | | | | | PRED_UNIFY: (148), (910) imply: % 140.16/19.51 | | | | | | (911) $false % 140.16/19.51 | | | | | | % 140.16/19.51 | | | | | | CLOSE: (911) is inconsistent. % 140.16/19.51 | | | | | | % 140.16/19.51 | | | | | Case 2: % 140.16/19.51 | | | | | | % 140.16/19.51 | | | | | | (912) ~ leq(n0, all_71_25) | (a_select3(q, pv10, n0) = all_71_0 % 140.16/19.51 | | | | | | & $i(all_71_0)) % 140.16/19.51 | | | | | | % 140.16/19.51 | | | | | | BETA: splitting (912) gives: % 140.16/19.51 | | | | | | % 140.16/19.51 | | | | | | Case 1: % 140.16/19.51 | | | | | | | % 140.16/19.51 | | | | | | | (913) ~ leq(n0, all_71_25) % 140.16/19.51 | | | | | | | % 140.16/19.51 | | | | | | | REDUCE: (776), (913) imply: % 140.16/19.51 | | | | | | | (914) ~ leq(n0, n3) % 140.16/19.51 | | | | | | | % 140.16/19.51 | | | | | | | PRED_UNIFY: (906), (914) imply: % 140.16/19.51 | | | | | | | (915) $false % 140.16/19.51 | | | | | | | % 140.16/19.51 | | | | | | | CLOSE: (915) is inconsistent. % 140.16/19.51 | | | | | | | % 140.16/19.51 | | | | | | Case 2: % 140.16/19.51 | | | | | | | % 140.16/19.51 | | | | | | | (916) a_select3(q, pv10, n0) = all_71_0 & $i(all_71_0) % 140.16/19.51 | | | | | | | % 140.16/19.51 | | | | | | | REF_CLOSE: (27), (134), (905), (916) are inconsistent by sub-proof % 140.16/19.51 | | | | | | | #6. % 140.16/19.51 | | | | | | | % 140.16/19.51 | | | | | | End of split % 140.16/19.51 | | | | | | % 140.16/19.51 | | | | | End of split % 140.16/19.51 | | | | | % 140.16/19.51 | | | | End of split % 140.16/19.51 | | | | % 140.16/19.51 | | | End of split % 140.16/19.51 | | | % 140.16/19.51 | | Case 2: % 140.16/19.51 | | | % 140.16/19.51 | | | (917) pv10 = n0 % 140.16/19.51 | | | (918) ~ gt(pv10, n0) % 140.16/19.51 | | | % 140.16/19.51 | | | REDUCE: (137), (917) imply: % 140.16/19.51 | | | (919) a_select3(q, n0, all_71_12) = all_71_10 % 140.16/19.51 | | | % 140.16/19.51 | | | REDUCE: (917), (918) imply: % 140.16/19.51 | | | (920) ~ gt(n0, n0) % 140.16/19.51 | | | % 140.16/19.51 | | | BETA: splitting (104) gives: % 140.16/19.51 | | | % 140.16/19.51 | | | Case 1: % 140.16/19.51 | | | | % 140.16/19.51 | | | | (921) gt(all_71_26, pv12) % 140.16/19.51 | | | | % 140.16/19.51 | | | | REDUCE: (119), (921) imply: % 140.16/19.51 | | | | (922) gt(n4, pv12) % 140.16/19.51 | | | | % 140.16/19.51 | | | | GROUND_INST: instantiating (1) with pv12, n4, n3, simplifying with (22), % 140.16/19.51 | | | | (101), (109), (922) gives: % 140.16/19.51 | | | | (923) leq(pv12, n3) % 140.16/19.51 | | | | % 140.16/19.51 | | | | GROUND_INST: instantiating (7) with all_71_25, n2, pv12, n3, simplifying % 140.16/19.51 | | | | with (90), (91), (117), (125), (923) gives: % 140.16/19.51 | | | | (924) leq(all_71_25, n2) % 140.16/19.51 | | | | % 140.16/19.51 | | | | GROUND_INST: instantiating (leq_gt2) with pv12, n3, simplifying with % 140.16/19.51 | | | | (22), (98), (923) gives: % 140.16/19.51 | | | | (925) pv12 = n3 | gt(n3, pv12) % 140.16/19.51 | | | | % 140.16/19.51 | | | | GROUND_INST: instantiating (transitivity_leq) with all_71_12, all_71_25, % 140.16/19.51 | | | | n2, simplifying with (58), (91), (117), (136), (924) gives: % 140.16/19.51 | | | | (926) leq(all_71_12, n2) % 140.16/19.51 | | | | % 140.16/19.51 | | | | GROUND_INST: instantiating (leq_gt2) with all_71_25, n2, simplifying % 140.16/19.51 | | | | with (91), (117), (924) gives: % 140.16/19.51 | | | | (927) all_71_25 = n2 | gt(n2, all_71_25) % 140.16/19.51 | | | | % 140.16/19.51 | | | | GROUND_INST: instantiating (leq_gt2) with all_71_12, n2, simplifying % 140.16/19.51 | | | | with (58), (91), (926) gives: % 140.16/19.51 | | | | (928) all_71_12 = n2 | gt(n2, all_71_12) % 140.16/19.51 | | | | % 140.16/19.51 | | | | BETA: splitting (123) gives: % 140.16/19.51 | | | | % 140.16/19.51 | | | | Case 1: % 140.16/19.51 | | | | | % 140.16/19.51 | | | | | (929) pv12 = n0 % 140.16/19.51 | | | | | % 140.16/19.51 | | | | | REDUCE: (156), (929) imply: % 140.16/19.51 | | | | | (930) gt(n0, n0) % 140.16/19.51 | | | | | % 140.16/19.51 | | | | | PRED_UNIFY: (920), (930) imply: % 140.16/19.51 | | | | | (931) $false % 140.16/19.51 | | | | | % 140.16/19.51 | | | | | CLOSE: (931) is inconsistent. % 140.16/19.51 | | | | | % 140.16/19.51 | | | | Case 2: % 140.16/19.51 | | | | | % 140.16/19.51 | | | | | (932) pv12 = n4 | pv12 = n3 | pv12 = n2 | pv12 = n1 % 140.16/19.51 | | | | | % 140.16/19.51 | | | | | BETA: splitting (149) gives: % 140.16/19.51 | | | | | % 140.16/19.51 | | | | | Case 1: % 140.16/19.51 | | | | | | % 140.16/19.51 | | | | | | (933) gt(all_71_12, n0) % 140.16/19.51 | | | | | | % 140.16/19.51 | | | | | | BETA: splitting (154) gives: % 140.16/19.51 | | | | | | % 140.16/19.51 | | | | | | Case 1: % 140.16/19.51 | | | | | | | % 140.16/19.52 | | | | | | | (934) gt(all_71_25, all_71_12) % 140.16/19.52 | | | | | | | % 140.16/19.52 | | | | | | | BETA: splitting (158) gives: % 140.16/19.52 | | | | | | | % 140.16/19.52 | | | | | | | Case 1: % 140.16/19.52 | | | | | | | | % 140.16/19.52 | | | | | | | | (935) gt(all_71_25, n0) % 140.16/19.52 | | | | | | | | % 140.16/19.52 | | | | | | | | BETA: splitting (157) gives: % 140.16/19.52 | | | | | | | | % 140.16/19.52 | | | | | | | | Case 1: % 140.16/19.52 | | | | | | | | | % 140.16/19.52 | | | | | | | | | (936) all_71_25 = n0 % 140.16/19.52 | | | | | | | | | % 140.16/19.52 | | | | | | | | | REDUCE: (935), (936) imply: % 140.16/19.52 | | | | | | | | | (937) gt(n0, n0) % 140.16/19.52 | | | | | | | | | % 140.16/19.52 | | | | | | | | | PRED_UNIFY: (920), (937) imply: % 140.16/19.52 | | | | | | | | | (938) $false % 140.16/19.52 | | | | | | | | | % 140.16/19.52 | | | | | | | | | CLOSE: (938) is inconsistent. % 140.16/19.52 | | | | | | | | | % 140.16/19.52 | | | | | | | | Case 2: % 140.16/19.52 | | | | | | | | | % 140.16/19.52 | | | | | | | | | (939) ~ (all_71_25 = n0) % 140.16/19.52 | | | | | | | | | % 140.16/19.52 | | | | | | | | | BETA: splitting (159) gives: % 140.16/19.52 | | | | | | | | | % 140.16/19.52 | | | | | | | | | Case 1: % 140.16/19.52 | | | | | | | | | | % 140.16/19.52 | | | | | | | | | | (940) all_71_12 = n0 % 140.16/19.52 | | | | | | | | | | % 140.16/19.52 | | | | | | | | | | REDUCE: (933), (940) imply: % 140.16/19.52 | | | | | | | | | | (941) gt(n0, n0) % 140.16/19.52 | | | | | | | | | | % 140.16/19.52 | | | | | | | | | | PRED_UNIFY: (920), (941) imply: % 140.16/19.52 | | | | | | | | | | (942) $false % 140.16/19.52 | | | | | | | | | | % 140.16/19.52 | | | | | | | | | | CLOSE: (942) is inconsistent. % 140.16/19.52 | | | | | | | | | | % 140.16/19.52 | | | | | | | | | Case 2: % 140.16/19.52 | | | | | | | | | | % 140.16/19.52 | | | | | | | | | | (943) ~ (all_71_12 = n0) % 140.16/19.52 | | | | | | | | | | % 140.16/19.52 | | | | | | | | | | BETA: splitting (925) gives: % 140.16/19.52 | | | | | | | | | | % 140.16/19.52 | | | | | | | | | | Case 1: % 140.16/19.52 | | | | | | | | | | | % 140.16/19.52 | | | | | | | | | | | (944) gt(n3, pv12) % 140.16/19.52 | | | | | | | | | | | % 140.16/19.52 | | | | | | | | | | | REF_CLOSE: (1), (11), (22), (24), (25), (58), (90), (91), % 140.16/19.52 | | | | | | | | | | | (105), (107), (117), (118), (125), (135), (153), % 140.16/19.52 | | | | | | | | | | | (920), (927), (928), (932), (934), (935), (939), % 140.16/19.52 | | | | | | | | | | | (943), (944), (irreflexivity_gt), % 140.16/19.52 | | | | | | | | | | | (transitivity_gt) are inconsistent by sub-proof % 140.16/19.52 | | | | | | | | | | | #15. % 140.16/19.52 | | | | | | | | | | | % 140.16/19.52 | | | | | | | | | | Case 2: % 140.16/19.52 | | | | | | | | | | | % 140.16/19.52 | | | | | | | | | | | (945) pv12 = n3 % 140.16/19.52 | | | | | | | | | | | % 140.16/19.52 | | | | | | | | | | | REDUCE: (118), (945) imply: % 140.16/19.52 | | | | | | | | | | | (946) pred(n3) = all_71_25 % 140.16/19.52 | | | | | | | | | | | % 140.16/19.52 | | | | | | | | | | | GROUND_INST: instantiating (24) with n2, all_71_25, n3, % 140.16/19.52 | | | | | | | | | | | simplifying with (108), (946) gives: % 140.16/19.52 | | | | | | | | | | | (947) all_71_25 = n2 % 140.16/19.52 | | | | | | | | | | | % 140.16/19.52 | | | | | | | | | | | REDUCE: (934), (947) imply: % 140.16/19.52 | | | | | | | | | | | (948) gt(n2, all_71_12) % 140.16/19.52 | | | | | | | | | | | % 140.16/19.52 | | | | | | | | | | | GROUND_INST: instantiating (1) with all_71_12, n2, n1, % 140.16/19.52 | | | | | | | | | | | simplifying with (58), (91), (107), (948) gives: % 140.16/19.52 | | | | | | | | | | | (949) leq(all_71_12, n1) % 140.16/19.52 | | | | | | | | | | | % 140.16/19.52 | | | | | | | | | | | GROUND_INST: instantiating (11) with all_71_12, simplifying % 140.16/19.52 | | | | | | | | | | | with (58), (135), (949) gives: % 140.16/19.52 | | | | | | | | | | | (950) all_71_12 = n1 | all_71_12 = n0 % 140.16/19.52 | | | | | | | | | | | % 140.16/19.52 | | | | | | | | | | | BETA: splitting (950) gives: % 140.16/19.52 | | | | | | | | | | | % 140.16/19.52 | | | | | | | | | | | Case 1: % 140.16/19.52 | | | | | | | | | | | | % 140.16/19.52 | | | | | | | | | | | | (951) all_71_12 = n0 % 140.16/19.52 | | | | | | | | | | | | % 140.16/19.52 | | | | | | | | | | | | REDUCE: (943), (951) imply: % 140.16/19.52 | | | | | | | | | | | | (952) $false % 140.16/19.52 | | | | | | | | | | | | % 140.16/19.52 | | | | | | | | | | | | CLOSE: (952) is inconsistent. % 140.16/19.52 | | | | | | | | | | | | % 140.16/19.52 | | | | | | | | | | | Case 2: % 140.16/19.52 | | | | | | | | | | | | % 140.16/19.52 | | | | | | | | | | | | (953) all_71_12 = n1 % 140.16/19.52 | | | | | | | | | | | | % 140.16/19.52 | | | | | | | | | | | | REDUCE: (138), (953) imply: % 140.16/19.52 | | | | | | | | | | | | (954) a_select3(center, n1, n0) = all_71_9 % 140.16/19.52 | | | | | | | | | | | | % 140.16/19.52 | | | | | | | | | | | | REDUCE: (919), (953) imply: % 140.16/19.52 | | | | | | | | | | | | (955) a_select3(q, n0, n1) = all_71_10 % 140.16/19.52 | | | | | | | | | | | | % 140.16/19.52 | | | | | | | | | | | | REDUCE: (926), (953) imply: % 140.16/19.52 | | | | | | | | | | | | (956) leq(n1, n2) % 140.16/19.52 | | | | | | | | | | | | % 140.16/19.52 | | | | | | | | | | | | REDUCE: (135), (953) imply: % 140.16/19.52 | | | | | | | | | | | | (957) leq(n0, n1) % 140.16/19.52 | | | | | | | | | | | | % 140.16/19.52 | | | | | | | | | | | | GROUND_INST: instantiating (65) with n1, all_71_11, all_71_9, % 140.16/19.52 | | | | | | | | | | | | all_71_8, all_71_7, all_71_6, all_71_5, all_71_4, % 140.16/19.52 | | | | | | | | | | | | all_71_3, all_71_2, all_71_1, all_71_0, % 140.16/19.52 | | | | | | | | | | | | simplifying with (59), (80), (139), (141), (142), % 140.16/19.52 | | | | | | | | | | | | (143), (144), (145), (146), (147), (954), (957) % 140.16/19.52 | | | | | | | | | | | | gives: % 140.16/19.52 | | | | | | | | | | | | (958) ~ (sum(n0, all_71_26, all_71_2) = all_71_1) | ~ % 140.16/19.52 | | | | | | | | | | | | leq(n1, all_71_25) | (a_select3(q, pv10, n1) = % 140.16/19.52 | | | | | | | | | | | | all_71_0 & $i(all_71_0)) % 140.16/19.52 | | | | | | | | | | | | % 140.16/19.52 | | | | | | | | | | | | BETA: splitting (958) gives: % 140.16/19.52 | | | | | | | | | | | | % 140.16/19.52 | | | | | | | | | | | | Case 1: % 140.16/19.52 | | | | | | | | | | | | | % 140.16/19.52 | | | | | | | | | | | | | (959) ~ (sum(n0, all_71_26, all_71_2) = all_71_1) % 140.16/19.52 | | | | | | | | | | | | | % 140.16/19.52 | | | | | | | | | | | | | REDUCE: (119), (959) imply: % 140.16/19.52 | | | | | | | | | | | | | (960) ~ (sum(n0, n4, all_71_2) = all_71_1) % 140.16/19.52 | | | | | | | | | | | | | % 140.16/19.52 | | | | | | | | | | | | | PRED_UNIFY: (148), (960) imply: % 140.16/19.52 | | | | | | | | | | | | | (961) $false % 140.16/19.52 | | | | | | | | | | | | | % 140.16/19.52 | | | | | | | | | | | | | CLOSE: (961) is inconsistent. % 140.16/19.52 | | | | | | | | | | | | | % 140.16/19.52 | | | | | | | | | | | | Case 2: % 140.16/19.52 | | | | | | | | | | | | | % 140.16/19.52 | | | | | | | | | | | | | (962) ~ leq(n1, all_71_25) | (a_select3(q, pv10, n1) = % 140.16/19.52 | | | | | | | | | | | | | all_71_0 & $i(all_71_0)) % 140.16/19.52 | | | | | | | | | | | | | % 140.16/19.52 | | | | | | | | | | | | | BETA: splitting (962) gives: % 140.16/19.52 | | | | | | | | | | | | | % 140.16/19.52 | | | | | | | | | | | | | Case 1: % 140.16/19.52 | | | | | | | | | | | | | | % 140.16/19.52 | | | | | | | | | | | | | | (963) ~ leq(n1, all_71_25) % 140.16/19.52 | | | | | | | | | | | | | | % 140.16/19.52 | | | | | | | | | | | | | | REDUCE: (947), (963) imply: % 140.16/19.52 | | | | | | | | | | | | | | (964) ~ leq(n1, n2) % 140.16/19.52 | | | | | | | | | | | | | | % 140.16/19.52 | | | | | | | | | | | | | | PRED_UNIFY: (956), (964) imply: % 140.16/19.52 | | | | | | | | | | | | | | (965) $false % 140.16/19.52 | | | | | | | | | | | | | | % 140.16/19.52 | | | | | | | | | | | | | | CLOSE: (965) is inconsistent. % 140.16/19.52 | | | | | | | | | | | | | | % 140.16/19.52 | | | | | | | | | | | | | Case 2: % 140.16/19.52 | | | | | | | | | | | | | | % 140.16/19.52 | | | | | | | | | | | | | | (966) a_select3(q, pv10, n1) = all_71_0 & $i(all_71_0) % 140.16/19.52 | | | | | | | | | | | | | | % 140.16/19.52 | | | | | | | | | | | | | | REF_CLOSE: (27), (134), (917), (955), (966) are inconsistent % 140.16/19.52 | | | | | | | | | | | | | | by sub-proof #2. % 140.16/19.52 | | | | | | | | | | | | | | % 140.16/19.52 | | | | | | | | | | | | | End of split % 140.16/19.52 | | | | | | | | | | | | | % 140.16/19.52 | | | | | | | | | | | | End of split % 140.16/19.52 | | | | | | | | | | | | % 140.16/19.52 | | | | | | | | | | | End of split % 140.16/19.52 | | | | | | | | | | | % 140.16/19.52 | | | | | | | | | | End of split % 140.16/19.52 | | | | | | | | | | % 140.16/19.52 | | | | | | | | | End of split % 140.16/19.52 | | | | | | | | | % 140.16/19.52 | | | | | | | | End of split % 140.16/19.52 | | | | | | | | % 140.16/19.52 | | | | | | | Case 2: % 140.16/19.52 | | | | | | | | % 140.16/19.52 | | | | | | | | (967) all_71_25 = n0 % 140.16/19.52 | | | | | | | | (968) ~ gt(all_71_25, n0) % 140.16/19.52 | | | | | | | | % 140.16/19.52 | | | | | | | | REDUCE: (934), (967) imply: % 140.16/19.52 | | | | | | | | (969) gt(n0, all_71_12) % 140.16/19.52 | | | | | | | | % 140.16/19.52 | | | | | | | | GROUND_INST: instantiating (transitivity_gt) with n0, all_71_12, % 140.16/19.52 | | | | | | | | n0, simplifying with (19), (58), (920), (933), % 140.16/19.52 | | | | | | | | (969) gives: % 140.16/19.52 | | | | | | | | (970) $false % 140.16/19.52 | | | | | | | | % 140.16/19.52 | | | | | | | | CLOSE: (970) is inconsistent. % 140.16/19.52 | | | | | | | | % 140.16/19.52 | | | | | | | End of split % 140.16/19.52 | | | | | | | % 140.16/19.52 | | | | | | Case 2: % 140.16/19.52 | | | | | | | % 140.16/19.52 | | | | | | | (971) all_71_12 = all_71_25 % 140.16/19.52 | | | | | | | (972) ~ gt(all_71_25, all_71_12) % 140.16/19.52 | | | | | | | % 140.16/19.52 | | | | | | | REDUCE: (138), (971) imply: % 140.16/19.52 | | | | | | | (973) a_select3(center, all_71_25, n0) = all_71_9 % 140.16/19.52 | | | | | | | % 140.16/19.52 | | | | | | | REDUCE: (919), (971) imply: % 140.16/19.52 | | | | | | | (974) a_select3(q, n0, all_71_25) = all_71_10 % 140.16/19.52 | | | | | | | % 140.16/19.52 | | | | | | | REDUCE: (933), (971) imply: % 140.16/19.52 | | | | | | | (975) gt(all_71_25, n0) % 140.16/19.52 | | | | | | | % 140.16/19.52 | | | | | | | REDUCE: (971), (972) imply: % 140.16/19.52 | | | | | | | (976) ~ gt(all_71_25, all_71_25) % 140.16/19.52 | | | | | | | % 140.16/19.52 | | | | | | | BETA: splitting (161) gives: % 140.16/19.52 | | | | | | | % 140.16/19.52 | | | | | | | Case 1: % 140.16/19.52 | | | | | | | | % 140.16/19.52 | | | | | | | | (977) gt(pv12, n1) % 140.16/19.52 | | | | | | | | % 140.16/19.52 | | | | | | | | GROUND_INST: instantiating (1) with n1, pv12, all_71_25, % 140.16/19.52 | | | | | | | | simplifying with (22), (80), (118), (977) gives: % 140.16/19.52 | | | | | | | | (978) leq(n1, all_71_25) % 140.16/19.52 | | | | | | | | % 140.16/19.52 | | | | | | | | BETA: splitting (157) gives: % 140.16/19.52 | | | | | | | | % 140.16/19.52 | | | | | | | | Case 1: % 140.16/19.52 | | | | | | | | | % 140.16/19.52 | | | | | | | | | (979) all_71_25 = n0 % 140.16/19.52 | | | | | | | | | % 140.16/19.52 | | | | | | | | | REDUCE: (975), (979) imply: % 140.16/19.52 | | | | | | | | | (980) gt(n0, n0) % 140.16/19.52 | | | | | | | | | % 140.16/19.52 | | | | | | | | | PRED_UNIFY: (920), (980) imply: % 140.16/19.52 | | | | | | | | | (981) $false % 140.16/19.52 | | | | | | | | | % 140.16/19.52 | | | | | | | | | CLOSE: (981) is inconsistent. % 140.16/19.52 | | | | | | | | | % 140.16/19.52 | | | | | | | | Case 2: % 140.16/19.52 | | | | | | | | | % 140.16/19.52 | | | | | | | | | (982) ~ (all_71_25 = n0) % 140.16/19.52 | | | | | | | | | % 140.16/19.52 | | | | | | | | | BETA: splitting (925) gives: % 140.16/19.52 | | | | | | | | | % 140.16/19.52 | | | | | | | | | Case 1: % 140.16/19.52 | | | | | | | | | | % 140.16/19.52 | | | | | | | | | | (983) gt(n3, pv12) % 140.16/19.52 | | | | | | | | | | % 140.16/19.52 | | | | | | | | | | BETA: splitting (927) gives: % 140.16/19.52 | | | | | | | | | | % 140.16/19.52 | | | | | | | | | | Case 1: % 140.16/19.52 | | | | | | | | | | | % 140.16/19.52 | | | | | | | | | | | (984) gt(n2, all_71_25) % 140.16/19.52 | | | | | | | | | | | % 140.16/19.52 | | | | | | | | | | | GROUND_INST: instantiating (1) with all_71_25, n2, n1, % 140.16/19.52 | | | | | | | | | | | simplifying with (91), (107), (117), (984) gives: % 140.16/19.52 | | | | | | | | | | | (985) leq(all_71_25, n1) % 140.16/19.52 | | | | | | | | | | | % 140.16/19.52 | | | | | | | | | | | BETA: splitting (932) gives: % 140.16/19.52 | | | | | | | | | | | % 140.16/19.52 | | | | | | | | | | | Case 1: % 140.16/19.52 | | | | | | | | | | | | % 140.16/19.52 | | | | | | | | | | | | (986) pv12 = n1 % 140.16/19.52 | | | | | | | | | | | | % 140.16/19.52 | | | | | | | | | | | | REF_CLOSE: (24), (105), (118), (920), (975), (986) are % 140.16/19.52 | | | | | | | | | | | | inconsistent by sub-proof #16. % 140.16/19.52 | | | | | | | | | | | | % 140.16/19.52 | | | | | | | | | | | Case 2: % 140.16/19.52 | | | | | | | | | | | | % 140.16/19.52 | | | | | | | | | | | | % 140.16/19.52 | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_71_25, simplifying % 140.16/19.52 | | | | | | | | | | | | with (117), (153), (985) gives: % 140.16/19.52 | | | | | | | | | | | | (987) all_71_25 = n1 | all_71_25 = n0 % 140.16/19.52 | | | | | | | | | | | | % 140.16/19.52 | | | | | | | | | | | | BETA: splitting (987) gives: % 140.16/19.52 | | | | | | | | | | | | % 140.16/19.52 | | | | | | | | | | | | Case 1: % 140.16/19.52 | | | | | | | | | | | | | % 140.16/19.52 | | | | | | | | | | | | | (988) all_71_25 = n0 % 140.16/19.52 | | | | | | | | | | | | | % 140.16/19.52 | | | | | | | | | | | | | REDUCE: (982), (988) imply: % 140.16/19.52 | | | | | | | | | | | | | (989) $false % 140.16/19.52 | | | | | | | | | | | | | % 140.16/19.52 | | | | | | | | | | | | | CLOSE: (989) is inconsistent. % 140.16/19.52 | | | | | | | | | | | | | % 140.16/19.52 | | | | | | | | | | | | Case 2: % 140.16/19.52 | | | | | | | | | | | | | % 140.16/19.52 | | | | | | | | | | | | | (990) all_71_25 = n1 % 140.16/19.52 | | | | | | | | | | | | | % 140.16/19.52 | | | | | | | | | | | | | REDUCE: (973), (990) imply: % 140.16/19.52 | | | | | | | | | | | | | (991) a_select3(center, n1, n0) = all_71_9 % 140.16/19.52 | | | | | | | | | | | | | % 140.16/19.52 | | | | | | | | | | | | | REDUCE: (974), (990) imply: % 140.16/19.52 | | | | | | | | | | | | | (992) a_select3(q, n0, n1) = all_71_10 % 140.16/19.52 | | | | | | | | | | | | | % 140.16/19.52 | | | | | | | | | | | | | REDUCE: (978), (990) imply: % 140.16/19.52 | | | | | | | | | | | | | (993) leq(n1, n1) % 140.16/19.52 | | | | | | | | | | | | | % 140.16/19.52 | | | | | | | | | | | | | REDUCE: (153), (990) imply: % 140.16/19.52 | | | | | | | | | | | | | (994) leq(n0, n1) % 140.16/19.52 | | | | | | | | | | | | | % 140.16/19.52 | | | | | | | | | | | | | GROUND_INST: instantiating (65) with n1, all_71_11, all_71_9, % 140.16/19.52 | | | | | | | | | | | | | all_71_8, all_71_7, all_71_6, all_71_5, all_71_4, % 140.16/19.52 | | | | | | | | | | | | | all_71_3, all_71_2, all_71_1, all_71_0, % 140.16/19.52 | | | | | | | | | | | | | simplifying with (59), (80), (139), (141), (142), % 140.16/19.52 | | | | | | | | | | | | | (143), (144), (145), (146), (147), (991), (994) % 140.16/19.52 | | | | | | | | | | | | | gives: % 140.16/19.52 | | | | | | | | | | | | | (995) ~ (sum(n0, all_71_26, all_71_2) = all_71_1) | ~ % 140.16/19.52 | | | | | | | | | | | | | leq(n1, all_71_25) | (a_select3(q, pv10, n1) = % 140.16/19.52 | | | | | | | | | | | | | all_71_0 & $i(all_71_0)) % 140.16/19.52 | | | | | | | | | | | | | % 140.16/19.52 | | | | | | | | | | | | | BETA: splitting (995) gives: % 140.16/19.52 | | | | | | | | | | | | | % 140.16/19.52 | | | | | | | | | | | | | Case 1: % 140.16/19.52 | | | | | | | | | | | | | | % 140.16/19.52 | | | | | | | | | | | | | | (996) ~ (sum(n0, all_71_26, all_71_2) = all_71_1) % 140.16/19.52 | | | | | | | | | | | | | | % 140.16/19.52 | | | | | | | | | | | | | | REDUCE: (119), (996) imply: % 140.16/19.52 | | | | | | | | | | | | | | (997) ~ (sum(n0, n4, all_71_2) = all_71_1) % 140.16/19.52 | | | | | | | | | | | | | | % 140.16/19.52 | | | | | | | | | | | | | | PRED_UNIFY: (148), (997) imply: % 140.16/19.52 | | | | | | | | | | | | | | (998) $false % 140.16/19.52 | | | | | | | | | | | | | | % 140.16/19.52 | | | | | | | | | | | | | | CLOSE: (998) is inconsistent. % 140.16/19.52 | | | | | | | | | | | | | | % 140.16/19.52 | | | | | | | | | | | | | Case 2: % 140.16/19.52 | | | | | | | | | | | | | | % 140.16/19.52 | | | | | | | | | | | | | | (999) ~ leq(n1, all_71_25) | (a_select3(q, pv10, n1) = % 140.16/19.52 | | | | | | | | | | | | | | all_71_0 & $i(all_71_0)) % 140.16/19.52 | | | | | | | | | | | | | | % 140.16/19.52 | | | | | | | | | | | | | | BETA: splitting (999) gives: % 140.16/19.52 | | | | | | | | | | | | | | % 140.16/19.52 | | | | | | | | | | | | | | Case 1: % 140.16/19.52 | | | | | | | | | | | | | | | % 140.16/19.52 | | | | | | | | | | | | | | | (1000) ~ leq(n1, all_71_25) % 140.16/19.52 | | | | | | | | | | | | | | | % 140.16/19.52 | | | | | | | | | | | | | | | REDUCE: (990), (1000) imply: % 140.16/19.52 | | | | | | | | | | | | | | | (1001) ~ leq(n1, n1) % 140.16/19.52 | | | | | | | | | | | | | | | % 140.16/19.52 | | | | | | | | | | | | | | | PRED_UNIFY: (993), (1001) imply: % 140.16/19.52 | | | | | | | | | | | | | | | (1002) $false % 140.16/19.52 | | | | | | | | | | | | | | | % 140.16/19.52 | | | | | | | | | | | | | | | CLOSE: (1002) is inconsistent. % 140.16/19.52 | | | | | | | | | | | | | | | % 140.16/19.52 | | | | | | | | | | | | | | Case 2: % 140.16/19.52 | | | | | | | | | | | | | | | % 140.16/19.52 | | | | | | | | | | | | | | | (1003) a_select3(q, pv10, n1) = all_71_0 & $i(all_71_0) % 140.16/19.52 | | | | | | | | | | | | | | | % 140.16/19.52 | | | | | | | | | | | | | | | ALPHA: (1003) implies: % 140.16/19.52 | | | | | | | | | | | | | | | (1004) a_select3(q, pv10, n1) = all_71_0 % 140.16/19.52 | | | | | | | | | | | | | | | % 140.16/19.52 | | | | | | | | | | | | | | | REDUCE: (917), (1004) imply: % 140.16/19.52 | | | | | | | | | | | | | | | (1005) a_select3(q, n0, n1) = all_71_0 % 140.16/19.52 | | | | | | | | | | | | | | | % 140.16/19.52 | | | | | | | | | | | | | | | GROUND_INST: instantiating (27) with all_71_10, all_71_0, n1, % 140.16/19.52 | | | | | | | | | | | | | | | n0, q, simplifying with (992), (1005) gives: % 140.16/19.52 | | | | | | | | | | | | | | | (1006) all_71_0 = all_71_10 % 140.16/19.52 | | | | | | | | | | | | | | | % 140.16/19.52 | | | | | | | | | | | | | | | REDUCE: (134), (1006) imply: % 140.16/19.52 | | | | | | | | | | | | | | | (1007) $false % 140.16/19.52 | | | | | | | | | | | | | | | % 140.16/19.52 | | | | | | | | | | | | | | | CLOSE: (1007) is inconsistent. % 140.16/19.52 | | | | | | | | | | | | | | | % 140.16/19.53 | | | | | | | | | | | | | | End of split % 140.16/19.53 | | | | | | | | | | | | | | % 140.16/19.53 | | | | | | | | | | | | | End of split % 140.16/19.53 | | | | | | | | | | | | | % 140.16/19.53 | | | | | | | | | | | | End of split % 140.16/19.53 | | | | | | | | | | | | % 140.16/19.53 | | | | | | | | | | | End of split % 140.16/19.53 | | | | | | | | | | | % 140.16/19.53 | | | | | | | | | | Case 2: % 140.16/19.53 | | | | | | | | | | | % 140.16/19.53 | | | | | | | | | | | (1008) all_71_25 = n2 % 140.16/19.53 | | | | | | | | | | | % 140.16/19.53 | | | | | | | | | | | REDUCE: (125), (1008) imply: % 140.16/19.53 | | | | | | | | | | | (1009) succ(n2) = pv12 % 140.16/19.53 | | | | | | | | | | | % 140.16/19.53 | | | | | | | | | | | REF_CLOSE: (22), (25), (90), (983), (1009), % 140.16/19.53 | | | | | | | | | | | (irreflexivity_gt) are inconsistent by sub-proof % 140.16/19.53 | | | | | | | | | | | #23. % 140.16/19.53 | | | | | | | | | | | % 140.16/19.53 | | | | | | | | | | End of split % 140.16/19.53 | | | | | | | | | | % 140.16/19.53 | | | | | | | | | Case 2: % 140.16/19.53 | | | | | | | | | | % 140.16/19.53 | | | | | | | | | | (1010) pv12 = n3 % 140.16/19.53 | | | | | | | | | | % 140.16/19.53 | | | | | | | | | | REDUCE: (118), (1010) imply: % 140.16/19.53 | | | | | | | | | | (1011) pred(n3) = all_71_25 % 140.16/19.53 | | | | | | | | | | % 140.16/19.53 | | | | | | | | | | GROUND_INST: instantiating (24) with n2, all_71_25, n3, % 140.16/19.53 | | | | | | | | | | simplifying with (108), (1011) gives: % 140.16/19.53 | | | | | | | | | | (1012) all_71_25 = n2 % 140.16/19.53 | | | | | | | | | | % 140.16/19.53 | | | | | | | | | | REDUCE: (973), (1012) imply: % 140.16/19.53 | | | | | | | | | | (1013) a_select3(center, n2, n0) = all_71_9 % 140.16/19.53 | | | | | | | | | | % 140.16/19.53 | | | | | | | | | | REDUCE: (974), (1012) imply: % 140.16/19.53 | | | | | | | | | | (1014) a_select3(q, n0, n2) = all_71_10 % 140.16/19.53 | | | | | | | | | | % 140.16/19.53 | | | | | | | | | | REDUCE: (924), (1012) imply: % 140.16/19.53 | | | | | | | | | | (1015) leq(n2, n2) % 140.16/19.53 | | | | | | | | | | % 140.16/19.53 | | | | | | | | | | REDUCE: (153), (1012) imply: % 140.16/19.53 | | | | | | | | | | (1016) leq(n0, n2) % 140.16/19.53 | | | | | | | | | | % 140.16/19.53 | | | | | | | | | | GROUND_INST: instantiating (65) with n2, all_71_11, all_71_9, % 140.16/19.53 | | | | | | | | | | all_71_8, all_71_7, all_71_6, all_71_5, all_71_4, % 140.16/19.53 | | | | | | | | | | all_71_3, all_71_2, all_71_1, all_71_0, % 140.16/19.53 | | | | | | | | | | simplifying with (59), (91), (139), (141), (142), % 140.16/19.53 | | | | | | | | | | (143), (144), (145), (146), (147), (1013), (1016) % 140.16/19.53 | | | | | | | | | | gives: % 140.16/19.53 | | | | | | | | | | (1017) ~ (sum(n0, all_71_26, all_71_2) = all_71_1) | ~ % 140.16/19.53 | | | | | | | | | | leq(n2, all_71_25) | (a_select3(q, pv10, n2) = % 140.16/19.53 | | | | | | | | | | all_71_0 & $i(all_71_0)) % 140.16/19.53 | | | | | | | | | | % 140.16/19.53 | | | | | | | | | | BETA: splitting (1017) gives: % 140.16/19.53 | | | | | | | | | | % 140.16/19.53 | | | | | | | | | | Case 1: % 140.16/19.53 | | | | | | | | | | | % 140.16/19.53 | | | | | | | | | | | (1018) ~ (sum(n0, all_71_26, all_71_2) = all_71_1) % 140.16/19.53 | | | | | | | | | | | % 140.16/19.53 | | | | | | | | | | | REDUCE: (119), (1018) imply: % 140.16/19.53 | | | | | | | | | | | (1019) ~ (sum(n0, n4, all_71_2) = all_71_1) % 140.16/19.53 | | | | | | | | | | | % 140.16/19.53 | | | | | | | | | | | PRED_UNIFY: (148), (1019) imply: % 140.16/19.53 | | | | | | | | | | | (1020) $false % 140.16/19.53 | | | | | | | | | | | % 140.16/19.53 | | | | | | | | | | | CLOSE: (1020) is