0.00/0.04 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.04 % Command : princess-casc +printProof -timeout=%d %s 0.03/0.26 % Computer : n014.star.cs.uiowa.edu 0.03/0.26 % Model : x86_64 x86_64 0.03/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz 0.03/0.26 % Memory : 32218.625MB 0.03/0.26 % OS : Linux 3.10.0-693.2.2.el7.x86_64 0.03/0.26 % CPULimit : 300 0.03/0.26 % DateTime : Sat Jul 14 04:52:09 CDT 2018 0.03/0.26 % CPUTime : 0.06/0.47 ________ _____ 0.06/0.47 ___ __ \_________(_)________________________________ 0.06/0.47 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ 0.06/0.47 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) 0.06/0.47 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ 0.06/0.47 0.06/0.47 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic 0.06/0.47 (CASC 2017-07-17) 0.06/0.47 0.06/0.47 (c) Philipp Rümmer, 2009-2017 0.06/0.47 (contributions by Peter Backeman, Peter Baumgartner, 0.06/0.47 Angelo Brillout, Aleksandar Zeljic) 0.06/0.47 Free software under GNU Lesser General Public License (LGPL). 0.06/0.47 Bug reports to ph_r@gmx.net 0.06/0.47 0.06/0.47 For more information, visit http://www.philipp.ruemmer.org/princess.shtml 0.06/0.47 0.06/0.47 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... 0.06/0.51 Prover 0: Options: +triggersInConjecture -genTotalityAxioms=ctors +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=off 2.43/1.27 Prover 0: Warning: using theory to encode multiplication: GroebnerMultiplication 2.43/1.27 Prover 0: Preprocessing ... 6.96/2.57 Prover 0: Proving ... 12.94/4.35 Prover 1: Options: +triggersInConjecture -genTotalityAxioms=none -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=off 13.94/4.60 Prover 1: Warning: using theory to encode multiplication: GroebnerMultiplication 13.94/4.60 Prover 1: Preprocessing ... 14.96/4.97 Prover 1: Warning: ignoring some quantifiers 15.28/5.03 Prover 1: Constructing countermodel ... 17.02/5.54 Prover 1: gave up 17.02/5.54 Prover 2: Options: +triggersInConjecture -genTotalityAxioms=all -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=off 17.65/5.75 Prover 2: Warning: using theory to encode multiplication: GroebnerMultiplication 17.65/5.75 Prover 2: Preprocessing ... 19.22/6.25 Prover 2: Proving ... 24.18/7.83 Prover 3: Options: +triggersInConjecture -genTotalityAxioms=none -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=off 24.85/8.04 Prover 3: Warning: using theory to encode multiplication: GroebnerMultiplication 24.85/8.04 Prover 3: Preprocessing ... 25.38/8.22 Prover 3: Warning: ignoring some quantifiers 25.38/8.24 Prover 3: Constructing countermodel ... 25.81/8.38 Prover 3: gave up 25.81/8.38 Prover 4: Options: +triggersInConjecture -genTotalityAxioms=none -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=off 26.29/8.55 Prover 4: Warning: using theory to encode multiplication: GroebnerMultiplication 26.29/8.55 Prover 4: Preprocessing ... 27.01/8.77 Prover 4: Warning: ignoring some quantifiers 27.25/8.81 Prover 4: Constructing countermodel ... 78.01/38.63 Prover 4: stopped 78.40/38.83 Prover 5: Options: +triggersInConjecture -genTotalityAxioms=none +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=off 78.69/38.95 Prover 5: Warning: using theory to encode multiplication: GroebnerMultiplication 78.69/38.96 Prover 5: Preprocessing ... 79.45/39.21 Prover 5: Proving ... 93.34/45.01 Prover 5: stopped 93.67/45.20 Prover 6: Options: -triggersInConjecture -genTotalityAxioms=none +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=off 94.07/45.34 Prover 6: Warning: using theory to encode multiplication: GroebnerMultiplication 94.07/45.34 Prover 6: Preprocessing ... 94.53/45.48 Prover 6: Proving ... 115.06/53.73 Prover 6: stopped 115.28/53.94 Prover 7: Options: +triggersInConjecture -genTotalityAxioms=none +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=off 115.52/54.05 Prover 7: Warning: using theory to encode multiplication: GroebnerMultiplication 115.52/54.05 Prover 7: Preprocessing ... 115.96/54.19 Prover 7: Warning: ignoring some quantifiers 116.11/54.26 Prover 7: Constructing countermodel ... 124.03/60.13 Prover 2: stopped 124.27/60.33 Prover 8: Options: +triggersInConjecture -genTotalityAxioms=ctors -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=off 124.37/60.45 Prover 8: Warning: using theory to encode multiplication: GroebnerMultiplication 124.37/60.45 Prover 8: Preprocessing ... 124.80/60.57 Prover 8: Warning: ignoring some quantifiers 124.80/60.61 Prover 8: Constructing countermodel ... 126.59/61.24 Prover 8: gave up 126.59/61.24 Prover 9: Options: +triggersInConjecture -genTotalityAxioms=none -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=off 126.70/61.34 Prover 9: Warning: using theory to encode multiplication: GroebnerMultiplication 126.70/61.34 Prover 9: Preprocessing ... 126.99/61.49 Prover 9: Warning: ignoring some quantifiers 126.99/61.50 Prover 9: Constructing countermodel ... 173.61/103.15 Prover 9: stopped 173.81/103.35 Prover 10: Options: +triggersInConjecture -genTotalityAxioms=none +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=off 173.99/103.46 Prover 10: Warning: using theory to encode multiplication: GroebnerMultiplication 173.99/103.46 Prover 10: Preprocessing ... 174.18/103.55 Prover 10: Warning: ignoring some quantifiers 174.31/103.58 Prover 10: Constructing countermodel ... 185.32/112.92 Prover 10: gave up 185.32/112.92 Prover 11: Options: +triggersInConjecture -genTotalityAxioms=none +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=off 185.58/113.05 Prover 11: Warning: using theory to encode multiplication: GroebnerMultiplication 185.58/113.05 Prover 11: Preprocessing ... 185.90/113.17 Prover 11: Warning: ignoring some quantifiers 185.90/113.22 Prover 11: Constructing countermodel ... 202.28/126.25 Prover 11: Found proof (size 58262) 202.28/126.25 Prover 11: proved (13332ms) 202.28/126.26 Prover 0: stopped 202.29/126.26 Prover 7: stopped 202.29/126.26 202.29/126.26 VALID 202.29/126.26 % SZS status Theorem for theBenchmark 202.29/126.26 202.75/126.57 % SZS output start Proof for theBenchmark 202.75/126.60 Assumptions after simplification: 202.75/126.60 --------------------------------- 202.75/126.60 202.75/126.60 (array_eq_def) 202.86/126.62 ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: $int] 202.86/126.62 : ! [v5: $int] : ! [v6: $int] : ( ~ (map_eq_sub1(v0, v4, v5, 0, v3) = v6) | 202.86/126.62 ~ (length1(v0, v1) = v3) | ~ (elts(v0, v2) = v5) | ~ (elts(v0, v1) = v4) | 202.86/126.62 ~ in_ty(v0) | ? [v7: $int] : ((v7 = v3 & v6 = 0 & length1(v0, v2) = v3) | 202.86/126.62 ( ~ (v7 = 0) & array_eq(v0, v1, v2) = v7))) & ! [v0: $int] : ! [v1: 202.86/126.62 $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: $int] : ! [v5: $int] : ( ~ 202.86/126.62 (map_eq_sub1(v0, v4, v5, 0, v3) = 0) | ~ (length1(v0, v1) = v3) | ~ 202.86/126.62 (elts(v0, v2) = v5) | ~ (elts(v0, v1) = v4) | ~ in_ty(v0) | ? [v6: $int] 202.86/126.62 : ((v6 = 0 & array_eq(v0, v1, v2) = 0) | ( ~ (v6 = v3) & length1(v0, v2) = 202.86/126.62 v6))) & ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : 202.86/126.62 (v3 = 0 | ~ (array_eq(v0, v1, v2) = v3) | ~ in_ty(v0) | ? [v4: $int] : ? 202.86/126.62 [v5: $int] : ? [v6: $int] : ? [v7: $int] : ? [v8: $int] : (length1(v0, 202.86/126.62 v1) = v5 & (( ~ (v8 = 0) & map_eq_sub1(v0, v6, v7, 0, v5) = v8 & 202.86/126.62 elts(v0, v2) = v7 & elts(v0, v1) = v6 & in_uni(v7) & in_uni(v6)) | ( ~ 202.86/126.62 (v5 = v4) & length1(v0, v2) = v4)))) & ! [v0: $int] : ! [v1: $int] : 202.86/126.62 ! [v2: $int] : ( ~ (array_eq(v0, v1, v2) = 0) | ~ in_ty(v0) | ? [v3: $int] 202.86/126.62 : ? [v4: $int] : ? [v5: $int] : (map_eq_sub1(v0, v4, v5, 0, v3) = 0 & 202.86/126.62 length1(v0, v2) = v3 & length1(v0, v1) = v3 & elts(v0, v2) = v5 & elts(v0, 202.86/126.62 v1) = v4 & in_uni(v5) & in_uni(v4))) 202.86/126.62 202.86/126.62 (array_eq_sub_def) 202.86/126.63 ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: $int] 202.86/126.63 : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ (map_eq_sub1(v0, v5, v6, 202.86/126.63 v3, v4) = v7) | ~ (elts(v0, v2) = v6) | ~ (elts(v0, v1) = v5) | ~ 202.86/126.63 in_ty(v0) | ? [v8: $int] : ? [v9: $int] : ((v9 = v8 & v7 = 0 & $lesseq(v4, 202.86/126.63 v8) & $lesseq(v3, v8) & $lesseq(0, v4) & $lesseq(0, v3) & length1(v0, 202.86/126.63 v2) = v8 & length1(v0, v1) = v8) | ( ~ (v8 = 0) & array_eq_sub1(v0, 202.86/126.63 v1, v2, v3, v4) = v8))) & ! [v0: $int] : ! [v1: $int] : ! [v2: 202.86/126.63 $int] : ! [v3: $int] : ! [v4: $int] : ! [v5: $int] : ! [v6: $int] : ( ~ 202.86/126.63 ($lesseq(0, v4)) | ~ ($lesseq(0, v3)) | ~ (map_eq_sub1(v0, v5, v6, v3, v4) 202.86/126.63 = 0) | ~ (elts(v0, v2) = v6) | ~ (elts(v0, v1) = v5) | ~ in_ty(v0) | ? 202.86/126.63 [v7: $int] : ? [v8: $int] : ((v7 = 0 & array_eq_sub1(v0, v1, v2, v3, v4) = 202.86/126.63 0) | (length1(v0, v1) = v7 & ( ~ ($lesseq(v4, v7)) | ~ ($lesseq(v3, 202.86/126.63 v7)) | ( ~ (v8 = v7) & length1(v0, v2) = v8))))) & ! [v0: $int] : 202.86/126.63 ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: $int] : ! [v5: $int] 202.86/126.64 : (v5 = 0 | ~ ($lesseq(0, v4)) | ~ ($lesseq(0, v3)) | ~ (array_eq_sub1(v0, 202.86/126.64 v1, v2, v3, v4) = v5) | ~ in_ty(v0) | ? [v6: $int] : ? [v7: $int] : 202.86/126.64 ? [v8: $int] : (( ~ (v8 = 0) & map_eq_sub1(v0, v6, v7, v3, v4) = v8 & 202.86/126.64 elts(v0, v2) = v7 & elts(v0, v1) = v6 & in_uni(v7) & in_uni(v6)) | ( ~ 202.86/126.64 (v7 = v6) & length1(v0, v2) = v7 & length1(v0, v1) = v6) | ($lesseq(1, 202.86/126.64 $difference(v4, v6)) & length1(v0, v1) = v6) | ($lesseq(1, 202.86/126.64 $difference(v3, v6)) & length1(v0, v1) = v6))) & ! [v0: $int] : ! 202.86/126.64 [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: $int] : ( ~ ($lesseq(v4, 202.86/126.64 -1)) | ~ (array_eq_sub1(v0, v1, v2, v3, v4) = 0) | ~ in_ty(v0)) & ! 202.86/126.64 [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: $int] : ( 202.86/126.64 ~ ($lesseq(v3, -1)) | ~ (array_eq_sub1(v0, v1, v2, v3, v4) = 0) | ~ 202.86/126.64 in_ty(v0)) & ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : 202.86/126.64 ! [v4: $int] : ( ~ (array_eq_sub1(v0, v1, v2, v3, v4) = 0) | ~ in_ty(v0) | 202.86/126.64 ? [v5: $int] : ? [v6: $int] : ? [v7: $int] : ($lesseq(v4, v5) & 202.86/126.64 $lesseq(v3, v5) & map_eq_sub1(v0, v6, v7, v3, v4) = 0 & length1(v0, v2) = 202.86/126.64 v5 & length1(v0, v1) = v5 & elts(v0, v2) = v7 & elts(v0, v1) = v6 & 202.86/126.64 in_uni(v7) & in_uni(v6))) 202.86/126.64 202.86/126.64 (array_inversion3) 202.86/126.64 ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ( ~ (length1(v0, v1) = v2) | 202.86/126.64 ~ in_ty(v0) | ? [v3: $int] : (mk_array2(v0, v2, v3) = v1 & elts(v0, v1) = 202.86/126.64 v3 & in_uni(v3) & in_uni(v1))) & ! [v0: $int] : ! [v1: $int] : ! [v2: 202.86/126.64 $int] : ( ~ (elts(v0, v1) = v2) | ~ in_ty(v0) | ? [v3: $int] : 202.86/126.64 (length1(v0, v1) = v3 & mk_array2(v0, v3, v2) = v1 & in_uni(v1))) 202.86/126.64 202.86/126.64 (bridgeR) 202.86/126.64 ! [v0: $int] : ! [v1: $int] : ( ~ (tb2t(v0) = v1) | ~ in_uni(v0) | t2tb(v1) 202.86/126.64 = v0) 202.86/126.64 202.86/126.64 (bridgeR1) 202.86/126.64 ! [v0: $int] : ! [v1: $int] : ( ~ (tb2t1(v0) = v1) | ~ in_uni(v0) | 202.86/126.64 t2tb1(v1) = v0) 202.86/126.64 202.86/126.64 (elts_def2) 202.86/126.64 in_ty(int) & ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ( ~ 202.86/126.64 (mk_array3(v0, v1) = v2) | ~ in_map_int_int(v1) | ? [v3: $int] : ? [v4: 202.86/126.64 $int] : (tb2t(v4) = v1 & t2tb2(v2) = v3 & elts(int, v3) = v4 & in_uni(v4) 202.86/126.64 & in_uni(v3))) 202.86/126.64 202.86/126.64 (get_def) 202.86/126.64 in_ty(int) & ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : 202.86/126.64 ! [v4: $int] : ! [v5: $int] : ( ~ (tb2t(v3) = v4) | ~ (get3(v4, v1) = v5) | 202.86/126.64 ~ (t2tb2(v0) = v2) | ~ (elts(int, v2) = v3) | ~ in_array_int(v0) | ? [v6: 202.86/126.64 $int] : (tb2t1(v6) = v5 & get4(int, v2, v1) = v6 & in_uni(v6))) & ! [v0: 202.86/126.64 $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ( ~ (t2tb2(v0) = v2) 202.86/126.64 | ~ (get4(int, v2, v1) = v3) | ~ in_array_int(v0) | ? [v4: $int] : ? 202.86/126.64 [v5: $int] : ? [v6: $int] : (tb2t(v4) = v5 & tb2t1(v3) = v6 & get3(v5, v1) 202.86/126.64 = v6 & elts(int, v2) = v4 & in_map_int_int(v5) & in_uni(v4))) 202.86/126.64 202.86/126.64 (get_def1) 202.86/126.64 in_ty(int) & ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : 202.86/126.64 ! [v4: $int] : ! [v5: $int] : ( ~ (elts(v0, v1) = v3) | ~ (t2tb1(v2) = v4) | 202.86/126.64 ~ (get(v0, int, v3, v4) = v5) | ~ in_ty(v0) | (get4(v0, v1, v2) = v5 & 202.86/126.64 in_uni(v5))) & ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: 202.86/126.64 $int] : ( ~ (get4(v0, v1, v2) = v3) | ~ in_ty(v0) | ? [v4: $int] : ? [v5: 202.86/126.64 $int] : (elts(v0, v1) = v4 & t2tb1(v2) = v5 & get(v0, int, v4, v5) = v3 & 202.86/126.64 in_uni(v5) & in_uni(v4) & in_uni(v3))) 202.86/126.64 202.86/126.64 (length_def2) 202.86/126.64 in_ty(int) & ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ( ~ 202.86/126.64 (mk_array3(v0, v1) = v2) | ~ in_map_int_int(v1) | ? [v3: $int] : 202.86/126.64 (t2tb2(v2) = v3 & length1(int, v3) = v0 & in_uni(v3))) 202.86/126.64 202.86/126.64 (map_eq_sub_def) 202.86/126.65 in_ty(int) & ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : 202.86/126.65 ! [v4: $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ ($lesseq(1, 202.86/126.65 $difference(v3, v6))) | ~ ($lesseq(v2, v6)) | ~ (map_eq_sub1(int, v4, 202.86/126.65 v5, v2, v3) = 0) | ~ (t2tb(v1) = v5) | ~ (t2tb(v0) = v4) | ~ 202.86/126.65 (get3(v1, v6) = v7) | ~ in_map_int_int(v0) | get3(v0, v6) = v7) & ! [v0: 202.86/126.65 $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: $int] : ! 202.86/126.65 [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ ($lesseq(1, $difference(v3, 202.86/126.65 v6))) | ~ ($lesseq(v2, v6)) | ~ (map_eq_sub1(int, v4, v5, v2, v3) = 202.86/126.65 0) | ~ (t2tb(v1) = v5) | ~ (t2tb(v0) = v4) | ~ (get3(v0, v6) = v7) | ~ 202.86/126.65 in_map_int_int(v0) | get3(v1, v6) = v7) & ! [v0: $int] : ! [v1: $int] : ! 202.86/126.65 [v2: $int] : ! [v3: $int] : ! [v4: $int] : ! [v5: $int] : ! [v6: $int] : 202.86/126.65 (v6 = 0 | ~ (map_eq_sub1(int, v4, v5, v2, v3) = v6) | ~ (t2tb(v1) = v5) | ~ 202.86/126.65 (t2tb(v0) = v4) | ~ in_map_int_int(v0) | ? [v7: $int] : ? [v8: $int] : ? 202.86/126.65 [v9: $int] : ( ~ (v9 = v8) & $lesseq(1, $difference(v3, v7)) & $lesseq(v2, 202.86/126.65 v7) & get3(v1, v7) = v9 & get3(v0, v7) = v8)) 202.86/126.65 202.86/126.65 (map_eq_sub_def1) 202.86/126.65 in_ty(int) & ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : 202.86/126.65 ! [v4: $int] : ! [v5: $int] : ! [v6: $int] : ( ~ ($lesseq(1, $difference(v4, 202.86/126.65 v5))) | ~ ($lesseq(v3, v5)) | ~ (map_eq_sub1(v0, v1, v2, v3, v4) = 202.86/126.65 0) | ~ (t2tb1(v5) = v6) | ~ in_ty(v0) | ? [v7: $int] : (get(v0, int, 202.86/126.65 v2, v6) = v7 & get(v0, int, v1, v6) = v7 & in_uni(v7))) & ! [v0: $int] 202.86/126.65 : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: $int] : ! [v5: 202.86/126.65 $int] : (v5 = 0 | ~ (map_eq_sub1(v0, v1, v2, v3, v4) = v5) | ~ in_ty(v0) | 202.86/126.65 ? [v6: $int] : ? [v7: $int] : ? [v8: $int] : ? [v9: $int] : ( ~ (v9 = 202.86/126.65 v8) & $lesseq(1, $difference(v4, v6)) & $lesseq(v3, v6) & t2tb1(v6) = v7 202.86/126.65 & get(v0, int, v2, v7) = v8 & get(v0, int, v1, v7) = v9 & in_uni(v9) & 202.86/126.65 in_uni(v8) & in_uni(v7))) 202.86/126.65 202.86/126.65 (permut_all_def) 203.01/126.67 ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: $int] 203.01/126.67 : ! [v5: $int] : ! [v6: $int] : ( ~ (permut2(v0, v3, v4, 0, v5) = v6) | ~ 203.01/126.67 (length1(v0, v1) = v5) | ~ (elts(v0, v2) = v4) | ~ (elts(v0, v1) = v3) | 203.01/126.67 ~ in_ty(v0) | ? [v7: $int] : ((v7 = v5 & v6 = 0 & length1(v0, v2) = v5) | ( 203.01/126.67 ~ (v7 = 0) & permut_all(v0, v1, v2) = v7))) & ! [v0: $int] : ! [v1: 203.01/126.67 $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: $int] : ! [v5: $int] : ( ~ 203.01/126.67 (permut2(v0, v3, v4, 0, v5) = 0) | ~ (length1(v0, v1) = v5) | ~ (elts(v0, 203.01/126.67 v2) = v4) | ~ (elts(v0, v1) = v3) | ~ in_ty(v0) | ? [v6: $int] : ((v6 203.01/126.67 = 0 & permut_all(v0, v1, v2) = 0) | ( ~ (v6 = v5) & length1(v0, v2) = 203.01/126.67 v6))) & ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : 203.01/126.67 (v3 = 0 | ~ (permut_all(v0, v1, v2) = v3) | ~ in_ty(v0) | ? [v4: $int] : ? 203.01/126.67 [v5: $int] : ? [v6: $int] : ? [v7: $int] : (length1(v0, v1) = v6 & (( ~ 203.01/126.67 (v7 = v6) & length1(v0, v2) = v7) | ( ~ (v7 = 0) & permut2(v0, v4, v5, 203.01/126.67 0, v6) = v7 & elts(v0, v2) = v5 & elts(v0, v1) = v4 & in_uni(v5) & 203.01/126.67 in_uni(v4))))) & ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ( ~ 203.01/126.67 (permut_all(v0, v1, v2) = 0) | ~ in_ty(v0) | ? [v3: $int] : ? [v4: $int] 203.01/126.67 : ? [v5: $int] : (permut2(v0, v3, v4, 0, v5) = 0 & length1(v0, v2) = v5 & 203.01/126.67 length1(v0, v1) = v5 & elts(v0, v2) = v4 & elts(v0, v1) = v3 & in_uni(v4) 203.01/126.67 & in_uni(v3))) 203.01/126.67 203.01/126.67 (permut_def1) 203.01/126.67 ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: $int] 203.01/126.67 : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ (permut2(v0, v5, v6, v3, 203.01/126.67 v4) = v7) | ~ (elts(v0, v2) = v6) | ~ (elts(v0, v1) = v5) | ~ 203.01/126.67 in_ty(v0) | ? [v8: $int] : ? [v9: $int] : ((v9 = v8 & v7 = 0 & $lesseq(v4, 203.01/126.67 v8) & $lesseq(v3, v8) & $lesseq(0, v4) & $lesseq(0, v3) & length1(v0, 203.01/126.67 v2) = v8 & length1(v0, v1) = v8) | ( ~ (v8 = 0) & permut3(v0, v1, v2, 203.01/126.67 v3, v4) = v8))) & ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! 203.01/126.67 [v3: $int] : ! [v4: $int] : ! [v5: $int] : ! [v6: $int] : ( ~ ($lesseq(0, 203.01/126.67 v4)) | ~ ($lesseq(0, v3)) | ~ (permut2(v0, v5, v6, v3, v4) = 0) | ~ 203.01/126.67 (elts(v0, v2) = v6) | ~ (elts(v0, v1) = v5) | ~ in_ty(v0) | ? [v7: $int] 203.01/126.67 : ? [v8: $int] : ((v7 = 0 & permut3(v0, v1, v2, v3, v4) = 0) | (length1(v0, 203.01/126.67 v1) = v7 & ( ~ ($lesseq(v4, v7)) | ~ ($lesseq(v3, v7)) | ( ~ (v8 = 203.01/126.67 v7) & length1(v0, v2) = v8))))) & ! [v0: $int] : ! [v1: $int] : 203.01/126.67 ! [v2: $int] : ! [v3: $int] : ! [v4: $int] : ! [v5: $int] : (v5 = 0 | ~ 203.01/126.67 ($lesseq(0, v4)) | ~ ($lesseq(0, v3)) | ~ (permut3(v0, v1, v2, v3, v4) = 203.01/126.67 v5) | ~ in_ty(v0) | ? [v6: $int] : ? [v7: $int] : ? [v8: $int] : (( ~ 203.01/126.67 (v8 = 0) & permut2(v0, v6, v7, v3, v4) = v8 & elts(v0, v2) = v7 & 203.01/126.67 elts(v0, v1) = v6 & in_uni(v7) & in_uni(v6)) | ( ~ (v7 = v6) & 203.01/126.67 length1(v0, v2) = v7 & length1(v0, v1) = v6) | (length1(v0, v1) = v6 & ( 203.01/126.67 ~ ($lesseq(v4, v6)) | ~ ($lesseq(v3, v6)))))) & ! [v0: $int] : ! 203.01/126.67 [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: $int] : ( ~ ($lesseq(v4, 203.01/126.67 -1)) | ~ (permut3(v0, v1, v2, v3, v4) = 0) | ~ in_ty(v0)) & ! [v0: 203.01/126.67 $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: $int] : ( ~ 203.01/126.67 ($lesseq(v3, -1)) | ~ (permut3(v0, v1, v2, v3, v4) = 0) | ~ in_ty(v0)) & 203.01/126.67 ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: $int] : 203.01/126.67 ( ~ (permut3(v0, v1, v2, v3, v4) = 0) | ~ in_ty(v0) | ? [v5: $int] : ? [v6: 203.01/126.67 $int] : ? [v7: $int] : ($lesseq(v4, v5) & $lesseq(v3, v5) & permut2(v0, 203.01/126.67 v6, v7, v3, v4) = 0 & length1(v0, v2) = v5 & length1(v0, v1) = v5 & 203.01/126.67 elts(v0, v2) = v7 & elts(v0, v1) = v6 & in_uni(v7) & in_uni(v6))) 203.01/126.67 203.01/126.67 (permut_exists) 203.01/126.68 in_ty(int) & ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : 203.01/126.68 ! [v4: $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ ($lesseq(1, 203.01/126.68 $difference(v3, v4))) | ~ ($lesseq(v2, v4)) | ~ (permut2(int, v5, v6, 203.01/126.68 v2, v3) = 0) | ~ (t2tb(v1) = v6) | ~ (t2tb(v0) = v5) | ~ (get3(v1, 203.01/126.68 v4) = v7) | ~ in_map_int_int(v0) | ? [v8: $int] : ($lesseq(1, 203.01/126.68 $difference(v3, v8)) & $lesseq(v2, v8) & get3(v0, v8) = v7)) 203.01/126.68 203.01/126.68 (permut_exists1) 203.01/126.68 in_ty(int) & ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : 203.01/126.68 ! [v4: $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ ($lesseq(1, 203.01/126.68 $difference(v4, v5))) | ~ ($lesseq(v3, v5)) | ~ (permut2(v0, v1, v2, 203.01/126.68 v3, v4) = 0) | ~ (t2tb1(v5) = v6) | ~ (get(v0, int, v2, v6) = v7) | ~ 203.01/126.68 in_ty(v0) | ? [v8: $int] : ? [v9: $int] : ($lesseq(1, $difference(v4, v8)) 203.01/126.68 & $lesseq(v3, v8) & t2tb1(v8) = v9 & get(v0, int, v1, v9) = v7 & 203.01/126.68 in_uni(v9) & in_uni(v7))) 203.01/126.68 203.01/126.68 (permut_sub_def) 203.01/126.68 in_ty(int) & ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : 203.01/126.68 ! [v4: $int] : ! [v5: $int] : ! [v6: $int] : ( ~ (permut3(int, v4, v5, v2, 203.01/126.68 v3) = v6) | ~ (t2tb2(v1) = v5) | ~ (t2tb2(v0) = v4) | ~ 203.01/126.68 in_array_int(v0) | ? [v7: $int] : ? [v8: $int] : ? [v9: $int] : ? [v10: 203.01/126.68 $int] : ? [v11: $int] : ((v11 = 0 & v9 = 0 & v6 = 0 & map_eq_sub1(int, 203.01/126.68 v7, v8, v3, v10) = 0 & map_eq_sub1(int, v7, v8, 0, v2) = 0 & 203.01/126.68 length1(int, v4) = v10 & elts(int, v5) = v8 & elts(int, v4) = v7 & 203.01/126.68 in_uni(v8) & in_uni(v7)) | ( ~ (v7 = 0) & permut_sub3(v0, v1, v2, v3) = 203.01/126.68 v7))) & ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : 203.01/126.68 ! [v4: $int] : ! [v5: $int] : ( ~ (permut3(int, v4, v5, v2, v3) = 0) | ~ 203.01/126.68 (t2tb2(v1) = v5) | ~ (t2tb2(v0) = v4) | ~ in_array_int(v0) | ? [v6: $int] 203.01/126.68 : ? [v7: $int] : ? [v8: $int] : ? [v9: $int] : ((v6 = 0 & permut_sub3(v0, 203.01/126.68 v1, v2, v3) = 0) | (elts(int, v5) = v7 & elts(int, v4) = v6 & 203.01/126.68 in_uni(v7) & in_uni(v6) & (( ~ (v9 = 0) & map_eq_sub1(int, v6, v7, v3, 203.01/126.68 v8) = v9 & length1(int, v4) = v8) | ( ~ (v8 = 0) & 203.01/126.68 map_eq_sub1(int, v6, v7, 0, v2) = v8))))) & ! [v0: $int] : ! [v1: 203.01/126.68 $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: $int] : (v4 = 0 | ~ 203.01/126.68 (permut_sub3(v0, v1, v2, v3) = v4) | ~ in_array_int(v0) | ? [v5: $int] : 203.01/126.68 ? [v6: $int] : ? [v7: $int] : ? [v8: $int] : ? [v9: $int] : ? [v10: 203.01/126.68 $int] : (t2tb2(v1) = v7 & t2tb2(v0) = v5 & in_uni(v7) & in_uni(v5) & (( ~ 203.01/126.68 (v8 = 0) & permut3(int, v5, v7, v2, v3) = v8) | (elts(int, v7) = v8 & 203.01/126.68 elts(int, v5) = v6 & in_uni(v8) & in_uni(v6) & (( ~ (v10 = 0) & 203.01/126.68 map_eq_sub1(int, v6, v8, v3, v9) = v10 & length1(int, v5) = v9) | 203.01/126.68 ( ~ (v9 = 0) & map_eq_sub1(int, v6, v8, 0, v2) = v9)))))) & ! [v0: 203.01/126.68 $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ( ~ (permut_sub3(v0, 203.01/126.68 v1, v2, v3) = 0) | ~ in_array_int(v0) | ? [v4: $int] : ? [v5: $int] : 203.01/126.68 ? [v6: $int] : ? [v7: $int] : ? [v8: $int] : (map_eq_sub1(int, v5, v7, 203.01/126.68 v3, v8) = 0 & map_eq_sub1(int, v5, v7, 0, v2) = 0 & permut3(int, v4, v6, 203.01/126.68 v2, v3) = 0 & t2tb2(v1) = v6 & t2tb2(v0) = v4 & length1(int, v4) = v8 & 203.01/126.68 elts(int, v6) = v7 & elts(int, v4) = v5 & in_uni(v7) & in_uni(v6) & 203.01/126.68 in_uni(v5) & in_uni(v4))) 203.01/126.68 203.01/126.68 (permut_sub_def1) 203.01/126.68 ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: $int] 203.01/126.68 : ! [v5: $int] : (v5 = 0 | ~ (permut_sub2(v0, v1, v2, v3, v4) = v5) | ~ 203.01/126.68 in_ty(v0) | ? [v6: $int] : ? [v7: $int] : ? [v8: $int] : ? [v9: $int] : 203.01/126.68 (( ~ (v9 = 0) & map_eq_sub1(v0, v6, v7, v4, v8) = v9 & length1(v0, v1) = v8 203.01/126.68 & elts(v0, v2) = v7 & elts(v0, v1) = v6 & in_uni(v7) & in_uni(v6)) | ( ~ 203.01/126.68 (v8 = 0) & map_eq_sub1(v0, v6, v7, 0, v3) = v8 & elts(v0, v2) = v7 & 203.01/126.68 elts(v0, v1) = v6 & in_uni(v7) & in_uni(v6)) | ( ~ (v6 = 0) & 203.01/126.68 permut3(v0, v1, v2, v3, v4) = v6))) & ! [v0: $int] : ! [v1: $int] : ! 203.01/126.68 [v2: $int] : ! [v3: $int] : ! [v4: $int] : ! [v5: $int] : ( ~ (permut3(v0, 203.01/126.68 v1, v2, v3, v4) = v5) | ~ in_ty(v0) | ? [v6: $int] : ? [v7: $int] : 203.01/126.68 ? [v8: $int] : ? [v9: $int] : ? [v10: $int] : ((v10 = 0 & v9 = 0 & v5 = 0 203.01/126.68 & map_eq_sub1(v0, v6, v7, v4, v8) = 0 & map_eq_sub1(v0, v6, v7, 0, v3) = 203.01/126.68 0 & length1(v0, v1) = v8 & elts(v0, v2) = v7 & elts(v0, v1) = v6 & 203.01/126.68 in_uni(v7) & in_uni(v6)) | ( ~ (v6 = 0) & permut_sub2(v0, v1, v2, v3, 203.01/126.68 v4) = v6))) & ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: 203.01/126.68 $int] : ! [v4: $int] : ( ~ (permut_sub2(v0, v1, v2, v3, v4) = 0) | ~ 203.01/126.68 in_ty(v0) | ? [v5: $int] : ? [v6: $int] : ? [v7: $int] : (map_eq_sub1(v0, 203.01/126.68 v5, v6, v4, v7) = 0 & map_eq_sub1(v0, v5, v6, 0, v3) = 0 & permut3(v0, 203.01/126.68 v1, v2, v3, v4) = 0 & length1(v0, v1) = v7 & elts(v0, v2) = v6 & 203.01/126.68 elts(v0, v1) = v5 & in_uni(v6) & in_uni(v5))) & ! [v0: $int] : ! [v1: 203.01/126.69 $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: $int] : ( ~ (permut3(v0, v1, 203.01/126.69 v2, v3, v4) = 0) | ~ in_ty(v0) | ? [v5: $int] : ? [v6: $int] : ? 203.01/126.69 [v7: $int] : ? [v8: $int] : ((v5 = 0 & permut_sub2(v0, v1, v2, v3, v4) = 0) 203.01/126.69 | (elts(v0, v2) = v6 & elts(v0, v1) = v5 & in_uni(v6) & in_uni(v5) & (( ~ 203.01/126.69 (v8 = 0) & map_eq_sub1(v0, v5, v6, v4, v7) = v8 & length1(v0, v1) = 203.01/126.69 v7) | ( ~ (v7 = 0) & map_eq_sub1(v0, v5, v6, 0, v3) = v7))))) 203.01/126.69 203.01/126.69 (permut_sub_weakening) 203.01/126.69 in_ty(int) & ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : 203.01/126.69 ! [v4: $int] : ! [v5: $int] : ! [v6: $int] : (v6 = 0 | ~ ($lesseq(v3, v5)) 203.01/126.69 | ~ ($lesseq(v4, v2)) | ~ ($lesseq(0, v4)) | ~ (permut_sub3(v0, v1, v4, 203.01/126.69 v5) = v6) | ~ (permut_sub3(v0, v1, v2, v3) = 0) | ~ in_array_int(v0) | 203.01/126.69 ? [v7: $int] : ? [v8: $int] : ($lesseq(1, $difference(v5, v8)) & t2tb2(v0) 203.01/126.69 = v7 & length1(int, v7) = v8 & in_uni(v7))) 203.01/126.69 203.01/126.69 (permut_trans) 203.01/126.69 ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: $int] 203.01/126.69 : ! [v5: $int] : ! [v6: $int] : (v6 = 0 | ~ (permut2(v0, v2, v3, v4, v5) = 203.01/126.69 0) | ~ (permut2(v0, v1, v3, v4, v5) = v6) | ~ in_ty(v0) | ? [v7: $int] 203.01/126.69 : ( ~ (v7 = 0) & permut2(v0, v1, v2, v4, v5) = v7)) & ! [v0: $int] : ! 203.01/126.69 [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: $int] : ! [v5: $int] : 203.01/126.69 ! [v6: $int] : (v6 = 0 | ~ (permut2(v0, v1, v3, v4, v5) = v6) | ~ 203.01/126.69 (permut2(v0, v1, v2, v4, v5) = 0) | ~ in_ty(v0) | ? [v7: $int] : ( ~ (v7 = 203.01/126.69 0) & permut2(v0, v2, v3, v4, v5) = v7)) & ! [v0: $int] : ! [v1: $int] 203.01/126.69 : ! [v2: $int] : ! [v3: $int] : ! [v4: $int] : ! [v5: $int] : ( ~ 203.01/126.69 (permut2(v0, v2, v3, v4, v5) = 0) | ~ (permut2(v0, v1, v2, v4, v5) = 0) | 203.01/126.69 ~ in_ty(v0) | permut2(v0, v1, v3, v4, v5) = 0) 203.01/126.69 203.01/126.69 (qs_partition_def) 203.01/126.70 in_ty(int) & ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : 203.01/126.70 ! [v4: $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : (v7 = 0 | ~ 203.01/126.70 (qs_partition1(v0, v1, v2, v3, v4, v5, v6) = v7) | ~ in_array_int(v0) | ? 203.01/126.70 [v8: $int] : ? [v9: $int] : ? [v10: $int] : ? [v11: $int] : (( ~ (v8 = 0) 203.01/126.70 & permut_sub3(v0, v1, v2, $sum(v3, 1)) = v8) | (t2tb2(v1) = v8 & 203.01/126.70 in_uni(v8) & (( ~ (v11 = v6) & $lesseq(1, $difference(v4, v9)) & 203.01/126.70 $lesseq(1, $difference(v9, v5)) & tb2t1(v10) = v11 & get4(int, v8, 203.01/126.70 v9) = v10 & in_uni(v10)) | ($lesseq(1, $difference(v6, v11)) & 203.01/126.70 $lesseq(v9, v3) & $lesseq(v4, v9) & tb2t1(v10) = v11 & get4(int, v8, 203.01/126.70 v9) = v10 & in_uni(v10)) | ($lesseq(1, $difference(v11, v6)) & 203.01/126.70 $lesseq(v9, v5) & $lesseq(v2, v9) & tb2t1(v10) = v11 & get4(int, v8, 203.01/126.70 v9) = v10 & in_uni(v10)))))) & ! [v0: $int] : ! [v1: $int] : ! 203.01/126.70 [v2: $int] : ! [v3: $int] : ! [v4: $int] : ! [v5: $int] : ! [v6: $int] : ( 203.01/126.70 ~ (qs_partition1(v0, v1, v2, v3, v4, v5, v6) = 0) | ~ in_array_int(v0) | ? 203.01/126.70 [v7: $int] : (permut_sub3(v0, v1, v2, $sum(v3, 1)) = 0 & t2tb2(v1) = v7 & 203.01/126.70 in_uni(v7) & ! [v8: $int] : ! [v9: $int] : ( ~ ($lesseq(v8, v5)) | ~ 203.01/126.70 ($lesseq(v2, v8)) | ~ (get4(int, v7, v8) = v9) | ? [v10: $int] : 203.01/126.70 ($lesseq(v10, v6) & tb2t1(v9) = v10)) & ! [v8: $int] : ! [v9: $int] : 203.01/126.70 ( ~ ($lesseq(1, $difference(v4, v8))) | ~ ($lesseq(1, $difference(v8, 203.01/126.70 v5))) | ~ (get4(int, v7, v8) = v9) | tb2t1(v9) = v6) & ! [v8: 203.01/126.70 $int] : ! [v9: $int] : ( ~ ($lesseq(v8, v3)) | ~ ($lesseq(v4, v8)) | 203.01/126.70 ~ (get4(int, v7, v8) = v9) | ? [v10: $int] : ($lesseq(v6, v10) & 203.01/126.70 tb2t1(v9) = v10)))) 203.01/126.70 203.01/126.70 (sorted_def) 203.01/126.70 in_ty(int) & ! [v0: $int] : ! [v1: $int] : (v1 = 0 | ~ (sorted1(v0) = v1) | 203.01/126.70 ~ in_array_int(v0) | ? [v2: $int] : ? [v3: $int] : ? [v4: $int] : ? 203.01/126.70 [v5: $int] : ? [v6: $int] : ( ~ (v6 = 0) & sorted_sub2(v4, 0, v5) = v6 & 203.01/126.70 tb2t(v3) = v4 & t2tb2(v0) = v2 & length1(int, v2) = v5 & elts(int, v2) = 203.01/126.70 v3 & in_map_int_int(v4) & in_uni(v3) & in_uni(v2))) & ! [v0: $int] : ! 203.01/126.70 [v1: $int] : ( ~ (t2tb2(v0) = v1) | ~ in_array_int(v0) | ? [v2: $int] : ? 203.01/126.70 [v3: $int] : ? [v4: $int] : ? [v5: $int] : ((v5 = 0 & sorted_sub2(v3, 0, 203.01/126.70 v4) = 0 & tb2t(v2) = v3 & length1(int, v1) = v4 & elts(int, v1) = v2 & 203.01/126.70 in_map_int_int(v3) & in_uni(v2)) | ( ~ (v2 = 0) & sorted1(v0) = v2))) & 203.01/126.70 ! [v0: $int] : ! [v1: $int] : ( ~ (t2tb2(v0) = v1) | ~ in_array_int(v0) | ? 203.01/126.70 [v2: $int] : ? [v3: $int] : ? [v4: $int] : ? [v5: $int] : ((v2 = 0 & 203.01/126.70 sorted1(v0) = 0) | ( ~ (v5 = 0) & sorted_sub2(v3, 0, v4) = v5 & tb2t(v2) 203.01/126.70 = v3 & length1(int, v1) = v4 & elts(int, v1) = v2 & in_map_int_int(v3) & 203.01/126.70 in_uni(v2)))) & ! [v0: $int] : ( ~ (sorted1(v0) = 0) | ~ 203.01/126.70 in_array_int(v0) | ? [v1: $int] : ? [v2: $int] : ? [v3: $int] : ? [v4: 203.01/126.70 $int] : (sorted_sub2(v3, 0, v4) = 0 & tb2t(v2) = v3 & t2tb2(v0) = v1 & 203.01/126.70 length1(int, v1) = v4 & elts(int, v1) = v2 & in_map_int_int(v3) & 203.01/126.70 in_uni(v2) & in_uni(v1))) 203.01/126.70 203.01/126.70 (wP_parameter_quicksort) 203.01/126.70 ? [v0: $int] : ? [v1: $int] : ? [v2: $int] : ? [v3: $int] : ? [v4: $int] 203.01/126.70 : ? [v5: $int] : ? [v6: $int] : ? [v7: $int] : ? [v8: $int] : ? [v9: 203.01/126.70 $int] : ? [v10: $int] : ? [v11: $int] : ? [v12: $int] : ? [v13: $int] : 203.01/126.70 ( ~ (v13 = 0) & $lesseq(v6, v3) & $lesseq(1, $difference(v6, v5)) & $lesseq(0, 203.01/126.70 v6) & $lesseq(1, $difference(v0, v5)) & $lesseq(v2, v5) & $lesseq(1, 203.01/126.70 $difference(v0, v3)) & $lesseq(0, v2) & qs_partition1(v10, v12, v2, v3, 203.01/126.70 v6, v5, 42) = v13 & qs_partition1(v8, v10, v2, v3, v6, v5, 42) = 0 & 203.01/126.70 mk_array3(v0, v11) = v12 & mk_array3(v0, v9) = v10 & mk_array3(v0, v7) = v8 203.01/126.70 & mk_array3(v0, v1) = v4 & sorted_sub2(v11, v6, $sum(v3, 1)) = 0 & 203.01/126.70 sorted_sub2(v9, v2, $sum(v5, 1)) = 0 & permut_sub3(v10, v12, v6, $sum(v3, 203.01/126.70 1)) = 0 & permut_sub3(v8, v10, v2, $sum(v5, 1)) = 0 & permut_sub3(v4, 203.01/126.70 v8, v2, $sum(v3, 1)) = 0 & in_array_int(v12) & in_array_int(v10) & 203.01/126.70 in_array_int(v8) & in_array_int(v4) & in_map_int_int(v11) & 203.01/126.70 in_map_int_int(v9) & in_map_int_int(v7) & in_map_int_int(v1) & ! [v14: 203.01/126.70 $int] : ! [v15: $int] : (v15 = 42 | ~ ($lesseq(1, $difference(v6, v14))) 203.01/126.70 | ~ ($lesseq(1, $difference(v14, v5))) | ~ (get3(v7, v14) = v15)) & ! 203.01/126.70 [v14: $int] : ! [v15: $int] : ( ~ ($lesseq(v15, 41)) | ~ ($lesseq(v14, 203.01/126.70 v3)) | ~ ($lesseq(v6, v14)) | ~ (get3(v7, v14) = v15)) & ! [v14: 203.01/126.70 $int] : ! [v15: $int] : ( ~ ($lesseq(43, v15)) | ~ ($lesseq(v14, v5)) | 203.01/126.70 ~ ($lesseq(v2, v14)) | ~ (get3(v7, v14) = v15))) 203.01/126.70 203.01/126.71 (axioms) 203.01/126.72 in_array_int(constant_in_array_int) & in_map_int_int(constant_in_map_int_int) 203.01/126.72 & in_uni(constant_in_uni) & ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! 203.01/126.72 [v3: $int] : ! [v4: $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : 203.01/126.72 ! [v8: $int] : (v1 = v0 | ~ (qs_partition1(v8, v7, v6, v5, v4, v3, v2) = v1) 203.01/126.72 | ~ (qs_partition1(v8, v7, v6, v5, v4, v3, v2) = v0)) & ! [v0: $int] : ! 203.01/126.72 [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: $int] : ! [v5: $int] : 203.01/126.72 ! [v6: $int] : ! [v7: $int] : ! [v8: $int] : (v1 = v0 | ~ (exchange2(v8, 203.01/126.72 v7, v6, v5, v4, v3, v2) = v1) | ~ (exchange2(v8, v7, v6, v5, v4, v3, 203.01/126.72 v2) = v0)) & ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: 203.01/126.72 $int] : ! [v4: $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ 203.01/126.72 (array_eq_sub1(v6, v5, v4, v3, v2) = v1) | ~ (array_eq_sub1(v6, v5, v4, v3, 203.01/126.72 v2) = v0)) & ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: 203.01/126.72 $int] : ! [v4: $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ 203.01/126.72 (map_eq_sub1(v6, v5, v4, v3, v2) = v1) | ~ (map_eq_sub1(v6, v5, v4, v3, v2) 203.01/126.72 = v0)) & ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : 203.01/126.72 ! [v4: $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ (permut_sub2(v6, 203.01/126.72 v5, v4, v3, v2) = v1) | ~ (permut_sub2(v6, v5, v4, v3, v2) = v0)) & ! 203.01/126.72 [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: $int] : 203.01/126.72 ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ (permut3(v6, v5, v4, v3, v2) = 203.01/126.72 v1) | ~ (permut3(v6, v5, v4, v3, v2) = v0)) & ! [v0: $int] : ! [v1: 203.01/126.72 $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: $int] : ! [v5: $int] : ! 203.01/126.72 [v6: $int] : (v1 = v0 | ~ (set(v6, v5, v4, v3, v2) = v1) | ~ (set(v6, v5, 203.01/126.72 v4, v3, v2) = v0)) & ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! 203.01/126.72 [v3: $int] : ! [v4: $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ 203.01/126.72 (exchange3(v6, v5, v4, v3, v2) = v1) | ~ (exchange3(v6, v5, v4, v3, v2) = 203.01/126.72 v0)) & ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! 203.01/126.72 [v4: $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ (permut2(v6, v5, 203.01/126.72 v4, v3, v2) = v1) | ~ (permut2(v6, v5, v4, v3, v2) = v0)) & ! [v0: 203.01/126.72 $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: $int] : ! 203.01/126.72 [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ (occ1(v6, v5, v4, v3, v2) = v1) | 203.01/126.72 ~ (occ1(v6, v5, v4, v3, v2) = v0)) & ! [v0: $int] : ! [v1: $int] : ! [v2: 203.01/126.72 $int] : ! [v3: $int] : ! [v4: $int] : ! [v5: $int] : (v1 = v0 | ~ 203.01/126.72 (match_bool1(v5, v4, v3, v2) = v1) | ~ (match_bool1(v5, v4, v3, v2) = v0)) 203.01/126.72 & ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 203.01/126.72 $int] : ! [v5: $int] : (v1 = v0 | ~ (set2(v5, v4, v3, v2) = v1) | ~ 203.01/126.72 (set2(v5, v4, v3, v2) = v0)) & ! [v0: $int] : ! [v1: $int] : ! [v2: $int] 203.01/126.72 : ! [v3: $int] : ! [v4: $int] : ! [v5: $int] : (v1 = v0 | ~ 203.01/126.72 (permut_sub3(v5, v4, v3, v2) = v1) | ~ (permut_sub3(v5, v4, v3, v2) = v0)) 203.01/126.72 & ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 203.01/126.72 $int] : ! [v5: $int] : (v1 = v0 | ~ (get(v5, v4, v3, v2) = v1) | ~ 203.01/126.72 (get(v5, v4, v3, v2) = v0)) & ! [v0: $int] : ! [v1: $int] : ! [v2: $int] 203.01/126.72 : ! [v3: $int] : ! [v4: $int] : (v1 = v0 | ~ (array_eq(v4, v3, v2) = v1) | 203.01/126.72 ~ (array_eq(v4, v3, v2) = v0)) & ! [v0: $int] : ! [v1: $int] : ! [v2: 203.01/126.72 $int] : ! [v3: $int] : ! [v4: $int] : (v1 = v0 | ~ (sorted_sub3(v4, v3, 203.01/126.72 v2) = v1) | ~ (sorted_sub3(v4, v3, v2) = v0)) & ! [v0: $int] : ! [v1: 203.01/126.72 $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: $int] : (v1 = v0 | ~ 203.01/126.72 (sorted_sub2(v4, v3, v2) = v1) | ~ (sorted_sub2(v4, v3, v2) = v0)) & ! 203.01/126.72 [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: $int] : 203.01/126.72 (v1 = v0 | ~ (permut_all(v4, v3, v2) = v1) | ~ (permut_all(v4, v3, v2) = 203.01/126.72 v0)) & ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! 203.01/126.72 [v4: $int] : (v1 = v0 | ~ (make1(v4, v3, v2) = v1) | ~ (make1(v4, v3, v2) = 203.01/126.72 v0)) & ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! 203.01/126.72 [v4: $int] : (v1 = v0 | ~ (mk_array2(v4, v3, v2) = v1) | ~ (mk_array2(v4, 203.01/126.72 v3, v2) = v0)) & ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: 203.01/126.72 $int] : ! [v4: $int] : (v1 = v0 | ~ (const(v4, v3, v2) = v1) | ~ 203.01/126.72 (const(v4, v3, v2) = v0)) & ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : 203.01/126.72 ! [v3: $int] : ! [v4: $int] : (v1 = v0 | ~ (get4(v4, v3, v2) = v1) | ~ 203.01/126.72 (get4(v4, v3, v2) = v0)) & ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : 203.01/126.72 ! [v3: $int] : (v1 = v0 | ~ (contents(v3, v2) = v1) | ~ (contents(v3, v2) = 203.01/126.72 v0)) & ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 203.01/126.72 = v0 | ~ (mk_ref(v3, v2) = v1) | ~ (mk_ref(v3, v2) = v0)) & ! [v0: $int] 203.01/126.72 : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 | ~ (map(v3, v2) = 203.01/126.72 v1) | ~ (map(v3, v2) = v0)) & ! [v0: $int] : ! [v1: $int] : ! [v2: 203.01/126.72 $int] : ! [v3: $int] : (v1 = v0 | ~ (mk_array3(v3, v2) = v1) | ~ 203.01/126.72 (mk_array3(v3, v2) = v0)) & ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : 203.01/126.72 ! [v3: $int] : (v1 = v0 | ~ (get3(v3, v2) = v1) | ~ (get3(v3, v2) = v0)) & 203.01/126.72 ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 | ~ 203.01/126.72 (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) & ! [v0: $int] : ! 203.01/126.72 [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 | ~ (sort1(v3, v2) = 203.01/126.72 v1) | ~ (sort1(v3, v2) = v0)) & ! [v0: $int] : ! [v1: $int] : ! [v2: 203.01/126.72 $int] : ! [v3: $int] : (v1 = v0 | ~ (elts(v3, v2) = v1) | ~ (elts(v3, v2) 203.01/126.72 = v0)) & ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ 203.01/126.72 (sorted1(v2) = v1) | ~ (sorted1(v2) = v0)) & ! [v0: $int] : ! [v1: $int] 203.01/126.72 : ! [v2: $int] : (v1 = v0 | ~ (ref(v2) = v1) | ~ (ref(v2) = v0)) & ! [v0: 203.01/126.72 $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ (tb2t2(v2) = v1) | ~ 203.01/126.72 (tb2t2(v2) = v0)) & ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 203.01/126.72 | ~ (witness1(v2) = v1) | ~ (witness1(v2) = v0)) & ! [v0: $int] : ! [v1: 203.01/126.72 $int] : ! [v2: $int] : (v1 = v0 | ~ (tb2t(v2) = v1) | ~ (tb2t(v2) = v0)) 203.01/126.72 & ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ (tb2t1(v2) = 203.01/126.72 v1) | ~ (tb2t1(v2) = v0)) & ! [v0: $int] : ! [v1: $int] : ! [v2: $int] 203.01/126.72 : (v1 = v0 | ~ (t2tb(v2) = v1) | ~ (t2tb(v2) = v0)) & ! [v0: $int] : ! 203.01/126.72 [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ (array(v2) = v1) | ~ (array(v2) = 203.01/126.72 v0)) & ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ 203.01/126.72 (t2tb2(v2) = v1) | ~ (t2tb2(v2) = v0)) & ! [v0: $int] : ! [v1: $int] : ! 203.01/126.72 [v2: $int] : (v1 = v0 | ~ (t2tb1(v2) = v1) | ~ (t2tb1(v2) = v0)) 203.01/126.72 203.01/126.72 Further assumptions not needed in the proof: 203.01/126.72 -------------------------------------------- 203.01/126.72 array_inversion2, bool_inversion, bridgeL, bridgeL1, bridgeL2, bridgeR2, 203.01/126.72 compatOrderMult, const, const1, const_sort1, contents_def1, contents_sort1, 203.01/126.72 elts_def3, elts_sort1, exchange_def, exchange_def1, exchange_def2, 203.01/126.72 exchange_permut_all, exchange_permut_sub, exchange_permut_sub1, exchange_set, 203.01/126.72 exchange_set1, get_sort3, get_sort4, length_def3, make_def, make_def1, 203.01/126.72 make_sort1, match_bool_False, match_bool_True, match_bool_sort1, mk_array_sort2, 203.01/126.72 mk_ref_sort1, occ_append, occ_bounds, occ_empty, occ_eq, occ_eq1, occ_exists, 203.01/126.72 occ_exists1, occ_neq, occ_neq1, occ_pos, occ_pos1, occ_right_add, 203.01/126.72 occ_right_add1, occ_right_no_add, occ_right_no_add1, permut_def, 203.01/126.72 permut_sub_weakening1, ref_inversion1, select_eq, select_eq1, select_neq, 203.01/126.72 select_neq1, set_def, set_def1, set_sort2, set_sort3, sorted_sub_def, 203.01/126.72 sorted_sub_def1, t2tb_sort, t2tb_sort1, t2tb_sort2, true_False, 203.01/126.72 tuple0_inversion, witness_sort1 203.01/126.72 203.01/126.72 Those formulas are unsatisfiable: 203.01/126.72 --------------------------------- 203.01/126.72 203.01/126.72 Begin of proof 203.01/126.72 | 203.01/126.72 | ALPHA: (get_def1) implies: 203.01/126.73 | (1) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ( ~ 203.01/126.73 | (get4(v0, v1, v2) = v3) | ~ in_ty(v0) | ? [v4: $int] : ? [v5: 203.01/126.73 | $int] : (elts(v0, v1) = v4 & t2tb1(v2) = v5 & get(v0, int, v4, v5) 203.01/126.73 | = v3 & in_uni(v5) & in_uni(v4) & in_uni(v3))) 203.01/126.73 | (2) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 203.01/126.73 | $int] : ! [v5: $int] : ( ~ (elts(v0, v1) = v3) | ~ (t2tb1(v2) = v4) 203.01/126.73 | | ~ (get(v0, int, v3, v4) = v5) | ~ in_ty(v0) | (get4(v0, v1, v2) = 203.01/126.73 | v5 & in_uni(v5))) 203.01/126.73 | 203.01/126.73 | ALPHA: (permut_sub_weakening) implies: 203.01/126.73 | (3) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 203.01/126.73 | $int] : ! [v5: $int] : ! [v6: $int] : (v6 = 0 | ~ ($lesseq(v3, 203.01/126.73 | v5)) | ~ ($lesseq(v4, v2)) | ~ ($lesseq(0, v4)) | ~ 203.01/126.73 | (permut_sub3(v0, v1, v4, v5) = v6) | ~ (permut_sub3(v0, v1, v2, v3) 203.01/126.73 | = 0) | ~ in_array_int(v0) | ? [v7: $int] : ? [v8: $int] : 203.01/126.73 | ($lesseq(1, $difference(v5, v8)) & t2tb2(v0) = v7 & length1(int, v7) 203.01/126.73 | = v8 & in_uni(v7))) 203.01/126.73 | 203.01/126.73 | ALPHA: (get_def) implies: 203.01/126.73 | (4) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ( ~ 203.01/126.73 | (t2tb2(v0) = v2) | ~ (get4(int, v2, v1) = v3) | ~ in_array_int(v0) 203.01/126.73 | | ? [v4: $int] : ? [v5: $int] : ? [v6: $int] : (tb2t(v4) = v5 & 203.01/126.73 | tb2t1(v3) = v6 & get3(v5, v1) = v6 & elts(int, v2) = v4 & 203.01/126.73 | in_map_int_int(v5) & in_uni(v4))) 203.01/126.73 | 203.01/126.73 | ALPHA: (permut_all_def) implies: 203.01/126.73 | (5) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 203.01/126.73 | $int] : ! [v5: $int] : ( ~ (permut2(v0, v3, v4, 0, v5) = 0) | ~ 203.01/126.73 | (length1(v0, v1) = v5) | ~ (elts(v0, v2) = v4) | ~ (elts(v0, v1) = 203.01/126.73 | v3) | ~ in_ty(v0) | ? [v6: $int] : ((v6 = 0 & permut_all(v0, v1, 203.01/126.73 | v2) = 0) | ( ~ (v6 = v5) & length1(v0, v2) = v6))) 203.01/126.73 | (6) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 203.01/126.73 | $int] : ! [v5: $int] : ! [v6: $int] : ( ~ (permut2(v0, v3, v4, 0, 203.01/126.73 | v5) = v6) | ~ (length1(v0, v1) = v5) | ~ (elts(v0, v2) = v4) | 203.01/126.73 | ~ (elts(v0, v1) = v3) | ~ in_ty(v0) | ? [v7: $int] : ((v7 = v5 & v6 203.01/126.73 | = 0 & length1(v0, v2) = v5) | ( ~ (v7 = 0) & permut_all(v0, v1, 203.01/126.73 | v2) = v7))) 203.01/126.73 | 203.01/126.73 | ALPHA: (permut_exists1) implies: 203.01/126.73 | (7) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 203.01/126.73 | $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 203.01/126.73 | ($lesseq(1, $difference(v4, v5))) | ~ ($lesseq(v3, v5)) | ~ 203.01/126.73 | (permut2(v0, v1, v2, v3, v4) = 0) | ~ (t2tb1(v5) = v6) | ~ (get(v0, 203.01/126.73 | int, v2, v6) = v7) | ~ in_ty(v0) | ? [v8: $int] : ? [v9: $int] 203.01/126.73 | : ($lesseq(1, $difference(v4, v8)) & $lesseq(v3, v8) & t2tb1(v8) = v9 203.01/126.73 | & get(v0, int, v1, v9) = v7 & in_uni(v9) & in_uni(v7))) 203.01/126.73 | 203.01/126.73 | ALPHA: (elts_def2) implies: 203.01/126.74 | (8) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ( ~ (mk_array3(v0, v1) 203.01/126.74 | = v2) | ~ in_map_int_int(v1) | ? [v3: $int] : ? [v4: $int] : 203.01/126.74 | (tb2t(v4) = v1 & t2tb2(v2) = v3 & elts(int, v3) = v4 & in_uni(v4) & 203.01/126.74 | in_uni(v3))) 203.01/126.74 | 203.01/126.74 | ALPHA: (permut_exists) implies: 203.01/126.74 | (9) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 203.01/126.74 | $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 203.01/126.74 | ($lesseq(1, $difference(v3, v4))) | ~ ($lesseq(v2, v4)) | ~ 203.01/126.74 | (permut2(int, v5, v6, v2, v3) = 0) | ~ (t2tb(v1) = v6) | ~ 203.01/126.74 | (t2tb(v0) = v5) | ~ (get3(v1, v4) = v7) | ~ in_map_int_int(v0) | ? 203.01/126.74 | [v8: $int] : ($lesseq(1, $difference(v3, v8)) & $lesseq(v2, v8) & 203.01/126.74 | get3(v0, v8) = v7)) 203.01/126.74 | 203.01/126.74 | ALPHA: (permut_def1) implies: 203.34/126.75 | (10) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! 203.34/126.75 | [v4: $int] : ( ~ (permut3(v0, v1, v2, v3, v4) = 0) | ~ in_ty(v0) | ? 203.34/126.75 | [v5: $int] : ? [v6: $int] : ? [v7: $int] : ($lesseq(v4, v5) & 203.34/126.75 | $lesseq(v3, v5) & permut2(v0, v6, v7, v3, v4) = 0 & length1(v0, 203.34/126.75 | v2) = v5 & length1(v0, v1) = v5 & elts(v0, v2) = v7 & elts(v0, 203.34/126.75 | v1) = v6 & in_uni(v7) & in_uni(v6))) 203.34/126.75 | (11) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! 203.34/126.75 | [v4: $int] : ( ~ ($lesseq(v4, -1)) | ~ (permut3(v0, v1, v2, v3, v4) = 203.34/126.75 | 0) | ~ in_ty(v0)) 203.34/126.75 | (12) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! 203.34/126.75 | [v4: $int] : ! [v5: $int] : ! [v6: $int] : ( ~ ($lesseq(0, v4)) | ~ 203.34/126.75 | ($lesseq(0, v3)) | ~ (permut2(v0, v5, v6, v3, v4) = 0) | ~ 203.34/126.75 | (elts(v0, v2) = v6) | ~ (elts(v0, v1) = v5) | ~ in_ty(v0) | ? 203.34/126.75 | [v7: $int] : ? [v8: $int] : ((v7 = 0 & permut3(v0, v1, v2, v3, v4) 203.34/126.75 | = 0) | (length1(v0, v1) = v7 & ( ~ ($lesseq(v4, v7)) | ~ 203.34/126.75 | ($lesseq(v3, v7)) | ( ~ (v8 = v7) & length1(v0, v2) = v8))))) 203.34/126.75 | (13) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! 203.34/126.75 | [v4: $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 203.34/126.75 | (permut2(v0, v5, v6, v3, v4) = v7) | ~ (elts(v0, v2) = v6) | ~ 203.34/126.75 | (elts(v0, v1) = v5) | ~ in_ty(v0) | ? [v8: $int] : ? [v9: $int] : 203.34/126.75 | ((v9 = v8 & v7 = 0 & $lesseq(v4, v8) & $lesseq(v3, v8) & $lesseq(0, 203.34/126.75 | v4) & $lesseq(0, v3) & length1(v0, v2) = v8 & length1(v0, v1) 203.34/126.75 | = v8) | ( ~ (v8 = 0) & permut3(v0, v1, v2, v3, v4) = v8))) 203.34/126.75 | 203.34/126.75 | ALPHA: (map_eq_sub_def1) implies: 203.34/126.75 | (14) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! 203.34/126.75 | [v4: $int] : ! [v5: $int] : ! [v6: $int] : ( ~ ($lesseq(1, 203.34/126.75 | $difference(v4, v5))) | ~ ($lesseq(v3, v5)) | ~ 203.34/126.75 | (map_eq_sub1(v0, v1, v2, v3, v4) = 0) | ~ (t2tb1(v5) = v6) | ~ 203.34/126.75 | in_ty(v0) | ? [v7: $int] : (get(v0, int, v2, v6) = v7 & get(v0, 203.34/126.75 | int, v1, v6) = v7 & in_uni(v7))) 203.34/126.75 | 203.34/126.75 | ALPHA: (array_eq_def) implies: 203.34/126.75 | (15) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! 203.34/126.75 | [v4: $int] : ! [v5: $int] : ( ~ (map_eq_sub1(v0, v4, v5, 0, v3) = 0) 203.34/126.75 | | ~ (length1(v0, v1) = v3) | ~ (elts(v0, v2) = v5) | ~ (elts(v0, 203.34/126.75 | v1) = v4) | ~ in_ty(v0) | ? [v6: $int] : ((v6 = 0 & 203.34/126.75 | array_eq(v0, v1, v2) = 0) | ( ~ (v6 = v3) & length1(v0, v2) = 203.34/126.75 | v6))) 203.34/126.75 | 203.34/126.75 | ALPHA: (length_def2) implies: 203.34/126.75 | (16) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ( ~ (mk_array3(v0, v1) 203.34/126.75 | = v2) | ~ in_map_int_int(v1) | ? [v3: $int] : (t2tb2(v2) = v3 & 203.34/126.75 | length1(int, v3) = v0 & in_uni(v3))) 203.34/126.75 | 203.34/126.75 | ALPHA: (sorted_def) implies: 203.34/126.75 | (17) ! [v0: $int] : ! [v1: $int] : ( ~ (t2tb2(v0) = v1) | ~ 203.34/126.75 | in_array_int(v0) | ? [v2: $int] : ? [v3: $int] : ? [v4: $int] : 203.34/126.75 | ? [v5: $int] : ((v2 = 0 & sorted1(v0) = 0) | ( ~ (v5 = 0) & 203.34/126.75 | sorted_sub2(v3, 0, v4) = v5 & tb2t(v2) = v3 & length1(int, v1) = 203.34/126.75 | v4 & elts(int, v1) = v2 & in_map_int_int(v3) & in_uni(v2)))) 203.34/126.75 | (18) ! [v0: $int] : ! [v1: $int] : ( ~ (t2tb2(v0) = v1) | ~ 203.34/126.75 | in_array_int(v0) | ? [v2: $int] : ? [v3: $int] : ? [v4: $int] : 203.34/126.75 | ? [v5: $int] : ((v5 = 0 & sorted_sub2(v3, 0, v4) = 0 & tb2t(v2) = v3 203.34/126.75 | & length1(int, v1) = v4 & elts(int, v1) = v2 & 203.34/126.75 | in_map_int_int(v3) & in_uni(v2)) | ( ~ (v2 = 0) & sorted1(v0) = 203.34/126.75 | v2))) 203.34/126.75 | 203.34/126.75 | ALPHA: (permut_trans) implies: 203.34/126.75 | (19) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! 203.34/126.75 | [v4: $int] : ! [v5: $int] : ( ~ (permut2(v0, v2, v3, v4, v5) = 0) | 203.34/126.75 | ~ (permut2(v0, v1, v2, v4, v5) = 0) | ~ in_ty(v0) | permut2(v0, v1, 203.34/126.75 | v3, v4, v5) = 0) 203.34/126.75 | 203.34/126.75 | ALPHA: (map_eq_sub_def) implies: 203.34/126.75 | (20) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! 203.34/126.75 | [v4: $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 203.34/126.75 | ($lesseq(1, $difference(v3, v6))) | ~ ($lesseq(v2, v6)) | ~ 203.34/126.75 | (map_eq_sub1(int, v4, v5, v2, v3) = 0) | ~ (t2tb(v1) = v5) | ~ 203.34/126.75 | (t2tb(v0) = v4) | ~ (get3(v1, v6) = v7) | ~ in_map_int_int(v0) | 203.34/126.75 | get3(v0, v6) = v7) 203.34/126.75 | 203.34/126.75 | ALPHA: (permut_sub_def) implies: 203.34/126.75 | (21) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ( ~ 203.34/126.75 | (permut_sub3(v0, v1, v2, v3) = 0) | ~ in_array_int(v0) | ? [v4: 203.34/126.75 | $int] : ? [v5: $int] : ? [v6: $int] : ? [v7: $int] : ? [v8: 203.34/126.75 | $int] : (map_eq_sub1(int, v5, v7, v3, v8) = 0 & map_eq_sub1(int, 203.34/126.75 | v5, v7, 0, v2) = 0 & permut3(int, v4, v6, v2, v3) = 0 & 203.34/126.75 | t2tb2(v1) = v6 & t2tb2(v0) = v4 & length1(int, v4) = v8 & 203.34/126.75 | elts(int, v6) = v7 & elts(int, v4) = v5 & in_uni(v7) & in_uni(v6) 203.34/126.75 | & in_uni(v5) & in_uni(v4))) 203.34/126.75 | (22) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! 203.34/126.75 | [v4: $int] : ! [v5: $int] : ( ~ (permut3(int, v4, v5, v2, v3) = 0) | 203.34/126.75 | ~ (t2tb2(v1) = v5) | ~ (t2tb2(v0) = v4) | ~ in_array_int(v0) | ? 203.34/126.75 | [v6: $int] : ? [v7: $int] : ? [v8: $int] : ? [v9: $int] : ((v6 = 203.34/126.75 | 0 & permut_sub3(v0, v1, v2, v3) = 0) | (elts(int, v5) = v7 & 203.34/126.75 | elts(int, v4) = v6 & in_uni(v7) & in_uni(v6) & (( ~ (v9 = 0) & 203.34/126.75 | map_eq_sub1(int, v6, v7, v3, v8) = v9 & length1(int, v4) = 203.34/126.75 | v8) | ( ~ (v8 = 0) & map_eq_sub1(int, v6, v7, 0, v2) = 203.34/126.75 | v8))))) 203.34/126.75 | (23) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! 203.34/126.75 | [v4: $int] : ! [v5: $int] : ! [v6: $int] : ( ~ (permut3(int, v4, v5, 203.34/126.75 | v2, v3) = v6) | ~ (t2tb2(v1) = v5) | ~ (t2tb2(v0) = v4) | ~ 203.34/126.75 | in_array_int(v0) | ? [v7: $int] : ? [v8: $int] : ? [v9: $int] : 203.34/126.75 | ? [v10: $int] : ? [v11: $int] : ((v11 = 0 & v9 = 0 & v6 = 0 & 203.34/126.75 | map_eq_sub1(int, v7, v8, v3, v10) = 0 & map_eq_sub1(int, v7, v8, 203.34/126.75 | 0, v2) = 0 & length1(int, v4) = v10 & elts(int, v5) = v8 & 203.34/126.75 | elts(int, v4) = v7 & in_uni(v8) & in_uni(v7)) | ( ~ (v7 = 0) & 203.34/126.75 | permut_sub3(v0, v1, v2, v3) = v7))) 203.34/126.75 | 203.34/126.75 | ALPHA: (array_eq_sub_def) implies: 203.34/126.75 | (24) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! 203.34/126.75 | [v4: $int] : ! [v5: $int] : ! [v6: $int] : ( ~ ($lesseq(0, v4)) | ~ 203.34/126.75 | ($lesseq(0, v3)) | ~ (map_eq_sub1(v0, v5, v6, v3, v4) = 0) | ~ 203.34/126.75 | (elts(v0, v2) = v6) | ~ (elts(v0, v1) = v5) | ~ in_ty(v0) | ? 203.34/126.75 | [v7: $int] : ? [v8: $int] : ((v7 = 0 & array_eq_sub1(v0, v1, v2, 203.34/126.75 | v3, v4) = 0) | (length1(v0, v1) = v7 & ( ~ ($lesseq(v4, v7)) | 203.34/126.75 | ~ ($lesseq(v3, v7)) | ( ~ (v8 = v7) & length1(v0, v2) = 203.34/126.75 | v8))))) 203.34/126.76 | (25) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! 203.34/126.76 | [v4: $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 203.34/126.76 | (map_eq_sub1(v0, v5, v6, v3, v4) = v7) | ~ (elts(v0, v2) = v6) | ~ 203.34/126.76 | (elts(v0, v1) = v5) | ~ in_ty(v0) | ? [v8: $int] : ? [v9: $int] : 203.34/126.76 | ((v9 = v8 & v7 = 0 & $lesseq(v4, v8) & $lesseq(v3, v8) & $lesseq(0, 203.34/126.76 | v4) & $lesseq(0, v3) & length1(v0, v2) = v8 & length1(v0, v1) 203.34/126.76 | = v8) | ( ~ (v8 = 0) & array_eq_sub1(v0, v1, v2, v3, v4) = v8))) 203.34/126.76 | 203.34/126.76 | ALPHA: (permut_sub_def1) implies: 203.34/126.76 | (26) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! 203.34/126.76 | [v4: $int] : ( ~ (permut3(v0, v1, v2, v3, v4) = 0) | ~ in_ty(v0) | ? 203.34/126.76 | [v5: $int] : ? [v6: $int] : ? [v7: $int] : ? [v8: $int] : ((v5 = 203.34/126.76 | 0 & permut_sub2(v0, v1, v2, v3, v4) = 0) | (elts(v0, v2) = v6 & 203.34/126.76 | elts(v0, v1) = v5 & in_uni(v6) & in_uni(v5) & (( ~ (v8 = 0) & 203.34/126.76 | map_eq_sub1(v0, v5, v6, v4, v7) = v8 & length1(v0, v1) = v7) 203.34/126.76 | | ( ~ (v7 = 0) & map_eq_sub1(v0, v5, v6, 0, v3) = v7))))) 203.34/126.76 | (27) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! 203.34/126.76 | [v4: $int] : ! [v5: $int] : ( ~ (permut3(v0, v1, v2, v3, v4) = v5) | 203.34/126.76 | ~ in_ty(v0) | ? [v6: $int] : ? [v7: $int] : ? [v8: $int] : ? 203.34/126.76 | [v9: $int] : ? [v10: $int] : ((v10 = 0 & v9 = 0 & v5 = 0 & 203.34/126.76 | map_eq_sub1(v0, v6, v7, v4, v8) = 0 & map_eq_sub1(v0, v6, v7, 0, 203.34/126.76 | v3) = 0 & length1(v0, v1) = v8 & elts(v0, v2) = v7 & elts(v0, 203.34/126.76 | v1) = v6 & in_uni(v7) & in_uni(v6)) | ( ~ (v6 = 0) & 203.34/126.76 | permut_sub2(v0, v1, v2, v3, v4) = v6))) 203.34/126.76 | (28) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! 203.34/126.76 | [v4: $int] : ! [v5: $int] : (v5 = 0 | ~ (permut_sub2(v0, v1, v2, v3, 203.34/126.76 | v4) = v5) | ~ in_ty(v0) | ? [v6: $int] : ? [v7: $int] : ? 203.34/126.76 | [v8: $int] : ? [v9: $int] : (( ~ (v9 = 0) & map_eq_sub1(v0, v6, v7, 203.34/126.76 | v4, v8) = v9 & length1(v0, v1) = v8 & elts(v0, v2) = v7 & 203.34/126.76 | elts(v0, v1) = v6 & in_uni(v7) & in_uni(v6)) | ( ~ (v8 = 0) & 203.34/126.76 | map_eq_sub1(v0, v6, v7, 0, v3) = v8 & elts(v0, v2) = v7 & 203.34/126.76 | elts(v0, v1) = v6 & in_uni(v7) & in_uni(v6)) | ( ~ (v6 = 0) & 203.34/126.76 | permut3(v0, v1, v2, v3, v4) = v6))) 203.34/126.76 | 203.34/126.76 | ALPHA: (array_inversion3) implies: 203.34/126.76 | (29) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ( ~ (elts(v0, v1) = 203.34/126.76 | v2) | ~ in_ty(v0) | ? [v3: $int] : (length1(v0, v1) = v3 & 203.34/126.76 | mk_array2(v0, v3, v2) = v1 & in_uni(v1))) 203.34/126.76 | (30) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ( ~ (length1(v0, v1) = 203.34/126.76 | v2) | ~ in_ty(v0) | ? [v3: $int] : (mk_array2(v0, v2, v3) = v1 & 203.34/126.76 | elts(v0, v1) = v3 & in_uni(v3) & in_uni(v1))) 203.34/126.76 | 203.34/126.76 | ALPHA: (qs_partition_def) implies: 203.34/126.76 | (31) in_ty(int) 203.34/126.76 | (32) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! 203.34/126.76 | [v4: $int] : ! [v5: $int] : ! [v6: $int] : ( ~ (qs_partition1(v0, 203.34/126.76 | v1, v2, v3, v4, v5, v6) = 0) | ~ in_array_int(v0) | ? [v7: 203.34/126.76 | $int] : (permut_sub3(v0, v1, v2, $sum(v3, 1)) = 0 & t2tb2(v1) = v7 203.34/126.76 | & in_uni(v7) & ! [v8: $int] : ! [v9: $int] : ( ~ ($lesseq(v8, 203.34/126.76 | v5)) | ~ ($lesseq(v2, v8)) | ~ (get4(int, v7, v8) = v9) | 203.34/126.76 | ? [v10: $int] : ($lesseq(v10, v6) & tb2t1(v9) = v10)) & ! [v8: 203.34/126.76 | $int] : ! [v9: $int] : ( ~ ($lesseq(1, $difference(v4, v8))) | 203.34/126.76 | ~ ($lesseq(1, $difference(v8, v5))) | ~ (get4(int, v7, v8) = 203.34/126.76 | v9) | tb2t1(v9) = v6) & ! [v8: $int] : ! [v9: $int] : ( ~ 203.34/126.76 | ($lesseq(v8, v3)) | ~ ($lesseq(v4, v8)) | ~ (get4(int, v7, v8) 203.34/126.76 | = v9) | ? [v10: $int] : ($lesseq(v6, v10) & tb2t1(v9) = 203.34/126.76 | v10)))) 203.34/126.76 | (33) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! 203.34/126.76 | [v4: $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : (v7 = 0 | 203.34/126.76 | ~ (qs_partition1(v0, v1, v2, v3, v4, v5, v6) = v7) | ~ 203.34/126.76 | in_array_int(v0) | ? [v8: $int] : ? [v9: $int] : ? [v10: $int] : 203.34/126.76 | ? [v11: $int] : (( ~ (v8 = 0) & permut_sub3(v0, v1, v2, $sum(v3, 1)) 203.34/126.76 | = v8) | (t2tb2(v1) = v8 & in_uni(v8) & (( ~ (v11 = v6) & 203.34/126.76 | $lesseq(1, $difference(v4, v9)) & $lesseq(1, $difference(v9, 203.34/126.76 | v5)) & tb2t1(v10) = v11 & get4(int, v8, v9) = v10 & 203.34/126.76 | in_uni(v10)) | ($lesseq(1, $difference(v6, v11)) & 203.34/126.76 | $lesseq(v9, v3) & $lesseq(v4, v9) & tb2t1(v10) = v11 & 203.34/126.76 | get4(int, v8, v9) = v10 & in_uni(v10)) | ($lesseq(1, 203.34/126.76 | $difference(v11, v6)) & $lesseq(v9, v5) & $lesseq(v2, v9) 203.34/126.76 | & tb2t1(v10) = v11 & get4(int, v8, v9) = v10 & 203.34/126.76 | in_uni(v10)))))) 203.34/126.76 | 203.34/126.76 | ALPHA: (axioms) implies: 203.34/126.77 | (34) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ 203.34/126.77 | (t2tb2(v2) = v1) | ~ (t2tb2(v2) = v0)) 203.34/126.77 | (35) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ 203.34/126.77 | (tb2t1(v2) = v1) | ~ (tb2t1(v2) = v0)) 203.34/126.77 | (36) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ 203.34/126.77 | (tb2t(v2) = v1) | ~ (tb2t(v2) = v0)) 203.34/126.77 | (37) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ 203.34/126.77 | (sorted1(v2) = v1) | ~ (sorted1(v2) = v0)) 203.34/126.77 | (38) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = 203.34/126.77 | v0 | ~ (elts(v3, v2) = v1) | ~ (elts(v3, v2) = v0)) 203.34/126.77 | (39) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = 203.34/126.77 | v0 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 203.34/126.77 | (40) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! 203.34/126.77 | [v4: $int] : (v1 = v0 | ~ (sorted_sub2(v4, v3, v2) = v1) | ~ 203.34/126.77 | (sorted_sub2(v4, v3, v2) = v0)) 203.34/126.77 | (41) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! 203.34/126.77 | [v4: $int] : ! [v5: $int] : (v1 = v0 | ~ (permut_sub3(v5, v4, v3, 203.34/126.77 | v2) = v1) | ~ (permut_sub3(v5, v4, v3, v2) = v0)) 203.34/126.77 | (42) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! 203.34/126.77 | [v4: $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ 203.34/126.77 | (permut3(v6, v5, v4, v3, v2) = v1) | ~ (permut3(v6, v5, v4, v3, v2) 203.34/126.77 | = v0)) 203.34/126.77 | (43) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! 203.34/126.77 | [v4: $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ 203.34/126.77 | (permut_sub2(v6, v5, v4, v3, v2) = v1) | ~ (permut_sub2(v6, v5, v4, 203.34/126.77 | v3, v2) = v0)) 203.34/126.77 | (44) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! 203.34/126.77 | [v4: $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ 203.34/126.77 | (map_eq_sub1(v6, v5, v4, v3, v2) = v1) | ~ (map_eq_sub1(v6, v5, v4, 203.34/126.77 | v3, v2) = v0)) 203.34/126.77 | (45) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! 203.34/126.77 | [v4: $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ 203.34/126.77 | (array_eq_sub1(v6, v5, v4, v3, v2) = v1) | ~ (array_eq_sub1(v6, v5, 203.34/126.77 | v4, v3, v2) = v0)) 203.34/126.77 | 203.34/126.77 | DELTA: instantiating (wP_parameter_quicksort) with fresh symbols all_86_0, 203.34/126.77 | all_86_1, all_86_2, all_86_3, all_86_4, all_86_5, all_86_6, all_86_7, 203.34/126.77 | all_86_8, all_86_9, all_86_10, all_86_11, all_86_12, all_86_13 gives: 203.34/126.77 | (46) ~ (all_86_0 = 0) & $lesseq(all_86_7, all_86_10) & $lesseq(1, 203.34/126.77 | $difference(all_86_7, all_86_8)) & $lesseq(0, all_86_7) & $lesseq(1, 203.34/126.77 | $difference(all_86_13, all_86_8)) & $lesseq(all_86_11, all_86_8) & 203.34/126.77 | $lesseq(1, $difference(all_86_13, all_86_10)) & $lesseq(0, all_86_11) 203.34/126.77 | & qs_partition1(all_86_3, all_86_1, all_86_11, all_86_10, all_86_7, 203.34/126.77 | all_86_8, 42) = all_86_0 & qs_partition1(all_86_5, all_86_3, 203.34/126.77 | all_86_11, all_86_10, all_86_7, all_86_8, 42) = 0 & 203.34/126.77 | mk_array3(all_86_13, all_86_2) = all_86_1 & mk_array3(all_86_13, 203.34/126.77 | all_86_4) = all_86_3 & mk_array3(all_86_13, all_86_6) = all_86_5 & 203.34/126.77 | mk_array3(all_86_13, all_86_12) = all_86_9 & sorted_sub2(all_86_2, 203.34/126.77 | all_86_7, $sum(all_86_10, 1)) = 0 & sorted_sub2(all_86_4, all_86_11, 203.34/126.77 | $sum(all_86_8, 1)) = 0 & permut_sub3(all_86_3, all_86_1, all_86_7, 203.34/126.77 | $sum(all_86_10, 1)) = 0 & permut_sub3(all_86_5, all_86_3, all_86_11, 203.34/126.77 | $sum(all_86_8, 1)) = 0 & permut_sub3(all_86_9, all_86_5, all_86_11, 203.34/126.77 | $sum(all_86_10, 1)) = 0 & in_array_int(all_86_1) & 203.34/126.77 | in_array_int(all_86_3) & in_array_int(all_86_5) & 203.34/126.77 | in_array_int(all_86_9) & in_map_int_int(all_86_2) & 203.34/126.77 | in_map_int_int(all_86_4) & in_map_int_int(all_86_6) & 203.34/126.77 | in_map_int_int(all_86_12) & ! [v0: $int] : ! [v1: $int] : (v1 = 42 | 203.34/126.77 | ~ ($lesseq(1, $difference(all_86_7, v0))) | ~ ($lesseq(1, 203.34/126.77 | $difference(v0, all_86_8))) | ~ (get3(all_86_6, v0) = v1)) & ! 203.34/126.77 | [v0: $int] : ! [v1: $int] : ( ~ ($lesseq(v1, 41)) | ~ ($lesseq(v0, 203.34/126.77 | all_86_10)) | ~ ($lesseq(all_86_7, v0)) | ~ (get3(all_86_6, 203.34/126.77 | v0) = v1)) & ! [v0: $int] : ! [v1: $int] : ( ~ ($lesseq(43, 203.34/126.77 | v1)) | ~ ($lesseq(v0, all_86_8)) | ~ ($lesseq(all_86_11, v0)) 203.34/126.77 | | ~ (get3(all_86_6, v0) = v1)) 203.34/126.77 | 203.34/126.77 | ALPHA: (46) implies: 203.34/126.77 | (47) ~ (all_86_0 = 0) 203.34/126.77 | (48) $lesseq(0, all_86_11) 203.34/126.77 | (49) $lesseq(1, $difference(all_86_13, all_86_10)) 203.34/126.77 | (50) $lesseq(all_86_11, all_86_8) 203.34/126.77 | (51) $lesseq(0, all_86_7) 203.34/126.77 | (52) $lesseq(1, $difference(all_86_7, all_86_8)) 203.34/126.77 | (53) $lesseq(all_86_7, all_86_10) 203.34/126.77 | (54) in_map_int_int(all_86_12) 203.34/126.77 | (55) in_map_int_int(all_86_6) 203.34/126.77 | (56) in_map_int_int(all_86_4) 203.34/126.77 | (57) in_map_int_int(all_86_2) 203.34/126.77 | (58) in_array_int(all_86_9) 203.34/126.77 | (59) in_array_int(all_86_5) 203.34/126.77 | (60) in_array_int(all_86_3) 203.34/126.77 | (61) in_array_int(all_86_1) 203.34/126.77 | (62) permut_sub3(all_86_9, all_86_5, all_86_11, $sum(all_86_10, 1)) = 0 203.34/126.77 | (63) permut_sub3(all_86_5, all_86_3, all_86_11, $sum(all_86_8, 1)) = 0 203.34/126.78 | (64) permut_sub3(all_86_3, all_86_1, all_86_7, $sum(all_86_10, 1)) = 0 203.34/126.78 | (65) mk_array3(all_86_13, all_86_12) = all_86_9 203.34/126.78 | (66) mk_array3(all_86_13, all_86_6) = all_86_5 203.34/126.78 | (67) mk_array3(all_86_13, all_86_4) = all_86_3 203.34/126.78 | (68) mk_array3(all_86_13, all_86_2) = all_86_1 203.34/126.78 | (69) qs_partition1(all_86_5, all_86_3, all_86_11, all_86_10, all_86_7, 203.34/126.78 | all_86_8, 42) = 0 203.34/126.78 | (70) qs_partition1(all_86_3, all_86_1, all_86_11, all_86_10, all_86_7, 203.34/126.78 | all_86_8, 42) = all_86_0 203.34/126.78 | (71) ! [v0: $int] : ! [v1: $int] : ( ~ ($lesseq(43, v1)) | ~ 203.34/126.78 | ($lesseq(v0, all_86_8)) | ~ ($lesseq(all_86_11, v0)) | ~ 203.34/126.78 | (get3(all_86_6, v0) = v1)) 203.34/126.78 | (72) ! [v0: $int] : ! [v1: $int] : (v1 = 42 | ~ ($lesseq(1, 203.34/126.78 | $difference(all_86_7, v0))) | ~ ($lesseq(1, $difference(v0, 203.34/126.78 | all_86_8))) | ~ (get3(all_86_6, v0) = v1)) 203.34/126.78 | 203.34/126.78 | COMBINE_INEQS: (52), (53) imply: 203.34/126.78 | (73) $lesseq(1, $difference(all_86_10, all_86_8)) 203.34/126.78 | 203.34/126.78 | COMBINE_INEQS: (50), (73) imply: 203.34/126.78 | (74) $lesseq(1, $difference(all_86_10, all_86_11)) 203.34/126.78 | 203.34/126.78 | COMBINE_INEQS: (49), (74) imply: 203.34/126.78 | (75) $lesseq(2, $difference(all_86_13, all_86_11)) 203.34/126.78 | 203.34/126.78 | GROUND_INST: instantiating (33) with all_86_3, all_86_1, all_86_11, all_86_10, 203.34/126.78 | all_86_7, all_86_8, 42, all_86_0, simplifying with (60), (70) 203.34/126.78 | gives: 203.34/126.78 | (76) all_86_0 = 0 | ? [v0: $int] : ? [v1: $int] : ? [v2: $int] : ? [v3: 203.34/126.78 | $int] : (( ~ (v0 = 0) & permut_sub3(all_86_3, all_86_1, all_86_11, 203.34/126.78 | $sum(all_86_10, 1)) = v0) | (t2tb2(all_86_1) = v0 & in_uni(v0) & 203.34/126.78 | (( ~ (v3 = 42) & $lesseq(1, $difference(all_86_7, v1)) & 203.34/126.78 | $lesseq(1, $difference(v1, all_86_8)) & tb2t1(v2) = v3 & 203.34/126.78 | get4(int, v0, v1) = v2 & in_uni(v2)) | ($lesseq(v3, 41) & 203.34/126.78 | $lesseq(v1, all_86_10) & $lesseq(all_86_7, v1) & tb2t1(v2) = 203.34/126.78 | v3 & get4(int, v0, v1) = v2 & in_uni(v2)) | ($lesseq(43, v3) & 203.34/126.78 | $lesseq(v1, all_86_8) & $lesseq(all_86_11, v1) & tb2t1(v2) = 203.34/126.78 | v3 & get4(int, v0, v1) = v2 & in_uni(v2))))) 203.34/126.78 | 203.34/126.78 | GROUND_INST: instantiating (32) with all_86_5, all_86_3, all_86_11, all_86_10, 203.34/126.78 | all_86_7, all_86_8, 42, simplifying with (59), (69) gives: 203.34/126.78 | (77) ? [v0: $int] : (permut_sub3(all_86_5, all_86_3, all_86_11, 203.34/126.78 | $sum(all_86_10, 1)) = 0 & t2tb2(all_86_3) = v0 & in_uni(v0) & ! 203.34/126.78 | [v1: $int] : ! [v2: $int] : ( ~ ($lesseq(1, $difference(all_86_7, 203.34/126.78 | v1))) | ~ ($lesseq(1, $difference(v1, all_86_8))) | ~ 203.34/126.78 | (get4(int, v0, v1) = v2) | tb2t1(v2) = 42) & ! [v1: $int] : ! 203.34/126.78 | [v2: $int] : ( ~ ($lesseq(v1, all_86_8)) | ~ ($lesseq(all_86_11, 203.34/126.78 | v1)) | ~ (get4(int, v0, v1) = v2) | ? [v3: $int] : 203.34/126.78 | ($lesseq(v3, 42) & tb2t1(v2) = v3)) & ! [v1: $int] : ! [v2: 203.34/126.78 | $int] : ( ~ ($lesseq(v1, all_86_10)) | ~ ($lesseq(all_86_7, v1)) 203.34/126.78 | | ~ (get4(int, v0, v1) = v2) | ? [v3: $int] : ($lesseq(42, v3) & 203.34/126.78 | tb2t1(v2) = v3))) 203.34/126.78 | 203.34/126.78 | GROUND_INST: instantiating (8) with all_86_13, all_86_2, all_86_1, simplifying 203.34/126.78 | with (57), (68) gives: 203.34/126.78 | (78) ? [v0: $int] : ? [v1: $int] : (tb2t(v1) = all_86_2 & t2tb2(all_86_1) 203.34/126.78 | = v0 & elts(int, v0) = v1 & in_uni(v1) & in_uni(v0)) 203.34/126.78 | 203.34/126.78 | GROUND_INST: instantiating (16) with all_86_13, all_86_2, all_86_1, 203.34/126.78 | simplifying with (57), (68) gives: 203.34/126.78 | (79) ? [v0: $int] : (t2tb2(all_86_1) = v0 & length1(int, v0) = all_86_13 & 203.34/126.78 | in_uni(v0)) 203.34/126.78 | 203.34/126.79 | GROUND_INST: instantiating (8) with all_86_13, all_86_4, all_86_3, simplifying 203.34/126.79 | with (56), (67) gives: 203.34/126.79 | (80) ? [v0: $int] : ? [v1: $int] : (tb2t(v1) = all_86_4 & t2tb2(all_86_3) 203.34/126.79 | = v0 & elts(int, v0) = v1 & in_uni(v1) & in_uni(v0)) 203.34/126.79 | 203.34/126.79 | GROUND_INST: instantiating (16) with all_86_13, all_86_4, all_86_3, 203.34/126.79 | simplifying with (56), (67) gives: 203.34/126.79 | (81) ? [v0: $int] : (t2tb2(all_86_3) = v0 & length1(int, v0) = all_86_13 & 203.34/126.79 | in_uni(v0)) 203.34/126.79 | 203.34/126.79 | GROUND_INST: instantiating (8) with all_86_13, all_86_6, all_86_5, simplifying 203.34/126.79 | with (55), (66) gives: 203.34/126.79 | (82) ? [v0: $int] : ? [v1: $int] : (tb2t(v1) = all_86_6 & t2tb2(all_86_5) 203.34/126.79 | = v0 & elts(int, v0) = v1 & in_uni(v1) & in_uni(v0)) 203.34/126.79 | 203.34/126.79 | GROUND_INST: instantiating (16) with all_86_13, all_86_6, all_86_5, 203.34/126.79 | simplifying with (55), (66) gives: 203.34/126.79 | (83) ? [v0: $int] : (t2tb2(all_86_5) = v0 & length1(int, v0) = all_86_13 & 203.34/126.79 | in_uni(v0)) 203.34/126.79 | 203.34/126.79 | GROUND_INST: instantiating (8) with all_86_13, all_86_12, all_86_9, 203.34/126.79 | simplifying with (54), (65) gives: 203.34/126.79 | (84) ? [v0: $int] : ? [v1: $int] : (tb2t(v1) = all_86_12 & 203.34/126.79 | t2tb2(all_86_9) = v0 & elts(int, v0) = v1 & in_uni(v1) & in_uni(v0)) 203.34/126.79 | 203.34/126.79 | GROUND_INST: instantiating (16) with all_86_13, all_86_12, all_86_9, 203.34/126.79 | simplifying with (54), (65) gives: 203.34/126.79 | (85) ? [v0: $int] : (t2tb2(all_86_9) = v0 & length1(int, v0) = all_86_13 & 203.34/126.79 | in_uni(v0)) 203.34/126.79 | 203.34/126.79 | GROUND_INST: instantiating (21) with all_86_3, all_86_1, all_86_7, 203.34/126.79 | $sum(all_86_10, 1), simplifying with (60), (64) gives: 203.34/126.79 | (86) ? [v0: $int] : ? [v1: $int] : ? [v2: $int] : ? [v3: $int] : ? 203.34/126.79 | [v4: $int] : (map_eq_sub1(int, v1, v3, $sum(all_86_10, 1), v4) = 0 & 203.34/126.79 | map_eq_sub1(int, v1, v3, 0, all_86_7) = 0 & permut3(int, v0, v2, 203.34/126.79 | all_86_7, $sum(all_86_10, 1)) = 0 & t2tb2(all_86_1) = v2 & 203.34/126.79 | t2tb2(all_86_3) = v0 & length1(int, v0) = v4 & elts(int, v2) = v3 & 203.34/126.79 | elts(int, v0) = v1 & in_uni(v3) & in_uni(v2) & in_uni(v1) & 203.34/126.79 | in_uni(v0)) 203.34/126.79 | 203.34/126.79 | GROUND_INST: instantiating (21) with all_86_5, all_86_3, all_86_11, 203.34/126.79 | $sum(all_86_8, 1), simplifying with (59), (63) gives: 203.34/126.79 | (87) ? [v0: $int] : ? [v1: $int] : ? [v2: $int] : ? [v3: $int] : ? 203.34/126.79 | [v4: $int] : (map_eq_sub1(int, v1, v3, $sum(all_86_8, 1), v4) = 0 & 203.34/126.79 | map_eq_sub1(int, v1, v3, 0, all_86_11) = 0 & permut3(int, v0, v2, 203.34/126.79 | all_86_11, $sum(all_86_8, 1)) = 0 & t2tb2(all_86_3) = v2 & 203.34/126.79 | t2tb2(all_86_5) = v0 & length1(int, v0) = v4 & elts(int, v2) = v3 & 203.34/126.79 | elts(int, v0) = v1 & in_uni(v3) & in_uni(v2) & in_uni(v1) & 203.34/126.79 | in_uni(v0)) 203.34/126.79 | 203.34/126.79 | GROUND_INST: instantiating (21) with all_86_9, all_86_5, all_86_11, 203.34/126.79 | $sum(all_86_10, 1), simplifying with (58), (62) gives: 203.34/126.79 | (88) ? [v0: $int] : ? [v1: $int] : ? [v2: $int] : ? [v3: $int] : ? 203.34/126.79 | [v4: $int] : (map_eq_sub1(int, v1, v3, $sum(all_86_10, 1), v4) = 0 & 203.34/126.79 | map_eq_sub1(int, v1, v3, 0, all_86_11) = 0 & permut3(int, v0, v2, 203.34/126.79 | all_86_11, $sum(all_86_10, 1)) = 0 & t2tb2(all_86_5) = v2 & 203.34/126.79 | t2tb2(all_86_9) = v0 & length1(int, v0) = v4 & elts(int, v2) = v3 & 203.34/126.79 | elts(int, v0) = v1 & in_uni(v3) & in_uni(v2) & in_uni(v1) & 203.34/126.79 | in_uni(v0)) 203.34/126.79 | 203.34/126.79 | DELTA: instantiating (88) with fresh symbols all_103_0, all_103_1, all_103_2, 203.34/126.79 | all_103_3, all_103_4 gives: 203.34/126.79 | (89) map_eq_sub1(int, all_103_3, all_103_1, $sum(all_86_10, 1), all_103_0) 203.34/126.79 | = 0 & map_eq_sub1(int, all_103_3, all_103_1, 0, all_86_11) = 0 & 203.34/126.79 | permut3(int, all_103_4, all_103_2, all_86_11, $sum(all_86_10, 1)) = 0 203.34/126.79 | & t2tb2(all_86_5) = all_103_2 & t2tb2(all_86_9) = all_103_4 & 203.34/126.79 | length1(int, all_103_4) = all_103_0 & elts(int, all_103_2) = all_103_1 203.34/126.79 | & elts(int, all_103_4) = all_103_3 & in_uni(all_103_1) & 203.34/126.79 | in_uni(all_103_2) & in_uni(all_103_3) & in_uni(all_103_4) 203.34/126.79 | 203.34/126.79 | ALPHA: (89) implies: 203.34/126.79 | (90) elts(int, all_103_4) = all_103_3 203.34/126.79 | (91) elts(int, all_103_2) = all_103_1 203.34/126.79 | (92) length1(int, all_103_4) = all_103_0 203.34/126.79 | (93) t2tb2(all_86_9) = all_103_4 203.34/126.79 | (94) t2tb2(all_86_5) = all_103_2 203.34/126.79 | (95) permut3(int, all_103_4, all_103_2, all_86_11, $sum(all_86_10, 1)) = 0 203.34/126.79 | (96) map_eq_sub1(int, all_103_3, all_103_1, 0, all_86_11) = 0 203.34/126.79 | (97) map_eq_sub1(int, all_103_3, all_103_1, $sum(all_86_10, 1), all_103_0) 203.34/126.79 | = 0 203.34/126.79 | 203.34/126.79 | DELTA: instantiating (86) with fresh symbols all_105_0, all_105_1, all_105_2, 203.34/126.79 | all_105_3, all_105_4 gives: 203.34/126.79 | (98) map_eq_sub1(int, all_105_3, all_105_1, $sum(all_86_10, 1), all_105_0) 203.34/126.79 | = 0 & map_eq_sub1(int, all_105_3, all_105_1, 0, all_86_7) = 0 & 203.34/126.79 | permut3(int, all_105_4, all_105_2, all_86_7, $sum(all_86_10, 1)) = 0 & 203.34/126.79 | t2tb2(all_86_1) = all_105_2 & t2tb2(all_86_3) = all_105_4 & 203.34/126.79 | length1(int, all_105_4) = all_105_0 & elts(int, all_105_2) = all_105_1 203.34/126.79 | & elts(int, all_105_4) = all_105_3 & in_uni(all_105_1) & 203.34/126.79 | in_uni(all_105_2) & in_uni(all_105_3) & in_uni(all_105_4) 203.34/126.79 | 203.34/126.79 | ALPHA: (98) implies: 203.34/126.79 | (99) elts(int, all_105_4) = all_105_3 203.34/126.79 | (100) elts(int, all_105_2) = all_105_1 203.34/126.79 | (101) length1(int, all_105_4) = all_105_0 203.34/126.79 | (102) t2tb2(all_86_3) = all_105_4 203.34/126.79 | (103) t2tb2(all_86_1) = all_105_2 203.34/126.79 | (104) permut3(int, all_105_4, all_105_2, all_86_7, $sum(all_86_10, 1)) = 0 203.34/126.79 | (105) map_eq_sub1(int, all_105_3, all_105_1, 0, all_86_7) = 0 203.34/126.79 | (106) map_eq_sub1(int, all_105_3, all_105_1, $sum(all_86_10, 1), all_105_0) 203.34/126.79 | = 0 203.34/126.79 | 203.34/126.79 | DELTA: instantiating (84) with fresh symbols all_107_0, all_107_1 gives: 203.34/126.79 | (107) tb2t(all_107_0) = all_86_12 & t2tb2(all_86_9) = all_107_1 & elts(int, 203.34/126.79 | all_107_1) = all_107_0 & in_uni(all_107_0) & in_uni(all_107_1) 203.34/126.79 | 203.34/126.79 | ALPHA: (107) implies: 203.34/126.79 | (108) in_uni(all_107_0) 203.34/126.79 | (109) elts(int, all_107_1) = all_107_0 203.34/126.79 | (110) t2tb2(all_86_9) = all_107_1 203.34/126.79 | (111) tb2t(all_107_0) = all_86_12 203.34/126.79 | 203.34/126.79 | DELTA: instantiating (83) with fresh symbol all_109_0 gives: 203.34/126.79 | (112) t2tb2(all_86_5) = all_109_0 & length1(int, all_109_0) = all_86_13 & 203.34/126.79 | in_uni(all_109_0) 203.34/126.79 | 203.34/126.79 | ALPHA: (112) implies: 203.34/126.79 | (113) length1(int, all_109_0) = all_86_13 203.34/126.79 | (114) t2tb2(all_86_5) = all_109_0 203.34/126.79 | 203.34/126.79 | DELTA: instantiating (85) with fresh symbol all_111_0 gives: 203.34/126.79 | (115) t2tb2(all_86_9) = all_111_0 & length1(int, all_111_0) = all_86_13 & 203.34/126.79 | in_uni(all_111_0) 203.34/126.79 | 203.34/126.79 | ALPHA: (115) implies: 203.34/126.79 | (116) length1(int, all_111_0) = all_86_13 203.34/126.79 | (117) t2tb2(all_86_9) = all_111_0 203.34/126.79 | 203.34/126.79 | DELTA: instantiating (87) with fresh symbols all_113_0, all_113_1, all_113_2, 203.34/126.79 | all_113_3, all_113_4 gives: 203.53/126.80 | (118) map_eq_sub1(int, all_113_3, all_113_1, $sum(all_86_8, 1), all_113_0) 203.53/126.80 | = 0 & map_eq_sub1(int, all_113_3, all_113_1, 0, all_86_11) = 0 & 203.53/126.80 | permut3(int, all_113_4, all_113_2, all_86_11, $sum(all_86_8, 1)) = 0 203.53/126.80 | & t2tb2(all_86_3) = all_113_2 & t2tb2(all_86_5) = all_113_4 & 203.53/126.80 | length1(int, all_113_4) = all_113_0 & elts(int, all_113_2) = 203.53/126.80 | all_113_1 & elts(int, all_113_4) = all_113_3 & in_uni(all_113_1) & 203.53/126.80 | in_uni(all_113_2) & in_uni(all_113_3) & in_uni(all_113_4) 203.53/126.80 | 203.53/126.80 | ALPHA: (118) implies: 203.53/126.80 | (119) in_uni(all_113_3) 203.53/126.80 | (120) in_uni(all_113_1) 203.53/126.80 | (121) elts(int, all_113_4) = all_113_3 203.53/126.80 | (122) elts(int, all_113_2) = all_113_1 203.53/126.80 | (123) length1(int, all_113_4) = all_113_0 203.53/126.80 | (124) t2tb2(all_86_5) = all_113_4 203.53/126.80 | (125) t2tb2(all_86_3) = all_113_2 203.53/126.80 | (126) permut3(int, all_113_4, all_113_2, all_86_11, $sum(all_86_8, 1)) = 0 203.53/126.80 | (127) map_eq_sub1(int, all_113_3, all_113_1, 0, all_86_11) = 0 203.53/126.80 | (128) map_eq_sub1(int, all_113_3, all_113_1, $sum(all_86_8, 1), all_113_0) 203.53/126.80 | = 0 203.53/126.80 | 203.53/126.80 | DELTA: instantiating (82) with fresh symbols all_115_0, all_115_1 gives: 203.53/126.80 | (129) tb2t(all_115_0) = all_86_6 & t2tb2(all_86_5) = all_115_1 & elts(int, 203.53/126.80 | all_115_1) = all_115_0 & in_uni(all_115_0) & in_uni(all_115_1) 203.53/126.80 | 203.53/126.80 | ALPHA: (129) implies: 203.53/126.80 | (130) elts(int, all_115_1) = all_115_0 203.53/126.80 | (131) t2tb2(all_86_5) = all_115_1 203.53/126.80 | (132) tb2t(all_115_0) = all_86_6 203.53/126.80 | 203.53/126.80 | DELTA: instantiating (80) with fresh symbols all_117_0, all_117_1 gives: 203.53/126.80 | (133) tb2t(all_117_0) = all_86_4 & t2tb2(all_86_3) = all_117_1 & elts(int, 203.53/126.80 | all_117_1) = all_117_0 & in_uni(all_117_0) & in_uni(all_117_1) 203.53/126.80 | 203.53/126.80 | ALPHA: (133) implies: 203.53/126.80 | (134) elts(int, all_117_1) = all_117_0 203.53/126.80 | (135) t2tb2(all_86_3) = all_117_1 203.53/126.80 | (136) tb2t(all_117_0) = all_86_4 203.53/126.80 | 203.53/126.80 | DELTA: instantiating (79) with fresh symbol all_119_0 gives: 203.53/126.80 | (137) t2tb2(all_86_1) = all_119_0 & length1(int, all_119_0) = all_86_13 & 203.53/126.80 | in_uni(all_119_0) 203.53/126.80 | 203.53/126.80 | ALPHA: (137) implies: 203.53/126.80 | (138) length1(int, all_119_0) = all_86_13 203.53/126.80 | (139) t2tb2(all_86_1) = all_119_0 203.53/126.80 | 203.53/126.80 | DELTA: instantiating (81) with fresh symbol all_121_0 gives: 203.53/126.80 | (140) t2tb2(all_86_3) = all_121_0 & length1(int, all_121_0) = all_86_13 & 203.53/126.80 | in_uni(all_121_0) 203.53/126.80 | 203.53/126.80 | ALPHA: (140) implies: 203.53/126.80 | (141) length1(int, all_121_0) = all_86_13 203.53/126.80 | (142) t2tb2(all_86_3) = all_121_0 203.53/126.80 | 203.53/126.80 | DELTA: instantiating (78) with fresh symbols all_123_0, all_123_1 gives: 203.53/126.80 | (143) tb2t(all_123_0) = all_86_2 & t2tb2(all_86_1) = all_123_1 & elts(int, 203.53/126.80 | all_123_1) = all_123_0 & in_uni(all_123_0) & in_uni(all_123_1) 203.53/126.80 | 203.53/126.80 | ALPHA: (143) implies: 203.53/126.80 | (144) in_uni(all_123_0) 203.53/126.80 | (145) elts(int, all_123_1) = all_123_0 203.53/126.80 | (146) t2tb2(all_86_1) = all_123_1 203.53/126.80 | (147) tb2t(all_123_0) = all_86_2 203.53/126.80 | 203.53/126.80 | DELTA: instantiating (77) with fresh symbol all_125_0 gives: 203.53/126.80 | (148) permut_sub3(all_86_5, all_86_3, all_86_11, $sum(all_86_10, 1)) = 0 & 203.53/126.80 | t2tb2(all_86_3) = all_125_0 & in_uni(all_125_0) & ! [v0: $int] : ! 203.53/126.80 | [v1: $int] : ( ~ ($lesseq(1, $difference(all_86_7, v0))) | ~ 203.53/126.80 | ($lesseq(1, $difference(v0, all_86_8))) | ~ (get4(int, all_125_0, 203.53/126.80 | v0) = v1) | tb2t1(v1) = 42) & ! [v0: $int] : ! [v1: $int] : ( 203.53/126.80 | ~ ($lesseq(v0, all_86_8)) | ~ ($lesseq(all_86_11, v0)) | ~ 203.53/126.80 | (get4(int, all_125_0, v0) = v1) | ? [v2: $int] : ($lesseq(v2, 42) 203.53/126.80 | & tb2t1(v1) = v2)) & ! [v0: $int] : ! [v1: $int] : ( ~ 203.53/126.80 | ($lesseq(v0, all_86_10)) | ~ ($lesseq(all_86_7, v0)) | ~ 203.53/126.80 | (get4(int, all_125_0, v0) = v1) | ? [v2: $int] : ($lesseq(42, v2) 203.53/126.80 | & tb2t1(v1) = v2)) 203.53/126.80 | 203.53/126.80 | ALPHA: (148) implies: 203.53/126.80 | (149) t2tb2(all_86_3) = all_125_0 203.53/126.80 | (150) permut_sub3(all_86_5, all_86_3, all_86_11, $sum(all_86_10, 1)) = 0 203.53/126.80 | (151) ! [v0: $int] : ! [v1: $int] : ( ~ ($lesseq(v0, all_86_10)) | ~ 203.53/126.80 | ($lesseq(all_86_7, v0)) | ~ (get4(int, all_125_0, v0) = v1) | ? 203.53/126.80 | [v2: $int] : ($lesseq(42, v2) & tb2t1(v1) = v2)) 203.53/126.80 | 203.53/126.80 | BETA: splitting (76) gives: 203.53/126.80 | 203.53/126.80 | Case 1: 203.53/126.80 | | 203.53/126.80 | | (152) all_86_0 = 0 203.53/126.80 | | 203.53/126.80 | | REDUCE: (47), (152) imply: 203.53/126.80 | | (153) ~ (0 = 0) 203.53/126.81 | | 203.53/126.81 | | CLOSE: (153) is inconsistent. 203.53/126.81 | | 203.53/126.81 | Case 2: 203.53/126.81 | | 203.53/126.81 | | (154) ? [v0: $int] : ? [v1: $int] : ? [v2: $int] : ? [v3: $int] : (( 203.53/126.81 | | ~ (v0 = 0) & permut_sub3(all_86_3, all_86_1, all_86_11, 203.53/126.81 | | $sum(all_86_10, 1)) = v0) | (t2tb2(all_86_1) = v0 & 203.53/126.81 | | in_uni(v0) & (( ~ (v3 = 42) & $lesseq(1, $difference(all_86_7, 203.53/126.81 | | v1)) & $lesseq(1, $difference(v1, all_86_8)) & 203.53/126.81 | | tb2t1(v2) = v3 & get4(int, v0, v1) = v2 & in_uni(v2)) | 203.53/126.81 | | ($lesseq(v3, 41) & $lesseq(v1, all_86_10) & $lesseq(all_86_7, 203.53/126.81 | | v1) & tb2t1(v2) = v3 & get4(int, v0, v1) = v2 & 203.53/126.81 | | in_uni(v2)) | ($lesseq(43, v3) & $lesseq(v1, all_86_8) & 203.53/126.81 | | $lesseq(all_86_11, v1) & tb2t1(v2) = v3 & get4(int, v0, v1) 203.53/126.81 | | = v2 & in_uni(v2))))) 203.53/126.81 | | 203.53/126.81 | | DELTA: instantiating (154) with fresh symbols all_133_0, all_133_1, 203.53/126.81 | | all_133_2, all_133_3 gives: 203.53/126.82 | | (155) ( ~ (all_133_3 = 0) & permut_sub3(all_86_3, all_86_1, all_86_11, 203.53/126.82 | | $sum(all_86_10, 1)) = all_133_3) | (t2tb2(all_86_1) = all_133_3 203.53/126.82 | | & in_uni(all_133_3) & (( ~ (all_133_0 = 42) & $lesseq(1, 203.53/126.82 | | $difference(all_86_7, all_133_2)) & $lesseq(1, 203.53/126.82 | | $difference(all_133_2, all_86_8)) & tb2t1(all_133_1) = 203.53/126.82 | | all_133_0 & get4(int, all_133_3, all_133_2) = all_133_1 & 203.53/126.82 | | in_uni(all_133_1)) | ($lesseq(all_133_0, 41) & 203.53/126.82 | | $lesseq(all_133_2, all_86_10) & $lesseq(all_86_7, all_133_2) 203.53/126.82 | | & tb2t1(all_133_1) = all_133_0 & get4(int, all_133_3, 203.53/126.82 | | all_133_2) = all_133_1 & in_uni(all_133_1)) | ($lesseq(43, 203.53/126.82 | | all_133_0) & $lesseq(all_133_2, all_86_8) & 203.53/126.82 | | $lesseq(all_86_11, all_133_2) & tb2t1(all_133_1) = all_133_0 203.53/126.82 | | & get4(int, all_133_3, all_133_2) = all_133_1 & 203.53/126.82 | | in_uni(all_133_1)))) 203.53/126.82 | | 203.53/126.82 | | GROUND_INST: instantiating (11) with int, all_113_4, all_113_2, all_86_11, 203.53/126.82 | | $sum(all_86_8, 1), simplifying with (31), (126) gives: 203.53/126.82 | | (156) $lesseq(-1, all_86_8) 203.53/126.82 | | 203.53/126.82 | | GROUND_INST: instantiating (34) with all_123_1, all_119_0, all_86_1, 203.53/126.82 | | simplifying with (139), (146) gives: 203.53/126.82 | | (157) all_123_1 = all_119_0 203.53/126.82 | | 203.53/126.82 | | GROUND_INST: instantiating (34) with all_123_1, all_105_2, all_86_1, 203.53/126.82 | | simplifying with (103), (146) gives: 203.53/126.82 | | (158) all_123_1 = all_105_2 203.53/126.82 | | 203.53/126.82 | | GROUND_INST: instantiating (34) with all_125_0, all_121_0, all_86_3, 203.53/126.82 | | simplifying with (142), (149) gives: 203.53/126.82 | | (159) all_125_0 = all_121_0 203.53/126.82 | | 203.53/126.82 | | GROUND_INST: instantiating (34) with all_121_0, all_117_1, all_86_3, 203.53/126.82 | | simplifying with (135), (142) gives: 203.53/126.82 | | (160) all_121_0 = all_117_1 203.53/126.82 | | 203.53/126.82 | | GROUND_INST: instantiating (34) with all_117_1, all_113_2, all_86_3, 203.53/126.82 | | simplifying with (125), (135) gives: 203.53/126.82 | | (161) all_117_1 = all_113_2 203.53/126.82 | | 203.53/126.82 | | GROUND_INST: instantiating (34) with all_125_0, all_105_4, all_86_3, 203.53/126.82 | | simplifying with (102), (149) gives: 203.53/126.82 | | (162) all_125_0 = all_105_4 203.53/126.82 | | 203.53/126.82 | | GROUND_INST: instantiating (34) with all_115_1, all_113_4, all_86_5, 203.53/126.82 | | simplifying with (124), (131) gives: 203.53/126.82 | | (163) all_115_1 = all_113_4 203.53/126.82 | | 203.53/126.82 | | GROUND_INST: instantiating (34) with all_115_1, all_109_0, all_86_5, 203.53/126.82 | | simplifying with (114), (131) gives: 203.53/126.82 | | (164) all_115_1 = all_109_0 203.53/126.82 | | 203.53/126.82 | | GROUND_INST: instantiating (34) with all_115_1, all_103_2, all_86_5, 203.53/126.82 | | simplifying with (94), (131) gives: 203.53/126.82 | | (165) all_115_1 = all_103_2 203.53/126.82 | | 203.53/126.82 | | GROUND_INST: instantiating (34) with all_111_0, all_107_1, all_86_9, 203.53/126.82 | | simplifying with (110), (117) gives: 203.53/126.82 | | (166) all_111_0 = all_107_1 203.53/126.82 | | 203.53/126.82 | | GROUND_INST: instantiating (34) with all_111_0, all_103_4, all_86_9, 203.53/126.82 | | simplifying with (93), (117) gives: 203.53/126.82 | | (167) all_111_0 = all_103_4 203.53/126.82 | | 203.53/126.82 | | COMBINE_EQS: (159), (162) imply: 203.53/126.82 | | (168) all_121_0 = all_105_4 203.53/126.82 | | 203.53/126.82 | | SIMP: (168) implies: 203.53/126.82 | | (169) all_121_0 = all_105_4 203.53/126.82 | | 203.53/126.82 | | COMBINE_EQS: (157), (158) imply: 203.53/126.82 | | (170) all_119_0 = all_105_2 203.53/126.82 | | 203.53/126.82 | | COMBINE_EQS: (160), (169) imply: 203.53/126.82 | | (171) all_117_1 = all_105_4 203.53/126.82 | | 203.53/126.82 | | SIMP: (171) implies: 203.53/126.82 | | (172) all_117_1 = all_105_4 203.53/126.82 | | 203.53/126.82 | | COMBINE_EQS: (161), (172) imply: 203.53/126.82 | | (173) all_113_2 = all_105_4 203.53/126.82 | | 203.53/126.82 | | SIMP: (173) implies: 203.53/126.82 | | (174) all_113_2 = all_105_4 203.53/126.82 | | 203.53/126.82 | | COMBINE_EQS: (163), (165) imply: 203.53/126.82 | | (175) all_113_4 = all_103_2 203.53/126.82 | | 203.53/126.82 | | COMBINE_EQS: (163), (164) imply: 203.53/126.82 | | (176) all_113_4 = all_109_0 203.53/126.82 | | 203.53/126.82 | | COMBINE_EQS: (175), (176) imply: 203.53/126.82 | | (177) all_109_0 = all_103_2 203.53/126.82 | | 203.53/126.82 | | COMBINE_EQS: (166), (167) imply: 203.53/126.82 | | (178) all_107_1 = all_103_4 203.53/126.82 | | 203.53/126.82 | | REDUCE: (126), (174), (175) imply: 203.53/126.82 | | (179) permut3(int, all_103_2, all_105_4, all_86_11, $sum(all_86_8, 1)) = 203.53/126.82 | | 0 203.53/126.82 | | 203.53/126.82 | | REDUCE: (141), (169) imply: 203.53/126.82 | | (180) length1(int, all_105_4) = all_86_13 203.53/126.82 | | 203.53/126.82 | | REDUCE: (138), (170) imply: 203.53/126.82 | | (181) length1(int, all_105_2) = all_86_13 203.53/126.82 | | 203.53/126.82 | | REDUCE: (123), (175) imply: 203.53/126.82 | | (182) length1(int, all_103_2) = all_113_0 203.53/126.82 | | 203.53/126.82 | | REDUCE: (116), (167) imply: 203.53/126.82 | | (183) length1(int, all_103_4) = all_86_13 203.53/126.82 | | 203.53/126.82 | | REDUCE: (113), (177) imply: 203.53/126.82 | | (184) length1(int, all_103_2) = all_86_13 203.53/126.82 | | 203.53/126.82 | | REDUCE: (145), (158) imply: 203.53/126.82 | | (185) elts(int, all_105_2) = all_123_0 203.53/126.82 | | 203.53/126.82 | | REDUCE: (134), (172) imply: 203.53/126.82 | | (186) elts(int, all_105_4) = all_117_0 203.53/126.82 | | 203.53/126.82 | | REDUCE: (130), (165) imply: 203.53/126.82 | | (187) elts(int, all_103_2) = all_115_0 203.53/126.82 | | 203.53/126.82 | | REDUCE: (122), (174) imply: 203.53/126.82 | | (188) elts(int, all_105_4) = all_113_1 203.53/126.82 | | 203.53/126.82 | | REDUCE: (121), (175) imply: 203.53/126.82 | | (189) elts(int, all_103_2) = all_113_3 203.53/126.82 | | 203.53/126.82 | | REDUCE: (109), (178) imply: 203.53/126.82 | | (190) elts(int, all_103_4) = all_107_0 203.53/126.82 | | 203.53/126.82 | | GROUND_INST: instantiating (39) with all_105_0, all_86_13, all_105_4, int, 203.53/126.82 | | simplifying with (101), (180) gives: 203.53/126.82 | | (191) all_105_0 = all_86_13 203.53/126.82 | | 203.53/126.82 | | GROUND_INST: instantiating (39) with all_113_0, all_86_13, all_103_2, int, 203.53/126.82 | | simplifying with (182), (184) gives: 203.53/126.82 | | (192) all_113_0 = all_86_13 203.53/126.82 | | 203.53/126.82 | | GROUND_INST: instantiating (39) with all_103_0, all_86_13, all_103_4, int, 203.53/126.82 | | simplifying with (92), (183) gives: 203.53/126.82 | | (193) all_103_0 = all_86_13 203.53/126.82 | | 203.53/126.82 | | GROUND_INST: instantiating (38) with all_105_1, all_123_0, all_105_2, int, 203.53/126.82 | | simplifying with (100), (185) gives: 203.53/126.82 | | (194) all_123_0 = all_105_1 203.53/126.82 | | 203.53/126.82 | | GROUND_INST: instantiating (38) with all_105_3, all_117_0, all_105_4, int, 203.53/126.82 | | simplifying with (99), (186) gives: 203.53/126.82 | | (195) all_117_0 = all_105_3 203.53/126.82 | | 203.53/126.82 | | GROUND_INST: instantiating (38) with all_117_0, all_113_1, all_105_4, int, 203.53/126.82 | | simplifying with (186), (188) gives: 203.53/126.82 | | (196) all_117_0 = all_113_1 203.53/126.82 | | 203.53/126.82 | | GROUND_INST: instantiating (38) with all_103_1, all_115_0, all_103_2, int, 203.53/126.82 | | simplifying with (91), (187) gives: 203.53/126.82 | | (197) all_115_0 = all_103_1 203.53/126.82 | | 203.53/126.82 | | GROUND_INST: instantiating (38) with all_115_0, all_113_3, all_103_2, int, 203.53/126.82 | | simplifying with (187), (189) gives: 203.53/126.82 | | (198) all_115_0 = all_113_3 203.53/126.82 | | 203.53/126.82 | | GROUND_INST: instantiating (38) with all_103_3, all_107_0, all_103_4, int, 203.53/126.82 | | simplifying with (90), (190) gives: 203.53/126.82 | | (199) all_107_0 = all_103_3 203.53/126.82 | | 203.53/126.82 | | COMBINE_EQS: (195), (196) imply: 203.53/126.82 | | (200) all_113_1 = all_105_3 203.53/126.82 | | 203.53/126.82 | | COMBINE_EQS: (197), (198) imply: 203.53/126.82 | | (201) all_113_3 = all_103_1 203.53/126.82 | | 203.53/126.82 | | SIMP: (201) implies: 203.53/126.82 | | (202) all_113_3 = all_103_1 203.53/126.82 | | 203.53/126.82 | | REDUCE: (128), (192), (200), (202) imply: 203.53/126.82 | | (203) map_eq_sub1(int, all_103_1, all_105_3, $sum(all_86_8, 1), 203.53/126.82 | | all_86_13) = 0 203.53/126.82 | | 203.53/126.82 | | REDUCE: (127), (200), (202) imply: 203.53/126.82 | | (204) map_eq_sub1(int, all_103_1, all_105_3, 0, all_86_11) = 0 203.53/126.82 | | 203.53/126.82 | | REDUCE: (106), (191) imply: 203.53/126.82 | | (205) map_eq_sub1(int, all_105_3, all_105_1, $sum(all_86_10, 1), 203.53/126.82 | | all_86_13) = 0 203.53/126.82 | | 203.53/126.82 | | REDUCE: (97), (193) imply: 203.53/126.82 | | (206) map_eq_sub1(int, all_103_3, all_103_1, $sum(all_86_10, 1), 203.53/126.82 | | all_86_13) = 0 203.53/126.82 | | 203.53/126.82 | | REDUCE: (147), (194) imply: 203.53/126.82 | | (207) tb2t(all_105_1) = all_86_2 203.53/126.82 | | 203.53/126.82 | | REDUCE: (136), (195) imply: 203.53/126.82 | | (208) tb2t(all_105_3) = all_86_4 203.53/126.82 | | 203.53/126.82 | | REDUCE: (132), (197) imply: 203.53/126.82 | | (209) tb2t(all_103_1) = all_86_6 203.53/126.82 | | 203.53/126.82 | | REDUCE: (111), (199) imply: 203.53/126.82 | | (210) tb2t(all_103_3) = all_86_12 203.53/126.82 | | 203.53/126.82 | | REDUCE: (144), (194) imply: 203.53/126.82 | | (211) in_uni(all_105_1) 203.53/126.82 | | 203.53/126.82 | | REDUCE: (120), (200) imply: 203.53/126.82 | | (212) in_uni(all_105_3) 203.53/126.82 | | 203.53/126.82 | | REDUCE: (119), (202) imply: 203.53/126.82 | | (213) in_uni(all_103_1) 203.53/126.82 | | 203.53/126.82 | | REDUCE: (108), (199) imply: 203.53/126.82 | | (214) in_uni(all_103_3) 203.53/126.82 | | 203.53/126.82 | | GROUND_INST: instantiating (26) with int, all_105_4, all_105_2, all_86_7, 203.53/126.82 | | $sum(all_86_10, 1), simplifying with (31), (104) gives: 203.53/126.83 | | (215) ? [v0: $int] : ? [v1: $int] : ? [v2: $int] : ? [v3: $int] : 203.53/126.83 | | ((v0 = 0 & permut_sub2(int, all_105_4, all_105_2, all_86_7, 203.53/126.83 | | $sum(all_86_10, 1)) = 0) | (elts(int, all_105_2) = v1 & 203.53/126.83 | | elts(int, all_105_4) = v0 & in_uni(v1) & in_uni(v0) & (( ~ (v3 203.53/126.83 | | = 0) & map_eq_sub1(int, v0, v1, $sum(all_86_10, 1), v2) = 203.53/126.83 | | v3 & length1(int, all_105_4) = v2) | ( ~ (v2 = 0) & 203.53/126.83 | | map_eq_sub1(int, v0, v1, 0, all_86_7) = v2)))) 203.53/126.83 | | 203.53/126.83 | | GROUND_INST: instantiating (10) with int, all_105_4, all_105_2, all_86_7, 203.53/126.83 | | $sum(all_86_10, 1), simplifying with (31), (104) gives: 203.53/126.83 | | (216) ? [v0: $int] : ? [v1: $int] : ? [v2: $int] : ($lesseq(all_86_7, 203.53/126.83 | | v0) & $lesseq(1, $difference(v0, all_86_10)) & permut2(int, v1, 203.53/126.83 | | v2, all_86_7, $sum(all_86_10, 1)) = 0 & length1(int, all_105_2) 203.53/126.83 | | = v0 & length1(int, all_105_4) = v0 & elts(int, all_105_2) = v2 & 203.53/126.83 | | elts(int, all_105_4) = v1 & in_uni(v2) & in_uni(v1)) 203.53/126.83 | | 203.53/126.83 | | GROUND_INST: instantiating (27) with int, all_105_4, all_105_2, all_86_7, 203.53/126.83 | | $sum(all_86_10, 1), 0, simplifying with (31), (104) gives: 203.53/126.83 | | (217) ? [v0: $int] : ? [v1: $int] : ? [v2: $int] : ? [v3: $int] : ? 203.53/126.83 | | [v4: $int] : ((v4 = 0 & v3 = 0 & map_eq_sub1(int, v0, v1, 203.53/126.83 | | $sum(all_86_10, 1), v2) = 0 & map_eq_sub1(int, v0, v1, 0, 203.53/126.83 | | all_86_7) = 0 & length1(int, all_105_4) = v2 & elts(int, 203.53/126.83 | | all_105_2) = v1 & elts(int, all_105_4) = v0 & in_uni(v1) & 203.53/126.83 | | in_uni(v0)) | ( ~ (v0 = 0) & permut_sub2(int, all_105_4, 203.53/126.83 | | all_105_2, all_86_7, $sum(all_86_10, 1)) = v0)) 203.53/126.83 | | 203.53/126.83 | | GROUND_INST: instantiating (26) with int, all_103_2, all_105_4, all_86_11, 203.53/126.83 | | $sum(all_86_8, 1), simplifying with (31), (179) gives: 203.53/126.83 | | (218) ? [v0: $int] : ? [v1: $int] : ? [v2: $int] : ? [v3: $int] : 203.53/126.83 | | ((v0 = 0 & permut_sub2(int, all_103_2, all_105_4, all_86_11, 203.53/126.83 | | $sum(all_86_8, 1)) = 0) | (elts(int, all_105_4) = v1 & 203.53/126.83 | | elts(int, all_103_2) = v0 & in_uni(v1) & in_uni(v0) & (( ~ (v3 203.53/126.83 | | = 0) & map_eq_sub1(int, v0, v1, $sum(all_86_8, 1), v2) = 203.53/126.83 | | v3 & length1(int, all_103_2) = v2) | ( ~ (v2 = 0) & 203.53/126.83 | | map_eq_sub1(int, v0, v1, 0, all_86_11) = v2)))) 203.53/126.83 | | 203.53/126.83 | | GROUND_INST: instantiating (10) with int, all_103_2, all_105_4, all_86_11, 203.53/126.83 | | $sum(all_86_8, 1), simplifying with (31), (179) gives: 203.53/126.83 | | (219) ? [v0: $int] : ? [v1: $int] : ? [v2: $int] : ($lesseq(1, 203.53/126.83 | | $difference(v0, all_86_8)) & $lesseq(all_86_11, v0) & 203.53/126.83 | | permut2(int, v1, v2, all_86_11, $sum(all_86_8, 1)) = 0 & 203.53/126.83 | | length1(int, all_105_4) = v0 & length1(int, all_103_2) = v0 & 203.53/126.83 | | elts(int, all_105_4) = v2 & elts(int, all_103_2) = v1 & 203.53/126.83 | | in_uni(v2) & in_uni(v1)) 203.53/126.83 | | 203.53/126.83 | | GROUND_INST: instantiating (27) with int, all_103_2, all_105_4, all_86_11, 203.53/126.83 | | $sum(all_86_8, 1), 0, simplifying with (31), (179) gives: 203.53/126.83 | | (220) ? [v0: $int] : ? [v1: $int] : ? [v2: $int] : ? [v3: $int] : ? 203.53/126.83 | | [v4: $int] : ((v4 = 0 & v3 = 0 & map_eq_sub1(int, v0, v1, 203.53/126.83 | | $sum(all_86_8, 1), v2) = 0 & map_eq_sub1(int, v0, v1, 0, 203.53/126.83 | | all_86_11) = 0 & length1(int, all_103_2) = v2 & elts(int, 203.53/126.83 | | all_105_4) = v1 & elts(int, all_103_2) = v0 & in_uni(v1) & 203.53/126.83 | | in_uni(v0)) | ( ~ (v0 = 0) & permut_sub2(int, all_103_2, 203.53/126.83 | | all_105_4, all_86_11, $sum(all_86_8, 1)) = v0)) 203.53/126.83 | | 203.53/126.83 | | GROUND_INST: instantiating (26) with int, all_103_4, all_103_2, all_86_11, 203.53/126.83 | | $sum(all_86_10, 1), simplifying with (31), (95) gives: 203.53/126.83 | | (221) ? [v0: $int] : ? [v1: $int] : ? [v2: $int] : ? [v3: $int] : 203.53/126.83 | | ((v0 = 0 & permut_sub2(int, all_103_4, all_103_2, all_86_11, 203.53/126.83 | | $sum(all_86_10, 1)) = 0) | (elts(int, all_103_2) = v1 & 203.53/126.83 | | elts(int, all_103_4) = v0 & in_uni(v1) & in_uni(v0) & (( ~ (v3 203.53/126.83 | | = 0) & map_eq_sub1(int, v0, v1, $sum(all_86_10, 1), v2) = 203.53/126.83 | | v3 & length1(int, all_103_4) = v2) | ( ~ (v2 = 0) & 203.53/126.83 | | map_eq_sub1(int, v0, v1, 0, all_86_11) = v2)))) 203.53/126.83 | | 203.53/126.83 | | GROUND_INST: instantiating (10) with int, all_103_4, all_103_2, all_86_11, 203.53/126.83 | | $sum(all_86_10, 1), simplifying with (31), (95) gives: 203.53/126.83 | | (222) ? [v0: $int] : ? [v1: $int] : ? [v2: $int] : ($lesseq(1, 203.53/126.83 | | $difference(v0, all_86_10)) & $lesseq(all_86_11, v0) & 203.53/126.83 | | permut2(int, v1, v2, all_86_11, $sum(all_86_10, 1)) = 0 & 203.53/126.83 | | length1(int, all_103_2) = v0 & length1(int, all_103_4) = v0 & 203.53/126.83 | | elts(int, all_103_2) = v2 & elts(int, all_103_4) = v1 & 203.53/126.83 | | in_uni(v2) & in_uni(v1)) 203.53/126.83 | | 203.53/126.83 | | GROUND_INST: instantiating (27) with int, all_103_4, all_103_2, all_86_11, 203.53/126.83 | | $sum(all_86_10, 1), 0, simplifying with (31), (95) gives: 203.53/126.83 | | (223) ? [v0: $int] : ? [v1: $int] : ? [v2: $int] : ? [v3: $int] : ? 203.53/126.83 | | [v4: $int] : ((v4 = 0 & v3 = 0 & map_eq_sub1(int, v0, v1, 203.53/126.83 | | $sum(all_86_10, 1), v2) = 0 & map_eq_sub1(int, v0, v1, 0, 203.53/126.83 | | all_86_11) = 0 & length1(int, all_103_4) = v2 & elts(int, 203.53/126.83 | | all_103_2) = v1 & elts(int, all_103_4) = v0 & in_uni(v1) & 203.53/126.83 | | in_uni(v0)) | ( ~ (v0 = 0) & permut_sub2(int, all_103_4, 203.53/126.83 | | all_103_2, all_86_11, $sum(all_86_10, 1)) = v0)) 203.53/126.83 | | 203.53/126.83 | | GROUND_INST: instantiating (bridgeR) with all_105_1, all_86_2, simplifying 203.53/126.83 | | with (207), (211) gives: 203.53/126.83 | | (224) t2tb(all_86_2) = all_105_1 203.53/126.83 | | 203.53/126.83 | | GROUND_INST: instantiating (bridgeR) with all_105_3, all_86_4, simplifying 203.53/126.83 | | with (208), (212) gives: 203.53/126.83 | | (225) t2tb(all_86_4) = all_105_3 203.53/126.83 | | 203.53/126.83 | | GROUND_INST: instantiating (bridgeR) with all_103_1, all_86_6, simplifying 203.53/126.83 | | with (209), (213) gives: 203.53/126.83 | | (226) t2tb(all_86_6) = all_103_1 203.53/126.83 | | 203.53/126.83 | | GROUND_INST: instantiating (bridgeR) with all_103_3, all_86_12, simplifying 203.53/126.83 | | with (210), (214) gives: 203.53/126.83 | | (227) t2tb(all_86_12) = all_103_3 203.53/126.83 | | 203.53/126.83 | | GROUND_INST: instantiating (21) with all_86_5, all_86_3, all_86_11, 203.53/126.83 | | $sum(all_86_10, 1), simplifying with (59), (150) gives: 203.53/126.83 | | (228) ? [v0: $int] : ? [v1: $int] : ? [v2: $int] : ? [v3: $int] : ? 203.53/126.83 | | [v4: $int] : (map_eq_sub1(int, v1, v3, $sum(all_86_10, 1), v4) = 0 203.53/126.83 | | & map_eq_sub1(int, v1, v3, 0, all_86_11) = 0 & permut3(int, v0, 203.53/126.83 | | v2, all_86_11, $sum(all_86_10, 1)) = 0 & t2tb2(all_86_3) = v2 & 203.53/126.83 | | t2tb2(all_86_5) = v0 & length1(int, v0) = v4 & elts(int, v2) = v3 203.53/126.83 | | & elts(int, v0) = v1 & in_uni(v3) & in_uni(v2) & in_uni(v1) & 203.53/126.83 | | in_uni(v0)) 203.53/126.83 | | 203.53/126.83 | | GROUND_INST: instantiating (18) with all_86_1, all_105_2, simplifying with 203.53/126.83 | | (61), (103) gives: 203.53/126.83 | | (229) ? [v0: $int] : ? [v1: $int] : ? [v2: $int] : ? [v3: $int] : 203.53/126.83 | | ((v3 = 0 & sorted_sub2(v1, 0, v2) = 0 & tb2t(v0) = v1 & 203.53/126.83 | | length1(int, all_105_2) = v2 & elts(int, all_105_2) = v0 & 203.53/126.83 | | in_map_int_int(v1) & in_uni(v0)) | ( ~ (v0 = 0) & 203.53/126.83 | | sorted1(all_86_1) = v0)) 203.53/126.83 | | 203.53/126.83 | | GROUND_INST: instantiating (17) with all_86_1, all_105_2, simplifying with 203.53/126.83 | | (61), (103) gives: 203.53/126.83 | | (230) ? [v0: $int] : ? [v1: $int] : ? [v2: $int] : ? [v3: $int] : 203.53/126.83 | | ((v0 = 0 & sorted1(all_86_1) = 0) | ( ~ (v3 = 0) & sorted_sub2(v1, 203.53/126.83 | | 0, v2) = v3 & tb2t(v0) = v1 & length1(int, all_105_2) = v2 & 203.53/126.83 | | elts(int, all_105_2) = v0 & in_map_int_int(v1) & in_uni(v0))) 203.53/126.83 | | 203.53/126.83 | | GROUND_INST: instantiating (30) with int, all_105_2, all_86_13, simplifying 203.53/126.83 | | with (31), (181) gives: 203.53/126.83 | | (231) ? [v0: $int] : (mk_array2(int, all_86_13, v0) = all_105_2 & 203.53/126.83 | | elts(int, all_105_2) = v0 & in_uni(v0) & in_uni(all_105_2)) 203.53/126.83 | | 203.53/126.83 | | GROUND_INST: instantiating (30) with int, all_105_4, all_86_13, simplifying 203.53/126.83 | | with (31), (180) gives: 203.53/126.83 | | (232) ? [v0: $int] : (mk_array2(int, all_86_13, v0) = all_105_4 & 203.53/126.83 | | elts(int, all_105_4) = v0 & in_uni(v0) & in_uni(all_105_4)) 203.53/126.83 | | 203.53/126.83 | | GROUND_INST: instantiating (30) with int, all_103_2, all_86_13, simplifying 203.53/126.83 | | with (31), (184) gives: 203.53/126.83 | | (233) ? [v0: $int] : (mk_array2(int, all_86_13, v0) = all_103_2 & 203.53/126.83 | | elts(int, all_103_2) = v0 & in_uni(v0) & in_uni(all_103_2)) 203.53/126.84 | | 203.53/126.84 | | GROUND_INST: instantiating (30) with int, all_103_4, all_86_13, simplifying 203.53/126.84 | | with (31), (183) gives: 203.53/126.84 | | (234) ? [v0: $int] : (mk_array2(int, all_86_13, v0) = all_103_4 & 203.53/126.84 | | elts(int, all_103_4) = v0 & in_uni(v0) & in_uni(all_103_4)) 203.53/126.84 | | 203.53/126.84 | | GROUND_INST: instantiating (29) with int, all_105_2, all_105_1, simplifying 203.53/126.84 | | with (31), (100) gives: 203.53/126.84 | | (235) ? [v0: $int] : (length1(int, all_105_2) = v0 & mk_array2(int, v0, 203.53/126.84 | | all_105_1) = all_105_2 & in_uni(all_105_2)) 203.53/126.84 | | 203.53/126.84 | | GROUND_INST: instantiating (25) with int, all_105_4, all_105_2, 203.53/126.84 | | $sum(all_86_10, 1), all_86_13, all_105_3, all_105_1, 0, 203.53/126.84 | | simplifying with (31), (99), (100), (205) gives: 203.53/126.84 | | (236) ? [v0: $int] : ? [v1: $int] : ((v1 = v0 & $lesseq(1, 203.53/126.84 | | $difference(v0, all_86_10)) & $lesseq(all_86_13, v0) & 203.53/126.84 | | $lesseq(-1, all_86_10) & $lesseq(0, all_86_13) & length1(int, 203.53/126.84 | | all_105_2) = v0 & length1(int, all_105_4) = v0) | ( ~ (v0 = 203.53/126.84 | | 0) & array_eq_sub1(int, all_105_4, all_105_2, $sum(all_86_10, 203.53/126.84 | | 1), all_86_13) = v0)) 203.53/126.84 | | 203.53/126.84 | | GROUND_INST: instantiating (24) with int, all_105_4, all_105_2, 203.53/126.84 | | $sum(all_86_10, 1), all_86_13, all_105_3, all_105_1, 203.53/126.84 | | simplifying with (31), (99), (100), (205) gives: 203.53/126.84 | | (237) ~ ($lesseq(-1, all_86_10)) | ~ ($lesseq(0, all_86_13)) | ? [v0: 203.53/126.84 | | $int] : ? [v1: $int] : ((v0 = 0 & array_eq_sub1(int, all_105_4, 203.53/126.84 | | all_105_2, $sum(all_86_10, 1), all_86_13) = 0) | 203.53/126.84 | | (length1(int, all_105_4) = v0 & ( ~ ($lesseq(1, $difference(v0, 203.53/126.84 | | all_86_10))) | ~ ($lesseq(all_86_13, v0)) | ( ~ (v1 = 203.53/126.84 | | v0) & length1(int, all_105_2) = v1)))) 203.53/126.84 | | 203.53/126.84 | | GROUND_INST: instantiating (25) with int, all_105_4, all_105_2, 0, all_86_7, 203.53/126.84 | | all_105_3, all_105_1, 0, simplifying with (31), (99), (100), 203.53/126.84 | | (105) gives: 203.53/126.84 | | (238) ? [v0: $int] : ? [v1: $int] : ((v1 = v0 & $lesseq(all_86_7, v0) & 203.53/126.84 | | $lesseq(0, v0) & $lesseq(0, all_86_7) & length1(int, all_105_2) 203.53/126.84 | | = v0 & length1(int, all_105_4) = v0) | ( ~ (v0 = 0) & 203.53/126.84 | | array_eq_sub1(int, all_105_4, all_105_2, 0, all_86_7) = v0)) 203.53/126.84 | | 203.53/126.84 | | GROUND_INST: instantiating (24) with int, all_105_4, all_105_2, 0, all_86_7, 203.53/126.84 | | all_105_3, all_105_1, simplifying with (31), (99), (100), (105) 203.53/126.84 | | gives: 203.53/126.85 | | (239) ~ ($lesseq(0, all_86_7)) | ? [v0: $int] : ? [v1: $int] : ((v0 = 203.53/126.85 | | 0 & array_eq_sub1(int, all_105_4, all_105_2, 0, all_86_7) = 0) 203.53/126.85 | | | (length1(int, all_105_4) = v0 & ( ~ ($lesseq(all_86_7, v0)) | 203.53/126.85 | | ~ ($lesseq(0, v0)) | ( ~ (v1 = v0) & length1(int, all_105_2) 203.53/126.85 | | = v1)))) 203.53/126.85 | | 203.53/126.85 | | GROUND_INST: instantiating (15) with int, all_105_4, all_105_2, all_86_13, 203.53/126.85 | | all_105_3, all_105_1, simplifying with (31), (99), (100), (180) 203.53/126.85 | | gives: 203.53/126.85 | | (240) ~ (map_eq_sub1(int, all_105_3, all_105_1, 0, all_86_13) = 0) | ? 203.53/126.85 | | [v0: $int] : ((v0 = 0 & array_eq(int, all_105_4, all_105_2) = 0) | 203.53/126.85 | | ( ~ (v0 = all_86_13) & length1(int, all_105_2) = v0)) 203.53/126.85 | | 203.53/126.85 | | GROUND_INST: instantiating (29) with int, all_105_4, all_105_3, simplifying 203.53/126.85 | | with (31), (99) gives: 203.53/126.85 | | (241) ? [v0: $int] : (length1(int, all_105_4) = v0 & mk_array2(int, v0, 203.53/126.85 | | all_105_3) = all_105_4 & in_uni(all_105_4)) 203.53/126.85 | | 203.53/126.85 | | GROUND_INST: instantiating (25) with int, all_103_2, all_105_4, 203.53/126.85 | | $sum(all_86_8, 1), all_86_13, all_103_1, all_105_3, 0, 203.53/126.85 | | simplifying with (31), (91), (99), (203) gives: 203.53/126.85 | | (242) ? [v0: $int] : ? [v1: $int] : ((v1 = v0 & $lesseq(1, 203.53/126.85 | | $difference(v0, all_86_8)) & $lesseq(all_86_13, v0) & 203.53/126.85 | | $lesseq(-1, all_86_8) & $lesseq(0, all_86_13) & length1(int, 203.53/126.85 | | all_105_4) = v0 & length1(int, all_103_2) = v0) | ( ~ (v0 = 203.53/126.85 | | 0) & array_eq_sub1(int, all_103_2, all_105_4, $sum(all_86_8, 203.53/126.85 | | 1), all_86_13) = v0)) 203.53/126.85 | | 203.53/126.85 | | GROUND_INST: instantiating (24) with int, all_103_2, all_105_4, 203.53/126.85 | | $sum(all_86_8, 1), all_86_13, all_103_1, all_105_3, simplifying 203.53/126.85 | | with (31), (91), (99), (203) gives: 203.53/126.85 | | (243) ~ ($lesseq(-1, all_86_8)) | ~ ($lesseq(0, all_86_13)) | ? [v0: 203.53/126.85 | | $int] : ? [v1: $int] : ((v0 = 0 & array_eq_sub1(int, all_103_2, 203.53/126.85 | | all_105_4, $sum(all_86_8, 1), all_86_13) = 0) | (length1(int, 203.53/126.85 | | all_103_2) = v0 & ( ~ ($lesseq(1, $difference(v0, all_86_8))) 203.53/126.85 | | | ~ ($lesseq(all_86_13, v0)) | ( ~ (v1 = v0) & length1(int, 203.53/126.85 | | all_105_4) = v1)))) 203.53/126.85 | | 203.53/126.85 | | GROUND_INST: instantiating (15) with int, all_103_2, all_105_4, all_86_13, 203.53/126.85 | | all_103_1, all_105_3, simplifying with (31), (91), (99), (184) 203.53/126.85 | | gives: 203.53/126.85 | | (244) ~ (map_eq_sub1(int, all_103_1, all_105_3, 0, all_86_13) = 0) | ? 203.53/126.85 | | [v0: $int] : ((v0 = 0 & array_eq(int, all_103_2, all_105_4) = 0) | 203.53/126.85 | | ( ~ (v0 = all_86_13) & length1(int, all_105_4) = v0)) 203.53/126.85 | | 203.53/126.85 | | GROUND_INST: instantiating (25) with int, all_103_2, all_105_4, 0, 203.53/126.85 | | all_86_11, all_103_1, all_105_3, 0, simplifying with (31), 203.53/126.85 | | (91), (99), (204) gives: 203.53/126.85 | | (245) ? [v0: $int] : ? [v1: $int] : ((v1 = v0 & $lesseq(all_86_11, v0) 203.53/126.85 | | & $lesseq(0, v0) & $lesseq(0, all_86_11) & length1(int, 203.53/126.85 | | all_105_4) = v0 & length1(int, all_103_2) = v0) | ( ~ (v0 = 203.53/126.85 | | 0) & array_eq_sub1(int, all_103_2, all_105_4, 0, all_86_11) = 203.53/126.85 | | v0)) 203.53/126.85 | | 203.53/126.85 | | GROUND_INST: instantiating (24) with int, all_103_2, all_105_4, 0, 203.53/126.85 | | all_86_11, all_103_1, all_105_3, simplifying with (31), (91), 203.53/126.85 | | (99), (204) gives: 203.53/126.85 | | (246) ~ ($lesseq(0, all_86_11)) | ? [v0: $int] : ? [v1: $int] : ((v0 = 203.53/126.85 | | 0 & array_eq_sub1(int, all_103_2, all_105_4, 0, all_86_11) = 0) 203.53/126.85 | | | (length1(int, all_103_2) = v0 & ( ~ ($lesseq(all_86_11, v0)) | 203.53/126.85 | | ~ ($lesseq(0, v0)) | ( ~ (v1 = v0) & length1(int, all_105_4) 203.53/126.85 | | = v1)))) 203.53/126.85 | | 203.53/126.85 | | GROUND_INST: instantiating (29) with int, all_103_2, all_103_1, simplifying 203.53/126.85 | | with (31), (91) gives: 203.53/126.85 | | (247) ? [v0: $int] : (length1(int, all_103_2) = v0 & mk_array2(int, v0, 203.53/126.85 | | all_103_1) = all_103_2 & in_uni(all_103_2)) 203.53/126.85 | | 203.53/126.85 | | GROUND_INST: instantiating (25) with int, all_103_4, all_103_2, 203.53/126.85 | | $sum(all_86_10, 1), all_86_13, all_103_3, all_103_1, 0, 203.53/126.85 | | simplifying with (31), (90), (91), (206) gives: 203.53/126.85 | | (248) ? [v0: $int] : ? [v1: $int] : ((v1 = v0 & $lesseq(1, 203.53/126.85 | | $difference(v0, all_86_10)) & $lesseq(all_86_13, v0) & 203.53/126.85 | | $lesseq(-1, all_86_10) & $lesseq(0, all_86_13) & length1(int, 203.53/126.85 | | all_103_2) = v0 & length1(int, all_103_4) = v0) | ( ~ (v0 = 203.53/126.85 | | 0) & array_eq_sub1(int, all_103_4, all_103_2, $sum(all_86_10, 203.53/126.85 | | 1), all_86_13) = v0)) 203.53/126.85 | | 203.53/126.85 | | GROUND_INST: instantiating (24) with int, all_103_4, all_103_2, 203.53/126.85 | | $sum(all_86_10, 1), all_86_13, all_103_3, all_103_1, 203.53/126.85 | | simplifying with (31), (90), (91), (206) gives: 203.53/126.85 | | (249) ~ ($lesseq(-1, all_86_10)) | ~ ($lesseq(0, all_86_13)) | ? [v0: 203.53/126.85 | | $int] : ? [v1: $int] : ((v0 = 0 & array_eq_sub1(int, all_103_4, 203.53/126.85 | | all_103_2, $sum(all_86_10, 1), all_86_13) = 0) | 203.53/126.85 | | (length1(int, all_103_4) = v0 & ( ~ ($lesseq(1, $difference(v0, 203.53/126.85 | | all_86_10))) | ~ ($lesseq(all_86_13, v0)) | ( ~ (v1 = 203.53/126.85 | | v0) & length1(int, all_103_2) = v1)))) 203.53/126.85 | | 203.53/126.85 | | GROUND_INST: instantiating (25) with int, all_103_4, all_103_2, 0, 203.53/126.85 | | all_86_11, all_103_3, all_103_1, 0, simplifying with (31), 203.53/126.85 | | (90), (91), (96) gives: 203.53/126.85 | | (250) ? [v0: $int] : ? [v1: $int] : ((v1 = v0 & $lesseq(all_86_11, v0) 203.53/126.85 | | & $lesseq(0, v0) & $lesseq(0, all_86_11) & length1(int, 203.53/126.85 | | all_103_2) = v0 & length1(int, all_103_4) = v0) | ( ~ (v0 = 203.53/126.85 | | 0) & array_eq_sub1(int, all_103_4, all_103_2, 0, all_86_11) = 203.53/126.85 | | v0)) 203.53/126.85 | | 203.53/126.85 | | GROUND_INST: instantiating (24) with int, all_103_4, all_103_2, 0, 203.53/126.85 | | all_86_11, all_103_3, all_103_1, simplifying with (31), (90), 203.53/126.85 | | (91), (96) gives: 203.73/126.85 | | (251) ~ ($lesseq(0, all_86_11)) | ? [v0: $int] : ? [v1: $int] : ((v0 = 203.73/126.85 | | 0 & array_eq_sub1(int, all_103_4, all_103_2, 0, all_86_11) = 0) 203.73/126.85 | | | (length1(int, all_103_4) = v0 & ( ~ ($lesseq(all_86_11, v0)) | 203.73/126.85 | | ~ ($lesseq(0, v0)) | ( ~ (v1 = v0) & length1(int, all_103_2) 203.73/126.85 | | = v1)))) 203.73/126.85 | | 203.73/126.85 | | GROUND_INST: instantiating (29) with int, all_103_4, all_103_3, simplifying 203.73/126.85 | | with (31), (90) gives: 203.73/126.85 | | (252) ? [v0: $int] : (length1(int, all_103_4) = v0 & mk_array2(int, v0, 203.73/126.85 | | all_103_3) = all_103_4 & in_uni(all_103_4)) 203.73/126.85 | | 203.73/126.85 | | DELTA: instantiating (241) with fresh symbol all_151_0 gives: 203.73/126.85 | | (253) length1(int, all_105_4) = all_151_0 & mk_array2(int, all_151_0, 203.73/126.85 | | all_105_3) = all_105_4 & in_uni(all_105_4) 203.73/126.85 | | 203.73/126.85 | | ALPHA: (253) implies: 203.73/126.85 | | (254) length1(int, all_105_4) = all_151_0 203.73/126.85 | | 203.73/126.85 | | DELTA: instantiating (236) with fresh symbols all_153_0, all_153_1 gives: 203.73/126.85 | | (255) (all_153_0 = all_153_1 & $lesseq(1, $difference(all_153_1, 203.73/126.85 | | all_86_10)) & $lesseq(all_86_13, all_153_1) & $lesseq(-1, 203.73/126.85 | | all_86_10) & $lesseq(0, all_86_13) & length1(int, all_105_2) = 203.73/126.85 | | all_153_1 & length1(int, all_105_4) = all_153_1) | ( ~ (all_153_1 203.73/126.85 | | = 0) & array_eq_sub1(int, all_105_4, all_105_2, $sum(all_86_10, 203.73/126.85 | | 1), all_86_13) = all_153_1) 203.73/126.85 | | 203.73/126.85 | | DELTA: instantiating (228) with fresh symbols all_156_0, all_156_1, 203.73/126.85 | | all_156_2, all_156_3, all_156_4 gives: 203.73/126.85 | | (256) map_eq_sub1(int, all_156_3, all_156_1, $sum(all_86_10, 1), 203.73/126.85 | | all_156_0) = 0 & map_eq_sub1(int, all_156_3, all_156_1, 0, 203.73/126.85 | | all_86_11) = 0 & permut3(int, all_156_4, all_156_2, all_86_11, 203.73/126.85 | | $sum(all_86_10, 1)) = 0 & t2tb2(all_86_3) = all_156_2 & 203.73/126.85 | | t2tb2(all_86_5) = all_156_4 & length1(int, all_156_4) = all_156_0 & 203.73/126.85 | | elts(int, all_156_2) = all_156_1 & elts(int, all_156_4) = all_156_3 203.73/126.85 | | & in_uni(all_156_1) & in_uni(all_156_2) & in_uni(all_156_3) & 203.73/126.85 | | in_uni(all_156_4) 203.73/126.85 | | 203.73/126.85 | | ALPHA: (256) implies: 203.73/126.85 | | (257) elts(int, all_156_4) = all_156_3 203.73/126.85 | | (258) elts(int, all_156_2) = all_156_1 203.73/126.85 | | (259) length1(int, all_156_4) = all_156_0 203.73/126.85 | | (260) t2tb2(all_86_5) = all_156_4 203.73/126.85 | | (261) t2tb2(all_86_3) = all_156_2 203.73/126.85 | | (262) permut3(int, all_156_4, all_156_2, all_86_11, $sum(all_86_10, 1)) = 203.73/126.85 | | 0 203.73/126.85 | | (263) map_eq_sub1(int, all_156_3, all_156_1, 0, all_86_11) = 0 203.73/126.85 | | (264) map_eq_sub1(int, all_156_3, all_156_1, $sum(all_86_10, 1), 203.73/126.85 | | all_156_0) = 0 203.73/126.85 | | 203.73/126.85 | | DELTA: instantiating (252) with fresh symbol all_160_0 gives: 203.73/126.85 | | (265) length1(int, all_103_4) = all_160_0 & mk_array2(int, all_160_0, 203.73/126.85 | | all_103_3) = all_103_4 & in_uni(all_103_4) 203.73/126.85 | | 203.73/126.85 | | ALPHA: (265) implies: 203.73/126.85 | | (266) length1(int, all_103_4) = all_160_0 203.73/126.85 | | 203.73/126.85 | | DELTA: instantiating (247) with fresh symbol all_164_0 gives: 203.73/126.85 | | (267) length1(int, all_103_2) = all_164_0 & mk_array2(int, all_164_0, 203.73/126.85 | | all_103_1) = all_103_2 & in_uni(all_103_2) 203.73/126.85 | | 203.73/126.85 | | ALPHA: (267) implies: 203.73/126.85 | | (268) length1(int, all_103_2) = all_164_0 203.73/126.85 | | 203.73/126.85 | | DELTA: instantiating (242) with fresh symbols all_168_0, all_168_1 gives: 203.73/126.85 | | (269) (all_168_0 = all_168_1 & $lesseq(1, $difference(all_168_1, 203.73/126.85 | | all_86_8)) & $lesseq(all_86_13, all_168_1) & $lesseq(-1, 203.73/126.85 | | all_86_8) & $lesseq(0, all_86_13) & length1(int, all_105_4) = 203.73/126.85 | | all_168_1 & length1(int, all_103_2) = all_168_1) | ( ~ (all_168_1 203.73/126.85 | | = 0) & array_eq_sub1(int, all_103_2, all_105_4, $sum(all_86_8, 203.73/126.85 | | 1), all_86_13) = all_168_1) 203.73/126.85 | | 203.73/126.85 | | DELTA: instantiating (238) with fresh symbols all_169_0, all_169_1 gives: 203.73/126.85 | | (270) (all_169_0 = all_169_1 & $lesseq(all_86_7, all_169_1) & $lesseq(0, 203.73/126.85 | | all_169_1) & $lesseq(0, all_86_7) & length1(int, all_105_2) = 203.73/126.85 | | all_169_1 & length1(int, all_105_4) = all_169_1) | ( ~ (all_169_1 203.73/126.85 | | = 0) & array_eq_sub1(int, all_105_4, all_105_2, 0, all_86_7) = 203.73/126.85 | | all_169_1) 203.73/126.85 | | 203.73/126.85 | | DELTA: instantiating (245) with fresh symbols all_170_0, all_170_1 gives: 203.73/126.85 | | (271) (all_170_0 = all_170_1 & $lesseq(all_86_11, all_170_1) & $lesseq(0, 203.73/126.85 | | all_170_1) & $lesseq(0, all_86_11) & length1(int, all_105_4) = 203.73/126.85 | | all_170_1 & length1(int, all_103_2) = all_170_1) | ( ~ (all_170_1 203.73/126.85 | | = 0) & array_eq_sub1(int, all_103_2, all_105_4, 0, all_86_11) = 203.73/126.85 | | all_170_1) 203.73/126.85 | | 203.73/126.85 | | DELTA: instantiating (250) with fresh symbols all_171_0, all_171_1 gives: 203.73/126.85 | | (272) (all_171_0 = all_171_1 & $lesseq(all_86_11, all_171_1) & $lesseq(0, 203.73/126.85 | | all_171_1) & $lesseq(0, all_86_11) & length1(int, all_103_2) = 203.73/126.85 | | all_171_1 & length1(int, all_103_4) = all_171_1) | ( ~ (all_171_1 203.73/126.85 | | = 0) & array_eq_sub1(int, all_103_4, all_103_2, 0, all_86_11) = 203.73/126.85 | | all_171_1) 203.73/126.85 | | 203.73/126.85 | | DELTA: instantiating (222) with fresh symbols all_172_0, all_172_1, 203.73/126.85 | | all_172_2 gives: 203.73/126.85 | | (273) $lesseq(1, $difference(all_172_2, all_86_10)) & $lesseq(all_86_11, 203.73/126.85 | | all_172_2) & permut2(int, all_172_1, all_172_0, all_86_11, 203.73/126.85 | | $sum(all_86_10, 1)) = 0 & length1(int, all_103_2) = all_172_2 & 203.73/126.85 | | length1(int, all_103_4) = all_172_2 & elts(int, all_103_2) = 203.73/126.85 | | all_172_0 & elts(int, all_103_4) = all_172_1 & in_uni(all_172_0) & 203.73/126.85 | | in_uni(all_172_1) 203.73/126.85 | | 203.73/126.85 | | ALPHA: (273) implies: 203.73/126.85 | | (274) $lesseq(1, $difference(all_172_2, all_86_10)) 203.73/126.85 | | (275) elts(int, all_103_4) = all_172_1 203.73/126.85 | | (276) elts(int, all_103_2) = all_172_0 203.73/126.85 | | (277) length1(int, all_103_4) = all_172_2 203.73/126.85 | | (278) length1(int, all_103_2) = all_172_2 203.73/126.85 | | (279) permut2(int, all_172_1, all_172_0, all_86_11, $sum(all_86_10, 1)) = 203.73/126.85 | | 0 203.73/126.85 | | 203.73/126.85 | | DELTA: instantiating (220) with fresh symbols all_177_0, all_177_1, 203.73/126.85 | | all_177_2, all_177_3, all_177_4 gives: 203.73/126.85 | | (280) (all_177_0 = 0 & all_177_1 = 0 & map_eq_sub1(int, all_177_4, 203.73/126.85 | | all_177_3, $sum(all_86_8, 1), all_177_2) = 0 & map_eq_sub1(int, 203.73/126.85 | | all_177_4, all_177_3, 0, all_86_11) = 0 & length1(int, 203.73/126.85 | | all_103_2) = all_177_2 & elts(int, all_105_4) = all_177_3 & 203.73/126.85 | | elts(int, all_103_2) = all_177_4 & in_uni(all_177_3) & 203.73/126.85 | | in_uni(all_177_4)) | ( ~ (all_177_4 = 0) & permut_sub2(int, 203.73/126.85 | | all_103_2, all_105_4, all_86_11, $sum(all_86_8, 1)) = 203.73/126.85 | | all_177_4) 203.73/126.85 | | 203.73/126.85 | | DELTA: instantiating (219) with fresh symbols all_178_0, all_178_1, 203.73/126.85 | | all_178_2 gives: 203.73/126.85 | | (281) $lesseq(1, $difference(all_178_2, all_86_8)) & $lesseq(all_86_11, 203.73/126.85 | | all_178_2) & permut2(int, all_178_1, all_178_0, all_86_11, 203.73/126.85 | | $sum(all_86_8, 1)) = 0 & length1(int, all_105_4) = all_178_2 & 203.73/126.85 | | length1(int, all_103_2) = all_178_2 & elts(int, all_105_4) = 203.73/126.85 | | all_178_0 & elts(int, all_103_2) = all_178_1 & in_uni(all_178_0) & 203.73/126.85 | | in_uni(all_178_1) 203.73/126.85 | | 203.73/126.85 | | ALPHA: (281) implies: 203.73/126.85 | | (282) elts(int, all_103_2) = all_178_1 203.73/126.85 | | (283) elts(int, all_105_4) = all_178_0 203.73/126.85 | | (284) length1(int, all_103_2) = all_178_2 203.73/126.85 | | (285) length1(int, all_105_4) = all_178_2 203.73/126.85 | | (286) permut2(int, all_178_1, all_178_0, all_86_11, $sum(all_86_8, 1)) = 203.73/126.85 | | 0 203.73/126.85 | | 203.73/126.85 | | DELTA: instantiating (218) with fresh symbols all_181_0, all_181_1, 203.73/126.85 | | all_181_2, all_181_3 gives: 203.73/126.85 | | (287) (all_181_3 = 0 & permut_sub2(int, all_103_2, all_105_4, all_86_11, 203.73/126.85 | | $sum(all_86_8, 1)) = 0) | (elts(int, all_105_4) = all_181_2 & 203.73/126.85 | | elts(int, all_103_2) = all_181_3 & in_uni(all_181_2) & 203.73/126.85 | | in_uni(all_181_3) & (( ~ (all_181_0 = 0) & map_eq_sub1(int, 203.73/126.85 | | all_181_3, all_181_2, $sum(all_86_8, 1), all_181_1) = 203.73/126.85 | | all_181_0 & length1(int, all_103_2) = all_181_1) | ( ~ 203.73/126.85 | | (all_181_1 = 0) & map_eq_sub1(int, all_181_3, all_181_2, 0, 203.73/126.85 | | all_86_11) = all_181_1))) 203.73/126.85 | | 203.73/126.85 | | DELTA: instantiating (216) with fresh symbols all_184_0, all_184_1, 203.73/126.85 | | all_184_2 gives: 203.73/126.85 | | (288) $lesseq(all_86_7, all_184_2) & $lesseq(1, $difference(all_184_2, 203.73/126.85 | | all_86_10)) & permut2(int, all_184_1, all_184_0, all_86_7, 203.73/126.85 | | $sum(all_86_10, 1)) = 0 & length1(int, all_105_2) = all_184_2 & 203.73/126.85 | | length1(int, all_105_4) = all_184_2 & elts(int, all_105_2) = 203.73/126.85 | | all_184_0 & elts(int, all_105_4) = all_184_1 & in_uni(all_184_0) & 203.73/126.85 | | in_uni(all_184_1) 203.73/126.85 | | 203.73/126.85 | | ALPHA: (288) implies: 203.73/126.85 | | (289) $lesseq(all_86_7, all_184_2) 203.73/126.85 | | (290) elts(int, all_105_4) = all_184_1 203.73/126.86 | | (291) elts(int, all_105_2) = all_184_0 203.73/126.86 | | (292) length1(int, all_105_2) = all_184_2 203.73/126.86 | | (293) permut2(int, all_184_1, all_184_0, all_86_7, $sum(all_86_10, 1)) = 203.73/126.86 | | 0 203.73/126.86 | | 203.73/126.86 | | DELTA: instantiating (215) with fresh symbols all_187_0, all_187_1, 203.73/126.86 | | all_187_2, all_187_3 gives: 203.73/126.86 | | (294) (all_187_3 = 0 & permut_sub2(int, all_105_4, all_105_2, all_86_7, 203.73/126.86 | | $sum(all_86_10, 1)) = 0) | (elts(int, all_105_2) = all_187_2 & 203.73/126.86 | | elts(int, all_105_4) = all_187_3 & in_uni(all_187_2) & 203.73/126.86 | | in_uni(all_187_3) & (( ~ (all_187_0 = 0) & map_eq_sub1(int, 203.73/126.86 | | all_187_3, all_187_2, $sum(all_86_10, 1), all_187_1) = 203.73/126.86 | | all_187_0 & length1(int, all_105_4) = all_187_1) | ( ~ 203.73/126.86 | | (all_187_1 = 0) & map_eq_sub1(int, all_187_3, all_187_2, 0, 203.73/126.86 | | all_86_7) = all_187_1))) 203.73/126.86 | | 203.73/126.86 | | DELTA: instantiating (217) with fresh symbols all_190_0, all_190_1, 203.73/126.86 | | all_190_2, all_190_3, all_190_4 gives: 203.73/126.86 | | (295) (all_190_0 = 0 & all_190_1 = 0 & map_eq_sub1(int, all_190_4, 203.73/126.86 | | all_190_3, $sum(all_86_10, 1), all_190_2) = 0 & 203.73/126.86 | | map_eq_sub1(int, all_190_4, all_190_3, 0, all_86_7) = 0 & 203.73/126.86 | | length1(int, all_105_4) = all_190_2 & elts(int, all_105_2) = 203.73/126.86 | | all_190_3 & elts(int, all_105_4) = all_190_4 & in_uni(all_190_3) 203.73/126.86 | | & in_uni(all_190_4)) | ( ~ (all_190_4 = 0) & permut_sub2(int, 203.73/126.86 | | all_105_4, all_105_2, all_86_7, $sum(all_86_10, 1)) = 203.73/126.86 | | all_190_4) 203.73/126.86 | | 203.73/126.86 | | DELTA: instantiating (221) with fresh symbols all_191_0, all_191_1, 203.73/126.86 | | all_191_2, all_191_3 gives: 203.73/126.86 | | (296) (all_191_3 = 0 & permut_sub2(int, all_103_4, all_103_2, all_86_11, 203.73/126.86 | | $sum(all_86_10, 1)) = 0) | (elts(int, all_103_2) = all_191_2 & 203.73/126.86 | | elts(int, all_103_4) = all_191_3 & in_uni(all_191_2) & 203.73/126.86 | | in_uni(all_191_3) & (( ~ (all_191_0 = 0) & map_eq_sub1(int, 203.73/126.86 | | all_191_3, all_191_2, $sum(all_86_10, 1), all_191_1) = 203.73/126.86 | | all_191_0 & length1(int, all_103_4) = all_191_1) | ( ~ 203.73/126.86 | | (all_191_1 = 0) & map_eq_sub1(int, all_191_3, all_191_2, 0, 203.73/126.86 | | all_86_11) = all_191_1))) 203.73/126.86 | | 203.73/126.86 | | DELTA: instantiating (223) with fresh symbols all_192_0, all_192_1, 203.73/126.86 | | all_192_2, all_192_3, all_192_4 gives: 203.73/126.86 | | (297) (all_192_0 = 0 & all_192_1 = 0 & map_eq_sub1(int, all_192_4, 203.73/126.86 | | all_192_3, $sum(all_86_10, 1), all_192_2) = 0 & 203.73/126.86 | | map_eq_sub1(int, all_192_4, all_192_3, 0, all_86_11) = 0 & 203.73/126.86 | | length1(int, all_103_4) = all_192_2 & elts(int, all_103_2) = 203.73/126.86 | | all_192_3 & elts(int, all_103_4) = all_192_4 & in_uni(all_192_3) 203.73/126.86 | | & in_uni(all_192_4)) | ( ~ (all_192_4 = 0) & permut_sub2(int, 203.73/126.86 | | all_103_4, all_103_2, all_86_11, $sum(all_86_10, 1)) = 203.73/126.86 | | all_192_4) 203.73/126.86 | | 203.73/126.86 | | DELTA: instantiating (248) with fresh symbols all_193_0, all_193_1 gives: 203.73/126.86 | | (298) (all_193_0 = all_193_1 & $lesseq(1, $difference(all_193_1, 203.73/126.86 | | all_86_10)) & $lesseq(all_86_13, all_193_1) & $lesseq(-1, 203.73/126.86 | | all_86_10) & $lesseq(0, all_86_13) & length1(int, all_103_2) = 203.73/126.86 | | all_193_1 & length1(int, all_103_4) = all_193_1) | ( ~ (all_193_1 203.73/126.86 | | = 0) & array_eq_sub1(int, all_103_4, all_103_2, $sum(all_86_10, 203.73/126.86 | | 1), all_86_13) = all_193_1) 203.73/126.86 | | 203.73/126.86 | | DELTA: instantiating (234) with fresh symbol all_194_0 gives: 203.73/126.86 | | (299) mk_array2(int, all_86_13, all_194_0) = all_103_4 & elts(int, 203.73/126.86 | | all_103_4) = all_194_0 & in_uni(all_194_0) & in_uni(all_103_4) 203.73/126.86 | | 203.73/126.86 | | ALPHA: (299) implies: 203.73/126.86 | | (300) elts(int, all_103_4) = all_194_0 203.73/126.86 | | 203.73/126.86 | | DELTA: instantiating (233) with fresh symbol all_196_0 gives: 203.73/126.86 | | (301) mk_array2(int, all_86_13, all_196_0) = all_103_2 & elts(int, 203.73/126.86 | | all_103_2) = all_196_0 & in_uni(all_196_0) & in_uni(all_103_2) 203.73/126.86 | | 203.73/126.86 | | ALPHA: (301) implies: 203.73/126.86 | | (302) elts(int, all_103_2) = all_196_0 203.73/126.86 | | 203.73/126.86 | | DELTA: instantiating (235) with fresh symbol all_198_0 gives: 203.73/126.86 | | (303) length1(int, all_105_2) = all_198_0 & mk_array2(int, all_198_0, 203.73/126.86 | | all_105_1) = all_105_2 & in_uni(all_105_2) 203.73/126.86 | | 203.73/126.86 | | ALPHA: (303) implies: 203.73/126.86 | | (304) length1(int, all_105_2) = all_198_0 203.73/126.86 | | 203.73/126.86 | | DELTA: instantiating (230) with fresh symbols all_200_0, all_200_1, 203.73/126.86 | | all_200_2, all_200_3 gives: 203.73/126.86 | | (305) (all_200_3 = 0 & sorted1(all_86_1) = 0) | ( ~ (all_200_0 = 0) & 203.73/126.86 | | sorted_sub2(all_200_2, 0, all_200_1) = all_200_0 & 203.73/126.86 | | tb2t(all_200_3) = all_200_2 & length1(int, all_105_2) = all_200_1 203.73/126.86 | | & elts(int, all_105_2) = all_200_3 & in_map_int_int(all_200_2) & 203.73/126.86 | | in_uni(all_200_3)) 203.73/126.86 | | 203.73/126.86 | | DELTA: instantiating (232) with fresh symbol all_201_0 gives: 203.73/126.86 | | (306) mk_array2(int, all_86_13, all_201_0) = all_105_4 & elts(int, 203.73/126.86 | | all_105_4) = all_201_0 & in_uni(all_201_0) & in_uni(all_105_4) 203.73/126.86 | | 203.73/126.86 | | ALPHA: (306) implies: 203.73/126.86 | | (307) elts(int, all_105_4) = all_201_0 203.73/126.86 | | 203.73/126.86 | | DELTA: instantiating (231) with fresh symbol all_203_0 gives: 203.73/126.86 | | (308) mk_array2(int, all_86_13, all_203_0) = all_105_2 & elts(int, 203.73/126.86 | | all_105_2) = all_203_0 & in_uni(all_203_0) & in_uni(all_105_2) 203.73/126.86 | | 203.73/126.86 | | ALPHA: (308) implies: 203.73/126.86 | | (309) elts(int, all_105_2) = all_203_0 203.73/126.86 | | 203.73/126.86 | | DELTA: instantiating (229) with fresh symbols all_205_0, all_205_1, 203.73/126.86 | | all_205_2, all_205_3 gives: 203.73/126.86 | | (310) (all_205_0 = 0 & sorted_sub2(all_205_2, 0, all_205_1) = 0 & 203.73/126.86 | | tb2t(all_205_3) = all_205_2 & length1(int, all_105_2) = all_205_1 203.73/126.86 | | & elts(int, all_105_2) = all_205_3 & in_map_int_int(all_205_2) & 203.73/126.86 | | in_uni(all_205_3)) | ( ~ (all_205_3 = 0) & sorted1(all_86_1) = 203.73/126.86 | | all_205_3) 203.73/126.86 | | 203.73/126.86 | | BETA: splitting (246) gives: 203.73/126.86 | | 203.73/126.86 | | Case 1: 203.73/126.86 | | | 203.73/126.86 | | | (311) $lesseq(all_86_11, -1) 203.73/126.86 | | | 203.73/126.86 | | | COMBINE_INEQS: (48), (311) imply: 203.73/126.86 | | | (312) $lesseq(0, -1) 203.73/126.86 | | | 203.73/126.86 | | | CLOSE: (312) is inconsistent. 203.73/126.86 | | | 203.73/126.86 | | Case 2: 203.73/126.86 | | | 203.73/126.86 | | | (313) ? [v0: $int] : ? [v1: $int] : ((v0 = 0 & array_eq_sub1(int, 203.73/126.86 | | | all_103_2, all_105_4, 0, all_86_11) = 0) | (length1(int, 203.73/126.86 | | | all_103_2) = v0 & ( ~ ($lesseq(all_86_11, v0)) | ~ 203.73/126.86 | | | ($lesseq(0, v0)) | ( ~ (v1 = v0) & length1(int, all_105_4) 203.73/126.86 | | | = v1)))) 203.73/126.86 | | | 203.73/126.86 | | | DELTA: instantiating (313) with fresh symbols all_211_0, all_211_1 gives: 203.73/126.86 | | | (314) (all_211_1 = 0 & array_eq_sub1(int, all_103_2, all_105_4, 0, 203.73/126.86 | | | all_86_11) = 0) | (length1(int, all_103_2) = all_211_1 & ( ~ 203.73/126.86 | | | ($lesseq(all_86_11, all_211_1)) | ~ ($lesseq(0, all_211_1)) 203.73/126.86 | | | | ( ~ (all_211_0 = all_211_1) & length1(int, all_105_4) = 203.73/126.86 | | | all_211_0))) 203.73/126.86 | | | 203.73/126.86 | | | BETA: splitting (251) gives: 203.73/126.86 | | | 203.73/126.86 | | | Case 1: 203.73/126.86 | | | | 203.73/126.86 | | | | (315) $lesseq(all_86_11, -1) 203.73/126.86 | | | | 203.73/126.86 | | | | COMBINE_INEQS: (48), (315) imply: 203.73/126.86 | | | | (316) $lesseq(0, -1) 203.73/126.86 | | | | 203.73/126.86 | | | | CLOSE: (316) is inconsistent. 203.73/126.86 | | | | 203.73/126.86 | | | Case 2: 203.73/126.86 | | | | 203.73/126.86 | | | | (317) ? [v0: $int] : ? [v1: $int] : ((v0 = 0 & array_eq_sub1(int, 203.73/126.86 | | | | all_103_4, all_103_2, 0, all_86_11) = 0) | (length1(int, 203.73/126.86 | | | | all_103_4) = v0 & ( ~ ($lesseq(all_86_11, v0)) | ~ 203.73/126.86 | | | | ($lesseq(0, v0)) | ( ~ (v1 = v0) & length1(int, 203.73/126.86 | | | | all_103_2) = v1)))) 203.73/126.86 | | | | 203.73/126.86 | | | | COMBINE_INEQS: (48), (75) imply: 203.73/126.86 | | | | (318) $lesseq(2, all_86_13) 203.73/126.86 | | | | 203.73/126.86 | | | | DELTA: instantiating (317) with fresh symbols all_215_0, all_215_1 203.73/126.86 | | | | gives: 203.73/126.86 | | | | (319) (all_215_1 = 0 & array_eq_sub1(int, all_103_4, all_103_2, 0, 203.73/126.86 | | | | all_86_11) = 0) | (length1(int, all_103_4) = all_215_1 & ( 203.73/126.86 | | | | ~ ($lesseq(all_86_11, all_215_1)) | ~ ($lesseq(0, 203.73/126.86 | | | | all_215_1)) | ( ~ (all_215_0 = all_215_1) & 203.73/126.86 | | | | length1(int, all_103_2) = all_215_0))) 203.73/126.86 | | | | 203.73/126.86 | | | | BETA: splitting (239) gives: 203.73/126.86 | | | | 203.73/126.86 | | | | Case 1: 203.73/126.86 | | | | | 203.73/126.86 | | | | | (320) $lesseq(all_86_7, -1) 203.73/126.86 | | | | | 203.73/126.86 | | | | | COMBINE_INEQS: (51), (320) imply: 203.73/126.86 | | | | | (321) $lesseq(0, -1) 203.73/126.86 | | | | | 203.73/126.86 | | | | | CLOSE: (321) is inconsistent. 203.73/126.86 | | | | | 203.73/126.86 | | | | Case 2: 203.73/126.86 | | | | | 203.73/126.86 | | | | | (322) ? [v0: $int] : ? [v1: $int] : ((v0 = 0 & array_eq_sub1(int, 203.73/126.86 | | | | | all_105_4, all_105_2, 0, all_86_7) = 0) | (length1(int, 203.73/126.86 | | | | | all_105_4) = v0 & ( ~ ($lesseq(all_86_7, v0)) | ~ 203.73/126.86 | | | | | ($lesseq(0, v0)) | ( ~ (v1 = v0) & length1(int, 203.73/126.86 | | | | | all_105_2) = v1)))) 203.73/126.86 | | | | | 203.73/126.86 | | | | | COMBINE_INEQS: (51), (53) imply: 203.73/126.86 | | | | | (323) $lesseq(0, all_86_10) 203.73/126.86 | | | | | 203.73/126.86 | | | | | DELTA: instantiating (322) with fresh symbols all_219_0, all_219_1 203.73/126.86 | | | | | gives: 203.73/126.86 | | | | | (324) (all_219_1 = 0 & array_eq_sub1(int, all_105_4, all_105_2, 0, 203.73/126.86 | | | | | all_86_7) = 0) | (length1(int, all_105_4) = all_219_1 & ( 203.73/126.86 | | | | | ~ ($lesseq(all_86_7, all_219_1)) | ~ ($lesseq(0, 203.73/126.86 | | | | | all_219_1)) | ( ~ (all_219_0 = all_219_1) & 203.73/126.86 | | | | | length1(int, all_105_2) = all_219_0))) 203.73/126.86 | | | | | 203.73/126.86 | | | | | BETA: splitting (237) gives: 203.73/126.86 | | | | | 203.73/126.86 | | | | | Case 1: 203.73/126.86 | | | | | | 203.73/126.86 | | | | | | (325) $lesseq(all_86_13, -1) 203.73/126.86 | | | | | | 203.73/126.86 | | | | | | COMBINE_INEQS: (318), (325) imply: 203.73/126.86 | | | | | | (326) $lesseq(0, -1) 203.73/126.86 | | | | | | 203.73/126.86 | | | | | | CLOSE: (326) is inconsistent. 203.73/126.86 | | | | | | 203.73/126.86 | | | | | Case 2: 203.73/126.86 | | | | | | 203.78/126.87 | | | | | | (327) ~ ($lesseq(-1, all_86_10)) | ? [v0: $int] : ? [v1: $int] 203.78/126.87 | | | | | | : ((v0 = 0 & array_eq_sub1(int, all_105_4, all_105_2, 203.78/126.87 | | | | | | $sum(all_86_10, 1), all_86_13) = 0) | (length1(int, 203.78/126.87 | | | | | | all_105_4) = v0 & ( ~ ($lesseq(1, $difference(v0, 203.78/126.87 | | | | | | all_86_10))) | ~ ($lesseq(all_86_13, v0)) | ( 203.78/126.87 | | | | | | ~ (v1 = v0) & length1(int, all_105_2) = v1)))) 203.78/126.87 | | | | | | 203.78/126.87 | | | | | | BETA: splitting (249) gives: 203.78/126.87 | | | | | | 203.78/126.87 | | | | | | Case 1: 203.78/126.87 | | | | | | | 203.78/126.87 | | | | | | | (328) $lesseq(all_86_13, -1) 203.78/126.87 | | | | | | | 203.78/126.87 | | | | | | | COMBINE_INEQS: (318), (328) imply: 203.78/126.87 | | | | | | | (329) $lesseq(0, -1) 203.78/126.87 | | | | | | | 203.78/126.87 | | | | | | | CLOSE: (329) is inconsistent. 203.78/126.87 | | | | | | | 203.78/126.87 | | | | | | Case 2: 203.78/126.87 | | | | | | | 203.78/126.87 | | | | | | | (330) ~ ($lesseq(-1, all_86_10)) | ? [v0: $int] : ? [v1: 203.78/126.87 | | | | | | | $int] : ((v0 = 0 & array_eq_sub1(int, all_103_4, 203.78/126.87 | | | | | | | all_103_2, $sum(all_86_10, 1), all_86_13) = 0) | 203.78/126.87 | | | | | | | (length1(int, all_103_4) = v0 & ( ~ ($lesseq(1, 203.78/126.87 | | | | | | | $difference(v0, all_86_10))) | ~ 203.78/126.87 | | | | | | | ($lesseq(all_86_13, v0)) | ( ~ (v1 = v0) & 203.78/126.87 | | | | | | | length1(int, all_103_2) = v1)))) 203.78/126.87 | | | | | | | 203.78/126.87 | | | | | | | BETA: splitting (243) gives: 203.78/126.87 | | | | | | | 203.78/126.87 | | | | | | | Case 1: 203.78/126.87 | | | | | | | | 203.78/126.87 | | | | | | | | (331) $lesseq(all_86_13, -1) 203.78/126.87 | | | | | | | | 203.78/126.87 | | | | | | | | COMBINE_INEQS: (318), (331) imply: 203.78/126.87 | | | | | | | | (332) $lesseq(0, -1) 203.78/126.87 | | | | | | | | 203.78/126.87 | | | | | | | | CLOSE: (332) is inconsistent. 203.78/126.87 | | | | | | | | 203.78/126.87 | | | | | | | Case 2: 203.78/126.87 | | | | | | | | 203.78/126.87 | | | | | | | | (333) ~ ($lesseq(-1, all_86_8)) | ? [v0: $int] : ? [v1: 203.78/126.87 | | | | | | | | $int] : ((v0 = 0 & array_eq_sub1(int, all_103_2, 203.78/126.87 | | | | | | | | all_105_4, $sum(all_86_8, 1), all_86_13) = 0) | 203.78/126.87 | | | | | | | | (length1(int, all_103_2) = v0 & ( ~ ($lesseq(1, 203.78/126.87 | | | | | | | | $difference(v0, all_86_8))) | ~ 203.78/126.87 | | | | | | | | ($lesseq(all_86_13, v0)) | ( ~ (v1 = v0) & 203.78/126.87 | | | | | | | | length1(int, all_105_4) = v1)))) 203.78/126.87 | | | | | | | | 203.78/126.87 | | | | | | | | BETA: splitting (327) gives: 203.78/126.87 | | | | | | | | 203.78/126.87 | | | | | | | | Case 1: 203.78/126.87 | | | | | | | | | 203.78/126.87 | | | | | | | | | (334) $lesseq(all_86_10, -2) 203.78/126.87 | | | | | | | | | 203.78/126.87 | | | | | | | | | COMBINE_INEQS: (323), (334) imply: 203.78/126.87 | | | | | | | | | (335) $lesseq(0, -1) 203.78/126.87 | | | | | | | | | 203.78/126.87 | | | | | | | | | CLOSE: (335) is inconsistent. 203.78/126.87 | | | | | | | | | 203.78/126.87 | | | | | | | | Case 2: 203.78/126.87 | | | | | | | | | 203.78/126.87 | | | | | | | | | (336) ? [v0: $int] : ? [v1: $int] : ((v0 = 0 & 203.78/126.87 | | | | | | | | | array_eq_sub1(int, all_105_4, all_105_2, 203.78/126.87 | | | | | | | | | $sum(all_86_10, 1), all_86_13) = 0) | 203.78/126.87 | | | | | | | | | (length1(int, all_105_4) = v0 & ( ~ ($lesseq(1, 203.78/126.87 | | | | | | | | | $difference(v0, all_86_10))) | ~ 203.78/126.87 | | | | | | | | | ($lesseq(all_86_13, v0)) | ( ~ (v1 = v0) & 203.78/126.87 | | | | | | | | | length1(int, all_105_2) = v1)))) 203.78/126.87 | | | | | | | | | 203.78/126.87 | | | | | | | | | DELTA: instantiating (336) with fresh symbols all_234_0, 203.78/126.87 | | | | | | | | | all_234_1 gives: 203.78/126.87 | | | | | | | | | (337) (all_234_1 = 0 & array_eq_sub1(int, all_105_4, 203.78/126.87 | | | | | | | | | all_105_2, $sum(all_86_10, 1), all_86_13) = 0) | 203.78/126.87 | | | | | | | | | (length1(int, all_105_4) = all_234_1 & ( ~ 203.78/126.87 | | | | | | | | | ($lesseq(1, $difference(all_234_1, all_86_10))) | 203.78/126.87 | | | | | | | | | ~ ($lesseq(all_86_13, all_234_1)) | ( ~ 203.78/126.87 | | | | | | | | | (all_234_0 = all_234_1) & length1(int, 203.78/126.87 | | | | | | | | | all_105_2) = all_234_0))) 203.78/126.87 | | | | | | | | | 203.78/126.87 | | | | | | | | | BETA: splitting (330) gives: 203.78/126.87 | | | | | | | | | 203.78/126.87 | | | | | | | | | Case 1: 203.78/126.87 | | | | | | | | | | 203.78/126.87 | | | | | | | | | | (338) $lesseq(all_86_10, -2) 203.78/126.87 | | | | | | | | | | 203.78/126.87 | | | | | | | | | | COMBINE_INEQS: (323), (338) imply: 203.78/126.87 | | | | | | | | | | (339) $lesseq(0, -1) 203.78/126.87 | | | | | | | | | | 203.78/126.87 | | | | | | | | | | CLOSE: (339) is inconsistent. 203.78/126.87 | | | | | | | | | | 203.78/126.87 | | | | | | | | | Case 2: 203.78/126.87 | | | | | | | | | | 203.78/126.87 | | | | | | | | | | (340) ? [v0: $int] : ? [v1: $int] : ((v0 = 0 & 203.78/126.87 | | | | | | | | | | array_eq_sub1(int, all_103_4, all_103_2, 203.78/126.87 | | | | | | | | | | $sum(all_86_10, 1), all_86_13) = 0) | 203.78/126.87 | | | | | | | | | | (length1(int, all_103_4) = v0 & ( ~ ($lesseq(1, 203.78/126.87 | | | | | | | | | | $difference(v0, all_86_10))) | ~ 203.78/126.87 | | | | | | | | | | ($lesseq(all_86_13, v0)) | ( ~ (v1 = v0) & 203.78/126.87 | | | | | | | | | | length1(int, all_103_2) = v1)))) 203.78/126.87 | | | | | | | | | | 203.78/126.87 | | | | | | | | | | DELTA: instantiating (340) with fresh symbols all_238_0, 203.78/126.87 | | | | | | | | | | all_238_1 gives: 203.78/126.87 | | | | | | | | | | (341) (all_238_1 = 0 & array_eq_sub1(int, all_103_4, 203.78/126.87 | | | | | | | | | | all_103_2, $sum(all_86_10, 1), all_86_13) = 0) 203.78/126.87 | | | | | | | | | | | (length1(int, all_103_4) = all_238_1 & ( ~ 203.78/126.87 | | | | | | | | | | ($lesseq(1, $difference(all_238_1, all_86_10))) 203.78/126.87 | | | | | | | | | | | ~ ($lesseq(all_86_13, all_238_1)) | ( ~ 203.78/126.87 | | | | | | | | | | (all_238_0 = all_238_1) & length1(int, 203.78/126.87 | | | | | | | | | | all_103_2) = all_238_0))) 203.78/126.87 | | | | | | | | | | 203.78/126.87 | | | | | | | | | | BETA: splitting (333) gives: 203.78/126.87 | | | | | | | | | | 203.78/126.87 | | | | | | | | | | Case 1: 203.78/126.87 | | | | | | | | | | | 203.78/126.87 | | | | | | | | | | | (342) $lesseq(all_86_8, -2) 203.78/126.87 | | | | | | | | | | | 203.78/126.87 | | | | | | | | | | | COMBINE_INEQS: (156), (342) imply: 203.78/126.87 | | | | | | | | | | | (343) $lesseq(0, -1) 203.78/126.87 | | | | | | | | | | | 203.78/126.87 | | | | | | | | | | | CLOSE: (343) is inconsistent. 203.78/126.87 | | | | | | | | | | | 203.78/126.87 | | | | | | | | | | Case 2: 203.78/126.87 | | | | | | | | | | | 203.78/126.87 | | | | | | | | | | | (344) ? [v0: $int] : ? [v1: $int] : ((v0 = 0 & 203.78/126.87 | | | | | | | | | | | array_eq_sub1(int, all_103_2, all_105_4, 203.78/126.87 | | | | | | | | | | | $sum(all_86_8, 1), all_86_13) = 0) | 203.78/126.87 | | | | | | | | | | | (length1(int, all_103_2) = v0 & ( ~ ($lesseq(1, 203.78/126.87 | | | | | | | | | | | $difference(v0, all_86_8))) | ~ 203.78/126.87 | | | | | | | | | | | ($lesseq(all_86_13, v0)) | ( ~ (v1 = v0) & 203.78/126.87 | | | | | | | | | | | length1(int, all_105_4) = v1)))) 203.78/126.87 | | | | | | | | | | | 203.78/126.87 | | | | | | | | | | | DELTA: instantiating (344) with fresh symbols all_242_0, 203.78/126.87 | | | | | | | | | | | all_242_1 gives: 203.78/126.87 | | | | | | | | | | | (345) (all_242_1 = 0 & array_eq_sub1(int, all_103_2, 203.78/126.87 | | | | | | | | | | | all_105_4, $sum(all_86_8, 1), all_86_13) = 0) 203.78/126.87 | | | | | | | | | | | | (length1(int, all_103_2) = all_242_1 & ( ~ 203.78/126.87 | | | | | | | | | | | ($lesseq(1, $difference(all_242_1, all_86_8))) 203.78/126.87 | | | | | | | | | | | | ~ ($lesseq(all_86_13, all_242_1)) | ( ~ 203.78/126.87 | | | | | | | | | | | (all_242_0 = all_242_1) & length1(int, 203.78/126.87 | | | | | | | | | | | all_105_4) = all_242_0))) 203.78/126.87 | | | | | | | | | | | 203.78/126.87 | | | | | | | | | | | GROUND_INST: instantiating (34) with all_105_4, all_156_2, 203.78/126.87 | | | | | | | | | | | all_86_3, simplifying with (102), (261) gives: 203.78/126.87 | | | | | | | | | | | (346) all_156_2 = all_105_4 203.78/126.87 | | | | | | | | | | | 203.78/126.87 | | | | | | | | | | | GROUND_INST: instantiating (34) with all_103_2, all_156_4, 203.78/126.87 | | | | | | | | | | | all_86_5, simplifying with (94), (260) gives: 203.78/126.87 | | | | | | | | | | | (347) all_156_4 = all_103_2 203.78/126.87 | | | | | | | | | | | 203.78/126.87 | | | | | | | | | | | GROUND_INST: instantiating (39) with all_86_13, all_198_0, 203.78/126.87 | | | | | | | | | | | all_105_2, int, simplifying with (181), (304) 203.78/126.87 | | | | | | | | | | | gives: 203.78/126.87 | | | | | | | | | | | (348) all_198_0 = all_86_13 203.78/126.87 | | | | | | | | | | | 203.78/126.87 | | | | | | | | | | | GROUND_INST: instantiating (39) with all_198_0, all_184_2, 203.78/126.87 | | | | | | | | | | | all_105_2, int, simplifying with (292), (304) 203.78/126.87 | | | | | | | | | | | gives: 203.78/126.87 | | | | | | | | | | | (349) all_198_0 = all_184_2 203.78/126.87 | | | | | | | | | | | 203.78/126.87 | | | | | | | | | | | GROUND_INST: instantiating (39) with all_178_2, all_151_0, 203.78/126.87 | | | | | | | | | | | all_105_4, int, simplifying with (254), (285) 203.78/126.87 | | | | | | | | | | | gives: 203.78/126.87 | | | | | | | | | | | (350) all_178_2 = all_151_0 203.78/126.87 | | | | | | | | | | | 203.78/126.87 | | | | | | | | | | | GROUND_INST: instantiating (39) with all_178_2, all_172_2, 203.78/126.87 | | | | | | | | | | | all_103_2, int, simplifying with (278), (284) 203.78/126.87 | | | | | | | | | | | gives: 203.78/126.87 | | | | | | | | | | | (351) all_178_2 = all_172_2 203.78/126.87 | | | | | | | | | | | 203.78/126.87 | | | | | | | | | | | GROUND_INST: instantiating (39) with all_178_2, all_164_0, 203.78/126.87 | | | | | | | | | | | all_103_2, int, simplifying with (268), (284) 203.78/126.87 | | | | | | | | | | | gives: 203.78/126.87 | | | | | | | | | | | (352) all_178_2 = all_164_0 203.78/126.87 | | | | | | | | | | | 203.78/126.87 | | | | | | | | | | | GROUND_INST: instantiating (39) with all_86_13, all_172_2, 203.78/126.87 | | | | | | | | | | | all_103_4, int, simplifying with (183), (277) 203.78/126.87 | | | | | | | | | | | gives: 203.78/126.87 | | | | | | | | | | | (353) all_172_2 = all_86_13 203.78/126.87 | | | | | | | | | | | 203.78/126.87 | | | | | | | | | | | GROUND_INST: instantiating (39) with all_172_2, all_160_0, 203.78/126.87 | | | | | | | | | | | all_103_4, int, simplifying with (266), (277) 203.78/126.87 | | | | | | | | | | | gives: 203.78/126.87 | | | | | | | | | | | (354) all_172_2 = all_160_0 203.78/126.87 | | | | | | | | | | | 203.78/126.88 | | | | | | | | | | | GROUND_INST: instantiating (38) with all_105_1, all_203_0, 203.78/126.88 | | | | | | | | | | | all_105_2, int, simplifying with (100), (309) 203.78/126.88 | | | | | | | | | | | gives: 203.78/126.88 | | | | | | | | | | | (355) all_203_0 = all_105_1 203.78/126.88 | | | | | | | | | | | 203.78/126.88 | | | | | | | | | | | GROUND_INST: instantiating (38) with all_203_0, all_184_0, 203.78/126.88 | | | | | | | | | | | all_105_2, int, simplifying with (291), (309) 203.78/126.88 | | | | | | | | | | | gives: 203.78/126.88 | | | | | | | | | | | (356) all_203_0 = all_184_0 203.78/126.88 | | | | | | | | | | | 203.78/126.88 | | | | | | | | | | | GROUND_INST: instantiating (38) with all_105_3, all_201_0, 203.78/126.88 | | | | | | | | | | | all_105_4, int, simplifying with (99), (307) 203.78/126.88 | | | | | | | | | | | gives: 203.78/126.88 | | | | | | | | | | | (357) all_201_0 = all_105_3 203.78/126.88 | | | | | | | | | | | 203.78/126.88 | | | | | | | | | | | GROUND_INST: instantiating (38) with all_201_0, all_184_1, 203.78/126.88 | | | | | | | | | | | all_105_4, int, simplifying with (290), (307) 203.78/126.88 | | | | | | | | | | | gives: 203.78/126.88 | | | | | | | | | | | (358) all_201_0 = all_184_1 203.78/126.88 | | | | | | | | | | | 203.78/126.88 | | | | | | | | | | | GROUND_INST: instantiating (38) with all_201_0, all_178_0, 203.78/126.88 | | | | | | | | | | | all_105_4, int, simplifying with (283), (307) 203.78/126.88 | | | | | | | | | | | gives: 203.78/126.88 | | | | | | | | | | | (359) all_201_0 = all_178_0 203.78/126.88 | | | | | | | | | | | 203.78/126.88 | | | | | | | | | | | GROUND_INST: instantiating (38) with all_103_1, all_196_0, 203.78/126.88 | | | | | | | | | | | all_103_2, int, simplifying with (91), (302) 203.78/126.88 | | | | | | | | | | | gives: 203.78/126.88 | | | | | | | | | | | (360) all_196_0 = all_103_1 203.78/126.88 | | | | | | | | | | | 203.78/126.88 | | | | | | | | | | | GROUND_INST: instantiating (38) with all_196_0, all_178_1, 203.78/126.88 | | | | | | | | | | | all_103_2, int, simplifying with (282), (302) 203.78/126.88 | | | | | | | | | | | gives: 203.78/126.88 | | | | | | | | | | | (361) all_196_0 = all_178_1 203.78/126.88 | | | | | | | | | | | 203.78/126.88 | | | | | | | | | | | GROUND_INST: instantiating (38) with all_196_0, all_172_0, 203.78/126.88 | | | | | | | | | | | all_103_2, int, simplifying with (276), (302) 203.78/126.88 | | | | | | | | | | | gives: 203.78/126.88 | | | | | | | | | | | (362) all_196_0 = all_172_0 203.78/126.88 | | | | | | | | | | | 203.78/126.88 | | | | | | | | | | | GROUND_INST: instantiating (38) with all_103_3, all_194_0, 203.78/126.88 | | | | | | | | | | | all_103_4, int, simplifying with (90), (300) 203.78/126.88 | | | | | | | | | | | gives: 203.78/126.88 | | | | | | | | | | | (363) all_194_0 = all_103_3 203.78/126.88 | | | | | | | | | | | 203.78/126.88 | | | | | | | | | | | GROUND_INST: instantiating (38) with all_194_0, all_172_1, 203.78/126.88 | | | | | | | | | | | all_103_4, int, simplifying with (275), (300) 203.78/126.88 | | | | | | | | | | | gives: 203.78/126.88 | | | | | | | | | | | (364) all_194_0 = all_172_1 203.78/126.88 | | | | | | | | | | | 203.78/126.88 | | | | | | | | | | | COMBINE_EQS: (355), (356) imply: 203.78/126.88 | | | | | | | | | | | (365) all_184_0 = all_105_1 203.78/126.88 | | | | | | | | | | | 203.78/126.88 | | | | | | | | | | | SIMP: (365) implies: 203.78/126.88 | | | | | | | | | | | (366) all_184_0 = all_105_1 203.78/126.88 | | | | | | | | | | | 203.78/126.88 | | | | | | | | | | | COMBINE_EQS: (358), (359) imply: 203.78/126.88 | | | | | | | | | | | (367) all_184_1 = all_178_0 203.78/126.88 | | | | | | | | | | | 203.78/126.88 | | | | | | | | | | | COMBINE_EQS: (357), (358) imply: 203.78/126.88 | | | | | | | | | | | (368) all_184_1 = all_105_3 203.78/126.88 | | | | | | | | | | | 203.78/126.88 | | | | | | | | | | | COMBINE_EQS: (348), (349) imply: 203.78/126.88 | | | | | | | | | | | (369) all_184_2 = all_86_13 203.78/126.88 | | | | | | | | | | | 203.78/126.88 | | | | | | | | | | | SIMP: (369) implies: 203.78/126.88 | | | | | | | | | | | (370) all_184_2 = all_86_13 203.78/126.88 | | | | | | | | | | | 203.78/126.88 | | | | | | | | | | | COMBINE_EQS: (360), (361) imply: 203.78/126.88 | | | | | | | | | | | (371) all_178_1 = all_103_1 203.78/126.88 | | | | | | | | | | | 203.78/126.88 | | | | | | | | | | | COMBINE_EQS: (361), (362) imply: 203.78/126.88 | | | | | | | | | | | (372) all_178_1 = all_172_0 203.78/126.88 | | | | | | | | | | | 203.78/126.88 | | | | | | | | | | | COMBINE_EQS: (363), (364) imply: 203.78/126.88 | | | | | | | | | | | (373) all_172_1 = all_103_3 203.78/126.88 | | | | | | | | | | | 203.78/126.88 | | | | | | | | | | | COMBINE_EQS: (367), (368) imply: 203.78/126.88 | | | | | | | | | | | (374) all_178_0 = all_105_3 203.78/126.88 | | | | | | | | | | | 203.78/126.88 | | | | | | | | | | | SIMP: (374) implies: 203.78/126.88 | | | | | | | | | | | (375) all_178_0 = all_105_3 203.78/126.88 | | | | | | | | | | | 203.78/126.88 | | | | | | | | | | | COMBINE_EQS: (371), (372) imply: 203.78/126.88 | | | | | | | | | | | (376) all_172_0 = all_103_1 203.78/126.88 | | | | | | | | | | | 203.78/126.88 | | | | | | | | | | | SIMP: (376) implies: 203.78/126.88 | | | | | | | | | | | (377) all_172_0 = all_103_1 203.78/126.88 | | | | | | | | | | | 203.78/126.88 | | | | | | | | | | | COMBINE_EQS: (350), (352) imply: 203.78/126.88 | | | | | | | | | | | (378) all_164_0 = all_151_0 203.78/126.88 | | | | | | | | | | | 203.78/126.88 | | | | | | | | | | | COMBINE_EQS: (351), (352) imply: 203.78/126.88 | | | | | | | | | | | (379) all_172_2 = all_164_0 203.78/126.88 | | | | | | | | | | | 203.78/126.88 | | | | | | | | | | | SIMP: (379) implies: 203.78/126.88 | | | | | | | | | | | (380) all_172_2 = all_164_0 203.78/126.88 | | | | | | | | | | | 203.78/126.88 | | | | | | | | | | | COMBINE_EQS: (353), (354) imply: 203.78/126.88 | | | | | | | | | | | (381) all_160_0 = all_86_13 203.78/126.88 | | | | | | | | | | | 203.78/126.88 | | | | | | | | | | | COMBINE_EQS: (354), (380) imply: 203.78/126.88 | | | | | | | | | | | (382) all_164_0 = all_160_0 203.78/126.88 | | | | | | | | | | | 203.78/126.88 | | | | | | | | | | | SIMP: (382) implies: 203.78/126.88 | | | | | | | | | | | (383) all_164_0 = all_160_0 203.78/126.88 | | | | | | | | | | | 203.78/126.88 | | | | | | | | | | | COMBINE_EQS: (378), (383) imply: 203.78/126.88 | | | | | | | | | | | (384) all_160_0 = all_151_0 203.78/126.88 | | | | | | | | | | | 203.78/126.88 | | | | | | | | | | | SIMP: (384) implies: 203.78/126.88 | | | | | | | | | | | (385) all_160_0 = all_151_0 203.78/126.88 | | | | | | | | | | | 203.78/126.88 | | | | | | | | | | | COMBINE_EQS: (381), (385) imply: 203.78/126.88 | | | | | | | | | | | (386) all_151_0 = all_86_13 203.78/126.88 | | | | | | | | | | | 203.78/126.88 | | | | | | | | | | | SIMP: (386) implies: 203.78/126.88 | | | | | | | | | | | (387) all_151_0 = all_86_13 203.78/126.88 | | | | | | | | | | | 203.78/126.88 | | | | | | | | | | | COMBINE_EQS: (378), (387) imply: 203.78/126.88 | | | | | | | | | | | (388) all_164_0 = all_86_13 203.78/126.88 | | | | | | | | | | | 203.78/126.88 | | | | | | | | | | | REDUCE: (289), (370) imply: 203.78/126.88 | | | | | | | | | | | (389) $lesseq(all_86_7, all_86_13) 203.78/126.88 | | | | | | | | | | | 203.78/126.88 | | | | | | | | | | | REDUCE: (262), (346), (347) imply: 203.78/126.88 | | | | | | | | | | | (390) permut3(int, all_103_2, all_105_4, all_86_11, 203.78/126.88 | | | | | | | | | | | $sum(all_86_10, 1)) = 0 203.78/126.88 | | | | | | | | | | | 203.78/126.88 | | | | | | | | | | | REDUCE: (293), (366), (368) imply: 203.78/126.88 | | | | | | | | | | | (391) permut2(int, all_105_3, all_105_1, all_86_7, 203.78/126.88 | | | | | | | | | | | $sum(all_86_10, 1)) = 0 203.78/126.88 | | | | | | | | | | | 203.78/126.88 | | | | | | | | | | | REDUCE: (286), (371), (375) imply: 203.78/126.88 | | | | | | | | | | | (392) permut2(int, all_103_1, all_105_3, all_86_11, 203.78/126.88 | | | | | | | | | | | $sum(all_86_8, 1)) = 0 203.78/126.88 | | | | | | | | | | | 203.78/126.88 | | | | | | | | | | | REDUCE: (279), (373), (377) imply: 203.78/126.88 | | | | | | | | | | | (393) permut2(int, all_103_3, all_103_1, all_86_11, 203.78/126.88 | | | | | | | | | | | $sum(all_86_10, 1)) = 0 203.78/126.88 | | | | | | | | | | | 203.78/126.88 | | | | | | | | | | | REDUCE: (259), (347) imply: 203.78/126.88 | | | | | | | | | | | (394) length1(int, all_103_2) = all_156_0 203.78/126.88 | | | | | | | | | | | 203.78/126.88 | | | | | | | | | | | REDUCE: (258), (346) imply: 203.78/126.88 | | | | | | | | | | | (395) elts(int, all_105_4) = all_156_1 203.78/126.88 | | | | | | | | | | | 203.78/126.88 | | | | | | | | | | | REDUCE: (257), (347) imply: 203.78/126.88 | | | | | | | | | | | (396) elts(int, all_103_2) = all_156_3 203.78/126.88 | | | | | | | | | | | 203.78/126.88 | | | | | | | | | | | BETA: splitting (314) gives: 203.78/126.88 | | | | | | | | | | | 203.78/126.88 | | | | | | | | | | | Case 1: 203.78/126.88 | | | | | | | | | | | | 203.78/126.88 | | | | | | | | | | | | (397) all_211_1 = 0 & array_eq_sub1(int, all_103_2, 203.78/126.88 | | | | | | | | | | | | all_105_4, 0, all_86_11) = 0 203.78/126.88 | | | | | | | | | | | | 203.78/126.88 | | | | | | | | | | | | ALPHA: (397) implies: 203.78/126.88 | | | | | | | | | | | | (398) array_eq_sub1(int, all_103_2, all_105_4, 0, 203.78/126.88 | | | | | | | | | | | | all_86_11) = 0 203.78/126.88 | | | | | | | | | | | | 203.78/126.88 | | | | | | | | | | | | BETA: splitting (341) gives: 203.78/126.88 | | | | | | | | | | | | 203.78/126.88 | | | | | | | | | | | | Case 1: 203.78/126.88 | | | | | | | | | | | | | 203.78/126.88 | | | | | | | | | | | | | (399) all_238_1 = 0 & array_eq_sub1(int, all_103_4, 203.78/126.88 | | | | | | | | | | | | | all_103_2, $sum(all_86_10, 1), all_86_13) = 0 203.78/126.88 | | | | | | | | | | | | | 203.78/126.88 | | | | | | | | | | | | | ALPHA: (399) implies: 203.78/126.88 | | | | | | | | | | | | | (400) array_eq_sub1(int, all_103_4, all_103_2, 203.78/126.88 | | | | | | | | | | | | | $sum(all_86_10, 1), all_86_13) = 0 203.78/126.88 | | | | | | | | | | | | | 203.78/126.88 | | | | | | | | | | | | | BETA: splitting (287) gives: 203.78/126.88 | | | | | | | | | | | | | 203.78/126.88 | | | | | | | | | | | | | Case 1: 203.78/126.88 | | | | | | | | | | | | | | 203.78/126.88 | | | | | | | | | | | | | | (401) all_181_3 = 0 & permut_sub2(int, all_103_2, 203.78/126.88 | | | | | | | | | | | | | | all_105_4, all_86_11, $sum(all_86_8, 1)) = 0 203.78/126.88 | | | | | | | | | | | | | | 203.78/126.88 | | | | | | | | | | | | | | ALPHA: (401) implies: 203.78/126.88 | | | | | | | | | | | | | | (402) permut_sub2(int, all_103_2, all_105_4, all_86_11, 203.78/126.88 | | | | | | | | | | | | | | $sum(all_86_8, 1)) = 0 203.78/126.88 | | | | | | | | | | | | | | 203.78/126.88 | | | | | | | | | | | | | | BETA: splitting (280) gives: 203.78/126.88 | | | | | | | | | | | | | | 203.78/126.88 | | | | | | | | | | | | | | Case 1: 203.78/126.88 | | | | | | | | | | | | | | | 203.78/126.89 | | | | | | | | | | | | | | | (403) all_177_0 = 0 & all_177_1 = 0 & map_eq_sub1(int, 203.78/126.89 | | | | | | | | | | | | | | | all_177_4, all_177_3, $sum(all_86_8, 1), 203.78/126.89 | | | | | | | | | | | | | | | all_177_2) = 0 & map_eq_sub1(int, all_177_4, 203.78/126.89 | | | | | | | | | | | | | | | all_177_3, 0, all_86_11) = 0 & length1(int, 203.78/126.89 | | | | | | | | | | | | | | | all_103_2) = all_177_2 & elts(int, all_105_4) = 203.78/126.89 | | | | | | | | | | | | | | | all_177_3 & elts(int, all_103_2) = all_177_4 & 203.78/126.89 | | | | | | | | | | | | | | | in_uni(all_177_3) & in_uni(all_177_4) 203.78/126.89 | | | | | | | | | | | | | | | 203.78/126.89 | | | | | | | | | | | | | | | ALPHA: (403) implies: 203.78/126.89 | | | | | | | | | | | | | | | (404) elts(int, all_103_2) = all_177_4 203.78/126.89 | | | | | | | | | | | | | | | (405) elts(int, all_105_4) = all_177_3 203.78/126.89 | | | | | | | | | | | | | | | (406) length1(int, all_103_2) = all_177_2 203.78/126.89 | | | | | | | | | | | | | | | (407) map_eq_sub1(int, all_177_4, all_177_3, 203.78/126.89 | | | | | | | | | | | | | | | $sum(all_86_8, 1), all_177_2) = 0 203.78/126.89 | | | | | | | | | | | | | | | 203.78/126.89 | | | | | | | | | | | | | | | BETA: splitting (271) gives: 203.78/126.89 | | | | | | | | | | | | | | | 203.78/126.89 | | | | | | | | | | | | | | | Case 1: 203.78/126.89 | | | | | | | | | | | | | | | | 203.78/126.89 | | | | | | | | | | | | | | | | (408) all_170_0 = all_170_1 & $lesseq(all_86_11, 203.78/126.89 | | | | | | | | | | | | | | | | all_170_1) & $lesseq(0, all_170_1) & $lesseq(0, 203.78/126.89 | | | | | | | | | | | | | | | | all_86_11) & length1(int, all_105_4) = all_170_1 203.78/126.89 | | | | | | | | | | | | | | | | & length1(int, all_103_2) = all_170_1 203.78/126.89 | | | | | | | | | | | | | | | | 203.78/126.89 | | | | | | | | | | | | | | | | ALPHA: (408) implies: 203.78/126.89 | | | | | | | | | | | | | | | | (409) length1(int, all_103_2) = all_170_1 203.78/126.89 | | | | | | | | | | | | | | | | (410) length1(int, all_105_4) = all_170_1 203.78/126.89 | | | | | | | | | | | | | | | | 203.78/126.89 | | | | | | | | | | | | | | | | BETA: splitting (337) gives: 203.78/126.89 | | | | | | | | | | | | | | | | 203.78/126.89 | | | | | | | | | | | | | | | | Case 1: 203.78/126.89 | | | | | | | | | | | | | | | | | 203.78/126.89 | | | | | | | | | | | | | | | | | (411) all_234_1 = 0 & array_eq_sub1(int, all_105_4, 203.78/126.89 | | | | | | | | | | | | | | | | | all_105_2, $sum(all_86_10, 1), all_86_13) = 0 203.78/126.89 | | | | | | | | | | | | | | | | | 203.78/126.89 | | | | | | | | | | | | | | | | | ALPHA: (411) implies: 203.78/126.89 | | | | | | | | | | | | | | | | | (412) array_eq_sub1(int, all_105_4, all_105_2, 203.78/126.89 | | | | | | | | | | | | | | | | | $sum(all_86_10, 1), all_86_13) = 0 203.78/126.89 | | | | | | | | | | | | | | | | | 203.78/126.89 | | | | | | | | | | | | | | | | | BETA: splitting (255) gives: 203.78/126.89 | | | | | | | | | | | | | | | | | 203.78/126.89 | | | | | | | | | | | | | | | | | Case 1: 203.78/126.89 | | | | | | | | | | | | | | | | | | 203.78/126.89 | | | | | | | | | | | | | | | | | | (413) all_153_0 = all_153_1 & $lesseq(1, 203.78/126.89 | | | | | | | | | | | | | | | | | | $difference(all_153_1, all_86_10)) & 203.78/126.89 | | | | | | | | | | | | | | | | | | $lesseq(all_86_13, all_153_1) & $lesseq(-1, 203.78/126.89 | | | | | | | | | | | | | | | | | | all_86_10) & $lesseq(0, all_86_13) & 203.78/126.89 | | | | | | | | | | | | | | | | | | length1(int, all_105_2) = all_153_1 & length1(int, 203.78/126.89 | | | | | | | | | | | | | | | | | | all_105_4) = all_153_1 203.78/126.89 | | | | | | | | | | | | | | | | | | 203.78/126.89 | | | | | | | | | | | | | | | | | | ALPHA: (413) implies: 203.78/126.89 | | | | | | | | | | | | | | | | | | (414) $lesseq(1, $difference(all_153_1, all_86_10)) 203.78/126.89 | | | | | | | | | | | | | | | | | | (415) length1(int, all_105_4) = all_153_1 203.78/126.89 | | | | | | | | | | | | | | | | | | (416) length1(int, all_105_2) = all_153_1 203.78/126.89 | | | | | | | | | | | | | | | | | | 203.78/126.89 | | | | | | | | | | | | | | | | | | BETA: splitting (298) gives: 203.78/126.89 | | | | | | | | | | | | | | | | | | 203.78/126.89 | | | | | | | | | | | | | | | | | | Case 1: 203.78/126.89 | | | | | | | | | | | | | | | | | | | 203.78/126.89 | | | | | | | | | | | | | | | | | | | (417) all_193_0 = all_193_1 & $lesseq(1, 203.78/126.89 | | | | | | | | | | | | | | | | | | | $difference(all_193_1, all_86_10)) & 203.78/126.89 | | | | | | | | | | | | | | | | | | | $lesseq(all_86_13, all_193_1) & $lesseq(-1, 203.78/126.89 | | | | | | | | | | | | | | | | | | | all_86_10) & $lesseq(0, all_86_13) & 203.78/126.89 | | | | | | | | | | | | | | | | | | | length1(int, all_103_2) = all_193_1 & length1(int, 203.78/126.89 | | | | | | | | | | | | | | | | | | | all_103_4) = all_193_1 203.78/126.89 | | | | | | | | | | | | | | | | | | | 203.78/126.89 | | | | | | | | | | | | | | | | | | | ALPHA: (417) implies: 203.78/126.89 | | | | | | | | | | | | | | | | | | | (418) length1(int, all_103_4) = all_193_1 203.78/126.89 | | | | | | | | | | | | | | | | | | | (419) length1(int, all_103_2) = all_193_1 203.78/126.89 | | | | | | | | | | | | | | | | | | | 203.78/126.89 | | | | | | | | | | | | | | | | | | | BETA: splitting (296) gives: 203.78/126.89 | | | | | | | | | | | | | | | | | | | 203.78/126.89 | | | | | | | | | | | | | | | | | | | Case 1: 203.78/126.89 | | | | | | | | | | | | | | | | | | | | 203.78/126.89 | | | | | | | | | | | | | | | | | | | | (420) all_191_3 = 0 & permut_sub2(int, all_103_4, 203.78/126.89 | | | | | | | | | | | | | | | | | | | | all_103_2, all_86_11, $sum(all_86_10, 1)) = 0 203.78/126.89 | | | | | | | | | | | | | | | | | | | | 203.78/126.89 | | | | | | | | | | | | | | | | | | | | ALPHA: (420) implies: 203.78/126.89 | | | | | | | | | | | | | | | | | | | | (421) permut_sub2(int, all_103_4, all_103_2, all_86_11, 203.78/126.89 | | | | | | | | | | | | | | | | | | | | $sum(all_86_10, 1)) = 0 203.78/126.89 | | | | | | | | | | | | | | | | | | | | 203.78/126.89 | | | | | | | | | | | | | | | | | | | | BETA: splitting (294) gives: 203.78/126.89 | | | | | | | | | | | | | | | | | | | | 203.78/126.89 | | | | | | | | | | | | | | | | | | | | Case 1: 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | (422) all_187_3 = 0 & permut_sub2(int, all_105_4, 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | all_105_2, all_86_7, $sum(all_86_10, 1)) = 0 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | ALPHA: (422) implies: 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | (423) permut_sub2(int, all_105_4, all_105_2, all_86_7, 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | $sum(all_86_10, 1)) = 0 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (295) gives: 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | Case 1: 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | (424) all_190_0 = 0 & all_190_1 = 0 & map_eq_sub1(int, 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | all_190_4, all_190_3, $sum(all_86_10, 1), 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | all_190_2) = 0 & map_eq_sub1(int, all_190_4, 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | all_190_3, 0, all_86_7) = 0 & length1(int, 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | all_105_4) = all_190_2 & elts(int, all_105_2) = 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | all_190_3 & elts(int, all_105_4) = all_190_4 & 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | in_uni(all_190_3) & in_uni(all_190_4) 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (424) implies: 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | (425) elts(int, all_105_4) = all_190_4 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | (426) elts(int, all_105_2) = all_190_3 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | (427) length1(int, all_105_4) = all_190_2 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | (428) map_eq_sub1(int, all_190_4, all_190_3, 0, 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | all_86_7) = 0 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | (429) map_eq_sub1(int, all_190_4, all_190_3, 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | $sum(all_86_10, 1), all_190_2) = 0 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (297) gives: 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | Case 1: 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | (430) all_192_0 = 0 & all_192_1 = 0 & map_eq_sub1(int, 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | all_192_4, all_192_3, $sum(all_86_10, 1), 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | all_192_2) = 0 & map_eq_sub1(int, all_192_4, 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | all_192_3, 0, all_86_11) = 0 & length1(int, 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | all_103_4) = all_192_2 & elts(int, all_103_2) = 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | all_192_3 & elts(int, all_103_4) = all_192_4 & 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | in_uni(all_192_3) & in_uni(all_192_4) 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (430) implies: 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | (431) elts(int, all_103_4) = all_192_4 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | (432) elts(int, all_103_2) = all_192_3 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | (433) length1(int, all_103_4) = all_192_2 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | (434) map_eq_sub1(int, all_192_4, all_192_3, 0, 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | all_86_11) = 0 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | (435) map_eq_sub1(int, all_192_4, all_192_3, 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | $sum(all_86_10, 1), all_192_2) = 0 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (324) gives: 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | Case 1: 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | | 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | | (436) all_219_1 = 0 & array_eq_sub1(int, all_105_4, 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | | all_105_2, 0, all_86_7) = 0 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | | 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (436) implies: 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | | (437) array_eq_sub1(int, all_105_4, all_105_2, 0, 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | | all_86_7) = 0 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | | 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (270) gives: 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | | 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | | | 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | | | (438) all_169_0 = all_169_1 & $lesseq(all_86_7, 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | | | all_169_1) & $lesseq(0, all_169_1) & $lesseq(0, 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | | | all_86_7) & length1(int, all_105_2) = all_169_1 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | | | & length1(int, all_105_4) = all_169_1 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | | | 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (438) implies: 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | | | (439) $lesseq(all_86_7, all_169_1) 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | | | (440) length1(int, all_105_4) = all_169_1 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | | | 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (319) gives: 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | | | 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | | | | 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | | | | (441) all_215_1 = 0 & array_eq_sub1(int, all_103_4, 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, 0, all_86_11) = 0 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | | | | 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (441) implies: 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | | | | (442) array_eq_sub1(int, all_103_4, all_103_2, 0, 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | | | | all_86_11) = 0 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | | | | 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (345) gives: 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | | | | 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | (443) all_242_1 = 0 & array_eq_sub1(int, all_103_2, 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, $sum(all_86_8, 1), all_86_13) = 0 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (443) implies: 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | (444) array_eq_sub1(int, all_103_2, all_105_4, 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | $sum(all_86_8, 1), all_86_13) = 0 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (269) gives: 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (445) all_168_0 = all_168_1 & $lesseq(1, 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $difference(all_168_1, all_86_8)) & 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $lesseq(all_86_13, all_168_1) & $lesseq(-1, 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_86_8) & $lesseq(0, all_86_13) & length1(int, 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4) = all_168_1 & length1(int, all_103_2) 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_168_1 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (445) implies: 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (446) length1(int, all_103_2) = all_168_1 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (447) length1(int, all_105_4) = all_168_1 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (272) gives: 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (448) all_171_0 = all_171_1 & $lesseq(all_86_11, 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_171_1) & $lesseq(0, all_171_1) & $lesseq(0, 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_86_11) & length1(int, all_103_2) = all_171_1 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & length1(int, all_103_4) = all_171_1 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (448) implies: 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (449) length1(int, all_103_4) = all_171_1 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (450) length1(int, all_103_2) = all_171_1 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_190_2, all_170_1, 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (410), (427) 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (451) all_190_2 = all_170_1 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_190_2, all_169_1, 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (427), (440) 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (452) all_190_2 = all_169_1 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_190_2, all_168_1, 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (427), (447) 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (453) all_190_2 = all_168_1 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_168_1, all_153_1, 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (415), (447) 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (454) all_168_1 = all_153_1 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_86_13, all_177_2, 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (184), (406) 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (455) all_177_2 = all_86_13 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_177_2, all_171_1, 203.78/126.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (406), (450) 203.78/126.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 203.78/126.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (456) all_177_2 = all_171_1 203.78/126.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.78/126.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_171_1, all_170_1, 203.78/126.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (409), (450) 203.78/126.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 203.78/126.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (457) all_171_1 = all_170_1 203.78/126.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.78/126.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_193_1, all_168_1, 203.78/126.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (419), (446) 203.78/126.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 203.78/126.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (458) all_193_1 = all_168_1 203.78/126.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.78/126.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_193_1, all_156_0, 203.78/126.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (394), (419) 203.78/126.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 203.78/126.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (459) all_193_1 = all_156_0 203.78/126.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.78/126.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_193_1, all_192_2, 203.78/126.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (418), (433) 203.78/126.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 203.78/126.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (460) all_193_1 = all_192_2 203.78/126.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.78/126.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_105_1, all_190_3, 203.78/126.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_2, int, simplifying with (100), (426) 203.78/126.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 203.78/126.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (461) all_190_3 = all_105_1 203.78/126.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.78/126.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_105_3, all_190_4, 203.78/126.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (99), (425) 203.78/126.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 203.78/126.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (462) all_190_4 = all_105_3 203.78/126.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.78/126.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_190_4, all_177_3, 203.78/126.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (405), (425) 203.78/126.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 203.78/126.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (463) all_190_4 = all_177_3 203.78/126.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.78/126.