inconsistent. % 140.16/19.53 | | | | | | | | | | | % 140.16/19.53 | | | | | | | | | | Case 2: % 140.16/19.53 | | | | | | | | | | | % 140.16/19.53 | | | | | | | | | | | (1021) ~ leq(n2, all_71_25) | (a_select3(q, pv10, n2) = % 140.16/19.53 | | | | | | | | | | | all_71_0 & $i(all_71_0)) % 140.16/19.53 | | | | | | | | | | | % 140.16/19.53 | | | | | | | | | | | BETA: splitting (1021) gives: % 140.16/19.53 | | | | | | | | | | | % 140.16/19.53 | | | | | | | | | | | Case 1: % 140.16/19.53 | | | | | | | | | | | | % 140.16/19.53 | | | | | | | | | | | | (1022) ~ leq(n2, all_71_25) % 140.16/19.53 | | | | | | | | | | | | % 140.16/19.53 | | | | | | | | | | | | REDUCE: (1012), (1022) imply: % 140.16/19.53 | | | | | | | | | | | | (1023) ~ leq(n2, n2) % 140.16/19.53 | | | | | | | | | | | | % 140.16/19.53 | | | | | | | | | | | | PRED_UNIFY: (1015), (1023) imply: % 140.16/19.53 | | | | | | | | | | | | (1024) $false % 140.16/19.53 | | | | | | | | | | | | % 140.16/19.53 | | | | | | | | | | | | CLOSE: (1024) is inconsistent. % 140.16/19.53 | | | | | | | | | | | | % 140.16/19.53 | | | | | | | | | | | Case 2: % 140.16/19.53 | | | | | | | | | | | | % 140.16/19.53 | | | | | | | | | | | | (1025) a_select3(q, pv10, n2) = all_71_0 & $i(all_71_0) % 140.16/19.53 | | | | | | | | | | | | % 140.16/19.53 | | | | | | | | | | | | ALPHA: (1025) implies: % 140.16/19.53 | | | | | | | | | | | | (1026) a_select3(q, pv10, n2) = all_71_0 % 140.16/19.53 | | | | | | | | | | | | % 140.16/19.53 | | | | | | | | | | | | REDUCE: (917), (1026) imply: % 140.16/19.53 | | | | | | | | | | | | (1027) a_select3(q, n0, n2) = all_71_0 % 140.16/19.53 | | | | | | | | | | | | % 140.16/19.53 | | | | | | | | | | | | GROUND_INST: instantiating (27) with all_71_10, all_71_0, n2, % 140.16/19.53 | | | | | | | | | | | | n0, q, simplifying with (1014), (1027) gives: % 140.16/19.53 | | | | | | | | | | | | (1028) all_71_0 = all_71_10 % 140.16/19.53 | | | | | | | | | | | | % 140.16/19.53 | | | | | | | | | | | | REDUCE: (134), (1028) imply: % 140.16/19.53 | | | | | | | | | | | | (1029) $false % 140.16/19.53 | | | | | | | | | | | | % 140.16/19.53 | | | | | | | | | | | | CLOSE: (1029) is inconsistent. % 140.16/19.53 | | | | | | | | | | | | % 140.16/19.53 | | | | | | | | | | | End of split % 140.16/19.53 | | | | | | | | | | | % 140.16/19.53 | | | | | | | | | | End of split % 140.16/19.53 | | | | | | | | | | % 140.16/19.53 | | | | | | | | | End of split % 140.16/19.53 | | | | | | | | | % 140.16/19.53 | | | | | | | | End of split % 140.16/19.53 | | | | | | | | % 140.16/19.53 | | | | | | | Case 2: % 140.16/19.53 | | | | | | | | % 140.16/19.53 | | | | | | | | (1030) pv12 = n1 % 140.16/19.53 | | | | | | | | % 140.16/19.53 | | | | | | | | REF_CLOSE: (24), (105), (118), (920), (975), (1030) are % 140.16/19.53 | | | | | | | | inconsistent by sub-proof #16. % 140.16/19.53 | | | | | | | | % 140.16/19.53 | | | | | | | End of split % 140.16/19.53 | | | | | | | % 140.16/19.53 | | | | | | End of split % 140.16/19.53 | | | | | | % 140.16/19.53 | | | | | Case 2: % 140.16/19.53 | | | | | | % 140.16/19.53 | | | | | | (1031) all_71_12 = n0 % 140.16/19.53 | | | | | | (1032) ~ gt(all_71_12, n0) % 140.16/19.53 | | | | | | % 140.16/19.53 | | | | | | REDUCE: (138), (1031) imply: % 140.16/19.53 | | | | | | (1033) a_select3(center, n0, n0) = all_71_9 % 140.16/19.53 | | | | | | % 140.16/19.53 | | | | | | REDUCE: (919), (1031) imply: % 140.16/19.53 | | | | | | (1034) a_select3(q, n0, n0) = all_71_10 % 140.16/19.53 | | | | | | % 140.16/19.53 | | | | | | REDUCE: (135), (1031) imply: % 140.16/19.53 | | | | | | (1035) leq(n0, n0) % 140.16/19.53 | | | | | | % 140.16/19.53 | | | | | | BETA: splitting (154) gives: % 140.16/19.53 | | | | | | % 140.16/19.53 | | | | | | Case 1: % 140.16/19.53 | | | | | | | % 140.16/19.53 | | | | | | | (1036) gt(all_71_25, all_71_12) % 140.16/19.53 | | | | | | | % 140.16/19.53 | | | | | | | REDUCE: (1031), (1036) imply: % 140.16/19.53 | | | | | | | (1037) gt(all_71_25, n0) % 140.16/19.53 | | | | | | | % 140.16/19.53 | | | | | | | BETA: splitting (157) gives: % 140.16/19.53 | | | | | | | % 140.16/19.53 | | | | | | | Case 1: % 140.16/19.53 | | | | | | | | % 140.16/19.53 | | | | | | | | (1038) all_71_25 = n0 % 140.16/19.53 | | | | | | | | % 140.16/19.53 | | | | | | | | REDUCE: (1037), (1038) imply: % 140.16/19.53 | | | | | | | | (1039) gt(n0, n0) % 140.16/19.53 | | | | | | | | % 140.16/19.53 | | | | | | | | PRED_UNIFY: (920), (1039) imply: % 140.16/19.53 | | | | | | | | (1040) $false % 140.16/19.53 | | | | | | | | % 140.16/19.53 | | | | | | | | CLOSE: (1040) is inconsistent. % 140.16/19.53 | | | | | | | | % 140.16/19.53 | | | | | | | Case 2: % 140.16/19.53 | | | | | | | | % 140.16/19.53 | | | | | | | | (1041) ~ (all_71_25 = n0) % 140.16/19.53 | | | | | | | | % 140.16/19.53 | | | | | | | | BETA: splitting (925) gives: % 140.16/19.53 | | | | | | | | % 140.16/19.53 | | | | | | | | Case 1: % 140.16/19.53 | | | | | | | | | % 140.16/19.53 | | | | | | | | | (1042) gt(n3, pv12) % 140.16/19.53 | | | | | | | | | % 140.16/19.53 | | | | | | | | | BETA: splitting (927) gives: % 140.16/19.53 | | | | | | | | | % 140.16/19.53 | | | | | | | | | Case 1: % 140.16/19.53 | | | | | | | | | | % 140.16/19.53 | | | | | | | | | | (1043) gt(n2, all_71_25) % 140.16/19.53 | | | | | | | | | | % 140.16/19.53 | | | | | | | | | | GROUND_INST: instantiating (1) with all_71_25, n2, n1, % 140.16/19.53 | | | | | | | | | | simplifying with (91), (107), (117), (1043) gives: % 140.16/19.53 | | | | | | | | | | (1044) leq(all_71_25, n1) % 140.16/19.53 | | | | | | | | | | % 140.16/19.53 | | | | | | | | | | GROUND_INST: instantiating (11) with all_71_25, simplifying % 140.16/19.53 | | | | | | | | | | with (117), (153), (1044) gives: % 140.16/19.53 | | | | | | | | | | (1045) all_71_25 = n1 | all_71_25 = n0 % 140.16/19.53 | | | | | | | | | | % 140.16/19.53 | | | | | | | | | | BETA: splitting (1045) gives: % 140.16/19.53 | | | | | | | | | | % 140.16/19.53 | | | | | | | | | | Case 1: % 140.16/19.53 | | | | | | | | | | | % 140.16/19.53 | | | | | | | | | | | (1046) all_71_25 = n0 % 140.16/19.53 | | | | | | | | | | | % 140.16/19.53 | | | | | | | | | | | REDUCE: (1041), (1046) imply: % 140.16/19.53 | | | | | | | | | | | (1047) $false % 140.16/19.53 | | | | | | | | | | | % 140.16/19.53 | | | | | | | | | | | CLOSE: (1047) is inconsistent. % 140.16/19.53 | | | | | | | | | | | % 140.16/19.53 | | | | | | | | | | Case 2: % 140.16/19.53 | | | | | | | | | | | % 140.16/19.53 | | | | | | | | | | | (1048) all_71_25 = n1 % 140.16/19.53 | | | | | | | | | | | % 140.16/19.53 | | | | | | | | | | | REDUCE: (153), (1048) imply: % 140.16/19.53 | | | | | | | | | | | (1049) leq(n0, n1) % 140.16/19.53 | | | | | | | | | | | % 140.16/19.53 | | | | | | | | | | | GROUND_INST: instantiating (65) with n0, all_71_11, all_71_9, % 140.16/19.53 | | | | | | | | | | | all_71_8, all_71_7, all_71_6, all_71_5, all_71_4, % 140.16/19.53 | | | | | | | | | | | all_71_3, all_71_2, all_71_1, all_71_0, % 140.16/19.53 | | | | | | | | | | | simplifying with (19), (59), (139), (141), (142), % 140.16/19.53 | | | | | | | | | | | (143), (144), (145), (146), (147), (1033), (1035) % 140.16/19.53 | | | | | | | | | | | gives: % 140.16/19.53 | | | | | | | | | | | (1050) ~ (sum(n0, all_71_26, all_71_2) = all_71_1) | ~ % 140.16/19.53 | | | | | | | | | | | leq(n0, all_71_25) | (a_select3(q, pv10, n0) = % 140.16/19.53 | | | | | | | | | | | all_71_0 & $i(all_71_0)) % 140.16/19.53 | | | | | | | | | | | % 140.16/19.53 | | | | | | | | | | | BETA: splitting (1050) gives: % 140.16/19.53 | | | | | | | | | | | % 140.16/19.53 | | | | | | | | | | | Case 1: % 140.16/19.53 | | | | | | | | | | | | % 140.16/19.53 | | | | | | | | | | | | (1051) ~ (sum(n0, all_71_26, all_71_2) = all_71_1) % 140.16/19.53 | | | | | | | | | | | | % 140.16/19.53 | | | | | | | | | | | | REDUCE: (119), (1051) imply: % 140.16/19.53 | | | | | | | | | | | | (1052) ~ (sum(n0, n4, all_71_2) = all_71_1) % 140.16/19.53 | | | | | | | | | | | | % 140.16/19.53 | | | | | | | | | | | | PRED_UNIFY: (148), (1052) imply: % 140.16/19.53 | | | | | | | | | | | | (1053) $false % 140.16/19.53 | | | | | | | | | | | | % 140.16/19.53 | | | | | | | | | | | | CLOSE: (1053) is inconsistent. % 140.16/19.53 | | | | | | | | | | | | % 140.16/19.53 | | | | | | | | | | | Case 2: % 140.16/19.53 | | | | | | | | | | | | % 140.16/19.53 | | | | | | | | | | | | (1054) ~ leq(n0, all_71_25) | (a_select3(q, pv10, n0) = % 140.16/19.53 | | | | | | | | | | | | all_71_0 & $i(all_71_0)) % 140.16/19.53 | | | | | | | | | | | | % 140.16/19.53 | | | | | | | | | | | | BETA: splitting (1054) gives: % 140.16/19.53 | | | | | | | | | | | | % 140.16/19.53 | | | | | | | | | | | | Case 1: % 140.16/19.53 | | | | | | | | | | | | | % 140.16/19.53 | | | | | | | | | | | | | (1055) ~ leq(n0, all_71_25) % 140.16/19.53 | | | | | | | | | | | | | % 140.16/19.53 | | | | | | | | | | | | | REDUCE: (1048), (1055) imply: % 140.16/19.53 | | | | | | | | | | | | | (1056) ~ leq(n0, n1) % 140.16/19.53 | | | | | | | | | | | | | % 140.16/19.53 | | | | | | | | | | | | | PRED_UNIFY: (1049), (1056) imply: % 140.16/19.53 | | | | | | | | | | | | | (1057) $false % 140.16/19.53 | | | | | | | | | | | | | % 140.16/19.53 | | | | | | | | | | | | | CLOSE: (1057) is inconsistent. % 140.16/19.53 | | | | | | | | | | | | | % 140.16/19.53 | | | | | | | | | | | | Case 2: % 140.16/19.53 | | | | | | | | | | | | | % 140.16/19.53 | | | | | | | | | | | | | (1058) a_select3(q, pv10, n0) = all_71_0 & $i(all_71_0) % 140.16/19.53 | | | | | | | | | | | | | % 140.16/19.53 | | | | | | | | | | | | | REF_CLOSE: (27), (134), (917), (1034), (1058) are % 140.16/19.53 | | | | | | | | | | | | | inconsistent by sub-proof #1. % 140.16/19.53 | | | | | | | | | | | | | % 140.16/19.53 | | | | | | | | | | | | End of split % 140.16/19.53 | | | | | | | | | | | | % 140.16/19.53 | | | | | | | | | | | End of split % 140.16/19.53 | | | | | | | | | | | % 140.16/19.53 | | | | | | | | | | End of split % 140.16/19.53 | | | | | | | | | | % 140.16/19.53 | | | | | | | | | Case 2: % 140.16/19.53 | | | | | | | | | | % 140.16/19.53 | | | | | | | | | | (1059) all_71_25 = n2 % 140.16/19.53 | | | | | | | | | | % 140.16/19.53 | | | | | | | | | | REDUCE: (125), (1059) imply: % 140.16/19.53 | | | | | | | | | | (1060) succ(n2) = pv12 % 140.16/19.53 | | | | | | | | | | % 140.16/19.53 | | | | | | | | | | REF_CLOSE: (22), (25), (90), (1042), (1060), % 140.16/19.53 | | | | | | | | | | (irreflexivity_gt) are inconsistent by sub-proof % 140.16/19.53 | | | | | | | | | | #23. % 140.16/19.53 | | | | | | | | | | % 140.16/19.53 | | | | | | | | | End of split % 140.16/19.53 | | | | | | | | | % 140.16/19.53 | | | | | | | | Case 2: % 140.16/19.53 | | | | | | | | | % 140.16/19.53 | | | | | | | | | (1061) pv12 = n3 % 140.16/19.53 | | | | | | | | | % 140.16/19.53 | | | | | | | | | REDUCE: (118), (1061) imply: % 140.16/19.53 | | | | | | | | | (1062) pred(n3) = all_71_25 % 140.16/19.53 | | | | | | | | | % 140.16/19.53 | | | | | | | | | GROUND_INST: instantiating (24) with n2, all_71_25, n3, % 140.16/19.53 | | | | | | | | | simplifying with (108), (1062) gives: % 140.16/19.53 | | | | | | | | | (1063) all_71_25 = n2 % 140.16/19.53 | | | | | | | | | % 140.16/19.53 | | | | | | | | | REDUCE: (153), (1063) imply: % 140.16/19.53 | | | | | | | | | (1064) leq(n0, n2) % 140.16/19.53 | | | | | | | | | % 140.16/19.53 | | | | | | | | | GROUND_INST: instantiating (65) with n0, all_71_11, all_71_9, % 140.16/19.53 | | | | | | | | | all_71_8, all_71_7, all_71_6, all_71_5, all_71_4, % 140.16/19.53 | | | | | | | | | all_71_3, all_71_2, all_71_1, all_71_0, % 140.16/19.53 | | | | | | | | | simplifying with (19), (59), (139), (141), (142), % 140.16/19.53 | | | | | | | | | (143), (144), (145), (146), (147), (1033), (1035) % 140.16/19.53 | | | | | | | | | gives: % 140.16/19.53 | | | | | | | | | (1065) ~ (sum(n0, all_71_26, all_71_2) = all_71_1) | ~ % 140.16/19.53 | | | | | | | | | leq(n0, all_71_25) | (a_select3(q, pv10, n0) = % 140.16/19.53 | | | | | | | | | all_71_0 & $i(all_71_0)) % 140.16/19.53 | | | | | | | | | % 140.16/19.53 | | | | | | | | | BETA: splitting (1065) gives: % 140.16/19.53 | | | | | | | | | % 140.16/19.53 | | | | | | | | | Case 1: % 140.16/19.53 | | | | | | | | | | % 140.16/19.53 | | | | | | | | | | (1066) ~ (sum(n0, all_71_26, all_71_2) = all_71_1) % 140.16/19.53 | | | | | | | | | | % 140.16/19.53 | | | | | | | | | | REDUCE: (119), (1066) imply: % 140.16/19.53 | | | | | | | | | | (1067) ~ (sum(n0, n4, all_71_2) = all_71_1) % 140.16/19.53 | | | | | | | | | | % 140.16/19.53 | | | | | | | | | | PRED_UNIFY: (148), (1067) imply: % 140.16/19.53 | | | | | | | | | | (1068) $false % 140.16/19.53 | | | | | | | | | | % 140.16/19.53 | | | | | | | | | | CLOSE: (1068) is inconsistent. % 140.16/19.53 | | | | | | | | | | % 140.16/19.53 | | | | | | | | | Case 2: % 140.16/19.53 | | | | | | | | | | % 140.16/19.53 | | | | | | | | | | (1069) ~ leq(n0, all_71_25) | (a_select3(q, pv10, n0) = % 140.16/19.53 | | | | | | | | | | all_71_0 & $i(all_71_0)) % 140.16/19.53 | | | | | | | | | | % 140.16/19.53 | | | | | | | | | | BETA: splitting (1069) gives: % 140.16/19.53 | | | | | | | | | | % 140.16/19.53 | | | | | | | | | | Case 1: % 140.16/19.53 | | | | | | | | | | | % 140.16/19.53 | | | | | | | | | | | (1070) ~ leq(n0, all_71_25) % 140.16/19.53 | | | | | | | | | | | % 140.16/19.53 | | | | | | | | | | | REDUCE: (1063), (1070) imply: % 140.16/19.53 | | | | | | | | | | | (1071) ~ leq(n0, n2) % 140.16/19.53 | | | | | | | | | | | % 140.16/19.53 | | | | | | | | | | | PRED_UNIFY: (1064), (1071) imply: % 140.16/19.53 | | | | | | | | | | | (1072) $false % 140.16/19.53 | | | | | | | | | | | % 140.16/19.53 | | | | | | | | | | | CLOSE: (1072) is inconsistent. % 140.16/19.53 | | | | | | | | | | | % 140.16/19.53 | | | | | | | | | | Case 2: % 140.16/19.53 | | | | | | | | | | | % 