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_177_3, all_156_1, 203.78/126.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (395), (405) 203.78/126.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 203.78/126.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (464) all_177_3 = all_156_1 203.78/126.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.78/126.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_103_1, all_192_3, 203.78/126.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (91), (432) 203.78/126.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 203.78/126.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (465) all_192_3 = all_103_1 203.78/126.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.78/126.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_192_3, all_177_4, 203.78/126.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (404), (432) 203.78/126.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 203.78/126.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (466) all_192_3 = all_177_4 203.78/126.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.78/126.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_177_4, all_156_3, 203.78/126.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (396), (404) 203.78/126.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 203.78/126.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (467) all_177_4 = all_156_3 203.78/126.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.78/126.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_103_3, all_192_4, 203.78/126.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (90), (431) 203.78/126.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 203.78/126.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (468) all_192_4 = all_103_3 203.78/126.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.78/126.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (459), (460) imply: 203.78/126.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (469) all_192_2 = all_156_0 203.78/126.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.78/126.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (458), (460) imply: 203.78/126.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (470) all_192_2 = all_168_1 203.78/126.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.78/126.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (469), (470) imply: 203.78/126.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (471) all_168_1 = all_156_0 203.78/126.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.78/126.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (471) implies: 203.78/126.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (472) all_168_1 = all_156_0 203.78/126.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.78/126.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (465), (466) imply: 203.78/126.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (473) all_177_4 = all_103_1 203.78/126.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.78/126.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (473) implies: 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (474) all_177_4 = all_103_1 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (451), (452) imply: 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (475) all_170_1 = all_169_1 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (475) implies: 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (476) all_170_1 = all_169_1 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (452), (453) imply: 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (477) all_169_1 = all_168_1 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (462), (463) imply: 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (478) all_177_3 = all_105_3 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (478) implies: 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (479) all_177_3 = all_105_3 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (455), (456) imply: 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (480) all_171_1 = all_86_13 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (480) implies: 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (481) all_171_1 = all_86_13 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (464), (479) imply: 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (482) all_156_1 = all_105_3 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (482) implies: 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (483) all_156_1 = all_105_3 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (467), (474) imply: 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (484) all_156_3 = all_103_1 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (484) implies: 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (485) all_156_3 = all_103_1 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (457), (481) imply: 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (486) all_170_1 = all_86_13 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (476), (486) imply: 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (487) all_169_1 = all_86_13 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (487) implies: 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (488) all_169_1 = all_86_13 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (477), (488) imply: 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (489) all_168_1 = all_86_13 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (489) implies: 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (490) all_168_1 = all_86_13 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (472), (490) imply: 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (491) all_156_0 = all_86_13 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (491) implies: 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (492) all_156_0 = all_86_13 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (454), (490) imply: 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (493) all_153_1 = all_86_13 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (493) implies: 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (494) all_153_1 = all_86_13 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (452), (488) imply: 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (495) all_190_2 = all_86_13 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (469), (492) imply: 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (496) all_192_2 = all_86_13 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (264), (483), (485), (492) imply: 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (497) map_eq_sub1(int, all_103_1, all_105_3, 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $sum(all_86_10, 1), all_86_13) = 0 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (24) with int, all_103_2, all_105_4, 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $sum(all_86_10, 1), all_86_13, all_103_1, 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_3, simplifying with (31), (91), (99), 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (497) gives: 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (498) ~ ($lesseq(-1, all_86_10)) | ~ ($lesseq(0, 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_86_13)) | ? [v0: $int] : ? [v1: $int] : 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((v0 = 0 & array_eq_sub1(int, all_103_2, 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, $sum(all_86_10, 1), all_86_13) = 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 0) | (length1(int, all_103_2) = v0 & ( ~ 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ($lesseq(1, $difference(v0, all_86_10))) | 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ ($lesseq(all_86_13, v0)) | ( ~ (v1 = v0) & 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | length1(int, all_105_4) = v1)))) 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with int, all_103_2, all_105_4, 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_86_11, $sum(all_86_10, 1), simplifying with 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (31), (390) gives: 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (499) ? [v0: $int] : ? [v1: $int] : ? [v2: $int] : 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ($lesseq(1, $difference(v0, all_86_10)) & 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $lesseq(all_86_11, v0) & permut2(int, v1, v2, 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_86_11, $sum(all_86_10, 1)) = 0 & 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | length1(int, all_105_4) = v0 & length1(int, 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2) = v0 & elts(int, all_105_4) = v2 & 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | elts(int, all_103_2) = v1 & in_uni(v2) & 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | in_uni(v1)) 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (5) with int, all_105_4, all_105_2, 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_3, all_105_1, all_86_13, simplifying with 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (31), (99), (100), (180) gives: 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (500) ~ (permut2(int, all_105_3, all_105_1, 0, 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_86_13) = 0) | ? [v0: $int] : ((v0 = 0 & 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | permut_all(int, all_105_4, all_105_2) = 0) | ( 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (v0 = all_86_13) & length1(int, all_105_2) = 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | v0)) 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (5) with int, all_103_2, all_105_4, 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_1, all_105_3, all_86_13, simplifying with 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (31), (91), (99), (184) gives: 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (501) ~ (permut2(int, all_103_1, all_105_3, 0, 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_86_13) = 0) | ? [v0: $int] : ((v0 = 0 & 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | permut_all(int, all_103_2, all_105_4) = 0) | ( 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (v0 = all_86_13) & length1(int, all_105_4) = 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | v0)) 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (5) with int, all_103_4, all_103_2, 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_3, all_103_1, all_86_13, simplifying with 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (31), (90), (91), (183) gives: 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (502) ~ (permut2(int, all_103_3, all_103_1, 0, 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_86_13) = 0) | ? [v0: $int] : ((v0 = 0 & 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | permut_all(int, all_103_4, all_103_2) = 0) | ( 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (v0 = all_86_13) & length1(int, all_103_2) = 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | v0)) 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (499) with fresh symbols all_366_0, 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_366_1, all_366_2 gives: 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (503) $lesseq(1, $difference(all_366_2, all_86_10)) & 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $lesseq(all_86_11, all_366_2) & permut2(int, 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_366_1, all_366_0, all_86_11, $sum(all_86_10, 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 1)) = 0 & length1(int, all_105_4) = all_366_2 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & length1(int, all_103_2) = all_366_2 & elts(int, 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4) = all_366_0 & elts(int, all_103_2) = 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_366_1 & in_uni(all_366_0) & in_uni(all_366_1) 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (503) implies: 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (504) $lesseq(1, $difference(all_366_2, all_86_10)) 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (505) elts(int, all_103_2) = all_366_1 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (506) elts(int, all_105_4) = all_366_0 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (507) length1(int, all_103_2) = all_366_2 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (508) length1(int, all_105_4) = all_366_2 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (509) permut2(int, all_366_1, all_366_0, all_86_11, 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $sum(all_86_10, 1)) = 0 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (498) gives: 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (510) $lesseq(all_86_13, -1) 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_INEQS: (318), (510) imply: 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (511) $lesseq(0, -1) 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (511) is inconsistent. 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (512) ~ ($lesseq(-1, all_86_10)) | ? [v0: $int] : ? 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | [v1: $int] : ((v0 = 0 & array_eq_sub1(int, 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, all_105_4, $sum(all_86_10, 1), 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_86_13) = 0) | (length1(int, all_103_2) = 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | v0 & ( ~ ($lesseq(1, $difference(v0, 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_86_10))) | ~ ($lesseq(all_86_13, 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | v0)) | ( ~ (v1 = v0) & length1(int, 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4) = v1)))) 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (512) gives: 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (513) $lesseq(all_86_10, -2) 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_INEQS: (323), (513) imply: 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (514) $lesseq(0, -1) 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (514) is inconsistent. 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_86_13, all_366_2, 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (184), (507) 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (515) all_366_2 = all_86_13 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_105_3, all_366_0, 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (99), (506) 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (516) all_366_0 = all_105_3 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_103_1, all_366_1, 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (91), (505) 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (517) all_366_1 = all_103_1 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (509), (516), (517) imply: 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (518) permut2(int, all_103_1, all_105_3, all_86_11, 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $sum(all_86_10, 1)) = 0 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (155) gives: 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (519) ~ (all_133_3 = 0) & permut_sub3(all_86_3, 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_86_1, all_86_11, $sum(all_86_10, 1)) = 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_133_3 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (519) implies: 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (520) ~ (all_133_3 = 0) 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (521) permut_sub3(all_86_3, all_86_1, all_86_11, 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $sum(all_86_10, 1)) = all_133_3 203.78/126.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_86_3, all_86_1, 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_86_7, $sum(all_86_10, 1), all_86_11, 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $sum(all_86_10, 1), all_133_3, simplifying with 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (60), (64), (521) gives: 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (522) all_133_3 = 0 | ~ ($lesseq(all_86_11, all_86_7)) 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ ($lesseq(0, all_86_11)) | ? [v0: $int] : ? 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | [v1: $int] : ($lesseq(v1, all_86_10) & 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | t2tb2(all_86_3) = v0 & length1(int, v0) = v1 & 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | in_uni(v0)) 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (522) gives: 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (523) $lesseq(all_86_11, -1) 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_INEQS: (48), (523) imply: 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (524) $lesseq(0, -1) 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (524) is inconsistent. 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (525) all_133_3 = 0 | ~ ($lesseq(all_86_11, all_86_7)) 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ? [v0: $int] : ? [v1: $int] : ($lesseq(v1, 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_86_10) & t2tb2(all_86_3) = v0 & 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | length1(int, v0) = v1 & in_uni(v0)) 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (525) gives: 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (526) $lesseq(1, $difference(all_86_11, all_86_7)) 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_INEQS: (52), (526) imply: 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (527) $lesseq(2, $difference(all_86_11, all_86_8)) 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_INEQS: (50), (527) imply: 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (528) $lesseq(0, -1) 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (528) is inconsistent. 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (529) all_133_3 = 0 | ? [v0: $int] : ? [v1: $int] : 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ($lesseq(v1, all_86_10) & t2tb2(all_86_3) = v0 & 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | length1(int, v0) = v1 & in_uni(v0)) 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (529) gives: 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (530) all_133_3 = 0 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (520), (530) imply: 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (531) ~ (0 = 0) 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (531) is inconsistent. 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (532) ? [v0: $int] : ? [v1: $int] : ($lesseq(v1, 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_86_10) & t2tb2(all_86_3) = v0 & 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | length1(int, v0) = v1 & in_uni(v0)) 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (532) with fresh symbols all_622_0, 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_622_1 gives: 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (533) $lesseq(all_622_0, all_86_10) & t2tb2(all_86_3) = 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_622_1 & length1(int, all_622_1) = all_622_0 & 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | in_uni(all_622_1) 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (533) implies: 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (534) $lesseq(all_622_0, all_86_10) 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (535) length1(int, all_622_1) = all_622_0 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (536) t2tb2(all_86_3) = all_622_1 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (34) with all_105_4, all_622_1, 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_86_3, simplifying with (102), (536) gives: 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (537) all_622_1 = all_105_4 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (535), (537) imply: 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (538) length1(int, all_105_4) = all_622_0 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_86_13, all_622_0, 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (180), (538) 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (539) all_622_0 = all_86_13 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (534), (539) imply: 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (540) $lesseq(all_86_13, all_86_10) 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_INEQS: (49), (540) imply: 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (541) $lesseq(0, -1) 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (541) is inconsistent. 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (542) t2tb2(all_86_1) = all_133_3 & in_uni(all_133_3) & 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (( ~ (all_133_0 = 42) & $lesseq(1, 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $difference(all_86_7, all_133_2)) & 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $lesseq(1, $difference(all_133_2, all_86_8)) & 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | tb2t1(all_133_1) = all_133_0 & get4(int, 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_133_3, all_133_2) = all_133_1 & 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | in_uni(all_133_1)) | ($lesseq(all_133_0, 41) & 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $lesseq(all_133_2, all_86_10) & 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $lesseq(all_86_7, all_133_2) & 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | tb2t1(all_133_1) = all_133_0 & get4(int, 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_133_3, all_133_2) = all_133_1 & 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | in_uni(all_133_1)) | ($lesseq(43, all_133_0) & 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $lesseq(all_133_2, all_86_8) & 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $lesseq(all_86_11, all_133_2) & 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | tb2t1(all_133_1) = all_133_0 & get4(int, 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_133_3, all_133_2) = all_133_1 & 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | in_uni(all_133_1))) 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (542) implies: 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (543) t2tb2(all_86_1) = all_133_3 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (544) ( ~ (all_133_0 = 42) & $lesseq(1, 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $difference(all_86_7, all_133_2)) & $lesseq(1, 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $difference(all_133_2, all_86_8)) & 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | tb2t1(all_133_1) = all_133_0 & get4(int, 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_133_3, all_133_2) = all_133_1 & 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | in_uni(all_133_1)) | ($lesseq(all_133_0, 41) & 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $lesseq(all_133_2, all_86_10) & 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $lesseq(all_86_7, all_133_2) & tb2t1(all_133_1) 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_133_0 & get4(int, all_133_3, all_133_2) = 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_133_1 & in_uni(all_133_1)) | ($lesseq(43, 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_133_0) & $lesseq(all_133_2, all_86_8) & 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $lesseq(all_86_11, all_133_2) & tb2t1(all_133_1) 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_133_0 & get4(int, all_133_3, all_133_2) = 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_133_1 & in_uni(all_133_1)) 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (34) with all_105_2, all_133_3, 203.95/126.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_86_1, simplifying with (103), (543) gives: 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (545) all_133_3 = all_105_2 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (240) gives: 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (546) ~ (map_eq_sub1(int, all_105_3, all_105_1, 0, 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_86_13) = 0) 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (105), (546) imply: 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (547) ~ (all_86_7 = all_86_13) 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | STRENGTHEN: (389), (547) imply: 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (548) $lesseq(1, $difference(all_86_13, all_86_7)) 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (244) gives: 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (549) ~ (map_eq_sub1(int, all_103_1, all_105_3, 0, 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_86_13) = 0) 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (203), (549) imply: 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (550) ~ (all_86_8 = -1) 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | STRENGTHEN: (156), (550) imply: 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (551) $lesseq(0, all_86_8) 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_INEQS: (52), (548) imply: 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (552) $lesseq(2, $difference(all_86_13, all_86_8)) 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_INEQS: (73), (551) imply: 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (553) $lesseq(1, all_86_10) 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (305) gives: 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (554) all_200_3 = 0 & sorted1(all_86_1) = 0 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (554) implies: 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (555) sorted1(all_86_1) = 0 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (310) gives: 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (556) all_205_0 = 0 & sorted_sub2(all_205_2, 0, 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_205_1) = 0 & tb2t(all_205_3) = all_205_2 & 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | length1(int, all_105_2) = all_205_1 & elts(int, 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_2) = all_205_3 & 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | in_map_int_int(all_205_2) & in_uni(all_205_3) 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (556) implies: 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (557) elts(int, all_105_2) = all_205_3 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (558) tb2t(all_205_3) = all_205_2 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_105_1, all_205_3, 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_2, int, simplifying with (100), (557) 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (559) all_205_3 = all_105_1 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (558), (559) imply: 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (560) tb2t(all_105_1) = all_205_2 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (36) with all_86_2, all_205_2, 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_1, simplifying with (207), (560) gives: 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (561) all_205_2 = all_86_2 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (19) with int, all_103_3, all_103_1, 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_3, all_86_11, $sum(all_86_10, 1), 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (31), (393), (518) gives: 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (562) permut2(int, all_103_3, all_105_3, all_86_11, 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $sum(all_86_10, 1)) = 0 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (4), (7), (9), (12), (13), (14), (19), 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (20), (22), (23), (24), (26), (27), (28), (31), 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (35), (36), (38), (39), (41), (42), (43), (44), 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (48), (49), (50), (52), (53), (54), (55), (56), 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (58), (60), (61), (71), (72), (90), (91), (93), 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (99), (100), (102), (103), (105), (151), (162), 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (180), (183), (184), (203), (205), (207), (224), 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (225), (226), (227), (318), (391), (392), (393), 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (501), (502), (518), (544), (545), (548), (551), 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (552), (553), (562) are inconsistent by sub-proof 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #132. 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (563) ~ (all_205_3 = 0) & sorted1(all_86_1) = all_205_3 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (563) implies: 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (564) ~ (all_205_3 = 0) 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (565) sorted1(all_86_1) = all_205_3 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (37) with all_205_3, 0, all_86_1, 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (555), (565) gives: 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (566) all_205_3 = 0 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (564), (566) imply: 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (567) ~ (0 = 0) 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (567) is inconsistent. 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (568) ~ (all_200_0 = 0) & sorted_sub2(all_200_2, 0, 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_200_1) = all_200_0 & tb2t(all_200_3) = 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_200_2 & length1(int, all_105_2) = all_200_1 & 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | elts(int, all_105_2) = all_200_3 & 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | in_map_int_int(all_200_2) & in_uni(all_200_3) 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (568) implies: 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (569) ~ (all_200_0 = 0) 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (570) elts(int, all_105_2) = all_200_3 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (571) length1(int, all_105_2) = all_200_1 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (572) tb2t(all_200_3) = all_200_2 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (573) sorted_sub2(all_200_2, 0, all_200_1) = all_200_0 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_86_13, all_200_1, 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_2, int, simplifying with (181), (571) 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (574) all_200_1 = all_86_13 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_105_1, all_200_3, 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_2, int, simplifying with (100), (570) 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (575) all_200_3 = all_105_1 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (573), (574) imply: 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (576) sorted_sub2(all_200_2, 0, all_86_13) = all_200_0 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (572), (575) imply: 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (577) tb2t(all_105_1) = all_200_2 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (36) with all_86_2, all_200_2, 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_1, simplifying with (207), (577) gives: 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (578) all_200_2 = all_86_2 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (576), (578) imply: 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (579) sorted_sub2(all_86_2, 0, all_86_13) = all_200_0 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (310) gives: 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (580) all_205_0 = 0 & sorted_sub2(all_205_2, 0, 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_205_1) = 0 & tb2t(all_205_3) = all_205_2 & 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | length1(int, all_105_2) = all_205_1 & elts(int, 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_2) = all_205_3 & 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | in_map_int_int(all_205_2) & in_uni(all_205_3) 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (580) implies: 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (581) elts(int, all_105_2) = all_205_3 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (582) length1(int, all_105_2) = all_205_1 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (583) tb2t(all_205_3) = all_205_2 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (584) sorted_sub2(all_205_2, 0, all_205_1) = 0 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (38), (39), (40), (100), (181), (207), 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (569), (579), (581), (582), (583), (584) are 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #131. 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (19) with int, all_103_3, all_103_1, 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_3, all_86_11, $sum(all_86_10, 1), 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (31), (393), (518) gives: 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (585) permut2(int, all_103_3, all_105_3, all_86_11, 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $sum(all_86_10, 1)) = 0 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (4), (7), (9), (12), (13), (14), (19), 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (20), (22), (23), (24), (26), (27), (28), (31), 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (35), (36), (38), (39), (41), (42), (43), (44), 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (48), (49), (50), (52), (53), (54), (55), (56), 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (58), (60), (61), (71), (72), (90), (91), (93), 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (99), (100), (102), (103), (105), (151), (162), 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (180), (183), (184), (203), (205), (207), (224), 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (225), (226), (227), (318), (391), (392), (393), 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (501), (502), (518), (544), (545), (548), (551), 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (552), (553), (585) are inconsistent by sub-proof 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #132. 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split 203.95/126.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (586) map_eq_sub1(int, all_103_1, all_105_3, 0, 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_86_13) = 0 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (305) gives: 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (587) all_200_3 = 0 & sorted1(all_86_1) = 0 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (587) implies: 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (588) sorted1(all_86_1) = 0 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (310) gives: 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (589) all_205_0 = 0 & sorted_sub2(all_205_2, 0, 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_205_1) = 0 & tb2t(all_205_3) = all_205_2 & 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | length1(int, all_105_2) = all_205_1 & elts(int, 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_2) = all_205_3 & 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | in_map_int_int(all_205_2) & in_uni(all_205_3) 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (589) implies: 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (590) elts(int, all_105_2) = all_205_3 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (591) length1(int, all_105_2) = all_205_1 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (592) tb2t(all_205_3) = all_205_2 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_86_13, all_205_1, 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_2, int, simplifying with (181), (591) 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (593) all_205_1 = all_86_13 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_105_1, all_205_3, 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_2, int, simplifying with (100), (590) 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (594) all_205_3 = all_105_1 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (592), (594) imply: 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (595) tb2t(all_105_1) = all_205_2 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (36) with all_86_2, all_205_2, 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_1, simplifying with (207), (595) gives: 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (596) all_205_2 = all_86_2 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (19) with int, all_103_1, all_105_3, 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_1, all_86_11, $sum(all_86_10, 1), 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (31), (518) gives: 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (597) ~ (permut2(int, all_105_3, all_105_1, all_86_11, 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $sum(all_86_10, 1)) = 0) | permut2(int, 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_1, all_105_1, all_86_11, $sum(all_86_10, 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 1)) = 0 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (4), (6), (7), (9), (12), (13), (14), 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (19), (20), (24), (27), (28), (31), (35), (36), 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (38), (39), (42), (48), (49), (50), (51), (52), 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (53), (54), (55), (56), (60), (61), (71), (72), 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (90), (91), (96), (99), (100), (102), (103), 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (105), (151), (156), (162), (180), (181), (183), 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (184), (203), (205), (206), (207), (224), (225), 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (226), (227), (318), (323), (391), (392), (393), 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (500), (501), (502), (518), (544), (545), (548), 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (586), (597), (bridgeR1) are inconsistent by 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #112. 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (598) ~ (all_205_3 = 0) & sorted1(all_86_1) = all_205_3 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (598) implies: 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (599) ~ (all_205_3 = 0) 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (600) sorted1(all_86_1) = all_205_3 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (37), (588), (599), (600) are inconsistent by 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #111. 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (601) ~ (all_200_0 = 0) & sorted_sub2(all_200_2, 0, 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_200_1) = all_200_0 & tb2t(all_200_3) = 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_200_2 & length1(int, all_105_2) = all_200_1 & 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | elts(int, all_105_2) = all_200_3 & 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | in_map_int_int(all_200_2) & in_uni(all_200_3) 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (601) implies: 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (602) ~ (all_200_0 = 0) 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (603) elts(int, all_105_2) = all_200_3 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (604) length1(int, all_105_2) = all_200_1 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (605) tb2t(all_200_3) = all_200_2 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (606) sorted_sub2(all_200_2, 0, all_200_1) = all_200_0 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_86_13, all_200_1, 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_2, int, simplifying with (181), (604) 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (607) all_200_1 = all_86_13 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_105_1, all_200_3, 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_2, int, simplifying with (100), (603) 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (608) all_200_3 = all_105_1 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (606), (607) imply: 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (609) sorted_sub2(all_200_2, 0, all_86_13) = all_200_0 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (605), (608) imply: 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (610) tb2t(all_105_1) = all_200_2 203.95/126.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (36) with all_86_2, all_200_2, 203.95/126.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_1, simplifying with (207), (610) gives: 203.95/126.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (611) all_200_2 = all_86_2 203.95/126.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (609), (611) imply: 203.95/126.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (612) sorted_sub2(all_86_2, 0, all_86_13) = all_200_0 203.95/126.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (310) gives: 203.95/126.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: 203.95/126.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (613) all_205_0 = 0 & sorted_sub2(all_205_2, 0, 203.95/126.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_205_1) = 0 & tb2t(all_205_3) = all_205_2 & 203.95/126.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | length1(int, all_105_2) = all_205_1 & elts(int, 203.95/126.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_2) = all_205_3 & 203.95/126.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | in_map_int_int(all_205_2) & in_uni(all_205_3) 203.95/126.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (613) implies: 203.95/126.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (614) elts(int, all_105_2) = all_205_3 203.95/126.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (615) length1(int, all_105_2) = all_205_1 203.95/126.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (616) tb2t(all_205_3) = all_205_2 203.95/126.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (617) sorted_sub2(all_205_2, 0, all_205_1) = 0 203.95/126.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (38), (39), (40), (100), (181), (207), 203.95/126.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (602), (612), (614), (615), (616), (617) are 203.95/126.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #131. 203.95/126.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: 203.95/126.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (19) with int, all_103_1, all_105_3, 203.95/126.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_1, all_86_11, $sum(all_86_10, 1), 203.95/126.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (31), (518) gives: 203.95/126.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (618) ~ (permut2(int, all_105_3, all_105_1, all_86_11, 203.95/126.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $sum(all_86_10, 1)) = 0) | permut2(int, 203.95/126.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_1, all_105_1, all_86_11, $sum(all_86_10, 203.95/126.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 1)) = 0 203.95/126.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (4), (6), (7), (9), (12), (13), (14), 203.95/126.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (19), (20), (24), (27), (28), (31), (35), (36), 203.95/126.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (38), (39), (42), (48), (49), (50), (51), (52), 203.95/126.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (53), (54), (55), (56), (60), (61), (71), (72), 203.95/126.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (90), (91), (96), (99), (100), (102), (103), 203.95/126.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (105), (151), (156), (162), (180), (181), (183), 203.95/126.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (184), (203), (205), (206), (207), (224), (225), 203.95/126.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (226), (227), (318), (323), (391), (392), (393), 203.95/126.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (500), (501), (502), (518), (544), (545), (548), 203.95/126.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (586), (618), (bridgeR1) are inconsistent by 203.95/126.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #112. 203.95/126.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split 203.95/126.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split 203.95/126.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split 203.95/126.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: 203.95/126.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (619) map_eq_sub1(int, all_105_3, all_105_1, 0, 203.95/126.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_86_13) = 0 203.95/126.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (244) gives: 203.95/126.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: 203.95/126.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (620) ~ (map_eq_sub1(int, all_103_1, all_105_3, 0, 203.95/126.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_86_13) = 0) 203.95/126.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (203), (620) imply: 203.95/126.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (621) ~ (all_86_8 = -1) 203.95/126.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | STRENGTHEN: (156), (621) imply: 203.95/126.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (622) $lesseq(0, all_86_8) 203.95/126.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 203.95/126.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_INEQS: (73), (622) imply: 203.95/126.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (623) $lesseq(1, all_86_10) 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (305) gives: 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (624) all_200_3 = 0 & sorted1(all_86_1) = 0 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (624) implies: 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (625) sorted1(all_86_1) = 0 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (310) gives: 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (626) all_205_0 = 0 & sorted_sub2(all_205_2, 0, 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_205_1) = 0 & tb2t(all_205_3) = all_205_2 & 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | length1(int, all_105_2) = all_205_1 & elts(int, 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_2) = all_205_3 & 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | in_map_int_int(all_205_2) & in_uni(all_205_3) 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (626) implies: 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (627) elts(int, all_105_2) = all_205_3 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (628) tb2t(all_205_3) = all_205_2 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_105_1, all_205_3, 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_2, int, simplifying with (100), (627) 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (629) all_205_3 = all_105_1 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (628), (629) imply: 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (630) tb2t(all_105_1) = all_205_2 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (36) with all_86_2, all_205_2, 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_1, simplifying with (207), (630) gives: 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (631) all_205_2 = all_86_2 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (19) with int, all_103_3, all_103_1, 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_3, all_86_11, $sum(all_86_10, 1), 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (31), (393), (518) gives: 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (632) permut2(int, all_103_3, all_105_3, all_86_11, 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $sum(all_86_10, 1)) = 0 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (4), (7), (9), (12), (13), (14), (19), 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (20), (22), (23), (24), (26), (27), (28), (31), 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (35), (36), (38), (39), (41), (42), (43), (48), 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (49), (50), (52), (53), (54), (55), (56), (58), 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (60), (61), (71), (72), (75), (90), (91), (93), 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (96), (99), (100), (102), (103), (105), (151), 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (162), (180), (183), (184), (203), (205), (206), 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (207), (224), (225), (226), (227), (318), (389), 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (391), (392), (393), (501), (502), (518), (544), 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (545), (619), (622), (623), (632), (bridgeR1) are 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #104. 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (633) ~ (all_205_3 = 0) & sorted1(all_86_1) = all_205_3 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (633) implies: 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (634) ~ (all_205_3 = 0) 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (635) sorted1(all_86_1) = all_205_3 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (37), (625), (634), (635) are inconsistent by 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #111. 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (636) ~ (all_200_0 = 0) & sorted_sub2(all_200_2, 0, 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_200_1) = all_200_0 & tb2t(all_200_3) = 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_200_2 & length1(int, all_105_2) = all_200_1 & 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | elts(int, all_105_2) = all_200_3 & 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | in_map_int_int(all_200_2) & in_uni(all_200_3) 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (636) implies: 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (637) ~ (all_200_0 = 0) 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (638) elts(int, all_105_2) = all_200_3 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (639) length1(int, all_105_2) = all_200_1 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (640) tb2t(all_200_3) = all_200_2 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (641) sorted_sub2(all_200_2, 0, all_200_1) = all_200_0 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_86_13, all_200_1, 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_2, int, simplifying with (181), (639) 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (642) all_200_1 = all_86_13 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_105_1, all_200_3, 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_2, int, simplifying with (100), (638) 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (643) all_200_3 = all_105_1 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (641), (642) imply: 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (644) sorted_sub2(all_200_2, 0, all_86_13) = all_200_0 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (640), (643) imply: 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (645) tb2t(all_105_1) = all_200_2 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (36) with all_86_2, all_200_2, 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_1, simplifying with (207), (645) gives: 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (646) all_200_2 = all_86_2 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (644), (646) imply: 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (647) sorted_sub2(all_86_2, 0, all_86_13) = all_200_0 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (310) gives: 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (648) all_205_0 = 0 & sorted_sub2(all_205_2, 0, 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_205_1) = 0 & tb2t(all_205_3) = all_205_2 & 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | length1(int, all_105_2) = all_205_1 & elts(int, 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_2) = all_205_3 & 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | in_map_int_int(all_205_2) & in_uni(all_205_3) 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (648) implies: 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (649) elts(int, all_105_2) = all_205_3 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (650) length1(int, all_105_2) = all_205_1 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (651) tb2t(all_205_3) = all_205_2 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (652) sorted_sub2(all_205_2, 0, all_205_1) = 0 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (38), (39), (40), (100), (181), (207), 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (637), (647), (649), (650), (651), (652) are 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #131. 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (19) with int, all_103_3, all_103_1, 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_3, all_86_11, $sum(all_86_10, 1), 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (31), (393), (518) gives: 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (653) permut2(int, all_103_3, all_105_3, all_86_11, 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $sum(all_86_10, 1)) = 0 204.07/126.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (4), (7), (9), (12), (13), (14), (19), 204.07/126.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (20), (22), (23), (24), (26), (27), (28), (31), 204.07/126.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (35), (36), (38), (39), (41), (42), (43), (48), 204.07/126.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (49), (50), (52), (53), (54), (55), (56), (58), 204.07/126.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (60), (61), (71), (72), (75), (90), (91), (93), 204.07/126.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (96), (99), (100), (102), (103), (105), (151), 204.07/126.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (162), (180), (183), (184), (203), (205), (206), 204.07/126.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (207), (224), (225), (226), (227), (318), (389), 204.07/126.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (391), (392), (393), (501), (502), (518), (544), 204.07/126.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (545), (619), (622), (623), (653), (bridgeR1) are 204.07/126.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #104. 204.07/126.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split 204.07/126.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split 204.07/126.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: 204.07/126.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (654) map_eq_sub1(int, all_103_1, all_105_3, 0, 204.07/126.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_86_13) = 0 204.07/126.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (305) gives: 204.07/126.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: 204.07/126.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (655) all_200_3 = 0 & sorted1(all_86_1) = 0 204.07/126.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (655) implies: 204.07/126.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (656) sorted1(all_86_1) = 0 204.07/126.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (310) gives: 204.07/126.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: 204.07/126.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (657) all_205_0 = 0 & sorted_sub2(all_205_2, 0, 204.07/126.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_205_1) = 0 & tb2t(all_205_3) = all_205_2 & 204.07/126.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | length1(int, all_105_2) = all_205_1 & elts(int, 204.07/126.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_2) = all_205_3 & 204.07/126.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | in_map_int_int(all_205_2) & in_uni(all_205_3) 204.07/126.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (657) implies: 204.07/126.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (658) elts(int, all_105_2) = all_205_3 204.07/126.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (659) length1(int, all_105_2) = all_205_1 204.07/126.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (660) tb2t(all_205_3) = all_205_2 204.07/126.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (4), (6), (7), (9), (12), (13), (14), 204.07/126.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (19), (20), (24), (25), (27), (28), (31), (35), 204.07/126.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (36), (38), (39), (42), (45), (48), (49), (50), 204.07/126.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (51), (52), (53), (54), (55), (56), (60), (61), 204.07/126.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (71), (72), (90), (91), (96), (99), (100), (102), 204.07/126.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (103), (105), (151), (156), (162), (180), (181), 204.07/126.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (183), (184), (203), (205), (206), (207), (224), 204.07/126.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (225), (226), (227), (318), (389), (391), (392), 204.07/126.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (393), (500), (501), (502), (518), (544), (545), 204.07/126.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (619), (654), (658), (659), (660), (bridgeR1) are 204.07/126.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #84. 204.07/126.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: 204.07/126.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (661) ~ (all_205_3 = 0) & sorted1(all_86_1) = all_205_3 204.07/126.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (661) implies: 204.07/126.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (662) ~ (all_205_3 = 0) 204.07/126.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (663) sorted1(all_86_1) = all_205_3 204.07/126.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (37), (656), (662), (663) are inconsistent by 204.07/126.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #111. 204.07/126.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split 204.07/126.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: 204.07/126.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (664) ~ (all_200_0 = 0) & sorted_sub2(all_200_2, 0, 204.07/126.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_200_1) = all_200_0 & tb2t(all_200_3) = 204.07/126.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_200_2 & length1(int, all_105_2) = all_200_1 & 204.07/126.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | elts(int, all_105_2) = all_200_3 & 204.07/126.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | in_map_int_int(all_200_2) & in_uni(all_200_3) 204.07/126.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (664) implies: 204.07/126.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (665) elts(int, all_105_2) = all_200_3 204.07/126.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (666) length1(int, all_105_2) = all_200_1 204.07/126.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (667) tb2t(all_200_3) = all_200_2 204.07/126.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_86_13, all_200_1, 204.07/126.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_2, int, simplifying with (181), (666) 204.07/126.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.07/126.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (668) all_200_1 = all_86_13 204.07/126.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_105_1, all_200_3, 204.07/126.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_2, int, simplifying with (100), (665) 204.07/126.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.07/126.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (669) all_200_3 = all_105_1 204.07/126.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (667), (669) imply: 204.07/126.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (670) tb2t(all_105_1) = all_200_2 204.07/126.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (36) with all_86_2, all_200_2, 204.07/126.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_1, simplifying with (207), (670) gives: 204.07/126.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (671) all_200_2 = all_86_2 204.07/126.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (310) gives: 204.07/126.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: 204.07/126.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (672) all_205_0 = 0 & sorted_sub2(all_205_2, 0, 204.07/126.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_205_1) = 0 & tb2t(all_205_3) = all_205_2 & 204.07/126.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | length1(int, all_105_2) = all_205_1 & elts(int, 204.07/126.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_2) = all_205_3 & 204.07/126.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | in_map_int_int(all_205_2) & in_uni(all_205_3) 204.07/126.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (672) implies: 204.07/126.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (673) elts(int, all_105_2) = all_205_3 204.07/126.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (674) length1(int, all_105_2) = all_205_1 204.07/126.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (675) tb2t(all_205_3) = all_205_2 204.07/126.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (4), (6), (7), (9), (12), (13), (14), 204.07/126.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (19), (20), (24), (25), (27), (28), (31), (35), 204.07/126.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (36), (38), (39), (42), (45), (48), (49), (50), 204.07/126.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (51), (52), (53), (54), (55), (56), (60), (61), 204.07/126.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (71), (72), (90), (91), (96), (99), (100), (102), 204.07/126.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (103), (105), (151), (156), (162), (180), (181), 204.07/126.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (183), (184), (203), (205), (206), (207), (224), 204.07/126.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (225), (226), (227), (318), (389), (391), (392), 204.07/126.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (393), (500), (501), (502), (518), (544), (545), 204.07/126.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (619), (654), (673), (674), (675), (bridgeR1) are 204.07/126.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #84. 204.07/126.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: 204.07/126.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (25) with int, all_103_2, all_105_4, 204.07/126.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 0, all_86_13, all_103_1, all_105_3, 0, simplifying 204.07/126.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | with (31), (91), (99), (654) gives: 204.07/126.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (676) ? [v0: $int] : ? [v1: $int] : ((v1 = v0 & 204.07/126.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $lesseq(all_86_13, v0) & $lesseq(0, v0) & 204.07/126.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $lesseq(0, all_86_13) & length1(int, 204.07/126.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4) = v0 & length1(int, all_103_2) = 204.07/126.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | v0) | ( ~ (v0 = 0) & array_eq_sub1(int, 204.07/126.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, all_105_4, 0, all_86_13) = v0)) 204.07/126.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (24) with int, all_103_2, all_105_4, 204.07/126.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 0, all_86_13, all_103_1, all_105_3, simplifying 204.07/126.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | with (31), (91), (99), (654) gives: 204.07/126.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (677) ~ ($lesseq(0, all_86_13)) | ? [v0: $int] : ? 204.07/126.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | [v1: $int] : ((v0 = 0 & array_eq_sub1(int, 204.07/126.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, all_105_4, 0, all_86_13) = 0) | 204.07/126.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (length1(int, all_103_2) = v0 & ( ~ 204.07/126.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ($lesseq(all_86_13, v0)) | ~ ($lesseq(0, 204.07/126.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | v0)) | ( ~ (v1 = v0) & length1(int, 204.07/126.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4) = v1)))) 204.07/126.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (19) with int, all_103_1, all_105_3, 204.07/126.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_1, all_86_11, $sum(all_86_10, 1), 204.07/126.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (31), (518) gives: 204.07/126.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (678) ~ (permut2(int, all_105_3, all_105_1, all_86_11, 204.07/126.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $sum(all_86_10, 1)) = 0) | permut2(int, 204.07/126.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_1, all_105_1, all_86_11, $sum(all_86_10, 204.07/126.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 1)) = 0 204.07/126.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (19) with int, all_103_3, all_103_1, 204.07/126.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_3, all_86_11, $sum(all_86_10, 1), 204.07/126.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (31), (393), (518) gives: 204.07/126.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (679) permut2(int, all_103_3, all_105_3, all_86_11, 204.07/126.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $sum(all_86_10, 1)) = 0 204.07/126.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (676) with fresh symbols all_601_0, 204.07/126.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_601_1 gives: 204.07/126.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (680) (all_601_0 = all_601_1 & $lesseq(all_86_13, 204.07/126.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_601_1) & $lesseq(0, all_601_1) & 204.07/126.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $lesseq(0, all_86_13) & length1(int, all_105_4) 204.07/126.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_601_1 & length1(int, all_103_2) = 204.07/126.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_601_1) | ( ~ (all_601_1 = 0) & 204.07/126.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | array_eq_sub1(int, all_103_2, all_105_4, 0, 204.07/126.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_86_13) = all_601_1) 204.07/126.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (677) gives: 204.07/126.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: 204.07/126.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (681) $lesseq(all_86_13, -1) 204.07/126.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_INEQS: (318), (681) imply: 204.07/126.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (682) $lesseq(0, -1) 204.07/126.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (682) is inconsistent. 204.07/126.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (683) ? [v0: $int] : ? [v1: $int] : ((v0 = 0 & 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | array_eq_sub1(int, all_103_2, all_105_4, 0, 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_86_13) = 0) | (length1(int, all_103_2) = 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | v0 & ( ~ ($lesseq(all_86_13, v0)) | ~ 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ($lesseq(0, v0)) | ( ~ (v1 = v0) & 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | length1(int, all_105_4) = v1)))) 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (683) with fresh symbols all_626_0, 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_626_1 gives: 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (684) (all_626_1 = 0 & array_eq_sub1(int, all_103_2, 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, 0, all_86_13) = 0) | (length1(int, 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2) = all_626_1 & ( ~ 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ($lesseq(all_86_13, all_626_1)) | ~ 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ($lesseq(0, all_626_1)) | ( ~ (all_626_0 = 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_626_1) & length1(int, all_105_4) = 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_626_0))) 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (684) gives: 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (685) all_626_1 = 0 & array_eq_sub1(int, all_103_2, 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, 0, all_86_13) = 0 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (685) implies: 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (686) array_eq_sub1(int, all_103_2, all_105_4, 0, 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_86_13) = 0 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (680) gives: 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (687) all_601_0 = all_601_1 & $lesseq(all_86_13, 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_601_1) & $lesseq(0, all_601_1) & $lesseq(0, 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_86_13) & length1(int, all_105_4) = all_601_1 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & length1(int, all_103_2) = all_601_1 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (687) implies: 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (688) length1(int, all_103_2) = all_601_1 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (689) length1(int, all_105_4) = all_601_1 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_86_13, all_601_1, 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (184), (688) 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (690) all_601_1 = all_86_13 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (501) gives: 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (691) ~ (permut2(int, all_103_1, all_105_3, 0, 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_86_13) = 0) 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (392), (691) imply: 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (692) ~ ($difference(all_86_8, all_86_13) = -1) | ~ 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_86_11 = 0) 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (4), (7), (9), (12), (13), (14), (20), 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (24), (27), (28), (31), (35), (36), (38), (39), 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (42), (48), (49), (50), (51), (52), (53), (55), 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (56), (60), (61), (71), (72), (90), (96), (99), 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (100), (102), (103), (105), (151), (156), (162), 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (180), (181), (183), (203), (205), (206), (207), 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (224), (225), (226), (318), (323), (389), (391), 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (392), (500), (518), (544), (545), (619), (654), 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (679), (691), (692), (bridgeR1) are inconsistent 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #98. 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (693) permut2(int, all_103_1, all_105_3, 0, all_86_13) = 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 0 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (4), (6), (7), (9), (12), (13), (14), 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (19), (20), (24), (27), (28), (31), (35), (36), 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (38), (39), (42), (48), (49), (50), (51), (52), 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (53), (54), (55), (56), (60), (61), (71), (72), 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (75), (90), (91), (96), (99), (100), (102), (103), 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (105), (151), (156), (162), (180), (181), (183), 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (184), (203), (205), (206), (207), (224), (225), 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (226), (227), (318), (323), (389), (391), (392), 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (393), (500), (502), (544), (545), (619), (654), 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (678), (679), (693), (bridgeR1) are inconsistent 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #86. 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (694) ~ (all_601_1 = 0) & array_eq_sub1(int, all_103_2, 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, 0, all_86_13) = all_601_1 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (694) implies: 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (695) ~ (all_601_1 = 0) 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (696) array_eq_sub1(int, all_103_2, all_105_4, 0, 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_86_13) = all_601_1 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (45) with 0, all_601_1, all_86_13, 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 0, all_105_4, all_103_2, int, simplifying with 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (686), (696) gives: 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (697) all_601_1 = 0 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (695), (697) imply: 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (698) ~ (0 = 0) 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (698) is inconsistent. 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (699) length1(int, all_103_2) = all_626_1 & ( ~ 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ($lesseq(all_86_13, all_626_1)) | ~ ($lesseq(0, 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_626_1)) | ( ~ (all_626_0 = all_626_1) & 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | length1(int, all_105_4) = all_626_0)) 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (699) implies: 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (700) length1(int, all_103_2) = all_626_1 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (701) ~ ($lesseq(all_86_13, all_626_1)) | ~ 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ($lesseq(0, all_626_1)) | ( ~ (all_626_0 = 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_626_1) & length1(int, all_105_4) = 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_626_0) 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_86_13, all_626_1, 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (184), (700) 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (702) all_626_1 = all_86_13 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (701) gives: 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: 204.07/126.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (703) $lesseq(all_626_1, -1) 204.07/127.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (702), (703) imply: 204.07/127.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (704) $lesseq(all_86_13, -1) 204.07/127.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_INEQS: (318), (704) imply: 204.07/127.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (705) $lesseq(0, -1) 204.07/127.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (705) is inconsistent. 204.07/127.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: 204.07/127.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (706) ~ ($lesseq(all_86_13, all_626_1)) | ( ~ 204.07/127.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_626_0 = all_626_1) & length1(int, 204.07/127.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4) = all_626_0) 204.07/127.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (706) gives: 204.07/127.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: 204.07/127.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (707) $lesseq(1, $difference(all_86_13, all_626_1)) 204.07/127.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (702), (707) imply: 204.07/127.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (708) $lesseq(0, -1) 204.07/127.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (708) is inconsistent. 204.07/127.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: 204.07/127.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (709) ~ (all_626_0 = all_626_1) & length1(int, 204.07/127.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4) = all_626_0 204.07/127.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (709) implies: 204.07/127.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (710) ~ (all_626_0 = all_626_1) 204.07/127.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (711) length1(int, all_105_4) = all_626_0 204.07/127.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (702), (710) imply: 204.07/127.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (712) ~ (all_626_0 = all_86_13) 204.07/127.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_86_13, all_626_0, 204.07/127.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (180), (711) 204.07/127.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.07/127.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (713) all_626_0 = all_86_13 204.07/127.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (712), (713) imply: 204.07/127.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (714) ~ (0 = 0) 204.07/127.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (714) is inconsistent. 204.07/127.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split 204.07/127.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split 204.07/127.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split 204.07/127.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split 204.07/127.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split 204.07/127.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split 204.07/127.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split 204.07/127.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split 204.07/127.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split 204.07/127.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split 204.07/127.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split 204.07/127.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (715) ~ (all_171_1 = 0) & array_eq_sub1(int, all_103_4, 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, 0, all_86_11) = all_171_1 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (715) implies: 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (716) ~ (all_171_1 = 0) 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (717) array_eq_sub1(int, all_103_4, all_103_2, 0, 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_86_11) = all_171_1 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (45) with all_171_1, 0, all_86_11, 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 0, all_103_2, all_103_4, int, simplifying with 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (442), (717) gives: 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (718) all_171_1 = 0 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (716), (718) imply: 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (719) ~ (0 = 0) 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (719) is inconsistent. 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (720) ~ (all_168_1 = 0) & array_eq_sub1(int, all_103_2, 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, $sum(all_86_8, 1), all_86_13) = 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_168_1 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (444), (720) are inconsistent by sub-proof 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #83. 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | (721) length1(int, all_103_2) = all_242_1 & ( ~ 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | ($lesseq(1, $difference(all_242_1, all_86_8))) | 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ ($lesseq(all_86_13, all_242_1)) | ( ~ 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_242_0 = all_242_1) & length1(int, 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4) = all_242_0)) 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (721) implies: 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | (722) length1(int, all_103_2) = all_242_1 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | (723) ~ ($lesseq(1, $difference(all_242_1, all_86_8))) 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ ($lesseq(all_86_13, all_242_1)) | ( ~ 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_242_0 = all_242_1) & length1(int, 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4) = all_242_0) 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (272) gives: 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (724) all_171_0 = all_171_1 & $lesseq(all_86_11, 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_171_1) & $lesseq(0, all_171_1) & $lesseq(0, 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_86_11) & length1(int, all_103_2) = all_171_1 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & length1(int, all_103_4) = all_171_1 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (724) implies: 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (725) length1(int, all_103_4) = all_171_1 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (726) length1(int, all_103_2) = all_171_1 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_190_2, all_170_1, 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (410), (427) 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (727) all_190_2 = all_170_1 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_190_2, all_169_1, 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (427), (440) 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (728) all_190_2 = all_169_1 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_169_1, all_153_1, 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (415), (440) 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (729) all_169_1 = all_153_1 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_242_1, all_193_1, 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (419), (722) 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (730) all_242_1 = all_193_1 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_86_13, all_177_2, 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (184), (406) 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (731) all_177_2 = all_86_13 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_177_2, all_170_1, 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (406), (409) 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (732) all_177_2 = all_170_1 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_171_1, all_170_1, 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (409), (726) 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (733) all_171_1 = all_170_1 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_242_1, all_156_0, 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (394), (722) 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (734) all_242_1 = all_156_0 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_193_1, all_192_2, 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (418), (433) 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (735) all_193_1 = all_192_2 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_192_2, all_171_1, 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (433), (725) 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (736) all_192_2 = all_171_1 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (730), (734) imply: 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (737) all_193_1 = all_156_0 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (737) implies: 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (738) all_193_1 = all_156_0 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (735), (738) imply: 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (739) all_192_2 = all_156_0 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (739) implies: 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (740) all_192_2 = all_156_0 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (736), (740) imply: 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (741) all_171_1 = all_156_0 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (741) implies: 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (742) all_171_1 = all_156_0 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (727), (728) imply: 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (743) all_170_1 = all_169_1 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (731), (732) imply: 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (744) all_170_1 = all_86_13 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (744) implies: 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (745) all_170_1 = all_86_13 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (733), (742) imply: 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (746) all_170_1 = all_156_0 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (746) implies: 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (747) all_170_1 = all_156_0 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (743), (747) imply: 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (748) all_169_1 = all_156_0 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (748) implies: 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (749) all_169_1 = all_156_0 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (745), (747) imply: 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (750) all_156_0 = all_86_13 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (729), (749) imply: 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (751) all_156_0 = all_153_1 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (751) implies: 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (752) all_156_0 = all_153_1 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (750), (752) imply: 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (753) all_153_1 = all_86_13 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (753) implies: 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (754) all_153_1 = all_86_13 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (729), (754) imply: 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (755) all_169_1 = all_86_13 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (734), (750) imply: 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (756) all_242_1 = all_86_13 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (723) gives: 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (757) $lesseq(1, $difference(all_86_13, all_242_1)) 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (756), (757) imply: 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (758) $lesseq(0, -1) 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (758) is inconsistent. 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (759) ~ ($lesseq(1, $difference(all_242_1, all_86_8))) 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ( ~ (all_242_0 = all_242_1) & length1(int, 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4) = all_242_0) 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (52), (180), (389), (756), (759) are 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #82. 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (760) ~ (all_171_1 = 0) & array_eq_sub1(int, all_103_4, 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, 0, all_86_11) = all_171_1 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (442), (760) are inconsistent by sub-proof 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #81. 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | (761) length1(int, all_103_4) = all_215_1 & ( ~ 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | ($lesseq(all_86_11, all_215_1)) | ~ ($lesseq(0, 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | all_215_1)) | ( ~ (all_215_0 = all_215_1) & 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | length1(int, all_103_2) = all_215_0)) 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (761) implies: 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | (762) length1(int, all_103_4) = all_215_1 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | (763) ~ ($lesseq(all_86_11, all_215_1)) | ~ 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | ($lesseq(0, all_215_1)) | ( ~ (all_215_0 = 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | all_215_1) & length1(int, all_103_2) = 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | all_215_0) 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (345) gives: 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | (764) all_242_1 = 0 & array_eq_sub1(int, all_103_2, 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, $sum(all_86_8, 1), all_86_13) = 0 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (764) implies: 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | (765) array_eq_sub1(int, all_103_2, all_105_4, 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | $sum(all_86_8, 1), all_86_13) = 0 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (269) gives: 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (766) all_168_0 = all_168_1 & $lesseq(1, 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $difference(all_168_1, all_86_8)) & 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $lesseq(all_86_13, all_168_1) & $lesseq(-1, 204.07/127.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_86_8) & $lesseq(0, all_86_13) & length1(int, 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4) = all_168_1 & length1(int, all_103_2) 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_168_1 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (766) implies: 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (767) length1(int, all_103_2) = all_168_1 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (768) length1(int, all_105_4) = all_168_1 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_190_2, all_170_1, 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (410), (427) 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (769) all_190_2 = all_170_1 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_170_1, all_169_1, 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (410), (440) 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (770) all_170_1 = all_169_1 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_169_1, all_168_1, 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (440), (768) 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (771) all_169_1 = all_168_1 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_190_2, all_153_1, 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (415), (427) 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (772) all_190_2 = all_153_1 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_193_1, all_177_2, 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (406), (419) 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (773) all_193_1 = all_177_2 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_193_1, all_156_0, 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (394), (419) 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (774) all_193_1 = all_156_0 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_168_1, all_156_0, 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (394), (767) 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (775) all_168_1 = all_156_0 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_86_13, all_215_1, 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (183), (762) 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (776) all_215_1 = all_86_13 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_215_1, all_193_1, 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (418), (762) 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (777) all_215_1 = all_193_1 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_215_1, all_192_2, 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (433), (762) 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (778) all_215_1 = all_192_2 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (776), (778) imply: 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (779) all_192_2 = all_86_13 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (777), (778) imply: 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (780) all_193_1 = all_192_2 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (780) implies: 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (781) all_193_1 = all_192_2 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (773), (781) imply: 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (782) all_192_2 = all_177_2 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (782) implies: 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (783) all_192_2 = all_177_2 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (773), (774) imply: 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (784) all_177_2 = all_156_0 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (779), (783) imply: 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (785) all_177_2 = all_86_13 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (785) implies: 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (786) all_177_2 = all_86_13 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (769), (772) imply: 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (787) all_170_1 = all_153_1 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (787) implies: 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (788) all_170_1 = all_153_1 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (784), (786) imply: 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (789) all_156_0 = all_86_13 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (789) implies: 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (790) all_156_0 = all_86_13 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (770), (788) imply: 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (791) all_169_1 = all_153_1 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (791) implies: 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (792) all_169_1 = all_153_1 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (771), (792) imply: 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (793) all_168_1 = all_153_1 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (775), (793) imply: 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (794) all_156_0 = all_153_1 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (794) implies: 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (795) all_156_0 = all_153_1 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (790), (795) imply: 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (796) all_153_1 = all_86_13 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (796) implies: 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (797) all_153_1 = all_86_13 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (763) gives: 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (798) $lesseq(all_215_1, -1) 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (776), (798) imply: 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (799) $lesseq(all_86_13, -1) 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (48), (49), (50), (52), (53), (799) are 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #80. 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (800) ~ ($lesseq(all_86_11, all_215_1)) | ( ~ 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_215_0 = all_215_1) & length1(int, 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2) = all_215_0) 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (49), (50), (52), (53), (184), (776), (800) 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #78. 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (801) ~ (all_168_1 = 0) & array_eq_sub1(int, all_103_2, 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, $sum(all_86_8, 1), all_86_13) = 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_168_1 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (765), (801) are inconsistent by sub-proof 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #83. 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | (802) length1(int, all_103_2) = all_242_1 & ( ~ 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | ($lesseq(1, $difference(all_242_1, all_86_8))) | 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ ($lesseq(all_86_13, all_242_1)) | ( ~ 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_242_0 = all_242_1) & length1(int, 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4) = all_242_0)) 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (802) implies: 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | (803) length1(int, all_103_2) = all_242_1 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | (804) ~ ($lesseq(1, $difference(all_242_1, all_86_8))) 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ ($lesseq(all_86_13, all_242_1)) | ( ~ 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_242_0 = all_242_1) & length1(int, 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4) = all_242_0) 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (52), (180), (394), (406), (409), (410), 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | (415), (419), (427), (439), (440), (803), (804) 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #76. 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | End of split 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | (805) ~ (all_169_1 = 0) & array_eq_sub1(int, all_105_4, 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | all_105_2, 0, all_86_7) = all_169_1 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (437), (805) are inconsistent by sub-proof 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | #75. 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | End of split 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | Case 2: 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | (806) length1(int, all_105_4) = all_219_1 & ( ~ 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | ($lesseq(all_86_7, all_219_1)) | ~ ($lesseq(0, 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | all_219_1)) | ( ~ (all_219_0 = all_219_1) & 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | length1(int, all_105_2) = all_219_0)) 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (806) implies: 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | (807) length1(int, all_105_4) = all_219_1 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | (808) ~ ($lesseq(all_86_7, all_219_1)) | ~ ($lesseq(0, 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | all_219_1)) | ( ~ (all_219_0 = all_219_1) & 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | length1(int, all_105_2) = all_219_0) 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (319) gives: 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | (809) all_215_1 = 0 & array_eq_sub1(int, all_103_4, 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, 0, all_86_11) = 0 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (809) implies: 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | (810) array_eq_sub1(int, all_103_4, all_103_2, 0, 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | all_86_11) = 0 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (345) gives: 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | (811) all_242_1 = 0 & array_eq_sub1(int, all_103_2, 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, $sum(all_86_8, 1), all_86_13) = 0 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (811) implies: 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | (812) array_eq_sub1(int, all_103_2, all_105_4, 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | $sum(all_86_8, 1), all_86_13) = 0 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (45), (50), (52), (53), (183), (269), (272), 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | (389), (394), (406), (409), (414), (415), (416), 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | (418), (419), (427), (807), (808), (810), (812) 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #73. 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | (813) length1(int, all_103_2) = all_242_1 & ( ~ 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | ($lesseq(1, $difference(all_242_1, all_86_8))) | 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | ~ ($lesseq(all_86_13, all_242_1)) | ( ~ 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_242_0 = all_242_1) & length1(int, 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4) = all_242_0)) 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (813) implies: 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | (814) length1(int, all_103_2) = all_242_1 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | (815) ~ ($lesseq(1, $difference(all_242_1, all_86_8))) 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ ($lesseq(all_86_13, all_242_1)) | ( ~ 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_242_0 = all_242_1) & length1(int, 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4) = all_242_0) 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (272) gives: 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | (816) all_171_0 = all_171_1 & $lesseq(all_86_11, 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_171_1) & $lesseq(0, all_171_1) & $lesseq(0, 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_86_11) & length1(int, all_103_2) = all_171_1 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | & length1(int, all_103_4) = all_171_1 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (816) implies: 204.07/127.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | (817) length1(int, all_103_4) = all_171_1 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | (818) length1(int, all_103_2) = all_171_1 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_219_1, all_190_2, 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (427), (807) 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | (819) all_219_1 = all_190_2 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_190_2, all_170_1, 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (410), (427) 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | (820) all_190_2 = all_170_1 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_219_1, all_153_1, 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (415), (807) 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | (821) all_219_1 = all_153_1 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_242_1, all_193_1, 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (419), (814) 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | (822) all_242_1 = all_193_1 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_86_13, all_177_2, 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (184), (406) 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | (823) all_177_2 = all_86_13 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_177_2, all_170_1, 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (406), (409) 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | (824) all_177_2 = all_170_1 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_171_1, all_170_1, 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (409), (818) 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | (825) all_171_1 = all_170_1 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_242_1, all_156_0, 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (394), (814) 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | (826) all_242_1 = all_156_0 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_193_1, all_192_2, 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (418), (433) 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | (827) all_193_1 = all_192_2 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_192_2, all_171_1, 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (433), (817) 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | (828) all_192_2 = all_171_1 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (822), (826) imply: 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | (829) all_193_1 = all_156_0 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (829) implies: 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | (830) all_193_1 = all_156_0 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (819), (821) imply: 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | (831) all_190_2 = all_153_1 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (831) implies: 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | (832) all_190_2 = all_153_1 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (827), (830) imply: 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | (833) all_192_2 = all_156_0 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (833) implies: 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | (834) all_192_2 = all_156_0 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (828), (834) imply: 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | (835) all_171_1 = all_156_0 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (835) implies: 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | (836) all_171_1 = all_156_0 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (820), (832) imply: 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | (837) all_170_1 = all_153_1 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (823), (824) imply: 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | (838) all_170_1 = all_86_13 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (838) implies: 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | (839) all_170_1 = all_86_13 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (825), (836) imply: 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | (840) all_170_1 = all_156_0 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (840) implies: 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | (841) all_170_1 = all_156_0 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (839), (841) imply: 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | (842) all_156_0 = all_86_13 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (837), (841) imply: 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | (843) all_156_0 = all_153_1 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (842), (843) imply: 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | (844) all_153_1 = all_86_13 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (826), (842) imply: 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | (845) all_242_1 = all_86_13 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (52), (180), (389), (815), (845) are 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #77. 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | (846) ~ (all_171_1 = 0) & array_eq_sub1(int, all_103_4, 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, 0, all_86_11) = all_171_1 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (810), (846) are inconsistent by sub-proof 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | #81. 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | End of split 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | (847) length1(int, all_103_4) = all_215_1 & ( ~ 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | ($lesseq(all_86_11, all_215_1)) | ~ ($lesseq(0, 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | all_215_1)) | ( ~ (all_215_0 = all_215_1) & 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | length1(int, all_103_2) = all_215_0)) 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (847) implies: 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | (848) length1(int, all_103_4) = all_215_1 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | (849) ~ ($lesseq(all_86_11, all_215_1)) | ~ 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | ($lesseq(0, all_215_1)) | ( ~ (all_215_0 = 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | all_215_1) & length1(int, all_103_2) = 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | all_215_0) 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (45), (48), (50), (52), (53), (183), (184), 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | (269), (345), (394), (406), (409), (410), (414), 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | (415), (418), (419), (433), (807), (848), (849) 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #70. 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | End of split 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | End of split 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | Case 2: 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | (850) ~ (all_192_4 = 0) & permut_sub2(int, all_103_4, 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | all_103_2, all_86_11, $sum(all_86_10, 1)) = 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | all_192_4 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (43), (421), (850) are inconsistent by sub-proof 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | #69. 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | End of split 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | Case 2: 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | (851) ~ (all_190_4 = 0) & permut_sub2(int, all_105_4, 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | all_105_2, all_86_7, $sum(all_86_10, 1)) = 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | all_190_4 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (43), (423), (851) are inconsistent by sub-proof 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | #68. 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | | 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | End of split 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | 204.07/127.03 | | | | | | | | | | | | | | | | | | | | Case 2: 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | (852) elts(int, all_105_2) = all_187_2 & elts(int, 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | all_105_4) = all_187_3 & in_uni(all_187_2) & 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | in_uni(all_187_3) & (( ~ (all_187_0 = 0) & 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | map_eq_sub1(int, all_187_3, all_187_2, 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | $sum(all_86_10, 1), all_187_1) = all_187_0 & 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | length1(int, all_105_4) = all_187_1) | ( ~ 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | (all_187_1 = 0) & map_eq_sub1(int, all_187_3, 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | all_187_2, 0, all_86_7) = all_187_1)) 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | 204.07/127.03 | | | | | | | | | | | | | | | | | | | | | ALPHA: (852) implies: 204.07/127.04 | | | | | | | | | | | | | | | | | | | | | (853) elts(int, all_105_4) = all_187_3 204.07/127.04 | | | | | | | | | | | | | | | | | | | | | (854) elts(int, all_105_2) = all_187_2 204.07/127.04 | | | | | | | | | | | | | | | | | | | | | (855) ( ~ (all_187_0 = 0) & map_eq_sub1(int, all_187_3, 204.07/127.04 | | | | | | | | | | | | | | | | | | | | | all_187_2, $sum(all_86_10, 1), all_187_1) = 204.07/127.04 | | | | | | | | | | | | | | | | | | | | | all_187_0 & length1(int, all_105_4) = all_187_1) 204.07/127.04 | | | | | | | | | | | | | | | | | | | | | | ( ~ (all_187_1 = 0) & map_eq_sub1(int, 204.07/127.04 | | | | | | | | | | | | | | | | | | | | | all_187_3, all_187_2, 0, all_86_7) = 204.07/127.04 | | | | | | | | | | | | | | | | | | | | | all_187_1) 204.07/127.04 | | | | | | | | | | | | | | | | | | | | | 204.07/127.04 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (297) gives: 204.07/127.04 | | | | | | | | | | | | | | | | | | | | | 204.07/127.04 | | | | | | | | | | | | | | | | | | | | | Case 1: 204.07/127.04 | | | | | | | | | | | | | | | | | | | | | | 204.07/127.04 | | | | | | | | | | | | | | | | | | | | | | (856) all_192_0 = 0 & all_192_1 = 0 & map_eq_sub1(int, 204.07/127.04 | | | | | | | | | | | | | | | | | | | | | | all_192_4, all_192_3, $sum(all_86_10, 1), 204.07/127.04 | | | | | | | | | | | | | | | | | | | | | | all_192_2) = 0 & map_eq_sub1(int, all_192_4, 204.07/127.04 | | | | | | | | | | | | | | | | | | | | | | all_192_3, 0, all_86_11) = 0 & length1(int, 204.07/127.04 | | | | | | | | | | | | | | | | | | | | | | all_103_4) = all_192_2 & elts(int, all_103_2) = 204.07/127.04 | | | | | | | | | | | | | | | | | | | | | | all_192_3 & elts(int, all_103_4) = all_192_4 & 204.07/127.04 | | | | | | | | | | | | | | | | | | | | | | in_uni(all_192_3) & in_uni(all_192_4) 204.07/127.04 | | | | | | | | | | | | | | | | | | | | | | 204.07/127.04 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (856) implies: 204.07/127.04 | | | | | | | | | | | | | | | | | | | | | | (857) length1(int, all_103_4) = all_192_2 204.07/127.04 | | | | | | | | | | | | | | | | | | | | | | 204.07/127.04 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (319) gives: 204.07/127.04 | | | | | | | | | | | | | | | | | | | | | | 204.07/127.04 | | | | | | | | | | | | | | | | | | | | | | Case 1: 204.07/127.04 | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.04 | | | | | | | | | | | | | | | | | | | | | | | (858) all_215_1 = 0 & array_eq_sub1(int, all_103_4, 204.07/127.04 | | | | | | | | | | | | | | | | | | | | | | | all_103_2, 0, all_86_11) = 0 204.07/127.04 | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.04 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (858) implies: 204.07/127.04 | | | | | | | | | | | | | | | | | | | | | | | (859) array_eq_sub1(int, all_103_4, all_103_2, 0, 204.07/127.04 | | | | | | | | | | | | | | | | | | | | | | | all_86_11) = 0 204.07/127.04 | | | | | | | | | | | | | | | | | | | | | | | 204.07/127.04 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (39), (44), (45), (99), (100), (105), (180), 204.07/127.04 | | | | | | | | | | | | | | | | | | | | | | | (184), (205), (269), (270), (272), (324), (345), 204.07/127.04 | | | | | | | | | | | | | | | | | | | | | | | (394), (395), (405), (406), (409), (410), (415), 204.07/127.04 | | | | | | | | | | | | | | | | | | | | | | | (418), (419), (853), (854), (855), (859) are 204.07/127.04 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #63. 204.07/127.04 | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | Case 2: 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | (860) length1(int, all_103_4) = all_215_1 & ( ~ 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | ($lesseq(all_86_11, all_215_1)) | ~ ($lesseq(0, 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | all_215_1)) | ( ~ (all_215_0 = all_215_1) & 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | length1(int, all_103_2) = all_215_0)) 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (860) implies: 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | (861) length1(int, all_103_4) = all_215_1 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | (862) ~ ($lesseq(all_86_11, all_215_1)) | ~ 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | ($lesseq(0, all_215_1)) | ( ~ (all_215_0 = 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | all_215_1) & length1(int, all_103_2) = 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | all_215_0) 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (324) gives: 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | Case 1: 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | (863) all_219_1 = 0 & array_eq_sub1(int, all_105_4, 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | all_105_2, 0, all_86_7) = 0 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (863) implies: 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | (864) array_eq_sub1(int, all_105_4, all_105_2, 0, 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | all_86_7) = 0 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (270) gives: 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | (865) all_169_0 = all_169_1 & $lesseq(all_86_7, 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | all_169_1) & $lesseq(0, all_169_1) & $lesseq(0, 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | all_86_7) & length1(int, all_105_2) = all_169_1 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | & length1(int, all_105_4) = all_169_1 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (865) implies: 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | (866) length1(int, all_105_4) = all_169_1 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (345) gives: 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | (867) all_242_1 = 0 & array_eq_sub1(int, all_103_2, 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, $sum(all_86_8, 1), all_86_13) = 0 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (867) implies: 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | (868) array_eq_sub1(int, all_103_2, all_105_4, 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | $sum(all_86_8, 1), all_86_13) = 0 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (269) gives: 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | (869) all_168_0 = all_168_1 & $lesseq(1, 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | $difference(all_168_1, all_86_8)) & 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | $lesseq(all_86_13, all_168_1) & $lesseq(-1, 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_86_8) & $lesseq(0, all_86_13) & length1(int, 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4) = all_168_1 & length1(int, all_103_2) 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_168_1 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (869) implies: 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | (870) length1(int, all_103_2) = all_168_1 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | (871) length1(int, all_105_4) = all_168_1 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (48), (50), (52), (53), (184), (394), (406), 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | (410), (414), (415), (418), (419), (861), (862), 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | (866), (870), (871) are inconsistent by sub-proof 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | #62. 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | (872) ~ (all_168_1 = 0) & array_eq_sub1(int, all_103_2, 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, $sum(all_86_8, 1), all_86_13) = 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_168_1 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (868), (872) are inconsistent by sub-proof 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | #83. 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | (873) length1(int, all_103_2) = all_242_1 & ( ~ 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | ($lesseq(1, $difference(all_242_1, all_86_8))) | 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | ~ ($lesseq(all_86_13, all_242_1)) | ( ~ 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_242_0 = all_242_1) & length1(int, 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4) = all_242_0)) 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (873) implies: 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | (874) length1(int, all_103_2) = all_242_1 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_170_1, all_169_1, 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (410), (866) 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | (875) all_170_1 = all_169_1 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_169_1, all_153_1, 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (415), (866) 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | (876) all_169_1 = all_153_1 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_242_1, all_193_1, 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (419), (874) 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | (877) all_242_1 = all_193_1 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_193_1, all_177_2, 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (406), (419) 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | (878) all_193_1 = all_177_2 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_86_13, all_170_1, 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (184), (409) 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | (879) all_170_1 = all_86_13 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_193_1, all_170_1, 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (409), (419) 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | (880) all_193_1 = all_170_1 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_242_1, all_156_0, 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (394), (874) 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | (881) all_242_1 = all_156_0 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_86_13, all_215_1, 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (183), (861) 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | (882) all_215_1 = all_86_13 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_215_1, all_192_2, 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (857), (861) 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | (883) all_215_1 = all_192_2 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (877), (881) imply: 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | (884) all_193_1 = all_156_0 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (884) implies: 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | (885) all_193_1 = all_156_0 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (882), (883) imply: 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | (886) all_192_2 = all_86_13 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (878), (880) imply: 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | (887) all_177_2 = all_170_1 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (878), (885) imply: 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | (888) all_177_2 = all_156_0 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (887), (888) imply: 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | (889) all_170_1 = all_156_0 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (889) implies: 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | (890) all_170_1 = all_156_0 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (875), (879) imply: 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | (891) all_169_1 = all_86_13 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (891) implies: 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | (892) all_169_1 = all_86_13 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (879), (890) imply: 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | (893) all_156_0 = all_86_13 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (893) implies: 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | (894) all_156_0 = all_86_13 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (876), (892) imply: 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | (895) all_153_1 = all_86_13 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (48), (50), (52), (53), (394), (414), (862), 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | (882), (894), (895) are inconsistent by sub-proof 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | #72. 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | End of split 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | (896) ~ (all_169_1 = 0) & array_eq_sub1(int, all_105_4, 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | all_105_2, 0, all_86_7) = all_169_1 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (864), (896) are inconsistent by sub-proof 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | #75. 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | End of split 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | Case 2: 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | (897) length1(int, all_105_4) = all_219_1 & ( ~ 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | ($lesseq(all_86_7, all_219_1)) | ~ ($lesseq(0, 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | all_219_1)) | ( ~ (all_219_0 = all_219_1) & 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | length1(int, all_105_2) = all_219_0)) 204.33/127.04 | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.05 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (897) implies: 204.33/127.05 | | | | | | | | | | | | | | | | | | | | | | | | (898) length1(int, all_105_4) = all_219_1 204.33/127.05 | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.05 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (45), (48), (50), (52), (53), (183), (184), 204.33/127.05 | | | | | | | | | | | | | | | | | | | | | | | | (269), (345), (394), (406), (409), (410), (414), 204.33/127.05 | | | | | | | | | | | | | | | | | | | | | | | | (415), (418), (419), (857), (861), (862), (898) 204.33/127.05 | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #70. 204.33/127.05 | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.05 | | | | | | | | | | | | | | | | | | | | | | | End of split 204.33/127.05 | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.05 | | | | | | | | | | | | | | | | | | | | | | End of split 204.33/127.05 | | | | | | | | | | | | | | | | | | | | | | 204.33/127.05 | | | | | | | | | | | | | | | | | | | | | Case 2: 204.33/127.05 | | | | | | | | | | | | | | | | | | | | | | 204.33/127.05 | | | | | | | | | | | | | | | | | | | | | | (899) ~ (all_192_4 = 0) & permut_sub2(int, all_103_4, 204.33/127.05 | | | | | | | | | | | | | | | | | | | | | | all_103_2, all_86_11, $sum(all_86_10, 1)) = 204.33/127.05 | | | | | | | | | | | | | | | | | | | | | | all_192_4 204.33/127.05 | | | | | | | | | | | | | | | | | | | | | | 204.33/127.05 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (43), (421), (899) are inconsistent by sub-proof 204.33/127.05 | | | | | | | | | | | | | | | | | | | | | | #69. 204.33/127.05 | | | | | | | | | | | | | | | | | | | | | | 204.33/127.05 | | | | | | | | | | | | | | | | | | | | | End of split 204.33/127.05 | | | | | | | | | | | | | | | | | | | | | 204.33/127.05 | | | | | | | | | | | | | | | | | | | | End of split 204.33/127.05 | | | | | | | | | | | | | | | | | | | | 204.33/127.05 | | | | | | | | | | | | | | | | | | | Case 2: 204.33/127.05 | | | | | | | | | | | | | | | | | | | | 204.33/127.05 | | | | | | | | | | | | | | | | | | | | (900) elts(int, all_103_2) = all_191_2 & elts(int, 204.33/127.05 | | | | | | | | | | | | | | | | | | | | all_103_4) = all_191_3 & in_uni(all_191_2) & 204.33/127.05 | | | | | | | | | | | | | | | | | | | | in_uni(all_191_3) & (( ~ (all_191_0 = 0) & 204.33/127.05 | | | | | | | | | | | | | | | | | | | | map_eq_sub1(int, all_191_3, all_191_2, 204.33/127.05 | | | | | | | | | | | | | | | | | | | | $sum(all_86_10, 1), all_191_1) = all_191_0 & 204.33/127.05 | | | | | | | | | | | | | | | | | | | | length1(int, all_103_4) = all_191_1) | ( ~ 204.33/127.05 | | | | | | | | | | | | | | | | | | | | (all_191_1 = 0) & map_eq_sub1(int, all_191_3, 204.33/127.05 | | | | | | | | | | | | | | | | | | | | all_191_2, 0, all_86_11) = all_191_1)) 204.33/127.05 | | | | | | | | | | | | | | | | | | | | 204.33/127.05 | | | | | | | | | | | | | | | | | | | | ALPHA: (900) implies: 204.33/127.05 | | | | | | | | | | | | | | | | | | | | (901) elts(int, all_103_4) = all_191_3 204.33/127.05 | | | | | | | | | | | | | | | | | | | | (902) elts(int, all_103_2) = all_191_2 204.33/127.05 | | | | | | | | | | | | | | | | | | | | (903) ( ~ (all_191_0 = 0) & map_eq_sub1(int, all_191_3, 204.33/127.05 | | | | | | | | | | | | | | | | | | | | all_191_2, $sum(all_86_10, 1), all_191_1) = 204.33/127.05 | | | | | | | | | | | | | | | | | | | | all_191_0 & length1(int, all_103_4) = all_191_1) 204.33/127.05 | | | | | | | | | | | | | | | | | | | | | ( ~ (all_191_1 = 0) & map_eq_sub1(int, 204.33/127.05 | | | | | | | | | | | | | | | | | | | | all_191_3, all_191_2, 0, all_86_11) = 204.33/127.05 | | | | | | | | | | | | | | | | | | | | all_191_1) 204.33/127.05 | | | | | | | | | | | | | | | | | | | | 204.33/127.05 | | | | | | | | | | | | | | | | | | | | BETA: splitting (294) gives: 204.33/127.05 | | | | | | | | | | | | | | | | | | | | 204.33/127.05 | | | | | | | | | | | | | | | | | | | | Case 1: 204.33/127.05 | | | | | | | | | | | | | | | | | | | | | 204.33/127.05 | | | | | | | | | | | | | | | | | | | | | (904) all_187_3 = 0 & permut_sub2(int, all_105_4, 204.33/127.05 | | | | | | | | | | | | | | | | | | | | | all_105_2, all_86_7, $sum(all_86_10, 1)) = 0 204.33/127.05 | | | | | | | | | | | | | | | | | | | | | 204.33/127.05 | | | | | | | | | | | | | | | | | | | | | ALPHA: (904) implies: 204.33/127.05 | | | | | | | | | | | | | | | | | | | | | (905) permut_sub2(int, all_105_4, all_105_2, all_86_7, 204.33/127.05 | | | | | | | | | | | | | | | | | | | | | $sum(all_86_10, 1)) = 0 204.33/127.05 | | | | | | | | | | | | | | | | | | | | | 204.33/127.05 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (295) gives: 204.33/127.05 | | | | | | | | | | | | | | | | | | | | | 204.33/127.05 | | | | | | | | | | | | | | | | | | | | | Case 1: 204.33/127.05 | | | | | | | | | | | | | | | | | | | | | | 204.33/127.05 | | | | | | | | | | | | | | | | | | | | | | (906) all_190_0 = 0 & all_190_1 = 0 & map_eq_sub1(int, 204.33/127.05 | | | | | | | | | | | | | | | | | | | | | | all_190_4, all_190_3, $sum(all_86_10, 1), 204.33/127.05 | | | | | | | | | | | | | | | | | | | | | | all_190_2) = 0 & map_eq_sub1(int, all_190_4, 204.33/127.05 | | | | | | | | | | | | | | | | | | | | | | all_190_3, 0, all_86_7) = 0 & length1(int, 204.33/127.05 | | | | | | | | | | | | | | | | | | | | | | all_105_4) = all_190_2 & elts(int, all_105_2) = 204.33/127.05 | | | | | | | | | | | | | | | | | | | | | | all_190_3 & elts(int, all_105_4) = all_190_4 & 204.33/127.05 | | | | | | | | | | | | | | | | | | | | | | in_uni(all_190_3) & in_uni(all_190_4) 204.33/127.05 | | | | | | | | | | | | | | | | | | | | | | 204.33/127.05 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (906) implies: 204.33/127.05 | | | | | | | | | | | | | | | | | | | | | | (907) length1(int, all_105_4) = all_190_2 204.33/127.05 | | | | | | | | | | | | | | | | | | | | | | 204.33/127.05 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (319) gives: 204.33/127.05 | | | | | | | | | | | | | | | | | | | | | | 204.33/127.05 | | | | | | | | | | | | | | | | | | | | | | Case 1: 204.33/127.05 | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.05 | | | | | | | | | | | | | | | | | | | | | | | (908) all_215_1 = 0 & array_eq_sub1(int, all_103_4, 204.33/127.05 | | | | | | | | | | | | | | | | | | | | | | | all_103_2, 0, all_86_11) = 0 204.33/127.05 | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.05 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (908) implies: 204.33/127.05 | | | | | | | | | | | | | | | | | | | | | | | (909) array_eq_sub1(int, all_103_4, all_103_2, 0, 204.33/127.05 | | | | | | | | | | | | | | | | | | | | | | | all_86_11) = 0 204.33/127.05 | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.05 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (272) gives: 204.33/127.05 | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.05 | | | | | | | | | | | | | | | | | | | | | | | Case 1: 204.33/127.05 | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.05 | | | | | | | | | | | | | | | | | | | | | | | | (910) all_171_0 = all_171_1 & $lesseq(all_86_11, 204.33/127.05 | | | | | | | | | | | | | | | | | | | | | | | | all_171_1) & $lesseq(0, all_171_1) & $lesseq(0, 204.33/127.05 | | | | | | | | | | | | | | | | | | | | | | | | all_86_11) & length1(int, all_103_2) = all_171_1 204.33/127.05 | | | | | | | | | | | | | | | | | | | | | | | | & length1(int, all_103_4) = all_171_1 204.33/127.05 | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.05 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (910) implies: 204.33/127.05 | | | | | | | | | | | | | | | | | | | | | | | | (911) length1(int, all_103_4) = all_171_1 204.33/127.05 | | | | | | | | | | | | | | | | | | | | | | | | (912) length1(int, all_103_2) = all_171_1 204.33/127.05 | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.05 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (324) gives: 204.33/127.05 | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.05 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: 204.33/127.05 | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.05 | | | | | | | | | | | | | | | | | | | | | | | | | (913) all_219_1 = 0 & array_eq_sub1(int, all_105_4, 204.33/127.05 | | | | | | | | | | | | | | | | | | | | | | | | | all_105_2, 0, all_86_7) = 0 204.33/127.05 | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.05 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (913) implies: 204.33/127.05 | | | | | | | | | | | | | | | | | | | | | | | | | (914) array_eq_sub1(int, all_105_4, all_105_2, 0, 204.33/127.05 | | | | | | | | | | | | | | | | | | | | | | | | | all_86_7) = 0 204.33/127.05 | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.05 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (270) gives: 204.33/127.05 | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.05 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: 204.33/127.05 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.05 | | | | | | | | | | | | | | | | | | | | | | | | | | (915) all_169_0 = all_169_1 & $lesseq(all_86_7, 204.33/127.05 | | | | | | | | | | | | | | | | | | | | | | | | | | all_169_1) & $lesseq(0, all_169_1) & $lesseq(0, 204.33/127.05 | | | | | | | | | | | | | | | | | | | | | | | | | | all_86_7) & length1(int, all_105_2) = all_169_1 204.33/127.05 | | | | | | | | | | | | | | | | | | | | | | | | | | & length1(int, all_105_4) = all_169_1 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (915) implies: 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | (916) $lesseq(all_86_7, all_169_1) 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | (917) length1(int, all_105_4) = all_169_1 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (345) gives: 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | (918) all_242_1 = 0 & array_eq_sub1(int, all_103_2, 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, $sum(all_86_8, 1), all_86_13) = 0 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (918) implies: 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | (919) array_eq_sub1(int, all_103_2, all_105_4, 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | $sum(all_86_8, 1), all_86_13) = 0 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (39), (44), (45), (90), (91), (96), (183), 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | (206), (269), (394), (396), (404), (406), (409), 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | (418), (419), (901), (902), (903), (911), (912), 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | (919) are inconsistent by sub-proof #60. 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | (920) length1(int, all_103_2) = all_242_1 & ( ~ 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | ($lesseq(1, $difference(all_242_1, all_86_8))) | 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ ($lesseq(all_86_13, all_242_1)) | ( ~ 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_242_0 = all_242_1) & length1(int, 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4) = all_242_0)) 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (920) implies: 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | (921) length1(int, all_103_2) = all_242_1 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | (922) ~ ($lesseq(1, $difference(all_242_1, all_86_8))) 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ ($lesseq(all_86_13, all_242_1)) | ( ~ 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_242_0 = all_242_1) & length1(int, 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4) = all_242_0) 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (52), (180), (394), (406), (409), (410), 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | (415), (419), (907), (916), (917), (921), (922) 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #76. 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | (923) ~ (all_169_1 = 0) & array_eq_sub1(int, all_105_4, 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_2, 0, all_86_7) = all_169_1 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (914), (923) are inconsistent by sub-proof 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | #75. 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | End of split 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | (924) length1(int, all_105_4) = all_219_1 & ( ~ 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | ($lesseq(all_86_7, all_219_1)) | ~ ($lesseq(0, 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | all_219_1)) | ( ~ (all_219_0 = all_219_1) & 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | length1(int, all_105_2) = all_219_0)) 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (924) implies: 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | (925) length1(int, all_105_4) = all_219_1 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | (926) ~ ($lesseq(all_86_7, all_219_1)) | ~ ($lesseq(0, 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | all_219_1)) | ( ~ (all_219_0 = all_219_1) & 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | length1(int, all_105_2) = all_219_0) 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (345) gives: 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | (927) all_242_1 = 0 & array_eq_sub1(int, all_103_2, 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, $sum(all_86_8, 1), all_86_13) = 0 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (927) implies: 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | (928) array_eq_sub1(int, all_103_2, all_105_4, 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | $sum(all_86_8, 1), all_86_13) = 0 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (45), (50), (52), (53), (183), (269), (272), 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | (389), (394), (406), (409), (414), (415), (416), 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | (418), (419), (907), (909), (925), (926), (928) 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #73. 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | (929) length1(int, all_103_2) = all_242_1 & ( ~ 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | ($lesseq(1, $difference(all_242_1, all_86_8))) | 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | ~ ($lesseq(all_86_13, all_242_1)) | ( ~ 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_242_0 = all_242_1) & length1(int, 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4) = all_242_0)) 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (929) implies: 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | (930) length1(int, all_103_2) = all_242_1 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_219_1, all_170_1, 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (410), (925) 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | (931) all_219_1 = all_170_1 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_219_1, all_153_1, 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (415), (925) 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | (932) all_219_1 = all_153_1 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_242_1, all_193_1, 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (419), (930) 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | (933) all_242_1 = all_193_1 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_193_1, all_177_2, 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (406), (419) 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | (934) all_193_1 = all_177_2 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_242_1, all_171_1, 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (912), (930) 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | (935) all_242_1 = all_171_1 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_193_1, all_170_1, 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (409), (419) 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | (936) all_193_1 = all_170_1 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_193_1, all_156_0, 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (394), (419) 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | (937) all_193_1 = all_156_0 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_86_13, all_193_1, 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (183), (418) 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | (938) all_193_1 = all_86_13 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (933), (935) imply: 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | (939) all_193_1 = all_171_1 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (939) implies: 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | (940) all_193_1 = all_171_1 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (931), (932) imply: 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | (941) all_170_1 = all_153_1 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (941) implies: 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | (942) all_170_1 = all_153_1 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (934), (937) imply: 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | (943) all_177_2 = all_156_0 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (934), (938) imply: 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | (944) all_177_2 = all_86_13 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (934), (940) imply: 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | (945) all_177_2 = all_171_1 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (934), (936) imply: 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | (946) all_177_2 = all_170_1 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (944), (945) imply: 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | (947) all_171_1 = all_86_13 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (943), (945) imply: 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | (948) all_171_1 = all_156_0 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (945), (946) imply: 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | (949) all_171_1 = all_170_1 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (948), (949) imply: 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | (950) all_170_1 = all_156_0 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (950) implies: 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | (951) all_170_1 = all_156_0 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (947), (948) imply: 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | (952) all_156_0 = all_86_13 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (942), (951) imply: 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | (953) all_156_0 = all_153_1 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (953) implies: 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | (954) all_156_0 = all_153_1 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (952), (954) imply: 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | (955) all_153_1 = all_86_13 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (48), (50), (52), (53), (389), (414), (416), 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | (926), (932), (955) are inconsistent by sub-proof 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | #58. 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | End of split 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | End of split 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | Case 2: 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | (956) ~ (all_171_1 = 0) & array_eq_sub1(int, all_103_4, 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, 0, all_86_11) = all_171_1 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (909), (956) are inconsistent by sub-proof 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | #81. 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | End of split 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | Case 2: 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | (957) length1(int, all_103_4) = all_215_1 & ( ~ 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | ($lesseq(all_86_11, all_215_1)) | ~ ($lesseq(0, 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | all_215_1)) | ( ~ (all_215_0 = all_215_1) & 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | length1(int, all_103_2) = all_215_0)) 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (957) implies: 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | (958) length1(int, all_103_4) = all_215_1 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | (959) ~ ($lesseq(all_86_11, all_215_1)) | ~ 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | ($lesseq(0, all_215_1)) | ( ~ (all_215_0 = 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | all_215_1) & length1(int, all_103_2) = 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | all_215_0) 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (324) gives: 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | Case 1: 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | (960) all_219_1 = 0 & array_eq_sub1(int, all_105_4, 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | all_105_2, 0, all_86_7) = 0 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (960) implies: 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | (961) array_eq_sub1(int, all_105_4, all_105_2, 0, 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | all_86_7) = 0 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (345) gives: 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | (962) all_242_1 = 0 & array_eq_sub1(int, all_103_2, 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, $sum(all_86_8, 1), all_86_13) = 0 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (962) implies: 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | (963) array_eq_sub1(int, all_103_2, all_105_4, 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | $sum(all_86_8, 1), all_86_13) = 0 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (269) gives: 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | (964) all_168_0 = all_168_1 & $lesseq(1, 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | $difference(all_168_1, all_86_8)) & 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | $lesseq(all_86_13, all_168_1) & $lesseq(-1, 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | all_86_8) & $lesseq(0, all_86_13) & length1(int, 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4) = all_168_1 & length1(int, all_103_2) 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | = all_168_1 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (964) implies: 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | (965) length1(int, all_103_2) = all_168_1 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | (966) length1(int, all_105_4) = all_168_1 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (270) gives: 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | (967) all_169_0 = all_169_1 & $lesseq(all_86_7, 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_169_1) & $lesseq(0, all_169_1) & $lesseq(0, 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_86_7) & length1(int, all_105_2) = all_169_1 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | & length1(int, all_105_4) = all_169_1 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (967) implies: 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | (968) length1(int, all_105_4) = all_169_1 204.33/127.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (48), (50), (52), (53), (184), (394), (406), 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | (410), (414), (415), (418), (419), (958), (959), 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | (965), (966), (968) are inconsistent by sub-proof 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | #62. 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | (969) ~ (all_169_1 = 0) & array_eq_sub1(int, all_105_4, 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_2, 0, all_86_7) = all_169_1 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (961), (969) are inconsistent by sub-proof 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | #75. 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | | (970) ~ (all_168_1 = 0) & array_eq_sub1(int, all_103_2, 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, $sum(all_86_8, 1), all_86_13) = 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | | all_168_1 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (963), (970) are inconsistent by sub-proof 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | | #83. 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | End of split 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | (971) length1(int, all_103_2) = all_242_1 & ( ~ 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | ($lesseq(1, $difference(all_242_1, all_86_8))) | 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | ~ ($lesseq(all_86_13, all_242_1)) | ( ~ 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | (all_242_0 = all_242_1) & length1(int, 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4) = all_242_0)) 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (971) implies: 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | (972) length1(int, all_103_2) = all_242_1 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | (973) ~ ($lesseq(1, $difference(all_242_1, all_86_8))) 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | | ~ ($lesseq(all_86_13, all_242_1)) | ( ~ 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | (all_242_0 = all_242_1) & length1(int, 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4) = all_242_0) 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (270) gives: 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | | (974) all_169_0 = all_169_1 & $lesseq(all_86_7, 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | | all_169_1) & $lesseq(0, all_169_1) & $lesseq(0, 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | | all_86_7) & length1(int, all_105_2) = all_169_1 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | | & length1(int, all_105_4) = all_169_1 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (974) implies: 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | | (975) $lesseq(all_86_7, all_169_1) 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | | (976) length1(int, all_105_4) = all_169_1 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (52), (180), (394), (406), (409), (410), 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | | (415), (419), (907), (972), (973), (975), (976) 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #76. 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | | (977) ~ (all_169_1 = 0) & array_eq_sub1(int, all_105_4, 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_2, 0, all_86_7) = all_169_1 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (961), (977) are inconsistent by sub-proof 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | | #75. 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | End of split 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | End of split 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | Case 2: 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | (978) length1(int, all_105_4) = all_219_1 & ( ~ 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | ($lesseq(all_86_7, all_219_1)) | ~ ($lesseq(0, 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | all_219_1)) | ( ~ (all_219_0 = all_219_1) & 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | length1(int, all_105_2) = all_219_0)) 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (978) implies: 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | (979) length1(int, all_105_4) = all_219_1 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (345) gives: 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | (980) all_242_1 = 0 & array_eq_sub1(int, all_103_2, 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, $sum(all_86_8, 1), all_86_13) = 0 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (980) implies: 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | (981) array_eq_sub1(int, all_103_2, all_105_4, 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | $sum(all_86_8, 1), all_86_13) = 0 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (45), (48), (50), (52), (53), (183), (184), 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | (269), (394), (406), (409), (410), (414), (415), 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | (419), (958), (959), (979), (981) are inconsistent 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #71. 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | (982) length1(int, all_103_2) = all_242_1 & ( ~ 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | ($lesseq(1, $difference(all_242_1, all_86_8))) | 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | ~ ($lesseq(all_86_13, all_242_1)) | ( ~ 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | (all_242_0 = all_242_1) & length1(int, 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4) = all_242_0)) 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (982) implies: 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | (983) length1(int, all_103_2) = all_242_1 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | (984) ~ ($lesseq(1, $difference(all_242_1, all_86_8))) 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | | ~ ($lesseq(all_86_13, all_242_1)) | ( ~ 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | (all_242_0 = all_242_1) & length1(int, 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4) = all_242_0) 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_219_1, all_190_2, 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (907), (979) 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | (985) all_219_1 = all_190_2 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_190_2, all_170_1, 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (410), (907) 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | (986) all_190_2 = all_170_1 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_219_1, all_153_1, 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (415), (979) 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | (987) all_219_1 = all_153_1 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_242_1, all_177_2, 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (406), (983) 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | (988) all_242_1 = all_177_2 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_193_1, all_177_2, 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (406), (419) 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | (989) all_193_1 = all_177_2 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_242_1, all_170_1, 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (409), (983) 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | (990) all_242_1 = all_170_1 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_86_13, all_215_1, 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (183), (958) 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | (991) all_215_1 = all_86_13 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_215_1, all_193_1, 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (418), (958) 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | (992) all_215_1 = all_193_1 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (988), (990) imply: 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | (993) all_177_2 = all_170_1 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (993) implies: 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | (994) all_177_2 = all_170_1 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (985), (987) imply: 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | (995) all_190_2 = all_153_1 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (995) implies: 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | (996) all_190_2 = all_153_1 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (991), (992) imply: 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | (997) all_193_1 = all_86_13 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (989), (997) imply: 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | (998) all_177_2 = all_86_13 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (998) implies: 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | (999) all_177_2 = all_86_13 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (986), (996) imply: 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | (1000) all_170_1 = all_153_1 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1000) implies: 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | (1001) all_170_1 = all_153_1 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (994), (999) imply: 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | (1002) all_170_1 = all_86_13 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1001), (1002) imply: 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | (1003) all_153_1 = all_86_13 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1003) implies: 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | (1004) all_153_1 = all_86_13 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (990), (1002) imply: 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | (1005) all_242_1 = all_86_13 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (52), (180), (389), (984), (1005) are 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #77. 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | End of split 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | End of split 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | | 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | End of split 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | Case 2: 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | (1006) ~ (all_190_4 = 0) & permut_sub2(int, all_105_4, 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | all_105_2, all_86_7, $sum(all_86_10, 1)) = 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | all_190_4 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (43), (905), (1006) are inconsistent by sub-proof 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | #68. 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | End of split 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | 204.33/127.07 | | | | | | | | | | | | | | | | | | | | Case 2: 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | (1007) elts(int, all_105_2) = all_187_2 & elts(int, 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | all_105_4) = all_187_3 & in_uni(all_187_2) & 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | in_uni(all_187_3) & (( ~ (all_187_0 = 0) & 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | map_eq_sub1(int, all_187_3, all_187_2, 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | $sum(all_86_10, 1), all_187_1) = all_187_0 & 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | length1(int, all_105_4) = all_187_1) | ( ~ 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | (all_187_1 = 0) & map_eq_sub1(int, all_187_3, 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | all_187_2, 0, all_86_7) = all_187_1)) 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | ALPHA: (1007) implies: 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | (1008) elts(int, all_105_4) = all_187_3 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | (1009) elts(int, all_105_2) = all_187_2 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | (1010) ( ~ (all_187_0 = 0) & map_eq_sub1(int, all_187_3, 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | all_187_2, $sum(all_86_10, 1), all_187_1) = 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | all_187_0 & length1(int, all_105_4) = all_187_1) 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | | ( ~ (all_187_1 = 0) & map_eq_sub1(int, 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | all_187_3, all_187_2, 0, all_86_7) = 204.33/127.07 | | | | | | | | | | | | | | | | | | | | | all_187_1) 204.33/127.08 | | | | | | | | | | | | | | | | | | | | | 204.33/127.08 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (319) gives: 204.33/127.08 | | | | | | | | | | | | | | | | | | | | | 204.33/127.08 | | | | | | | | | | | | | | | | | | | | | Case 1: 204.33/127.08 | | | | | | | | | | | | | | | | | | | | | | 204.33/127.08 | | | | | | | | | | | | | | | | | | | | | | (1011) all_215_1 = 0 & array_eq_sub1(int, all_103_4, 204.33/127.08 | | | | | | | | | | | | | | | | | | | | | | all_103_2, 0, all_86_11) = 0 204.33/127.08 | | | | | | | | | | | | | | | | | | | | | | 204.33/127.08 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1011) implies: 204.33/127.08 | | | | | | | | | | | | | | | | | | | | | | (1012) array_eq_sub1(int, all_103_4, all_103_2, 0, 204.33/127.08 | | | | | | | | | | | | | | | | | | | | | | all_86_11) = 0 204.33/127.08 | | | | | | | | | | | | | | | | | | | | | | 204.33/127.08 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (39), (44), (45), (99), (100), (105), (180), 204.33/127.08 | | | | | | | | | | | | | | | | | | | | | | (184), (205), (269), (270), (272), (324), (345), 204.33/127.08 | | | | | | | | | | | | | | | | | | | | | | (394), (395), (405), (406), (409), (410), (415), 204.33/127.08 | | | | | | | | | | | | | | | | | | | | | | (418), (419), (1008), (1009), (1010), (1012) are 204.33/127.08 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #63. 204.33/127.08 | | | | | | | | | | | | | | | | | | | | | | 204.33/127.08 | | | | | | | | | | | | | | | | | | | | | Case 2: 204.33/127.08 | | | | | | | | | | | | | | | | | | | | | | 204.33/127.08 | | | | | | | | | | | | | | | | | | | | | | (1013) length1(int, all_103_4) = all_215_1 & ( ~ 204.33/127.08 | | | | | | | | | | | | | | | | | | | | | | ($lesseq(all_86_11, all_215_1)) | ~ ($lesseq(0, 204.33/127.08 | | | | | | | | | | | | | | | | | | | | | | all_215_1)) | ( ~ (all_215_0 = all_215_1) & 204.33/127.08 | | | | | | | | | | | | | | | | | | | | | | length1(int, all_103_2) = all_215_0)) 204.33/127.08 | | | | | | | | | | | | | | | | | | | | | | 204.33/127.08 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1013) implies: 204.33/127.08 | | | | | | | | | | | | | | | | | | | | | | (1014) length1(int, all_103_4) = all_215_1 204.33/127.08 | | | | | | | | | | | | | | | | | | | | | | 204.33/127.08 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (39), (44), (90), (91), (96), (183), (206), 204.33/127.08 | | | | | | | | | | | | | | | | | | | | | | (396), (404), (418), (901), (902), (903), (1014) 204.33/127.08 | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #56. 204.33/127.08 | | | | | | | | | | | | | | | | | | | | | | 204.33/127.08 | | | | | | | | | | | | | | | | | | | | | End of split 204.33/127.08 | | | | | | | | | | | | | | | | | | | | | 204.33/127.08 | | | | | | | | | | | | | | | | | | | | End of split 204.33/127.08 | | | | | | | | | | | | | | | | | | | | 204.33/127.08 | | | | | | | | | | | | | | | | | | | End of split 204.33/127.08 | | | | | | | | | | | | | | | | | | | 204.33/127.08 | | | | | | | | | | | | | | | | | | Case 2: 204.33/127.08 | | | | | | | | | | | | | | | | | | | 204.33/127.08 | | | | | | | | | | | | | | | | | | | (1015) ~ (all_193_1 = 0) & array_eq_sub1(int, all_103_4, 204.33/127.08 | | | | | | | | | | | | | | | | | | | all_103_2, $sum(all_86_10, 1), all_86_13) = 204.33/127.08 | | | | | | | | | | | | | | | | | | | all_193_1 204.33/127.08 | | | | | | | | | | | | | | | | | | | 204.33/127.08 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (400), (1015) are inconsistent by sub-proof 204.33/127.08 | | | | | | | | | | | | | | | | | | | #55. 204.33/127.08 | | | | | | | | | | | | | | | | | | | 204.33/127.08 | | | | | | | | | | | | | | | | | | End of split 204.33/127.08 | | | | | | | | | | | | | | | | | | 204.33/127.08 | | | | | | | | | | | | | | | | | Case 2: 204.33/127.08 | | | | | | | | | | | | | | | | | | 204.33/127.08 | | | | | | | | | | | | | | | | | | (1016) ~ (all_153_1 = 0) & array_eq_sub1(int, all_105_4, 204.33/127.08 | | | | | | | | | | | | | | | | | | all_105_2, $sum(all_86_10, 1), all_86_13) = 204.33/127.08 | | | | | | | | | | | | | | | | | | all_153_1 204.33/127.08 | | | | | | | | | | | | | | | | | | 204.33/127.08 | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (412), (1016) are inconsistent by sub-proof 204.33/127.08 | | | | | | | | | | | | | | | | | | #54. 204.33/127.08 | | | | | | | | | | | | | | | | | | 204.33/127.08 | | | | | | | | | | | | | | | | | End of split 204.33/127.08 | | | | | | | | | | | | | | | | | 204.33/127.08 | | | | | | | | | | | | | | | | Case 2: 204.33/127.08 | | | | | | | | | | | | | | | | | 204.33/127.08 | | | | | | | | | | | | | | | | | (1017) length1(int, all_105_4) = all_234_1 & ( ~ 204.33/127.08 | | | | | | | | | | | | | | | | | ($lesseq(1, $difference(all_234_1, all_86_10))) 204.33/127.08 | | | | | | | | | | | | | | | | | | ~ ($lesseq(all_86_13, all_234_1)) | ( ~ 204.33/127.08 | | | | | | | | | | | | | | | | | (all_234_0 = all_234_1) & length1(int, 204.33/127.08 | | | | | | | | | | | | | | | | | all_105_2) = all_234_0)) 204.33/127.08 | | | | | | | | | | | | | | | | | 204.33/127.08 | | | | | | | | | | | | | | | | | ALPHA: (1017) implies: 204.33/127.08 | | | | | | | | | | | | | | | | | (1018) length1(int, all_105_4) = all_234_1 204.47/127.08 | | | | | | | | | | | | | | | | | (1019) ~ ($lesseq(1, $difference(all_234_1, all_86_10))) 204.47/127.08 | | | | | | | | | | | | | | | | | | ~ ($lesseq(all_86_13, all_234_1)) | ( ~ 204.47/127.08 | | | | | | | | | | | | | | | | | (all_234_0 = all_234_1) & length1(int, 204.47/127.08 | | | | | | | | | | | | | | | | | all_105_2) = all_234_0) 204.47/127.08 | | | | | | | | | | | | | | | | | 204.47/127.08 | | | | | | | | | | | | | | | | | BETA: splitting (298) gives: 204.47/127.08 | | | | | | | | | | | | | | | | | 204.47/127.08 | | | | | | | | | | | | | | | | | Case 1: 204.47/127.08 | | | | | | | | | | | | | | | | | | 204.47/127.08 | | | | | | | | | | | | | | | | | | (1020) all_193_0 = all_193_1 & $lesseq(1, 204.47/127.08 | | | | | | | | | | | | | | | | | | $difference(all_193_1, all_86_10)) & 204.47/127.08 | | | | | | | | | | | | | | | | | | $lesseq(all_86_13, all_193_1) & $lesseq(-1, 204.47/127.08 | | | | | | | | | | | | | | | | | | all_86_10) & $lesseq(0, all_86_13) & 204.47/127.08 | | | | | | | | | | | | | | | | | | length1(int, all_103_2) = all_193_1 & length1(int, 204.47/127.08 | | | | | | | | | | | | | | | | | | all_103_4) = all_193_1 204.47/127.08 | | | | | | | | | | | | | | | | | | 204.47/127.08 | | | | | | | | | | | | | | | | | | ALPHA: (1020) implies: 204.47/127.08 | | | | | | | | | | | | | | | | | | (1021) $lesseq(1, $difference(all_193_1, all_86_10)) 204.47/127.08 | | | | | | | | | | | | | | | | | | (1022) length1(int, all_103_4) = all_193_1 204.47/127.08 | | | | | | | | | | | | | | | | | | (1023) length1(int, all_103_2) = all_193_1 204.47/127.08 | | | | | | | | | | | | | | | | | | 204.47/127.08 | | | | | | | | | | | | | | | | | | BETA: splitting (319) gives: 204.47/127.08 | | | | | | | | | | | | | | | | | | 204.47/127.08 | | | | | | | | | | | | | | | | | | Case 1: 204.47/127.08 | | | | | | | | | | | | | | | | | | | 204.47/127.08 | | | | | | | | | | | | | | | | | | | (1024) all_215_1 = 0 & array_eq_sub1(int, all_103_4, 204.47/127.08 | | | | | | | | | | | | | | | | | | | all_103_2, 0, all_86_11) = 0 204.47/127.08 | | | | | | | | | | | | | | | | | | | 204.47/127.08 | | | | | | | | | | | | | | | | | | | ALPHA: (1024) implies: 204.47/127.08 | | | | | | | | | | | | | | | | | | | (1025) array_eq_sub1(int, all_103_4, all_103_2, 0, 204.47/127.08 | | | | | | | | | | | | | | | | | | | all_86_11) = 0 204.47/127.08 | | | | | | | | | | | | | | | | | | | 204.47/127.08 | | | | | | | | | | | | | | | | | | | BETA: splitting (324) gives: 204.47/127.08 | | | | | | | | | | | | | | | | | | | 204.47/127.08 | | | | | | | | | | | | | | | | | | | Case 1: 204.47/127.08 | | | | | | | | | | | | | | | | | | | | 204.47/127.08 | | | | | | | | | | | | | | | | | | | | (1026) all_219_1 = 0 & array_eq_sub1(int, all_105_4, 204.47/127.08 | | | | | | | | | | | | | | | | | | | | all_105_2, 0, all_86_7) = 0 204.47/127.08 | | | | | | | | | | | | | | | | | | | | 204.47/127.08 | | | | | | | | | | | | | | | | | | | | ALPHA: (1026) implies: 204.47/127.08 | | | | | | | | | | | | | | | | | | | | (1027) array_eq_sub1(int, all_105_4, all_105_2, 0, 204.47/127.08 | | | | | | | | | | | | | | | | | | | | all_86_7) = 0 204.47/127.08 | | | | | | | | | | | | | | | | | | | | 204.47/127.08 | | | | | | | | | | | | | | | | | | | | BETA: splitting (270) gives: 204.47/127.08 | | | | | | | | | | | | | | | | | | | | 204.47/127.08 | | | | | | | | | | | | | | | | | | | | Case 1: 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | (1028) all_169_0 = all_169_1 & $lesseq(all_86_7, 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | all_169_1) & $lesseq(0, all_169_1) & $lesseq(0, 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | all_86_7) & length1(int, all_105_2) = all_169_1 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | & length1(int, all_105_4) = all_169_1 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | ALPHA: (1028) implies: 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | (1029) $lesseq(all_86_7, all_169_1) 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | (1030) length1(int, all_105_4) = all_169_1 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | (1031) length1(int, all_105_2) = all_169_1 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (345) gives: 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | Case 1: 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | | 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | | (1032) all_242_1 = 0 & array_eq_sub1(int, all_103_2, 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | | all_105_4, $sum(all_86_8, 1), all_86_13) = 0 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | | 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (45), (180), (183), (269), (406), (409), 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | | (410), (1018), (1019), (1021), (1022), (1030), 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | | (1031), (1032) are inconsistent by sub-proof #52. 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | | 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | Case 2: 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | | 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | | (1033) length1(int, all_103_2) = all_242_1 & ( ~ 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | | ($lesseq(1, $difference(all_242_1, all_86_8))) | 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | | ~ ($lesseq(all_86_13, all_242_1)) | ( ~ 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | | (all_242_0 = all_242_1) & length1(int, 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | | all_105_4) = all_242_0)) 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | | 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1033) implies: 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | | (1034) length1(int, all_103_2) = all_242_1 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | | (1035) ~ ($lesseq(1, $difference(all_242_1, all_86_8))) 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | | | ~ ($lesseq(all_86_13, all_242_1)) | ( ~ 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | | (all_242_0 = all_242_1) & length1(int, 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | | all_105_4) = all_242_0) 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | | 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (272) gives: 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | | 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | | Case 1: 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | | | (1036) all_171_0 = all_171_1 & $lesseq(all_86_11, 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | | | all_171_1) & $lesseq(0, all_171_1) & $lesseq(0, 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | | | all_86_11) & length1(int, all_103_2) = all_171_1 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | | | & length1(int, all_103_4) = all_171_1 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1036) implies: 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | | | (1037) length1(int, all_103_4) = all_171_1 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_234_1, all_170_1, 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (410), (1018) 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | | | gives: 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | | | (1038) all_234_1 = all_170_1 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_234_1, all_169_1, 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (1018), (1030) 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | | | gives: 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | | | (1039) all_234_1 = all_169_1 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_242_1, all_193_1, 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (1023), (1034) 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | | | gives: 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | | | (1040) all_242_1 = all_193_1 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_86_13, all_177_2, 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (184), (406) 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | | | gives: 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | | | (1041) all_177_2 = all_86_13 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_193_1, all_177_2, 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (406), (1023) 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | | | gives: 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | | | (1042) all_193_1 = all_177_2 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_242_1, all_170_1, 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (409), (1034) 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | | | gives: 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | | | (1043) all_242_1 = all_170_1 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_193_1, all_171_1, 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (1022), (1037) 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | | | gives: 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | | | (1044) all_193_1 = all_171_1 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1040), (1043) imply: 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | | | (1045) all_193_1 = all_170_1 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1045) implies: 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | | | (1046) all_193_1 = all_170_1 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1038), (1039) imply: 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | | | (1047) all_170_1 = all_169_1 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1047) implies: 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | | | (1048) all_170_1 = all_169_1 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1042), (1044) imply: 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | | | (1049) all_177_2 = all_171_1 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1049) implies: 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | | | (1050) all_177_2 = all_171_1 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1044), (1046) imply: 204.47/127.08 | | | | | | | | | | | | | | | | | | | | | | | (1051) all_171_1 = all_170_1 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1041), (1050) imply: 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | | (1052) all_171_1 = all_86_13 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1052) implies: 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | | (1053) all_171_1 = all_86_13 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1051), (1053) imply: 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | | (1054) all_170_1 = all_86_13 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1054) implies: 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | | (1055) all_170_1 = all_86_13 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1048), (1055) imply: 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | | (1056) all_169_1 = all_86_13 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1056) implies: 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | | (1057) all_169_1 = all_86_13 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1043), (1055) imply: 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | | (1058) all_242_1 = all_86_13 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (52), (180), (389), (1035), (1058) are 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #77. 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | Case 2: 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | | (1059) ~ (all_171_1 = 0) & array_eq_sub1(int, all_103_4, 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | | all_103_2, 0, all_86_11) = all_171_1 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (1025), (1059) are inconsistent by sub-proof 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | | #81. 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | End of split 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | End of split 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | 204.47/127.09 | | | | | | | | | | | | | | | | | | | | Case 2: 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | (1060) ~ (all_169_1 = 0) & array_eq_sub1(int, all_105_4, 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | all_105_2, 0, all_86_7) = all_169_1 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (1027), (1060) are inconsistent by sub-proof 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | #75. 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | 204.47/127.09 | | | | | | | | | | | | | | | | | | | | End of split 204.47/127.09 | | | | | | | | | | | | | | | | | | | | 204.47/127.09 | | | | | | | | | | | | | | | | | | | Case 2: 204.47/127.09 | | | | | | | | | | | | | | | | | | | | 204.47/127.09 | | | | | | | | | | | | | | | | | | | | (1061) length1(int, all_105_4) = all_219_1 & ( ~ 204.47/127.09 | | | | | | | | | | | | | | | | | | | | ($lesseq(all_86_7, all_219_1)) | ~ ($lesseq(0, 204.47/127.09 | | | | | | | | | | | | | | | | | | | | all_219_1)) | ( ~ (all_219_0 = all_219_1) & 204.47/127.09 | | | | | | | | | | | | | | | | | | | | length1(int, all_105_2) = all_219_0)) 204.47/127.09 | | | | | | | | | | | | | | | | | | | | 204.47/127.09 | | | | | | | | | | | | | | | | | | | | ALPHA: (1061) implies: 204.47/127.09 | | | | | | | | | | | | | | | | | | | | (1062) length1(int, all_105_4) = all_219_1 204.47/127.09 | | | | | | | | | | | | | | | | | | | | (1063) ~ ($lesseq(all_86_7, all_219_1)) | ~ ($lesseq(0, 204.47/127.09 | | | | | | | | | | | | | | | | | | | | all_219_1)) | ( ~ (all_219_0 = all_219_1) & 204.47/127.09 | | | | | | | | | | | | | | | | | | | | length1(int, all_105_2) = all_219_0) 204.47/127.09 | | | | | | | | | | | | | | | | | | | | 204.47/127.09 | | | | | | | | | | | | | | | | | | | | BETA: splitting (272) gives: 204.47/127.09 | | | | | | | | | | | | | | | | | | | | 204.47/127.09 | | | | | | | | | | | | | | | | | | | | Case 1: 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | (1064) all_171_0 = all_171_1 & $lesseq(all_86_11, 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | all_171_1) & $lesseq(0, all_171_1) & $lesseq(0, 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | all_86_11) & length1(int, all_103_2) = all_171_1 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | & length1(int, all_103_4) = all_171_1 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | ALPHA: (1064) implies: 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | (1065) length1(int, all_103_4) = all_171_1 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | (1066) length1(int, all_103_2) = all_171_1 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (296) gives: 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | Case 1: 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | (1067) all_191_3 = 0 & permut_sub2(int, all_103_4, 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | all_103_2, all_86_11, $sum(all_86_10, 1)) = 0 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1067) implies: 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | (1068) permut_sub2(int, all_103_4, all_103_2, all_86_11, 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | $sum(all_86_10, 1)) = 0 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (43), (48), (50), (52), (53), (181), (183), 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | (297), (389), (409), (410), (1021), (1022), 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | (1062), (1063), (1065), (1066), (1068) are 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #51. 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | Case 2: 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | (1069) elts(int, all_103_2) = all_191_2 & elts(int, 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | all_103_4) = all_191_3 & in_uni(all_191_2) & 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | in_uni(all_191_3) & (( ~ (all_191_0 = 0) & 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | map_eq_sub1(int, all_191_3, all_191_2, 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | $sum(all_86_10, 1), all_191_1) = all_191_0 & 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | length1(int, all_103_4) = all_191_1) | ( ~ 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | (all_191_1 = 0) & map_eq_sub1(int, all_191_3, 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | all_191_2, 0, all_86_11) = all_191_1)) 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1069) implies: 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | (1070) elts(int, all_103_4) = all_191_3 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | (1071) elts(int, all_103_2) = all_191_2 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | (1072) ( ~ (all_191_0 = 0) & map_eq_sub1(int, all_191_3, 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | all_191_2, $sum(all_86_10, 1), all_191_1) = 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | all_191_0 & length1(int, all_103_4) = all_191_1) 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | | ( ~ (all_191_1 = 0) & map_eq_sub1(int, 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | all_191_3, all_191_2, 0, all_86_11) = 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | all_191_1) 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (272) gives: 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | Case 1: 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (345) gives: 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | | Case 1: 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | | | (1073) all_242_1 = 0 & array_eq_sub1(int, all_103_2, 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, $sum(all_86_8, 1), all_86_13) = 0 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1073) implies: 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | | | (1074) array_eq_sub1(int, all_103_2, all_105_4, 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | | | $sum(all_86_8, 1), all_86_13) = 0 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (39), (44), (45), (90), (91), (96), (183), 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | | | (206), (269), (394), (396), (404), (406), (409), 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | | | (1022), (1023), (1065), (1066), (1070), (1071), 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | | | (1072), (1074) are inconsistent by sub-proof #60. 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | | Case 2: 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | | | (1075) length1(int, all_103_2) = all_242_1 & ( ~ 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | | | ($lesseq(1, $difference(all_242_1, all_86_8))) | 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | | | ~ ($lesseq(all_86_13, all_242_1)) | ( ~ 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | | | (all_242_0 = all_242_1) & length1(int, 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | | | all_105_4) = all_242_0)) 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (39), (44), (90), (91), (96), (184), (206), 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | | | (396), (404), (1065), (1066), (1070), (1071), 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | | | (1072), (1075) are inconsistent by sub-proof #50. 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | | End of split 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | Case 2: 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | | (1076) ~ (all_171_1 = 0) & array_eq_sub1(int, all_103_4, 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | | all_103_2, 0, all_86_11) = all_171_1 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (1025), (1076) are inconsistent by sub-proof 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | | #81. 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | End of split 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | End of split 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | 204.47/127.09 | | | | | | | | | | | | | | | | | | | | Case 2: 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | (1077) ~ (all_171_1 = 0) & array_eq_sub1(int, all_103_4, 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | all_103_2, 0, all_86_11) = all_171_1 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (1025), (1077) are inconsistent by sub-proof 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | #81. 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | 204.47/127.09 | | | | | | | | | | | | | | | | | | | | End of split 204.47/127.09 | | | | | | | | | | | | | | | | | | | | 204.47/127.09 | | | | | | | | | | | | | | | | | | | End of split 204.47/127.09 | | | | | | | | | | | | | | | | | | | 204.47/127.09 | | | | | | | | | | | | | | | | | | Case 2: 204.47/127.09 | | | | | | | | | | | | | | | | | | | 204.47/127.09 | | | | | | | | | | | | | | | | | | | (1078) length1(int, all_103_4) = all_215_1 & ( ~ 204.47/127.09 | | | | | | | | | | | | | | | | | | | ($lesseq(all_86_11, all_215_1)) | ~ ($lesseq(0, 204.47/127.09 | | | | | | | | | | | | | | | | | | | all_215_1)) | ( ~ (all_215_0 = all_215_1) & 204.47/127.09 | | | | | | | | | | | | | | | | | | | length1(int, all_103_2) = all_215_0)) 204.47/127.09 | | | | | | | | | | | | | | | | | | | 204.47/127.09 | | | | | | | | | | | | | | | | | | | ALPHA: (1078) implies: 204.47/127.09 | | | | | | | | | | | | | | | | | | | (1079) length1(int, all_103_4) = all_215_1 204.47/127.09 | | | | | | | | | | | | | | | | | | | 204.47/127.09 | | | | | | | | | | | | | | | | | | | BETA: splitting (324) gives: 204.47/127.09 | | | | | | | | | | | | | | | | | | | 204.47/127.09 | | | | | | | | | | | | | | | | | | | Case 1: 204.47/127.09 | | | | | | | | | | | | | | | | | | | | 204.47/127.09 | | | | | | | | | | | | | | | | | | | | (1080) all_219_1 = 0 & array_eq_sub1(int, all_105_4, 204.47/127.09 | | | | | | | | | | | | | | | | | | | | all_105_2, 0, all_86_7) = 0 204.47/127.09 | | | | | | | | | | | | | | | | | | | | 204.47/127.09 | | | | | | | | | | | | | | | | | | | | ALPHA: (1080) implies: 204.47/127.09 | | | | | | | | | | | | | | | | | | | | (1081) array_eq_sub1(int, all_105_4, all_105_2, 0, 204.47/127.09 | | | | | | | | | | | | | | | | | | | | all_86_7) = 0 204.47/127.09 | | | | | | | | | | | | | | | | | | | | 204.47/127.09 | | | | | | | | | | | | | | | | | | | | BETA: splitting (270) gives: 204.47/127.09 | | | | | | | | | | | | | | | | | | | | 204.47/127.09 | | | | | | | | | | | | | | | | | | | | Case 1: 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | (1082) all_169_0 = all_169_1 & $lesseq(all_86_7, 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | all_169_1) & $lesseq(0, all_169_1) & $lesseq(0, 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | all_86_7) & length1(int, all_105_2) = all_169_1 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | & length1(int, all_105_4) = all_169_1 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | ALPHA: (1082) implies: 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | (1083) $lesseq(all_86_7, all_169_1) 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | (1084) length1(int, all_105_4) = all_169_1 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | (1085) length1(int, all_105_2) = all_169_1 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (345) gives: 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | Case 1: 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | (1086) all_242_1 = 0 & array_eq_sub1(int, all_103_2, 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | all_105_4, $sum(all_86_8, 1), all_86_13) = 0 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (45), (180), (183), (269), (406), (409), 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | (410), (1018), (1019), (1021), (1022), (1084), 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | (1085), (1086) are inconsistent by sub-proof #52. 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | | 204.47/127.09 | | | | | | | | | | | | | | | | | | | | | Case 2: 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | (1087) length1(int, all_103_2) = all_242_1 & ( ~ 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | ($lesseq(1, $difference(all_242_1, all_86_8))) | 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | ~ ($lesseq(all_86_13, all_242_1)) | ( ~ 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | (all_242_0 = all_242_1) & length1(int, 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | all_105_4) = all_242_0)) 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1087) implies: 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | (1088) length1(int, all_103_2) = all_242_1 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | (1089) ~ ($lesseq(1, $difference(all_242_1, all_86_8))) 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | ~ ($lesseq(all_86_13, all_242_1)) | ( ~ 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | (all_242_0 = all_242_1) & length1(int, 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | all_105_4) = all_242_0) 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (296) gives: 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | Case 1: 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | (1090) all_191_3 = 0 & permut_sub2(int, all_103_4, 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | all_103_2, all_86_11, $sum(all_86_10, 1)) = 0 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1090) implies: 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | (1091) permut_sub2(int, all_103_4, all_103_2, all_86_11, 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | $sum(all_86_10, 1)) = 0 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (297) gives: 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | Case 1: 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | (1092) all_192_0 = 0 & all_192_1 = 0 & map_eq_sub1(int, 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | all_192_4, all_192_3, $sum(all_86_10, 1), 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | all_192_2) = 0 & map_eq_sub1(int, all_192_4, 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | all_192_3, 0, all_86_11) = 0 & length1(int, 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | all_103_4) = all_192_2 & elts(int, all_103_2) = 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | all_192_3 & elts(int, all_103_4) = all_192_4 & 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | in_uni(all_192_3) & in_uni(all_192_4) 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1092) implies: 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | (1093) length1(int, all_103_4) = all_192_2 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_234_1, all_170_1, 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (410), (1018) 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | (1094) all_234_1 = all_170_1 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_234_1, all_169_1, 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (1018), (1084) 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | (1095) all_234_1 = all_169_1 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_242_1, all_177_2, 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (406), (1088) 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | (1096) all_242_1 = all_177_2 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_193_1, all_177_2, 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (406), (1023) 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | (1097) all_193_1 = all_177_2 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_193_1, all_170_1, 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (409), (1023) 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | (1098) all_193_1 = all_170_1 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_242_1, all_156_0, 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (394), (1088) 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | (1099) all_242_1 = all_156_0 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_86_13, all_215_1, 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (183), (1079) 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | (1100) all_215_1 = all_86_13 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_215_1, all_193_1, 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (1022), (1079) 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | (1101) all_215_1 = all_193_1 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_215_1, all_192_2, 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (1079), (1093) 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | (1102) all_215_1 = all_192_2 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1096), (1099) imply: 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | (1103) all_177_2 = all_156_0 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1103) implies: 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | (1104) all_177_2 = all_156_0 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1094), (1095) imply: 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | (1105) all_170_1 = all_169_1 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1105) implies: 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | (1106) all_170_1 = all_169_1 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1101), (1102) imply: 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | (1107) all_193_1 = all_192_2 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1107) implies: 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | (1108) all_193_1 = all_192_2 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1100), (1102) imply: 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | (1109) all_192_2 = all_86_13 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1098), (1108) imply: 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | (1110) all_192_2 = all_170_1 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1110) implies: 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | (1111) all_192_2 = all_170_1 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1097), (1098) imply: 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | (1112) all_177_2 = all_170_1 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1112) implies: 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | (1113) all_177_2 = all_170_1 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1109), (1111) imply: 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | (1114) all_170_1 = all_86_13 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1114) implies: 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | (1115) all_170_1 = all_86_13 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1104), (1113) imply: 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | (1116) all_170_1 = all_156_0 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1116) implies: 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | (1117) all_170_1 = all_156_0 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1106), (1115) imply: 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | (1118) all_169_1 = all_86_13 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1118) implies: 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | (1119) all_169_1 = all_86_13 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1115), (1117) imply: 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | (1120) all_156_0 = all_86_13 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (52), (1083), (1084), (1089), (1099), 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | (1119), (1120) are inconsistent by sub-proof #49. 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | Case 2: 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | (1121) ~ (all_192_4 = 0) & permut_sub2(int, all_103_4, 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, all_86_11, $sum(all_86_10, 1)) = 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | all_192_4 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (43), (1091), (1121) are inconsistent by sub-proof 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | #69. 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | End of split 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | Case 2: 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | (1122) elts(int, all_103_2) = all_191_2 & elts(int, 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | all_103_4) = all_191_3 & in_uni(all_191_2) & 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | in_uni(all_191_3) & (( ~ (all_191_0 = 0) & 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | map_eq_sub1(int, all_191_3, all_191_2, 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | $sum(all_86_10, 1), all_191_1) = all_191_0 & 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | length1(int, all_103_4) = all_191_1) | ( ~ 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | (all_191_1 = 0) & map_eq_sub1(int, all_191_3, 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | all_191_2, 0, all_86_11) = all_191_1)) 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1122) implies: 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | (1123) elts(int, all_103_4) = all_191_3 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | (1124) elts(int, all_103_2) = all_191_2 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | (1125) ( ~ (all_191_0 = 0) & map_eq_sub1(int, all_191_3, 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | all_191_2, $sum(all_86_10, 1), all_191_1) = 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | all_191_0 & length1(int, all_103_4) = all_191_1) 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | | ( ~ (all_191_1 = 0) & map_eq_sub1(int, 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | all_191_3, all_191_2, 0, all_86_11) = 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | all_191_1) 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (39), (44), (90), (91), (96), (183), (206), 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | (396), (404), (1022), (1079), (1123), (1124), 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | (1125) are inconsistent by sub-proof #56. 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | End of split 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | | 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | End of split 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | 204.47/127.10 | | | | | | | | | | | | | | | | | | | | Case 2: 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | (1126) ~ (all_169_1 = 0) & array_eq_sub1(int, all_105_4, 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | all_105_2, 0, all_86_7) = all_169_1 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (1081), (1126) are inconsistent by sub-proof 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | #75. 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | 204.47/127.10 | | | | | | | | | | | | | | | | | | | | End of split 204.47/127.10 | | | | | | | | | | | | | | | | | | | | 204.47/127.10 | | | | | | | | | | | | | | | | | | | Case 2: 204.47/127.10 | | | | | | | | | | | | | | | | | | | | 204.47/127.10 | | | | | | | | | | | | | | | | | | | | (1127) length1(int, all_105_4) = all_219_1 & ( ~ 204.47/127.10 | | | | | | | | | | | | | | | | | | | | ($lesseq(all_86_7, all_219_1)) | ~ ($lesseq(0, 204.47/127.10 | | | | | | | | | | | | | | | | | | | | all_219_1)) | ( ~ (all_219_0 = all_219_1) & 204.47/127.10 | | | | | | | | | | | | | | | | | | | | length1(int, all_105_2) = all_219_0)) 204.47/127.10 | | | | | | | | | | | | | | | | | | | | 204.47/127.10 | | | | | | | | | | | | | | | | | | | | ALPHA: (1127) implies: 204.47/127.10 | | | | | | | | | | | | | | | | | | | | (1128) length1(int, all_105_4) = all_219_1 204.47/127.10 | | | | | | | | | | | | | | | | | | | | (1129) ~ ($lesseq(all_86_7, all_219_1)) | ~ ($lesseq(0, 204.47/127.10 | | | | | | | | | | | | | | | | | | | | all_219_1)) | ( ~ (all_219_0 = all_219_1) & 204.47/127.10 | | | | | | | | | | | | | | | | | | | | length1(int, all_105_2) = all_219_0) 204.47/127.10 | | | | | | | | | | | | | | | | | | | | 204.47/127.10 | | | | | | | | | | | | | | | | | | | | BETA: splitting (345) gives: 204.47/127.10 | | | | | | | | | | | | | | | | | | | | 204.47/127.10 | | | | | | | | | | | | | | | | | | | | Case 1: 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | (1130) all_242_1 = 0 & array_eq_sub1(int, all_103_2, 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | all_105_4, $sum(all_86_8, 1), all_86_13) = 0 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | 204.47/127.10 | | | | | | | | | | | | | | | | | | | | | ALPHA: (1130) implies: 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | (1131) array_eq_sub1(int, all_103_2, all_105_4, 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | $sum(all_86_8, 1), all_86_13) = 0 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (269) gives: 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | Case 1: 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | | 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | | (1132) all_168_0 = all_168_1 & $lesseq(1, 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | | $difference(all_168_1, all_86_8)) & 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | | $lesseq(all_86_13, all_168_1) & $lesseq(-1, 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | | all_86_8) & $lesseq(0, all_86_13) & length1(int, 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | | all_105_4) = all_168_1 & length1(int, all_103_2) 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | | = all_168_1 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | | 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1132) implies: 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | | (1133) length1(int, all_105_4) = all_168_1 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | | 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_234_1, all_219_1, 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (1018), (1128) 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | | gives: 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | | (1134) all_234_1 = all_219_1 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | | 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_219_1, all_170_1, 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (410), (1128) 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | | gives: 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | | (1135) all_219_1 = all_170_1 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | | 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_234_1, all_168_1, 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (1018), (1133) 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | | gives: 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | | (1136) all_234_1 = all_168_1 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | | 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_193_1, all_177_2, 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (406), (1023) 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | | gives: 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | | (1137) all_193_1 = all_177_2 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | | 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_177_2, all_170_1, 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (406), (409) 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | | gives: 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | | (1138) all_177_2 = all_170_1 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | | 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_86_13, all_215_1, 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (183), (1079) 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | | gives: 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | | (1139) all_215_1 = all_86_13 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | | 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_215_1, all_193_1, 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (1022), (1079) 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | | gives: 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | | (1140) all_215_1 = all_193_1 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | | 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1134), (1136) imply: 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | | (1141) all_219_1 = all_168_1 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | | 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | | SIMP: (1141) implies: 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | | (1142) all_219_1 = all_168_1 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | | 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1135), (1142) imply: 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | | (1143) all_170_1 = all_168_1 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | | 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | | SIMP: (1143) implies: 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | | (1144) all_170_1 = all_168_1 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | | 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1139), (1140) imply: 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | | (1145) all_193_1 = all_86_13 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | | 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1137), (1145) imply: 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | | (1146) all_177_2 = all_86_13 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | | 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | | SIMP: (1146) implies: 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | | (1147) all_177_2 = all_86_13 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | | 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1138), (1147) imply: 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | | (1148) all_170_1 = all_86_13 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | | 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | | SIMP: (1148) implies: 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | | (1149) all_170_1 = all_86_13 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | | 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1144), (1149) imply: 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | | (1150) all_168_1 = all_86_13 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | | 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1142), (1150) imply: 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | | (1151) all_219_1 = all_86_13 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | | 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (48), (49), (50), (52), (53), (181), (389), 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | | (1129), (1151) are inconsistent by sub-proof #59. 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | | 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | Case 2: 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | | 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | | (1152) ~ (all_168_1 = 0) & array_eq_sub1(int, all_103_2, 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | | all_105_4, $sum(all_86_8, 1), all_86_13) = 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | | all_168_1 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | | 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (1131), (1152) are inconsistent by sub-proof 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | | #83. 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | | 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | End of split 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | 204.47/127.11 | | | | | | | | | | | | | | | | | | | | Case 2: 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | (1153) length1(int, all_103_2) = all_242_1 & ( ~ 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | ($lesseq(1, $difference(all_242_1, all_86_8))) | 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | ~ ($lesseq(all_86_13, all_242_1)) | ( ~ 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | (all_242_0 = all_242_1) & length1(int, 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | all_105_4) = all_242_0)) 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | ALPHA: (1153) implies: 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | (1154) length1(int, all_103_2) = all_242_1 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_234_1, all_219_1, 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (1018), (1128) 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | gives: 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | (1155) all_234_1 = all_219_1 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_234_1, all_170_1, 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (410), (1018) 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | gives: 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | (1156) all_234_1 = all_170_1 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_242_1, all_177_2, 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (406), (1154) 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | gives: 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | (1157) all_242_1 = all_177_2 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_193_1, all_177_2, 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (406), (1023) 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | gives: 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | (1158) all_193_1 = all_177_2 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_242_1, all_170_1, 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (409), (1154) 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | gives: 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | (1159) all_242_1 = all_170_1 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_242_1, all_156_0, 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (394), (1154) 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | gives: 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | (1160) all_242_1 = all_156_0 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_86_13, all_215_1, 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (183), (1079) 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | gives: 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | (1161) all_215_1 = all_86_13 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_215_1, all_193_1, 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (1022), (1079) 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | gives: 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | (1162) all_215_1 = all_193_1 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1159), (1160) imply: 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | (1163) all_170_1 = all_156_0 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1157), (1159) imply: 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | (1164) all_177_2 = all_170_1 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | SIMP: (1164) implies: 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | (1165) all_177_2 = all_170_1 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1155), (1156) imply: 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | (1166) all_219_1 = all_170_1 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | SIMP: (1166) implies: 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | (1167) all_219_1 = all_170_1 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1161), (1162) imply: 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | (1168) all_193_1 = all_86_13 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | SIMP: (1168) implies: 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | (1169) all_193_1 = all_86_13 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1158), (1169) imply: 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | (1170) all_177_2 = all_86_13 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | SIMP: (1170) implies: 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | (1171) all_177_2 = all_86_13 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1165), (1171) imply: 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | (1172) all_170_1 = all_86_13 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | SIMP: (1172) implies: 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | (1173) all_170_1 = all_86_13 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1163), (1173) imply: 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | (1174) all_156_0 = all_86_13 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1167), (1173) imply: 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | (1175) all_219_1 = all_86_13 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (48), (49), (50), (52), (53), (181), (389), 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | (1129), (1175) are inconsistent by sub-proof #59. 204.47/127.11 | | | | | | | | | | | | | | | | | | | | | 204.47/127.11 | | | | | | | | | | | | | | | | | | | | End of split 204.47/127.11 | | | | | | | | | | | | | | | | | | | | 204.47/127.11 | | | | | | | | | | | | | | | | | | | End of split 204.47/127.11 | | | | | | | | | | | | | | | | | | | 204.47/127.11 | | | | | | | | | | | | | | | | | | End of split 204.47/127.11 | | | | | | | | | | | | | | | | | | 204.47/127.11 | | | | | | | | | | | | | | | | | Case 2: 204.47/127.11 | | | | | | | | | | | | | | | | | | 204.47/127.11 | | | | | | | | | | | | | | | | | | (1176) ~ (all_193_1 = 0) & array_eq_sub1(int, all_103_4, 204.47/127.11 | | | | | | | | | | | | | | | | | | all_103_2, $sum(all_86_10, 1), all_86_13) = 204.47/127.11 | | | | | | | | | | | | | | | | | | all_193_1 204.47/127.11 | | | | | | | | | | | | | | | | | | 204.47/127.11 | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (400), (1176) are inconsistent by sub-proof 204.47/127.11 | | | | | | | | | | | | | | | | | | #55. 204.47/127.11 | | | | | | | | | | | | | | | | | | 204.47/127.11 | | | | | | | | | | | | | | | | | End of split 204.47/127.11 | | | | | | | | | | | | | | | | | 204.47/127.11 | | | | | | | | | | | | | | | | End of split 204.47/127.11 | | | | | | | | | | | | | | | | 204.47/127.11 | | | | | | | | | | | | | | | Case 2: 204.47/127.11 | | | | | | | | | | | | | | | | 204.47/127.11 | | | | | | | | | | | | | | | | (1177) ~ (all_170_1 = 0) & array_eq_sub1(int, all_103_2, 204.47/127.11 | | | | | | | | | | | | | | | | all_105_4, 0, all_86_11) = all_170_1 204.47/127.11 | | | | | | | | | | | | | | | | 204.47/127.11 | | | | | | | | | | | | | | | | REF_CLOSE: (45), (398), (1177) are inconsistent by sub-proof 204.47/127.11 | | | | | | | | | | | | | | | | #48. 204.47/127.11 | | | | | | | | | | | | | | | | 204.47/127.12 | | | | | | | | | | | | | | | End of split 204.47/127.12 | | | | | | | | | | | | | | | 204.47/127.12 | | | | | | | | | | | | | | Case 2: 204.47/127.12 | | | | | | | | | | | | | | | 204.47/127.12 | | | | | | | | | | | | | | | (1178) ~ (all_177_4 = 0) & permut_sub2(int, all_103_2, 204.47/127.12 | | | | | | | | | | | | | | | all_105_4, all_86_11, $sum(all_86_8, 1)) = 204.47/127.12 | | | | | | | | | | | | | | | all_177_4 204.47/127.12 | | | | | | | | | | | | | | | 204.47/127.12 | | | | | | | | | | | | | | | REF_CLOSE: (43), (402), (1178) are inconsistent by sub-proof 204.47/127.12 | | | | | | | | | | | | | | | #47. 204.47/127.12 | | | | | | | | | | | | | | | 204.47/127.12 | | | | | | | | | | | | | | End of split 204.47/127.12 | | | | | | | | | | | | | | 204.47/127.12 | | | | | | | | | | | | | Case 2: 204.47/127.12 | | | | | | | | | | | | | | 204.47/127.12 | | | | | | | | | | | | | | (1179) elts(int, all_105_4) = all_181_2 & elts(int, 204.47/127.12 | | | | | | | | | | | | | | all_103_2) = all_181_3 & in_uni(all_181_2) & 204.47/127.12 | | | | | | | | | | | | | | in_uni(all_181_3) & (( ~ (all_181_0 = 0) & 204.47/127.12 | | | | | | | | | | | | | | map_eq_sub1(int, all_181_3, all_181_2, 204.47/127.12 | | | | | | | | | | | | | | $sum(all_86_8, 1), all_181_1) = all_181_0 & 204.47/127.12 | | | | | | | | | | | | | | length1(int, all_103_2) = all_181_1) | ( ~ 204.47/127.12 | | | | | | | | | | | | | | (all_181_1 = 0) & map_eq_sub1(int, all_181_3, 204.47/127.12 | | | | | | | | | | | | | | all_181_2, 0, all_86_11) = all_181_1)) 204.47/127.12 | | | | | | | | | | | | | | 204.47/127.12 | | | | | | | | | | | | | | ALPHA: (1179) implies: 204.47/127.12 | | | | | | | | | | | | | | (1180) elts(int, all_103_2) = all_181_3 204.47/127.12 | | | | | | | | | | | | | | (1181) elts(int, all_105_4) = all_181_2 204.47/127.12 | | | | | | | | | | | | | | (1182) ( ~ (all_181_0 = 0) & map_eq_sub1(int, all_181_3, 204.47/127.12 | | | | | | | | | | | | | | all_181_2, $sum(all_86_8, 1), all_181_1) = 204.47/127.12 | | | | | | | | | | | | | | all_181_0 & length1(int, all_103_2) = all_181_1) 204.47/127.12 | | | | | | | | | | | | | | | ( ~ (all_181_1 = 0) & map_eq_sub1(int, 204.47/127.12 | | | | | | | | | | | | | | all_181_3, all_181_2, 0, all_86_11) = 204.47/127.12 | | | | | | | | | | | | | | all_181_1) 204.47/127.12 | | | | | | | | | | | | | | 204.47/127.12 | | | | | | | | | | | | | | BETA: splitting (271) gives: 204.47/127.12 | | | | | | | | | | | | | | 204.47/127.12 | | | | | | | | | | | | | | Case 1: 204.47/127.12 | | | | | | | | | | | | | | | 204.47/127.12 | | | | | | | | | | | | | | | (1183) all_170_0 = all_170_1 & $lesseq(all_86_11, 204.47/127.12 | | | | | | | | | | | | | | | all_170_1) & $lesseq(0, all_170_1) & $lesseq(0, 204.47/127.12 | | | | | | | | | | | | | | | all_86_11) & length1(int, all_105_4) = all_170_1 204.47/127.12 | | | | | | | | | | | | | | | & length1(int, all_103_2) = all_170_1 204.47/127.12 | | | | | | | | | | | | | | | 204.47/127.12 | | | | | | | | | | | | | | | ALPHA: (1183) implies: 204.47/127.12 | | | | | | | | | | | | | | | (1184) length1(int, all_103_2) = all_170_1 204.47/127.12 | | | | | | | | | | | | | | | (1185) length1(int, all_105_4) = all_170_1 204.47/127.12 | | | | | | | | | | | | | | | 204.47/127.12 | | | | | | | | | | | | | | | BETA: splitting (296) gives: 204.47/127.12 | | | | | | | | | | | | | | | 204.47/127.12 | | | | | | | | | | | | | | | Case 1: 204.47/127.12 | | | | | | | | | | | | | | | | 204.47/127.12 | | | | | | | | | | | | | | | | (1186) all_191_3 = 0 & permut_sub2(int, all_103_4, 204.47/127.12 | | | | | | | | | | | | | | | | all_103_2, all_86_11, $sum(all_86_10, 1)) = 0 204.47/127.12 | | | | | | | | | | | | | | | | 204.47/127.12 | | | | | | | | | | | | | | | | ALPHA: (1186) implies: 204.47/127.12 | | | | | | | | | | | | | | | | (1187) permut_sub2(int, all_103_4, all_103_2, all_86_11, 204.47/127.12 | | | | | | | | | | | | | | | | $sum(all_86_10, 1)) = 0 204.47/127.12 | | | | | | | | | | | | | | | | 204.47/127.12 | | | | | | | | | | | | | | | | BETA: splitting (294) gives: 204.47/127.12 | | | | | | | | | | | | | | | | 204.47/127.12 | | | | | | | | | | | | | | | | Case 1: 204.47/127.12 | | | | | | | | | | | | | | | | | 204.47/127.12 | | | | | | | | | | | | | | | | | (1188) all_187_3 = 0 & permut_sub2(int, all_105_4, 204.47/127.12 | | | | | | | | | | | | | | | | | all_105_2, all_86_7, $sum(all_86_10, 1)) = 0 204.47/127.12 | | | | | | | | | | | | | | | | | 204.47/127.12 | | | | | | | | | | | | | | | | | ALPHA: (1188) implies: 204.47/127.12 | | | | | | | | | | | | | | | | | (1189) permut_sub2(int, all_105_4, all_105_2, all_86_7, 204.47/127.12 | | | | | | | | | | | | | | | | | $sum(all_86_10, 1)) = 0 204.47/127.12 | | | | | | | | | | | | | | | | | 204.47/127.12 | | | | | | | | | | | | | | | | | BETA: splitting (337) gives: 204.47/127.12 | | | | | | | | | | | | | | | | | 204.47/127.12 | | | | | | | | | | | | | | | | | Case 1: 204.47/127.12 | | | | | | | | | | | | | | | | | | 204.47/127.12 | | | | | | | | | | | | | | | | | | (1190) all_234_1 = 0 & array_eq_sub1(int, all_105_4, 204.47/127.12 | | | | | | | | | | | | | | | | | | all_105_2, $sum(all_86_10, 1), all_86_13) = 0 204.47/127.12 | | | | | | | | | | | | | | | | | | 204.47/127.12 | | | | | | | | | | | | | | | | | | ALPHA: (1190) implies: 204.47/127.12 | | | | | | | | | | | | | | | | | | (1191) array_eq_sub1(int, all_105_4, all_105_2, 204.47/127.12 | | | | | | | | | | | | | | | | | | $sum(all_86_10, 1), all_86_13) = 0 204.47/127.12 | | | | | | | | | | | | | | | | | | 204.47/127.12 | | | | | | | | | | | | | | | | | | BETA: splitting (255) gives: 204.47/127.12 | | | | | | | | | | | | | | | | | | 204.47/127.12 | | | | | | | | | | | | | | | | | | Case 1: 204.47/127.12 | | | | | | | | | | | | | | | | | | | 204.47/127.12 | | | | | | | | | | | | | | | | | | | (1192) all_153_0 = all_153_1 & $lesseq(1, 204.47/127.12 | | | | | | | | | | | | | | | | | | | $difference(all_153_1, all_86_10)) & 204.47/127.12 | | | | | | | | | | | | | | | | | | | $lesseq(all_86_13, all_153_1) & $lesseq(-1, 204.47/127.12 | | | | | | | | | | | | | | | | | | | all_86_10) & $lesseq(0, all_86_13) & 204.47/127.12 | | | | | | | | | | | | | | | | | | | length1(int, all_105_2) = all_153_1 & length1(int, 204.47/127.12 | | | | | | | | | | | | | | | | | | | all_105_4) = all_153_1 204.47/127.12 | | | | | | | | | | | | | | | | | | | 204.47/127.12 | | | | | | | | | | | | | | | | | | | ALPHA: (1192) implies: 204.47/127.12 | | | | | | | | | | | | | | | | | | | (1193) $lesseq(1, $difference(all_153_1, all_86_10)) 204.47/127.12 | | | | | | | | | | | | | | | | | | | (1194) length1(int, all_105_4) = all_153_1 204.47/127.12 | | | | | | | | | | | | | | | | | | | (1195) length1(int, all_105_2) = all_153_1 204.47/127.12 | | | | | | | | | | | | | | | | | | | 204.47/127.12 | | | | | | | | | | | | | | | | | | | BETA: splitting (298) gives: 204.47/127.12 | | | | | | | | | | | | | | | | | | | 204.47/127.12 | | | | | | | | | | | | | | | | | | | Case 1: 204.47/127.12 | | | | | | | | | | | | | | | | | | | | 204.47/127.12 | | | | | | | | | | | | | | | | | | | | (1196) all_193_0 = all_193_1 & $lesseq(1, 204.47/127.12 | | | | | | | | | | | | | | | | | | | | $difference(all_193_1, all_86_10)) & 204.47/127.12 | | | | | | | | | | | | | | | | | | | | $lesseq(all_86_13, all_193_1) & $lesseq(-1, 204.47/127.12 | | | | | | | | | | | | | | | | | | | | all_86_10) & $lesseq(0, all_86_13) & 204.47/127.12 | | | | | | | | | | | | | | | | | | | | length1(int, all_103_2) = all_193_1 & length1(int, 204.47/127.12 | | | | | | | | | | | | | | | | | | | | all_103_4) = all_193_1 204.47/127.12 | | | | | | | | | | | | | | | | | | | | 204.47/127.12 | | | | | | | | | | | | | | | | | | | | ALPHA: (1196) implies: 204.47/127.12 | | | | | | | | | | | | | | | | | | | | (1197) $lesseq(1, $difference(all_193_1, all_86_10)) 204.47/127.12 | | | | | | | | | | | | | | | | | | | | (1198) length1(int, all_103_4) = all_193_1 204.47/127.12 | | | | | | | | | | | | | | | | | | | | (1199) length1(int, all_103_2) = all_193_1 204.47/127.12 | | | | | | | | | | | | | | | | | | | | 204.47/127.12 | | | | | | | | | | | | | | | | | | | | BETA: splitting (295) gives: 204.47/127.12 | | | | | | | | | | | | | | | | | | | | 204.47/127.12 | | | | | | | | | | | | | | | | | | | | Case 1: 204.47/127.12 | | | | | | | | | | | | | | | | | | | | | 204.47/127.12 | | | | | | | | | | | | | | | | | | | | | (1200) all_190_0 = 0 & all_190_1 = 0 & map_eq_sub1(int, 204.47/127.12 | | | | | | | | | | | | | | | | | | | | | all_190_4, all_190_3, $sum(all_86_10, 1), 204.47/127.12 | | | | | | | | | | | | | | | | | | | | | all_190_2) = 0 & map_eq_sub1(int, all_190_4, 204.47/127.12 | | | | | | | | | | | | | | | | | | | | | all_190_3, 0, all_86_7) = 0 & length1(int, 204.47/127.12 | | | | | | | | | | | | | | | | | | | | | all_105_4) = all_190_2 & elts(int, all_105_2) = 204.47/127.12 | | | | | | | | | | | | | | | | | | | | | all_190_3 & elts(int, all_105_4) = all_190_4 & 204.47/127.12 | | | | | | | | | | | | | | | | | | | | | in_uni(all_190_3) & in_uni(all_190_4) 204.47/127.12 | | | | | | | | | | | | | | | | | | | | | 204.47/127.12 | | | | | | | | | | | | | | | | | | | | | ALPHA: (1200) implies: 204.47/127.12 | | | | | | | | | | | | | | | | | | | | | (1201) elts(int, all_105_4) = all_190_4 204.47/127.12 | | | | | | | | | | | | | | | | | | | | | (1202) length1(int, all_105_4) = all_190_2 204.47/127.12 | | | | | | | | | | | | | | | | | | | | | 204.47/127.12 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (297) gives: 204.47/127.12 | | | | | | | | | | | | | | | | | | | | | 204.47/127.12 | | | | | | | | | | | | | | | | | | | | | Case 1: 204.47/127.12 | | | | | | | | | | | | | | | | | | | | | | 204.47/127.12 | | | | | | | | | | | | | | | | | | | | | | (1203) all_192_0 = 0 & all_192_1 = 0 & map_eq_sub1(int, 204.47/127.12 | | | | | | | | | | | | | | | | | | | | | | all_192_4, all_192_3, $sum(all_86_10, 1), 204.47/127.12 | | | | | | | | | | | | | | | | | | | | | | all_192_2) = 0 & map_eq_sub1(int, all_192_4, 204.47/127.12 | | | | | | | | | | | | | | | | | | | | | | all_192_3, 0, all_86_11) = 0 & length1(int, 204.47/127.12 | | | | | | | | | | | | | | | | | | | | | | all_103_4) = all_192_2 & elts(int, all_103_2) = 204.47/127.12 | | | | | | | | | | | | | | | | | | | | | | all_192_3 & elts(int, all_103_4) = all_192_4 & 204.47/127.12 | | | | | | | | | | | | | | | | | | | | | | in_uni(all_192_3) & in_uni(all_192_4) 204.47/127.12 | | | | | | | | | | | | | | | | | | | | | | 204.47/127.12 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1203) implies: 204.47/127.12 | | | | | | | | | | | | | | | | | | | | | | (1204) elts(int, all_103_2) = all_192_3 204.47/127.12 | | | | | | | | | | | | | | | | | | | | | | (1205) length1(int, all_103_4) = all_192_2 204.47/127.12 | | | | | | | | | | | | | | | | | | | | | | 204.47/127.12 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (319) gives: 204.47/127.12 | | | | | | | | | | | | | | | | | | | | | | 204.47/127.12 | | | | | | | | | | | | | | | | | | | | | | Case 1: 204.47/127.12 | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.12 | | | | | | | | | | | | | | | | | | | | | | | (1206) all_215_1 = 0 & array_eq_sub1(int, all_103_4, 204.47/127.12 | | | | | | | | | | | | | | | | | | | | | | | all_103_2, 0, all_86_11) = 0 204.47/127.12 | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.12 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1206) implies: 204.47/127.12 | | | | | | | | | | | | | | | | | | | | | | | (1207) array_eq_sub1(int, all_103_4, all_103_2, 0, 204.47/127.12 | | | | | | | | | | | | | | | | | | | | | | | all_86_11) = 0 204.47/127.12 | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.12 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (39), (43), (44), (45), (50), (52), (53), 204.47/127.12 | | | | | | | | | | | | | | | | | | | | | | | (91), (99), (180), (181), (183), (203), (263), 204.47/127.12 | | | | | | | | | | | | | | | | | | | | | | | (269), (270), (272), (297), (324), (345), (389), 204.47/127.12 | | | | | | | | | | | | | | | | | | | | | | | (394), (395), (396), (1180), (1181), (1182), 204.47/127.12 | | | | | | | | | | | | | | | | | | | | | | | (1184), (1185), (1187), (1197), (1198), (1199), 204.47/127.12 | | | | | | | | | | | | | | | | | | | | | | | (1201), (1202), (1204), (1205), (1207) are 204.47/127.12 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #43. 204.47/127.12 | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.12 | | | | | | | | | | | | | | | | | | | | | | Case 2: 204.47/127.12 | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.12 | | | | | | | | | | | | | | | | | | | | | | | (1208) length1(int, all_103_4) = all_215_1 & ( ~ 204.47/127.12 | | | | | | | | | | | | | | | | | | | | | | | ($lesseq(all_86_11, all_215_1)) | ~ ($lesseq(0, 204.47/127.12 | | | | | | | | | | | | | | | | | | | | | | | all_215_1)) | ( ~ (all_215_0 = all_215_1) & 204.47/127.12 | | | | | | | | | | | | | | | | | | | | | | | length1(int, all_103_2) = all_215_0)) 204.47/127.12 | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.12 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1208) implies: 204.47/127.12 | | | | | | | | | | | | | | | | | | | | | | | (1209) length1(int, all_103_4) = all_215_1 204.47/127.12 | | | | | | | | | | | | | | | | | | | | | | | (1210) ~ ($lesseq(all_86_11, all_215_1)) | ~ 204.47/127.12 | | | | | | | | | | | | | | | | | | | | | | | ($lesseq(0, all_215_1)) | ( ~ (all_215_0 = 204.47/127.12 | | | | | | | | | | | | | | | | | | | | | | | all_215_1) & length1(int, all_103_2) = 204.47/127.12 | | | | | | | | | | | | | | | | | | | | | | | all_215_0) 204.47/127.12 | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.12 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (324) gives: 204.47/127.12 | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.12 | | | | | | | | | | | | | | | | | | | | | | | Case 1: 204.47/127.12 | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.12 | | | | | | | | | | | | | | | | | | | | | | | | (1211) all_219_1 = 0 & array_eq_sub1(int, all_105_4, 204.47/127.12 | | | | | | | | | | | | | | | | | | | | | | | | all_105_2, 0, all_86_7) = 0 204.47/127.12 | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.12 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1211) implies: 204.47/127.12 | | | | | | | | | | | | | | | | | | | | | | | | (1212) array_eq_sub1(int, all_105_4, all_105_2, 0, 204.47/127.12 | | | | | | | | | | | | | | | | | | | | | | | | all_86_7) = 0 204.47/127.12 | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.12 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (270) gives: 204.47/127.12 | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.12 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: 204.47/127.12 | | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.12 | | | | | | | | | | | | | | | | | | | | | | | | | (1213) all_169_0 = all_169_1 & $lesseq(all_86_7, 204.47/127.12 | | | | | | | | | | | | | | | | | | | | | | | | | all_169_1) & $lesseq(0, all_169_1) & $lesseq(0, 204.47/127.12 | | | | | | | | | | | | | | | | | | | | | | | | | all_86_7) & length1(int, all_105_2) = all_169_1 204.47/127.12 | | | | | | | | | | | | | | | | | | | | | | | | | & length1(int, all_105_4) = all_169_1 204.47/127.12 | | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.12 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1213) implies: 204.47/127.12 | | | | | | | | | | | | | | | | | | | | | | | | | (1214) length1(int, all_105_4) = all_169_1 204.47/127.12 | | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.12 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (345) gives: 204.47/127.12 | | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.12 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: 204.47/127.12 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.12 | | | | | | | | | | | | | | | | | | | | | | | | | | (1215) all_242_1 = 0 & array_eq_sub1(int, all_103_2, 204.47/127.12 | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, $sum(all_86_8, 1), all_86_13) = 0 204.47/127.12 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.12 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1215) implies: 204.47/127.12 | | | | | | | | | | | | | | | | | | | | | | | | | | (1216) array_eq_sub1(int, all_103_2, all_105_4, 204.47/127.12 | | | | | | | | | | | | | | | | | | | | | | | | | | $sum(all_86_8, 1), all_86_13) = 0 204.47/127.12 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.12 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (45), (48), (50), (52), (53), (183), (269), 204.47/127.12 | | | | | | | | | | | | | | | | | | | | | | | | | | (394), (1184), (1185), (1193), (1194), (1198), 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | (1199), (1202), (1209), (1210), (1214), (1216) are 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #42. 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | (1217) length1(int, all_103_2) = all_242_1 & ( ~ 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | ($lesseq(1, $difference(all_242_1, all_86_8))) | 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | ~ ($lesseq(all_86_13, all_242_1)) | ( ~ 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_242_0 = all_242_1) & length1(int, 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4) = all_242_0)) 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1217) implies: 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | (1218) length1(int, all_103_2) = all_242_1 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (39), (44), (91), (99), (180), (203), (263), 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | (394), (395), (396), (1180), (1181), (1182), 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | (1184), (1185), (1201), (1202), (1204), (1214), 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | (1218) are inconsistent by sub-proof #40. 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | End of split 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | (1219) ~ (all_169_1 = 0) & array_eq_sub1(int, all_105_4, 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | all_105_2, 0, all_86_7) = all_169_1 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (1212), (1219) are inconsistent by sub-proof 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | #75. 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | End of split 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | Case 2: 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | (1220) length1(int, all_105_4) = all_219_1 & ( ~ 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | ($lesseq(all_86_7, all_219_1)) | ~ ($lesseq(0, 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | all_219_1)) | ( ~ (all_219_0 = all_219_1) & 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | length1(int, all_105_2) = all_219_0)) 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1220) implies: 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | (1221) length1(int, all_105_4) = all_219_1 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | (1222) ~ ($lesseq(all_86_7, all_219_1)) | ~ ($lesseq(0, 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | all_219_1)) | ( ~ (all_219_0 = all_219_1) & 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | length1(int, all_105_2) = all_219_0) 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (345) gives: 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | (1223) all_242_1 = 0 & array_eq_sub1(int, all_103_2, 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, $sum(all_86_8, 1), all_86_13) = 0 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1223) implies: 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | (1224) array_eq_sub1(int, all_103_2, all_105_4, 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | $sum(all_86_8, 1), all_86_13) = 0 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (269) gives: 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | (1225) all_168_0 = all_168_1 & $lesseq(1, 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | $difference(all_168_1, all_86_8)) & 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | $lesseq(all_86_13, all_168_1) & $lesseq(-1, 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | all_86_8) & $lesseq(0, all_86_13) & length1(int, 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4) = all_168_1 & length1(int, all_103_2) 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | = all_168_1 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1225) implies: 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | (1226) length1(int, all_105_4) = all_168_1 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_219_1, all_170_1, 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (1185), (1221) 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | (1227) all_219_1 = all_170_1 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_190_2, all_170_1, 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (1185), (1202) 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | (1228) all_190_2 = all_170_1 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_190_2, all_168_1, 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (1202), (1226) 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | (1229) all_190_2 = all_168_1 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_219_1, all_153_1, 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (1194), (1221) 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | (1230) all_219_1 = all_153_1 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_193_1, all_170_1, 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (1184), (1199) 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | (1231) all_193_1 = all_170_1 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_86_13, all_215_1, 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (183), (1209) 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | (1232) all_215_1 = all_86_13 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_215_1, all_193_1, 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (1198), (1209) 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | (1233) all_215_1 = all_193_1 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_215_1, all_192_2, 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (1205), (1209) 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | (1234) all_215_1 = all_192_2 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1227), (1230) imply: 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | (1235) all_170_1 = all_153_1 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1235) implies: 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | (1236) all_170_1 = all_153_1 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1232), (1233) imply: 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | (1237) all_193_1 = all_86_13 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1233), (1234) imply: 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | (1238) all_193_1 = all_192_2 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1231), (1238) imply: 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | (1239) all_192_2 = all_170_1 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1237), (1238) imply: 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | (1240) all_192_2 = all_86_13 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1239), (1240) imply: 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | (1241) all_170_1 = all_86_13 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1241) implies: 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | (1242) all_170_1 = all_86_13 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1228), (1229) imply: 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | (1243) all_170_1 = all_168_1 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1243) implies: 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | (1244) all_170_1 = all_168_1 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1236), (1244) imply: 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | (1245) all_168_1 = all_153_1 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1242), (1244) imply: 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | (1246) all_168_1 = all_86_13 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1245), (1246) imply: 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | (1247) all_153_1 = all_86_13 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1247) implies: 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | (1248) all_153_1 = all_86_13 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (48), (50), (52), (53), (389), (1193), 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | (1195), (1222), (1230), (1248) are inconsistent by 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #58. 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | (1249) ~ (all_168_1 = 0) & array_eq_sub1(int, all_103_2, 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, $sum(all_86_8, 1), all_86_13) = 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | all_168_1 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (1224), (1249) are inconsistent by sub-proof 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | #83. 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | End of split 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | (1250) length1(int, all_103_2) = all_242_1 & ( ~ 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | ($lesseq(1, $difference(all_242_1, all_86_8))) | 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | ~ ($lesseq(all_86_13, all_242_1)) | ( ~ 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | (all_242_0 = all_242_1) & length1(int, 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4) = all_242_0)) 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1250) implies: 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | (1251) length1(int, all_103_2) = all_242_1 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_219_1, all_190_2, 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (1202), (1221) 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | (1252) all_219_1 = all_190_2 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_190_2, all_170_1, 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (1185), (1202) 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | (1253) all_190_2 = all_170_1 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_219_1, all_153_1, 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (1194), (1221) 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | (1254) all_219_1 = all_153_1 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_242_1, all_170_1, 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (1184), (1251) 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | (1255) all_242_1 = all_170_1 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_193_1, all_170_1, 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (1184), (1199) 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | (1256) all_193_1 = all_170_1 204.47/127.13 | | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.14 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_242_1, all_156_0, 204.47/127.14 | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (394), (1251) 204.47/127.14 | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.47/127.14 | | | | | | | | | | | | | | | | | | | | | | | | | (1257) all_242_1 = all_156_0 204.47/127.14 | | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.14 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_86_13, all_193_1, 204.47/127.14 | | | | | | | | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (183), (1198) 204.47/127.14 | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.47/127.14 | | | | | | | | | | | | | | | | | | | | | | | | | (1258) all_193_1 = all_86_13 204.47/127.14 | | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.14 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_215_1, all_193_1, 204.47/127.14 | | | | | | | | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (1198), (1209) 204.47/127.14 | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.47/127.14 | | | | | | | | | | | | | | | | | | | | | | | | | (1259) all_215_1 = all_193_1 204.47/127.14 | | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.14 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_215_1, all_192_2, 204.47/127.14 | | | | | | | | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (1205), (1209) 204.47/127.14 | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.47/127.14 | | | | | | | | | | | | | | | | | | | | | | | | | (1260) all_215_1 = all_192_2 204.47/127.14 | | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.14 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1255), (1257) imply: 204.47/127.14 | | | | | | | | | | | | | | | | | | | | | | | | | (1261) all_170_1 = all_156_0 204.47/127.14 | | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.14 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1261) implies: 204.47/127.14 | | | | | | | | | | | | | | | | | | | | | | | | | (1262) all_170_1 = all_156_0 204.47/127.14 | | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.14 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1252), (1254) imply: 204.47/127.14 | | | | | | | | | | | | | | | | | | | | | | | | | (1263) all_190_2 = all_153_1 204.47/127.14 | | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.14 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1263) implies: 204.47/127.14 | | | | | | | | | | | | | | | | | | | | | | | | | (1264) all_190_2 = all_153_1 204.47/127.14 | | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.14 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1259), (1260) imply: 204.47/127.14 | | | | | | | | | | | | | | | | | | | | | | | | | (1265) all_193_1 = all_192_2 204.47/127.14 | | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.14 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1265) implies: 204.47/127.14 | | | | | | | | | | | | | | | | | | | | | | | | | (1266) all_193_1 = all_192_2 204.47/127.14 | | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.14 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1256), (1266) imply: 204.47/127.14 | | | | | | | | | | | | | | | | | | | | | | | | | (1267) all_192_2 = all_170_1 204.47/127.14 | | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.14 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1258), (1266) imply: 204.47/127.14 | | | | | | | | | | | | | | | | | | | | | | | | | (1268) all_192_2 = all_86_13 204.47/127.14 | | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.14 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1267), (1268) imply: 204.47/127.14 | | | | | | | | | | | | | | | | | | | | | | | | | (1269) all_170_1 = all_86_13 204.47/127.14 | | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.14 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1269) implies: 204.47/127.14 | | | | | | | | | | | | | | | | | | | | | | | | | (1270) all_170_1 = all_86_13 204.47/127.14 | | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.14 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1253), (1264) imply: 204.47/127.14 | | | | | | | | | | | | | | | | | | | | | | | | | (1271) all_170_1 = all_153_1 204.47/127.14 | | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.14 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1271) implies: 204.47/127.14 | | | | | | | | | | | | | | | | | | | | | | | | | (1272) all_170_1 = all_153_1 204.47/127.14 | | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.14 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1262), (1270) imply: 204.47/127.14 | | | | | | | | | | | | | | | | | | | | | | | | | (1273) all_156_0 = all_86_13 204.47/127.14 | | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.14 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1262), (1272) imply: 204.47/127.14 | | | | | | | | | | | | | | | | | | | | | | | | | (1274) all_156_0 = all_153_1 204.47/127.14 | | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.14 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1273), (1274) imply: 204.47/127.14 | | | | | | | | | | | | | | | | | | | | | | | | | (1275) all_153_1 = all_86_13 204.47/127.14 | | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.14 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1275) implies: 204.47/127.14 | | | | | | | | | | | | | | | | | | | | | | | | | (1276) all_153_1 = all_86_13 204.47/127.14 | | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.14 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1260), (1268) imply: 204.47/127.14 | | | | | | | | | | | | | | | | | | | | | | | | | (1277) all_215_1 = all_86_13 204.47/127.14 | | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.14 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (48), (50), (52), (53), (394), (1193), 204.47/127.14 | | | | | | | | | | | | | | | | | | | | | | | | | (1210), (1273), (1276), (1277) are inconsistent by 204.47/127.14 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #72. 204.47/127.14 | | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.14 | | | | | | | | | | | | | | | | | | | | | | | | End of split 204.47/127.14 | | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.14 | | | | | | | | | | | | | | | | | | | | | | | End of split 204.47/127.14 | | | | | | | | | | | | | | | | | | | | | | | 204.47/127.14 | | | | | | | | | | | | | | | | | | | | | | End of split 204.47/127.14 | | | | | | | | | | | | | | | | | | | | | | 204.47/127.14 | | | | | | | | | | | | | | | | | | | | | Case 2: 204.47/127.14 | | | | | | | | | | | | | | | | | | | | | | 204.47/127.14 | | | | | | | | | | | | | | | | | | | | | | (1278) ~ (all_192_4 = 0) & permut_sub2(int, all_103_4, 204.47/127.14 | | | | | | | | | | | | | | | | | | | | | | all_103_2, all_86_11, $sum(all_86_10, 1)) = 204.47/127.14 | | | | | | | | | | | | | | | | | | | | | | all_192_4 204.47/127.14 | | | | | | | | | | | | | | | | | | | | | | 204.47/127.14 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (43), (1187), (1278) are inconsistent by sub-proof 204.47/127.14 | | | | | | | | | | | | | | | | | | | | | | #69. 204.47/127.14 | | | | | | | | | | | | | | | | | | | | | | 204.47/127.14 | | | | | | | | | | | | | | | | | | | | | End of split 204.47/127.14 | | | | | | | | | | | | | | | | | | | | | 204.47/127.14 | | | | | | | | | | | | | | | | | | | | Case 2: 204.47/127.14 | | | | | | | | | | | | | | | | | | | | | 204.47/127.14 | | | | | | | | | | | | | | | | | | | | | (1279) ~ (all_190_4 = 0) & permut_sub2(int, all_105_4, 204.47/127.14 | | | | | | | | | | | | | | | | | | | | | all_105_2, all_86_7, $sum(all_86_10, 1)) = 204.47/127.14 | | | | | | | | | | | | | | | | | | | | | all_190_4 204.47/127.14 | | | | | | | | | | | | | | | | | | | | | 204.47/127.14 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (43), (1189), (1279) are inconsistent by sub-proof 204.47/127.14 | | | | | | | | | | | | | | | | | | | | | #68. 204.47/127.14 | | | | | | | | | | | | | | | | | | | | | 204.64/127.14 | | | | | | | | | | | | | | | | | | | | End of split 204.64/127.14 | | | | | | | | | | | | | | | | | | | | 204.64/127.14 | | | | | | | | | | | | | | | | | | | Case 2: 204.64/127.14 | | | | | | | | | | | | | | | | | | | | 204.64/127.14 | | | | | | | | | | | | | | | | | | | | (1280) ~ (all_193_1 = 0) & array_eq_sub1(int, all_103_4, 204.64/127.14 | | | | | | | | | | | | | | | | | | | | all_103_2, $sum(all_86_10, 1), all_86_13) = 204.64/127.14 | | | | | | | | | | | | | | | | | | | | all_193_1 204.64/127.14 | | | | | | | | | | | | | | | | | | | | 204.64/127.14 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (400), (1280) are inconsistent by sub-proof 204.64/127.14 | | | | | | | | | | | | | | | | | | | | #55. 204.64/127.14 | | | | | | | | | | | | | | | | | | | | 204.64/127.14 | | | | | | | | | | | | | | | | | | | End of split 204.64/127.14 | | | | | | | | | | | | | | | | | | | 204.64/127.14 | | | | | | | | | | | | | | | | | | Case 2: 204.64/127.14 | | | | | | | | | | | | | | | | | | | 204.64/127.14 | | | | | | | | | | | | | | | | | | | (1281) ~ (all_153_1 = 0) & array_eq_sub1(int, all_105_4, 204.64/127.14 | | | | | | | | | | | | | | | | | | | all_105_2, $sum(all_86_10, 1), all_86_13) = 204.64/127.14 | | | | | | | | | | | | | | | | | | | all_153_1 204.64/127.14 | | | | | | | | | | | | | | | | | | | 204.64/127.14 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (1191), (1281) are inconsistent by sub-proof 204.64/127.14 | | | | | | | | | | | | | | | | | | | #54. 204.64/127.14 | | | | | | | | | | | | | | | | | | | 204.64/127.14 | | | | | | | | | | | | | | | | | | End of split 204.64/127.14 | | | | | | | | | | | | | | | | | | 204.64/127.14 | | | | | | | | | | | | | | | | | Case 2: 204.64/127.14 | | | | | | | | | | | | | | | | | | 204.64/127.14 | | | | | | | | | | | | | | | | | | (1282) length1(int, all_105_4) = all_234_1 & ( ~ 204.64/127.14 | | | | | | | | | | | | | | | | | | ($lesseq(1, $difference(all_234_1, all_86_10))) 204.64/127.14 | | | | | | | | | | | | | | | | | | | ~ ($lesseq(all_86_13, all_234_1)) | ( ~ 204.64/127.14 | | | | | | | | | | | | | | | | | | (all_234_0 = all_234_1) & length1(int, 204.64/127.14 | | | | | | | | | | | | | | | | | | all_105_2) = all_234_0)) 204.64/127.14 | | | | | | | | | | | | | | | | | | 204.64/127.14 | | | | | | | | | | | | | | | | | | ALPHA: (1282) implies: 204.64/127.14 | | | | | | | | | | | | | | | | | | (1283) length1(int, all_105_4) = all_234_1 204.64/127.14 | | | | | | | | | | | | | | | | | | (1284) ~ ($lesseq(1, $difference(all_234_1, all_86_10))) 204.64/127.14 | | | | | | | | | | | | | | | | | | | ~ ($lesseq(all_86_13, all_234_1)) | ( ~ 204.64/127.14 | | | | | | | | | | | | | | | | | | (all_234_0 = all_234_1) & length1(int, 204.64/127.14 | | | | | | | | | | | | | | | | | | all_105_2) = all_234_0) 204.64/127.14 | | | | | | | | | | | | | | | | | | 204.64/127.14 | | | | | | | | | | | | | | | | | | BETA: splitting (298) gives: 204.64/127.14 | | | | | | | | | | | | | | | | | | 204.64/127.14 | | | | | | | | | | | | | | | | | | Case 1: 204.64/127.14 | | | | | | | | | | | | | | | | | | | 204.64/127.14 | | | | | | | | | | | | | | | | | | | (1285) all_193_0 = all_193_1 & $lesseq(1, 204.64/127.14 | | | | | | | | | | | | | | | | | | | $difference(all_193_1, all_86_10)) & 204.64/127.14 | | | | | | | | | | | | | | | | | | | $lesseq(all_86_13, all_193_1) & $lesseq(-1, 204.64/127.14 | | | | | | | | | | | | | | | | | | | all_86_10) & $lesseq(0, all_86_13) & 204.64/127.14 | | | | | | | | | | | | | | | | | | | length1(int, all_103_2) = all_193_1 & length1(int, 204.64/127.14 | | | | | | | | | | | | | | | | | | | all_103_4) = all_193_1 204.64/127.14 | | | | | | | | | | | | | | | | | | | 204.64/127.14 | | | | | | | | | | | | | | | | | | | ALPHA: (1285) implies: 204.64/127.14 | | | | | | | | | | | | | | | | | | | (1286) $lesseq(1, $difference(all_193_1, all_86_10)) 204.64/127.14 | | | | | | | | | | | | | | | | | | | (1287) length1(int, all_103_4) = all_193_1 204.64/127.14 | | | | | | | | | | | | | | | | | | | (1288) length1(int, all_103_2) = all_193_1 204.64/127.14 | | | | | | | | | | | | | | | | | | | 204.64/127.14 | | | | | | | | | | | | | | | | | | | BETA: splitting (295) gives: 204.64/127.14 | | | | | | | | | | | | | | | | | | | 204.64/127.14 | | | | | | | | | | | | | | | | | | | Case 1: 204.64/127.14 | | | | | | | | | | | | | | | | | | | | 204.64/127.14 | | | | | | | | | | | | | | | | | | | | (1289) all_190_0 = 0 & all_190_1 = 0 & map_eq_sub1(int, 204.64/127.14 | | | | | | | | | | | | | | | | | | | | all_190_4, all_190_3, $sum(all_86_10, 1), 204.64/127.14 | | | | | | | | | | | | | | | | | | | | all_190_2) = 0 & map_eq_sub1(int, all_190_4, 204.64/127.14 | | | | | | | | | | | | | | | | | | | | all_190_3, 0, all_86_7) = 0 & length1(int, 204.64/127.14 | | | | | | | | | | | | | | | | | | | | all_105_4) = all_190_2 & elts(int, all_105_2) = 204.64/127.14 | | | | | | | | | | | | | | | | | | | | all_190_3 & elts(int, all_105_4) = all_190_4 & 204.64/127.14 | | | | | | | | | | | | | | | | | | | | in_uni(all_190_3) & in_uni(all_190_4) 204.64/127.14 | | | | | | | | | | | | | | | | | | | | 204.64/127.14 | | | | | | | | | | | | | | | | | | | | ALPHA: (1289) implies: 204.64/127.14 | | | | | | | | | | | | | | | | | | | | (1290) elts(int, all_105_4) = all_190_4 204.64/127.14 | | | | | | | | | | | | | | | | | | | | (1291) length1(int, all_105_4) = all_190_2 204.64/127.14 | | | | | | | | | | | | | | | | | | | | 204.64/127.14 | | | | | | | | | | | | | | | | | | | | BETA: splitting (297) gives: 204.64/127.14 | | | | | | | | | | | | | | | | | | | | 204.64/127.14 | | | | | | | | | | | | | | | | | | | | Case 1: 204.64/127.14 | | | | | | | | | | | | | | | | | | | | | 204.64/127.14 | | | | | | | | | | | | | | | | | | | | | (1292) all_192_0 = 0 & all_192_1 = 0 & map_eq_sub1(int, 204.64/127.14 | | | | | | | | | | | | | | | | | | | | | all_192_4, all_192_3, $sum(all_86_10, 1), 204.64/127.14 | | | | | | | | | | | | | | | | | | | | | all_192_2) = 0 & map_eq_sub1(int, all_192_4, 204.64/127.14 | | | | | | | | | | | | | | | | | | | | | all_192_3, 0, all_86_11) = 0 & length1(int, 204.64/127.14 | | | | | | | | | | | | | | | | | | | | | all_103_4) = all_192_2 & elts(int, all_103_2) = 204.64/127.14 | | | | | | | | | | | | | | | | | | | | | all_192_3 & elts(int, all_103_4) = all_192_4 & 204.64/127.14 | | | | | | | | | | | | | | | | | | | | | in_uni(all_192_3) & in_uni(all_192_4) 204.64/127.14 | | | | | | | | | | | | | | | | | | | | | 204.64/127.14 | | | | | | | | | | | | | | | | | | | | | ALPHA: (1292) implies: 204.64/127.14 | | | | | | | | | | | | | | | | | | | | | (1293) elts(int, all_103_2) = all_192_3 204.64/127.14 | | | | | | | | | | | | | | | | | | | | | (1294) length1(int, all_103_4) = all_192_2 204.64/127.14 | | | | | | | | | | | | | | | | | | | | | 204.64/127.14 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (324) gives: 204.64/127.14 | | | | | | | | | | | | | | | | | | | | | 204.64/127.14 | | | | | | | | | | | | | | | | | | | | | Case 1: 204.64/127.14 | | | | | | | | | | | | | | | | | | | | | | 204.64/127.14 | | | | | | | | | | | | | | | | | | | | | | (1295) all_219_1 = 0 & array_eq_sub1(int, all_105_4, 204.64/127.14 | | | | | | | | | | | | | | | | | | | | | | all_105_2, 0, all_86_7) = 0 204.64/127.14 | | | | | | | | | | | | | | | | | | | | | | 204.64/127.14 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1295) implies: 204.64/127.14 | | | | | | | | | | | | | | | | | | | | | | (1296) array_eq_sub1(int, all_105_4, all_105_2, 0, 204.64/127.14 | | | | | | | | | | | | | | | | | | | | | | all_86_7) = 0 204.64/127.14 | | | | | | | | | | | | | | | | | | | | | | 204.64/127.14 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (270) gives: 204.64/127.14 | | | | | | | | | | | | | | | | | | | | | | 204.64/127.14 | | | | | | | | | | | | | | | | | | | | | | Case 1: 204.64/127.14 | | | | | | | | | | | | | | | | | | | | | | | 204.64/127.14 | | | | | | | | | | | | | | | | | | | | | | | (1297) all_169_0 = all_169_1 & $lesseq(all_86_7, 204.64/127.14 | | | | | | | | | | | | | | | | | | | | | | | all_169_1) & $lesseq(0, all_169_1) & $lesseq(0, 204.64/127.14 | | | | | | | | | | | | | | | | | | | | | | | all_86_7) & length1(int, all_105_2) = all_169_1 204.64/127.14 | | | | | | | | | | | | | | | | | | | | | | | & length1(int, all_105_4) = all_169_1 204.64/127.14 | | | | | | | | | | | | | | | | | | | | | | | 204.64/127.14 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1297) implies: 204.64/127.14 | | | | | | | | | | | | | | | | | | | | | | | (1298) length1(int, all_105_4) = all_169_1 204.64/127.14 | | | | | | | | | | | | | | | | | | | | | | | 204.64/127.14 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (319) gives: 204.64/127.14 | | | | | | | | | | | | | | | | | | | | | | | 204.64/127.14 | | | | | | | | | | | | | | | | | | | | | | | Case 1: 204.64/127.14 | | | | | | | | | | | | | | | | | | | | | | | | 204.64/127.14 | | | | | | | | | | | | | | | | | | | | | | | | (1299) all_215_1 = 0 & array_eq_sub1(int, all_103_4, 204.64/127.14 | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, 0, all_86_11) = 0 204.64/127.14 | | | | | | | | | | | | | | | | | | | | | | | | 204.64/127.14 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1299) implies: 204.64/127.14 | | | | | | | | | | | | | | | | | | | | | | | | (1300) array_eq_sub1(int, all_103_4, all_103_2, 0, 204.64/127.14 | | | | | | | | | | | | | | | | | | | | | | | | all_86_11) = 0 204.64/127.14 | | | | | | | | | | | | | | | | | | | | | | | | 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (39), (43), (44), (45), (50), (52), (53), 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | (91), (99), (180), (181), (183), (203), (263), 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | (269), (270), (272), (297), (324), (345), (389), 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | (394), (395), (396), (1180), (1181), (1182), 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | (1184), (1185), (1187), (1286), (1287), (1288), 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | (1290), (1291), (1293), (1294), (1300) are 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #43. 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | Case 2: 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | (1301) length1(int, all_103_4) = all_215_1 & ( ~ 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | ($lesseq(all_86_11, all_215_1)) | ~ ($lesseq(0, 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | all_215_1)) | ( ~ (all_215_0 = all_215_1) & 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | length1(int, all_103_2) = all_215_0)) 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1301) implies: 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | (1302) length1(int, all_103_4) = all_215_1 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (345) gives: 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | (1303) all_242_1 = 0 & array_eq_sub1(int, all_103_2, 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, $sum(all_86_8, 1), all_86_13) = 0 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1303) implies: 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | (1304) array_eq_sub1(int, all_103_2, all_105_4, 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | $sum(all_86_8, 1), all_86_13) = 0 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (269) gives: 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (1305) all_168_0 = all_168_1 & $lesseq(1, 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | $difference(all_168_1, all_86_8)) & 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | $lesseq(all_86_13, all_168_1) & $lesseq(-1, 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | all_86_8) & $lesseq(0, all_86_13) & length1(int, 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4) = all_168_1 & length1(int, all_103_2) 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | = all_168_1 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1305) implies: 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (1306) length1(int, all_103_2) = all_168_1 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (1307) length1(int, all_105_4) = all_168_1 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_234_1, all_170_1, 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (1185), (1283) 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (1308) all_234_1 = all_170_1 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_190_2, all_170_1, 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (1185), (1291) 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (1309) all_190_2 = all_170_1 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_190_2, all_169_1, 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (1291), (1298) 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (1310) all_190_2 = all_169_1 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_234_1, all_168_1, 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (1283), (1307) 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (1311) all_234_1 = all_168_1 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_193_1, all_170_1, 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (1184), (1288) 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (1312) all_193_1 = all_170_1 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_168_1, all_156_0, 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (394), (1306) 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (1313) all_168_1 = all_156_0 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_86_13, all_215_1, 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (183), (1302) 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (1314) all_215_1 = all_86_13 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_215_1, all_193_1, 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (1287), (1302) 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (1315) all_215_1 = all_193_1 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_215_1, all_192_2, 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (1294), (1302) 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (1316) all_215_1 = all_192_2 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_105_3, all_190_4, 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (99), (1290) 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (1317) all_190_4 = all_105_3 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_190_4, all_181_2, 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (1181), (1290) 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (1318) all_190_4 = all_181_2 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_181_2, all_156_1, 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (395), (1181) 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (1319) all_181_2 = all_156_1 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_103_1, all_181_3, 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (91), (1180) 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (1320) all_181_3 = all_103_1 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_192_3, all_181_3, 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (1180), (1293) 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (1321) all_192_3 = all_181_3 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_192_3, all_156_3, 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (396), (1293) 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (1322) all_192_3 = all_156_3 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1308), (1311) imply: 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (1323) all_170_1 = all_168_1 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1323) implies: 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (1324) all_170_1 = all_168_1 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1314), (1315) imply: 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (1325) all_193_1 = all_86_13 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1315), (1316) imply: 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (1326) all_193_1 = all_192_2 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1312), (1326) imply: 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (1327) all_192_2 = all_170_1 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1325), (1326) imply: 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (1328) all_192_2 = all_86_13 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1327), (1328) imply: 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (1329) all_170_1 = all_86_13 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1329) implies: 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (1330) all_170_1 = all_86_13 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1321), (1322) imply: 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (1331) all_181_3 = all_156_3 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1331) implies: 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (1332) all_181_3 = all_156_3 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1309), (1310) imply: 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (1333) all_170_1 = all_169_1 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1333) implies: 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (1334) all_170_1 = all_169_1 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1317), (1318) imply: 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (1335) all_181_2 = all_105_3 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1335) implies: 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (1336) all_181_2 = all_105_3 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1319), (1336) imply: 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (1337) all_156_1 = all_105_3 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1337) implies: 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (1338) all_156_1 = all_105_3 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1320), (1332) imply: 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (1339) all_156_3 = all_103_1 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1324), (1334) imply: 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (1340) all_169_1 = all_168_1 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1330), (1334) imply: 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (1341) all_169_1 = all_86_13 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (44), (203), (263), (394), (1182), (1313), 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (1332), (1336), (1338), (1339), (1340), (1341) are 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #39. 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (1342) ~ (all_168_1 = 0) & array_eq_sub1(int, all_103_2, 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, $sum(all_86_8, 1), all_86_13) = 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | all_168_1 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (1304), (1342) are inconsistent by sub-proof 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | #83. 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | End of split 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | (1343) length1(int, all_103_2) = all_242_1 & ( ~ 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | ($lesseq(1, $difference(all_242_1, all_86_8))) | 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | ~ ($lesseq(all_86_13, all_242_1)) | ( ~ 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | (all_242_0 = all_242_1) & length1(int, 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4) = all_242_0)) 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1343) implies: 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | (1344) length1(int, all_103_2) = all_242_1 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (39), (44), (91), (99), (180), (203), (263), 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | (394), (395), (396), (1180), (1181), (1182), 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | (1184), (1185), (1290), (1291), (1293), (1298), 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | (1344) are inconsistent by sub-proof #40. 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | | 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | End of split 204.64/127.15 | | | | | | | | | | | | | | | | | | | | | | | | 204.64/127.16 | | | | | | | | | | | | | | | | | | | | | | | End of split 204.64/127.16 | | | | | | | | | | | | | | | | | | | | | | | 204.64/127.16 | | | | | | | | | | | | | | | | | | | | | | Case 2: 204.64/127.16 | | | | | | | | | | | | | | | | | | | | | | | 204.64/127.16 | | | | | | | | | | | | | | | | | | | | | | | (1345) ~ (all_169_1 = 0) & array_eq_sub1(int, all_105_4, 204.64/127.16 | | | | | | | | | | | | | | | | | | | | | | | all_105_2, 0, all_86_7) = all_169_1 204.64/127.16 | | | | | | | | | | | | | | | | | | | | | | | 204.64/127.16 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (1296), (1345) are inconsistent by sub-proof 204.64/127.16 | | | | | | | | | | | | | | | | | | | | | | | #75. 204.64/127.16 | | | | | | | | | | | | | | | | | | | | | | | 204.64/127.16 | | | | | | | | | | | | | | | | | | | | | | End of split 204.64/127.16 | | | | | | | | | | | | | | | | | | | | | | 204.64/127.16 | | | | | | | | | | | | | | | | | | | | | Case 2: 204.64/127.16 | | | | | | | | | | | | | | | | | | | | | | 204.64/127.16 | | | | | | | | | | | | | | | | | | | | | | (1346) length1(int, all_105_4) = all_219_1 & ( ~ 204.64/127.16 | | | | | | | | | | | | | | | | | | | | | | ($lesseq(all_86_7, all_219_1)) | ~ ($lesseq(0, 204.64/127.16 | | | | | | | | | | | | | | | | | | | | | | all_219_1)) | ( ~ (all_219_0 = all_219_1) & 204.64/127.16 | | | | | | | | | | | | | | | | | | | | | | length1(int, all_105_2) = all_219_0)) 204.64/127.16 | | | | | | | | | | | | | | | | | | | | | | 204.64/127.16 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1346) implies: 204.64/127.16 | | | | | | | | | | | | | | | | | | | | | | (1347) length1(int, all_105_4) = all_219_1 204.64/127.16 | | | | | | | | | | | | | | | | | | | | | | 204.64/127.16 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (319) gives: 204.64/127.16 | | | | | | | | | | | | | | | | | | | | | | 204.64/127.16 | | | | | | | | | | | | | | | | | | | | | | Case 1: 204.64/127.16 | | | | | | | | | | | | | | | | | | | | | | | 204.64/127.16 | | | | | | | | | | | | | | | | | | | | | | | (1348) all_215_1 = 0 & array_eq_sub1(int, all_103_4, 204.64/127.16 | | | | | | | | | | | | | | | | | | | | | | | all_103_2, 0, all_86_11) = 0 204.64/127.16 | | | | | | | | | | | | | | | | | | | | | | | 204.64/127.16 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1348) implies: 204.64/127.16 | | | | | | | | | | | | | | | | | | | | | | | (1349) array_eq_sub1(int, all_103_4, all_103_2, 0, 204.64/127.16 | | | | | | | | | | | | | | | | | | | | | | | all_86_11) = 0 204.64/127.16 | | | | | | | | | | | | | | | | | | | | | | | 204.64/127.16 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (39), (43), (44), (45), (50), (52), (53), 204.64/127.16 | | | | | | | | | | | | | | | | | | | | | | | (91), (99), (180), (181), (183), (203), (263), 204.64/127.16 | | | | | | | | | | | | | | | | | | | | | | | (269), (270), (272), (297), (324), (345), (389), 204.64/127.16 | | | | | | | | | | | | | | | | | | | | | | | (394), (395), (396), (1180), (1181), (1182), 204.64/127.16 | | | | | | | | | | | | | | | | | | | | | | | (1184), (1185), (1187), (1286), (1287), (1288), 204.64/127.16 | | | | | | | | | | | | | | | | | | | | | | | (1290), (1291), (1293), (1294), (1349) are 204.64/127.16 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #43. 204.64/127.16 | | | | | | | | | | | | | | | | | | | | | | | 204.64/127.16 | | | | | | | | | | | | | | | | | | | | | | Case 2: 204.64/127.16 | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | (1350) length1(int, all_103_4) = all_215_1 & ( ~ 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | ($lesseq(all_86_11, all_215_1)) | ~ ($lesseq(0, 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | all_215_1)) | ( ~ (all_215_0 = all_215_1) & 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | length1(int, all_103_2) = all_215_0)) 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1350) implies: 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | (1351) length1(int, all_103_4) = all_215_1 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (345) gives: 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | Case 1: 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | (1352) all_242_1 = 0 & array_eq_sub1(int, all_103_2, 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, $sum(all_86_8, 1), all_86_13) = 0 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (45), (181), (183), (269), (1184), (1185), 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | (1283), (1284), (1286), (1287), (1288), (1291), 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | (1347), (1351), (1352) are inconsistent by 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #37. 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | Case 2: 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | (1353) length1(int, all_103_2) = all_242_1 & ( ~ 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | ($lesseq(1, $difference(all_242_1, all_86_8))) | 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | ~ ($lesseq(all_86_13, all_242_1)) | ( ~ 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | (all_242_0 = all_242_1) & length1(int, 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | all_105_4) = all_242_0)) 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1353) implies: 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | (1354) length1(int, all_103_2) = all_242_1 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_86_13, all_219_1, 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (180), (1347) 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | (1355) all_219_1 = all_86_13 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_234_1, all_219_1, 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (1283), (1347) 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | (1356) all_234_1 = all_219_1 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_219_1, all_190_2, 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (1291), (1347) 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | (1357) all_219_1 = all_190_2 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_234_1, all_170_1, 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (1185), (1283) 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | (1358) all_234_1 = all_170_1 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_242_1, all_193_1, 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (1288), (1354) 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | (1359) all_242_1 = all_193_1 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_193_1, all_170_1, 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (1184), (1288) 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | (1360) all_193_1 = all_170_1 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_242_1, all_156_0, 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (394), (1354) 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | (1361) all_242_1 = all_156_0 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_105_3, all_190_4, 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (99), (1290) 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | (1362) all_190_4 = all_105_3 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_190_4, all_181_2, 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (1181), (1290) 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | (1363) all_190_4 = all_181_2 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_181_2, all_156_1, 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (395), (1181) 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | (1364) all_181_2 = all_156_1 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_103_1, all_181_3, 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (91), (1180) 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | (1365) all_181_3 = all_103_1 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_192_3, all_181_3, 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (1180), (1293) 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | (1366) all_192_3 = all_181_3 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_192_3, all_156_3, 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (396), (1293) 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | (1367) all_192_3 = all_156_3 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1359), (1361) imply: 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | (1368) all_193_1 = all_156_0 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1368) implies: 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | (1369) all_193_1 = all_156_0 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1356), (1358) imply: 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | (1370) all_219_1 = all_170_1 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1370) implies: 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | (1371) all_219_1 = all_170_1 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1355), (1357) imply: 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | (1372) all_190_2 = all_86_13 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1357), (1371) imply: 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | (1373) all_190_2 = all_170_1 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1360), (1369) imply: 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | (1374) all_170_1 = all_156_0 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1374) implies: 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | (1375) all_170_1 = all_156_0 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1366), (1367) imply: 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | (1376) all_181_3 = all_156_3 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1376) implies: 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | (1377) all_181_3 = all_156_3 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1372), (1373) imply: 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | (1378) all_170_1 = all_86_13 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1378) implies: 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | (1379) all_170_1 = all_86_13 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1362), (1363) imply: 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | (1380) all_181_2 = all_105_3 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1380) implies: 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | (1381) all_181_2 = all_105_3 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (44), (203), (263), (394), (1182), (1364), 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | (1365), (1375), (1377), (1379), (1381) are 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #36. 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | End of split 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | End of split 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | | 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | End of split 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | 204.71/127.16 | | | | | | | | | | | | | | | | | | | | Case 2: 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | (1382) ~ (all_192_4 = 0) & permut_sub2(int, all_103_4, 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | all_103_2, all_86_11, $sum(all_86_10, 1)) = 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | all_192_4 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (43), (1187), (1382) are inconsistent by sub-proof 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | #69. 204.71/127.16 | | | | | | | | | | | | | | | | | | | | | 204.71/127.16 | | | | | | | | | | | | | | | | | | | | End of split 204.71/127.16 | | | | | | | | | | | | | | | | | | | | 204.71/127.16 | | | | | | | | | | | | | | | | | | | Case 2: 204.71/127.16 | | | | | | | | | | | | | | | | | | | | 204.71/127.16 | | | | | | | | | | | | | | | | | | | | (1383) ~ (all_190_4 = 0) & permut_sub2(int, all_105_4, 204.71/127.16 | | | | | | | | | | | | | | | | | | | | all_105_2, all_86_7, $sum(all_86_10, 1)) = 204.71/127.16 | | | | | | | | | | | | | | | | | | | | all_190_4 204.71/127.16 | | | | | | | | | | | | | | | | | | | | 204.71/127.17 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (43), (1189), (1383) are inconsistent by sub-proof 204.71/127.17 | | | | | | | | | | | | | | | | | | | | #68. 204.71/127.17 | | | | | | | | | | | | | | | | | | | | 204.71/127.17 | | | | | | | | | | | | | | | | | | | End of split 204.71/127.17 | | | | | | | | | | | | | | | | | | | 204.71/127.17 | | | | | | | | | | | | | | | | | | Case 2: 204.71/127.17 | | | | | | | | | | | | | | | | | | | 204.71/127.17 | | | | | | | | | | | | | | | | | | | (1384) ~ (all_193_1 = 0) & array_eq_sub1(int, all_103_4, 204.71/127.17 | | | | | | | | | | | | | | | | | | | all_103_2, $sum(all_86_10, 1), all_86_13) = 204.71/127.17 | | | | | | | | | | | | | | | | | | | all_193_1 204.71/127.17 | | | | | | | | | | | | | | | | | | | 204.71/127.17 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (400), (1384) are inconsistent by sub-proof 204.71/127.17 | | | | | | | | | | | | | | | | | | | #55. 204.71/127.17 | | | | | | | | | | | | | | | | | | | 204.71/127.17 | | | | | | | | | | | | | | | | | | End of split 204.71/127.17 | | | | | | | | | | | | | | | | | | 204.71/127.17 | | | | | | | | | | | | | | | | | End of split 204.71/127.17 | | | | | | | | | | | | | | | | | 204.71/127.17 | | | | | | | | | | | | | | | | Case 2: 204.71/127.17 | | | | | | | | | | | | | | | | | 204.71/127.17 | | | | | | | | | | | | | | | | | (1385) elts(int, all_105_2) = all_187_2 & elts(int, 204.71/127.17 | | | | | | | | | | | | | | | | | all_105_4) = all_187_3 & in_uni(all_187_2) & 204.71/127.17 | | | | | | | | | | | | | | | | | in_uni(all_187_3) & (( ~ (all_187_0 = 0) & 204.71/127.17 | | | | | | | | | | | | | | | | | map_eq_sub1(int, all_187_3, all_187_2, 204.71/127.17 | | | | | | | | | | | | | | | | | $sum(all_86_10, 1), all_187_1) = all_187_0 & 204.71/127.17 | | | | | | | | | | | | | | | | | length1(int, all_105_4) = all_187_1) | ( ~ 204.71/127.17 | | | | | | | | | | | | | | | | | (all_187_1 = 0) & map_eq_sub1(int, all_187_3, 204.71/127.17 | | | | | | | | | | | | | | | | | all_187_2, 0, all_86_7) = all_187_1)) 204.71/127.17 | | | | | | | | | | | | | | | | | 204.71/127.17 | | | | | | | | | | | | | | | | | ALPHA: (1385) implies: 204.71/127.17 | | | | | | | | | | | | | | | | | (1386) elts(int, all_105_4) = all_187_3 204.71/127.17 | | | | | | | | | | | | | | | | | (1387) elts(int, all_105_2) = all_187_2 204.71/127.17 | | | | | | | | | | | | | | | | | (1388) ( ~ (all_187_0 = 0) & map_eq_sub1(int, all_187_3, 204.71/127.17 | | | | | | | | | | | | | | | | | all_187_2, $sum(all_86_10, 1), all_187_1) = 204.71/127.17 | | | | | | | | | | | | | | | | | all_187_0 & length1(int, all_105_4) = all_187_1) 204.71/127.17 | | | | | | | | | | | | | | | | | | ( ~ (all_187_1 = 0) & map_eq_sub1(int, 204.71/127.17 | | | | | | | | | | | | | | | | | all_187_3, all_187_2, 0, all_86_7) = 204.71/127.17 | | | | | | | | | | | | | | | | | all_187_1) 204.71/127.17 | | | | | | | | | | | | | | | | | 204.71/127.17 | | | | | | | | | | | | | | | | | BETA: splitting (337) gives: 204.71/127.17 | | | | | | | | | | | | | | | | | 204.71/127.17 | | | | | | | | | | | | | | | | | Case 1: 204.71/127.17 | | | | | | | | | | | | | | | | | | 204.71/127.17 | | | | | | | | | | | | | | | | | | (1389) all_234_1 = 0 & array_eq_sub1(int, all_105_4, 204.71/127.17 | | | | | | | | | | | | | | | | | | all_105_2, $sum(all_86_10, 1), all_86_13) = 0 204.71/127.17 | | | | | | | | | | | | | | | | | | 204.71/127.17 | | | | | | | | | | | | | | | | | | ALPHA: (1389) implies: 204.71/127.17 | | | | | | | | | | | | | | | | | | (1390) array_eq_sub1(int, all_105_4, all_105_2, 204.71/127.17 | | | | | | | | | | | | | | | | | | $sum(all_86_10, 1), all_86_13) = 0 204.71/127.17 | | | | | | | | | | | | | | | | | | 204.71/127.17 | | | | | | | | | | | | | | | | | | BETA: splitting (255) gives: 204.71/127.17 | | | | | | | | | | | | | | | | | | 204.71/127.17 | | | | | | | | | | | | | | | | | | Case 1: 204.71/127.17 | | | | | | | | | | | | | | | | | | | 204.71/127.17 | | | | | | | | | | | | | | | | | | | (1391) all_153_0 = all_153_1 & $lesseq(1, 204.71/127.17 | | | | | | | | | | | | | | | | | | | $difference(all_153_1, all_86_10)) & 204.71/127.17 | | | | | | | | | | | | | | | | | | | $lesseq(all_86_13, all_153_1) & $lesseq(-1, 204.71/127.17 | | | | | | | | | | | | | | | | | | | all_86_10) & $lesseq(0, all_86_13) & 204.71/127.17 | | | | | | | | | | | | | | | | | | | length1(int, all_105_2) = all_153_1 & length1(int, 204.71/127.17 | | | | | | | | | | | | | | | | | | | all_105_4) = all_153_1 204.71/127.17 | | | | | | | | | | | | | | | | | | | 204.71/127.17 | | | | | | | | | | | | | | | | | | | ALPHA: (1391) implies: 204.71/127.17 | | | | | | | | | | | | | | | | | | | (1392) $lesseq(1, $difference(all_153_1, all_86_10)) 204.71/127.17 | | | | | | | | | | | | | | | | | | | (1393) length1(int, all_105_4) = all_153_1 204.71/127.17 | | | | | | | | | | | | | | | | | | | 204.71/127.17 | | | | | | | | | | | | | | | | | | | BETA: splitting (297) gives: 204.71/127.17 | | | | | | | | | | | | | | | | | | | 204.71/127.17 | | | | | | | | | | | | | | | | | | | Case 1: 204.71/127.17 | | | | | | | | | | | | | | | | | | | | 204.71/127.17 | | | | | | | | | | | | | | | | | | | | (1394) all_192_0 = 0 & all_192_1 = 0 & map_eq_sub1(int, 204.71/127.17 | | | | | | | | | | | | | | | | | | | | all_192_4, all_192_3, $sum(all_86_10, 1), 204.71/127.17 | | | | | | | | | | | | | | | | | | | | all_192_2) = 0 & map_eq_sub1(int, all_192_4, 204.71/127.17 | | | | | | | | | | | | | | | | | | | | all_192_3, 0, all_86_11) = 0 & length1(int, 204.71/127.17 | | | | | | | | | | | | | | | | | | | | all_103_4) = all_192_2 & elts(int, all_103_2) = 204.71/127.17 | | | | | | | | | | | | | | | | | | | | all_192_3 & elts(int, all_103_4) = all_192_4 & 204.71/127.17 | | | | | | | | | | | | | | | | | | | | in_uni(all_192_3) & in_uni(all_192_4) 204.71/127.17 | | | | | | | | | | | | | | | | | | | | 204.71/127.17 | | | | | | | | | | | | | | | | | | | | ALPHA: (1394) implies: 204.71/127.17 | | | | | | | | | | | | | | | | | | | | (1395) elts(int, all_103_2) = all_192_3 204.71/127.17 | | | | | | | | | | | | | | | | | | | | 204.71/127.17 | | | | | | | | | | | | | | | | | | | | BETA: splitting (298) gives: 204.71/127.17 | | | | | | | | | | | | | | | | | | | | 204.71/127.17 | | | | | | | | | | | | | | | | | | | | Case 1: 204.71/127.17 | | | | | | | | | | | | | | | | | | | | | 204.71/127.17 | | | | | | | | | | | | | | | | | | | | | (1396) all_193_0 = all_193_1 & $lesseq(1, 204.71/127.17 | | | | | | | | | | | | | | | | | | | | | $difference(all_193_1, all_86_10)) & 204.71/127.17 | | | | | | | | | | | | | | | | | | | | | $lesseq(all_86_13, all_193_1) & $lesseq(-1, 204.71/127.17 | | | | | | | | | | | | | | | | | | | | | all_86_10) & $lesseq(0, all_86_13) & 204.71/127.17 | | | | | | | | | | | | | | | | | | | | | length1(int, all_103_2) = all_193_1 & length1(int, 204.71/127.17 | | | | | | | | | | | | | | | | | | | | | all_103_4) = all_193_1 204.71/127.17 | | | | | | | | | | | | | | | | | | | | | 204.71/127.17 | | | | | | | | | | | | | | | | | | | | | ALPHA: (1396) implies: 204.71/127.17 | | | | | | | | | | | | | | | | | | | | | (1397) $lesseq(1, $difference(all_193_1, all_86_10)) 204.71/127.17 | | | | | | | | | | | | | | | | | | | | | (1398) length1(int, all_103_4) = all_193_1 204.71/127.17 | | | | | | | | | | | | | | | | | | | | | (1399) length1(int, all_103_2) = all_193_1 204.71/127.17 | | | | | | | | | | | | | | | | | | | | | 204.71/127.17 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (324) gives: 204.71/127.17 | | | | | | | | | | | | | | | | | | | | | 204.71/127.17 | | | | | | | | | | | | | | | | | | | | | Case 1: 204.71/127.17 | | | | | | | | | | | | | | | | | | | | | | 204.71/127.17 | | | | | | | | | | | | | | | | | | | | | | (1400) all_219_1 = 0 & array_eq_sub1(int, all_105_4, 204.71/127.17 | | | | | | | | | | | | | | | | | | | | | | all_105_2, 0, all_86_7) = 0 204.71/127.17 | | | | | | | | | | | | | | | | | | | | | | 204.71/127.17 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1400) implies: 204.71/127.17 | | | | | | | | | | | | | | | | | | | | | | (1401) array_eq_sub1(int, all_105_4, all_105_2, 0, 204.71/127.17 | | | | | | | | | | | | | | | | | | | | | | all_86_7) = 0 204.71/127.17 | | | | | | | | | | | | | | | | | | | | | | 204.71/127.17 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (270) gives: 204.71/127.17 | | | | | | | | | | | | | | | | | | | | | | 204.71/127.17 | | | | | | | | | | | | | | | | | | | | | | Case 1: 204.71/127.17 | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.17 | | | | | | | | | | | | | | | | | | | | | | | (1402) all_169_0 = all_169_1 & $lesseq(all_86_7, 204.71/127.17 | | | | | | | | | | | | | | | | | | | | | | | all_169_1) & $lesseq(0, all_169_1) & $lesseq(0, 204.71/127.17 | | | | | | | | | | | | | | | | | | | | | | | all_86_7) & length1(int, all_105_2) = all_169_1 204.71/127.17 | | | | | | | | | | | | | | | | | | | | | | | & length1(int, all_105_4) = all_169_1 204.71/127.17 | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.17 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1402) implies: 204.71/127.17 | | | | | | | | | | | | | | | | | | | | | | | (1403) length1(int, all_105_4) = all_169_1 204.71/127.17 | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.17 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (39), (44), (99), (100), (105), (184), 204.71/127.17 | | | | | | | | | | | | | | | | | | | | | | | (205), (1181), (1184), (1185), (1386), (1387), 204.71/127.17 | | | | | | | | | | | | | | | | | | | | | | | (1388), (1393), (1403) are inconsistent by 204.71/127.17 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #35. 204.71/127.17 | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.17 | | | | | | | | | | | | | | | | | | | | | | Case 2: 204.71/127.17 | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.17 | | | | | | | | | | | | | | | | | | | | | | | (1404) ~ (all_169_1 = 0) & array_eq_sub1(int, all_105_4, 204.71/127.17 | | | | | | | | | | | | | | | | | | | | | | | all_105_2, 0, all_86_7) = all_169_1 204.71/127.17 | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.17 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (1401), (1404) are inconsistent by sub-proof 204.71/127.17 | | | | | | | | | | | | | | | | | | | | | | | #75. 204.71/127.17 | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.17 | | | | | | | | | | | | | | | | | | | | | | End of split 204.71/127.17 | | | | | | | | | | | | | | | | | | | | | | 204.71/127.17 | | | | | | | | | | | | | | | | | | | | | Case 2: 204.71/127.17 | | | | | | | | | | | | | | | | | | | | | | 204.71/127.17 | | | | | | | | | | | | | | | | | | | | | | (1405) length1(int, all_105_4) = all_219_1 & ( ~ 204.71/127.17 | | | | | | | | | | | | | | | | | | | | | | ($lesseq(all_86_7, all_219_1)) | ~ ($lesseq(0, 204.71/127.17 | | | | | | | | | | | | | | | | | | | | | | all_219_1)) | ( ~ (all_219_0 = all_219_1) & 204.71/127.17 | | | | | | | | | | | | | | | | | | | | | | length1(int, all_105_2) = all_219_0)) 204.71/127.17 | | | | | | | | | | | | | | | | | | | | | | 204.71/127.17 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1405) implies: 204.71/127.17 | | | | | | | | | | | | | | | | | | | | | | (1406) length1(int, all_105_4) = all_219_1 204.71/127.17 | | | | | | | | | | | | | | | | | | | | | | (1407) ~ ($lesseq(all_86_7, all_219_1)) | ~ ($lesseq(0, 204.71/127.17 | | | | | | | | | | | | | | | | | | | | | | all_219_1)) | ( ~ (all_219_0 = all_219_1) & 204.71/127.17 | | | | | | | | | | | | | | | | | | | | | | length1(int, all_105_2) = all_219_0) 204.71/127.17 | | | | | | | | | | | | | | | | | | | | | | 204.71/127.17 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (319) gives: 204.71/127.17 | | | | | | | | | | | | | | | | | | | | | | 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | Case 1: 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | (1408) all_215_1 = 0 & array_eq_sub1(int, all_103_4, 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | all_103_2, 0, all_86_11) = 0 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (43), (45), (50), (52), (53), (181), (183), 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | (272), (297), (389), (1184), (1185), (1187), 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | (1397), (1398), (1406), (1407), (1408) are 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #34. 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | Case 2: 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | (1409) length1(int, all_103_4) = all_215_1 & ( ~ 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | ($lesseq(all_86_11, all_215_1)) | ~ ($lesseq(0, 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | all_215_1)) | ( ~ (all_215_0 = all_215_1) & 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | length1(int, all_103_2) = all_215_0)) 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1409) implies: 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | (1410) length1(int, all_103_4) = all_215_1 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | (1411) ~ ($lesseq(all_86_11, all_215_1)) | ~ 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | ($lesseq(0, all_215_1)) | ( ~ (all_215_0 = 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | all_215_1) & length1(int, all_103_2) = 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | all_215_0) 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (345) gives: 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | Case 1: 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | | (1412) all_242_1 = 0 & array_eq_sub1(int, all_103_2, 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, $sum(all_86_8, 1), all_86_13) = 0 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1412) implies: 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | | (1413) array_eq_sub1(int, all_103_2, all_105_4, 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | | $sum(all_86_8, 1), all_86_13) = 0 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (45), (48), (50), (52), (53), (183), (269), 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | | (394), (1184), (1185), (1392), (1393), (1398), 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | | (1399), (1406), (1410), (1411), (1413) are 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #32. 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | Case 2: 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | | (1414) length1(int, all_103_2) = all_242_1 & ( ~ 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | | ($lesseq(1, $difference(all_242_1, all_86_8))) | 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | | ~ ($lesseq(all_86_13, all_242_1)) | ( ~ 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | | (all_242_0 = all_242_1) & length1(int, 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | | all_105_4) = all_242_0)) 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1414) implies: 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | | (1415) length1(int, all_103_2) = all_242_1 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (39), (44), (91), (99), (180), (203), (263), 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | | (394), (395), (396), (1180), (1181), (1182), 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | | (1184), (1185), (1386), (1395), (1399), (1406), 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | | (1415) are inconsistent by sub-proof #31. 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | End of split 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | End of split 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | End of split 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | 204.71/127.18 | | | | | | | | | | | | | | | | | | | | Case 2: 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | (1416) ~ (all_193_1 = 0) & array_eq_sub1(int, all_103_4, 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | all_103_2, $sum(all_86_10, 1), all_86_13) = 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | all_193_1 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (400), (1416) are inconsistent by sub-proof 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | #55. 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | 204.71/127.18 | | | | | | | | | | | | | | | | | | | | End of split 204.71/127.18 | | | | | | | | | | | | | | | | | | | | 204.71/127.18 | | | | | | | | | | | | | | | | | | | Case 2: 204.71/127.18 | | | | | | | | | | | | | | | | | | | | 204.71/127.18 | | | | | | | | | | | | | | | | | | | | (1417) ~ (all_192_4 = 0) & permut_sub2(int, all_103_4, 204.71/127.18 | | | | | | | | | | | | | | | | | | | | all_103_2, all_86_11, $sum(all_86_10, 1)) = 204.71/127.18 | | | | | | | | | | | | | | | | | | | | all_192_4 204.71/127.18 | | | | | | | | | | | | | | | | | | | | 204.71/127.18 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (43), (1187), (1417) are inconsistent by sub-proof 204.71/127.18 | | | | | | | | | | | | | | | | | | | | #69. 204.71/127.18 | | | | | | | | | | | | | | | | | | | | 204.71/127.18 | | | | | | | | | | | | | | | | | | | End of split 204.71/127.18 | | | | | | | | | | | | | | | | | | | 204.71/127.18 | | | | | | | | | | | | | | | | | | Case 2: 204.71/127.18 | | | | | | | | | | | | | | | | | | | 204.71/127.18 | | | | | | | | | | | | | | | | | | | (1418) ~ (all_153_1 = 0) & array_eq_sub1(int, all_105_4, 204.71/127.18 | | | | | | | | | | | | | | | | | | | all_105_2, $sum(all_86_10, 1), all_86_13) = 204.71/127.18 | | | | | | | | | | | | | | | | | | | all_153_1 204.71/127.18 | | | | | | | | | | | | | | | | | | | 204.71/127.18 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (1390), (1418) are inconsistent by sub-proof 204.71/127.18 | | | | | | | | | | | | | | | | | | | #54. 204.71/127.18 | | | | | | | | | | | | | | | | | | | 204.71/127.18 | | | | | | | | | | | | | | | | | | End of split 204.71/127.18 | | | | | | | | | | | | | | | | | | 204.71/127.18 | | | | | | | | | | | | | | | | | Case 2: 204.71/127.18 | | | | | | | | | | | | | | | | | | 204.71/127.18 | | | | | | | | | | | | | | | | | | (1419) length1(int, all_105_4) = all_234_1 & ( ~ 204.71/127.18 | | | | | | | | | | | | | | | | | | ($lesseq(1, $difference(all_234_1, all_86_10))) 204.71/127.18 | | | | | | | | | | | | | | | | | | | ~ ($lesseq(all_86_13, all_234_1)) | ( ~ 204.71/127.18 | | | | | | | | | | | | | | | | | | (all_234_0 = all_234_1) & length1(int, 204.71/127.18 | | | | | | | | | | | | | | | | | | all_105_2) = all_234_0)) 204.71/127.18 | | | | | | | | | | | | | | | | | | 204.71/127.18 | | | | | | | | | | | | | | | | | | ALPHA: (1419) implies: 204.71/127.18 | | | | | | | | | | | | | | | | | | (1420) length1(int, all_105_4) = all_234_1 204.71/127.18 | | | | | | | | | | | | | | | | | | (1421) ~ ($lesseq(1, $difference(all_234_1, all_86_10))) 204.71/127.18 | | | | | | | | | | | | | | | | | | | ~ ($lesseq(all_86_13, all_234_1)) | ( ~ 204.71/127.18 | | | | | | | | | | | | | | | | | | (all_234_0 = all_234_1) & length1(int, 204.71/127.18 | | | | | | | | | | | | | | | | | | all_105_2) = all_234_0) 204.71/127.18 | | | | | | | | | | | | | | | | | | 204.71/127.18 | | | | | | | | | | | | | | | | | | BETA: splitting (297) gives: 204.71/127.18 | | | | | | | | | | | | | | | | | | 204.71/127.18 | | | | | | | | | | | | | | | | | | Case 1: 204.71/127.18 | | | | | | | | | | | | | | | | | | | 204.71/127.18 | | | | | | | | | | | | | | | | | | | (1422) all_192_0 = 0 & all_192_1 = 0 & map_eq_sub1(int, 204.71/127.18 | | | | | | | | | | | | | | | | | | | all_192_4, all_192_3, $sum(all_86_10, 1), 204.71/127.18 | | | | | | | | | | | | | | | | | | | all_192_2) = 0 & map_eq_sub1(int, all_192_4, 204.71/127.18 | | | | | | | | | | | | | | | | | | | all_192_3, 0, all_86_11) = 0 & length1(int, 204.71/127.18 | | | | | | | | | | | | | | | | | | | all_103_4) = all_192_2 & elts(int, all_103_2) = 204.71/127.18 | | | | | | | | | | | | | | | | | | | all_192_3 & elts(int, all_103_4) = all_192_4 & 204.71/127.18 | | | | | | | | | | | | | | | | | | | in_uni(all_192_3) & in_uni(all_192_4) 204.71/127.18 | | | | | | | | | | | | | | | | | | | 204.71/127.18 | | | | | | | | | | | | | | | | | | | ALPHA: (1422) implies: 204.71/127.18 | | | | | | | | | | | | | | | | | | | (1423) elts(int, all_103_2) = all_192_3 204.71/127.18 | | | | | | | | | | | | | | | | | | | (1424) length1(int, all_103_4) = all_192_2 204.71/127.18 | | | | | | | | | | | | | | | | | | | 204.71/127.18 | | | | | | | | | | | | | | | | | | | BETA: splitting (298) gives: 204.71/127.18 | | | | | | | | | | | | | | | | | | | 204.71/127.18 | | | | | | | | | | | | | | | | | | | Case 1: 204.71/127.18 | | | | | | | | | | | | | | | | | | | | 204.71/127.18 | | | | | | | | | | | | | | | | | | | | (1425) all_193_0 = all_193_1 & $lesseq(1, 204.71/127.18 | | | | | | | | | | | | | | | | | | | | $difference(all_193_1, all_86_10)) & 204.71/127.18 | | | | | | | | | | | | | | | | | | | | $lesseq(all_86_13, all_193_1) & $lesseq(-1, 204.71/127.18 | | | | | | | | | | | | | | | | | | | | all_86_10) & $lesseq(0, all_86_13) & 204.71/127.18 | | | | | | | | | | | | | | | | | | | | length1(int, all_103_2) = all_193_1 & length1(int, 204.71/127.18 | | | | | | | | | | | | | | | | | | | | all_103_4) = all_193_1 204.71/127.18 | | | | | | | | | | | | | | | | | | | | 204.71/127.18 | | | | | | | | | | | | | | | | | | | | ALPHA: (1425) implies: 204.71/127.18 | | | | | | | | | | | | | | | | | | | | (1426) $lesseq(1, $difference(all_193_1, all_86_10)) 204.71/127.18 | | | | | | | | | | | | | | | | | | | | (1427) length1(int, all_103_4) = all_193_1 204.71/127.18 | | | | | | | | | | | | | | | | | | | | (1428) length1(int, all_103_2) = all_193_1 204.71/127.18 | | | | | | | | | | | | | | | | | | | | 204.71/127.18 | | | | | | | | | | | | | | | | | | | | BETA: splitting (324) gives: 204.71/127.18 | | | | | | | | | | | | | | | | | | | | 204.71/127.18 | | | | | | | | | | | | | | | | | | | | Case 1: 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | (1429) all_219_1 = 0 & array_eq_sub1(int, all_105_4, 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | all_105_2, 0, all_86_7) = 0 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | ALPHA: (1429) implies: 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | (1430) array_eq_sub1(int, all_105_4, all_105_2, 0, 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | all_86_7) = 0 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (45), (180), (183), (270), (1420), (1421), 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | (1426), (1427), (1430) are inconsistent by 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | sub-proof #29. 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | 204.71/127.18 | | | | | | | | | | | | | | | | | | | | Case 2: 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | (1431) length1(int, all_105_4) = all_219_1 & ( ~ 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | ($lesseq(all_86_7, all_219_1)) | ~ ($lesseq(0, 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | all_219_1)) | ( ~ (all_219_0 = all_219_1) & 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | length1(int, all_105_2) = all_219_0)) 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | ALPHA: (1431) implies: 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | (1432) length1(int, all_105_4) = all_219_1 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | (1433) ~ ($lesseq(all_86_7, all_219_1)) | ~ ($lesseq(0, 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | all_219_1)) | ( ~ (all_219_0 = all_219_1) & 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | length1(int, all_105_2) = all_219_0) 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (319) gives: 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | Case 1: 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | (1434) all_215_1 = 0 & array_eq_sub1(int, all_103_4, 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | all_103_2, 0, all_86_11) = 0 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (43), (45), (50), (52), (53), (181), (183), 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | (272), (297), (389), (1184), (1185), (1187), 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | (1426), (1427), (1432), (1433), (1434) are 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #34. 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | Case 2: 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | (1435) length1(int, all_103_4) = all_215_1 & ( ~ 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | ($lesseq(all_86_11, all_215_1)) | ~ ($lesseq(0, 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | all_215_1)) | ( ~ (all_215_0 = all_215_1) & 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | length1(int, all_103_2) = all_215_0)) 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1435) implies: 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | (1436) length1(int, all_103_4) = all_215_1 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (345) gives: 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | Case 1: 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | (1437) all_242_1 = 0 & array_eq_sub1(int, all_103_2, 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | all_105_4, $sum(all_86_8, 1), all_86_13) = 0 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1437) implies: 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | (1438) array_eq_sub1(int, all_103_2, all_105_4, 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | $sum(all_86_8, 1), all_86_13) = 0 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (269) gives: 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | Case 1: 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | | (1439) all_168_0 = all_168_1 & $lesseq(1, 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | | $difference(all_168_1, all_86_8)) & 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | | $lesseq(all_86_13, all_168_1) & $lesseq(-1, 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | | all_86_8) & $lesseq(0, all_86_13) & length1(int, 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | | all_105_4) = all_168_1 & length1(int, all_103_2) 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | | = all_168_1 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1439) implies: 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | | (1440) length1(int, all_103_2) = all_168_1 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | | (1441) length1(int, all_105_4) = all_168_1 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_234_1, all_170_1, 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (1185), (1420) 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | | (1442) all_234_1 = all_170_1 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_234_1, all_168_1, 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (1420), (1441) 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | | (1443) all_234_1 = all_168_1 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_193_1, all_168_1, 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (1428), (1440) 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | | (1444) all_193_1 = all_168_1 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_170_1, all_156_0, 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (394), (1184) 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | | (1445) all_170_1 = all_156_0 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_86_13, all_215_1, 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (183), (1436) 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | | (1446) all_215_1 = all_86_13 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_215_1, all_193_1, 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (1427), (1436) 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | | (1447) all_215_1 = all_193_1 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_193_1, all_192_2, 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (1424), (1427) 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | | (1448) all_193_1 = all_192_2 204.71/127.18 | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_105_3, all_187_3, 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (99), (1386) 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | (1449) all_187_3 = all_105_3 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_187_3, all_181_2, 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (1181), (1386) 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | (1450) all_187_3 = all_181_2 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_181_2, all_156_1, 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (395), (1181) 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | (1451) all_181_2 = all_156_1 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_103_1, all_192_3, 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (91), (1423) 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | (1452) all_192_3 = all_103_1 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_192_3, all_181_3, 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (1180), (1423) 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | (1453) all_192_3 = all_181_3 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_192_3, all_156_3, 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (396), (1423) 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | (1454) all_192_3 = all_156_3 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1442), (1443) imply: 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | (1455) all_170_1 = all_168_1 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1446), (1447) imply: 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | (1456) all_193_1 = all_86_13 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1456) implies: 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | (1457) all_193_1 = all_86_13 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1444), (1448) imply: 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | (1458) all_192_2 = all_168_1 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1448), (1457) imply: 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | (1459) all_192_2 = all_86_13 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1458), (1459) imply: 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | (1460) all_168_1 = all_86_13 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1460) implies: 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | (1461) all_168_1 = all_86_13 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1452), (1453) imply: 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | (1462) all_181_3 = all_103_1 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1453), (1454) imply: 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | (1463) all_181_3 = all_156_3 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1449), (1450) imply: 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | (1464) all_181_2 = all_105_3 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1464) implies: 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | (1465) all_181_2 = all_105_3 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1451), (1465) imply: 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | (1466) all_156_1 = all_105_3 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1462), (1463) imply: 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | (1467) all_156_3 = all_103_1 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1445), (1455) imply: 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | (1468) all_168_1 = all_156_0 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1468) implies: 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | (1469) all_168_1 = all_156_0 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1461), (1469) imply: 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | (1470) all_156_0 = all_86_13 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (44), (203), (263), (394), (1182), (1451), 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | (1463), (1466), (1467), (1470) are inconsistent by 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #41. 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | Case 2: 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | (1471) ~ (all_168_1 = 0) & array_eq_sub1(int, all_103_2, 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, $sum(all_86_8, 1), all_86_13) = 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | all_168_1 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (1438), (1471) are inconsistent by sub-proof 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | #83. 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | End of split 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | Case 2: 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | (1472) length1(int, all_103_2) = all_242_1 & ( ~ 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | ($lesseq(1, $difference(all_242_1, all_86_8))) | 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | ~ ($lesseq(all_86_13, all_242_1)) | ( ~ 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | (all_242_0 = all_242_1) & length1(int, 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | all_105_4) = all_242_0)) 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1472) implies: 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | (1473) length1(int, all_103_2) = all_242_1 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (39), (44), (91), (99), (180), (203), (263), 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | (394), (395), (396), (1180), (1181), (1182), 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | (1184), (1185), (1386), (1423), (1428), (1432), 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | (1473) are inconsistent by sub-proof #31. 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | End of split 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | End of split 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | 204.71/127.19 | | | | | | | | | | | | | | | | | | | | End of split 204.71/127.19 | | | | | | | | | | | | | | | | | | | | 204.71/127.19 | | | | | | | | | | | | | | | | | | | Case 2: 204.71/127.19 | | | | | | | | | | | | | | | | | | | | 204.71/127.19 | | | | | | | | | | | | | | | | | | | | (1474) ~ (all_193_1 = 0) & array_eq_sub1(int, all_103_4, 204.71/127.19 | | | | | | | | | | | | | | | | | | | | all_103_2, $sum(all_86_10, 1), all_86_13) = 204.71/127.19 | | | | | | | | | | | | | | | | | | | | all_193_1 204.71/127.19 | | | | | | | | | | | | | | | | | | | | 204.71/127.19 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (400), (1474) are inconsistent by sub-proof 204.71/127.19 | | | | | | | | | | | | | | | | | | | | #55. 204.71/127.19 | | | | | | | | | | | | | | | | | | | | 204.71/127.19 | | | | | | | | | | | | | | | | | | | End of split 204.71/127.19 | | | | | | | | | | | | | | | | | | | 204.71/127.19 | | | | | | | | | | | | | | | | | | Case 2: 204.71/127.19 | | | | | | | | | | | | | | | | | | | 204.71/127.19 | | | | | | | | | | | | | | | | | | | (1475) ~ (all_192_4 = 0) & permut_sub2(int, all_103_4, 204.71/127.19 | | | | | | | | | | | | | | | | | | | all_103_2, all_86_11, $sum(all_86_10, 1)) = 204.71/127.19 | | | | | | | | | | | | | | | | | | | all_192_4 204.71/127.19 | | | | | | | | | | | | | | | | | | | 204.71/127.19 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (43), (1187), (1475) are inconsistent by sub-proof 204.71/127.19 | | | | | | | | | | | | | | | | | | | #69. 204.71/127.19 | | | | | | | | | | | | | | | | | | | 204.71/127.19 | | | | | | | | | | | | | | | | | | End of split 204.71/127.19 | | | | | | | | | | | | | | | | | | 204.71/127.19 | | | | | | | | | | | | | | | | | End of split 204.71/127.19 | | | | | | | | | | | | | | | | | 204.71/127.19 | | | | | | | | | | | | | | | | End of split 204.71/127.19 | | | | | | | | | | | | | | | | 204.71/127.19 | | | | | | | | | | | | | | | Case 2: 204.71/127.19 | | | | | | | | | | | | | | | | 204.71/127.19 | | | | | | | | | | | | | | | | (1476) elts(int, all_103_2) = all_191_2 & elts(int, 204.71/127.19 | | | | | | | | | | | | | | | | all_103_4) = all_191_3 & in_uni(all_191_2) & 204.71/127.19 | | | | | | | | | | | | | | | | in_uni(all_191_3) & (( ~ (all_191_0 = 0) & 204.71/127.19 | | | | | | | | | | | | | | | | map_eq_sub1(int, all_191_3, all_191_2, 204.71/127.19 | | | | | | | | | | | | | | | | $sum(all_86_10, 1), all_191_1) = all_191_0 & 204.71/127.19 | | | | | | | | | | | | | | | | length1(int, all_103_4) = all_191_1) | ( ~ 204.71/127.19 | | | | | | | | | | | | | | | | (all_191_1 = 0) & map_eq_sub1(int, all_191_3, 204.71/127.19 | | | | | | | | | | | | | | | | all_191_2, 0, all_86_11) = all_191_1)) 204.71/127.19 | | | | | | | | | | | | | | | | 204.71/127.19 | | | | | | | | | | | | | | | | ALPHA: (1476) implies: 204.71/127.19 | | | | | | | | | | | | | | | | (1477) elts(int, all_103_4) = all_191_3 204.71/127.19 | | | | | | | | | | | | | | | | (1478) elts(int, all_103_2) = all_191_2 204.71/127.19 | | | | | | | | | | | | | | | | (1479) ( ~ (all_191_0 = 0) & map_eq_sub1(int, all_191_3, 204.71/127.19 | | | | | | | | | | | | | | | | all_191_2, $sum(all_86_10, 1), all_191_1) = 204.71/127.19 | | | | | | | | | | | | | | | | all_191_0 & length1(int, all_103_4) = all_191_1) 204.71/127.19 | | | | | | | | | | | | | | | | | ( ~ (all_191_1 = 0) & map_eq_sub1(int, 204.71/127.19 | | | | | | | | | | | | | | | | all_191_3, all_191_2, 0, all_86_11) = 204.71/127.19 | | | | | | | | | | | | | | | | all_191_1) 204.71/127.19 | | | | | | | | | | | | | | | | 204.71/127.19 | | | | | | | | | | | | | | | | BETA: splitting (294) gives: 204.71/127.19 | | | | | | | | | | | | | | | | 204.71/127.19 | | | | | | | | | | | | | | | | Case 1: 204.71/127.19 | | | | | | | | | | | | | | | | | 204.71/127.19 | | | | | | | | | | | | | | | | | (1480) all_187_3 = 0 & permut_sub2(int, all_105_4, 204.71/127.19 | | | | | | | | | | | | | | | | | all_105_2, all_86_7, $sum(all_86_10, 1)) = 0 204.71/127.19 | | | | | | | | | | | | | | | | | 204.71/127.19 | | | | | | | | | | | | | | | | | ALPHA: (1480) implies: 204.71/127.19 | | | | | | | | | | | | | | | | | (1481) permut_sub2(int, all_105_4, all_105_2, all_86_7, 204.71/127.19 | | | | | | | | | | | | | | | | | $sum(all_86_10, 1)) = 0 204.71/127.19 | | | | | | | | | | | | | | | | | 204.71/127.19 | | | | | | | | | | | | | | | | | BETA: splitting (298) gives: 204.71/127.19 | | | | | | | | | | | | | | | | | 204.71/127.19 | | | | | | | | | | | | | | | | | Case 1: 204.71/127.19 | | | | | | | | | | | | | | | | | | 204.71/127.19 | | | | | | | | | | | | | | | | | | (1482) all_193_0 = all_193_1 & $lesseq(1, 204.71/127.19 | | | | | | | | | | | | | | | | | | $difference(all_193_1, all_86_10)) & 204.71/127.19 | | | | | | | | | | | | | | | | | | $lesseq(all_86_13, all_193_1) & $lesseq(-1, 204.71/127.19 | | | | | | | | | | | | | | | | | | all_86_10) & $lesseq(0, all_86_13) & 204.71/127.19 | | | | | | | | | | | | | | | | | | length1(int, all_103_2) = all_193_1 & length1(int, 204.71/127.19 | | | | | | | | | | | | | | | | | | all_103_4) = all_193_1 204.71/127.19 | | | | | | | | | | | | | | | | | | 204.71/127.19 | | | | | | | | | | | | | | | | | | ALPHA: (1482) implies: 204.71/127.19 | | | | | | | | | | | | | | | | | | (1483) $lesseq(1, $difference(all_193_1, all_86_10)) 204.71/127.19 | | | | | | | | | | | | | | | | | | (1484) length1(int, all_103_4) = all_193_1 204.71/127.19 | | | | | | | | | | | | | | | | | | (1485) length1(int, all_103_2) = all_193_1 204.71/127.19 | | | | | | | | | | | | | | | | | | 204.71/127.19 | | | | | | | | | | | | | | | | | | BETA: splitting (319) gives: 204.71/127.19 | | | | | | | | | | | | | | | | | | 204.71/127.19 | | | | | | | | | | | | | | | | | | Case 1: 204.71/127.19 | | | | | | | | | | | | | | | | | | | 204.71/127.19 | | | | | | | | | | | | | | | | | | | (1486) all_215_1 = 0 & array_eq_sub1(int, all_103_4, 204.71/127.19 | | | | | | | | | | | | | | | | | | | all_103_2, 0, all_86_11) = 0 204.71/127.19 | | | | | | | | | | | | | | | | | | | 204.71/127.19 | | | | | | | | | | | | | | | | | | | ALPHA: (1486) implies: 204.71/127.19 | | | | | | | | | | | | | | | | | | | (1487) array_eq_sub1(int, all_103_4, all_103_2, 0, 204.71/127.19 | | | | | | | | | | | | | | | | | | | all_86_11) = 0 204.71/127.19 | | | | | | | | | | | | | | | | | | | 204.71/127.19 | | | | | | | | | | | | | | | | | | | BETA: splitting (272) gives: 204.71/127.19 | | | | | | | | | | | | | | | | | | | 204.71/127.19 | | | | | | | | | | | | | | | | | | | Case 1: 204.71/127.19 | | | | | | | | | | | | | | | | | | | | 204.71/127.19 | | | | | | | | | | | | | | | | | | | | (1488) all_171_0 = all_171_1 & $lesseq(all_86_11, 204.71/127.19 | | | | | | | | | | | | | | | | | | | | all_171_1) & $lesseq(0, all_171_1) & $lesseq(0, 204.71/127.19 | | | | | | | | | | | | | | | | | | | | all_86_11) & length1(int, all_103_2) = all_171_1 204.71/127.19 | | | | | | | | | | | | | | | | | | | | & length1(int, all_103_4) = all_171_1 204.71/127.19 | | | | | | | | | | | | | | | | | | | | 204.71/127.19 | | | | | | | | | | | | | | | | | | | | ALPHA: (1488) implies: 204.71/127.19 | | | | | | | | | | | | | | | | | | | | (1489) length1(int, all_103_4) = all_171_1 204.71/127.19 | | | | | | | | | | | | | | | | | | | | (1490) length1(int, all_103_2) = all_171_1 204.71/127.19 | | | | | | | | | | | | | | | | | | | | 204.71/127.19 | | | | | | | | | | | | | | | | | | | | BETA: splitting (295) gives: 204.71/127.19 | | | | | | | | | | | | | | | | | | | | 204.71/127.19 | | | | | | | | | | | | | | | | | | | | Case 1: 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | (1491) all_190_0 = 0 & all_190_1 = 0 & map_eq_sub1(int, 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | all_190_4, all_190_3, $sum(all_86_10, 1), 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | all_190_2) = 0 & map_eq_sub1(int, all_190_4, 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | all_190_3, 0, all_86_7) = 0 & length1(int, 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | all_105_4) = all_190_2 & elts(int, all_105_2) = 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | all_190_3 & elts(int, all_105_4) = all_190_4 & 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | in_uni(all_190_3) & in_uni(all_190_4) 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | ALPHA: (1491) implies: 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | (1492) elts(int, all_105_4) = all_190_4 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | (1493) length1(int, all_105_4) = all_190_2 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (324) gives: 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | Case 1: 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | (1494) all_219_1 = 0 & array_eq_sub1(int, all_105_4, 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | all_105_2, 0, all_86_7) = 0 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1494) implies: 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | (1495) array_eq_sub1(int, all_105_4, all_105_2, 0, 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | all_86_7) = 0 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (270) gives: 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | Case 1: 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | (1496) all_169_0 = all_169_1 & $lesseq(all_86_7, 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | all_169_1) & $lesseq(0, all_169_1) & $lesseq(0, 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | all_86_7) & length1(int, all_105_2) = all_169_1 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | & length1(int, all_105_4) = all_169_1 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1496) implies: 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | (1497) length1(int, all_105_4) = all_169_1 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | (1498) length1(int, all_105_2) = all_169_1 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (337) gives: 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | Case 1: 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | (1499) all_234_1 = 0 & array_eq_sub1(int, all_105_4, 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | all_105_2, $sum(all_86_10, 1), all_86_13) = 0 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1499) implies: 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | (1500) array_eq_sub1(int, all_105_4, all_105_2, 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | $sum(all_86_10, 1), all_86_13) = 0 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (255) gives: 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | | (1501) all_153_0 = all_153_1 & $lesseq(1, 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | | $difference(all_153_1, all_86_10)) & 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | | $lesseq(all_86_13, all_153_1) & $lesseq(-1, 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | | all_86_10) & $lesseq(0, all_86_13) & 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | | length1(int, all_105_2) = all_153_1 & length1(int, 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4) = all_153_1 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1501) implies: 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | | (1502) length1(int, all_105_4) = all_153_1 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (345) gives: 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | | | (1503) all_242_1 = 0 & array_eq_sub1(int, all_103_2, 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, $sum(all_86_8, 1), all_86_13) = 0 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1503) implies: 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | | | (1504) array_eq_sub1(int, all_103_2, all_105_4, 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | | | $sum(all_86_8, 1), all_86_13) = 0 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (269) gives: 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: 204.71/127.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1505) all_168_0 = all_168_1 & $lesseq(1, 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | $difference(all_168_1, all_86_8)) & 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | $lesseq(all_86_13, all_168_1) & $lesseq(-1, 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_86_8) & $lesseq(0, all_86_13) & length1(int, 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4) = all_168_1 & length1(int, all_103_2) 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_168_1 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1505) implies: 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1506) length1(int, all_105_4) = all_168_1 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_190_2, all_170_1, 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (1185), (1493) 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1507) all_190_2 = all_170_1 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_86_13, all_169_1, 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (180), (1497) 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1508) all_169_1 = all_86_13 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_170_1, all_169_1, 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (1185), (1497) 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1509) all_170_1 = all_169_1 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_190_2, all_168_1, 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (1493), (1506) 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1510) all_190_2 = all_168_1 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_171_1, all_170_1, 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (1184), (1490) 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1511) all_171_1 = all_170_1 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_193_1, all_156_0, 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (394), (1485) 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1512) all_193_1 = all_156_0 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_193_1, all_171_1, 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (1484), (1489) 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1513) all_193_1 = all_171_1 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_105_3, all_190_4, 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (99), (1492) 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1514) all_190_4 = all_105_3 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_190_4, all_181_2, 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (1181), (1492) 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1515) all_190_4 = all_181_2 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_181_2, all_156_1, 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (395), (1181) 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1516) all_181_2 = all_156_1 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_103_1, all_181_3, 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (91), (1180) 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1517) all_181_3 = all_103_1 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_191_2, all_181_3, 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (1180), (1478) 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1518) all_191_2 = all_181_3 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_191_2, all_156_3, 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (396), (1478) 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1519) all_191_2 = all_156_3 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1512), (1513) imply: 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1520) all_171_1 = all_156_0 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1520) implies: 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1521) all_171_1 = all_156_0 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1518), (1519) imply: 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1522) all_181_3 = all_156_3 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1522) implies: 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1523) all_181_3 = all_156_3 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1507), (1510) imply: 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1524) all_170_1 = all_168_1 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1524) implies: 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1525) all_170_1 = all_168_1 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1514), (1515) imply: 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1526) all_181_2 = all_105_3 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1526) implies: 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1527) all_181_2 = all_105_3 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1516), (1527) imply: 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1528) all_156_1 = all_105_3 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1528) implies: 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1529) all_156_1 = all_105_3 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1517), (1523) imply: 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1530) all_156_3 = all_103_1 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1511), (1521) imply: 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1531) all_170_1 = all_156_0 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1531) implies: 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1532) all_170_1 = all_156_0 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1509), (1525) imply: 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1533) all_169_1 = all_168_1 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1533) implies: 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1534) all_169_1 = all_168_1 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1525), (1532) imply: 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1535) all_168_1 = all_156_0 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (44), (203), (263), (394), (1182), (1508), 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1523), (1527), (1529), (1530), (1534), (1535) are 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #39. 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1536) ~ (all_168_1 = 0) & array_eq_sub1(int, all_103_2, 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, $sum(all_86_8, 1), all_86_13) = 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_168_1 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (1504), (1536) are inconsistent by sub-proof 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | #83. 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | (1537) length1(int, all_103_2) = all_242_1 & ( ~ 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | ($lesseq(1, $difference(all_242_1, all_86_8))) | 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | ~ ($lesseq(all_86_13, all_242_1)) | ( ~ 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_242_0 = all_242_1) & length1(int, 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4) = all_242_0)) 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1537) implies: 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | (1538) length1(int, all_103_2) = all_242_1 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (39), (44), (90), (91), (96), (183), (206), 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | (394), (396), (1180), (1184), (1185), (1477), 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | (1478), (1479), (1484), (1485), (1489), (1490), 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | (1493), (1502), (1538) are inconsistent by 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #28. 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | End of split 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | (1539) ~ (all_153_1 = 0) & array_eq_sub1(int, all_105_4, 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | all_105_2, $sum(all_86_10, 1), all_86_13) = 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | all_153_1 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (1500), (1539) are inconsistent by sub-proof 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | #54. 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | End of split 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | Case 2: 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | (1540) length1(int, all_105_4) = all_234_1 & ( ~ 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | ($lesseq(1, $difference(all_234_1, all_86_10))) 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | ~ ($lesseq(all_86_13, all_234_1)) | ( ~ 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | (all_234_0 = all_234_1) & length1(int, 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | all_105_2) = all_234_0)) 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1540) implies: 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | (1541) length1(int, all_105_4) = all_234_1 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | (1542) ~ ($lesseq(1, $difference(all_234_1, all_86_10))) 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | | ~ ($lesseq(all_86_13, all_234_1)) | ( ~ 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | (all_234_0 = all_234_1) & length1(int, 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | all_105_2) = all_234_0) 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (180), (183), (1483), (1484), (1497), 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | (1498), (1541), (1542) are inconsistent by 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #30. 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | End of split 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | Case 2: 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | (1543) ~ (all_169_1 = 0) & array_eq_sub1(int, all_105_4, 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | all_105_2, 0, all_86_7) = all_169_1 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (1495), (1543) are inconsistent by sub-proof 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | #75. 