140.16/19.53 | | | | | | | | | | | (1073) a_select3(q, pv10, n0) = all_71_0 & $i(all_71_0) % 140.16/19.53 | | | | | | | | | | | % 140.16/19.53 | | | | | | | | | | | REF_CLOSE: (27), (134), (917), (1034), (1073) are % 140.16/19.53 | | | | | | | | | | | inconsistent by sub-proof #1. % 140.16/19.53 | | | | | | | | | | | % 140.16/19.53 | | | | | | | | | | End of split % 140.16/19.53 | | | | | | | | | | % 140.16/19.53 | | | | | | | | | End of split % 140.16/19.53 | | | | | | | | | % 140.16/19.53 | | | | | | | | End of split % 140.16/19.53 | | | | | | | | % 140.16/19.53 | | | | | | | End of split % 140.16/19.53 | | | | | | | % 140.16/19.53 | | | | | | Case 2: % 140.16/19.53 | | | | | | | % 140.16/19.53 | | | | | | | (1074) all_71_12 = all_71_25 % 140.16/19.53 | | | | | | | % 140.16/19.53 | | | | | | | COMBINE_EQS: (1031), (1074) imply: % 140.16/19.53 | | | | | | | (1075) all_71_25 = n0 % 140.16/19.53 | | | | | | | % 140.16/19.53 | | | | | | | SIMP: (1075) implies: % 140.16/19.53 | | | | | | | (1076) all_71_25 = n0 % 140.16/19.53 | | | | | | | % 140.16/19.54 | | | | | | | GROUND_INST: instantiating (65) with n0, all_71_11, all_71_9, % 140.16/19.54 | | | | | | | all_71_8, all_71_7, all_71_6, all_71_5, all_71_4, % 140.16/19.54 | | | | | | | all_71_3, all_71_2, all_71_1, all_71_0, simplifying % 140.16/19.54 | | | | | | | with (19), (59), (139), (141), (142), (143), (144), % 140.16/19.54 | | | | | | | (145), (146), (147), (1033), (1035) gives: % 140.16/19.54 | | | | | | | (1077) ~ (sum(n0, all_71_26, all_71_2) = all_71_1) | ~ % 140.16/19.54 | | | | | | | leq(n0, all_71_25) | (a_select3(q, pv10, n0) = all_71_0 % 140.16/19.54 | | | | | | | & $i(all_71_0)) % 140.16/19.54 | | | | | | | % 140.16/19.54 | | | | | | | BETA: splitting (1077) gives: % 140.16/19.54 | | | | | | | % 140.16/19.54 | | | | | | | Case 1: % 140.16/19.54 | | | | | | | | % 140.16/19.54 | | | | | | | | (1078) ~ (sum(n0, all_71_26, all_71_2) = all_71_1) % 140.16/19.54 | | | | | | | | % 140.16/19.54 | | | | | | | | REDUCE: (119), (1078) imply: % 140.16/19.54 | | | | | | | | (1079) ~ (sum(n0, n4, all_71_2) = all_71_1) % 140.16/19.54 | | | | | | | | % 140.16/19.54 | | | | | | | | PRED_UNIFY: (148), (1079) imply: % 140.16/19.54 | | | | | | | | (1080) $false % 140.16/19.54 | | | | | | | | % 140.16/19.54 | | | | | | | | CLOSE: (1080) is inconsistent. % 140.16/19.54 | | | | | | | | % 140.16/19.54 | | | | | | | Case 2: % 140.16/19.54 | | | | | | | | % 140.16/19.54 | | | | | | | | (1081) ~ leq(n0, all_71_25) | (a_select3(q, pv10, n0) = % 140.16/19.54 | | | | | | | | all_71_0 & $i(all_71_0)) % 140.16/19.54 | | | | | | | | % 140.16/19.54 | | | | | | | | BETA: splitting (1081) gives: % 140.16/19.54 | | | | | | | | % 140.16/19.54 | | | | | | | | Case 1: % 140.16/19.54 | | | | | | | | | % 140.16/19.54 | | | | | | | | | (1082) ~ leq(n0, all_71_25) % 140.40/19.54 | | | | | | | | | % 140.40/19.54 | | | | | | | | | REDUCE: (1076), (1082) imply: % 140.40/19.54 | | | | | | | | | (1083) ~ leq(n0, n0) % 140.40/19.54 | | | | | | | | | % 140.40/19.54 | | | | | | | | | PRED_UNIFY: (1035), (1083) imply: % 140.40/19.54 | | | | | | | | | (1084) $false % 140.40/19.54 | | | | | | | | | % 140.40/19.54 | | | | | | | | | CLOSE: (1084) is inconsistent. % 140.40/19.54 | | | | | | | | | % 140.40/19.54 | | | | | | | | Case 2: % 140.40/19.54 | | | | | | | | | % 140.40/19.54 | | | | | | | | | (1085) a_select3(q, pv10, n0) = all_71_0 & $i(all_71_0) % 140.40/19.54 | | | | | | | | | % 140.40/19.54 | | | | | | | | | REF_CLOSE: (27), (134), (917), (1034), (1085) are inconsistent % 140.40/19.54 | | | | | | | | | by sub-proof #1. % 140.40/19.54 | | | | | | | | | % 140.40/19.54 | | | | | | | | End of split % 140.40/19.54 | | | | | | | | % 140.40/19.54 | | | | | | | End of split % 140.40/19.54 | | | | | | | % 140.40/19.54 | | | | | | End of split % 140.40/19.54 | | | | | | % 140.40/19.54 | | | | | End of split % 140.40/19.54 | | | | | % 140.40/19.54 | | | | End of split % 140.40/19.54 | | | | % 140.40/19.54 | | | Case 2: % 140.40/19.54 | | | | % 140.40/19.54 | | | | (1086) all_71_26 = pv12 % 140.40/19.54 | | | | % 140.40/19.54 | | | | COMBINE_EQS: (119), (1086) imply: % 140.40/19.54 | | | | (1087) pv12 = n4 % 140.40/19.54 | | | | % 140.40/19.54 | | | | REDUCE: (118), (1087) imply: % 140.40/19.54 | | | | (1088) pred(n4) = all_71_25 % 140.40/19.54 | | | | % 140.40/19.54 | | | | GROUND_INST: instantiating (24) with n3, all_71_25, n4, simplifying with % 140.40/19.54 | | | | (109), (1088) gives: % 140.40/19.54 | | | | (1089) all_71_25 = n3 % 140.40/19.54 | | | | % 140.40/19.54 | | | | BETA: splitting (149) gives: % 140.40/19.54 | | | | % 140.40/19.54 | | | | Case 1: % 140.40/19.54 | | | | | % 140.40/19.54 | | | | | (1090) gt(all_71_12, n0) % 140.40/19.54 | | | | | % 140.40/19.54 | | | | | BETA: splitting (154) gives: % 140.40/19.54 | | | | | % 140.40/19.54 | | | | | Case 1: % 140.40/19.54 | | | | | | % 140.40/19.54 | | | | | | (1091) gt(all_71_25, all_71_12) % 140.40/19.54 | | | | | | % 140.40/19.54 | | | | | | REDUCE: (1089), (1091) imply: % 140.40/19.54 | | | | | | (1092) gt(n3, all_71_12) % 140.40/19.54 | | | | | | % 140.40/19.54 | | | | | | GROUND_INST: instantiating (1) with all_71_12, n3, n2, simplifying % 140.40/19.54 | | | | | | with (58), (98), (108), (1092) gives: % 140.40/19.54 | | | | | | (1093) leq(all_71_12, n2) % 140.40/19.54 | | | | | | % 140.40/19.54 | | | | | | GROUND_INST: instantiating (leq_gt2) with all_71_12, n2, simplifying % 140.40/19.54 | | | | | | with (58), (91), (1093) gives: % 140.40/19.54 | | | | | | (1094) all_71_12 = n2 | gt(n2, all_71_12) % 140.40/19.54 | | | | | | % 140.40/19.54 | | | | | | BETA: splitting (159) gives: % 140.40/19.54 | | | | | | % 140.40/19.54 | | | | | | Case 1: % 140.40/19.54 | | | | | | | % 140.40/19.54 | | | | | | | (1095) all_71_12 = n0 % 140.40/19.54 | | | | | | | % 140.40/19.54 | | | | | | | REDUCE: (1090), (1095) imply: % 140.40/19.54 | | | | | | | (1096) gt(n0, n0) % 140.40/19.54 | | | | | | | % 140.40/19.54 | | | | | | | PRED_UNIFY: (920), (1096) imply: % 140.40/19.54 | | | | | | | (1097) $false % 140.40/19.54 | | | | | | | % 140.40/19.54 | | | | | | | CLOSE: (1097) is inconsistent. % 140.40/19.54 | | | | | | | % 140.40/19.54 | | | | | | Case 2: % 140.40/19.54 | | | | | | | % 140.40/19.54 | | | | | | | (1098) ~ (all_71_12 = n0) % 140.40/19.54 | | | | | | | % 140.40/19.54 | | | | | | | BETA: splitting (1094) gives: % 140.40/19.54 | | | | | | | % 140.40/19.54 | | | | | | | Case 1: % 140.40/19.54 | | | | | | | | % 140.40/19.54 | | | | | | | | (1099) gt(n2, all_71_12) % 140.40/19.54 | | | | | | | | % 140.40/19.54 | | | | | | | | GROUND_INST: instantiating (1) with all_71_12, n2, n1, % 140.40/19.54 | | | | | | | | simplifying with (58), (91), (107), (1099) gives: % 140.40/19.54 | | | | | | | | (1100) leq(all_71_12, n1) % 140.40/19.54 | | | | | | | | % 140.40/19.54 | | | | | | | | GROUND_INST: instantiating (11) with all_71_12, simplifying with % 140.40/19.54 | | | | | | | | (58), (135), (1100) gives: % 140.40/19.54 | | | | | | | | (1101) all_71_12 = n1 | all_71_12 = n0 % 140.40/19.54 | | | | | | | | % 140.40/19.54 | | | | | | | | BETA: splitting (1101) gives: % 140.40/19.54 | | | | | | | | % 140.40/19.54 | | | | | | | | Case 1: % 140.40/19.54 | | | | | | | | | % 140.40/19.54 | | | | | | | | | (1102) all_71_12 = n0 % 140.40/19.54 | | | | | | | | | % 140.40/19.54 | | | | | | | | | REDUCE: (1098), (1102) imply: % 140.40/19.54 | | | | | | | | | (1103) $false % 140.40/19.54 | | | | | | | | | % 140.40/19.54 | | | | | | | | | CLOSE: (1103) is inconsistent. % 140.40/19.54 | | | | | | | | | % 140.40/19.54 | | | | | | | | Case 2: % 140.40/19.54 | | | | | | | | | % 140.40/19.54 | | | | | | | | | (1104) all_71_12 = n1 % 140.40/19.54 | | | | | | | | | % 140.40/19.54 | | | | | | | | | REDUCE: (138), (1104) imply: % 140.40/19.54 | | | | | | | | | (1105) a_select3(center, n1, n0) = all_71_9 % 140.40/19.54 | | | | | | | | | % 140.40/19.54 | | | | | | | | | REDUCE: (919), (1104) imply: % 140.40/19.54 | | | | | | | | | (1106) a_select3(q, n0, n1) = all_71_10 % 140.40/19.54 | | | | | | | | | % 140.40/19.54 | | | | | | | | | REDUCE: (152), (1104) imply: % 140.40/19.54 | | | | | | | | | (1107) leq(n1, n3) % 140.40/19.54 | | | | | | | | | % 140.40/19.54 | | | | | | | | | REDUCE: (135), (1104) imply: % 140.40/19.54 | | | | | | | | | (1108) leq(n0, n1) % 140.40/19.54 | | | | | | | | | % 140.40/19.54 | | | | | | | | | GROUND_INST: instantiating (65) with n1, all_71_11, all_71_9, % 140.40/19.54 | | | | | | | | | all_71_8, all_71_7, all_71_6, all_71_5, all_71_4, % 140.40/19.54 | | | | | | | | | all_71_3, all_71_2, all_71_1, all_71_0, % 140.40/19.54 | | | | | | | | | simplifying with (59), (80), (139), (141), (142), % 140.40/19.54 | | | | | | | | | (143), (144), (145), (146), (147), (1105), (1108) % 140.40/19.54 | | | | | | | | | gives: % 140.40/19.54 | | | | | | | | | (1109) ~ (sum(n0, all_71_26, all_71_2) = all_71_1) | ~ % 140.40/19.54 | | | | | | | | | leq(n1, all_71_25) | (a_select3(q, pv10, n1) = % 140.40/19.54 | | | | | | | | | all_71_0 & $i(all_71_0)) % 140.40/19.54 | | | | | | | | | % 140.40/19.54 | | | | | | | | | BETA: splitting (1109) gives: % 140.40/19.54 | | | | | | | | | % 140.40/19.54 | | | | | | | | | Case 1: % 140.40/19.54 | | | | | | | | | | % 140.40/19.54 | | | | | | | | | | (1110) ~ (sum(n0, all_71_26, all_71_2) = all_71_1) % 140.40/19.54 | | | | | | | | | | % 140.40/19.54 | | | | | | | | | | REDUCE: (119), (1110) imply: % 140.40/19.54 | | | | | | | | | | (1111) ~ (sum(n0, n4, all_71_2) = all_71_1) % 140.40/19.54 | | | | | | | | | | % 140.40/19.54 | | | | | | | | | | PRED_UNIFY: (148), (1111) imply: % 140.40/19.54 | | | | | | | | | | (1112) $false % 140.40/19.54 | | | | | | | | | | % 140.40/19.54 | | | | | | | | | | CLOSE: (1112) is inconsistent. % 140.40/19.54 | | | | | | | | | | % 140.40/19.54 | | | | | | | | | Case 2: % 140.40/19.54 | | | | | | | | | | % 140.40/19.54 | | | | | | | | | | (1113) ~ leq(n1, all_71_25) | (a_select3(q, pv10, n1) = % 140.40/19.54 | | | | | | | | | | all_71_0 & $i(all_71_0)) % 140.40/19.54 | | | | | | | | | | % 140.40/19.54 | | | | | | | | | | BETA: splitting (1113) gives: % 140.40/19.54 | | | | | | | | | | % 140.40/19.54 | | | | | | | | | | Case 1: % 140.40/19.54 | | | | | | | | | | | % 140.40/19.54 | | | | | | | | | | | (1114) ~ leq(n1, all_71_25) % 140.40/19.54 | | | | | | | | | | | % 140.40/19.54 | | | | | | | | | | | REDUCE: (1089), (1114) imply: % 140.40/19.54 | | | | | | | | | | | (1115) ~ leq(n1, n3) % 140.40/19.54 | | | | | | | | | | | % 140.40/19.54 | | | | | | | | | | | PRED_UNIFY: (1107), (1115) imply: % 140.40/19.54 | | | | | | | | | | | (1116) $false % 140.40/19.54 | | | | | | | | | | | % 140.40/19.54 | | | | | | | | | | | CLOSE: (1116) is inconsistent. % 140.40/19.54 | | | | | | | | | | | % 140.40/19.54 | | | | | | | | | | Case 2: % 140.40/19.54 | | | | | | | | | | | % 140.40/19.54 | | | | | | | | | | | (1117) a_select3(q, pv10, n1) = all_71_0 & $i(all_71_0) % 140.40/19.54 | | | | | | | | | | | % 140.40/19.54 | | | | | | | | | | | REF_CLOSE: (27), (134), (917), (1106), (1117) are % 140.40/19.54 | | | | | | | | | | | inconsistent by sub-proof #2. % 140.40/19.54 | | | | | | | | | | | % 140.40/19.54 | | | | | | | | | | End of split % 140.40/19.54 | | | | | | | | | | % 140.40/19.54 | | | | | | | | | End of split % 140.40/19.54 | | | | | | | | | % 140.40/19.54 | | | | | | | | End of split % 140.40/19.54 | | | | | | | | % 140.40/19.54 | | | | | | | Case 2: % 140.40/19.54 | | | | | | | | % 140.40/19.54 | | | | | | | | (1118) all_71_12 = n2 % 140.40/19.54 | | | | | | | | % 140.40/19.54 | | | | | | | | REDUCE: (138), (1118) imply: % 140.40/19.54 | | | | | | | | (1119) a_select3(center, n2, n0) = all_71_9 % 140.40/19.54 | | | | | | | | % 140.40/19.54 | | | | | | | | REDUCE: (919), (1118) imply: % 140.40/19.54 | | | | | | | | (1120) a_select3(q, n0, n2) = all_71_10 % 140.40/19.54 | | | | | | | | % 140.40/19.54 | | | | | | | | REDUCE: (152), (1118) imply: % 140.40/19.54 | | | | | | | | (1121) leq(n2, n3) % 140.40/19.54 | | | | | | | | % 140.40/19.54 | | | | | | | | REDUCE: (135), (1118) imply: % 140.40/19.54 | | | | | | | | (1122) leq(n0, n2) % 140.40/19.54 | | | | | | | | % 140.40/19.54 | | | | | | | | GROUND_INST: instantiating (65) with n2, all_71_11, all_71_9, % 140.40/19.54 | | | | | | | | all_71_8, all_71_7, all_71_6, all_71_5, all_71_4, % 140.40/19.54 | | | | | | | | all_71_3, all_71_2, all_71_1, all_71_0, simplifying % 140.40/19.54 | | | | | | | | with (59), (91), (139), (141), (142), (143), (144), % 140.40/19.54 | | | | | | | | (145), (146), (147), (1119), (1122) gives: % 140.40/19.54 | | | | | | | | (1123) ~ (sum(n0, all_71_26, all_71_2) = all_71_1) | ~ % 140.40/19.54 | | | | | | | | leq(n2, all_71_25) | (a_select3(q, pv10, n2) = % 140.40/19.54 | | | | | | | | all_71_0 & $i(all_71_0)) % 140.40/19.54 | | | | | | | | % 140.40/19.54 | | | | | | | | BETA: splitting (1123) gives: % 140.40/19.54 | | | | | | | | % 140.40/19.54 | | | | | | | | Case 1: % 140.40/19.54 | | | | | | | | | % 140.40/19.54 | | | | | | | | | (1124) ~ (sum(n0, all_71_26, all_71_2) = all_71_1) % 140.40/19.54 | | | | | | | | | % 140.40/19.54 | | | | | | | | | REDUCE: (119), (1124) imply: % 140.40/19.54 | | | | | | | | | (1125) ~ (sum(n0, n4, all_71_2) = all_71_1) % 140.40/19.54 | | | | | | | | | % 140.40/19.54 | | | | | | | | | PRED_UNIFY: (148), (1125) imply: % 140.40/19.54 | | | | | | | | | (1126) $false % 140.40/19.54 | | | | | | | | | % 140.40/19.54 | | | | | | | | | CLOSE: (1126) is inconsistent. % 140.40/19.54 | | | | | | | | | % 140.40/19.54 | | | | | | | | Case 2: % 140.40/19.54 | | | | | | | | | % 140.40/19.54 | | | | | | | | | (1127) ~ leq(n2, all_71_25) | (a_select3(q, pv10, n2) = % 140.40/19.54 | | | | | | | | | all_71_0 & $i(all_71_0)) % 140.40/19.54 | | | | | | | | | % 