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | End of split 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | Case 2: 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | (1544) length1(int, all_105_4) = all_219_1 & ( ~ 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | ($lesseq(all_86_7, all_219_1)) | ~ ($lesseq(0, 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | all_219_1)) | ( ~ (all_219_0 = all_219_1) & 204.71/127.20 | | | | | | | | | | | | | | | | | | | | | | length1(int, all_105_2) = all_219_0)) 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1544) implies: 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | (1545) length1(int, all_105_4) = all_219_1 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (337) gives: 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | Case 1: 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | (1546) all_234_1 = 0 & array_eq_sub1(int, all_105_4, 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | all_105_2, $sum(all_86_10, 1), all_86_13) = 0 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1546) implies: 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | (1547) array_eq_sub1(int, all_105_4, all_105_2, 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | $sum(all_86_10, 1), all_86_13) = 0 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (255) gives: 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | Case 1: 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | (1548) all_153_0 = all_153_1 & $lesseq(1, 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | $difference(all_153_1, all_86_10)) & 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | $lesseq(all_86_13, all_153_1) & $lesseq(-1, 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | all_86_10) & $lesseq(0, all_86_13) & 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | length1(int, all_105_2) = all_153_1 & length1(int, 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | all_105_4) = all_153_1 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1548) implies: 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | (1549) length1(int, all_105_4) = all_153_1 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (345) gives: 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | (1550) all_242_1 = 0 & array_eq_sub1(int, all_103_2, 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, $sum(all_86_8, 1), all_86_13) = 0 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1550) implies: 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | (1551) array_eq_sub1(int, all_103_2, all_105_4, 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | $sum(all_86_8, 1), all_86_13) = 0 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (269) gives: 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | (1552) all_168_0 = all_168_1 & $lesseq(1, 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | $difference(all_168_1, all_86_8)) & 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | $lesseq(all_86_13, all_168_1) & $lesseq(-1, 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | all_86_8) & $lesseq(0, all_86_13) & length1(int, 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4) = all_168_1 & length1(int, all_103_2) 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | = all_168_1 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1552) implies: 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | (1553) length1(int, all_105_4) = all_168_1 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_219_1, all_170_1, 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (1185), (1545) 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | (1554) all_219_1 = all_170_1 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_190_2, all_170_1, 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (1185), (1493) 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | (1555) all_190_2 = all_170_1 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_190_2, all_168_1, 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (1493), (1553) 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | (1556) all_190_2 = all_168_1 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_219_1, all_153_1, 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (1545), (1549) 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | (1557) all_219_1 = all_153_1 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_86_13, all_170_1, 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (184), (1184) 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | (1558) all_170_1 = all_86_13 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_171_1, all_170_1, 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (1184), (1490) 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | (1559) all_171_1 = all_170_1 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_193_1, all_156_0, 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (394), (1485) 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | (1560) all_193_1 = all_156_0 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_193_1, all_171_1, 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (1484), (1489) 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | (1561) all_193_1 = all_171_1 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_105_3, all_190_4, 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (99), (1492) 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | (1562) all_190_4 = all_105_3 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_190_4, all_181_2, 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (1181), (1492) 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | (1563) all_190_4 = all_181_2 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_181_2, all_156_1, 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (395), (1181) 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | (1564) all_181_2 = all_156_1 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_103_1, all_181_3, 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (91), (1180) 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | (1565) all_181_3 = all_103_1 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_191_2, all_181_3, 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (1180), (1478) 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | (1566) all_191_2 = all_181_3 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_191_2, all_156_3, 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (396), (1478) 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | (1567) all_191_2 = all_156_3 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1554), (1557) imply: 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | (1568) all_170_1 = all_153_1 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1568) implies: 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | (1569) all_170_1 = all_153_1 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1560), (1561) imply: 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | (1570) all_171_1 = all_156_0 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1570) implies: 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | (1571) all_171_1 = all_156_0 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1566), (1567) imply: 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | (1572) all_181_3 = all_156_3 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1572) implies: 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | (1573) all_181_3 = all_156_3 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1555), (1556) imply: 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | (1574) all_170_1 = all_168_1 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1574) implies: 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | (1575) all_170_1 = all_168_1 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1562), (1563) imply: 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | (1576) all_181_2 = all_105_3 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1576) implies: 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | (1577) all_181_2 = all_105_3 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1564), (1577) imply: 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | (1578) all_156_1 = all_105_3 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1578) implies: 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | (1579) all_156_1 = all_105_3 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1565), (1573) imply: 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | (1580) all_156_3 = all_103_1 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1559), (1571) imply: 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | (1581) all_170_1 = all_156_0 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1581) implies: 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | (1582) all_170_1 = all_156_0 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1569), (1575) imply: 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | (1583) all_168_1 = all_153_1 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1558), (1575) imply: 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | (1584) all_168_1 = all_86_13 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1575), (1582) imply: 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | (1585) all_168_1 = all_156_0 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1584), (1585) imply: 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | (1586) all_156_0 = all_86_13 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1583), (1585) imply: 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | (1587) all_156_0 = all_153_1 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1586), (1587) imply: 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | (1588) all_153_1 = all_86_13 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (44), (203), (263), (394), (1182), (1565), 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | (1577), (1579), (1580), (1586) are inconsistent by 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #44. 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | (1589) ~ (all_168_1 = 0) & array_eq_sub1(int, all_103_2, 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, $sum(all_86_8, 1), all_86_13) = 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | all_168_1 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (1551), (1589) are inconsistent by sub-proof 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | #83. 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | End of split 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | (1590) length1(int, all_103_2) = all_242_1 & ( ~ 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | ($lesseq(1, $difference(all_242_1, all_86_8))) | 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | ~ ($lesseq(all_86_13, all_242_1)) | ( ~ 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | (all_242_0 = all_242_1) & length1(int, 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4) = all_242_0)) 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1590) implies: 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | (1591) length1(int, all_103_2) = all_242_1 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (39), (44), (90), (91), (96), (183), (206), 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | (394), (396), (1180), (1184), (1185), (1477), 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | (1478), (1479), (1484), (1485), (1489), (1490), 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | (1493), (1549), (1591) are inconsistent by 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #28. 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | End of split 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | Case 2: 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | (1592) ~ (all_153_1 = 0) & array_eq_sub1(int, all_105_4, 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | all_105_2, $sum(all_86_10, 1), all_86_13) = 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | all_153_1 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (1547), (1592) are inconsistent by sub-proof 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | #54. 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | End of split 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | Case 2: 204.71/127.21 | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.21 | | | | | | | | | | | | | | | | | | | | | | | (1593) length1(int, all_105_4) = all_234_1 & ( ~ 204.89/127.21 | | | | | | | | | | | | | | | | | | | | | | | ($lesseq(1, $difference(all_234_1, all_86_10))) 204.89/127.21 | | | | | | | | | | | | | | | | | | | | | | | | ~ ($lesseq(all_86_13, all_234_1)) | ( ~ 204.89/127.21 | | | | | | | | | | | | | | | | | | | | | | | (all_234_0 = all_234_1) & length1(int, 204.89/127.21 | | | | | | | | | | | | | | | | | | | | | | | all_105_2) = all_234_0)) 204.89/127.21 | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.21 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1593) implies: 204.89/127.21 | | | | | | | | | | | | | | | | | | | | | | | (1594) length1(int, all_105_4) = all_234_1 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | (1595) ~ ($lesseq(1, $difference(all_234_1, all_86_10))) 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | ~ ($lesseq(all_86_13, all_234_1)) | ( ~ 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | (all_234_0 = all_234_1) & length1(int, 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | all_105_2) = all_234_0) 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (345) gives: 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | Case 1: 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | (1596) all_242_1 = 0 & array_eq_sub1(int, all_103_2, 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, $sum(all_86_8, 1), all_86_13) = 0 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1596) implies: 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | (1597) array_eq_sub1(int, all_103_2, all_105_4, 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | $sum(all_86_8, 1), all_86_13) = 0 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (269) gives: 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | (1598) all_168_0 = all_168_1 & $lesseq(1, 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | $difference(all_168_1, all_86_8)) & 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | $lesseq(all_86_13, all_168_1) & $lesseq(-1, 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | all_86_8) & $lesseq(0, all_86_13) & length1(int, 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4) = all_168_1 & length1(int, all_103_2) 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | = all_168_1 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1598) implies: 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | (1599) length1(int, all_105_4) = all_168_1 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_234_1, all_219_1, 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (1545), (1594) 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | (1600) all_234_1 = all_219_1 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_86_13, all_190_2, 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (180), (1493) 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | (1601) all_190_2 = all_86_13 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_219_1, all_190_2, 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (1493), (1545) 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | (1602) all_219_1 = all_190_2 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_234_1, all_170_1, 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (1185), (1594) 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | (1603) all_234_1 = all_170_1 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_190_2, all_168_1, 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (1493), (1599) 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | (1604) all_190_2 = all_168_1 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_171_1, all_170_1, 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (1184), (1490) 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | (1605) all_171_1 = all_170_1 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_193_1, all_156_0, 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (394), (1485) 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | (1606) all_193_1 = all_156_0 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_193_1, all_171_1, 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (1484), (1489) 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | (1607) all_193_1 = all_171_1 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_105_3, all_190_4, 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (99), (1492) 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | (1608) all_190_4 = all_105_3 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_190_4, all_181_2, 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (1181), (1492) 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | (1609) all_190_4 = all_181_2 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_181_2, all_156_1, 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (395), (1181) 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | (1610) all_181_2 = all_156_1 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_103_1, all_181_3, 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (91), (1180) 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | (1611) all_181_3 = all_103_1 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_191_2, all_181_3, 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (1180), (1478) 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | (1612) all_191_2 = all_181_3 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_191_2, all_156_3, 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (396), (1478) 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | (1613) all_191_2 = all_156_3 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1600), (1603) imply: 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | (1614) all_219_1 = all_170_1 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1614) implies: 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | (1615) all_219_1 = all_170_1 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1602), (1615) imply: 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | (1616) all_190_2 = all_170_1 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1616) implies: 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | (1617) all_190_2 = all_170_1 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1606), (1607) imply: 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | (1618) all_171_1 = all_156_0 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1618) implies: 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | (1619) all_171_1 = all_156_0 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1612), (1613) imply: 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | (1620) all_181_3 = all_156_3 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1620) implies: 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | (1621) all_181_3 = all_156_3 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1604), (1617) imply: 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | (1622) all_170_1 = all_168_1 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1601), (1617) imply: 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | (1623) all_170_1 = all_86_13 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1608), (1609) imply: 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | (1624) all_181_2 = all_105_3 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1624) implies: 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | (1625) all_181_2 = all_105_3 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1610), (1625) imply: 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | (1626) all_156_1 = all_105_3 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1626) implies: 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | (1627) all_156_1 = all_105_3 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1611), (1621) imply: 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | (1628) all_156_3 = all_103_1 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1605), (1619) imply: 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | (1629) all_170_1 = all_156_0 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1629) implies: 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | (1630) all_170_1 = all_156_0 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1622), (1623) imply: 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | (1631) all_168_1 = all_86_13 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1622), (1630) imply: 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | (1632) all_168_1 = all_156_0 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1631), (1632) imply: 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | (1633) all_156_0 = all_86_13 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (44), (203), (263), (394), (1182), (1611), 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | (1625), (1627), (1628), (1633) are inconsistent by 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #44. 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | (1634) ~ (all_168_1 = 0) & array_eq_sub1(int, all_103_2, 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, $sum(all_86_8, 1), all_86_13) = 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | all_168_1 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (1597), (1634) are inconsistent by sub-proof 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | #83. 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | End of split 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | Case 2: 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | (1635) length1(int, all_103_2) = all_242_1 & ( ~ 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | ($lesseq(1, $difference(all_242_1, all_86_8))) | 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | ~ ($lesseq(all_86_13, all_242_1)) | ( ~ 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | (all_242_0 = all_242_1) & length1(int, 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | all_105_4) = all_242_0)) 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1635) implies: 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | (1636) length1(int, all_103_2) = all_242_1 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_234_1, all_170_1, 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (1185), (1594) 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | (1637) all_234_1 = all_170_1 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_242_1, all_193_1, 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (1485), (1636) 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | (1638) all_242_1 = all_193_1 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_242_1, all_170_1, 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (1184), (1636) 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | (1639) all_242_1 = all_170_1 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_171_1, all_156_0, 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (394), (1490) 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | (1640) all_171_1 = all_156_0 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_86_13, all_171_1, 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (183), (1489) 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | (1641) all_171_1 = all_86_13 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_193_1, all_171_1, 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (1484), (1489) 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | gives: 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | (1642) all_193_1 = all_171_1 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1638), (1639) imply: 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | (1643) all_193_1 = all_170_1 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1643) implies: 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | (1644) all_193_1 = all_170_1 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1642), (1644) imply: 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | (1645) all_171_1 = all_170_1 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1645) implies: 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | (1646) all_171_1 = all_170_1 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1640), (1646) imply: 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | (1647) all_170_1 = all_156_0 204.89/127.22 | | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1641), (1646) imply: 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | | (1648) all_170_1 = all_86_13 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1647), (1648) imply: 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | | (1649) all_156_0 = all_86_13 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1644), (1648) imply: 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | | (1650) all_193_1 = all_86_13 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1637), (1648) imply: 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | | (1651) all_234_1 = all_86_13 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (49), (181), (1595), (1651) are inconsistent 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #38. 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | End of split 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | End of split 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | End of split 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | 204.89/127.23 | | | | | | | | | | | | | | | | | | | | Case 2: 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | (1652) ~ (all_190_4 = 0) & permut_sub2(int, all_105_4, 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | all_105_2, all_86_7, $sum(all_86_10, 1)) = 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | all_190_4 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (43), (1481), (1652) are inconsistent by sub-proof 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | #68. 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | 204.89/127.23 | | | | | | | | | | | | | | | | | | | | End of split 204.89/127.23 | | | | | | | | | | | | | | | | | | | | 204.89/127.23 | | | | | | | | | | | | | | | | | | | Case 2: 204.89/127.23 | | | | | | | | | | | | | | | | | | | | 204.89/127.23 | | | | | | | | | | | | | | | | | | | | (1653) ~ (all_171_1 = 0) & array_eq_sub1(int, all_103_4, 204.89/127.23 | | | | | | | | | | | | | | | | | | | | all_103_2, 0, all_86_11) = all_171_1 204.89/127.23 | | | | | | | | | | | | | | | | | | | | 204.89/127.23 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (1487), (1653) are inconsistent by sub-proof 204.89/127.23 | | | | | | | | | | | | | | | | | | | | #81. 204.89/127.23 | | | | | | | | | | | | | | | | | | | | 204.89/127.23 | | | | | | | | | | | | | | | | | | | End of split 204.89/127.23 | | | | | | | | | | | | | | | | | | | 204.89/127.23 | | | | | | | | | | | | | | | | | | Case 2: 204.89/127.23 | | | | | | | | | | | | | | | | | | | 204.89/127.23 | | | | | | | | | | | | | | | | | | | (1654) length1(int, all_103_4) = all_215_1 & ( ~ 204.89/127.23 | | | | | | | | | | | | | | | | | | | ($lesseq(all_86_11, all_215_1)) | ~ ($lesseq(0, 204.89/127.23 | | | | | | | | | | | | | | | | | | | all_215_1)) | ( ~ (all_215_0 = all_215_1) & 204.89/127.23 | | | | | | | | | | | | | | | | | | | length1(int, all_103_2) = all_215_0)) 204.89/127.23 | | | | | | | | | | | | | | | | | | | 204.89/127.23 | | | | | | | | | | | | | | | | | | | ALPHA: (1654) implies: 204.89/127.23 | | | | | | | | | | | | | | | | | | | (1655) length1(int, all_103_4) = all_215_1 204.89/127.23 | | | | | | | | | | | | | | | | | | | (1656) ~ ($lesseq(all_86_11, all_215_1)) | ~ 204.89/127.23 | | | | | | | | | | | | | | | | | | | ($lesseq(0, all_215_1)) | ( ~ (all_215_0 = 204.89/127.23 | | | | | | | | | | | | | | | | | | | all_215_1) & length1(int, all_103_2) = 204.89/127.23 | | | | | | | | | | | | | | | | | | | all_215_0) 204.89/127.23 | | | | | | | | | | | | | | | | | | | 204.89/127.23 | | | | | | | | | | | | | | | | | | | BETA: splitting (295) gives: 204.89/127.23 | | | | | | | | | | | | | | | | | | | 204.89/127.23 | | | | | | | | | | | | | | | | | | | Case 1: 204.89/127.23 | | | | | | | | | | | | | | | | | | | | 204.89/127.23 | | | | | | | | | | | | | | | | | | | | (1657) all_190_0 = 0 & all_190_1 = 0 & map_eq_sub1(int, 204.89/127.23 | | | | | | | | | | | | | | | | | | | | all_190_4, all_190_3, $sum(all_86_10, 1), 204.89/127.23 | | | | | | | | | | | | | | | | | | | | all_190_2) = 0 & map_eq_sub1(int, all_190_4, 204.89/127.23 | | | | | | | | | | | | | | | | | | | | all_190_3, 0, all_86_7) = 0 & length1(int, 204.89/127.23 | | | | | | | | | | | | | | | | | | | | all_105_4) = all_190_2 & elts(int, all_105_2) = 204.89/127.23 | | | | | | | | | | | | | | | | | | | | all_190_3 & elts(int, all_105_4) = all_190_4 & 204.89/127.23 | | | | | | | | | | | | | | | | | | | | in_uni(all_190_3) & in_uni(all_190_4) 204.89/127.23 | | | | | | | | | | | | | | | | | | | | 204.89/127.23 | | | | | | | | | | | | | | | | | | | | ALPHA: (1657) implies: 204.89/127.23 | | | | | | | | | | | | | | | | | | | | (1658) elts(int, all_105_4) = all_190_4 204.89/127.23 | | | | | | | | | | | | | | | | | | | | (1659) length1(int, all_105_4) = all_190_2 204.89/127.23 | | | | | | | | | | | | | | | | | | | | 204.89/127.23 | | | | | | | | | | | | | | | | | | | | BETA: splitting (324) gives: 204.89/127.23 | | | | | | | | | | | | | | | | | | | | 204.89/127.23 | | | | | | | | | | | | | | | | | | | | Case 1: 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | (1660) all_219_1 = 0 & array_eq_sub1(int, all_105_4, 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | all_105_2, 0, all_86_7) = 0 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | ALPHA: (1660) implies: 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | (1661) array_eq_sub1(int, all_105_4, all_105_2, 0, 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | all_86_7) = 0 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (270) gives: 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | Case 1: 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | (1662) all_169_0 = all_169_1 & $lesseq(all_86_7, 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | all_169_1) & $lesseq(0, all_169_1) & $lesseq(0, 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | all_86_7) & length1(int, all_105_2) = all_169_1 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | & length1(int, all_105_4) = all_169_1 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1662) implies: 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | (1663) length1(int, all_105_4) = all_169_1 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (337) gives: 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | Case 1: 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | (1664) all_234_1 = 0 & array_eq_sub1(int, all_105_4, 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | all_105_2, $sum(all_86_10, 1), all_86_13) = 0 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1664) implies: 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | (1665) array_eq_sub1(int, all_105_4, all_105_2, 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | $sum(all_86_10, 1), all_86_13) = 0 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (255) gives: 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | Case 1: 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | | (1666) all_153_0 = all_153_1 & $lesseq(1, 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | | $difference(all_153_1, all_86_10)) & 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | | $lesseq(all_86_13, all_153_1) & $lesseq(-1, 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | | all_86_10) & $lesseq(0, all_86_13) & 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | | length1(int, all_105_2) = all_153_1 & length1(int, 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | | all_105_4) = all_153_1 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1666) implies: 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | | (1667) $lesseq(1, $difference(all_153_1, all_86_10)) 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | | (1668) length1(int, all_105_4) = all_153_1 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (345) gives: 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | | | (1669) all_242_1 = 0 & array_eq_sub1(int, all_103_2, 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, $sum(all_86_8, 1), all_86_13) = 0 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1669) implies: 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | | | (1670) array_eq_sub1(int, all_103_2, all_105_4, 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | | | $sum(all_86_8, 1), all_86_13) = 0 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (45), (48), (50), (52), (53), (183), (269), 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | | | (394), (1184), (1185), (1484), (1485), (1655), 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | | | (1656), (1659), (1663), (1667), (1668), (1670) are 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #42. 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | | | (1671) length1(int, all_103_2) = all_242_1 & ( ~ 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | | | ($lesseq(1, $difference(all_242_1, all_86_8))) | 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | | | ~ ($lesseq(all_86_13, all_242_1)) | ( ~ 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | | | (all_242_0 = all_242_1) & length1(int, 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4) = all_242_0)) 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1671) implies: 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | | | (1672) length1(int, all_103_2) = all_242_1 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (39), (44), (91), (99), (180), (203), (263), 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | | | (394), (395), (396), (1180), (1181), (1182), 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | | | (1184), (1185), (1478), (1485), (1658), (1659), 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | | | (1672) are inconsistent by sub-proof #27. 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | | End of split 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | Case 2: 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | | (1673) ~ (all_153_1 = 0) & array_eq_sub1(int, all_105_4, 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | | all_105_2, $sum(all_86_10, 1), all_86_13) = 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | | all_153_1 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (1665), (1673) are inconsistent by sub-proof 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | | #54. 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | End of split 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | Case 2: 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | (1674) length1(int, all_105_4) = all_234_1 & ( ~ 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | ($lesseq(1, $difference(all_234_1, all_86_10))) 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | | ~ ($lesseq(all_86_13, all_234_1)) | ( ~ 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | (all_234_0 = all_234_1) & length1(int, 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | all_105_2) = all_234_0)) 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1674) implies: 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | (1675) length1(int, all_105_4) = all_234_1 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | (1676) ~ ($lesseq(1, $difference(all_234_1, all_86_10))) 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | | ~ ($lesseq(all_86_13, all_234_1)) | ( ~ 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | (all_234_0 = all_234_1) & length1(int, 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | all_105_2) = all_234_0) 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (45), (180), (183), (270), (1483), (1484), 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | (1661), (1675), (1676) are inconsistent by 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #29. 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | End of split 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | Case 2: 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | (1677) ~ (all_169_1 = 0) & array_eq_sub1(int, all_105_4, 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | all_105_2, 0, all_86_7) = all_169_1 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (1661), (1677) are inconsistent by sub-proof 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | #75. 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | End of split 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | 204.89/127.23 | | | | | | | | | | | | | | | | | | | | Case 2: 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | (1678) length1(int, all_105_4) = all_219_1 & ( ~ 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | ($lesseq(all_86_7, all_219_1)) | ~ ($lesseq(0, 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | all_219_1)) | ( ~ (all_219_0 = all_219_1) & 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | length1(int, all_105_2) = all_219_0)) 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | ALPHA: (1678) implies: 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | (1679) length1(int, all_105_4) = all_219_1 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (337) gives: 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | Case 1: 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | (1680) all_234_1 = 0 & array_eq_sub1(int, all_105_4, 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | all_105_2, $sum(all_86_10, 1), all_86_13) = 0 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1680) implies: 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | (1681) array_eq_sub1(int, all_105_4, all_105_2, 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | $sum(all_86_10, 1), all_86_13) = 0 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (255) gives: 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | Case 1: 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | (1682) all_153_0 = all_153_1 & $lesseq(1, 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | $difference(all_153_1, all_86_10)) & 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | $lesseq(all_86_13, all_153_1) & $lesseq(-1, 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | all_86_10) & $lesseq(0, all_86_13) & 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | length1(int, all_105_2) = all_153_1 & length1(int, 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | all_105_4) = all_153_1 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1682) implies: 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | (1683) $lesseq(1, $difference(all_153_1, all_86_10)) 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | (1684) length1(int, all_105_4) = all_153_1 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (345) gives: 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | Case 1: 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | | (1685) all_242_1 = 0 & array_eq_sub1(int, all_103_2, 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, $sum(all_86_8, 1), all_86_13) = 0 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1685) implies: 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | | (1686) array_eq_sub1(int, all_103_2, all_105_4, 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | | $sum(all_86_8, 1), all_86_13) = 0 204.89/127.23 | | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (45), (48), (50), (52), (53), (183), (269), 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | | | | (394), (1184), (1185), (1484), (1485), (1655), 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | | | | (1656), (1679), (1683), (1684), (1686) are 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #32. 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | | | Case 2: 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | | | | (1687) length1(int, all_103_2) = all_242_1 & ( ~ 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | | | | ($lesseq(1, $difference(all_242_1, all_86_8))) | 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | | | | ~ ($lesseq(all_86_13, all_242_1)) | ( ~ 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | | | | (all_242_0 = all_242_1) & length1(int, 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | | | | all_105_4) = all_242_0)) 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1687) implies: 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | | | | (1688) length1(int, all_103_2) = all_242_1 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (39), (44), (91), (99), (180), (203), (263), 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | | | | (394), (395), (396), (1180), (1181), (1182), 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | | | | (1184), (1185), (1478), (1485), (1658), (1659), 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | | | | (1688) are inconsistent by sub-proof #27. 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | | | End of split 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | | Case 2: 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | | | (1689) ~ (all_153_1 = 0) & array_eq_sub1(int, all_105_4, 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | | | all_105_2, $sum(all_86_10, 1), all_86_13) = 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | | | all_153_1 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (1681), (1689) are inconsistent by sub-proof 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | | | #54. 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | | End of split 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | | 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | Case 2: 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | | 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | | (1690) length1(int, all_105_4) = all_234_1 & ( ~ 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | | ($lesseq(1, $difference(all_234_1, all_86_10))) 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | | | ~ ($lesseq(all_86_13, all_234_1)) | ( ~ 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | | (all_234_0 = all_234_1) & length1(int, 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | | all_105_2) = all_234_0)) 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | | 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1690) implies: 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | | (1691) length1(int, all_105_4) = all_234_1 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | | (1692) ~ ($lesseq(1, $difference(all_234_1, all_86_10))) 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | | | ~ ($lesseq(all_86_13, all_234_1)) | ( ~ 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | | (all_234_0 = all_234_1) & length1(int, 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | | all_105_2) = all_234_0) 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | | 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (345) gives: 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | | 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | | Case 1: 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | | | (1693) all_242_1 = 0 & array_eq_sub1(int, all_103_2, 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | | | all_105_4, $sum(all_86_8, 1), all_86_13) = 0 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (45), (181), (183), (269), (1184), (1185), 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | | | (1483), (1484), (1485), (1655), (1659), (1679), 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | | | (1691), (1692), (1693) are inconsistent by 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #37. 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | | Case 2: 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | | | (1694) length1(int, all_103_2) = all_242_1 & ( ~ 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | | | ($lesseq(1, $difference(all_242_1, all_86_8))) | 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | | | ~ ($lesseq(all_86_13, all_242_1)) | ( ~ 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | | | (all_242_0 = all_242_1) & length1(int, 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | | | all_105_4) = all_242_0)) 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1694) implies: 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | | | (1695) length1(int, all_103_2) = all_242_1 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (39), (44), (91), (99), (180), (203), (263), 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | | | (394), (395), (396), (1180), (1181), (1182), 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | | | (1184), (1185), (1478), (1485), (1658), (1659), 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | | | (1695) are inconsistent by sub-proof #27. 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | | End of split 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | | 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | End of split 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | 204.89/127.24 | | | | | | | | | | | | | | | | | | | | End of split 204.89/127.24 | | | | | | | | | | | | | | | | | | | | 204.89/127.24 | | | | | | | | | | | | | | | | | | | Case 2: 204.89/127.24 | | | | | | | | | | | | | | | | | | | | 204.89/127.24 | | | | | | | | | | | | | | | | | | | | (1696) ~ (all_190_4 = 0) & permut_sub2(int, all_105_4, 204.89/127.24 | | | | | | | | | | | | | | | | | | | | all_105_2, all_86_7, $sum(all_86_10, 1)) = 204.89/127.24 | | | | | | | | | | | | | | | | | | | | all_190_4 204.89/127.24 | | | | | | | | | | | | | | | | | | | | 204.89/127.24 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (43), (1481), (1696) are inconsistent by sub-proof 204.89/127.24 | | | | | | | | | | | | | | | | | | | | #68. 204.89/127.24 | | | | | | | | | | | | | | | | | | | | 204.89/127.24 | | | | | | | | | | | | | | | | | | | End of split 204.89/127.24 | | | | | | | | | | | | | | | | | | | 204.89/127.24 | | | | | | | | | | | | | | | | | | End of split 204.89/127.24 | | | | | | | | | | | | | | | | | | 204.89/127.24 | | | | | | | | | | | | | | | | | Case 2: 204.89/127.24 | | | | | | | | | | | | | | | | | | 204.89/127.24 | | | | | | | | | | | | | | | | | | (1697) ~ (all_193_1 = 0) & array_eq_sub1(int, all_103_4, 204.89/127.24 | | | | | | | | | | | | | | | | | | all_103_2, $sum(all_86_10, 1), all_86_13) = 204.89/127.24 | | | | | | | | | | | | | | | | | | all_193_1 204.89/127.24 | | | | | | | | | | | | | | | | | | 204.89/127.24 | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (400), (1697) are inconsistent by sub-proof 204.89/127.24 | | | | | | | | | | | | | | | | | | #55. 204.89/127.24 | | | | | | | | | | | | | | | | | | 204.89/127.24 | | | | | | | | | | | | | | | | | End of split 204.89/127.24 | | | | | | | | | | | | | | | | | 204.89/127.24 | | | | | | | | | | | | | | | | Case 2: 204.89/127.24 | | | | | | | | | | | | | | | | | 204.89/127.24 | | | | | | | | | | | | | | | | | (1698) elts(int, all_105_2) = all_187_2 & elts(int, 204.89/127.24 | | | | | | | | | | | | | | | | | all_105_4) = all_187_3 & in_uni(all_187_2) & 204.89/127.24 | | | | | | | | | | | | | | | | | in_uni(all_187_3) & (( ~ (all_187_0 = 0) & 204.89/127.24 | | | | | | | | | | | | | | | | | map_eq_sub1(int, all_187_3, all_187_2, 204.89/127.24 | | | | | | | | | | | | | | | | | $sum(all_86_10, 1), all_187_1) = all_187_0 & 204.89/127.24 | | | | | | | | | | | | | | | | | length1(int, all_105_4) = all_187_1) | ( ~ 204.89/127.24 | | | | | | | | | | | | | | | | | (all_187_1 = 0) & map_eq_sub1(int, all_187_3, 204.89/127.24 | | | | | | | | | | | | | | | | | all_187_2, 0, all_86_7) = all_187_1)) 204.89/127.24 | | | | | | | | | | | | | | | | | 204.89/127.24 | | | | | | | | | | | | | | | | | ALPHA: (1698) implies: 204.89/127.24 | | | | | | | | | | | | | | | | | (1699) elts(int, all_105_4) = all_187_3 204.89/127.24 | | | | | | | | | | | | | | | | | (1700) elts(int, all_105_2) = all_187_2 204.89/127.24 | | | | | | | | | | | | | | | | | (1701) ( ~ (all_187_0 = 0) & map_eq_sub1(int, all_187_3, 204.89/127.24 | | | | | | | | | | | | | | | | | all_187_2, $sum(all_86_10, 1), all_187_1) = 204.89/127.24 | | | | | | | | | | | | | | | | | all_187_0 & length1(int, all_105_4) = all_187_1) 204.89/127.24 | | | | | | | | | | | | | | | | | | ( ~ (all_187_1 = 0) & map_eq_sub1(int, 204.89/127.24 | | | | | | | | | | | | | | | | | all_187_3, all_187_2, 0, all_86_7) = 204.89/127.24 | | | | | | | | | | | | | | | | | all_187_1) 204.89/127.24 | | | | | | | | | | | | | | | | | 204.89/127.24 | | | | | | | | | | | | | | | | | BETA: splitting (298) gives: 204.89/127.24 | | | | | | | | | | | | | | | | | 204.89/127.24 | | | | | | | | | | | | | | | | | Case 1: 204.89/127.24 | | | | | | | | | | | | | | | | | | 204.89/127.24 | | | | | | | | | | | | | | | | | | (1702) all_193_0 = all_193_1 & $lesseq(1, 204.89/127.24 | | | | | | | | | | | | | | | | | | $difference(all_193_1, all_86_10)) & 204.89/127.24 | | | | | | | | | | | | | | | | | | $lesseq(all_86_13, all_193_1) & $lesseq(-1, 204.89/127.24 | | | | | | | | | | | | | | | | | | all_86_10) & $lesseq(0, all_86_13) & 204.89/127.24 | | | | | | | | | | | | | | | | | | length1(int, all_103_2) = all_193_1 & length1(int, 204.89/127.24 | | | | | | | | | | | | | | | | | | all_103_4) = all_193_1 204.89/127.24 | | | | | | | | | | | | | | | | | | 204.89/127.24 | | | | | | | | | | | | | | | | | | ALPHA: (1702) implies: 204.89/127.24 | | | | | | | | | | | | | | | | | | (1703) $lesseq(1, $difference(all_193_1, all_86_10)) 204.89/127.24 | | | | | | | | | | | | | | | | | | (1704) length1(int, all_103_4) = all_193_1 204.89/127.24 | | | | | | | | | | | | | | | | | | (1705) length1(int, all_103_2) = all_193_1 204.89/127.24 | | | | | | | | | | | | | | | | | | 204.89/127.24 | | | | | | | | | | | | | | | | | | BETA: splitting (319) gives: 204.89/127.24 | | | | | | | | | | | | | | | | | | 204.89/127.24 | | | | | | | | | | | | | | | | | | Case 1: 204.89/127.24 | | | | | | | | | | | | | | | | | | | 204.89/127.24 | | | | | | | | | | | | | | | | | | | (1706) all_215_1 = 0 & array_eq_sub1(int, all_103_4, 204.89/127.24 | | | | | | | | | | | | | | | | | | | all_103_2, 0, all_86_11) = 0 204.89/127.24 | | | | | | | | | | | | | | | | | | | 204.89/127.24 | | | | | | | | | | | | | | | | | | | ALPHA: (1706) implies: 204.89/127.24 | | | | | | | | | | | | | | | | | | | (1707) array_eq_sub1(int, all_103_4, all_103_2, 0, 204.89/127.24 | | | | | | | | | | | | | | | | | | | all_86_11) = 0 204.89/127.24 | | | | | | | | | | | | | | | | | | | 204.89/127.24 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (39), (44), (45), (90), (91), (96), (183), 204.89/127.24 | | | | | | | | | | | | | | | | | | | (206), (272), (394), (396), (1180), (1477), 204.89/127.24 | | | | | | | | | | | | | | | | | | | (1478), (1479), (1704), (1705), (1707) are 204.89/127.24 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #26. 204.89/127.24 | | | | | | | | | | | | | | | | | | | 204.89/127.24 | | | | | | | | | | | | | | | | | | Case 2: 204.89/127.24 | | | | | | | | | | | | | | | | | | | 204.89/127.24 | | | | | | | | | | | | | | | | | | | (1708) length1(int, all_103_4) = all_215_1 & ( ~ 204.89/127.24 | | | | | | | | | | | | | | | | | | | ($lesseq(all_86_11, all_215_1)) | ~ ($lesseq(0, 204.89/127.24 | | | | | | | | | | | | | | | | | | | all_215_1)) | ( ~ (all_215_0 = all_215_1) & 204.89/127.24 | | | | | | | | | | | | | | | | | | | length1(int, all_103_2) = all_215_0)) 204.89/127.24 | | | | | | | | | | | | | | | | | | | 204.89/127.24 | | | | | | | | | | | | | | | | | | | ALPHA: (1708) implies: 204.89/127.24 | | | | | | | | | | | | | | | | | | | (1709) length1(int, all_103_4) = all_215_1 204.89/127.24 | | | | | | | | | | | | | | | | | | | (1710) ~ ($lesseq(all_86_11, all_215_1)) | ~ 204.89/127.24 | | | | | | | | | | | | | | | | | | | ($lesseq(0, all_215_1)) | ( ~ (all_215_0 = 204.89/127.24 | | | | | | | | | | | | | | | | | | | all_215_1) & length1(int, all_103_2) = 204.89/127.24 | | | | | | | | | | | | | | | | | | | all_215_0) 204.89/127.24 | | | | | | | | | | | | | | | | | | | 204.89/127.24 | | | | | | | | | | | | | | | | | | | BETA: splitting (324) gives: 204.89/127.24 | | | | | | | | | | | | | | | | | | | 204.89/127.24 | | | | | | | | | | | | | | | | | | | Case 1: 204.89/127.24 | | | | | | | | | | | | | | | | | | | | 204.89/127.24 | | | | | | | | | | | | | | | | | | | | (1711) all_219_1 = 0 & array_eq_sub1(int, all_105_4, 204.89/127.24 | | | | | | | | | | | | | | | | | | | | all_105_2, 0, all_86_7) = 0 204.89/127.24 | | | | | | | | | | | | | | | | | | | | 204.89/127.24 | | | | | | | | | | | | | | | | | | | | ALPHA: (1711) implies: 204.89/127.24 | | | | | | | | | | | | | | | | | | | | (1712) array_eq_sub1(int, all_105_4, all_105_2, 0, 204.89/127.24 | | | | | | | | | | | | | | | | | | | | all_86_7) = 0 204.89/127.24 | | | | | | | | | | | | | | | | | | | | 204.89/127.24 | | | | | | | | | | | | | | | | | | | | BETA: splitting (270) gives: 204.89/127.24 | | | | | | | | | | | | | | | | | | | | 204.89/127.24 | | | | | | | | | | | | | | | | | | | | Case 1: 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | (1713) all_169_0 = all_169_1 & $lesseq(all_86_7, 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | all_169_1) & $lesseq(0, all_169_1) & $lesseq(0, 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | all_86_7) & length1(int, all_105_2) = all_169_1 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | & length1(int, all_105_4) = all_169_1 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | ALPHA: (1713) implies: 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | (1714) length1(int, all_105_4) = all_169_1 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (337) gives: 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | Case 1: 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | | 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | | (1715) all_234_1 = 0 & array_eq_sub1(int, all_105_4, 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | | all_105_2, $sum(all_86_10, 1), all_86_13) = 0 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | | 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1715) implies: 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | | (1716) array_eq_sub1(int, all_105_4, all_105_2, 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | | $sum(all_86_10, 1), all_86_13) = 0 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | | 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (39), (44), (45), (99), (100), (105), (184), 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | | (205), (255), (1181), (1184), (1185), (1699), 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | | (1700), (1701), (1714), (1716) are inconsistent by 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | | sub-proof #25. 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | | 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | Case 2: 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | | 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | | (1717) length1(int, all_105_4) = all_234_1 & ( ~ 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | | ($lesseq(1, $difference(all_234_1, all_86_10))) 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | | | ~ ($lesseq(all_86_13, all_234_1)) | ( ~ 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | | (all_234_0 = all_234_1) & length1(int, 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | | all_105_2) = all_234_0)) 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | | 204.89/127.24 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1717) implies: 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | (1718) length1(int, all_105_4) = all_234_1 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | (1719) ~ ($lesseq(1, $difference(all_234_1, all_86_10))) 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | ~ ($lesseq(all_86_13, all_234_1)) | ( ~ 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | (all_234_0 = all_234_1) & length1(int, 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | all_105_2) = all_234_0) 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (45), (180), (183), (270), (1703), (1704), 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | (1712), (1718), (1719) are inconsistent by 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | sub-proof #29. 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | End of split 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | 204.89/127.25 | | | | | | | | | | | | | | | | | | | | Case 2: 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | (1720) ~ (all_169_1 = 0) & array_eq_sub1(int, all_105_4, 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | all_105_2, 0, all_86_7) = all_169_1 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (1712), (1720) are inconsistent by sub-proof 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | #75. 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | 204.89/127.25 | | | | | | | | | | | | | | | | | | | | End of split 204.89/127.25 | | | | | | | | | | | | | | | | | | | | 204.89/127.25 | | | | | | | | | | | | | | | | | | | Case 2: 204.89/127.25 | | | | | | | | | | | | | | | | | | | | 204.89/127.25 | | | | | | | | | | | | | | | | | | | | (1721) length1(int, all_105_4) = all_219_1 & ( ~ 204.89/127.25 | | | | | | | | | | | | | | | | | | | | ($lesseq(all_86_7, all_219_1)) | ~ ($lesseq(0, 204.89/127.25 | | | | | | | | | | | | | | | | | | | | all_219_1)) | ( ~ (all_219_0 = all_219_1) & 204.89/127.25 | | | | | | | | | | | | | | | | | | | | length1(int, all_105_2) = all_219_0)) 204.89/127.25 | | | | | | | | | | | | | | | | | | | | 204.89/127.25 | | | | | | | | | | | | | | | | | | | | ALPHA: (1721) implies: 204.89/127.25 | | | | | | | | | | | | | | | | | | | | (1722) length1(int, all_105_4) = all_219_1 204.89/127.25 | | | | | | | | | | | | | | | | | | | | 204.89/127.25 | | | | | | | | | | | | | | | | | | | | BETA: splitting (337) gives: 204.89/127.25 | | | | | | | | | | | | | | | | | | | | 204.89/127.25 | | | | | | | | | | | | | | | | | | | | Case 1: 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | (1723) all_234_1 = 0 & array_eq_sub1(int, all_105_4, 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | all_105_2, $sum(all_86_10, 1), all_86_13) = 0 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | ALPHA: (1723) implies: 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | (1724) array_eq_sub1(int, all_105_4, all_105_2, 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | $sum(all_86_10, 1), all_86_13) = 0 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (255) gives: 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | Case 1: 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | (1725) all_153_0 = all_153_1 & $lesseq(1, 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | $difference(all_153_1, all_86_10)) & 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | $lesseq(all_86_13, all_153_1) & $lesseq(-1, 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | all_86_10) & $lesseq(0, all_86_13) & 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | length1(int, all_105_2) = all_153_1 & length1(int, 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | all_105_4) = all_153_1 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1725) implies: 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | (1726) $lesseq(1, $difference(all_153_1, all_86_10)) 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | (1727) length1(int, all_105_4) = all_153_1 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (345) gives: 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | Case 1: 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | (1728) all_242_1 = 0 & array_eq_sub1(int, all_103_2, 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | all_105_4, $sum(all_86_8, 1), all_86_13) = 0 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1728) implies: 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | (1729) array_eq_sub1(int, all_103_2, all_105_4, 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | $sum(all_86_8, 1), all_86_13) = 0 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (45), (48), (50), (52), (53), (183), (269), 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | (394), (1184), (1185), (1704), (1705), (1709), 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | (1710), (1722), (1726), (1727), (1729) are 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #32. 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | Case 2: 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | (1730) length1(int, all_103_2) = all_242_1 & ( ~ 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | ($lesseq(1, $difference(all_242_1, all_86_8))) | 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | ~ ($lesseq(all_86_13, all_242_1)) | ( ~ 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | (all_242_0 = all_242_1) & length1(int, 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | all_105_4) = all_242_0)) 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1730) implies: 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | (1731) length1(int, all_103_2) = all_242_1 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_219_1, all_170_1, 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (1185), (1722) 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | gives: 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | (1732) all_219_1 = all_170_1 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_219_1, all_153_1, 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (1722), (1727) 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | gives: 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | (1733) all_219_1 = all_153_1 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_242_1, all_193_1, 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (1705), (1731) 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | gives: 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | (1734) all_242_1 = all_193_1 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_242_1, all_170_1, 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (1184), (1731) 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | gives: 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | (1735) all_242_1 = all_170_1 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_193_1, all_156_0, 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (394), (1705) 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | gives: 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | (1736) all_193_1 = all_156_0 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_86_13, all_215_1, 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (183), (1709) 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | gives: 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | (1737) all_215_1 = all_86_13 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_215_1, all_193_1, 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (1704), (1709) 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | gives: 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | (1738) all_215_1 = all_193_1 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_105_3, all_187_3, 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (99), (1699) 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | gives: 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | (1739) all_187_3 = all_105_3 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_187_3, all_181_2, 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (1181), (1699) 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | gives: 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | (1740) all_187_3 = all_181_2 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_187_3, all_156_1, 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (395), (1699) 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | gives: 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | (1741) all_187_3 = all_156_1 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_103_1, all_181_3, 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (91), (1180) 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | gives: 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | (1742) all_181_3 = all_103_1 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_191_2, all_181_3, 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (1180), (1478) 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | gives: 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | (1743) all_191_2 = all_181_3 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_191_2, all_156_3, 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (396), (1478) 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | gives: 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | (1744) all_191_2 = all_156_3 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1734), (1735) imply: 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | (1745) all_193_1 = all_170_1 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1745) implies: 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | (1746) all_193_1 = all_170_1 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1732), (1733) imply: 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | (1747) all_170_1 = all_153_1 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1747) implies: 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | (1748) all_170_1 = all_153_1 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1737), (1738) imply: 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | (1749) all_193_1 = all_86_13 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1749) implies: 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | (1750) all_193_1 = all_86_13 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1736), (1746) imply: 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | (1751) all_170_1 = all_156_0 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1746), (1750) imply: 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | (1752) all_170_1 = all_86_13 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1743), (1744) imply: 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | (1753) all_181_3 = all_156_3 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1753) implies: 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | (1754) all_181_3 = all_156_3 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1740), (1741) imply: 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | (1755) all_181_2 = all_156_1 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1739), (1740) imply: 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | (1756) all_181_2 = all_105_3 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1755), (1756) imply: 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | (1757) all_156_1 = all_105_3 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1742), (1754) imply: 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | (1758) all_156_3 = all_103_1 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1748), (1751) imply: 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | (1759) all_156_0 = all_153_1 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1751), (1752) imply: 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | (1760) all_156_0 = all_86_13 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1759), (1760) imply: 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | (1761) all_153_1 = all_86_13 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (44), (203), (263), (394), (1182), (1742), 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | (1756), (1757), (1758), (1760) are inconsistent by 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #44. 204.89/127.25 | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.25 | | | | | | | | | | | | | | | | | | | | | | End of split 205.00/127.25 | | | | | | | | | | | | | | | | | | | | | | 205.00/127.25 | | | | | | | | | | | | | | | | | | | | | Case 2: 205.00/127.25 | | | | | | | | | | | | | | | | | | | | | | 205.00/127.25 | | | | | | | | | | | | | | | | | | | | | | (1762) ~ (all_153_1 = 0) & array_eq_sub1(int, all_105_4, 205.00/127.25 | | | | | | | | | | | | | | | | | | | | | | all_105_2, $sum(all_86_10, 1), all_86_13) = 205.00/127.25 | | | | | | | | | | | | | | | | | | | | | | all_153_1 205.00/127.25 | | | | | | | | | | | | | | | | | | | | | | 205.00/127.25 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (1724), (1762) are inconsistent by sub-proof 205.00/127.25 | | | | | | | | | | | | | | | | | | | | | | #54. 205.00/127.25 | | | | | | | | | | | | | | | | | | | | | | 205.00/127.25 | | | | | | | | | | | | | | | | | | | | | End of split 205.00/127.25 | | | | | | | | | | | | | | | | | | | | | 205.00/127.25 | | | | | | | | | | | | | | | | | | | | Case 2: 205.00/127.25 | | | | | | | | | | | | | | | | | | | | | 205.00/127.25 | | | | | | | | | | | | | | | | | | | | | (1763) length1(int, all_105_4) = all_234_1 & ( ~ 205.00/127.25 | | | | | | | | | | | | | | | | | | | | | ($lesseq(1, $difference(all_234_1, all_86_10))) 205.00/127.25 | | | | | | | | | | | | | | | | | | | | | | ~ ($lesseq(all_86_13, all_234_1)) | ( ~ 205.00/127.25 | | | | | | | | | | | | | | | | | | | | | (all_234_0 = all_234_1) & length1(int, 205.00/127.25 | | | | | | | | | | | | | | | | | | | | | all_105_2) = all_234_0)) 205.00/127.25 | | | | | | | | | | | | | | | | | | | | | 205.00/127.25 | | | | | | | | | | | | | | | | | | | | | ALPHA: (1763) implies: 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | (1764) length1(int, all_105_4) = all_234_1 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | (1765) ~ ($lesseq(1, $difference(all_234_1, all_86_10))) 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | ~ ($lesseq(all_86_13, all_234_1)) | ( ~ 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | (all_234_0 = all_234_1) & length1(int, 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | all_105_2) = all_234_0) 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (345) gives: 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | Case 1: 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | (1766) all_242_1 = 0 & array_eq_sub1(int, all_103_2, 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | all_105_4, $sum(all_86_8, 1), all_86_13) = 0 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1766) implies: 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | (1767) array_eq_sub1(int, all_103_2, all_105_4, 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | $sum(all_86_8, 1), all_86_13) = 0 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (269) gives: 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | Case 1: 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | | (1768) all_168_0 = all_168_1 & $lesseq(1, 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | | $difference(all_168_1, all_86_8)) & 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | | $lesseq(all_86_13, all_168_1) & $lesseq(-1, 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | | all_86_8) & $lesseq(0, all_86_13) & length1(int, 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | | all_105_4) = all_168_1 & length1(int, all_103_2) 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | | = all_168_1 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1768) implies: 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | | (1769) length1(int, all_105_4) = all_168_1 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_86_13, all_234_1, 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (180), (1764) 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | | gives: 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | | (1770) all_234_1 = all_86_13 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_234_1, all_219_1, 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (1722), (1764) 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | | gives: 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | | (1771) all_234_1 = all_219_1 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_219_1, all_170_1, 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (1185), (1722) 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | | gives: 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | | (1772) all_219_1 = all_170_1 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_234_1, all_168_1, 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (1764), (1769) 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | | gives: 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | | (1773) all_234_1 = all_168_1 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_193_1, all_170_1, 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (1184), (1705) 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | | gives: 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | | (1774) all_193_1 = all_170_1 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_193_1, all_156_0, 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (394), (1705) 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | | gives: 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | | (1775) all_193_1 = all_156_0 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1771), (1773) imply: 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | | (1776) all_219_1 = all_168_1 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1776) implies: 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | | (1777) all_219_1 = all_168_1 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1770), (1773) imply: 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | | (1778) all_168_1 = all_86_13 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1772), (1777) imply: 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | | (1779) all_170_1 = all_168_1 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1774), (1775) imply: 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | | (1780) all_170_1 = all_156_0 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1780) implies: 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | | (1781) all_170_1 = all_156_0 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1779), (1781) imply: 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | | (1782) all_168_1 = all_156_0 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1782) implies: 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | | (1783) all_168_1 = all_156_0 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1778), (1783) imply: 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | | (1784) all_156_0 = all_86_13 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1775), (1784) imply: 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | | (1785) all_193_1 = all_86_13 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (49), (181), (1765), (1770) are inconsistent 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #38. 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | Case 2: 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | | (1786) ~ (all_168_1 = 0) & array_eq_sub1(int, all_103_2, 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | | all_105_4, $sum(all_86_8, 1), all_86_13) = 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | | all_168_1 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (1767), (1786) are inconsistent by sub-proof 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | | #83. 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | End of split 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | Case 2: 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | (1787) length1(int, all_103_2) = all_242_1 & ( ~ 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | ($lesseq(1, $difference(all_242_1, all_86_8))) | 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | ~ ($lesseq(all_86_13, all_242_1)) | ( ~ 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | (all_242_0 = all_242_1) & length1(int, 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | all_105_4) = all_242_0)) 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1787) implies: 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | (1788) length1(int, all_103_2) = all_242_1 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_242_1, all_193_1, 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (1705), (1788) 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | gives: 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | (1789) all_242_1 = all_193_1 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_242_1, all_170_1, 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (1184), (1788) 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | gives: 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | (1790) all_242_1 = all_170_1 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_86_13, all_215_1, 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (183), (1709) 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | gives: 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | (1791) all_215_1 = all_86_13 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_215_1, all_193_1, 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (1704), (1709) 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | gives: 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | (1792) all_215_1 = all_193_1 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_105_1, all_187_2, 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | all_105_2, int, simplifying with (100), (1700) 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | gives: 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | (1793) all_187_2 = all_105_1 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_105_3, all_187_3, 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (99), (1699) 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | gives: 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | (1794) all_187_3 = all_105_3 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_187_3, all_181_2, 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (1181), (1699) 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | gives: 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | (1795) all_187_3 = all_181_2 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_187_3, all_156_1, 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (395), (1699) 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | gives: 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | (1796) all_187_3 = all_156_1 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1789), (1790) imply: 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | (1797) all_193_1 = all_170_1 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | SIMP: (1797) implies: 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | (1798) all_193_1 = all_170_1 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1791), (1792) imply: 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | (1799) all_193_1 = all_86_13 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | SIMP: (1799) implies: 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | (1800) all_193_1 = all_86_13 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1798), (1800) imply: 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | (1801) all_170_1 = all_86_13 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1795), (1796) imply: 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | (1802) all_181_2 = all_156_1 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1794), (1795) imply: 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | (1803) all_181_2 = all_105_3 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1802), (1803) imply: 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | (1804) all_156_1 = all_105_3 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (44), (105), (180), (205), (1701), (1793), 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | (1794) are inconsistent by sub-proof #66. 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | | 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | End of split 205.00/127.26 | | | | | | | | | | | | | | | | | | | | | 205.00/127.26 | | | | | | | | | | | | | | | | | | | | End of split 205.00/127.26 | | | | | | | | | | | | | | | | | | | | 205.00/127.26 | | | | | | | | | | | | | | | | | | | End of split 205.00/127.26 | | | | | | | | | | | | | | | | | | | 205.00/127.26 | | | | | | | | | | | | | | | | | | End of split 205.00/127.26 | | | | | | | | | | | | | | | | | | 205.00/127.26 | | | | | | | | | | | | | | | | | Case 2: 205.00/127.26 | | | | | | | | | | | | | | | | | | 205.00/127.26 | | | | | | | | | | | | | | | | | | (1805) ~ (all_193_1 = 0) & array_eq_sub1(int, all_103_4, 205.00/127.26 | | | | | | | | | | | | | | | | | | all_103_2, $sum(all_86_10, 1), all_86_13) = 205.00/127.26 | | | | | | | | | | | | | | | | | | all_193_1 205.00/127.26 | | | | | | | | | | | | | | | | | | 205.00/127.26 | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (400), (1805) are inconsistent by sub-proof 205.00/127.26 | | | | | | | | | | | | | | | | | | #55. 205.00/127.26 | | | | | | | | | | | | | | | | | | 205.00/127.26 | | | | | | | | | | | | | | | | | End of split 205.00/127.26 | | | | | | | | | | | | | | | | | 205.00/127.26 | | | | | | | | | | | | | | | | End of split 205.00/127.26 | | | | | | | | | | | | | | | | 205.00/127.26 | | | | | | | | | | | | | | | End of split 205.00/127.26 | | | | | | | | | | | | | | | 205.00/127.26 | | | | | | | | | | | | | | Case 2: 205.00/127.26 | | | | | | | | | | | | | | | 205.00/127.26 | | | | | | | | | | | | | | | (1806) ~ (all_170_1 = 0) & array_eq_sub1(int, all_103_2, 205.00/127.26 | | | | | | | | | | | | | | | all_105_4, 0, all_86_11) = all_170_1 205.00/127.26 | | | | | | | | | | | | | | | 205.00/127.26 | | | | | | | | | | | | | | | REF_CLOSE: (45), (398), (1806) are inconsistent by sub-proof 205.00/127.26 | | | | | | | | | | | | | | | #48. 205.00/127.26 | | | | | | | | | | | | | | | 205.00/127.26 | | | | | | | | | | | | | | End of split 205.00/127.26 | | | | | | | | | | | | | | 205.00/127.26 | | | | | | | | | | | | | End of split 205.00/127.26 | | | | | | | | | | | | | 205.00/127.26 | | | | | | | | | | | | Case 2: 205.00/127.26 | | | | | | | | | | | | | 205.00/127.26 | | | | | | | | | | | | | (1807) length1(int, all_103_4) = all_238_1 & ( ~ 205.00/127.26 | | | | | | | | | | | | | ($lesseq(1, $difference(all_238_1, all_86_10))) 205.00/127.26 | | | | | | | | | | | | | | ~ ($lesseq(all_86_13, all_238_1)) | ( ~ 205.00/127.26 | | | | | | | | | | | | | (all_238_0 = all_238_1) & length1(int, 205.00/127.26 | | | | | | | | | | | | | all_103_2) = all_238_0)) 205.00/127.26 | | | | | | | | | | | | | 205.00/127.26 | | | | | | | | | | | | | ALPHA: (1807) implies: 205.00/127.26 | | | | | | | | | | | | | (1808) length1(int, all_103_4) = all_238_1 205.00/127.26 | | | | | | | | | | | | | (1809) ~ ($lesseq(1, $difference(all_238_1, all_86_10))) 205.00/127.26 | | | | | | | | | | | | | | ~ ($lesseq(all_86_13, all_238_1)) | ( ~ 205.00/127.26 | | | | | | | | | | | | | (all_238_0 = all_238_1) & length1(int, 205.00/127.26 | | | | | | | | | | | | | all_103_2) = all_238_0) 205.00/127.26 | | | | | | | | | | | | | 205.00/127.26 | | | | | | | | | | | | | BETA: splitting (294) gives: 205.00/127.26 | | | | | | | | | | | | | 205.00/127.26 | | | | | | | | | | | | | Case 1: 205.00/127.26 | | | | | | | | | | | | | | 205.00/127.27 | | | | | | | | | | | | | | (1810) all_187_3 = 0 & permut_sub2(int, all_105_4, 205.00/127.27 | | | | | | | | | | | | | | all_105_2, all_86_7, $sum(all_86_10, 1)) = 0 205.00/127.27 | | | | | | | | | | | | | | 205.00/127.27 | | | | | | | | | | | | | | ALPHA: (1810) implies: 205.00/127.27 | | | | | | | | | | | | | | (1811) permut_sub2(int, all_105_4, all_105_2, all_86_7, 205.00/127.27 | | | | | | | | | | | | | | $sum(all_86_10, 1)) = 0 205.00/127.27 | | | | | | | | | | | | | | 205.00/127.27 | | | | | | | | | | | | | | BETA: splitting (287) gives: 205.00/127.27 | | | | | | | | | | | | | | 205.00/127.27 | | | | | | | | | | | | | | Case 1: 205.00/127.27 | | | | | | | | | | | | | | | 205.00/127.27 | | | | | | | | | | | | | | | (1812) all_181_3 = 0 & permut_sub2(int, all_103_2, 205.00/127.27 | | | | | | | | | | | | | | | all_105_4, all_86_11, $sum(all_86_8, 1)) = 0 205.00/127.27 | | | | | | | | | | | | | | | 205.00/127.27 | | | | | | | | | | | | | | | ALPHA: (1812) implies: 205.00/127.27 | | | | | | | | | | | | | | | (1813) permut_sub2(int, all_103_2, all_105_4, all_86_11, 205.00/127.27 | | | | | | | | | | | | | | | $sum(all_86_8, 1)) = 0 205.00/127.27 | | | | | | | | | | | | | | | 205.00/127.27 | | | | | | | | | | | | | | | BETA: splitting (280) gives: 205.00/127.27 | | | | | | | | | | | | | | | 205.00/127.27 | | | | | | | | | | | | | | | Case 1: 205.00/127.27 | | | | | | | | | | | | | | | | 205.00/127.27 | | | | | | | | | | | | | | | | (1814) all_177_0 = 0 & all_177_1 = 0 & map_eq_sub1(int, 205.00/127.27 | | | | | | | | | | | | | | | | all_177_4, all_177_3, $sum(all_86_8, 1), 205.00/127.27 | | | | | | | | | | | | | | | | all_177_2) = 0 & map_eq_sub1(int, all_177_4, 205.00/127.27 | | | | | | | | | | | | | | | | all_177_3, 0, all_86_11) = 0 & length1(int, 205.00/127.27 | | | | | | | | | | | | | | | | all_103_2) = all_177_2 & elts(int, all_105_4) = 205.00/127.27 | | | | | | | | | | | | | | | | all_177_3 & elts(int, all_103_2) = all_177_4 & 205.00/127.27 | | | | | | | | | | | | | | | | in_uni(all_177_3) & in_uni(all_177_4) 205.00/127.27 | | | | | | | | | | | | | | | | 205.00/127.27 | | | | | | | | | | | | | | | | ALPHA: (1814) implies: 205.00/127.27 | | | | | | | | | | | | | | | | (1815) length1(int, all_103_2) = all_177_2 205.00/127.27 | | | | | | | | | | | | | | | | 205.00/127.27 | | | | | | | | | | | | | | | | BETA: splitting (337) gives: 205.00/127.27 | | | | | | | | | | | | | | | | 205.00/127.27 | | | | | | | | | | | | | | | | Case 1: 205.00/127.27 | | | | | | | | | | | | | | | | | 205.00/127.27 | | | | | | | | | | | | | | | | | (1816) all_234_1 = 0 & array_eq_sub1(int, all_105_4, 205.00/127.27 | | | | | | | | | | | | | | | | | all_105_2, $sum(all_86_10, 1), all_86_13) = 0 205.00/127.27 | | | | | | | | | | | | | | | | | 205.00/127.27 | | | | | | | | | | | | | | | | | ALPHA: (1816) implies: 205.00/127.27 | | | | | | | | | | | | | | | | | (1817) array_eq_sub1(int, all_105_4, all_105_2, 205.00/127.27 | | | | | | | | | | | | | | | | | $sum(all_86_10, 1), all_86_13) = 0 205.00/127.27 | | | | | | | | | | | | | | | | | 205.00/127.27 | | | | | | | | | | | | | | | | | BETA: splitting (255) gives: 205.00/127.27 | | | | | | | | | | | | | | | | | 205.00/127.27 | | | | | | | | | | | | | | | | | Case 1: 205.00/127.27 | | | | | | | | | | | | | | | | | | 205.00/127.27 | | | | | | | | | | | | | | | | | | (1818) all_153_0 = all_153_1 & $lesseq(1, 205.00/127.27 | | | | | | | | | | | | | | | | | | $difference(all_153_1, all_86_10)) & 205.00/127.27 | | | | | | | | | | | | | | | | | | $lesseq(all_86_13, all_153_1) & $lesseq(-1, 205.00/127.27 | | | | | | | | | | | | | | | | | | all_86_10) & $lesseq(0, all_86_13) & 205.00/127.27 | | | | | | | | | | | | | | | | | | length1(int, all_105_2) = all_153_1 & length1(int, 205.00/127.27 | | | | | | | | | | | | | | | | | | all_105_4) = all_153_1 205.00/127.27 | | | | | | | | | | | | | | | | | | 205.00/127.27 | | | | | | | | | | | | | | | | | | ALPHA: (1818) implies: 205.00/127.27 | | | | | | | | | | | | | | | | | | (1819) $lesseq(1, $difference(all_153_1, all_86_10)) 205.00/127.27 | | | | | | | | | | | | | | | | | | (1820) length1(int, all_105_4) = all_153_1 205.00/127.27 | | | | | | | | | | | | | | | | | | (1821) length1(int, all_105_2) = all_153_1 205.00/127.27 | | | | | | | | | | | | | | | | | | 205.00/127.27 | | | | | | | | | | | | | | | | | | BETA: splitting (319) gives: 205.00/127.27 | | | | | | | | | | | | | | | | | | 205.00/127.27 | | | | | | | | | | | | | | | | | | Case 1: 205.00/127.27 | | | | | | | | | | | | | | | | | | | 205.00/127.27 | | | | | | | | | | | | | | | | | | | (1822) all_215_1 = 0 & array_eq_sub1(int, all_103_4, 205.00/127.27 | | | | | | | | | | | | | | | | | | | all_103_2, 0, all_86_11) = 0 205.00/127.27 | | | | | | | | | | | | | | | | | | | 205.00/127.27 | | | | | | | | | | | | | | | | | | | ALPHA: (1822) implies: 205.00/127.27 | | | | | | | | | | | | | | | | | | | (1823) array_eq_sub1(int, all_103_4, all_103_2, 0, 205.00/127.27 | | | | | | | | | | | | | | | | | | | all_86_11) = 0 205.00/127.27 | | | | | | | | | | | | | | | | | | | 205.00/127.27 | | | | | | | | | | | | | | | | | | | BETA: splitting (271) gives: 205.00/127.27 | | | | | | | | | | | | | | | | | | | 205.00/127.27 | | | | | | | | | | | | | | | | | | | Case 1: 205.00/127.27 | | | | | | | | | | | | | | | | | | | | 205.00/127.27 | | | | | | | | | | | | | | | | | | | | (1824) all_170_0 = all_170_1 & $lesseq(all_86_11, 205.00/127.27 | | | | | | | | | | | | | | | | | | | | all_170_1) & $lesseq(0, all_170_1) & $lesseq(0, 205.00/127.27 | | | | | | | | | | | | | | | | | | | | all_86_11) & length1(int, all_105_4) = all_170_1 205.00/127.27 | | | | | | | | | | | | | | | | | | | | & length1(int, all_103_2) = all_170_1 205.00/127.27 | | | | | | | | | | | | | | | | | | | | 205.00/127.27 | | | | | | | | | | | | | | | | | | | | ALPHA: (1824) implies: 205.00/127.27 | | | | | | | | | | | | | | | | | | | | (1825) length1(int, all_103_2) = all_170_1 205.00/127.27 | | | | | | | | | | | | | | | | | | | | (1826) length1(int, all_105_4) = all_170_1 205.00/127.27 | | | | | | | | | | | | | | | | | | | | 205.00/127.27 | | | | | | | | | | | | | | | | | | | | BETA: splitting (272) gives: 205.00/127.27 | | | | | | | | | | | | | | | | | | | | 205.00/127.27 | | | | | | | | | | | | | | | | | | | | Case 1: 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | (1827) all_171_0 = all_171_1 & $lesseq(all_86_11, 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | all_171_1) & $lesseq(0, all_171_1) & $lesseq(0, 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | all_86_11) & length1(int, all_103_2) = all_171_1 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | & length1(int, all_103_4) = all_171_1 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | ALPHA: (1827) implies: 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | (1828) length1(int, all_103_4) = all_171_1 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | (1829) length1(int, all_103_2) = all_171_1 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (295) gives: 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | Case 1: 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | (1830) all_190_0 = 0 & all_190_1 = 0 & map_eq_sub1(int, 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | all_190_4, all_190_3, $sum(all_86_10, 1), 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | all_190_2) = 0 & map_eq_sub1(int, all_190_4, 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | all_190_3, 0, all_86_7) = 0 & length1(int, 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | all_105_4) = all_190_2 & elts(int, all_105_2) = 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | all_190_3 & elts(int, all_105_4) = all_190_4 & 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | in_uni(all_190_3) & in_uni(all_190_4) 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1830) implies: 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | (1831) length1(int, all_105_4) = all_190_2 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (296) gives: 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | Case 1: 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | (1832) all_191_3 = 0 & permut_sub2(int, all_103_4, 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | all_103_2, all_86_11, $sum(all_86_10, 1)) = 0 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1832) implies: 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | (1833) permut_sub2(int, all_103_4, all_103_2, all_86_11, 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | $sum(all_86_10, 1)) = 0 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (297) gives: 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | Case 1: 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | (1834) all_192_0 = 0 & all_192_1 = 0 & map_eq_sub1(int, 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | all_192_4, all_192_3, $sum(all_86_10, 1), 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | all_192_2) = 0 & map_eq_sub1(int, all_192_4, 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | all_192_3, 0, all_86_11) = 0 & length1(int, 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | all_103_4) = all_192_2 & elts(int, all_103_2) = 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | all_192_3 & elts(int, all_103_4) = all_192_4 & 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | in_uni(all_192_3) & in_uni(all_192_4) 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1834) implies: 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | (1835) length1(int, all_103_4) = all_192_2 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (324) gives: 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | (1836) all_219_1 = 0 & array_eq_sub1(int, all_105_4, 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | all_105_2, 0, all_86_7) = 0 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1836) implies: 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | (1837) array_eq_sub1(int, all_105_4, all_105_2, 0, 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | all_86_7) = 0 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (270) gives: 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | (1838) all_169_0 = all_169_1 & $lesseq(all_86_7, 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | all_169_1) & $lesseq(0, all_169_1) & $lesseq(0, 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | all_86_7) & length1(int, all_105_2) = all_169_1 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | & length1(int, all_105_4) = all_169_1 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1838) implies: 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | (1839) length1(int, all_105_4) = all_169_1 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (345) gives: 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1840) all_242_1 = 0 & array_eq_sub1(int, all_103_2, 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, $sum(all_86_8, 1), all_86_13) = 0 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1840) implies: 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1841) array_eq_sub1(int, all_103_2, all_105_4, 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | $sum(all_86_8, 1), all_86_13) = 0 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (269) gives: 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1842) all_168_0 = all_168_1 & $lesseq(1, 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $difference(all_168_1, all_86_8)) & 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $lesseq(all_86_13, all_168_1) & $lesseq(-1, 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_86_8) & $lesseq(0, all_86_13) & length1(int, 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4) = all_168_1 & length1(int, all_103_2) 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_168_1 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1842) implies: 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1843) length1(int, all_103_2) = all_168_1 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1844) length1(int, all_105_4) = all_168_1 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_190_2, all_169_1, 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (1831), (1839) 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1845) all_190_2 = all_169_1 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_169_1, all_168_1, 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (1839), (1844) 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1846) all_169_1 = all_168_1 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_190_2, all_153_1, 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (1820), (1831) 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1847) all_190_2 = all_153_1 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_86_13, all_177_2, 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (184), (1815) 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1848) all_177_2 = all_86_13 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_177_2, all_171_1, 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (1815), (1829) 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1849) all_177_2 = all_171_1 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_177_2, all_170_1, 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (1815), (1825) 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1850) all_177_2 = all_170_1 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_177_2, all_156_0, 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (394), (1815) 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1851) all_177_2 = all_156_0 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_168_1, all_156_0, 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (394), (1843) 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1852) all_168_1 = all_156_0 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_238_1, all_192_2, 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (1808), (1835) 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1853) all_238_1 = all_192_2 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_238_1, all_171_1, 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (1808), (1828) 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1854) all_238_1 = all_171_1 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1853), (1854) imply: 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1855) all_192_2 = all_171_1 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1845), (1847) imply: 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1856) all_169_1 = all_153_1 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1856) implies: 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1857) all_169_1 = all_153_1 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1849), (1850) imply: 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1858) all_171_1 = all_170_1 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1848), (1849) imply: 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1859) all_171_1 = all_86_13 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1849), (1851) imply: 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1860) all_171_1 = all_156_0 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1858), (1860) imply: 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1861) all_170_1 = all_156_0 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1858), (1859) imply: 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1862) all_170_1 = all_86_13 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1861), (1862) imply: 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1863) all_156_0 = all_86_13 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1863) implies: 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1864) all_156_0 = all_86_13 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1846), (1857) imply: 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1865) all_168_1 = all_153_1 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1852), (1865) imply: 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1866) all_156_0 = all_153_1 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1866) implies: 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1867) all_156_0 = all_153_1 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1864), (1867) imply: 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1868) all_153_1 = all_86_13 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1868) implies: 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1869) all_153_1 = all_86_13 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1855), (1859) imply: 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1870) all_192_2 = all_86_13 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1853), (1870) imply: 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1871) all_238_1 = all_86_13 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1809) gives: 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1872) $lesseq(1, $difference(all_86_13, all_238_1)) 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1871), (1872) imply: 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1873) $lesseq(0, -1) 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1873) is inconsistent. 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1874) ~ ($lesseq(1, $difference(all_238_1, all_86_10))) 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ( ~ (all_238_0 = all_238_1) & length1(int, 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2) = all_238_0) 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (49), (184), (1871), (1874) are inconsistent 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #24. 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1875) ~ (all_168_1 = 0) & array_eq_sub1(int, all_103_2, 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, $sum(all_86_8, 1), all_86_13) = 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_168_1 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (1841), (1875) are inconsistent by sub-proof 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #83. 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1876) length1(int, all_103_2) = all_242_1 & ( ~ 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | ($lesseq(1, $difference(all_242_1, all_86_8))) | 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ ($lesseq(all_86_13, all_242_1)) | ( ~ 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_242_0 = all_242_1) & length1(int, 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4) = all_242_0)) 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1876) implies: 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1877) length1(int, all_103_2) = all_242_1 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_190_2, all_169_1, 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (1831), (1839) 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1878) all_190_2 = all_169_1 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_170_1, all_169_1, 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (1826), (1839) 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1879) all_170_1 = all_169_1 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_190_2, all_153_1, 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (1820), (1831) 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1880) all_190_2 = all_153_1 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_86_13, all_177_2, 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (184), (1815) 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1881) all_177_2 = all_86_13 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_242_1, all_177_2, 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (1815), (1877) 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1882) all_242_1 = all_177_2 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_177_2, all_171_1, 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (1815), (1829) 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1883) all_177_2 = all_171_1 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_242_1, all_170_1, 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (1825), (1877) 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1884) all_242_1 = all_170_1 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_242_1, all_156_0, 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (394), (1877) 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1885) all_242_1 = all_156_0 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_86_13, all_238_1, 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (183), (1808) 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1886) all_238_1 = all_86_13 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1882), (1884) imply: 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1887) all_177_2 = all_170_1 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1887) implies: 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1888) all_177_2 = all_170_1 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1884), (1885) imply: 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1889) all_170_1 = all_156_0 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1878), (1880) imply: 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1890) all_169_1 = all_153_1 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1890) implies: 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1891) all_169_1 = all_153_1 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1881), (1883) imply: 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1892) all_171_1 = all_86_13 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1883), (1888) imply: 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1893) all_171_1 = all_170_1 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1892), (1893) imply: 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1894) all_170_1 = all_86_13 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1894) implies: 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1895) all_170_1 = all_86_13 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1889), (1895) imply: 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1896) all_156_0 = all_86_13 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1896) implies: 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1897) all_156_0 = all_86_13 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1879), (1895) imply: 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1898) all_169_1 = all_86_13 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1898) implies: 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1899) all_169_1 = all_86_13 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1891), (1899) imply: 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1900) all_153_1 = all_86_13 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (394), (1809), (1819), (1886), (1897), 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1900) are inconsistent by sub-proof #23. 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | (1901) ~ (all_169_1 = 0) & array_eq_sub1(int, all_105_4, 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_2, 0, all_86_7) = all_169_1 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (1837), (1901) are inconsistent by sub-proof 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | #75. 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | End of split 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | (1902) length1(int, all_105_4) = all_219_1 & ( ~ 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | ($lesseq(all_86_7, all_219_1)) | ~ ($lesseq(0, 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | all_219_1)) | ( ~ (all_219_0 = all_219_1) & 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | length1(int, all_105_2) = all_219_0)) 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1902) implies: 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | (1903) length1(int, all_105_4) = all_219_1 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | (1904) ~ ($lesseq(all_86_7, all_219_1)) | ~ ($lesseq(0, 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | all_219_1)) | ( ~ (all_219_0 = all_219_1) & 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | length1(int, all_105_2) = all_219_0) 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (345) gives: 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | (1905) all_242_1 = 0 & array_eq_sub1(int, all_103_2, 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, $sum(all_86_8, 1), all_86_13) = 0 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1905) implies: 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | (1906) array_eq_sub1(int, all_103_2, all_105_4, 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | $sum(all_86_8, 1), all_86_13) = 0 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (269) gives: 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1907) all_168_0 = all_168_1 & $lesseq(1, 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | $difference(all_168_1, all_86_8)) & 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | $lesseq(all_86_13, all_168_1) & $lesseq(-1, 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_86_8) & $lesseq(0, all_86_13) & length1(int, 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4) = all_168_1 & length1(int, all_103_2) 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_168_1 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1907) implies: 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1908) length1(int, all_103_2) = all_168_1 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_219_1, all_190_2, 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (1831), (1903) 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1909) all_219_1 = all_190_2 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_190_2, all_170_1, 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (1826), (1831) 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1910) all_190_2 = all_170_1 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_219_1, all_153_1, 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (1820), (1903) 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1911) all_219_1 = all_153_1 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_177_2, all_171_1, 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (1815), (1829) 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1912) all_177_2 = all_171_1 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_177_2, all_170_1, 205.00/127.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (1815), (1825) 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1913) all_177_2 = all_170_1 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_177_2, all_168_1, 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (1815), (1908) 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1914) all_177_2 = all_168_1 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_86_13, all_238_1, 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (183), (1808) 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1915) all_238_1 = all_86_13 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_238_1, all_192_2, 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (1808), (1835) 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1916) all_238_1 = all_192_2 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_238_1, all_171_1, 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (1808), (1828) 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1917) all_238_1 = all_171_1 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1916), (1917) imply: 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1918) all_192_2 = all_171_1 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1915), (1916) imply: 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1919) all_192_2 = all_86_13 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1909), (1911) imply: 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1920) all_190_2 = all_153_1 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1920) implies: 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1921) all_190_2 = all_153_1 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1918), (1919) imply: 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1922) all_171_1 = all_86_13 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1922) implies: 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1923) all_171_1 = all_86_13 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1910), (1921) imply: 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1924) all_170_1 = all_153_1 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1924) implies: 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1925) all_170_1 = all_153_1 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1913), (1914) imply: 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1926) all_170_1 = all_168_1 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1912), (1913) imply: 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1927) all_171_1 = all_170_1 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1927) implies: 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1928) all_171_1 = all_170_1 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1923), (1928) imply: 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1929) all_170_1 = all_86_13 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1929) implies: 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1930) all_170_1 = all_86_13 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1926), (1930) imply: 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1931) all_168_1 = all_86_13 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1925), (1926) imply: 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1932) all_168_1 = all_153_1 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1931), (1932) imply: 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1933) all_153_1 = all_86_13 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1933) implies: 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1934) all_153_1 = all_86_13 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (48), (50), (52), (53), (389), (1819), 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1821), (1904), (1911), (1934) are inconsistent by 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #58. 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1935) ~ (all_168_1 = 0) & array_eq_sub1(int, all_103_2, 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, $sum(all_86_8, 1), all_86_13) = 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_168_1 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (1906), (1935) are inconsistent by sub-proof 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | #83. 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | (1936) length1(int, all_103_2) = all_242_1 & ( ~ 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | ($lesseq(1, $difference(all_242_1, all_86_8))) | 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | ~ ($lesseq(all_86_13, all_242_1)) | ( ~ 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_242_0 = all_242_1) & length1(int, 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4) = all_242_0)) 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1936) implies: 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | (1937) length1(int, all_103_2) = all_242_1 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_219_1, all_170_1, 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (1826), (1903) 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | (1938) all_219_1 = all_170_1 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_219_1, all_153_1, 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (1820), (1903) 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | (1939) all_219_1 = all_153_1 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_86_13, all_177_2, 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (184), (1815) 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | (1940) all_177_2 = all_86_13 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_242_1, all_177_2, 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (1815), (1937) 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | (1941) all_242_1 = all_177_2 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_177_2, all_171_1, 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (1815), (1829) 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | (1942) all_177_2 = all_171_1 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_242_1, all_170_1, 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (1825), (1937) 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | (1943) all_242_1 = all_170_1 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1941), (1943) imply: 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | (1944) all_177_2 = all_170_1 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1944) implies: 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | (1945) all_177_2 = all_170_1 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1938), (1939) imply: 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | (1946) all_170_1 = all_153_1 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1946) implies: 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | (1947) all_170_1 = all_153_1 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1940), (1942) imply: 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | (1948) all_171_1 = all_86_13 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1942), (1945) imply: 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | (1949) all_171_1 = all_170_1 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1948), (1949) imply: 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | (1950) all_170_1 = all_86_13 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1947), (1950) imply: 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | (1951) all_153_1 = all_86_13 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1951) implies: 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | (1952) all_153_1 = all_86_13 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (48), (50), (52), (53), (389), (1819), 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | (1821), (1904), (1939), (1952) are inconsistent by 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #58. 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | End of split 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | End of split 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | Case 2: 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | (1953) ~ (all_192_4 = 0) & permut_sub2(int, all_103_4, 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, all_86_11, $sum(all_86_10, 1)) = 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | all_192_4 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (43), (1833), (1953) are inconsistent by sub-proof 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | #69. 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | End of split 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | Case 2: 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | (1954) elts(int, all_103_2) = all_191_2 & elts(int, 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | all_103_4) = all_191_3 & in_uni(all_191_2) & 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | in_uni(all_191_3) & (( ~ (all_191_0 = 0) & 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | map_eq_sub1(int, all_191_3, all_191_2, 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | $sum(all_86_10, 1), all_191_1) = all_191_0 & 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | length1(int, all_103_4) = all_191_1) | ( ~ 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | (all_191_1 = 0) & map_eq_sub1(int, all_191_3, 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | all_191_2, 0, all_86_11) = all_191_1)) 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1954) implies: 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | (1955) elts(int, all_103_4) = all_191_3 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | (1956) elts(int, all_103_2) = all_191_2 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | (1957) ( ~ (all_191_0 = 0) & map_eq_sub1(int, all_191_3, 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | all_191_2, $sum(all_86_10, 1), all_191_1) = 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | all_191_0 & length1(int, all_103_4) = all_191_1) 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | | ( ~ (all_191_1 = 0) & map_eq_sub1(int, 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | all_191_3, all_191_2, 0, all_86_11) = 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | all_191_1) 205.00/127.29 | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_86_13, all_177_2, 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (184), (1815) 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | gives: 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | (1958) all_177_2 = all_86_13 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_177_2, all_171_1, 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (1815), (1829) 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | gives: 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | (1959) all_177_2 = all_171_1 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_171_1, all_170_1, 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (1825), (1829) 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | gives: 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | (1960) all_171_1 = all_170_1 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_103_1, all_191_2, 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (91), (1956) 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | gives: 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | (1961) all_191_2 = all_103_1 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_103_3, all_191_3, 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (90), (1955) 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | gives: 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | (1962) all_191_3 = all_103_3 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1958), (1959) imply: 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | (1963) all_171_1 = all_86_13 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1963) implies: 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | (1964) all_171_1 = all_86_13 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1960), (1964) imply: 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | (1965) all_170_1 = all_86_13 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (44), (96), (183), (206), (1957), (1961), 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | (1962) are inconsistent by sub-proof #57. 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | End of split 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | Case 2: 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | (1966) ~ (all_190_4 = 0) & permut_sub2(int, all_105_4, 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | all_105_2, all_86_7, $sum(all_86_10, 1)) = 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | all_190_4 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (43), (1811), (1966) are inconsistent by sub-proof 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | #68. 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | End of split 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | 205.00/127.30 | | | | | | | | | | | | | | | | | | | | Case 2: 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | (1967) ~ (all_171_1 = 0) & array_eq_sub1(int, all_103_4, 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | all_103_2, 0, all_86_11) = all_171_1 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (1823), (1967) are inconsistent by sub-proof 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | #81. 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | 205.00/127.30 | | | | | | | | | | | | | | | | | | | | End of split 205.00/127.30 | | | | | | | | | | | | | | | | | | | | 205.00/127.30 | | | | | | | | | | | | | | | | | | | Case 2: 205.00/127.30 | | | | | | | | | | | | | | | | | | | | 205.00/127.30 | | | | | | | | | | | | | | | | | | | | (1968) ~ (all_170_1 = 0) & array_eq_sub1(int, all_103_2, 205.00/127.30 | | | | | | | | | | | | | | | | | | | | all_105_4, 0, all_86_11) = all_170_1 205.00/127.30 | | | | | | | | | | | | | | | | | | | | 205.00/127.30 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (398), (1968) are inconsistent by sub-proof 205.00/127.30 | | | | | | | | | | | | | | | | | | | | #48. 205.00/127.30 | | | | | | | | | | | | | | | | | | | | 205.00/127.30 | | | | | | | | | | | | | | | | | | | End of split 205.00/127.30 | | | | | | | | | | | | | | | | | | | 205.00/127.30 | | | | | | | | | | | | | | | | | | Case 2: 205.00/127.30 | | | | | | | | | | | | | | | | | | | 205.00/127.30 | | | | | | | | | | | | | | | | | | | (1969) length1(int, all_103_4) = all_215_1 & ( ~ 205.00/127.30 | | | | | | | | | | | | | | | | | | | ($lesseq(all_86_11, all_215_1)) | ~ ($lesseq(0, 205.00/127.30 | | | | | | | | | | | | | | | | | | | all_215_1)) | ( ~ (all_215_0 = all_215_1) & 205.00/127.30 | | | | | | | | | | | | | | | | | | | length1(int, all_103_2) = all_215_0)) 205.00/127.30 | | | | | | | | | | | | | | | | | | | 205.00/127.30 | | | | | | | | | | | | | | | | | | | ALPHA: (1969) implies: 205.00/127.30 | | | | | | | | | | | | | | | | | | | (1970) length1(int, all_103_4) = all_215_1 205.00/127.30 | | | | | | | | | | | | | | | | | | | (1971) ~ ($lesseq(all_86_11, all_215_1)) | ~ 205.00/127.30 | | | | | | | | | | | | | | | | | | | ($lesseq(0, all_215_1)) | ( ~ (all_215_0 = 205.00/127.30 | | | | | | | | | | | | | | | | | | | all_215_1) & length1(int, all_103_2) = 205.00/127.30 | | | | | | | | | | | | | | | | | | | all_215_0) 205.00/127.30 | | | | | | | | | | | | | | | | | | | 205.00/127.30 | | | | | | | | | | | | | | | | | | | BETA: splitting (271) gives: 205.00/127.30 | | | | | | | | | | | | | | | | | | | 205.00/127.30 | | | | | | | | | | | | | | | | | | | Case 1: 205.00/127.30 | | | | | | | | | | | | | | | | | | | | 205.00/127.30 | | | | | | | | | | | | | | | | | | | | (1972) all_170_0 = all_170_1 & $lesseq(all_86_11, 205.00/127.30 | | | | | | | | | | | | | | | | | | | | all_170_1) & $lesseq(0, all_170_1) & $lesseq(0, 205.00/127.30 | | | | | | | | | | | | | | | | | | | | all_86_11) & length1(int, all_105_4) = all_170_1 205.00/127.30 | | | | | | | | | | | | | | | | | | | | & length1(int, all_103_2) = all_170_1 205.00/127.30 | | | | | | | | | | | | | | | | | | | | 205.00/127.30 | | | | | | | | | | | | | | | | | | | | ALPHA: (1972) implies: 205.00/127.30 | | | | | | | | | | | | | | | | | | | | (1973) length1(int, all_103_2) = all_170_1 205.00/127.30 | | | | | | | | | | | | | | | | | | | | (1974) length1(int, all_105_4) = all_170_1 205.00/127.30 | | | | | | | | | | | | | | | | | | | | 205.00/127.30 | | | | | | | | | | | | | | | | | | | | BETA: splitting (295) gives: 205.00/127.30 | | | | | | | | | | | | | | | | | | | | 205.00/127.30 | | | | | | | | | | | | | | | | | | | | Case 1: 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | (1975) all_190_0 = 0 & all_190_1 = 0 & map_eq_sub1(int, 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | all_190_4, all_190_3, $sum(all_86_10, 1), 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | all_190_2) = 0 & map_eq_sub1(int, all_190_4, 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | all_190_3, 0, all_86_7) = 0 & length1(int, 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | all_105_4) = all_190_2 & elts(int, all_105_2) = 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | all_190_3 & elts(int, all_105_4) = all_190_4 & 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | in_uni(all_190_3) & in_uni(all_190_4) 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | ALPHA: (1975) implies: 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | (1976) length1(int, all_105_4) = all_190_2 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (324) gives: 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | Case 1: 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | (1977) all_219_1 = 0 & array_eq_sub1(int, all_105_4, 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | all_105_2, 0, all_86_7) = 0 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1977) implies: 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | (1978) array_eq_sub1(int, all_105_4, all_105_2, 0, 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | all_86_7) = 0 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (270) gives: 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | Case 1: 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | (1979) all_169_0 = all_169_1 & $lesseq(all_86_7, 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | all_169_1) & $lesseq(0, all_169_1) & $lesseq(0, 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | all_86_7) & length1(int, all_105_2) = all_169_1 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | & length1(int, all_105_4) = all_169_1 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1979) implies: 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | (1980) length1(int, all_105_4) = all_169_1 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (345) gives: 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | Case 1: 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | (1981) all_242_1 = 0 & array_eq_sub1(int, all_103_2, 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, $sum(all_86_8, 1), all_86_13) = 0 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1981) implies: 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | (1982) array_eq_sub1(int, all_103_2, all_105_4, 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | $sum(all_86_8, 1), all_86_13) = 0 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (269) gives: 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | (1983) all_168_0 = all_168_1 & $lesseq(1, 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | $difference(all_168_1, all_86_8)) & 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | $lesseq(all_86_13, all_168_1) & $lesseq(-1, 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | all_86_8) & $lesseq(0, all_86_13) & length1(int, 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4) = all_168_1 & length1(int, all_103_2) 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | = all_168_1 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1983) implies: 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | (1984) length1(int, all_105_4) = all_168_1 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_190_2, all_170_1, 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (1974), (1976) 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | (1985) all_190_2 = all_170_1 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_86_13, all_169_1, 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (180), (1980) 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | (1986) all_169_1 = all_86_13 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_170_1, all_169_1, 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (1974), (1980) 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | (1987) all_170_1 = all_169_1 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_190_2, all_168_1, 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (1976), (1984) 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | (1988) all_190_2 = all_168_1 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_170_1, all_153_1, 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (1820), (1974) 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | (1989) all_170_1 = all_153_1 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_177_2, all_170_1, 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (1815), (1973) 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | (1990) all_177_2 = all_170_1 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_177_2, all_156_0, 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (394), (1815) 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | (1991) all_177_2 = all_156_0 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_86_13, all_238_1, 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (183), (1808) 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | (1992) all_238_1 = all_86_13 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_238_1, all_215_1, 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (1808), (1970) 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | (1993) all_238_1 = all_215_1 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1992), (1993) imply: 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | (1994) all_215_1 = all_86_13 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1994) implies: 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | (1995) all_215_1 = all_86_13 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1985), (1988) imply: 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | (1996) all_170_1 = all_168_1 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1996) implies: 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | (1997) all_170_1 = all_168_1 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1990), (1991) imply: 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | (1998) all_170_1 = all_156_0 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1998) implies: 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | (1999) all_170_1 = all_156_0 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1989), (1997) imply: 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | (2000) all_168_1 = all_153_1 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1987), (1997) imply: 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | (2001) all_169_1 = all_168_1 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2001) implies: 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | (2002) all_169_1 = all_168_1 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1997), (1999) imply: 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | (2003) all_168_1 = all_156_0 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1986), (2002) imply: 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | (2004) all_168_1 = all_86_13 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2004) implies: 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | (2005) all_168_1 = all_86_13 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2000), (2005) imply: 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | (2006) all_153_1 = all_86_13 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2006) implies: 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | (2007) all_153_1 = all_86_13 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2003), (2005) imply: 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | (2008) all_156_0 = all_86_13 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2008) implies: 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | (2009) all_156_0 = all_86_13 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (48), (50), (52), (53), (394), (1819), 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | (1971), (1995), (2007), (2009) are inconsistent by 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #72. 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | (2010) ~ (all_168_1 = 0) & array_eq_sub1(int, all_103_2, 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, $sum(all_86_8, 1), all_86_13) = 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | all_168_1 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (1982), (2010) are inconsistent by sub-proof 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | #83. 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | End of split 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | Case 2: 205.00/127.30 | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | (2011) length1(int, all_103_2) = all_242_1 & ( ~ 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | ($lesseq(1, $difference(all_242_1, all_86_8))) | 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | ~ ($lesseq(all_86_13, all_242_1)) | ( ~ 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | (all_242_0 = all_242_1) & length1(int, 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | all_105_4) = all_242_0)) 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2011) implies: 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | (2012) length1(int, all_103_2) = all_242_1 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (48), (50), (52), (53), (183), (184), (394), 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | (1808), (1815), (1819), (1820), (1970), (1971), 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | (1973), (1974), (1980), (2012) are inconsistent by 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #22. 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | End of split 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | Case 2: 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | (2013) ~ (all_169_1 = 0) & array_eq_sub1(int, all_105_4, 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | all_105_2, 0, all_86_7) = all_169_1 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (1978), (2013) are inconsistent by sub-proof 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | #75. 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | End of split 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | Case 2: 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | (2014) length1(int, all_105_4) = all_219_1 & ( ~ 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | ($lesseq(all_86_7, all_219_1)) | ~ ($lesseq(0, 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | all_219_1)) | ( ~ (all_219_0 = all_219_1) & 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | length1(int, all_105_2) = all_219_0)) 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2014) implies: 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | (2015) length1(int, all_105_4) = all_219_1 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (345) gives: 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | Case 1: 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | (2016) all_242_1 = 0 & array_eq_sub1(int, all_103_2, 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | all_105_4, $sum(all_86_8, 1), all_86_13) = 0 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2016) implies: 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | (2017) array_eq_sub1(int, all_103_2, all_105_4, 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | $sum(all_86_8, 1), all_86_13) = 0 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (269) gives: 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | Case 1: 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | (2018) all_168_0 = all_168_1 & $lesseq(1, 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | $difference(all_168_1, all_86_8)) & 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | $lesseq(all_86_13, all_168_1) & $lesseq(-1, 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | all_86_8) & $lesseq(0, all_86_13) & length1(int, 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | all_105_4) = all_168_1 & length1(int, all_103_2) 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | = all_168_1 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2018) implies: 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | (2019) length1(int, all_105_4) = all_168_1 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_219_1, all_170_1, 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (1974), (2015) 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | (2020) all_219_1 = all_170_1 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_190_2, all_170_1, 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (1974), (1976) 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | (2021) all_190_2 = all_170_1 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_190_2, all_168_1, 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (1976), (2019) 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | (2022) all_190_2 = all_168_1 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_219_1, all_153_1, 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (1820), (2015) 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | (2023) all_219_1 = all_153_1 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_86_13, all_177_2, 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (184), (1815) 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | (2024) all_177_2 = all_86_13 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_177_2, all_156_0, 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (394), (1815) 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | (2025) all_177_2 = all_156_0 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_170_1, all_156_0, 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (394), (1973) 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | (2026) all_170_1 = all_156_0 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_86_13, all_238_1, 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (183), (1808) 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | (2027) all_238_1 = all_86_13 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_238_1, all_215_1, 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (1808), (1970) 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | (2028) all_238_1 = all_215_1 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2027), (2028) imply: 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | (2029) all_215_1 = all_86_13 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2020), (2023) imply: 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | (2030) all_170_1 = all_153_1 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2030) implies: 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | (2031) all_170_1 = all_153_1 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2021), (2022) imply: 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | (2032) all_170_1 = all_168_1 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2032) implies: 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | (2033) all_170_1 = all_168_1 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2024), (2025) imply: 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | (2034) all_156_0 = all_86_13 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2034) implies: 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | (2035) all_156_0 = all_86_13 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2026), (2033) imply: 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | (2036) all_168_1 = all_156_0 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2031), (2033) imply: 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | (2037) all_168_1 = all_153_1 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2036), (2037) imply: 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | (2038) all_156_0 = all_153_1 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (48), (50), (52), (53), (394), (1819), 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | (1971), (2029), (2035), (2038) are inconsistent by 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #33. 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | Case 2: 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | (2039) ~ (all_168_1 = 0) & array_eq_sub1(int, all_103_2, 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, $sum(all_86_8, 1), all_86_13) = 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | all_168_1 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (2017), (2039) are inconsistent by sub-proof 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | #83. 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | End of split 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | Case 2: 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | (2040) length1(int, all_103_2) = all_242_1 & ( ~ 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | ($lesseq(1, $difference(all_242_1, all_86_8))) | 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | ~ ($lesseq(all_86_13, all_242_1)) | ( ~ 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | (all_242_0 = all_242_1) & length1(int, 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | all_105_4) = all_242_0)) 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2040) implies: 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | (2041) length1(int, all_103_2) = all_242_1 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | (2042) ~ ($lesseq(1, $difference(all_242_1, all_86_8))) 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | | ~ ($lesseq(all_86_13, all_242_1)) | ( ~ 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | (all_242_0 = all_242_1) & length1(int, 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | all_105_4) = all_242_0) 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_219_1, all_190_2, 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (1976), (2015) 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | gives: 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | (2043) all_219_1 = all_190_2 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_219_1, all_170_1, 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (1974), (2015) 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | gives: 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | (2044) all_219_1 = all_170_1 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_190_2, all_153_1, 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (1820), (1976) 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | gives: 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | (2045) all_190_2 = all_153_1 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_86_13, all_242_1, 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (184), (2041) 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | gives: 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | (2046) all_242_1 = all_86_13 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_242_1, all_177_2, 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (1815), (2041) 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | gives: 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | (2047) all_242_1 = all_177_2 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_177_2, all_170_1, 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (1815), (1973) 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | gives: 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | (2048) all_177_2 = all_170_1 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_242_1, all_156_0, 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (394), (2041) 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | gives: 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | (2049) all_242_1 = all_156_0 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2046), (2049) imply: 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | (2050) all_156_0 = all_86_13 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2047), (2049) imply: 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | (2051) all_177_2 = all_156_0 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2051) implies: 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | (2052) all_177_2 = all_156_0 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2043), (2044) imply: 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | (2053) all_190_2 = all_170_1 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2053) implies: 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | (2054) all_190_2 = all_170_1 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2045), (2054) imply: 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | (2055) all_170_1 = all_153_1 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2055) implies: 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | (2056) all_170_1 = all_153_1 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2048), (2052) imply: 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | (2057) all_170_1 = all_156_0 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2056), (2057) imply: 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | (2058) all_156_0 = all_153_1 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2058) implies: 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | (2059) all_156_0 = all_153_1 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2050), (2059) imply: 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | (2060) all_153_1 = all_86_13 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2060) implies: 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | (2061) all_153_1 = all_86_13 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (52), (180), (389), (2042), (2046) are 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #77. 205.00/127.31 | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | | End of split 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | | 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | End of split 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | 205.00/127.32 | | | | | | | | | | | | | | | | | | | | Case 2: 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | (2062) ~ (all_190_4 = 0) & permut_sub2(int, all_105_4, 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | all_105_2, all_86_7, $sum(all_86_10, 1)) = 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | all_190_4 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (43), (1811), (2062) are inconsistent by sub-proof 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | #68. 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | 205.00/127.32 | | | | | | | | | | | | | | | | | | | | End of split 205.00/127.32 | | | | | | | | | | | | | | | | | | | | 205.00/127.32 | | | | | | | | | | | | | | | | | | | Case 2: 205.00/127.32 | | | | | | | | | | | | | | | | | | | | 205.00/127.32 | | | | | | | | | | | | | | | | | | | | (2063) ~ (all_170_1 = 0) & array_eq_sub1(int, all_103_2, 205.00/127.32 | | | | | | | | | | | | | | | | | | | | all_105_4, 0, all_86_11) = all_170_1 205.00/127.32 | | | | | | | | | | | | | | | | | | | | 205.00/127.32 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (398), (2063) are inconsistent by sub-proof 205.00/127.32 | | | | | | | | | | | | | | | | | | | | #48. 205.00/127.32 | | | | | | | | | | | | | | | | | | | | 205.00/127.32 | | | | | | | | | | | | | | | | | | | End of split 205.00/127.32 | | | | | | | | | | | | | | | | | | | 205.00/127.32 | | | | | | | | | | | | | | | | | | End of split 205.00/127.32 | | | | | | | | | | | | | | | | | | 205.00/127.32 | | | | | | | | | | | | | | | | | Case 2: 205.00/127.32 | | | | | | | | | | | | | | | | | | 205.00/127.32 | | | | | | | | | | | | | | | | | | (2064) ~ (all_153_1 = 0) & array_eq_sub1(int, all_105_4, 205.00/127.32 | | | | | | | | | | | | | | | | | | all_105_2, $sum(all_86_10, 1), all_86_13) = 205.00/127.32 | | | | | | | | | | | | | | | | | | all_153_1 205.00/127.32 | | | | | | | | | | | | | | | | | | 205.00/127.32 | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (1817), (2064) are inconsistent by sub-proof 205.00/127.32 | | | | | | | | | | | | | | | | | | #54. 205.00/127.32 | | | | | | | | | | | | | | | | | | 205.00/127.32 | | | | | | | | | | | | | | | | | End of split 205.00/127.32 | | | | | | | | | | | | | | | | | 205.00/127.32 | | | | | | | | | | | | | | | | Case 2: 205.00/127.32 | | | | | | | | | | | | | | | | | 205.00/127.32 | | | | | | | | | | | | | | | | | (2065) length1(int, all_105_4) = all_234_1 & ( ~ 205.00/127.32 | | | | | | | | | | | | | | | | | ($lesseq(1, $difference(all_234_1, all_86_10))) 205.00/127.32 | | | | | | | | | | | | | | | | | | ~ ($lesseq(all_86_13, all_234_1)) | ( ~ 205.00/127.32 | | | | | | | | | | | | | | | | | (all_234_0 = all_234_1) & length1(int, 205.00/127.32 | | | | | | | | | | | | | | | | | all_105_2) = all_234_0)) 205.00/127.32 | | | | | | | | | | | | | | | | | 205.00/127.32 | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (43), (45), (49), (180), (181), (184), 205.00/127.32 | | | | | | | | | | | | | | | | | (270), (271), (295), (324), (398), (1811), (2065) 205.00/127.32 | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #21. 205.00/127.32 | | | | | | | | | | | | | | | | | 205.00/127.32 | | | | | | | | | | | | | | | | End of split 205.00/127.32 | | | | | | | | | | | | | | | | 205.00/127.32 | | | | | | | | | | | | | | | Case 2: 205.00/127.32 | | | | | | | | | | | | | | | | 205.00/127.32 | | | | | | | | | | | | | | | | (2066) ~ (all_177_4 = 0) & permut_sub2(int, all_103_2, 205.00/127.32 | | | | | | | | | | | | | | | | all_105_4, all_86_11, $sum(all_86_8, 1)) = 205.00/127.32 | | | | | | | | | | | | | | | | all_177_4 205.00/127.32 | | | | | | | | | | | | | | | | 205.00/127.32 | | | | | | | | | | | | | | | | REF_CLOSE: (43), (1813), (2066) are inconsistent by sub-proof 205.00/127.32 | | | | | | | | | | | | | | | | #47. 205.00/127.32 | | | | | | | | | | | | | | | | 205.00/127.32 | | | | | | | | | | | | | | | End of split 205.00/127.32 | | | | | | | | | | | | | | | 205.00/127.32 | | | | | | | | | | | | | | Case 2: 205.00/127.32 | | | | | | | | | | | | | | | 205.00/127.32 | | | | | | | | | | | | | | | (2067) elts(int, all_105_4) = all_181_2 & elts(int, 205.00/127.32 | | | | | | | | | | | | | | | all_103_2) = all_181_3 & in_uni(all_181_2) & 205.00/127.32 | | | | | | | | | | | | | | | in_uni(all_181_3) & (( ~ (all_181_0 = 0) & 205.00/127.32 | | | | | | | | | | | | | | | map_eq_sub1(int, all_181_3, all_181_2, 205.00/127.32 | | | | | | | | | | | | | | | $sum(all_86_8, 1), all_181_1) = all_181_0 & 205.00/127.32 | | | | | | | | | | | | | | | length1(int, all_103_2) = all_181_1) | ( ~ 205.00/127.32 | | | | | | | | | | | | | | | (all_181_1 = 0) & map_eq_sub1(int, all_181_3, 205.00/127.32 | | | | | | | | | | | | | | | all_181_2, 0, all_86_11) = all_181_1)) 205.00/127.32 | | | | | | | | | | | | | | | 205.00/127.32 | | | | | | | | | | | | | | | ALPHA: (2067) implies: 205.00/127.32 | | | | | | | | | | | | | | | (2068) elts(int, all_103_2) = all_181_3 205.00/127.32 | | | | | | | | | | | | | | | (2069) elts(int, all_105_4) = all_181_2 205.00/127.32 | | | | | | | | | | | | | | | (2070) ( ~ (all_181_0 = 0) & map_eq_sub1(int, all_181_3, 205.00/127.32 | | | | | | | | | | | | | | | all_181_2, $sum(all_86_8, 1), all_181_1) = 205.00/127.32 | | | | | | | | | | | | | | | all_181_0 & length1(int, all_103_2) = all_181_1) 205.00/127.32 | | | | | | | | | | | | | | | | ( ~ (all_181_1 = 0) & map_eq_sub1(int, 205.00/127.32 | | | | | | | | | | | | | | | all_181_3, all_181_2, 0, all_86_11) = 205.00/127.32 | | | | | | | | | | | | | | | all_181_1) 205.00/127.32 | | | | | | | | | | | | | | | 205.00/127.32 | | | | | | | | | | | | | | | BETA: splitting (337) gives: 205.00/127.32 | | | | | | | | | | | | | | | 205.00/127.32 | | | | | | | | | | | | | | | Case 1: 205.00/127.32 | | | | | | | | | | | | | | | | 205.00/127.32 | | | | | | | | | | | | | | | | (2071) all_234_1 = 0 & array_eq_sub1(int, all_105_4, 205.00/127.32 | | | | | | | | | | | | | | | | all_105_2, $sum(all_86_10, 1), all_86_13) = 0 205.00/127.32 | | | | | | | | | | | | | | | | 205.00/127.32 | | | | | | | | | | | | | | | | ALPHA: (2071) implies: 205.00/127.32 | | | | | | | | | | | | | | | | (2072) array_eq_sub1(int, all_105_4, all_105_2, 205.00/127.32 | | | | | | | | | | | | | | | | $sum(all_86_10, 1), all_86_13) = 0 205.00/127.32 | | | | | | | | | | | | | | | | 205.00/127.32 | | | | | | | | | | | | | | | | BETA: splitting (255) gives: 205.00/127.32 | | | | | | | | | | | | | | | | 205.00/127.32 | | | | | | | | | | | | | | | | Case 1: 205.00/127.32 | | | | | | | | | | | | | | | | | 205.00/127.32 | | | | | | | | | | | | | | | | | (2073) all_153_0 = all_153_1 & $lesseq(1, 205.00/127.32 | | | | | | | | | | | | | | | | | $difference(all_153_1, all_86_10)) & 205.00/127.32 | | | | | | | | | | | | | | | | | $lesseq(all_86_13, all_153_1) & $lesseq(-1, 205.00/127.32 | | | | | | | | | | | | | | | | | all_86_10) & $lesseq(0, all_86_13) & 205.00/127.32 | | | | | | | | | | | | | | | | | length1(int, all_105_2) = all_153_1 & length1(int, 205.00/127.32 | | | | | | | | | | | | | | | | | all_105_4) = all_153_1 205.00/127.32 | | | | | | | | | | | | | | | | | 205.00/127.32 | | | | | | | | | | | | | | | | | ALPHA: (2073) implies: 205.00/127.32 | | | | | | | | | | | | | | | | | (2074) $lesseq(1, $difference(all_153_1, all_86_10)) 205.00/127.32 | | | | | | | | | | | | | | | | | (2075) length1(int, all_105_4) = all_153_1 205.00/127.32 | | | | | | | | | | | | | | | | | (2076) length1(int, all_105_2) = all_153_1 205.00/127.32 | | | | | | | | | | | | | | | | | 205.00/127.32 | | | | | | | | | | | | | | | | | BETA: splitting (319) gives: 205.00/127.32 | | | | | | | | | | | | | | | | | 205.00/127.32 | | | | | | | | | | | | | | | | | Case 1: 205.00/127.32 | | | | | | | | | | | | | | | | | | 205.00/127.32 | | | | | | | | | | | | | | | | | | (2077) all_215_1 = 0 & array_eq_sub1(int, all_103_4, 205.00/127.32 | | | | | | | | | | | | | | | | | | all_103_2, 0, all_86_11) = 0 205.00/127.32 | | | | | | | | | | | | | | | | | | 205.00/127.32 | | | | | | | | | | | | | | | | | | ALPHA: (2077) implies: 205.00/127.32 | | | | | | | | | | | | | | | | | | (2078) array_eq_sub1(int, all_103_4, all_103_2, 0, 205.00/127.32 | | | | | | | | | | | | | | | | | | all_86_11) = 0 205.00/127.32 | | | | | | | | | | | | | | | | | | 205.00/127.32 | | | | | | | | | | | | | | | | | | BETA: splitting (271) gives: 205.00/127.32 | | | | | | | | | | | | | | | | | | 205.00/127.32 | | | | | | | | | | | | | | | | | | Case 1: 205.00/127.32 | | | | | | | | | | | | | | | | | | | 205.00/127.32 | | | | | | | | | | | | | | | | | | | (2079) all_170_0 = all_170_1 & $lesseq(all_86_11, 205.00/127.32 | | | | | | | | | | | | | | | | | | | all_170_1) & $lesseq(0, all_170_1) & $lesseq(0, 205.00/127.32 | | | | | | | | | | | | | | | | | | | all_86_11) & length1(int, all_105_4) = all_170_1 205.00/127.32 | | | | | | | | | | | | | | | | | | | & length1(int, all_103_2) = all_170_1 205.00/127.32 | | | | | | | | | | | | | | | | | | | 205.00/127.32 | | | | | | | | | | | | | | | | | | | ALPHA: (2079) implies: 205.00/127.32 | | | | | | | | | | | | | | | | | | | (2080) length1(int, all_103_2) = all_170_1 205.00/127.32 | | | | | | | | | | | | | | | | | | | (2081) length1(int, all_105_4) = all_170_1 205.00/127.32 | | | | | | | | | | | | | | | | | | | 205.00/127.32 | | | | | | | | | | | | | | | | | | | BETA: splitting (272) gives: 205.00/127.32 | | | | | | | | | | | | | | | | | | | 205.00/127.32 | | | | | | | | | | | | | | | | | | | Case 1: 205.00/127.32 | | | | | | | | | | | | | | | | | | | | 205.00/127.32 | | | | | | | | | | | | | | | | | | | | (2082) all_171_0 = all_171_1 & $lesseq(all_86_11, 205.00/127.32 | | | | | | | | | | | | | | | | | | | | all_171_1) & $lesseq(0, all_171_1) & $lesseq(0, 205.00/127.32 | | | | | | | | | | | | | | | | | | | | all_86_11) & length1(int, all_103_2) = all_171_1 205.00/127.32 | | | | | | | | | | | | | | | | | | | | & length1(int, all_103_4) = all_171_1 205.00/127.32 | | | | | | | | | | | | | | | | | | | | 205.00/127.32 | | | | | | | | | | | | | | | | | | | | ALPHA: (2082) implies: 205.00/127.32 | | | | | | | | | | | | | | | | | | | | (2083) length1(int, all_103_4) = all_171_1 205.00/127.32 | | | | | | | | | | | | | | | | | | | | (2084) length1(int, all_103_2) = all_171_1 205.00/127.32 | | | | | | | | | | | | | | | | | | | | 205.00/127.32 | | | | | | | | | | | | | | | | | | | | BETA: splitting (295) gives: 205.00/127.32 | | | | | | | | | | | | | | | | | | | | 205.00/127.32 | | | | | | | | | | | | | | | | | | | | Case 1: 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | (2085) all_190_0 = 0 & all_190_1 = 0 & map_eq_sub1(int, 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | all_190_4, all_190_3, $sum(all_86_10, 1), 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | all_190_2) = 0 & map_eq_sub1(int, all_190_4, 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | all_190_3, 0, all_86_7) = 0 & length1(int, 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | all_105_4) = all_190_2 & elts(int, all_105_2) = 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | all_190_3 & elts(int, all_105_4) = all_190_4 & 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | in_uni(all_190_3) & in_uni(all_190_4) 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | ALPHA: (2085) implies: 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | (2086) elts(int, all_105_4) = all_190_4 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | (2087) length1(int, all_105_4) = all_190_2 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (296) gives: 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | Case 1: 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | | 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | | (2088) all_191_3 = 0 & permut_sub2(int, all_103_4, 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | | all_103_2, all_86_11, $sum(all_86_10, 1)) = 0 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | | 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2088) implies: 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | | (2089) permut_sub2(int, all_103_4, all_103_2, all_86_11, 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | | $sum(all_86_10, 1)) = 0 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | | 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (297) gives: 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | | 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | | Case 1: 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | | | (2090) all_192_0 = 0 & all_192_1 = 0 & map_eq_sub1(int, 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | | | all_192_4, all_192_3, $sum(all_86_10, 1), 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | | | all_192_2) = 0 & map_eq_sub1(int, all_192_4, 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | | | all_192_3, 0, all_86_11) = 0 & length1(int, 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | | | all_103_4) = all_192_2 & elts(int, all_103_2) = 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | | | all_192_3 & elts(int, all_103_4) = all_192_4 & 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | | | in_uni(all_192_3) & in_uni(all_192_4) 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2090) implies: 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | | | (2091) elts(int, all_103_2) = all_192_3 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | | | (2092) length1(int, all_103_4) = all_192_2 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (324) gives: 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | | | Case 1: 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | | | | (2093) all_219_1 = 0 & array_eq_sub1(int, all_105_4, 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | | | | all_105_2, 0, all_86_7) = 0 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2093) implies: 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | | | | (2094) array_eq_sub1(int, all_105_4, all_105_2, 0, 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | | | | all_86_7) = 0 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (270) gives: 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | | | | | (2095) all_169_0 = all_169_1 & $lesseq(all_86_7, 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | | | | | all_169_1) & $lesseq(0, all_169_1) & $lesseq(0, 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | | | | | all_86_7) & length1(int, all_105_2) = all_169_1 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | | | | | & length1(int, all_105_4) = all_169_1 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2095) implies: 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | | | | | (2096) length1(int, all_105_4) = all_169_1 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (345) gives: 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (2097) all_242_1 = 0 & array_eq_sub1(int, all_103_2, 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, $sum(all_86_8, 1), all_86_13) = 0 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2097) implies: 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (2098) array_eq_sub1(int, all_103_2, all_105_4, 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | | | | | | $sum(all_86_8, 1), all_86_13) = 0 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (39), (44), (45), (91), (99), (180), (203), 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (263), (269), (394), (395), (396), (2068), (2069), 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (2070), (2080), (2084), (2086), (2087), (2091), 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (2096), (2098) are inconsistent by sub-proof #45. 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (2099) length1(int, all_103_2) = all_242_1 & ( ~ 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | | | | | | ($lesseq(1, $difference(all_242_1, all_86_8))) | 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | | | | | | ~ ($lesseq(all_86_13, all_242_1)) | ( ~ 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_242_0 = all_242_1) & length1(int, 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4) = all_242_0)) 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2099) implies: 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (2100) length1(int, all_103_2) = all_242_1 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (39), (44), (91), (99), (180), (203), (263), 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (394), (395), (396), (2068), (2069), (2070), 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (2080), (2081), (2086), (2087), (2091), (2096), 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (2100) are inconsistent by sub-proof #40. 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | | | | | End of split 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | | | | | (2101) ~ (all_169_1 = 0) & array_eq_sub1(int, all_105_4, 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | | | | | all_105_2, 0, all_86_7) = all_169_1 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (2094), (2101) are inconsistent by sub-proof 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | | | | | #75. 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | | | | End of split 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | | | Case 2: 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | | | | (2102) length1(int, all_105_4) = all_219_1 & ( ~ 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | | | | ($lesseq(all_86_7, all_219_1)) | ~ ($lesseq(0, 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | | | | all_219_1)) | ( ~ (all_219_0 = all_219_1) & 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | | | | length1(int, all_105_2) = all_219_0)) 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2102) implies: 205.00/127.32 | | | | | | | | | | | | | | | | | | | | | | | | (2103) length1(int, all_105_4) = all_219_1 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | (2104) ~ ($lesseq(all_86_7, all_219_1)) | ~ ($lesseq(0, 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | all_219_1)) | ( ~ (all_219_0 = all_219_1) & 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | length1(int, all_105_2) = all_219_0) 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (345) gives: 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | (2105) all_242_1 = 0 & array_eq_sub1(int, all_103_2, 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, $sum(all_86_8, 1), all_86_13) = 0 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2105) implies: 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | (2106) array_eq_sub1(int, all_103_2, all_105_4, 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | $sum(all_86_8, 1), all_86_13) = 0 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (269) gives: 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | (2107) all_168_0 = all_168_1 & $lesseq(1, 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | $difference(all_168_1, all_86_8)) & 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | $lesseq(all_86_13, all_168_1) & $lesseq(-1, 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | all_86_8) & $lesseq(0, all_86_13) & length1(int, 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4) = all_168_1 & length1(int, all_103_2) 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | = all_168_1 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2107) implies: 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | (2108) length1(int, all_103_2) = all_168_1 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | (2109) length1(int, all_105_4) = all_168_1 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_219_1, all_190_2, 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (2087), (2103) 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | (2110) all_219_1 = all_190_2 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_190_2, all_168_1, 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (2087), (2109) 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | (2111) all_190_2 = all_168_1 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_219_1, all_153_1, 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (2075), (2103) 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | (2112) all_219_1 = all_153_1 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_171_1, all_170_1, 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (2080), (2084) 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | (2113) all_171_1 = all_170_1 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_170_1, all_156_0, 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (394), (2080) 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | (2114) all_170_1 = all_156_0 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_168_1, all_156_0, 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (394), (2108) 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | (2115) all_168_1 = all_156_0 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_86_13, all_238_1, 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (183), (1808) 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | (2116) all_238_1 = all_86_13 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_238_1, all_192_2, 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (1808), (2092) 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | (2117) all_238_1 = all_192_2 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_238_1, all_171_1, 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (1808), (2083) 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | (2118) all_238_1 = all_171_1 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2116), (2117) imply: 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | (2119) all_192_2 = all_86_13 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2117), (2118) imply: 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | (2120) all_192_2 = all_171_1 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2110), (2112) imply: 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | (2121) all_190_2 = all_153_1 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2121) implies: 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | (2122) all_190_2 = all_153_1 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2119), (2120) imply: 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | (2123) all_171_1 = all_86_13 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2111), (2122) imply: 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | (2124) all_168_1 = all_153_1 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2113), (2123) imply: 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | (2125) all_170_1 = all_86_13 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2125) implies: 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | (2126) all_170_1 = all_86_13 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2114), (2126) imply: 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | (2127) all_156_0 = all_86_13 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2127) implies: 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | (2128) all_156_0 = all_86_13 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2115), (2124) imply: 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | (2129) all_156_0 = all_153_1 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2129) implies: 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | (2130) all_156_0 = all_153_1 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2128), (2130) imply: 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | (2131) all_153_1 = all_86_13 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2131) implies: 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | (2132) all_153_1 = all_86_13 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (48), (50), (52), (53), (389), (2074), 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | (2076), (2104), (2112), (2132) are inconsistent by 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #58. 