140.40/19.54 | | | | | | | | | BETA: splitting (1127) gives: % 140.40/19.54 | | | | | | | | | % 140.40/19.54 | | | | | | | | | Case 1: % 140.40/19.54 | | | | | | | | | | % 140.40/19.54 | | | | | | | | | | (1128) ~ leq(n2, all_71_25) % 140.40/19.54 | | | | | | | | | | % 140.40/19.54 | | | | | | | | | | REDUCE: (1089), (1128) imply: % 140.40/19.54 | | | | | | | | | | (1129) ~ leq(n2, n3) % 140.40/19.54 | | | | | | | | | | % 140.40/19.54 | | | | | | | | | | PRED_UNIFY: (1121), (1129) imply: % 140.40/19.54 | | | | | | | | | | (1130) $false % 140.40/19.54 | | | | | | | | | | % 140.40/19.54 | | | | | | | | | | CLOSE: (1130) is inconsistent. % 140.40/19.54 | | | | | | | | | | % 140.40/19.54 | | | | | | | | | Case 2: % 140.40/19.54 | | | | | | | | | | % 140.40/19.54 | | | | | | | | | | (1131) a_select3(q, pv10, n2) = all_71_0 & $i(all_71_0) % 140.40/19.54 | | | | | | | | | | % 140.40/19.54 | | | | | | | | | | ALPHA: (1131) implies: % 140.40/19.54 | | | | | | | | | | (1132) a_select3(q, pv10, n2) = all_71_0 % 140.40/19.54 | | | | | | | | | | % 140.40/19.54 | | | | | | | | | | REDUCE: (917), (1132) imply: % 140.40/19.54 | | | | | | | | | | (1133) a_select3(q, n0, n2) = all_71_0 % 140.40/19.54 | | | | | | | | | | % 140.40/19.54 | | | | | | | | | | GROUND_INST: instantiating (27) with all_71_10, all_71_0, n2, % 140.40/19.54 | | | | | | | | | | n0, q, simplifying with (1120), (1133) gives: % 140.40/19.54 | | | | | | | | | | (1134) all_71_0 = all_71_10 % 140.40/19.54 | | | | | | | | | | % 140.40/19.54 | | | | | | | | | | REDUCE: (134), (1134) imply: % 140.40/19.54 | | | | | | | | | | (1135) $false % 140.40/19.54 | | | | | | | | | | % 140.40/19.54 | | | | | | | | | | CLOSE: (1135) is inconsistent. % 140.40/19.54 | | | | | | | | | | % 140.40/19.54 | | | | | | | | | End of split % 140.40/19.54 | | | | | | | | | % 140.40/19.54 | | | | | | | | End of split % 140.40/19.54 | | | | | | | | % 140.40/19.54 | | | | | | | End of split % 140.40/19.54 | | | | | | | % 140.40/19.54 | | | | | | End of split % 140.40/19.54 | | | | | | % 140.40/19.54 | | | | | Case 2: % 140.40/19.54 | | | | | | % 140.40/19.54 | | | | | | (1136) all_71_12 = all_71_25 % 140.40/19.54 | | | | | | % 140.40/19.54 | | | | | | COMBINE_EQS: (1089), (1136) imply: % 140.40/19.54 | | | | | | (1137) all_71_12 = n3 % 140.40/19.54 | | | | | | % 140.40/19.54 | | | | | | REDUCE: (138), (1137) imply: % 140.40/19.54 | | | | | | (1138) a_select3(center, n3, n0) = all_71_9 % 140.40/19.54 | | | | | | % 140.40/19.54 | | | | | | REDUCE: (919), (1137) imply: % 140.40/19.54 | | | | | | (1139) a_select3(q, n0, n3) = all_71_10 % 140.40/19.54 | | | | | | % 140.40/19.54 | | | | | | REDUCE: (152), (1137) imply: % 140.40/19.54 | | | | | | (1140) leq(n3, n3) % 140.40/19.54 | | | | | | % 140.40/19.54 | | | | | | REDUCE: (135), (1137) imply: % 140.40/19.54 | | | | | | (1141) leq(n0, n3) % 140.40/19.54 | | | | | | % 140.40/19.54 | | | | | | GROUND_INST: instantiating (65) with n3, all_71_11, all_71_9, % 140.40/19.54 | | | | | | all_71_8, all_71_7, all_71_6, all_71_5, all_71_4, % 140.40/19.54 | | | | | | all_71_3, all_71_2, all_71_1, all_71_0, simplifying % 140.40/19.54 | | | | | | with (59), (98), (139), (141), (142), (143), (144), % 140.40/19.54 | | | | | | (145), (146), (147), (1138), (1141) gives: % 140.40/19.54 | | | | | | (1142) ~ (sum(n0, all_71_26, all_71_2) = all_71_1) | ~ leq(n3, % 140.40/19.54 | | | | | | all_71_25) | (a_select3(q, pv10, n3) = all_71_0 & % 140.40/19.54 | | | | | | $i(all_71_0)) % 140.40/19.54 | | | | | | % 140.40/19.54 | | | | | | BETA: splitting (1142) gives: % 140.40/19.54 | | | | | | % 140.40/19.54 | | | | | | Case 1: % 140.40/19.54 | | | | | | | % 140.40/19.54 | | | | | | | (1143) ~ (sum(n0, all_71_26, all_71_2) = all_71_1) % 140.40/19.54 | | | | | | | % 140.40/19.54 | | | | | | | REDUCE: (119), (1143) imply: % 140.40/19.55 | | | | | | | (1144) ~ (sum(n0, n4, all_71_2) = all_71_1) % 140.40/19.55 | | | | | | | % 140.40/19.55 | | | | | | | PRED_UNIFY: (148), (1144) imply: % 140.40/19.55 | | | | | | | (1145) $false % 140.40/19.55 | | | | | | | % 140.40/19.55 | | | | | | | CLOSE: (1145) is inconsistent. % 140.40/19.55 | | | | | | | % 140.40/19.55 | | | | | | Case 2: % 140.40/19.55 | | | | | | | % 140.40/19.55 | | | | | | | (1146) ~ leq(n3, all_71_25) | (a_select3(q, pv10, n3) = % 140.40/19.55 | | | | | | | all_71_0 & $i(all_71_0)) % 140.40/19.55 | | | | | | | % 140.40/19.55 | | | | | | | BETA: splitting (1146) gives: % 140.40/19.55 | | | | | | | % 140.40/19.55 | | | | | | | Case 1: % 140.40/19.55 | | | | | | | | % 140.40/19.55 | | | | | | | | (1147) ~ leq(n3, all_71_25) % 140.40/19.55 | | | | | | | | % 140.40/19.55 | | | | | | | | REDUCE: (1089), (1147) imply: % 140.40/19.55 | | | | | | | | (1148) ~ leq(n3, n3) % 140.40/19.55 | | | | | | | | % 140.40/19.55 | | | | | | | | PRED_UNIFY: (1140), (1148) imply: % 140.40/19.55 | | | | | | | | (1149) $false % 140.40/19.55 | | | | | | | | % 140.40/19.55 | | | | | | | | CLOSE: (1149) is inconsistent. % 140.40/19.55 | | | | | | | | % 140.40/19.55 | | | | | | | Case 2: % 140.40/19.55 | | | | | | | | % 140.40/19.55 | | | | | | | | (1150) a_select3(q, pv10, n3) = all_71_0 & $i(all_71_0) % 140.40/19.55 | | | | | | | | % 140.40/19.55 | | | | | | | | ALPHA: (1150) implies: % 140.40/19.55 | | | | | | | | (1151) a_select3(q, pv10, n3) = all_71_0 % 140.40/19.55 | | | | | | | | % 140.40/19.55 | | | | | | | | REDUCE: (917), (1151) imply: % 140.40/19.55 | | | | | | | | (1152) a_select3(q, n0, n3) = all_71_0 % 140.40/19.55 | | | | | | | | % 140.40/19.55 | | | | | | | | GROUND_INST: instantiating (27) with all_71_10, all_71_0, n3, % 140.40/19.55 | | | | | | | | n0, q, simplifying with (1139), (1152) gives: % 140.40/19.55 | | | | | | | | (1153) all_71_0 = all_71_10 % 140.40/19.55 | | | | | | | | % 140.40/19.55 | | | | | | | | REDUCE: (134), (1153) imply: % 140.40/19.55 | | | | | | | | (1154) $false % 140.40/19.55 | | | | | | | | % 140.40/19.55 | | | | | | | | CLOSE: (1154) is inconsistent. % 140.40/19.55 | | | | | | | | % 140.40/19.55 | | | | | | | End of split % 140.40/19.55 | | | | | | | % 140.40/19.55 | | | | | | End of split % 140.40/19.55 | | | | | | % 140.40/19.55 | | | | | End of split % 140.40/19.55 | | | | | % 140.40/19.55 | | | | Case 2: % 140.40/19.55 | | | | | % 140.40/19.55 | | | | | (1155) all_71_12 = n0 % 140.40/19.55 | | | | | % 140.40/19.55 | | | | | REDUCE: (138), (1155) imply: % 140.40/19.55 | | | | | (1156) a_select3(center, n0, n0) = all_71_9 % 140.40/19.55 | | | | | % 140.40/19.55 | | | | | REDUCE: (919), (1155) imply: % 140.40/19.55 | | | | | (1157) a_select3(q, n0, n0) = all_71_10 % 140.40/19.55 | | | | | % 140.40/19.55 | | | | | REDUCE: (152), (1155) imply: % 140.40/19.55 | | | | | (1158) leq(n0, n3) % 140.40/19.55 | | | | | % 140.40/19.55 | | | | | REDUCE: (135), (1155) imply: % 140.40/19.55 | | | | | (1159) leq(n0, n0) % 140.40/19.55 | | | | | % 140.40/19.55 | | | | | GROUND_INST: instantiating (65) with n0, all_71_11, all_71_9, % 140.40/19.55 | | | | | all_71_8, all_71_7, all_71_6, all_71_5, all_71_4, % 140.40/19.55 | | | | | all_71_3, all_71_2, all_71_1, all_71_0, simplifying with % 140.40/19.55 | | | | | (19), (59), (139), (141), (142), (143), (144), (145), % 140.40/19.55 | | | | | (146), (147), (1156), (1159) gives: % 140.40/19.55 | | | | | (1160) ~ (sum(n0, all_71_26, all_71_2) = all_71_1) | ~ leq(n0, % 140.40/19.55 | | | | | all_71_25) | (a_select3(q, pv10, n0) = all_71_0 & % 140.40/19.55 | | | | | $i(all_71_0)) % 140.40/19.55 | | | | | % 140.40/19.55 | | | | | BETA: splitting (1160) gives: % 140.40/19.55 | | | | | % 140.40/19.55 | | | | | Case 1: % 140.40/19.55 | | | | | | % 140.40/19.55 | | | | | | (1161) ~ (sum(n0, all_71_26, all_71_2) = all_71_1) % 140.40/19.55 | | | | | | % 140.40/19.55 | | | | | | REDUCE: (119), (1161) imply: % 140.40/19.55 | | | | | | (1162) ~ (sum(n0, n4, all_71_2) = all_71_1) % 140.40/19.55 | | | | | | % 140.40/19.55 | | | | | | PRED_UNIFY: (148), (1162) imply: % 140.40/19.55 | | | | | | (1163) $false % 140.40/19.55 | | | | | | % 140.40/19.55 | | | | | | CLOSE: (1163) is inconsistent. % 140.40/19.55 | | | | | | % 140.40/19.55 | | | | | Case 2: % 140.40/19.55 | | | | | | % 140.40/19.55 | | | | | | (1164) ~ leq(n0, all_71_25) | (a_select3(q, pv10, n0) = all_71_0 % 140.40/19.55 | | | | | | & $i(all_71_0)) % 140.40/19.55 | | | | | | % 140.40/19.55 | | | | | | BETA: splitting (1164) gives: % 140.40/19.55 | | | | | | % 140.40/19.55 | | | | | | Case 1: % 140.40/19.55 | | | | | | | % 140.40/19.55 | | | | | | | (1165) ~ leq(n0, all_71_25) % 140.40/19.55 | | | | | | | % 140.40/19.55 | | | | | | | REDUCE: (1089), (1165) imply: % 140.40/19.55 | | | | | | | (1166) ~ leq(n0, n3) % 140.40/19.55 | | | | | | | % 140.40/19.55 | | | | | | | PRED_UNIFY: (1158), (1166) imply: % 140.40/19.55 | | | | | | | (1167) $false % 140.40/19.55 | | | | | | | % 140.40/19.55 | | | | | | | CLOSE: (1167) is inconsistent. % 140.40/19.55 | | | | | | | % 140.40/19.55 | | | | | | Case 2: % 140.40/19.55 | | | | | | | % 140.40/19.55 | | | | | | | (1168) a_select3(q, pv10, n0) = all_71_0 & $i(all_71_0) % 140.40/19.55 | | | | | | | % 140.40/19.55 | | | | | | | REF_CLOSE: (27), (134), (917), (1157), (1168) are inconsistent by % 140.40/19.55 | | | | | | | sub-proof #1. % 140.40/19.55 | | | | | | | % 140.40/19.55 | | | | | | End of split % 140.40/19.55 | | | | | | % 140.40/19.55 | | | | | End of split % 140.40/19.55 | | | | | % 140.40/19.55 | | | | End of split % 140.40/19.55 | | | | % 140.40/19.55 | | | End of split % 140.40/19.55 | | | % 140.40/19.55 | | End of split % 140.40/19.55 | | % 140.40/19.55 | Case 2: % 140.40/19.55 | | % 140.40/19.55 | | (1169) ( ~ (all_71_13 = n1) & sum(n0, all_71_26, all_71_14) = all_71_13 & % 140.40/19.55 | | a_select3(q, all_71_16, all_71_15) = all_71_14 & $i(all_71_13) & % 140.40/19.55 | | $i(all_71_14) & leq(all_71_16, all_71_23) & leq(n0, all_71_16)) % 140.40/19.55 | | | ( ~ (all_71_17 = n0) & times(all_71_20, all_71_20) = all_71_19 & % 140.40/19.55 | | sqrt(all_71_19) = all_71_18 & minus(all_71_21, all_71_24) = % 140.40/19.55 | | all_71_20 & minus(n0, n1) = all_71_22 & sum(n0, all_71_22, % 140.40/19.55 | | all_71_18) = all_71_17 & a_select3(center, pv71, n0) = % 140.40/19.55 | | all_71_21 & $i(all_71_17) & $i(all_71_18) & $i(all_71_19) & % 140.40/19.55 | | $i(all_71_20) & $i(all_71_21) & $i(all_71_22)) % 140.40/19.55 | | % 140.40/19.55 | | BETA: splitting (1169) gives: % 140.40/19.55 | | % 140.40/19.55 | | Case 1: % 140.40/19.55 | | | % 140.40/19.55 | | | (1170) ~ (all_71_13 = n1) & sum(n0, all_71_26, all_71_14) = all_71_13 % 140.40/19.55 | | | & a_select3(q, all_71_16, all_71_15) = all_71_14 & $i(all_71_13) % 140.40/19.55 | | | & $i(all_71_14) & leq(all_71_16, all_71_23) & leq(n0, all_71_16) % 140.40/19.55 | | | % 140.40/19.55 | | | ALPHA: (1170) implies: % 140.40/19.55 | | | (1171) ~ (all_71_13 = n1) % 140.40/19.55 | | | (1172) leq(n0, all_71_16) % 140.40/19.55 | | | (1173) leq(all_71_16, all_71_23) % 140.40/19.55 | | | (1174) a_select3(q, all_71_16, all_71_15) = all_71_14 % 140.40/19.55 | | | (1175) sum(n0, all_71_26, all_71_14) = all_71_13 % 140.40/19.55 | | | % 140.40/19.55 | | | REDUCE: (119), (1175) imply: % 140.40/19.55 | | | (1176) sum(n0, n4, all_71_14) = all_71_13 % 140.40/19.55 | | | % 140.40/19.55 | | | GROUND_INST: instantiating (64) with all_71_16, all_71_15, all_71_14, % 140.40/19.55 | | | simplifying with (56), (57), (1172), (1173), (1174) gives: % 140.40/19.55 | | | (1177) sum(n0, all_71_26, all_71_14) = n1 % 140.40/19.55 | | | % 140.40/19.55 | | | REDUCE: (119), (1177) imply: % 140.40/19.55 | | | (1178) sum(n0, n4, all_71_14) = n1 % 140.40/19.55 | | | % 140.40/19.55 | | | GROUND_INST: instantiating (28) with all_71_13, n1, all_71_14, n4, n0, % 140.40/19.55 | | | simplifying with (1176), (1178) gives: % 140.40/19.55 | | | (1179) all_71_13 = n1 % 140.40/19.55 | | | % 140.40/19.55 | | | REDUCE: (1171), (1179) imply: % 140.40/19.55 | | | (1180) $false % 140.40/19.55 | | | % 140.40/19.55 | | | CLOSE: (1180) is inconsistent. % 140.40/19.55 | | | % 140.40/19.55 | | Case 2: % 140.40/19.55 | | | % 140.40/19.55 | | | (1181) ~ (all_71_17 = n0) & times(all_71_20, all_71_20) = all_71_19 & % 140.40/19.55 | | | sqrt(all_71_19) = all_71_18 & minus(all_71_21, all_71_24) = % 140.40/19.55 | | | all_71_20 & minus(n0, n1) = all_71_22 & sum(n0, all_71_22, % 140.40/19.55 | | | all_71_18) = all_71_17 & a_select3(center, pv71, n0) = % 140.40/19.55 | | | all_71_21 & $i(all_71_17) & $i(all_71_18) & $i(all_71_19) & % 140.40/19.55 | | | $i(all_71_20) & $i(all_71_21) & $i(all_71_22) % 140.40/19.55 | | | % 140.40/19.55 | | | ALPHA: (1181) implies: % 140.40/19.55 | | | (1182) ~ (all_71_17 = n0) % 140.40/19.55 | | | (1183) $i(all_71_18) % 140.40/19.55 | | | (1184) sum(n0, all_71_22, all_71_18) = all_71_17 % 140.40/19.55 | | | (1185) minus(n0, n1) = all_71_22 % 140.40/19.55 | | | % 140.40/19.55 | | | GROUND_INST: instantiating (5) with n0, all_71_22, simplifying with (19), % 140.40/19.55 | | | (1185) gives: % 140.40/19.55 | | | (1186) pred(n0) = all_71_22 & $i(all_71_22) % 140.40/19.55 | | | % 140.40/19.55 | | | ALPHA: (1186) implies: % 140.40/19.55 | | | (1187) pred(n0) = all_71_22 % 140.40/19.55 | | | % 140.40/19.55 | | | GROUND_INST: instantiating (24) with tptp_minus_1, all_71_22, n0, % 140.40/19.55 | | | simplifying with (106), (1187) gives: % 140.40/19.55 | | | (1188) all_71_22 = tptp_minus_1 % 140.40/19.55 | | | % 140.40/19.55 | | | REDUCE: (1184), (1188) imply: % 140.40/19.55 | | | (1189) sum(n0, tptp_minus_1, all_71_18) = all_71_17 % 140.40/19.55 | | | % 140.40/19.55 | | | GROUND_INST: instantiating (3) with all_71_18, all_71_17, simplifying with % 140.40/19.55 | | | (1183), (1189) gives: % 140.40/19.55 | | | (1190) all_71_17 = n0 % 140.40/19.55 | | | % 140.40/19.55 | | | REDUCE: (1182), (1190) imply: % 140.40/19.55 | | | (1191) $false % 140.40/19.55 | | | % 140.40/19.55 | | | CLOSE: (1191) is inconsistent. % 140.40/19.55 | | | % 140.40/19.55 | | End of split % 140.40/19.55 | | % 140.40/19.55 | End of split % 140.40/19.55 | % 140.40/19.55 End of proof % 140.40/19.55 % 140.40/19.55 Sub-proof #1 shows that the following formulas are inconsistent: % 140.40/19.55 ---------------------------------------------------------------- % 140.40/19.55 (1) pv10 = n0 % 140.40/19.55 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 140.40/19.55 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 140.40/19.55 v0)) % 140.40/19.55 (3) ~ (all_71_0 = all_71_10) % 140.40/19.55 (4) a_select3(q, n0, n0) = all_71_10 % 140.40/19.55 (5) a_select3(q, pv10, n0) = all_71_0 & $i(all_71_0) % 140.40/19.55 % 140.40/19.55 Begin of proof % 140.40/19.55 | % 140.40/19.55 | ALPHA: (5) implies: % 140.40/19.55 | (6) a_select3(q, pv10, n0) = all_71_0 % 140.40/19.55 | % 140.40/19.55 | REDUCE: (1), (6) imply: % 140.40/19.55 | (7) a_select3(q, n0, n0) = all_71_0 % 140.40/19.55 | % 140.40/19.55 | GROUND_INST: instantiating (2) with all_71_10, all_71_0, n0, n0, q, % 140.40/19.55 | simplifying with (4), (7) gives: % 140.40/19.55 | (8) all_71_0 = all_71_10 % 140.40/19.55 | % 140.40/19.55 | REDUCE: (3), (8) imply: % 140.40/19.55 | (9) $false % 140.40/19.55 | % 140.40/19.55 | CLOSE: (9) is inconsistent. % 140.40/19.55 | % 140.40/19.55 End of proof % 140.40/19.55 % 140.40/19.55 Sub-proof #2 shows that the following formulas are inconsistent: % 140.40/19.55 ---------------------------------------------------------------- % 140.40/19.56 (1) pv10 = n0 % 140.40/19.56 (2) a_select3(q, pv10, n1) = all_71_0 & $i(all_71_0) % 140.40/19.56 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 140.40/19.56 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 140.40/19.56 v0)) % 140.40/19.56 (4) ~ (all_71_0 = all_71_10) % 140.40/19.56 (5) a_select3(q, n0, n1) = all_71_10 % 140.40/19.56 % 140.40/19.56 Begin of proof % 140.40/19.56 | % 140.40/19.56 | ALPHA: (2) implies: % 140.40/19.56 | (6) a_select3(q, pv10, n1) = all_71_0 % 140.40/19.56 | % 140.40/19.56 | REDUCE: (1), (6) imply: % 140.40/19.56 | (7) a_select3(q, n0, n1) = all_71_0 % 140.40/19.56 | % 140.40/19.56 | GROUND_INST: instantiating (3) with all_71_10, all_71_0, n1, n0, q, % 140.40/19.56 | simplifying with (5), (7) gives: % 140.40/19.56 | (8) all_71_0 = all_71_10 % 140.40/19.56 | % 140.40/19.56 | REDUCE: (4), (8) imply: % 140.40/19.56 | (9) $false % 140.40/19.56 | % 140.40/19.56 | CLOSE: (9) is inconsistent. % 140.40/19.56 | % 140.40/19.56 End of proof % 140.40/19.56 % 140.40/19.56 Sub-proof #3 shows that the following formulas are inconsistent: % 140.40/19.56 ---------------------------------------------------------------- % 140.40/19.56 (1) ~ (sum(n0, all_71_26, all_71_2) = all_71_1) | ~ leq(n2, all_71_25) | % 140.40/19.56 (a_select3(q, pv10, n2) = all_71_0 & $i(all_71_0)) % 140.49/19.56 (2) sum(n0, n4, all_71_2) = all_71_1 % 140.49/19.56 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 140.49/19.56 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 140.49/19.56 v0)) % 140.49/19.56 (4) ~ (all_71_0 = all_71_10) % 140.49/19.56 (5) leq(n2, n3) % 140.49/19.56 (6) a_select3(q, pv10, n2) = all_71_10 % 140.49/19.56 (7) all_71_25 = n3 % 140.49/19.56 (8) all_71_26 = n4 % 140.49/19.56 % 140.49/19.56 Begin of proof % 140.49/19.56 | % 140.49/19.56 | BETA: splitting (1) gives: % 140.49/19.56 | % 140.49/19.56 | Case 1: % 140.49/19.56 | | % 140.49/19.56 | | (9) ~ (sum(n0, all_71_26, all_71_2) = all_71_1) % 140.49/19.56 | | % 140.49/19.56 | | REDUCE: (8), (9) imply: % 140.49/19.56 | | (10) ~ (sum(n0, n4, all_71_2) = all_71_1) % 140.49/19.56 | | % 140.49/19.56 | | PRED_UNIFY: (2), (10) imply: % 140.49/19.56 | | (11) $false % 140.49/19.56 | | % 140.49/19.56 | | CLOSE: (11) is inconsistent. % 140.49/19.56 | | % 140.49/19.56 | Case 2: % 140.49/19.56 | | % 140.49/19.56 | | (12) ~ leq(n2, all_71_25) | (a_select3(q, pv10, n2) = all_71_0 & % 140.49/19.56 | | $i(all_71_0)) % 140.49/19.56 | | % 140.49/19.56 | | BETA: splitting (12) gives: % 140.49/19.56 | | % 140.49/19.56 | | Case 1: % 140.49/19.56 | | | % 140.49/19.56 | | | (13) ~ leq(n2, all_71_25) % 140.49/19.56 | | | % 140.49/19.56 | | | REDUCE: (7), (13) imply: % 140.49/19.56 | | | (14) ~ leq(n2, n3) % 140.49/19.56 | | | % 140.49/19.56 | | | PRED_UNIFY: (5), (14) imply: % 140.49/19.56 | | | (15) $false % 140.49/19.56 | | | % 140.49/19.56 | | | CLOSE: (15) is inconsistent. % 140.49/19.56 | | | % 140.49/19.56 | | Case 2: % 140.49/19.56 | | | % 140.49/19.56 | | | (16) a_select3(q, pv10, n2) = all_71_0 & $i(all_71_0) % 140.49/19.56 | | | % 140.49/19.56 | | | ALPHA: (16) implies: % 140.49/19.56 | | | (17) a_select3(q, pv10, n2) = all_71_0 % 140.49/19.56 | | | % 140.49/19.56 | | | GROUND_INST: instantiating (3) with all_71_10, all_71_0, n2, pv10, q, % 140.49/19.56 | | | simplifying with (6), (17) gives: % 140.49/19.56 | | | (18) all_71_0 = all_71_10 % 140.49/19.56 | | | % 140.49/19.56 | | | REDUCE: (4), (18) imply: % 140.49/19.56 | | | (19) $false % 140.49/19.56 | | | % 140.49/19.56 | | | CLOSE: (19) is inconsistent. % 140.49/19.56 | | | % 140.49/19.56 | | End of split % 140.49/19.56 | | % 140.49/19.56 | End of split % 140.49/19.56 | % 140.49/19.56 End of proof % 140.49/19.56 % 140.49/19.56 Sub-proof #4 shows that the following formulas are inconsistent: % 140.49/19.56 ---------------------------------------------------------------- % 140.49/19.56 (1) sum(n0, n4, all_71_2) = all_71_1 % 140.49/19.56 (2) a_select3(q, pv10, n1) = all_71_10 % 140.49/19.56 (3) leq(n1, n3) % 140.49/19.56 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 140.49/19.56 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 140.49/19.56 v0)) % 140.49/19.56 (5) ~ (all_71_0 = all_71_10) % 140.49/19.56 (6) ~ (sum(n0, all_71_26, all_71_2) = all_71_1) | ~ leq(n1, all_71_25) | % 140.49/19.56 (a_select3(q, pv10, n1) = all_71_0 & $i(all_71_0)) % 140.49/19.56 (7) all_71_25 = n3 % 140.49/19.56 (8) all_71_26 = n4 % 140.49/19.56 % 140.49/19.56 Begin of proof % 140.49/19.56 | % 140.49/19.56 | BETA: splitting (6) gives: % 140.49/19.56 | % 140.49/19.56 | Case 1: % 140.49/19.56 | | % 140.49/19.56 | | (9) ~ (sum(n0, all_71_26, all_71_2) = all_71_1) % 140.49/19.56 | | % 140.49/19.56 | | REDUCE: (8), (9) imply: % 140.49/19.56 | | (10) ~ (sum(n0, n4, all_71_2) = all_71_1) % 140.49/19.56 | | % 140.49/19.56 | | PRED_UNIFY: (1), (10) imply: % 140.49/19.56 | | (11) $false % 140.49/19.56 | | % 140.49/19.56 | | CLOSE: (11) is inconsistent. % 140.49/19.56 | | % 140.49/19.56 | Case 2: % 140.49/19.56 | | % 140.49/19.56 | | (12) ~ leq(n1, all_71_25) | (a_select3(q, pv10, n1) = all_71_0 & % 140.49/19.56 | | $i(all_71_0)) % 140.49/19.56 | | % 140.49/19.56 | | BETA: splitting (12) gives: % 140.49/19.56 | | % 140.49/19.56 | | Case 1: % 140.49/19.56 | | | % 140.49/19.56 | | | (13) ~ leq(n1, all_71_25) % 140.49/19.56 | | | % 140.49/19.56 | | | REDUCE: (7), (13) imply: % 140.49/19.56 | | | (14) ~ leq(n1, n3) % 140.49/19.56 | | | % 140.49/19.56 | | | PRED_UNIFY: (3), (14) imply: % 140.49/19.56 | | | (15) $false % 140.49/19.56 | | | % 140.49/19.56 | | | CLOSE: (15) is inconsistent. % 140.49/19.56 | | | % 140.49/19.56 | | Case 2: % 140.49/19.56 | | | % 140.49/19.56 | | | (16) a_select3(q, pv10, n1) = all_71_0 & $i(all_71_0) % 140.49/19.56 | | | % 140.49/19.56 | | | REF_CLOSE: (2), (4), (5), (16) are inconsistent by sub-proof #22. % 140.49/19.56 | | | % 140.49/19.56 | | End of split % 140.49/19.56 | | % 140.49/19.56 | End of split % 140.49/19.56 | % 140.49/19.56 End of proof % 140.49/19.56 % 140.49/19.56 Sub-proof #5 shows that the following formulas are inconsistent: % 140.49/19.56 ---------------------------------------------------------------- % 140.49/19.56 (1) a_select3(q, n1, n0) = all_71_10 % 140.49/19.56 (2) pv10 = n1 % 140.49/19.56 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 140.49/19.56 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 140.49/19.56 v0)) % 140.49/19.56 (4) ~ (all_71_0 = all_71_10) % 140.49/19.56 (5) a_select3(q, pv10, n0) = all_71_0 & $i(all_71_0) % 140.49/19.56 % 140.49/19.56 Begin of proof % 140.49/19.56 | % 140.49/19.56 | ALPHA: (5) implies: % 140.49/19.56 | (6) a_select3(q, pv10, n0) = all_71_0 % 140.49/19.56 | % 140.49/19.56 | REDUCE: (2), (6) imply: % 140.49/19.56 | (7) a_select3(q, n1, n0) = all_71_0 % 140.49/19.56 | % 140.49/19.56 | GROUND_INST: instantiating (3) with all_71_10, all_71_0, n0, n1, q, % 140.49/19.56 | simplifying with (1), (7) gives: % 140.49/19.56 | (8) all_71_0 = all_71_10 % 140.49/19.56 | % 140.49/19.56 | REDUCE: (4), (8) imply: % 140.49/19.56 | (9) $false % 140.49/19.56 | % 140.49/19.56 | CLOSE: (9) is inconsistent. % 140.49/19.56 | % 140.49/19.56 End of proof % 140.49/19.56 % 140.49/19.56 Sub-proof #6 shows that the following formulas are inconsistent: % 140.49/19.56 ---------------------------------------------------------------- % 140.49/19.56 (1) a_select3(q, pv10, n0) = all_71_0 & $i(all_71_0) % 140.49/19.56 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 140.49/19.56 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 140.49/19.56 v0)) % 140.49/19.56 (3) a_select3(q, pv10, n0) = all_71_10 % 140.49/19.56 (4) ~ (all_71_0 = all_71_10) % 140.49/19.56 % 140.49/19.56 Begin of proof % 140.49/19.56 | % 140.49/19.56 | ALPHA: (1) implies: % 140.49/19.56 | (5) a_select3(q, pv10, n0) = all_71_0 % 140.49/19.56 | % 140.49/19.56 | GROUND_INST: instantiating (2) with all_71_10, all_71_0, n0, pv10, q, % 140.49/19.56 | simplifying with (3), (5) gives: % 140.49/19.56 | (6) all_71_0 = all_71_10 % 140.49/19.56 | % 140.49/19.56 | REDUCE: (4), (6) imply: % 140.49/19.56 | (7) $false % 140.49/19.56 | % 140.49/19.56 | CLOSE: (7) is inconsistent. % 140.49/19.56 | % 140.49/19.56 End of proof % 140.49/19.56 % 140.49/19.56 Sub-proof #7 shows that the following formulas are inconsistent: % 140.49/19.56 ---------------------------------------------------------------- % 140.49/19.56 (1) pv10 = n1 % 140.49/19.56 (2) a_select3(q, pv10, n1) = all_71_0 & $i(all_71_0) % 140.49/19.56 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 140.49/19.56 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 140.49/19.56 v0)) % 140.49/19.56 (4) ~ (all_71_0 = all_71_10) % 140.49/19.56 (5) a_select3(q, n1, n1) = all_71_10 % 140.49/19.56 % 140.49/19.56 Begin of proof % 140.49/19.56 | % 140.49/19.56 | ALPHA: (2) implies: % 140.49/19.56 | (6) a_select3(q, pv10, n1) = all_71_0 % 140.49/19.56 | % 140.49/19.56 | REDUCE: (1), (6) imply: % 140.49/19.56 | (7) a_select3(q, n1, n1) = all_71_0 % 140.49/19.56 | % 140.49/19.56 | GROUND_INST: instantiating (3) with all_71_10, all_71_0, n1, n1, q, % 140.49/19.56 | simplifying with (5), (7) gives: % 140.49/19.56 | (8) all_71_0 = all_71_10 % 140.49/19.56 | % 140.49/19.56 | REDUCE: (4), (8) imply: % 140.49/19.56 | (9) $false % 140.49/19.56 | % 140.49/19.56 | CLOSE: (9) is inconsistent. % 140.49/19.56 | % 140.49/19.56 End of proof % 140.49/19.56 % 140.49/19.56 Sub-proof #8 shows that the following formulas are inconsistent: % 140.49/19.56 ---------------------------------------------------------------- % 140.49/19.56 (1) $i(all_71_11) % 140.49/19.56 (2) sqrt(all_71_7) = all_71_6 % 140.49/19.56 (3) times(all_71_8, all_71_8) = all_71_7 % 140.49/19.56 (4) leq(n0, n2) % 140.49/19.56 (5) sum(n0, n4, all_71_2) = all_71_1 % 140.49/19.56 (6) sqrt(all_71_3) = all_71_2 % 140.49/19.56 (7) leq(n2, n2) % 140.49/19.56 (8) all_71_25 = n2 % 140.49/19.56 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 140.49/19.56 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 140.49/19.56 v0)) % 140.49/19.57 (10) ~ (all_71_0 = all_71_10) % 140.49/19.57 (11) divide(all_71_6, all_71_1) = all_71_0 % 140.49/19.57 (12) a_select3(center, all_71_11, n0) = all_71_5 % 140.49/19.57 (13) minus(all_71_9, all_71_24) = all_71_8 % 140.49/19.57 (14) times(all_71_4, all_71_4) = all_71_3 % 140.49/19.57 (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 140.49/19.57 [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! % 140.49/19.57 [v10: $i] : ! [v11: $i] : ( ~ (times(v7, v7) = v8) | ~ (times(v3, v3) % 140.49/19.57 = v4) | ~ (sqrt(v8) = v9) | ~ (sqrt(v4) = v5) | ~ (divide(v5, % 140.49/19.57 v10) = v11) | ~ (minus(v6, all_71_24) = v7) | ~ (minus(v2, % 140.49/19.57 all_71_24) = v3) | ~ (sum(n0, all_71_26, v9) = v10) | ~ % 140.49/19.57 (a_select3(center, v1, n0) = v6) | ~ (a_select3(center, v0, n0) = v2) % 140.49/19.57 | ~ $i(v1) | ~ $i(v0) | ~ leq(v0, all_71_25) | ~ leq(n0, v0) | % 140.49/19.57 (a_select3(q, pv10, v0) = v11 & $i(v11))) % 140.49/19.57 (16) $i(n2) % 140.49/19.57 (17) a_select3(q, pv10, n2) = all_71_10 % 140.49/19.57 (18) a_select3(center, n2, n0) = all_71_9 % 140.49/19.57 (19) minus(all_71_5, all_71_24) = all_71_4 % 140.49/19.57 (20) all_71_26 = n4 % 140.49/19.57 % 140.49/19.57 Begin of proof % 140.49/19.57 | % 140.49/19.57 | GROUND_INST: instantiating (15) with n2, all_71_11, all_71_9, all_71_8, % 140.49/19.57 | all_71_7, all_71_6, all_71_5, all_71_4, all_71_3, all_71_2, % 140.49/19.57 | all_71_1, all_71_0, simplifying with (1), (2), (3), (4), (6), % 140.49/19.57 | (11), (12), (13), (14), (16), (18), (19) gives: % 140.49/19.57 | (21) ~ (sum(n0, all_71_26, all_71_2) = all_71_1) | ~ leq(n2, all_71_25) | % 140.49/19.57 | (a_select3(q, pv10, n2) = all_71_0 & $i(all_71_0)) % 140.49/19.57 | % 140.49/19.57 | BETA: splitting (21) gives: % 140.49/19.57 | % 140.49/19.57 | Case 1: % 140.49/19.57 | | % 140.49/19.57 | | (22) ~ (sum(n0, all_71_26, all_71_2) = all_71_1) % 140.49/19.57 | | % 140.49/19.57 | | REDUCE: (20), (22) imply: % 140.49/19.57 | | (23) ~ (sum(n0, n4, all_71_2) = all_71_1) % 140.49/19.57 | | % 140.49/19.57 | | PRED_UNIFY: (5), (23) imply: % 140.49/19.57 | | (24) $false % 140.49/19.57 | | % 140.49/19.57 | | CLOSE: (24) is inconsistent. % 140.49/19.57 | | % 140.49/19.57 | Case 2: % 140.49/19.57 | | % 140.49/19.57 | | (25) ~ leq(n2, all_71_25) | (a_select3(q, pv10, n2) = all_71_0 & % 140.49/19.57 | | $i(all_71_0)) % 140.49/19.57 | | % 140.49/19.57 | | BETA: splitting (25) gives: % 140.49/19.57 | | % 140.49/19.57 | | Case 1: % 140.49/19.57 | | | % 140.49/19.57 | | | (26) ~ leq(n2, all_71_25) % 140.49/19.57 | | | % 140.49/19.57 | | | REDUCE: (8), (26) imply: % 140.49/19.57 | | | (27) ~ leq(n2, n2) % 140.49/19.57 | | | % 140.49/19.57 | | | PRED_UNIFY: (7), (27) imply: % 140.49/19.57 | | | (28) $false % 140.49/19.57 | | | % 140.49/19.57 | | | CLOSE: (28) is inconsistent. % 140.49/19.57 | | | % 140.49/19.57 | | Case 2: % 140.49/19.57 | | | % 140.49/19.57 | | | (29) a_select3(q, pv10, n2) = all_71_0 & $i(all_71_0) % 140.49/19.57 | | | % 140.49/19.57 | | | ALPHA: (29) implies: % 140.49/19.57 | | | (30) a_select3(q, pv10, n2) = all_71_0 % 140.49/19.57 | | | % 140.49/19.57 | | | GROUND_INST: instantiating (9) with all_71_10, all_71_0, n2, pv10, q, % 140.49/19.57 | | | simplifying with (17), (30) gives: % 140.49/19.57 | | | (31) all_71_0 = all_71_10 % 140.49/19.57 | | | % 140.49/19.57 | | | REDUCE: (10), (31) imply: % 140.49/19.57 | | | (32) $false % 140.49/19.57 | | | % 140.49/19.57 | | | CLOSE: (32) is inconsistent. % 140.49/19.57 | | | % 140.49/19.57 | | End of split % 140.49/19.57 | | % 140.49/19.57 | End of split % 140.49/19.57 | % 140.49/19.57 End of proof % 140.49/19.57 % 140.49/19.57 Sub-proof #9 shows that the following formulas are inconsistent: % 140.49/19.57 ---------------------------------------------------------------- % 140.49/19.57 (1) pv10 = n3 % 140.49/19.57 (2) pred(pv10) = all_71_23 % 140.49/19.57 (3) $i(all_71_23) % 140.49/19.57 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (pred(v2) = v1) | % 140.49/19.57 ~ (pred(v2) = v0)) % 140.49/19.57 (5) ! [v0: $i] : ( ~ $i(v0) | ~ gt(v0, v0)) % 140.49/19.57 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 140.49/19.57 (minus(v3, v2) = v1) | ~ (minus(v3, v2) = v0)) % 140.49/19.57 (7) gt(all_71_23, n2) % 140.49/19.57 (8) pred(n3) = n2 % 140.49/19.57 (9) minus(pv10, n1) = all_71_23 % 140.49/19.57 % 140.49/19.57 Begin of proof % 140.49/19.57 | % 140.49/19.57 | REDUCE: (1), (9) imply: % 140.49/19.57 | (10) minus(n3, n1) = all_71_23 % 140.49/19.57 | % 140.49/19.57 | REDUCE: (1), (2) imply: % 140.49/19.57 | (11) pred(n3) = all_71_23 % 140.49/19.57 | % 140.49/19.57 | GROUND_INST: instantiating (4) with n2, all_71_23, n3, simplifying with (8), % 140.49/19.57 | (11) gives: % 140.49/19.57 | (12) all_71_23 = n2 % 140.49/19.57 | % 140.49/19.57 | REDUCE: (10), (12) imply: % 140.49/19.57 | (13) minus(n3, n1) = n2 % 140.49/19.57 | % 140.49/19.57 | REF_CLOSE: (3), (5), (6), (7), (10), (13) are inconsistent by sub-proof #21. % 140.49/19.57 | % 140.49/19.57 End of proof % 140.49/19.57 % 140.49/19.57 Sub-proof #10 shows that the following formulas are inconsistent: % 140.49/19.57 ---------------------------------------------------------------- % 140.49/19.57 (1) pred(n4) = all_71_23 % 140.49/19.57 (2) pred(n4) = n3 % 140.49/19.57 (3) $i(all_71_23) % 140.49/19.57 (4) gt(all_71_23, n3) % 140.49/19.57 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (pred(v2) = v1) | % 140.49/19.57 ~ (pred(v2) = v0)) % 140.49/19.57 (6) ! [v0: $i] : ( ~ $i(v0) | ~ gt(v0, v0)) % 140.49/19.57 % 140.49/19.57 Begin of proof % 140.49/19.57 | % 140.49/19.57 | GROUND_INST: instantiating (5) with n3, all_71_23, n4, simplifying with (1), % 140.49/19.57 | (2) gives: % 140.49/19.57 | (7) all_71_23 = n3 % 140.49/19.57 | % 140.49/19.57 | REDUCE: (3), (7) imply: % 140.49/19.57 | (8) $i(n3) % 140.49/19.57 | % 140.49/19.57 | REDUCE: (4), (7) imply: % 140.49/19.57 | (9) gt(n3, n3) % 140.49/19.57 | % 140.49/19.57 | GROUND_INST: instantiating (6) with n3, simplifying with (8), (9) gives: % 140.49/19.57 | (10) $false % 140.49/19.57 | % 140.49/19.57 | CLOSE: (10) is inconsistent. % 140.49/19.57 | % 140.49/19.57 End of proof % 140.49/19.57 % 140.49/19.57 Sub-proof #11 shows that the following formulas are inconsistent: % 140.49/19.57 ---------------------------------------------------------------- % 140.49/19.57 (1) $i(all_71_23) % 140.49/19.57 (2) minus(n5, n1) = n4 % 140.49/19.57 (3) ! [v0: $i] : ( ~ $i(v0) | ~ gt(v0, v0)) % 140.49/19.57 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 140.49/19.57 (minus(v3, v2) = v1) | ~ (minus(v3, v2) = v0)) % 140.49/19.57 (5) gt(all_71_23, n4) % 140.49/19.57 (6) pv10 = n5 % 140.49/19.57 (7) minus(pv10, n1) = all_71_23 % 140.49/19.57 % 140.49/19.57 Begin of proof % 140.49/19.57 | % 140.49/19.57 | REDUCE: (6), (7) imply: % 140.49/19.57 | (8) minus(n5, n1) = all_71_23 % 140.49/19.57 | % 140.49/19.57 | GROUND_INST: instantiating (4) with n4, all_71_23, n1, n5, simplifying with % 140.49/19.57 | (2), (8) gives: % 140.49/19.57 | (9) all_71_23 = n4 % 140.49/19.57 | % 140.49/19.57 | REDUCE: (1), (9) imply: % 140.49/19.57 | (10) $i(n4) % 140.49/19.57 | % 140.49/19.57 | REDUCE: (5), (9) imply: % 140.49/19.57 | (11) gt(n4, n4) % 140.49/19.57 | % 140.49/19.57 | GROUND_INST: instantiating (3) with n4, simplifying with (10), (11) gives: % 140.49/19.57 | (12) $false % 140.49/19.57 | % 140.49/19.57 | CLOSE: (12) is inconsistent. % 140.49/19.57 | % 140.49/19.57 End of proof % 140.49/19.57 % 140.49/19.57 Sub-proof #12 shows that the following formulas are inconsistent: % 140.49/19.57 ---------------------------------------------------------------- % 140.49/19.57 (1) $i(all_71_11) % 140.49/19.57 (2) sqrt(all_71_7) = all_71_6 % 140.49/19.57 (3) $i(n1) % 140.49/19.57 (4) times(all_71_8, all_71_8) = all_71_7 % 140.49/19.57 (5) sum(n0, n4, all_71_2) = all_71_1 % 140.49/19.57 (6) sqrt(all_71_3) = all_71_2 % 140.49/19.57 (7) a_select3(center, n1, n0) = all_71_9 % 140.49/19.57 (8) leq(n1, n1) % 140.49/19.57 (9) a_select3(q, pv10, n1) = all_71_10 % 140.49/19.57 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 140.49/19.57 (v1 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 140.49/19.57 v0)) % 140.49/19.57 (11) ~ (all_71_0 = all_71_10) % 140.49/19.57 (12) divide(all_71_6, all_71_1) = all_71_0 % 140.49/19.57 (13) all_71_25 = n1 % 140.49/19.57 (14) leq(n0, n1) % 140.49/19.57 (15) a_select3(center, all_71_11, n0) = all_71_5 % 140.49/19.57 (16) minus(all_71_9, all_71_24) = all_71_8 % 140.49/19.57 (17) times(all_71_4, all_71_4) = all_71_3 % 140.49/19.58 (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 140.49/19.58 [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! % 140.49/19.58 [v10: $i] : ! [v11: $i] : ( ~ (times(v7, v7) = v8) | ~ (times(v3, v3) % 140.49/19.58 = v4) | ~ (sqrt(v8) = v9) | ~ (sqrt(v4) = v5) | ~ (divide(v5, % 140.49/19.58 v10) = v11) | ~ (minus(v6, all_71_24) = v7) | ~ (minus(v2, % 140.49/19.58 all_71_24) = v3) | ~ (sum(n0, all_71_26, v9) = v10) | ~ % 140.49/19.58 (a_select3(center, v1, n0) = v6) | ~ (a_select3(center, v0, n0) = v2) % 140.49/19.58 | ~ $i(v1) | ~ $i(v0) | ~ leq(v0, all_71_25) | ~ leq(n0, v0) | % 140.49/19.58 (a_select3(q, pv10, v0) = v11 & $i(v11))) % 140.49/19.58 (19) minus(all_71_5, all_71_24) = all_71_4 % 140.49/19.58 (20) all_71_26 = n4 % 140.49/19.58 % 140.49/19.58 Begin of proof % 140.49/19.58 | % 140.49/19.58 | GROUND_INST: instantiating (18) with n1, all_71_11, all_71_9, all_71_8, % 140.49/19.58 | all_71_7, all_71_6, all_71_5, all_71_4, all_71_3, all_71_2, % 140.49/19.58 | all_71_1, all_71_0, simplifying with (1), (2), (3), (4), (6), % 140.49/19.58 | (7), (12), (14), (15), (16), (17), (19) gives: % 140.49/19.58 | (21) ~ (sum(n0, all_71_26, all_71_2) = all_71_1) | ~ leq(n1, all_71_25) | % 140.49/19.58 | (a_select3(q, pv10, n1) = all_71_0 & $i(all_71_0)) % 140.49/19.58 | % 140.49/19.58 | BETA: splitting (21) gives: % 140.49/19.58 | % 140.49/19.58 | Case 1: % 140.49/19.58 | | % 140.49/19.58 | | (22) ~ (sum(n0, all_71_26, all_71_2) = all_71_1) % 140.49/19.58 | | % 140.49/19.58 | | REDUCE: (20), (22) imply: % 140.49/19.58 | | (23) ~ (sum(n0, n4, all_71_2) = all_71_1) % 140.49/19.58 | | % 140.49/19.58 | | PRED_UNIFY: (5), (23) imply: % 140.49/19.58 | | (24) $false % 140.49/19.58 | | % 140.49/19.58 | | CLOSE: (24) is inconsistent. % 140.49/19.58 | | % 140.49/19.58 | Case 2: % 140.49/19.58 | | % 140.49/19.58 | | (25) ~ leq(n1, all_71_25) | (a_select3(q, pv10, n1) = all_71_0 & % 140.49/19.58 | | $i(all_71_0)) % 140.49/19.58 | | % 140.49/19.58 | | BETA: splitting (25) gives: % 140.49/19.58 | | % 140.49/19.58 | | Case 1: % 140.49/19.58 | | | % 140.49/19.58 | | | (26) ~ leq(n1, all_71_25) % 140.49/19.58 | | | % 140.49/19.58 | | | REDUCE: (13), (26) imply: % 140.49/19.58 | | | (27) ~ leq(n1, n1) % 140.49/19.58 | | | % 140.49/19.58 | | | PRED_UNIFY: (8), (27) imply: % 140.49/19.58 | | | (28) $false % 140.49/19.58 | | | % 140.49/19.58 | | | CLOSE: (28) is inconsistent. % 140.49/19.58 | | | % 140.49/19.58 | | Case 2: % 140.49/19.58 | | | % 140.49/19.58 | | | (29) a_select3(q, pv10, n1) = all_71_0 & $i(all_71_0) % 140.49/19.58 | | | % 140.49/19.58 | | | ALPHA: (29) implies: % 140.49/19.58 | | | (30) a_select3(q, pv10, n1) = all_71_0 % 140.49/19.58 | | | % 140.49/19.58 | | | GROUND_INST: instantiating (10) with all_71_10, all_71_0, n1, pv10, q, % 140.49/19.58 | | | simplifying with (9), (30) gives: % 140.49/19.58 | | | (31) all_71_0 = all_71_10 % 140.49/19.58 | | | % 140.49/19.58 | | | REDUCE: (11), (31) imply: % 140.49/19.58 | | | (32) $false % 140.49/19.58 | | | % 140.49/19.58 | | | CLOSE: (32) is inconsistent. % 140.49/19.58 | | | % 140.49/19.58 | | End of split % 140.49/19.58 | | % 140.49/19.58 | End of split % 140.49/19.58 | % 140.49/19.58 End of proof % 140.49/19.58 % 140.49/19.58 Sub-proof #13 shows that the following formulas are inconsistent: % 140.49/19.58 ---------------------------------------------------------------- % 140.49/19.58 (1) $i(pv12) % 140.49/19.58 (2) pv12 = n1 % 140.49/19.58 (3) gt(pv12, n1) % 140.49/19.58 (4) ! [v0: $i] : ( ~ $i(v0) | ~ gt(v0, v0)) % 140.49/19.58 % 140.49/19.58 Begin of proof % 140.49/19.58 | % 140.49/19.58 | REDUCE: (1), (2) imply: % 140.49/19.58 | (5) $i(n1) % 140.49/19.58 | % 140.49/19.58 | REDUCE: (2), (3) imply: % 140.49/19.58 | (6) gt(n1, n1) % 140.49/19.58 | % 140.49/19.58 | GROUND_INST: instantiating (4) with n1, simplifying with (5), (6) gives: % 140.49/19.58 | (7) $false % 140.49/19.58 | % 140.49/19.58 | CLOSE: (7) is inconsistent. % 140.49/19.58 | % 140.49/19.58 End of proof % 140.49/19.58 % 140.49/19.58 Sub-proof #14 shows that the following formulas are inconsistent: % 140.49/19.58 ---------------------------------------------------------------- % 140.49/19.58 (1) gt(all_71_25, n0) % 140.49/19.58 (2) all_71_25 = n0 % 140.49/19.58 (3) ~ gt(all_71_25, all_71_25) % 140.49/19.58 % 140.49/19.58 Begin of proof % 140.49/19.58 | % 140.49/19.58 | REDUCE: (1), (2) imply: % 140.49/19.58 | (4) gt(n0, n0) % 140.49/19.58 | % 140.49/19.58 | REDUCE: (2), (3) imply: % 140.49/19.58 | (5) ~ gt(n0, n0) % 140.49/19.58 | % 140.49/19.58 | PRED_UNIFY: (4), (5) imply: % 140.49/19.58 | (6) $false % 140.49/19.58 | % 140.49/19.58 | CLOSE: (6) is inconsistent. % 140.49/19.58 | % 140.49/19.58 End of proof % 140.49/19.58 % 140.49/19.58 Sub-proof #15 shows that the following formulas are inconsistent: % 140.49/19.58 ---------------------------------------------------------------- % 140.49/19.58 (1) gt(all_71_25, n0) % 140.49/19.58 (2) pred(n2) = n1 % 140.49/19.58 (3) ~ (all_71_25 = n0) % 140.49/19.58 (4) all_71_12 = n2 | gt(n2, all_71_12) % 140.49/19.58 (5) $i(all_71_25) % 140.49/19.58 (6) gt(all_71_25, all_71_12) % 140.49/19.58 (7) pred(n1) = n0 % 140.49/19.58 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (pred(v2) = v1) | % 140.49/19.58 ~ (pred(v2) = v0)) % 140.49/19.58 (9) succ(n2) = n3 % 140.49/19.58 (10) ! [v0: $i] : ( ~ $i(v0) | ~ gt(v0, v0)) % 140.49/19.58 (11) ~ (all_71_12 = n0) % 140.49/19.58 (12) ! [v0: $i] : (v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0, n1) | ~ % 140.49/19.58 leq(n0, v0)) % 140.49/19.58 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (pred(v1) = v2) | ~ % 140.49/19.58 $i(v1) | ~ $i(v0) | ~ gt(v1, v0) | leq(v0, v2)) % 140.49/19.58 (14) pv12 = n4 | pv12 = n3 | pv12 = n2 | pv12 = n1 % 140.49/19.58 (15) $i(all_71_12) % 140.49/19.58 (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 140.49/19.58 $i(v0) | ~ gt(v1, v2) | ~ gt(v0, v1) | gt(v0, v2)) % 140.49/19.58 (17) gt(n3, pv12) % 140.49/19.58 (18) leq(n0, all_71_12) % 140.49/19.58 (19) $i(pv12) % 140.49/19.58 (20) succ(all_71_25) = pv12 % 140.49/19.58 (21) all_71_25 = n2 | gt(n2, all_71_25) % 140.49/19.58 (22) $i(n2) % 140.49/19.58 (23) leq(n0, all_71_25) % 140.49/19.58 (24) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (succ(v2) = v1) % 140.49/19.58 | ~ (succ(v2) = v0)) % 140.49/19.58 (25) ~ gt(n0, n0) % 140.49/19.58 (26) pred(pv12) = all_71_25 % 140.49/19.58 % 140.49/19.58 Begin of proof % 140.49/19.58 | % 140.49/19.58 | BETA: splitting (21) gives: % 140.49/19.58 | % 140.49/19.58 | Case 1: % 140.49/19.58 | | % 140.49/19.58 | | (27) gt(n2, all_71_25) % 140.49/19.58 | | % 140.49/19.58 | | BETA: splitting (4) gives: % 140.49/19.58 | | % 140.49/19.58 | | Case 1: % 140.49/19.58 | | | % 140.49/19.58 | | | (28) gt(n2, all_71_12) % 140.49/19.58 | | | % 140.49/19.58 | | | GROUND_INST: instantiating (13) with all_71_25, n2, n1, simplifying with % 140.49/19.58 | | | (2), (5), (22), (27) gives: % 140.49/19.58 | | | (29) leq(all_71_25, n1) % 140.49/19.58 | | | % 140.49/19.58 | | | GROUND_INST: instantiating (13) with all_71_12, n2, n1, simplifying with % 140.49/19.58 | | | (2), (15), (22), (28) gives: % 140.49/19.58 | | | (30) leq(all_71_12, n1) % 140.49/19.58 | | | % 140.49/19.58 | | | BETA: splitting (14) gives: % 140.49/19.58 | | | % 140.49/19.58 | | | Case 1: % 140.49/19.58 | | | | % 140.49/19.58 | | | | (31) pv12 = n1 % 140.49/19.58 | | | | % 140.49/19.58 | | | | REF_CLOSE: (1), (7), (8), (25), (26), (31) are