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | (2133) ~ (all_168_1 = 0) & array_eq_sub1(int, all_103_2, 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, $sum(all_86_8, 1), all_86_13) = 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | all_168_1 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (2106), (2133) are inconsistent by sub-proof 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | #83. 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | End of split 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | (2134) length1(int, all_103_2) = all_242_1 & ( ~ 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | ($lesseq(1, $difference(all_242_1, all_86_8))) | 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | ~ ($lesseq(all_86_13, all_242_1)) | ( ~ 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | (all_242_0 = all_242_1) & length1(int, 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4) = all_242_0)) 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2134) implies: 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | (2135) length1(int, all_103_2) = all_242_1 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_219_1, all_190_2, 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (2087), (2103) 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | (2136) all_219_1 = all_190_2 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_190_2, all_170_1, 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (2081), (2087) 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | (2137) all_190_2 = all_170_1 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_219_1, all_153_1, 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (2075), (2103) 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | (2138) all_219_1 = all_153_1 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_242_1, all_171_1, 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (2084), (2135) 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | (2139) all_242_1 = all_171_1 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_242_1, all_170_1, 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (2080), (2135) 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | (2140) all_242_1 = all_170_1 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_242_1, all_156_0, 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (394), (2135) 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | (2141) all_242_1 = all_156_0 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_86_13, all_238_1, 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (183), (1808) 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | (2142) all_238_1 = all_86_13 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_238_1, all_192_2, 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (1808), (2092) 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | (2143) all_238_1 = all_192_2 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_192_2, all_171_1, 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (2083), (2092) 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | (2144) all_192_2 = all_171_1 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2140), (2141) imply: 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | (2145) all_170_1 = all_156_0 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2145) implies: 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | (2146) all_170_1 = all_156_0 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2139), (2141) imply: 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | (2147) all_171_1 = all_156_0 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2147) implies: 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | (2148) all_171_1 = all_156_0 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2142), (2143) imply: 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | (2149) all_192_2 = all_86_13 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2149) implies: 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | (2150) all_192_2 = all_86_13 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2136), (2138) imply: 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | (2151) all_190_2 = all_153_1 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2151) implies: 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | (2152) all_190_2 = all_153_1 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2144), (2150) imply: 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | (2153) all_171_1 = all_86_13 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2153) implies: 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | (2154) all_171_1 = all_86_13 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2137), (2152) imply: 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | (2155) all_170_1 = all_153_1 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2155) implies: 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | (2156) all_170_1 = all_153_1 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2148), (2154) imply: 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | (2157) all_156_0 = all_86_13 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2157) implies: 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | (2158) all_156_0 = all_86_13 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2146), (2156) imply: 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | (2159) all_156_0 = all_153_1 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (394), (1809), (2074), (2142), (2158), 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | (2159) are inconsistent by sub-proof #20. 205.00/127.33 | | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.34 | | | | | | | | | | | | | | | | | | | | | | | | End of split 205.00/127.34 | | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.34 | | | | | | | | | | | | | | | | | | | | | | | End of split 205.00/127.34 | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.34 | | | | | | | | | | | | | | | | | | | | | | Case 2: 205.00/127.34 | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.34 | | | | | | | | | | | | | | | | | | | | | | | (2160) ~ (all_192_4 = 0) & permut_sub2(int, all_103_4, 205.00/127.34 | | | | | | | | | | | | | | | | | | | | | | | all_103_2, all_86_11, $sum(all_86_10, 1)) = 205.00/127.34 | | | | | | | | | | | | | | | | | | | | | | | all_192_4 205.00/127.34 | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.34 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (43), (2089), (2160) are inconsistent by sub-proof 205.00/127.34 | | | | | | | | | | | | | | | | | | | | | | | #69. 205.00/127.34 | | | | | | | | | | | | | | | | | | | | | | | 205.00/127.34 | | | | | | | | | | | | | | | | | | | | | | End of split 205.00/127.34 | | | | | | | | | | | | | | | | | | | | | | 205.00/127.34 | | | | | | | | | | | | | | | | | | | | | Case 2: 205.00/127.34 | | | | | | | | | | | | | | | | | | | | | | 205.25/127.34 | | | | | | | | | | | | | | | | | | | | | | (2161) elts(int, all_103_2) = all_191_2 & elts(int, 205.25/127.34 | | | | | | | | | | | | | | | | | | | | | | all_103_4) = all_191_3 & in_uni(all_191_2) & 205.25/127.34 | | | | | | | | | | | | | | | | | | | | | | in_uni(all_191_3) & (( ~ (all_191_0 = 0) & 205.25/127.34 | | | | | | | | | | | | | | | | | | | | | | map_eq_sub1(int, all_191_3, all_191_2, 205.25/127.34 | | | | | | | | | | | | | | | | | | | | | | $sum(all_86_10, 1), all_191_1) = all_191_0 & 205.25/127.34 | | | | | | | | | | | | | | | | | | | | | | length1(int, all_103_4) = all_191_1) | ( ~ 205.25/127.34 | | | | | | | | | | | | | | | | | | | | | | (all_191_1 = 0) & map_eq_sub1(int, all_191_3, 205.25/127.34 | | | | | | | | | | | | | | | | | | | | | | all_191_2, 0, all_86_11) = all_191_1)) 205.25/127.34 | | | | | | | | | | | | | | | | | | | | | | 205.25/127.34 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2161) implies: 205.25/127.34 | | | | | | | | | | | | | | | | | | | | | | (2162) elts(int, all_103_4) = all_191_3 205.25/127.34 | | | | | | | | | | | | | | | | | | | | | | (2163) elts(int, all_103_2) = all_191_2 205.25/127.34 | | | | | | | | | | | | | | | | | | | | | | (2164) ( ~ (all_191_0 = 0) & map_eq_sub1(int, all_191_3, 205.25/127.34 | | | | | | | | | | | | | | | | | | | | | | all_191_2, $sum(all_86_10, 1), all_191_1) = 205.25/127.34 | | | | | | | | | | | | | | | | | | | | | | all_191_0 & length1(int, all_103_4) = all_191_1) 205.25/127.34 | | | | | | | | | | | | | | | | | | | | | | | ( ~ (all_191_1 = 0) & map_eq_sub1(int, 205.25/127.34 | | | | | | | | | | | | | | | | | | | | | | all_191_3, all_191_2, 0, all_86_11) = 205.25/127.34 | | | | | | | | | | | | | | | | | | | | | | all_191_1) 205.25/127.34 | | | | | | | | | | | | | | | | | | | | | | 205.25/127.34 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (39), (44), (90), (91), (96), (183), (206), 205.25/127.34 | | | | | | | | | | | | | | | | | | | | | | (1808), (2083), (2162), (2163), (2164) are 205.25/127.34 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #19. 205.25/127.34 | | | | | | | | | | | | | | | | | | | | | | 205.25/127.34 | | | | | | | | | | | | | | | | | | | | | End of split 205.25/127.34 | | | | | | | | | | | | | | | | | | | | | 205.25/127.34 | | | | | | | | | | | | | | | | | | | | Case 2: 205.25/127.34 | | | | | | | | | | | | | | | | | | | | | 205.25/127.34 | | | | | | | | | | | | | | | | | | | | | (2165) ~ (all_190_4 = 0) & permut_sub2(int, all_105_4, 205.25/127.34 | | | | | | | | | | | | | | | | | | | | | all_105_2, all_86_7, $sum(all_86_10, 1)) = 205.25/127.34 | | | | | | | | | | | | | | | | | | | | | all_190_4 205.25/127.34 | | | | | | | | | | | | | | | | | | | | | 205.25/127.34 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (43), (1811), (2165) are inconsistent by sub-proof 205.25/127.34 | | | | | | | | | | | | | | | | | | | | | #68. 205.25/127.34 | | | | | | | | | | | | | | | | | | | | | 205.25/127.34 | | | | | | | | | | | | | | | | | | | | End of split 205.25/127.34 | | | | | | | | | | | | | | | | | | | | 205.25/127.34 | | | | | | | | | | | | | | | | | | | Case 2: 205.25/127.34 | | | | | | | | | | | | | | | | | | | | 205.25/127.34 | | | | | | | | | | | | | | | | | | | | (2166) ~ (all_171_1 = 0) & array_eq_sub1(int, all_103_4, 205.25/127.34 | | | | | | | | | | | | | | | | | | | | all_103_2, 0, all_86_11) = all_171_1 205.25/127.34 | | | | | | | | | | | | | | | | | | | | 205.25/127.34 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (2078), (2166) are inconsistent by sub-proof 205.25/127.34 | | | | | | | | | | | | | | | | | | | | #81. 205.25/127.34 | | | | | | | | | | | | | | | | | | | | 205.25/127.34 | | | | | | | | | | | | | | | | | | | End of split 205.25/127.34 | | | | | | | | | | | | | | | | | | | 205.25/127.34 | | | | | | | | | | | | | | | | | | Case 2: 205.25/127.34 | | | | | | | | | | | | | | | | | | | 205.25/127.34 | | | | | | | | | | | | | | | | | | | (2167) ~ (all_170_1 = 0) & array_eq_sub1(int, all_103_2, 205.25/127.34 | | | | | | | | | | | | | | | | | | | all_105_4, 0, all_86_11) = all_170_1 205.25/127.34 | | | | | | | | | | | | | | | | | | | 205.25/127.34 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (398), (2167) are inconsistent by sub-proof 205.25/127.34 | | | | | | | | | | | | | | | | | | | #48. 205.25/127.34 | | | | | | | | | | | | | | | | | | | 205.25/127.34 | | | | | | | | | | | | | | | | | | End of split 205.25/127.34 | | | | | | | | | | | | | | | | | | 205.25/127.34 | | | | | | | | | | | | | | | | | Case 2: 205.25/127.34 | | | | | | | | | | | | | | | | | | 205.25/127.34 | | | | | | | | | | | | | | | | | | (2168) length1(int, all_103_4) = all_215_1 & ( ~ 205.25/127.34 | | | | | | | | | | | | | | | | | | ($lesseq(all_86_11, all_215_1)) | ~ ($lesseq(0, 205.25/127.34 | | | | | | | | | | | | | | | | | | all_215_1)) | ( ~ (all_215_0 = all_215_1) & 205.25/127.34 | | | | | | | | | | | | | | | | | | length1(int, all_103_2) = all_215_0)) 205.25/127.34 | | | | | | | | | | | | | | | | | | 205.25/127.34 | | | | | | | | | | | | | | | | | | ALPHA: (2168) implies: 205.25/127.34 | | | | | | | | | | | | | | | | | | (2169) length1(int, all_103_4) = all_215_1 205.25/127.34 | | | | | | | | | | | | | | | | | | 205.25/127.34 | | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (39), (43), (44), (90), (91), (96), (99), 205.25/127.34 | | | | | | | | | | | | | | | | | | (183), (184), (203), (206), (263), (295), (296), 205.25/127.34 | | | | | | | | | | | | | | | | | | (297), (394), (395), (396), (1808), (1811), 205.25/127.34 | | | | | | | | | | | | | | | | | | (2068), (2069), (2070), (2169) are inconsistent by 205.25/127.34 | | | | | | | | | | | | | | | | | | sub-proof #15. 205.25/127.34 | | | | | | | | | | | | | | | | | | 205.25/127.34 | | | | | | | | | | | | | | | | | End of split 205.25/127.34 | | | | | | | | | | | | | | | | | 205.25/127.34 | | | | | | | | | | | | | | | | Case 2: 205.25/127.34 | | | | | | | | | | | | | | | | | 205.25/127.34 | | | | | | | | | | | | | | | | | (2170) ~ (all_153_1 = 0) & array_eq_sub1(int, all_105_4, 205.25/127.34 | | | | | | | | | | | | | | | | | all_105_2, $sum(all_86_10, 1), all_86_13) = 205.25/127.34 | | | | | | | | | | | | | | | | | all_153_1 205.25/127.34 | | | | | | | | | | | | | | | | | 205.25/127.34 | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (2072), (2170) are inconsistent by sub-proof 205.25/127.34 | | | | | | | | | | | | | | | | | #54. 205.25/127.34 | | | | | | | | | | | | | | | | | 205.25/127.34 | | | | | | | | | | | | | | | | End of split 205.25/127.34 | | | | | | | | | | | | | | | | 205.25/127.34 | | | | | | | | | | | | | | | Case 2: 205.25/127.34 | | | | | | | | | | | | | | | | 205.25/127.34 | | | | | | | | | | | | | | | | (2171) length1(int, all_105_4) = all_234_1 & ( ~ 205.25/127.34 | | | | | | | | | | | | | | | | ($lesseq(1, $difference(all_234_1, all_86_10))) 205.25/127.34 | | | | | | | | | | | | | | | | | ~ ($lesseq(all_86_13, all_234_1)) | ( ~ 205.25/127.34 | | | | | | | | | | | | | | | | (all_234_0 = all_234_1) & length1(int, 205.25/127.34 | | | | | | | | | | | | | | | | all_105_2) = all_234_0)) 205.25/127.34 | | | | | | | | | | | | | | | | 205.25/127.34 | | | | | | | | | | | | | | | | REF_CLOSE: (39), (43), (45), (49), (180), (181), (184), 205.25/127.34 | | | | | | | | | | | | | | | | (270), (271), (295), (324), (398), (1811), (2171) 205.25/127.34 | | | | | | | | | | | | | | | | are inconsistent by sub-proof #21. 205.25/127.34 | | | | | | | | | | | | | | | | 205.25/127.34 | | | | | | | | | | | | | | | End of split 205.25/127.34 | | | | | | | | | | | | | | | 205.25/127.34 | | | | | | | | | | | | | | End of split 205.25/127.34 | | | | | | | | | | | | | | 205.25/127.34 | | | | | | | | | | | | | Case 2: 205.25/127.34 | | | | | | | | | | | | | | 205.25/127.34 | | | | | | | | | | | | | | (2172) elts(int, all_105_2) = all_187_2 & elts(int, 205.25/127.34 | | | | | | | | | | | | | | all_105_4) = all_187_3 & in_uni(all_187_2) & 205.25/127.34 | | | | | | | | | | | | | | in_uni(all_187_3) & (( ~ (all_187_0 = 0) & 205.25/127.34 | | | | | | | | | | | | | | map_eq_sub1(int, all_187_3, all_187_2, 205.25/127.34 | | | | | | | | | | | | | | $sum(all_86_10, 1), all_187_1) = all_187_0 & 205.25/127.34 | | | | | | | | | | | | | | length1(int, all_105_4) = all_187_1) | ( ~ 205.25/127.34 | | | | | | | | | | | | | | (all_187_1 = 0) & map_eq_sub1(int, all_187_3, 205.25/127.34 | | | | | | | | | | | | | | all_187_2, 0, all_86_7) = all_187_1)) 205.25/127.34 | | | | | | | | | | | | | | 205.25/127.34 | | | | | | | | | | | | | | ALPHA: (2172) implies: 205.25/127.34 | | | | | | | | | | | | | | (2173) elts(int, all_105_4) = all_187_3 205.25/127.34 | | | | | | | | | | | | | | (2174) elts(int, all_105_2) = all_187_2 205.25/127.34 | | | | | | | | | | | | | | (2175) ( ~ (all_187_0 = 0) & map_eq_sub1(int, all_187_3, 205.25/127.34 | | | | | | | | | | | | | | all_187_2, $sum(all_86_10, 1), all_187_1) = 205.25/127.34 | | | | | | | | | | | | | | all_187_0 & length1(int, all_105_4) = all_187_1) 205.25/127.34 | | | | | | | | | | | | | | | ( ~ (all_187_1 = 0) & map_eq_sub1(int, 205.25/127.34 | | | | | | | | | | | | | | all_187_3, all_187_2, 0, all_86_7) = 205.25/127.34 | | | | | | | | | | | | | | all_187_1) 205.25/127.34 | | | | | | | | | | | | | | 205.25/127.34 | | | | | | | | | | | | | | BETA: splitting (319) gives: 205.25/127.34 | | | | | | | | | | | | | | 205.25/127.34 | | | | | | | | | | | | | | Case 1: 205.25/127.34 | | | | | | | | | | | | | | | 205.25/127.34 | | | | | | | | | | | | | | | (2176) all_215_1 = 0 & array_eq_sub1(int, all_103_4, 205.25/127.34 | | | | | | | | | | | | | | | all_103_2, 0, all_86_11) = 0 205.25/127.34 | | | | | | | | | | | | | | | 205.25/127.34 | | | | | | | | | | | | | | | ALPHA: (2176) implies: 205.25/127.34 | | | | | | | | | | | | | | | (2177) array_eq_sub1(int, all_103_4, all_103_2, 0, 205.25/127.34 | | | | | | | | | | | | | | | all_86_11) = 0 205.25/127.34 | | | | | | | | | | | | | | | 205.25/127.34 | | | | | | | | | | | | | | | BETA: splitting (324) gives: 205.25/127.34 | | | | | | | | | | | | | | | 205.25/127.34 | | | | | | | | | | | | | | | Case 1: 205.25/127.34 | | | | | | | | | | | | | | | | 205.25/127.34 | | | | | | | | | | | | | | | | (2178) all_219_1 = 0 & array_eq_sub1(int, all_105_4, 205.25/127.34 | | | | | | | | | | | | | | | | all_105_2, 0, all_86_7) = 0 205.25/127.34 | | | | | | | | | | | | | | | | 205.25/127.34 | | | | | | | | | | | | | | | | ALPHA: (2178) implies: 205.25/127.34 | | | | | | | | | | | | | | | | (2179) array_eq_sub1(int, all_105_4, all_105_2, 0, 205.25/127.34 | | | | | | | | | | | | | | | | all_86_7) = 0 205.25/127.34 | | | | | | | | | | | | | | | | 205.25/127.34 | | | | | | | | | | | | | | | | BETA: splitting (337) gives: 205.25/127.34 | | | | | | | | | | | | | | | | 205.25/127.34 | | | | | | | | | | | | | | | | Case 1: 205.25/127.34 | | | | | | | | | | | | | | | | | 205.25/127.34 | | | | | | | | | | | | | | | | | (2180) all_234_1 = 0 & array_eq_sub1(int, all_105_4, 205.25/127.34 | | | | | | | | | | | | | | | | | all_105_2, $sum(all_86_10, 1), all_86_13) = 0 205.25/127.34 | | | | | | | | | | | | | | | | | 205.25/127.34 | | | | | | | | | | | | | | | | | ALPHA: (2180) implies: 205.25/127.34 | | | | | | | | | | | | | | | | | (2181) array_eq_sub1(int, all_105_4, all_105_2, 205.25/127.34 | | | | | | | | | | | | | | | | | $sum(all_86_10, 1), all_86_13) = 0 205.25/127.34 | | | | | | | | | | | | | | | | | 205.25/127.34 | | | | | | | | | | | | | | | | | BETA: splitting (345) gives: 205.25/127.34 | | | | | | | | | | | | | | | | | 205.25/127.34 | | | | | | | | | | | | | | | | | Case 1: 205.25/127.34 | | | | | | | | | | | | | | | | | | 205.25/127.34 | | | | | | | | | | | | | | | | | | (2182) all_242_1 = 0 & array_eq_sub1(int, all_103_2, 205.25/127.34 | | | | | | | | | | | | | | | | | | all_105_4, $sum(all_86_8, 1), all_86_13) = 0 205.25/127.34 | | | | | | | | | | | | | | | | | | 205.25/127.34 | | | | | | | | | | | | | | | | | | ALPHA: (2182) implies: 205.25/127.34 | | | | | | | | | | | | | | | | | | (2183) array_eq_sub1(int, all_103_2, all_105_4, 205.25/127.34 | | | | | | | | | | | | | | | | | | $sum(all_86_8, 1), all_86_13) = 0 205.25/127.34 | | | | | | | | | | | | | | | | | | 205.25/127.34 | | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (39), (44), (45), (99), (100), (105), (180), 205.25/127.34 | | | | | | | | | | | | | | | | | | (205), (255), (269), (270), (271), (394), (398), 205.25/127.34 | | | | | | | | | | | | | | | | | | (2173), (2174), (2175), (2179), (2181), (2183) are 205.25/127.34 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #14. 205.25/127.34 | | | | | | | | | | | | | | | | | | 205.25/127.34 | | | | | | | | | | | | | | | | | Case 2: 205.25/127.34 | | | | | | | | | | | | | | | | | | 205.25/127.34 | | | | | | | | | | | | | | | | | | (2184) length1(int, all_103_2) = all_242_1 & ( ~ 205.25/127.34 | | | | | | | | | | | | | | | | | | ($lesseq(1, $difference(all_242_1, all_86_8))) | 205.25/127.34 | | | | | | | | | | | | | | | | | | ~ ($lesseq(all_86_13, all_242_1)) | ( ~ 205.25/127.34 | | | | | | | | | | | | | | | | | | (all_242_0 = all_242_1) & length1(int, 205.25/127.34 | | | | | | | | | | | | | | | | | | all_105_4) = all_242_0)) 205.25/127.34 | | | | | | | | | | | | | | | | | | 205.25/127.34 | | | | | | | | | | | | | | | | | | ALPHA: (2184) implies: 205.25/127.34 | | | | | | | | | | | | | | | | | | (2185) length1(int, all_103_2) = all_242_1 205.25/127.34 | | | | | | | | | | | | | | | | | | 205.25/127.34 | | | | | | | | | | | | | | | | | | BETA: splitting (255) gives: 205.25/127.34 | | | | | | | | | | | | | | | | | | 205.25/127.34 | | | | | | | | | | | | | | | | | | Case 1: 205.25/127.34 | | | | | | | | | | | | | | | | | | | 205.25/127.34 | | | | | | | | | | | | | | | | | | | (2186) all_153_0 = all_153_1 & $lesseq(1, 205.25/127.34 | | | | | | | | | | | | | | | | | | | $difference(all_153_1, all_86_10)) & 205.25/127.34 | | | | | | | | | | | | | | | | | | | $lesseq(all_86_13, all_153_1) & $lesseq(-1, 205.25/127.34 | | | | | | | | | | | | | | | | | | | all_86_10) & $lesseq(0, all_86_13) & 205.25/127.34 | | | | | | | | | | | | | | | | | | | length1(int, all_105_2) = all_153_1 & length1(int, 205.25/127.34 | | | | | | | | | | | | | | | | | | | all_105_4) = all_153_1 205.25/127.34 | | | | | | | | | | | | | | | | | | | 205.25/127.34 | | | | | | | | | | | | | | | | | | | ALPHA: (2186) implies: 205.25/127.34 | | | | | | | | | | | | | | | | | | | (2187) length1(int, all_105_4) = all_153_1 205.25/127.34 | | | | | | | | | | | | | | | | | | | 205.25/127.34 | | | | | | | | | | | | | | | | | | | BETA: splitting (287) gives: 205.25/127.34 | | | | | | | | | | | | | | | | | | | 205.25/127.34 | | | | | | | | | | | | | | | | | | | Case 1: 205.25/127.34 | | | | | | | | | | | | | | | | | | | | 205.25/127.34 | | | | | | | | | | | | | | | | | | | | (2188) all_181_3 = 0 & permut_sub2(int, all_103_2, 205.25/127.34 | | | | | | | | | | | | | | | | | | | | all_105_4, all_86_11, $sum(all_86_8, 1)) = 0 205.25/127.34 | | | | | | | | | | | | | | | | | | | | 205.25/127.34 | | | | | | | | | | | | | | | | | | | | ALPHA: (2188) implies: 205.25/127.34 | | | | | | | | | | | | | | | | | | | | (2189) permut_sub2(int, all_103_2, all_105_4, all_86_11, 205.25/127.34 | | | | | | | | | | | | | | | | | | | | $sum(all_86_8, 1)) = 0 205.25/127.34 | | | | | | | | | | | | | | | | | | | | 205.25/127.34 | | | | | | | | | | | | | | | | | | | | BETA: splitting (280) gives: 205.25/127.34 | | | | | | | | | | | | | | | | | | | | 205.25/127.34 | | | | | | | | | | | | | | | | | | | | Case 1: 205.25/127.34 | | | | | | | | | | | | | | | | | | | | | 205.25/127.34 | | | | | | | | | | | | | | | | | | | | | (2190) all_177_0 = 0 & all_177_1 = 0 & map_eq_sub1(int, 205.25/127.34 | | | | | | | | | | | | | | | | | | | | | all_177_4, all_177_3, $sum(all_86_8, 1), 205.25/127.34 | | | | | | | | | | | | | | | | | | | | | all_177_2) = 0 & map_eq_sub1(int, all_177_4, 205.25/127.34 | | | | | | | | | | | | | | | | | | | | | all_177_3, 0, all_86_11) = 0 & length1(int, 205.25/127.34 | | | | | | | | | | | | | | | | | | | | | all_103_2) = all_177_2 & elts(int, all_105_4) = 205.25/127.34 | | | | | | | | | | | | | | | | | | | | | all_177_3 & elts(int, all_103_2) = all_177_4 & 205.25/127.34 | | | | | | | | | | | | | | | | | | | | | in_uni(all_177_3) & in_uni(all_177_4) 205.25/127.34 | | | | | | | | | | | | | | | | | | | | | 205.25/127.34 | | | | | | | | | | | | | | | | | | | | | ALPHA: (2190) implies: 205.25/127.34 | | | | | | | | | | | | | | | | | | | | | (2191) elts(int, all_105_4) = all_177_3 205.25/127.34 | | | | | | | | | | | | | | | | | | | | | (2192) length1(int, all_103_2) = all_177_2 205.25/127.34 | | | | | | | | | | | | | | | | | | | | | 205.25/127.34 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (270) gives: 205.25/127.34 | | | | | | | | | | | | | | | | | | | | | 205.25/127.34 | | | | | | | | | | | | | | | | | | | | | Case 1: 205.25/127.34 | | | | | | | | | | | | | | | | | | | | | | 205.25/127.34 | | | | | | | | | | | | | | | | | | | | | | (2193) all_169_0 = all_169_1 & $lesseq(all_86_7, 205.25/127.34 | | | | | | | | | | | | | | | | | | | | | | all_169_1) & $lesseq(0, all_169_1) & $lesseq(0, 205.25/127.34 | | | | | | | | | | | | | | | | | | | | | | all_86_7) & length1(int, all_105_2) = all_169_1 205.25/127.34 | | | | | | | | | | | | | | | | | | | | | | & length1(int, all_105_4) = all_169_1 205.25/127.34 | | | | | | | | | | | | | | | | | | | | | | 205.25/127.34 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2193) implies: 205.25/127.34 | | | | | | | | | | | | | | | | | | | | | | (2194) length1(int, all_105_4) = all_169_1 205.25/127.34 | | | | | | | | | | | | | | | | | | | | | | 205.25/127.34 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (271) gives: 205.25/127.34 | | | | | | | | | | | | | | | | | | | | | | 205.25/127.34 | | | | | | | | | | | | | | | | | | | | | | Case 1: 205.25/127.34 | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.34 | | | | | | | | | | | | | | | | | | | | | | | (2195) all_170_0 = all_170_1 & $lesseq(all_86_11, 205.25/127.34 | | | | | | | | | | | | | | | | | | | | | | | all_170_1) & $lesseq(0, all_170_1) & $lesseq(0, 205.25/127.34 | | | | | | | | | | | | | | | | | | | | | | | all_86_11) & length1(int, all_105_4) = all_170_1 205.25/127.34 | | | | | | | | | | | | | | | | | | | | | | | & length1(int, all_103_2) = all_170_1 205.25/127.34 | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.34 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2195) implies: 205.25/127.34 | | | | | | | | | | | | | | | | | | | | | | | (2196) length1(int, all_103_2) = all_170_1 205.25/127.34 | | | | | | | | | | | | | | | | | | | | | | | (2197) length1(int, all_105_4) = all_170_1 205.25/127.34 | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.34 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (272) gives: 205.25/127.34 | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.34 | | | | | | | | | | | | | | | | | | | | | | | Case 1: 205.25/127.34 | | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | (2198) all_171_0 = all_171_1 & $lesseq(all_86_11, 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | all_171_1) & $lesseq(0, all_171_1) & $lesseq(0, 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | all_86_11) & length1(int, all_103_2) = all_171_1 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | & length1(int, all_103_4) = all_171_1 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2198) implies: 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | (2199) length1(int, all_103_2) = all_171_1 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_170_1, all_169_1, 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (2194), (2197) 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | (2200) all_170_1 = all_169_1 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_170_1, all_153_1, 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (2187), (2197) 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | (2201) all_170_1 = all_153_1 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_86_13, all_177_2, 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (184), (2192) 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | (2202) all_177_2 = all_86_13 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_242_1, all_177_2, 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (2185), (2192) 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | (2203) all_242_1 = all_177_2 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_177_2, all_171_1, 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (2192), (2199) 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | (2204) all_177_2 = all_171_1 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_177_2, all_170_1, 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (2192), (2196) 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | (2205) all_177_2 = all_170_1 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_242_1, all_156_0, 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (394), (2185) 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | (2206) all_242_1 = all_156_0 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_105_1, all_187_2, 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | all_105_2, int, simplifying with (100), (2174) 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | (2207) all_187_2 = all_105_1 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_105_3, all_187_3, 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (99), (2173) 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | (2208) all_187_3 = all_105_3 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_187_3, all_177_3, 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (2173), (2191) 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | (2209) all_187_3 = all_177_3 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_187_3, all_156_1, 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (395), (2173) 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | (2210) all_187_3 = all_156_1 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2203), (2206) imply: 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | (2211) all_177_2 = all_156_0 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2211) implies: 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | (2212) all_177_2 = all_156_0 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2209), (2210) imply: 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | (2213) all_177_3 = all_156_1 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2208), (2209) imply: 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | (2214) all_177_3 = all_105_3 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2204), (2205) imply: 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | (2215) all_171_1 = all_170_1 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2202), (2204) imply: 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | (2216) all_171_1 = all_86_13 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2204), (2212) imply: 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | (2217) all_171_1 = all_156_0 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2213), (2214) imply: 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | (2218) all_156_1 = all_105_3 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2216), (2217) imply: 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | (2219) all_156_0 = all_86_13 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2215), (2217) imply: 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | (2220) all_170_1 = all_156_0 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2220) implies: 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | (2221) all_170_1 = all_156_0 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2200), (2201) imply: 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | (2222) all_169_1 = all_153_1 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2200), (2221) imply: 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | (2223) all_169_1 = all_156_0 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2222), (2223) imply: 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | (2224) all_156_0 = all_153_1 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2224) implies: 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | (2225) all_156_0 = all_153_1 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2219), (2225) imply: 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | (2226) all_153_1 = all_86_13 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2226) implies: 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | (2227) all_153_1 = all_86_13 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (44), (105), (180), (205), (2175), (2207), 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | (2208) are inconsistent by sub-proof #66. 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | Case 2: 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | (2228) ~ (all_171_1 = 0) & array_eq_sub1(int, all_103_4, 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, 0, all_86_11) = all_171_1 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (2177), (2228) are inconsistent by sub-proof 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | #81. 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | End of split 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | Case 2: 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | (2229) ~ (all_170_1 = 0) & array_eq_sub1(int, all_103_2, 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | all_105_4, 0, all_86_11) = all_170_1 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (398), (2229) are inconsistent by sub-proof 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | #48. 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | End of split 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | Case 2: 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | (2230) ~ (all_169_1 = 0) & array_eq_sub1(int, all_105_4, 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | all_105_2, 0, all_86_7) = all_169_1 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (2179), (2230) are inconsistent by sub-proof 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | #75. 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | | 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | End of split 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | 205.25/127.35 | | | | | | | | | | | | | | | | | | | | Case 2: 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | (2231) ~ (all_177_4 = 0) & permut_sub2(int, all_103_2, 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | all_105_4, all_86_11, $sum(all_86_8, 1)) = 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | all_177_4 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (43), (2189), (2231) are inconsistent by sub-proof 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | #47. 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | 205.25/127.35 | | | | | | | | | | | | | | | | | | | | End of split 205.25/127.35 | | | | | | | | | | | | | | | | | | | | 205.25/127.35 | | | | | | | | | | | | | | | | | | | Case 2: 205.25/127.35 | | | | | | | | | | | | | | | | | | | | 205.25/127.35 | | | | | | | | | | | | | | | | | | | | (2232) elts(int, all_105_4) = all_181_2 & elts(int, 205.25/127.35 | | | | | | | | | | | | | | | | | | | | all_103_2) = all_181_3 & in_uni(all_181_2) & 205.25/127.35 | | | | | | | | | | | | | | | | | | | | in_uni(all_181_3) & (( ~ (all_181_0 = 0) & 205.25/127.35 | | | | | | | | | | | | | | | | | | | | map_eq_sub1(int, all_181_3, all_181_2, 205.25/127.35 | | | | | | | | | | | | | | | | | | | | $sum(all_86_8, 1), all_181_1) = all_181_0 & 205.25/127.35 | | | | | | | | | | | | | | | | | | | | length1(int, all_103_2) = all_181_1) | ( ~ 205.25/127.35 | | | | | | | | | | | | | | | | | | | | (all_181_1 = 0) & map_eq_sub1(int, all_181_3, 205.25/127.35 | | | | | | | | | | | | | | | | | | | | all_181_2, 0, all_86_11) = all_181_1)) 205.25/127.35 | | | | | | | | | | | | | | | | | | | | 205.25/127.35 | | | | | | | | | | | | | | | | | | | | ALPHA: (2232) implies: 205.25/127.35 | | | | | | | | | | | | | | | | | | | | (2233) elts(int, all_105_4) = all_181_2 205.25/127.35 | | | | | | | | | | | | | | | | | | | | 205.25/127.35 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (39), (44), (45), (99), (100), (105), (184), 205.25/127.35 | | | | | | | | | | | | | | | | | | | | (205), (255), (270), (271), (398), (2173), (2174), 205.25/127.35 | | | | | | | | | | | | | | | | | | | | (2175), (2179), (2181), (2233) are inconsistent by 205.25/127.35 | | | | | | | | | | | | | | | | | | | | sub-proof #13. 205.25/127.35 | | | | | | | | | | | | | | | | | | | | 205.25/127.35 | | | | | | | | | | | | | | | | | | | End of split 205.25/127.35 | | | | | | | | | | | | | | | | | | | 205.25/127.35 | | | | | | | | | | | | | | | | | | Case 2: 205.25/127.35 | | | | | | | | | | | | | | | | | | | 205.25/127.35 | | | | | | | | | | | | | | | | | | | (2234) ~ (all_153_1 = 0) & array_eq_sub1(int, all_105_4, 205.25/127.35 | | | | | | | | | | | | | | | | | | | all_105_2, $sum(all_86_10, 1), all_86_13) = 205.25/127.35 | | | | | | | | | | | | | | | | | | | all_153_1 205.25/127.35 | | | | | | | | | | | | | | | | | | | 205.25/127.35 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (2181), (2234) are inconsistent by sub-proof 205.25/127.35 | | | | | | | | | | | | | | | | | | | #54. 205.25/127.35 | | | | | | | | | | | | | | | | | | | 205.25/127.35 | | | | | | | | | | | | | | | | | | End of split 205.25/127.35 | | | | | | | | | | | | | | | | | | 205.25/127.35 | | | | | | | | | | | | | | | | | End of split 205.25/127.35 | | | | | | | | | | | | | | | | | 205.25/127.35 | | | | | | | | | | | | | | | | Case 2: 205.25/127.35 | | | | | | | | | | | | | | | | | 205.25/127.35 | | | | | | | | | | | | | | | | | (2235) length1(int, all_105_4) = all_234_1 & ( ~ 205.25/127.35 | | | | | | | | | | | | | | | | | ($lesseq(1, $difference(all_234_1, all_86_10))) 205.25/127.35 | | | | | | | | | | | | | | | | | | ~ ($lesseq(all_86_13, all_234_1)) | ( ~ 205.25/127.35 | | | | | | | | | | | | | | | | | (all_234_0 = all_234_1) & length1(int, 205.25/127.35 | | | | | | | | | | | | | | | | | all_105_2) = all_234_0)) 205.25/127.35 | | | | | | | | | | | | | | | | | 205.25/127.35 | | | | | | | | | | | | | | | | | ALPHA: (2235) implies: 205.25/127.35 | | | | | | | | | | | | | | | | | (2236) length1(int, all_105_4) = all_234_1 205.25/127.35 | | | | | | | | | | | | | | | | | (2237) ~ ($lesseq(1, $difference(all_234_1, all_86_10))) 205.25/127.35 | | | | | | | | | | | | | | | | | | ~ ($lesseq(all_86_13, all_234_1)) | ( ~ 205.25/127.35 | | | | | | | | | | | | | | | | | (all_234_0 = all_234_1) & length1(int, 205.25/127.35 | | | | | | | | | | | | | | | | | all_105_2) = all_234_0) 205.25/127.35 | | | | | | | | | | | | | | | | | 205.25/127.35 | | | | | | | | | | | | | | | | | BETA: splitting (345) gives: 205.25/127.35 | | | | | | | | | | | | | | | | | 205.25/127.35 | | | | | | | | | | | | | | | | | Case 1: 205.25/127.35 | | | | | | | | | | | | | | | | | | 205.25/127.35 | | | | | | | | | | | | | | | | | | (2238) all_242_1 = 0 & array_eq_sub1(int, all_103_2, 205.25/127.35 | | | | | | | | | | | | | | | | | | all_105_4, $sum(all_86_8, 1), all_86_13) = 0 205.25/127.35 | | | | | | | | | | | | | | | | | | 205.25/127.35 | | | | | | | | | | | | | | | | | | ALPHA: (2238) implies: 205.25/127.35 | | | | | | | | | | | | | | | | | | (2239) array_eq_sub1(int, all_103_2, all_105_4, 205.25/127.35 | | | | | | | | | | | | | | | | | | $sum(all_86_8, 1), all_86_13) = 0 205.25/127.35 | | | | | | | | | | | | | | | | | | 205.25/127.35 | | | | | | | | | | | | | | | | | | BETA: splitting (269) gives: 205.25/127.35 | | | | | | | | | | | | | | | | | | 205.25/127.35 | | | | | | | | | | | | | | | | | | Case 1: 205.25/127.35 | | | | | | | | | | | | | | | | | | | 205.25/127.35 | | | | | | | | | | | | | | | | | | | (2240) all_168_0 = all_168_1 & $lesseq(1, 205.25/127.35 | | | | | | | | | | | | | | | | | | | $difference(all_168_1, all_86_8)) & 205.25/127.35 | | | | | | | | | | | | | | | | | | | $lesseq(all_86_13, all_168_1) & $lesseq(-1, 205.25/127.35 | | | | | | | | | | | | | | | | | | | all_86_8) & $lesseq(0, all_86_13) & length1(int, 205.25/127.35 | | | | | | | | | | | | | | | | | | | all_105_4) = all_168_1 & length1(int, all_103_2) 205.25/127.35 | | | | | | | | | | | | | | | | | | | = all_168_1 205.25/127.35 | | | | | | | | | | | | | | | | | | | 205.25/127.35 | | | | | | | | | | | | | | | | | | | ALPHA: (2240) implies: 205.25/127.35 | | | | | | | | | | | | | | | | | | | (2241) length1(int, all_105_4) = all_168_1 205.25/127.35 | | | | | | | | | | | | | | | | | | | 205.25/127.35 | | | | | | | | | | | | | | | | | | | BETA: splitting (270) gives: 205.25/127.35 | | | | | | | | | | | | | | | | | | | 205.25/127.35 | | | | | | | | | | | | | | | | | | | Case 1: 205.25/127.35 | | | | | | | | | | | | | | | | | | | | 205.25/127.35 | | | | | | | | | | | | | | | | | | | | (2242) all_169_0 = all_169_1 & $lesseq(all_86_7, 205.25/127.35 | | | | | | | | | | | | | | | | | | | | all_169_1) & $lesseq(0, all_169_1) & $lesseq(0, 205.25/127.35 | | | | | | | | | | | | | | | | | | | | all_86_7) & length1(int, all_105_2) = all_169_1 205.25/127.35 | | | | | | | | | | | | | | | | | | | | & length1(int, all_105_4) = all_169_1 205.25/127.35 | | | | | | | | | | | | | | | | | | | | 205.25/127.35 | | | | | | | | | | | | | | | | | | | | ALPHA: (2242) implies: 205.25/127.35 | | | | | | | | | | | | | | | | | | | | (2243) length1(int, all_105_4) = all_169_1 205.25/127.35 | | | | | | | | | | | | | | | | | | | | (2244) length1(int, all_105_2) = all_169_1 205.25/127.35 | | | | | | | | | | | | | | | | | | | | 205.25/127.35 | | | | | | | | | | | | | | | | | | | | BETA: splitting (271) gives: 205.25/127.35 | | | | | | | | | | | | | | | | | | | | 205.25/127.35 | | | | | | | | | | | | | | | | | | | | Case 1: 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | (2245) all_170_0 = all_170_1 & $lesseq(all_86_11, 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | all_170_1) & $lesseq(0, all_170_1) & $lesseq(0, 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | all_86_11) & length1(int, all_105_4) = all_170_1 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | & length1(int, all_103_2) = all_170_1 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | ALPHA: (2245) implies: 205.25/127.35 | | | | | | | | | | | | | | | | | | | | | (2246) length1(int, all_103_2) = all_170_1 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | (2247) length1(int, all_105_4) = all_170_1 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (272) gives: 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | Case 1: 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | (2248) all_171_0 = all_171_1 & $lesseq(all_86_11, 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | all_171_1) & $lesseq(0, all_171_1) & $lesseq(0, 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | all_86_11) & length1(int, all_103_2) = all_171_1 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | & length1(int, all_103_4) = all_171_1 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2248) implies: 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | (2249) length1(int, all_103_4) = all_171_1 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | (2250) length1(int, all_103_2) = all_171_1 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (296) gives: 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | Case 1: 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | (2251) all_191_3 = 0 & permut_sub2(int, all_103_4, 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | all_103_2, all_86_11, $sum(all_86_10, 1)) = 0 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2251) implies: 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | (2252) permut_sub2(int, all_103_4, all_103_2, all_86_11, 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | $sum(all_86_10, 1)) = 0 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (297) gives: 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | Case 1: 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | | (2253) all_192_0 = 0 & all_192_1 = 0 & map_eq_sub1(int, 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | | all_192_4, all_192_3, $sum(all_86_10, 1), 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | | all_192_2) = 0 & map_eq_sub1(int, all_192_4, 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | | all_192_3, 0, all_86_11) = 0 & length1(int, 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | | all_103_4) = all_192_2 & elts(int, all_103_2) = 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | | all_192_3 & elts(int, all_103_4) = all_192_4 & 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | | in_uni(all_192_3) & in_uni(all_192_4) 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2253) implies: 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | | (2254) length1(int, all_103_4) = all_192_2 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_234_1, all_170_1, 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (2236), (2247) 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | | (2255) all_234_1 = all_170_1 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_170_1, all_169_1, 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (2243), (2247) 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | | (2256) all_170_1 = all_169_1 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_234_1, all_168_1, 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (2236), (2241) 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | | (2257) all_234_1 = all_168_1 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_171_1, all_170_1, 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (2246), (2250) 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | | (2258) all_171_1 = all_170_1 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_86_13, all_238_1, 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (183), (1808) 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | | (2259) all_238_1 = all_86_13 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_238_1, all_192_2, 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (1808), (2254) 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | | (2260) all_238_1 = all_192_2 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_238_1, all_171_1, 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (1808), (2249) 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | | (2261) all_238_1 = all_171_1 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2259), (2260) imply: 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | | (2262) all_192_2 = all_86_13 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2260), (2261) imply: 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | | (2263) all_192_2 = all_171_1 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2255), (2257) imply: 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | | (2264) all_170_1 = all_168_1 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2264) implies: 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | | (2265) all_170_1 = all_168_1 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2262), (2263) imply: 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | | (2266) all_171_1 = all_86_13 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2266) implies: 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | | (2267) all_171_1 = all_86_13 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2258), (2267) imply: 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | | (2268) all_170_1 = all_86_13 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2268) implies: 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | | (2269) all_170_1 = all_86_13 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2256), (2269) imply: 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | | (2270) all_169_1 = all_86_13 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2256), (2265) imply: 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | | (2271) all_169_1 = all_168_1 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2270), (2271) imply: 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | | (2272) all_168_1 = all_86_13 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2257), (2272) imply: 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | | (2273) all_234_1 = all_86_13 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (49), (181), (2237), (2273) are inconsistent 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #38. 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | Case 2: 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | | (2274) ~ (all_192_4 = 0) & permut_sub2(int, all_103_4, 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, all_86_11, $sum(all_86_10, 1)) = 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | | all_192_4 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (43), (2252), (2274) are inconsistent by sub-proof 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | | #69. 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | End of split 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | Case 2: 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | (2275) elts(int, all_103_2) = all_191_2 & elts(int, 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | all_103_4) = all_191_3 & in_uni(all_191_2) & 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | in_uni(all_191_3) & (( ~ (all_191_0 = 0) & 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | map_eq_sub1(int, all_191_3, all_191_2, 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | $sum(all_86_10, 1), all_191_1) = all_191_0 & 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | length1(int, all_103_4) = all_191_1) | ( ~ 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | (all_191_1 = 0) & map_eq_sub1(int, all_191_3, 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | all_191_2, 0, all_86_11) = all_191_1)) 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2275) implies: 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | (2276) elts(int, all_103_4) = all_191_3 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | (2277) elts(int, all_103_2) = all_191_2 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | (2278) ( ~ (all_191_0 = 0) & map_eq_sub1(int, all_191_3, 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | all_191_2, $sum(all_86_10, 1), all_191_1) = 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | all_191_0 & length1(int, all_103_4) = all_191_1) 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | | ( ~ (all_191_1 = 0) & map_eq_sub1(int, 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | all_191_3, all_191_2, 0, all_86_11) = 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | all_191_1) 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (39), (44), (90), (91), (96), (183), (206), 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | (1808), (2249), (2276), (2277), (2278) are 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #19. 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | End of split 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | Case 2: 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | (2279) ~ (all_171_1 = 0) & array_eq_sub1(int, all_103_4, 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | all_103_2, 0, all_86_11) = all_171_1 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (2177), (2279) are inconsistent by sub-proof 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | #81. 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | End of split 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | 205.25/127.36 | | | | | | | | | | | | | | | | | | | | Case 2: 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | (2280) ~ (all_170_1 = 0) & array_eq_sub1(int, all_103_2, 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | all_105_4, 0, all_86_11) = all_170_1 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (398), (2280) are inconsistent by sub-proof 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | #48. 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | 205.25/127.36 | | | | | | | | | | | | | | | | | | | | End of split 205.25/127.36 | | | | | | | | | | | | | | | | | | | | 205.25/127.36 | | | | | | | | | | | | | | | | | | | Case 2: 205.25/127.36 | | | | | | | | | | | | | | | | | | | | 205.25/127.36 | | | | | | | | | | | | | | | | | | | | (2281) ~ (all_169_1 = 0) & array_eq_sub1(int, all_105_4, 205.25/127.36 | | | | | | | | | | | | | | | | | | | | all_105_2, 0, all_86_7) = all_169_1 205.25/127.36 | | | | | | | | | | | | | | | | | | | | 205.25/127.36 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (2179), (2281) are inconsistent by sub-proof 205.25/127.36 | | | | | | | | | | | | | | | | | | | | #75. 205.25/127.36 | | | | | | | | | | | | | | | | | | | | 205.25/127.36 | | | | | | | | | | | | | | | | | | | End of split 205.25/127.36 | | | | | | | | | | | | | | | | | | | 205.25/127.36 | | | | | | | | | | | | | | | | | | Case 2: 205.25/127.36 | | | | | | | | | | | | | | | | | | | 205.25/127.36 | | | | | | | | | | | | | | | | | | | (2282) ~ (all_168_1 = 0) & array_eq_sub1(int, all_103_2, 205.25/127.36 | | | | | | | | | | | | | | | | | | | all_105_4, $sum(all_86_8, 1), all_86_13) = 205.25/127.36 | | | | | | | | | | | | | | | | | | | all_168_1 205.25/127.36 | | | | | | | | | | | | | | | | | | | 205.25/127.36 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (2239), (2282) are inconsistent by sub-proof 205.25/127.36 | | | | | | | | | | | | | | | | | | | #83. 205.25/127.36 | | | | | | | | | | | | | | | | | | | 205.25/127.36 | | | | | | | | | | | | | | | | | | End of split 205.25/127.36 | | | | | | | | | | | | | | | | | | 205.25/127.36 | | | | | | | | | | | | | | | | | Case 2: 205.25/127.36 | | | | | | | | | | | | | | | | | | 205.25/127.36 | | | | | | | | | | | | | | | | | | (2283) length1(int, all_103_2) = all_242_1 & ( ~ 205.25/127.36 | | | | | | | | | | | | | | | | | | ($lesseq(1, $difference(all_242_1, all_86_8))) | 205.25/127.36 | | | | | | | | | | | | | | | | | | ~ ($lesseq(all_86_13, all_242_1)) | ( ~ 205.25/127.36 | | | | | | | | | | | | | | | | | | (all_242_0 = all_242_1) & length1(int, 205.25/127.36 | | | | | | | | | | | | | | | | | | all_105_4) = all_242_0)) 205.25/127.36 | | | | | | | | | | | | | | | | | | 205.25/127.36 | | | | | | | | | | | | | | | | | | ALPHA: (2283) implies: 205.25/127.36 | | | | | | | | | | | | | | | | | | (2284) length1(int, all_103_2) = all_242_1 205.25/127.36 | | | | | | | | | | | | | | | | | | (2285) ~ ($lesseq(1, $difference(all_242_1, all_86_8))) 205.25/127.36 | | | | | | | | | | | | | | | | | | | ~ ($lesseq(all_86_13, all_242_1)) | ( ~ 205.25/127.36 | | | | | | | | | | | | | | | | | | (all_242_0 = all_242_1) & length1(int, 205.25/127.36 | | | | | | | | | | | | | | | | | | all_105_4) = all_242_0) 205.25/127.36 | | | | | | | | | | | | | | | | | | 205.25/127.36 | | | | | | | | | | | | | | | | | | BETA: splitting (270) gives: 205.25/127.36 | | | | | | | | | | | | | | | | | | 205.25/127.36 | | | | | | | | | | | | | | | | | | Case 1: 205.25/127.36 | | | | | | | | | | | | | | | | | | | 205.25/127.36 | | | | | | | | | | | | | | | | | | | (2286) all_169_0 = all_169_1 & $lesseq(all_86_7, 205.25/127.36 | | | | | | | | | | | | | | | | | | | all_169_1) & $lesseq(0, all_169_1) & $lesseq(0, 205.25/127.36 | | | | | | | | | | | | | | | | | | | all_86_7) & length1(int, all_105_2) = all_169_1 205.25/127.36 | | | | | | | | | | | | | | | | | | | & length1(int, all_105_4) = all_169_1 205.25/127.36 | | | | | | | | | | | | | | | | | | | 205.25/127.36 | | | | | | | | | | | | | | | | | | | ALPHA: (2286) implies: 205.25/127.36 | | | | | | | | | | | | | | | | | | | (2287) $lesseq(all_86_7, all_169_1) 205.25/127.36 | | | | | | | | | | | | | | | | | | | (2288) length1(int, all_105_4) = all_169_1 205.25/127.36 | | | | | | | | | | | | | | | | | | | 205.25/127.36 | | | | | | | | | | | | | | | | | | | BETA: splitting (271) gives: 205.25/127.36 | | | | | | | | | | | | | | | | | | | 205.25/127.36 | | | | | | | | | | | | | | | | | | | Case 1: 205.25/127.36 | | | | | | | | | | | | | | | | | | | | 205.25/127.36 | | | | | | | | | | | | | | | | | | | | (2289) all_170_0 = all_170_1 & $lesseq(all_86_11, 205.25/127.36 | | | | | | | | | | | | | | | | | | | | all_170_1) & $lesseq(0, all_170_1) & $lesseq(0, 205.25/127.36 | | | | | | | | | | | | | | | | | | | | all_86_11) & length1(int, all_105_4) = all_170_1 205.25/127.36 | | | | | | | | | | | | | | | | | | | | & length1(int, all_103_2) = all_170_1 205.25/127.36 | | | | | | | | | | | | | | | | | | | | 205.25/127.36 | | | | | | | | | | | | | | | | | | | | ALPHA: (2289) implies: 205.25/127.36 | | | | | | | | | | | | | | | | | | | | (2290) length1(int, all_103_2) = all_170_1 205.25/127.36 | | | | | | | | | | | | | | | | | | | | (2291) length1(int, all_105_4) = all_170_1 205.25/127.36 | | | | | | | | | | | | | | | | | | | | 205.25/127.36 | | | | | | | | | | | | | | | | | | | | BETA: splitting (272) gives: 205.25/127.36 | | | | | | | | | | | | | | | | | | | | 205.25/127.36 | | | | | | | | | | | | | | | | | | | | Case 1: 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | (2292) all_171_0 = all_171_1 & $lesseq(all_86_11, 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | all_171_1) & $lesseq(0, all_171_1) & $lesseq(0, 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | all_86_11) & length1(int, all_103_2) = all_171_1 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | & length1(int, all_103_4) = all_171_1 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | ALPHA: (2292) implies: 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | (2293) length1(int, all_103_4) = all_171_1 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | (2294) length1(int, all_103_2) = all_171_1 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (296) gives: 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | Case 1: 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | (2295) all_191_3 = 0 & permut_sub2(int, all_103_4, 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | all_103_2, all_86_11, $sum(all_86_10, 1)) = 0 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2295) implies: 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | (2296) permut_sub2(int, all_103_4, all_103_2, all_86_11, 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | $sum(all_86_10, 1)) = 0 205.25/127.36 | | | | | | | | | | | | | | | | | | | | | | 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (297) gives: 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | Case 1: 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | | (2297) all_192_0 = 0 & all_192_1 = 0 & map_eq_sub1(int, 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | | all_192_4, all_192_3, $sum(all_86_10, 1), 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | | all_192_2) = 0 & map_eq_sub1(int, all_192_4, 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | | all_192_3, 0, all_86_11) = 0 & length1(int, 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | | all_103_4) = all_192_2 & elts(int, all_103_2) = 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | | all_192_3 & elts(int, all_103_4) = all_192_4 & 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | | in_uni(all_192_3) & in_uni(all_192_4) 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2297) implies: 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | | (2298) length1(int, all_103_4) = all_192_2 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_234_1, all_170_1, 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (2236), (2291) 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | | gives: 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | | (2299) all_234_1 = all_170_1 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_234_1, all_169_1, 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (2236), (2288) 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | | gives: 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | | (2300) all_234_1 = all_169_1 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_242_1, all_170_1, 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (2284), (2290) 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | | gives: 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | | (2301) all_242_1 = all_170_1 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_171_1, all_170_1, 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (2290), (2294) 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | | gives: 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | | (2302) all_171_1 = all_170_1 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_242_1, all_156_0, 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (394), (2284) 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | | gives: 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | | (2303) all_242_1 = all_156_0 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_86_13, all_192_2, 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (183), (2298) 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | | gives: 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | | (2304) all_192_2 = all_86_13 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_238_1, all_192_2, 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (1808), (2298) 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | | gives: 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | | (2305) all_238_1 = all_192_2 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_238_1, all_171_1, 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (1808), (2293) 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | | gives: 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | | (2306) all_238_1 = all_171_1 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2301), (2303) imply: 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | | (2307) all_170_1 = all_156_0 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2307) implies: 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | | (2308) all_170_1 = all_156_0 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2305), (2306) imply: 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | | (2309) all_192_2 = all_171_1 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2309) implies: 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | | (2310) all_192_2 = all_171_1 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2299), (2300) imply: 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | | (2311) all_170_1 = all_169_1 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2304), (2310) imply: 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | | (2312) all_171_1 = all_86_13 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2302), (2312) imply: 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | | (2313) all_170_1 = all_86_13 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2313) implies: 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | | (2314) all_170_1 = all_86_13 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2308), (2311) imply: 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | | (2315) all_169_1 = all_156_0 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2311), (2314) imply: 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | | (2316) all_169_1 = all_86_13 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2315), (2316) imply: 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | | (2317) all_156_0 = all_86_13 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (52), (2285), (2287), (2288), (2303), 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | | (2316), (2317) are inconsistent by sub-proof #49. 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | Case 2: 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | | (2318) ~ (all_192_4 = 0) & permut_sub2(int, all_103_4, 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | | all_103_2, all_86_11, $sum(all_86_10, 1)) = 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | | all_192_4 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (43), (2296), (2318) are inconsistent by sub-proof 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | | #69. 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | End of split 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | Case 2: 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | (2319) elts(int, all_103_2) = all_191_2 & elts(int, 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | all_103_4) = all_191_3 & in_uni(all_191_2) & 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | in_uni(all_191_3) & (( ~ (all_191_0 = 0) & 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | map_eq_sub1(int, all_191_3, all_191_2, 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | $sum(all_86_10, 1), all_191_1) = all_191_0 & 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | length1(int, all_103_4) = all_191_1) | ( ~ 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | (all_191_1 = 0) & map_eq_sub1(int, all_191_3, 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | all_191_2, 0, all_86_11) = all_191_1)) 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2319) implies: 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | (2320) elts(int, all_103_4) = all_191_3 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | (2321) elts(int, all_103_2) = all_191_2 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | (2322) ( ~ (all_191_0 = 0) & map_eq_sub1(int, all_191_3, 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | all_191_2, $sum(all_86_10, 1), all_191_1) = 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | all_191_0 & length1(int, all_103_4) = all_191_1) 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | | ( ~ (all_191_1 = 0) & map_eq_sub1(int, 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | all_191_3, all_191_2, 0, all_86_11) = 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | all_191_1) 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (39), (44), (90), (91), (96), (183), (206), 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | (1808), (2293), (2320), (2321), (2322) are 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #19. 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | End of split 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | 205.25/127.37 | | | | | | | | | | | | | | | | | | | | Case 2: 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | (2323) ~ (all_171_1 = 0) & array_eq_sub1(int, all_103_4, 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | all_103_2, 0, all_86_11) = all_171_1 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (2177), (2323) are inconsistent by sub-proof 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | #81. 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | 205.25/127.37 | | | | | | | | | | | | | | | | | | | | End of split 205.25/127.37 | | | | | | | | | | | | | | | | | | | | 205.25/127.37 | | | | | | | | | | | | | | | | | | | Case 2: 205.25/127.37 | | | | | | | | | | | | | | | | | | | | 205.25/127.37 | | | | | | | | | | | | | | | | | | | | (2324) ~ (all_170_1 = 0) & array_eq_sub1(int, all_103_2, 205.25/127.37 | | | | | | | | | | | | | | | | | | | | all_105_4, 0, all_86_11) = all_170_1 205.25/127.37 | | | | | | | | | | | | | | | | | | | | 205.25/127.37 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (398), (2324) are inconsistent by sub-proof 205.25/127.37 | | | | | | | | | | | | | | | | | | | | #48. 205.25/127.37 | | | | | | | | | | | | | | | | | | | | 205.25/127.37 | | | | | | | | | | | | | | | | | | | End of split 205.25/127.37 | | | | | | | | | | | | | | | | | | | 205.25/127.37 | | | | | | | | | | | | | | | | | | Case 2: 205.25/127.37 | | | | | | | | | | | | | | | | | | | 205.25/127.37 | | | | | | | | | | | | | | | | | | | (2325) ~ (all_169_1 = 0) & array_eq_sub1(int, all_105_4, 205.25/127.37 | | | | | | | | | | | | | | | | | | | all_105_2, 0, all_86_7) = all_169_1 205.25/127.37 | | | | | | | | | | | | | | | | | | | 205.25/127.37 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (2179), (2325) are inconsistent by sub-proof 205.25/127.37 | | | | | | | | | | | | | | | | | | | #75. 205.25/127.37 | | | | | | | | | | | | | | | | | | | 205.25/127.37 | | | | | | | | | | | | | | | | | | End of split 205.25/127.37 | | | | | | | | | | | | | | | | | | 205.25/127.37 | | | | | | | | | | | | | | | | | End of split 205.25/127.37 | | | | | | | | | | | | | | | | | 205.25/127.37 | | | | | | | | | | | | | | | | End of split 205.25/127.37 | | | | | | | | | | | | | | | | 205.25/127.37 | | | | | | | | | | | | | | | Case 2: 205.25/127.37 | | | | | | | | | | | | | | | | 205.25/127.37 | | | | | | | | | | | | | | | | (2326) length1(int, all_105_4) = all_219_1 & ( ~ 205.25/127.37 | | | | | | | | | | | | | | | | ($lesseq(all_86_7, all_219_1)) | ~ ($lesseq(0, 205.25/127.37 | | | | | | | | | | | | | | | | all_219_1)) | ( ~ (all_219_0 = all_219_1) & 205.25/127.37 | | | | | | | | | | | | | | | | length1(int, all_105_2) = all_219_0)) 205.25/127.37 | | | | | | | | | | | | | | | | 205.25/127.37 | | | | | | | | | | | | | | | | ALPHA: (2326) implies: 205.25/127.37 | | | | | | | | | | | | | | | | (2327) length1(int, all_105_4) = all_219_1 205.25/127.37 | | | | | | | | | | | | | | | | (2328) ~ ($lesseq(all_86_7, all_219_1)) | ~ ($lesseq(0, 205.25/127.37 | | | | | | | | | | | | | | | | all_219_1)) | ( ~ (all_219_0 = all_219_1) & 205.25/127.37 | | | | | | | | | | | | | | | | length1(int, all_105_2) = all_219_0) 205.25/127.37 | | | | | | | | | | | | | | | | 205.25/127.37 | | | | | | | | | | | | | | | | BETA: splitting (345) gives: 205.25/127.37 | | | | | | | | | | | | | | | | 205.25/127.37 | | | | | | | | | | | | | | | | Case 1: 205.25/127.37 | | | | | | | | | | | | | | | | | 205.25/127.37 | | | | | | | | | | | | | | | | | (2329) all_242_1 = 0 & array_eq_sub1(int, all_103_2, 205.25/127.37 | | | | | | | | | | | | | | | | | all_105_4, $sum(all_86_8, 1), all_86_13) = 0 205.25/127.37 | | | | | | | | | | | | | | | | | 205.25/127.37 | | | | | | | | | | | | | | | | | ALPHA: (2329) implies: 205.25/127.37 | | | | | | | | | | | | | | | | | (2330) array_eq_sub1(int, all_103_2, all_105_4, 205.25/127.37 | | | | | | | | | | | | | | | | | $sum(all_86_8, 1), all_86_13) = 0 205.25/127.37 | | | | | | | | | | | | | | | | | 205.25/127.37 | | | | | | | | | | | | | | | | | BETA: splitting (337) gives: 205.25/127.37 | | | | | | | | | | | | | | | | | 205.25/127.37 | | | | | | | | | | | | | | | | | Case 1: 205.25/127.37 | | | | | | | | | | | | | | | | | | 205.25/127.37 | | | | | | | | | | | | | | | | | | (2331) all_234_1 = 0 & array_eq_sub1(int, all_105_4, 205.25/127.37 | | | | | | | | | | | | | | | | | | all_105_2, $sum(all_86_10, 1), all_86_13) = 0 205.25/127.37 | | | | | | | | | | | | | | | | | | 205.25/127.37 | | | | | | | | | | | | | | | | | | ALPHA: (2331) implies: 205.25/127.37 | | | | | | | | | | | | | | | | | | (2332) array_eq_sub1(int, all_105_4, all_105_2, 205.25/127.37 | | | | | | | | | | | | | | | | | | $sum(all_86_10, 1), all_86_13) = 0 205.25/127.37 | | | | | | | | | | | | | | | | | | 205.25/127.37 | | | | | | | | | | | | | | | | | | BETA: splitting (255) gives: 205.25/127.37 | | | | | | | | | | | | | | | | | | 205.25/127.37 | | | | | | | | | | | | | | | | | | Case 1: 205.25/127.37 | | | | | | | | | | | | | | | | | | | 205.25/127.37 | | | | | | | | | | | | | | | | | | | (2333) all_153_0 = all_153_1 & $lesseq(1, 205.25/127.37 | | | | | | | | | | | | | | | | | | | $difference(all_153_1, all_86_10)) & 205.25/127.37 | | | | | | | | | | | | | | | | | | | $lesseq(all_86_13, all_153_1) & $lesseq(-1, 205.25/127.37 | | | | | | | | | | | | | | | | | | | all_86_10) & $lesseq(0, all_86_13) & 205.25/127.37 | | | | | | | | | | | | | | | | | | | length1(int, all_105_2) = all_153_1 & length1(int, 205.25/127.37 | | | | | | | | | | | | | | | | | | | all_105_4) = all_153_1 205.25/127.37 | | | | | | | | | | | | | | | | | | | 205.25/127.37 | | | | | | | | | | | | | | | | | | | ALPHA: (2333) implies: 205.25/127.37 | | | | | | | | | | | | | | | | | | | (2334) length1(int, all_105_4) = all_153_1 205.25/127.37 | | | | | | | | | | | | | | | | | | | 205.25/127.37 | | | | | | | | | | | | | | | | | | | BETA: splitting (269) gives: 205.25/127.37 | | | | | | | | | | | | | | | | | | | 205.25/127.37 | | | | | | | | | | | | | | | | | | | Case 1: 205.25/127.37 | | | | | | | | | | | | | | | | | | | | 205.25/127.37 | | | | | | | | | | | | | | | | | | | | (2335) all_168_0 = all_168_1 & $lesseq(1, 205.25/127.37 | | | | | | | | | | | | | | | | | | | | $difference(all_168_1, all_86_8)) & 205.25/127.37 | | | | | | | | | | | | | | | | | | | | $lesseq(all_86_13, all_168_1) & $lesseq(-1, 205.25/127.37 | | | | | | | | | | | | | | | | | | | | all_86_8) & $lesseq(0, all_86_13) & length1(int, 205.25/127.37 | | | | | | | | | | | | | | | | | | | | all_105_4) = all_168_1 & length1(int, all_103_2) 205.25/127.37 | | | | | | | | | | | | | | | | | | | | = all_168_1 205.25/127.37 | | | | | | | | | | | | | | | | | | | | 205.25/127.37 | | | | | | | | | | | | | | | | | | | | ALPHA: (2335) implies: 205.25/127.37 | | | | | | | | | | | | | | | | | | | | (2336) length1(int, all_103_2) = all_168_1 205.25/127.37 | | | | | | | | | | | | | | | | | | | | 205.25/127.37 | | | | | | | | | | | | | | | | | | | | BETA: splitting (271) gives: 205.25/127.37 | | | | | | | | | | | | | | | | | | | | 205.25/127.37 | | | | | | | | | | | | | | | | | | | | Case 1: 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | (2337) all_170_0 = all_170_1 & $lesseq(all_86_11, 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | all_170_1) & $lesseq(0, all_170_1) & $lesseq(0, 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | all_86_11) & length1(int, all_105_4) = all_170_1 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | & length1(int, all_103_2) = all_170_1 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | ALPHA: (2337) implies: 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | (2338) length1(int, all_103_2) = all_170_1 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | (2339) length1(int, all_105_4) = all_170_1 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (272) gives: 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | Case 1: 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | (2340) all_171_0 = all_171_1 & $lesseq(all_86_11, 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | all_171_1) & $lesseq(0, all_171_1) & $lesseq(0, 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | all_86_11) & length1(int, all_103_2) = all_171_1 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | & length1(int, all_103_4) = all_171_1 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2340) implies: 205.25/127.37 | | | | | | | | | | | | | | | | | | | | | | (2341) length1(int, all_103_4) = all_171_1 205.25/127.38 | | | | | | | | | | | | | | | | | | | | | | (2342) length1(int, all_103_2) = all_171_1 205.25/127.38 | | | | | | | | | | | | | | | | | | | | | | 205.25/127.38 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (296) gives: 205.25/127.38 | | | | | | | | | | | | | | | | | | | | | | 205.25/127.38 | | | | | | | | | | | | | | | | | | | | | | Case 1: 205.25/127.38 | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.38 | | | | | | | | | | | | | | | | | | | | | | | (2343) all_191_3 = 0 & permut_sub2(int, all_103_4, 205.25/127.38 | | | | | | | | | | | | | | | | | | | | | | | all_103_2, all_86_11, $sum(all_86_10, 1)) = 0 205.25/127.38 | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.38 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2343) implies: 205.25/127.38 | | | | | | | | | | | | | | | | | | | | | | | (2344) permut_sub2(int, all_103_4, all_103_2, all_86_11, 205.25/127.38 | | | | | | | | | | | | | | | | | | | | | | | $sum(all_86_10, 1)) = 0 205.25/127.38 | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.38 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (297) gives: 205.25/127.38 | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.38 | | | | | | | | | | | | | | | | | | | | | | | Case 1: 205.25/127.38 | | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.38 | | | | | | | | | | | | | | | | | | | | | | | | (2345) all_192_0 = 0 & all_192_1 = 0 & map_eq_sub1(int, 205.25/127.38 | | | | | | | | | | | | | | | | | | | | | | | | all_192_4, all_192_3, $sum(all_86_10, 1), 205.25/127.38 | | | | | | | | | | | | | | | | | | | | | | | | all_192_2) = 0 & map_eq_sub1(int, all_192_4, 205.25/127.38 | | | | | | | | | | | | | | | | | | | | | | | | all_192_3, 0, all_86_11) = 0 & length1(int, 205.25/127.38 | | | | | | | | | | | | | | | | | | | | | | | | all_103_4) = all_192_2 & elts(int, all_103_2) = 205.25/127.38 | | | | | | | | | | | | | | | | | | | | | | | | all_192_3 & elts(int, all_103_4) = all_192_4 & 205.25/127.38 | | | | | | | | | | | | | | | | | | | | | | | | in_uni(all_192_3) & in_uni(all_192_4) 205.25/127.38 | | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.38 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2345) implies: 205.25/127.38 | | | | | | | | | | | | | | | | | | | | | | | | (2346) length1(int, all_103_4) = all_192_2 205.25/127.38 | | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.38 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_219_1, all_170_1, 205.25/127.38 | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (2327), (2339) 205.25/127.38 | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.25/127.38 | | | | | | | | | | | | | | | | | | | | | | | | (2347) all_219_1 = all_170_1 205.25/127.38 | | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.38 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_219_1, all_153_1, 205.25/127.38 | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (2327), (2334) 205.25/127.38 | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.25/127.38 | | | | | | | | | | | | | | | | | | | | | | | | (2348) all_219_1 = all_153_1 205.25/127.38 | | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.38 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_171_1, all_170_1, 205.25/127.38 | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (2338), (2342) 205.25/127.38 | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.25/127.38 | | | | | | | | | | | | | | | | | | | | | | | | (2349) all_171_1 = all_170_1 205.25/127.38 | | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.38 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_170_1, all_168_1, 205.25/127.38 | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (2336), (2338) 205.25/127.38 | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.25/127.38 | | | | | | | | | | | | | | | | | | | | | | | | (2350) all_170_1 = all_168_1 205.25/127.38 | | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.38 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_86_13, all_238_1, 205.25/127.38 | | | | | | | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (183), (1808) 205.25/127.38 | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.25/127.38 | | | | | | | | | | | | | | | | | | | | | | | | (2351) all_238_1 = all_86_13 205.25/127.38 | | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.38 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_238_1, all_192_2, 205.25/127.38 | | | | | | | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (1808), (2346) 205.25/127.38 | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.25/127.38 | | | | | | | | | | | | | | | | | | | | | | | | (2352) all_238_1 = all_192_2 205.25/127.38 | | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.38 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_238_1, all_171_1, 205.25/127.38 | | | | | | | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (1808), (2341) 205.25/127.38 | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.25/127.38 | | | | | | | | | | | | | | | | | | | | | | | | (2353) all_238_1 = all_171_1 205.25/127.38 | | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.38 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_105_1, all_187_2, 205.25/127.38 | | | | | | | | | | | | | | | | | | | | | | | | all_105_2, int, simplifying with (100), (2174) 205.25/127.38 | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.25/127.38 | | | | | | | | | | | | | | | | | | | | | | | | (2354) all_187_2 = all_105_1 205.25/127.38 | | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.38 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_105_3, all_187_3, 205.25/127.38 | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (99), (2173) 205.25/127.38 | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.25/127.38 | | | | | | | | | | | | | | | | | | | | | | | | (2355) all_187_3 = all_105_3 205.25/127.38 | | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.38 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2351), (2352) imply: 205.25/127.38 | | | | | | | | | | | | | | | | | | | | | | | | (2356) all_192_2 = all_86_13 205.25/127.38 | | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.38 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2352), (2353) imply: 205.25/127.38 | | | | | | | | | | | | | | | | | | | | | | | | (2357) all_192_2 = all_171_1 205.25/127.38 | | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.38 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2347), (2348) imply: 205.25/127.38 | | | | | | | | | | | | | | | | | | | | | | | | (2358) all_170_1 = all_153_1 205.25/127.38 | | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.38 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2358) implies: 205.25/127.38 | | | | | | | | | | | | | | | | | | | | | | | | (2359) all_170_1 = all_153_1 205.25/127.38 | | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.38 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2356), (2357) imply: 205.25/127.38 | | | | | | | | | | | | | | | | | | | | | | | | (2360) all_171_1 = all_86_13 205.25/127.38 | | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.38 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2349), (2360) imply: 205.25/127.38 | | | | | | | | | | | | | | | | | | | | | | | | (2361) all_170_1 = all_86_13 205.25/127.38 | | | | | | | | | | | | | | | | | | | | | | | | 205.25/127.38 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2361) implies: 205.38/127.38 | | | | | | | | | | | | | | | | | | | | | | | | (2362) all_170_1 = all_86_13 205.38/127.38 | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.38 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2350), (2359) imply: 205.38/127.38 | | | | | | | | | | | | | | | | | | | | | | | | (2363) all_168_1 = all_153_1 205.38/127.38 | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.38 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2350), (2362) imply: 205.38/127.38 | | | | | | | | | | | | | | | | | | | | | | | | (2364) all_168_1 = all_86_13 205.38/127.38 | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.38 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2363), (2364) imply: 205.38/127.38 | | | | | | | | | | | | | | | | | | | | | | | | (2365) all_153_1 = all_86_13 205.38/127.38 | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.38 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2365) implies: 205.38/127.38 | | | | | | | | | | | | | | | | | | | | | | | | (2366) all_153_1 = all_86_13 205.38/127.38 | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.38 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (44), (105), (180), (205), (2175), (2354), 205.38/127.38 | | | | | | | | | | | | | | | | | | | | | | | | (2355) are inconsistent by sub-proof #66. 205.38/127.38 | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.38 | | | | | | | | | | | | | | | | | | | | | | | Case 2: 205.38/127.38 | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.38 | | | | | | | | | | | | | | | | | | | | | | | | (2367) ~ (all_192_4 = 0) & permut_sub2(int, all_103_4, 205.38/127.38 | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, all_86_11, $sum(all_86_10, 1)) = 205.38/127.38 | | | | | | | | | | | | | | | | | | | | | | | | all_192_4 205.38/127.38 | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.38 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (43), (2344), (2367) are inconsistent by sub-proof 205.38/127.38 | | | | | | | | | | | | | | | | | | | | | | | | #69. 205.38/127.38 | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.38 | | | | | | | | | | | | | | | | | | | | | | | End of split 205.38/127.38 | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.38 | | | | | | | | | | | | | | | | | | | | | | Case 2: 205.38/127.38 | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.38 | | | | | | | | | | | | | | | | | | | | | | | (2368) elts(int, all_103_2) = all_191_2 & elts(int, 205.38/127.38 | | | | | | | | | | | | | | | | | | | | | | | all_103_4) = all_191_3 & in_uni(all_191_2) & 205.38/127.38 | | | | | | | | | | | | | | | | | | | | | | | in_uni(all_191_3) & (( ~ (all_191_0 = 0) & 205.38/127.38 | | | | | | | | | | | | | | | | | | | | | | | map_eq_sub1(int, all_191_3, all_191_2, 205.38/127.38 | | | | | | | | | | | | | | | | | | | | | | | $sum(all_86_10, 1), all_191_1) = all_191_0 & 205.38/127.38 | | | | | | | | | | | | | | | | | | | | | | | length1(int, all_103_4) = all_191_1) | ( ~ 205.38/127.38 | | | | | | | | | | | | | | | | | | | | | | | (all_191_1 = 0) & map_eq_sub1(int, all_191_3, 205.38/127.38 | | | | | | | | | | | | | | | | | | | | | | | all_191_2, 0, all_86_11) = all_191_1)) 205.38/127.38 | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.38 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2368) implies: 205.38/127.38 | | | | | | | | | | | | | | | | | | | | | | | (2369) elts(int, all_103_4) = all_191_3 205.38/127.38 | | | | | | | | | | | | | | | | | | | | | | | (2370) elts(int, all_103_2) = all_191_2 205.38/127.38 | | | | | | | | | | | | | | | | | | | | | | | (2371) ( ~ (all_191_0 = 0) & map_eq_sub1(int, all_191_3, 205.38/127.38 | | | | | | | | | | | | | | | | | | | | | | | all_191_2, $sum(all_86_10, 1), all_191_1) = 205.38/127.38 | | | | | | | | | | | | | | | | | | | | | | | all_191_0 & length1(int, all_103_4) = all_191_1) 205.38/127.38 | | | | | | | | | | | | | | | | | | | | | | | | ( ~ (all_191_1 = 0) & map_eq_sub1(int, 205.38/127.38 | | | | | | | | | | | | | | | | | | | | | | | all_191_3, all_191_2, 0, all_86_11) = 205.38/127.38 | | | | | | | | | | | | | | | | | | | | | | | all_191_1) 205.38/127.38 | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.38 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (39), (44), (90), (91), (96), (183), (206), 205.38/127.38 | | | | | | | | | | | | | | | | | | | | | | | (1808), (2341), (2369), (2370), (2371) are 205.38/127.38 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #19. 205.38/127.38 | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.38 | | | | | | | | | | | | | | | | | | | | | | End of split 205.38/127.38 | | | | | | | | | | | | | | | | | | | | | | 205.38/127.38 | | | | | | | | | | | | | | | | | | | | | Case 2: 205.38/127.38 | | | | | | | | | | | | | | | | | | | | | | 205.38/127.38 | | | | | | | | | | | | | | | | | | | | | | (2372) ~ (all_171_1 = 0) & array_eq_sub1(int, all_103_4, 205.38/127.38 | | | | | | | | | | | | | | | | | | | | | | all_103_2, 0, all_86_11) = all_171_1 205.38/127.38 | | | | | | | | | | | | | | | | | | | | | | 205.38/127.38 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (2177), (2372) are inconsistent by sub-proof 205.38/127.38 | | | | | | | | | | | | | | | | | | | | | | #81. 205.38/127.38 | | | | | | | | | | | | | | | | | | | | | | 205.38/127.38 | | | | | | | | | | | | | | | | | | | | | End of split 205.38/127.38 | | | | | | | | | | | | | | | | | | | | | 205.38/127.38 | | | | | | | | | | | | | | | | | | | | Case 2: 205.38/127.38 | | | | | | | | | | | | | | | | | | | | | 205.38/127.38 | | | | | | | | | | | | | | | | | | | | | (2373) ~ (all_170_1 = 0) & array_eq_sub1(int, all_103_2, 205.38/127.38 | | | | | | | | | | | | | | | | | | | | | all_105_4, 0, all_86_11) = all_170_1 205.38/127.38 | | | | | | | | | | | | | | | | | | | | | 205.38/127.38 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (398), (2373) are inconsistent by sub-proof 205.38/127.38 | | | | | | | | | | | | | | | | | | | | | #48. 205.38/127.38 | | | | | | | | | | | | | | | | | | | | | 205.38/127.38 | | | | | | | | | | | | | | | | | | | | End of split 205.38/127.38 | | | | | | | | | | | | | | | | | | | | 205.38/127.38 | | | | | | | | | | | | | | | | | | | Case 2: 205.38/127.38 | | | | | | | | | | | | | | | | | | | | 205.38/127.38 | | | | | | | | | | | | | | | | | | | | (2374) ~ (all_168_1 = 0) & array_eq_sub1(int, all_103_2, 205.38/127.38 | | | | | | | | | | | | | | | | | | | | all_105_4, $sum(all_86_8, 1), all_86_13) = 205.38/127.38 | | | | | | | | | | | | | | | | | | | | all_168_1 205.38/127.38 | | | | | | | | | | | | | | | | | | | | 205.38/127.38 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (2330), (2374) are inconsistent by sub-proof 205.38/127.38 | | | | | | | | | | | | | | | | | | | | #83. 205.38/127.38 | | | | | | | | | | | | | | | | | | | | 205.38/127.38 | | | | | | | | | | | | | | | | | | | End of split 205.38/127.38 | | | | | | | | | | | | | | | | | | | 205.38/127.38 | | | | | | | | | | | | | | | | | | Case 2: 205.38/127.38 | | | | | | | | | | | | | | | | | | | 205.38/127.38 | | | | | | | | | | | | | | | | | | | (2375) ~ (all_153_1 = 0) & array_eq_sub1(int, all_105_4, 205.38/127.38 | | | | | | | | | | | | | | | | | | | all_105_2, $sum(all_86_10, 1), all_86_13) = 205.38/127.38 | | | | | | | | | | | | | | | | | | | all_153_1 205.38/127.38 | | | | | | | | | | | | | | | | | | | 205.38/127.38 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (2332), (2375) are inconsistent by sub-proof 205.38/127.38 | | | | | | | | | | | | | | | | | | | #54. 205.38/127.38 | | | | | | | | | | | | | | | | | | | 205.38/127.38 | | | | | | | | | | | | | | | | | | End of split 205.38/127.38 | | | | | | | | | | | | | | | | | | 205.38/127.38 | | | | | | | | | | | | | | | | | Case 2: 205.38/127.38 | | | | | | | | | | | | | | | | | | 205.38/127.38 | | | | | | | | | | | | | | | | | | (2376) length1(int, all_105_4) = all_234_1 & ( ~ 205.38/127.38 | | | | | | | | | | | | | | | | | | ($lesseq(1, $difference(all_234_1, all_86_10))) 205.38/127.38 | | | | | | | | | | | | | | | | | | | ~ ($lesseq(all_86_13, all_234_1)) | ( ~ 205.38/127.38 | | | | | | | | | | | | | | | | | | (all_234_0 = all_234_1) & length1(int, 205.38/127.38 | | | | | | | | | | | | | | | | | | all_105_2) = all_234_0)) 205.38/127.38 | | | | | | | | | | | | | | | | | | 205.38/127.38 | | | | | | | | | | | | | | | | | | ALPHA: (2376) implies: 205.38/127.38 | | | | | | | | | | | | | | | | | | (2377) length1(int, all_105_4) = all_234_1 205.38/127.38 | | | | | | | | | | | | | | | | | | (2378) ~ ($lesseq(1, $difference(all_234_1, all_86_10))) 205.38/127.38 | | | | | | | | | | | | | | | | | | | ~ ($lesseq(all_86_13, all_234_1)) | ( ~ 205.38/127.38 | | | | | | | | | | | | | | | | | | (all_234_0 = all_234_1) & length1(int, 205.38/127.38 | | | | | | | | | | | | | | | | | | all_105_2) = all_234_0) 205.38/127.38 | | | | | | | | | | | | | | | | | | 205.38/127.38 | | | | | | | | | | | | | | | | | | BETA: splitting (269) gives: 205.38/127.38 | | | | | | | | | | | | | | | | | | 205.38/127.38 | | | | | | | | | | | | | | | | | | Case 1: 205.38/127.38 | | | | | | | | | | | | | | | | | | | 205.38/127.38 | | | | | | | | | | | | | | | | | | | (2379) all_168_0 = all_168_1 & $lesseq(1, 205.38/127.38 | | | | | | | | | | | | | | | | | | | $difference(all_168_1, all_86_8)) & 205.38/127.38 | | | | | | | | | | | | | | | | | | | $lesseq(all_86_13, all_168_1) & $lesseq(-1, 205.38/127.38 | | | | | | | | | | | | | | | | | | | all_86_8) & $lesseq(0, all_86_13) & length1(int, 205.38/127.38 | | | | | | | | | | | | | | | | | | | all_105_4) = all_168_1 & length1(int, all_103_2) 205.38/127.38 | | | | | | | | | | | | | | | | | | | = all_168_1 205.38/127.38 | | | | | | | | | | | | | | | | | | | 205.38/127.38 | | | | | | | | | | | | | | | | | | | ALPHA: (2379) implies: 205.38/127.38 | | | | | | | | | | | | | | | | | | | (2380) length1(int, all_103_2) = all_168_1 205.38/127.38 | | | | | | | | | | | | | | | | | | | (2381) length1(int, all_105_4) = all_168_1 205.38/127.38 | | | | | | | | | | | | | | | | | | | 205.38/127.38 | | | | | | | | | | | | | | | | | | | BETA: splitting (287) gives: 205.38/127.38 | | | | | | | | | | | | | | | | | | | 205.38/127.38 | | | | | | | | | | | | | | | | | | | Case 1: 205.38/127.38 | | | | | | | | | | | | | | | | | | | | 205.38/127.38 | | | | | | | | | | | | | | | | | | | | (2382) all_181_3 = 0 & permut_sub2(int, all_103_2, 205.38/127.38 | | | | | | | | | | | | | | | | | | | | all_105_4, all_86_11, $sum(all_86_8, 1)) = 0 205.38/127.38 | | | | | | | | | | | | | | | | | | | | 205.38/127.38 | | | | | | | | | | | | | | | | | | | | ALPHA: (2382) implies: 205.38/127.38 | | | | | | | | | | | | | | | | | | | | (2383) permut_sub2(int, all_103_2, all_105_4, all_86_11, 205.38/127.38 | | | | | | | | | | | | | | | | | | | | $sum(all_86_8, 1)) = 0 205.38/127.38 | | | | | | | | | | | | | | | | | | | | 205.38/127.38 | | | | | | | | | | | | | | | | | | | | BETA: splitting (280) gives: 205.38/127.38 | | | | | | | | | | | | | | | | | | | | 205.38/127.38 | | | | | | | | | | | | | | | | | | | | Case 1: 205.38/127.38 | | | | | | | | | | | | | | | | | | | | | 205.38/127.38 | | | | | | | | | | | | | | | | | | | | | (2384) all_177_0 = 0 & all_177_1 = 0 & map_eq_sub1(int, 205.38/127.38 | | | | | | | | | | | | | | | | | | | | | all_177_4, all_177_3, $sum(all_86_8, 1), 205.38/127.38 | | | | | | | | | | | | | | | | | | | | | all_177_2) = 0 & map_eq_sub1(int, all_177_4, 205.38/127.38 | | | | | | | | | | | | | | | | | | | | | all_177_3, 0, all_86_11) = 0 & length1(int, 205.38/127.38 | | | | | | | | | | | | | | | | | | | | | all_103_2) = all_177_2 & elts(int, all_105_4) = 205.38/127.38 | | | | | | | | | | | | | | | | | | | | | all_177_3 & elts(int, all_103_2) = all_177_4 & 205.38/127.38 | | | | | | | | | | | | | | | | | | | | | in_uni(all_177_3) & in_uni(all_177_4) 205.38/127.38 | | | | | | | | | | | | | | | | | | | | | 205.38/127.38 | | | | | | | | | | | | | | | | | | | | | ALPHA: (2384) implies: 205.38/127.38 | | | | | | | | | | | | | | | | | | | | | (2385) length1(int, all_103_2) = all_177_2 205.38/127.38 | | | | | | | | | | | | | | | | | | | | | 205.38/127.38 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (271) gives: 205.38/127.38 | | | | | | | | | | | | | | | | | | | | | 205.38/127.38 | | | | | | | | | | | | | | | | | | | | | Case 1: 205.38/127.38 | | | | | | | | | | | | | | | | | | | | | | 205.38/127.38 | | | | | | | | | | | | | | | | | | | | | | (2386) all_170_0 = all_170_1 & $lesseq(all_86_11, 205.38/127.38 | | | | | | | | | | | | | | | | | | | | | | all_170_1) & $lesseq(0, all_170_1) & $lesseq(0, 205.38/127.38 | | | | | | | | | | | | | | | | | | | | | | all_86_11) & length1(int, all_105_4) = all_170_1 205.38/127.38 | | | | | | | | | | | | | | | | | | | | | | & length1(int, all_103_2) = all_170_1 205.38/127.38 | | | | | | | | | | | | | | | | | | | | | | 205.38/127.38 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2386) implies: 205.38/127.38 | | | | | | | | | | | | | | | | | | | | | | (2387) length1(int, all_103_2) = all_170_1 205.38/127.38 | | | | | | | | | | | | | | | | | | | | | | (2388) length1(int, all_105_4) = all_170_1 205.38/127.38 | | | | | | | | | | | | | | | | | | | | | | 205.38/127.38 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (272) gives: 205.38/127.38 | | | | | | | | | | | | | | | | | | | | | | 205.38/127.38 | | | | | | | | | | | | | | | | | | | | | | Case 1: 205.38/127.38 | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | (2389) all_171_0 = all_171_1 & $lesseq(all_86_11, 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | all_171_1) & $lesseq(0, all_171_1) & $lesseq(0, 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | all_86_11) & length1(int, all_103_2) = all_171_1 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | & length1(int, all_103_4) = all_171_1 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2389) implies: 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | (2390) length1(int, all_103_2) = all_171_1 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (345) gives: 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | Case 1: 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (269) gives: 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_234_1, all_168_1, 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (2377), (2381) 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | | (2391) all_234_1 = all_168_1 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_86_13, all_177_2, 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (184), (2385) 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | | (2392) all_177_2 = all_86_13 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_177_2, all_170_1, 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (2385), (2387) 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | | (2393) all_177_2 = all_170_1 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_171_1, all_170_1, 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (2387), (2390) 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | | (2394) all_171_1 = all_170_1 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_171_1, all_168_1, 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (2380), (2390) 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | | (2395) all_171_1 = all_168_1 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_170_1, all_156_0, 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (394), (2387) 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | | (2396) all_170_1 = all_156_0 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2392), (2393) imply: 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | | (2397) all_170_1 = all_86_13 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2397) implies: 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | | (2398) all_170_1 = all_86_13 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2394), (2395) imply: 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | | (2399) all_170_1 = all_168_1 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2399) implies: 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | | (2400) all_170_1 = all_168_1 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2398), (2400) imply: 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | | (2401) all_168_1 = all_86_13 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2396), (2400) imply: 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | | (2402) all_168_1 = all_156_0 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2401), (2402) imply: 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | | (2403) all_156_0 = all_86_13 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2391), (2401) imply: 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | | (2404) all_234_1 = all_86_13 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (49), (181), (2378), (2404) are inconsistent 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #38. 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | | (2405) ~ (all_168_1 = 0) & array_eq_sub1(int, all_103_2, 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, $sum(all_86_8, 1), all_86_13) = 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | | all_168_1 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (2330), (2405) are inconsistent by sub-proof 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | | #83. 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | End of split 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | Case 2: 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | (2406) length1(int, all_103_2) = all_242_1 & ( ~ 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | ($lesseq(1, $difference(all_242_1, all_86_8))) | 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | ~ ($lesseq(all_86_13, all_242_1)) | ( ~ 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | (all_242_0 = all_242_1) & length1(int, 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | all_105_4) = all_242_0)) 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2406) implies: 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | (2407) length1(int, all_103_2) = all_242_1 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_234_1, all_170_1, 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (2377), (2388) 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | (2408) all_234_1 = all_170_1 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_86_13, all_177_2, 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (184), (2385) 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | (2409) all_177_2 = all_86_13 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_242_1, all_171_1, 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (2390), (2407) 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | (2410) all_242_1 = all_171_1 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_177_2, all_171_1, 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (2385), (2390) 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | (2411) all_177_2 = all_171_1 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_242_1, all_170_1, 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (2387), (2407) 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | (2412) all_242_1 = all_170_1 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2410), (2412) imply: 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | (2413) all_171_1 = all_170_1 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2413) implies: 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | (2414) all_171_1 = all_170_1 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2409), (2411) imply: 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | (2415) all_171_1 = all_86_13 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2415) implies: 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | (2416) all_171_1 = all_86_13 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2414), (2416) imply: 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | (2417) all_170_1 = all_86_13 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2417) implies: 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | (2418) all_170_1 = all_86_13 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2408), (2418) imply: 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | (2419) all_234_1 = all_86_13 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (49), (181), (2378), (2419) are inconsistent 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #38. 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | End of split 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | Case 2: 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | (2420) ~ (all_171_1 = 0) & array_eq_sub1(int, all_103_4, 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | all_103_2, 0, all_86_11) = all_171_1 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (2177), (2420) are inconsistent by sub-proof 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | #81. 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | End of split 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | Case 2: 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | (2421) ~ (all_170_1 = 0) & array_eq_sub1(int, all_103_2, 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | all_105_4, 0, all_86_11) = all_170_1 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (398), (2421) are inconsistent by sub-proof 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | #48. 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | End of split 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | 205.38/127.39 | | | | | | | | | | | | | | | | | | | | Case 2: 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | (2422) ~ (all_177_4 = 0) & permut_sub2(int, all_103_2, 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | all_105_4, all_86_11, $sum(all_86_8, 1)) = 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | all_177_4 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (43), (2383), (2422) are inconsistent by sub-proof 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | #47. 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | 205.38/127.39 | | | | | | | | | | | | | | | | | | | | End of split 205.38/127.39 | | | | | | | | | | | | | | | | | | | | 205.38/127.39 | | | | | | | | | | | | | | | | | | | Case 2: 205.38/127.39 | | | | | | | | | | | | | | | | | | | | 205.38/127.39 | | | | | | | | | | | | | | | | | | | | (2423) elts(int, all_105_4) = all_181_2 & elts(int, 205.38/127.39 | | | | | | | | | | | | | | | | | | | | all_103_2) = all_181_3 & in_uni(all_181_2) & 205.38/127.39 | | | | | | | | | | | | | | | | | | | | in_uni(all_181_3) & (( ~ (all_181_0 = 0) & 205.38/127.39 | | | | | | | | | | | | | | | | | | | | map_eq_sub1(int, all_181_3, all_181_2, 205.38/127.39 | | | | | | | | | | | | | | | | | | | | $sum(all_86_8, 1), all_181_1) = all_181_0 & 205.38/127.39 | | | | | | | | | | | | | | | | | | | | length1(int, all_103_2) = all_181_1) | ( ~ 205.38/127.39 | | | | | | | | | | | | | | | | | | | | (all_181_1 = 0) & map_eq_sub1(int, all_181_3, 205.38/127.39 | | | | | | | | | | | | | | | | | | | | all_181_2, 0, all_86_11) = all_181_1)) 205.38/127.39 | | | | | | | | | | | | | | | | | | | | 205.38/127.39 | | | | | | | | | | | | | | | | | | | | ALPHA: (2423) implies: 205.38/127.39 | | | | | | | | | | | | | | | | | | | | (2424) elts(int, all_103_2) = all_181_3 205.38/127.39 | | | | | | | | | | | | | | | | | | | | (2425) elts(int, all_105_4) = all_181_2 205.38/127.39 | | | | | | | | | | | | | | | | | | | | (2426) ( ~ (all_181_0 = 0) & map_eq_sub1(int, all_181_3, 205.38/127.39 | | | | | | | | | | | | | | | | | | | | all_181_2, $sum(all_86_8, 1), all_181_1) = 205.38/127.39 | | | | | | | | | | | | | | | | | | | | all_181_0 & length1(int, all_103_2) = all_181_1) 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | ( ~ (all_181_1 = 0) & map_eq_sub1(int, 205.38/127.39 | | | | | | | | | | | | | | | | | | | | all_181_3, all_181_2, 0, all_86_11) = 205.38/127.39 | | | | | | | | | | | | | | | | | | | | all_181_1) 205.38/127.39 | | | | | | | | | | | | | | | | | | | | 205.38/127.39 | | | | | | | | | | | | | | | | | | | | BETA: splitting (271) gives: 205.38/127.39 | | | | | | | | | | | | | | | | | | | | 205.38/127.39 | | | | | | | | | | | | | | | | | | | | Case 1: 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | (2427) all_170_0 = all_170_1 & $lesseq(all_86_11, 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | all_170_1) & $lesseq(0, all_170_1) & $lesseq(0, 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | all_86_11) & length1(int, all_105_4) = all_170_1 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | & length1(int, all_103_2) = all_170_1 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | ALPHA: (2427) implies: 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | (2428) length1(int, all_105_4) = all_170_1 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (272) gives: 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | Case 1: 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | (2429) all_171_0 = all_171_1 & $lesseq(all_86_11, 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | all_171_1) & $lesseq(0, all_171_1) & $lesseq(0, 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | all_86_11) & length1(int, all_103_2) = all_171_1 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | & length1(int, all_103_4) = all_171_1 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2429) implies: 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | (2430) length1(int, all_103_4) = all_171_1 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | (2431) length1(int, all_103_2) = all_171_1 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (296) gives: 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | Case 1: 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | (2432) all_191_3 = 0 & permut_sub2(int, all_103_4, 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | all_103_2, all_86_11, $sum(all_86_10, 1)) = 0 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2432) implies: 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | (2433) permut_sub2(int, all_103_4, all_103_2, all_86_11, 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | $sum(all_86_10, 1)) = 0 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (297) gives: 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | Case 1: 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | (2434) all_192_0 = 0 & all_192_1 = 0 & map_eq_sub1(int, 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | all_192_4, all_192_3, $sum(all_86_10, 1), 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | all_192_2) = 0 & map_eq_sub1(int, all_192_4, 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | all_192_3, 0, all_86_11) = 0 & length1(int, 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | all_103_4) = all_192_2 & elts(int, all_103_2) = 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | all_192_3 & elts(int, all_103_4) = all_192_4 & 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | in_uni(all_192_3) & in_uni(all_192_4) 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2434) implies: 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | (2435) elts(int, all_103_2) = all_192_3 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_86_13, all_219_1, 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (180), (2327) 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | (2436) all_219_1 = all_86_13 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_234_1, all_219_1, 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (2327), (2377) 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | (2437) all_234_1 = all_219_1 205.38/127.39 | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_234_1, all_170_1, 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (2377), (2428) 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | (2438) all_234_1 = all_170_1 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_234_1, all_168_1, 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (2377), (2381) 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | (2439) all_234_1 = all_168_1 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_171_1, all_168_1, 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (2380), (2431) 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | (2440) all_171_1 = all_168_1 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_171_1, all_156_0, 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (394), (2431) 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | (2441) all_171_1 = all_156_0 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_105_3, all_187_3, 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (99), (2173) 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | (2442) all_187_3 = all_105_3 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_187_3, all_181_2, 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (2173), (2425) 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | (2443) all_187_3 = all_181_2 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_181_2, all_156_1, 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (395), (2425) 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | (2444) all_181_2 = all_156_1 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_103_1, all_192_3, 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (91), (2435) 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | (2445) all_192_3 = all_103_1 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_192_3, all_181_3, 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (2424), (2435) 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | (2446) all_192_3 = all_181_3 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_192_3, all_156_3, 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (396), (2435) 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | (2447) all_192_3 = all_156_3 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2437), (2438) imply: 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | (2448) all_219_1 = all_170_1 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2448) implies: 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | (2449) all_219_1 = all_170_1 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2438), (2439) imply: 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | (2450) all_170_1 = all_168_1 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2436), (2449) imply: 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | (2451) all_170_1 = all_86_13 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2451) implies: 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | (2452) all_170_1 = all_86_13 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2445), (2446) imply: 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | (2453) all_181_3 = all_103_1 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2446), (2447) imply: 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | (2454) all_181_3 = all_156_3 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2442), (2443) imply: 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | (2455) all_181_2 = all_105_3 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2455) implies: 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | (2456) all_181_2 = all_105_3 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2444), (2456) imply: 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | (2457) all_156_1 = all_105_3 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2453), (2454) imply: 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | (2458) all_156_3 = all_103_1 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2458) implies: 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | (2459) all_156_3 = all_103_1 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2440), (2441) imply: 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | (2460) all_168_1 = all_156_0 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2460) implies: 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | (2461) all_168_1 = all_156_0 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2450), (2452) imply: 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | (2462) all_168_1 = all_86_13 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2462) implies: 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | (2463) all_168_1 = all_86_13 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2461), (2463) imply: 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | (2464) all_156_0 = all_86_13 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2464) implies: 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | (2465) all_156_0 = all_86_13 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (44), (203), (263), (394), (2426), (2453), 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | (2456), (2457), (2459), (2465) are inconsistent by 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #44. 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | Case 2: 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | (2466) ~ (all_192_4 = 0) & permut_sub2(int, all_103_4, 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, all_86_11, $sum(all_86_10, 1)) = 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | all_192_4 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (43), (2433), (2466) are inconsistent by sub-proof 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | #69. 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | End of split 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | Case 2: 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | (2467) elts(int, all_103_2) = all_191_2 & elts(int, 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | all_103_4) = all_191_3 & in_uni(all_191_2) & 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | in_uni(all_191_3) & (( ~ (all_191_0 = 0) & 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | map_eq_sub1(int, all_191_3, all_191_2, 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | $sum(all_86_10, 1), all_191_1) = all_191_0 & 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | length1(int, all_103_4) = all_191_1) | ( ~ 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | (all_191_1 = 0) & map_eq_sub1(int, all_191_3, 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | all_191_2, 0, all_86_11) = all_191_1)) 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2467) implies: 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | (2468) elts(int, all_103_4) = all_191_3 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | (2469) elts(int, all_103_2) = all_191_2 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | (2470) ( ~ (all_191_0 = 0) & map_eq_sub1(int, all_191_3, 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | all_191_2, $sum(all_86_10, 1), all_191_1) = 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | all_191_0 & length1(int, all_103_4) = all_191_1) 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | | ( ~ (all_191_1 = 0) & map_eq_sub1(int, 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | all_191_3, all_191_2, 0, all_86_11) = 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | all_191_1) 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (39), (44), (90), (91), (96), (183), (206), 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | (1808), (2430), (2468), (2469), (2470) are 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #19. 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | End of split 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | Case 2: 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | (2471) ~ (all_171_1 = 0) & array_eq_sub1(int, all_103_4, 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | all_103_2, 0, all_86_11) = all_171_1 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (2177), (2471) are inconsistent by sub-proof 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | #81. 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | End of split 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | 205.38/127.40 | | | | | | | | | | | | | | | | | | | | Case 2: 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | (2472) ~ (all_170_1 = 0) & array_eq_sub1(int, all_103_2, 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | all_105_4, 0, all_86_11) = all_170_1 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (398), (2472) are inconsistent by sub-proof 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | #48. 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | 205.38/127.40 | | | | | | | | | | | | | | | | | | | | End of split 205.38/127.40 | | | | | | | | | | | | | | | | | | | | 205.38/127.40 | | | | | | | | | | | | | | | | | | | End of split 205.38/127.40 | | | | | | | | | | | | | | | | | | | 205.38/127.40 | | | | | | | | | | | | | | | | | | Case 2: 205.38/127.40 | | | | | | | | | | | | | | | | | | | 205.38/127.40 | | | | | | | | | | | | | | | | | | | (2473) ~ (all_168_1 = 0) & array_eq_sub1(int, all_103_2, 205.38/127.40 | | | | | | | | | | | | | | | | | | | all_105_4, $sum(all_86_8, 1), all_86_13) = 205.38/127.40 | | | | | | | | | | | | | | | | | | | all_168_1 205.38/127.40 | | | | | | | | | | | | | | | | | | | 205.38/127.40 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (2330), (2473) are inconsistent by sub-proof 205.38/127.40 | | | | | | | | | | | | | | | | | | | #83. 205.38/127.40 | | | | | | | | | | | | | | | | | | | 205.38/127.40 | | | | | | | | | | | | | | | | | | End of split 205.38/127.40 | | | | | | | | | | | | | | | | | | 205.38/127.40 | | | | | | | | | | | | | | | | | End of split 205.38/127.40 | | | | | | | | | | | | | | | | | 205.38/127.40 | | | | | | | | | | | | | | | | Case 2: 205.38/127.40 | | | | | | | | | | | | | | | | | 205.38/127.40 | | | | | | | | | | | | | | | | | (2474) length1(int, all_103_2) = all_242_1 & ( ~ 205.38/127.40 | | | | | | | | | | | | | | | | | ($lesseq(1, $difference(all_242_1, all_86_8))) | 205.38/127.40 | | | | | | | | | | | | | | | | | ~ ($lesseq(all_86_13, all_242_1)) | ( ~ 205.38/127.40 | | | | | | | | | | | | | | | | | (all_242_0 = all_242_1) & length1(int, 205.38/127.40 | | | | | | | | | | | | | | | | | all_105_4) = all_242_0)) 205.38/127.40 | | | | | | | | | | | | | | | | | 205.38/127.40 | | | | | | | | | | | | | | | | | ALPHA: (2474) implies: 205.38/127.40 | | | | | | | | | | | | | | | | | (2475) length1(int, all_103_2) = all_242_1 205.38/127.40 | | | | | | | | | | | | | | | | | 205.38/127.40 | | | | | | | | | | | | | | | | | BETA: splitting (337) gives: 205.38/127.40 | | | | | | | | | | | | | | | | | 205.38/127.40 | | | | | | | | | | | | | | | | | Case 1: 205.38/127.40 | | | | | | | | | | | | | | | | | | 205.38/127.40 | | | | | | | | | | | | | | | | | | (2476) all_234_1 = 0 & array_eq_sub1(int, all_105_4, 205.38/127.40 | | | | | | | | | | | | | | | | | | all_105_2, $sum(all_86_10, 1), all_86_13) = 0 205.38/127.40 | | | | | | | | | | | | | | | | | | 205.38/127.40 | | | | | | | | | | | | | | | | | | ALPHA: (2476) implies: 205.38/127.40 | | | | | | | | | | | | | | | | | | (2477) array_eq_sub1(int, all_105_4, all_105_2, 205.38/127.40 | | | | | | | | | | | | | | | | | | $sum(all_86_10, 1), all_86_13) = 0 205.38/127.40 | | | | | | | | | | | | | | | | | | 205.38/127.40 | | | | | | | | | | | | | | | | | | BETA: splitting (255) gives: 205.38/127.40 | | | | | | | | | | | | | | | | | | 205.38/127.40 | | | | | | | | | | | | | | | | | | Case 1: 205.38/127.40 | | | | | | | | | | | | | | | | | | | 205.38/127.40 | | | | | | | | | | | | | | | | | | | (2478) all_153_0 = all_153_1 & $lesseq(1, 205.38/127.40 | | | | | | | | | | | | | | | | | | | $difference(all_153_1, all_86_10)) & 205.38/127.40 | | | | | | | | | | | | | | | | | | | $lesseq(all_86_13, all_153_1) & $lesseq(-1, 205.38/127.40 | | | | | | | | | | | | | | | | | | | all_86_10) & $lesseq(0, all_86_13) & 205.38/127.40 | | | | | | | | | | | | | | | | | | | length1(int, all_105_2) = all_153_1 & length1(int, 205.38/127.40 | | | | | | | | | | | | | | | | | | | all_105_4) = all_153_1 205.38/127.40 | | | | | | | | | | | | | | | | | | | 205.38/127.40 | | | | | | | | | | | | | | | | | | | ALPHA: (2478) implies: 205.38/127.40 | | | | | | | | | | | | | | | | | | | (2479) $lesseq(1, $difference(all_153_1, all_86_10)) 205.38/127.40 | | | | | | | | | | | | | | | | | | | (2480) length1(int, all_105_4) = all_153_1 205.38/127.40 | | | | | | | | | | | | | | | | | | | (2481) length1(int, all_105_2) = all_153_1 205.38/127.40 | | | | | | | | | | | | | | | | | | | 205.38/127.40 | | | | | | | | | | | | | | | | | | | BETA: splitting (271) gives: 205.38/127.40 | | | | | | | | | | | | | | | | | | | 205.38/127.40 | | | | | | | | | | | | | | | | | | | Case 1: 205.38/127.40 | | | | | | | | | | | | | | | | | | | | 205.38/127.40 | | | | | | | | | | | | | | | | | | | | (2482) all_170_0 = all_170_1 & $lesseq(all_86_11, 205.38/127.40 | | | | | | | | | | | | | | | | | | | | all_170_1) & $lesseq(0, all_170_1) & $lesseq(0, 205.38/127.40 | | | | | | | | | | | | | | | | | | | | all_86_11) & length1(int, all_105_4) = all_170_1 205.38/127.40 | | | | | | | | | | | | | | | | | | | | & length1(int, all_103_2) = all_170_1 205.38/127.40 | | | | | | | | | | | | | | | | | | | | 205.38/127.40 | | | | | | | | | | | | | | | | | | | | ALPHA: (2482) implies: 205.38/127.40 | | | | | | | | | | | | | | | | | | | | (2483) length1(int, all_103_2) = all_170_1 205.38/127.40 | | | | | | | | | | | | | | | | | | | | (2484) length1(int, all_105_4) = all_170_1 205.38/127.40 | | | | | | | | | | | | | | | | | | | | 205.38/127.40 | | | | | | | | | | | | | | | | | | | | BETA: splitting (272) gives: 205.38/127.40 | | | | | | | | | | | | | | | | | | | | 205.38/127.40 | | | | | | | | | | | | | | | | | | | | Case 1: 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | (2485) all_171_0 = all_171_1 & $lesseq(all_86_11, 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | all_171_1) & $lesseq(0, all_171_1) & $lesseq(0, 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | all_86_11) & length1(int, all_103_2) = all_171_1 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | & length1(int, all_103_4) = all_171_1 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | ALPHA: (2485) implies: 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | (2486) length1(int, all_103_4) = all_171_1 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | (2487) length1(int, all_103_2) = all_171_1 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (296) gives: 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | Case 1: 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | (2488) all_191_3 = 0 & permut_sub2(int, all_103_4, 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | all_103_2, all_86_11, $sum(all_86_10, 1)) = 0 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2488) implies: 205.38/127.40 | | | | | | | | | | | | | | | | | | | | | | (2489) permut_sub2(int, all_103_4, all_103_2, all_86_11, 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | $sum(all_86_10, 1)) = 0 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (297) gives: 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | Case 1: 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | (2490) all_192_0 = 0 & all_192_1 = 0 & map_eq_sub1(int, 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | all_192_4, all_192_3, $sum(all_86_10, 1), 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | all_192_2) = 0 & map_eq_sub1(int, all_192_4, 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | all_192_3, 0, all_86_11) = 0 & length1(int, 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | all_103_4) = all_192_2 & elts(int, all_103_2) = 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | all_192_3 & elts(int, all_103_4) = all_192_4 & 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | in_uni(all_192_3) & in_uni(all_192_4) 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2490) implies: 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | (2491) length1(int, all_103_4) = all_192_2 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_219_1, all_170_1, 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (2327), (2484) 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | gives: 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | (2492) all_219_1 = all_170_1 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_219_1, all_153_1, 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (2327), (2480) 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | gives: 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | (2493) all_219_1 = all_153_1 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_242_1, all_170_1, 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (2475), (2483) 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | gives: 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | (2494) all_242_1 = all_170_1 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_171_1, all_170_1, 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (2483), (2487) 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | gives: 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | (2495) all_171_1 = all_170_1 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_242_1, all_156_0, 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (394), (2475) 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | gives: 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | (2496) all_242_1 = all_156_0 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_86_13, all_192_2, 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (183), (2491) 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | gives: 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | (2497) all_192_2 = all_86_13 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_238_1, all_192_2, 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (1808), (2491) 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | gives: 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | (2498) all_238_1 = all_192_2 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_238_1, all_171_1, 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (1808), (2486) 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | gives: 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | (2499) all_238_1 = all_171_1 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2494), (2496) imply: 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | (2500) all_170_1 = all_156_0 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2500) implies: 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | (2501) all_170_1 = all_156_0 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2498), (2499) imply: 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | (2502) all_192_2 = all_171_1 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2502) implies: 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | (2503) all_192_2 = all_171_1 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2492), (2493) imply: 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | (2504) all_170_1 = all_153_1 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2497), (2503) imply: 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | (2505) all_171_1 = all_86_13 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2495), (2505) imply: 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | (2506) all_170_1 = all_86_13 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2506) implies: 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | (2507) all_170_1 = all_86_13 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2501), (2504) imply: 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | (2508) all_156_0 = all_153_1 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2501), (2507) imply: 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | (2509) all_156_0 = all_86_13 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2508), (2509) imply: 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | (2510) all_153_1 = all_86_13 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2510) implies: 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | (2511) all_153_1 = all_86_13 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2492), (2507) imply: 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | (2512) all_219_1 = all_86_13 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (48), (49), (50), (52), (53), (181), (389), 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | (2328), (2512) are inconsistent by sub-proof #59. 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | Case 2: 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | (2513) ~ (all_192_4 = 0) & permut_sub2(int, all_103_4, 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | all_103_2, all_86_11, $sum(all_86_10, 1)) = 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | all_192_4 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (43), (2489), (2513) are inconsistent by sub-proof 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | #69. 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | End of split 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | Case 2: 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | (2514) elts(int, all_103_2) = all_191_2 & elts(int, 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | all_103_4) = all_191_3 & in_uni(all_191_2) & 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | in_uni(all_191_3) & (( ~ (all_191_0 = 0) & 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | map_eq_sub1(int, all_191_3, all_191_2, 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | $sum(all_86_10, 1), all_191_1) = all_191_0 & 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | length1(int, all_103_4) = all_191_1) | ( ~ 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | (all_191_1 = 0) & map_eq_sub1(int, all_191_3, 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | all_191_2, 0, all_86_11) = all_191_1)) 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2514) implies: 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | (2515) elts(int, all_103_4) = all_191_3 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | (2516) elts(int, all_103_2) = all_191_2 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | (2517) ( ~ (all_191_0 = 0) & map_eq_sub1(int, all_191_3, 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | all_191_2, $sum(all_86_10, 1), all_191_1) = 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | all_191_0 & length1(int, all_103_4) = all_191_1) 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | | ( ~ (all_191_1 = 0) & map_eq_sub1(int, 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | all_191_3, all_191_2, 0, all_86_11) = 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | all_191_1) 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (39), (44), (90), (91), (96), (183), (206), 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | (1808), (2486), (2515), (2516), (2517) are 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #19. 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | | 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | End of split 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | 205.38/127.41 | | | | | | | | | | | | | | | | | | | | Case 2: 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | (2518) ~ (all_171_1 = 0) & array_eq_sub1(int, all_103_4, 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | all_103_2, 0, all_86_11) = all_171_1 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (2177), (2518) are inconsistent by sub-proof 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | #81. 205.38/127.41 | | | | | | | | | | | | | | | | | | | | | 205.38/127.41 | | | | | | | | | | | | | | | | | | | | End of split 205.38/127.41 | | | | | | | | | | | | | | | | | | | | 205.38/127.41 | | | | | | | | | | | | | | | | | | | Case 2: 205.38/127.41 | | | | | | | | | | | | | | | | | | | | 205.38/127.41 | | | | | | | | | | | | | | | | | | | | (2519) ~ (all_170_1 = 0) & array_eq_sub1(int, all_103_2, 205.38/127.41 | | | | | | | | | | | | | | | | | | | | all_105_4, 0, all_86_11) = all_170_1 205.38/127.41 | | | | | | | | | | | | | | | | | | | | 205.38/127.41 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (398), (2519) are inconsistent by sub-proof 205.38/127.41 | | | | | | | | | | | | | | | | | | | | #48. 205.38/127.41 | | | | | | | | | | | | | | | | | | | | 205.38/127.41 | | | | | | | | | | | | | | | | | | | End of split 205.38/127.41 | | | | | | | | | | | | | | | | | | | 205.38/127.41 | | | | | | | | | | | | | | | | | | Case 2: 205.38/127.41 | | | | | | | | | | | | | | | | | | | 205.38/127.41 | | | | | | | | | | | | | | | | | | | (2520) ~ (all_153_1 = 0) & array_eq_sub1(int, all_105_4, 205.38/127.41 | | | | | | | | | | | | | | | | | | | all_105_2, $sum(all_86_10, 1), all_86_13) = 205.38/127.41 | | | | | | | | | | | | | | | | | | | all_153_1 205.38/127.41 | | | | | | | | | | | | | | | | | | | 205.38/127.41 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (2477), (2520) are inconsistent by sub-proof 205.38/127.41 | | | | | | | | | | | | | | | | | | | #54. 205.38/127.41 | | | | | | | | | | | | | | | | | | | 205.38/127.41 | | | | | | | | | | | | | | | | | | End of split 205.38/127.41 | | | | | | | | | | | | | | | | | | 205.38/127.41 | | | | | | | | | | | | | | | | | Case 2: 205.38/127.41 | | | | | | | | | | | | | | | | | | 205.38/127.41 | | | | | | | | | | | | | | | | | | (2521) length1(int, all_105_4) = all_234_1 & ( ~ 205.38/127.41 | | | | | | | | | | | | | | | | | | ($lesseq(1, $difference(all_234_1, all_86_10))) 205.38/127.41 | | | | | | | | | | | | | | | | | | | ~ ($lesseq(all_86_13, all_234_1)) | ( ~ 205.38/127.41 | | | | | | | | | | | | | | | | | | (all_234_0 = all_234_1) & length1(int, 205.38/127.41 | | | | | | | | | | | | | | | | | | all_105_2) = all_234_0)) 205.38/127.41 | | | | | | | | | | | | | | | | | | 205.38/127.41 | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (49), (180), (181), (2521) are inconsistent 205.38/127.41 | | | | | | | | | | | | | | | | | | by sub-proof #12. 205.38/127.41 | | | | | | | | | | | | | | | | | | 205.38/127.41 | | | | | | | | | | | | | | | | | End of split 205.38/127.41 | | | | | | | | | | | | | | | | | 205.38/127.41 | | | | | | | | | | | | | | | | End of split 205.38/127.41 | | | | | | | | | | | | | | | | 205.38/127.41 | | | | | | | | | | | | | | | End of split 205.38/127.41 | | | | | | | | | | | | | | | 205.38/127.41 | | | | | | | | | | | | | | Case 2: 205.38/127.41 | | | | | | | | | | | | | | | 205.38/127.41 | | | | | | | | | | | | | | | (2522) length1(int, all_103_4) = all_215_1 & ( ~ 205.38/127.41 | | | | | | | | | | | | | | | ($lesseq(all_86_11, all_215_1)) | ~ ($lesseq(0, 205.38/127.41 | | | | | | | | | | | | | | | all_215_1)) | ( ~ (all_215_0 = all_215_1) & 205.38/127.41 | | | | | | | | | | | | | | | length1(int, all_103_2) = all_215_0)) 205.38/127.41 | | | | | | | | | | | | | | | 205.38/127.41 | | | | | | | | | | | | | | | ALPHA: (2522) implies: 205.38/127.41 | | | | | | | | | | | | | | | (2523) length1(int, all_103_4) = all_215_1 205.38/127.41 | | | | | | | | | | | | | | | (2524) ~ ($lesseq(all_86_11, all_215_1)) | ~ 205.38/127.41 | | | | | | | | | | | | | | | ($lesseq(0, all_215_1)) | ( ~ (all_215_0 = 205.38/127.41 | | | | | | | | | | | | | | | all_215_1) & length1(int, all_103_2) = 205.38/127.41 | | | | | | | | | | | | | | | all_215_0) 205.38/127.41 | | | | | | | | | | | | | | | 205.38/127.41 | | | | | | | | | | | | | | | BETA: splitting (324) gives: 205.38/127.41 | | | | | | | | | | | | | | | 205.38/127.41 | | | | | | | | | | | | | | | Case 1: 205.38/127.41 | | | | | | | | | | | | | | | | 205.38/127.41 | | | | | | | | | | | | | | | | (2525) all_219_1 = 0 & array_eq_sub1(int, all_105_4, 205.38/127.41 | | | | | | | | | | | | | | | | all_105_2, 0, all_86_7) = 0 205.38/127.41 | | | | | | | | | | | | | | | | 205.38/127.41 | | | | | | | | | | | | | | | | ALPHA: (2525) implies: 205.38/127.41 | | | | | | | | | | | | | | | | (2526) array_eq_sub1(int, all_105_4, all_105_2, 0, 205.38/127.41 | | | | | | | | | | | | | | | | all_86_7) = 0 205.38/127.41 | | | | | | | | | | | | | | | | 205.38/127.41 | | | | | | | | | | | | | | | | BETA: splitting (337) gives: 205.38/127.41 | | | | | | | | | | | | | | | | 205.38/127.41 | | | | | | | | | | | | | | | | Case 1: 205.38/127.41 | | | | | | | | | | | | | | | | | 205.38/127.41 | | | | | | | | | | | | | | | | | (2527) all_234_1 = 0 & array_eq_sub1(int, all_105_4, 205.38/127.41 | | | | | | | | | | | | | | | | | all_105_2, $sum(all_86_10, 1), all_86_13) = 0 205.38/127.41 | | | | | | | | | | | | | | | | | 205.38/127.41 | | | | | | | | | | | | | | | | | ALPHA: (2527) implies: 205.38/127.41 | | | | | | | | | | | | | | | | | (2528) array_eq_sub1(int, all_105_4, all_105_2, 205.38/127.41 | | | | | | | | | | | | | | | | | $sum(all_86_10, 1), all_86_13) = 0 205.38/127.41 | | | | | | | | | | | | | | | | | 205.38/127.41 | | | | | | | | | | | | | | | | | BETA: splitting (345) gives: 205.38/127.41 | | | | | | | | | | | | | | | | | 205.38/127.41 | | | | | | | | | | | | | | | | | Case 1: 205.38/127.41 | | | | | | | | | | | | | | | | | | 205.38/127.41 | | | | | | | | | | | | | | | | | | (2529) all_242_1 = 0 & array_eq_sub1(int, all_103_2, 205.38/127.41 | | | | | | | | | | | | | | | | | | all_105_4, $sum(all_86_8, 1), all_86_13) = 0 205.38/127.41 | | | | | | | | | | | | | | | | | | 205.38/127.41 | | | | | | | | | | | | | | | | | | ALPHA: (2529) implies: 205.38/127.41 | | | | | | | | | | | | | | | | | | (2530) array_eq_sub1(int, all_103_2, all_105_4, 205.38/127.41 | | | | | | | | | | | | | | | | | | $sum(all_86_8, 1), all_86_13) = 0 205.38/127.41 | | | | | | | | | | | | | | | | | | 205.38/127.41 | | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (39), (44), (45), (99), (100), (105), (180), 205.38/127.41 | | | | | | | | | | | | | | | | | | (205), (255), (269), (270), (271), (394), (398), 205.38/127.41 | | | | | | | | | | | | | | | | | | (2173), (2174), (2175), (2526), (2528), (2530) are 205.38/127.41 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #14. 205.38/127.41 | | | | | | | | | | | | | | | | | | 205.38/127.41 | | | | | | | | | | | | | | | | | Case 2: 205.38/127.41 | | | | | | | | | | | | | | | | | | 205.38/127.41 | | | | | | | | | | | | | | | | | | (2531) length1(int, all_103_2) = all_242_1 & ( ~ 205.38/127.41 | | | | | | | | | | | | | | | | | | ($lesseq(1, $difference(all_242_1, all_86_8))) | 205.38/127.41 | | | | | | | | | | | | | | | | | | ~ ($lesseq(all_86_13, all_242_1)) | ( ~ 205.38/127.41 | | | | | | | | | | | | | | | | | | (all_242_0 = all_242_1) & length1(int, 205.38/127.41 | | | | | | | | | | | | | | | | | | all_105_4) = all_242_0)) 205.38/127.41 | | | | | | | | | | | | | | | | | | 205.38/127.41 | | | | | | | | | | | | | | | | | | ALPHA: (2531) implies: 205.38/127.41 | | | | | | | | | | | | | | | | | | (2532) length1(int, all_103_2) = all_242_1 205.38/127.41 | | | | | | | | | | | | | | | | | | 205.38/127.41 | | | | | | | | | | | | | | | | | | BETA: splitting (255) gives: 205.38/127.41 | | | | | | | | | | | | | | | | | | 205.38/127.41 | | | | | | | | | | | | | | | | | | Case 1: 205.38/127.41 | | | | | | | | | | | | | | | | | | | 205.38/127.41 | | | | | | | | | | | | | | | | | | | (2533) all_153_0 = all_153_1 & $lesseq(1, 205.38/127.41 | | | | | | | | | | | | | | | | | | | $difference(all_153_1, all_86_10)) & 205.38/127.41 | | | | | | | | | | | | | | | | | | | $lesseq(all_86_13, all_153_1) & $lesseq(-1, 205.38/127.41 | | | | | | | | | | | | | | | | | | | all_86_10) & $lesseq(0, all_86_13) & 205.38/127.42 | | | | | | | | | | | | | | | | | | | length1(int, all_105_2) = all_153_1 & length1(int, 205.38/127.42 | | | | | | | | | | | | | | | | | | | all_105_4) = all_153_1 205.38/127.42 | | | | | | | | | | | | | | | | | | | 205.38/127.42 | | | | | | | | | | | | | | | | | | | ALPHA: (2533) implies: 205.38/127.42 | | | | | | | | | | | | | | | | | | | (2534) $lesseq(1, $difference(all_153_1, all_86_10)) 205.38/127.42 | | | | | | | | | | | | | | | | | | | (2535) length1(int, all_105_4) = all_153_1 205.38/127.42 | | | | | | | | | | | | | | | | | | | 205.38/127.42 | | | | | | | | | | | | | | | | | | | BETA: splitting (287) gives: 205.38/127.42 | | | | | | | | | | | | | | | | | | | 205.38/127.42 | | | | | | | | | | | | | | | | | | | Case 1: 205.38/127.42 | | | | | | | | | | | | | | | | | | | | 205.38/127.42 | | | | | | | | | | | | | | | | | | | | (2536) all_181_3 = 0 & permut_sub2(int, all_103_2, 205.38/127.42 | | | | | | | | | | | | | | | | | | | | all_105_4, all_86_11, $sum(all_86_8, 1)) = 0 205.38/127.42 | | | | | | | | | | | | | | | | | | | | 205.38/127.42 | | | | | | | | | | | | | | | | | | | | ALPHA: (2536) implies: 205.38/127.42 | | | | | | | | | | | | | | | | | | | | (2537) permut_sub2(int, all_103_2, all_105_4, all_86_11, 205.38/127.42 | | | | | | | | | | | | | | | | | | | | $sum(all_86_8, 1)) = 0 205.38/127.42 | | | | | | | | | | | | | | | | | | | | 205.38/127.42 | | | | | | | | | | | | | | | | | | | | BETA: splitting (280) gives: 205.38/127.42 | | | | | | | | | | | | | | | | | | | | 205.38/127.42 | | | | | | | | | | | | | | | | | | | | Case 1: 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | (2538) all_177_0 = 0 & all_177_1 = 0 & map_eq_sub1(int, 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | all_177_4, all_177_3, $sum(all_86_8, 1), 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | all_177_2) = 0 & map_eq_sub1(int, all_177_4, 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | all_177_3, 0, all_86_11) = 0 & length1(int, 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | all_103_2) = all_177_2 & elts(int, all_105_4) = 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | all_177_3 & elts(int, all_103_2) = all_177_4 & 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | in_uni(all_177_3) & in_uni(all_177_4) 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | ALPHA: (2538) implies: 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | (2539) length1(int, all_103_2) = all_177_2 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (270) gives: 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | Case 1: 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | (2540) all_169_0 = all_169_1 & $lesseq(all_86_7, 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | all_169_1) & $lesseq(0, all_169_1) & $lesseq(0, 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | all_86_7) & length1(int, all_105_2) = all_169_1 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | & length1(int, all_105_4) = all_169_1 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2540) implies: 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | (2541) length1(int, all_105_4) = all_169_1 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (271) gives: 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | Case 1: 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | | (2542) all_170_0 = all_170_1 & $lesseq(all_86_11, 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | | all_170_1) & $lesseq(0, all_170_1) & $lesseq(0, 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | | all_86_11) & length1(int, all_105_4) = all_170_1 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | | & length1(int, all_103_2) = all_170_1 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2542) implies: 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | | (2543) length1(int, all_103_2) = all_170_1 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | | (2544) length1(int, all_105_4) = all_170_1 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (48), (50), (52), (53), (183), (184), (394), 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | | (1808), (2523), (2524), (2532), (2534), (2535), 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | | (2539), (2541), (2543), (2544) are inconsistent by 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #22. 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | Case 2: 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | | (2545) ~ (all_170_1 = 0) & array_eq_sub1(int, all_103_2, 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | | all_105_4, 0, all_86_11) = all_170_1 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (398), (2545) are inconsistent by sub-proof 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | | #48. 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | End of split 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | Case 2: 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | (2546) ~ (all_169_1 = 0) & array_eq_sub1(int, all_105_4, 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | all_105_2, 0, all_86_7) = all_169_1 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (2526), (2546) are inconsistent by sub-proof 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | #75. 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | End of split 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | 205.38/127.42 | | | | | | | | | | | | | | | | | | | | Case 2: 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | (2547) ~ (all_177_4 = 0) & permut_sub2(int, all_103_2, 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | all_105_4, all_86_11, $sum(all_86_8, 1)) = 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | all_177_4 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (43), (2537), (2547) are inconsistent by sub-proof 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | #47. 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | 205.38/127.42 | | | | | | | | | | | | | | | | | | | | End of split 205.38/127.42 | | | | | | | | | | | | | | | | | | | | 205.38/127.42 | | | | | | | | | | | | | | | | | | | Case 2: 205.38/127.42 | | | | | | | | | | | | | | | | | | | | 205.38/127.42 | | | | | | | | | | | | | | | | | | | | (2548) elts(int, all_105_4) = all_181_2 & elts(int, 205.38/127.42 | | | | | | | | | | | | | | | | | | | | all_103_2) = all_181_3 & in_uni(all_181_2) & 205.38/127.42 | | | | | | | | | | | | | | | | | | | | in_uni(all_181_3) & (( ~ (all_181_0 = 0) & 205.38/127.42 | | | | | | | | | | | | | | | | | | | | map_eq_sub1(int, all_181_3, all_181_2, 205.38/127.42 | | | | | | | | | | | | | | | | | | | | $sum(all_86_8, 1), all_181_1) = all_181_0 & 205.38/127.42 | | | | | | | | | | | | | | | | | | | | length1(int, all_103_2) = all_181_1) | ( ~ 205.38/127.42 | | | | | | | | | | | | | | | | | | | | (all_181_1 = 0) & map_eq_sub1(int, all_181_3, 205.38/127.42 | | | | | | | | | | | | | | | | | | | | all_181_2, 0, all_86_11) = all_181_1)) 205.38/127.42 | | | | | | | | | | | | | | | | | | | | 205.38/127.42 | | | | | | | | | | | | | | | | | | | | ALPHA: (2548) implies: 205.38/127.42 | | | | | | | | | | | | | | | | | | | | (2549) elts(int, all_105_4) = all_181_2 205.38/127.42 | | | | | | | | | | | | | | | | | | | | 205.38/127.42 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (39), (44), (45), (99), (100), (105), (184), 205.38/127.42 | | | | | | | | | | | | | | | | | | | | (205), (255), (270), (271), (398), (2173), (2174), 205.38/127.42 | | | | | | | | | | | | | | | | | | | | (2175), (2526), (2528), (2549) are inconsistent by 205.38/127.42 | | | | | | | | | | | | | | | | | | | | sub-proof #13. 205.38/127.42 | | | | | | | | | | | | | | | | | | | | 205.38/127.42 | | | | | | | | | | | | | | | | | | | End of split 205.38/127.42 | | | | | | | | | | | | | | | | | | | 205.38/127.42 | | | | | | | | | | | | | | | | | | Case 2: 205.38/127.42 | | | | | | | | | | | | | | | | | | | 205.38/127.42 | | | | | | | | | | | | | | | | | | | (2550) ~ (all_153_1 = 0) & array_eq_sub1(int, all_105_4, 205.38/127.42 | | | | | | | | | | | | | | | | | | | all_105_2, $sum(all_86_10, 1), all_86_13) = 205.38/127.42 | | | | | | | | | | | | | | | | | | | all_153_1 205.38/127.42 | | | | | | | | | | | | | | | | | | | 205.38/127.42 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (2528), (2550) are inconsistent by sub-proof 205.38/127.42 | | | | | | | | | | | | | | | | | | | #54. 205.38/127.42 | | | | | | | | | | | | | | | | | | | 205.38/127.42 | | | | | | | | | | | | | | | | | | End of split 205.38/127.42 | | | | | | | | | | | | | | | | | | 205.38/127.42 | | | | | | | | | | | | | | | | | End of split 205.38/127.42 | | | | | | | | | | | | | | | | | 205.38/127.42 | | | | | | | | | | | | | | | | Case 2: 205.38/127.42 | | | | | | | | | | | | | | | | | 205.38/127.42 | | | | | | | | | | | | | | | | | (2551) length1(int, all_105_4) = all_234_1 & ( ~ 205.38/127.42 | | | | | | | | | | | | | | | | | ($lesseq(1, $difference(all_234_1, all_86_10))) 205.38/127.42 | | | | | | | | | | | | | | | | | | ~ ($lesseq(all_86_13, all_234_1)) | ( ~ 205.38/127.42 | | | | | | | | | | | | | | | | | (all_234_0 = all_234_1) & length1(int, 205.38/127.42 | | | | | | | | | | | | | | | | | all_105_2) = all_234_0)) 205.38/127.42 | | | | | | | | | | | | | | | | | 205.38/127.42 | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (49), (180), (181), (2551) are inconsistent 205.38/127.42 | | | | | | | | | | | | | | | | | by sub-proof #12. 205.38/127.42 | | | | | | | | | | | | | | | | | 205.38/127.42 | | | | | | | | | | | | | | | | End of split 205.38/127.42 | | | | | | | | | | | | | | | | 205.38/127.42 | | | | | | | | | | | | | | | Case 2: 205.38/127.42 | | | | | | | | | | | | | | | | 205.38/127.42 | | | | | | | | | | | | | | | | (2552) length1(int, all_105_4) = all_219_1 & ( ~ 205.38/127.42 | | | | | | | | | | | | | | | | ($lesseq(all_86_7, all_219_1)) | ~ ($lesseq(0, 205.38/127.42 | | | | | | | | | | | | | | | | all_219_1)) | ( ~ (all_219_0 = all_219_1) & 205.38/127.42 | | | | | | | | | | | | | | | | length1(int, all_105_2) = all_219_0)) 205.38/127.42 | | | | | | | | | | | | | | | | 205.38/127.42 | | | | | | | | | | | | | | | | ALPHA: (2552) implies: 205.38/127.42 | | | | | | | | | | | | | | | | (2553) length1(int, all_105_4) = all_219_1 205.38/127.42 | | | | | | | | | | | | | | | | 205.38/127.42 | | | | | | | | | | | | | | | | BETA: splitting (337) gives: 205.38/127.42 | | | | | | | | | | | | | | | | 205.38/127.42 | | | | | | | | | | | | | | | | Case 1: 205.38/127.42 | | | | | | | | | | | | | | | | | 205.38/127.42 | | | | | | | | | | | | | | | | | (2554) all_234_1 = 0 & array_eq_sub1(int, all_105_4, 205.38/127.42 | | | | | | | | | | | | | | | | | all_105_2, $sum(all_86_10, 1), all_86_13) = 0 205.38/127.42 | | | | | | | | | | | | | | | | | 205.38/127.42 | | | | | | | | | | | | | | | | | ALPHA: (2554) implies: 205.38/127.42 | | | | | | | | | | | | | | | | | (2555) array_eq_sub1(int, all_105_4, all_105_2, 205.38/127.42 | | | | | | | | | | | | | | | | | $sum(all_86_10, 1), all_86_13) = 0 205.38/127.42 | | | | | | | | | | | | | | | | | 205.38/127.42 | | | | | | | | | | | | | | | | | BETA: splitting (345) gives: 205.38/127.42 | | | | | | | | | | | | | | | | | 205.38/127.42 | | | | | | | | | | | | | | | | | Case 1: 205.38/127.42 | | | | | | | | | | | | | | | | | | 205.38/127.42 | | | | | | | | | | | | | | | | | | (2556) all_242_1 = 0 & array_eq_sub1(int, all_103_2, 205.38/127.42 | | | | | | | | | | | | | | | | | | all_105_4, $sum(all_86_8, 1), all_86_13) = 0 205.38/127.42 | | | | | | | | | | | | | | | | | | 205.38/127.42 | | | | | | | | | | | | | | | | | | ALPHA: (2556) implies: 205.38/127.42 | | | | | | | | | | | | | | | | | | (2557) array_eq_sub1(int, all_103_2, all_105_4, 205.38/127.42 | | | | | | | | | | | | | | | | | | $sum(all_86_8, 1), all_86_13) = 0 205.38/127.42 | | | | | | | | | | | | | | | | | | 205.38/127.42 | | | | | | | | | | | | | | | | | | BETA: splitting (255) gives: 205.38/127.42 | | | | | | | | | | | | | | | | | | 205.38/127.42 | | | | | | | | | | | | | | | | | | Case 1: 205.38/127.42 | | | | | | | | | | | | | | | | | | | 205.38/127.42 | | | | | | | | | | | | | | | | | | | (2558) all_153_0 = all_153_1 & $lesseq(1, 205.38/127.42 | | | | | | | | | | | | | | | | | | | $difference(all_153_1, all_86_10)) & 205.38/127.42 | | | | | | | | | | | | | | | | | | | $lesseq(all_86_13, all_153_1) & $lesseq(-1, 205.38/127.42 | | | | | | | | | | | | | | | | | | | all_86_10) & $lesseq(0, all_86_13) & 205.38/127.42 | | | | | | | | | | | | | | | | | | | length1(int, all_105_2) = all_153_1 & length1(int, 205.38/127.42 | | | | | | | | | | | | | | | | | | | all_105_4) = all_153_1 205.38/127.42 | | | | | | | | | | | | | | | | | | | 205.38/127.42 | | | | | | | | | | | | | | | | | | | ALPHA: (2558) implies: 205.38/127.42 | | | | | | | | | | | | | | | | | | | (2559) length1(int, all_105_4) = all_153_1 205.38/127.42 | | | | | | | | | | | | | | | | | | | 205.38/127.42 | | | | | | | | | | | | | | | | | | | BETA: splitting (287) gives: 205.38/127.42 | | | | | | | | | | | | | | | | | | | 205.38/127.42 | | | | | | | | | | | | | | | | | | | Case 1: 205.38/127.42 | | | | | | | | | | | | | | | | | | | | 205.38/127.42 | | | | | | | | | | | | | | | | | | | | (2560) all_181_3 = 0 & permut_sub2(int, all_103_2, 205.38/127.42 | | | | | | | | | | | | | | | | | | | | all_105_4, all_86_11, $sum(all_86_8, 1)) = 0 205.38/127.42 | | | | | | | | | | | | | | | | | | | | 205.38/127.42 | | | | | | | | | | | | | | | | | | | | ALPHA: (2560) implies: 205.38/127.42 | | | | | | | | | | | | | | | | | | | | (2561) permut_sub2(int, all_103_2, all_105_4, all_86_11, 205.38/127.42 | | | | | | | | | | | | | | | | | | | | $sum(all_86_8, 1)) = 0 205.38/127.42 | | | | | | | | | | | | | | | | | | | | 205.38/127.42 | | | | | | | | | | | | | | | | | | | | BETA: splitting (269) gives: 205.38/127.42 | | | | | | | | | | | | | | | | | | | | 205.38/127.42 | | | | | | | | | | | | | | | | | | | | Case 1: 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | (2562) all_168_0 = all_168_1 & $lesseq(1, 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | $difference(all_168_1, all_86_8)) & 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | $lesseq(all_86_13, all_168_1) & $lesseq(-1, 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | all_86_8) & $lesseq(0, all_86_13) & length1(int, 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | all_105_4) = all_168_1 & length1(int, all_103_2) 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | = all_168_1 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | ALPHA: (2562) implies: 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | (2563) length1(int, all_103_2) = all_168_1 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (271) gives: 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | Case 1: 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | (2564) all_170_0 = all_170_1 & $lesseq(all_86_11, 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | all_170_1) & $lesseq(0, all_170_1) & $lesseq(0, 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | all_86_11) & length1(int, all_105_4) = all_170_1 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | & length1(int, all_103_2) = all_170_1 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2564) implies: 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | (2565) length1(int, all_103_2) = all_170_1 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | (2566) length1(int, all_105_4) = all_170_1 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (280) gives: 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | Case 1: 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | | (2567) all_177_0 = 0 & all_177_1 = 0 & map_eq_sub1(int, 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | | all_177_4, all_177_3, $sum(all_86_8, 1), 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | | all_177_2) = 0 & map_eq_sub1(int, all_177_4, 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | | all_177_3, 0, all_86_11) = 0 & length1(int, 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | | all_103_2) = all_177_2 & elts(int, all_105_4) = 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | | all_177_3 & elts(int, all_103_2) = all_177_4 & 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | | in_uni(all_177_3) & in_uni(all_177_4) 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2567) implies: 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | | (2568) elts(int, all_105_4) = all_177_3 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | | (2569) length1(int, all_103_2) = all_177_2 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_219_1, all_170_1, 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (2553), (2566) 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | | gives: 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | | (2570) all_219_1 = all_170_1 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_219_1, all_153_1, 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (2553), (2559) 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | | gives: 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | | (2571) all_219_1 = all_153_1 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_86_13, all_177_2, 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (184), (2569) 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | | gives: 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | | (2572) all_177_2 = all_86_13 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_170_1, all_168_1, 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (2563), (2565) 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | | gives: 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | | (2573) all_170_1 = all_168_1 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_177_2, all_156_0, 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (394), (2569) 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | | gives: 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | | (2574) all_177_2 = all_156_0 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_168_1, all_156_0, 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (394), (2563) 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | | gives: 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | | (2575) all_168_1 = all_156_0 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_105_1, all_187_2, 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | | all_105_2, int, simplifying with (100), (2174) 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | | gives: 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | | (2576) all_187_2 = all_105_1 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_105_3, all_177_3, 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (99), (2568) 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | | gives: 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | | (2577) all_177_3 = all_105_3 205.38/127.42 | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_187_3, all_177_3, 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (2173), (2568) 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | | gives: 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | | (2578) all_187_3 = all_177_3 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_187_3, all_156_1, 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (395), (2173) 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | | gives: 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | | (2579) all_187_3 = all_156_1 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2570), (2571) imply: 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | | (2580) all_170_1 = all_153_1 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2580) implies: 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | | (2581) all_170_1 = all_153_1 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2578), (2579) imply: 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | | (2582) all_177_3 = all_156_1 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2582) implies: 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | | (2583) all_177_3 = all_156_1 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2572), (2574) imply: 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | | (2584) all_156_0 = all_86_13 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2584) implies: 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | | (2585) all_156_0 = all_86_13 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2577), (2583) imply: 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | | (2586) all_156_1 = all_105_3 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2573), (2581) imply: 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | | (2587) all_168_1 = all_153_1 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2587) implies: 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | | (2588) all_168_1 = all_153_1 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2575), (2588) imply: 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | | (2589) all_156_0 = all_153_1 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2589) implies: 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | | (2590) all_156_0 = all_153_1 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2585), (2590) imply: 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | | (2591) all_153_1 = all_86_13 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (44), (105), (205), (2175), (2559), (2576), 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | | (2579), (2586), (2591) are inconsistent by 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #64. 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | Case 2: 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | | (2592) ~ (all_177_4 = 0) & permut_sub2(int, all_103_2, 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | | all_105_4, all_86_11, $sum(all_86_8, 1)) = 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | | all_177_4 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (43), (2561), (2592) are inconsistent by sub-proof 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | | #47. 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | End of split 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | Case 2: 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | (2593) ~ (all_170_1 = 0) & array_eq_sub1(int, all_103_2, 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | all_105_4, 0, all_86_11) = all_170_1 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (398), (2593) are inconsistent by sub-proof 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | #48. 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | End of split 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | 205.38/127.43 | | | | | | | | | | | | | | | | | | | | Case 2: 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | (2594) ~ (all_168_1 = 0) & array_eq_sub1(int, all_103_2, 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | all_105_4, $sum(all_86_8, 1), all_86_13) = 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | all_168_1 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (2557), (2594) are inconsistent by sub-proof 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | #83. 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | 205.38/127.43 | | | | | | | | | | | | | | | | | | | | End of split 205.38/127.43 | | | | | | | | | | | | | | | | | | | | 205.38/127.43 | | | | | | | | | | | | | | | | | | | Case 2: 205.38/127.43 | | | | | | | | | | | | | | | | | | | | 205.38/127.43 | | | | | | | | | | | | | | | | | | | | (2595) elts(int, all_105_4) = all_181_2 & elts(int, 205.38/127.43 | | | | | | | | | | | | | | | | | | | | all_103_2) = all_181_3 & in_uni(all_181_2) & 205.38/127.43 | | | | | | | | | | | | | | | | | | | | in_uni(all_181_3) & (( ~ (all_181_0 = 0) & 205.38/127.43 | | | | | | | | | | | | | | | | | | | | map_eq_sub1(int, all_181_3, all_181_2, 205.38/127.43 | | | | | | | | | | | | | | | | | | | | $sum(all_86_8, 1), all_181_1) = all_181_0 & 205.38/127.43 | | | | | | | | | | | | | | | | | | | | length1(int, all_103_2) = all_181_1) | ( ~ 205.38/127.43 | | | | | | | | | | | | | | | | | | | | (all_181_1 = 0) & map_eq_sub1(int, all_181_3, 205.38/127.43 | | | | | | | | | | | | | | | | | | | | all_181_2, 0, all_86_11) = all_181_1)) 205.38/127.43 | | | | | | | | | | | | | | | | | | | | 205.38/127.43 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (39), (43), (44), (90), (91), (96), (99), 205.38/127.43 | | | | | | | | | | | | | | | | | | | | (183), (184), (203), (206), (263), (296), (297), 205.38/127.43 | | | | | | | | | | | | | | | | | | | | (394), (395), (396), (1808), (2173), (2523), 205.38/127.43 | | | | | | | | | | | | | | | | | | | | (2595) are inconsistent by sub-proof #10. 205.38/127.43 | | | | | | | | | | | | | | | | | | | | 205.38/127.43 | | | | | | | | | | | | | | | | | | | End of split 205.38/127.43 | | | | | | | | | | | | | | | | | | | 205.38/127.43 | | | | | | | | | | | | | | | | | | Case 2: 205.38/127.43 | | | | | | | | | | | | | | | | | | | 205.38/127.43 | | | | | | | | | | | | | | | | | | | (2596) ~ (all_153_1 = 0) & array_eq_sub1(int, all_105_4, 205.38/127.43 | | | | | | | | | | | | | | | | | | | all_105_2, $sum(all_86_10, 1), all_86_13) = 205.38/127.43 | | | | | | | | | | | | | | | | | | | all_153_1 205.38/127.43 | | | | | | | | | | | | | | | | | | | 205.38/127.43 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (2555), (2596) are inconsistent by sub-proof 205.38/127.43 | | | | | | | | | | | | | | | | | | | #54. 205.38/127.43 | | | | | | | | | | | | | | | | | | | 205.38/127.43 | | | | | | | | | | | | | | | | | | End of split 205.38/127.43 | | | | | | | | | | | | | | | | | | 205.38/127.43 | | | | | | | | | | | | | | | | | Case 2: 205.38/127.43 | | | | | | | | | | | | | | | | | | 205.38/127.43 | | | | | | | | | | | | | | | | | | (2597) length1(int, all_103_2) = all_242_1 & ( ~ 205.38/127.43 | | | | | | | | | | | | | | | | | | ($lesseq(1, $difference(all_242_1, all_86_8))) | 205.38/127.43 | | | | | | | | | | | | | | | | | | ~ ($lesseq(all_86_13, all_242_1)) | ( ~ 205.38/127.43 | | | | | | | | | | | | | | | | | | (all_242_0 = all_242_1) & length1(int, 205.38/127.43 | | | | | | | | | | | | | | | | | | all_105_4) = all_242_0)) 205.38/127.43 | | | | | | | | | | | | | | | | | | 205.38/127.43 | | | | | | | | | | | | | | | | | | ALPHA: (2597) implies: 205.38/127.43 | | | | | | | | | | | | | | | | | | (2598) length1(int, all_103_2) = all_242_1 205.38/127.43 | | | | | | | | | | | | | | | | | | 205.38/127.43 | | | | | | | | | | | | | | | | | | BETA: splitting (255) gives: 205.38/127.43 | | | | | | | | | | | | | | | | | | 205.38/127.43 | | | | | | | | | | | | | | | | | | Case 1: 205.38/127.43 | | | | | | | | | | | | | | | | | | | 205.38/127.43 | | | | | | | | | | | | | | | | | | | (2599) all_153_0 = all_153_1 & $lesseq(1, 205.38/127.43 | | | | | | | | | | | | | | | | | | | $difference(all_153_1, all_86_10)) & 205.38/127.43 | | | | | | | | | | | | | | | | | | | $lesseq(all_86_13, all_153_1) & $lesseq(-1, 205.38/127.43 | | | | | | | | | | | | | | | | | | | all_86_10) & $lesseq(0, all_86_13) & 205.38/127.43 | | | | | | | | | | | | | | | | | | | length1(int, all_105_2) = all_153_1 & length1(int, 205.38/127.43 | | | | | | | | | | | | | | | | | | | all_105_4) = all_153_1 205.38/127.43 | | | | | | | | | | | | | | | | | | | 205.38/127.43 | | | | | | | | | | | | | | | | | | | ALPHA: (2599) implies: 205.38/127.43 | | | | | | | | | | | | | | | | | | | (2600) $lesseq(1, $difference(all_153_1, all_86_10)) 205.38/127.43 | | | | | | | | | | | | | | | | | | | (2601) length1(int, all_105_4) = all_153_1 205.38/127.43 | | | | | | | | | | | | | | | | | | | 205.38/127.43 | | | | | | | | | | | | | | | | | | | BETA: splitting (287) gives: 205.38/127.43 | | | | | | | | | | | | | | | | | | | 205.38/127.43 | | | | | | | | | | | | | | | | | | | Case 1: 205.38/127.43 | | | | | | | | | | | | | | | | | | | | 205.38/127.43 | | | | | | | | | | | | | | | | | | | | (2602) all_181_3 = 0 & permut_sub2(int, all_103_2, 205.38/127.43 | | | | | | | | | | | | | | | | | | | | all_105_4, all_86_11, $sum(all_86_8, 1)) = 0 205.38/127.43 | | | | | | | | | | | | | | | | | | | | 205.38/127.43 | | | | | | | | | | | | | | | | | | | | ALPHA: (2602) implies: 205.38/127.43 | | | | | | | | | | | | | | | | | | | | (2603) permut_sub2(int, all_103_2, all_105_4, all_86_11, 205.38/127.43 | | | | | | | | | | | | | | | | | | | | $sum(all_86_8, 1)) = 0 205.38/127.43 | | | | | | | | | | | | | | | | | | | | 205.38/127.43 | | | | | | | | | | | | | | | | | | | | BETA: splitting (280) gives: 205.38/127.43 | | | | | | | | | | | | | | | | | | | | 205.38/127.43 | | | | | | | | | | | | | | | | | | | | Case 1: 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | (2604) all_177_0 = 0 & all_177_1 = 0 & map_eq_sub1(int, 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | all_177_4, all_177_3, $sum(all_86_8, 1), 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | all_177_2) = 0 & map_eq_sub1(int, all_177_4, 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | all_177_3, 0, all_86_11) = 0 & length1(int, 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | all_103_2) = all_177_2 & elts(int, all_105_4) = 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | all_177_3 & elts(int, all_103_2) = all_177_4 & 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | in_uni(all_177_3) & in_uni(all_177_4) 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | ALPHA: (2604) implies: 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | (2605) length1(int, all_103_2) = all_177_2 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (271) gives: 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | Case 1: 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | (2606) all_170_0 = all_170_1 & $lesseq(all_86_11, 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | all_170_1) & $lesseq(0, all_170_1) & $lesseq(0, 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | all_86_11) & length1(int, all_105_4) = all_170_1 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | & length1(int, all_103_2) = all_170_1 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2606) implies: 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | (2607) length1(int, all_103_2) = all_170_1 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | (2608) length1(int, all_105_4) = all_170_1 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_219_1, all_170_1, 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (2553), (2608) 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | gives: 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | (2609) all_219_1 = all_170_1 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_219_1, all_153_1, 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (2553), (2601) 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | gives: 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | (2610) all_219_1 = all_153_1 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_86_13, all_177_2, 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (184), (2605) 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | gives: 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | (2611) all_177_2 = all_86_13 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_242_1, all_177_2, 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (2598), (2605) 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | gives: 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | (2612) all_242_1 = all_177_2 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_177_2, all_170_1, 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (2605), (2607) 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | gives: 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | (2613) all_177_2 = all_170_1 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_242_1, all_156_0, 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (394), (2598) 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | gives: 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | (2614) all_242_1 = all_156_0 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_86_13, all_238_1, 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (183), (1808) 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | gives: 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | (2615) all_238_1 = all_86_13 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_238_1, all_215_1, 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (1808), (2523) 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | gives: 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | (2616) all_238_1 = all_215_1 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2612), (2614) imply: 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | (2617) all_177_2 = all_156_0 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | SIMP: (2617) implies: 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | (2618) all_177_2 = all_156_0 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2615), (2616) imply: 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | (2619) all_215_1 = all_86_13 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2609), (2610) imply: 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | (2620) all_170_1 = all_153_1 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | SIMP: (2620) implies: 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | (2621) all_170_1 = all_153_1 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2611), (2618) imply: 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | (2622) all_156_0 = all_86_13 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2613), (2618) imply: 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | (2623) all_170_1 = all_156_0 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | SIMP: (2623) implies: 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | (2624) all_170_1 = all_156_0 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2621), (2624) imply: 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | (2625) all_156_0 = all_153_1 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (48), (50), (52), (53), (394), (2524), 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | (2600), (2619), (2622), (2625) are inconsistent by 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | sub-proof #33. 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | Case 2: 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | (2626) ~ (all_170_1 = 0) & array_eq_sub1(int, all_103_2, 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | all_105_4, 0, all_86_11) = all_170_1 205.38/127.43 | | | | | | | | | | | | | | | | | | | | | | 205.38/127.44 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (398), (2626) are inconsistent by sub-proof 205.38/127.44 | | | | | | | | | | | | | | | | | | | | | | #48. 205.38/127.44 | | | | | | | | | | | | | | | | | | | | | | 205.38/127.44 | | | | | | | | | | | | | | | | | | | | | End of split 205.38/127.44 | | | | | | | | | | | | | | | | | | | | | 205.38/127.44 | | | | | | | | | | | | | | | | | | | | Case 2: 205.38/127.44 | | | | | | | | | | | | | | | | | | | | | 205.38/127.44 | | | | | | | | | | | | | | | | | | | | | (2627) ~ (all_177_4 = 0) & permut_sub2(int, all_103_2, 205.38/127.44 | | | | | | | | | | | | | | | | | | | | | all_105_4, all_86_11, $sum(all_86_8, 1)) = 205.38/127.44 | | | | | | | | | | | | | | | | | | | | | all_177_4 205.38/127.44 | | | | | | | | | | | | | | | | | | | | | 205.38/127.44 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (43), (2603), (2627) are inconsistent by sub-proof 205.38/127.44 | | | | | | | | | | | | | | | | | | | | | #47. 205.38/127.44 | | | | | | | | | | | | | | | | | | | | | 205.38/127.44 | | | | | | | | | | | | | | | | | | | | End of split 205.38/127.44 | | | | | | | | | | | | | | | | | | | | 205.38/127.44 | | | | | | | | | | | | | | | | | | | Case 2: 205.38/127.44 | | | | | | | | | | | | | | | | | | | | 205.38/127.44 | | | | | | | | | | | | | | | | | | | | (2628) elts(int, all_105_4) = all_181_2 & elts(int, 205.38/127.44 | | | | | | | | | | | | | | | | | | | | all_103_2) = all_181_3 & in_uni(all_181_2) & 205.38/127.44 | | | | | | | | | | | | | | | | | | | | in_uni(all_181_3) & (( ~ (all_181_0 = 0) & 205.38/127.44 | | | | | | | | | | | | | | | | | | | | map_eq_sub1(int, all_181_3, all_181_2, 205.38/127.44 | | | | | | | | | | | | | | | | | | | | $sum(all_86_8, 1), all_181_1) = all_181_0 & 205.38/127.44 | | | | | | | | | | | | | | | | | | | | length1(int, all_103_2) = all_181_1) | ( ~ 205.38/127.44 | | | | | | | | | | | | | | | | | | | | (all_181_1 = 0) & map_eq_sub1(int, all_181_3, 205.38/127.44 | | | | | | | | | | | | | | | | | | | | all_181_2, 0, all_86_11) = all_181_1)) 205.38/127.44 | | | | | | | | | | | | | | | | | | | | 205.38/127.44 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (39), (43), (44), (90), (91), (96), (99), 205.38/127.44 | | | | | | | | | | | | | | | | | | | | (183), (184), (203), (206), (263), (296), (297), 205.38/127.44 | | | | | | | | | | | | | | | | | | | | (394), (395), (396), (1808), (2173), (2523), 205.38/127.44 | | | | | | | | | | | | | | | | | | | | (2628) are inconsistent by sub-proof #10. 205.38/127.44 | | | | | | | | | | | | | | | | | | | | 205.38/127.44 | | | | | | | | | | | | | | | | | | | End of split 205.38/127.44 | | | | | | | | | | | | | | | | | | | 205.38/127.44 | | | | | | | | | | | | | | | | | | Case 2: 205.38/127.44 | | | | | | | | | | | | | | | | | | | 205.38/127.44 | | | | | | | | | | | | | | | | | | | (2629) ~ (all_153_1 = 0) & array_eq_sub1(int, all_105_4, 205.38/127.44 | | | | | | | | | | | | | | | | | | | all_105_2, $sum(all_86_10, 1), all_86_13) = 205.38/127.44 | | | | | | | | | | | | | | | | | | | all_153_1 205.38/127.44 | | | | | | | | | | | | | | | | | | | 205.38/127.44 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (2555), (2629) are inconsistent by sub-proof 205.38/127.44 | | | | | | | | | | | | | | | | | | | #54. 205.38/127.44 | | | | | | | | | | | | | | | | | | | 205.38/127.44 | | | | | | | | | | | | | | | | | | End of split 205.38/127.44 | | | | | | | | | | | | | | | | | | 205.38/127.44 | | | | | | | | | | | | | | | | | End of split 205.38/127.44 | | | | | | | | | | | | | | | | | 205.38/127.44 | | | | | | | | | | | | | | | | Case 2: 205.38/127.44 | | | | | | | | | | | | | | | | | 205.38/127.44 | | | | | | | | | | | | | | | | | (2630) length1(int, all_105_4) = all_234_1 & ( ~ 205.38/127.44 | | | | | | | | | | | | | | | | | ($lesseq(1, $difference(all_234_1, all_86_10))) 205.38/127.44 | | | | | | | | | | | | | | | | | | ~ ($lesseq(all_86_13, all_234_1)) | ( ~ 205.38/127.44 | | | | | | | | | | | | | | | | | (all_234_0 = all_234_1) & length1(int, 205.38/127.44 | | | | | | | | | | | | | | | | | all_105_2) = all_234_0)) 205.38/127.44 | | | | | | | | | | | | | | | | | 205.38/127.44 | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (49), (180), (181), (2630) are inconsistent 205.38/127.44 | | | | | | | | | | | | | | | | | by sub-proof #12. 205.38/127.44 | | | | | | | | | | | | | | | | | 205.38/127.44 | | | | | | | | | | | | | | | | End of split 205.38/127.44 | | | | | | | | | | | | | | | | 205.38/127.44 | | | | | | | | | | | | | | | End of split 205.38/127.44 | | | | | | | | | | | | | | | 205.38/127.44 | | | | | | | | | | | | | | End of split 205.38/127.44 | | | | | | | | | | | | | | 205.38/127.44 | | | | | | | | | | | | | End of split 205.38/127.44 | | | | | | | | | | | | | 205.38/127.44 | | | | | | | | | | | | End of split 205.38/127.44 | | | | | | | | | | | | 205.38/127.44 | | | | | | | | | | | Case 2: 205.38/127.44 | | | | | | | | | | | | 205.38/127.44 | | | | | | | | | | | | (2631) length1(int, all_103_2) = all_211_1 & ( ~ 205.38/127.44 | | | | | | | | | | | | ($lesseq(all_86_11, all_211_1)) | ~ ($lesseq(0, 205.38/127.44 | | | | | | | | | | | | all_211_1)) | ( ~ (all_211_0 = all_211_1) & 205.38/127.44 | | | | | | | | | | | | length1(int, all_105_4) = all_211_0)) 205.38/127.44 | | | | | | | | | | | | 205.38/127.44 | | | | | | | | | | | | ALPHA: (2631) implies: 205.38/127.44 | | | | | | | | | | | | (2632) length1(int, all_103_2) = all_211_1 205.38/127.44 | | | | | | | | | | | | (2633) ~ ($lesseq(all_86_11, all_211_1)) | ~ 205.38/127.44 | | | | | | | | | | | | ($lesseq(0, all_211_1)) | ( ~ (all_211_0 = 205.38/127.44 | | | | | | | | | | | | all_211_1) & length1(int, all_105_4) = 205.38/127.44 | | | | | | | | | | | | all_211_0) 205.38/127.44 | | | | | | | | | | | | 205.38/127.44 | | | | | | | | | | | | BETA: splitting (341) gives: 205.38/127.44 | | | | | | | | | | | | 205.38/127.44 | | | | | | | | | | | | Case 1: 205.38/127.44 | | | | | | | | | | | | | 205.38/127.44 | | | | | | | | | | | | | (2634) all_238_1 = 0 & array_eq_sub1(int, all_103_4, 205.38/127.44 | | | | | | | | | | | | | all_103_2, $sum(all_86_10, 1), all_86_13) = 0 205.38/127.44 | | | | | | | | | | | | | 205.38/127.44 | | | | | | | | | | | | | ALPHA: (2634) implies: 205.38/127.44 | | | | | | | | | | | | | (2635) array_eq_sub1(int, all_103_4, all_103_2, 205.38/127.44 | | | | | | | | | | | | | $sum(all_86_10, 1), all_86_13) = 0 205.38/127.44 | | | | | | | | | | | | | 205.38/127.44 | | | | | | | | | | | | | BETA: splitting (296) gives: 205.38/127.44 | | | | | | | | | | | | | 205.38/127.44 | | | | | | | | | | | | | Case 1: 205.38/127.44 | | | | | | | | | | | | | | 205.38/127.44 | | | | | | | | | | | | | | (2636) all_191_3 = 0 & permut_sub2(int, all_103_4, 205.38/127.44 | | | | | | | | | | | | | | all_103_2, all_86_11, $sum(all_86_10, 1)) = 0 205.38/127.44 | | | | | | | | | | | | | | 205.38/127.44 | | | | | | | | | | | | | | ALPHA: (2636) implies: 205.38/127.44 | | | | | | | | | | | | | | (2637) permut_sub2(int, all_103_4, all_103_2, all_86_11, 205.38/127.44 | | | | | | | | | | | | | | $sum(all_86_10, 1)) = 0 205.38/127.44 | | | | | | | | | | | | | | 205.38/127.44 | | | | | | | | | | | | | | BETA: splitting (294) gives: 205.38/127.44 | | | | | | | | | | | | | | 205.38/127.44 | | | | | | | | | | | | | | Case 1: 205.38/127.44 | | | | | | | | | | | | | | | 205.38/127.44 | | | | | | | | | | | | | | | (2638) all_187_3 = 0 & permut_sub2(int, all_105_4, 205.38/127.44 | | | | | | | | | | | | | | | all_105_2, all_86_7, $sum(all_86_10, 1)) = 0 205.38/127.44 | | | | | | | | | | | | | | | 205.38/127.44 | | | | | | | | | | | | | | | ALPHA: (2638) implies: 205.38/127.44 | | | | | | | | | | | | | | | (2639) permut_sub2(int, all_105_4, all_105_2, all_86_7, 205.38/127.44 | | | | | | | | | | | | | | | $sum(all_86_10, 1)) = 0 205.38/127.44 | | | | | | | | | | | | | | | 205.38/127.44 | | | | | | | | | | | | | | | BETA: splitting (319) gives: 205.38/127.44 | | | | | | | | | | | | | | | 205.38/127.44 | | | | | | | | | | | | | | | Case 1: 205.38/127.44 | | | | | | | | | | | | | | | | 205.38/127.44 | | | | | | | | | | | | | | | | (2640) all_215_1 = 0 & array_eq_sub1(int, all_103_4, 205.38/127.44 | | | | | | | | | | | | | | | | all_103_2, 0, all_86_11) = 0 205.38/127.44 | | | | | | | | | | | | | | | | 205.38/127.44 | | | | | | | | | | | | | | | | ALPHA: (2640) implies: 205.38/127.44 | | | | | | | | | | | | | | | | (2641) array_eq_sub1(int, all_103_4, all_103_2, 0, 205.38/127.44 | | | | | | | | | | | | | | | | all_86_11) = 0 205.38/127.44 | | | | | | | | | | | | | | | | 205.38/127.44 | | | | | | | | | | | | | | | | BETA: splitting (295) gives: 205.38/127.44 | | | | | | | | | | | | | | | | 205.38/127.44 | | | | | | | | | | | | | | | | Case 1: 205.38/127.44 | | | | | | | | | | | | | | | | | 205.38/127.44 | | | | | | | | | | | | | | | | | (2642) all_190_0 = 0 & all_190_1 = 0 & map_eq_sub1(int, 205.38/127.44 | | | | | | | | | | | | | | | | | all_190_4, all_190_3, $sum(all_86_10, 1), 205.38/127.44 | | | | | | | | | | | | | | | | | all_190_2) = 0 & map_eq_sub1(int, all_190_4, 205.38/127.44 | | | | | | | | | | | | | | | | | all_190_3, 0, all_86_7) = 0 & length1(int, 205.38/127.44 | | | | | | | | | | | | | | | | | all_105_4) = all_190_2 & elts(int, all_105_2) = 205.38/127.44 | | | | | | | | | | | | | | | | | all_190_3 & elts(int, all_105_4) = all_190_4 & 205.38/127.44 | | | | | | | | | | | | | | | | | in_uni(all_190_3) & in_uni(all_190_4) 205.38/127.44 | | | | | | | | | | | | | | | | | 205.38/127.44 | | | | | | | | | | | | | | | | | ALPHA: (2642) implies: 205.38/127.44 | | | | | | | | | | | | | | | | | (2643) elts(int, all_105_4) = all_190_4 205.38/127.44 | | | | | | | | | | | | | | | | | (2644) length1(int, all_105_4) = all_190_2 205.38/127.44 | | | | | | | | | | | | | | | | | 205.38/127.44 | | | | | | | | | | | | | | | | | BETA: splitting (324) gives: 205.38/127.44 | | | | | | | | | | | | | | | | | 205.38/127.44 | | | | | | | | | | | | | | | | | Case 1: 205.38/127.44 | | | | | | | | | | | | | | | | | | 205.38/127.44 | | | | | | | | | | | | | | | | | | (2645) all_219_1 = 0 & array_eq_sub1(int, all_105_4, 205.38/127.44 | | | | | | | | | | | | | | | | | | all_105_2, 0, all_86_7) = 0 205.38/127.44 | | | | | | | | | | | | | | | | | | 205.38/127.44 | | | | | | | | | | | | | | | | | | ALPHA: (2645) implies: 205.38/127.45 | | | | | | | | | | | | | | | | | | (2646) array_eq_sub1(int, all_105_4, all_105_2, 0, 205.38/127.45 | | | | | | | | | | | | | | | | | | all_86_7) = 0 205.38/127.45 | | | | | | | | | | | | | | | | | | 205.38/127.45 | | | | | | | | | | | | | | | | | | BETA: splitting (287) gives: 205.38/127.45 | | | | | | | | | | | | | | | | | | 205.38/127.45 | | | | | | | | | | | | | | | | | | Case 1: 205.38/127.45 | | | | | | | | | | | | | | | | | | | 205.38/127.45 | | | | | | | | | | | | | | | | | | | (2647) all_181_3 = 0 & permut_sub2(int, all_103_2, 205.38/127.45 | | | | | | | | | | | | | | | | | | | all_105_4, all_86_11, $sum(all_86_8, 1)) = 0 205.38/127.45 | | | | | | | | | | | | | | | | | | | 205.38/127.45 | | | | | | | | | | | | | | | | | | | ALPHA: (2647) implies: 205.38/127.45 | | | | | | | | | | | | | | | | | | | (2648) permut_sub2(int, all_103_2, all_105_4, all_86_11, 205.38/127.45 | | | | | | | | | | | | | | | | | | | $sum(all_86_8, 1)) = 0 205.38/127.45 | | | | | | | | | | | | | | | | | | | 205.38/127.45 | | | | | | | | | | | | | | | | | | | BETA: splitting (280) gives: 205.38/127.45 | | | | | | | | | | | | | | | | | | | 205.38/127.45 | | | | | | | | | | | | | | | | | | | Case 1: 205.38/127.45 | | | | | | | | | | | | | | | | | | | | 205.38/127.45 | | | | | | | | | | | | | | | | | | | | (2649) all_177_0 = 0 & all_177_1 = 0 & map_eq_sub1(int, 205.38/127.45 | | | | | | | | | | | | | | | | | | | | all_177_4, all_177_3, $sum(all_86_8, 1), 205.38/127.45 | | | | | | | | | | | | | | | | | | | | all_177_2) = 0 & map_eq_sub1(int, all_177_4, 205.38/127.45 | | | | | | | | | | | | | | | | | | | | all_177_3, 0, all_86_11) = 0 & length1(int, 205.38/127.45 | | | | | | | | | | | | | | | | | | | | all_103_2) = all_177_2 & elts(int, all_105_4) = 205.38/127.45 | | | | | | | | | | | | | | | | | | | | all_177_3 & elts(int, all_103_2) = all_177_4 & 205.38/127.45 | | | | | | | | | | | | | | | | | | | | in_uni(all_177_3) & in_uni(all_177_4) 205.38/127.45 | | | | | | | | | | | | | | | | | | | | 205.38/127.45 | | | | | | | | | | | | | | | | | | | | ALPHA: (2649) implies: 205.38/127.45 | | | | | | | | | | | | | | | | | | | | (2650) length1(int, all_103_2) = all_177_2 205.38/127.45 | | | | | | | | | | | | | | | | | | | | 205.38/127.45 | | | | | | | | | | | | | | | | | | | | BETA: splitting (337) gives: 205.38/127.45 | | | | | | | | | | | | | | | | | | | | 205.38/127.45 | | | | | | | | | | | | | | | | | | | | Case 1: 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | (2651) all_234_1 = 0 & array_eq_sub1(int, all_105_4, 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | all_105_2, $sum(all_86_10, 1), all_86_13) = 0 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | ALPHA: (2651) implies: 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | (2652) array_eq_sub1(int, all_105_4, all_105_2, 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | $sum(all_86_10, 1), all_86_13) = 0 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (270) gives: 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | Case 1: 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | (2653) all_169_0 = all_169_1 & $lesseq(all_86_7, 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | all_169_1) & $lesseq(0, all_169_1) & $lesseq(0, 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | all_86_7) & length1(int, all_105_2) = all_169_1 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | & length1(int, all_105_4) = all_169_1 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2653) implies: 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | (2654) $lesseq(all_86_7, all_169_1) 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | (2655) length1(int, all_105_4) = all_169_1 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (255) gives: 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | Case 1: 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | (2656) all_153_0 = all_153_1 & $lesseq(1, 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | $difference(all_153_1, all_86_10)) & 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | $lesseq(all_86_13, all_153_1) & $lesseq(-1, 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | all_86_10) & $lesseq(0, all_86_13) & 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | length1(int, all_105_2) = all_153_1 & length1(int, 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | all_105_4) = all_153_1 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2656) implies: 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | (2657) $lesseq(1, $difference(all_153_1, all_86_10)) 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | (2658) length1(int, all_105_4) = all_153_1 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (272) gives: 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | Case 1: 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | (2659) all_171_0 = all_171_1 & $lesseq(all_86_11, 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | all_171_1) & $lesseq(0, all_171_1) & $lesseq(0, 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | all_86_11) & length1(int, all_103_2) = all_171_1 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | & length1(int, all_103_4) = all_171_1 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2659) implies: 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | (2660) length1(int, all_103_4) = all_171_1 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (345) gives: 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | (2661) all_242_1 = 0 & array_eq_sub1(int, all_103_2, 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, $sum(all_86_8, 1), all_86_13) = 0 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2661) implies: 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | (2662) array_eq_sub1(int, all_103_2, all_105_4, 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | $sum(all_86_8, 1), all_86_13) = 0 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (45), (48), (50), (52), (53), (180), (184), 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | (269), (2632), (2633), (2644), (2650), (2655), 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | (2657), (2658), (2662) are inconsistent by 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #8. 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | (2663) length1(int, all_103_2) = all_242_1 & ( ~ 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | ($lesseq(1, $difference(all_242_1, all_86_8))) | 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | ~ ($lesseq(all_86_13, all_242_1)) | ( ~ 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | (all_242_0 = all_242_1) & length1(int, 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4) = all_242_0)) 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2663) implies: 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | (2664) length1(int, all_103_2) = all_242_1 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | (2665) ~ ($lesseq(1, $difference(all_242_1, all_86_8))) 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | ~ ($lesseq(all_86_13, all_242_1)) | ( ~ 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | (all_242_0 = all_242_1) & length1(int, 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4) = all_242_0) 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (298) gives: 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | (2666) all_193_0 = all_193_1 & $lesseq(1, 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | $difference(all_193_1, all_86_10)) & 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | $lesseq(all_86_13, all_193_1) & $lesseq(-1, 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | all_86_10) & $lesseq(0, all_86_13) & 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | length1(int, all_103_2) = all_193_1 & length1(int, 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_4) = all_193_1 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2666) implies: 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | (2667) length1(int, all_103_4) = all_193_1 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | (2668) length1(int, all_103_2) = all_193_1 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (297) gives: 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2669) all_192_0 = 0 & all_192_1 = 0 & map_eq_sub1(int, 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_192_4, all_192_3, $sum(all_86_10, 1), 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_192_2) = 0 & map_eq_sub1(int, all_192_4, 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_192_3, 0, all_86_11) = 0 & length1(int, 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_4) = all_192_2 & elts(int, all_103_2) = 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_192_3 & elts(int, all_103_4) = all_192_4 & 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | in_uni(all_192_3) & in_uni(all_192_4) 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2669) implies: 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2670) length1(int, all_103_4) = all_192_2 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_86_13, all_190_2, 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (180), (2644) 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2671) all_190_2 = all_86_13 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_190_2, all_169_1, 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (2644), (2655) 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2672) all_190_2 = all_169_1 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_169_1, all_153_1, 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (2655), (2658) 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2673) all_169_1 = all_153_1 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_242_1, all_193_1, 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (2664), (2668) 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2674) all_242_1 = all_193_1 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_211_1, all_193_1, 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (2632), (2668) 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2675) all_211_1 = all_193_1 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_211_1, all_177_2, 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (2632), (2650) 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2676) all_211_1 = all_177_2 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_242_1, all_156_0, 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (394), (2664) 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2677) all_242_1 = all_156_0 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_86_13, all_192_2, 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (183), (2670) 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2678) all_192_2 = all_86_13 205.38/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_193_1, all_171_1, 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (2660), (2667) 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2679) all_193_1 = all_171_1 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_192_2, all_171_1, 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (2660), (2670) 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2680) all_192_2 = all_171_1 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2674), (2677) imply: 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2681) all_193_1 = all_156_0 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2681) implies: 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2682) all_193_1 = all_156_0 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2675), (2676) imply: 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2683) all_193_1 = all_177_2 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2683) implies: 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2684) all_193_1 = all_177_2 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2682), (2684) imply: 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2685) all_177_2 = all_156_0 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2679), (2684) imply: 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2686) all_177_2 = all_171_1 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2678), (2680) imply: 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2687) all_171_1 = all_86_13 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2687) implies: 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2688) all_171_1 = all_86_13 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2671), (2672) imply: 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2689) all_169_1 = all_86_13 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2689) implies: 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2690) all_169_1 = all_86_13 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2685), (2686) imply: 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2691) all_171_1 = all_156_0 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2691) implies: 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2692) all_171_1 = all_156_0 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2688), (2692) imply: 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2693) all_156_0 = all_86_13 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2693) implies: 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2694) all_156_0 = all_86_13 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2673), (2690) imply: 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2695) all_153_1 = all_86_13 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2677), (2694) imply: 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2696) all_242_1 = all_86_13 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (52), (180), (389), (2665), (2696) are 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #77. 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2697) ~ (all_192_4 = 0) & permut_sub2(int, all_103_4, 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, all_86_11, $sum(all_86_10, 1)) = 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_192_4 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (43), (2637), (2697) are inconsistent by sub-proof 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | #69. 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | (2698) ~ (all_193_1 = 0) & array_eq_sub1(int, all_103_4, 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, $sum(all_86_10, 1), all_86_13) = 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | all_193_1 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (2635), (2698) are inconsistent by sub-proof 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | #55. 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | End of split 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | | End of split 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | Case 2: 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | | (2699) ~ (all_171_1 = 0) & array_eq_sub1(int, all_103_4, 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, 0, all_86_11) = all_171_1 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (2641), (2699) are inconsistent by sub-proof 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | | #81. 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | End of split 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | Case 2: 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | (2700) ~ (all_153_1 = 0) & array_eq_sub1(int, all_105_4, 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | all_105_2, $sum(all_86_10, 1), all_86_13) = 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | all_153_1 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (2652), (2700) are inconsistent by sub-proof 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | #54. 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | End of split 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | Case 2: 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | (2701) ~ (all_169_1 = 0) & array_eq_sub1(int, all_105_4, 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | all_105_2, 0, all_86_7) = all_169_1 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (2646), (2701) are inconsistent by sub-proof 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | #75. 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | End of split 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | 205.57/127.45 | | | | | | | | | | | | | | | | | | | | Case 2: 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | (2702) length1(int, all_105_4) = all_234_1 & ( ~ 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | ($lesseq(1, $difference(all_234_1, all_86_10))) 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | ~ ($lesseq(all_86_13, all_234_1)) | ( ~ 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | (all_234_0 = all_234_1) & length1(int, 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | all_105_2) = all_234_0)) 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (49), (180), (181), (2702) are inconsistent 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | by sub-proof #12. 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | 205.57/127.45 | | | | | | | | | | | | | | | | | | | | End of split 205.57/127.45 | | | | | | | | | | | | | | | | | | | | 205.57/127.45 | | | | | | | | | | | | | | | | | | | Case 2: 205.57/127.45 | | | | | | | | | | | | | | | | | | | | 205.57/127.45 | | | | | | | | | | | | | | | | | | | | (2703) ~ (all_177_4 = 0) & permut_sub2(int, all_103_2, 205.57/127.45 | | | | | | | | | | | | | | | | | | | | all_105_4, all_86_11, $sum(all_86_8, 1)) = 205.57/127.45 | | | | | | | | | | | | | | | | | | | | all_177_4 205.57/127.45 | | | | | | | | | | | | | | | | | | | | 205.57/127.45 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (43), (2648), (2703) are inconsistent by sub-proof 205.57/127.45 | | | | | | | | | | | | | | | | | | | | #47. 205.57/127.45 | | | | | | | | | | | | | | | | | | | | 205.57/127.45 | | | | | | | | | | | | | | | | | | | End of split 205.57/127.45 | | | | | | | | | | | | | | | | | | | 205.57/127.45 | | | | | | | | | | | | | | | | | | Case 2: 205.57/127.45 | | | | | | | | | | | | | | | | | | | 205.57/127.45 | | | | | | | | | | | | | | | | | | | (2704) elts(int, all_105_4) = all_181_2 & elts(int, 205.57/127.45 | | | | | | | | | | | | | | | | | | | all_103_2) = all_181_3 & in_uni(all_181_2) & 205.57/127.45 | | | | | | | | | | | | | | | | | | | in_uni(all_181_3) & (( ~ (all_181_0 = 0) & 205.57/127.45 | | | | | | | | | | | | | | | | | | | map_eq_sub1(int, all_181_3, all_181_2, 205.57/127.45 | | | | | | | | | | | | | | | | | | | $sum(all_86_8, 1), all_181_1) = all_181_0 & 205.57/127.45 | | | | | | | | | | | | | | | | | | | length1(int, all_103_2) = all_181_1) | ( ~ 205.57/127.45 | | | | | | | | | | | | | | | | | | | (all_181_1 = 0) & map_eq_sub1(int, all_181_3, 205.57/127.45 | | | | | | | | | | | | | | | | | | | all_181_2, 0, all_86_11) = all_181_1)) 205.57/127.45 | | | | | | | | | | | | | | | | | | | 205.57/127.45 | | | | | | | | | | | | | | | | | | | ALPHA: (2704) implies: 205.57/127.45 | | | | | | | | | | | | | | | | | | | (2705) elts(int, all_103_2) = all_181_3 205.57/127.45 | | | | | | | | | | | | | | | | | | | (2706) elts(int, all_105_4) = all_181_2 205.57/127.45 | | | | | | | | | | | | | | | | | | | (2707) ( ~ (all_181_0 = 0) & map_eq_sub1(int, all_181_3, 205.57/127.45 | | | | | | | | | | | | | | | | | | | all_181_2, $sum(all_86_8, 1), all_181_1) = 205.57/127.45 | | | | | | | | | | | | | | | | | | | all_181_0 & length1(int, all_103_2) = all_181_1) 205.57/127.45 | | | | | | | | | | | | | | | | | | | | ( ~ (all_181_1 = 0) & map_eq_sub1(int, 205.57/127.45 | | | | | | | | | | | | | | | | | | | all_181_3, all_181_2, 0, all_86_11) = 205.57/127.45 | | | | | | | | | | | | | | | | | | | all_181_1) 205.57/127.45 | | | | | | | | | | | | | | | | | | | 205.57/127.45 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (39), (43), (44), (91), (99), (184), (203), 205.57/127.45 | | | | | | | | | | | | | | | | | | | (263), (297), (394), (395), (396), (2637), (2643), 205.57/127.45 | | | | | | | | | | | | | | | | | | | (2705), (2706), (2707) are inconsistent by 205.57/127.45 | | | | | | | | | | | | | | | | | | | sub-proof #17. 205.57/127.45 | | | | | | | | | | | | | | | | | | | 205.57/127.45 | | | | | | | | | | | | | | | | | | End of split 205.57/127.45 | | | | | | | | | | | | | | | | | | 205.57/127.45 | | | | | | | | | | | | | | | | | Case 2: 205.57/127.45 | | | | | | | | | | | | | | | | | | 205.57/127.45 | | | | | | | | | | | | | | | | | | (2708) length1(int, all_105_4) = all_219_1 & ( ~ 205.57/127.45 | | | | | | | | | | | | | | | | | | ($lesseq(all_86_7, all_219_1)) | ~ ($lesseq(0, 205.57/127.45 | | | | | | | | | | | | | | | | | | all_219_1)) | ( ~ (all_219_0 = all_219_1) & 205.57/127.45 | | | | | | | | | | | | | | | | | | length1(int, all_105_2) = all_219_0)) 205.57/127.45 | | | | | | | | | | | | | | | | | | 205.57/127.45 | | | | | | | | | | | | | | | | | | ALPHA: (2708) implies: 205.57/127.45 | | | | | | | | | | | | | | | | | | (2709) length1(int, all_105_4) = all_219_1 205.57/127.45 | | | | | | | | | | | | | | | | | | 205.57/127.45 | | | | | | | | | | | | | | | | | | BETA: splitting (287) gives: 205.57/127.45 | | | | | | | | | | | | | | | | | | 205.57/127.45 | | | | | | | | | | | | | | | | | | Case 1: 205.57/127.45 | | | | | | | | | | | | | | | | | | | 205.57/127.45 | | | | | | | | | | | | | | | | | | | (2710) all_181_3 = 0 & permut_sub2(int, all_103_2, 205.57/127.45 | | | | | | | | | | | | | | | | | | | all_105_4, all_86_11, $sum(all_86_8, 1)) = 0 205.57/127.45 | | | | | | | | | | | | | | | | | | | 205.57/127.45 | | | | | | | | | | | | | | | | | | | ALPHA: (2710) implies: 205.57/127.45 | | | | | | | | | | | | | | | | | | | (2711) permut_sub2(int, all_103_2, all_105_4, all_86_11, 205.57/127.45 | | | | | | | | | | | | | | | | | | | $sum(all_86_8, 1)) = 0 205.57/127.45 | | | | | | | | | | | | | | | | | | | 205.57/127.45 | | | | | | | | | | | | | | | | | | | BETA: splitting (280) gives: 205.57/127.45 | | | | | | | | | | | | | | | | | | | 205.57/127.45 | | | | | | | | | | | | | | | | | | | Case 1: 205.57/127.45 | | | | | | | | | | | | | | | | | | | | 205.57/127.45 | | | | | | | | | | | | | | | | | | | | (2712) all_177_0 = 0 & all_177_1 = 0 & map_eq_sub1(int, 205.57/127.45 | | | | | | | | | | | | | | | | | | | | all_177_4, all_177_3, $sum(all_86_8, 1), 205.57/127.45 | | | | | | | | | | | | | | | | | | | | all_177_2) = 0 & map_eq_sub1(int, all_177_4, 205.57/127.45 | | | | | | | | | | | | | | | | | | | | all_177_3, 0, all_86_11) = 0 & length1(int, 205.57/127.45 | | | | | | | | | | | | | | | | | | | | all_103_2) = all_177_2 & elts(int, all_105_4) = 205.57/127.45 | | | | | | | | | | | | | | | | | | | | all_177_3 & elts(int, all_103_2) = all_177_4 & 205.57/127.45 | | | | | | | | | | | | | | | | | | | | in_uni(all_177_3) & in_uni(all_177_4) 205.57/127.45 | | | | | | | | | | | | | | | | | | | | 205.57/127.45 | | | | | | | | | | | | | | | | | | | | ALPHA: (2712) implies: 205.57/127.45 | | | | | | | | | | | | | | | | | | | | (2713) length1(int, all_103_2) = all_177_2 205.57/127.45 | | | | | | | | | | | | | | | | | | | | 205.57/127.45 | | | | | | | | | | | | | | | | | | | | BETA: splitting (337) gives: 205.57/127.45 | | | | | | | | | | | | | | | | | | | | 205.57/127.45 | | | | | | | | | | | | | | | | | | | | Case 1: 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | (2714) all_234_1 = 0 & array_eq_sub1(int, all_105_4, 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | all_105_2, $sum(all_86_10, 1), all_86_13) = 0 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | ALPHA: (2714) implies: 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | (2715) array_eq_sub1(int, all_105_4, all_105_2, 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | $sum(all_86_10, 1), all_86_13) = 0 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (255) gives: 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | Case 1: 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | (2716) all_153_0 = all_153_1 & $lesseq(1, 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | $difference(all_153_1, all_86_10)) & 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | $lesseq(all_86_13, all_153_1) & $lesseq(-1, 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | all_86_10) & $lesseq(0, all_86_13) & 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | length1(int, all_105_2) = all_153_1 & length1(int, 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | all_105_4) = all_153_1 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | 205.57/127.45 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2716) implies: 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | (2717) $lesseq(1, $difference(all_153_1, all_86_10)) 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | (2718) length1(int, all_105_4) = all_153_1 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (345) gives: 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | Case 1: 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | (2719) all_242_1 = 0 & array_eq_sub1(int, all_103_2, 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | all_105_4, $sum(all_86_8, 1), all_86_13) = 0 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2719) implies: 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | (2720) array_eq_sub1(int, all_103_2, all_105_4, 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | $sum(all_86_8, 1), all_86_13) = 0 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (269) gives: 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | Case 1: 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | (2721) all_168_0 = all_168_1 & $lesseq(1, 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | $difference(all_168_1, all_86_8)) & 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | $lesseq(all_86_13, all_168_1) & $lesseq(-1, 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | all_86_8) & $lesseq(0, all_86_13) & length1(int, 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | all_105_4) = all_168_1 & length1(int, all_103_2) 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | = all_168_1 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2721) implies: 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | (2722) length1(int, all_103_2) = all_168_1 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | (2723) length1(int, all_105_4) = all_168_1 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (272) gives: 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | (2724) all_171_0 = all_171_1 & $lesseq(all_86_11, 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | all_171_1) & $lesseq(0, all_171_1) & $lesseq(0, 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | all_86_11) & length1(int, all_103_2) = all_171_1 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | & length1(int, all_103_4) = all_171_1 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2724) implies: 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | (2725) length1(int, all_103_4) = all_171_1 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | (2726) length1(int, all_103_2) = all_171_1 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (297) gives: 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | (2727) all_192_0 = 0 & all_192_1 = 0 & map_eq_sub1(int, 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | all_192_4, all_192_3, $sum(all_86_10, 1), 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | all_192_2) = 0 & map_eq_sub1(int, all_192_4, 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | all_192_3, 0, all_86_11) = 0 & length1(int, 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_4) = all_192_2 & elts(int, all_103_2) = 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | all_192_3 & elts(int, all_103_4) = all_192_4 & 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | in_uni(all_192_3) & in_uni(all_192_4) 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2727) implies: 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | (2728) length1(int, all_103_4) = all_192_2 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (298) gives: 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2729) all_193_0 = all_193_1 & $lesseq(1, 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | $difference(all_193_1, all_86_10)) & 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | $lesseq(all_86_13, all_193_1) & $lesseq(-1, 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_86_10) & $lesseq(0, all_86_13) & 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | length1(int, all_103_2) = all_193_1 & length1(int, 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_4) = all_193_1 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2729) implies: 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2730) length1(int, all_103_4) = all_193_1 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2731) length1(int, all_103_2) = all_193_1 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_219_1, all_190_2, 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (2644), (2709) 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2732) all_219_1 = all_190_2 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_190_2, all_168_1, 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (2644), (2723) 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2733) all_190_2 = all_168_1 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_219_1, all_153_1, 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (2709), (2718) 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2734) all_219_1 = all_153_1 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_211_1, all_193_1, 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (2632), (2731) 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2735) all_211_1 = all_193_1 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_86_13, all_177_2, 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (184), (2713) 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2736) all_177_2 = all_86_13 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_177_2, all_168_1, 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (2713), (2722) 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2737) all_177_2 = all_168_1 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_171_1, all_168_1, 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (2722), (2726) 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2738) all_171_1 = all_168_1 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_211_1, all_156_0, 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (394), (2632) 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2739) all_211_1 = all_156_0 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_193_1, all_192_2, 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (2728), (2730) 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2740) all_193_1 = all_192_2 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_192_2, all_171_1, 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (2725), (2728) 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2741) all_192_2 = all_171_1 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2732), (2734) imply: 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2742) all_190_2 = all_153_1 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2742) implies: 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2743) all_190_2 = all_153_1 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2735), (2739) imply: 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2744) all_193_1 = all_156_0 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2740), (2744) imply: 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2745) all_192_2 = all_156_0 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2745) implies: 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2746) all_192_2 = all_156_0 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2741), (2746) imply: 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2747) all_171_1 = all_156_0 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2747) implies: 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2748) all_171_1 = all_156_0 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2733), (2743) imply: 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2749) all_168_1 = all_153_1 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2736), (2737) imply: 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2750) all_168_1 = all_86_13 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2750) implies: 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2751) all_168_1 = all_86_13 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2738), (2748) imply: 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2752) all_168_1 = all_156_0 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2752) implies: 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2753) all_168_1 = all_156_0 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2749), (2753) imply: 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2754) all_156_0 = all_153_1 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2751), (2753) imply: 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2755) all_156_0 = all_86_13 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2754), (2755) imply: 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2756) all_153_1 = all_86_13 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2744), (2755) imply: 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2757) all_193_1 = all_86_13 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2735), (2757) imply: 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2758) all_211_1 = all_86_13 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (48), (50), (52), (53), (2633), (2717), 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2718), (2756), (2758) are inconsistent by 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #7. 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2759) ~ (all_193_1 = 0) & array_eq_sub1(int, all_103_4, 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, $sum(all_86_10, 1), all_86_13) = 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_193_1 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (2635), (2759) are inconsistent by sub-proof 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | #55. 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | (2760) ~ (all_192_4 = 0) & permut_sub2(int, all_103_4, 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, all_86_11, $sum(all_86_10, 1)) = 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | all_192_4 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (43), (2637), (2760) are inconsistent by sub-proof 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | #69. 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | End of split 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | (2761) ~ (all_171_1 = 0) & array_eq_sub1(int, all_103_4, 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, 0, all_86_11) = all_171_1 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (2641), (2761) are inconsistent by sub-proof 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | #81. 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | End of split 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | Case 2: 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | (2762) ~ (all_168_1 = 0) & array_eq_sub1(int, all_103_2, 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, $sum(all_86_8, 1), all_86_13) = 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | all_168_1 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (2720), (2762) are inconsistent by sub-proof 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | #83. 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | End of split 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | Case 2: 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | (2763) length1(int, all_103_2) = all_242_1 & ( ~ 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | ($lesseq(1, $difference(all_242_1, all_86_8))) | 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | ~ ($lesseq(all_86_13, all_242_1)) | ( ~ 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | (all_242_0 = all_242_1) & length1(int, 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | all_105_4) = all_242_0)) 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2763) implies: 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | (2764) length1(int, all_103_2) = all_242_1 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (272) gives: 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | Case 1: 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | (2765) all_171_0 = all_171_1 & $lesseq(all_86_11, 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | all_171_1) & $lesseq(0, all_171_1) & $lesseq(0, 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | all_86_11) & length1(int, all_103_2) = all_171_1 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | & length1(int, all_103_4) = all_171_1 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2765) implies: 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | (2766) length1(int, all_103_4) = all_171_1 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (298) gives: 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | (2767) all_193_0 = all_193_1 & $lesseq(1, 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | $difference(all_193_1, all_86_10)) & 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | $lesseq(all_86_13, all_193_1) & $lesseq(-1, 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | all_86_10) & $lesseq(0, all_86_13) & 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | length1(int, all_103_2) = all_193_1 & length1(int, 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | all_103_4) = all_193_1 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2767) implies: 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | (2768) length1(int, all_103_4) = all_193_1 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | (2769) length1(int, all_103_2) = all_193_1 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (297) gives: 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: 205.57/127.46 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | (2770) all_192_0 = 0 & all_192_1 = 0 & map_eq_sub1(int, 205.57/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | all_192_4, all_192_3, $sum(all_86_10, 1), 205.57/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | all_192_2) = 0 & map_eq_sub1(int, all_192_4, 205.57/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | all_192_3, 0, all_86_11) = 0 & length1(int, 205.57/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_4) = all_192_2 & elts(int, all_103_2) = 205.57/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | all_192_3 & elts(int, all_103_4) = all_192_4 & 205.57/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | in_uni(all_192_3) & in_uni(all_192_4) 205.57/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2770) implies: 205.57/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | (2771) length1(int, all_103_4) = all_192_2 205.57/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_86_13, all_190_2, 205.57/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (180), (2644) 205.57/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.57/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | (2772) all_190_2 = all_86_13 205.57/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_219_1, all_190_2, 205.57/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (2644), (2709) 205.57/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.57/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | (2773) all_219_1 = all_190_2 205.57/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_219_1, all_153_1, 205.57/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (2709), (2718) 205.57/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.57/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | (2774) all_219_1 = all_153_1 205.57/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_242_1, all_193_1, 205.57/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (2764), (2769) 205.57/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.57/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | (2775) all_242_1 = all_193_1 205.57/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_211_1, all_193_1, 205.57/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (2632), (2769) 205.57/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.57/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | (2776) all_211_1 = all_193_1 205.57/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_211_1, all_177_2, 205.57/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (2632), (2713) 205.57/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.57/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | (2777) all_211_1 = all_177_2 205.57/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_242_1, all_156_0, 205.57/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (394), (2764) 205.57/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.57/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | (2778) all_242_1 = all_156_0 205.57/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_86_13, all_192_2, 205.57/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (183), (2771) 205.57/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.57/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | (2779) all_192_2 = all_86_13 205.57/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_193_1, all_192_2, 205.57/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (2768), (2771) 205.57/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.57/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | (2780) all_193_1 = all_192_2 205.57/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_192_2, all_171_1, 205.57/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (2766), (2771) 205.57/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.57/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | (2781) all_192_2 = all_171_1 205.57/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2775), (2778) imply: 205.57/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | (2782) all_193_1 = all_156_0 205.57/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2782) implies: 205.57/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | (2783) all_193_1 = all_156_0 205.57/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2773), (2774) imply: 205.57/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | (2784) all_190_2 = all_153_1 205.57/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2784) implies: 205.57/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | (2785) all_190_2 = all_153_1 205.57/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2776), (2777) imply: 205.57/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | (2786) all_193_1 = all_177_2 205.57/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2786) implies: 205.57/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | (2787) all_193_1 = all_177_2 205.57/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2783), (2787) imply: 205.57/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | (2788) all_177_2 = all_156_0 205.57/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2780), (2787) imply: 205.57/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | (2789) all_192_2 = all_177_2 205.57/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2789) implies: 205.57/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | (2790) all_192_2 = all_177_2 205.57/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2781), (2790) imply: 205.57/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | (2791) all_177_2 = all_171_1 205.57/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.57/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2779), (2790) imply: 205.57/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | (2792) all_177_2 = all_86_13 205.57/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2772), (2785) imply: 205.64/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | (2793) all_153_1 = all_86_13 205.64/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2791), (2792) imply: 205.64/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | (2794) all_171_1 = all_86_13 205.64/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2788), (2791) imply: 205.64/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | (2795) all_171_1 = all_156_0 205.64/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2794), (2795) imply: 205.64/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | (2796) all_156_0 = all_86_13 205.64/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2777), (2792) imply: 205.64/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | (2797) all_211_1 = all_86_13 205.64/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (48), (50), (52), (53), (2633), (2717), 205.64/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | (2718), (2793), (2797) are inconsistent by 205.64/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #7. 205.64/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: 205.64/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | (2798) ~ (all_192_4 = 0) & permut_sub2(int, all_103_4, 205.64/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, all_86_11, $sum(all_86_10, 1)) = 205.64/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | all_192_4 205.64/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (43), (2637), (2798) are inconsistent by sub-proof 205.64/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | #69. 205.64/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | End of split 205.64/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.47 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: 205.64/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | (2799) ~ (all_193_1 = 0) & array_eq_sub1(int, all_103_4, 205.64/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, $sum(all_86_10, 1), all_86_13) = 205.64/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | all_193_1 205.64/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (2635), (2799) are inconsistent by sub-proof 205.64/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | #55. 205.64/127.47 | | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.47 | | | | | | | | | | | | | | | | | | | | | | | | End of split 205.64/127.47 | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.47 | | | | | | | | | | | | | | | | | | | | | | | Case 2: 205.64/127.47 | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.47 | | | | | | | | | | | | | | | | | | | | | | | | (2800) ~ (all_171_1 = 0) & array_eq_sub1(int, all_103_4, 205.64/127.47 | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, 0, all_86_11) = all_171_1 205.64/127.47 | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.47 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (2641), (2800) are inconsistent by sub-proof 205.64/127.47 | | | | | | | | | | | | | | | | | | | | | | | | #81. 205.64/127.47 | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.47 | | | | | | | | | | | | | | | | | | | | | | | End of split 205.64/127.47 | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.47 | | | | | | | | | | | | | | | | | | | | | | End of split 205.64/127.47 | | | | | | | | | | | | | | | | | | | | | | 205.64/127.47 | | | | | | | | | | | | | | | | | | | | | Case 2: 205.64/127.47 | | | | | | | | | | | | | | | | | | | | | | 205.64/127.47 | | | | | | | | | | | | | | | | | | | | | | (2801) ~ (all_153_1 = 0) & array_eq_sub1(int, all_105_4, 205.64/127.47 | | | | | | | | | | | | | | | | | | | | | | all_105_2, $sum(all_86_10, 1), all_86_13) = 205.64/127.47 | | | | | | | | | | | | | | | | | | | | | | all_153_1 205.64/127.47 | | | | | | | | | | | | | | | | | | | | | | 205.64/127.47 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (2715), (2801) are inconsistent by sub-proof 205.64/127.47 | | | | | | | | | | | | | | | | | | | | | | #54. 205.64/127.47 | | | | | | | | | | | | | | | | | | | | | | 205.64/127.47 | | | | | | | | | | | | | | | | | | | | | End of split 205.64/127.47 | | | | | | | | | | | | | | | | | | | | | 205.64/127.47 | | | | | | | | | | | | | | | | | | | | Case 2: 205.64/127.47 | | | | | | | | | | | | | | | | | | | | | 205.64/127.47 | | | | | | | | | | | | | | | | | | | | | (2802) length1(int, all_105_4) = all_234_1 & ( ~ 205.64/127.47 | | | | | | | | | | | | | | | | | | | | | ($lesseq(1, $difference(all_234_1, all_86_10))) 205.64/127.47 | | | | | | | | | | | | | | | | | | | | | | ~ ($lesseq(all_86_13, all_234_1)) | ( ~ 205.64/127.47 | | | | | | | | | | | | | | | | | | | | | (all_234_0 = all_234_1) & length1(int, 205.64/127.47 | | | | | | | | | | | | | | | | | | | | | all_105_2) = all_234_0)) 205.64/127.47 | | | | | | | | | | | | | | | | | | | | | 205.64/127.47 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (49), (180), (181), (2802) are inconsistent 205.64/127.47 | | | | | | | | | | | | | | | | | | | | | by sub-proof #12. 205.64/127.47 | | | | | | | | | | | | | | | | | | | | | 205.64/127.47 | | | | | | | | | | | | | | | | | | | | End of split 205.64/127.47 | | | | | | | | | | | | | | | | | | | | 205.64/127.47 | | | | | | | | | | | | | | | | | | | Case 2: 205.64/127.47 | | | | | | | | | | | | | | | | | | | | 205.64/127.47 | | | | | | | | | | | | | | | | | | | | (2803) ~ (all_177_4 = 0) & permut_sub2(int, all_103_2, 205.64/127.47 | | | | | | | | | | | | | | | | | | | | all_105_4, all_86_11, $sum(all_86_8, 1)) = 205.64/127.47 | | | | | | | | | | | | | | | | | | | | all_177_4 205.64/127.47 | | | | | | | | | | | | | | | | | | | | 205.64/127.47 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (43), (2711), (2803) are inconsistent by sub-proof 205.64/127.47 | | | | | | | | | | | | | | | | | | | | #47. 205.64/127.47 | | | | | | | | | | | | | | | | | | | | 205.64/127.47 | | | | | | | | | | | | | | | | | | | End of split 205.64/127.47 | | | | | | | | | | | | | | | | | | | 205.64/127.47 | | | | | | | | | | | | | | | | | | Case 2: 205.64/127.47 | | | | | | | | | | | | | | | | | | | 205.64/127.47 | | | | | | | | | | | | | | | | | | | (2804) elts(int, all_105_4) = all_181_2 & elts(int, 205.64/127.47 | | | | | | | | | | | | | | | | | | | all_103_2) = all_181_3 & in_uni(all_181_2) & 205.64/127.47 | | | | | | | | | | | | | | | | | | | in_uni(all_181_3) & (( ~ (all_181_0 = 0) & 205.64/127.47 | | | | | | | | | | | | | | | | | | | map_eq_sub1(int, all_181_3, all_181_2, 205.64/127.47 | | | | | | | | | | | | | | | | | | | $sum(all_86_8, 1), all_181_1) = all_181_0 & 205.64/127.47 | | | | | | | | | | | | | | | | | | | length1(int, all_103_2) = all_181_1) | ( ~ 205.64/127.47 | | | | | | | | | | | | | | | | | | | (all_181_1 = 0) & map_eq_sub1(int, all_181_3, 205.64/127.47 | | | | | | | | | | | | | | | | | | | all_181_2, 0, all_86_11) = all_181_1)) 205.64/127.47 | | | | | | | | | | | | | | | | | | | 205.64/127.47 | | | | | | | | | | | | | | | | | | | ALPHA: (2804) implies: 205.64/127.47 | | | | | | | | | | | | | | | | | | | (2805) elts(int, all_103_2) = all_181_3 205.64/127.47 | | | | | | | | | | | | | | | | | | | (2806) elts(int, all_105_4) = all_181_2 205.64/127.47 | | | | | | | | | | | | | | | | | | | (2807) ( ~ (all_181_0 = 0) & map_eq_sub1(int, all_181_3, 205.64/127.47 | | | | | | | | | | | | | | | | | | | all_181_2, $sum(all_86_8, 1), all_181_1) = 205.64/127.47 | | | | | | | | | | | | | | | | | | | all_181_0 & length1(int, all_103_2) = all_181_1) 205.64/127.47 | | | | | | | | | | | | | | | | | | | | ( ~ (all_181_1 = 0) & map_eq_sub1(int, 205.64/127.47 | | | | | | | | | | | | | | | | | | | all_181_3, all_181_2, 0, all_86_11) = 205.64/127.47 | | | | | | | | | | | | | | | | | | | all_181_1) 205.64/127.47 | | | | | | | | | | | | | | | | | | | 205.64/127.47 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (39), (43), (44), (91), (99), (184), (203), 205.64/127.47 | | | | | | | | | | | | | | | | | | | (263), (297), (394), (395), (396), (2637), (2643), 205.64/127.47 | | | | | | | | | | | | | | | | | | | (2805), (2806), (2807) are inconsistent by 205.64/127.47 | | | | | | | | | | | | | | | | | | | sub-proof #17. 205.64/127.47 | | | | | | | | | | | | | | | | | | | 205.64/127.47 | | | | | | | | | | | | | | | | | | End of split 205.64/127.47 | | | | | | | | | | | | | | | | | | 205.64/127.47 | | | | | | | | | | | | | | | | | End of split 205.64/127.47 | | | | | | | | | | | | | | | | | 205.64/127.47 | | | | | | | | | | | | | | | | Case 2: 205.64/127.47 | | | | | | | | | | | | | | | | | 205.64/127.47 | | | | | | | | | | | | | | | | | (2808) ~ (all_190_4 = 0) & permut_sub2(int, all_105_4, 205.64/127.47 | | | | | | | | | | | | | | | | | all_105_2, all_86_7, $sum(all_86_10, 1)) = 205.64/127.47 | | | | | | | | | | | | | | | | | all_190_4 205.64/127.47 | | | | | | | | | | | | | | | | | 205.64/127.47 | | | | | | | | | | | | | | | | | REF_CLOSE: (43), (2639), (2808) are inconsistent by sub-proof 205.64/127.47 | | | | | | | | | | | | | | | | | #68. 205.64/127.47 | | | | | | | | | | | | | | | | | 205.64/127.47 | | | | | | | | | | | | | | | | End of split 205.64/127.47 | | | | | | | | | | | | | | | | 205.64/127.47 | | | | | | | | | | | | | | | Case 2: 205.64/127.47 | | | | | | | | | | | | | | | | 205.64/127.47 | | | | | | | | | | | | | | | | (2809) length1(int, all_103_4) = all_215_1 & ( ~ 205.64/127.47 | | | | | | | | | | | | | | | | ($lesseq(all_86_11, all_215_1)) | ~ ($lesseq(0, 205.64/127.47 | | | | | | | | | | | | | | | | all_215_1)) | ( ~ (all_215_0 = all_215_1) & 205.64/127.47 | | | | | | | | | | | | | | | | length1(int, all_103_2) = all_215_0)) 205.64/127.47 | | | | | | | | | | | | | | | | 205.64/127.47 | | | | | | | | | | | | | | | | ALPHA: (2809) implies: 205.64/127.47 | | | | | | | | | | | | | | | | (2810) length1(int, all_103_4) = all_215_1 205.64/127.47 | | | | | | | | | | | | | | | | (2811) ~ ($lesseq(all_86_11, all_215_1)) | ~ 205.64/127.47 | | | | | | | | | | | | | | | | ($lesseq(0, all_215_1)) | ( ~ (all_215_0 = 205.64/127.47 | | | | | | | | | | | | | | | | all_215_1) & length1(int, all_103_2) = 205.64/127.47 | | | | | | | | | | | | | | | | all_215_0) 205.64/127.47 | | | | | | | | | | | | | | | | 205.64/127.47 | | | | | | | | | | | | | | | | BETA: splitting (295) gives: 205.64/127.47 | | | | | | | | | | | | | | | | 205.64/127.47 | | | | | | | | | | | | | | | | Case 1: 205.64/127.47 | | | | | | | | | | | | | | | | | 205.64/127.47 | | | | | | | | | | | | | | | | | (2812) all_190_0 = 0 & all_190_1 = 0 & map_eq_sub1(int, 205.64/127.47 | | | | | | | | | | | | | | | | | all_190_4, all_190_3, $sum(all_86_10, 1), 205.64/127.47 | | | | | | | | | | | | | | | | | all_190_2) = 0 & map_eq_sub1(int, all_190_4, 205.64/127.47 | | | | | | | | | | | | | | | | | all_190_3, 0, all_86_7) = 0 & length1(int, 205.64/127.47 | | | | | | | | | | | | | | | | | all_105_4) = all_190_2 & elts(int, all_105_2) = 205.64/127.47 | | | | | | | | | | | | | | | | | all_190_3 & elts(int, all_105_4) = all_190_4 & 205.64/127.47 | | | | | | | | | | | | | | | | | in_uni(all_190_3) & in_uni(all_190_4) 205.64/127.47 | | | | | | | | | | | | | | | | | 205.64/127.47 | | | | | | | | | | | | | | | | | ALPHA: (2812) implies: 205.64/127.47 | | | | | | | | | | | | | | | | | (2813) elts(int, all_105_4) = all_190_4 205.64/127.47 | | | | | | | | | | | | | | | | | (2814) length1(int, all_105_4) = all_190_2 205.64/127.47 | | | | | | | | | | | | | | | | | 205.64/127.48 | | | | | | | | | | | | | | | | | BETA: splitting (324) gives: 205.64/127.48 | | | | | | | | | | | | | | | | | 205.64/127.48 | | | | | | | | | | | | | | | | | Case 1: 205.64/127.48 | | | | | | | | | | | | | | | | | | 205.64/127.48 | | | | | | | | | | | | | | | | | | (2815) all_219_1 = 0 & array_eq_sub1(int, all_105_4, 205.64/127.48 | | | | | | | | | | | | | | | | | | all_105_2, 0, all_86_7) = 0 205.64/127.48 | | | | | | | | | | | | | | | | | | 205.64/127.48 | | | | | | | | | | | | | | | | | | ALPHA: (2815) implies: 205.64/127.48 | | | | | | | | | | | | | | | | | | (2816) array_eq_sub1(int, all_105_4, all_105_2, 0, 205.64/127.48 | | | | | | | | | | | | | | | | | | all_86_7) = 0 205.64/127.48 | | | | | | | | | | | | | | | | | | 205.64/127.48 | | | | | | | | | | | | | | | | | | BETA: splitting (287) gives: 205.64/127.48 | | | | | | | | | | | | | | | | | | 205.64/127.48 | | | | | | | | | | | | | | | | | | Case 1: 205.64/127.48 | | | | | | | | | | | | | | | | | | | 205.64/127.48 | | | | | | | | | | | | | | | | | | | (2817) all_181_3 = 0 & permut_sub2(int, all_103_2, 205.64/127.48 | | | | | | | | | | | | | | | | | | | all_105_4, all_86_11, $sum(all_86_8, 1)) = 0 205.64/127.48 | | | | | | | | | | | | | | | | | | | 205.64/127.48 | | | | | | | | | | | | | | | | | | | ALPHA: (2817) implies: 205.64/127.48 | | | | | | | | | | | | | | | | | | | (2818) permut_sub2(int, all_103_2, all_105_4, all_86_11, 205.64/127.48 | | | | | | | | | | | | | | | | | | | $sum(all_86_8, 1)) = 0 205.64/127.48 | | | | | | | | | | | | | | | | | | | 205.64/127.48 | | | | | | | | | | | | | | | | | | | BETA: splitting (280) gives: 205.64/127.48 | | | | | | | | | | | | | | | | | | | 205.64/127.48 | | | | | | | | | | | | | | | | | | | Case 1: 205.64/127.48 | | | | | | | | | | | | | | | | | | | | 205.64/127.48 | | | | | | | | | | | | | | | | | | | | (2819) all_177_0 = 0 & all_177_1 = 0 & map_eq_sub1(int, 205.64/127.48 | | | | | | | | | | | | | | | | | | | | all_177_4, all_177_3, $sum(all_86_8, 1), 205.64/127.48 | | | | | | | | | | | | | | | | | | | | all_177_2) = 0 & map_eq_sub1(int, all_177_4, 205.64/127.48 | | | | | | | | | | | | | | | | | | | | all_177_3, 0, all_86_11) = 0 & length1(int, 205.64/127.48 | | | | | | | | | | | | | | | | | | | | all_103_2) = all_177_2 & elts(int, all_105_4) = 205.64/127.48 | | | | | | | | | | | | | | | | | | | | all_177_3 & elts(int, all_103_2) = all_177_4 & 205.64/127.48 | | | | | | | | | | | | | | | | | | | | in_uni(all_177_3) & in_uni(all_177_4) 205.64/127.48 | | | | | | | | | | | | | | | | | | | | 205.64/127.48 | | | | | | | | | | | | | | | | | | | | ALPHA: (2819) implies: 205.64/127.48 | | | | | | | | | | | | | | | | | | | | (2820) length1(int, all_103_2) = all_177_2 205.64/127.48 | | | | | | | | | | | | | | | | | | | | 205.64/127.48 | | | | | | | | | | | | | | | | | | | | BETA: splitting (337) gives: 205.64/127.48 | | | | | | | | | | | | | | | | | | | | 205.64/127.48 | | | | | | | | | | | | | | | | | | | | Case 1: 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | (2821) all_234_1 = 0 & array_eq_sub1(int, all_105_4, 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | all_105_2, $sum(all_86_10, 1), all_86_13) = 0 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | ALPHA: (2821) implies: 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | (2822) array_eq_sub1(int, all_105_4, all_105_2, 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | $sum(all_86_10, 1), all_86_13) = 0 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (270) gives: 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | Case 1: 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | (2823) all_169_0 = all_169_1 & $lesseq(all_86_7, 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | all_169_1) & $lesseq(0, all_169_1) & $lesseq(0, 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | all_86_7) & length1(int, all_105_2) = all_169_1 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | & length1(int, all_105_4) = all_169_1 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2823) implies: 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | (2824) length1(int, all_105_4) = all_169_1 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (255) gives: 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | Case 1: 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | (2825) all_153_0 = all_153_1 & $lesseq(1, 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | $difference(all_153_1, all_86_10)) & 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | $lesseq(all_86_13, all_153_1) & $lesseq(-1, 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | all_86_10) & $lesseq(0, all_86_13) & 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | length1(int, all_105_2) = all_153_1 & length1(int, 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | all_105_4) = all_153_1 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2825) implies: 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | (2826) $lesseq(1, $difference(all_153_1, all_86_10)) 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | (2827) length1(int, all_105_4) = all_153_1 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (298) gives: 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | Case 1: 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | (2828) all_193_0 = all_193_1 & $lesseq(1, 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | $difference(all_193_1, all_86_10)) & 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | $lesseq(all_86_13, all_193_1) & $lesseq(-1, 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | all_86_10) & $lesseq(0, all_86_13) & 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | length1(int, all_103_2) = all_193_1 & length1(int, 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | all_103_4) = all_193_1 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2828) implies: 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | (2829) length1(int, all_103_4) = all_193_1 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | (2830) length1(int, all_103_2) = all_193_1 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (345) gives: 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | (2831) all_242_1 = 0 & array_eq_sub1(int, all_103_2, 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, $sum(all_86_8, 1), all_86_13) = 0 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2831) implies: 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | (2832) array_eq_sub1(int, all_103_2, all_105_4, 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | $sum(all_86_8, 1), all_86_13) = 0 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (45), (48), (50), (52), (53), (180), (184), 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | (269), (2632), (2633), (2814), (2820), (2824), 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | (2826), (2827), (2832) are inconsistent by 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #8. 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | (2833) length1(int, all_103_2) = all_242_1 & ( ~ 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | ($lesseq(1, $difference(all_242_1, all_86_8))) | 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | ~ ($lesseq(all_86_13, all_242_1)) | ( ~ 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | (all_242_0 = all_242_1) & length1(int, 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4) = all_242_0)) 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2833) implies: 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | (2834) length1(int, all_103_2) = all_242_1 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_86_13, all_190_2, 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (180), (2814) 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | (2835) all_190_2 = all_86_13 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_190_2, all_169_1, 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (2814), (2824) 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | (2836) all_190_2 = all_169_1 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_190_2, all_153_1, 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (2814), (2827) 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | (2837) all_190_2 = all_153_1 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_86_13, all_211_1, 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (184), (2632) 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | (2838) all_211_1 = all_86_13 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_211_1, all_193_1, 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (2632), (2830) 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | (2839) all_211_1 = all_193_1 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_242_1, all_177_2, 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (2820), (2834) 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | (2840) all_242_1 = all_177_2 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_211_1, all_177_2, 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (2632), (2820) 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | (2841) all_211_1 = all_177_2 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_242_1, all_156_0, 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (394), (2834) 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | (2842) all_242_1 = all_156_0 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_215_1, all_193_1, 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (2810), (2829) 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | (2843) all_215_1 = all_193_1 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2840), (2842) imply: 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | (2844) all_177_2 = all_156_0 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2844) implies: 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | (2845) all_177_2 = all_156_0 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2838), (2839) imply: 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | (2846) all_193_1 = all_86_13 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2839), (2841) imply: 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | (2847) all_193_1 = all_177_2 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2846), (2847) imply: 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | (2848) all_177_2 = all_86_13 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2848) implies: 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | (2849) all_177_2 = all_86_13 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2836), (2837) imply: 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | (2850) all_169_1 = all_153_1 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2835), (2836) imply: 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | (2851) all_169_1 = all_86_13 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2845), (2849) imply: 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | (2852) all_156_0 = all_86_13 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2852) implies: 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | (2853) all_156_0 = all_86_13 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2850), (2851) imply: 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | (2854) all_153_1 = all_86_13 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2843), (2846) imply: 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | (2855) all_215_1 = all_86_13 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (48), (50), (52), (53), (394), (2811), 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | (2826), (2853), (2854), (2855) are inconsistent by 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #72. 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | End of split 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | Case 2: 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | (2856) ~ (all_193_1 = 0) & array_eq_sub1(int, all_103_4, 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, $sum(all_86_10, 1), all_86_13) = 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | all_193_1 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (2635), (2856) are inconsistent by sub-proof 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | #55. 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | End of split 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | Case 2: 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | (2857) ~ (all_153_1 = 0) & array_eq_sub1(int, all_105_4, 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | all_105_2, $sum(all_86_10, 1), all_86_13) = 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | all_153_1 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (2822), (2857) are inconsistent by sub-proof 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | #54. 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | End of split 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | Case 2: 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | (2858) ~ (all_169_1 = 0) & array_eq_sub1(int, all_105_4, 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | all_105_2, 0, all_86_7) = all_169_1 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (2816), (2858) are inconsistent by sub-proof 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | #75. 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | End of split 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | 205.64/127.48 | | | | | | | | | | | | | | | | | | | | Case 2: 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | (2859) length1(int, all_105_4) = all_234_1 & ( ~ 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | ($lesseq(1, $difference(all_234_1, all_86_10))) 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | | ~ ($lesseq(all_86_13, all_234_1)) | ( ~ 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | (all_234_0 = all_234_1) & length1(int, 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | all_105_2) = all_234_0)) 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (49), (180), (181), (2859) are inconsistent 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | by sub-proof #12. 205.64/127.48 | | | | | | | | | | | | | | | | | | | | | 205.64/127.48 | | | | | | | | | | | | | | | | | | | | End of split 205.64/127.48 | | | | | | | | | | | | | | | | | | | | 205.64/127.48 | | | | | | | | | | | | | | | | | | | Case 2: 205.64/127.48 | | | | | | | | | | | | | | | | | | | | 205.64/127.48 | | | | | | | | | | | | | | | | | | | | (2860) ~ (all_177_4 = 0) & permut_sub2(int, all_103_2, 205.64/127.48 | | | | | | | | | | | | | | | | | | | | all_105_4, all_86_11, $sum(all_86_8, 1)) = 205.64/127.48 | | | | | | | | | | | | | | | | | | | | all_177_4 205.64/127.48 | | | | | | | | | | | | | | | | | | | | 205.64/127.48 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (43), (2818), (2860) are inconsistent by sub-proof 205.64/127.48 | | | | | | | | | | | | | | | | | | | | #47. 205.64/127.48 | | | | | | | | | | | | | | | | | | | | 205.64/127.48 | | | | | | | | | | | | | | | | | | | End of split 205.64/127.48 | | | | | | | | | | | | | | | | | | | 205.64/127.48 | | | | | | | | | | | | | | | | | | Case 2: 205.64/127.48 | | | | | | | | | | | | | | | | | | | 205.64/127.48 | | | | | | | | | | | | | | | | | | | (2861) elts(int, all_105_4) = all_181_2 & elts(int, 205.64/127.48 | | | | | | | | | | | | | | | | | | | all_103_2) = all_181_3 & in_uni(all_181_2) & 205.64/127.48 | | | | | | | | | | | | | | | | | | | in_uni(all_181_3) & (( ~ (all_181_0 = 0) & 205.64/127.48 | | | | | | | | | | | | | | | | | | | map_eq_sub1(int, all_181_3, all_181_2, 205.64/127.48 | | | | | | | | | | | | | | | | | | | $sum(all_86_8, 1), all_181_1) = all_181_0 & 205.64/127.48 | | | | | | | | | | | | | | | | | | | length1(int, all_103_2) = all_181_1) | ( ~ 205.64/127.48 | | | | | | | | | | | | | | | | | | | (all_181_1 = 0) & map_eq_sub1(int, all_181_3, 205.64/127.48 | | | | | | | | | | | | | | | | | | | all_181_2, 0, all_86_11) = all_181_1)) 205.64/127.48 | | | | | | | | | | | | | | | | | | | 205.64/127.48 | | | | | | | | | | | | | | | | | | | ALPHA: (2861) implies: 205.64/127.49 | | | | | | | | | | | | | | | | | | | (2862) elts(int, all_103_2) = all_181_3 205.64/127.49 | | | | | | | | | | | | | | | | | | | (2863) elts(int, all_105_4) = all_181_2 205.64/127.49 | | | | | | | | | | | | | | | | | | | (2864) ( ~ (all_181_0 = 0) & map_eq_sub1(int, all_181_3, 205.64/127.49 | | | | | | | | | | | | | | | | | | | all_181_2, $sum(all_86_8, 1), all_181_1) = 205.64/127.49 | | | | | | | | | | | | | | | | | | | all_181_0 & length1(int, all_103_2) = all_181_1) 205.64/127.49 | | | | | | | | | | | | | | | | | | | | ( ~ (all_181_1 = 0) & map_eq_sub1(int, 205.64/127.49 | | | | | | | | | | | | | | | | | | | all_181_3, all_181_2, 0, all_86_11) = 205.64/127.49 | | | | | | | | | | | | | | | | | | | all_181_1) 205.64/127.49 | | | | | | | | | | | | | | | | | | | 205.64/127.49 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (39), (43), (44), (91), (99), (184), (203), 205.64/127.49 | | | | | | | | | | | | | | | | | | | (263), (297), (394), (395), (396), (2637), (2813), 205.64/127.49 | | | | | | | | | | | | | | | | | | | (2862), (2863), (2864) are inconsistent by 205.64/127.49 | | | | | | | | | | | | | | | | | | | sub-proof #17. 205.64/127.49 | | | | | | | | | | | | | | | | | | | 205.64/127.49 | | | | | | | | | | | | | | | | | | End of split 205.64/127.49 | | | | | | | | | | | | | | | | | | 205.64/127.49 | | | | | | | | | | | | | | | | | Case 2: 205.64/127.49 | | | | | | | | | | | | | | | | | | 205.64/127.49 | | | | | | | | | | | | | | | | | | (2865) length1(int, all_105_4) = all_219_1 & ( ~ 205.64/127.49 | | | | | | | | | | | | | | | | | | ($lesseq(all_86_7, all_219_1)) | ~ ($lesseq(0, 205.64/127.49 | | | | | | | | | | | | | | | | | | all_219_1)) | ( ~ (all_219_0 = all_219_1) & 205.64/127.49 | | | | | | | | | | | | | | | | | | length1(int, all_105_2) = all_219_0)) 205.64/127.49 | | | | | | | | | | | | | | | | | | 205.64/127.49 | | | | | | | | | | | | | | | | | | ALPHA: (2865) implies: 205.64/127.49 | | | | | | | | | | | | | | | | | | (2866) length1(int, all_105_4) = all_219_1 205.64/127.49 | | | | | | | | | | | | | | | | | | 205.64/127.49 | | | | | | | | | | | | | | | | | | BETA: splitting (287) gives: 205.64/127.49 | | | | | | | | | | | | | | | | | | 205.64/127.49 | | | | | | | | | | | | | | | | | | Case 1: 205.64/127.49 | | | | | | | | | | | | | | | | | | | 205.64/127.49 | | | | | | | | | | | | | | | | | | | (2867) all_181_3 = 0 & permut_sub2(int, all_103_2, 205.64/127.49 | | | | | | | | | | | | | | | | | | | all_105_4, all_86_11, $sum(all_86_8, 1)) = 0 205.64/127.49 | | | | | | | | | | | | | | | | | | | 205.64/127.49 | | | | | | | | | | | | | | | | | | | ALPHA: (2867) implies: 205.64/127.49 | | | | | | | | | | | | | | | | | | | (2868) permut_sub2(int, all_103_2, all_105_4, all_86_11, 205.64/127.49 | | | | | | | | | | | | | | | | | | | $sum(all_86_8, 1)) = 0 205.64/127.49 | | | | | | | | | | | | | | | | | | | 205.64/127.49 | | | | | | | | | | | | | | | | | | | BETA: splitting (280) gives: 205.64/127.49 | | | | | | | | | | | | | | | | | | | 205.64/127.49 | | | | | | | | | | | | | | | | | | | Case 1: 205.64/127.49 | | | | | | | | | | | | | | | | | | | | 205.64/127.49 | | | | | | | | | | | | | | | | | | | | (2869) all_177_0 = 0 & all_177_1 = 0 & map_eq_sub1(int, 205.64/127.49 | | | | | | | | | | | | | | | | | | | | all_177_4, all_177_3, $sum(all_86_8, 1), 205.64/127.49 | | | | | | | | | | | | | | | | | | | | all_177_2) = 0 & map_eq_sub1(int, all_177_4, 205.64/127.49 | | | | | | | | | | | | | | | | | | | | all_177_3, 0, all_86_11) = 0 & length1(int, 205.64/127.49 | | | | | | | | | | | | | | | | | | | | all_103_2) = all_177_2 & elts(int, all_105_4) = 205.64/127.49 | | | | | | | | | | | | | | | | | | | | all_177_3 & elts(int, all_103_2) = all_177_4 & 205.64/127.49 | | | | | | | | | | | | | | | | | | | | in_uni(all_177_3) & in_uni(all_177_4) 205.64/127.49 | | | | | | | | | | | | | | | | | | | | 205.64/127.49 | | | | | | | | | | | | | | | | | | | | ALPHA: (2869) implies: 205.64/127.49 | | | | | | | | | | | | | | | | | | | | (2870) length1(int, all_103_2) = all_177_2 205.64/127.49 | | | | | | | | | | | | | | | | | | | | 205.64/127.49 | | | | | | | | | | | | | | | | | | | | BETA: splitting (337) gives: 205.64/127.49 | | | | | | | | | | | | | | | | | | | | 205.64/127.49 | | | | | | | | | | | | | | | | | | | | Case 1: 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | (2871) all_234_1 = 0 & array_eq_sub1(int, all_105_4, 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | all_105_2, $sum(all_86_10, 1), all_86_13) = 0 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | ALPHA: (2871) implies: 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | (2872) array_eq_sub1(int, all_105_4, all_105_2, 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | $sum(all_86_10, 1), all_86_13) = 0 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (255) gives: 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | Case 1: 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | (2873) all_153_0 = all_153_1 & $lesseq(1, 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | $difference(all_153_1, all_86_10)) & 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | $lesseq(all_86_13, all_153_1) & $lesseq(-1, 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | all_86_10) & $lesseq(0, all_86_13) & 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | length1(int, all_105_2) = all_153_1 & length1(int, 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | all_105_4) = all_153_1 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2873) implies: 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | (2874) $lesseq(1, $difference(all_153_1, all_86_10)) 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | (2875) length1(int, all_105_4) = all_153_1 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (345) gives: 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | Case 1: 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | (2876) all_242_1 = 0 & array_eq_sub1(int, all_103_2, 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | all_105_4, $sum(all_86_8, 1), all_86_13) = 0 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2876) implies: 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | (2877) array_eq_sub1(int, all_103_2, all_105_4, 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | $sum(all_86_8, 1), all_86_13) = 0 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (269) gives: 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | Case 1: 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | (2878) all_168_0 = all_168_1 & $lesseq(1, 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | $difference(all_168_1, all_86_8)) & 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | $lesseq(all_86_13, all_168_1) & $lesseq(-1, 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | all_86_8) & $lesseq(0, all_86_13) & length1(int, 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | all_105_4) = all_168_1 & length1(int, all_103_2) 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | = all_168_1 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2878) implies: 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | (2879) length1(int, all_103_2) = all_168_1 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | (2880) length1(int, all_105_4) = all_168_1 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (298) gives: 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | (2881) all_193_0 = all_193_1 & $lesseq(1, 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | $difference(all_193_1, all_86_10)) & 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | $lesseq(all_86_13, all_193_1) & $lesseq(-1, 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | all_86_10) & $lesseq(0, all_86_13) & 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | length1(int, all_103_2) = all_193_1 & length1(int, 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | all_103_4) = all_193_1 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2881) implies: 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | (2882) length1(int, all_103_4) = all_193_1 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | (2883) length1(int, all_103_2) = all_193_1 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (297) gives: 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | (2884) all_192_0 = 0 & all_192_1 = 0 & map_eq_sub1(int, 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | all_192_4, all_192_3, $sum(all_86_10, 1), 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | all_192_2) = 0 & map_eq_sub1(int, all_192_4, 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | all_192_3, 0, all_86_11) = 0 & length1(int, 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_4) = all_192_2 & elts(int, all_103_2) = 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | all_192_3 & elts(int, all_103_4) = all_192_4 & 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | in_uni(all_192_3) & in_uni(all_192_4) 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2884) implies: 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | (2885) length1(int, all_103_4) = all_192_2 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_219_1, all_190_2, 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (2814), (2866) 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | (2886) all_219_1 = all_190_2 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_190_2, all_168_1, 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (2814), (2880) 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | (2887) all_190_2 = all_168_1 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_219_1, all_153_1, 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (2866), (2875) 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | (2888) all_219_1 = all_153_1 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_211_1, all_193_1, 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (2632), (2883) 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | (2889) all_211_1 = all_193_1 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_211_1, all_177_2, 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (2632), (2870) 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | (2890) all_211_1 = all_177_2 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_193_1, all_156_0, 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (394), (2883) 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | (2891) all_193_1 = all_156_0 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_168_1, all_156_0, 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (394), (2879) 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | (2892) all_168_1 = all_156_0 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_86_13, all_215_1, 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (183), (2810) 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | (2893) all_215_1 = all_86_13 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_215_1, all_192_2, 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (2810), (2885) 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | (2894) all_215_1 = all_192_2 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_193_1, all_192_2, 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (2882), (2885) 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | (2895) all_193_1 = all_192_2 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2886), (2888) imply: 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | (2896) all_190_2 = all_153_1 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2896) implies: 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | (2897) all_190_2 = all_153_1 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2893), (2894) imply: 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | (2898) all_192_2 = all_86_13 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2898) implies: 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | (2899) all_192_2 = all_86_13 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2889), (2890) imply: 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | (2900) all_193_1 = all_177_2 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2900) implies: 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | (2901) all_193_1 = all_177_2 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2895), (2901) imply: 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | (2902) all_192_2 = all_177_2 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2902) implies: 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | (2903) all_192_2 = all_177_2 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2891), (2901) imply: 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | (2904) all_177_2 = all_156_0 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2899), (2903) imply: 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | (2905) all_177_2 = all_86_13 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2905) implies: 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | (2906) all_177_2 = all_86_13 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2887), (2897) imply: 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | (2907) all_168_1 = all_153_1 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2904), (2906) imply: 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | (2908) all_156_0 = all_86_13 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2908) implies: 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | (2909) all_156_0 = all_86_13 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2892), (2907) imply: 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | (2910) all_156_0 = all_153_1 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (48), (50), (52), (53), (394), (2811), 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | (2874), (2893), (2909), (2910) are inconsistent by 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #33. 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | (2911) ~ (all_192_4 = 0) & permut_sub2(int, all_103_4, 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, all_86_11, $sum(all_86_10, 1)) = 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | all_192_4 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (43), (2637), (2911) are inconsistent by sub-proof 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | #69. 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | End of split 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | (2912) ~ (all_193_1 = 0) & array_eq_sub1(int, all_103_4, 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, $sum(all_86_10, 1), all_86_13) = 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | all_193_1 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (2635), (2912) are inconsistent by sub-proof 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | #55. 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | End of split 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | Case 2: 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | (2913) ~ (all_168_1 = 0) & array_eq_sub1(int, all_103_2, 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, $sum(all_86_8, 1), all_86_13) = 205.64/127.49 | | | | | | | | | | | | | | | | | | | | | | | | all_168_1 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (2877), (2913) are inconsistent by sub-proof 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | #83. 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | End of split 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | Case 2: 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | (2914) length1(int, all_103_2) = all_242_1 & ( ~ 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | ($lesseq(1, $difference(all_242_1, all_86_8))) | 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | ~ ($lesseq(all_86_13, all_242_1)) | ( ~ 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | (all_242_0 = all_242_1) & length1(int, 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | all_105_4) = all_242_0)) 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2914) implies: 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | (2915) length1(int, all_103_2) = all_242_1 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (298) gives: 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | Case 1: 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | (2916) all_193_0 = all_193_1 & $lesseq(1, 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | $difference(all_193_1, all_86_10)) & 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | $lesseq(all_86_13, all_193_1) & $lesseq(-1, 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | all_86_10) & $lesseq(0, all_86_13) & 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | length1(int, all_103_2) = all_193_1 & length1(int, 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | all_103_4) = all_193_1 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2916) implies: 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | (2917) length1(int, all_103_4) = all_193_1 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | (2918) length1(int, all_103_2) = all_193_1 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_86_13, all_190_2, 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (180), (2814) 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | (2919) all_190_2 = all_86_13 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_219_1, all_190_2, 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (2814), (2866) 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | (2920) all_219_1 = all_190_2 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_219_1, all_153_1, 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (2866), (2875) 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | (2921) all_219_1 = all_153_1 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_86_13, all_211_1, 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (184), (2632) 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | (2922) all_211_1 = all_86_13 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_211_1, all_193_1, 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (2632), (2918) 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | (2923) all_211_1 = all_193_1 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_242_1, all_177_2, 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (2870), (2915) 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | (2924) all_242_1 = all_177_2 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_211_1, all_177_2, 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (2632), (2870) 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | (2925) all_211_1 = all_177_2 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_242_1, all_156_0, 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (394), (2915) 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | (2926) all_242_1 = all_156_0 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_215_1, all_193_1, 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (2810), (2917) 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | (2927) all_215_1 = all_193_1 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2924), (2926) imply: 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | (2928) all_177_2 = all_156_0 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2928) implies: 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | (2929) all_177_2 = all_156_0 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2920), (2921) imply: 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | (2930) all_190_2 = all_153_1 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2930) implies: 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | (2931) all_190_2 = all_153_1 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2922), (2923) imply: 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | (2932) all_193_1 = all_86_13 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2923), (2925) imply: 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | (2933) all_193_1 = all_177_2 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2932), (2933) imply: 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | (2934) all_177_2 = all_86_13 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2934) implies: 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | (2935) all_177_2 = all_86_13 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2919), (2931) imply: 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | (2936) all_153_1 = all_86_13 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2929), (2935) imply: 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | (2937) all_156_0 = all_86_13 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2937) implies: 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | (2938) all_156_0 = all_86_13 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2927), (2932) imply: 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | (2939) all_215_1 = all_86_13 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (48), (50), (52), (53), (394), (2811), 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | (2874), (2936), (2938), (2939) are inconsistent by 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #72. 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | Case 2: 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | (2940) ~ (all_193_1 = 0) & array_eq_sub1(int, all_103_4, 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, $sum(all_86_10, 1), all_86_13) = 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | all_193_1 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (2635), (2940) are inconsistent by sub-proof 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | #55. 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | End of split 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | End of split 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | Case 2: 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | (2941) ~ (all_153_1 = 0) & array_eq_sub1(int, all_105_4, 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | all_105_2, $sum(all_86_10, 1), all_86_13) = 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | all_153_1 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (2872), (2941) are inconsistent by sub-proof 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | #54. 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | End of split 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | 205.64/127.50 | | | | | | | | | | | | | | | | | | | | Case 2: 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | (2942) length1(int, all_105_4) = all_234_1 & ( ~ 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | ($lesseq(1, $difference(all_234_1, all_86_10))) 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | | ~ ($lesseq(all_86_13, all_234_1)) | ( ~ 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | (all_234_0 = all_234_1) & length1(int, 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | all_105_2) = all_234_0)) 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (49), (180), (181), (2942) are inconsistent 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | by sub-proof #12. 205.64/127.50 | | | | | | | | | | | | | | | | | | | | | 205.64/127.50 | | | | | | | | | | | | | | | | | | | | End of split 205.64/127.50 | | | | | | | | | | | | | | | | | | | | 205.64/127.50 | | | | | | | | | | | | | | | | | | | Case 2: 205.64/127.50 | | | | | | | | | | | | | | | | | | | | 205.64/127.50 | | | | | | | | | | | | | | | | | | | | (2943) ~ (all_177_4 = 0) & permut_sub2(int, all_103_2, 205.64/127.50 | | | | | | | | | | | | | | | | | | | | all_105_4, all_86_11, $sum(all_86_8, 1)) = 205.64/127.50 | | | | | | | | | | | | | | | | | | | | all_177_4 205.64/127.50 | | | | | | | | | | | | | | | | | | | | 205.64/127.50 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (43), (2868), (2943) are inconsistent by sub-proof 205.64/127.50 | | | | | | | | | | | | | | | | | | | | #47. 205.64/127.50 | | | | | | | | | | | | | | | | | | | | 205.64/127.50 | | | | | | | | | | | | | | | | | | | End of split 205.64/127.50 | | | | | | | | | | | | | | | | | | | 205.64/127.50 | | | | | | | | | | | | | | | | | | Case 2: 205.64/127.50 | | | | | | | | | | | | | | | | | | | 205.64/127.50 | | | | | | | | | | | | | | | | | | | (2944) elts(int, all_105_4) = all_181_2 & elts(int, 205.64/127.50 | | | | | | | | | | | | | | | | | | | all_103_2) = all_181_3 & in_uni(all_181_2) & 205.64/127.50 | | | | | | | | | | | | | | | | | | | in_uni(all_181_3) & (( ~ (all_181_0 = 0) & 205.64/127.50 | | | | | | | | | | | | | | | | | | | map_eq_sub1(int, all_181_3, all_181_2, 205.64/127.50 | | | | | | | | | | | | | | | | | | | $sum(all_86_8, 1), all_181_1) = all_181_0 & 205.64/127.50 | | | | | | | | | | | | | | | | | | | length1(int, all_103_2) = all_181_1) | ( ~ 205.64/127.50 | | | | | | | | | | | | | | | | | | | (all_181_1 = 0) & map_eq_sub1(int, all_181_3, 205.64/127.50 | | | | | | | | | | | | | | | | | | | all_181_2, 0, all_86_11) = all_181_1)) 205.64/127.50 | | | | | | | | | | | | | | | | | | | 205.64/127.50 | | | | | | | | | | | | | | | | | | | ALPHA: (2944) implies: 205.64/127.50 | | | | | | | | | | | | | | | | | | | (2945) elts(int, all_103_2) = all_181_3 205.64/127.50 | | | | | | | | | | | | | | | | | | | (2946) elts(int, all_105_4) = all_181_2 205.64/127.50 | | | | | | | | | | | | | | | | | | | (2947) ( ~ (all_181_0 = 0) & map_eq_sub1(int, all_181_3, 205.64/127.50 | | | | | | | | | | | | | | | | | | | all_181_2, $sum(all_86_8, 1), all_181_1) = 205.64/127.50 | | | | | | | | | | | | | | | | | | | all_181_0 & length1(int, all_103_2) = all_181_1) 205.64/127.50 | | | | | | | | | | | | | | | | | | | | ( ~ (all_181_1 = 0) & map_eq_sub1(int, 205.64/127.50 | | | | | | | | | | | | | | | | | | | all_181_3, all_181_2, 0, all_86_11) = 205.64/127.50 | | | | | | | | | | | | | | | | | | | all_181_1) 205.64/127.50 | | | | | | | | | | | | | | | | | | | 205.64/127.50 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (39), (43), (44), (91), (99), (184), (203), 205.64/127.50 | | | | | | | | | | | | | | | | | | | (263), (297), (394), (395), (396), (2637), (2813), 205.64/127.50 | | | | | | | | | | | | | | | | | | | (2945), (2946), (2947) are inconsistent by 205.64/127.50 | | | | | | | | | | | | | | | | | | | sub-proof #17. 205.64/127.50 | | | | | | | | | | | | | | | | | | | 205.64/127.50 | | | | | | | | | | | | | | | | | | End of split 205.64/127.50 | | | | | | | | | | | | | | | | | | 205.64/127.50 | | | | | | | | | | | | | | | | | End of split 205.64/127.50 | | | | | | | | | | | | | | | | | 205.64/127.50 | | | | | | | | | | | | | | | | Case 2: 205.64/127.50 | | | | | | | | | | | | | | | | | 205.64/127.50 | | | | | | | | | | | | | | | | | (2948) ~ (all_190_4 = 0) & permut_sub2(int, all_105_4, 205.64/127.50 | | | | | | | | | | | | | | | | | all_105_2, all_86_7, $sum(all_86_10, 1)) = 205.64/127.50 | | | | | | | | | | | | | | | | | all_190_4 205.64/127.50 | | | | | | | | | | | | | | | | | 205.64/127.50 | | | | | | | | | | | | | | | | | REF_CLOSE: (43), (2639), (2948) are inconsistent by sub-proof 205.64/127.50 | | | | | | | | | | | | | | | | | #68. 205.64/127.50 | | | | | | | | | | | | | | | | | 205.64/127.50 | | | | | | | | | | | | | | | | End of split 205.64/127.50 | | | | | | | | | | | | | | | | 205.64/127.50 | | | | | | | | | | | | | | | End of split 205.64/127.50 | | | | | | | | | | | | | | | 205.64/127.50 | | | | | | | | | | | | | | Case 2: 205.64/127.50 | | | | | | | | | | | | | | | 205.64/127.50 | | | | | | | | | | | | | | | (2949) elts(int, all_105_2) = all_187_2 & elts(int, 205.64/127.50 | | | | | | | | | | | | | | | all_105_4) = all_187_3 & in_uni(all_187_2) & 205.64/127.50 | | | | | | | | | | | | | | | in_uni(all_187_3) & (( ~ (all_187_0 = 0) & 205.64/127.50 | | | | | | | | | | | | | | | map_eq_sub1(int, all_187_3, all_187_2, 205.64/127.50 | | | | | | | | | | | | | | | $sum(all_86_10, 1), all_187_1) = all_187_0 & 205.64/127.50 | | | | | | | | | | | | | | | length1(int, all_105_4) = all_187_1) | ( ~ 205.64/127.50 | | | | | | | | | | | | | | | (all_187_1 = 0) & map_eq_sub1(int, all_187_3, 205.64/127.50 | | | | | | | | | | | | | | | all_187_2, 0, all_86_7) = all_187_1)) 205.64/127.50 | | | | | | | | | | | | | | | 205.64/127.50 | | | | | | | | | | | | | | | ALPHA: (2949) implies: 205.64/127.50 | | | | | | | | | | | | | | | (2950) elts(int, all_105_4) = all_187_3 205.64/127.50 | | | | | | | | | | | | | | | (2951) elts(int, all_105_2) = all_187_2 205.64/127.50 | | | | | | | | | | | | | | | (2952) ( ~ (all_187_0 = 0) & map_eq_sub1(int, all_187_3, 205.64/127.50 | | | | | | | | | | | | | | | all_187_2, $sum(all_86_10, 1), all_187_1) = 205.64/127.50 | | | | | | | | | | | | | | | all_187_0 & length1(int, all_105_4) = all_187_1) 205.64/127.50 | | | | | | | | | | | | | | | | ( ~ (all_187_1 = 0) & map_eq_sub1(int, 205.64/127.50 | | | | | | | | | | | | | | | all_187_3, all_187_2, 0, all_86_7) = 205.64/127.50 | | | | | | | | | | | | | | | all_187_1) 205.64/127.50 | | | | | | | | | | | | | | | 205.64/127.50 | | | | | | | | | | | | | | | BETA: splitting (298) gives: 205.64/127.50 | | | | | | | | | | | | | | | 205.64/127.50 | | | | | | | | | | | | | | | Case 1: 205.64/127.50 | | | | | | | | | | | | | | | | 205.64/127.50 | | | | | | | | | | | | | | | | (2953) all_193_0 = all_193_1 & $lesseq(1, 205.64/127.50 | | | | | | | | | | | | | | | | $difference(all_193_1, all_86_10)) & 205.64/127.50 | | | | | | | | | | | | | | | | $lesseq(all_86_13, all_193_1) & $lesseq(-1, 205.64/127.50 | | | | | | | | | | | | | | | | all_86_10) & $lesseq(0, all_86_13) & 205.64/127.50 | | | | | | | | | | | | | | | | length1(int, all_103_2) = all_193_1 & length1(int, 205.64/127.50 | | | | | | | | | | | | | | | | all_103_4) = all_193_1 205.64/127.50 | | | | | | | | | | | | | | | | 205.64/127.50 | | | | | | | | | | | | | | | | ALPHA: (2953) implies: 205.64/127.50 | | | | | | | | | | | | | | | | (2954) $lesseq(1, $difference(all_193_1, all_86_10)) 205.64/127.50 | | | | | | | | | | | | | | | | (2955) length1(int, all_103_4) = all_193_1 205.64/127.50 | | | | | | | | | | | | | | | | (2956) length1(int, all_103_2) = all_193_1 205.64/127.50 | | | | | | | | | | | | | | | | 205.64/127.50 | | | | | | | | | | | | | | | | BETA: splitting (324) gives: 205.64/127.50 | | | | | | | | | | | | | | | | 205.64/127.50 | | | | | | | | | | | | | | | | Case 1: 205.64/127.50 | | | | | | | | | | | | | | | | | 205.64/127.50 | | | | | | | | | | | | | | | | | (2957) all_219_1 = 0 & array_eq_sub1(int, all_105_4, 205.64/127.50 | | | | | | | | | | | | | | | | | all_105_2, 0, all_86_7) = 0 205.64/127.50 | | | | | | | | | | | | | | | | | 205.64/127.50 | | | | | | | | | | | | | | | | | ALPHA: (2957) implies: 205.64/127.50 | | | | | | | | | | | | | | | | | (2958) array_eq_sub1(int, all_105_4, all_105_2, 0, 205.64/127.50 | | | | | | | | | | | | | | | | | all_86_7) = 0 205.64/127.50 | | | | | | | | | | | | | | | | | 205.64/127.51 | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (39), (44), (45), (99), (100), (105), (180), 205.64/127.51 | | | | | | | | | | | | | | | | | (183), (205), (255), (270), (337), (2950), (2951), 205.64/127.51 | | | | | | | | | | | | | | | | | (2952), (2954), (2955), (2958) are inconsistent by 205.64/127.51 | | | | | | | | | | | | | | | | | sub-proof #5. 205.64/127.51 | | | | | | | | | | | | | | | | | 205.64/127.51 | | | | | | | | | | | | | | | | Case 2: 205.64/127.51 | | | | | | | | | | | | | | | | | 205.64/127.51 | | | | | | | | | | | | | | | | | (2959) length1(int, all_105_4) = all_219_1 & ( ~ 205.64/127.51 | | | | | | | | | | | | | | | | | ($lesseq(all_86_7, all_219_1)) | ~ ($lesseq(0, 205.64/127.51 | | | | | | | | | | | | | | | | | all_219_1)) | ( ~ (all_219_0 = all_219_1) & 205.64/127.51 | | | | | | | | | | | | | | | | | length1(int, all_105_2) = all_219_0)) 205.64/127.51 | | | | | | | | | | | | | | | | | 205.64/127.51 | | | | | | | | | | | | | | | | | ALPHA: (2959) implies: 205.64/127.51 | | | | | | | | | | | | | | | | | (2960) length1(int, all_105_4) = all_219_1 205.64/127.51 | | | | | | | | | | | | | | | | | 205.64/127.51 | | | | | | | | | | | | | | | | | BETA: splitting (287) gives: 205.64/127.51 | | | | | | | | | | | | | | | | | 205.64/127.51 | | | | | | | | | | | | | | | | | Case 1: 205.64/127.51 | | | | | | | | | | | | | | | | | | 205.64/127.51 | | | | | | | | | | | | | | | | | | (2961) all_181_3 = 0 & permut_sub2(int, all_103_2, 205.64/127.51 | | | | | | | | | | | | | | | | | | all_105_4, all_86_11, $sum(all_86_8, 1)) = 0 205.64/127.51 | | | | | | | | | | | | | | | | | | 205.64/127.51 | | | | | | | | | | | | | | | | | | ALPHA: (2961) implies: 205.64/127.51 | | | | | | | | | | | | | | | | | | (2962) permut_sub2(int, all_103_2, all_105_4, all_86_11, 205.64/127.51 | | | | | | | | | | | | | | | | | | $sum(all_86_8, 1)) = 0 205.64/127.51 | | | | | | | | | | | | | | | | | | 205.64/127.51 | | | | | | | | | | | | | | | | | | BETA: splitting (297) gives: 205.64/127.51 | | | | | | | | | | | | | | | | | | 205.64/127.51 | | | | | | | | | | | | | | | | | | Case 1: 205.64/127.51 | | | | | | | | | | | | | | | | | | | 205.64/127.51 | | | | | | | | | | | | | | | | | | | (2963) all_192_0 = 0 & all_192_1 = 0 & map_eq_sub1(int, 205.64/127.51 | | | | | | | | | | | | | | | | | | | all_192_4, all_192_3, $sum(all_86_10, 1), 205.64/127.51 | | | | | | | | | | | | | | | | | | | all_192_2) = 0 & map_eq_sub1(int, all_192_4, 205.64/127.51 | | | | | | | | | | | | | | | | | | | all_192_3, 0, all_86_11) = 0 & length1(int, 205.64/127.51 | | | | | | | | | | | | | | | | | | | all_103_4) = all_192_2 & elts(int, all_103_2) = 205.64/127.51 | | | | | | | | | | | | | | | | | | | all_192_3 & elts(int, all_103_4) = all_192_4 & 205.64/127.51 | | | | | | | | | | | | | | | | | | | in_uni(all_192_3) & in_uni(all_192_4) 205.64/127.51 | | | | | | | | | | | | | | | | | | | 205.64/127.51 | | | | | | | | | | | | | | | | | | | ALPHA: (2963) implies: 205.64/127.51 | | | | | | | | | | | | | | | | | | | (2964) length1(int, all_103_4) = all_192_2 205.64/127.51 | | | | | | | | | | | | | | | | | | | 205.64/127.51 | | | | | | | | | | | | | | | | | | | BETA: splitting (280) gives: 205.64/127.51 | | | | | | | | | | | | | | | | | | | 205.64/127.51 | | | | | | | | | | | | | | | | | | | Case 1: 205.64/127.51 | | | | | | | | | | | | | | | | | | | | 205.64/127.51 | | | | | | | | | | | | | | | | | | | | (2965) all_177_0 = 0 & all_177_1 = 0 & map_eq_sub1(int, 205.64/127.51 | | | | | | | | | | | | | | | | | | | | all_177_4, all_177_3, $sum(all_86_8, 1), 205.64/127.51 | | | | | | | | | | | | | | | | | | | | all_177_2) = 0 & map_eq_sub1(int, all_177_4, 205.64/127.51 | | | | | | | | | | | | | | | | | | | | all_177_3, 0, all_86_11) = 0 & length1(int, 205.64/127.51 | | | | | | | | | | | | | | | | | | | | all_103_2) = all_177_2 & elts(int, all_105_4) = 205.64/127.51 | | | | | | | | | | | | | | | | | | | | all_177_3 & elts(int, all_103_2) = all_177_4 & 205.64/127.51 | | | | | | | | | | | | | | | | | | | | in_uni(all_177_3) & in_uni(all_177_4) 205.64/127.51 | | | | | | | | | | | | | | | | | | | | 205.64/127.51 | | | | | | | | | | | | | | | | | | | | ALPHA: (2965) implies: 205.64/127.51 | | | | | | | | | | | | | | | | | | | | (2966) length1(int, all_103_2) = all_177_2 205.64/127.51 | | | | | | | | | | | | | | | | | | | | 205.64/127.51 | | | | | | | | | | | | | | | | | | | | BETA: splitting (337) gives: 205.64/127.51 | | | | | | | | | | | | | | | | | | | | 205.64/127.51 | | | | | | | | | | | | | | | | | | | | Case 1: 205.64/127.51 | | | | | | | | | | | | | | | | | | | | | 205.64/127.51 | | | | | | | | | | | | | | | | | | | | | (2967) all_234_1 = 0 & array_eq_sub1(int, all_105_4, 205.64/127.51 | | | | | | | | | | | | | | | | | | | | | all_105_2, $sum(all_86_10, 1), all_86_13) = 0 205.64/127.51 | | | | | | | | | | | | | | | | | | | | | 205.64/127.51 | | | | | | | | | | | | | | | | | | | | | ALPHA: (2967) implies: 205.64/127.51 | | | | | | | | | | | | | | | | | | | | | (2968) array_eq_sub1(int, all_105_4, all_105_2, 205.64/127.51 | | | | | | | | | | | | | | | | | | | | | $sum(all_86_10, 1), all_86_13) = 0 205.64/127.51 | | | | | | | | | | | | | | | | | | | | | 205.64/127.51 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (255) gives: 205.64/127.51 | | | | | | | | | | | | | | | | | | | | | 205.64/127.51 | | | | | | | | | | | | | | | | | | | | | Case 1: 205.64/127.51 | | | | | | | | | | | | | | | | | | | | | | 205.64/127.51 | | | | | | | | | | | | | | | | | | | | | | (2969) all_153_0 = all_153_1 & $lesseq(1, 205.64/127.51 | | | | | | | | | | | | | | | | | | | | | | $difference(all_153_1, all_86_10)) & 205.64/127.51 | | | | | | | | | | | | | | | | | | | | | | $lesseq(all_86_13, all_153_1) & $lesseq(-1, 205.64/127.51 | | | | | | | | | | | | | | | | | | | | | | all_86_10) & $lesseq(0, all_86_13) & 205.64/127.51 | | | | | | | | | | | | | | | | | | | | | | length1(int, all_105_2) = all_153_1 & length1(int, 205.64/127.51 | | | | | | | | | | | | | | | | | | | | | | all_105_4) = all_153_1 205.64/127.51 | | | | | | | | | | | | | | | | | | | | | | 205.64/127.51 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2969) implies: 205.64/127.51 | | | | | | | | | | | | | | | | | | | | | | (2970) $lesseq(1, $difference(all_153_1, all_86_10)) 205.64/127.51 | | | | | | | | | | | | | | | | | | | | | | (2971) length1(int, all_105_4) = all_153_1 205.64/127.51 | | | | | | | | | | | | | | | | | | | | | | 205.64/127.51 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_86_13, all_219_1, 205.64/127.51 | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (180), (2960) 205.64/127.51 | | | | | | | | | | | | | | | | | | | | | | gives: 205.64/127.51 | | | | | | | | | | | | | | | | | | | | | | (2972) all_219_1 = all_86_13 205.64/127.51 | | | | | | | | | | | | | | | | | | | | | | 205.64/127.51 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_219_1, all_153_1, 205.64/127.51 | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (2960), (2971) 205.64/127.51 | | | | | | | | | | | | | | | | | | | | | | gives: 205.64/127.51 | | | | | | | | | | | | | | | | | | | | | | (2973) all_219_1 = all_153_1 205.64/127.51 | | | | | | | | | | | | | | | | | | | | | | 205.64/127.51 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_211_1, all_193_1, 205.64/127.51 | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (2632), (2956) 205.64/127.51 | | | | | | | | | | | | | | | | | | | | | | gives: 205.64/127.51 | | | | | | | | | | | | | | | | | | | | | | (2974) all_211_1 = all_193_1 205.64/127.51 | | | | | | | | | | | | | | | | | | | | | | 205.64/127.51 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_211_1, all_177_2, 205.64/127.51 | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (2632), (2966) 205.64/127.51 | | | | | | | | | | | | | | | | | | | | | | gives: 205.64/127.51 | | | | | | | | | | | | | | | | | | | | | | (2975) all_211_1 = all_177_2 205.64/127.51 | | | | | | | | | | | | | | | | | | | | | | 205.64/127.51 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_86_13, all_192_2, 205.64/127.51 | | | | | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (183), (2964) 205.64/127.51 | | | | | | | | | | | | | | | | | | | | | | gives: 205.64/127.51 | | | | | | | | | | | | | | | | | | | | | | (2976) all_192_2 = all_86_13 205.64/127.51 | | | | | | | | | | | | | | | | | | | | | | 205.64/127.51 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_193_1, all_192_2, 205.64/127.51 | | | | | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (2955), (2964) 205.64/127.51 | | | | | | | | | | | | | | | | | | | | | | gives: 205.64/127.51 | | | | | | | | | | | | | | | | | | | | | | (2977) all_193_1 = all_192_2 205.64/127.51 | | | | | | | | | | | | | | | | | | | | | | 205.64/127.51 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2972), (2973) imply: 205.64/127.51 | | | | | | | | | | | | | | | | | | | | | | (2978) all_153_1 = all_86_13 205.64/127.51 | | | | | | | | | | | | | | | | | | | | | | 205.64/127.51 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2974), (2975) imply: 205.64/127.51 | | | | | | | | | | | | | | | | | | | | | | (2979) all_193_1 = all_177_2 205.64/127.51 | | | | | | | | | | | | | | | | | | | | | | 205.64/127.51 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2977), (2979) imply: 205.64/127.51 | | | | | | | | | | | | | | | | | | | | | | (2980) all_192_2 = all_177_2 205.64/127.51 | | | | | | | | | | | | | | | | | | | | | | 205.64/127.51 | | | | | | | | | | | | | | | | | | | | | | SIMP: (2980) implies: 205.64/127.51 | | | | | | | | | | | | | | | | | | | | | | (2981) all_192_2 = all_177_2 205.64/127.51 | | | | | | | | | | | | | | | | | | | | | | 205.64/127.51 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2976), (2981) imply: 205.64/127.51 | | | | | | | | | | | | | | | | | | | | | | (2982) all_177_2 = all_86_13 205.64/127.51 | | | | | | | | | | | | | | | | | | | | | | 205.64/127.51 | | | | | | | | | | | | | | | | | | | | | | SIMP: (2982) implies: 205.64/127.51 | | | | | | | | | | | | | | | | | | | | | | (2983) all_177_2 = all_86_13 205.64/127.51 | | | | | | | | | | | | | | | | | | | | | | 205.64/127.51 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2979), (2983) imply: 205.64/127.51 | | | | | | | | | | | | | | | | | | | | | | (2984) all_193_1 = all_86_13 205.64/127.51 | | | | | | | | | | | | | | | | | | | | | | 205.64/127.51 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2974), (2984) imply: 205.64/127.51 | | | | | | | | | | | | | | | | | | | | | | (2985) all_211_1 = all_86_13 205.64/127.51 | | | | | | | | | | | | | | | | | | | | | | 205.64/127.51 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (48), (50), (52), (53), (2633), (2970), 205.64/127.51 | | | | | | | | | | | | | | | | | | | | | | (2971), (2978), (2985) are inconsistent by 205.64/127.51 | | | | | | | | | | | | | | | | | | | | | | sub-proof #7. 205.64/127.51 | | | | | | | | | | | | | | | | | | | | | | 205.64/127.51 | | | | | | | | | | | | | | | | | | | | | Case 2: 205.64/127.51 | | | | | | | | | | | | | | | | | | | | | | 205.64/127.51 | | | | | | | | | | | | | | | | | | | | | | (2986) ~ (all_153_1 = 0) & array_eq_sub1(int, all_105_4, 205.64/127.51 | | | | | | | | | | | | | | | | | | | | | | all_105_2, $sum(all_86_10, 1), all_86_13) = 205.64/127.51 | | | | | | | | | | | | | | | | | | | | | | all_153_1 205.64/127.51 | | | | | | | | | | | | | | | | | | | | | | 205.64/127.51 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (2968), (2986) are inconsistent by sub-proof 205.64/127.51 | | | | | | | | | | | | | | | | | | | | | | #54. 205.64/127.51 | | | | | | | | | | | | | | | | | | | | | | 205.64/127.51 | | | | | | | | | | | | | | | | | | | | | End of split 205.64/127.51 | | | | | | | | | | | | | | | | | | | | | 205.64/127.51 | | | | | | | | | | | | | | | | | | | | Case 2: 205.64/127.51 | | | | | | | | | | | | | | | | | | | | | 205.64/127.51 | | | | | | | | | | | | | | | | | | | | | (2987) length1(int, all_105_4) = all_234_1 & ( ~ 205.64/127.51 | | | | | | | | | | | | | | | | | | | | | ($lesseq(1, $difference(all_234_1, all_86_10))) 205.64/127.51 | | | | | | | | | | | | | | | | | | | | | | ~ ($lesseq(all_86_13, all_234_1)) | ( ~ 205.64/127.51 | | | | | | | | | | | | | | | | | | | | | (all_234_0 = all_234_1) & length1(int, 205.64/127.51 | | | | | | | | | | | | | | | | | | | | | all_105_2) = all_234_0)) 205.64/127.51 | | | | | | | | | | | | | | | | | | | | | 205.64/127.51 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (49), (180), (181), (2987) are inconsistent 205.64/127.51 | | | | | | | | | | | | | | | | | | | | | by sub-proof #12. 205.64/127.51 | | | | | | | | | | | | | | | | | | | | | 205.64/127.51 | | | | | | | | | | | | | | | | | | | | End of split 205.64/127.51 | | | | | | | | | | | | | | | | | | | | 205.64/127.51 | | | | | | | | | | | | | | | | | | | Case 2: 205.64/127.51 | | | | | | | | | | | | | | | | | | | | 205.64/127.51 | | | | | | | | | | | | | | | | | | | | (2988) ~ (all_177_4 = 0) & permut_sub2(int, all_103_2, 205.64/127.51 | | | | | | | | | | | | | | | | | | | | all_105_4, all_86_11, $sum(all_86_8, 1)) = 205.64/127.51 | | | | | | | | | | | | | | | | | | | | all_177_4 205.64/127.51 | | | | | | | | | | | | | | | | | | | | 205.64/127.51 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (43), (2962), (2988) are inconsistent by sub-proof 205.64/127.51 | | | | | | | | | | | | | | | | | | | | #47. 205.64/127.51 | | | | | | | | | | | | | | | | | | | | 205.64/127.51 | | | | | | | | | | | | | | | | | | | End of split 205.64/127.51 | | | | | | | | | | | | | | | | | | | 205.64/127.51 | | | | | | | | | | | | | | | | | | Case 2: 205.64/127.51 | | | | | | | | | | | | | | | | | | | 205.64/127.51 | | | | | | | | | | | | | | | | | | | (2989) ~ (all_192_4 = 0) & permut_sub2(int, all_103_4, 205.64/127.51 | | | | | | | | | | | | | | | | | | | all_103_2, all_86_11, $sum(all_86_10, 1)) = 205.64/127.51 | | | | | | | | | | | | | | | | | | | all_192_4 205.64/127.51 | | | | | | | | | | | | | | | | | | | 205.64/127.51 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (43), (2637), (2989) are inconsistent by sub-proof 205.64/127.51 | | | | | | | | | | | | | | | | | | | #69. 205.64/127.51 | | | | | | | | | | | | | | | | | | | 205.64/127.51 | | | | | | | | | | | | | | | | | | End of split 205.64/127.51 | | | | | | | | | | | | | | | | | | 205.64/127.51 | | | | | | | | | | | | | | | | | Case 2: 205.64/127.51 | | | | | | | | | | | | | | | | | | 205.64/127.51 | | | | | | | | | | | | | | | | | | (2990) elts(int, all_105_4) = all_181_2 & elts(int, 205.64/127.51 | | | | | | | | | | | | | | | | | | all_103_2) = all_181_3 & in_uni(all_181_2) & 205.64/127.51 | | | | | | | | | | | | | | | | | | in_uni(all_181_3) & (( ~ (all_181_0 = 0) & 205.64/127.51 | | | | | | | | | | | | | | | | | | map_eq_sub1(int, all_181_3, all_181_2, 205.64/127.51 | | | | | | | | | | | | | | | | | | $sum(all_86_8, 1), all_181_1) = all_181_0 & 205.64/127.51 | | | | | | | | | | | | | | | | | | length1(int, all_103_2) = all_181_1) | ( ~ 205.64/127.51 | | | | | | | | | | | | | | | | | | (all_181_1 = 0) & map_eq_sub1(int, all_181_3, 205.64/127.51 | | | | | | | | | | | | | | | | | | all_181_2, 0, all_86_11) = all_181_1)) 205.64/127.51 | | | | | | | | | | | | | | | | | | 205.64/127.51 | | | | | | | | | | | | | | | | | | ALPHA: (2990) implies: 205.64/127.51 | | | | | | | | | | | | | | | | | | (2991) elts(int, all_103_2) = all_181_3 205.64/127.51 | | | | | | | | | | | | | | | | | | (2992) elts(int, all_105_4) = all_181_2 205.64/127.51 | | | | | | | | | | | | | | | | | | (2993) ( ~ (all_181_0 = 0) & map_eq_sub1(int, all_181_3, 205.64/127.51 | | | | | | | | | | | | | | | | | | all_181_2, $sum(all_86_8, 1), all_181_1) = 205.64/127.51 | | | | | | | | | | | | | | | | | | all_181_0 & length1(int, all_103_2) = all_181_1) 205.64/127.51 | | | | | | | | | | | | | | | | | | | ( ~ (all_181_1 = 0) & map_eq_sub1(int, 205.64/127.51 | | | | | | | | | | | | | | | | | | all_181_3, all_181_2, 0, all_86_11) = 205.64/127.51 | | | | | | | | | | | | | | | | | | all_181_1) 205.64/127.51 | | | | | | | | | | | | | | | | | | 205.64/127.51 | | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (39), (43), (44), (91), (99), (184), (203), 205.64/127.51 | | | | | | | | | | | | | | | | | | (263), (297), (394), (395), (396), (2637), (2950), 205.64/127.51 | | | | | | | | | | | | | | | | | | (2991), (2992), (2993) are inconsistent by 205.64/127.51 | | | | | | | | | | | | | | | | | | sub-proof #11. 205.64/127.51 | | | | | | | | | | | | | | | | | | 205.64/127.51 | | | | | | | | | | | | | | | | | End of split 205.64/127.51 | | | | | | | | | | | | | | | | | 205.64/127.51 | | | | | | | | | | | | | | | | End of split 205.64/127.51 | | | | | | | | | | | | | | | | 205.64/127.51 | | | | | | | | | | | | | | | Case 2: 205.64/127.51 | | | | | | | | | | | | | | | | 205.64/127.51 | | | | | | | | | | | | | | | | (2994) ~ (all_193_1 = 0) & array_eq_sub1(int, all_103_4, 205.64/127.51 | | | | | | | | | | | | | | | | all_103_2, $sum(all_86_10, 1), all_86_13) = 205.64/127.51 | | | | | | | | | | | | | | | | all_193_1 205.64/127.51 | | | | | | | | | | | | | | | | 205.64/127.51 | | | | | | | | | | | | | | | | REF_CLOSE: (45), (2635), (2994) are inconsistent by sub-proof 205.64/127.51 | | | | | | | | | | | | | | | | #55. 205.64/127.51 | | | | | | | | | | | | | | | | 205.64/127.51 | | | | | | | | | | | | | | | End of split 205.64/127.51 | | | | | | | | | | | | | | | 205.64/127.51 | | | | | | | | | | | | | | End of split 205.64/127.51 | | | | | | | | | | | | | | 205.64/127.51 | | | | | | | | | | | | | Case 2: 205.64/127.51 | | | | | | | | | | | | | | 205.64/127.51 | | | | | | | | | | | | | | (2995) elts(int, all_103_2) = all_191_2 & elts(int, 205.64/127.51 | | | | | | | | | | | | | | all_103_4) = all_191_3 & in_uni(all_191_2) & 205.64/127.51 | | | | | | | | | | | | | | in_uni(all_191_3) & (( ~ (all_191_0 = 0) & 205.64/127.51 | | | | | | | | | | | | | | map_eq_sub1(int, all_191_3, all_191_2, 205.64/127.51 | | | | | | | | | | | | | | $sum(all_86_10, 1), all_191_1) = all_191_0 & 205.64/127.51 | | | | | | | | | | | | | | length1(int, all_103_4) = all_191_1) | ( ~ 205.64/127.51 | | | | | | | | | | | | | | (all_191_1 = 0) & map_eq_sub1(int, all_191_3, 205.64/127.51 | | | | | | | | | | | | | | all_191_2, 0, all_86_11) = all_191_1)) 205.64/127.51 | | | | | | | | | | | | | | 205.64/127.51 | | | | | | | | | | | | | | ALPHA: (2995) implies: 205.64/127.51 | | | | | | | | | | | | | | (2996) elts(int, all_103_4) = all_191_3 205.64/127.51 | | | | | | | | | | | | | | (2997) elts(int, all_103_2) = all_191_2 205.64/127.51 | | | | | | | | | | | | | | (2998) ( ~ (all_191_0 = 0) & map_eq_sub1(int, all_191_3, 205.64/127.51 | | | | | | | | | | | | | | all_191_2, $sum(all_86_10, 1), all_191_1) = 205.64/127.51 | | | | | | | | | | | | | | all_191_0 & length1(int, all_103_4) = all_191_1) 205.64/127.51 | | | | | | | | | | | | | | | ( ~ (all_191_1 = 0) & map_eq_sub1(int, 205.64/127.51 | | | | | | | | | | | | | | all_191_3, all_191_2, 0, all_86_11) = 205.64/127.51 | | | | | | | | | | | | | | all_191_1) 205.64/127.51 | | | | | | | | | | | | | | 205.64/127.51 | | | | | | | | | | | | | | BETA: splitting (287) gives: 205.64/127.51 | | | | | | | | | | | | | | 205.64/127.51 | | | | | | | | | | | | | | Case 1: 205.64/127.51 | | | | | | | | | | | | | | | 205.64/127.51 | | | | | | | | | | | | | | | (2999) all_181_3 = 0 & permut_sub2(int, all_103_2, 205.64/127.51 | | | | | | | | | | | | | | | all_105_4, all_86_11, $sum(all_86_8, 1)) = 0 205.64/127.51 | | | | | | | | | | | | | | | 205.64/127.51 | | | | | | | | | | | | | | | ALPHA: (2999) implies: 205.64/127.51 | | | | | | | | | | | | | | | (3000) permut_sub2(int, all_103_2, all_105_4, all_86_11, 205.64/127.51 | | | | | | | | | | | | | | | $sum(all_86_8, 1)) = 0 205.64/127.51 | | | | | | | | | | | | | | | 205.64/127.51 | | | | | | | | | | | | | | | BETA: splitting (280) gives: 205.64/127.51 | | | | | | | | | | | | | | | 205.64/127.51 | | | | | | | | | | | | | | | Case 1: 205.64/127.51 | | | | | | | | | | | | | | | | 205.64/127.52 | | | | | | | | | | | | | | | | (3001) all_177_0 = 0 & all_177_1 = 0 & map_eq_sub1(int, 205.64/127.52 | | | | | | | | | | | | | | | | all_177_4, all_177_3, $sum(all_86_8, 1), 205.64/127.52 | | | | | | | | | | | | | | | | all_177_2) = 0 & map_eq_sub1(int, all_177_4, 205.64/127.52 | | | | | | | | | | | | | | | | all_177_3, 0, all_86_11) = 0 & length1(int, 205.64/127.52 | | | | | | | | | | | | | | | | all_103_2) = all_177_2 & elts(int, all_105_4) = 205.64/127.52 | | | | | | | | | | | | | | | | all_177_3 & elts(int, all_103_2) = all_177_4 & 205.64/127.52 | | | | | | | | | | | | | | | | in_uni(all_177_3) & in_uni(all_177_4) 205.64/127.52 | | | | | | | | | | | | | | | | 205.64/127.52 | | | | | | | | | | | | | | | | ALPHA: (3001) implies: 205.64/127.52 | | | | | | | | | | | | | | | | (3002) elts(int, all_103_2) = all_177_4 205.64/127.52 | | | | | | | | | | | | | | | | (3003) length1(int, all_103_2) = all_177_2 205.64/127.52 | | | | | | | | | | | | | | | | 205.64/127.52 | | | | | | | | | | | | | | | | BETA: splitting (294) gives: 205.64/127.52 | | | | | | | | | | | | | | | | 205.64/127.52 | | | | | | | | | | | | | | | | Case 1: 205.64/127.52 | | | | | | | | | | | | | | | | | 205.64/127.52 | | | | | | | | | | | | | | | | | (3004) all_187_3 = 0 & permut_sub2(int, all_105_4, 205.64/127.52 | | | | | | | | | | | | | | | | | all_105_2, all_86_7, $sum(all_86_10, 1)) = 0 205.64/127.52 | | | | | | | | | | | | | | | | | 205.64/127.52 | | | | | | | | | | | | | | | | | ALPHA: (3004) implies: 205.64/127.52 | | | | | | | | | | | | | | | | | (3005) permut_sub2(int, all_105_4, all_105_2, all_86_7, 205.64/127.52 | | | | | | | | | | | | | | | | | $sum(all_86_10, 1)) = 0 205.64/127.52 | | | | | | | | | | | | | | | | | 205.64/127.52 | | | | | | | | | | | | | | | | | BETA: splitting (337) gives: 205.64/127.52 | | | | | | | | | | | | | | | | | 205.64/127.52 | | | | | | | | | | | | | | | | | Case 1: 205.64/127.52 | | | | | | | | | | | | | | | | | | 205.64/127.52 | | | | | | | | | | | | | | | | | | (3006) all_234_1 = 0 & array_eq_sub1(int, all_105_4, 205.64/127.52 | | | | | | | | | | | | | | | | | | all_105_2, $sum(all_86_10, 1), all_86_13) = 0 205.64/127.52 | | | | | | | | | | | | | | | | | | 205.64/127.52 | | | | | | | | | | | | | | | | | | ALPHA: (3006) implies: 205.64/127.52 | | | | | | | | | | | | | | | | | | (3007) array_eq_sub1(int, all_105_4, all_105_2, 205.64/127.52 | | | | | | | | | | | | | | | | | | $sum(all_86_10, 1), all_86_13) = 0 205.64/127.52 | | | | | | | | | | | | | | | | | | 205.64/127.52 | | | | | | | | | | | | | | | | | | BETA: splitting (255) gives: 205.64/127.52 | | | | | | | | | | | | | | | | | | 205.64/127.52 | | | | | | | | | | | | | | | | | | Case 1: 205.64/127.52 | | | | | | | | | | | | | | | | | | | 205.64/127.52 | | | | | | | | | | | | | | | | | | | (3008) all_153_0 = all_153_1 & $lesseq(1, 205.64/127.52 | | | | | | | | | | | | | | | | | | | $difference(all_153_1, all_86_10)) & 205.64/127.52 | | | | | | | | | | | | | | | | | | | $lesseq(all_86_13, all_153_1) & $lesseq(-1, 205.64/127.52 | | | | | | | | | | | | | | | | | | | all_86_10) & $lesseq(0, all_86_13) & 205.64/127.52 | | | | | | | | | | | | | | | | | | | length1(int, all_105_2) = all_153_1 & length1(int, 205.64/127.52 | | | | | | | | | | | | | | | | | | | all_105_4) = all_153_1 205.64/127.52 | | | | | | | | | | | | | | | | | | | 205.64/127.52 | | | | | | | | | | | | | | | | | | | ALPHA: (3008) implies: 205.64/127.52 | | | | | | | | | | | | | | | | | | | (3009) $lesseq(1, $difference(all_153_1, all_86_10)) 205.64/127.52 | | | | | | | | | | | | | | | | | | | (3010) length1(int, all_105_4) = all_153_1 205.64/127.52 | | | | | | | | | | | | | | | | | | | (3011) length1(int, all_105_2) = all_153_1 205.64/127.52 | | | | | | | | | | | | | | | | | | | 205.64/127.52 | | | | | | | | | | | | | | | | | | | BETA: splitting (298) gives: 205.64/127.52 | | | | | | | | | | | | | | | | | | | 205.64/127.52 | | | | | | | | | | | | | | | | | | | Case 1: 205.64/127.52 | | | | | | | | | | | | | | | | | | | | 205.64/127.52 | | | | | | | | | | | | | | | | | | | | (3012) all_193_0 = all_193_1 & $lesseq(1, 205.64/127.52 | | | | | | | | | | | | | | | | | | | | $difference(all_193_1, all_86_10)) & 205.64/127.52 | | | | | | | | | | | | | | | | | | | | $lesseq(all_86_13, all_193_1) & $lesseq(-1, 205.64/127.52 | | | | | | | | | | | | | | | | | | | | all_86_10) & $lesseq(0, all_86_13) & 205.64/127.52 | | | | | | | | | | | | | | | | | | | | length1(int, all_103_2) = all_193_1 & length1(int, 205.64/127.52 | | | | | | | | | | | | | | | | | | | | all_103_4) = all_193_1 205.64/127.52 | | | | | | | | | | | | | | | | | | | | 205.64/127.52 | | | | | | | | | | | | | | | | | | | | ALPHA: (3012) implies: 205.64/127.52 | | | | | | | | | | | | | | | | | | | | (3013) length1(int, all_103_4) = all_193_1 205.64/127.52 | | | | | | | | | | | | | | | | | | | | (3014) length1(int, all_103_2) = all_193_1 205.64/127.52 | | | | | | | | | | | | | | | | | | | | 205.64/127.52 | | | | | | | | | | | | | | | | | | | | BETA: splitting (295) gives: 205.64/127.52 | | | | | | | | | | | | | | | | | | | | 205.64/127.52 | | | | | | | | | | | | | | | | | | | | Case 1: 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | (3015) all_190_0 = 0 & all_190_1 = 0 & map_eq_sub1(int, 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | all_190_4, all_190_3, $sum(all_86_10, 1), 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | all_190_2) = 0 & map_eq_sub1(int, all_190_4, 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | all_190_3, 0, all_86_7) = 0 & length1(int, 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | all_105_4) = all_190_2 & elts(int, all_105_2) = 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | all_190_3 & elts(int, all_105_4) = all_190_4 & 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | in_uni(all_190_3) & in_uni(all_190_4) 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | ALPHA: (3015) implies: 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | (3016) length1(int, all_105_4) = all_190_2 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (319) gives: 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | Case 1: 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | (3017) all_215_1 = 0 & array_eq_sub1(int, all_103_4, 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | all_103_2, 0, all_86_11) = 0 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3017) implies: 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | (3018) array_eq_sub1(int, all_103_4, all_103_2, 0, 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | all_86_11) = 0 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (272) gives: 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | Case 1: 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | | (3019) all_171_0 = all_171_1 & $lesseq(all_86_11, 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | | all_171_1) & $lesseq(0, all_171_1) & $lesseq(0, 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | | all_86_11) & length1(int, all_103_2) = all_171_1 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | | & length1(int, all_103_4) = all_171_1 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3019) implies: 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | | (3020) length1(int, all_103_4) = all_171_1 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | | (3021) length1(int, all_103_2) = all_171_1 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (324) gives: 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | | Case 1: 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | | | (3022) all_219_1 = 0 & array_eq_sub1(int, all_105_4, 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | | | all_105_2, 0, all_86_7) = 0 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3022) implies: 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | | | (3023) array_eq_sub1(int, all_105_4, all_105_2, 0, 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | | | all_86_7) = 0 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (345) gives: 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | | | | (3024) all_242_1 = 0 & array_eq_sub1(int, all_103_2, 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, $sum(all_86_8, 1), all_86_13) = 0 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3024) implies: 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | | | | (3025) array_eq_sub1(int, all_103_2, all_105_4, 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | | | | $sum(all_86_8, 1), all_86_13) = 0 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (270) gives: 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | | | | | (3026) all_169_0 = all_169_1 & $lesseq(all_86_7, 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | | | | | all_169_1) & $lesseq(0, all_169_1) & $lesseq(0, 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | | | | | all_86_7) & length1(int, all_105_2) = all_169_1 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | | | | | & length1(int, all_105_4) = all_169_1 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3026) implies: 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | | | | | (3027) length1(int, all_105_4) = all_169_1 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (45), (48), (50), (52), (53), (180), (184), 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | | | | | (269), (2632), (2633), (3003), (3009), (3010), 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | | | | | (3016), (3025), (3027) are inconsistent by 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #8. 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | | | | | (3028) ~ (all_169_1 = 0) & array_eq_sub1(int, all_105_4, 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_2, 0, all_86_7) = all_169_1 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (3023), (3028) are inconsistent by sub-proof 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | | | | | #75. 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | | | | End of split 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | | | | (3029) length1(int, all_103_2) = all_242_1 & ( ~ 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | | | | ($lesseq(1, $difference(all_242_1, all_86_8))) | 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | | | | ~ ($lesseq(all_86_13, all_242_1)) | ( ~ 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | | | | (all_242_0 = all_242_1) & length1(int, 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4) = all_242_0)) 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (39), (44), (90), (91), (96), (184), (206), 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | | | | (396), (2996), (2997), (2998), (3002), (3020), 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | | | | (3021), (3029) are inconsistent by sub-proof #50. 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | | | End of split 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | | Case 2: 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | | | (3030) length1(int, all_105_4) = all_219_1 & ( ~ 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | | | ($lesseq(all_86_7, all_219_1)) | ~ ($lesseq(0, 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | | | all_219_1)) | ( ~ (all_219_0 = all_219_1) & 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | | | length1(int, all_105_2) = all_219_0)) 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3030) implies: 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | | | (3031) length1(int, all_105_4) = all_219_1 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | | | (3032) ~ ($lesseq(all_86_7, all_219_1)) | ~ ($lesseq(0, 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | | | all_219_1)) | ( ~ (all_219_0 = all_219_1) & 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | | | length1(int, all_105_2) = all_219_0) 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (39), (44), (45), (48), (50), (52), (53), 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | | | (90), (91), (96), (184), (206), (269), (345), 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | | | (389), (394), (396), (2632), (2996), (2997), 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | | | (2998), (3002), (3003), (3009), (3010), (3011), 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | | | (3014), (3020), (3021), (3031), (3032) are 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #4. 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | | End of split 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | Case 2: 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | | (3033) ~ (all_171_1 = 0) & array_eq_sub1(int, all_103_4, 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | | all_103_2, 0, all_86_11) = all_171_1 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (3018), (3033) are inconsistent by sub-proof 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | | #81. 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | | 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | End of split 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | Case 2: 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | (3034) length1(int, all_103_4) = all_215_1 & ( ~ 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | ($lesseq(all_86_11, all_215_1)) | ~ ($lesseq(0, 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | all_215_1)) | ( ~ (all_215_0 = all_215_1) & 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | length1(int, all_103_2) = all_215_0)) 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3034) implies: 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | (3035) length1(int, all_103_4) = all_215_1 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (39), (44), (90), (91), (96), (183), (206), 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | (396), (2996), (2997), (2998), (3002), (3013), 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | (3035) are inconsistent by sub-proof #56. 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | | 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | End of split 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | 205.64/127.52 | | | | | | | | | | | | | | | | | | | | Case 2: 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | (3036) ~ (all_190_4 = 0) & permut_sub2(int, all_105_4, 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | all_105_2, all_86_7, $sum(all_86_10, 1)) = 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | all_190_4 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (43), (3005), (3036) are inconsistent by sub-proof 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | #68. 205.64/127.52 | | | | | | | | | | | | | | | | | | | | | 205.64/127.52 | | | | | | | | | | | | | | | | | | | | End of split 205.64/127.52 | | | | | | | | | | | | | | | | | | | | 205.64/127.52 | | | | | | | | | | | | | | | | | | | Case 2: 205.64/127.52 | | | | | | | | | | | | | | | | | | | | 205.64/127.52 | | | | | | | | | | | | | | | | | | | | (3037) ~ (all_193_1 = 0) & array_eq_sub1(int, all_103_4, 205.64/127.52 | | | | | | | | | | | | | | | | | | | | all_103_2, $sum(all_86_10, 1), all_86_13) = 205.64/127.52 | | | | | | | | | | | | | | | | | | | | all_193_1 205.64/127.52 | | | | | | | | | | | | | | | | | | | | 205.64/127.52 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (2635), (3037) are inconsistent by sub-proof 205.64/127.52 | | | | | | | | | | | | | | | | | | | | #55. 205.64/127.52 | | | | | | | | | | | | | | | | | | | | 205.64/127.52 | | | | | | | | | | | | | | | | | | | End of split 205.64/127.52 | | | | | | | | | | | | | | | | | | | 205.64/127.52 | | | | | | | | | | | | | | | | | | Case 2: 205.64/127.52 | | | | | | | | | | | | | | | | | | | 205.64/127.52 | | | | | | | | | | | | | | | | | | | (3038) ~ (all_153_1 = 0) & array_eq_sub1(int, all_105_4, 205.64/127.52 | | | | | | | | | | | | | | | | | | | all_105_2, $sum(all_86_10, 1), all_86_13) = 205.64/127.52 | | | | | | | | | | | | | | | | | | | all_153_1 205.64/127.52 | | | | | | | | | | | | | | | | | | | 205.64/127.52 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (3007), (3038) are inconsistent by sub-proof 205.64/127.52 | | | | | | | | | | | | | | | | | | | #54. 205.64/127.52 | | | | | | | | | | | | | | | | | | | 205.64/127.52 | | | | | | | | | | | | | | | | | | End of split 205.64/127.52 | | | | | | | | | | | | | | | | | | 205.64/127.52 | | | | | | | | | | | | | | | | | Case 2: 205.64/127.52 | | | | | | | | | | | | | | | | | | 205.64/127.52 | | | | | | | | | | | | | | | | | | (3039) length1(int, all_105_4) = all_234_1 & ( ~ 205.64/127.52 | | | | | | | | | | | | | | | | | | ($lesseq(1, $difference(all_234_1, all_86_10))) 205.64/127.52 | | | | | | | | | | | | | | | | | | | ~ ($lesseq(all_86_13, all_234_1)) | ( ~ 205.64/127.52 | | | | | | | | | | | | | | | | | | (all_234_0 = all_234_1) & length1(int, 205.64/127.52 | | | | | | | | | | | | | | | | | | all_105_2) = all_234_0)) 205.64/127.52 | | | | | | | | | | | | | | | | | | 205.64/127.52 | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (49), (180), (181), (3039) are inconsistent 205.64/127.52 | | | | | | | | | | | | | | | | | | by sub-proof #12. 205.64/127.52 | | | | | | | | | | | | | | | | | | 205.64/127.52 | | | | | | | | | | | | | | | | | End of split 205.64/127.52 | | | | | | | | | | | | | | | | | 205.64/127.52 | | | | | | | | | | | | | | | | Case 2: 205.64/127.52 | | | | | | | | | | | | | | | | | 205.64/127.52 | | | | | | | | | | | | | | | | | (3040) elts(int, all_105_2) = all_187_2 & elts(int, 205.64/127.52 | | | | | | | | | | | | | | | | | all_105_4) = all_187_3 & in_uni(all_187_2) & 205.64/127.52 | | | | | | | | | | | | | | | | | in_uni(all_187_3) & (( ~ (all_187_0 = 0) & 205.64/127.52 | | | | | | | | | | | | | | | | | map_eq_sub1(int, all_187_3, all_187_2, 205.64/127.52 | | | | | | | | | | | | | | | | | $sum(all_86_10, 1), all_187_1) = all_187_0 & 205.64/127.52 | | | | | | | | | | | | | | | | | length1(int, all_105_4) = all_187_1) | ( ~ 205.64/127.52 | | | | | | | | | | | | | | | | | (all_187_1 = 0) & map_eq_sub1(int, all_187_3, 205.64/127.53 | | | | | | | | | | | | | | | | | all_187_2, 0, all_86_7) = all_187_1)) 205.64/127.53 | | | | | | | | | | | | | | | | | 205.64/127.53 | | | | | | | | | | | | | | | | | ALPHA: (3040) implies: 205.64/127.53 | | | | | | | | | | | | | | | | | (3041) elts(int, all_105_4) = all_187_3 205.64/127.53 | | | | | | | | | | | | | | | | | (3042) elts(int, all_105_2) = all_187_2 205.64/127.53 | | | | | | | | | | | | | | | | | (3043) ( ~ (all_187_0 = 0) & map_eq_sub1(int, all_187_3, 205.64/127.53 | | | | | | | | | | | | | | | | | all_187_2, $sum(all_86_10, 1), all_187_1) = 205.64/127.53 | | | | | | | | | | | | | | | | | all_187_0 & length1(int, all_105_4) = all_187_1) 205.64/127.53 | | | | | | | | | | | | | | | | | | ( ~ (all_187_1 = 0) & map_eq_sub1(int, 205.64/127.53 | | | | | | | | | | | | | | | | | all_187_3, all_187_2, 0, all_86_7) = 205.64/127.53 | | | | | | | | | | | | | | | | | all_187_1) 205.64/127.53 | | | | | | | | | | | | | | | | | 205.64/127.53 | | | | | | | | | | | | | | | | | BETA: splitting (337) gives: 205.64/127.53 | | | | | | | | | | | | | | | | | 205.64/127.53 | | | | | | | | | | | | | | | | | Case 1: 205.64/127.53 | | | | | | | | | | | | | | | | | | 205.82/127.53 | | | | | | | | | | | | | | | | | | (3044) all_234_1 = 0 & array_eq_sub1(int, all_105_4, 205.82/127.53 | | | | | | | | | | | | | | | | | | all_105_2, $sum(all_86_10, 1), all_86_13) = 0 205.82/127.53 | | | | | | | | | | | | | | | | | | 205.82/127.53 | | | | | | | | | | | | | | | | | | ALPHA: (3044) implies: 205.82/127.53 | | | | | | | | | | | | | | | | | | (3045) array_eq_sub1(int, all_105_4, all_105_2, 205.82/127.53 | | | | | | | | | | | | | | | | | | $sum(all_86_10, 1), all_86_13) = 0 205.82/127.53 | | | | | | | | | | | | | | | | | | 205.82/127.53 | | | | | | | | | | | | | | | | | | BETA: splitting (298) gives: 205.82/127.53 | | | | | | | | | | | | | | | | | | 205.82/127.53 | | | | | | | | | | | | | | | | | | Case 1: 205.82/127.53 | | | | | | | | | | | | | | | | | | | 205.82/127.53 | | | | | | | | | | | | | | | | | | | (3046) all_193_0 = all_193_1 & $lesseq(1, 205.82/127.53 | | | | | | | | | | | | | | | | | | | $difference(all_193_1, all_86_10)) & 205.82/127.53 | | | | | | | | | | | | | | | | | | | $lesseq(all_86_13, all_193_1) & $lesseq(-1, 205.82/127.53 | | | | | | | | | | | | | | | | | | | all_86_10) & $lesseq(0, all_86_13) & 205.82/127.53 | | | | | | | | | | | | | | | | | | | length1(int, all_103_2) = all_193_1 & length1(int, 205.82/127.53 | | | | | | | | | | | | | | | | | | | all_103_4) = all_193_1 205.82/127.53 | | | | | | | | | | | | | | | | | | | 205.82/127.53 | | | | | | | | | | | | | | | | | | | ALPHA: (3046) implies: 205.82/127.53 | | | | | | | | | | | | | | | | | | | (3047) $lesseq(1, $difference(all_193_1, all_86_10)) 205.82/127.53 | | | | | | | | | | | | | | | | | | | (3048) length1(int, all_103_4) = all_193_1 205.82/127.53 | | | | | | | | | | | | | | | | | | | (3049) length1(int, all_103_2) = all_193_1 205.82/127.53 | | | | | | | | | | | | | | | | | | | 205.82/127.53 | | | | | | | | | | | | | | | | | | | BETA: splitting (319) gives: 205.82/127.53 | | | | | | | | | | | | | | | | | | | 205.82/127.53 | | | | | | | | | | | | | | | | | | | Case 1: 205.82/127.53 | | | | | | | | | | | | | | | | | | | | 205.82/127.53 | | | | | | | | | | | | | | | | | | | | (3050) all_215_1 = 0 & array_eq_sub1(int, all_103_4, 205.82/127.53 | | | | | | | | | | | | | | | | | | | | all_103_2, 0, all_86_11) = 0 205.82/127.53 | | | | | | | | | | | | | | | | | | | | 205.82/127.53 | | | | | | | | | | | | | | | | | | | | ALPHA: (3050) implies: 205.82/127.53 | | | | | | | | | | | | | | | | | | | | (3051) array_eq_sub1(int, all_103_4, all_103_2, 0, 205.82/127.53 | | | | | | | | | | | | | | | | | | | | all_86_11) = 0 205.82/127.53 | | | | | | | | | | | | | | | | | | | | 205.82/127.53 | | | | | | | | | | | | | | | | | | | | BETA: splitting (272) gives: 205.82/127.53 | | | | | | | | | | | | | | | | | | | | 205.82/127.53 | | | | | | | | | | | | | | | | | | | | Case 1: 205.82/127.53 | | | | | | | | | | | | | | | | | | | | | 205.82/127.53 | | | | | | | | | | | | | | | | | | | | | (3052) all_171_0 = all_171_1 & $lesseq(all_86_11, 205.82/127.53 | | | | | | | | | | | | | | | | | | | | | all_171_1) & $lesseq(0, all_171_1) & $lesseq(0, 205.82/127.53 | | | | | | | | | | | | | | | | | | | | | all_86_11) & length1(int, all_103_2) = all_171_1 205.82/127.53 | | | | | | | | | | | | | | | | | | | | | & length1(int, all_103_4) = all_171_1 205.82/127.53 | | | | | | | | | | | | | | | | | | | | | 205.82/127.53 | | | | | | | | | | | | | | | | | | | | | ALPHA: (3052) implies: 205.82/127.53 | | | | | | | | | | | | | | | | | | | | | (3053) length1(int, all_103_4) = all_171_1 205.82/127.53 | | | | | | | | | | | | | | | | | | | | | (3054) length1(int, all_103_2) = all_171_1 205.82/127.53 | | | | | | | | | | | | | | | | | | | | | 205.82/127.53 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (255) gives: 205.82/127.53 | | | | | | | | | | | | | | | | | | | | | 205.82/127.53 | | | | | | | | | | | | | | | | | | | | | Case 1: 205.82/127.53 | | | | | | | | | | | | | | | | | | | | | | 205.82/127.53 | | | | | | | | | | | | | | | | | | | | | | (3055) all_153_0 = all_153_1 & $lesseq(1, 205.82/127.53 | | | | | | | | | | | | | | | | | | | | | | $difference(all_153_1, all_86_10)) & 205.82/127.53 | | | | | | | | | | | | | | | | | | | | | | $lesseq(all_86_13, all_153_1) & $lesseq(-1, 205.82/127.53 | | | | | | | | | | | | | | | | | | | | | | all_86_10) & $lesseq(0, all_86_13) & 205.82/127.53 | | | | | | | | | | | | | | | | | | | | | | length1(int, all_105_2) = all_153_1 & length1(int, 205.82/127.53 | | | | | | | | | | | | | | | | | | | | | | all_105_4) = all_153_1 205.82/127.53 | | | | | | | | | | | | | | | | | | | | | | 205.82/127.53 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3055) implies: 205.82/127.53 | | | | | | | | | | | | | | | | | | | | | | (3056) $lesseq(1, $difference(all_153_1, all_86_10)) 205.82/127.53 | | | | | | | | | | | | | | | | | | | | | | (3057) length1(int, all_105_4) = all_153_1 205.82/127.53 | | | | | | | | | | | | | | | | | | | | | | (3058) length1(int, all_105_2) = all_153_1 205.82/127.53 | | | | | | | | | | | | | | | | | | | | | | 205.82/127.53 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (324) gives: 205.82/127.53 | | | | | | | | | | | | | | | | | | | | | | 205.82/127.53 | | | | | | | | | | | | | | | | | | | | | | Case 1: 205.82/127.53 | | | | | | | | | | | | | | | | | | | | | | | 205.82/127.53 | | | | | | | | | | | | | | | | | | | | | | | (3059) all_219_1 = 0 & array_eq_sub1(int, all_105_4, 205.82/127.53 | | | | | | | | | | | | | | | | | | | | | | | all_105_2, 0, all_86_7) = 0 205.82/127.53 | | | | | | | | | | | | | | | | | | | | | | | 205.82/127.53 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3059) implies: 205.82/127.53 | | | | | | | | | | | | | | | | | | | | | | | (3060) array_eq_sub1(int, all_105_4, all_105_2, 0, 205.82/127.53 | | | | | | | | | | | | | | | | | | | | | | | all_86_7) = 0 205.82/127.53 | | | | | | | | | | | | | | | | | | | | | | | 205.82/127.53 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (39), (44), (45), (99), (100), (105), (180), 205.82/127.53 | | | | | | | | | | | | | | | | | | | | | | | (183), (205), (255), (270), (337), (3041), (3042), 205.82/127.53 | | | | | | | | | | | | | | | | | | | | | | | (3043), (3047), (3048), (3060) are inconsistent by 205.82/127.53 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #5. 205.82/127.53 | | | | | | | | | | | | | | | | | | | | | | | 205.82/127.53 | | | | | | | | | | | | | | | | | | | | | | Case 2: 205.82/127.53 | | | | | | | | | | | | | | | | | | | | | | | 205.82/127.53 | | | | | | | | | | | | | | | | | | | | | | | (3061) length1(int, all_105_4) = all_219_1 & ( ~ 205.82/127.53 | | | | | | | | | | | | | | | | | | | | | | | ($lesseq(all_86_7, all_219_1)) | ~ ($lesseq(0, 205.82/127.53 | | | | | | | | | | | | | | | | | | | | | | | all_219_1)) | ( ~ (all_219_0 = all_219_1) & 205.82/127.53 | | | | | | | | | | | | | | | | | | | | | | | length1(int, all_105_2) = all_219_0)) 205.82/127.53 | | | | | | | | | | | | | | | | | | | | | | | 205.82/127.53 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3061) implies: 205.82/127.53 | | | | | | | | | | | | | | | | | | | | | | | (3062) length1(int, all_105_4) = all_219_1 205.82/127.53 | | | | | | | | | | | | | | | | | | | | | | | (3063) ~ ($lesseq(all_86_7, all_219_1)) | ~ ($lesseq(0, 205.82/127.53 | | | | | | | | | | | | | | | | | | | | | | | all_219_1)) | ( ~ (all_219_0 = all_219_1) & 205.82/127.53 | | | | | | | | | | | | | | | | | | | | | | | length1(int, all_105_2) = all_219_0) 205.82/127.53 | | | | | | | | | | | | | | | | | | | | | | | 205.82/127.53 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (39), (44), (45), (48), (50), (52), (53), 205.82/127.53 | | | | | | | | | | | | | | | | | | | | | | | (90), (91), (96), (184), (206), (269), (345), 205.82/127.53 | | | | | | | | | | | | | | | | | | | | | | | (389), (394), (396), (2632), (2996), (2997), 205.82/127.53 | | | | | | | | | | | | | | | | | | | | | | | (2998), (3002), (3003), (3049), (3053), (3054), 205.82/127.53 | | | | | | | | | | | | | | | | | | | | | | | (3056), (3057), (3058), (3062), (3063) are 205.82/127.53 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #4. 205.82/127.53 | | | | | | | | | | | | | | | | | | | | | | | 205.82/127.53 | | | | | | | | | | | | | | | | | | | | | | End of split 205.82/127.53 | | | | | | | | | | | | | | | | | | | | | | 205.82/127.53 | | | | | | | | | | | | | | | | | | | | | Case 2: 205.82/127.53 | | | | | | | | | | | | | | | | | | | | | | 205.82/127.53 | | | | | | | | | | | | | | | | | | | | | | (3064) ~ (all_153_1 = 0) & array_eq_sub1(int, all_105_4, 205.82/127.53 | | | | | | | | | | | | | | | | | | | | | | all_105_2, $sum(all_86_10, 1), all_86_13) = 205.82/127.53 | | | | | | | | | | | | | | | | | | | | | | all_153_1 205.82/127.53 | | | | | | | | | | | | | | | | | | | | | | 205.82/127.53 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (3045), (3064) are inconsistent by sub-proof 205.82/127.53 | | | | | | | | | | | | | | | | | | | | | | #54. 205.82/127.53 | | | | | | | | | | | | | | | | | | | | | | 205.82/127.53 | | | | | | | | | | | | | | | | | | | | | End of split 205.82/127.53 | | | | | | | | | | | | | | | | | | | | | 205.82/127.53 | | | | | | | | | | | | | | | | | | | | Case 2: 205.82/127.53 | | | | | | | | | | | | | | | | | | | | | 205.82/127.53 | | | | | | | | | | | | | | | | | | | | | (3065) ~ (all_171_1 = 0) & array_eq_sub1(int, all_103_4, 205.82/127.53 | | | | | | | | | | | | | | | | | | | | | all_103_2, 0, all_86_11) = all_171_1 205.82/127.53 | | | | | | | | | | | | | | | | | | | | | 205.82/127.53 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (3051), (3065) are inconsistent by sub-proof 205.82/127.53 | | | | | | | | | | | | | | | | | | | | | #81. 205.82/127.53 | | | | | | | | | | | | | | | | | | | | | 205.82/127.53 | | | | | | | | | | | | | | | | | | | | End of split 205.82/127.53 | | | | | | | | | | | | | | | | | | | | 205.82/127.53 | | | | | | | | | | | | | | | | | | | Case 2: 205.82/127.53 | | | | | | | | | | | | | | | | | | | | 205.82/127.53 | | | | | | | | | | | | | | | | | | | | (3066) length1(int, all_103_4) = all_215_1 & ( ~ 205.82/127.53 | | | | | | | | | | | | | | | | | | | | ($lesseq(all_86_11, all_215_1)) | ~ ($lesseq(0, 205.82/127.53 | | | | | | | | | | | | | | | | | | | | all_215_1)) | ( ~ (all_215_0 = all_215_1) & 205.82/127.53 | | | | | | | | | | | | | | | | | | | | length1(int, all_103_2) = all_215_0)) 205.82/127.53 | | | | | | | | | | | | | | | | | | | | 205.82/127.53 | | | | | | | | | | | | | | | | | | | | ALPHA: (3066) implies: 205.82/127.53 | | | | | | | | | | | | | | | | | | | | (3067) length1(int, all_103_4) = all_215_1 205.82/127.53 | | | | | | | | | | | | | | | | | | | | 205.82/127.53 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (39), (44), (90), (91), (96), (183), (206), 205.82/127.53 | | | | | | | | | | | | | | | | | | | | (396), (2996), (2997), (2998), (3002), (3048), 205.82/127.53 | | | | | | | | | | | | | | | | | | | | (3067) are inconsistent by sub-proof #56. 205.82/127.53 | | | | | | | | | | | | | | | | | | | | 205.82/127.53 | | | | | | | | | | | | | | | | | | | End of split 205.82/127.53 | | | | | | | | | | | | | | | | | | | 205.82/127.53 | | | | | | | | | | | | | | | | | | Case 2: 205.82/127.53 | | | | | | | | | | | | | | | | | | | 205.82/127.53 | | | | | | | | | | | | | | | | | | | (3068) ~ (all_193_1 = 0) & array_eq_sub1(int, all_103_4, 205.82/127.53 | | | | | | | | | | | | | | | | | | | all_103_2, $sum(all_86_10, 1), all_86_13) = 205.82/127.53 | | | | | | | | | | | | | | | | | | | all_193_1 205.82/127.53 | | | | | | | | | | | | | | | | | | | 205.82/127.53 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (2635), (3068) are inconsistent by sub-proof 205.82/127.53 | | | | | | | | | | | | | | | | | | | #55. 205.82/127.53 | | | | | | | | | | | | | | | | | | | 205.82/127.53 | | | | | | | | | | | | | | | | | | End of split 205.82/127.53 | | | | | | | | | | | | | | | | | | 205.82/127.53 | | | | | | | | | | | | | | | | | Case 2: 205.82/127.53 | | | | | | | | | | | | | | | | | | 205.82/127.53 | | | | | | | | | | | | | | | | | | (3069) length1(int, all_105_4) = all_234_1 & ( ~ 205.82/127.53 | | | | | | | | | | | | | | | | | | ($lesseq(1, $difference(all_234_1, all_86_10))) 205.82/127.53 | | | | | | | | | | | | | | | | | | | ~ ($lesseq(all_86_13, all_234_1)) | ( ~ 205.82/127.53 | | | | | | | | | | | | | | | | | | (all_234_0 = all_234_1) & length1(int, 205.82/127.53 | | | | | | | | | | | | | | | | | | all_105_2) = all_234_0)) 205.82/127.53 | | | | | | | | | | | | | | | | | | 205.82/127.53 | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (49), (180), (181), (3069) are inconsistent 205.82/127.53 | | | | | | | | | | | | | | | | | | by sub-proof #12. 205.82/127.53 | | | | | | | | | | | | | | | | | | 205.82/127.53 | | | | | | | | | | | | | | | | | End of split 205.82/127.53 | | | | | | | | | | | | | | | | | 205.82/127.53 | | | | | | | | | | | | | | | | End of split 205.82/127.53 | | | | | | | | | | | | | | | | 205.82/127.53 | | | | | | | | | | | | | | | Case 2: 205.82/127.53 | | | | | | | | | | | | | | | | 205.82/127.53 | | | | | | | | | | | | | | | | (3070) ~ (all_177_4 = 0) & permut_sub2(int, all_103_2, 205.82/127.53 | | | | | | | | | | | | | | | | all_105_4, all_86_11, $sum(all_86_8, 1)) = 205.82/127.53 | | | | | | | | | | | | | | | | all_177_4 205.82/127.53 | | | | | | | | | | | | | | | | 205.82/127.53 | | | | | | | | | | | | | | | | REF_CLOSE: (43), (3000), (3070) are inconsistent by sub-proof 205.82/127.53 | | | | | | | | | | | | | | | | #47. 