inconsistent by sub-proof % 140.49/19.58 | | | | #16. % 140.49/19.58 | | | | % 140.49/19.58 | | | Case 2: % 140.49/19.58 | | | | % 140.49/19.58 | | | | % 140.49/19.58 | | | | GROUND_INST: instantiating (12) with all_71_25, simplifying with (5), % 140.49/19.58 | | | | (23), (29) gives: % 140.49/19.58 | | | | (32) all_71_25 = n1 | all_71_25 = n0 % 140.49/19.58 | | | | % 140.49/19.58 | | | | GROUND_INST: instantiating (12) with all_71_12, simplifying with (15), % 140.49/19.58 | | | | (18), (30) gives: % 140.49/19.58 | | | | (33) all_71_12 = n1 | all_71_12 = n0 % 140.49/19.58 | | | | % 140.49/19.58 | | | | REF_CLOSE: (3), (5), (6), (10), (11), (32), (33) are inconsistent by % 140.49/19.58 | | | | sub-proof #24. % 140.49/19.58 | | | | % 140.49/19.58 | | | End of split % 140.49/19.58 | | | % 140.49/19.58 | | Case 2: % 140.49/19.58 | | | % 140.49/19.58 | | | (34) all_71_12 = n2 % 140.49/19.58 | | | (35) ~ gt(n2, all_71_12) % 140.49/19.58 | | | % 140.49/19.58 | | | REDUCE: (6), (34) imply: % 140.49/19.58 | | | (36) gt(all_71_25, n2) % 140.49/19.58 | | | % 140.49/19.58 | | | REDUCE: (34), (35) imply: % 140.49/19.58 | | | (37) ~ gt(n2, n2) % 140.49/19.58 | | | % 140.49/19.58 | | | GROUND_INST: instantiating (16) with n2, all_71_25, n2, simplifying with % 140.49/19.58 | | | (5), (22), (27), (36), (37) gives: % 140.49/19.58 | | | (38) $false % 140.49/19.58 | | | % 140.49/19.58 | | | CLOSE: (38) is inconsistent. % 140.49/19.58 | | | % 140.49/19.58 | | End of split % 140.49/19.58 | | % 140.49/19.58 | Case 2: % 140.49/19.58 | | % 140.49/19.58 | | (39) all_71_25 = n2 % 140.49/19.58 | | % 140.49/19.58 | | REDUCE: (20), (39) imply: % 140.49/19.58 | | (40) succ(n2) = pv12 % 140.49/19.58 | | % 140.49/19.58 | | REF_CLOSE: (9), (10), (17), (19), (24), (40) are inconsistent by sub-proof % 140.49/19.58 | | #23. % 140.49/19.58 | | % 140.49/19.58 | End of split % 140.49/19.58 | % 140.49/19.58 End of proof % 140.49/19.58 % 140.49/19.58 Sub-proof #16 shows that the following formulas are inconsistent: % 140.49/19.58 ---------------------------------------------------------------- % 140.49/19.58 (1) gt(all_71_25, n0) % 140.49/19.58 (2) pv12 = n1 % 140.49/19.58 (3) pred(n1) = n0 % 140.49/19.58 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (pred(v2) = v1) | % 140.49/19.58 ~ (pred(v2) = v0)) % 140.49/19.58 (5) ~ gt(n0, n0) % 140.49/19.58 (6) pred(pv12) = all_71_25 % 140.49/19.58 % 140.49/19.58 Begin of proof % 140.49/19.58 | % 140.49/19.58 | REDUCE: (2), (6) imply: % 140.49/19.58 | (7) pred(n1) = all_71_25 % 140.49/19.58 | % 140.49/19.58 | GROUND_INST: instantiating (4) with n0, all_71_25, n1, simplifying with (3), % 140.49/19.58 | (7) gives: % 140.49/19.58 | (8) all_71_25 = n0 % 140.49/19.58 | % 140.49/19.58 | REDUCE: (1), (8) imply: % 140.49/19.58 | (9) gt(n0, n0) % 140.49/19.58 | % 140.49/19.58 | PRED_UNIFY: (5), (9) imply: % 140.49/19.58 | (10) $false % 140.49/19.58 | % 140.49/19.58 | CLOSE: (10) is inconsistent. % 140.49/19.58 | % 140.49/19.58 End of proof % 140.49/19.58 % 140.49/19.58 Sub-proof #17 shows that the following formulas are inconsistent: % 140.49/19.58 ---------------------------------------------------------------- % 140.49/19.58 (1) gt(all_71_23, n0) % 140.49/19.58 (2) pred(pv10) = all_71_23 % 140.49/19.58 (3) $i(all_71_23) % 140.49/19.58 (4) pv10 = n1 % 140.49/19.58 (5) pred(n1) = n0 % 140.49/19.59 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (pred(v2) = v1) | % 140.49/19.59 ~ (pred(v2) = v0)) % 140.49/19.59 (7) ! [v0: $i] : ( ~ $i(v0) | ~ gt(v0, v0)) % 140.49/19.59 % 140.49/19.59 Begin of proof % 140.49/19.59 | % 140.49/19.59 | REDUCE: (2), (4) imply: % 140.49/19.59 | (8) pred(n1) = all_71_23 % 140.49/19.59 | % 140.49/19.59 | GROUND_INST: instantiating (6) with n0, all_71_23, n1, simplifying with (5), % 140.49/19.59 | (8) gives: % 140.49/19.59 | (9) all_71_23 = n0 % 140.49/19.59 | % 140.49/19.59 | REDUCE: (3), (9) imply: % 140.49/19.59 | (10) $i(n0) % 140.49/19.59 | % 140.49/19.59 | REDUCE: (1), (9) imply: % 140.49/19.59 | (11) gt(n0, n0) % 140.49/19.59 | % 140.49/19.59 | GROUND_INST: instantiating (7) with n0, simplifying with (10), (11) gives: % 140.49/19.59 | (12) $false % 140.49/19.59 | % 140.49/19.59 | CLOSE: (12) is inconsistent. % 140.49/19.59 | % 140.49/19.59 End of proof % 140.49/19.59 % 140.49/19.59 Sub-proof #18 shows that the following formulas are inconsistent: % 140.49/19.59 ---------------------------------------------------------------- % 140.49/19.59 (1) a_select3(q, pv10, n1) = all_71_0 & $i(all_71_0) % 140.49/19.59 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 140.49/19.59 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 140.49/19.59 v0)) % 140.49/19.59 (3) ~ (all_71_0 = all_71_10) % 140.49/19.59 (4) pv10 = n2 % 140.49/19.59 (5) a_select3(q, n2, n1) = all_71_10 % 140.49/19.59 % 140.49/19.59 Begin of proof % 140.49/19.59 | % 140.49/19.59 | ALPHA: (1) implies: % 140.49/19.59 | (6) a_select3(q, pv10, n1) = all_71_0 % 140.49/19.59 | % 140.49/19.59 | REDUCE: (4), (6) imply: % 140.49/19.59 | (7) a_select3(q, n2, n1) = all_71_0 % 140.49/19.59 | % 140.49/19.59 | GROUND_INST: instantiating (2) with all_71_10, all_71_0, n1, n2, q, % 140.49/19.59 | simplifying with (5), (7) gives: % 140.49/19.59 | (8) all_71_0 = all_71_10 % 140.49/19.59 | % 140.49/19.59 | REDUCE: (3), (8) imply: % 140.49/19.59 | (9) $false % 140.49/19.59 | % 140.49/19.59 | CLOSE: (9) is inconsistent. % 140.49/19.59 | % 140.49/19.59 End of proof % 140.49/19.59 % 140.49/19.59 Sub-proof #19 shows that the following formulas are inconsistent: % 140.49/19.59 ---------------------------------------------------------------- % 140.49/19.59 (1) $i(all_71_23) % 140.49/19.59 (2) all_71_23 = n1 % 140.49/19.59 (3) gt(all_71_23, n1) % 140.49/19.59 (4) ! [v0: $i] : ( ~ $i(v0) | ~ gt(v0, v0)) % 140.49/19.59 % 140.49/19.59 Begin of proof % 140.49/19.59 | % 140.49/19.59 | REDUCE: (1), (2) imply: % 140.49/19.59 | (5) $i(n1) % 140.49/19.59 | % 140.49/19.59 | REDUCE: (2), (3) imply: % 140.49/19.59 | (6) gt(n1, n1) % 140.49/19.59 | % 140.49/19.59 | GROUND_INST: instantiating (4) with n1, simplifying with (5), (6) gives: % 140.49/19.59 | (7) $false % 140.49/19.59 | % 140.49/19.59 | CLOSE: (7) is inconsistent. % 140.49/19.59 | % 140.49/19.59 End of proof % 140.49/19.59 % 140.49/19.59 Sub-proof #20 shows that the following formulas are inconsistent: % 140.49/19.59 ---------------------------------------------------------------- % 140.49/19.59 (1) a_select3(q, n3, n1) = all_71_10 % 140.49/19.59 (2) pv10 = n3 % 140.49/19.59 (3) a_select3(q, pv10, n1) = all_71_0 & $i(all_71_0) % 140.49/19.59 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 140.49/19.59 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 140.49/19.59 v0)) % 140.49/19.59 (5) ~ (all_71_0 = all_71_10) % 140.49/19.59 % 140.49/19.59 Begin of proof % 140.49/19.59 | % 140.49/19.59 | ALPHA: (3) implies: % 140.49/19.59 | (6) a_select3(q, pv10, n1) = all_71_0 % 140.49/19.59 | % 140.49/19.59 | REDUCE: (2), (6) imply: % 140.49/19.59 | (7) a_select3(q, n3, n1) = all_71_0 % 140.49/19.59 | % 140.49/19.59 | GROUND_INST: instantiating (4) with all_71_10, all_71_0, n1, n3, q, % 140.49/19.59 | simplifying with (1), (7) gives: % 140.49/19.59 | (8) all_71_0 = all_71_10 % 140.49/19.59 | % 140.49/19.59 | REDUCE: (5), (8) imply: % 140.49/19.59 | (9) $false % 140.49/19.59 | % 140.49/19.59 | CLOSE: (9) is inconsistent. % 140.49/19.59 | % 140.49/19.59 End of proof % 140.49/19.59 % 140.49/19.59 Sub-proof #21 shows that the following formulas are inconsistent: % 140.49/19.59 ---------------------------------------------------------------- % 140.49/19.59 (1) minus(n3, n1) = all_71_23 % 140.49/19.59 (2) $i(all_71_23) % 140.49/19.59 (3) minus(n3, n1) = n2 % 140.49/19.59 (4) ! [v0: $i] : ( ~ $i(v0) | ~ gt(v0, v0)) % 140.49/19.59 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 140.49/19.59 (minus(v3, v2) = v1) | ~ (minus(v3, v2) = v0)) % 140.49/19.59 (6) gt(all_71_23, n2) % 140.49/19.59 % 140.49/19.59 Begin of proof % 140.49/19.59 | % 140.49/19.59 | GROUND_INST: instantiating (5) with n2, all_71_23, n1, n3, simplifying with % 140.49/19.59 | (1), (3) gives: % 140.49/19.59 | (7) all_71_23 = n2 % 140.49/19.59 | % 140.49/19.59 | REDUCE: (2), (7) imply: % 140.49/19.59 | (8) $i(n2) % 140.49/19.59 | % 140.49/19.59 | REDUCE: (6), (7) imply: % 140.49/19.59 | (9) gt(n2, n2) % 140.49/19.59 | % 140.49/19.59 | GROUND_INST: instantiating (4) with n2, simplifying with (8), (9) gives: % 140.49/19.59 | (10) $false % 140.49/19.59 | % 140.49/19.59 | CLOSE: (10) is inconsistent. % 140.49/19.59 | % 140.49/19.59 End of proof % 140.49/19.59 % 140.49/19.59 Sub-proof #22 shows that the following formulas are inconsistent: % 140.49/19.59 ---------------------------------------------------------------- % 140.49/19.59 (1) a_select3(q, pv10, n1) = all_71_0 & $i(all_71_0) % 140.49/19.59 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 140.49/19.59 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = % 140.49/19.59 v0)) % 140.49/19.59 (3) a_select3(q, pv10, n1) = all_71_10 % 140.49/19.59 (4) ~ (all_71_0 = all_71_10) % 140.49/19.59 % 140.49/19.59 Begin of proof % 140.49/19.59 | % 140.49/19.59 | ALPHA: (1) implies: % 140.49/19.59 | (5) a_select3(q, pv10, n1) = all_71_0 % 140.49/19.59 | % 140.49/19.59 | GROUND_INST: instantiating (2) with all_71_10, all_71_0, n1, pv10, q, % 140.49/19.59 | simplifying with (3), (5) gives: % 140.49/19.59 | (6) all_71_0 = all_71_10 % 140.49/19.59 | % 140.49/19.59 | REDUCE: (4), (6) imply: % 140.49/19.59 | (7) $false % 140.49/19.59 | % 140.49/19.59 | CLOSE: (7) is inconsistent. % 140.49/19.59 | % 140.49/19.59 End of proof % 140.49/19.59 % 140.49/19.59 Sub-proof #23 shows that the following formulas are inconsistent: % 140.49/19.59 ---------------------------------------------------------------- % 140.49/19.59 (1) succ(n2) = n3 % 140.49/19.59 (2) ! [v0: $i] : ( ~ $i(v0) | ~ gt(v0, v0)) % 140.49/19.59 (3) succ(n2) = pv12 % 140.49/19.59 (4) gt(n3, pv12) % 140.49/19.59 (5) $i(pv12) % 140.49/19.59 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (succ(v2) = v1) | % 140.49/19.59 ~ (succ(v2) = v0)) % 140.49/19.59 % 140.49/19.59 Begin of proof % 140.49/19.59 | % 140.49/19.59 | GROUND_INST: instantiating (6) with n3, pv12, n2, simplifying with (1), (3) % 140.49/19.59 | gives: % 140.49/19.59 | (7) pv12 = n3 % 140.49/19.59 | % 140.49/19.59 | REDUCE: (5), (7) imply: % 140.49/19.59 | (8) $i(n3) % 140.49/19.59 | % 140.49/19.59 | REDUCE: (4), (7) imply: % 140.49/19.59 | (9) gt(n3, n3) % 140.49/19.59 | % 140.49/19.59 | GROUND_INST: instantiating (2) with n3, simplifying with (8), (9) gives: % 140.49/19.59 | (10) $false % 140.49/19.59 | % 140.49/19.59 | CLOSE: (10) is inconsistent. % 140.49/19.59 | % 140.49/19.59 End of proof % 140.49/19.59 % 140.49/19.59 Sub-proof #24 shows that the following formulas are inconsistent: % 140.49/19.59 ---------------------------------------------------------------- % 140.49/19.59 (1) ~ (all_71_25 = n0) % 140.49/19.59 (2) $i(all_71_25) % 140.49/19.59 (3) gt(all_71_25, all_71_12) % 140.49/19.59 (4) all_71_25 = n1 | all_71_25 = n0 % 140.49/19.59 (5) ! [v0: $i] : ( ~ $i(v0) | ~ gt(v0, v0)) % 140.49/19.59 (6) ~ (all_71_12 = n0) % 140.49/19.59 (7) all_71_12 = n1 | all_71_12 = n0 % 140.49/19.59 % 140.49/19.59 Begin of proof % 140.49/19.59 | % 140.49/19.59 | BETA: splitting (7) gives: % 140.49/19.59 | % 140.49/19.59 | Case 1: % 140.49/19.59 | | % 140.49/19.59 | | (8) all_71_12 = n0 % 140.49/19.59 | | % 140.49/19.59 | | REDUCE: (6), (8) imply: % 140.49/19.59 | | (9) $false % 140.49/19.59 | | % 140.49/19.59 | | CLOSE: (9) is inconsistent. % 140.49/19.59 | | % 140.49/19.59 | Case 2: % 140.49/19.59 | | % 140.49/19.59 | | (10) all_71_12 = n1 % 140.49/19.59 | | % 140.49/19.59 | | REDUCE: (3), (10) imply: % 140.49/19.59 | | (11) gt(all_71_25, n1) % 140.49/19.59 | | % 140.49/19.59 | | BETA: splitting (4) gives: % 140.49/19.59 | | % 140.49/19.59 | | Case 1: % 140.49/19.59 | | | % 140.49/19.59 | | | (12) all_71_25 = n0 % 140.49/19.59 | | | % 140.49/19.59 | | | REDUCE: (1), (12) imply: % 140.49/19.59 | | | (13) $false % 140.49/19.59 | | | % 140.49/19.59 | | | CLOSE: (13) is inconsistent. % 140.49/19.59 | | | % 140.49/19.59 | | Case 2: % 140.49/19.59 | | | % 140.49/19.59 | | | (14) all_71_25 = n1 % 140.49/19.59 | | | % 140.49/19.59 | | | REDUCE: (2), (14) imply: % 140.49/19.59 | | | (15) $i(n1) % 140.49/19.59 | | | % 140.49/19.59 | | | REDUCE: (11), (14) imply: % 140.49/19.59 | | | (16) gt(n1, n1) % 140.49/19.59 | | | % 140.49/19.59 | | | GROUND_INST: instantiating (5) with n1, simplifying with (15), (16) gives: % 140.49/19.59 | | | (17) $false % 140.49/19.59 | | | % 140.49/19.59 | | | CLOSE: (17) is inconsistent. % 140.49/19.59 | | | % 140.49/19.59 | | End of split % 140.49/19.59 | | % 140.49/19.59 | End of split % 140.49/19.59 | % 140.49/19.59 End of proof % 140.49/19.59 % 140.49/19.59 Sub-proof #25 shows that the following formulas are inconsistent: % 140.49/19.59 ---------------------------------------------------------------- % 140.49/19.59 (1) $i(all_71_12) % 140.49/19.59 (2) all_71_12 = n0 % 140.49/19.59 (3) gt(all_71_12, n0) % 140.49/19.59 (4) ! [v0: $i] : ( ~ $i(v0) | ~ gt(v0, v0)) % 140.49/19.59 % 140.49/19.59 Begin of proof % 140.49/19.59 | % 140.49/19.59 | REDUCE: (1), (2) imply: % 140.49/19.59 | (5) $i(n0) % 140.49/19.59 | % 140.49/19.59 | REDUCE: (2), (3) imply: % 140.49/19.59 | (6) gt(n0, n0) % 140.49/19.59 | % 140.49/19.59 | GROUND_INST: instantiating (4) with n0, simplifying with (5), (6) gives: % 140.49/19.59 | (7) $false % 140.49/19.59 | % 140.49/19.59 | CLOSE: (7) is inconsistent. % 140.49/19.59 | % 140.49/19.59 End of proof % 140.49/19.59 % SZS output end Proof for theBenchmark % 140.49/19.59 % 140.49/19.59 19059ms %------------------------------------------------------------------------------