205.82/127.53 | | | | | | | | | | | | | | | | 205.82/127.53 | | | | | | | | | | | | | | | End of split 205.82/127.53 | | | | | | | | | | | | | | | 205.82/127.53 | | | | | | | | | | | | | | Case 2: 205.82/127.53 | | | | | | | | | | | | | | | 205.82/127.53 | | | | | | | | | | | | | | | (3071) elts(int, all_105_4) = all_181_2 & elts(int, 205.82/127.53 | | | | | | | | | | | | | | | all_103_2) = all_181_3 & in_uni(all_181_2) & 205.82/127.53 | | | | | | | | | | | | | | | in_uni(all_181_3) & (( ~ (all_181_0 = 0) & 205.82/127.53 | | | | | | | | | | | | | | | map_eq_sub1(int, all_181_3, all_181_2, 205.82/127.53 | | | | | | | | | | | | | | | $sum(all_86_8, 1), all_181_1) = all_181_0 & 205.82/127.53 | | | | | | | | | | | | | | | length1(int, all_103_2) = all_181_1) | ( ~ 205.82/127.53 | | | | | | | | | | | | | | | (all_181_1 = 0) & map_eq_sub1(int, all_181_3, 205.82/127.53 | | | | | | | | | | | | | | | all_181_2, 0, all_86_11) = all_181_1)) 205.82/127.53 | | | | | | | | | | | | | | | 205.82/127.53 | | | | | | | | | | | | | | | ALPHA: (3071) implies: 205.82/127.53 | | | | | | | | | | | | | | | (3072) elts(int, all_103_2) = all_181_3 205.82/127.53 | | | | | | | | | | | | | | | 205.82/127.53 | | | | | | | | | | | | | | | BETA: splitting (298) gives: 205.82/127.53 | | | | | | | | | | | | | | | 205.82/127.53 | | | | | | | | | | | | | | | Case 1: 205.82/127.53 | | | | | | | | | | | | | | | | 205.82/127.53 | | | | | | | | | | | | | | | | (3073) all_193_0 = all_193_1 & $lesseq(1, 205.82/127.53 | | | | | | | | | | | | | | | | $difference(all_193_1, all_86_10)) & 205.82/127.53 | | | | | | | | | | | | | | | | $lesseq(all_86_13, all_193_1) & $lesseq(-1, 205.82/127.53 | | | | | | | | | | | | | | | | all_86_10) & $lesseq(0, all_86_13) & 205.82/127.53 | | | | | | | | | | | | | | | | length1(int, all_103_2) = all_193_1 & length1(int, 205.82/127.53 | | | | | | | | | | | | | | | | all_103_4) = all_193_1 205.82/127.53 | | | | | | | | | | | | | | | | 205.82/127.53 | | | | | | | | | | | | | | | | ALPHA: (3073) implies: 205.82/127.53 | | | | | | | | | | | | | | | | (3074) length1(int, all_103_4) = all_193_1 205.82/127.53 | | | | | | | | | | | | | | | | (3075) length1(int, all_103_2) = all_193_1 205.82/127.53 | | | | | | | | | | | | | | | | 205.82/127.53 | | | | | | | | | | | | | | | | BETA: splitting (319) gives: 205.82/127.53 | | | | | | | | | | | | | | | | 205.82/127.53 | | | | | | | | | | | | | | | | Case 1: 205.82/127.53 | | | | | | | | | | | | | | | | | 205.82/127.53 | | | | | | | | | | | | | | | | | (3076) all_215_1 = 0 & array_eq_sub1(int, all_103_4, 205.82/127.53 | | | | | | | | | | | | | | | | | all_103_2, 0, all_86_11) = 0 205.82/127.53 | | | | | | | | | | | | | | | | | 205.82/127.53 | | | | | | | | | | | | | | | | | ALPHA: (3076) implies: 205.82/127.53 | | | | | | | | | | | | | | | | | (3077) array_eq_sub1(int, all_103_4, all_103_2, 0, 205.82/127.53 | | | | | | | | | | | | | | | | | all_86_11) = 0 205.82/127.53 | | | | | | | | | | | | | | | | | 205.82/127.53 | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (39), (44), (45), (90), (91), (96), (183), 205.82/127.53 | | | | | | | | | | | | | | | | | (206), (272), (394), (396), (2996), (2997), 205.82/127.53 | | | | | | | | | | | | | | | | | (2998), (3072), (3074), (3075), (3077) are 205.82/127.53 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #26. 205.82/127.53 | | | | | | | | | | | | | | | | | 205.82/127.53 | | | | | | | | | | | | | | | | Case 2: 205.82/127.53 | | | | | | | | | | | | | | | | | 205.82/127.53 | | | | | | | | | | | | | | | | | (3078) length1(int, all_103_4) = all_215_1 & ( ~ 205.82/127.53 | | | | | | | | | | | | | | | | | ($lesseq(all_86_11, all_215_1)) | ~ ($lesseq(0, 205.82/127.53 | | | | | | | | | | | | | | | | | all_215_1)) | ( ~ (all_215_0 = all_215_1) & 205.82/127.53 | | | | | | | | | | | | | | | | | length1(int, all_103_2) = all_215_0)) 205.82/127.53 | | | | | | | | | | | | | | | | | 205.82/127.53 | | | | | | | | | | | | | | | | | ALPHA: (3078) implies: 205.82/127.53 | | | | | | | | | | | | | | | | | (3079) length1(int, all_103_4) = all_215_1 205.82/127.53 | | | | | | | | | | | | | | | | | 205.82/127.53 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_86_13, all_215_1, 205.82/127.53 | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (183), (3079) 205.82/127.53 | | | | | | | | | | | | | | | | | gives: 205.82/127.53 | | | | | | | | | | | | | | | | | (3080) all_215_1 = all_86_13 205.82/127.53 | | | | | | | | | | | | | | | | | 205.82/127.53 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_215_1, all_193_1, 205.82/127.54 | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (3074), (3079) 205.82/127.54 | | | | | | | | | | | | | | | | | gives: 205.82/127.54 | | | | | | | | | | | | | | | | | (3081) all_215_1 = all_193_1 205.82/127.54 | | | | | | | | | | | | | | | | | 205.82/127.54 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_103_1, all_191_2, 205.82/127.54 | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (91), (2997) 205.82/127.54 | | | | | | | | | | | | | | | | | gives: 205.82/127.54 | | | | | | | | | | | | | | | | | (3082) all_191_2 = all_103_1 205.82/127.54 | | | | | | | | | | | | | | | | | 205.82/127.54 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_191_2, all_181_3, 205.82/127.54 | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (2997), (3072) 205.82/127.54 | | | | | | | | | | | | | | | | | gives: 205.82/127.54 | | | | | | | | | | | | | | | | | (3083) all_191_2 = all_181_3 205.82/127.54 | | | | | | | | | | | | | | | | | 205.82/127.54 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_103_3, all_191_3, 205.82/127.54 | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (90), (2996) 205.82/127.54 | | | | | | | | | | | | | | | | | gives: 205.82/127.54 | | | | | | | | | | | | | | | | | (3084) all_191_3 = all_103_3 205.82/127.54 | | | | | | | | | | | | | | | | | 205.82/127.54 | | | | | | | | | | | | | | | | | COMBINE_EQS: (3080), (3081) imply: 205.82/127.54 | | | | | | | | | | | | | | | | | (3085) all_193_1 = all_86_13 205.82/127.54 | | | | | | | | | | | | | | | | | 205.82/127.54 | | | | | | | | | | | | | | | | | COMBINE_EQS: (3082), (3083) imply: 205.82/127.54 | | | | | | | | | | | | | | | | | (3086) all_181_3 = all_103_1 205.82/127.54 | | | | | | | | | | | | | | | | | 205.82/127.54 | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (44), (96), (183), (206), (2998), (3082), 205.82/127.54 | | | | | | | | | | | | | | | | | (3084) are inconsistent by sub-proof #57. 205.82/127.54 | | | | | | | | | | | | | | | | | 205.82/127.54 | | | | | | | | | | | | | | | | End of split 205.82/127.54 | | | | | | | | | | | | | | | | 205.82/127.54 | | | | | | | | | | | | | | | Case 2: 205.82/127.54 | | | | | | | | | | | | | | | | 205.82/127.54 | | | | | | | | | | | | | | | | (3087) ~ (all_193_1 = 0) & array_eq_sub1(int, all_103_4, 205.82/127.54 | | | | | | | | | | | | | | | | all_103_2, $sum(all_86_10, 1), all_86_13) = 205.82/127.54 | | | | | | | | | | | | | | | | all_193_1 205.82/127.54 | | | | | | | | | | | | | | | | 205.82/127.54 | | | | | | | | | | | | | | | | REF_CLOSE: (45), (2635), (3087) are inconsistent by sub-proof 205.82/127.54 | | | | | | | | | | | | | | | | #55. 205.82/127.54 | | | | | | | | | | | | | | | | 205.82/127.54 | | | | | | | | | | | | | | | End of split 205.82/127.54 | | | | | | | | | | | | | | | 205.82/127.54 | | | | | | | | | | | | | | End of split 205.82/127.54 | | | | | | | | | | | | | | 205.82/127.54 | | | | | | | | | | | | | End of split 205.82/127.54 | | | | | | | | | | | | | 205.82/127.54 | | | | | | | | | | | | Case 2: 205.82/127.54 | | | | | | | | | | | | | 205.82/127.54 | | | | | | | | | | | | | (3088) length1(int, all_103_4) = all_238_1 & ( ~ 205.82/127.54 | | | | | | | | | | | | | ($lesseq(1, $difference(all_238_1, all_86_10))) 205.82/127.54 | | | | | | | | | | | | | | ~ ($lesseq(all_86_13, all_238_1)) | ( ~ 205.82/127.54 | | | | | | | | | | | | | (all_238_0 = all_238_1) & length1(int, 205.82/127.54 | | | | | | | | | | | | | all_103_2) = all_238_0)) 205.82/127.54 | | | | | | | | | | | | | 205.82/127.54 | | | | | | | | | | | | | ALPHA: (3088) implies: 205.82/127.54 | | | | | | | | | | | | | (3089) length1(int, all_103_4) = all_238_1 205.82/127.54 | | | | | | | | | | | | | (3090) ~ ($lesseq(1, $difference(all_238_1, all_86_10))) 205.82/127.54 | | | | | | | | | | | | | | ~ ($lesseq(all_86_13, all_238_1)) | ( ~ 205.82/127.54 | | | | | | | | | | | | | (all_238_0 = all_238_1) & length1(int, 205.82/127.54 | | | | | | | | | | | | | all_103_2) = all_238_0) 205.82/127.54 | | | | | | | | | | | | | 205.82/127.54 | | | | | | | | | | | | | BETA: splitting (294) gives: 205.82/127.54 | | | | | | | | | | | | | 205.82/127.54 | | | | | | | | | | | | | Case 1: 205.82/127.54 | | | | | | | | | | | | | | 205.82/127.54 | | | | | | | | | | | | | | (3091) all_187_3 = 0 & permut_sub2(int, all_105_4, 205.82/127.54 | | | | | | | | | | | | | | all_105_2, all_86_7, $sum(all_86_10, 1)) = 0 205.82/127.54 | | | | | | | | | | | | | | 205.82/127.54 | | | | | | | | | | | | | | ALPHA: (3091) implies: 205.82/127.54 | | | | | | | | | | | | | | (3092) permut_sub2(int, all_105_4, all_105_2, all_86_7, 205.82/127.54 | | | | | | | | | | | | | | $sum(all_86_10, 1)) = 0 205.82/127.54 | | | | | | | | | | | | | | 205.82/127.54 | | | | | | | | | | | | | | BETA: splitting (337) gives: 205.82/127.54 | | | | | | | | | | | | | | 205.82/127.54 | | | | | | | | | | | | | | Case 1: 205.82/127.54 | | | | | | | | | | | | | | | 205.82/127.54 | | | | | | | | | | | | | | | (3093) all_234_1 = 0 & array_eq_sub1(int, all_105_4, 205.82/127.54 | | | | | | | | | | | | | | | all_105_2, $sum(all_86_10, 1), all_86_13) = 0 205.82/127.54 | | | | | | | | | | | | | | | 205.82/127.54 | | | | | | | | | | | | | | | ALPHA: (3093) implies: 205.82/127.54 | | | | | | | | | | | | | | | (3094) array_eq_sub1(int, all_105_4, all_105_2, 205.82/127.54 | | | | | | | | | | | | | | | $sum(all_86_10, 1), all_86_13) = 0 205.82/127.54 | | | | | | | | | | | | | | | 205.82/127.54 | | | | | | | | | | | | | | | BETA: splitting (296) gives: 205.82/127.54 | | | | | | | | | | | | | | | 205.82/127.54 | | | | | | | | | | | | | | | Case 1: 205.82/127.54 | | | | | | | | | | | | | | | | 205.82/127.54 | | | | | | | | | | | | | | | | (3095) all_191_3 = 0 & permut_sub2(int, all_103_4, 205.82/127.54 | | | | | | | | | | | | | | | | all_103_2, all_86_11, $sum(all_86_10, 1)) = 0 205.82/127.54 | | | | | | | | | | | | | | | | 205.82/127.54 | | | | | | | | | | | | | | | | ALPHA: (3095) implies: 205.82/127.54 | | | | | | | | | | | | | | | | (3096) permut_sub2(int, all_103_4, all_103_2, all_86_11, 205.82/127.54 | | | | | | | | | | | | | | | | $sum(all_86_10, 1)) = 0 205.82/127.54 | | | | | | | | | | | | | | | | 205.82/127.54 | | | | | | | | | | | | | | | | BETA: splitting (319) gives: 205.82/127.54 | | | | | | | | | | | | | | | | 205.82/127.54 | | | | | | | | | | | | | | | | Case 1: 205.82/127.54 | | | | | | | | | | | | | | | | | 205.82/127.54 | | | | | | | | | | | | | | | | | (3097) all_215_1 = 0 & array_eq_sub1(int, all_103_4, 205.82/127.54 | | | | | | | | | | | | | | | | | all_103_2, 0, all_86_11) = 0 205.82/127.54 | | | | | | | | | | | | | | | | | 205.82/127.54 | | | | | | | | | | | | | | | | | ALPHA: (3097) implies: 205.82/127.54 | | | | | | | | | | | | | | | | | (3098) array_eq_sub1(int, all_103_4, all_103_2, 0, 205.82/127.54 | | | | | | | | | | | | | | | | | all_86_11) = 0 205.82/127.54 | | | | | | | | | | | | | | | | | 205.82/127.54 | | | | | | | | | | | | | | | | | BETA: splitting (272) gives: 205.82/127.54 | | | | | | | | | | | | | | | | | 205.82/127.54 | | | | | | | | | | | | | | | | | Case 1: 205.82/127.54 | | | | | | | | | | | | | | | | | | 205.82/127.54 | | | | | | | | | | | | | | | | | | (3099) all_171_0 = all_171_1 & $lesseq(all_86_11, 205.82/127.54 | | | | | | | | | | | | | | | | | | all_171_1) & $lesseq(0, all_171_1) & $lesseq(0, 205.82/127.54 | | | | | | | | | | | | | | | | | | all_86_11) & length1(int, all_103_2) = all_171_1 205.82/127.54 | | | | | | | | | | | | | | | | | | & length1(int, all_103_4) = all_171_1 205.82/127.54 | | | | | | | | | | | | | | | | | | 205.82/127.54 | | | | | | | | | | | | | | | | | | ALPHA: (3099) implies: 205.82/127.54 | | | | | | | | | | | | | | | | | | (3100) length1(int, all_103_4) = all_171_1 205.82/127.54 | | | | | | | | | | | | | | | | | | (3101) length1(int, all_103_2) = all_171_1 205.82/127.54 | | | | | | | | | | | | | | | | | | 205.82/127.54 | | | | | | | | | | | | | | | | | | BETA: splitting (255) gives: 205.82/127.54 | | | | | | | | | | | | | | | | | | 205.82/127.54 | | | | | | | | | | | | | | | | | | Case 1: 205.82/127.54 | | | | | | | | | | | | | | | | | | | 205.82/127.54 | | | | | | | | | | | | | | | | | | | (3102) all_153_0 = all_153_1 & $lesseq(1, 205.82/127.54 | | | | | | | | | | | | | | | | | | | $difference(all_153_1, all_86_10)) & 205.82/127.54 | | | | | | | | | | | | | | | | | | | $lesseq(all_86_13, all_153_1) & $lesseq(-1, 205.82/127.54 | | | | | | | | | | | | | | | | | | | all_86_10) & $lesseq(0, all_86_13) & 205.82/127.54 | | | | | | | | | | | | | | | | | | | length1(int, all_105_2) = all_153_1 & length1(int, 205.82/127.54 | | | | | | | | | | | | | | | | | | | all_105_4) = all_153_1 205.82/127.54 | | | | | | | | | | | | | | | | | | | 205.82/127.54 | | | | | | | | | | | | | | | | | | | ALPHA: (3102) implies: 205.82/127.54 | | | | | | | | | | | | | | | | | | | (3103) $lesseq(1, $difference(all_153_1, all_86_10)) 205.82/127.54 | | | | | | | | | | | | | | | | | | | (3104) length1(int, all_105_4) = all_153_1 205.82/127.54 | | | | | | | | | | | | | | | | | | | 205.82/127.54 | | | | | | | | | | | | | | | | | | | BETA: splitting (287) gives: 205.82/127.54 | | | | | | | | | | | | | | | | | | | 205.82/127.54 | | | | | | | | | | | | | | | | | | | Case 1: 205.82/127.54 | | | | | | | | | | | | | | | | | | | | 205.82/127.54 | | | | | | | | | | | | | | | | | | | | (3105) all_181_3 = 0 & permut_sub2(int, all_103_2, 205.82/127.54 | | | | | | | | | | | | | | | | | | | | all_105_4, all_86_11, $sum(all_86_8, 1)) = 0 205.82/127.54 | | | | | | | | | | | | | | | | | | | | 205.82/127.54 | | | | | | | | | | | | | | | | | | | | ALPHA: (3105) implies: 205.82/127.54 | | | | | | | | | | | | | | | | | | | | (3106) permut_sub2(int, all_103_2, all_105_4, all_86_11, 205.82/127.54 | | | | | | | | | | | | | | | | | | | | $sum(all_86_8, 1)) = 0 205.82/127.54 | | | | | | | | | | | | | | | | | | | | 205.82/127.54 | | | | | | | | | | | | | | | | | | | | BETA: splitting (280) gives: 205.82/127.54 | | | | | | | | | | | | | | | | | | | | 205.82/127.54 | | | | | | | | | | | | | | | | | | | | Case 1: 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | (3107) all_177_0 = 0 & all_177_1 = 0 & map_eq_sub1(int, 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | all_177_4, all_177_3, $sum(all_86_8, 1), 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | all_177_2) = 0 & map_eq_sub1(int, all_177_4, 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | all_177_3, 0, all_86_11) = 0 & length1(int, 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | all_103_2) = all_177_2 & elts(int, all_105_4) = 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | all_177_3 & elts(int, all_103_2) = all_177_4 & 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | in_uni(all_177_3) & in_uni(all_177_4) 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | ALPHA: (3107) implies: 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | (3108) length1(int, all_103_2) = all_177_2 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (295) gives: 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | Case 1: 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | (3109) all_190_0 = 0 & all_190_1 = 0 & map_eq_sub1(int, 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | all_190_4, all_190_3, $sum(all_86_10, 1), 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | all_190_2) = 0 & map_eq_sub1(int, all_190_4, 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | all_190_3, 0, all_86_7) = 0 & length1(int, 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | all_105_4) = all_190_2 & elts(int, all_105_2) = 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | all_190_3 & elts(int, all_105_4) = all_190_4 & 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | in_uni(all_190_3) & in_uni(all_190_4) 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3109) implies: 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | (3110) length1(int, all_105_4) = all_190_2 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (324) gives: 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | Case 1: 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | | 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | | (3111) all_219_1 = 0 & array_eq_sub1(int, all_105_4, 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | | all_105_2, 0, all_86_7) = 0 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | | 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3111) implies: 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | | (3112) array_eq_sub1(int, all_105_4, all_105_2, 0, 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | | all_86_7) = 0 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | | 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (270) gives: 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | | 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | | Case 1: 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | | | 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | | | (3113) all_169_0 = all_169_1 & $lesseq(all_86_7, 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | | | all_169_1) & $lesseq(0, all_169_1) & $lesseq(0, 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | | | all_86_7) & length1(int, all_105_2) = all_169_1 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | | | & length1(int, all_105_4) = all_169_1 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | | | 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3113) implies: 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | | | (3114) length1(int, all_105_4) = all_169_1 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | | | 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (297) gives: 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | | | 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | | | | 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | | | | (3115) all_192_0 = 0 & all_192_1 = 0 & map_eq_sub1(int, 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | | | | all_192_4, all_192_3, $sum(all_86_10, 1), 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | | | | all_192_2) = 0 & map_eq_sub1(int, all_192_4, 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | | | | all_192_3, 0, all_86_11) = 0 & length1(int, 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | | | | all_103_4) = all_192_2 & elts(int, all_103_2) = 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | | | | all_192_3 & elts(int, all_103_4) = all_192_4 & 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | | | | in_uni(all_192_3) & in_uni(all_192_4) 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | | | | 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3115) implies: 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | | | | (3116) length1(int, all_103_4) = all_192_2 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | | | | 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (345) gives: 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | | | | 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | | | | | (3117) all_242_1 = 0 & array_eq_sub1(int, all_103_2, 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, $sum(all_86_8, 1), all_86_13) = 0 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3117) implies: 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | | | | | (3118) array_eq_sub1(int, all_103_2, all_105_4, 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | | | | | $sum(all_86_8, 1), all_86_13) = 0 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (45), (48), (50), (52), (53), (180), (184), 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | | | | | (269), (2632), (2633), (3103), (3104), (3108), 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | | | | | (3110), (3114), (3118) are inconsistent by 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #8. 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | | | | | (3119) length1(int, all_103_2) = all_242_1 & ( ~ 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | | | | | ($lesseq(1, $difference(all_242_1, all_86_8))) | 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | | | | | ~ ($lesseq(all_86_13, all_242_1)) | ( ~ 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_242_0 = all_242_1) & length1(int, 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4) = all_242_0)) 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3119) implies: 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | | | | | (3120) length1(int, all_103_2) = all_242_1 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_86_13, all_169_1, 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (180), (3114) 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | | | | | (3121) all_169_1 = all_86_13 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_190_2, all_169_1, 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (3110), (3114) 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | | | | | (3122) all_190_2 = all_169_1 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_190_2, all_153_1, 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (3104), (3110) 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | | | | | (3123) all_190_2 = all_153_1 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_86_13, all_211_1, 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (184), (2632) 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | | | | | (3124) all_211_1 = all_86_13 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_211_1, all_177_2, 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (2632), (3108) 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | | | | | (3125) all_211_1 = all_177_2 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_242_1, all_171_1, 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (3101), (3120) 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | | | | | (3126) all_242_1 = all_171_1 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_211_1, all_171_1, 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (2632), (3101) 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | | | | | (3127) all_211_1 = all_171_1 205.82/127.54 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_242_1, all_156_0, 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (394), (3120) 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | | | | | (3128) all_242_1 = all_156_0 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_238_1, all_192_2, 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (3089), (3116) 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | | | | | (3129) all_238_1 = all_192_2 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_238_1, all_171_1, 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (3089), (3100) 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | | | | | (3130) all_238_1 = all_171_1 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3126), (3128) imply: 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | | | | | (3131) all_171_1 = all_156_0 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3131) implies: 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | | | | | (3132) all_171_1 = all_156_0 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3129), (3130) imply: 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | | | | | (3133) all_192_2 = all_171_1 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3124), (3125) imply: 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | | | | | (3134) all_177_2 = all_86_13 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3125), (3127) imply: 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | | | | | (3135) all_177_2 = all_171_1 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3122), (3123) imply: 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | | | | | (3136) all_169_1 = all_153_1 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3136) implies: 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | | | | | (3137) all_169_1 = all_153_1 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3134), (3135) imply: 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | | | | | (3138) all_171_1 = all_86_13 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3138) implies: 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | | | | | (3139) all_171_1 = all_86_13 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3132), (3139) imply: 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | | | | | (3140) all_156_0 = all_86_13 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3121), (3137) imply: 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | | | | | (3141) all_153_1 = all_86_13 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3141) implies: 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | | | | | (3142) all_153_1 = all_86_13 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3133), (3139) imply: 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | | | | | (3143) all_192_2 = all_86_13 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3129), (3143) imply: 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | | | | | (3144) all_238_1 = all_86_13 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (394), (3090), (3103), (3140), (3142), 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | | | | | (3144) are inconsistent by sub-proof #23. 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | | | | | 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | | | | End of split 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | | | | 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | | | | 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | | | | (3145) ~ (all_192_4 = 0) & permut_sub2(int, all_103_4, 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, all_86_11, $sum(all_86_10, 1)) = 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | | | | all_192_4 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | | | | 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (43), (3096), (3145) are inconsistent by sub-proof 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | | | | #69. 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | | | | 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | | | End of split 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | | | 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | | Case 2: 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | | | 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | | | (3146) ~ (all_169_1 = 0) & array_eq_sub1(int, all_105_4, 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | | | all_105_2, 0, all_86_7) = all_169_1 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | | | 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (3112), (3146) are inconsistent by sub-proof 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | | | #75. 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | | | 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | | End of split 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | | 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | Case 2: 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | | 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | | (3147) length1(int, all_105_4) = all_219_1 & ( ~ 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | | ($lesseq(all_86_7, all_219_1)) | ~ ($lesseq(0, 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | | all_219_1)) | ( ~ (all_219_0 = all_219_1) & 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | | length1(int, all_105_2) = all_219_0)) 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | | 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3147) implies: 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | | (3148) length1(int, all_105_4) = all_219_1 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | | 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (48), (50), (52), (53), (180), (184), 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | | (2632), (2633), (3103), (3104), (3108), (3110), 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | | (3148) are inconsistent by sub-proof #3. 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | | 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | End of split 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | Case 2: 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | (3149) ~ (all_190_4 = 0) & permut_sub2(int, all_105_4, 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | all_105_2, all_86_7, $sum(all_86_10, 1)) = 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | all_190_4 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (43), (3092), (3149) are inconsistent by sub-proof 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | #68. 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | | 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | End of split 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | 205.82/127.55 | | | | | | | | | | | | | | | | | | | | Case 2: 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | (3150) ~ (all_177_4 = 0) & permut_sub2(int, all_103_2, 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | all_105_4, all_86_11, $sum(all_86_8, 1)) = 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | all_177_4 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (43), (3106), (3150) are inconsistent by sub-proof 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | #47. 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | 205.82/127.55 | | | | | | | | | | | | | | | | | | | | End of split 205.82/127.55 | | | | | | | | | | | | | | | | | | | | 205.82/127.55 | | | | | | | | | | | | | | | | | | | Case 2: 205.82/127.55 | | | | | | | | | | | | | | | | | | | | 205.82/127.55 | | | | | | | | | | | | | | | | | | | | (3151) elts(int, all_105_4) = all_181_2 & elts(int, 205.82/127.55 | | | | | | | | | | | | | | | | | | | | all_103_2) = all_181_3 & in_uni(all_181_2) & 205.82/127.55 | | | | | | | | | | | | | | | | | | | | in_uni(all_181_3) & (( ~ (all_181_0 = 0) & 205.82/127.55 | | | | | | | | | | | | | | | | | | | | map_eq_sub1(int, all_181_3, all_181_2, 205.82/127.55 | | | | | | | | | | | | | | | | | | | | $sum(all_86_8, 1), all_181_1) = all_181_0 & 205.82/127.55 | | | | | | | | | | | | | | | | | | | | length1(int, all_103_2) = all_181_1) | ( ~ 205.82/127.55 | | | | | | | | | | | | | | | | | | | | (all_181_1 = 0) & map_eq_sub1(int, all_181_3, 205.82/127.55 | | | | | | | | | | | | | | | | | | | | all_181_2, 0, all_86_11) = all_181_1)) 205.82/127.55 | | | | | | | | | | | | | | | | | | | | 205.82/127.55 | | | | | | | | | | | | | | | | | | | | ALPHA: (3151) implies: 205.82/127.55 | | | | | | | | | | | | | | | | | | | | (3152) elts(int, all_103_2) = all_181_3 205.82/127.55 | | | | | | | | | | | | | | | | | | | | (3153) elts(int, all_105_4) = all_181_2 205.82/127.55 | | | | | | | | | | | | | | | | | | | | (3154) ( ~ (all_181_0 = 0) & map_eq_sub1(int, all_181_3, 205.82/127.55 | | | | | | | | | | | | | | | | | | | | all_181_2, $sum(all_86_8, 1), all_181_1) = 205.82/127.55 | | | | | | | | | | | | | | | | | | | | all_181_0 & length1(int, all_103_2) = all_181_1) 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | ( ~ (all_181_1 = 0) & map_eq_sub1(int, 205.82/127.55 | | | | | | | | | | | | | | | | | | | | all_181_3, all_181_2, 0, all_86_11) = 205.82/127.55 | | | | | | | | | | | | | | | | | | | | all_181_1) 205.82/127.55 | | | | | | | | | | | | | | | | | | | | 205.82/127.55 | | | | | | | | | | | | | | | | | | | | BETA: splitting (295) gives: 205.82/127.55 | | | | | | | | | | | | | | | | | | | | 205.82/127.55 | | | | | | | | | | | | | | | | | | | | Case 1: 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | (3155) all_190_0 = 0 & all_190_1 = 0 & map_eq_sub1(int, 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | all_190_4, all_190_3, $sum(all_86_10, 1), 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | all_190_2) = 0 & map_eq_sub1(int, all_190_4, 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | all_190_3, 0, all_86_7) = 0 & length1(int, 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | all_105_4) = all_190_2 & elts(int, all_105_2) = 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | all_190_3 & elts(int, all_105_4) = all_190_4 & 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | in_uni(all_190_3) & in_uni(all_190_4) 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | ALPHA: (3155) implies: 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | (3156) elts(int, all_105_4) = all_190_4 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (39), (43), (44), (91), (99), (184), (203), 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | (263), (297), (394), (395), (396), (3096), (3152), 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | (3153), (3154), (3156) are inconsistent by 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | sub-proof #17. 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | 205.82/127.55 | | | | | | | | | | | | | | | | | | | | Case 2: 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | (3157) ~ (all_190_4 = 0) & permut_sub2(int, all_105_4, 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | all_105_2, all_86_7, $sum(all_86_10, 1)) = 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | all_190_4 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (43), (3092), (3157) are inconsistent by sub-proof 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | #68. 205.82/127.55 | | | | | | | | | | | | | | | | | | | | | 205.82/127.55 | | | | | | | | | | | | | | | | | | | | End of split 205.82/127.55 | | | | | | | | | | | | | | | | | | | | 205.82/127.55 | | | | | | | | | | | | | | | | | | | End of split 205.82/127.55 | | | | | | | | | | | | | | | | | | | 205.82/127.55 | | | | | | | | | | | | | | | | | | Case 2: 205.82/127.55 | | | | | | | | | | | | | | | | | | | 205.82/127.55 | | | | | | | | | | | | | | | | | | | (3158) ~ (all_153_1 = 0) & array_eq_sub1(int, all_105_4, 205.82/127.55 | | | | | | | | | | | | | | | | | | | all_105_2, $sum(all_86_10, 1), all_86_13) = 205.82/127.55 | | | | | | | | | | | | | | | | | | | all_153_1 205.82/127.55 | | | | | | | | | | | | | | | | | | | 205.82/127.55 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (3094), (3158) are inconsistent by sub-proof 205.82/127.55 | | | | | | | | | | | | | | | | | | | #54. 205.82/127.55 | | | | | | | | | | | | | | | | | | | 205.82/127.55 | | | | | | | | | | | | | | | | | | End of split 205.82/127.55 | | | | | | | | | | | | | | | | | | 205.82/127.55 | | | | | | | | | | | | | | | | | Case 2: 205.82/127.55 | | | | | | | | | | | | | | | | | | 205.82/127.55 | | | | | | | | | | | | | | | | | | (3159) ~ (all_171_1 = 0) & array_eq_sub1(int, all_103_4, 205.82/127.55 | | | | | | | | | | | | | | | | | | all_103_2, 0, all_86_11) = all_171_1 205.82/127.55 | | | | | | | | | | | | | | | | | | 205.82/127.55 | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (3098), (3159) are inconsistent by sub-proof 205.82/127.55 | | | | | | | | | | | | | | | | | | #81. 205.82/127.55 | | | | | | | | | | | | | | | | | | 205.82/127.55 | | | | | | | | | | | | | | | | | End of split 205.82/127.55 | | | | | | | | | | | | | | | | | 205.82/127.55 | | | | | | | | | | | | | | | | Case 2: 205.82/127.55 | | | | | | | | | | | | | | | | | 205.82/127.55 | | | | | | | | | | | | | | | | | (3160) length1(int, all_103_4) = all_215_1 & ( ~ 205.82/127.55 | | | | | | | | | | | | | | | | | ($lesseq(all_86_11, all_215_1)) | ~ ($lesseq(0, 205.82/127.55 | | | | | | | | | | | | | | | | | all_215_1)) | ( ~ (all_215_0 = all_215_1) & 205.82/127.55 | | | | | | | | | | | | | | | | | length1(int, all_103_2) = all_215_0)) 205.82/127.55 | | | | | | | | | | | | | | | | | 205.82/127.55 | | | | | | | | | | | | | | | | | ALPHA: (3160) implies: 205.82/127.55 | | | | | | | | | | | | | | | | | (3161) length1(int, all_103_4) = all_215_1 205.82/127.55 | | | | | | | | | | | | | | | | | 205.82/127.55 | | | | | | | | | | | | | | | | | BETA: splitting (255) gives: 205.82/127.55 | | | | | | | | | | | | | | | | | 205.82/127.55 | | | | | | | | | | | | | | | | | Case 1: 205.82/127.55 | | | | | | | | | | | | | | | | | | 205.82/127.55 | | | | | | | | | | | | | | | | | | (3162) all_153_0 = all_153_1 & $lesseq(1, 205.82/127.55 | | | | | | | | | | | | | | | | | | $difference(all_153_1, all_86_10)) & 205.82/127.55 | | | | | | | | | | | | | | | | | | $lesseq(all_86_13, all_153_1) & $lesseq(-1, 205.82/127.55 | | | | | | | | | | | | | | | | | | all_86_10) & $lesseq(0, all_86_13) & 205.82/127.55 | | | | | | | | | | | | | | | | | | length1(int, all_105_2) = all_153_1 & length1(int, 205.82/127.55 | | | | | | | | | | | | | | | | | | all_105_4) = all_153_1 205.82/127.55 | | | | | | | | | | | | | | | | | | 205.82/127.55 | | | | | | | | | | | | | | | | | | ALPHA: (3162) implies: 205.82/127.55 | | | | | | | | | | | | | | | | | | (3163) $lesseq(1, $difference(all_153_1, all_86_10)) 205.82/127.55 | | | | | | | | | | | | | | | | | | (3164) length1(int, all_105_4) = all_153_1 205.82/127.55 | | | | | | | | | | | | | | | | | | 205.82/127.55 | | | | | | | | | | | | | | | | | | BETA: splitting (295) gives: 205.82/127.55 | | | | | | | | | | | | | | | | | | 205.82/127.55 | | | | | | | | | | | | | | | | | | Case 1: 205.82/127.55 | | | | | | | | | | | | | | | | | | | 205.89/127.55 | | | | | | | | | | | | | | | | | | | (3165) all_190_0 = 0 & all_190_1 = 0 & map_eq_sub1(int, 205.89/127.55 | | | | | | | | | | | | | | | | | | | all_190_4, all_190_3, $sum(all_86_10, 1), 205.89/127.55 | | | | | | | | | | | | | | | | | | | all_190_2) = 0 & map_eq_sub1(int, all_190_4, 205.89/127.55 | | | | | | | | | | | | | | | | | | | all_190_3, 0, all_86_7) = 0 & length1(int, 205.89/127.55 | | | | | | | | | | | | | | | | | | | all_105_4) = all_190_2 & elts(int, all_105_2) = 205.89/127.55 | | | | | | | | | | | | | | | | | | | all_190_3 & elts(int, all_105_4) = all_190_4 & 205.89/127.55 | | | | | | | | | | | | | | | | | | | in_uni(all_190_3) & in_uni(all_190_4) 205.89/127.55 | | | | | | | | | | | | | | | | | | | 205.89/127.55 | | | | | | | | | | | | | | | | | | | ALPHA: (3165) implies: 205.89/127.55 | | | | | | | | | | | | | | | | | | | (3166) length1(int, all_105_4) = all_190_2 205.89/127.55 | | | | | | | | | | | | | | | | | | | 205.89/127.55 | | | | | | | | | | | | | | | | | | | BETA: splitting (287) gives: 205.89/127.55 | | | | | | | | | | | | | | | | | | | 205.89/127.55 | | | | | | | | | | | | | | | | | | | Case 1: 205.89/127.55 | | | | | | | | | | | | | | | | | | | | 205.89/127.55 | | | | | | | | | | | | | | | | | | | | (3167) all_181_3 = 0 & permut_sub2(int, all_103_2, 205.89/127.55 | | | | | | | | | | | | | | | | | | | | all_105_4, all_86_11, $sum(all_86_8, 1)) = 0 205.89/127.55 | | | | | | | | | | | | | | | | | | | | 205.89/127.55 | | | | | | | | | | | | | | | | | | | | ALPHA: (3167) implies: 205.89/127.55 | | | | | | | | | | | | | | | | | | | | (3168) permut_sub2(int, all_103_2, all_105_4, all_86_11, 205.89/127.55 | | | | | | | | | | | | | | | | | | | | $sum(all_86_8, 1)) = 0 205.89/127.55 | | | | | | | | | | | | | | | | | | | | 205.89/127.55 | | | | | | | | | | | | | | | | | | | | BETA: splitting (324) gives: 205.89/127.55 | | | | | | | | | | | | | | | | | | | | 205.89/127.55 | | | | | | | | | | | | | | | | | | | | Case 1: 205.89/127.55 | | | | | | | | | | | | | | | | | | | | | 205.89/127.55 | | | | | | | | | | | | | | | | | | | | | (3169) all_219_1 = 0 & array_eq_sub1(int, all_105_4, 205.89/127.55 | | | | | | | | | | | | | | | | | | | | | all_105_2, 0, all_86_7) = 0 205.89/127.55 | | | | | | | | | | | | | | | | | | | | | 205.89/127.55 | | | | | | | | | | | | | | | | | | | | | ALPHA: (3169) implies: 205.89/127.55 | | | | | | | | | | | | | | | | | | | | | (3170) array_eq_sub1(int, all_105_4, all_105_2, 0, 205.89/127.55 | | | | | | | | | | | | | | | | | | | | | all_86_7) = 0 205.89/127.55 | | | | | | | | | | | | | | | | | | | | | 205.89/127.55 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (280) gives: 205.89/127.55 | | | | | | | | | | | | | | | | | | | | | 205.89/127.55 | | | | | | | | | | | | | | | | | | | | | Case 1: 205.89/127.55 | | | | | | | | | | | | | | | | | | | | | | 205.89/127.55 | | | | | | | | | | | | | | | | | | | | | | (3171) all_177_0 = 0 & all_177_1 = 0 & map_eq_sub1(int, 205.89/127.55 | | | | | | | | | | | | | | | | | | | | | | all_177_4, all_177_3, $sum(all_86_8, 1), 205.89/127.55 | | | | | | | | | | | | | | | | | | | | | | all_177_2) = 0 & map_eq_sub1(int, all_177_4, 205.89/127.55 | | | | | | | | | | | | | | | | | | | | | | all_177_3, 0, all_86_11) = 0 & length1(int, 205.89/127.55 | | | | | | | | | | | | | | | | | | | | | | all_103_2) = all_177_2 & elts(int, all_105_4) = 205.89/127.55 | | | | | | | | | | | | | | | | | | | | | | all_177_3 & elts(int, all_103_2) = all_177_4 & 205.89/127.55 | | | | | | | | | | | | | | | | | | | | | | in_uni(all_177_3) & in_uni(all_177_4) 205.89/127.55 | | | | | | | | | | | | | | | | | | | | | | 205.89/127.55 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3171) implies: 205.89/127.55 | | | | | | | | | | | | | | | | | | | | | | (3172) length1(int, all_103_2) = all_177_2 205.89/127.55 | | | | | | | | | | | | | | | | | | | | | | 205.89/127.55 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (270) gives: 205.89/127.55 | | | | | | | | | | | | | | | | | | | | | | 205.89/127.55 | | | | | | | | | | | | | | | | | | | | | | Case 1: 205.89/127.55 | | | | | | | | | | | | | | | | | | | | | | | 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | (3173) all_169_0 = all_169_1 & $lesseq(all_86_7, 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | all_169_1) & $lesseq(0, all_169_1) & $lesseq(0, 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | all_86_7) & length1(int, all_105_2) = all_169_1 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | & length1(int, all_105_4) = all_169_1 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3173) implies: 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | (3174) length1(int, all_105_4) = all_169_1 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (345) gives: 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | Case 1: 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | | 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | | (3175) all_242_1 = 0 & array_eq_sub1(int, all_103_2, 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, $sum(all_86_8, 1), all_86_13) = 0 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | | 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3175) implies: 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | | (3176) array_eq_sub1(int, all_103_2, all_105_4, 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | | $sum(all_86_8, 1), all_86_13) = 0 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | | 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (45), (48), (50), (52), (53), (180), (184), 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | | (269), (2632), (2633), (3163), (3164), (3166), 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | | (3172), (3174), (3176) are inconsistent by 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #8. 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | | 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | Case 2: 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | | 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | | (3177) length1(int, all_103_2) = all_242_1 & ( ~ 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | | ($lesseq(1, $difference(all_242_1, all_86_8))) | 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | | ~ ($lesseq(all_86_13, all_242_1)) | ( ~ 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | | (all_242_0 = all_242_1) & length1(int, 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | | all_105_4) = all_242_0)) 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | | 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3177) implies: 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | | (3178) length1(int, all_103_2) = all_242_1 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | | 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_86_13, all_169_1, 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (180), (3174) 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | | (3179) all_169_1 = all_86_13 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | | 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_190_2, all_169_1, 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (3166), (3174) 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | | (3180) all_190_2 = all_169_1 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | | 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_190_2, all_153_1, 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (3164), (3166) 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | | (3181) all_190_2 = all_153_1 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | | 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_86_13, all_211_1, 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (184), (2632) 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | | (3182) all_211_1 = all_86_13 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | | 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_242_1, all_177_2, 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (3172), (3178) 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | | (3183) all_242_1 = all_177_2 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | | 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_211_1, all_177_2, 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (2632), (3172) 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | | (3184) all_211_1 = all_177_2 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | | 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_242_1, all_156_0, 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (394), (3178) 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | | (3185) all_242_1 = all_156_0 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | | 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_86_13, all_238_1, 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (183), (3089) 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | | (3186) all_238_1 = all_86_13 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | | 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3183), (3185) imply: 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | | (3187) all_177_2 = all_156_0 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | | 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3187) implies: 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | | (3188) all_177_2 = all_156_0 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | | 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3182), (3184) imply: 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | | (3189) all_177_2 = all_86_13 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | | 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3189) implies: 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | | (3190) all_177_2 = all_86_13 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | | 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3180), (3181) imply: 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | | (3191) all_169_1 = all_153_1 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | | 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3191) implies: 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | | (3192) all_169_1 = all_153_1 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | | 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3188), (3190) imply: 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | | (3193) all_156_0 = all_86_13 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | | 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3179), (3192) imply: 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | | (3194) all_153_1 = all_86_13 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | | 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3194) implies: 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | | (3195) all_153_1 = all_86_13 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | | 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (394), (3090), (3163), (3186), (3193), 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | | (3195) are inconsistent by sub-proof #23. 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | | 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | End of split 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | Case 2: 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | (3196) ~ (all_169_1 = 0) & array_eq_sub1(int, all_105_4, 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | all_105_2, 0, all_86_7) = all_169_1 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (3170), (3196) are inconsistent by sub-proof 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | #75. 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | | 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | End of split 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | Case 2: 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | (3197) ~ (all_177_4 = 0) & permut_sub2(int, all_103_2, 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | all_105_4, all_86_11, $sum(all_86_8, 1)) = 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | all_177_4 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (43), (3168), (3197) are inconsistent by sub-proof 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | #47. 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | End of split 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | 205.89/127.56 | | | | | | | | | | | | | | | | | | | | Case 2: 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | (3198) length1(int, all_105_4) = all_219_1 & ( ~ 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | ($lesseq(all_86_7, all_219_1)) | ~ ($lesseq(0, 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | all_219_1)) | ( ~ (all_219_0 = all_219_1) & 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | length1(int, all_105_2) = all_219_0)) 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | ALPHA: (3198) implies: 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | (3199) length1(int, all_105_4) = all_219_1 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (280) gives: 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | Case 1: 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | (3200) all_177_0 = 0 & all_177_1 = 0 & map_eq_sub1(int, 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | all_177_4, all_177_3, $sum(all_86_8, 1), 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | all_177_2) = 0 & map_eq_sub1(int, all_177_4, 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | all_177_3, 0, all_86_11) = 0 & length1(int, 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | all_103_2) = all_177_2 & elts(int, all_105_4) = 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | all_177_3 & elts(int, all_103_2) = all_177_4 & 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | in_uni(all_177_3) & in_uni(all_177_4) 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3200) implies: 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | (3201) length1(int, all_103_2) = all_177_2 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (48), (50), (52), (53), (180), (184), 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | (2632), (2633), (3163), (3164), (3166), (3199), 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | (3201) are inconsistent by sub-proof #3. 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | Case 2: 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | (3202) ~ (all_177_4 = 0) & permut_sub2(int, all_103_2, 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | all_105_4, all_86_11, $sum(all_86_8, 1)) = 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | all_177_4 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (43), (3168), (3202) are inconsistent by sub-proof 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | #47. 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | | 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | End of split 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | 205.89/127.56 | | | | | | | | | | | | | | | | | | | | End of split 205.89/127.56 | | | | | | | | | | | | | | | | | | | | 205.89/127.56 | | | | | | | | | | | | | | | | | | | Case 2: 205.89/127.56 | | | | | | | | | | | | | | | | | | | | 205.89/127.56 | | | | | | | | | | | | | | | | | | | | (3203) elts(int, all_105_4) = all_181_2 & elts(int, 205.89/127.56 | | | | | | | | | | | | | | | | | | | | all_103_2) = all_181_3 & in_uni(all_181_2) & 205.89/127.56 | | | | | | | | | | | | | | | | | | | | in_uni(all_181_3) & (( ~ (all_181_0 = 0) & 205.89/127.56 | | | | | | | | | | | | | | | | | | | | map_eq_sub1(int, all_181_3, all_181_2, 205.89/127.56 | | | | | | | | | | | | | | | | | | | | $sum(all_86_8, 1), all_181_1) = all_181_0 & 205.89/127.56 | | | | | | | | | | | | | | | | | | | | length1(int, all_103_2) = all_181_1) | ( ~ 205.89/127.56 | | | | | | | | | | | | | | | | | | | | (all_181_1 = 0) & map_eq_sub1(int, all_181_3, 205.89/127.56 | | | | | | | | | | | | | | | | | | | | all_181_2, 0, all_86_11) = all_181_1)) 205.89/127.56 | | | | | | | | | | | | | | | | | | | | 205.89/127.56 | | | | | | | | | | | | | | | | | | | | ALPHA: (3203) implies: 205.89/127.56 | | | | | | | | | | | | | | | | | | | | (3204) elts(int, all_103_2) = all_181_3 205.89/127.56 | | | | | | | | | | | | | | | | | | | | (3205) elts(int, all_105_4) = all_181_2 205.89/127.56 | | | | | | | | | | | | | | | | | | | | (3206) ( ~ (all_181_0 = 0) & map_eq_sub1(int, all_181_3, 205.89/127.56 | | | | | | | | | | | | | | | | | | | | all_181_2, $sum(all_86_8, 1), all_181_1) = 205.89/127.56 | | | | | | | | | | | | | | | | | | | | all_181_0 & length1(int, all_103_2) = all_181_1) 205.89/127.56 | | | | | | | | | | | | | | | | | | | | | ( ~ (all_181_1 = 0) & map_eq_sub1(int, 205.89/127.56 | | | | | | | | | | | | | | | | | | | | all_181_3, all_181_2, 0, all_86_11) = 205.89/127.56 | | | | | | | | | | | | | | | | | | | | all_181_1) 205.89/127.56 | | | | | | | | | | | | | | | | | | | | 205.89/127.56 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (39), (43), (44), (90), (91), (96), (99), 205.89/127.56 | | | | | | | | | | | | | | | | | | | | (183), (184), (203), (206), (263), (295), (296), 205.89/127.56 | | | | | | | | | | | | | | | | | | | | (297), (394), (395), (396), (3089), (3092), 205.89/127.56 | | | | | | | | | | | | | | | | | | | | (3161), (3204), (3205), (3206) are inconsistent by 205.89/127.56 | | | | | | | | | | | | | | | | | | | | sub-proof #15. 205.89/127.56 | | | | | | | | | | | | | | | | | | | | 205.89/127.56 | | | | | | | | | | | | | | | | | | | End of split 205.89/127.56 | | | | | | | | | | | | | | | | | | | 205.89/127.56 | | | | | | | | | | | | | | | | | | Case 2: 205.89/127.56 | | | | | | | | | | | | | | | | | | | 205.89/127.56 | | | | | | | | | | | | | | | | | | | (3207) ~ (all_190_4 = 0) & permut_sub2(int, all_105_4, 205.89/127.56 | | | | | | | | | | | | | | | | | | | all_105_2, all_86_7, $sum(all_86_10, 1)) = 205.89/127.56 | | | | | | | | | | | | | | | | | | | all_190_4 205.89/127.56 | | | | | | | | | | | | | | | | | | | 205.89/127.56 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (43), (3092), (3207) are inconsistent by sub-proof 205.89/127.56 | | | | | | | | | | | | | | | | | | | #68. 205.89/127.56 | | | | | | | | | | | | | | | | | | | 205.89/127.56 | | | | | | | | | | | | | | | | | | End of split 205.89/127.56 | | | | | | | | | | | | | | | | | | 205.89/127.56 | | | | | | | | | | | | | | | | | Case 2: 205.89/127.56 | | | | | | | | | | | | | | | | | | 205.89/127.56 | | | | | | | | | | | | | | | | | | (3208) ~ (all_153_1 = 0) & array_eq_sub1(int, all_105_4, 205.89/127.56 | | | | | | | | | | | | | | | | | | all_105_2, $sum(all_86_10, 1), all_86_13) = 205.89/127.56 | | | | | | | | | | | | | | | | | | all_153_1 205.89/127.56 | | | | | | | | | | | | | | | | | | 205.89/127.56 | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (3094), (3208) are inconsistent by sub-proof 205.89/127.56 | | | | | | | | | | | | | | | | | | #54. 205.89/127.56 | | | | | | | | | | | | | | | | | | 205.89/127.56 | | | | | | | | | | | | | | | | | End of split 205.89/127.56 | | | | | | | | | | | | | | | | | 205.89/127.56 | | | | | | | | | | | | | | | | End of split 205.89/127.56 | | | | | | | | | | | | | | | | 205.89/127.56 | | | | | | | | | | | | | | | Case 2: 205.89/127.56 | | | | | | | | | | | | | | | | 205.89/127.56 | | | | | | | | | | | | | | | | (3209) elts(int, all_103_2) = all_191_2 & elts(int, 205.89/127.56 | | | | | | | | | | | | | | | | all_103_4) = all_191_3 & in_uni(all_191_2) & 205.89/127.56 | | | | | | | | | | | | | | | | in_uni(all_191_3) & (( ~ (all_191_0 = 0) & 205.89/127.56 | | | | | | | | | | | | | | | | map_eq_sub1(int, all_191_3, all_191_2, 205.89/127.56 | | | | | | | | | | | | | | | | $sum(all_86_10, 1), all_191_1) = all_191_0 & 205.89/127.56 | | | | | | | | | | | | | | | | length1(int, all_103_4) = all_191_1) | ( ~ 205.89/127.56 | | | | | | | | | | | | | | | | (all_191_1 = 0) & map_eq_sub1(int, all_191_3, 205.89/127.56 | | | | | | | | | | | | | | | | all_191_2, 0, all_86_11) = all_191_1)) 205.89/127.56 | | | | | | | | | | | | | | | | 205.89/127.56 | | | | | | | | | | | | | | | | ALPHA: (3209) implies: 205.89/127.56 | | | | | | | | | | | | | | | | (3210) elts(int, all_103_4) = all_191_3 205.89/127.56 | | | | | | | | | | | | | | | | (3211) elts(int, all_103_2) = all_191_2 205.89/127.56 | | | | | | | | | | | | | | | | (3212) ( ~ (all_191_0 = 0) & map_eq_sub1(int, all_191_3, 205.89/127.56 | | | | | | | | | | | | | | | | all_191_2, $sum(all_86_10, 1), all_191_1) = 205.89/127.56 | | | | | | | | | | | | | | | | all_191_0 & length1(int, all_103_4) = all_191_1) 205.89/127.56 | | | | | | | | | | | | | | | | | ( ~ (all_191_1 = 0) & map_eq_sub1(int, 205.89/127.56 | | | | | | | | | | | | | | | | all_191_3, all_191_2, 0, all_86_11) = 205.89/127.56 | | | | | | | | | | | | | | | | all_191_1) 205.89/127.56 | | | | | | | | | | | | | | | | 205.89/127.57 | | | | | | | | | | | | | | | | REF_CLOSE: (38), (39), (44), (45), (90), (91), (96), (183), 205.89/127.57 | | | | | | | | | | | | | | | | (206), (272), (319), (3089), (3210), (3211), 205.89/127.57 | | | | | | | | | | | | | | | | (3212) are inconsistent by sub-proof #2. 205.89/127.57 | | | | | | | | | | | | | | | | 205.89/127.57 | | | | | | | | | | | | | | | End of split 205.89/127.57 | | | | | | | | | | | | | | | 205.89/127.57 | | | | | | | | | | | | | | Case 2: 205.89/127.57 | | | | | | | | | | | | | | | 205.89/127.57 | | | | | | | | | | | | | | | (3213) length1(int, all_105_4) = all_234_1 & ( ~ 205.89/127.57 | | | | | | | | | | | | | | | ($lesseq(1, $difference(all_234_1, all_86_10))) 205.89/127.57 | | | | | | | | | | | | | | | | ~ ($lesseq(all_86_13, all_234_1)) | ( ~ 205.89/127.57 | | | | | | | | | | | | | | | (all_234_0 = all_234_1) & length1(int, 205.89/127.57 | | | | | | | | | | | | | | | all_105_2) = all_234_0)) 205.89/127.57 | | | | | | | | | | | | | | | 205.89/127.57 | | | | | | | | | | | | | | | REF_CLOSE: (39), (49), (180), (181), (3213) are inconsistent 205.89/127.57 | | | | | | | | | | | | | | | by sub-proof #12. 205.89/127.57 | | | | | | | | | | | | | | | 205.89/127.57 | | | | | | | | | | | | | | End of split 205.89/127.57 | | | | | | | | | | | | | | 205.89/127.57 | | | | | | | | | | | | | Case 2: 205.89/127.57 | | | | | | | | | | | | | | 205.89/127.57 | | | | | | | | | | | | | | (3214) elts(int, all_105_2) = all_187_2 & elts(int, 205.89/127.57 | | | | | | | | | | | | | | all_105_4) = all_187_3 & in_uni(all_187_2) & 205.89/127.57 | | | | | | | | | | | | | | in_uni(all_187_3) & (( ~ (all_187_0 = 0) & 205.89/127.57 | | | | | | | | | | | | | | map_eq_sub1(int, all_187_3, all_187_2, 205.89/127.57 | | | | | | | | | | | | | | $sum(all_86_10, 1), all_187_1) = all_187_0 & 205.89/127.57 | | | | | | | | | | | | | | length1(int, all_105_4) = all_187_1) | ( ~ 205.89/127.57 | | | | | | | | | | | | | | (all_187_1 = 0) & map_eq_sub1(int, all_187_3, 205.89/127.57 | | | | | | | | | | | | | | all_187_2, 0, all_86_7) = all_187_1)) 205.89/127.57 | | | | | | | | | | | | | | 205.89/127.57 | | | | | | | | | | | | | | ALPHA: (3214) implies: 205.89/127.57 | | | | | | | | | | | | | | (3215) elts(int, all_105_4) = all_187_3 205.89/127.57 | | | | | | | | | | | | | | (3216) elts(int, all_105_2) = all_187_2 205.89/127.57 | | | | | | | | | | | | | | (3217) ( ~ (all_187_0 = 0) & map_eq_sub1(int, all_187_3, 205.89/127.57 | | | | | | | | | | | | | | all_187_2, $sum(all_86_10, 1), all_187_1) = 205.89/127.57 | | | | | | | | | | | | | | all_187_0 & length1(int, all_105_4) = all_187_1) 205.89/127.57 | | | | | | | | | | | | | | | ( ~ (all_187_1 = 0) & map_eq_sub1(int, 205.89/127.57 | | | | | | | | | | | | | | all_187_3, all_187_2, 0, all_86_7) = 205.89/127.57 | | | | | | | | | | | | | | all_187_1) 205.89/127.57 | | | | | | | | | | | | | | 205.89/127.57 | | | | | | | | | | | | | | BETA: splitting (337) gives: 205.89/127.57 | | | | | | | | | | | | | | 205.89/127.57 | | | | | | | | | | | | | | Case 1: 205.89/127.57 | | | | | | | | | | | | | | | 205.89/127.57 | | | | | | | | | | | | | | | (3218) all_234_1 = 0 & array_eq_sub1(int, all_105_4, 205.89/127.57 | | | | | | | | | | | | | | | all_105_2, $sum(all_86_10, 1), all_86_13) = 0 205.89/127.57 | | | | | | | | | | | | | | | 205.89/127.57 | | | | | | | | | | | | | | | ALPHA: (3218) implies: 205.89/127.57 | | | | | | | | | | | | | | | (3219) array_eq_sub1(int, all_105_4, all_105_2, 205.89/127.57 | | | | | | | | | | | | | | | $sum(all_86_10, 1), all_86_13) = 0 205.89/127.57 | | | | | | | | | | | | | | | 205.89/127.57 | | | | | | | | | | | | | | | BETA: splitting (296) gives: 205.89/127.57 | | | | | | | | | | | | | | | 205.89/127.57 | | | | | | | | | | | | | | | Case 1: 205.89/127.57 | | | | | | | | | | | | | | | | 205.89/127.57 | | | | | | | | | | | | | | | | (3220) all_191_3 = 0 & permut_sub2(int, all_103_4, 205.89/127.57 | | | | | | | | | | | | | | | | all_103_2, all_86_11, $sum(all_86_10, 1)) = 0 205.89/127.57 | | | | | | | | | | | | | | | | 205.89/127.57 | | | | | | | | | | | | | | | | ALPHA: (3220) implies: 205.89/127.57 | | | | | | | | | | | | | | | | (3221) permut_sub2(int, all_103_4, all_103_2, all_86_11, 205.89/127.57 | | | | | | | | | | | | | | | | $sum(all_86_10, 1)) = 0 205.89/127.57 | | | | | | | | | | | | | | | | 205.89/127.57 | | | | | | | | | | | | | | | | BETA: splitting (319) gives: 205.89/127.57 | | | | | | | | | | | | | | | | 205.89/127.57 | | | | | | | | | | | | | | | | Case 1: 205.89/127.57 | | | | | | | | | | | | | | | | | 205.89/127.57 | | | | | | | | | | | | | | | | | (3222) all_215_1 = 0 & array_eq_sub1(int, all_103_4, 205.89/127.57 | | | | | | | | | | | | | | | | | all_103_2, 0, all_86_11) = 0 205.89/127.57 | | | | | | | | | | | | | | | | | 205.89/127.57 | | | | | | | | | | | | | | | | | ALPHA: (3222) implies: 205.89/127.57 | | | | | | | | | | | | | | | | | (3223) array_eq_sub1(int, all_103_4, all_103_2, 0, 205.89/127.57 | | | | | | | | | | | | | | | | | all_86_11) = 0 205.89/127.57 | | | | | | | | | | | | | | | | | 205.89/127.57 | | | | | | | | | | | | | | | | | BETA: splitting (255) gives: 205.89/127.57 | | | | | | | | | | | | | | | | | 205.89/127.57 | | | | | | | | | | | | | | | | | Case 1: 205.89/127.57 | | | | | | | | | | | | | | | | | | 205.89/127.57 | | | | | | | | | | | | | | | | | | (3224) all_153_0 = all_153_1 & $lesseq(1, 205.89/127.57 | | | | | | | | | | | | | | | | | | $difference(all_153_1, all_86_10)) & 205.89/127.57 | | | | | | | | | | | | | | | | | | $lesseq(all_86_13, all_153_1) & $lesseq(-1, 205.89/127.57 | | | | | | | | | | | | | | | | | | all_86_10) & $lesseq(0, all_86_13) & 205.89/127.57 | | | | | | | | | | | | | | | | | | length1(int, all_105_2) = all_153_1 & length1(int, 205.89/127.57 | | | | | | | | | | | | | | | | | | all_105_4) = all_153_1 205.89/127.57 | | | | | | | | | | | | | | | | | | 205.89/127.57 | | | | | | | | | | | | | | | | | | ALPHA: (3224) implies: 205.89/127.57 | | | | | | | | | | | | | | | | | | (3225) $lesseq(1, $difference(all_153_1, all_86_10)) 205.89/127.57 | | | | | | | | | | | | | | | | | | (3226) length1(int, all_105_4) = all_153_1 205.89/127.57 | | | | | | | | | | | | | | | | | | 205.89/127.57 | | | | | | | | | | | | | | | | | | BETA: splitting (272) gives: 205.89/127.57 | | | | | | | | | | | | | | | | | | 205.89/127.57 | | | | | | | | | | | | | | | | | | Case 1: 205.89/127.57 | | | | | | | | | | | | | | | | | | | 205.89/127.57 | | | | | | | | | | | | | | | | | | | (3227) all_171_0 = all_171_1 & $lesseq(all_86_11, 205.89/127.57 | | | | | | | | | | | | | | | | | | | all_171_1) & $lesseq(0, all_171_1) & $lesseq(0, 205.89/127.57 | | | | | | | | | | | | | | | | | | | all_86_11) & length1(int, all_103_2) = all_171_1 205.89/127.57 | | | | | | | | | | | | | | | | | | | & length1(int, all_103_4) = all_171_1 205.89/127.57 | | | | | | | | | | | | | | | | | | | 205.89/127.57 | | | | | | | | | | | | | | | | | | | ALPHA: (3227) implies: 205.89/127.57 | | | | | | | | | | | | | | | | | | | (3228) length1(int, all_103_2) = all_171_1 205.89/127.57 | | | | | | | | | | | | | | | | | | | 205.89/127.57 | | | | | | | | | | | | | | | | | | | BETA: splitting (287) gives: 205.89/127.57 | | | | | | | | | | | | | | | | | | | 205.89/127.57 | | | | | | | | | | | | | | | | | | | Case 1: 205.89/127.57 | | | | | | | | | | | | | | | | | | | | 205.89/127.57 | | | | | | | | | | | | | | | | | | | | (3229) all_181_3 = 0 & permut_sub2(int, all_103_2, 205.89/127.57 | | | | | | | | | | | | | | | | | | | | all_105_4, all_86_11, $sum(all_86_8, 1)) = 0 205.89/127.57 | | | | | | | | | | | | | | | | | | | | 205.89/127.57 | | | | | | | | | | | | | | | | | | | | ALPHA: (3229) implies: 205.89/127.57 | | | | | | | | | | | | | | | | | | | | (3230) permut_sub2(int, all_103_2, all_105_4, all_86_11, 205.89/127.57 | | | | | | | | | | | | | | | | | | | | $sum(all_86_8, 1)) = 0 205.89/127.57 | | | | | | | | | | | | | | | | | | | | 205.89/127.57 | | | | | | | | | | | | | | | | | | | | BETA: splitting (280) gives: 205.89/127.57 | | | | | | | | | | | | | | | | | | | | 205.89/127.57 | | | | | | | | | | | | | | | | | | | | Case 1: 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | (3231) all_177_0 = 0 & all_177_1 = 0 & map_eq_sub1(int, 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | all_177_4, all_177_3, $sum(all_86_8, 1), 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | all_177_2) = 0 & map_eq_sub1(int, all_177_4, 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | all_177_3, 0, all_86_11) = 0 & length1(int, 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | all_103_2) = all_177_2 & elts(int, all_105_4) = 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | all_177_3 & elts(int, all_103_2) = all_177_4 & 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | in_uni(all_177_3) & in_uni(all_177_4) 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | ALPHA: (3231) implies: 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | (3232) length1(int, all_103_2) = all_177_2 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (324) gives: 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | Case 1: 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | (3233) all_219_1 = 0 & array_eq_sub1(int, all_105_4, 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | all_105_2, 0, all_86_7) = 0 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (39), (44), (45), (99), (100), (105), (180), 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | (205), (255), (270), (3215), (3216), (3217), 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | (3219), (3233) are inconsistent by sub-proof #1. 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | Case 2: 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | (3234) length1(int, all_105_4) = all_219_1 & ( ~ 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | ($lesseq(all_86_7, all_219_1)) | ~ ($lesseq(0, 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | all_219_1)) | ( ~ (all_219_0 = all_219_1) & 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | length1(int, all_105_2) = all_219_0)) 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3234) implies: 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | (3235) length1(int, all_105_4) = all_219_1 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (345) gives: 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | Case 1: 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | (3236) all_242_1 = 0 & array_eq_sub1(int, all_103_2, 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | all_105_4, $sum(all_86_8, 1), all_86_13) = 0 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3236) implies: 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | (3237) array_eq_sub1(int, all_103_2, all_105_4, 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | $sum(all_86_8, 1), all_86_13) = 0 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (269) gives: 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | Case 1: 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | | 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | | (3238) all_168_0 = all_168_1 & $lesseq(1, 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | | $difference(all_168_1, all_86_8)) & 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | | $lesseq(all_86_13, all_168_1) & $lesseq(-1, 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | | all_86_8) & $lesseq(0, all_86_13) & length1(int, 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | | all_105_4) = all_168_1 & length1(int, all_103_2) 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | | = all_168_1 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | | 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3238) implies: 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | | (3239) length1(int, all_103_2) = all_168_1 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | | (3240) length1(int, all_105_4) = all_168_1 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | | 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_219_1, all_168_1, 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (3235), (3240) 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | | (3241) all_219_1 = all_168_1 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | | 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_219_1, all_153_1, 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (3226), (3235) 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | | (3242) all_219_1 = all_153_1 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | | 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_86_13, all_177_2, 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (184), (3232) 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | | (3243) all_177_2 = all_86_13 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | | 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_211_1, all_177_2, 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (2632), (3232) 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | | (3244) all_211_1 = all_177_2 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | | 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_211_1, all_171_1, 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (2632), (3228) 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | | (3245) all_211_1 = all_171_1 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | | 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_177_2, all_156_0, 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (394), (3232) 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | | (3246) all_177_2 = all_156_0 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | | 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_168_1, all_156_0, 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (394), (3239) 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | | (3247) all_168_1 = all_156_0 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | | 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_86_13, all_238_1, 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (183), (3089) 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | | gives: 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | | (3248) all_238_1 = all_86_13 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | | 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3241), (3242) imply: 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | | (3249) all_168_1 = all_153_1 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | | 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3249) implies: 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | | (3250) all_168_1 = all_153_1 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | | 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3244), (3245) imply: 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | | (3251) all_177_2 = all_171_1 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | | 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3251) implies: 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | | (3252) all_177_2 = all_171_1 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | | 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3243), (3252) imply: 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | | (3253) all_171_1 = all_86_13 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | | 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3246), (3252) imply: 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | | (3254) all_171_1 = all_156_0 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | | 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3253), (3254) imply: 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | | (3255) all_156_0 = all_86_13 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | | 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3255) implies: 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | | (3256) all_156_0 = all_86_13 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | | 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3247), (3250) imply: 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | | (3257) all_156_0 = all_153_1 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | | 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (394), (3090), (3225), (3248), (3256), 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | | (3257) are inconsistent by sub-proof #20. 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | | 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | Case 2: 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | | 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | | (3258) ~ (all_168_1 = 0) & array_eq_sub1(int, all_103_2, 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | | all_105_4, $sum(all_86_8, 1), all_86_13) = 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | | all_168_1 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | | 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (3237), (3258) are inconsistent by sub-proof 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | | #83. 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | | 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | End of split 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | Case 2: 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | (3259) length1(int, all_103_2) = all_242_1 & ( ~ 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | ($lesseq(1, $difference(all_242_1, all_86_8))) | 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | ~ ($lesseq(all_86_13, all_242_1)) | ( ~ 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | (all_242_0 = all_242_1) & length1(int, 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | all_105_4) = all_242_0)) 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | 205.89/127.57 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3259) implies: 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | | | (3260) length1(int, all_103_2) = all_242_1 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | | | (3261) ~ ($lesseq(1, $difference(all_242_1, all_86_8))) 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | | | | ~ ($lesseq(all_86_13, all_242_1)) | ( ~ 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | | | (all_242_0 = all_242_1) & length1(int, 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | | | all_105_4) = all_242_0) 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | | | 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_86_13, all_219_1, 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (180), (3235) 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | | | gives: 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | | | (3262) all_219_1 = all_86_13 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | | | 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_219_1, all_153_1, 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (3226), (3235) 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | | | gives: 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | | | (3263) all_219_1 = all_153_1 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | | | 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_86_13, all_211_1, 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (184), (2632) 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | | | gives: 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | | | (3264) all_211_1 = all_86_13 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | | | 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_211_1, all_177_2, 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (2632), (3232) 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | | | gives: 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | | | (3265) all_211_1 = all_177_2 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | | | 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_242_1, all_171_1, 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (3228), (3260) 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | | | gives: 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | | | (3266) all_242_1 = all_171_1 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | | | 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_177_2, all_171_1, 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (3228), (3232) 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | | | gives: 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | | | (3267) all_177_2 = all_171_1 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | | | 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_242_1, all_156_0, 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (394), (3260) 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | | | gives: 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | | | (3268) all_242_1 = all_156_0 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | | | 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3266), (3268) imply: 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | | | (3269) all_171_1 = all_156_0 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | | | 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3269) implies: 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | | | (3270) all_171_1 = all_156_0 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | | | 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3262), (3263) imply: 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | | | (3271) all_153_1 = all_86_13 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | | | 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3264), (3265) imply: 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | | | (3272) all_177_2 = all_86_13 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | | | 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3272) implies: 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | | | (3273) all_177_2 = all_86_13 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | | | 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3267), (3273) imply: 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | | | (3274) all_171_1 = all_86_13 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | | | 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3274) implies: 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | | | (3275) all_171_1 = all_86_13 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | | | 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3270), (3275) imply: 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | | | (3276) all_156_0 = all_86_13 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | | | 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3276) implies: 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | | | (3277) all_156_0 = all_86_13 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | | | 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3268), (3277) imply: 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | | | (3278) all_242_1 = all_86_13 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | | | 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (52), (180), (389), (3261), (3278) are 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #77. 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | | | 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | | End of split 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | | 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | End of split 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | 205.89/127.58 | | | | | | | | | | | | | | | | | | | | Case 2: 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | (3279) ~ (all_177_4 = 0) & permut_sub2(int, all_103_2, 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | all_105_4, all_86_11, $sum(all_86_8, 1)) = 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | all_177_4 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (43), (3230), (3279) are inconsistent by sub-proof 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | #47. 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | 205.89/127.58 | | | | | | | | | | | | | | | | | | | | End of split 205.89/127.58 | | | | | | | | | | | | | | | | | | | | 205.89/127.58 | | | | | | | | | | | | | | | | | | | Case 2: 205.89/127.58 | | | | | | | | | | | | | | | | | | | | 205.89/127.58 | | | | | | | | | | | | | | | | | | | | (3280) elts(int, all_105_4) = all_181_2 & elts(int, 205.89/127.58 | | | | | | | | | | | | | | | | | | | | all_103_2) = all_181_3 & in_uni(all_181_2) & 205.89/127.58 | | | | | | | | | | | | | | | | | | | | in_uni(all_181_3) & (( ~ (all_181_0 = 0) & 205.89/127.58 | | | | | | | | | | | | | | | | | | | | map_eq_sub1(int, all_181_3, all_181_2, 205.89/127.58 | | | | | | | | | | | | | | | | | | | | $sum(all_86_8, 1), all_181_1) = all_181_0 & 205.89/127.58 | | | | | | | | | | | | | | | | | | | | length1(int, all_103_2) = all_181_1) | ( ~ 205.89/127.58 | | | | | | | | | | | | | | | | | | | | (all_181_1 = 0) & map_eq_sub1(int, all_181_3, 205.89/127.58 | | | | | | | | | | | | | | | | | | | | all_181_2, 0, all_86_11) = all_181_1)) 205.89/127.58 | | | | | | | | | | | | | | | | | | | | 205.89/127.58 | | | | | | | | | | | | | | | | | | | | ALPHA: (3280) implies: 205.89/127.58 | | | | | | | | | | | | | | | | | | | | (3281) elts(int, all_103_2) = all_181_3 205.89/127.58 | | | | | | | | | | | | | | | | | | | | (3282) elts(int, all_105_4) = all_181_2 205.89/127.58 | | | | | | | | | | | | | | | | | | | | (3283) ( ~ (all_181_0 = 0) & map_eq_sub1(int, all_181_3, 205.89/127.58 | | | | | | | | | | | | | | | | | | | | all_181_2, $sum(all_86_8, 1), all_181_1) = 205.89/127.58 | | | | | | | | | | | | | | | | | | | | all_181_0 & length1(int, all_103_2) = all_181_1) 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | ( ~ (all_181_1 = 0) & map_eq_sub1(int, 205.89/127.58 | | | | | | | | | | | | | | | | | | | | all_181_3, all_181_2, 0, all_86_11) = 205.89/127.58 | | | | | | | | | | | | | | | | | | | | all_181_1) 205.89/127.58 | | | | | | | | | | | | | | | | | | | | 205.89/127.58 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (39), (43), (44), (91), (99), (184), (203), 205.89/127.58 | | | | | | | | | | | | | | | | | | | | (263), (297), (394), (395), (396), (3215), (3221), 205.89/127.58 | | | | | | | | | | | | | | | | | | | | (3281), (3282), (3283) are inconsistent by 205.89/127.58 | | | | | | | | | | | | | | | | | | | | sub-proof #11. 205.89/127.58 | | | | | | | | | | | | | | | | | | | | 205.89/127.58 | | | | | | | | | | | | | | | | | | | End of split 205.89/127.58 | | | | | | | | | | | | | | | | | | | 205.89/127.58 | | | | | | | | | | | | | | | | | | Case 2: 205.89/127.58 | | | | | | | | | | | | | | | | | | | 205.89/127.58 | | | | | | | | | | | | | | | | | | | (3284) ~ (all_171_1 = 0) & array_eq_sub1(int, all_103_4, 205.89/127.58 | | | | | | | | | | | | | | | | | | | all_103_2, 0, all_86_11) = all_171_1 205.89/127.58 | | | | | | | | | | | | | | | | | | | 205.89/127.58 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (3223), (3284) are inconsistent by sub-proof 205.89/127.58 | | | | | | | | | | | | | | | | | | | #81. 205.89/127.58 | | | | | | | | | | | | | | | | | | | 205.89/127.58 | | | | | | | | | | | | | | | | | | End of split 205.89/127.58 | | | | | | | | | | | | | | | | | | 205.89/127.58 | | | | | | | | | | | | | | | | | Case 2: 205.89/127.58 | | | | | | | | | | | | | | | | | | 205.89/127.58 | | | | | | | | | | | | | | | | | | (3285) ~ (all_153_1 = 0) & array_eq_sub1(int, all_105_4, 205.89/127.58 | | | | | | | | | | | | | | | | | | all_105_2, $sum(all_86_10, 1), all_86_13) = 205.89/127.58 | | | | | | | | | | | | | | | | | | all_153_1 205.89/127.58 | | | | | | | | | | | | | | | | | | 205.89/127.58 | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (3219), (3285) are inconsistent by sub-proof 205.89/127.58 | | | | | | | | | | | | | | | | | | #54. 205.89/127.58 | | | | | | | | | | | | | | | | | | 205.89/127.58 | | | | | | | | | | | | | | | | | End of split 205.89/127.58 | | | | | | | | | | | | | | | | | 205.89/127.58 | | | | | | | | | | | | | | | | Case 2: 205.89/127.58 | | | | | | | | | | | | | | | | | 205.89/127.58 | | | | | | | | | | | | | | | | | (3286) length1(int, all_103_4) = all_215_1 & ( ~ 205.89/127.58 | | | | | | | | | | | | | | | | | ($lesseq(all_86_11, all_215_1)) | ~ ($lesseq(0, 205.89/127.58 | | | | | | | | | | | | | | | | | all_215_1)) | ( ~ (all_215_0 = all_215_1) & 205.89/127.58 | | | | | | | | | | | | | | | | | length1(int, all_103_2) = all_215_0)) 205.89/127.58 | | | | | | | | | | | | | | | | | 205.89/127.58 | | | | | | | | | | | | | | | | | ALPHA: (3286) implies: 205.89/127.58 | | | | | | | | | | | | | | | | | (3287) length1(int, all_103_4) = all_215_1 205.89/127.58 | | | | | | | | | | | | | | | | | 205.89/127.58 | | | | | | | | | | | | | | | | | BETA: splitting (255) gives: 205.89/127.58 | | | | | | | | | | | | | | | | | 205.89/127.58 | | | | | | | | | | | | | | | | | Case 1: 205.89/127.58 | | | | | | | | | | | | | | | | | | 205.89/127.58 | | | | | | | | | | | | | | | | | | (3288) all_153_0 = all_153_1 & $lesseq(1, 205.89/127.58 | | | | | | | | | | | | | | | | | | $difference(all_153_1, all_86_10)) & 205.89/127.58 | | | | | | | | | | | | | | | | | | $lesseq(all_86_13, all_153_1) & $lesseq(-1, 205.89/127.58 | | | | | | | | | | | | | | | | | | all_86_10) & $lesseq(0, all_86_13) & 205.89/127.58 | | | | | | | | | | | | | | | | | | length1(int, all_105_2) = all_153_1 & length1(int, 205.89/127.58 | | | | | | | | | | | | | | | | | | all_105_4) = all_153_1 205.89/127.58 | | | | | | | | | | | | | | | | | | 205.89/127.58 | | | | | | | | | | | | | | | | | | ALPHA: (3288) implies: 205.89/127.58 | | | | | | | | | | | | | | | | | | (3289) length1(int, all_105_4) = all_153_1 205.89/127.58 | | | | | | | | | | | | | | | | | | 205.89/127.58 | | | | | | | | | | | | | | | | | | BETA: splitting (287) gives: 205.89/127.58 | | | | | | | | | | | | | | | | | | 205.89/127.58 | | | | | | | | | | | | | | | | | | Case 1: 205.89/127.58 | | | | | | | | | | | | | | | | | | | 205.89/127.58 | | | | | | | | | | | | | | | | | | | (3290) all_181_3 = 0 & permut_sub2(int, all_103_2, 205.89/127.58 | | | | | | | | | | | | | | | | | | | all_105_4, all_86_11, $sum(all_86_8, 1)) = 0 205.89/127.58 | | | | | | | | | | | | | | | | | | | 205.89/127.58 | | | | | | | | | | | | | | | | | | | ALPHA: (3290) implies: 205.89/127.58 | | | | | | | | | | | | | | | | | | | (3291) permut_sub2(int, all_103_2, all_105_4, all_86_11, 205.89/127.58 | | | | | | | | | | | | | | | | | | | $sum(all_86_8, 1)) = 0 205.89/127.58 | | | | | | | | | | | | | | | | | | | 205.89/127.58 | | | | | | | | | | | | | | | | | | | BETA: splitting (280) gives: 205.89/127.58 | | | | | | | | | | | | | | | | | | | 205.89/127.58 | | | | | | | | | | | | | | | | | | | Case 1: 205.89/127.58 | | | | | | | | | | | | | | | | | | | | 205.89/127.58 | | | | | | | | | | | | | | | | | | | | (3292) all_177_0 = 0 & all_177_1 = 0 & map_eq_sub1(int, 205.89/127.58 | | | | | | | | | | | | | | | | | | | | all_177_4, all_177_3, $sum(all_86_8, 1), 205.89/127.58 | | | | | | | | | | | | | | | | | | | | all_177_2) = 0 & map_eq_sub1(int, all_177_4, 205.89/127.58 | | | | | | | | | | | | | | | | | | | | all_177_3, 0, all_86_11) = 0 & length1(int, 205.89/127.58 | | | | | | | | | | | | | | | | | | | | all_103_2) = all_177_2 & elts(int, all_105_4) = 205.89/127.58 | | | | | | | | | | | | | | | | | | | | all_177_3 & elts(int, all_103_2) = all_177_4 & 205.89/127.58 | | | | | | | | | | | | | | | | | | | | in_uni(all_177_3) & in_uni(all_177_4) 205.89/127.58 | | | | | | | | | | | | | | | | | | | | 205.89/127.58 | | | | | | | | | | | | | | | | | | | | ALPHA: (3292) implies: 205.89/127.58 | | | | | | | | | | | | | | | | | | | | (3293) elts(int, all_105_4) = all_177_3 205.89/127.58 | | | | | | | | | | | | | | | | | | | | 205.89/127.58 | | | | | | | | | | | | | | | | | | | | BETA: splitting (324) gives: 205.89/127.58 | | | | | | | | | | | | | | | | | | | | 205.89/127.58 | | | | | | | | | | | | | | | | | | | | Case 1: 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | (3294) all_219_1 = 0 & array_eq_sub1(int, all_105_4, 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | all_105_2, 0, all_86_7) = 0 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (39), (44), (45), (99), (100), (105), (180), 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | (205), (255), (270), (3215), (3216), (3217), 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | (3219), (3294) are inconsistent by sub-proof #1. 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | 205.89/127.58 | | | | | | | | | | | | | | | | | | | | Case 2: 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | (3295) length1(int, all_105_4) = all_219_1 & ( ~ 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | ($lesseq(all_86_7, all_219_1)) | ~ ($lesseq(0, 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | all_219_1)) | ( ~ (all_219_0 = all_219_1) & 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | length1(int, all_105_2) = all_219_0)) 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | ALPHA: (3295) implies: 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | (3296) length1(int, all_105_4) = all_219_1 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_86_13, all_219_1, 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (180), (3296) 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | gives: 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | (3297) all_219_1 = all_86_13 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_219_1, all_153_1, 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (3289), (3296) 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | gives: 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | (3298) all_219_1 = all_153_1 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_105_1, all_187_2, 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | all_105_2, int, simplifying with (100), (3216) 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | gives: 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | (3299) all_187_2 = all_105_1 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_105_3, all_177_3, 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (99), (3293) 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | gives: 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | (3300) all_177_3 = all_105_3 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_187_3, all_177_3, 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (3215), (3293) 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | gives: 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | (3301) all_187_3 = all_177_3 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_187_3, all_156_1, 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (395), (3215) 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | gives: 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | (3302) all_187_3 = all_156_1 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3297), (3298) imply: 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | (3303) all_153_1 = all_86_13 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | SIMP: (3303) implies: 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | (3304) all_153_1 = all_86_13 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3301), (3302) imply: 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | (3305) all_177_3 = all_156_1 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | SIMP: (3305) implies: 205.89/127.58 | | | | | | | | | | | | | | | | | | | | | (3306) all_177_3 = all_156_1 205.89/127.59 | | | | | | | | | | | | | | | | | | | | | 205.89/127.59 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3300), (3306) imply: 205.89/127.59 | | | | | | | | | | | | | | | | | | | | | (3307) all_156_1 = all_105_3 205.89/127.59 | | | | | | | | | | | | | | | | | | | | | 205.89/127.59 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3302), (3307) imply: 205.89/127.59 | | | | | | | | | | | | | | | | | | | | | (3308) all_187_3 = all_105_3 205.89/127.59 | | | | | | | | | | | | | | | | | | | | | 205.89/127.59 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (44), (105), (180), (205), (3217), (3299), 205.89/127.59 | | | | | | | | | | | | | | | | | | | | | (3308) are inconsistent by sub-proof #66. 205.89/127.59 | | | | | | | | | | | | | | | | | | | | | 205.89/127.59 | | | | | | | | | | | | | | | | | | | | End of split 205.89/127.59 | | | | | | | | | | | | | | | | | | | | 205.89/127.59 | | | | | | | | | | | | | | | | | | | Case 2: 205.89/127.59 | | | | | | | | | | | | | | | | | | | | 205.89/127.59 | | | | | | | | | | | | | | | | | | | | (3309) ~ (all_177_4 = 0) & permut_sub2(int, all_103_2, 205.89/127.59 | | | | | | | | | | | | | | | | | | | | all_105_4, all_86_11, $sum(all_86_8, 1)) = 205.89/127.59 | | | | | | | | | | | | | | | | | | | | all_177_4 205.89/127.59 | | | | | | | | | | | | | | | | | | | | 205.89/127.59 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (43), (3291), (3309) are inconsistent by sub-proof 205.89/127.59 | | | | | | | | | | | | | | | | | | | | #47. 205.89/127.59 | | | | | | | | | | | | | | | | | | | | 205.89/127.59 | | | | | | | | | | | | | | | | | | | End of split 205.89/127.59 | | | | | | | | | | | | | | | | | | | 205.89/127.59 | | | | | | | | | | | | | | | | | | Case 2: 205.89/127.59 | | | | | | | | | | | | | | | | | | | 205.89/127.59 | | | | | | | | | | | | | | | | | | | (3310) elts(int, all_105_4) = all_181_2 & elts(int, 205.89/127.59 | | | | | | | | | | | | | | | | | | | all_103_2) = all_181_3 & in_uni(all_181_2) & 205.89/127.59 | | | | | | | | | | | | | | | | | | | in_uni(all_181_3) & (( ~ (all_181_0 = 0) & 205.89/127.59 | | | | | | | | | | | | | | | | | | | map_eq_sub1(int, all_181_3, all_181_2, 205.89/127.59 | | | | | | | | | | | | | | | | | | | $sum(all_86_8, 1), all_181_1) = all_181_0 & 205.89/127.59 | | | | | | | | | | | | | | | | | | | length1(int, all_103_2) = all_181_1) | ( ~ 205.89/127.59 | | | | | | | | | | | | | | | | | | | (all_181_1 = 0) & map_eq_sub1(int, all_181_3, 205.89/127.59 | | | | | | | | | | | | | | | | | | | all_181_2, 0, all_86_11) = all_181_1)) 205.89/127.59 | | | | | | | | | | | | | | | | | | | 205.89/127.59 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (39), (43), (44), (90), (91), (96), (99), 205.89/127.59 | | | | | | | | | | | | | | | | | | | (183), (184), (203), (206), (263), (296), (297), 205.89/127.59 | | | | | | | | | | | | | | | | | | | (394), (395), (396), (3089), (3215), (3287), 205.89/127.59 | | | | | | | | | | | | | | | | | | | (3310) are inconsistent by sub-proof #10. 205.89/127.59 | | | | | | | | | | | | | | | | | | | 205.89/127.59 | | | | | | | | | | | | | | | | | | End of split 205.89/127.59 | | | | | | | | | | | | | | | | | | 205.89/127.59 | | | | | | | | | | | | | | | | | Case 2: 205.89/127.59 | | | | | | | | | | | | | | | | | | 205.89/127.59 | | | | | | | | | | | | | | | | | | (3311) ~ (all_153_1 = 0) & array_eq_sub1(int, all_105_4, 205.89/127.59 | | | | | | | | | | | | | | | | | | all_105_2, $sum(all_86_10, 1), all_86_13) = 205.89/127.59 | | | | | | | | | | | | | | | | | | all_153_1 205.89/127.59 | | | | | | | | | | | | | | | | | | 205.89/127.59 | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (3219), (3311) are inconsistent by sub-proof 205.89/127.59 | | | | | | | | | | | | | | | | | | #54. 205.89/127.59 | | | | | | | | | | | | | | | | | | 205.89/127.59 | | | | | | | | | | | | | | | | | End of split 205.89/127.59 | | | | | | | | | | | | | | | | | 205.89/127.59 | | | | | | | | | | | | | | | | End of split 205.89/127.59 | | | | | | | | | | | | | | | | 205.89/127.59 | | | | | | | | | | | | | | | Case 2: 205.89/127.59 | | | | | | | | | | | | | | | | 205.89/127.59 | | | | | | | | | | | | | | | | (3312) elts(int, all_103_2) = all_191_2 & elts(int, 205.89/127.59 | | | | | | | | | | | | | | | | all_103_4) = all_191_3 & in_uni(all_191_2) & 205.89/127.59 | | | | | | | | | | | | | | | | in_uni(all_191_3) & (( ~ (all_191_0 = 0) & 205.89/127.59 | | | | | | | | | | | | | | | | map_eq_sub1(int, all_191_3, all_191_2, 205.89/127.59 | | | | | | | | | | | | | | | | $sum(all_86_10, 1), all_191_1) = all_191_0 & 205.89/127.59 | | | | | | | | | | | | | | | | length1(int, all_103_4) = all_191_1) | ( ~ 205.89/127.59 | | | | | | | | | | | | | | | | (all_191_1 = 0) & map_eq_sub1(int, all_191_3, 205.89/127.59 | | | | | | | | | | | | | | | | all_191_2, 0, all_86_11) = all_191_1)) 205.89/127.59 | | | | | | | | | | | | | | | | 205.89/127.59 | | | | | | | | | | | | | | | | ALPHA: (3312) implies: 205.89/127.59 | | | | | | | | | | | | | | | | (3313) elts(int, all_103_4) = all_191_3 205.89/127.59 | | | | | | | | | | | | | | | | (3314) elts(int, all_103_2) = all_191_2 205.89/127.59 | | | | | | | | | | | | | | | | (3315) ( ~ (all_191_0 = 0) & map_eq_sub1(int, all_191_3, 205.89/127.59 | | | | | | | | | | | | | | | | all_191_2, $sum(all_86_10, 1), all_191_1) = 205.89/127.59 | | | | | | | | | | | | | | | | all_191_0 & length1(int, all_103_4) = all_191_1) 205.89/127.59 | | | | | | | | | | | | | | | | | ( ~ (all_191_1 = 0) & map_eq_sub1(int, 205.89/127.59 | | | | | | | | | | | | | | | | all_191_3, all_191_2, 0, all_86_11) = 205.89/127.59 | | | | | | | | | | | | | | | | all_191_1) 205.89/127.59 | | | | | | | | | | | | | | | | 205.89/127.59 | | | | | | | | | | | | | | | | REF_CLOSE: (38), (39), (44), (45), (90), (91), (96), (183), 205.89/127.59 | | | | | | | | | | | | | | | | (206), (272), (319), (3089), (3313), (3314), 205.89/127.59 | | | | | | | | | | | | | | | | (3315) are inconsistent by sub-proof #2. 205.89/127.59 | | | | | | | | | | | | | | | | 205.89/127.59 | | | | | | | | | | | | | | | End of split 205.89/127.59 | | | | | | | | | | | | | | | 205.89/127.59 | | | | | | | | | | | | | | Case 2: 205.89/127.59 | | | | | | | | | | | | | | | 205.89/127.59 | | | | | | | | | | | | | | | (3316) length1(int, all_105_4) = all_234_1 & ( ~ 205.89/127.59 | | | | | | | | | | | | | | | ($lesseq(1, $difference(all_234_1, all_86_10))) 205.89/127.59 | | | | | | | | | | | | | | | | ~ ($lesseq(all_86_13, all_234_1)) | ( ~ 205.89/127.59 | | | | | | | | | | | | | | | (all_234_0 = all_234_1) & length1(int, 205.89/127.59 | | | | | | | | | | | | | | | all_105_2) = all_234_0)) 205.89/127.59 | | | | | | | | | | | | | | | 205.89/127.59 | | | | | | | | | | | | | | | REF_CLOSE: (39), (49), (180), (181), (3316) are inconsistent 205.89/127.59 | | | | | | | | | | | | | | | by sub-proof #12. 205.89/127.59 | | | | | | | | | | | | | | | 205.89/127.59 | | | | | | | | | | | | | | End of split 205.89/127.59 | | | | | | | | | | | | | | 205.89/127.59 | | | | | | | | | | | | | End of split 205.89/127.59 | | | | | | | | | | | | | 205.89/127.59 | | | | | | | | | | | | End of split 205.89/127.59 | | | | | | | | | | | | 205.89/127.59 | | | | | | | | | | | End of split 205.89/127.59 | | | | | | | | | | | 205.89/127.59 | | | | | | | | | | End of split 205.89/127.59 | | | | | | | | | | 205.89/127.59 | | | | | | | | | End of split 205.89/127.59 | | | | | | | | | 205.89/127.59 | | | | | | | | End of split 205.89/127.59 | | | | | | | | 205.89/127.59 | | | | | | | End of split 205.89/127.59 | | | | | | | 205.89/127.59 | | | | | | End of split 205.89/127.59 | | | | | | 205.89/127.59 | | | | | End of split 205.89/127.59 | | | | | 205.89/127.59 | | | | End of split 205.89/127.59 | | | | 205.89/127.59 | | | End of split 205.89/127.59 | | | 205.89/127.59 | | End of split 205.89/127.59 | | 205.89/127.59 | End of split 205.89/127.59 | 205.89/127.59 End of proof 205.89/127.59 205.89/127.59 Sub-proof #1 shows that the following formulas are inconsistent: 205.89/127.59 ---------------------------------------------------------------- 205.89/127.59 (1) array_eq_sub1(int, all_105_4, all_105_2, $sum(all_86_10, 1), all_86_13) = 205.89/127.59 0 205.89/127.59 (2) all_219_1 = 0 & array_eq_sub1(int, all_105_4, all_105_2, 0, all_86_7) = 0 205.89/127.59 (3) elts(int, all_105_2) = all_187_2 205.89/127.59 (4) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 205.89/127.59 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ 205.89/127.59 (array_eq_sub1(v6, v5, v4, v3, v2) = v1) | ~ (array_eq_sub1(v6, v5, 205.89/127.59 v4, v3, v2) = v0)) 205.89/127.59 (5) elts(int, all_105_4) = all_187_3 205.89/127.59 (6) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 205.89/127.59 | ~ (elts(v3, v2) = v1) | ~ (elts(v3, v2) = v0)) 205.89/127.59 (7) length1(int, all_105_4) = all_86_13 205.89/127.59 (8) elts(int, all_105_4) = all_105_3 205.89/127.59 (9) map_eq_sub1(int, all_105_3, all_105_1, 0, all_86_7) = 0 205.89/127.59 (10) (all_169_0 = all_169_1 & $lesseq(all_86_7, all_169_1) & $lesseq(0, 205.89/127.59 all_169_1) & $lesseq(0, all_86_7) & length1(int, all_105_2) = 205.89/127.59 all_169_1 & length1(int, all_105_4) = all_169_1) | ( ~ (all_169_1 = 0) 205.89/127.59 & array_eq_sub1(int, all_105_4, all_105_2, 0, all_86_7) = all_169_1) 205.89/127.59 (11) elts(int, all_105_2) = all_105_1 205.89/127.59 (12) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 205.89/127.59 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ (map_eq_sub1(v6, 205.89/127.59 v5, v4, v3, v2) = v1) | ~ (map_eq_sub1(v6, v5, v4, v3, v2) = v0)) 205.89/127.59 (13) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 205.89/127.59 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 205.89/127.59 (14) (all_153_0 = all_153_1 & $lesseq(1, $difference(all_153_1, all_86_10)) & 205.89/127.59 $lesseq(all_86_13, all_153_1) & $lesseq(-1, all_86_10) & $lesseq(0, 205.89/127.59 all_86_13) & length1(int, all_105_2) = all_153_1 & length1(int, 205.89/127.59 all_105_4) = all_153_1) | ( ~ (all_153_1 = 0) & array_eq_sub1(int, 205.89/127.59 all_105_4, all_105_2, $sum(all_86_10, 1), all_86_13) = all_153_1) 205.89/127.60 (15) ( ~ (all_187_0 = 0) & map_eq_sub1(int, all_187_3, all_187_2, 205.89/127.60 $sum(all_86_10, 1), all_187_1) = all_187_0 & length1(int, all_105_4) 205.89/127.60 = all_187_1) | ( ~ (all_187_1 = 0) & map_eq_sub1(int, all_187_3, 205.89/127.60 all_187_2, 0, all_86_7) = all_187_1) 205.89/127.60 (16) map_eq_sub1(int, all_105_3, all_105_1, $sum(all_86_10, 1), all_86_13) = 205.89/127.60 0 205.89/127.60 205.89/127.60 Begin of proof 205.89/127.60 | 205.89/127.60 | ALPHA: (2) implies: 205.89/127.60 | (17) array_eq_sub1(int, all_105_4, all_105_2, 0, all_86_7) = 0 205.89/127.60 | 205.89/127.60 | BETA: splitting (10) gives: 205.89/127.60 | 205.89/127.60 | Case 1: 205.89/127.60 | | 205.89/127.60 | | (18) all_169_0 = all_169_1 & $lesseq(all_86_7, all_169_1) & $lesseq(0, 205.89/127.60 | | all_169_1) & $lesseq(0, all_86_7) & length1(int, all_105_2) = 205.89/127.60 | | all_169_1 & length1(int, all_105_4) = all_169_1 205.89/127.60 | | 205.89/127.60 | | ALPHA: (18) implies: 205.89/127.60 | | (19) length1(int, all_105_4) = all_169_1 205.89/127.60 | | 205.89/127.60 | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (11), (12), (13), (14), 205.89/127.60 | | (15), (16), (19) are inconsistent by sub-proof #6. 205.89/127.60 | | 205.89/127.60 | Case 2: 205.89/127.60 | | 205.89/127.60 | | (20) ~ (all_169_1 = 0) & array_eq_sub1(int, all_105_4, all_105_2, 0, 205.89/127.60 | | all_86_7) = all_169_1 205.89/127.60 | | 205.89/127.60 | | REF_CLOSE: (4), (17), (20) are inconsistent by sub-proof #75. 205.89/127.60 | | 205.89/127.60 | End of split 205.89/127.60 | 205.89/127.60 End of proof 205.89/127.60 205.89/127.60 Sub-proof #2 shows that the following formulas are inconsistent: 205.89/127.60 ---------------------------------------------------------------- 205.89/127.60 (1) elts(int, all_103_4) = all_191_3 205.89/127.60 (2) elts(int, all_103_4) = all_103_3 205.89/127.60 (3) length1(int, all_103_4) = all_86_13 205.89/127.60 (4) map_eq_sub1(int, all_103_3, all_103_1, $sum(all_86_10, 1), all_86_13) = 0 205.89/127.60 (5) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 205.89/127.60 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ 205.89/127.60 (array_eq_sub1(v6, v5, v4, v3, v2) = v1) | ~ (array_eq_sub1(v6, v5, 205.89/127.60 v4, v3, v2) = v0)) 205.89/127.60 (6) (all_171_0 = all_171_1 & $lesseq(all_86_11, all_171_1) & $lesseq(0, 205.89/127.60 all_171_1) & $lesseq(0, all_86_11) & length1(int, all_103_2) = 205.89/127.60 all_171_1 & length1(int, all_103_4) = all_171_1) | ( ~ (all_171_1 = 0) 205.89/127.60 & array_eq_sub1(int, all_103_4, all_103_2, 0, all_86_11) = all_171_1) 205.89/127.60 (7) elts(int, all_103_2) = all_191_2 205.89/127.60 (8) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 205.89/127.60 | ~ (elts(v3, v2) = v1) | ~ (elts(v3, v2) = v0)) 205.89/127.60 (9) length1(int, all_103_4) = all_238_1 205.89/127.60 (10) map_eq_sub1(int, all_103_3, all_103_1, 0, all_86_11) = 0 205.89/127.60 (11) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 205.89/127.60 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ (map_eq_sub1(v6, 205.89/127.60 v5, v4, v3, v2) = v1) | ~ (map_eq_sub1(v6, v5, v4, v3, v2) = v0)) 205.89/127.60 (12) (all_215_1 = 0 & array_eq_sub1(int, all_103_4, all_103_2, 0, all_86_11) 205.89/127.60 = 0) | (length1(int, all_103_4) = all_215_1 & ( ~ ($lesseq(all_86_11, 205.89/127.60 all_215_1)) | ~ ($lesseq(0, all_215_1)) | ( ~ (all_215_0 = 205.89/127.60 all_215_1) & length1(int, all_103_2) = all_215_0))) 205.89/127.60 (13) elts(int, all_103_2) = all_103_1 205.89/127.60 (14) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 205.89/127.60 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 205.89/127.60 (15) ( ~ (all_191_0 = 0) & map_eq_sub1(int, all_191_3, all_191_2, 205.89/127.60 $sum(all_86_10, 1), all_191_1) = all_191_0 & length1(int, all_103_4) 205.89/127.60 = all_191_1) | ( ~ (all_191_1 = 0) & map_eq_sub1(int, all_191_3, 205.89/127.60 all_191_2, 0, all_86_11) = all_191_1) 205.89/127.60 205.89/127.60 Begin of proof 205.89/127.60 | 205.89/127.60 | BETA: splitting (12) gives: 205.89/127.60 | 205.89/127.60 | Case 1: 205.89/127.60 | | 205.89/127.60 | | (16) all_215_1 = 0 & array_eq_sub1(int, all_103_4, all_103_2, 0, 205.89/127.60 | | all_86_11) = 0 205.89/127.60 | | 205.89/127.60 | | ALPHA: (16) implies: 205.89/127.60 | | (17) array_eq_sub1(int, all_103_4, all_103_2, 0, all_86_11) = 0 205.89/127.60 | | 205.89/127.60 | | BETA: splitting (6) gives: 205.89/127.60 | | 205.89/127.60 | | Case 1: 205.89/127.60 | | | 205.89/127.60 | | | (18) all_171_0 = all_171_1 & $lesseq(all_86_11, all_171_1) & $lesseq(0, 205.89/127.60 | | | all_171_1) & $lesseq(0, all_86_11) & length1(int, all_103_2) = 205.89/127.60 | | | all_171_1 & length1(int, all_103_4) = all_171_1 205.89/127.60 | | | 205.89/127.60 | | | ALPHA: (18) implies: 205.89/127.60 | | | (19) length1(int, all_103_4) = all_171_1 205.89/127.60 | | | 205.89/127.60 | | | REF_CLOSE: (1), (2), (3), (4), (7), (8), (9), (10), (11), (13), (14), 205.89/127.60 | | | (15), (19) are inconsistent by sub-proof #19. 205.89/127.60 | | | 205.89/127.60 | | Case 2: 205.89/127.60 | | | 205.89/127.60 | | | (20) ~ (all_171_1 = 0) & array_eq_sub1(int, all_103_4, all_103_2, 0, 205.89/127.60 | | | all_86_11) = all_171_1 205.89/127.60 | | | 205.89/127.60 | | | REF_CLOSE: (5), (17), (20) are inconsistent by sub-proof #81. 205.89/127.60 | | | 205.89/127.60 | | End of split 205.89/127.60 | | 205.89/127.60 | Case 2: 205.89/127.60 | | 205.89/127.60 | | (21) length1(int, all_103_4) = all_215_1 & ( ~ ($lesseq(all_86_11, 205.89/127.60 | | all_215_1)) | ~ ($lesseq(0, all_215_1)) | ( ~ (all_215_0 = 205.89/127.60 | | all_215_1) & length1(int, all_103_2) = all_215_0)) 205.89/127.60 | | 205.89/127.60 | | ALPHA: (21) implies: 205.89/127.60 | | (22) length1(int, all_103_4) = all_215_1 205.89/127.60 | | 205.89/127.60 | | REF_CLOSE: (1), (2), (3), (4), (7), (8), (9), (10), (11), (13), (14), (15), 205.89/127.60 | | (22) are inconsistent by sub-proof #16. 205.89/127.60 | | 205.89/127.60 | End of split 205.89/127.60 | 205.89/127.60 End of proof 205.89/127.60 205.89/127.60 Sub-proof #3 shows that the following formulas are inconsistent: 205.89/127.60 ---------------------------------------------------------------- 205.89/127.60 (1) length1(int, all_103_2) = all_86_13 205.89/127.60 (2) length1(int, all_105_4) = all_153_1 205.89/127.60 (3) length1(int, all_103_2) = all_211_1 205.89/127.60 (4) length1(int, all_105_4) = all_86_13 205.89/127.60 (5) $lesseq(1, $difference(all_153_1, all_86_10)) 205.89/127.60 (6) $lesseq(all_86_11, all_86_8) 205.89/127.60 (7) $lesseq(all_86_7, all_86_10) 205.89/127.60 (8) length1(int, all_105_4) = all_190_2 205.89/127.60 (9) $lesseq(1, $difference(all_86_7, all_86_8)) 205.89/127.60 (10) $lesseq(0, all_86_11) 205.89/127.60 (11) ~ ($lesseq(all_86_11, all_211_1)) | ~ ($lesseq(0, all_211_1)) | ( ~ 205.89/127.60 (all_211_0 = all_211_1) & length1(int, all_105_4) = all_211_0) 205.89/127.60 (12) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 205.89/127.60 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 205.89/127.60 (13) length1(int, all_103_2) = all_177_2 205.89/127.60 (14) length1(int, all_105_4) = all_219_1 205.89/127.60 205.89/127.60 Begin of proof 205.89/127.60 | 205.89/127.60 | GROUND_INST: instantiating (12) with all_86_13, all_190_2, all_105_4, int, 205.89/127.60 | simplifying with (4), (8) gives: 205.89/127.60 | (15) all_190_2 = all_86_13 205.89/127.60 | 205.89/127.60 | GROUND_INST: instantiating (12) with all_219_1, all_190_2, all_105_4, int, 205.89/127.60 | simplifying with (8), (14) gives: 205.89/127.60 | (16) all_219_1 = all_190_2 205.89/127.60 | 205.89/127.60 | GROUND_INST: instantiating (12) with all_219_1, all_153_1, all_105_4, int, 205.89/127.60 | simplifying with (2), (14) gives: 205.89/127.60 | (17) all_219_1 = all_153_1 205.89/127.60 | 205.89/127.60 | GROUND_INST: instantiating (12) with all_86_13, all_211_1, all_103_2, int, 205.89/127.60 | simplifying with (1), (3) gives: 205.89/127.60 | (18) all_211_1 = all_86_13 205.89/127.60 | 205.89/127.60 | GROUND_INST: instantiating (12) with all_211_1, all_177_2, all_103_2, int, 205.89/127.60 | simplifying with (3), (13) gives: 205.89/127.60 | (19) all_211_1 = all_177_2 205.89/127.60 | 205.89/127.60 | COMBINE_EQS: (16), (17) imply: 205.89/127.60 | (20) all_190_2 = all_153_1 205.89/127.60 | 205.89/127.60 | SIMP: (20) implies: 205.89/127.60 | (21) all_190_2 = all_153_1 205.89/127.60 | 205.89/127.60 | COMBINE_EQS: (18), (19) imply: 205.89/127.60 | (22) all_177_2 = all_86_13 205.89/127.60 | 205.89/127.60 | COMBINE_EQS: (15), (21) imply: 205.89/127.60 | (23) all_153_1 = all_86_13 205.89/127.60 | 205.89/127.60 | REF_CLOSE: (2), (5), (6), (7), (9), (10), (11), (12), (18), (23) are 205.89/127.60 | inconsistent by sub-proof #7. 205.89/127.60 | 205.89/127.60 End of proof 205.89/127.60 205.89/127.60 Sub-proof #4 shows that the following formulas are inconsistent: 205.89/127.60 ---------------------------------------------------------------- 205.89/127.60 (1) elts(int, all_103_4) = all_191_3 205.89/127.60 (2) length1(int, all_103_2) = all_86_13 205.89/127.60 (3) elts(int, all_103_4) = all_103_3 205.89/127.60 (4) length1(int, all_105_4) = all_153_1 205.89/127.60 (5) $lesseq(all_86_7, all_86_13) 205.89/127.60 (6) map_eq_sub1(int, all_103_3, all_103_1, $sum(all_86_10, 1), all_86_13) = 0 205.89/127.60 (7) length1(int, all_103_2) = all_211_1 205.89/127.60 (8) length1(int, all_103_2) = all_193_1 205.89/127.60 (9) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 205.89/127.60 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ 205.89/127.60 (array_eq_sub1(v6, v5, v4, v3, v2) = v1) | ~ (array_eq_sub1(v6, v5, 205.89/127.60 v4, v3, v2) = v0)) 205.89/127.60 (10) elts(int, all_103_2) = all_191_2 205.89/127.60 (11) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 205.89/127.60 | ~ (elts(v3, v2) = v1) | ~ (elts(v3, v2) = v0)) 205.89/127.60 (12) (all_242_1 = 0 & array_eq_sub1(int, all_103_2, all_105_4, $sum(all_86_8, 205.89/127.60 1), all_86_13) = 0) | (length1(int, all_103_2) = all_242_1 & ( ~ 205.89/127.60 ($lesseq(1, $difference(all_242_1, all_86_8))) | ~ 205.89/127.60 ($lesseq(all_86_13, all_242_1)) | ( ~ (all_242_0 = all_242_1) & 205.89/127.60 length1(int, all_105_4) = all_242_0))) 205.89/127.60 (13) $lesseq(1, $difference(all_153_1, all_86_10)) 205.89/127.60 (14) length1(int, all_103_4) = all_171_1 205.89/127.60 (15) map_eq_sub1(int, all_103_3, all_103_1, 0, all_86_11) = 0 205.89/127.60 (16) $lesseq(all_86_11, all_86_8) 205.89/127.60 (17) $lesseq(all_86_7, all_86_10) 205.89/127.61 (18) (all_168_0 = all_168_1 & $lesseq(1, $difference(all_168_1, all_86_8)) & 205.89/127.61 $lesseq(all_86_13, all_168_1) & $lesseq(-1, all_86_8) & $lesseq(0, 205.89/127.61 all_86_13) & length1(int, all_105_4) = all_168_1 & length1(int, 205.89/127.61 all_103_2) = all_168_1) | ( ~ (all_168_1 = 0) & array_eq_sub1(int, 205.89/127.61 all_103_2, all_105_4, $sum(all_86_8, 1), all_86_13) = all_168_1) 205.89/127.61 (19) elts(int, all_103_2) = all_177_4 205.89/127.61 (20) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 205.89/127.61 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ (map_eq_sub1(v6, 205.89/127.61 v5, v4, v3, v2) = v1) | ~ (map_eq_sub1(v6, v5, v4, v3, v2) = v0)) 205.89/127.61 (21) ~ ($lesseq(all_86_7, all_219_1)) | ~ ($lesseq(0, all_219_1)) | ( ~ 205.89/127.61 (all_219_0 = all_219_1) & length1(int, all_105_2) = all_219_0) 205.89/127.61 (22) $lesseq(1, $difference(all_86_7, all_86_8)) 205.89/127.61 (23) $lesseq(0, all_86_11) 205.89/127.61 (24) elts(int, all_103_2) = all_103_1 205.89/127.61 (25) length1(int, all_103_2) = all_171_1 205.89/127.61 (26) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 205.89/127.61 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 205.89/127.61 (27) length1(int, all_103_2) = all_177_2 205.89/127.61 (28) length1(int, all_105_4) = all_219_1 205.89/127.61 (29) length1(int, all_105_2) = all_153_1 205.89/127.61 (30) elts(int, all_103_2) = all_156_3 205.89/127.61 (31) length1(int, all_103_2) = all_156_0 205.89/127.61 (32) ( ~ (all_191_0 = 0) & map_eq_sub1(int, all_191_3, all_191_2, 205.89/127.61 $sum(all_86_10, 1), all_191_1) = all_191_0 & length1(int, all_103_4) 205.89/127.61 = all_191_1) | ( ~ (all_191_1 = 0) & map_eq_sub1(int, all_191_3, 205.89/127.61 all_191_2, 0, all_86_11) = all_191_1) 205.89/127.61 205.89/127.61 Begin of proof 205.89/127.61 | 205.89/127.61 | BETA: splitting (12) gives: 205.89/127.61 | 205.89/127.61 | Case 1: 205.89/127.61 | | 205.89/127.61 | | (33) all_242_1 = 0 & array_eq_sub1(int, all_103_2, all_105_4, 205.89/127.61 | | $sum(all_86_8, 1), all_86_13) = 0 205.89/127.61 | | 205.89/127.61 | | ALPHA: (33) implies: 205.89/127.61 | | (34) array_eq_sub1(int, all_103_2, all_105_4, $sum(all_86_8, 1), 205.89/127.61 | | all_86_13) = 0 205.89/127.61 | | 205.89/127.61 | | BETA: splitting (18) gives: 205.89/127.61 | | 205.89/127.61 | | Case 1: 205.89/127.61 | | | 205.89/127.61 | | | (35) all_168_0 = all_168_1 & $lesseq(1, $difference(all_168_1, 205.89/127.61 | | | all_86_8)) & $lesseq(all_86_13, all_168_1) & $lesseq(-1, 205.89/127.61 | | | all_86_8) & $lesseq(0, all_86_13) & length1(int, all_105_4) = 205.89/127.61 | | | all_168_1 & length1(int, all_103_2) = all_168_1 205.89/127.61 | | | 205.89/127.61 | | | ALPHA: (35) implies: 205.89/127.61 | | | (36) length1(int, all_103_2) = all_168_1 205.89/127.61 | | | (37) length1(int, all_105_4) = all_168_1 205.89/127.61 | | | 205.89/127.61 | | | GROUND_INST: instantiating (26) with all_219_1, all_168_1, all_105_4, int, 205.89/127.61 | | | simplifying with (28), (37) gives: 205.89/127.61 | | | (38) all_219_1 = all_168_1 205.89/127.61 | | | 205.89/127.61 | | | GROUND_INST: instantiating (26) with all_219_1, all_153_1, all_105_4, int, 205.89/127.61 | | | simplifying with (4), (28) gives: 205.89/127.61 | | | (39) all_219_1 = all_153_1 205.89/127.61 | | | 205.89/127.61 | | | GROUND_INST: instantiating (26) with all_211_1, all_193_1, all_103_2, int, 205.89/127.61 | | | simplifying with (7), (8) gives: 205.89/127.61 | | | (40) all_211_1 = all_193_1 205.89/127.61 | | | 205.89/127.61 | | | GROUND_INST: instantiating (26) with all_193_1, all_177_2, all_103_2, int, 205.89/127.61 | | | simplifying with (8), (27) gives: 205.89/127.61 | | | (41) all_193_1 = all_177_2 205.89/127.61 | | | 205.89/127.61 | | | GROUND_INST: instantiating (26) with all_211_1, all_171_1, all_103_2, int, 205.89/127.61 | | | simplifying with (7), (25) gives: 205.89/127.61 | | | (42) all_211_1 = all_171_1 205.89/127.61 | | | 205.89/127.61 | | | GROUND_INST: instantiating (26) with all_86_13, all_168_1, all_103_2, int, 205.89/127.61 | | | simplifying with (2), (36) gives: 205.89/127.61 | | | (43) all_168_1 = all_86_13 205.89/127.61 | | | 205.89/127.61 | | | GROUND_INST: instantiating (26) with all_177_2, all_168_1, all_103_2, int, 205.89/127.61 | | | simplifying with (27), (36) gives: 205.89/127.61 | | | (44) all_177_2 = all_168_1 205.89/127.61 | | | 205.89/127.61 | | | GROUND_INST: instantiating (26) with all_177_2, all_156_0, all_103_2, int, 205.89/127.61 | | | simplifying with (27), (31) gives: 205.89/127.61 | | | (45) all_177_2 = all_156_0 205.89/127.61 | | | 205.89/127.61 | | | COMBINE_EQS: (38), (39) imply: 205.89/127.61 | | | (46) all_168_1 = all_153_1 205.89/127.61 | | | 205.89/127.61 | | | SIMP: (46) implies: 205.89/127.61 | | | (47) all_168_1 = all_153_1 205.89/127.61 | | | 205.89/127.61 | | | COMBINE_EQS: (40), (42) imply: 205.89/127.61 | | | (48) all_193_1 = all_171_1 205.89/127.61 | | | 205.89/127.61 | | | SIMP: (48) implies: 205.89/127.61 | | | (49) all_193_1 = all_171_1 205.89/127.61 | | | 205.89/127.61 | | | COMBINE_EQS: (41), (49) imply: 205.89/127.61 | | | (50) all_177_2 = all_171_1 205.89/127.61 | | | 205.89/127.61 | | | SIMP: (50) implies: 205.89/127.61 | | | (51) all_177_2 = all_171_1 205.89/127.61 | | | 205.89/127.61 | | | COMBINE_EQS: (45), (51) imply: 205.89/127.61 | | | (52) all_171_1 = all_156_0 205.89/127.61 | | | 205.89/127.61 | | | COMBINE_EQS: (44), (51) imply: 205.89/127.61 | | | (53) all_171_1 = all_168_1 205.89/127.61 | | | 205.89/127.61 | | | COMBINE_EQS: (52), (53) imply: 205.89/127.61 | | | (54) all_168_1 = all_156_0 205.89/127.61 | | | 205.89/127.61 | | | SIMP: (54) implies: 205.89/127.61 | | | (55) all_168_1 = all_156_0 205.89/127.61 | | | 205.89/127.61 | | | COMBINE_EQS: (47), (55) imply: 205.89/127.61 | | | (56) all_156_0 = all_153_1 205.89/127.61 | | | 205.89/127.61 | | | COMBINE_EQS: (43), (55) imply: 205.89/127.61 | | | (57) all_156_0 = all_86_13 205.89/127.61 | | | 205.89/127.61 | | | COMBINE_EQS: (56), (57) imply: 205.89/127.61 | | | (58) all_153_1 = all_86_13 205.89/127.61 | | | 205.89/127.61 | | | SIMP: (58) implies: 205.89/127.61 | | | (59) all_153_1 = all_86_13 205.89/127.61 | | | 205.89/127.61 | | | REF_CLOSE: (5), (13), (16), (17), (21), (22), (23), (26), (29), (39), (59) 205.89/127.61 | | | are inconsistent by sub-proof #58. 205.89/127.61 | | | 205.89/127.61 | | Case 2: 205.89/127.61 | | | 205.89/127.61 | | | (60) ~ (all_168_1 = 0) & array_eq_sub1(int, all_103_2, all_105_4, 205.89/127.61 | | | $sum(all_86_8, 1), all_86_13) = all_168_1 205.89/127.61 | | | 205.89/127.61 | | | REF_CLOSE: (9), (34), (60) are inconsistent by sub-proof #83. 205.89/127.61 | | | 205.89/127.61 | | End of split 205.89/127.61 | | 205.89/127.61 | Case 2: 205.89/127.61 | | 205.89/127.61 | | (61) length1(int, all_103_2) = all_242_1 & ( ~ ($lesseq(1, 205.89/127.61 | | $difference(all_242_1, all_86_8))) | ~ ($lesseq(all_86_13, 205.89/127.61 | | all_242_1)) | ( ~ (all_242_0 = all_242_1) & length1(int, 205.89/127.61 | | all_105_4) = all_242_0)) 205.89/127.61 | | 205.89/127.61 | | REF_CLOSE: (1), (2), (3), (6), (10), (11), (14), (15), (19), (20), (24), 205.89/127.61 | | (25), (26), (30), (32), (61) are inconsistent by sub-proof #50. 205.89/127.61 | | 205.89/127.61 | End of split 205.89/127.61 | 205.89/127.61 End of proof 205.89/127.61 205.89/127.61 Sub-proof #5 shows that the following formulas are inconsistent: 205.89/127.61 ---------------------------------------------------------------- 205.89/127.61 (1) length1(int, all_103_4) = all_86_13 205.89/127.61 (2) elts(int, all_105_2) = all_187_2 205.89/127.61 (3) length1(int, all_103_4) = all_193_1 205.89/127.61 (4) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 205.89/127.61 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ 205.89/127.61 (array_eq_sub1(v6, v5, v4, v3, v2) = v1) | ~ (array_eq_sub1(v6, v5, 205.89/127.61 v4, v3, v2) = v0)) 205.89/127.61 (5) elts(int, all_105_4) = all_187_3 205.89/127.61 (6) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 205.89/127.61 | ~ (elts(v3, v2) = v1) | ~ (elts(v3, v2) = v0)) 205.89/127.61 (7) length1(int, all_105_4) = all_86_13 205.89/127.61 (8) elts(int, all_105_4) = all_105_3 205.89/127.61 (9) map_eq_sub1(int, all_105_3, all_105_1, 0, all_86_7) = 0 205.89/127.61 (10) (all_169_0 = all_169_1 & $lesseq(all_86_7, all_169_1) & $lesseq(0, 205.89/127.61 all_169_1) & $lesseq(0, all_86_7) & length1(int, all_105_2) = 205.89/127.61 all_169_1 & length1(int, all_105_4) = all_169_1) | ( ~ (all_169_1 = 0) 205.89/127.61 & array_eq_sub1(int, all_105_4, all_105_2, 0, all_86_7) = all_169_1) 205.89/127.61 (11) (all_234_1 = 0 & array_eq_sub1(int, all_105_4, all_105_2, 205.89/127.61 $sum(all_86_10, 1), all_86_13) = 0) | (length1(int, all_105_4) = 205.89/127.61 all_234_1 & ( ~ ($lesseq(1, $difference(all_234_1, all_86_10))) | ~ 205.89/127.61 ($lesseq(all_86_13, all_234_1)) | ( ~ (all_234_0 = all_234_1) & 205.89/127.61 length1(int, all_105_2) = all_234_0))) 205.89/127.61 (12) array_eq_sub1(int, all_105_4, all_105_2, 0, all_86_7) = 0 205.89/127.61 (13) elts(int, all_105_2) = all_105_1 205.89/127.61 (14) $lesseq(1, $difference(all_193_1, all_86_10)) 205.89/127.61 (15) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 205.89/127.61 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ (map_eq_sub1(v6, 205.89/127.61 v5, v4, v3, v2) = v1) | ~ (map_eq_sub1(v6, v5, v4, v3, v2) = v0)) 205.89/127.61 (16) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 205.89/127.61 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 205.89/127.61 (17) (all_153_0 = all_153_1 & $lesseq(1, $difference(all_153_1, all_86_10)) & 205.89/127.61 $lesseq(all_86_13, all_153_1) & $lesseq(-1, all_86_10) & $lesseq(0, 205.89/127.61 all_86_13) & length1(int, all_105_2) = all_153_1 & length1(int, 205.89/127.61 all_105_4) = all_153_1) | ( ~ (all_153_1 = 0) & array_eq_sub1(int, 205.89/127.61 all_105_4, all_105_2, $sum(all_86_10, 1), all_86_13) = all_153_1) 205.89/127.61 (18) ( ~ (all_187_0 = 0) & map_eq_sub1(int, all_187_3, all_187_2, 205.89/127.61 $sum(all_86_10, 1), all_187_1) = all_187_0 & length1(int, all_105_4) 205.89/127.61 = all_187_1) | ( ~ (all_187_1 = 0) & map_eq_sub1(int, all_187_3, 205.89/127.61 all_187_2, 0, all_86_7) = all_187_1) 205.89/127.61 (19) map_eq_sub1(int, all_105_3, all_105_1, $sum(all_86_10, 1), all_86_13) = 205.89/127.61 0 205.89/127.61 205.89/127.61 Begin of proof 205.89/127.61 | 205.89/127.61 | BETA: splitting (10) gives: 205.89/127.61 | 205.89/127.61 | Case 1: 205.89/127.61 | | 205.89/127.61 | | (20) all_169_0 = all_169_1 & $lesseq(all_86_7, all_169_1) & $lesseq(0, 205.89/127.61 | | all_169_1) & $lesseq(0, all_86_7) & length1(int, all_105_2) = 205.89/127.61 | | all_169_1 & length1(int, all_105_4) = all_169_1 205.89/127.61 | | 205.89/127.61 | | ALPHA: (20) implies: 205.89/127.61 | | (21) length1(int, all_105_4) = all_169_1 205.89/127.61 | | (22) length1(int, all_105_2) = all_169_1 205.89/127.61 | | 205.89/127.61 | | BETA: splitting (11) gives: 205.89/127.61 | | 205.89/127.61 | | Case 1: 205.89/127.61 | | | 205.89/127.62 | | | (23) all_234_1 = 0 & array_eq_sub1(int, all_105_4, all_105_2, 205.89/127.62 | | | $sum(all_86_10, 1), all_86_13) = 0 205.89/127.62 | | | 205.89/127.62 | | | ALPHA: (23) implies: 205.89/127.62 | | | (24) array_eq_sub1(int, all_105_4, all_105_2, $sum(all_86_10, 1), 205.89/127.62 | | | all_86_13) = 0 205.89/127.62 | | | 205.89/127.62 | | | REF_CLOSE: (2), (4), (5), (6), (7), (8), (9), (13), (15), (16), (17), 205.89/127.62 | | | (18), (19), (21), (24) are inconsistent by sub-proof #6. 205.89/127.62 | | | 205.89/127.62 | | Case 2: 205.89/127.62 | | | 205.89/127.62 | | | (25) length1(int, all_105_4) = all_234_1 & ( ~ ($lesseq(1, 205.89/127.62 | | | $difference(all_234_1, all_86_10))) | ~ ($lesseq(all_86_13, 205.89/127.62 | | | all_234_1)) | ( ~ (all_234_0 = all_234_1) & length1(int, 205.89/127.62 | | | all_105_2) = all_234_0)) 205.89/127.62 | | | 205.89/127.62 | | | ALPHA: (25) implies: 205.89/127.62 | | | (26) length1(int, all_105_4) = all_234_1 205.89/127.62 | | | (27) ~ ($lesseq(1, $difference(all_234_1, all_86_10))) | ~ 205.89/127.62 | | | ($lesseq(all_86_13, all_234_1)) | ( ~ (all_234_0 = all_234_1) & 205.89/127.62 | | | length1(int, all_105_2) = all_234_0) 205.89/127.62 | | | 205.89/127.62 | | | REF_CLOSE: (1), (3), (7), (14), (16), (21), (22), (26), (27) are 205.89/127.62 | | | inconsistent by sub-proof #30. 205.89/127.62 | | | 205.89/127.62 | | End of split 205.89/127.62 | | 205.89/127.62 | Case 2: 205.89/127.62 | | 205.89/127.62 | | (28) ~ (all_169_1 = 0) & array_eq_sub1(int, all_105_4, all_105_2, 0, 205.89/127.62 | | all_86_7) = all_169_1 205.89/127.62 | | 205.89/127.62 | | REF_CLOSE: (4), (12), (28) are inconsistent by sub-proof #75. 205.89/127.62 | | 205.89/127.62 | End of split 205.89/127.62 | 205.89/127.62 End of proof 205.89/127.62 205.89/127.62 Sub-proof #6 shows that the following formulas are inconsistent: 205.89/127.62 ---------------------------------------------------------------- 205.89/127.62 (1) array_eq_sub1(int, all_105_4, all_105_2, $sum(all_86_10, 1), all_86_13) = 205.89/127.62 0 205.89/127.62 (2) elts(int, all_105_2) = all_187_2 205.89/127.62 (3) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 205.89/127.62 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ 205.89/127.62 (array_eq_sub1(v6, v5, v4, v3, v2) = v1) | ~ (array_eq_sub1(v6, v5, 205.89/127.62 v4, v3, v2) = v0)) 205.89/127.62 (4) elts(int, all_105_4) = all_187_3 205.89/127.62 (5) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 205.89/127.62 | ~ (elts(v3, v2) = v1) | ~ (elts(v3, v2) = v0)) 205.89/127.62 (6) length1(int, all_105_4) = all_86_13 205.89/127.62 (7) elts(int, all_105_4) = all_105_3 205.89/127.62 (8) map_eq_sub1(int, all_105_3, all_105_1, 0, all_86_7) = 0 205.89/127.62 (9) elts(int, all_105_2) = all_105_1 205.89/127.62 (10) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 205.89/127.62 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ (map_eq_sub1(v6, 205.89/127.62 v5, v4, v3, v2) = v1) | ~ (map_eq_sub1(v6, v5, v4, v3, v2) = v0)) 205.89/127.62 (11) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 205.89/127.62 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 205.89/127.62 (12) (all_153_0 = all_153_1 & $lesseq(1, $difference(all_153_1, all_86_10)) & 205.89/127.62 $lesseq(all_86_13, all_153_1) & $lesseq(-1, all_86_10) & $lesseq(0, 205.89/127.62 all_86_13) & length1(int, all_105_2) = all_153_1 & length1(int, 205.89/127.62 all_105_4) = all_153_1) | ( ~ (all_153_1 = 0) & array_eq_sub1(int, 205.89/127.62 all_105_4, all_105_2, $sum(all_86_10, 1), all_86_13) = all_153_1) 205.89/127.62 (13) ( ~ (all_187_0 = 0) & map_eq_sub1(int, all_187_3, all_187_2, 205.89/127.62 $sum(all_86_10, 1), all_187_1) = all_187_0 & length1(int, all_105_4) 205.89/127.62 = all_187_1) | ( ~ (all_187_1 = 0) & map_eq_sub1(int, all_187_3, 205.89/127.62 all_187_2, 0, all_86_7) = all_187_1) 205.89/127.62 (14) map_eq_sub1(int, all_105_3, all_105_1, $sum(all_86_10, 1), all_86_13) = 205.89/127.62 0 205.89/127.62 (15) length1(int, all_105_4) = all_169_1 205.89/127.62 205.89/127.62 Begin of proof 205.89/127.62 | 205.89/127.62 | BETA: splitting (12) gives: 205.89/127.62 | 205.89/127.62 | Case 1: 205.89/127.62 | | 205.89/127.62 | | (16) all_153_0 = all_153_1 & $lesseq(1, $difference(all_153_1, 205.89/127.62 | | all_86_10)) & $lesseq(all_86_13, all_153_1) & $lesseq(-1, 205.89/127.62 | | all_86_10) & $lesseq(0, all_86_13) & length1(int, all_105_2) = 205.89/127.62 | | all_153_1 & length1(int, all_105_4) = all_153_1 205.89/127.62 | | 205.89/127.62 | | ALPHA: (16) implies: 205.89/127.62 | | (17) length1(int, all_105_4) = all_153_1 205.89/127.62 | | 205.89/127.62 | | GROUND_INST: instantiating (11) with all_86_13, all_169_1, all_105_4, int, 205.89/127.62 | | simplifying with (6), (15) gives: 205.89/127.62 | | (18) all_169_1 = all_86_13 205.89/127.62 | | 205.89/127.62 | | GROUND_INST: instantiating (11) with all_169_1, all_153_1, all_105_4, int, 205.89/127.62 | | simplifying with (15), (17) gives: 205.89/127.62 | | (19) all_169_1 = all_153_1 205.89/127.62 | | 205.89/127.62 | | GROUND_INST: instantiating (5) with all_105_1, all_187_2, all_105_2, int, 205.89/127.62 | | simplifying with (2), (9) gives: 205.89/127.62 | | (20) all_187_2 = all_105_1 205.89/127.62 | | 205.89/127.62 | | GROUND_INST: instantiating (5) with all_105_3, all_187_3, all_105_4, int, 205.89/127.62 | | simplifying with (4), (7) gives: 205.89/127.62 | | (21) all_187_3 = all_105_3 205.89/127.62 | | 205.89/127.62 | | COMBINE_EQS: (18), (19) imply: 205.89/127.62 | | (22) all_153_1 = all_86_13 205.89/127.62 | | 205.89/127.62 | | SIMP: (22) implies: 205.89/127.62 | | (23) all_153_1 = all_86_13 205.89/127.62 | | 205.89/127.62 | | REF_CLOSE: (6), (8), (10), (11), (13), (14), (20), (21) are inconsistent by 205.89/127.62 | | sub-proof #66. 205.89/127.62 | | 205.89/127.62 | Case 2: 205.89/127.62 | | 205.89/127.62 | | (24) ~ (all_153_1 = 0) & array_eq_sub1(int, all_105_4, all_105_2, 205.89/127.62 | | $sum(all_86_10, 1), all_86_13) = all_153_1 205.89/127.62 | | 205.89/127.62 | | REF_CLOSE: (1), (3), (24) are inconsistent by sub-proof #54. 205.89/127.62 | | 205.89/127.62 | End of split 205.89/127.62 | 205.89/127.62 End of proof 205.89/127.62 205.89/127.62 Sub-proof #7 shows that the following formulas are inconsistent: 205.89/127.62 ---------------------------------------------------------------- 205.89/127.62 (1) length1(int, all_105_4) = all_153_1 205.89/127.62 (2) all_153_1 = all_86_13 205.89/127.62 (3) $lesseq(1, $difference(all_153_1, all_86_10)) 205.89/127.62 (4) $lesseq(all_86_11, all_86_8) 205.89/127.62 (5) $lesseq(all_86_7, all_86_10) 205.89/127.62 (6) all_211_1 = all_86_13 205.89/127.62 (7) $lesseq(1, $difference(all_86_7, all_86_8)) 205.89/127.62 (8) $lesseq(0, all_86_11) 205.89/127.62 (9) ~ ($lesseq(all_86_11, all_211_1)) | ~ ($lesseq(0, all_211_1)) | ( ~ 205.89/127.62 (all_211_0 = all_211_1) & length1(int, all_105_4) = all_211_0) 205.89/127.62 (10) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 205.89/127.62 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 205.89/127.62 205.89/127.62 Begin of proof 205.89/127.62 | 205.89/127.62 | REDUCE: (2), (3) imply: 205.89/127.62 | (11) $lesseq(1, $difference(all_86_13, all_86_10)) 205.89/127.62 | 205.89/127.62 | REDUCE: (1), (2) imply: 205.89/127.62 | (12) length1(int, all_105_4) = all_86_13 205.89/127.62 | 205.89/127.62 | BETA: splitting (9) gives: 205.89/127.62 | 205.89/127.62 | Case 1: 205.89/127.62 | | 205.89/127.62 | | (13) $lesseq(all_211_1, -1) 205.89/127.62 | | 205.89/127.62 | | REDUCE: (6), (13) imply: 205.89/127.62 | | (14) $lesseq(all_86_13, -1) 205.89/127.62 | | 205.89/127.62 | | REF_CLOSE: (4), (5), (7), (8), (11), (14) are inconsistent by sub-proof #80. 205.89/127.62 | | 205.89/127.62 | Case 2: 205.89/127.62 | | 205.89/127.62 | | (15) ~ ($lesseq(all_86_11, all_211_1)) | ( ~ (all_211_0 = all_211_1) & 205.89/127.62 | | length1(int, all_105_4) = all_211_0) 205.89/127.62 | | 205.89/127.62 | | REF_CLOSE: (4), (5), (6), (7), (10), (11), (12), (15) are inconsistent by 205.89/127.62 | | sub-proof #9. 205.89/127.62 | | 205.89/127.62 | End of split 205.89/127.62 | 205.89/127.62 End of proof 205.89/127.62 205.89/127.62 Sub-proof #8 shows that the following formulas are inconsistent: 205.89/127.62 ---------------------------------------------------------------- 205.89/127.62 (1) length1(int, all_103_2) = all_86_13 205.89/127.62 (2) length1(int, all_105_4) = all_153_1 205.89/127.62 (3) length1(int, all_103_2) = all_211_1 205.89/127.62 (4) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 205.89/127.62 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ 205.89/127.62 (array_eq_sub1(v6, v5, v4, v3, v2) = v1) | ~ (array_eq_sub1(v6, v5, 205.89/127.62 v4, v3, v2) = v0)) 205.89/127.62 (5) length1(int, all_105_4) = all_86_13 205.89/127.62 (6) $lesseq(1, $difference(all_153_1, all_86_10)) 205.89/127.62 (7) $lesseq(all_86_11, all_86_8) 205.89/127.62 (8) $lesseq(all_86_7, all_86_10) 205.89/127.62 (9) (all_168_0 = all_168_1 & $lesseq(1, $difference(all_168_1, all_86_8)) & 205.89/127.62 $lesseq(all_86_13, all_168_1) & $lesseq(-1, all_86_8) & $lesseq(0, 205.89/127.62 all_86_13) & length1(int, all_105_4) = all_168_1 & length1(int, 205.89/127.62 all_103_2) = all_168_1) | ( ~ (all_168_1 = 0) & array_eq_sub1(int, 205.89/127.62 all_103_2, all_105_4, $sum(all_86_8, 1), all_86_13) = all_168_1) 205.89/127.62 (10) length1(int, all_105_4) = all_190_2 205.89/127.62 (11) $lesseq(1, $difference(all_86_7, all_86_8)) 205.89/127.62 (12) $lesseq(0, all_86_11) 205.89/127.62 (13) ~ ($lesseq(all_86_11, all_211_1)) | ~ ($lesseq(0, all_211_1)) | ( ~ 205.89/127.62 (all_211_0 = all_211_1) & length1(int, all_105_4) = all_211_0) 205.89/127.62 (14) array_eq_sub1(int, all_103_2, all_105_4, $sum(all_86_8, 1), all_86_13) = 205.89/127.62 0 205.89/127.62 (15) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 205.89/127.62 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 205.89/127.62 (16) length1(int, all_103_2) = all_177_2 205.89/127.62 (17) length1(int, all_105_4) = all_169_1 205.89/127.62 205.89/127.62 Begin of proof 205.89/127.62 | 205.89/127.62 | BETA: splitting (9) gives: 205.89/127.62 | 205.89/127.62 | Case 1: 205.89/127.62 | | 205.89/127.62 | | (18) all_168_0 = all_168_1 & $lesseq(1, $difference(all_168_1, all_86_8)) 205.89/127.62 | | & $lesseq(all_86_13, all_168_1) & $lesseq(-1, all_86_8) & $lesseq(0, 205.89/127.62 | | all_86_13) & length1(int, all_105_4) = all_168_1 & length1(int, 205.89/127.62 | | all_103_2) = all_168_1 205.89/127.62 | | 205.89/127.62 | | ALPHA: (18) implies: 205.89/127.62 | | (19) length1(int, all_105_4) = all_168_1 205.89/127.62 | | 205.89/127.62 | | GROUND_INST: instantiating (15) with all_86_13, all_190_2, all_105_4, int, 205.89/127.62 | | simplifying with (5), (10) gives: 205.89/127.62 | | (20) all_190_2 = all_86_13 205.89/127.62 | | 205.89/127.62 | | GROUND_INST: instantiating (15) with all_190_2, all_169_1, all_105_4, int, 205.89/127.62 | | simplifying with (10), (17) gives: 205.89/127.62 | | (21) all_190_2 = all_169_1 205.89/127.62 | | 205.89/127.62 | | GROUND_INST: instantiating (15) with all_190_2, all_168_1, all_105_4, int, 205.89/127.62 | | simplifying with (10), (19) gives: 205.89/127.62 | | (22) all_190_2 = all_168_1 205.89/127.62 | | 205.89/127.62 | | GROUND_INST: instantiating (15) with all_168_1, all_153_1, all_105_4, int, 205.89/127.62 | | simplifying with (2), (19) gives: 205.89/127.62 | | (23) all_168_1 = all_153_1 205.89/127.62 | | 205.89/127.62 | | GROUND_INST: instantiating (15) with all_86_13, all_211_1, all_103_2, int, 205.89/127.62 | | simplifying with (1), (3) gives: 205.89/127.62 | | (24) all_211_1 = all_86_13 205.89/127.62 | | 205.89/127.63 | | GROUND_INST: instantiating (15) with all_211_1, all_177_2, all_103_2, int, 205.89/127.63 | | simplifying with (3), (16) gives: 205.89/127.63 | | (25) all_211_1 = all_177_2 205.89/127.63 | | 205.89/127.63 | | COMBINE_EQS: (24), (25) imply: 205.89/127.63 | | (26) all_177_2 = all_86_13 205.89/127.63 | | 205.89/127.63 | | COMBINE_EQS: (21), (22) imply: 205.89/127.63 | | (27) all_169_1 = all_168_1 205.89/127.63 | | 205.89/127.63 | | COMBINE_EQS: (20), (21) imply: 205.89/127.63 | | (28) all_169_1 = all_86_13 205.89/127.63 | | 205.89/127.63 | | COMBINE_EQS: (27), (28) imply: 205.89/127.63 | | (29) all_168_1 = all_86_13 205.89/127.63 | | 205.89/127.63 | | SIMP: (29) implies: 205.89/127.63 | | (30) all_168_1 = all_86_13 205.89/127.63 | | 205.89/127.63 | | COMBINE_EQS: (23), (30) imply: 205.89/127.63 | | (31) all_153_1 = all_86_13 205.89/127.63 | | 205.89/127.63 | | SIMP: (31) implies: 205.89/127.63 | | (32) all_153_1 = all_86_13 205.89/127.63 | | 205.89/127.63 | | REDUCE: (6), (32) imply: 205.89/127.63 | | (33) $lesseq(1, $difference(all_86_13, all_86_10)) 205.89/127.63 | | 205.89/127.63 | | BETA: splitting (13) gives: 205.89/127.63 | | 205.89/127.63 | | Case 1: 205.89/127.63 | | | 205.89/127.63 | | | (34) $lesseq(all_211_1, -1) 205.89/127.63 | | | 205.89/127.63 | | | REDUCE: (24), (34) imply: 205.89/127.63 | | | (35) $lesseq(all_86_13, -1) 205.89/127.63 | | | 205.89/127.63 | | | REF_CLOSE: (7), (8), (11), (12), (33), (35) are inconsistent by sub-proof 205.89/127.63 | | | #80. 205.89/127.63 | | | 205.89/127.63 | | Case 2: 205.89/127.63 | | | 205.89/127.63 | | | (36) ~ ($lesseq(all_86_11, all_211_1)) | ( ~ (all_211_0 = all_211_1) & 205.89/127.63 | | | length1(int, all_105_4) = all_211_0) 205.89/127.63 | | | 205.89/127.63 | | | REF_CLOSE: (5), (7), (8), (11), (15), (24), (33), (36) are inconsistent by 205.89/127.63 | | | sub-proof #9. 205.89/127.63 | | | 205.89/127.63 | | End of split 205.89/127.63 | | 205.89/127.63 | Case 2: 205.89/127.63 | | 205.89/127.63 | | (37) ~ (all_168_1 = 0) & array_eq_sub1(int, all_103_2, all_105_4, 205.89/127.63 | | $sum(all_86_8, 1), all_86_13) = all_168_1 205.89/127.63 | | 205.89/127.63 | | REF_CLOSE: (4), (14), (37) are inconsistent by sub-proof #83. 205.89/127.63 | | 205.89/127.63 | End of split 205.89/127.63 | 205.89/127.63 End of proof 205.89/127.63 205.89/127.63 Sub-proof #9 shows that the following formulas are inconsistent: 205.89/127.63 ---------------------------------------------------------------- 205.89/127.63 (1) length1(int, all_105_4) = all_86_13 205.89/127.63 (2) $lesseq(all_86_11, all_86_8) 205.89/127.63 (3) $lesseq(all_86_7, all_86_10) 205.89/127.63 (4) all_211_1 = all_86_13 205.89/127.63 (5) $lesseq(1, $difference(all_86_7, all_86_8)) 205.89/127.63 (6) $lesseq(1, $difference(all_86_13, all_86_10)) 205.89/127.63 (7) ~ ($lesseq(all_86_11, all_211_1)) | ( ~ (all_211_0 = all_211_1) & 205.89/127.63 length1(int, all_105_4) = all_211_0) 205.89/127.63 (8) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 205.89/127.63 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 205.89/127.63 205.89/127.63 Begin of proof 205.89/127.63 | 205.89/127.63 | BETA: splitting (7) gives: 205.89/127.63 | 205.89/127.63 | Case 1: 205.89/127.63 | | 205.89/127.63 | | (9) $lesseq(1, $difference(all_86_11, all_211_1)) 205.89/127.63 | | 205.89/127.63 | | REDUCE: (4), (9) imply: 205.89/127.63 | | (10) $lesseq(1, $difference(all_86_11, all_86_13)) 205.89/127.63 | | 205.89/127.63 | | REF_CLOSE: (2), (3), (5), (6), (10) are inconsistent by sub-proof #79. 205.89/127.63 | | 205.89/127.63 | Case 2: 205.89/127.63 | | 205.89/127.63 | | (11) ~ (all_211_0 = all_211_1) & length1(int, all_105_4) = all_211_0 205.89/127.63 | | 205.89/127.63 | | ALPHA: (11) implies: 205.89/127.63 | | (12) ~ (all_211_0 = all_211_1) 205.89/127.63 | | (13) length1(int, all_105_4) = all_211_0 205.89/127.63 | | 205.89/127.63 | | REDUCE: (4), (12) imply: 205.89/127.63 | | (14) ~ (all_211_0 = all_86_13) 205.89/127.63 | | 205.89/127.63 | | GROUND_INST: instantiating (8) with all_86_13, all_211_0, all_105_4, int, 205.89/127.63 | | simplifying with (1), (13) gives: 205.89/127.63 | | (15) all_211_0 = all_86_13 205.89/127.63 | | 205.89/127.63 | | REDUCE: (14), (15) imply: 205.89/127.63 | | (16) ~ (0 = 0) 205.89/127.63 | | 205.89/127.63 | | CLOSE: (16) is inconsistent. 205.89/127.63 | | 205.89/127.63 | End of split 205.89/127.63 | 205.89/127.63 End of proof 205.89/127.63 205.89/127.63 Sub-proof #10 shows that the following formulas are inconsistent: 205.89/127.63 ---------------------------------------------------------------- 205.89/127.63 (1) length1(int, all_103_2) = all_86_13 205.89/127.63 (2) elts(int, all_103_4) = all_103_3 205.89/127.63 (3) length1(int, all_103_4) = all_86_13 205.89/127.63 (4) elts(int, all_105_4) = all_181_2 & elts(int, all_103_2) = all_181_3 & 205.89/127.63 in_uni(all_181_2) & in_uni(all_181_3) & (( ~ (all_181_0 = 0) & 205.89/127.63 map_eq_sub1(int, all_181_3, all_181_2, $sum(all_86_8, 1), all_181_1) 205.89/127.63 = all_181_0 & length1(int, all_103_2) = all_181_1) | ( ~ (all_181_1 = 205.89/127.63 0) & map_eq_sub1(int, all_181_3, all_181_2, 0, all_86_11) = 205.89/127.63 all_181_1)) 205.89/127.63 (5) map_eq_sub1(int, all_103_3, all_103_1, $sum(all_86_10, 1), all_86_13) = 0 205.89/127.63 (6) length1(int, all_103_4) = all_215_1 205.89/127.63 (7) map_eq_sub1(int, all_103_1, all_105_3, $sum(all_86_8, 1), all_86_13) = 0 205.89/127.63 (8) (all_192_0 = 0 & all_192_1 = 0 & map_eq_sub1(int, all_192_4, all_192_3, 205.89/127.63 $sum(all_86_10, 1), all_192_2) = 0 & map_eq_sub1(int, all_192_4, 205.89/127.63 all_192_3, 0, all_86_11) = 0 & length1(int, all_103_4) = all_192_2 & 205.89/127.63 elts(int, all_103_2) = all_192_3 & elts(int, all_103_4) = all_192_4 & 205.89/127.63 in_uni(all_192_3) & in_uni(all_192_4)) | ( ~ (all_192_4 = 0) & 205.89/127.63 permut_sub2(int, all_103_4, all_103_2, all_86_11, $sum(all_86_10, 1)) = 205.89/127.63 all_192_4) 205.89/127.63 (9) elts(int, all_105_4) = all_187_3 205.89/127.63 (10) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 205.89/127.63 | ~ (elts(v3, v2) = v1) | ~ (elts(v3, v2) = v0)) 205.89/127.63 (11) elts(int, all_105_4) = all_105_3 205.89/127.63 (12) elts(int, all_105_4) = all_156_1 205.89/127.63 (13) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 205.89/127.63 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ (permut_sub2(v6, 205.89/127.63 v5, v4, v3, v2) = v1) | ~ (permut_sub2(v6, v5, v4, v3, v2) = v0)) 205.89/127.63 (14) length1(int, all_103_4) = all_238_1 205.89/127.63 (15) map_eq_sub1(int, all_103_3, all_103_1, 0, all_86_11) = 0 205.89/127.63 (16) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 205.89/127.63 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ (map_eq_sub1(v6, 205.89/127.63 v5, v4, v3, v2) = v1) | ~ (map_eq_sub1(v6, v5, v4, v3, v2) = v0)) 205.89/127.63 (17) map_eq_sub1(int, all_156_3, all_156_1, 0, all_86_11) = 0 205.89/127.63 (18) elts(int, all_103_2) = all_103_1 205.89/127.63 (19) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 205.89/127.63 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 205.89/127.63 (20) (all_191_3 = 0 & permut_sub2(int, all_103_4, all_103_2, all_86_11, 205.89/127.63 $sum(all_86_10, 1)) = 0) | (elts(int, all_103_2) = all_191_2 & 205.89/127.63 elts(int, all_103_4) = all_191_3 & in_uni(all_191_2) & 205.89/127.63 in_uni(all_191_3) & (( ~ (all_191_0 = 0) & map_eq_sub1(int, all_191_3, 205.89/127.63 all_191_2, $sum(all_86_10, 1), all_191_1) = all_191_0 & 205.89/127.63 length1(int, all_103_4) = all_191_1) | ( ~ (all_191_1 = 0) & 205.89/127.63 map_eq_sub1(int, all_191_3, all_191_2, 0, all_86_11) = 205.89/127.63 all_191_1))) 205.89/127.63 (21) elts(int, all_103_2) = all_156_3 205.89/127.63 (22) length1(int, all_103_2) = all_156_0 205.89/127.63 205.89/127.63 Begin of proof 205.89/127.63 | 205.89/127.63 | ALPHA: (4) implies: 205.89/127.63 | (23) elts(int, all_103_2) = all_181_3 205.89/127.63 | (24) elts(int, all_105_4) = all_181_2 205.89/127.63 | (25) ( ~ (all_181_0 = 0) & map_eq_sub1(int, all_181_3, all_181_2, 205.89/127.63 | $sum(all_86_8, 1), all_181_1) = all_181_0 & length1(int, 205.89/127.63 | all_103_2) = all_181_1) | ( ~ (all_181_1 = 0) & map_eq_sub1(int, 205.89/127.63 | all_181_3, all_181_2, 0, all_86_11) = all_181_1) 205.89/127.63 | 205.89/127.63 | BETA: splitting (20) gives: 205.89/127.63 | 205.89/127.63 | Case 1: 205.89/127.63 | | 205.89/127.63 | | (26) all_191_3 = 0 & permut_sub2(int, all_103_4, all_103_2, all_86_11, 205.89/127.63 | | $sum(all_86_10, 1)) = 0 205.89/127.63 | | 205.89/127.63 | | ALPHA: (26) implies: 205.89/127.63 | | (27) permut_sub2(int, all_103_4, all_103_2, all_86_11, $sum(all_86_10, 205.89/127.63 | | 1)) = 0 205.89/127.63 | | 205.89/127.63 | | REF_CLOSE: (1), (7), (8), (9), (10), (11), (12), (13), (16), (17), (18), 205.89/127.63 | | (19), (21), (22), (23), (24), (25), (27) are inconsistent by 205.89/127.63 | | sub-proof #11. 205.89/127.63 | | 205.89/127.63 | Case 2: 205.89/127.63 | | 205.89/127.63 | | (28) elts(int, all_103_2) = all_191_2 & elts(int, all_103_4) = all_191_3 205.89/127.63 | | & in_uni(all_191_2) & in_uni(all_191_3) & (( ~ (all_191_0 = 0) & 205.89/127.63 | | map_eq_sub1(int, all_191_3, all_191_2, $sum(all_86_10, 1), 205.89/127.63 | | all_191_1) = all_191_0 & length1(int, all_103_4) = all_191_1) 205.89/127.63 | | | ( ~ (all_191_1 = 0) & map_eq_sub1(int, all_191_3, all_191_2, 0, 205.89/127.63 | | all_86_11) = all_191_1)) 205.89/127.63 | | 205.89/127.63 | | ALPHA: (28) implies: 205.89/127.63 | | (29) elts(int, all_103_4) = all_191_3 205.89/127.63 | | (30) elts(int, all_103_2) = all_191_2 205.89/127.63 | | (31) ( ~ (all_191_0 = 0) & map_eq_sub1(int, all_191_3, all_191_2, 205.89/127.63 | | $sum(all_86_10, 1), all_191_1) = all_191_0 & length1(int, 205.89/127.63 | | all_103_4) = all_191_1) | ( ~ (all_191_1 = 0) & map_eq_sub1(int, 205.89/127.63 | | all_191_3, all_191_2, 0, all_86_11) = all_191_1) 205.89/127.63 | | 205.89/127.63 | | REF_CLOSE: (2), (3), (5), (6), (10), (14), (15), (16), (18), (19), (29), 205.89/127.63 | | (30), (31) are inconsistent by sub-proof #16. 205.89/127.63 | | 205.89/127.63 | End of split 205.89/127.63 | 205.89/127.63 End of proof 205.89/127.63 205.89/127.63 Sub-proof #11 shows that the following formulas are inconsistent: 205.89/127.63 ---------------------------------------------------------------- 205.89/127.63 (1) length1(int, all_103_2) = all_86_13 205.89/127.63 (2) map_eq_sub1(int, all_103_1, all_105_3, $sum(all_86_8, 1), all_86_13) = 0 205.89/127.63 (3) ( ~ (all_181_0 = 0) & map_eq_sub1(int, all_181_3, all_181_2, 205.89/127.63 $sum(all_86_8, 1), all_181_1) = all_181_0 & length1(int, all_103_2) = 205.89/127.63 all_181_1) | ( ~ (all_181_1 = 0) & map_eq_sub1(int, all_181_3, 205.89/127.63 all_181_2, 0, all_86_11) = all_181_1) 205.89/127.63 (4) (all_192_0 = 0 & all_192_1 = 0 & map_eq_sub1(int, all_192_4, all_192_3, 205.89/127.63 $sum(all_86_10, 1), all_192_2) = 0 & map_eq_sub1(int, all_192_4, 205.89/127.63 all_192_3, 0, all_86_11) = 0 & length1(int, all_103_4) = all_192_2 & 205.89/127.63 elts(int, all_103_2) = all_192_3 & elts(int, all_103_4) = all_192_4 & 205.89/127.63 in_uni(all_192_3) & in_uni(all_192_4)) | ( ~ (all_192_4 = 0) & 205.89/127.63 permut_sub2(int, all_103_4, all_103_2, all_86_11, $sum(all_86_10, 1)) = 205.89/127.63 all_192_4) 206.14/127.64 (5) elts(int, all_105_4) = all_187_3 206.14/127.64 (6) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 206.14/127.64 | ~ (elts(v3, v2) = v1) | ~ (elts(v3, v2) = v0)) 206.14/127.64 (7) elts(int, all_105_4) = all_105_3 206.14/127.64 (8) elts(int, all_105_4) = all_156_1 206.14/127.64 (9) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.14/127.64 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ (permut_sub2(v6, 206.14/127.64 v5, v4, v3, v2) = v1) | ~ (permut_sub2(v6, v5, v4, v3, v2) = v0)) 206.14/127.64 (10) elts(int, all_103_2) = all_181_3 206.14/127.64 (11) elts(int, all_105_4) = all_181_2 206.14/127.64 (12) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.14/127.64 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ (map_eq_sub1(v6, 206.14/127.64 v5, v4, v3, v2) = v1) | ~ (map_eq_sub1(v6, v5, v4, v3, v2) = v0)) 206.14/127.64 (13) map_eq_sub1(int, all_156_3, all_156_1, 0, all_86_11) = 0 206.14/127.64 (14) permut_sub2(int, all_103_4, all_103_2, all_86_11, $sum(all_86_10, 1)) = 206.14/127.64 0 206.14/127.64 (15) elts(int, all_103_2) = all_103_1 206.14/127.64 (16) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 206.14/127.64 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 206.14/127.64 (17) elts(int, all_103_2) = all_156_3 206.14/127.64 (18) length1(int, all_103_2) = all_156_0 206.14/127.64 206.14/127.64 Begin of proof 206.14/127.64 | 206.14/127.64 | BETA: splitting (4) gives: 206.14/127.64 | 206.14/127.64 | Case 1: 206.14/127.64 | | 206.14/127.64 | | (19) all_192_0 = 0 & all_192_1 = 0 & map_eq_sub1(int, all_192_4, 206.14/127.64 | | all_192_3, $sum(all_86_10, 1), all_192_2) = 0 & map_eq_sub1(int, 206.14/127.64 | | all_192_4, all_192_3, 0, all_86_11) = 0 & length1(int, all_103_4) 206.14/127.64 | | = all_192_2 & elts(int, all_103_2) = all_192_3 & elts(int, 206.14/127.64 | | all_103_4) = all_192_4 & in_uni(all_192_3) & in_uni(all_192_4) 206.14/127.64 | | 206.14/127.64 | | ALPHA: (19) implies: 206.14/127.64 | | (20) elts(int, all_103_2) = all_192_3 206.14/127.64 | | 206.14/127.64 | | GROUND_INST: instantiating (16) with all_86_13, all_156_0, all_103_2, int, 206.14/127.64 | | simplifying with (1), (18) gives: 206.14/127.64 | | (21) all_156_0 = all_86_13 206.14/127.64 | | 206.14/127.64 | | GROUND_INST: instantiating (6) with all_105_3, all_181_2, all_105_4, int, 206.14/127.64 | | simplifying with (7), (11) gives: 206.14/127.64 | | (22) all_181_2 = all_105_3 206.14/127.64 | | 206.14/127.64 | | GROUND_INST: instantiating (6) with all_187_3, all_181_2, all_105_4, int, 206.14/127.64 | | simplifying with (5), (11) gives: 206.14/127.64 | | (23) all_187_3 = all_181_2 206.14/127.64 | | 206.14/127.64 | | GROUND_INST: instantiating (6) with all_187_3, all_156_1, all_105_4, int, 206.14/127.64 | | simplifying with (5), (8) gives: 206.14/127.64 | | (24) all_187_3 = all_156_1 206.14/127.64 | | 206.14/127.64 | | GROUND_INST: instantiating (6) with all_103_1, all_181_3, all_103_2, int, 206.14/127.64 | | simplifying with (10), (15) gives: 206.14/127.64 | | (25) all_181_3 = all_103_1 206.14/127.64 | | 206.14/127.64 | | GROUND_INST: instantiating (6) with all_192_3, all_181_3, all_103_2, int, 206.14/127.64 | | simplifying with (10), (20) gives: 206.14/127.64 | | (26) all_192_3 = all_181_3 206.14/127.64 | | 206.14/127.64 | | GROUND_INST: instantiating (6) with all_192_3, all_156_3, all_103_2, int, 206.14/127.64 | | simplifying with (17), (20) gives: 206.14/127.64 | | (27) all_192_3 = all_156_3 206.14/127.64 | | 206.14/127.64 | | COMBINE_EQS: (26), (27) imply: 206.14/127.64 | | (28) all_181_3 = all_156_3 206.14/127.64 | | 206.14/127.64 | | SIMP: (28) implies: 206.14/127.64 | | (29) all_181_3 = all_156_3 206.14/127.64 | | 206.14/127.64 | | COMBINE_EQS: (23), (24) imply: 206.14/127.64 | | (30) all_181_2 = all_156_1 206.14/127.64 | | 206.14/127.64 | | REF_CLOSE: (2), (3), (12), (13), (16), (18), (21), (22), (25), (29), (30) 206.14/127.64 | | are inconsistent by sub-proof #18. 206.14/127.64 | | 206.14/127.64 | Case 2: 206.14/127.64 | | 206.14/127.64 | | (31) ~ (all_192_4 = 0) & permut_sub2(int, all_103_4, all_103_2, 206.14/127.64 | | all_86_11, $sum(all_86_10, 1)) = all_192_4 206.14/127.64 | | 206.14/127.64 | | REF_CLOSE: (9), (14), (31) are inconsistent by sub-proof #69. 206.14/127.64 | | 206.14/127.64 | End of split 206.14/127.64 | 206.14/127.64 End of proof 206.14/127.64 206.14/127.64 Sub-proof #12 shows that the following formulas are inconsistent: 206.14/127.64 ---------------------------------------------------------------- 206.14/127.64 (1) length1(int, all_105_2) = all_86_13 206.14/127.64 (2) length1(int, all_105_4) = all_86_13 206.14/127.64 (3) length1(int, all_105_4) = all_234_1 & ( ~ ($lesseq(1, 206.14/127.64 $difference(all_234_1, all_86_10))) | ~ ($lesseq(all_86_13, 206.14/127.64 all_234_1)) | ( ~ (all_234_0 = all_234_1) & length1(int, all_105_2) 206.14/127.64 = all_234_0)) 206.14/127.64 (4) $lesseq(1, $difference(all_86_13, all_86_10)) 206.14/127.64 (5) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 206.14/127.64 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 206.14/127.64 206.14/127.64 Begin of proof 206.14/127.64 | 206.14/127.64 | ALPHA: (3) implies: 206.14/127.64 | (6) length1(int, all_105_4) = all_234_1 206.14/127.64 | (7) ~ ($lesseq(1, $difference(all_234_1, all_86_10))) | ~ 206.14/127.64 | ($lesseq(all_86_13, all_234_1)) | ( ~ (all_234_0 = all_234_1) & 206.14/127.64 | length1(int, all_105_2) = all_234_0) 206.14/127.64 | 206.14/127.64 | GROUND_INST: instantiating (5) with all_86_13, all_234_1, all_105_4, int, 206.14/127.64 | simplifying with (2), (6) gives: 206.14/127.64 | (8) all_234_1 = all_86_13 206.14/127.64 | 206.14/127.64 | REF_CLOSE: (1), (4), (5), (7), (8) are inconsistent by sub-proof #38. 206.14/127.64 | 206.14/127.64 End of proof 206.14/127.64 206.14/127.64 Sub-proof #13 shows that the following formulas are inconsistent: 206.14/127.64 ---------------------------------------------------------------- 206.14/127.64 (1) length1(int, all_103_2) = all_86_13 206.14/127.64 (2) array_eq_sub1(int, all_105_4, all_105_2, $sum(all_86_10, 1), all_86_13) = 206.14/127.64 0 206.14/127.64 (3) elts(int, all_105_2) = all_187_2 206.14/127.64 (4) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.14/127.64 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ 206.14/127.64 (array_eq_sub1(v6, v5, v4, v3, v2) = v1) | ~ (array_eq_sub1(v6, v5, 206.14/127.64 v4, v3, v2) = v0)) 206.14/127.64 (5) elts(int, all_105_4) = all_187_3 206.14/127.64 (6) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 206.14/127.64 | ~ (elts(v3, v2) = v1) | ~ (elts(v3, v2) = v0)) 206.14/127.64 (7) elts(int, all_105_4) = all_105_3 206.14/127.64 (8) map_eq_sub1(int, all_105_3, all_105_1, 0, all_86_7) = 0 206.14/127.64 (9) (all_169_0 = all_169_1 & $lesseq(all_86_7, all_169_1) & $lesseq(0, 206.14/127.64 all_169_1) & $lesseq(0, all_86_7) & length1(int, all_105_2) = 206.14/127.64 all_169_1 & length1(int, all_105_4) = all_169_1) | ( ~ (all_169_1 = 0) 206.14/127.64 & array_eq_sub1(int, all_105_4, all_105_2, 0, all_86_7) = all_169_1) 206.14/127.64 (10) (all_170_0 = all_170_1 & $lesseq(all_86_11, all_170_1) & $lesseq(0, 206.14/127.64 all_170_1) & $lesseq(0, all_86_11) & length1(int, all_105_4) = 206.14/127.64 all_170_1 & length1(int, all_103_2) = all_170_1) | ( ~ (all_170_1 = 0) 206.14/127.64 & array_eq_sub1(int, all_103_2, all_105_4, 0, all_86_11) = all_170_1) 206.14/127.64 (11) array_eq_sub1(int, all_105_4, all_105_2, 0, all_86_7) = 0 206.14/127.64 (12) elts(int, all_105_2) = all_105_1 206.14/127.64 (13) array_eq_sub1(int, all_103_2, all_105_4, 0, all_86_11) = 0 206.14/127.64 (14) elts(int, all_105_4) = all_181_2 206.14/127.64 (15) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.14/127.64 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ (map_eq_sub1(v6, 206.14/127.64 v5, v4, v3, v2) = v1) | ~ (map_eq_sub1(v6, v5, v4, v3, v2) = v0)) 206.14/127.64 (16) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 206.14/127.64 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 206.14/127.64 (17) (all_153_0 = all_153_1 & $lesseq(1, $difference(all_153_1, all_86_10)) & 206.14/127.64 $lesseq(all_86_13, all_153_1) & $lesseq(-1, all_86_10) & $lesseq(0, 206.14/127.64 all_86_13) & length1(int, all_105_2) = all_153_1 & length1(int, 206.14/127.64 all_105_4) = all_153_1) | ( ~ (all_153_1 = 0) & array_eq_sub1(int, 206.14/127.64 all_105_4, all_105_2, $sum(all_86_10, 1), all_86_13) = all_153_1) 206.14/127.64 (18) ( ~ (all_187_0 = 0) & map_eq_sub1(int, all_187_3, all_187_2, 206.14/127.64 $sum(all_86_10, 1), all_187_1) = all_187_0 & length1(int, all_105_4) 206.14/127.64 = all_187_1) | ( ~ (all_187_1 = 0) & map_eq_sub1(int, all_187_3, 206.14/127.64 all_187_2, 0, all_86_7) = all_187_1) 206.14/127.64 (19) map_eq_sub1(int, all_105_3, all_105_1, $sum(all_86_10, 1), all_86_13) = 206.14/127.64 0 206.14/127.64 206.14/127.64 Begin of proof 206.14/127.64 | 206.14/127.64 | BETA: splitting (9) gives: 206.14/127.64 | 206.14/127.64 | Case 1: 206.14/127.64 | | 206.14/127.64 | | (20) all_169_0 = all_169_1 & $lesseq(all_86_7, all_169_1) & $lesseq(0, 206.14/127.64 | | all_169_1) & $lesseq(0, all_86_7) & length1(int, all_105_2) = 206.14/127.64 | | all_169_1 & length1(int, all_105_4) = all_169_1 206.14/127.64 | | 206.14/127.64 | | ALPHA: (20) implies: 206.14/127.64 | | (21) length1(int, all_105_4) = all_169_1 206.14/127.64 | | 206.14/127.64 | | BETA: splitting (10) gives: 206.14/127.64 | | 206.14/127.64 | | Case 1: 206.14/127.64 | | | 206.14/127.64 | | | (22) all_170_0 = all_170_1 & $lesseq(all_86_11, all_170_1) & $lesseq(0, 206.14/127.64 | | | all_170_1) & $lesseq(0, all_86_11) & length1(int, all_105_4) = 206.14/127.64 | | | all_170_1 & length1(int, all_103_2) = all_170_1 206.14/127.64 | | | 206.14/127.64 | | | ALPHA: (22) implies: 206.14/127.64 | | | (23) length1(int, all_103_2) = all_170_1 206.14/127.64 | | | (24) length1(int, all_105_4) = all_170_1 206.14/127.64 | | | 206.14/127.64 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (12), (14), (15), (16), 206.14/127.64 | | | (17), (18), (19), (21), (23), (24) are inconsistent by 206.14/127.64 | | | sub-proof #25. 206.14/127.64 | | | 206.14/127.64 | | Case 2: 206.14/127.64 | | | 206.14/127.64 | | | (25) ~ (all_170_1 = 0) & array_eq_sub1(int, all_103_2, all_105_4, 0, 206.14/127.64 | | | all_86_11) = all_170_1 206.14/127.64 | | | 206.14/127.64 | | | REF_CLOSE: (4), (13), (25) are inconsistent by sub-proof #48. 206.14/127.64 | | | 206.14/127.64 | | End of split 206.14/127.64 | | 206.14/127.64 | Case 2: 206.14/127.64 | | 206.14/127.64 | | (26) ~ (all_169_1 = 0) & array_eq_sub1(int, all_105_4, all_105_2, 0, 206.14/127.64 | | all_86_7) = all_169_1 206.14/127.64 | | 206.14/127.64 | | REF_CLOSE: (4), (11), (26) are inconsistent by sub-proof #75. 206.14/127.64 | | 206.14/127.64 | End of split 206.14/127.64 | 206.14/127.64 End of proof 206.14/127.64 206.14/127.64 Sub-proof #14 shows that the following formulas are inconsistent: 206.14/127.64 ---------------------------------------------------------------- 206.14/127.64 (1) array_eq_sub1(int, all_105_4, all_105_2, $sum(all_86_10, 1), all_86_13) = 206.14/127.64 0 206.14/127.64 (2) elts(int, all_105_2) = all_187_2 206.14/127.64 (3) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.14/127.64 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ 206.14/127.64 (array_eq_sub1(v6, v5, v4, v3, v2) = v1) | ~ (array_eq_sub1(v6, v5, 206.14/127.64 v4, v3, v2) = v0)) 206.14/127.64 (4) elts(int, all_105_4) = all_187_3 206.14/127.64 (5) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 206.14/127.64 | ~ (elts(v3, v2) = v1) | ~ (elts(v3, v2) = v0)) 206.14/127.64 (6) length1(int, all_105_4) = all_86_13 206.14/127.64 (7) elts(int, all_105_4) = all_105_3 206.14/127.64 (8) map_eq_sub1(int, all_105_3, all_105_1, 0, all_86_7) = 0 206.14/127.64 (9) (all_169_0 = all_169_1 & $lesseq(all_86_7, all_169_1) & $lesseq(0, 206.14/127.64 all_169_1) & $lesseq(0, all_86_7) & length1(int, all_105_2) = 206.14/127.64 all_169_1 & length1(int, all_105_4) = all_169_1) | ( ~ (all_169_1 = 0) 206.14/127.64 & array_eq_sub1(int, all_105_4, all_105_2, 0, all_86_7) = all_169_1) 206.14/127.64 (10) (all_170_0 = all_170_1 & $lesseq(all_86_11, all_170_1) & $lesseq(0, 206.14/127.64 all_170_1) & $lesseq(0, all_86_11) & length1(int, all_105_4) = 206.14/127.64 all_170_1 & length1(int, all_103_2) = all_170_1) | ( ~ (all_170_1 = 0) 206.14/127.64 & array_eq_sub1(int, all_103_2, all_105_4, 0, all_86_11) = all_170_1) 206.14/127.64 (11) array_eq_sub1(int, all_105_4, all_105_2, 0, all_86_7) = 0 206.14/127.64 (12) elts(int, all_105_2) = all_105_1 206.14/127.64 (13) array_eq_sub1(int, all_103_2, all_105_4, 0, all_86_11) = 0 206.14/127.64 (14) (all_168_0 = all_168_1 & $lesseq(1, $difference(all_168_1, all_86_8)) & 206.14/127.64 $lesseq(all_86_13, all_168_1) & $lesseq(-1, all_86_8) & $lesseq(0, 206.14/127.64 all_86_13) & length1(int, all_105_4) = all_168_1 & length1(int, 206.14/127.64 all_103_2) = all_168_1) | ( ~ (all_168_1 = 0) & array_eq_sub1(int, 206.14/127.64 all_103_2, all_105_4, $sum(all_86_8, 1), all_86_13) = all_168_1) 206.14/127.64 (15) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.14/127.64 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ (map_eq_sub1(v6, 206.14/127.64 v5, v4, v3, v2) = v1) | ~ (map_eq_sub1(v6, v5, v4, v3, v2) = v0)) 206.14/127.64 (16) array_eq_sub1(int, all_103_2, all_105_4, $sum(all_86_8, 1), all_86_13) = 206.14/127.64 0 206.14/127.64 (17) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 206.14/127.64 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 206.14/127.65 (18) (all_153_0 = all_153_1 & $lesseq(1, $difference(all_153_1, all_86_10)) & 206.14/127.65 $lesseq(all_86_13, all_153_1) & $lesseq(-1, all_86_10) & $lesseq(0, 206.14/127.65 all_86_13) & length1(int, all_105_2) = all_153_1 & length1(int, 206.14/127.65 all_105_4) = all_153_1) | ( ~ (all_153_1 = 0) & array_eq_sub1(int, 206.14/127.65 all_105_4, all_105_2, $sum(all_86_10, 1), all_86_13) = all_153_1) 206.14/127.65 (19) ( ~ (all_187_0 = 0) & map_eq_sub1(int, all_187_3, all_187_2, 206.14/127.65 $sum(all_86_10, 1), all_187_1) = all_187_0 & length1(int, all_105_4) 206.14/127.65 = all_187_1) | ( ~ (all_187_1 = 0) & map_eq_sub1(int, all_187_3, 206.14/127.65 all_187_2, 0, all_86_7) = all_187_1) 206.14/127.65 (20) map_eq_sub1(int, all_105_3, all_105_1, $sum(all_86_10, 1), all_86_13) = 206.14/127.65 0 206.14/127.65 (21) length1(int, all_103_2) = all_156_0 206.14/127.65 206.14/127.65 Begin of proof 206.14/127.65 | 206.14/127.65 | BETA: splitting (18) gives: 206.14/127.65 | 206.14/127.65 | Case 1: 206.14/127.65 | | 206.14/127.65 | | (22) all_153_0 = all_153_1 & $lesseq(1, $difference(all_153_1, 206.14/127.65 | | all_86_10)) & $lesseq(all_86_13, all_153_1) & $lesseq(-1, 206.14/127.65 | | all_86_10) & $lesseq(0, all_86_13) & length1(int, all_105_2) = 206.14/127.65 | | all_153_1 & length1(int, all_105_4) = all_153_1 206.14/127.65 | | 206.14/127.65 | | ALPHA: (22) implies: 206.14/127.65 | | (23) length1(int, all_105_4) = all_153_1 206.14/127.65 | | 206.14/127.65 | | BETA: splitting (14) gives: 206.14/127.65 | | 206.14/127.65 | | Case 1: 206.14/127.65 | | | 206.14/127.65 | | | (24) all_168_0 = all_168_1 & $lesseq(1, $difference(all_168_1, 206.14/127.65 | | | all_86_8)) & $lesseq(all_86_13, all_168_1) & $lesseq(-1, 206.14/127.65 | | | all_86_8) & $lesseq(0, all_86_13) & length1(int, all_105_4) = 206.14/127.65 | | | all_168_1 & length1(int, all_103_2) = all_168_1 206.14/127.65 | | | 206.14/127.65 | | | ALPHA: (24) implies: 206.14/127.65 | | | (25) length1(int, all_103_2) = all_168_1 206.14/127.65 | | | (26) length1(int, all_105_4) = all_168_1 206.14/127.65 | | | 206.14/127.65 | | | BETA: splitting (9) gives: 206.14/127.65 | | | 206.14/127.65 | | | Case 1: 206.14/127.65 | | | | 206.14/127.65 | | | | (27) all_169_0 = all_169_1 & $lesseq(all_86_7, all_169_1) & 206.14/127.65 | | | | $lesseq(0, all_169_1) & $lesseq(0, all_86_7) & length1(int, 206.14/127.65 | | | | all_105_2) = all_169_1 & length1(int, all_105_4) = all_169_1 206.14/127.65 | | | | 206.14/127.65 | | | | ALPHA: (27) implies: 206.14/127.65 | | | | (28) length1(int, all_105_4) = all_169_1 206.14/127.65 | | | | 206.14/127.65 | | | | BETA: splitting (10) gives: 206.14/127.65 | | | | 206.14/127.65 | | | | Case 1: 206.14/127.65 | | | | | 206.14/127.65 | | | | | (29) all_170_0 = all_170_1 & $lesseq(all_86_11, all_170_1) & 206.14/127.65 | | | | | $lesseq(0, all_170_1) & $lesseq(0, all_86_11) & length1(int, 206.14/127.65 | | | | | all_105_4) = all_170_1 & length1(int, all_103_2) = all_170_1 206.14/127.65 | | | | | 206.14/127.65 | | | | | ALPHA: (29) implies: 206.14/127.65 | | | | | (30) length1(int, all_103_2) = all_170_1 206.14/127.65 | | | | | (31) length1(int, all_105_4) = all_170_1 206.14/127.65 | | | | | 206.14/127.65 | | | | | GROUND_INST: instantiating (17) with all_86_13, all_169_1, all_105_4, 206.14/127.65 | | | | | int, simplifying with (6), (28) gives: 206.14/127.65 | | | | | (32) all_169_1 = all_86_13 206.14/127.65 | | | | | 206.14/127.65 | | | | | GROUND_INST: instantiating (17) with all_169_1, all_168_1, all_105_4, 206.14/127.65 | | | | | int, simplifying with (26), (28) gives: 206.14/127.65 | | | | | (33) all_169_1 = all_168_1 206.14/127.65 | | | | | 206.14/127.65 | | | | | GROUND_INST: instantiating (17) with all_170_1, all_153_1, all_105_4, 206.14/127.65 | | | | | int, simplifying with (23), (31) gives: 206.14/127.65 | | | | | (34) all_170_1 = all_153_1 206.14/127.65 | | | | | 206.14/127.65 | | | | | GROUND_INST: instantiating (17) with all_170_1, all_156_0, all_103_2, 206.14/127.65 | | | | | int, simplifying with (21), (30) gives: 206.14/127.65 | | | | | (35) all_170_1 = all_156_0 206.14/127.65 | | | | | 206.14/127.65 | | | | | GROUND_INST: instantiating (17) with all_168_1, all_156_0, all_103_2, 206.14/127.65 | | | | | int, simplifying with (21), (25) gives: 206.14/127.65 | | | | | (36) all_168_1 = all_156_0 206.14/127.65 | | | | | 206.14/127.65 | | | | | GROUND_INST: instantiating (5) with all_105_1, all_187_2, all_105_2, 206.14/127.65 | | | | | int, simplifying with (2), (12) gives: 206.14/127.65 | | | | | (37) all_187_2 = all_105_1 206.14/127.65 | | | | | 206.14/127.65 | | | | | GROUND_INST: instantiating (5) with all_105_3, all_187_3, all_105_4, 206.14/127.65 | | | | | int, simplifying with (4), (7) gives: 206.14/127.65 | | | | | (38) all_187_3 = all_105_3 206.14/127.65 | | | | | 206.14/127.65 | | | | | COMBINE_EQS: (34), (35) imply: 206.14/127.65 | | | | | (39) all_156_0 = all_153_1 206.14/127.65 | | | | | 206.14/127.65 | | | | | SIMP: (39) implies: 206.14/127.65 | | | | | (40) all_156_0 = all_153_1 206.14/127.65 | | | | | 206.14/127.65 | | | | | COMBINE_EQS: (32), (33) imply: 206.14/127.65 | | | | | (41) all_168_1 = all_86_13 206.14/127.65 | | | | | 206.14/127.65 | | | | | COMBINE_EQS: (36), (41) imply: 206.14/127.65 | | | | | (42) all_156_0 = all_86_13 206.14/127.65 | | | | | 206.14/127.65 | | | | | SIMP: (42) implies: 206.14/127.65 | | | | | (43) all_156_0 = all_86_13 206.14/127.65 | | | | | 206.14/127.65 | | | | | COMBINE_EQS: (40), (43) imply: 206.14/127.65 | | | | | (44) all_153_1 = all_86_13 206.14/127.65 | | | | | 206.14/127.65 | | | | | REF_CLOSE: (6), (8), (15), (17), (19), (20), (37), (38) are 206.14/127.65 | | | | | inconsistent by sub-proof #66. 206.14/127.65 | | | | | 206.14/127.65 | | | | Case 2: 206.14/127.65 | | | | | 206.14/127.65 | | | | | (45) ~ (all_170_1 = 0) & array_eq_sub1(int, all_103_2, all_105_4, 206.14/127.65 | | | | | 0, all_86_11) = all_170_1 206.14/127.65 | | | | | 206.14/127.65 | | | | | REF_CLOSE: (3), (13), (45) are inconsistent by sub-proof #48. 206.14/127.65 | | | | | 206.14/127.65 | | | | End of split 206.14/127.65 | | | | 206.14/127.65 | | | Case 2: 206.14/127.65 | | | | 206.14/127.65 | | | | (46) ~ (all_169_1 = 0) & array_eq_sub1(int, all_105_4, all_105_2, 0, 206.14/127.65 | | | | all_86_7) = all_169_1 206.14/127.65 | | | | 206.14/127.65 | | | | REF_CLOSE: (3), (11), (46) are inconsistent by sub-proof #75. 206.14/127.65 | | | | 206.14/127.65 | | | End of split 206.14/127.65 | | | 206.14/127.65 | | Case 2: 206.14/127.65 | | | 206.14/127.65 | | | (47) ~ (all_168_1 = 0) & array_eq_sub1(int, all_103_2, all_105_4, 206.14/127.65 | | | $sum(all_86_8, 1), all_86_13) = all_168_1 206.14/127.65 | | | 206.14/127.65 | | | REF_CLOSE: (3), (16), (47) are inconsistent by sub-proof #83. 206.14/127.65 | | | 206.14/127.65 | | End of split 206.14/127.65 | | 206.14/127.65 | Case 2: 206.14/127.65 | | 206.14/127.65 | | (48) ~ (all_153_1 = 0) & array_eq_sub1(int, all_105_4, all_105_2, 206.14/127.65 | | $sum(all_86_10, 1), all_86_13) = all_153_1 206.14/127.65 | | 206.14/127.65 | | REF_CLOSE: (1), (3), (48) are inconsistent by sub-proof #54. 206.14/127.65 | | 206.14/127.65 | End of split 206.14/127.65 | 206.14/127.65 End of proof 206.14/127.65 206.14/127.65 Sub-proof #15 shows that the following formulas are inconsistent: 206.14/127.65 ---------------------------------------------------------------- 206.14/127.65 (1) length1(int, all_103_2) = all_86_13 206.14/127.65 (2) elts(int, all_103_4) = all_103_3 206.14/127.65 (3) (all_190_0 = 0 & all_190_1 = 0 & map_eq_sub1(int, all_190_4, all_190_3, 206.14/127.65 $sum(all_86_10, 1), all_190_2) = 0 & map_eq_sub1(int, all_190_4, 206.14/127.65 all_190_3, 0, all_86_7) = 0 & length1(int, all_105_4) = all_190_2 & 206.14/127.65 elts(int, all_105_2) = all_190_3 & elts(int, all_105_4) = all_190_4 & 206.14/127.65 in_uni(all_190_3) & in_uni(all_190_4)) | ( ~ (all_190_4 = 0) & 206.14/127.65 permut_sub2(int, all_105_4, all_105_2, all_86_7, $sum(all_86_10, 1)) = 206.14/127.65 all_190_4) 206.14/127.65 (4) length1(int, all_103_4) = all_86_13 206.14/127.65 (5) map_eq_sub1(int, all_103_3, all_103_1, $sum(all_86_10, 1), all_86_13) = 0 206.14/127.65 (6) length1(int, all_103_4) = all_215_1 206.14/127.65 (7) map_eq_sub1(int, all_103_1, all_105_3, $sum(all_86_8, 1), all_86_13) = 0 206.14/127.65 (8) ( ~ (all_181_0 = 0) & map_eq_sub1(int, all_181_3, all_181_2, 206.14/127.65 $sum(all_86_8, 1), all_181_1) = all_181_0 & length1(int, all_103_2) = 206.14/127.65 all_181_1) | ( ~ (all_181_1 = 0) & map_eq_sub1(int, all_181_3, 206.14/127.65 all_181_2, 0, all_86_11) = all_181_1) 206.14/127.65 (9) (all_192_0 = 0 & all_192_1 = 0 & map_eq_sub1(int, all_192_4, all_192_3, 206.14/127.65 $sum(all_86_10, 1), all_192_2) = 0 & map_eq_sub1(int, all_192_4, 206.14/127.65 all_192_3, 0, all_86_11) = 0 & length1(int, all_103_4) = all_192_2 & 206.14/127.65 elts(int, all_103_2) = all_192_3 & elts(int, all_103_4) = all_192_4 & 206.14/127.65 in_uni(all_192_3) & in_uni(all_192_4)) | ( ~ (all_192_4 = 0) & 206.14/127.65 permut_sub2(int, all_103_4, all_103_2, all_86_11, $sum(all_86_10, 1)) = 206.14/127.65 all_192_4) 206.14/127.65 (10) permut_sub2(int, all_105_4, all_105_2, all_86_7, $sum(all_86_10, 1)) = 0 206.14/127.65 (11) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 206.14/127.65 | ~ (elts(v3, v2) = v1) | ~ (elts(v3, v2) = v0)) 206.14/127.65 (12) elts(int, all_105_4) = all_105_3 206.14/127.65 (13) elts(int, all_105_4) = all_156_1 206.14/127.65 (14) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.14/127.65 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ (permut_sub2(v6, 206.14/127.65 v5, v4, v3, v2) = v1) | ~ (permut_sub2(v6, v5, v4, v3, v2) = v0)) 206.14/127.65 (15) length1(int, all_103_4) = all_238_1 206.14/127.65 (16) elts(int, all_103_2) = all_181_3 206.14/127.65 (17) map_eq_sub1(int, all_103_3, all_103_1, 0, all_86_11) = 0 206.14/127.65 (18) elts(int, all_105_4) = all_181_2 206.14/127.65 (19) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.14/127.65 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ (map_eq_sub1(v6, 206.14/127.65 v5, v4, v3, v2) = v1) | ~ (map_eq_sub1(v6, v5, v4, v3, v2) = v0)) 206.14/127.65 (20) map_eq_sub1(int, all_156_3, all_156_1, 0, all_86_11) = 0 206.14/127.65 (21) elts(int, all_103_2) = all_103_1 206.14/127.65 (22) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 206.14/127.65 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 206.14/127.65 (23) (all_191_3 = 0 & permut_sub2(int, all_103_4, all_103_2, all_86_11, 206.14/127.65 $sum(all_86_10, 1)) = 0) | (elts(int, all_103_2) = all_191_2 & 206.14/127.65 elts(int, all_103_4) = all_191_3 & in_uni(all_191_2) & 206.14/127.65 in_uni(all_191_3) & (( ~ (all_191_0 = 0) & map_eq_sub1(int, all_191_3, 206.14/127.65 all_191_2, $sum(all_86_10, 1), all_191_1) = all_191_0 & 206.14/127.65 length1(int, all_103_4) = all_191_1) | ( ~ (all_191_1 = 0) & 206.14/127.65 map_eq_sub1(int, all_191_3, all_191_2, 0, all_86_11) = 206.14/127.65 all_191_1))) 206.14/127.65 (24) elts(int, all_103_2) = all_156_3 206.14/127.65 (25) length1(int, all_103_2) = all_156_0 206.14/127.65 206.14/127.65 Begin of proof 206.14/127.65 | 206.14/127.65 | BETA: splitting (3) gives: 206.14/127.65 | 206.14/127.65 | Case 1: 206.14/127.65 | | 206.14/127.65 | | (26) all_190_0 = 0 & all_190_1 = 0 & map_eq_sub1(int, all_190_4, 206.14/127.65 | | all_190_3, $sum(all_86_10, 1), all_190_2) = 0 & map_eq_sub1(int, 206.14/127.65 | | all_190_4, all_190_3, 0, all_86_7) = 0 & length1(int, all_105_4) = 206.14/127.65 | | all_190_2 & elts(int, all_105_2) = all_190_3 & elts(int, all_105_4) 206.14/127.65 | | = all_190_4 & in_uni(all_190_3) & in_uni(all_190_4) 206.14/127.65 | | 206.14/127.65 | | ALPHA: (26) implies: 206.14/127.65 | | (27) elts(int, all_105_4) = all_190_4 206.14/127.65 | | 206.14/127.65 | | BETA: splitting (23) gives: 206.14/127.65 | | 206.14/127.65 | | Case 1: 206.14/127.65 | | | 206.14/127.65 | | | (28) all_191_3 = 0 & permut_sub2(int, all_103_4, all_103_2, all_86_11, 206.14/127.65 | | | $sum(all_86_10, 1)) = 0 206.14/127.65 | | | 206.14/127.65 | | | ALPHA: (28) implies: 206.14/127.65 | | | (29) permut_sub2(int, all_103_4, all_103_2, all_86_11, $sum(all_86_10, 206.14/127.65 | | | 1)) = 0 206.14/127.65 | | | 206.14/127.65 | | | REF_CLOSE: (1), (7), (8), (9), (11), (12), (13), (14), (16), (18), (19), 206.14/127.65 | | | (20), (21), (22), (24), (25), (27), (29) are inconsistent by 206.14/127.65 | | | sub-proof #17. 206.14/127.65 | | | 206.14/127.65 | | Case 2: 206.14/127.65 | | | 206.14/127.65 | | | (30) elts(int, all_103_2) = all_191_2 & elts(int, all_103_4) = 206.14/127.65 | | | all_191_3 & in_uni(all_191_2) & in_uni(all_191_3) & (( ~ 206.14/127.65 | | | (all_191_0 = 0) & map_eq_sub1(int, all_191_3, all_191_2, 206.14/127.65 | | | $sum(all_86_10, 1), all_191_1) = all_191_0 & length1(int, 206.14/127.65 | | | all_103_4) = all_191_1) | ( ~ (all_191_1 = 0) & 206.14/127.65 | | | map_eq_sub1(int, all_191_3, all_191_2, 0, all_86_11) = 206.14/127.65 | | | all_191_1)) 206.14/127.65 | | | 206.14/127.65 | | | ALPHA: (30) implies: 206.14/127.65 | | | (31) elts(int, all_103_4) = all_191_3 206.14/127.65 | | | (32) elts(int, all_103_2) = all_191_2 206.14/127.65 | | | (33) ( ~ (all_191_0 = 0) & map_eq_sub1(int, all_191_3, all_191_2, 206.14/127.65 | | | $sum(all_86_10, 1), all_191_1) = all_191_0 & length1(int, 206.14/127.66 | | | all_103_4) = all_191_1) | ( ~ (all_191_1 = 0) & 206.14/127.66 | | | map_eq_sub1(int, all_191_3, all_191_2, 0, all_86_11) = 206.14/127.66 | | | all_191_1) 206.14/127.66 | | | 206.14/127.66 | | | REF_CLOSE: (2), (4), (5), (6), (11), (15), (17), (19), (21), (22), (31), 206.14/127.66 | | | (32), (33) are inconsistent by sub-proof #16. 206.14/127.66 | | | 206.14/127.66 | | End of split 206.14/127.66 | | 206.14/127.66 | Case 2: 206.14/127.66 | | 206.14/127.66 | | (34) ~ (all_190_4 = 0) & permut_sub2(int, all_105_4, all_105_2, 206.14/127.66 | | all_86_7, $sum(all_86_10, 1)) = all_190_4 206.14/127.66 | | 206.14/127.66 | | REF_CLOSE: (10), (14), (34) are inconsistent by sub-proof #68. 206.14/127.66 | | 206.14/127.66 | End of split 206.14/127.66 | 206.14/127.66 End of proof 206.14/127.66 206.14/127.66 Sub-proof #16 shows that the following formulas are inconsistent: 206.14/127.66 ---------------------------------------------------------------- 206.14/127.66 (1) elts(int, all_103_4) = all_191_3 206.14/127.66 (2) elts(int, all_103_4) = all_103_3 206.14/127.66 (3) length1(int, all_103_4) = all_86_13 206.14/127.66 (4) map_eq_sub1(int, all_103_3, all_103_1, $sum(all_86_10, 1), all_86_13) = 0 206.14/127.66 (5) length1(int, all_103_4) = all_215_1 206.14/127.66 (6) elts(int, all_103_2) = all_191_2 206.14/127.66 (7) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 206.14/127.66 | ~ (elts(v3, v2) = v1) | ~ (elts(v3, v2) = v0)) 206.14/127.66 (8) length1(int, all_103_4) = all_238_1 206.14/127.66 (9) map_eq_sub1(int, all_103_3, all_103_1, 0, all_86_11) = 0 206.14/127.66 (10) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.14/127.66 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ (map_eq_sub1(v6, 206.14/127.66 v5, v4, v3, v2) = v1) | ~ (map_eq_sub1(v6, v5, v4, v3, v2) = v0)) 206.14/127.66 (11) elts(int, all_103_2) = all_103_1 206.14/127.66 (12) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 206.14/127.66 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 206.14/127.66 (13) ( ~ (all_191_0 = 0) & map_eq_sub1(int, all_191_3, all_191_2, 206.14/127.66 $sum(all_86_10, 1), all_191_1) = all_191_0 & length1(int, all_103_4) 206.14/127.66 = all_191_1) | ( ~ (all_191_1 = 0) & map_eq_sub1(int, all_191_3, 206.14/127.66 all_191_2, 0, all_86_11) = all_191_1) 206.14/127.66 206.14/127.66 Begin of proof 206.14/127.66 | 206.14/127.66 | GROUND_INST: instantiating (12) with all_86_13, all_238_1, all_103_4, int, 206.14/127.66 | simplifying with (3), (8) gives: 206.14/127.66 | (14) all_238_1 = all_86_13 206.14/127.66 | 206.14/127.66 | GROUND_INST: instantiating (12) with all_238_1, all_215_1, all_103_4, int, 206.14/127.66 | simplifying with (5), (8) gives: 206.14/127.66 | (15) all_238_1 = all_215_1 206.14/127.66 | 206.14/127.66 | GROUND_INST: instantiating (7) with all_103_1, all_191_2, all_103_2, int, 206.14/127.66 | simplifying with (6), (11) gives: 206.14/127.66 | (16) all_191_2 = all_103_1 206.14/127.66 | 206.14/127.66 | GROUND_INST: instantiating (7) with all_103_3, all_191_3, all_103_4, int, 206.14/127.66 | simplifying with (1), (2) gives: 206.14/127.66 | (17) all_191_3 = all_103_3 206.14/127.66 | 206.14/127.66 | COMBINE_EQS: (14), (15) imply: 206.14/127.66 | (18) all_215_1 = all_86_13 206.14/127.66 | 206.14/127.66 | SIMP: (18) implies: 206.14/127.66 | (19) all_215_1 = all_86_13 206.14/127.66 | 206.14/127.66 | REF_CLOSE: (3), (4), (9), (10), (12), (13), (16), (17) are inconsistent by 206.14/127.66 | sub-proof #57. 206.14/127.66 | 206.14/127.66 End of proof 206.14/127.66 206.14/127.66 Sub-proof #17 shows that the following formulas are inconsistent: 206.14/127.66 ---------------------------------------------------------------- 206.14/127.66 (1) length1(int, all_103_2) = all_86_13 206.14/127.66 (2) map_eq_sub1(int, all_103_1, all_105_3, $sum(all_86_8, 1), all_86_13) = 0 206.14/127.66 (3) ( ~ (all_181_0 = 0) & map_eq_sub1(int, all_181_3, all_181_2, 206.14/127.66 $sum(all_86_8, 1), all_181_1) = all_181_0 & length1(int, all_103_2) = 206.14/127.66 all_181_1) | ( ~ (all_181_1 = 0) & map_eq_sub1(int, all_181_3, 206.14/127.66 all_181_2, 0, all_86_11) = all_181_1) 206.14/127.66 (4) (all_192_0 = 0 & all_192_1 = 0 & map_eq_sub1(int, all_192_4, all_192_3, 206.14/127.66 $sum(all_86_10, 1), all_192_2) = 0 & map_eq_sub1(int, all_192_4, 206.14/127.66 all_192_3, 0, all_86_11) = 0 & length1(int, all_103_4) = all_192_2 & 206.14/127.66 elts(int, all_103_2) = all_192_3 & elts(int, all_103_4) = all_192_4 & 206.14/127.66 in_uni(all_192_3) & in_uni(all_192_4)) | ( ~ (all_192_4 = 0) & 206.14/127.66 permut_sub2(int, all_103_4, all_103_2, all_86_11, $sum(all_86_10, 1)) = 206.14/127.66 all_192_4) 206.14/127.66 (5) elts(int, all_105_4) = all_190_4 206.14/127.66 (6) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 206.14/127.66 | ~ (elts(v3, v2) = v1) | ~ (elts(v3, v2) = v0)) 206.14/127.66 (7) elts(int, all_105_4) = all_105_3 206.14/127.66 (8) elts(int, all_105_4) = all_156_1 206.14/127.66 (9) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.14/127.66 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ (permut_sub2(v6, 206.14/127.66 v5, v4, v3, v2) = v1) | ~ (permut_sub2(v6, v5, v4, v3, v2) = v0)) 206.14/127.66 (10) elts(int, all_103_2) = all_181_3 206.14/127.66 (11) elts(int, all_105_4) = all_181_2 206.14/127.66 (12) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.14/127.66 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ (map_eq_sub1(v6, 206.14/127.66 v5, v4, v3, v2) = v1) | ~ (map_eq_sub1(v6, v5, v4, v3, v2) = v0)) 206.14/127.66 (13) map_eq_sub1(int, all_156_3, all_156_1, 0, all_86_11) = 0 206.14/127.66 (14) permut_sub2(int, all_103_4, all_103_2, all_86_11, $sum(all_86_10, 1)) = 206.14/127.66 0 206.14/127.66 (15) elts(int, all_103_2) = all_103_1 206.14/127.66 (16) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 206.14/127.66 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 206.14/127.66 (17) elts(int, all_103_2) = all_156_3 206.14/127.66 (18) length1(int, all_103_2) = all_156_0 206.14/127.66 206.14/127.66 Begin of proof 206.14/127.66 | 206.14/127.66 | BETA: splitting (4) gives: 206.14/127.66 | 206.14/127.66 | Case 1: 206.14/127.66 | | 206.14/127.66 | | (19) all_192_0 = 0 & all_192_1 = 0 & map_eq_sub1(int, all_192_4, 206.14/127.66 | | all_192_3, $sum(all_86_10, 1), all_192_2) = 0 & map_eq_sub1(int, 206.14/127.66 | | all_192_4, all_192_3, 0, all_86_11) = 0 & length1(int, all_103_4) 206.14/127.66 | | = all_192_2 & elts(int, all_103_2) = all_192_3 & elts(int, 206.14/127.66 | | all_103_4) = all_192_4 & in_uni(all_192_3) & in_uni(all_192_4) 206.14/127.66 | | 206.14/127.66 | | ALPHA: (19) implies: 206.14/127.66 | | (20) elts(int, all_103_2) = all_192_3 206.14/127.66 | | 206.14/127.66 | | GROUND_INST: instantiating (16) with all_86_13, all_156_0, all_103_2, int, 206.14/127.66 | | simplifying with (1), (18) gives: 206.14/127.66 | | (21) all_156_0 = all_86_13 206.14/127.66 | | 206.14/127.66 | | GROUND_INST: instantiating (6) with all_105_3, all_181_2, all_105_4, int, 206.14/127.66 | | simplifying with (7), (11) gives: 206.14/127.66 | | (22) all_181_2 = all_105_3 206.14/127.66 | | 206.14/127.66 | | GROUND_INST: instantiating (6) with all_190_4, all_181_2, all_105_4, int, 206.14/127.66 | | simplifying with (5), (11) gives: 206.14/127.66 | | (23) all_190_4 = all_181_2 206.14/127.66 | | 206.14/127.66 | | GROUND_INST: instantiating (6) with all_190_4, all_156_1, all_105_4, int, 206.14/127.66 | | simplifying with (5), (8) gives: 206.14/127.66 | | (24) all_190_4 = all_156_1 206.14/127.66 | | 206.14/127.66 | | GROUND_INST: instantiating (6) with all_103_1, all_181_3, all_103_2, int, 206.14/127.66 | | simplifying with (10), (15) gives: 206.14/127.66 | | (25) all_181_3 = all_103_1 206.14/127.66 | | 206.14/127.66 | | GROUND_INST: instantiating (6) with all_192_3, all_181_3, all_103_2, int, 206.14/127.66 | | simplifying with (10), (20) gives: 206.14/127.66 | | (26) all_192_3 = all_181_3 206.14/127.66 | | 206.14/127.66 | | GROUND_INST: instantiating (6) with all_192_3, all_156_3, all_103_2, int, 206.14/127.66 | | simplifying with (17), (20) gives: 206.14/127.66 | | (27) all_192_3 = all_156_3 206.14/127.66 | | 206.14/127.66 | | COMBINE_EQS: (26), (27) imply: 206.14/127.66 | | (28) all_181_3 = all_156_3 206.14/127.66 | | 206.14/127.66 | | SIMP: (28) implies: 206.14/127.66 | | (29) all_181_3 = all_156_3 206.14/127.66 | | 206.14/127.66 | | COMBINE_EQS: (23), (24) imply: 206.14/127.66 | | (30) all_181_2 = all_156_1 206.14/127.66 | | 206.14/127.66 | | REF_CLOSE: (2), (3), (12), (13), (16), (18), (21), (22), (25), (29), (30) 206.14/127.66 | | are inconsistent by sub-proof #18. 206.14/127.66 | | 206.14/127.66 | Case 2: 206.14/127.66 | | 206.14/127.66 | | (31) ~ (all_192_4 = 0) & permut_sub2(int, all_103_4, all_103_2, 206.14/127.66 | | all_86_11, $sum(all_86_10, 1)) = all_192_4 206.14/127.66 | | 206.14/127.66 | | REF_CLOSE: (9), (14), (31) are inconsistent by sub-proof #69. 206.14/127.66 | | 206.14/127.66 | End of split 206.14/127.66 | 206.14/127.66 End of proof 206.14/127.66 206.14/127.66 Sub-proof #18 shows that the following formulas are inconsistent: 206.14/127.66 ---------------------------------------------------------------- 206.14/127.66 (1) all_181_2 = all_105_3 206.14/127.66 (2) all_181_3 = all_156_3 206.14/127.66 (3) all_156_0 = all_86_13 206.14/127.66 (4) map_eq_sub1(int, all_103_1, all_105_3, $sum(all_86_8, 1), all_86_13) = 0 206.14/127.66 (5) ( ~ (all_181_0 = 0) & map_eq_sub1(int, all_181_3, all_181_2, 206.14/127.66 $sum(all_86_8, 1), all_181_1) = all_181_0 & length1(int, all_103_2) = 206.14/127.66 all_181_1) | ( ~ (all_181_1 = 0) & map_eq_sub1(int, all_181_3, 206.14/127.66 all_181_2, 0, all_86_11) = all_181_1) 206.14/127.66 (6) all_181_3 = all_103_1 206.14/127.66 (7) all_181_2 = all_156_1 206.14/127.66 (8) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.14/127.66 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ (map_eq_sub1(v6, 206.14/127.66 v5, v4, v3, v2) = v1) | ~ (map_eq_sub1(v6, v5, v4, v3, v2) = v0)) 206.14/127.66 (9) map_eq_sub1(int, all_156_3, all_156_1, 0, all_86_11) = 0 206.14/127.66 (10) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 206.14/127.66 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 206.14/127.66 (11) length1(int, all_103_2) = all_156_0 206.14/127.66 206.14/127.66 Begin of proof 206.14/127.66 | 206.14/127.66 | SIMP: (7) implies: 206.14/127.66 | (12) all_181_2 = all_156_1 206.14/127.66 | 206.14/127.66 | COMBINE_EQS: (1), (12) imply: 206.14/127.66 | (13) all_156_1 = all_105_3 206.14/127.66 | 206.14/127.66 | COMBINE_EQS: (2), (6) imply: 206.14/127.66 | (14) all_156_3 = all_103_1 206.14/127.66 | 206.14/127.66 | REF_CLOSE: (1), (3), (4), (5), (6), (8), (9), (10), (11), (13), (14) are 206.14/127.66 | inconsistent by sub-proof #44. 206.14/127.66 | 206.14/127.66 End of proof 206.14/127.66 206.14/127.67 Sub-proof #19 shows that the following formulas are inconsistent: 206.14/127.67 ---------------------------------------------------------------- 206.14/127.67 (1) elts(int, all_103_4) = all_191_3 206.14/127.67 (2) elts(int, all_103_4) = all_103_3 206.14/127.67 (3) length1(int, all_103_4) = all_86_13 206.14/127.67 (4) map_eq_sub1(int, all_103_3, all_103_1, $sum(all_86_10, 1), all_86_13) = 0 206.14/127.67 (5) elts(int, all_103_2) = all_191_2 206.14/127.67 (6) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 206.14/127.67 | ~ (elts(v3, v2) = v1) | ~ (elts(v3, v2) = v0)) 206.14/127.67 (7) length1(int, all_103_4) = all_238_1 206.14/127.67 (8) length1(int, all_103_4) = all_171_1 206.14/127.67 (9) map_eq_sub1(int, all_103_3, all_103_1, 0, all_86_11) = 0 206.14/127.67 (10) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.14/127.67 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ (map_eq_sub1(v6, 206.14/127.67 v5, v4, v3, v2) = v1) | ~ (map_eq_sub1(v6, v5, v4, v3, v2) = v0)) 206.14/127.67 (11) elts(int, all_103_2) = all_103_1 206.14/127.67 (12) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 206.14/127.67 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 206.14/127.67 (13) ( ~ (all_191_0 = 0) & map_eq_sub1(int, all_191_3, all_191_2, 206.14/127.67 $sum(all_86_10, 1), all_191_1) = all_191_0 & length1(int, all_103_4) 206.14/127.67 = all_191_1) | ( ~ (all_191_1 = 0) & map_eq_sub1(int, all_191_3, 206.14/127.67 all_191_2, 0, all_86_11) = all_191_1) 206.14/127.67 206.14/127.67 Begin of proof 206.14/127.67 | 206.14/127.67 | GROUND_INST: instantiating (12) with all_86_13, all_238_1, all_103_4, int, 206.14/127.67 | simplifying with (3), (7) gives: 206.14/127.67 | (14) all_238_1 = all_86_13 206.14/127.67 | 206.14/127.67 | GROUND_INST: instantiating (12) with all_238_1, all_171_1, all_103_4, int, 206.14/127.67 | simplifying with (7), (8) gives: 206.14/127.67 | (15) all_238_1 = all_171_1 206.14/127.67 | 206.14/127.67 | GROUND_INST: instantiating (6) with all_103_1, all_191_2, all_103_2, int, 206.14/127.67 | simplifying with (5), (11) gives: 206.14/127.67 | (16) all_191_2 = all_103_1 206.14/127.67 | 206.14/127.67 | GROUND_INST: instantiating (6) with all_103_3, all_191_3, all_103_4, int, 206.14/127.67 | simplifying with (1), (2) gives: 206.14/127.67 | (17) all_191_3 = all_103_3 206.14/127.67 | 206.14/127.67 | COMBINE_EQS: (14), (15) imply: 206.14/127.67 | (18) all_171_1 = all_86_13 206.14/127.67 | 206.14/127.67 | SIMP: (18) implies: 206.14/127.67 | (19) all_171_1 = all_86_13 206.14/127.67 | 206.14/127.67 | REF_CLOSE: (3), (4), (9), (10), (12), (13), (16), (17) are inconsistent by 206.14/127.67 | sub-proof #57. 206.14/127.67 | 206.14/127.67 End of proof 206.14/127.67 206.14/127.67 Sub-proof #20 shows that the following formulas are inconsistent: 206.14/127.67 ---------------------------------------------------------------- 206.14/127.67 (1) all_156_0 = all_153_1 206.14/127.67 (2) all_156_0 = all_86_13 206.14/127.67 (3) ~ ($lesseq(1, $difference(all_238_1, all_86_10))) | ~ 206.14/127.67 ($lesseq(all_86_13, all_238_1)) | ( ~ (all_238_0 = all_238_1) & 206.14/127.67 length1(int, all_103_2) = all_238_0) 206.14/127.67 (4) $lesseq(1, $difference(all_153_1, all_86_10)) 206.14/127.67 (5) all_238_1 = all_86_13 206.14/127.67 (6) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 206.14/127.67 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 206.14/127.67 (7) length1(int, all_103_2) = all_156_0 206.14/127.67 206.14/127.67 Begin of proof 206.14/127.67 | 206.14/127.67 | SIMP: (1) implies: 206.14/127.67 | (8) all_156_0 = all_153_1 206.14/127.67 | 206.14/127.67 | COMBINE_EQS: (2), (8) imply: 206.14/127.67 | (9) all_153_1 = all_86_13 206.14/127.67 | 206.14/127.67 | SIMP: (9) implies: 206.14/127.67 | (10) all_153_1 = all_86_13 206.14/127.67 | 206.14/127.67 | REF_CLOSE: (2), (3), (4), (5), (6), (7), (10) are inconsistent by sub-proof 206.14/127.67 | #23. 206.14/127.67 | 206.14/127.67 End of proof 206.14/127.67 206.14/127.67 Sub-proof #21 shows that the following formulas are inconsistent: 206.14/127.67 ---------------------------------------------------------------- 206.14/127.67 (1) length1(int, all_103_2) = all_86_13 206.14/127.67 (2) length1(int, all_105_2) = all_86_13 206.14/127.67 (3) (all_190_0 = 0 & all_190_1 = 0 & map_eq_sub1(int, all_190_4, all_190_3, 206.14/127.67 $sum(all_86_10, 1), all_190_2) = 0 & map_eq_sub1(int, all_190_4, 206.14/127.67 all_190_3, 0, all_86_7) = 0 & length1(int, all_105_4) = all_190_2 & 206.14/127.67 elts(int, all_105_2) = all_190_3 & elts(int, all_105_4) = all_190_4 & 206.14/127.67 in_uni(all_190_3) & in_uni(all_190_4)) | ( ~ (all_190_4 = 0) & 206.14/127.67 permut_sub2(int, all_105_4, all_105_2, all_86_7, $sum(all_86_10, 1)) = 206.14/127.67 all_190_4) 206.14/127.67 (4) (all_219_1 = 0 & array_eq_sub1(int, all_105_4, all_105_2, 0, all_86_7) = 206.14/127.67 0) | (length1(int, all_105_4) = all_219_1 & ( ~ ($lesseq(all_86_7, 206.14/127.67 all_219_1)) | ~ ($lesseq(0, all_219_1)) | ( ~ (all_219_0 = 206.14/127.67 all_219_1) & length1(int, all_105_2) = all_219_0))) 206.14/127.67 (5) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.14/127.67 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ 206.14/127.67 (array_eq_sub1(v6, v5, v4, v3, v2) = v1) | ~ (array_eq_sub1(v6, v5, 206.14/127.67 v4, v3, v2) = v0)) 206.14/127.67 (6) permut_sub2(int, all_105_4, all_105_2, all_86_7, $sum(all_86_10, 1)) = 0 206.14/127.67 (7) length1(int, all_105_4) = all_86_13 206.14/127.67 (8) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.14/127.67 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ (permut_sub2(v6, 206.14/127.67 v5, v4, v3, v2) = v1) | ~ (permut_sub2(v6, v5, v4, v3, v2) = v0)) 206.14/127.67 (9) (all_169_0 = all_169_1 & $lesseq(all_86_7, all_169_1) & $lesseq(0, 206.14/127.67 all_169_1) & $lesseq(0, all_86_7) & length1(int, all_105_2) = 206.14/127.67 all_169_1 & length1(int, all_105_4) = all_169_1) | ( ~ (all_169_1 = 0) 206.14/127.67 & array_eq_sub1(int, all_105_4, all_105_2, 0, all_86_7) = all_169_1) 206.14/127.67 (10) (all_170_0 = all_170_1 & $lesseq(all_86_11, all_170_1) & $lesseq(0, 206.14/127.67 all_170_1) & $lesseq(0, all_86_11) & length1(int, all_105_4) = 206.14/127.67 all_170_1 & length1(int, all_103_2) = all_170_1) | ( ~ (all_170_1 = 0) 206.14/127.67 & array_eq_sub1(int, all_103_2, all_105_4, 0, all_86_11) = all_170_1) 206.14/127.67 (11) array_eq_sub1(int, all_103_2, all_105_4, 0, all_86_11) = 0 206.14/127.67 (12) length1(int, all_105_4) = all_234_1 & ( ~ ($lesseq(1, 206.14/127.67 $difference(all_234_1, all_86_10))) | ~ ($lesseq(all_86_13, 206.14/127.67 all_234_1)) | ( ~ (all_234_0 = all_234_1) & length1(int, 206.14/127.67 all_105_2) = all_234_0)) 206.14/127.67 (13) $lesseq(1, $difference(all_86_13, all_86_10)) 206.14/127.67 (14) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 206.14/127.67 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 206.14/127.67 206.14/127.67 Begin of proof 206.14/127.67 | 206.14/127.67 | ALPHA: (12) implies: 206.14/127.67 | (15) length1(int, all_105_4) = all_234_1 206.14/127.67 | (16) ~ ($lesseq(1, $difference(all_234_1, all_86_10))) | ~ 206.14/127.67 | ($lesseq(all_86_13, all_234_1)) | ( ~ (all_234_0 = all_234_1) & 206.14/127.67 | length1(int, all_105_2) = all_234_0) 206.14/127.67 | 206.14/127.67 | BETA: splitting (10) gives: 206.14/127.67 | 206.14/127.67 | Case 1: 206.14/127.67 | | 206.14/127.67 | | (17) all_170_0 = all_170_1 & $lesseq(all_86_11, all_170_1) & $lesseq(0, 206.14/127.67 | | all_170_1) & $lesseq(0, all_86_11) & length1(int, all_105_4) = 206.14/127.67 | | all_170_1 & length1(int, all_103_2) = all_170_1 206.14/127.67 | | 206.14/127.67 | | ALPHA: (17) implies: 206.14/127.67 | | (18) length1(int, all_103_2) = all_170_1 206.14/127.67 | | (19) length1(int, all_105_4) = all_170_1 206.14/127.67 | | 206.14/127.67 | | BETA: splitting (3) gives: 206.14/127.67 | | 206.14/127.67 | | Case 1: 206.14/127.67 | | | 206.14/127.67 | | | (20) all_190_0 = 0 & all_190_1 = 0 & map_eq_sub1(int, all_190_4, 206.14/127.67 | | | all_190_3, $sum(all_86_10, 1), all_190_2) = 0 & map_eq_sub1(int, 206.14/127.67 | | | all_190_4, all_190_3, 0, all_86_7) = 0 & length1(int, all_105_4) 206.14/127.67 | | | = all_190_2 & elts(int, all_105_2) = all_190_3 & elts(int, 206.14/127.67 | | | all_105_4) = all_190_4 & in_uni(all_190_3) & in_uni(all_190_4) 206.14/127.67 | | | 206.14/127.67 | | | ALPHA: (20) implies: 206.14/127.68 | | | (21) length1(int, all_105_4) = all_190_2 206.14/127.68 | | | 206.14/127.68 | | | BETA: splitting (4) gives: 206.14/127.68 | | | 206.14/127.68 | | | Case 1: 206.14/127.68 | | | | 206.14/127.68 | | | | (22) all_219_1 = 0 & array_eq_sub1(int, all_105_4, all_105_2, 0, 206.14/127.68 | | | | all_86_7) = 0 206.14/127.68 | | | | 206.14/127.68 | | | | ALPHA: (22) implies: 206.14/127.68 | | | | (23) array_eq_sub1(int, all_105_4, all_105_2, 0, all_86_7) = 0 206.14/127.68 | | | | 206.14/127.68 | | | | BETA: splitting (9) gives: 206.14/127.68 | | | | 206.14/127.68 | | | | Case 1: 206.14/127.68 | | | | | 206.14/127.68 | | | | | (24) all_169_0 = all_169_1 & $lesseq(all_86_7, all_169_1) & 206.14/127.68 | | | | | $lesseq(0, all_169_1) & $lesseq(0, all_86_7) & length1(int, 206.14/127.68 | | | | | all_105_2) = all_169_1 & length1(int, all_105_4) = all_169_1 206.14/127.68 | | | | | 206.14/127.68 | | | | | ALPHA: (24) implies: 206.14/127.68 | | | | | (25) length1(int, all_105_4) = all_169_1 206.14/127.68 | | | | | (26) length1(int, all_105_2) = all_169_1 206.14/127.68 | | | | | 206.14/127.68 | | | | | GROUND_INST: instantiating (14) with all_234_1, all_190_2, all_105_4, 206.14/127.68 | | | | | int, simplifying with (15), (21) gives: 206.14/127.68 | | | | | (27) all_234_1 = all_190_2 206.14/127.68 | | | | | 206.14/127.68 | | | | | GROUND_INST: instantiating (14) with all_190_2, all_170_1, all_105_4, 206.14/127.68 | | | | | int, simplifying with (19), (21) gives: 206.14/127.68 | | | | | (28) all_190_2 = all_170_1 206.14/127.68 | | | | | 206.14/127.68 | | | | | GROUND_INST: instantiating (14) with all_234_1, all_169_1, all_105_4, 206.14/127.68 | | | | | int, simplifying with (15), (25) gives: 206.14/127.68 | | | | | (29) all_234_1 = all_169_1 206.14/127.68 | | | | | 206.14/127.68 | | | | | GROUND_INST: instantiating (14) with all_86_13, all_170_1, all_103_2, 206.14/127.68 | | | | | int, simplifying with (1), (18) gives: 206.14/127.68 | | | | | (30) all_170_1 = all_86_13 206.14/127.68 | | | | | 206.14/127.68 | | | | | COMBINE_EQS: (27), (29) imply: 206.14/127.68 | | | | | (31) all_190_2 = all_169_1 206.14/127.68 | | | | | 206.14/127.68 | | | | | SIMP: (31) implies: 206.14/127.68 | | | | | (32) all_190_2 = all_169_1 206.14/127.68 | | | | | 206.14/127.68 | | | | | COMBINE_EQS: (28), (32) imply: 206.14/127.68 | | | | | (33) all_170_1 = all_169_1 206.14/127.68 | | | | | 206.14/127.68 | | | | | SIMP: (33) implies: 206.14/127.68 | | | | | (34) all_170_1 = all_169_1 206.14/127.68 | | | | | 206.14/127.68 | | | | | COMBINE_EQS: (30), (34) imply: 206.14/127.68 | | | | | (35) all_169_1 = all_86_13 206.14/127.68 | | | | | 206.14/127.68 | | | | | SIMP: (35) implies: 206.14/127.68 | | | | | (36) all_169_1 = all_86_13 206.14/127.68 | | | | | 206.14/127.68 | | | | | COMBINE_EQS: (29), (36) imply: 206.14/127.68 | | | | | (37) all_234_1 = all_86_13 206.14/127.68 | | | | | 206.14/127.68 | | | | | REF_CLOSE: (2), (13), (14), (16), (37) are inconsistent by sub-proof 206.14/127.68 | | | | | #38. 206.14/127.68 | | | | | 206.14/127.68 | | | | Case 2: 206.14/127.68 | | | | | 206.14/127.68 | | | | | (38) ~ (all_169_1 = 0) & array_eq_sub1(int, all_105_4, all_105_2, 206.14/127.68 | | | | | 0, all_86_7) = all_169_1 206.14/127.68 | | | | | 206.14/127.68 | | | | | REF_CLOSE: (5), (23), (38) are inconsistent by sub-proof #75. 206.14/127.68 | | | | | 206.14/127.68 | | | | End of split 206.14/127.68 | | | | 206.14/127.68 | | | Case 2: 206.14/127.68 | | | | 206.14/127.68 | | | | (39) length1(int, all_105_4) = all_219_1 & ( ~ ($lesseq(all_86_7, 206.14/127.68 | | | | all_219_1)) | ~ ($lesseq(0, all_219_1)) | ( ~ (all_219_0 206.14/127.68 | | | | = all_219_1) & length1(int, all_105_2) = all_219_0)) 206.14/127.68 | | | | 206.14/127.68 | | | | ALPHA: (39) implies: 206.14/127.68 | | | | (40) length1(int, all_105_4) = all_219_1 206.14/127.68 | | | | 206.14/127.68 | | | | GROUND_INST: instantiating (14) with all_86_13, all_219_1, all_105_4, 206.14/127.68 | | | | int, simplifying with (7), (40) gives: 206.14/127.68 | | | | (41) all_219_1 = all_86_13 206.14/127.68 | | | | 206.14/127.68 | | | | GROUND_INST: instantiating (14) with all_234_1, all_219_1, all_105_4, 206.14/127.68 | | | | int, simplifying with (15), (40) gives: 206.14/127.68 | | | | (42) all_234_1 = all_219_1 206.14/127.68 | | | | 206.14/127.68 | | | | GROUND_INST: instantiating (14) with all_219_1, all_190_2, all_105_4, 206.14/127.68 | | | | int, simplifying with (21), (40) gives: 206.14/127.68 | | | | (43) all_219_1 = all_190_2 206.14/127.68 | | | | 206.14/127.68 | | | | GROUND_INST: instantiating (14) with all_234_1, all_170_1, all_105_4, 206.14/127.68 | | | | int, simplifying with (15), (19) gives: 206.14/127.68 | | | | (44) all_234_1 = all_170_1 206.14/127.68 | | | | 206.14/127.68 | | | | COMBINE_EQS: (42), (44) imply: 206.14/127.68 | | | | (45) all_219_1 = all_170_1 206.14/127.68 | | | | 206.14/127.68 | | | | SIMP: (45) implies: 206.14/127.68 | | | | (46) all_219_1 = all_170_1 206.14/127.68 | | | | 206.14/127.68 | | | | COMBINE_EQS: (41), (43) imply: 206.14/127.68 | | | | (47) all_190_2 = all_86_13 206.14/127.68 | | | | 206.14/127.68 | | | | COMBINE_EQS: (43), (46) imply: 206.14/127.68 | | | | (48) all_190_2 = all_170_1 206.14/127.68 | | | | 206.14/127.68 | | | | COMBINE_EQS: (47), (48) imply: 206.14/127.68 | | | | (49) all_170_1 = all_86_13 206.14/127.68 | | | | 206.14/127.68 | | | | COMBINE_EQS: (44), (49) imply: 206.14/127.68 | | | | (50) all_234_1 = all_86_13 206.14/127.68 | | | | 206.14/127.68 | | | | REF_CLOSE: (2), (13), (14), (16), (50) are inconsistent by sub-proof 206.14/127.68 | | | | #38. 206.14/127.68 | | | | 206.14/127.68 | | | End of split 206.14/127.68 | | | 206.14/127.68 | | Case 2: 206.14/127.68 | | | 206.14/127.68 | | | (51) ~ (all_190_4 = 0) & permut_sub2(int, all_105_4, all_105_2, 206.14/127.68 | | | all_86_7, $sum(all_86_10, 1)) = all_190_4 206.14/127.68 | | | 206.14/127.68 | | | REF_CLOSE: (6), (8), (51) are inconsistent by sub-proof #68. 206.14/127.68 | | | 206.14/127.68 | | End of split 206.14/127.68 | | 206.14/127.68 | Case 2: 206.14/127.68 | | 206.14/127.68 | | (52) ~ (all_170_1 = 0) & array_eq_sub1(int, all_103_2, all_105_4, 0, 206.14/127.68 | | all_86_11) = all_170_1 206.14/127.68 | | 206.14/127.68 | | REF_CLOSE: (5), (11), (52) are inconsistent by sub-proof #48. 206.14/127.68 | | 206.14/127.68 | End of split 206.14/127.68 | 206.14/127.68 End of proof 206.14/127.68 206.14/127.68 Sub-proof #22 shows that the following formulas are inconsistent: 206.14/127.68 ---------------------------------------------------------------- 206.14/127.68 (1) length1(int, all_103_2) = all_86_13 206.14/127.68 (2) length1(int, all_103_2) = all_170_1 206.14/127.68 (3) length1(int, all_105_4) = all_153_1 206.14/127.68 (4) length1(int, all_103_4) = all_86_13 206.14/127.68 (5) length1(int, all_103_2) = all_242_1 206.14/127.68 (6) length1(int, all_103_4) = all_215_1 206.14/127.68 (7) ~ ($lesseq(all_86_11, all_215_1)) | ~ ($lesseq(0, all_215_1)) | ( ~ 206.14/127.68 (all_215_0 = all_215_1) & length1(int, all_103_2) = all_215_0) 206.14/127.68 (8) length1(int, all_103_4) = all_238_1 206.14/127.68 (9) $lesseq(1, $difference(all_153_1, all_86_10)) 206.14/127.68 (10) $lesseq(all_86_11, all_86_8) 206.14/127.68 (11) $lesseq(all_86_7, all_86_10) 206.14/127.68 (12) $lesseq(1, $difference(all_86_7, all_86_8)) 206.14/127.68 (13) $lesseq(0, all_86_11) 206.14/127.68 (14) length1(int, all_105_4) = all_170_1 206.14/127.68 (15) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 206.14/127.68 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 206.14/127.68 (16) length1(int, all_103_2) = all_177_2 206.14/127.68 (17) length1(int, all_103_2) = all_156_0 206.14/127.68 (18) length1(int, all_105_4) = all_169_1 206.14/127.68 206.14/127.68 Begin of proof 206.14/127.68 | 206.14/127.68 | GROUND_INST: instantiating (15) with all_170_1, all_169_1, all_105_4, int, 206.14/127.68 | simplifying with (14), (18) gives: 206.14/127.68 | (19) all_170_1 = all_169_1 206.14/127.68 | 206.14/127.68 | GROUND_INST: instantiating (15) with all_169_1, all_153_1, all_105_4, int, 206.14/127.68 | simplifying with (3), (18) gives: 206.26/127.68 | (20) all_169_1 = all_153_1 206.26/127.68 | 206.26/127.68 | GROUND_INST: instantiating (15) with all_86_13, all_177_2, all_103_2, int, 206.26/127.68 | simplifying with (1), (16) gives: 206.26/127.68 | (21) all_177_2 = all_86_13 206.26/127.68 | 206.26/127.68 | GROUND_INST: instantiating (15) with all_242_1, all_170_1, all_103_2, int, 206.26/127.68 | simplifying with (2), (5) gives: 206.26/127.68 | (22) all_242_1 = all_170_1 206.26/127.68 | 206.26/127.68 | GROUND_INST: instantiating (15) with all_177_2, all_170_1, all_103_2, int, 206.26/127.68 | simplifying with (2), (16) gives: 206.26/127.68 | (23) all_177_2 = all_170_1 206.26/127.68 | 206.26/127.68 | GROUND_INST: instantiating (15) with all_242_1, all_156_0, all_103_2, int, 206.26/127.68 | simplifying with (5), (17) gives: 206.26/127.68 | (24) all_242_1 = all_156_0 206.26/127.68 | 206.26/127.68 | GROUND_INST: instantiating (15) with all_86_13, all_238_1, all_103_4, int, 206.26/127.68 | simplifying with (4), (8) gives: 206.26/127.68 | (25) all_238_1 = all_86_13 206.26/127.68 | 206.26/127.68 | GROUND_INST: instantiating (15) with all_238_1, all_215_1, all_103_4, int, 206.26/127.68 | simplifying with (6), (8) gives: 206.26/127.68 | (26) all_238_1 = all_215_1 206.26/127.68 | 206.26/127.68 | COMBINE_EQS: (22), (24) imply: 206.26/127.68 | (27) all_170_1 = all_156_0 206.26/127.68 | 206.26/127.68 | SIMP: (27) implies: 206.26/127.68 | (28) all_170_1 = all_156_0 206.26/127.68 | 206.26/127.68 | COMBINE_EQS: (25), (26) imply: 206.26/127.68 | (29) all_215_1 = all_86_13 206.26/127.68 | 206.26/127.68 | SIMP: (29) implies: 206.26/127.68 | (30) all_215_1 = all_86_13 206.26/127.68 | 206.26/127.68 | COMBINE_EQS: (21), (23) imply: 206.26/127.68 | (31) all_170_1 = all_86_13 206.26/127.68 | 206.26/127.68 | SIMP: (31) implies: 206.26/127.68 | (32) all_170_1 = all_86_13 206.26/127.68 | 206.26/127.68 | COMBINE_EQS: (19), (32) imply: 206.26/127.68 | (33) all_169_1 = all_86_13 206.26/127.68 | 206.26/127.68 | SIMP: (33) implies: 206.26/127.68 | (34) all_169_1 = all_86_13 206.26/127.68 | 206.26/127.68 | COMBINE_EQS: (28), (32) imply: 206.26/127.68 | (35) all_156_0 = all_86_13 206.26/127.68 | 206.26/127.68 | SIMP: (35) implies: 206.26/127.68 | (36) all_156_0 = all_86_13 206.26/127.68 | 206.26/127.68 | COMBINE_EQS: (20), (34) imply: 206.26/127.68 | (37) all_153_1 = all_86_13 206.26/127.68 | 206.26/127.68 | SIMP: (37) implies: 206.26/127.68 | (38) all_153_1 = all_86_13 206.26/127.68 | 206.26/127.68 | REF_CLOSE: (7), (9), (10), (11), (12), (13), (15), (17), (30), (36), (38) are 206.26/127.68 | inconsistent by sub-proof #72. 206.26/127.68 | 206.26/127.68 End of proof 206.26/127.68 206.26/127.68 Sub-proof #23 shows that the following formulas are inconsistent: 206.26/127.68 ---------------------------------------------------------------- 206.26/127.68 (1) all_156_0 = all_86_13 206.26/127.68 (2) all_153_1 = all_86_13 206.26/127.68 (3) ~ ($lesseq(1, $difference(all_238_1, all_86_10))) | ~ 206.26/127.68 ($lesseq(all_86_13, all_238_1)) | ( ~ (all_238_0 = all_238_1) & 206.26/127.68 length1(int, all_103_2) = all_238_0) 206.26/127.68 (4) $lesseq(1, $difference(all_153_1, all_86_10)) 206.26/127.68 (5) all_238_1 = all_86_13 206.26/127.68 (6) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 206.26/127.68 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 206.26/127.68 (7) length1(int, all_103_2) = all_156_0 206.26/127.68 206.26/127.68 Begin of proof 206.26/127.68 | 206.26/127.68 | REDUCE: (2), (4) imply: 206.26/127.68 | (8) $lesseq(1, $difference(all_86_13, all_86_10)) 206.26/127.68 | 206.26/127.68 | REDUCE: (1), (7) imply: 206.26/127.68 | (9) length1(int, all_103_2) = all_86_13 206.26/127.68 | 206.26/127.68 | BETA: splitting (3) gives: 206.26/127.68 | 206.26/127.68 | Case 1: 206.26/127.68 | | 206.26/127.68 | | (10) $lesseq(1, $difference(all_86_13, all_238_1)) 206.26/127.68 | | 206.26/127.68 | | REDUCE: (5), (10) imply: 206.26/127.68 | | (11) $lesseq(0, -1) 206.26/127.68 | | 206.26/127.68 | | CLOSE: (11) is inconsistent. 206.26/127.68 | | 206.26/127.68 | Case 2: 206.26/127.68 | | 206.26/127.68 | | (12) ~ ($lesseq(1, $difference(all_238_1, all_86_10))) | ( ~ (all_238_0 206.26/127.68 | | = all_238_1) & length1(int, all_103_2) = all_238_0) 206.26/127.68 | | 206.26/127.68 | | REF_CLOSE: (5), (6), (8), (9), (12) are inconsistent by sub-proof #24. 206.26/127.68 | | 206.26/127.68 | End of split 206.26/127.68 | 206.26/127.68 End of proof 206.26/127.68 206.26/127.68 Sub-proof #24 shows that the following formulas are inconsistent: 206.26/127.68 ---------------------------------------------------------------- 206.26/127.68 (1) length1(int, all_103_2) = all_86_13 206.26/127.68 (2) $lesseq(1, $difference(all_86_13, all_86_10)) 206.26/127.68 (3) ~ ($lesseq(1, $difference(all_238_1, all_86_10))) | ( ~ (all_238_0 = 206.26/127.68 all_238_1) & length1(int, all_103_2) = all_238_0) 206.26/127.68 (4) all_238_1 = all_86_13 206.26/127.68 (5) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 206.26/127.68 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 206.26/127.68 206.26/127.68 Begin of proof 206.26/127.68 | 206.26/127.68 | BETA: splitting (3) gives: 206.26/127.68 | 206.26/127.68 | Case 1: 206.26/127.68 | | 206.26/127.68 | | (6) $lesseq(all_238_1, all_86_10) 206.26/127.68 | | 206.26/127.68 | | REDUCE: (4), (6) imply: 206.26/127.68 | | (7) $lesseq(all_86_13, all_86_10) 206.26/127.68 | | 206.26/127.68 | | COMBINE_INEQS: (2), (7) imply: 206.26/127.68 | | (8) $lesseq(0, -1) 206.26/127.68 | | 206.26/127.68 | | CLOSE: (8) is inconsistent. 206.26/127.68 | | 206.26/127.68 | Case 2: 206.26/127.68 | | 206.26/127.68 | | (9) ~ (all_238_0 = all_238_1) & length1(int, all_103_2) = all_238_0 206.26/127.68 | | 206.26/127.68 | | ALPHA: (9) implies: 206.26/127.68 | | (10) ~ (all_238_0 = all_238_1) 206.26/127.68 | | (11) length1(int, all_103_2) = all_238_0 206.26/127.68 | | 206.26/127.68 | | REDUCE: (4), (10) imply: 206.26/127.68 | | (12) ~ (all_238_0 = all_86_13) 206.26/127.68 | | 206.26/127.68 | | GROUND_INST: instantiating (5) with all_86_13, all_238_0, all_103_2, int, 206.26/127.68 | | simplifying with (1), (11) gives: 206.26/127.68 | | (13) all_238_0 = all_86_13 206.26/127.68 | | 206.26/127.68 | | REDUCE: (12), (13) imply: 206.26/127.68 | | (14) ~ (0 = 0) 206.26/127.68 | | 206.26/127.68 | | CLOSE: (14) is inconsistent. 206.26/127.68 | | 206.26/127.68 | End of split 206.26/127.68 | 206.26/127.68 End of proof 206.26/127.68 206.26/127.68 Sub-proof #25 shows that the following formulas are inconsistent: 206.26/127.68 ---------------------------------------------------------------- 206.26/127.68 (1) length1(int, all_103_2) = all_86_13 206.26/127.68 (2) length1(int, all_103_2) = all_170_1 206.26/127.68 (3) array_eq_sub1(int, all_105_4, all_105_2, $sum(all_86_10, 1), all_86_13) = 206.26/127.68 0 206.26/127.68 (4) elts(int, all_105_2) = all_187_2 206.26/127.68 (5) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.26/127.68 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ 206.26/127.68 (array_eq_sub1(v6, v5, v4, v3, v2) = v1) | ~ (array_eq_sub1(v6, v5, 206.26/127.68 v4, v3, v2) = v0)) 206.26/127.68 (6) elts(int, all_105_4) = all_187_3 206.26/127.68 (7) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 206.26/127.68 | ~ (elts(v3, v2) = v1) | ~ (elts(v3, v2) = v0)) 206.26/127.68 (8) elts(int, all_105_4) = all_105_3 206.26/127.68 (9) map_eq_sub1(int, all_105_3, all_105_1, 0, all_86_7) = 0 206.26/127.68 (10) elts(int, all_105_2) = all_105_1 206.26/127.68 (11) elts(int, all_105_4) = all_181_2 206.26/127.68 (12) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.26/127.68 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ (map_eq_sub1(v6, 206.26/127.68 v5, v4, v3, v2) = v1) | ~ (map_eq_sub1(v6, v5, v4, v3, v2) = v0)) 206.26/127.68 (13) length1(int, all_105_4) = all_170_1 206.26/127.68 (14) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 206.26/127.68 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 206.26/127.68 (15) (all_153_0 = all_153_1 & $lesseq(1, $difference(all_153_1, all_86_10)) & 206.26/127.68 $lesseq(all_86_13, all_153_1) & $lesseq(-1, all_86_10) & $lesseq(0, 206.26/127.68 all_86_13) & length1(int, all_105_2) = all_153_1 & length1(int, 206.26/127.68 all_105_4) = all_153_1) | ( ~ (all_153_1 = 0) & array_eq_sub1(int, 206.26/127.68 all_105_4, all_105_2, $sum(all_86_10, 1), all_86_13) = all_153_1) 206.26/127.68 (16) ( ~ (all_187_0 = 0) & map_eq_sub1(int, all_187_3, all_187_2, 206.26/127.68 $sum(all_86_10, 1), all_187_1) = all_187_0 & length1(int, all_105_4) 206.26/127.68 = all_187_1) | ( ~ (all_187_1 = 0) & map_eq_sub1(int, all_187_3, 206.26/127.68 all_187_2, 0, all_86_7) = all_187_1) 206.26/127.68 (17) map_eq_sub1(int, all_105_3, all_105_1, $sum(all_86_10, 1), all_86_13) = 206.26/127.68 0 206.26/127.68 (18) length1(int, all_105_4) = all_169_1 206.26/127.68 206.26/127.68 Begin of proof 206.26/127.68 | 206.26/127.68 | BETA: splitting (15) gives: 206.26/127.68 | 206.26/127.68 | Case 1: 206.26/127.68 | | 206.26/127.68 | | (19) all_153_0 = all_153_1 & $lesseq(1, $difference(all_153_1, 206.26/127.68 | | all_86_10)) & $lesseq(all_86_13, all_153_1) & $lesseq(-1, 206.26/127.68 | | all_86_10) & $lesseq(0, all_86_13) & length1(int, all_105_2) = 206.26/127.68 | | all_153_1 & length1(int, all_105_4) = all_153_1 206.26/127.68 | | 206.26/127.68 | | ALPHA: (19) implies: 206.26/127.68 | | (20) length1(int, all_105_4) = all_153_1 206.26/127.68 | | 206.26/127.70 | | REF_CLOSE: (1), (2), (4), (6), (7), (8), (9), (10), (11), (12), (13), (14), 206.26/127.70 | | (16), (17), (18), (20) are inconsistent by sub-proof #35. 206.26/127.70 | | 206.26/127.70 | Case 2: 206.26/127.70 | | 206.26/127.71 | | (21) ~ (all_153_1 = 0) & array_eq_sub1(int, all_105_4, all_105_2, 206.26/127.71 | | $sum(all_86_10, 1), all_86_13) = all_153_1 206.26/127.71 | | 206.26/127.71 | | REF_CLOSE: (3), (5), (21) are inconsistent by sub-proof #54. 206.26/127.71 | | 206.26/127.71 | End of split 206.26/127.71 | 206.26/127.71 End of proof 206.26/127.71 206.26/127.71 Sub-proof #26 shows that the following formulas are inconsistent: 206.26/127.71 ---------------------------------------------------------------- 206.26/127.71 (1) elts(int, all_103_4) = all_191_3 206.26/127.71 (2) elts(int, all_103_4) = all_103_3 206.26/127.71 (3) length1(int, all_103_4) = all_86_13 206.26/127.71 (4) map_eq_sub1(int, all_103_3, all_103_1, $sum(all_86_10, 1), all_86_13) = 0 206.26/127.71 (5) length1(int, all_103_2) = all_193_1 206.26/127.71 (6) length1(int, all_103_4) = all_193_1 206.26/127.71 (7) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.26/127.71 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ 206.26/127.71 (array_eq_sub1(v6, v5, v4, v3, v2) = v1) | ~ (array_eq_sub1(v6, v5, 206.26/127.71 v4, v3, v2) = v0)) 206.26/127.71 (8) (all_171_0 = all_171_1 & $lesseq(all_86_11, all_171_1) & $lesseq(0, 206.26/127.71 all_171_1) & $lesseq(0, all_86_11) & length1(int, all_103_2) = 206.26/127.71 all_171_1 & length1(int, all_103_4) = all_171_1) | ( ~ (all_171_1 = 0) 206.26/127.71 & array_eq_sub1(int, all_103_4, all_103_2, 0, all_86_11) = all_171_1) 206.26/127.71 (9) elts(int, all_103_2) = all_191_2 206.26/127.71 (10) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 206.26/127.71 | ~ (elts(v3, v2) = v1) | ~ (elts(v3, v2) = v0)) 206.26/127.71 (11) elts(int, all_103_2) = all_181_3 206.26/127.71 (12) map_eq_sub1(int, all_103_3, all_103_1, 0, all_86_11) = 0 206.26/127.71 (13) array_eq_sub1(int, all_103_4, all_103_2, 0, all_86_11) = 0 206.26/127.71 (14) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.26/127.71 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ (map_eq_sub1(v6, 206.26/127.71 v5, v4, v3, v2) = v1) | ~ (map_eq_sub1(v6, v5, v4, v3, v2) = v0)) 206.26/127.71 (15) elts(int, all_103_2) = all_103_1 206.26/127.71 (16) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 206.26/127.71 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 206.26/127.71 (17) elts(int, all_103_2) = all_156_3 206.26/127.71 (18) length1(int, all_103_2) = all_156_0 206.26/127.71 (19) ( ~ (all_191_0 = 0) & map_eq_sub1(int, all_191_3, all_191_2, 206.26/127.71 $sum(all_86_10, 1), all_191_1) = all_191_0 & length1(int, all_103_4) 206.26/127.71 = all_191_1) | ( ~ (all_191_1 = 0) & map_eq_sub1(int, all_191_3, 206.26/127.71 all_191_2, 0, all_86_11) = all_191_1) 206.26/127.71 206.26/127.71 Begin of proof 206.26/127.71 | 206.26/127.71 | BETA: splitting (8) gives: 206.26/127.71 | 206.26/127.71 | Case 1: 206.26/127.71 | | 206.26/127.71 | | (20) all_171_0 = all_171_1 & $lesseq(all_86_11, all_171_1) & $lesseq(0, 206.26/127.71 | | all_171_1) & $lesseq(0, all_86_11) & length1(int, all_103_2) = 206.26/127.71 | | all_171_1 & length1(int, all_103_4) = all_171_1 206.26/127.71 | | 206.26/127.71 | | ALPHA: (20) implies: 206.26/127.71 | | (21) length1(int, all_103_4) = all_171_1 206.26/127.71 | | 206.26/127.71 | | GROUND_INST: instantiating (16) with all_193_1, all_156_0, all_103_2, int, 206.26/127.71 | | simplifying with (5), (18) gives: 206.26/127.71 | | (22) all_193_1 = all_156_0 206.26/127.71 | | 206.26/127.71 | | GROUND_INST: instantiating (16) with all_86_13, all_171_1, all_103_4, int, 206.26/127.71 | | simplifying with (3), (21) gives: 206.26/127.71 | | (23) all_171_1 = all_86_13 206.26/127.71 | | 206.26/127.71 | | GROUND_INST: instantiating (16) with all_193_1, all_171_1, all_103_4, int, 206.26/127.71 | | simplifying with (6), (21) gives: 206.26/127.71 | | (24) all_193_1 = all_171_1 206.26/127.71 | | 206.26/127.71 | | GROUND_INST: instantiating (10) with all_103_1, all_191_2, all_103_2, int, 206.26/127.71 | | simplifying with (9), (15) gives: 206.26/127.71 | | (25) all_191_2 = all_103_1 206.26/127.71 | | 206.26/127.71 | | GROUND_INST: instantiating (10) with all_191_2, all_181_3, all_103_2, int, 206.26/127.71 | | simplifying with (9), (11) gives: 206.26/127.71 | | (26) all_191_2 = all_181_3 206.26/127.71 | | 206.26/127.71 | | GROUND_INST: instantiating (10) with all_191_2, all_156_3, all_103_2, int, 206.26/127.71 | | simplifying with (9), (17) gives: 206.26/127.71 | | (27) all_191_2 = all_156_3 206.26/127.71 | | 206.26/127.71 | | GROUND_INST: instantiating (10) with all_103_3, all_191_3, all_103_4, int, 206.26/127.71 | | simplifying with (1), (2) gives: 206.26/127.71 | | (28) all_191_3 = all_103_3 206.26/127.71 | | 206.26/127.71 | | COMBINE_EQS: (22), (24) imply: 206.26/127.71 | | (29) all_171_1 = all_156_0 206.26/127.71 | | 206.26/127.71 | | SIMP: (29) implies: 206.26/127.71 | | (30) all_171_1 = all_156_0 206.26/127.71 | | 206.26/127.71 | | COMBINE_EQS: (25), (26) imply: 206.26/127.71 | | (31) all_181_3 = all_103_1 206.26/127.71 | | 206.26/127.71 | | COMBINE_EQS: (26), (27) imply: 206.26/127.71 | | (32) all_181_3 = all_156_3 206.26/127.71 | | 206.26/127.71 | | COMBINE_EQS: (31), (32) imply: 206.26/127.71 | | (33) all_156_3 = all_103_1 206.26/127.71 | | 206.26/127.71 | | COMBINE_EQS: (23), (30) imply: 206.26/127.71 | | (34) all_156_0 = all_86_13 206.26/127.71 | | 206.26/127.71 | | REF_CLOSE: (3), (4), (12), (14), (16), (19), (25), (28) are inconsistent by 206.26/127.71 | | sub-proof #57. 206.26/127.71 | | 206.26/127.71 | Case 2: 206.26/127.71 | | 206.26/127.71 | | (35) ~ (all_171_1 = 0) & array_eq_sub1(int, all_103_4, all_103_2, 0, 206.26/127.71 | | all_86_11) = all_171_1 206.26/127.71 | | 206.26/127.71 | | REF_CLOSE: (7), (13), (35) are inconsistent by sub-proof #81. 206.26/127.71 | | 206.26/127.71 | End of split 206.26/127.71 | 206.26/127.71 End of proof 206.26/127.71 206.26/127.71 Sub-proof #27 shows that the following formulas are inconsistent: 206.26/127.71 ---------------------------------------------------------------- 206.26/127.71 (1) length1(int, all_103_2) = all_170_1 206.26/127.71 (2) length1(int, all_103_2) = all_242_1 206.26/127.71 (3) length1(int, all_103_2) = all_193_1 206.26/127.71 (4) map_eq_sub1(int, all_103_1, all_105_3, $sum(all_86_8, 1), all_86_13) = 0 206.26/127.71 (5) ( ~ (all_181_0 = 0) & map_eq_sub1(int, all_181_3, all_181_2, 206.26/127.71 $sum(all_86_8, 1), all_181_1) = all_181_0 & length1(int, all_103_2) = 206.26/127.71 all_181_1) | ( ~ (all_181_1 = 0) & map_eq_sub1(int, all_181_3, 206.26/127.71 all_181_2, 0, all_86_11) = all_181_1) 206.26/127.71 (6) elts(int, all_103_2) = all_191_2 206.26/127.71 (7) elts(int, all_105_4) = all_190_4 206.26/127.71 (8) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 206.26/127.71 | ~ (elts(v3, v2) = v1) | ~ (elts(v3, v2) = v0)) 206.26/127.71 (9) length1(int, all_105_4) = all_86_13 206.26/127.71 (10) elts(int, all_105_4) = all_105_3 206.26/127.71 (11) elts(int, all_105_4) = all_156_1 206.26/127.71 (12) elts(int, all_103_2) = all_181_3 206.26/127.71 (13) elts(int, all_105_4) = all_181_2 206.26/127.71 (14) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.26/127.71 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ (map_eq_sub1(v6, 206.26/127.71 v5, v4, v3, v2) = v1) | ~ (map_eq_sub1(v6, v5, v4, v3, v2) = v0)) 206.26/127.71 (15) map_eq_sub1(int, all_156_3, all_156_1, 0, all_86_11) = 0 206.26/127.71 (16) length1(int, all_105_4) = all_190_2 206.26/127.71 (17) length1(int, all_105_4) = all_170_1 206.26/127.71 (18) elts(int, all_103_2) = all_103_1 206.26/127.71 (19) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 206.26/127.71 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 206.26/127.71 (20) elts(int, all_103_2) = all_156_3 206.26/127.71 (21) length1(int, all_103_2) = all_156_0 206.26/127.71 206.26/127.71 Begin of proof 206.26/127.71 | 206.26/127.71 | GROUND_INST: instantiating (19) with all_86_13, all_190_2, all_105_4, int, 206.26/127.71 | simplifying with (9), (16) gives: 206.26/127.71 | (22) all_190_2 = all_86_13 206.26/127.71 | 206.26/127.71 | GROUND_INST: instantiating (19) with all_190_2, all_170_1, all_105_4, int, 206.26/127.71 | simplifying with (16), (17) gives: 206.26/127.71 | (23) all_190_2 = all_170_1 206.26/127.71 | 206.26/127.71 | GROUND_INST: instantiating (19) with all_242_1, all_193_1, all_103_2, int, 206.26/127.71 | simplifying with (2), (3) gives: 206.26/127.71 | (24) all_242_1 = all_193_1 206.26/127.71 | 206.26/127.71 | GROUND_INST: instantiating (19) with all_193_1, all_170_1, all_103_2, int, 206.26/127.71 | simplifying with (1), (3) gives: 206.26/127.71 | (25) all_193_1 = all_170_1 206.26/127.71 | 206.26/127.71 | GROUND_INST: instantiating (19) with all_242_1, all_156_0, all_103_2, int, 206.26/127.71 | simplifying with (2), (21) gives: 206.26/127.71 | (26) all_242_1 = all_156_0 206.26/127.71 | 206.26/127.71 | GROUND_INST: instantiating (8) with all_105_3, all_190_4, all_105_4, int, 206.26/127.71 | simplifying with (7), (10) gives: 206.26/127.71 | (27) all_190_4 = all_105_3 206.26/127.71 | 206.26/127.71 | GROUND_INST: instantiating (8) with all_190_4, all_181_2, all_105_4, int, 206.26/127.71 | simplifying with (7), (13) gives: 206.26/127.71 | (28) all_190_4 = all_181_2 206.26/127.71 | 206.26/127.71 | GROUND_INST: instantiating (8) with all_181_2, all_156_1, all_105_4, int, 206.26/127.71 | simplifying with (11), (13) gives: 206.26/127.71 | (29) all_181_2 = all_156_1 206.26/127.71 | 206.26/127.71 | GROUND_INST: instantiating (8) with all_103_1, all_191_2, all_103_2, int, 206.26/127.71 | simplifying with (6), (18) gives: 206.26/127.71 | (30) all_191_2 = all_103_1 206.26/127.71 | 206.26/127.71 | GROUND_INST: instantiating (8) with all_191_2, all_181_3, all_103_2, int, 206.26/127.71 | simplifying with (6), (12) gives: 206.26/127.71 | (31) all_191_2 = all_181_3 206.26/127.71 | 206.26/127.71 | GROUND_INST: instantiating (8) with all_181_3, all_156_3, all_103_2, int, 206.26/127.71 | simplifying with (12), (20) gives: 206.26/127.71 | (32) all_181_3 = all_156_3 206.26/127.71 | 206.26/127.71 | COMBINE_EQS: (24), (26) imply: 206.26/127.71 | (33) all_193_1 = all_156_0 206.26/127.71 | 206.26/127.71 | SIMP: (33) implies: 206.26/127.71 | (34) all_193_1 = all_156_0 206.26/127.71 | 206.26/127.71 | COMBINE_EQS: (25), (34) imply: 206.26/127.71 | (35) all_170_1 = all_156_0 206.26/127.71 | 206.26/127.71 | SIMP: (35) implies: 206.26/127.71 | (36) all_170_1 = all_156_0 206.26/127.71 | 206.26/127.71 | COMBINE_EQS: (30), (31) imply: 206.26/127.71 | (37) all_181_3 = all_103_1 206.26/127.71 | 206.26/127.71 | SIMP: (37) implies: 206.26/127.71 | (38) all_181_3 = all_103_1 206.26/127.71 | 206.26/127.71 | COMBINE_EQS: (22), (23) imply: 206.26/127.71 | (39) all_170_1 = all_86_13 206.26/127.71 | 206.26/127.71 | COMBINE_EQS: (27), (28) imply: 206.26/127.71 | (40) all_181_2 = all_105_3 206.26/127.71 | 206.26/127.71 | SIMP: (40) implies: 206.26/127.71 | (41) all_181_2 = all_105_3 206.26/127.71 | 206.26/127.71 | COMBINE_EQS: (29), (41) imply: 206.26/127.71 | (42) all_156_1 = all_105_3 206.26/127.71 | 206.26/127.71 | SIMP: (42) implies: 206.26/127.71 | (43) all_156_1 = all_105_3 206.26/127.71 | 206.26/127.71 | COMBINE_EQS: (32), (38) imply: 206.26/127.71 | (44) all_156_3 = all_103_1 206.26/127.71 | 206.26/127.71 | SIMP: (44) implies: 206.26/127.71 | (45) all_156_3 = all_103_1 206.26/127.71 | 206.26/127.71 | COMBINE_EQS: (36), (39) imply: 206.26/127.71 | (46) all_156_0 = all_86_13 206.26/127.71 | 206.26/127.71 | SIMP: (46) implies: 206.26/127.71 | (47) all_156_0 = all_86_13 206.26/127.71 | 206.26/127.71 | REF_CLOSE: (4), (5), (14), (15), (19), (21), (38), (41), (43), (45), (47) are 206.26/127.71 | inconsistent by sub-proof #44. 206.26/127.71 | 206.26/127.71 End of proof 206.26/127.71 206.26/127.71 Sub-proof #28 shows that the following formulas are inconsistent: 206.26/127.71 ---------------------------------------------------------------- 206.26/127.71 (1) elts(int, all_103_4) = all_191_3 206.26/127.71 (2) length1(int, all_103_2) = all_170_1 206.26/127.71 (3) elts(int, all_103_4) = all_103_3 206.26/127.71 (4) length1(int, all_105_4) = all_153_1 206.26/127.71 (5) length1(int, all_103_4) = all_86_13 206.26/127.71 (6) map_eq_sub1(int, all_103_3, all_103_1, $sum(all_86_10, 1), all_86_13) = 0 206.26/127.71 (7) length1(int, all_103_2) = all_242_1 206.26/127.71 (8) length1(int, all_103_2) = all_193_1 206.26/127.71 (9) length1(int, all_103_4) = all_193_1 206.26/127.71 (10) elts(int, all_103_2) = all_191_2 206.26/127.72 (11) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 206.26/127.72 | ~ (elts(v3, v2) = v1) | ~ (elts(v3, v2) = v0)) 206.26/127.72 (12) elts(int, all_103_2) = all_181_3 206.26/127.72 (13) length1(int, all_103_4) = all_171_1 206.26/127.72 (14) map_eq_sub1(int, all_103_3, all_103_1, 0, all_86_11) = 0 206.26/127.72 (15) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.26/127.72 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ (map_eq_sub1(v6, 206.26/127.72 v5, v4, v3, v2) = v1) | ~ (map_eq_sub1(v6, v5, v4, v3, v2) = v0)) 206.26/127.72 (16) length1(int, all_105_4) = all_190_2 206.26/127.72 (17) length1(int, all_105_4) = all_170_1 206.26/127.72 (18) elts(int, all_103_2) = all_103_1 206.26/127.72 (19) length1(int, all_103_2) = all_171_1 206.26/127.72 (20) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 206.26/127.72 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 206.26/127.72 (21) elts(int, all_103_2) = all_156_3 206.26/127.72 (22) length1(int, all_103_2) = all_156_0 206.26/127.72 (23) ( ~ (all_191_0 = 0) & map_eq_sub1(int, all_191_3, all_191_2, 206.26/127.72 $sum(all_86_10, 1), all_191_1) = all_191_0 & length1(int, all_103_4) 206.26/127.72 = all_191_1) | ( ~ (all_191_1 = 0) & map_eq_sub1(int, all_191_3, 206.26/127.72 all_191_2, 0, all_86_11) = all_191_1) 206.26/127.72 206.26/127.72 Begin of proof 206.26/127.72 | 206.26/127.72 | GROUND_INST: instantiating (20) with all_190_2, all_170_1, all_105_4, int, 206.26/127.72 | simplifying with (16), (17) gives: 206.26/127.72 | (24) all_190_2 = all_170_1 206.26/127.72 | 206.26/127.72 | GROUND_INST: instantiating (20) with all_190_2, all_153_1, all_105_4, int, 206.26/127.72 | simplifying with (4), (16) gives: 206.26/127.72 | (25) all_190_2 = all_153_1 206.26/127.72 | 206.26/127.72 | GROUND_INST: instantiating (20) with all_242_1, all_171_1, all_103_2, int, 206.26/127.72 | simplifying with (7), (19) gives: 206.26/127.72 | (26) all_242_1 = all_171_1 206.26/127.72 | 206.26/127.72 | GROUND_INST: instantiating (20) with all_242_1, all_170_1, all_103_2, int, 206.26/127.72 | simplifying with (2), (7) gives: 206.26/127.72 | (27) all_242_1 = all_170_1 206.26/127.72 | 206.26/127.72 | GROUND_INST: instantiating (20) with all_193_1, all_156_0, all_103_2, int, 206.26/127.72 | simplifying with (8), (22) gives: 206.26/127.72 | (28) all_193_1 = all_156_0 206.26/127.72 | 206.26/127.72 | GROUND_INST: instantiating (20) with all_171_1, all_156_0, all_103_2, int, 206.26/127.72 | simplifying with (19), (22) gives: 206.26/127.72 | (29) all_171_1 = all_156_0 206.26/127.72 | 206.26/127.72 | GROUND_INST: instantiating (20) with all_86_13, all_193_1, all_103_4, int, 206.26/127.72 | simplifying with (5), (9) gives: 206.26/127.72 | (30) all_193_1 = all_86_13 206.26/127.72 | 206.26/127.72 | GROUND_INST: instantiating (11) with all_103_1, all_181_3, all_103_2, int, 206.26/127.72 | simplifying with (12), (18) gives: 206.26/127.72 | (31) all_181_3 = all_103_1 206.26/127.72 | 206.26/127.72 | GROUND_INST: instantiating (11) with all_191_2, all_181_3, all_103_2, int, 206.26/127.72 | simplifying with (10), (12) gives: 206.26/127.72 | (32) all_191_2 = all_181_3 206.26/127.72 | 206.26/127.72 | GROUND_INST: instantiating (11) with all_191_2, all_156_3, all_103_2, int, 206.26/127.72 | simplifying with (10), (21) gives: 206.26/127.72 | (33) all_191_2 = all_156_3 206.26/127.72 | 206.26/127.72 | GROUND_INST: instantiating (11) with all_103_3, all_191_3, all_103_4, int, 206.26/127.72 | simplifying with (1), (3) gives: 206.26/127.72 | (34) all_191_3 = all_103_3 206.26/127.72 | 206.26/127.72 | COMBINE_EQS: (26), (27) imply: 206.26/127.72 | (35) all_171_1 = all_170_1 206.26/127.72 | 206.26/127.72 | SIMP: (35) implies: 206.26/127.72 | (36) all_171_1 = all_170_1 206.26/127.72 | 206.26/127.72 | COMBINE_EQS: (28), (30) imply: 206.26/127.72 | (37) all_156_0 = all_86_13 206.26/127.72 | 206.26/127.72 | SIMP: (37) implies: 206.26/127.72 | (38) all_156_0 = all_86_13 206.26/127.72 | 206.26/127.72 | COMBINE_EQS: (32), (33) imply: 206.26/127.72 | (39) all_181_3 = all_156_3 206.26/127.72 | 206.26/127.72 | SIMP: (39) implies: 206.26/127.72 | (40) all_181_3 = all_156_3 206.26/127.72 | 206.26/127.72 | COMBINE_EQS: (24), (25) imply: 206.26/127.72 | (41) all_170_1 = all_153_1 206.26/127.72 | 206.26/127.72 | SIMP: (41) implies: 206.26/127.72 | (42) all_170_1 = all_153_1 206.26/127.72 | 206.26/127.72 | COMBINE_EQS: (31), (40) imply: 206.26/127.72 | (43) all_156_3 = all_103_1 206.26/127.72 | 206.26/127.72 | COMBINE_EQS: (29), (36) imply: 206.26/127.72 | (44) all_170_1 = all_156_0 206.26/127.72 | 206.26/127.72 | COMBINE_EQS: (42), (44) imply: 206.26/127.72 | (45) all_156_0 = all_153_1 206.26/127.72 | 206.26/127.72 | SIMP: (45) implies: 206.26/127.72 | (46) all_156_0 = all_153_1 206.26/127.72 | 206.26/127.72 | COMBINE_EQS: (38), (46) imply: 206.26/127.72 | (47) all_153_1 = all_86_13 206.26/127.72 | 206.26/127.72 | COMBINE_EQS: (42), (47) imply: 206.26/127.72 | (48) all_170_1 = all_86_13 206.26/127.72 | 206.26/127.72 | COMBINE_EQS: (36), (48) imply: 206.26/127.72 | (49) all_171_1 = all_86_13 206.26/127.72 | 206.26/127.72 | COMBINE_EQS: (33), (43) imply: 206.26/127.72 | (50) all_191_2 = all_103_1 206.26/127.72 | 206.26/127.72 | REF_CLOSE: (5), (6), (14), (15), (20), (23), (34), (50) are inconsistent by 206.26/127.72 | sub-proof #57. 206.26/127.72 | 206.26/127.72 End of proof 206.26/127.72 206.26/127.72 Sub-proof #29 shows that the following formulas are inconsistent: 206.26/127.72 ---------------------------------------------------------------- 206.26/127.72 (1) length1(int, all_103_4) = all_86_13 206.26/127.72 (2) length1(int, all_103_4) = all_193_1 206.26/127.72 (3) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.26/127.72 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ 206.26/127.72 (array_eq_sub1(v6, v5, v4, v3, v2) = v1) | ~ (array_eq_sub1(v6, v5, 206.26/127.72 v4, v3, v2) = v0)) 206.26/127.72 (4) length1(int, all_105_4) = all_86_13 206.26/127.72 (5) (all_169_0 = all_169_1 & $lesseq(all_86_7, all_169_1) & $lesseq(0, 206.26/127.72 all_169_1) & $lesseq(0, all_86_7) & length1(int, all_105_2) = 206.26/127.72 all_169_1 & length1(int, all_105_4) = all_169_1) | ( ~ (all_169_1 = 0) 206.26/127.72 & array_eq_sub1(int, all_105_4, all_105_2, 0, all_86_7) = all_169_1) 206.26/127.72 (6) array_eq_sub1(int, all_105_4, all_105_2, 0, all_86_7) = 0 206.26/127.72 (7) length1(int, all_105_4) = all_234_1 206.26/127.72 (8) $lesseq(1, $difference(all_193_1, all_86_10)) 206.26/127.72 (9) ~ ($lesseq(1, $difference(all_234_1, all_86_10))) | ~ 206.26/127.72 ($lesseq(all_86_13, all_234_1)) | ( ~ (all_234_0 = all_234_1) & 206.26/127.72 length1(int, all_105_2) = all_234_0) 206.26/127.72 (10) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 206.26/127.72 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 206.26/127.72 206.26/127.72 Begin of proof 206.26/127.72 | 206.26/127.72 | BETA: splitting (5) gives: 206.26/127.72 | 206.26/127.72 | Case 1: 206.26/127.72 | | 206.26/127.72 | | (11) all_169_0 = all_169_1 & $lesseq(all_86_7, all_169_1) & $lesseq(0, 206.26/127.72 | | all_169_1) & $lesseq(0, all_86_7) & length1(int, all_105_2) = 206.26/127.72 | | all_169_1 & length1(int, all_105_4) = all_169_1 206.26/127.72 | | 206.26/127.72 | | ALPHA: (11) implies: 206.26/127.72 | | (12) length1(int, all_105_4) = all_169_1 206.26/127.72 | | (13) length1(int, all_105_2) = all_169_1 206.26/127.72 | | 206.26/127.72 | | REF_CLOSE: (1), (2), (4), (7), (8), (9), (10), (12), (13) are inconsistent 206.26/127.72 | | by sub-proof #30. 206.26/127.72 | | 206.26/127.72 | Case 2: 206.26/127.72 | | 206.26/127.72 | | (14) ~ (all_169_1 = 0) & array_eq_sub1(int, all_105_4, all_105_2, 0, 206.26/127.72 | | all_86_7) = all_169_1 206.26/127.72 | | 206.26/127.72 | | REF_CLOSE: (3), (6), (14) are inconsistent by sub-proof #75. 206.26/127.72 | | 206.26/127.72 | End of split 206.26/127.72 | 206.26/127.72 End of proof 206.26/127.72 206.26/127.72 Sub-proof #30 shows that the following formulas are inconsistent: 206.26/127.72 ---------------------------------------------------------------- 206.26/127.72 (1) length1(int, all_103_4) = all_86_13 206.26/127.72 (2) length1(int, all_103_4) = all_193_1 206.26/127.72 (3) length1(int, all_105_4) = all_86_13 206.26/127.72 (4) length1(int, all_105_4) = all_234_1 206.26/127.72 (5) $lesseq(1, $difference(all_193_1, all_86_10)) 206.26/127.72 (6) length1(int, all_105_2) = all_169_1 206.26/127.72 (7) ~ ($lesseq(1, $difference(all_234_1, all_86_10))) | ~ 206.26/127.72 ($lesseq(all_86_13, all_234_1)) | ( ~ (all_234_0 = all_234_1) & 206.26/127.72 length1(int, all_105_2) = all_234_0) 206.26/127.72 (8) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 206.26/127.72 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 206.26/127.72 (9) length1(int, all_105_4) = all_169_1 206.26/127.72 206.26/127.72 Begin of proof 206.26/127.72 | 206.26/127.72 | GROUND_INST: instantiating (8) with all_86_13, all_234_1, all_105_4, int, 206.26/127.72 | simplifying with (3), (4) gives: 206.26/127.72 | (10) all_234_1 = all_86_13 206.26/127.72 | 206.26/127.72 | GROUND_INST: instantiating (8) with all_234_1, all_169_1, all_105_4, int, 206.26/127.72 | simplifying with (4), (9) gives: 206.26/127.72 | (11) all_234_1 = all_169_1 206.26/127.72 | 206.26/127.72 | GROUND_INST: instantiating (8) with all_86_13, all_193_1, all_103_4, int, 206.26/127.72 | simplifying with (1), (2) gives: 206.26/127.72 | (12) all_193_1 = all_86_13 206.26/127.72 | 206.26/127.72 | COMBINE_EQS: (10), (11) imply: 206.26/127.72 | (13) all_169_1 = all_86_13 206.26/127.72 | 206.26/127.72 | REDUCE: (5), (12) imply: 206.26/127.72 | (14) $lesseq(1, $difference(all_86_13, all_86_10)) 206.26/127.72 | 206.26/127.72 | REDUCE: (6), (13) imply: 206.26/127.72 | (15) length1(int, all_105_2) = all_86_13 206.26/127.72 | 206.26/127.72 | REF_CLOSE: (7), (8), (10), (14), (15) are inconsistent by sub-proof #38. 206.26/127.72 | 206.26/127.72 End of proof 206.26/127.72 206.26/127.72 Sub-proof #31 shows that the following formulas are inconsistent: 206.26/127.72 ---------------------------------------------------------------- 206.26/127.72 (1) length1(int, all_103_2) = all_170_1 206.26/127.72 (2) length1(int, all_103_2) = all_242_1 206.26/127.72 (3) length1(int, all_103_2) = all_193_1 206.26/127.72 (4) map_eq_sub1(int, all_103_1, all_105_3, $sum(all_86_8, 1), all_86_13) = 0 206.26/127.72 (5) ( ~ (all_181_0 = 0) & map_eq_sub1(int, all_181_3, all_181_2, 206.26/127.72 $sum(all_86_8, 1), all_181_1) = all_181_0 & length1(int, all_103_2) = 206.26/127.72 all_181_1) | ( ~ (all_181_1 = 0) & map_eq_sub1(int, all_181_3, 206.26/127.72 all_181_2, 0, all_86_11) = all_181_1) 206.26/127.72 (6) elts(int, all_103_2) = all_192_3 206.26/127.72 (7) elts(int, all_105_4) = all_187_3 206.26/127.72 (8) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 206.26/127.72 | ~ (elts(v3, v2) = v1) | ~ (elts(v3, v2) = v0)) 206.26/127.72 (9) length1(int, all_105_4) = all_86_13 206.26/127.72 (10) elts(int, all_105_4) = all_105_3 206.26/127.72 (11) elts(int, all_105_4) = all_156_1 206.26/127.72 (12) elts(int, all_103_2) = all_181_3 206.26/127.72 (13) elts(int, all_105_4) = all_181_2 206.26/127.72 (14) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.26/127.72 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ (map_eq_sub1(v6, 206.26/127.72 v5, v4, v3, v2) = v1) | ~ (map_eq_sub1(v6, v5, v4, v3, v2) = v0)) 206.26/127.72 (15) map_eq_sub1(int, all_156_3, all_156_1, 0, all_86_11) = 0 206.26/127.72 (16) length1(int, all_105_4) = all_170_1 206.26/127.72 (17) elts(int, all_103_2) = all_103_1 206.26/127.72 (18) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 206.26/127.72 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 206.26/127.72 (19) length1(int, all_105_4) = all_219_1 206.26/127.72 (20) elts(int, all_103_2) = all_156_3 206.26/127.72 (21) length1(int, all_103_2) = all_156_0 206.26/127.72 206.26/127.72 Begin of proof 206.26/127.72 | 206.26/127.72 | GROUND_INST: instantiating (18) with all_86_13, all_219_1, all_105_4, int, 206.26/127.72 | simplifying with (9), (19) gives: 206.26/127.72 | (22) all_219_1 = all_86_13 206.26/127.72 | 206.26/127.72 | GROUND_INST: instantiating (18) with all_219_1, all_170_1, all_105_4, int, 206.26/127.72 | simplifying with (16), (19) gives: 206.26/127.72 | (23) all_219_1 = all_170_1 206.26/127.72 | 206.26/127.72 | GROUND_INST: instantiating (18) with all_242_1, all_193_1, all_103_2, int, 206.26/127.72 | simplifying with (2), (3) gives: 206.26/127.72 | (24) all_242_1 = all_193_1 206.26/127.72 | 206.26/127.72 | GROUND_INST: instantiating (18) with all_193_1, all_170_1, all_103_2, int, 206.26/127.72 | simplifying with (1), (3) gives: 206.26/127.72 | (25) all_193_1 = all_170_1 206.26/127.72 | 206.26/127.72 | GROUND_INST: instantiating (18) with all_242_1, all_156_0, all_103_2, int, 206.26/127.72 | simplifying with (2), (21) gives: 206.26/127.72 | (26) all_242_1 = all_156_0 206.26/127.72 | 206.26/127.72 | GROUND_INST: instantiating (8) with all_105_3, all_187_3, all_105_4, int, 206.26/127.72 | simplifying with (7), (10) gives: 206.26/127.72 | (27) all_187_3 = all_105_3 206.26/127.72 | 206.26/127.72 | GROUND_INST: instantiating (8) with all_187_3, all_181_2, all_105_4, int, 206.26/127.72 | simplifying with (7), (13) gives: 206.26/127.72 | (28) all_187_3 = all_181_2 206.26/127.72 | 206.26/127.72 | GROUND_INST: instantiating (8) with all_187_3, all_156_1, all_105_4, int, 206.26/127.72 | simplifying with (7), (11) gives: 206.26/127.72 | (29) all_187_3 = all_156_1 206.26/127.72 | 206.26/127.72 | GROUND_INST: instantiating (8) with all_103_1, all_181_3, all_103_2, int, 206.26/127.72 | simplifying with (12), (17) gives: 206.26/127.73 | (30) all_181_3 = all_103_1 206.26/127.73 | 206.26/127.73 | GROUND_INST: instantiating (8) with all_192_3, all_181_3, all_103_2, int, 206.26/127.73 | simplifying with (6), (12) gives: 206.26/127.73 | (31) all_192_3 = all_181_3 206.26/127.73 | 206.26/127.73 | GROUND_INST: instantiating (8) with all_192_3, all_156_3, all_103_2, int, 206.26/127.73 | simplifying with (6), (20) gives: 206.26/127.73 | (32) all_192_3 = all_156_3 206.26/127.73 | 206.26/127.73 | COMBINE_EQS: (24), (26) imply: 206.26/127.73 | (33) all_193_1 = all_156_0 206.26/127.73 | 206.26/127.73 | SIMP: (33) implies: 206.26/127.73 | (34) all_193_1 = all_156_0 206.26/127.73 | 206.26/127.73 | COMBINE_EQS: (22), (23) imply: 206.26/127.73 | (35) all_170_1 = all_86_13 206.26/127.73 | 206.26/127.73 | COMBINE_EQS: (25), (34) imply: 206.26/127.73 | (36) all_170_1 = all_156_0 206.26/127.73 | 206.26/127.73 | SIMP: (36) implies: 206.26/127.73 | (37) all_170_1 = all_156_0 206.26/127.73 | 206.26/127.73 | COMBINE_EQS: (31), (32) imply: 206.26/127.73 | (38) all_181_3 = all_156_3 206.26/127.73 | 206.26/127.73 | SIMP: (38) implies: 206.26/127.73 | (39) all_181_3 = all_156_3 206.26/127.73 | 206.26/127.73 | COMBINE_EQS: (27), (28) imply: 206.26/127.73 | (40) all_181_2 = all_105_3 206.26/127.73 | 206.26/127.73 | COMBINE_EQS: (28), (29) imply: 206.26/127.73 | (41) all_181_2 = all_156_1 206.26/127.73 | 206.26/127.73 | REF_CLOSE: (4), (5), (14), (15), (18), (21), (30), (35), (37), (39), (40), 206.26/127.73 | (41) are inconsistent by sub-proof #36. 206.26/127.73 | 206.26/127.73 End of proof 206.26/127.73 206.26/127.73 Sub-proof #32 shows that the following formulas are inconsistent: 206.26/127.73 ---------------------------------------------------------------- 206.26/127.73 (1) length1(int, all_103_2) = all_170_1 206.26/127.73 (2) length1(int, all_105_4) = all_153_1 206.26/127.73 (3) length1(int, all_103_4) = all_86_13 206.26/127.73 (4) length1(int, all_103_4) = all_215_1 206.26/127.73 (5) length1(int, all_103_2) = all_193_1 206.26/127.73 (6) ~ ($lesseq(all_86_11, all_215_1)) | ~ ($lesseq(0, all_215_1)) | ( ~ 206.26/127.73 (all_215_0 = all_215_1) & length1(int, all_103_2) = all_215_0) 206.26/127.73 (7) length1(int, all_103_4) = all_193_1 206.26/127.73 (8) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.26/127.73 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ 206.26/127.73 (array_eq_sub1(v6, v5, v4, v3, v2) = v1) | ~ (array_eq_sub1(v6, v5, 206.26/127.73 v4, v3, v2) = v0)) 206.26/127.73 (9) $lesseq(1, $difference(all_153_1, all_86_10)) 206.26/127.73 (10) $lesseq(all_86_11, all_86_8) 206.26/127.73 (11) $lesseq(all_86_7, all_86_10) 206.26/127.73 (12) (all_168_0 = all_168_1 & $lesseq(1, $difference(all_168_1, all_86_8)) & 206.26/127.73 $lesseq(all_86_13, all_168_1) & $lesseq(-1, all_86_8) & $lesseq(0, 206.26/127.73 all_86_13) & length1(int, all_105_4) = all_168_1 & length1(int, 206.26/127.73 all_103_2) = all_168_1) | ( ~ (all_168_1 = 0) & array_eq_sub1(int, 206.26/127.73 all_103_2, all_105_4, $sum(all_86_8, 1), all_86_13) = all_168_1) 206.26/127.73 (13) $lesseq(1, $difference(all_86_7, all_86_8)) 206.26/127.73 (14) $lesseq(0, all_86_11) 206.26/127.73 (15) length1(int, all_105_4) = all_170_1 206.26/127.73 (16) array_eq_sub1(int, all_103_2, all_105_4, $sum(all_86_8, 1), all_86_13) = 206.26/127.73 0 206.26/127.73 (17) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 206.26/127.73 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 206.26/127.73 (18) length1(int, all_105_4) = all_219_1 206.26/127.73 (19) length1(int, all_103_2) = all_156_0 206.26/127.73 206.26/127.73 Begin of proof 206.26/127.73 | 206.26/127.73 | BETA: splitting (12) gives: 206.26/127.73 | 206.26/127.73 | Case 1: 206.26/127.73 | | 206.26/127.73 | | (20) all_168_0 = all_168_1 & $lesseq(1, $difference(all_168_1, all_86_8)) 206.26/127.73 | | & $lesseq(all_86_13, all_168_1) & $lesseq(-1, all_86_8) & $lesseq(0, 206.26/127.73 | | all_86_13) & length1(int, all_105_4) = all_168_1 & length1(int, 206.26/127.73 | | all_103_2) = all_168_1 206.26/127.73 | | 206.26/127.73 | | ALPHA: (20) implies: 206.26/127.73 | | (21) length1(int, all_103_2) = all_168_1 206.26/127.73 | | 206.26/127.73 | | GROUND_INST: instantiating (17) with all_219_1, all_170_1, all_105_4, int, 206.26/127.73 | | simplifying with (15), (18) gives: 206.26/127.73 | | (22) all_219_1 = all_170_1 206.26/127.73 | | 206.26/127.73 | | GROUND_INST: instantiating (17) with all_219_1, all_153_1, all_105_4, int, 206.26/127.73 | | simplifying with (2), (18) gives: 206.26/127.73 | | (23) all_219_1 = all_153_1 206.26/127.73 | | 206.26/127.73 | | GROUND_INST: instantiating (17) with all_170_1, all_168_1, all_103_2, int, 206.26/127.73 | | simplifying with (1), (21) gives: 206.26/127.73 | | (24) all_170_1 = all_168_1 206.26/127.73 | | 206.26/127.73 | | GROUND_INST: instantiating (17) with all_193_1, all_156_0, all_103_2, int, 206.26/127.73 | | simplifying with (5), (19) gives: 206.26/127.73 | | (25) all_193_1 = all_156_0 206.26/127.73 | | 206.26/127.73 | | GROUND_INST: instantiating (17) with all_170_1, all_156_0, all_103_2, int, 206.26/127.73 | | simplifying with (1), (19) gives: 206.26/127.73 | | (26) all_170_1 = all_156_0 206.26/127.73 | | 206.26/127.73 | | GROUND_INST: instantiating (17) with all_86_13, all_215_1, all_103_4, int, 206.26/127.73 | | simplifying with (3), (4) gives: 206.26/127.73 | | (27) all_215_1 = all_86_13 206.26/127.73 | | 206.26/127.73 | | GROUND_INST: instantiating (17) with all_215_1, all_193_1, all_103_4, int, 206.26/127.73 | | simplifying with (4), (7) gives: 206.26/127.73 | | (28) all_215_1 = all_193_1 206.26/127.73 | | 206.26/127.73 | | COMBINE_EQS: (22), (23) imply: 206.26/127.73 | | (29) all_170_1 = all_153_1 206.26/127.73 | | 206.26/127.73 | | SIMP: (29) implies: 206.26/127.73 | | (30) all_170_1 = all_153_1 206.26/127.73 | | 206.26/127.73 | | COMBINE_EQS: (27), (28) imply: 206.26/127.73 | | (31) all_193_1 = all_86_13 206.26/127.73 | | 206.26/127.73 | | SIMP: (31) implies: 206.26/127.73 | | (32) all_193_1 = all_86_13 206.26/127.73 | | 206.26/127.73 | | COMBINE_EQS: (25), (32) imply: 206.26/127.73 | | (33) all_156_0 = all_86_13 206.26/127.73 | | 206.26/127.73 | | SIMP: (33) implies: 206.26/127.73 | | (34) all_156_0 = all_86_13 206.26/127.73 | | 206.26/127.73 | | COMBINE_EQS: (24), (30) imply: 206.26/127.73 | | (35) all_168_1 = all_153_1 206.26/127.73 | | 206.26/127.73 | | COMBINE_EQS: (24), (26) imply: 206.26/127.73 | | (36) all_168_1 = all_156_0 206.26/127.73 | | 206.26/127.73 | | COMBINE_EQS: (35), (36) imply: 206.26/127.73 | | (37) all_156_0 = all_153_1 206.26/127.73 | | 206.26/127.73 | | REF_CLOSE: (6), (9), (10), (11), (13), (14), (17), (19), (27), (34), (37) 206.26/127.73 | | are inconsistent by sub-proof #33. 206.26/127.73 | | 206.26/127.73 | Case 2: 206.26/127.73 | | 206.26/127.73 | | (38) ~ (all_168_1 = 0) & array_eq_sub1(int, all_103_2, all_105_4, 206.26/127.73 | | $sum(all_86_8, 1), all_86_13) = all_168_1 206.26/127.73 | | 206.26/127.73 | | REF_CLOSE: (8), (16), (38) are inconsistent by sub-proof #83. 206.26/127.73 | | 206.26/127.73 | End of split 206.26/127.73 | 206.26/127.73 End of proof 206.26/127.73 206.26/127.73 Sub-proof #33 shows that the following formulas are inconsistent: 206.26/127.73 ---------------------------------------------------------------- 206.26/127.73 (1) all_156_0 = all_153_1 206.26/127.73 (2) all_156_0 = all_86_13 206.26/127.73 (3) ~ ($lesseq(all_86_11, all_215_1)) | ~ ($lesseq(0, all_215_1)) | ( ~ 206.26/127.73 (all_215_0 = all_215_1) & length1(int, all_103_2) = all_215_0) 206.26/127.73 (4) $lesseq(1, $difference(all_153_1, all_86_10)) 206.26/127.73 (5) $lesseq(all_86_11, all_86_8) 206.26/127.73 (6) $lesseq(all_86_7, all_86_10) 206.26/127.73 (7) all_215_1 = all_86_13 206.26/127.73 (8) $lesseq(1, $difference(all_86_7, all_86_8)) 206.26/127.73 (9) $lesseq(0, all_86_11) 206.26/127.73 (10) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 206.26/127.73 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 206.26/127.73 (11) length1(int, all_103_2) = all_156_0 206.26/127.73 206.26/127.73 Begin of proof 206.26/127.73 | 206.26/127.73 | SIMP: (1) implies: 206.26/127.73 | (12) all_156_0 = all_153_1 206.26/127.73 | 206.26/127.73 | COMBINE_EQS: (2), (12) imply: 206.26/127.73 | (13) all_153_1 = all_86_13 206.26/127.73 | 206.26/127.73 | SIMP: (13) implies: 206.26/127.73 | (14) all_153_1 = all_86_13 206.26/127.73 | 206.26/127.73 | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (14) are 206.26/127.73 | inconsistent by sub-proof #72. 206.26/127.73 | 206.26/127.73 End of proof 206.26/127.73 206.26/127.73 Sub-proof #34 shows that the following formulas are inconsistent: 206.26/127.73 ---------------------------------------------------------------- 206.26/127.73 (1) length1(int, all_103_2) = all_170_1 206.26/127.73 (2) length1(int, all_105_2) = all_86_13 206.26/127.73 (3) length1(int, all_103_4) = all_86_13 206.26/127.73 (4) $lesseq(all_86_7, all_86_13) 206.26/127.73 (5) length1(int, all_103_4) = all_193_1 206.26/127.73 (6) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.26/127.73 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ 206.26/127.73 (array_eq_sub1(v6, v5, v4, v3, v2) = v1) | ~ (array_eq_sub1(v6, v5, 206.26/127.73 v4, v3, v2) = v0)) 206.26/127.73 (7) (all_171_0 = all_171_1 & $lesseq(all_86_11, all_171_1) & $lesseq(0, 206.26/127.73 all_171_1) & $lesseq(0, all_86_11) & length1(int, all_103_2) = 206.26/127.73 all_171_1 & length1(int, all_103_4) = all_171_1) | ( ~ (all_171_1 = 0) 206.26/127.73 & array_eq_sub1(int, all_103_4, all_103_2, 0, all_86_11) = all_171_1) 206.26/127.73 (8) (all_192_0 = 0 & all_192_1 = 0 & map_eq_sub1(int, all_192_4, all_192_3, 206.26/127.73 $sum(all_86_10, 1), all_192_2) = 0 & map_eq_sub1(int, all_192_4, 206.26/127.73 all_192_3, 0, all_86_11) = 0 & length1(int, all_103_4) = all_192_2 & 206.26/127.73 elts(int, all_103_2) = all_192_3 & elts(int, all_103_4) = all_192_4 & 206.26/127.73 in_uni(all_192_3) & in_uni(all_192_4)) | ( ~ (all_192_4 = 0) & 206.26/127.73 permut_sub2(int, all_103_4, all_103_2, all_86_11, $sum(all_86_10, 1)) = 206.26/127.73 all_192_4) 206.26/127.73 (9) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.26/127.73 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ (permut_sub2(v6, 206.26/127.73 v5, v4, v3, v2) = v1) | ~ (permut_sub2(v6, v5, v4, v3, v2) = v0)) 206.26/127.73 (10) $lesseq(1, $difference(all_193_1, all_86_10)) 206.26/127.73 (11) $lesseq(all_86_11, all_86_8) 206.26/127.73 (12) $lesseq(all_86_7, all_86_10) 206.26/127.73 (13) ~ ($lesseq(all_86_7, all_219_1)) | ~ ($lesseq(0, all_219_1)) | ( ~ 206.26/127.73 (all_219_0 = all_219_1) & length1(int, all_105_2) = all_219_0) 206.26/127.73 (14) $lesseq(1, $difference(all_86_7, all_86_8)) 206.26/127.73 (15) permut_sub2(int, all_103_4, all_103_2, all_86_11, $sum(all_86_10, 1)) = 206.26/127.73 0 206.26/127.73 (16) all_215_1 = 0 & array_eq_sub1(int, all_103_4, all_103_2, 0, all_86_11) = 206.26/127.73 0 206.26/127.73 (17) length1(int, all_105_4) = all_170_1 206.26/127.73 (18) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 206.26/127.73 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 206.26/127.73 (19) length1(int, all_105_4) = all_219_1 206.26/127.73 206.26/127.73 Begin of proof 206.26/127.73 | 206.26/127.73 | ALPHA: (16) implies: 206.26/127.73 | (20) array_eq_sub1(int, all_103_4, all_103_2, 0, all_86_11) = 0 206.26/127.73 | 206.26/127.73 | BETA: splitting (7) gives: 206.26/127.73 | 206.26/127.73 | Case 1: 206.26/127.73 | | 206.26/127.73 | | (21) all_171_0 = all_171_1 & $lesseq(all_86_11, all_171_1) & $lesseq(0, 206.26/127.73 | | all_171_1) & $lesseq(0, all_86_11) & length1(int, all_103_2) = 206.26/127.73 | | all_171_1 & length1(int, all_103_4) = all_171_1 206.26/127.73 | | 206.26/127.73 | | ALPHA: (21) implies: 206.26/127.73 | | (22) $lesseq(0, all_86_11) 206.26/127.73 | | (23) length1(int, all_103_4) = all_171_1 206.26/127.73 | | (24) length1(int, all_103_2) = all_171_1 206.26/127.73 | | 206.26/127.73 | | REF_CLOSE: (1), (2), (3), (4), (5), (8), (9), (10), (11), (12), (13), (14), 206.26/127.73 | | (15), (17), (18), (19), (22), (23), (24) are inconsistent by 206.26/127.73 | | sub-proof #51. 206.26/127.73 | | 206.26/127.73 | Case 2: 206.26/127.73 | | 206.26/127.73 | | (25) ~ (all_171_1 = 0) & array_eq_sub1(int, all_103_4, all_103_2, 0, 206.26/127.73 | | all_86_11) = all_171_1 206.26/127.73 | | 206.26/127.73 | | REF_CLOSE: (6), (20), (25) are inconsistent by sub-proof #81. 206.26/127.73 | | 206.26/127.73 | End of split 206.26/127.73 | 206.26/127.73 End of proof 206.26/127.73 206.26/127.73 Sub-proof #35 shows that the following formulas are inconsistent: 206.26/127.73 ---------------------------------------------------------------- 206.26/127.73 (1) length1(int, all_103_2) = all_86_13 206.26/127.73 (2) length1(int, all_103_2) = all_170_1 206.26/127.73 (3) length1(int, all_105_4) = all_153_1 206.26/127.73 (4) elts(int, all_105_2) = all_187_2 206.26/127.73 (5) elts(int, all_105_4) = all_187_3 206.26/127.73 (6) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 206.26/127.73 | ~ (elts(v3, v2) = v1) | ~ (elts(v3, v2) = v0)) 206.26/127.73 (7) elts(int, all_105_4) = all_105_3 206.26/127.73 (8) map_eq_sub1(int, all_105_3, all_105_1, 0, all_86_7) = 0 206.26/127.73 (9) elts(int, all_105_2) = all_105_1 206.26/127.73 (10) elts(int, all_105_4) = all_181_2 206.26/127.73 (11) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.26/127.73 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ (map_eq_sub1(v6, 206.26/127.73 v5, v4, v3, v2) = v1) | ~ (map_eq_sub1(v6, v5, v4, v3, v2) = v0)) 206.26/127.73 (12) length1(int, all_105_4) = all_170_1 206.26/127.73 (13) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 206.26/127.73 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 206.26/127.73 (14) ( ~ (all_187_0 = 0) & map_eq_sub1(int, all_187_3, all_187_2, 206.26/127.73 $sum(all_86_10, 1), all_187_1) = all_187_0 & length1(int, all_105_4) 206.26/127.73 = all_187_1) | ( ~ (all_187_1 = 0) & map_eq_sub1(int, all_187_3, 206.26/127.73 all_187_2, 0, all_86_7) = all_187_1) 206.26/127.73 (15) map_eq_sub1(int, all_105_3, all_105_1, $sum(all_86_10, 1), all_86_13) = 206.26/127.73 0 206.26/127.73 (16) length1(int, all_105_4) = all_169_1 206.26/127.73 206.26/127.73 Begin of proof 206.26/127.73 | 206.26/127.73 | GROUND_INST: instantiating (13) with all_170_1, all_169_1, all_105_4, int, 206.26/127.73 | simplifying with (12), (16) gives: 206.26/127.73 | (17) all_170_1 = all_169_1 206.26/127.73 | 206.26/127.73 | GROUND_INST: instantiating (13) with all_169_1, all_153_1, all_105_4, int, 206.26/127.73 | simplifying with (3), (16) gives: 206.26/127.73 | (18) all_169_1 = all_153_1 206.26/127.73 | 206.26/127.73 | GROUND_INST: instantiating (13) with all_86_13, all_170_1, all_103_2, int, 206.26/127.73 | simplifying with (1), (2) gives: 206.26/127.74 | (19) all_170_1 = all_86_13 206.26/127.74 | 206.26/127.74 | GROUND_INST: instantiating (6) with all_105_1, all_187_2, all_105_2, int, 206.26/127.74 | simplifying with (4), (9) gives: 206.26/127.74 | (20) all_187_2 = all_105_1 206.26/127.74 | 206.26/127.74 | GROUND_INST: instantiating (6) with all_105_3, all_187_3, all_105_4, int, 206.26/127.74 | simplifying with (5), (7) gives: 206.26/127.74 | (21) all_187_3 = all_105_3 206.26/127.74 | 206.26/127.74 | GROUND_INST: instantiating (6) with all_187_3, all_181_2, all_105_4, int, 206.26/127.74 | simplifying with (5), (10) gives: 206.26/127.74 | (22) all_187_3 = all_181_2 206.26/127.74 | 206.26/127.74 | COMBINE_EQS: (21), (22) imply: 206.26/127.74 | (23) all_181_2 = all_105_3 206.26/127.74 | 206.26/127.74 | COMBINE_EQS: (17), (19) imply: 206.26/127.74 | (24) all_169_1 = all_86_13 206.26/127.74 | 206.26/127.74 | SIMP: (24) implies: 206.26/127.74 | (25) all_169_1 = all_86_13 206.26/127.74 | 206.26/127.74 | COMBINE_EQS: (18), (25) imply: 206.26/127.74 | (26) all_153_1 = all_86_13 206.26/127.74 | 206.26/127.74 | REDUCE: (3), (26) imply: 206.26/127.74 | (27) length1(int, all_105_4) = all_86_13 206.26/127.74 | 206.26/127.74 | REF_CLOSE: (8), (11), (13), (14), (15), (20), (21), (27) are inconsistent by 206.26/127.74 | sub-proof #66. 206.26/127.74 | 206.26/127.74 End of proof 206.26/127.74 206.26/127.74 Sub-proof #36 shows that the following formulas are inconsistent: 206.26/127.74 ---------------------------------------------------------------- 206.26/127.74 (1) all_181_2 = all_105_3 206.26/127.74 (2) all_181_3 = all_156_3 206.26/127.74 (3) map_eq_sub1(int, all_103_1, all_105_3, $sum(all_86_8, 1), all_86_13) = 0 206.26/127.74 (4) ( ~ (all_181_0 = 0) & map_eq_sub1(int, all_181_3, all_181_2, 206.26/127.74 $sum(all_86_8, 1), all_181_1) = all_181_0 & length1(int, all_103_2) = 206.26/127.74 all_181_1) | ( ~ (all_181_1 = 0) & map_eq_sub1(int, all_181_3, 206.26/127.74 all_181_2, 0, all_86_11) = all_181_1) 206.26/127.74 (5) all_181_3 = all_103_1 206.26/127.74 (6) all_170_1 = all_86_13 206.26/127.74 (7) all_170_1 = all_156_0 206.26/127.74 (8) all_181_2 = all_156_1 206.26/127.74 (9) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.26/127.74 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ (map_eq_sub1(v6, 206.26/127.74 v5, v4, v3, v2) = v1) | ~ (map_eq_sub1(v6, v5, v4, v3, v2) = v0)) 206.26/127.74 (10) map_eq_sub1(int, all_156_3, all_156_1, 0, all_86_11) = 0 206.26/127.74 (11) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 206.26/127.74 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 206.26/127.74 (12) length1(int, all_103_2) = all_156_0 206.26/127.74 206.26/127.74 Begin of proof 206.26/127.74 | 206.26/127.74 | COMBINE_EQS: (1), (8) imply: 206.26/127.74 | (13) all_156_1 = all_105_3 206.26/127.74 | 206.26/127.74 | SIMP: (13) implies: 206.26/127.74 | (14) all_156_1 = all_105_3 206.26/127.74 | 206.26/127.74 | COMBINE_EQS: (2), (5) imply: 206.26/127.74 | (15) all_156_3 = all_103_1 206.26/127.74 | 206.26/127.74 | COMBINE_EQS: (6), (7) imply: 206.26/127.74 | (16) all_156_0 = all_86_13 206.26/127.74 | 206.26/127.74 | SIMP: (16) implies: 206.26/127.74 | (17) all_156_0 = all_86_13 206.26/127.74 | 206.26/127.74 | REF_CLOSE: (1), (3), (4), (5), (9), (10), (11), (12), (14), (15), (17) are 206.26/127.74 | inconsistent by sub-proof #44. 206.26/127.74 | 206.26/127.74 End of proof 206.26/127.74 206.26/127.74 Sub-proof #37 shows that the following formulas are inconsistent: 206.26/127.74 ---------------------------------------------------------------- 206.26/127.74 (1) length1(int, all_103_2) = all_170_1 206.26/127.74 (2) all_242_1 = 0 & array_eq_sub1(int, all_103_2, all_105_4, $sum(all_86_8, 206.26/127.74 1), all_86_13) = 0 206.26/127.74 (3) length1(int, all_105_2) = all_86_13 206.26/127.74 (4) length1(int, all_103_4) = all_86_13 206.26/127.74 (5) length1(int, all_103_4) = all_215_1 206.26/127.74 (6) length1(int, all_103_2) = all_193_1 206.26/127.74 (7) length1(int, all_103_4) = all_193_1 206.26/127.74 (8) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.26/127.74 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ 206.26/127.74 (array_eq_sub1(v6, v5, v4, v3, v2) = v1) | ~ (array_eq_sub1(v6, v5, 206.26/127.74 v4, v3, v2) = v0)) 206.26/127.74 (9) length1(int, all_105_4) = all_234_1 206.26/127.74 (10) $lesseq(1, $difference(all_193_1, all_86_10)) 206.26/127.74 (11) (all_168_0 = all_168_1 & $lesseq(1, $difference(all_168_1, all_86_8)) & 206.26/127.74 $lesseq(all_86_13, all_168_1) & $lesseq(-1, all_86_8) & $lesseq(0, 206.26/127.74 all_86_13) & length1(int, all_105_4) = all_168_1 & length1(int, 206.26/127.74 all_103_2) = all_168_1) | ( ~ (all_168_1 = 0) & array_eq_sub1(int, 206.26/127.74 all_103_2, all_105_4, $sum(all_86_8, 1), all_86_13) = all_168_1) 206.26/127.74 (12) length1(int, all_105_4) = all_190_2 206.26/127.74 (13) length1(int, all_105_4) = all_170_1 206.26/127.74 (14) ~ ($lesseq(1, $difference(all_234_1, all_86_10))) | ~ 206.26/127.74 ($lesseq(all_86_13, all_234_1)) | ( ~ (all_234_0 = all_234_1) & 206.26/127.74 length1(int, all_105_2) = all_234_0) 206.26/127.74 (15) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 206.26/127.74 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 206.26/127.74 (16) length1(int, all_105_4) = all_219_1 206.26/127.74 206.26/127.74 Begin of proof 206.26/127.74 | 206.26/127.74 | ALPHA: (2) implies: 206.26/127.74 | (17) array_eq_sub1(int, all_103_2, all_105_4, $sum(all_86_8, 1), all_86_13) 206.26/127.74 | = 0 206.26/127.74 | 206.26/127.74 | BETA: splitting (11) gives: 206.26/127.74 | 206.26/127.74 | Case 1: 206.26/127.74 | | 206.26/127.74 | | (18) all_168_0 = all_168_1 & $lesseq(1, $difference(all_168_1, all_86_8)) 206.26/127.74 | | & $lesseq(all_86_13, all_168_1) & $lesseq(-1, all_86_8) & $lesseq(0, 206.26/127.74 | | all_86_13) & length1(int, all_105_4) = all_168_1 & length1(int, 206.26/127.74 | | all_103_2) = all_168_1 206.26/127.74 | | 206.26/127.74 | | ALPHA: (18) implies: 206.26/127.74 | | (19) length1(int, all_105_4) = all_168_1 206.26/127.74 | | 206.26/127.74 | | GROUND_INST: instantiating (15) with all_234_1, all_219_1, all_105_4, int, 206.26/127.74 | | simplifying with (9), (16) gives: 206.26/127.74 | | (20) all_234_1 = all_219_1 206.48/127.74 | | 206.48/127.74 | | GROUND_INST: instantiating (15) with all_219_1, all_190_2, all_105_4, int, 206.48/127.74 | | simplifying with (12), (16) gives: 206.48/127.74 | | (21) all_219_1 = all_190_2 206.48/127.74 | | 206.48/127.74 | | GROUND_INST: instantiating (15) with all_190_2, all_170_1, all_105_4, int, 206.48/127.74 | | simplifying with (12), (13) gives: 206.48/127.74 | | (22) all_190_2 = all_170_1 206.48/127.74 | | 206.48/127.74 | | GROUND_INST: instantiating (15) with all_234_1, all_168_1, all_105_4, int, 206.48/127.74 | | simplifying with (9), (19) gives: 206.48/127.74 | | (23) all_234_1 = all_168_1 206.48/127.74 | | 206.48/127.74 | | GROUND_INST: instantiating (15) with all_193_1, all_170_1, all_103_2, int, 206.48/127.74 | | simplifying with (1), (6) gives: 206.48/127.74 | | (24) all_193_1 = all_170_1 206.48/127.74 | | 206.48/127.74 | | GROUND_INST: instantiating (15) with all_86_13, all_215_1, all_103_4, int, 206.48/127.74 | | simplifying with (4), (5) gives: 206.48/127.74 | | (25) all_215_1 = all_86_13 206.48/127.74 | | 206.48/127.74 | | GROUND_INST: instantiating (15) with all_215_1, all_193_1, all_103_4, int, 206.48/127.74 | | simplifying with (5), (7) gives: 206.48/127.74 | | (26) all_215_1 = all_193_1 206.48/127.74 | | 206.48/127.74 | | COMBINE_EQS: (20), (23) imply: 206.48/127.74 | | (27) all_219_1 = all_168_1 206.48/127.74 | | 206.48/127.74 | | SIMP: (27) implies: 206.48/127.74 | | (28) all_219_1 = all_168_1 206.48/127.74 | | 206.48/127.74 | | COMBINE_EQS: (21), (28) imply: 206.48/127.74 | | (29) all_190_2 = all_168_1 206.48/127.74 | | 206.48/127.74 | | SIMP: (29) implies: 206.48/127.74 | | (30) all_190_2 = all_168_1 206.48/127.74 | | 206.48/127.74 | | COMBINE_EQS: (25), (26) imply: 206.48/127.74 | | (31) all_193_1 = all_86_13 206.48/127.74 | | 206.48/127.74 | | SIMP: (31) implies: 206.48/127.74 | | (32) all_193_1 = all_86_13 206.48/127.74 | | 206.48/127.74 | | COMBINE_EQS: (24), (32) imply: 206.48/127.74 | | (33) all_170_1 = all_86_13 206.48/127.74 | | 206.48/127.74 | | SIMP: (33) implies: 206.48/127.74 | | (34) all_170_1 = all_86_13 206.48/127.74 | | 206.48/127.74 | | COMBINE_EQS: (22), (30) imply: 206.48/127.74 | | (35) all_170_1 = all_168_1 206.48/127.74 | | 206.48/127.74 | | SIMP: (35) implies: 206.48/127.74 | | (36) all_170_1 = all_168_1 206.48/127.74 | | 206.48/127.74 | | COMBINE_EQS: (34), (36) imply: 206.48/127.74 | | (37) all_168_1 = all_86_13 206.48/127.74 | | 206.48/127.74 | | SIMP: (37) implies: 206.48/127.74 | | (38) all_168_1 = all_86_13 206.48/127.74 | | 206.48/127.74 | | COMBINE_EQS: (23), (38) imply: 206.48/127.74 | | (39) all_234_1 = all_86_13 206.48/127.74 | | 206.48/127.74 | | REDUCE: (10), (32) imply: 206.48/127.74 | | (40) $lesseq(1, $difference(all_86_13, all_86_10)) 206.48/127.74 | | 206.48/127.74 | | REF_CLOSE: (3), (14), (15), (39), (40) are inconsistent by sub-proof #38. 206.48/127.74 | | 206.48/127.74 | Case 2: 206.48/127.74 | | 206.48/127.74 | | (41) ~ (all_168_1 = 0) & array_eq_sub1(int, all_103_2, all_105_4, 206.48/127.74 | | $sum(all_86_8, 1), all_86_13) = all_168_1 206.48/127.74 | | 206.48/127.74 | | REF_CLOSE: (8), (17), (41) are inconsistent by sub-proof #83. 206.48/127.74 | | 206.48/127.74 | End of split 206.48/127.74 | 206.48/127.74 End of proof 206.48/127.74 206.48/127.74 Sub-proof #38 shows that the following formulas are inconsistent: 206.48/127.74 ---------------------------------------------------------------- 206.48/127.74 (1) length1(int, all_105_2) = all_86_13 206.48/127.74 (2) all_234_1 = all_86_13 206.48/127.74 (3) $lesseq(1, $difference(all_86_13, all_86_10)) 206.48/127.74 (4) ~ ($lesseq(1, $difference(all_234_1, all_86_10))) | ~ 206.48/127.74 ($lesseq(all_86_13, all_234_1)) | ( ~ (all_234_0 = all_234_1) & 206.48/127.74 length1(int, all_105_2) = all_234_0) 206.48/127.74 (5) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 206.48/127.74 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 206.48/127.74 206.48/127.74 Begin of proof 206.48/127.74 | 206.48/127.74 | BETA: splitting (4) gives: 206.48/127.74 | 206.48/127.74 | Case 1: 206.48/127.74 | | 206.48/127.74 | | (6) $lesseq(1, $difference(all_86_13, all_234_1)) 206.48/127.74 | | 206.48/127.74 | | REDUCE: (2), (6) imply: 206.48/127.74 | | (7) $lesseq(0, -1) 206.48/127.74 | | 206.48/127.74 | | CLOSE: (7) is inconsistent. 206.48/127.74 | | 206.48/127.74 | Case 2: 206.48/127.74 | | 206.48/127.74 | | (8) ~ ($lesseq(1, $difference(all_234_1, all_86_10))) | ( ~ (all_234_0 = 206.48/127.74 | | all_234_1) & length1(int, all_105_2) = all_234_0) 206.48/127.74 | | 206.48/127.74 | | REF_CLOSE: (1), (2), (3), (5), (8) are inconsistent by sub-proof #53. 206.48/127.74 | | 206.48/127.74 | End of split 206.48/127.74 | 206.48/127.74 End of proof 206.48/127.74 206.48/127.74 Sub-proof #39 shows that the following formulas are inconsistent: 206.48/127.74 ---------------------------------------------------------------- 206.48/127.74 (1) all_181_2 = all_105_3 206.48/127.74 (2) all_181_3 = all_156_3 206.48/127.74 (3) all_169_1 = all_86_13 206.48/127.74 (4) map_eq_sub1(int, all_103_1, all_105_3, $sum(all_86_8, 1), all_86_13) = 0 206.48/127.74 (5) ( ~ (all_181_0 = 0) & map_eq_sub1(int, all_181_3, all_181_2, 206.48/127.74 $sum(all_86_8, 1), all_181_1) = all_181_0 & length1(int, all_103_2) = 206.48/127.74 all_181_1) | ( ~ (all_181_1 = 0) & map_eq_sub1(int, all_181_3, 206.48/127.74 all_181_2, 0, all_86_11) = all_181_1) 206.48/127.74 (6) all_169_1 = all_168_1 206.48/127.74 (7) all_156_1 = all_105_3 206.48/127.74 (8) all_168_1 = all_156_0 206.48/127.74 (9) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.48/127.74 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ (map_eq_sub1(v6, 206.48/127.74 v5, v4, v3, v2) = v1) | ~ (map_eq_sub1(v6, v5, v4, v3, v2) = v0)) 206.48/127.74 (10) map_eq_sub1(int, all_156_3, all_156_1, 0, all_86_11) = 0 206.48/127.74 (11) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 206.48/127.74 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 206.48/127.74 (12) all_156_3 = all_103_1 206.48/127.74 (13) length1(int, all_103_2) = all_156_0 206.48/127.74 206.48/127.74 Begin of proof 206.48/127.74 | 206.48/127.74 | COMBINE_EQS: (3), (6) imply: 206.48/127.74 | (14) all_168_1 = all_86_13 206.48/127.74 | 206.48/127.74 | SIMP: (14) implies: 206.48/127.74 | (15) all_168_1 = all_86_13 206.48/127.74 | 206.48/127.74 | COMBINE_EQS: (8), (15) imply: 206.48/127.74 | (16) all_156_0 = all_86_13 206.48/127.74 | 206.48/127.74 | SIMP: (16) implies: 206.48/127.74 | (17) all_156_0 = all_86_13 206.48/127.74 | 206.48/127.74 | COMBINE_EQS: (2), (12) imply: 206.48/127.74 | (18) all_181_3 = all_103_1 206.48/127.74 | 206.48/127.74 | REF_CLOSE: (1), (4), (5), (7), (9), (10), (11), (12), (13), (17), (18) are 206.48/127.74 | inconsistent by sub-proof #44. 206.48/127.74 | 206.48/127.74 End of proof 206.48/127.74 206.48/127.74 Sub-proof #40 shows that the following formulas are inconsistent: 206.48/127.74 ---------------------------------------------------------------- 206.48/127.74 (1) length1(int, all_103_2) = all_170_1 206.48/127.74 (2) length1(int, all_103_2) = all_242_1 206.48/127.74 (3) map_eq_sub1(int, all_103_1, all_105_3, $sum(all_86_8, 1), all_86_13) = 0 206.48/127.74 (4) ( ~ (all_181_0 = 0) & map_eq_sub1(int, all_181_3, all_181_2, 206.48/127.74 $sum(all_86_8, 1), all_181_1) = all_181_0 & length1(int, all_103_2) = 206.48/127.74 all_181_1) | ( ~ (all_181_1 = 0) & map_eq_sub1(int, all_181_3, 206.48/127.74 all_181_2, 0, all_86_11) = all_181_1) 206.48/127.74 (5) elts(int, all_103_2) = all_192_3 206.48/127.74 (6) elts(int, all_105_4) = all_190_4 206.48/127.74 (7) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 206.48/127.74 | ~ (elts(v3, v2) = v1) | ~ (elts(v3, v2) = v0)) 206.48/127.74 (8) length1(int, all_105_4) = all_86_13 206.48/127.74 (9) elts(int, all_105_4) = all_105_3 206.48/127.74 (10) elts(int, all_105_4) = all_156_1 206.48/127.74 (11) elts(int, all_103_2) = all_181_3 206.48/127.74 (12) elts(int, all_105_4) = all_181_2 206.48/127.75 (13) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.48/127.75 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ (map_eq_sub1(v6, 206.48/127.75 v5, v4, v3, v2) = v1) | ~ (map_eq_sub1(v6, v5, v4, v3, v2) = v0)) 206.48/127.75 (14) map_eq_sub1(int, all_156_3, all_156_1, 0, all_86_11) = 0 206.48/127.75 (15) length1(int, all_105_4) = all_190_2 206.48/127.75 (16) length1(int, all_105_4) = all_170_1 206.48/127.75 (17) elts(int, all_103_2) = all_103_1 206.48/127.75 (18) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 206.48/127.75 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 206.48/127.75 (19) elts(int, all_103_2) = all_156_3 206.48/127.75 (20) length1(int, all_103_2) = all_156_0 206.48/127.75 (21) length1(int, all_105_4) = all_169_1 206.48/127.75 206.48/127.75 Begin of proof 206.48/127.75 | 206.48/127.75 | GROUND_INST: instantiating (18) with all_86_13, all_190_2, all_105_4, int, 206.48/127.75 | simplifying with (8), (15) gives: 206.48/127.75 | (22) all_190_2 = all_86_13 206.48/127.75 | 206.48/127.75 | GROUND_INST: instantiating (18) with all_190_2, all_170_1, all_105_4, int, 206.48/127.75 | simplifying with (15), (16) gives: 206.48/127.75 | (23) all_190_2 = all_170_1 206.48/127.75 | 206.48/127.75 | GROUND_INST: instantiating (18) with all_170_1, all_169_1, all_105_4, int, 206.48/127.75 | simplifying with (16), (21) gives: 206.48/127.75 | (24) all_170_1 = all_169_1 206.48/127.75 | 206.48/127.75 | GROUND_INST: instantiating (18) with all_242_1, all_170_1, all_103_2, int, 206.48/127.75 | simplifying with (1), (2) gives: 206.48/127.75 | (25) all_242_1 = all_170_1 206.48/127.75 | 206.48/127.75 | GROUND_INST: instantiating (18) with all_242_1, all_156_0, all_103_2, int, 206.48/127.75 | simplifying with (2), (20) gives: 206.48/127.75 | (26) all_242_1 = all_156_0 206.48/127.75 | 206.48/127.75 | GROUND_INST: instantiating (7) with all_105_3, all_181_2, all_105_4, int, 206.48/127.75 | simplifying with (9), (12) gives: 206.48/127.75 | (27) all_181_2 = all_105_3 206.48/127.75 | 206.48/127.75 | GROUND_INST: instantiating (7) with all_190_4, all_181_2, all_105_4, int, 206.48/127.75 | simplifying with (6), (12) gives: 206.48/127.75 | (28) all_190_4 = all_181_2 206.48/127.75 | 206.48/127.75 | GROUND_INST: instantiating (7) with all_190_4, all_156_1, all_105_4, int, 206.48/127.75 | simplifying with (6), (10) gives: 206.48/127.75 | (29) all_190_4 = all_156_1 206.48/127.75 | 206.48/127.75 | GROUND_INST: instantiating (7) with all_103_1, all_181_3, all_103_2, int, 206.48/127.75 | simplifying with (11), (17) gives: 206.48/127.75 | (30) all_181_3 = all_103_1 206.48/127.75 | 206.48/127.75 | GROUND_INST: instantiating (7) with all_192_3, all_181_3, all_103_2, int, 206.48/127.75 | simplifying with (5), (11) gives: 206.48/127.75 | (31) all_192_3 = all_181_3 206.48/127.75 | 206.48/127.75 | GROUND_INST: instantiating (7) with all_192_3, all_156_3, all_103_2, int, 206.48/127.75 | simplifying with (5), (19) gives: 206.48/127.75 | (32) all_192_3 = all_156_3 206.48/127.75 | 206.48/127.75 | COMBINE_EQS: (25), (26) imply: 206.48/127.75 | (33) all_170_1 = all_156_0 206.48/127.75 | 206.48/127.75 | SIMP: (33) implies: 206.48/127.75 | (34) all_170_1 = all_156_0 206.48/127.75 | 206.48/127.75 | COMBINE_EQS: (31), (32) imply: 206.48/127.75 | (35) all_181_3 = all_156_3 206.48/127.75 | 206.48/127.75 | SIMP: (35) implies: 206.48/127.75 | (36) all_181_3 = all_156_3 206.48/127.75 | 206.48/127.75 | COMBINE_EQS: (22), (23) imply: 206.48/127.75 | (37) all_170_1 = all_86_13 206.48/127.75 | 206.48/127.75 | SIMP: (37) implies: 206.48/127.75 | (38) all_170_1 = all_86_13 206.48/127.75 | 206.48/127.75 | COMBINE_EQS: (28), (29) imply: 206.48/127.75 | (39) all_181_2 = all_156_1 206.48/127.75 | 206.48/127.75 | SIMP: (39) implies: 206.48/127.75 | (40) all_181_2 = all_156_1 206.48/127.75 | 206.48/127.75 | COMBINE_EQS: (27), (40) imply: 206.48/127.75 | (41) all_156_1 = all_105_3 206.48/127.75 | 206.48/127.75 | COMBINE_EQS: (30), (36) imply: 206.48/127.75 | (42) all_156_3 = all_103_1 206.48/127.75 | 206.48/127.75 | COMBINE_EQS: (24), (34) imply: 206.48/127.75 | (43) all_169_1 = all_156_0 206.48/127.75 | 206.48/127.75 | COMBINE_EQS: (24), (38) imply: 206.48/127.75 | (44) all_169_1 = all_86_13 206.48/127.75 | 206.48/127.75 | COMBINE_EQS: (43), (44) imply: 206.48/127.75 | (45) all_156_0 = all_86_13 206.48/127.75 | 206.48/127.75 | REF_CLOSE: (3), (4), (13), (14), (18), (20), (36), (40), (41), (42), (45) are 206.48/127.75 | inconsistent by sub-proof #41. 206.48/127.75 | 206.48/127.75 End of proof 206.48/127.75 206.48/127.75 Sub-proof #41 shows that the following formulas are inconsistent: 206.48/127.75 ---------------------------------------------------------------- 206.48/127.75 (1) all_181_3 = all_156_3 206.48/127.75 (2) map_eq_sub1(int, all_103_1, all_105_3, $sum(all_86_8, 1), all_86_13) = 0 206.48/127.75 (3) all_156_0 = all_86_13 206.48/127.75 (4) ( ~ (all_181_0 = 0) & map_eq_sub1(int, all_181_3, all_181_2, 206.48/127.75 $sum(all_86_8, 1), all_181_1) = all_181_0 & length1(int, all_103_2) = 206.48/127.75 all_181_1) | ( ~ (all_181_1 = 0) & map_eq_sub1(int, all_181_3, 206.48/127.75 all_181_2, 0, all_86_11) = all_181_1) 206.48/127.75 (5) all_156_1 = all_105_3 206.48/127.75 (6) all_181_2 = all_156_1 206.48/127.75 (7) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.48/127.75 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ (map_eq_sub1(v6, 206.48/127.75 v5, v4, v3, v2) = v1) | ~ (map_eq_sub1(v6, v5, v4, v3, v2) = v0)) 206.48/127.75 (8) map_eq_sub1(int, all_156_3, all_156_1, 0, all_86_11) = 0 206.48/127.75 (9) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 206.48/127.75 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 206.48/127.75 (10) all_156_3 = all_103_1 206.48/127.75 (11) length1(int, all_103_2) = all_156_0 206.48/127.75 206.48/127.75 Begin of proof 206.48/127.75 | 206.48/127.75 | SIMP: (3) implies: 206.48/127.75 | (12) all_156_0 = all_86_13 206.48/127.75 | 206.48/127.75 | COMBINE_EQS: (1), (10) imply: 206.48/127.75 | (13) all_181_3 = all_103_1 206.48/127.75 | 206.48/127.75 | COMBINE_EQS: (5), (6) imply: 206.48/127.75 | (14) all_181_2 = all_105_3 206.48/127.75 | 206.48/127.75 | REF_CLOSE: (2), (4), (5), (7), (8), (9), (10), (11), (12), (13), (14) are 206.48/127.75 | inconsistent by sub-proof #44. 206.48/127.75 | 206.48/127.75 End of proof 206.48/127.75 206.48/127.75 Sub-proof #42 shows that the following formulas are inconsistent: 206.48/127.75 ---------------------------------------------------------------- 206.48/127.75 (1) length1(int, all_103_2) = all_170_1 206.48/127.75 (2) length1(int, all_105_4) = all_153_1 206.48/127.75 (3) length1(int, all_103_4) = all_86_13 206.48/127.75 (4) length1(int, all_103_4) = all_215_1 206.48/127.75 (5) length1(int, all_103_2) = all_193_1 206.48/127.75 (6) ~ ($lesseq(all_86_11, all_215_1)) | ~ ($lesseq(0, all_215_1)) | ( ~ 206.48/127.75 (all_215_0 = all_215_1) & length1(int, all_103_2) = all_215_0) 206.48/127.75 (7) length1(int, all_103_4) = all_193_1 206.48/127.75 (8) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.48/127.75 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ 206.48/127.75 (array_eq_sub1(v6, v5, v4, v3, v2) = v1) | ~ (array_eq_sub1(v6, v5, 206.48/127.75 v4, v3, v2) = v0)) 206.48/127.75 (9) $lesseq(1, $difference(all_153_1, all_86_10)) 206.48/127.75 (10) $lesseq(all_86_11, all_86_8) 206.48/127.75 (11) $lesseq(all_86_7, all_86_10) 206.48/127.75 (12) (all_168_0 = all_168_1 & $lesseq(1, $difference(all_168_1, all_86_8)) & 206.48/127.75 $lesseq(all_86_13, all_168_1) & $lesseq(-1, all_86_8) & $lesseq(0, 206.48/127.75 all_86_13) & length1(int, all_105_4) = all_168_1 & length1(int, 206.48/127.75 all_103_2) = all_168_1) | ( ~ (all_168_1 = 0) & array_eq_sub1(int, 206.48/127.75 all_103_2, all_105_4, $sum(all_86_8, 1), all_86_13) = all_168_1) 206.48/127.75 (13) length1(int, all_105_4) = all_190_2 206.48/127.75 (14) $lesseq(1, $difference(all_86_7, all_86_8)) 206.48/127.75 (15) $lesseq(0, all_86_11) 206.48/127.75 (16) length1(int, all_105_4) = all_170_1 206.48/127.75 (17) array_eq_sub1(int, all_103_2, all_105_4, $sum(all_86_8, 1), all_86_13) = 206.48/127.75 0 206.48/127.75 (18) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 206.48/127.75 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 206.48/127.75 (19) length1(int, all_103_2) = all_156_0 206.48/127.75 (20) length1(int, all_105_4) = all_169_1 206.48/127.75 206.48/127.75 Begin of proof 206.48/127.75 | 206.48/127.75 | BETA: splitting (12) gives: 206.48/127.75 | 206.48/127.75 | Case 1: 206.48/127.75 | | 206.48/127.75 | | (21) all_168_0 = all_168_1 & $lesseq(1, $difference(all_168_1, all_86_8)) 206.48/127.75 | | & $lesseq(all_86_13, all_168_1) & $lesseq(-1, all_86_8) & $lesseq(0, 206.48/127.75 | | all_86_13) & length1(int, all_105_4) = all_168_1 & length1(int, 206.48/127.75 | | all_103_2) = all_168_1 206.48/127.75 | | 206.48/127.75 | | ALPHA: (21) implies: 206.48/127.75 | | (22) length1(int, all_103_2) = all_168_1 206.48/127.75 | | (23) length1(int, all_105_4) = all_168_1 206.48/127.75 | | 206.48/127.75 | | GROUND_INST: instantiating (18) with all_190_2, all_169_1, all_105_4, int, 206.48/127.75 | | simplifying with (13), (20) gives: 206.48/127.75 | | (24) all_190_2 = all_169_1 206.48/127.75 | | 206.48/127.75 | | GROUND_INST: instantiating (18) with all_170_1, all_169_1, all_105_4, int, 206.48/127.75 | | simplifying with (16), (20) gives: 206.48/127.75 | | (25) all_170_1 = all_169_1 206.48/127.75 | | 206.48/127.75 | | GROUND_INST: instantiating (18) with all_190_2, all_168_1, all_105_4, int, 206.48/127.75 | | simplifying with (13), (23) gives: 206.48/127.75 | | (26) all_190_2 = all_168_1 206.48/127.75 | | 206.48/127.75 | | GROUND_INST: instantiating (18) with all_169_1, all_153_1, all_105_4, int, 206.48/127.75 | | simplifying with (2), (20) gives: 206.48/127.75 | | (27) all_169_1 = all_153_1 206.48/127.75 | | 206.48/127.75 | | GROUND_INST: instantiating (18) with all_193_1, all_170_1, all_103_2, int, 206.48/127.75 | | simplifying with (1), (5) gives: 206.48/127.75 | | (28) all_193_1 = all_170_1 206.48/127.75 | | 206.48/127.75 | | GROUND_INST: instantiating (18) with all_168_1, all_156_0, all_103_2, int, 206.48/127.75 | | simplifying with (19), (22) gives: 206.48/127.75 | | (29) all_168_1 = all_156_0 206.48/127.75 | | 206.48/127.75 | | GROUND_INST: instantiating (18) with all_86_13, all_215_1, all_103_4, int, 206.48/127.75 | | simplifying with (3), (4) gives: 206.48/127.75 | | (30) all_215_1 = all_86_13 206.48/127.75 | | 206.48/127.75 | | GROUND_INST: instantiating (18) with all_215_1, all_193_1, all_103_4, int, 206.48/127.75 | | simplifying with (4), (7) gives: 206.48/127.75 | | (31) all_215_1 = all_193_1 206.48/127.75 | | 206.48/127.75 | | COMBINE_EQS: (30), (31) imply: 206.48/127.75 | | (32) all_193_1 = all_86_13 206.48/127.75 | | 206.48/127.75 | | COMBINE_EQS: (28), (32) imply: 206.48/127.75 | | (33) all_170_1 = all_86_13 206.48/127.75 | | 206.48/127.75 | | SIMP: (33) implies: 206.48/127.75 | | (34) all_170_1 = all_86_13 206.48/127.75 | | 206.48/127.75 | | COMBINE_EQS: (24), (26) imply: 206.48/127.75 | | (35) all_169_1 = all_168_1 206.48/127.75 | | 206.48/127.75 | | SIMP: (35) implies: 206.48/127.75 | | (36) all_169_1 = all_168_1 206.48/127.75 | | 206.48/127.75 | | COMBINE_EQS: (25), (34) imply: 206.48/127.75 | | (37) all_169_1 = all_86_13 206.48/127.75 | | 206.48/127.75 | | SIMP: (37) implies: 206.48/127.75 | | (38) all_169_1 = all_86_13 206.48/127.75 | | 206.48/127.75 | | COMBINE_EQS: (36), (38) imply: 206.48/127.75 | | (39) all_168_1 = all_86_13 206.48/127.75 | | 206.48/127.75 | | COMBINE_EQS: (27), (36) imply: 206.48/127.75 | | (40) all_168_1 = all_153_1 206.48/127.75 | | 206.48/127.75 | | COMBINE_EQS: (29), (39) imply: 206.48/127.75 | | (41) all_156_0 = all_86_13 206.48/127.75 | | 206.48/127.75 | | SIMP: (41) implies: 206.48/127.75 | | (42) all_156_0 = all_86_13 206.48/127.75 | | 206.48/127.75 | | COMBINE_EQS: (39), (40) imply: 206.48/127.75 | | (43) all_153_1 = all_86_13 206.48/127.75 | | 206.48/127.75 | | SIMP: (43) implies: 206.48/127.75 | | (44) all_153_1 = all_86_13 206.48/127.75 | | 206.48/127.75 | | REF_CLOSE: (6), (9), (10), (11), (14), (15), (18), (19), (30), (42), (44) 206.48/127.75 | | are inconsistent by sub-proof #72. 206.48/127.75 | | 206.48/127.75 | Case 2: 206.48/127.75 | | 206.48/127.75 | | (45) ~ (all_168_1 = 0) & array_eq_sub1(int, all_103_2, all_105_4, 206.48/127.75 | | $sum(all_86_8, 1), all_86_13) = all_168_1 206.48/127.75 | | 206.48/127.75 | | REF_CLOSE: (8), (17), (45) are inconsistent by sub-proof #83. 206.48/127.75 | | 206.48/127.75 | End of split 206.48/127.75 | 206.48/127.75 End of proof 206.48/127.75 206.48/127.75 Sub-proof #43 shows that the following formulas are inconsistent: 206.48/127.75 ---------------------------------------------------------------- 206.48/127.75 (1) length1(int, all_103_2) = all_170_1 206.48/127.75 (2) length1(int, all_105_2) = all_86_13 206.48/127.75 (3) length1(int, all_103_4) = all_86_13 206.48/127.75 (4) (all_219_1 = 0 & array_eq_sub1(int, all_105_4, all_105_2, 0, all_86_7) = 206.48/127.75 0) | (length1(int, all_105_4) = all_219_1 & ( ~ ($lesseq(all_86_7, 206.48/127.75 all_219_1)) | ~ ($lesseq(0, all_219_1)) | ( ~ (all_219_0 = 206.48/127.75 all_219_1) & length1(int, all_105_2) = all_219_0))) 206.48/127.75 (5) $lesseq(all_86_7, all_86_13) 206.48/127.75 (6) length1(int, all_103_2) = all_193_1 206.48/127.75 (7) length1(int, all_103_4) = all_192_2 206.48/127.75 (8) map_eq_sub1(int, all_103_1, all_105_3, $sum(all_86_8, 1), all_86_13) = 0 206.48/127.75 (9) length1(int, all_103_4) = all_193_1 206.48/127.75 (10) ( ~ (all_181_0 = 0) & map_eq_sub1(int, all_181_3, all_181_2, 206.48/127.75 $sum(all_86_8, 1), all_181_1) = all_181_0 & length1(int, all_103_2) 206.48/127.75 = all_181_1) | ( ~ (all_181_1 = 0) & map_eq_sub1(int, all_181_3, 206.48/127.75 all_181_2, 0, all_86_11) = all_181_1) 206.48/127.75 (11) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.48/127.75 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ 206.48/127.75 (array_eq_sub1(v6, v5, v4, v3, v2) = v1) | ~ (array_eq_sub1(v6, v5, 206.48/127.75 v4, v3, v2) = v0)) 206.48/127.75 (12) (all_171_0 = all_171_1 & $lesseq(all_86_11, all_171_1) & $lesseq(0, 206.48/127.75 all_171_1) & $lesseq(0, all_86_11) & length1(int, all_103_2) = 206.48/127.75 all_171_1 & length1(int, all_103_4) = all_171_1) | ( ~ (all_171_1 = 0) 206.48/127.75 & array_eq_sub1(int, all_103_4, all_103_2, 0, all_86_11) = all_171_1) 206.48/127.75 (13) elts(int, all_103_2) = all_192_3 206.48/127.75 (14) (all_192_0 = 0 & all_192_1 = 0 & map_eq_sub1(int, all_192_4, all_192_3, 206.48/127.75 $sum(all_86_10, 1), all_192_2) = 0 & map_eq_sub1(int, all_192_4, 206.48/127.75 all_192_3, 0, all_86_11) = 0 & length1(int, all_103_4) = all_192_2 & 206.48/127.75 elts(int, all_103_2) = all_192_3 & elts(int, all_103_4) = all_192_4 & 206.48/127.75 in_uni(all_192_3) & in_uni(all_192_4)) | ( ~ (all_192_4 = 0) & 206.48/127.75 permut_sub2(int, all_103_4, all_103_2, all_86_11, $sum(all_86_10, 1)) 206.48/127.75 = all_192_4) 206.48/127.75 (15) elts(int, all_105_4) = all_190_4 206.48/127.75 (16) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 206.48/127.75 | ~ (elts(v3, v2) = v1) | ~ (elts(v3, v2) = v0)) 206.48/127.75 (17) length1(int, all_105_4) = all_86_13 206.48/127.76 (18) elts(int, all_105_4) = all_105_3 206.48/127.76 (19) elts(int, all_105_4) = all_156_1 206.48/127.76 (20) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.48/127.76 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ (permut_sub2(v6, 206.48/127.76 v5, v4, v3, v2) = v1) | ~ (permut_sub2(v6, v5, v4, v3, v2) = v0)) 206.48/127.76 (21) (all_169_0 = all_169_1 & $lesseq(all_86_7, all_169_1) & $lesseq(0, 206.48/127.76 all_169_1) & $lesseq(0, all_86_7) & length1(int, all_105_2) = 206.48/127.76 all_169_1 & length1(int, all_105_4) = all_169_1) | ( ~ (all_169_1 = 0) 206.48/127.76 & array_eq_sub1(int, all_105_4, all_105_2, 0, all_86_7) = all_169_1) 206.48/127.76 (22) elts(int, all_103_2) = all_181_3 206.48/127.76 (23) (all_242_1 = 0 & array_eq_sub1(int, all_103_2, all_105_4, $sum(all_86_8, 206.48/127.76 1), all_86_13) = 0) | (length1(int, all_103_2) = all_242_1 & ( ~ 206.48/127.76 ($lesseq(1, $difference(all_242_1, all_86_8))) | ~ 206.48/127.76 ($lesseq(all_86_13, all_242_1)) | ( ~ (all_242_0 = all_242_1) & 206.48/127.76 length1(int, all_105_4) = all_242_0))) 206.48/127.76 (24) $lesseq(1, $difference(all_193_1, all_86_10)) 206.48/127.76 (25) $lesseq(all_86_11, all_86_8) 206.48/127.76 (26) $lesseq(all_86_7, all_86_10) 206.48/127.76 (27) array_eq_sub1(int, all_103_4, all_103_2, 0, all_86_11) = 0 206.48/127.76 (28) (all_168_0 = all_168_1 & $lesseq(1, $difference(all_168_1, all_86_8)) & 206.48/127.76 $lesseq(all_86_13, all_168_1) & $lesseq(-1, all_86_8) & $lesseq(0, 206.48/127.76 all_86_13) & length1(int, all_105_4) = all_168_1 & length1(int, 206.48/127.76 all_103_2) = all_168_1) | ( ~ (all_168_1 = 0) & array_eq_sub1(int, 206.48/127.76 all_103_2, all_105_4, $sum(all_86_8, 1), all_86_13) = all_168_1) 206.48/127.76 (29) elts(int, all_105_4) = all_181_2 206.48/127.76 (30) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.48/127.76 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ (map_eq_sub1(v6, 206.48/127.76 v5, v4, v3, v2) = v1) | ~ (map_eq_sub1(v6, v5, v4, v3, v2) = v0)) 206.48/127.76 (31) map_eq_sub1(int, all_156_3, all_156_1, 0, all_86_11) = 0 206.48/127.76 (32) length1(int, all_105_4) = all_190_2 206.48/127.76 (33) $lesseq(1, $difference(all_86_7, all_86_8)) 206.48/127.76 (34) permut_sub2(int, all_103_4, all_103_2, all_86_11, $sum(all_86_10, 1)) = 206.48/127.76 0 206.48/127.76 (35) length1(int, all_105_4) = all_170_1 206.48/127.76 (36) elts(int, all_103_2) = all_103_1 206.48/127.76 (37) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 206.48/127.76 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 206.48/127.76 (38) elts(int, all_103_2) = all_156_3 206.48/127.76 (39) length1(int, all_103_2) = all_156_0 206.48/127.76 206.48/127.76 Begin of proof 206.48/127.76 | 206.48/127.76 | BETA: splitting (12) gives: 206.48/127.76 | 206.48/127.76 | Case 1: 206.48/127.76 | | 206.48/127.76 | | (40) all_171_0 = all_171_1 & $lesseq(all_86_11, all_171_1) & $lesseq(0, 206.48/127.76 | | all_171_1) & $lesseq(0, all_86_11) & length1(int, all_103_2) = 206.48/127.76 | | all_171_1 & length1(int, all_103_4) = all_171_1 206.48/127.76 | | 206.48/127.76 | | ALPHA: (40) implies: 206.48/127.76 | | (41) $lesseq(0, all_86_11) 206.48/127.76 | | (42) length1(int, all_103_4) = all_171_1 206.48/127.76 | | (43) length1(int, all_103_2) = all_171_1 206.48/127.76 | | 206.48/127.76 | | BETA: splitting (4) gives: 206.48/127.76 | | 206.48/127.76 | | Case 1: 206.48/127.76 | | | 206.48/127.76 | | | (44) all_219_1 = 0 & array_eq_sub1(int, all_105_4, all_105_2, 0, 206.48/127.76 | | | all_86_7) = 0 206.48/127.76 | | | 206.48/127.76 | | | ALPHA: (44) implies: 206.48/127.76 | | | (45) array_eq_sub1(int, all_105_4, all_105_2, 0, all_86_7) = 0 206.48/127.76 | | | 206.48/127.76 | | | BETA: splitting (21) gives: 206.48/127.76 | | | 206.48/127.76 | | | Case 1: 206.48/127.76 | | | | 206.48/127.76 | | | | (46) all_169_0 = all_169_1 & $lesseq(all_86_7, all_169_1) & 206.48/127.76 | | | | $lesseq(0, all_169_1) & $lesseq(0, all_86_7) & length1(int, 206.48/127.76 | | | | all_105_2) = all_169_1 & length1(int, all_105_4) = all_169_1 206.48/127.76 | | | | 206.48/127.76 | | | | ALPHA: (46) implies: 206.48/127.76 | | | | (47) length1(int, all_105_4) = all_169_1 206.48/127.76 | | | | 206.48/127.76 | | | | BETA: splitting (23) gives: 206.48/127.76 | | | | 206.48/127.76 | | | | Case 1: 206.48/127.76 | | | | | 206.48/127.76 | | | | | (48) all_242_1 = 0 & array_eq_sub1(int, all_103_2, all_105_4, 206.48/127.76 | | | | | $sum(all_86_8, 1), all_86_13) = 0 206.48/127.76 | | | | | 206.48/127.76 | | | | | ALPHA: (48) implies: 206.48/127.76 | | | | | (49) array_eq_sub1(int, all_103_2, all_105_4, $sum(all_86_8, 1), 206.48/127.76 | | | | | all_86_13) = 0 206.48/127.76 | | | | | 206.48/127.76 | | | | | REF_CLOSE: (1), (8), (10), (11), (13), (15), (16), (17), (18), (19), 206.48/127.76 | | | | | (22), (28), (29), (30), (31), (32), (36), (37), (38), (39), 206.48/127.76 | | | | | (43), (47), (49) are inconsistent by sub-proof #45. 206.48/127.76 | | | | | 206.48/127.76 | | | | Case 2: 206.48/127.76 | | | | | 206.48/127.76 | | | | | (50) length1(int, all_103_2) = all_242_1 & ( ~ ($lesseq(1, 206.48/127.76 | | | | | $difference(all_242_1, all_86_8))) | ~ 206.48/127.76 | | | | | ($lesseq(all_86_13, all_242_1)) | ( ~ (all_242_0 = 206.48/127.76 | | | | | all_242_1) & length1(int, all_105_4) = all_242_0)) 206.53/127.76 | | | | | 206.53/127.76 | | | | | ALPHA: (50) implies: 206.53/127.76 | | | | | (51) length1(int, all_103_2) = all_242_1 206.53/127.76 | | | | | 206.53/127.76 | | | | | GROUND_INST: instantiating (37) with all_242_1, all_193_1, all_103_2, 206.53/127.76 | | | | | int, simplifying with (6), (51) gives: 206.53/127.76 | | | | | (52) all_242_1 = all_193_1 206.53/127.76 | | | | | 206.53/127.76 | | | | | GROUND_INST: instantiating (37) with all_242_1, all_156_0, all_103_2, 206.53/127.76 | | | | | int, simplifying with (39), (51) gives: 206.53/127.76 | | | | | (53) all_242_1 = all_156_0 206.53/127.76 | | | | | 206.53/127.76 | | | | | GROUND_INST: instantiating (37) with all_86_13, all_192_2, all_103_4, 206.53/127.76 | | | | | int, simplifying with (3), (7) gives: 206.53/127.76 | | | | | (54) all_192_2 = all_86_13 206.53/127.76 | | | | | 206.53/127.76 | | | | | GROUND_INST: instantiating (37) with all_193_1, all_192_2, all_103_4, 206.53/127.76 | | | | | int, simplifying with (7), (9) gives: 206.53/127.76 | | | | | (55) all_193_1 = all_192_2 206.53/127.76 | | | | | 206.53/127.76 | | | | | GROUND_INST: instantiating (37) with all_193_1, all_171_1, all_103_4, 206.53/127.76 | | | | | int, simplifying with (9), (42) gives: 206.53/127.76 | | | | | (56) all_193_1 = all_171_1 206.53/127.76 | | | | | 206.53/127.76 | | | | | GROUND_INST: instantiating (16) with all_105_3, all_190_4, all_105_4, 206.53/127.76 | | | | | int, simplifying with (15), (18) gives: 206.53/127.76 | | | | | (57) all_190_4 = all_105_3 206.53/127.76 | | | | | 206.53/127.76 | | | | | GROUND_INST: instantiating (16) with all_190_4, all_181_2, all_105_4, 206.53/127.76 | | | | | int, simplifying with (15), (29) gives: 206.53/127.76 | | | | | (58) all_190_4 = all_181_2 206.53/127.76 | | | | | 206.53/127.76 | | | | | GROUND_INST: instantiating (16) with all_181_2, all_156_1, all_105_4, 206.53/127.76 | | | | | int, simplifying with (19), (29) gives: 206.53/127.76 | | | | | (59) all_181_2 = all_156_1 206.53/127.76 | | | | | 206.53/127.76 | | | | | GROUND_INST: instantiating (16) with all_103_1, all_181_3, all_103_2, 206.53/127.76 | | | | | int, simplifying with (22), (36) gives: 206.53/127.76 | | | | | (60) all_181_3 = all_103_1 206.53/127.76 | | | | | 206.53/127.76 | | | | | GROUND_INST: instantiating (16) with all_192_3, all_181_3, all_103_2, 206.53/127.76 | | | | | int, simplifying with (13), (22) gives: 206.53/127.76 | | | | | (61) all_192_3 = all_181_3 206.53/127.76 | | | | | 206.53/127.76 | | | | | GROUND_INST: instantiating (16) with all_192_3, all_156_3, all_103_2, 206.53/127.76 | | | | | int, simplifying with (13), (38) gives: 206.53/127.76 | | | | | (62) all_192_3 = all_156_3 206.53/127.76 | | | | | 206.53/127.76 | | | | | COMBINE_EQS: (52), (53) imply: 206.53/127.76 | | | | | (63) all_193_1 = all_156_0 206.53/127.76 | | | | | 206.53/127.76 | | | | | SIMP: (63) implies: 206.53/127.76 | | | | | (64) all_193_1 = all_156_0 206.53/127.76 | | | | | 206.53/127.76 | | | | | COMBINE_EQS: (56), (64) imply: 206.53/127.76 | | | | | (65) all_171_1 = all_156_0 206.53/127.76 | | | | | 206.53/127.76 | | | | | COMBINE_EQS: (55), (56) imply: 206.53/127.76 | | | | | (66) all_192_2 = all_171_1 206.53/127.76 | | | | | 206.53/127.76 | | | | | SIMP: (66) implies: 206.53/127.76 | | | | | (67) all_192_2 = all_171_1 206.53/127.76 | | | | | 206.53/127.76 | | | | | COMBINE_EQS: (54), (67) imply: 206.53/127.76 | | | | | (68) all_171_1 = all_86_13 206.53/127.76 | | | | | 206.53/127.76 | | | | | SIMP: (68) implies: 206.53/127.76 | | | | | (69) all_171_1 = all_86_13 206.53/127.76 | | | | | 206.53/127.76 | | | | | COMBINE_EQS: (61), (62) imply: 206.53/127.76 | | | | | (70) all_181_3 = all_156_3 206.53/127.76 | | | | | 206.53/127.76 | | | | | SIMP: (70) implies: 206.53/127.76 | | | | | (71) all_181_3 = all_156_3 206.53/127.76 | | | | | 206.53/127.76 | | | | | COMBINE_EQS: (57), (58) imply: 206.53/127.76 | | | | | (72) all_181_2 = all_105_3 206.53/127.76 | | | | | 206.53/127.76 | | | | | SIMP: (72) implies: 206.53/127.76 | | | | | (73) all_181_2 = all_105_3 206.53/127.76 | | | | | 206.53/127.76 | | | | | COMBINE_EQS: (59), (73) imply: 206.53/127.76 | | | | | (74) all_156_1 = all_105_3 206.53/127.76 | | | | | 206.53/127.76 | | | | | SIMP: (74) implies: 206.53/127.76 | | | | | (75) all_156_1 = all_105_3 206.53/127.76 | | | | | 206.53/127.76 | | | | | COMBINE_EQS: (60), (71) imply: 206.53/127.76 | | | | | (76) all_156_3 = all_103_1 206.53/127.76 | | | | | 206.53/127.76 | | | | | COMBINE_EQS: (65), (69) imply: 206.53/127.76 | | | | | (77) all_156_0 = all_86_13 206.53/127.76 | | | | | 206.53/127.76 | | | | | SIMP: (77) implies: 206.53/127.76 | | | | | (78) all_156_0 = all_86_13 206.53/127.76 | | | | | 206.53/127.76 | | | | | REF_CLOSE: (8), (10), (30), (31), (37), (39), (60), (73), (75), (76), 206.53/127.76 | | | | | (78) are inconsistent by sub-proof #44. 206.53/127.76 | | | | | 206.53/127.76 | | | | End of split 206.53/127.76 | | | | 206.53/127.76 | | | Case 2: 206.53/127.76 | | | | 206.53/127.76 | | | | (79) ~ (all_169_1 = 0) & array_eq_sub1(int, all_105_4, all_105_2, 0, 206.53/127.76 | | | | all_86_7) = all_169_1 206.53/127.76 | | | | 206.53/127.76 | | | | REF_CLOSE: (11), (45), (79) are inconsistent by sub-proof #75. 206.53/127.76 | | | | 206.53/127.76 | | | End of split 206.53/127.76 | | | 206.53/127.76 | | Case 2: 206.53/127.76 | | | 206.53/127.76 | | | (80) length1(int, all_105_4) = all_219_1 & ( ~ ($lesseq(all_86_7, 206.53/127.76 | | | all_219_1)) | ~ ($lesseq(0, all_219_1)) | ( ~ (all_219_0 = 206.53/127.76 | | | all_219_1) & length1(int, all_105_2) = all_219_0)) 206.53/127.76 | | | 206.53/127.76 | | | ALPHA: (80) implies: 206.53/127.76 | | | (81) length1(int, all_105_4) = all_219_1 206.53/127.76 | | | (82) ~ ($lesseq(all_86_7, all_219_1)) | ~ ($lesseq(0, all_219_1)) | ( 206.53/127.76 | | | ~ (all_219_0 = all_219_1) & length1(int, all_105_2) = all_219_0) 206.53/127.76 | | | 206.53/127.76 | | | REF_CLOSE: (1), (2), (3), (5), (9), (14), (20), (24), (25), (26), (33), 206.53/127.76 | | | (34), (35), (37), (41), (42), (43), (81), (82) are inconsistent 206.53/127.76 | | | by sub-proof #51. 206.53/127.76 | | | 206.53/127.76 | | End of split 206.53/127.76 | | 206.53/127.76 | Case 2: 206.53/127.76 | | 206.53/127.76 | | (83) ~ (all_171_1 = 0) & array_eq_sub1(int, all_103_4, all_103_2, 0, 206.53/127.76 | | all_86_11) = all_171_1 206.53/127.76 | | 206.53/127.76 | | REF_CLOSE: (11), (27), (83) are inconsistent by sub-proof #81. 206.53/127.76 | | 206.53/127.76 | End of split 206.53/127.76 | 206.53/127.76 End of proof 206.53/127.76 206.53/127.76 Sub-proof #44 shows that the following formulas are inconsistent: 206.53/127.76 ---------------------------------------------------------------- 206.53/127.76 (1) all_181_2 = all_105_3 206.53/127.76 (2) all_156_0 = all_86_13 206.53/127.76 (3) map_eq_sub1(int, all_103_1, all_105_3, $sum(all_86_8, 1), all_86_13) = 0 206.53/127.76 (4) ( ~ (all_181_0 = 0) & map_eq_sub1(int, all_181_3, all_181_2, 206.53/127.76 $sum(all_86_8, 1), all_181_1) = all_181_0 & length1(int, all_103_2) = 206.53/127.76 all_181_1) | ( ~ (all_181_1 = 0) & map_eq_sub1(int, all_181_3, 206.53/127.76 all_181_2, 0, all_86_11) = all_181_1) 206.53/127.76 (5) all_181_3 = all_103_1 206.53/127.76 (6) all_156_1 = all_105_3 206.53/127.76 (7) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.53/127.76 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ (map_eq_sub1(v6, 206.53/127.76 v5, v4, v3, v2) = v1) | ~ (map_eq_sub1(v6, v5, v4, v3, v2) = v0)) 206.53/127.76 (8) map_eq_sub1(int, all_156_3, all_156_1, 0, all_86_11) = 0 206.53/127.76 (9) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 206.53/127.76 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 206.53/127.76 (10) all_156_3 = all_103_1 206.53/127.76 (11) length1(int, all_103_2) = all_156_0 206.53/127.76 206.53/127.76 Begin of proof 206.53/127.76 | 206.53/127.76 | REDUCE: (6), (8), (10) imply: 206.53/127.76 | (12) map_eq_sub1(int, all_103_1, all_105_3, 0, all_86_11) = 0 206.53/127.76 | 206.53/127.76 | REDUCE: (2), (11) imply: 206.53/127.76 | (13) length1(int, all_103_2) = all_86_13 206.53/127.76 | 206.53/127.76 | BETA: splitting (4) gives: 206.53/127.76 | 206.53/127.76 | Case 1: 206.53/127.76 | | 206.53/127.76 | | (14) ~ (all_181_0 = 0) & map_eq_sub1(int, all_181_3, all_181_2, 206.53/127.76 | | $sum(all_86_8, 1), all_181_1) = all_181_0 & length1(int, 206.53/127.76 | | all_103_2) = all_181_1 206.53/127.76 | | 206.53/127.76 | | ALPHA: (14) implies: 206.53/127.76 | | (15) ~ (all_181_0 = 0) 206.53/127.76 | | (16) length1(int, all_103_2) = all_181_1 206.53/127.76 | | (17) map_eq_sub1(int, all_181_3, all_181_2, $sum(all_86_8, 1), all_181_1) 206.53/127.76 | | = all_181_0 206.53/127.76 | | 206.53/127.76 | | REDUCE: (1), (5), (17) imply: 206.53/127.76 | | (18) map_eq_sub1(int, all_103_1, all_105_3, $sum(all_86_8, 1), all_181_1) 206.53/127.76 | | = all_181_0 206.53/127.76 | | 206.53/127.76 | | REF_CLOSE: (3), (7), (9), (13), (15), (16), (18) are inconsistent by 206.53/127.76 | | sub-proof #46. 206.53/127.76 | | 206.53/127.76 | Case 2: 206.53/127.76 | | 206.53/127.76 | | (19) ~ (all_181_1 = 0) & map_eq_sub1(int, all_181_3, all_181_2, 0, 206.53/127.76 | | all_86_11) = all_181_1 206.53/127.76 | | 206.53/127.76 | | ALPHA: (19) implies: 206.53/127.76 | | (20) ~ (all_181_1 = 0) 206.53/127.76 | | (21) map_eq_sub1(int, all_181_3, all_181_2, 0, all_86_11) = all_181_1 206.53/127.76 | | 206.53/127.76 | | REDUCE: (1), (5), (21) imply: 206.53/127.76 | | (22) map_eq_sub1(int, all_103_1, all_105_3, 0, all_86_11) = all_181_1 206.53/127.76 | | 206.53/127.76 | | GROUND_INST: instantiating (7) with 0, all_181_1, all_86_11, 0, all_105_3, 206.53/127.76 | | all_103_1, int, simplifying with (12), (22) gives: 206.53/127.76 | | (23) all_181_1 = 0 206.53/127.76 | | 206.53/127.76 | | REDUCE: (20), (23) imply: 206.53/127.77 | | (24) ~ (0 = 0) 206.53/127.77 | | 206.53/127.77 | | CLOSE: (24) is inconsistent. 206.53/127.77 | | 206.53/127.77 | End of split 206.53/127.77 | 206.53/127.77 End of proof 206.53/127.77 206.53/127.77 Sub-proof #45 shows that the following formulas are inconsistent: 206.53/127.77 ---------------------------------------------------------------- 206.53/127.77 (1) length1(int, all_103_2) = all_170_1 206.53/127.77 (2) map_eq_sub1(int, all_103_1, all_105_3, $sum(all_86_8, 1), all_86_13) = 0 206.53/127.77 (3) ( ~ (all_181_0 = 0) & map_eq_sub1(int, all_181_3, all_181_2, 206.53/127.77 $sum(all_86_8, 1), all_181_1) = all_181_0 & length1(int, all_103_2) = 206.53/127.77 all_181_1) | ( ~ (all_181_1 = 0) & map_eq_sub1(int, all_181_3, 206.53/127.77 all_181_2, 0, all_86_11) = all_181_1) 206.53/127.77 (4) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.53/127.77 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ 206.53/127.77 (array_eq_sub1(v6, v5, v4, v3, v2) = v1) | ~ (array_eq_sub1(v6, v5, 206.53/127.77 v4, v3, v2) = v0)) 206.53/127.77 (5) elts(int, all_103_2) = all_192_3 206.53/127.77 (6) elts(int, all_105_4) = all_190_4 206.53/127.77 (7) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 206.53/127.77 | ~ (elts(v3, v2) = v1) | ~ (elts(v3, v2) = v0)) 206.53/127.77 (8) length1(int, all_105_4) = all_86_13 206.53/127.77 (9) elts(int, all_105_4) = all_105_3 206.53/127.77 (10) elts(int, all_105_4) = all_156_1 206.53/127.77 (11) elts(int, all_103_2) = all_181_3 206.53/127.77 (12) (all_168_0 = all_168_1 & $lesseq(1, $difference(all_168_1, all_86_8)) & 206.53/127.77 $lesseq(all_86_13, all_168_1) & $lesseq(-1, all_86_8) & $lesseq(0, 206.53/127.77 all_86_13) & length1(int, all_105_4) = all_168_1 & length1(int, 206.53/127.77 all_103_2) = all_168_1) | ( ~ (all_168_1 = 0) & array_eq_sub1(int, 206.53/127.77 all_103_2, all_105_4, $sum(all_86_8, 1), all_86_13) = all_168_1) 206.53/127.77 (13) elts(int, all_105_4) = all_181_2 206.53/127.77 (14) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.53/127.77 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ (map_eq_sub1(v6, 206.53/127.77 v5, v4, v3, v2) = v1) | ~ (map_eq_sub1(v6, v5, v4, v3, v2) = v0)) 206.53/127.77 (15) map_eq_sub1(int, all_156_3, all_156_1, 0, all_86_11) = 0 206.53/127.77 (16) length1(int, all_105_4) = all_190_2 206.53/127.77 (17) elts(int, all_103_2) = all_103_1 206.53/127.77 (18) array_eq_sub1(int, all_103_2, all_105_4, $sum(all_86_8, 1), all_86_13) = 206.53/127.77 0 206.53/127.77 (19) length1(int, all_103_2) = all_171_1 206.53/127.77 (20) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 206.53/127.77 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 206.53/127.77 (21) elts(int, all_103_2) = all_156_3 206.53/127.77 (22) length1(int, all_103_2) = all_156_0 206.53/127.77 (23) length1(int, all_105_4) = all_169_1 206.53/127.77 206.53/127.77 Begin of proof 206.53/127.77 | 206.53/127.77 | BETA: splitting (12) gives: 206.53/127.77 | 206.53/127.77 | Case 1: 206.53/127.77 | | 206.53/127.77 | | (24) all_168_0 = all_168_1 & $lesseq(1, $difference(all_168_1, all_86_8)) 206.53/127.77 | | & $lesseq(all_86_13, all_168_1) & $lesseq(-1, all_86_8) & $lesseq(0, 206.53/127.77 | | all_86_13) & length1(int, all_105_4) = all_168_1 & length1(int, 206.53/127.77 | | all_103_2) = all_168_1 206.53/127.77 | | 206.53/127.77 | | ALPHA: (24) implies: 206.53/127.77 | | (25) length1(int, all_103_2) = all_168_1 206.53/127.77 | | (26) length1(int, all_105_4) = all_168_1 206.53/127.77 | | 206.53/127.77 | | GROUND_INST: instantiating (20) with all_86_13, all_190_2, all_105_4, int, 206.53/127.77 | | simplifying with (8), (16) gives: 206.53/127.77 | | (27) all_190_2 = all_86_13 206.53/127.77 | | 206.53/127.77 | | GROUND_INST: instantiating (20) with all_190_2, all_169_1, all_105_4, int, 206.53/127.77 | | simplifying with (16), (23) gives: 206.53/127.77 | | (28) all_190_2 = all_169_1 206.53/127.77 | | 206.53/127.77 | | GROUND_INST: instantiating (20) with all_169_1, all_168_1, all_105_4, int, 206.53/127.77 | | simplifying with (23), (26) gives: 206.53/127.77 | | (29) all_169_1 = all_168_1 206.53/127.77 | | 206.53/127.77 | | GROUND_INST: instantiating (20) with all_171_1, all_170_1, all_103_2, int, 206.53/127.77 | | simplifying with (1), (19) gives: 206.53/127.77 | | (30) all_171_1 = all_170_1 206.53/127.77 | | 206.53/127.77 | | GROUND_INST: instantiating (20) with all_171_1, all_168_1, all_103_2, int, 206.53/127.77 | | simplifying with (19), (25) gives: 206.53/127.77 | | (31) all_171_1 = all_168_1 206.53/127.77 | | 206.53/127.77 | | GROUND_INST: instantiating (20) with all_170_1, all_156_0, all_103_2, int, 206.53/127.77 | | simplifying with (1), (22) gives: 206.53/127.77 | | (32) all_170_1 = all_156_0 206.53/127.77 | | 206.53/127.77 | | GROUND_INST: instantiating (7) with all_105_3, all_190_4, all_105_4, int, 206.53/127.77 | | simplifying with (6), (9) gives: 206.53/127.77 | | (33) all_190_4 = all_105_3 206.53/127.77 | | 206.53/127.77 | | GROUND_INST: instantiating (7) with all_190_4, all_181_2, all_105_4, int, 206.53/127.77 | | simplifying with (6), (13) gives: 206.53/127.77 | | (34) all_190_4 = all_181_2 206.53/127.77 | | 206.53/127.77 | | GROUND_INST: instantiating (7) with all_181_2, all_156_1, all_105_4, int, 206.53/127.77 | | simplifying with (10), (13) gives: 206.53/127.77 | | (35) all_181_2 = all_156_1 206.53/127.77 | | 206.53/127.77 | | GROUND_INST: instantiating (7) with all_103_1, all_181_3, all_103_2, int, 206.53/127.77 | | simplifying with (11), (17) gives: 206.53/127.77 | | (36) all_181_3 = all_103_1 206.53/127.77 | | 206.53/127.77 | | GROUND_INST: instantiating (7) with all_192_3, all_181_3, all_103_2, int, 206.53/127.77 | | simplifying with (5), (11) gives: 206.53/127.77 | | (37) all_192_3 = all_181_3 206.53/127.77 | | 206.53/127.77 | | GROUND_INST: instantiating (7) with all_192_3, all_156_3, all_103_2, int, 206.53/127.77 | | simplifying with (5), (21) gives: 206.53/127.77 | | (38) all_192_3 = all_156_3 206.53/127.77 | | 206.53/127.77 | | COMBINE_EQS: (37), (38) imply: 206.53/127.77 | | (39) all_181_3 = all_156_3 206.53/127.77 | | 206.53/127.77 | | SIMP: (39) implies: 206.53/127.77 | | (40) all_181_3 = all_156_3 206.53/127.77 | | 206.53/127.77 | | COMBINE_EQS: (27), (28) imply: 206.53/127.77 | | (41) all_169_1 = all_86_13 206.53/127.77 | | 206.53/127.77 | | SIMP: (41) implies: 206.53/127.77 | | (42) all_169_1 = all_86_13 206.53/127.77 | | 206.53/127.77 | | COMBINE_EQS: (33), (34) imply: 206.53/127.77 | | (43) all_181_2 = all_105_3 206.53/127.77 | | 206.53/127.77 | | SIMP: (43) implies: 206.53/127.77 | | (44) all_181_2 = all_105_3 206.53/127.77 | | 206.53/127.77 | | COMBINE_EQS: (35), (44) imply: 206.53/127.77 | | (45) all_156_1 = all_105_3 206.53/127.77 | | 206.53/127.77 | | SIMP: (45) implies: 206.53/127.77 | | (46) all_156_1 = all_105_3 206.53/127.77 | | 206.53/127.77 | | COMBINE_EQS: (36), (40) imply: 206.53/127.77 | | (47) all_156_3 = all_103_1 206.53/127.77 | | 206.53/127.77 | | COMBINE_EQS: (30), (31) imply: 206.53/127.77 | | (48) all_170_1 = all_168_1 206.53/127.77 | | 206.53/127.77 | | SIMP: (48) implies: 206.53/127.77 | | (49) all_170_1 = all_168_1 206.53/127.77 | | 206.53/127.77 | | COMBINE_EQS: (32), (49) imply: 206.53/127.77 | | (50) all_168_1 = all_156_0 206.53/127.77 | | 206.53/127.77 | | SIMP: (50) implies: 206.53/127.77 | | (51) all_168_1 = all_156_0 206.53/127.77 | | 206.53/127.77 | | COMBINE_EQS: (29), (42) imply: 206.53/127.77 | | (52) all_168_1 = all_86_13 206.53/127.77 | | 206.53/127.77 | | SIMP: (52) implies: 206.53/127.77 | | (53) all_168_1 = all_86_13 206.53/127.77 | | 206.53/127.77 | | COMBINE_EQS: (51), (53) imply: 206.53/127.77 | | (54) all_156_0 = all_86_13 206.53/127.77 | | 206.53/127.77 | | SIMP: (54) implies: 206.53/127.77 | | (55) all_156_0 = all_86_13 206.53/127.77 | | 206.53/127.77 | | REDUCE: (15), (46), (47) imply: 206.53/127.77 | | (56) map_eq_sub1(int, all_103_1, all_105_3, 0, all_86_11) = 0 206.53/127.77 | | 206.53/127.77 | | REDUCE: (22), (55) imply: 206.53/127.77 | | (57) length1(int, all_103_2) = all_86_13 206.53/127.77 | | 206.53/127.77 | | BETA: splitting (3) gives: 206.53/127.77 | | 206.53/127.77 | | Case 1: 206.53/127.77 | | | 206.53/127.77 | | | (58) ~ (all_181_0 = 0) & map_eq_sub1(int, all_181_3, all_181_2, 206.53/127.77 | | | $sum(all_86_8, 1), all_181_1) = all_181_0 & length1(int, 206.53/127.77 | | | all_103_2) = all_181_1 206.53/127.77 | | | 206.53/127.77 | | | ALPHA: (58) implies: 206.53/127.77 | | | (59) ~ (all_181_0 = 0) 206.53/127.77 | | | (60) length1(int, all_103_2) = all_181_1 206.53/127.77 | | | (61) map_eq_sub1(int, all_181_3, all_181_2, $sum(all_86_8, 1), 206.53/127.77 | | | all_181_1) = all_181_0 206.53/127.77 | | | 206.53/127.77 | | | REDUCE: (36), (44), (61) imply: 206.53/127.77 | | | (62) map_eq_sub1(int, all_103_1, all_105_3, $sum(all_86_8, 1), 206.53/127.77 | | | all_181_1) = all_181_0 206.53/127.77 | | | 206.53/127.77 | | | REF_CLOSE: (2), (14), (20), (57), (59), (60), (62) are inconsistent by 206.53/127.77 | | | sub-proof #46. 206.53/127.77 | | | 206.53/127.77 | | Case 2: 206.53/127.77 | | | 206.53/127.77 | | | (63) ~ (all_181_1 = 0) & map_eq_sub1(int, all_181_3, all_181_2, 0, 206.53/127.77 | | | all_86_11) = all_181_1 206.53/127.77 | | | 206.53/127.77 | | | ALPHA: (63) implies: 206.53/127.77 | | | (64) ~ (all_181_1 = 0) 206.53/127.77 | | | (65) map_eq_sub1(int, all_181_3, all_181_2, 0, all_86_11) = all_181_1 206.53/127.77 | | | 206.53/127.77 | | | REDUCE: (36), (44), (65) imply: 206.53/127.77 | | | (66) map_eq_sub1(int, all_103_1, all_105_3, 0, all_86_11) = all_181_1 206.53/127.77 | | | 206.53/127.77 | | | GROUND_INST: instantiating (14) with 0, all_181_1, all_86_11, 0, 206.53/127.77 | | | all_105_3, all_103_1, int, simplifying with (56), (66) gives: 206.53/127.77 | | | (67) all_181_1 = 0 206.53/127.77 | | | 206.53/127.77 | | | REDUCE: (64), (67) imply: 206.53/127.77 | | | (68) ~ (0 = 0) 206.53/127.77 | | | 206.53/127.77 | | | CLOSE: (68) is inconsistent. 206.53/127.77 | | | 206.53/127.77 | | End of split 206.53/127.77 | | 206.53/127.77 | Case 2: 206.53/127.77 | | 206.53/127.77 | | (69) ~ (all_168_1 = 0) & array_eq_sub1(int, all_103_2, all_105_4, 206.53/127.77 | | $sum(all_86_8, 1), all_86_13) = all_168_1 206.53/127.77 | | 206.53/127.77 | | REF_CLOSE: (4), (18), (69) are inconsistent by sub-proof #83. 206.53/127.77 | | 206.53/127.77 | End of split 206.53/127.77 | 206.53/127.77 End of proof 206.53/127.77 206.53/127.77 Sub-proof #46 shows that the following formulas are inconsistent: 206.53/127.77 ---------------------------------------------------------------- 206.53/127.77 (1) length1(int, all_103_2) = all_86_13 206.53/127.77 (2) map_eq_sub1(int, all_103_1, all_105_3, $sum(all_86_8, 1), all_181_1) = 206.53/127.77 all_181_0 206.53/127.77 (3) map_eq_sub1(int, all_103_1, all_105_3, $sum(all_86_8, 1), all_86_13) = 0 206.53/127.77 (4) length1(int, all_103_2) = all_181_1 206.53/127.77 (5) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.53/127.77 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ (map_eq_sub1(v6, 206.53/127.77 v5, v4, v3, v2) = v1) | ~ (map_eq_sub1(v6, v5, v4, v3, v2) = v0)) 206.53/127.77 (6) ~ (all_181_0 = 0) 206.53/127.77 (7) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 206.53/127.77 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 206.53/127.77 206.53/127.77 Begin of proof 206.53/127.77 | 206.53/127.77 | GROUND_INST: instantiating (7) with all_86_13, all_181_1, all_103_2, int, 206.53/127.77 | simplifying with (1), (4) gives: 206.53/127.77 | (8) all_181_1 = all_86_13 206.53/127.77 | 206.53/127.77 | REDUCE: (2), (8) imply: 206.53/127.77 | (9) map_eq_sub1(int, all_103_1, all_105_3, $sum(all_86_8, 1), all_86_13) = 206.53/127.77 | all_181_0 206.53/127.77 | 206.53/127.77 | GROUND_INST: instantiating (5) with 0, all_181_0, all_86_13, $sum(all_86_8, 206.53/127.77 | 1), all_105_3, all_103_1, int, simplifying with (3), (9) gives: 206.53/127.77 | (10) all_181_0 = 0 206.53/127.77 | 206.53/127.77 | REDUCE: (6), (10) imply: 206.53/127.77 | (11) ~ (0 = 0) 206.53/127.77 | 206.53/127.77 | CLOSE: (11) is inconsistent. 206.53/127.77 | 206.53/127.77 End of proof 206.53/127.77 206.53/127.77 Sub-proof #47 shows that the following formulas are inconsistent: 206.53/127.77 ---------------------------------------------------------------- 206.53/127.77 (1) ~ (all_177_4 = 0) & permut_sub2(int, all_103_2, all_105_4, all_86_11, 206.53/127.77 $sum(all_86_8, 1)) = all_177_4 206.53/127.77 (2) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.53/127.77 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ (permut_sub2(v6, 206.53/127.77 v5, v4, v3, v2) = v1) | ~ (permut_sub2(v6, v5, v4, v3, v2) = v0)) 206.53/127.77 (3) permut_sub2(int, all_103_2, all_105_4, all_86_11, $sum(all_86_8, 1)) = 0 206.53/127.77 206.53/127.77 Begin of proof 206.53/127.77 | 206.53/127.77 | ALPHA: (1) implies: 206.53/127.77 | (4) ~ (all_177_4 = 0) 206.53/127.77 | (5) permut_sub2(int, all_103_2, all_105_4, all_86_11, $sum(all_86_8, 1)) = 206.53/127.77 | all_177_4 206.53/127.77 | 206.53/127.77 | GROUND_INST: instantiating (2) with all_177_4, 0, $sum(all_86_8, 1), 206.53/127.77 | all_86_11, all_105_4, all_103_2, int, simplifying with (3), (5) 206.53/127.77 | gives: 206.53/127.77 | (6) all_177_4 = 0 206.53/127.77 | 206.53/127.77 | REDUCE: (4), (6) imply: 206.53/127.77 | (7) ~ (0 = 0) 206.53/127.77 | 206.53/127.77 | CLOSE: (7) is inconsistent. 206.53/127.77 | 206.53/127.77 End of proof 206.53/127.77 206.53/127.77 Sub-proof #48 shows that the following formulas are inconsistent: 206.53/127.77 ---------------------------------------------------------------- 206.53/127.77 (1) ~ (all_170_1 = 0) & array_eq_sub1(int, all_103_2, all_105_4, 0, 206.53/127.77 all_86_11) = all_170_1 206.53/127.77 (2) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.53/127.77 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ 206.53/127.77 (array_eq_sub1(v6, v5, v4, v3, v2) = v1) | ~ (array_eq_sub1(v6, v5, 206.53/127.77 v4, v3, v2) = v0)) 206.53/127.77 (3) array_eq_sub1(int, all_103_2, all_105_4, 0, all_86_11) = 0 206.53/127.77 206.53/127.77 Begin of proof 206.53/127.77 | 206.53/127.77 | ALPHA: (1) implies: 206.53/127.77 | (4) ~ (all_170_1 = 0) 206.53/127.77 | (5) array_eq_sub1(int, all_103_2, all_105_4, 0, all_86_11) = all_170_1 206.53/127.77 | 206.53/127.77 | GROUND_INST: instantiating (2) with all_170_1, 0, all_86_11, 0, all_105_4, 206.53/127.77 | all_103_2, int, simplifying with (3), (5) gives: 206.53/127.77 | (6) all_170_1 = 0 206.53/127.77 | 206.53/127.77 | REDUCE: (4), (6) imply: 206.53/127.77 | (7) ~ (0 = 0) 206.53/127.77 | 206.53/127.77 | CLOSE: (7) is inconsistent. 206.53/127.77 | 206.53/127.77 End of proof 206.53/127.77 206.53/127.77 Sub-proof #49 shows that the following formulas are inconsistent: 206.53/127.77 ---------------------------------------------------------------- 206.53/127.77 (1) all_169_1 = all_86_13 206.53/127.77 (2) all_156_0 = all_86_13 206.53/127.77 (3) all_242_1 = all_156_0 206.53/127.77 (4) $lesseq(1, $difference(all_86_7, all_86_8)) 206.53/127.77 (5) ~ ($lesseq(1, $difference(all_242_1, all_86_8))) | ~ 206.53/127.77 ($lesseq(all_86_13, all_242_1)) | ( ~ (all_242_0 = all_242_1) & 206.53/127.77 length1(int, all_105_4) = all_242_0) 206.53/127.77 (6) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 206.53/127.77 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 206.53/127.77 (7) $lesseq(all_86_7, all_169_1) 206.53/127.77 (8) length1(int, all_105_4) = all_169_1 206.53/127.77 206.53/127.77 Begin of proof 206.53/127.77 | 206.53/127.77 | SIMP: (2) implies: 206.53/127.77 | (9) all_156_0 = all_86_13 206.53/127.77 | 206.53/127.78 | COMBINE_EQS: (3), (9) imply: 206.53/127.78 | (10) all_242_1 = all_86_13 206.53/127.78 | 206.53/127.78 | REDUCE: (1), (7) imply: 206.53/127.78 | (11) $lesseq(all_86_7, all_86_13) 206.53/127.78 | 206.53/127.78 | REDUCE: (1), (8) imply: 206.53/127.78 | (12) length1(int, all_105_4) = all_86_13 206.53/127.78 | 206.53/127.78 | REF_CLOSE: (4), (5), (6), (10), (11), (12) are inconsistent by sub-proof #77. 206.53/127.78 | 206.53/127.78 End of proof 206.53/127.78 206.53/127.78 Sub-proof #50 shows that the following formulas are inconsistent: 206.53/127.78 ---------------------------------------------------------------- 206.53/127.78 (1) elts(int, all_103_4) = all_191_3 206.53/127.78 (2) length1(int, all_103_2) = all_86_13 206.53/127.78 (3) elts(int, all_103_4) = all_103_3 206.53/127.78 (4) map_eq_sub1(int, all_103_3, all_103_1, $sum(all_86_10, 1), all_86_13) = 0 206.53/127.78 (5) elts(int, all_103_2) = all_191_2 206.53/127.78 (6) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 206.53/127.78 | ~ (elts(v3, v2) = v1) | ~ (elts(v3, v2) = v0)) 206.53/127.78 (7) length1(int, all_103_4) = all_171_1 206.53/127.78 (8) map_eq_sub1(int, all_103_3, all_103_1, 0, all_86_11) = 0 206.53/127.78 (9) elts(int, all_103_2) = all_177_4 206.53/127.78 (10) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.53/127.78 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ (map_eq_sub1(v6, 206.53/127.78 v5, v4, v3, v2) = v1) | ~ (map_eq_sub1(v6, v5, v4, v3, v2) = v0)) 206.53/127.78 (11) elts(int, all_103_2) = all_103_1 206.53/127.78 (12) length1(int, all_103_2) = all_171_1 206.53/127.78 (13) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 206.53/127.78 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 206.53/127.78 (14) length1(int, all_103_2) = all_242_1 & ( ~ ($lesseq(1, 206.53/127.78 $difference(all_242_1, all_86_8))) | ~ ($lesseq(all_86_13, 206.53/127.78 all_242_1)) | ( ~ (all_242_0 = all_242_1) & length1(int, 206.53/127.78 all_105_4) = all_242_0)) 206.53/127.78 (15) elts(int, all_103_2) = all_156_3 206.53/127.78 (16) ( ~ (all_191_0 = 0) & map_eq_sub1(int, all_191_3, all_191_2, 206.53/127.78 $sum(all_86_10, 1), all_191_1) = all_191_0 & length1(int, all_103_4) 206.53/127.78 = all_191_1) | ( ~ (all_191_1 = 0) & map_eq_sub1(int, all_191_3, 206.53/127.78 all_191_2, 0, all_86_11) = all_191_1) 206.53/127.78 206.53/127.78 Begin of proof 206.53/127.78 | 206.53/127.78 | ALPHA: (14) implies: 206.53/127.78 | (17) length1(int, all_103_2) = all_242_1 206.53/127.78 | 206.53/127.78 | GROUND_INST: instantiating (13) with all_86_13, all_242_1, all_103_2, int, 206.53/127.78 | simplifying with (2), (17) gives: 206.53/127.78 | (18) all_242_1 = all_86_13 206.53/127.78 | 206.53/127.78 | GROUND_INST: instantiating (13) with all_242_1, all_171_1, all_103_2, int, 206.53/127.78 | simplifying with (12), (17) gives: 206.53/127.78 | (19) all_242_1 = all_171_1 206.53/127.78 | 206.53/127.78 | GROUND_INST: instantiating (6) with all_103_1, all_177_4, all_103_2, int, 206.53/127.78 | simplifying with (9), (11) gives: 206.53/127.78 | (20) all_177_4 = all_103_1 206.53/127.78 | 206.53/127.78 | GROUND_INST: instantiating (6) with all_191_2, all_177_4, all_103_2, int, 206.53/127.78 | simplifying with (5), (9) gives: 206.53/127.78 | (21) all_191_2 = all_177_4 206.53/127.78 | 206.53/127.78 | GROUND_INST: instantiating (6) with all_191_2, all_156_3, all_103_2, int, 206.53/127.78 | simplifying with (5), (15) gives: 206.53/127.78 | (22) all_191_2 = all_156_3 206.53/127.78 | 206.53/127.78 | GROUND_INST: instantiating (6) with all_103_3, all_191_3, all_103_4, int, 206.53/127.78 | simplifying with (1), (3) gives: 206.53/127.78 | (23) all_191_3 = all_103_3 206.53/127.78 | 206.53/127.78 | COMBINE_EQS: (18), (19) imply: 206.53/127.78 | (24) all_171_1 = all_86_13 206.53/127.78 | 206.53/127.78 | COMBINE_EQS: (21), (22) imply: 206.53/127.78 | (25) all_177_4 = all_156_3 206.53/127.78 | 206.53/127.78 | SIMP: (25) implies: 206.53/127.78 | (26) all_177_4 = all_156_3 206.53/127.78 | 206.53/127.78 | COMBINE_EQS: (20), (26) imply: 206.53/127.78 | (27) all_156_3 = all_103_1 206.53/127.78 | 206.53/127.78 | COMBINE_EQS: (22), (27) imply: 206.53/127.78 | (28) all_191_2 = all_103_1 206.53/127.78 | 206.53/127.78 | REDUCE: (7), (24) imply: 206.53/127.78 | (29) length1(int, all_103_4) = all_86_13 206.53/127.78 | 206.53/127.78 | REF_CLOSE: (4), (8), (10), (13), (16), (23), (28), (29) are inconsistent by 206.53/127.78 | sub-proof #57. 206.53/127.78 | 206.53/127.78 End of proof 206.53/127.78 206.53/127.78 Sub-proof #51 shows that the following formulas are inconsistent: 206.53/127.78 ---------------------------------------------------------------- 206.53/127.78 (1) length1(int, all_103_2) = all_170_1 206.53/127.78 (2) length1(int, all_105_2) = all_86_13 206.53/127.78 (3) length1(int, all_103_4) = all_86_13 206.53/127.78 (4) $lesseq(all_86_7, all_86_13) 206.53/127.78 (5) length1(int, all_103_4) = all_193_1 206.53/127.78 (6) (all_192_0 = 0 & all_192_1 = 0 & map_eq_sub1(int, all_192_4, all_192_3, 206.53/127.78 $sum(all_86_10, 1), all_192_2) = 0 & map_eq_sub1(int, all_192_4, 206.53/127.78 all_192_3, 0, all_86_11) = 0 & length1(int, all_103_4) = all_192_2 & 206.53/127.78 elts(int, all_103_2) = all_192_3 & elts(int, all_103_4) = all_192_4 & 206.53/127.78 in_uni(all_192_3) & in_uni(all_192_4)) | ( ~ (all_192_4 = 0) & 206.53/127.78 permut_sub2(int, all_103_4, all_103_2, all_86_11, $sum(all_86_10, 1)) = 206.53/127.78 all_192_4) 206.53/127.78 (7) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.53/127.78 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ (permut_sub2(v6, 206.53/127.78 v5, v4, v3, v2) = v1) | ~ (permut_sub2(v6, v5, v4, v3, v2) = v0)) 206.53/127.78 (8) length1(int, all_103_4) = all_171_1 206.53/127.78 (9) $lesseq(1, $difference(all_193_1, all_86_10)) 206.53/127.78 (10) $lesseq(all_86_11, all_86_8) 206.53/127.78 (11) $lesseq(all_86_7, all_86_10) 206.53/127.78 (12) ~ ($lesseq(all_86_7, all_219_1)) | ~ ($lesseq(0, all_219_1)) | ( ~ 206.53/127.78 (all_219_0 = all_219_1) & length1(int, all_105_2) = all_219_0) 206.53/127.78 (13) $lesseq(1, $difference(all_86_7, all_86_8)) 206.53/127.78 (14) permut_sub2(int, all_103_4, all_103_2, all_86_11, $sum(all_86_10, 1)) = 206.53/127.78 0 206.53/127.78 (15) $lesseq(0, all_86_11) 206.53/127.78 (16) length1(int, all_105_4) = all_170_1 206.53/127.78 (17) length1(int, all_103_2) = all_171_1 206.53/127.78 (18) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 206.53/127.78 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 206.53/127.78 (19) length1(int, all_105_4) = all_219_1 206.53/127.78 206.53/127.78 Begin of proof 206.53/127.78 | 206.53/127.78 | BETA: splitting (6) gives: 206.53/127.78 | 206.53/127.78 | Case 1: 206.53/127.78 | | 206.53/127.78 | | (20) all_192_0 = 0 & all_192_1 = 0 & map_eq_sub1(int, all_192_4, 206.53/127.78 | | all_192_3, $sum(all_86_10, 1), all_192_2) = 0 & map_eq_sub1(int, 206.53/127.78 | | all_192_4, all_192_3, 0, all_86_11) = 0 & length1(int, all_103_4) 206.53/127.78 | | = all_192_2 & elts(int, all_103_2) = all_192_3 & elts(int, 206.53/127.78 | | all_103_4) = all_192_4 & in_uni(all_192_3) & in_uni(all_192_4) 206.53/127.78 | | 206.53/127.78 | | ALPHA: (20) implies: 206.53/127.78 | | (21) length1(int, all_103_4) = all_192_2 206.53/127.78 | | 206.53/127.78 | | GROUND_INST: instantiating (18) with all_219_1, all_170_1, all_105_4, int, 206.53/127.78 | | simplifying with (16), (19) gives: 206.53/127.78 | | (22) all_219_1 = all_170_1 206.53/127.78 | | 206.53/127.78 | | GROUND_INST: instantiating (18) with all_171_1, all_170_1, all_103_2, int, 206.53/127.78 | | simplifying with (1), (17) gives: 206.53/127.78 | | (23) all_171_1 = all_170_1 206.53/127.78 | | 206.53/127.78 | | GROUND_INST: instantiating (18) with all_86_13, all_193_1, all_103_4, int, 206.53/127.78 | | simplifying with (3), (5) gives: 206.53/127.78 | | (24) all_193_1 = all_86_13 206.53/127.78 | | 206.53/127.78 | | GROUND_INST: instantiating (18) with all_193_1, all_192_2, all_103_4, int, 206.53/127.78 | | simplifying with (5), (21) gives: 206.53/127.78 | | (25) all_193_1 = all_192_2 206.53/127.78 | | 206.53/127.78 | | GROUND_INST: instantiating (18) with all_192_2, all_171_1, all_103_4, int, 206.53/127.78 | | simplifying with (8), (21) gives: 206.53/127.78 | | (26) all_192_2 = all_171_1 206.53/127.78 | | 206.53/127.78 | | COMBINE_EQS: (24), (25) imply: 206.53/127.78 | | (27) all_192_2 = all_86_13 206.53/127.78 | | 206.53/127.78 | | SIMP: (27) implies: 206.53/127.78 | | (28) all_192_2 = all_86_13 206.53/127.78 | | 206.53/127.78 | | COMBINE_EQS: (26), (28) imply: 206.53/127.78 | | (29) all_171_1 = all_86_13 206.53/127.78 | | 206.53/127.78 | | SIMP: (29) implies: 206.53/127.78 | | (30) all_171_1 = all_86_13 206.53/127.78 | | 206.53/127.78 | | COMBINE_EQS: (23), (30) imply: 206.53/127.78 | | (31) all_170_1 = all_86_13 206.53/127.78 | | 206.53/127.78 | | SIMP: (31) implies: 206.53/127.78 | | (32) all_170_1 = all_86_13 206.53/127.78 | | 206.53/127.78 | | COMBINE_EQS: (22), (32) imply: 206.53/127.78 | | (33) all_219_1 = all_86_13 206.53/127.78 | | 206.53/127.78 | | REDUCE: (9), (24) imply: 206.53/127.78 | | (34) $lesseq(1, $difference(all_86_13, all_86_10)) 206.53/127.78 | | 206.53/127.78 | | REF_CLOSE: (2), (4), (10), (11), (12), (13), (15), (18), (33), (34) are 206.53/127.78 | | inconsistent by sub-proof #59. 206.53/127.78 | | 206.53/127.78 | Case 2: 206.53/127.78 | | 206.53/127.78 | | (35) ~ (all_192_4 = 0) & permut_sub2(int, all_103_4, all_103_2, 206.53/127.78 | | all_86_11, $sum(all_86_10, 1)) = all_192_4 206.53/127.78 | | 206.53/127.78 | | REF_CLOSE: (7), (14), (35) are inconsistent by sub-proof #69. 206.53/127.78 | | 206.53/127.78 | End of split 206.53/127.78 | 206.53/127.78 End of proof 206.53/127.78 206.53/127.78 Sub-proof #52 shows that the following formulas are inconsistent: 206.53/127.78 ---------------------------------------------------------------- 206.53/127.78 (1) length1(int, all_103_2) = all_170_1 206.53/127.78 (2) all_242_1 = 0 & array_eq_sub1(int, all_103_2, all_105_4, $sum(all_86_8, 206.53/127.78 1), all_86_13) = 0 206.53/127.78 (3) length1(int, all_103_4) = all_86_13 206.53/127.78 (4) length1(int, all_103_4) = all_193_1 206.53/127.78 (5) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.53/127.78 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ 206.53/127.78 (array_eq_sub1(v6, v5, v4, v3, v2) = v1) | ~ (array_eq_sub1(v6, v5, 206.53/127.78 v4, v3, v2) = v0)) 206.53/127.78 (6) length1(int, all_105_4) = all_86_13 206.53/127.78 (7) length1(int, all_105_4) = all_234_1 206.53/127.78 (8) $lesseq(1, $difference(all_193_1, all_86_10)) 206.53/127.78 (9) (all_168_0 = all_168_1 & $lesseq(1, $difference(all_168_1, all_86_8)) & 206.53/127.78 $lesseq(all_86_13, all_168_1) & $lesseq(-1, all_86_8) & $lesseq(0, 206.53/127.78 all_86_13) & length1(int, all_105_4) = all_168_1 & length1(int, 206.53/127.78 all_103_2) = all_168_1) | ( ~ (all_168_1 = 0) & array_eq_sub1(int, 206.53/127.78 all_103_2, all_105_4, $sum(all_86_8, 1), all_86_13) = all_168_1) 206.53/127.78 (10) length1(int, all_105_2) = all_169_1 206.53/127.78 (11) length1(int, all_105_4) = all_170_1 206.53/127.78 (12) ~ ($lesseq(1, $difference(all_234_1, all_86_10))) | ~ 206.53/127.78 ($lesseq(all_86_13, all_234_1)) | ( ~ (all_234_0 = all_234_1) & 206.53/127.78 length1(int, all_105_2) = all_234_0) 206.53/127.78 (13) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 206.53/127.78 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 206.53/127.78 (14) length1(int, all_103_2) = all_177_2 206.53/127.78 (15) length1(int, all_105_4) = all_169_1 206.53/127.78 206.53/127.78 Begin of proof 206.53/127.78 | 206.53/127.78 | ALPHA: (2) implies: 206.53/127.78 | (16) array_eq_sub1(int, all_103_2, all_105_4, $sum(all_86_8, 1), all_86_13) 206.53/127.78 | = 0 206.53/127.78 | 206.53/127.78 | BETA: splitting (9) gives: 206.53/127.78 | 206.53/127.78 | Case 1: 206.53/127.78 | | 206.53/127.78 | | (17) all_168_0 = all_168_1 & $lesseq(1, $difference(all_168_1, all_86_8)) 206.53/127.78 | | & $lesseq(all_86_13, all_168_1) & $lesseq(-1, all_86_8) & $lesseq(0, 206.53/127.78 | | all_86_13) & length1(int, all_105_4) = all_168_1 & length1(int, 206.53/127.78 | | all_103_2) = all_168_1 206.53/127.78 | | 206.53/127.78 | | ALPHA: (17) implies: 206.53/127.78 | | (18) length1(int, all_103_2) = all_168_1 206.53/127.78 | | (19) length1(int, all_105_4) = all_168_1 206.53/127.78 | | 206.53/127.78 | | GROUND_INST: instantiating (13) with all_86_13, all_169_1, all_105_4, int, 206.53/127.78 | | simplifying with (6), (15) gives: 206.53/127.78 | | (20) all_169_1 = all_86_13 206.53/127.78 | | 206.53/127.78 | | GROUND_INST: instantiating (13) with all_170_1, all_169_1, all_105_4, int, 206.53/127.78 | | simplifying with (11), (15) gives: 206.53/127.78 | | (21) all_170_1 = all_169_1 206.53/127.78 | | 206.53/127.78 | | GROUND_INST: instantiating (13) with all_234_1, all_168_1, all_105_4, int, 206.53/127.78 | | simplifying with (7), (19) gives: 206.53/127.78 | | (22) all_234_1 = all_168_1 206.53/127.78 | | 206.53/127.78 | | GROUND_INST: instantiating (13) with all_177_2, all_170_1, all_103_2, int, 206.53/127.78 | | simplifying with (1), (14) gives: 206.53/127.78 | | (23) all_177_2 = all_170_1 206.53/127.78 | | 206.53/127.78 | | GROUND_INST: instantiating (13) with all_177_2, all_168_1, all_103_2, int, 206.53/127.78 | | simplifying with (14), (18) gives: 206.53/127.78 | | (24) all_177_2 = all_168_1 206.53/127.78 | | 206.53/127.78 | | GROUND_INST: instantiating (13) with all_86_13, all_193_1, all_103_4, int, 206.53/127.78 | | simplifying with (3), (4) gives: 206.53/127.78 | | (25) all_193_1 = all_86_13 206.53/127.78 | | 206.53/127.78 | | COMBINE_EQS: (23), (24) imply: 206.53/127.78 | | (26) all_170_1 = all_168_1 206.53/127.78 | | 206.53/127.78 | | SIMP: (26) implies: 206.53/127.78 | | (27) all_170_1 = all_168_1 206.53/127.78 | | 206.53/127.78 | | COMBINE_EQS: (21), (27) imply: 206.53/127.78 | | (28) all_169_1 = all_168_1 206.53/127.78 | | 206.53/127.78 | | SIMP: (28) implies: 206.53/127.78 | | (29) all_169_1 = all_168_1 206.53/127.78 | | 206.53/127.78 | | COMBINE_EQS: (20), (29) imply: 206.53/127.78 | | (30) all_168_1 = all_86_13 206.53/127.78 | | 206.53/127.78 | | COMBINE_EQS: (22), (30) imply: 206.53/127.78 | | (31) all_234_1 = all_86_13 206.53/127.78 | | 206.53/127.78 | | REDUCE: (8), (25) imply: 206.53/127.78 | | (32) $lesseq(1, $difference(all_86_13, all_86_10)) 206.53/127.78 | | 206.53/127.78 | | REDUCE: (10), (20) imply: 206.53/127.78 | | (33) length1(int, all_105_2) = all_86_13 206.53/127.78 | | 206.53/127.78 | | BETA: splitting (12) gives: 206.53/127.78 | | 206.53/127.78 | | Case 1: 206.53/127.78 | | | 206.53/127.78 | | | (34) $lesseq(1, $difference(all_86_13, all_234_1)) 206.53/127.78 | | | 206.53/127.78 | | | REDUCE: (31), (34) imply: 206.53/127.78 | | | (35) $lesseq(0, -1) 206.53/127.78 | | | 206.53/127.78 | | | CLOSE: (35) is inconsistent. 206.53/127.78 | | | 206.53/127.78 | | Case 2: 206.53/127.78 | | | 206.53/127.78 | | | (36) ~ ($lesseq(1, $difference(all_234_1, all_86_10))) | ( ~ 206.53/127.78 | | | (all_234_0 = all_234_1) & length1(int, all_105_2) = all_234_0) 206.53/127.78 | | | 206.53/127.78 | | | REF_CLOSE: (13), (31), (32), (33), (36) are inconsistent by sub-proof #53. 206.53/127.78 | | | 206.53/127.78 | | End of split 206.53/127.78 | | 206.53/127.78 | Case 2: 206.53/127.78 | | 206.53/127.78 | | (37) ~ (all_168_1 = 0) & array_eq_sub1(int, all_103_2, all_105_4, 206.53/127.78 | | $sum(all_86_8, 1), all_86_13) = all_168_1 206.53/127.78 | | 206.53/127.78 | | REF_CLOSE: (5), (16), (37) are inconsistent by sub-proof #83. 206.53/127.78 | | 206.53/127.78 | End of split 206.53/127.78 | 206.53/127.78 End of proof 206.53/127.78 206.53/127.78 Sub-proof #53 shows that the following formulas are inconsistent: 206.53/127.78 ---------------------------------------------------------------- 206.53/127.78 (1) length1(int, all_105_2) = all_86_13 206.53/127.78 (2) ~ ($lesseq(1, $difference(all_234_1, all_86_10))) | ( ~ (all_234_0 = 206.53/127.78 all_234_1) & length1(int, all_105_2) = all_234_0) 206.53/127.78 (3) all_234_1 = all_86_13 206.53/127.78 (4) $lesseq(1, $difference(all_86_13, all_86_10)) 206.53/127.78 (5) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 206.53/127.78 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 206.53/127.78 206.53/127.78 Begin of proof 206.53/127.78 | 206.53/127.78 | BETA: splitting (2) gives: 206.53/127.78 | 206.53/127.78 | Case 1: 206.53/127.79 | | 206.53/127.79 | | (6) $lesseq(all_234_1, all_86_10) 206.53/127.79 | | 206.53/127.79 | | REDUCE: (3), (6) imply: 206.53/127.79 | | (7) $lesseq(all_86_13, all_86_10) 206.53/127.79 | | 206.53/127.79 | | COMBINE_INEQS: (4), (7) imply: 206.53/127.79 | | (8) $lesseq(0, -1) 206.53/127.79 | | 206.53/127.79 | | CLOSE: (8) is inconsistent. 206.53/127.79 | | 206.53/127.79 | Case 2: 206.53/127.79 | | 206.53/127.79 | | (9) ~ (all_234_0 = all_234_1) & length1(int, all_105_2) = all_234_0 206.53/127.79 | | 206.53/127.79 | | ALPHA: (9) implies: 206.53/127.79 | | (10) ~ (all_234_0 = all_234_1) 206.53/127.79 | | (11) length1(int, all_105_2) = all_234_0 206.53/127.79 | | 206.53/127.79 | | REDUCE: (3), (10) imply: 206.53/127.79 | | (12) ~ (all_234_0 = all_86_13) 206.53/127.79 | | 206.53/127.79 | | GROUND_INST: instantiating (5) with all_86_13, all_234_0, all_105_2, int, 206.53/127.79 | | simplifying with (1), (11) gives: 206.53/127.79 | | (13) all_234_0 = all_86_13 206.53/127.79 | | 206.53/127.79 | | REDUCE: (12), (13) imply: 206.53/127.79 | | (14) ~ (0 = 0) 206.53/127.79 | | 206.53/127.79 | | CLOSE: (14) is inconsistent. 206.53/127.79 | | 206.53/127.79 | End of split 206.53/127.79 | 206.53/127.79 End of proof 206.53/127.79 206.53/127.79 Sub-proof #54 shows that the following formulas are inconsistent: 206.53/127.79 ---------------------------------------------------------------- 206.53/127.79 (1) ~ (all_153_1 = 0) & array_eq_sub1(int, all_105_4, all_105_2, 206.53/127.79 $sum(all_86_10, 1), all_86_13) = all_153_1 206.53/127.79 (2) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.53/127.79 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ 206.53/127.79 (array_eq_sub1(v6, v5, v4, v3, v2) = v1) | ~ (array_eq_sub1(v6, v5, 206.53/127.79 v4, v3, v2) = v0)) 206.53/127.79 (3) array_eq_sub1(int, all_105_4, all_105_2, $sum(all_86_10, 1), all_86_13) = 206.53/127.79 0 206.53/127.79 206.53/127.79 Begin of proof 206.53/127.79 | 206.53/127.79 | ALPHA: (1) implies: 206.53/127.79 | (4) ~ (all_153_1 = 0) 206.53/127.79 | (5) array_eq_sub1(int, all_105_4, all_105_2, $sum(all_86_10, 1), all_86_13) 206.53/127.79 | = all_153_1 206.53/127.79 | 206.53/127.79 | GROUND_INST: instantiating (2) with all_153_1, 0, all_86_13, $sum(all_86_10, 206.53/127.79 | 1), all_105_2, all_105_4, int, simplifying with (3), (5) gives: 206.53/127.79 | (6) all_153_1 = 0 206.53/127.79 | 206.53/127.79 | REDUCE: (4), (6) imply: 206.53/127.79 | (7) ~ (0 = 0) 206.53/127.79 | 206.53/127.79 | CLOSE: (7) is inconsistent. 206.53/127.79 | 206.53/127.79 End of proof 206.53/127.79 206.53/127.79 Sub-proof #55 shows that the following formulas are inconsistent: 206.53/127.79 ---------------------------------------------------------------- 206.53/127.79 (1) ~ (all_193_1 = 0) & array_eq_sub1(int, all_103_4, all_103_2, 206.53/127.79 $sum(all_86_10, 1), all_86_13) = all_193_1 206.53/127.79 (2) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.53/127.79 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ 206.53/127.79 (array_eq_sub1(v6, v5, v4, v3, v2) = v1) | ~ (array_eq_sub1(v6, v5, 206.53/127.79 v4, v3, v2) = v0)) 206.53/127.79 (3) array_eq_sub1(int, all_103_4, all_103_2, $sum(all_86_10, 1), all_86_13) = 206.53/127.79 0 206.53/127.79 206.53/127.79 Begin of proof 206.53/127.79 | 206.53/127.79 | ALPHA: (1) implies: 206.53/127.79 | (4) ~ (all_193_1 = 0) 206.53/127.79 | (5) array_eq_sub1(int, all_103_4, all_103_2, $sum(all_86_10, 1), all_86_13) 206.53/127.79 | = all_193_1 206.53/127.79 | 206.53/127.79 | GROUND_INST: instantiating (2) with all_193_1, 0, all_86_13, $sum(all_86_10, 206.53/127.79 | 1), all_103_2, all_103_4, int, simplifying with (3), (5) gives: 206.53/127.79 | (6) all_193_1 = 0 206.53/127.79 | 206.53/127.79 | REDUCE: (4), (6) imply: 206.53/127.79 | (7) ~ (0 = 0) 206.53/127.79 | 206.53/127.79 | CLOSE: (7) is inconsistent. 206.53/127.79 | 206.53/127.79 End of proof 206.53/127.79 206.53/127.79 Sub-proof #56 shows that the following formulas are inconsistent: 206.53/127.79 ---------------------------------------------------------------- 206.53/127.79 (1) elts(int, all_103_4) = all_191_3 206.53/127.79 (2) elts(int, all_103_4) = all_103_3 206.53/127.79 (3) length1(int, all_103_4) = all_86_13 206.53/127.79 (4) map_eq_sub1(int, all_103_3, all_103_1, $sum(all_86_10, 1), all_86_13) = 0 206.53/127.79 (5) length1(int, all_103_4) = all_215_1 206.53/127.79 (6) length1(int, all_103_4) = all_193_1 206.53/127.79 (7) elts(int, all_103_2) = all_191_2 206.53/127.79 (8) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 206.53/127.79 | ~ (elts(v3, v2) = v1) | ~ (elts(v3, v2) = v0)) 206.53/127.79 (9) map_eq_sub1(int, all_103_3, all_103_1, 0, all_86_11) = 0 206.53/127.79 (10) elts(int, all_103_2) = all_177_4 206.53/127.79 (11) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.53/127.79 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ (map_eq_sub1(v6, 206.53/127.79 v5, v4, v3, v2) = v1) | ~ (map_eq_sub1(v6, v5, v4, v3, v2) = v0)) 206.53/127.79 (12) elts(int, all_103_2) = all_103_1 206.53/127.79 (13) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 206.53/127.79 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 206.53/127.79 (14) elts(int, all_103_2) = all_156_3 206.53/127.79 (15) ( ~ (all_191_0 = 0) & map_eq_sub1(int, all_191_3, all_191_2, 206.53/127.79 $sum(all_86_10, 1), all_191_1) = all_191_0 & length1(int, all_103_4) 206.53/127.79 = all_191_1) | ( ~ (all_191_1 = 0) & map_eq_sub1(int, all_191_3, 206.53/127.79 all_191_2, 0, all_86_11) = all_191_1) 206.53/127.79 206.53/127.79 Begin of proof 206.53/127.79 | 206.53/127.79 | GROUND_INST: instantiating (13) with all_86_13, all_215_1, all_103_4, int, 206.53/127.79 | simplifying with (3), (5) gives: 206.53/127.79 | (16) all_215_1 = all_86_13 206.53/127.79 | 206.53/127.79 | GROUND_INST: instantiating (13) with all_215_1, all_193_1, all_103_4, int, 206.53/127.79 | simplifying with (5), (6) gives: 206.53/127.79 | (17) all_215_1 = all_193_1 206.53/127.79 | 206.53/127.79 | GROUND_INST: instantiating (8) with all_103_1, all_191_2, all_103_2, int, 206.53/127.79 | simplifying with (7), (12) gives: 206.53/127.79 | (18) all_191_2 = all_103_1 206.53/127.79 | 206.53/127.79 | GROUND_INST: instantiating (8) with all_191_2, all_177_4, all_103_2, int, 206.53/127.79 | simplifying with (7), (10) gives: 206.53/127.79 | (19) all_191_2 = all_177_4 206.53/127.79 | 206.53/127.79 | GROUND_INST: instantiating (8) with all_191_2, all_156_3, all_103_2, int, 206.53/127.79 | simplifying with (7), (14) gives: 206.53/127.79 | (20) all_191_2 = all_156_3 206.53/127.79 | 206.53/127.79 | GROUND_INST: instantiating (8) with all_103_3, all_191_3, all_103_4, int, 206.53/127.79 | simplifying with (1), (2) gives: 206.53/127.79 | (21) all_191_3 = all_103_3 206.53/127.79 | 206.53/127.79 | COMBINE_EQS: (16), (17) imply: 206.53/127.79 | (22) all_193_1 = all_86_13 206.53/127.79 | 206.53/127.79 | COMBINE_EQS: (18), (19) imply: 206.53/127.79 | (23) all_177_4 = all_103_1 206.53/127.79 | 206.53/127.79 | COMBINE_EQS: (19), (20) imply: 206.53/127.79 | (24) all_177_4 = all_156_3 206.53/127.79 | 206.53/127.79 | COMBINE_EQS: (23), (24) imply: 206.53/127.79 | (25) all_156_3 = all_103_1 206.53/127.79 | 206.53/127.79 | REF_CLOSE: (3), (4), (9), (11), (13), (15), (18), (21) are inconsistent by 206.53/127.79 | sub-proof #57. 206.53/127.79 | 206.53/127.79 End of proof 206.53/127.79 206.53/127.79 Sub-proof #57 shows that the following formulas are inconsistent: 206.53/127.79 ---------------------------------------------------------------- 206.53/127.79 (1) all_191_3 = all_103_3 206.53/127.79 (2) length1(int, all_103_4) = all_86_13 206.53/127.79 (3) map_eq_sub1(int, all_103_3, all_103_1, $sum(all_86_10, 1), all_86_13) = 0 206.53/127.79 (4) map_eq_sub1(int, all_103_3, all_103_1, 0, all_86_11) = 0 206.53/127.79 (5) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.53/127.79 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ (map_eq_sub1(v6, 206.53/127.79 v5, v4, v3, v2) = v1) | ~ (map_eq_sub1(v6, v5, v4, v3, v2) = v0)) 206.53/127.79 (6) all_191_2 = all_103_1 206.53/127.79 (7) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 206.53/127.79 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 206.53/127.79 (8) ( ~ (all_191_0 = 0) & map_eq_sub1(int, all_191_3, all_191_2, 206.53/127.79 $sum(all_86_10, 1), all_191_1) = all_191_0 & length1(int, all_103_4) 206.53/127.79 = all_191_1) | ( ~ (all_191_1 = 0) & map_eq_sub1(int, all_191_3, 206.53/127.79 all_191_2, 0, all_86_11) = all_191_1) 206.53/127.79 206.53/127.79 Begin of proof 206.53/127.79 | 206.53/127.79 | BETA: splitting (8) gives: 206.53/127.79 | 206.53/127.79 | Case 1: 206.53/127.79 | | 206.53/127.79 | | (9) ~ (all_191_0 = 0) & map_eq_sub1(int, all_191_3, all_191_2, 206.53/127.79 | | $sum(all_86_10, 1), all_191_1) = all_191_0 & length1(int, 206.53/127.79 | | all_103_4) = all_191_1 206.53/127.79 | | 206.53/127.79 | | ALPHA: (9) implies: 206.53/127.79 | | (10) ~ (all_191_0 = 0) 206.53/127.79 | | (11) length1(int, all_103_4) = all_191_1 206.53/127.79 | | (12) map_eq_sub1(int, all_191_3, all_191_2, $sum(all_86_10, 1), 206.53/127.79 | | all_191_1) = all_191_0 206.53/127.79 | | 206.53/127.79 | | REDUCE: (1), (6), (12) imply: 206.53/127.79 | | (13) map_eq_sub1(int, all_103_3, all_103_1, $sum(all_86_10, 1), 206.53/127.79 | | all_191_1) = all_191_0 206.53/127.79 | | 206.53/127.79 | | REF_CLOSE: (2), (3), (5), (7), (10), (11), (13) are inconsistent by 206.53/127.79 | | sub-proof #61. 206.53/127.79 | | 206.53/127.79 | Case 2: 206.53/127.79 | | 206.53/127.79 | | (14) ~ (all_191_1 = 0) & map_eq_sub1(int, all_191_3, all_191_2, 0, 206.53/127.79 | | all_86_11) = all_191_1 206.53/127.79 | | 206.53/127.79 | | ALPHA: (14) implies: 206.53/127.79 | | (15) ~ (all_191_1 = 0) 206.53/127.79 | | (16) map_eq_sub1(int, all_191_3, all_191_2, 0, all_86_11) = all_191_1 206.53/127.79 | | 206.53/127.79 | | REDUCE: (1), (6), (16) imply: 206.53/127.79 | | (17) map_eq_sub1(int, all_103_3, all_103_1, 0, all_86_11) = all_191_1 206.53/127.79 | | 206.53/127.79 | | GROUND_INST: instantiating (5) with 0, all_191_1, all_86_11, 0, all_103_1, 206.53/127.79 | | all_103_3, int, simplifying with (4), (17) gives: 206.53/127.79 | | (18) all_191_1 = 0 206.53/127.79 | | 206.53/127.79 | | REDUCE: (15), (18) imply: 206.53/127.79 | | (19) ~ (0 = 0) 206.53/127.79 | | 206.53/127.79 | | CLOSE: (19) is inconsistent. 206.53/127.79 | | 206.53/127.79 | End of split 206.53/127.79 | 206.53/127.79 End of proof 206.53/127.79 206.53/127.79 Sub-proof #58 shows that the following formulas are inconsistent: 206.53/127.79 ---------------------------------------------------------------- 206.53/127.79 (1) $lesseq(all_86_7, all_86_13) 206.53/127.79 (2) all_153_1 = all_86_13 206.53/127.79 (3) $lesseq(1, $difference(all_153_1, all_86_10)) 206.53/127.79 (4) $lesseq(all_86_11, all_86_8) 206.53/127.79 (5) $lesseq(all_86_7, all_86_10) 206.53/127.79 (6) ~ ($lesseq(all_86_7, all_219_1)) | ~ ($lesseq(0, all_219_1)) | ( ~ 206.53/127.79 (all_219_0 = all_219_1) & length1(int, all_105_2) = all_219_0) 206.53/127.79 (7) $lesseq(1, $difference(all_86_7, all_86_8)) 206.53/127.79 (8) all_219_1 = all_153_1 206.53/127.79 (9) $lesseq(0, all_86_11) 206.53/127.79 (10) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 206.53/127.79 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 206.53/127.79 (11) length1(int, all_105_2) = all_153_1 206.53/127.79 206.53/127.79 Begin of proof 206.53/127.79 | 206.53/127.79 | COMBINE_EQS: (2), (8) imply: 206.53/127.79 | (12) all_219_1 = all_86_13 206.53/127.79 | 206.53/127.79 | REDUCE: (2), (3) imply: 206.53/127.79 | (13) $lesseq(1, $difference(all_86_13, all_86_10)) 206.53/127.79 | 206.53/127.79 | REDUCE: (2), (11) imply: 206.53/127.79 | (14) length1(int, all_105_2) = all_86_13 206.53/127.79 | 206.53/127.79 | REF_CLOSE: (1), (4), (5), (6), (7), (9), (10), (12), (13), (14) are 206.53/127.79 | inconsistent by sub-proof #59. 206.53/127.79 | 206.53/127.79 End of proof 206.53/127.79 206.53/127.79 Sub-proof #59 shows that the following formulas are inconsistent: 206.53/127.79 ---------------------------------------------------------------- 206.53/127.79 (1) length1(int, all_105_2) = all_86_13 206.53/127.79 (2) $lesseq(all_86_7, all_86_13) 206.53/127.79 (3) all_219_1 = all_86_13 206.53/127.79 (4) $lesseq(all_86_11, all_86_8) 206.53/127.79 (5) $lesseq(all_86_7, all_86_10) 206.53/127.79 (6) ~ ($lesseq(all_86_7, all_219_1)) | ~ ($lesseq(0, all_219_1)) | ( ~ 206.53/127.79 (all_219_0 = all_219_1) & length1(int, all_105_2) = all_219_0) 206.53/127.79 (7) $lesseq(1, $difference(all_86_7, all_86_8)) 206.53/127.79 (8) $lesseq(1, $difference(all_86_13, all_86_10)) 206.53/127.79 (9) $lesseq(0, all_86_11) 206.53/127.79 (10) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 206.53/127.79 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 206.53/127.79 206.53/127.79 Begin of proof 206.53/127.79 | 206.53/127.79 | BETA: splitting (6) gives: 206.53/127.79 | 206.53/127.79 | Case 1: 206.53/127.79 | | 206.53/127.79 | | (11) $lesseq(all_219_1, -1) 206.53/127.79 | | 206.53/127.79 | | REDUCE: (3), (11) imply: 206.53/127.79 | | (12) $lesseq(all_86_13, -1) 206.53/127.79 | | 206.53/127.79 | | REF_CLOSE: (4), (5), (7), (8), (9), (12) are inconsistent by sub-proof #80. 206.53/127.79 | | 206.53/127.79 | Case 2: 206.53/127.79 | | 206.53/127.79 | | (13) ~ ($lesseq(all_86_7, all_219_1)) | ( ~ (all_219_0 = all_219_1) & 206.53/127.79 | | length1(int, all_105_2) = all_219_0) 206.53/127.79 | | 206.53/127.79 | | REF_CLOSE: (1), (2), (3), (10), (13) are inconsistent by sub-proof #74. 206.53/127.79 | | 206.53/127.79 | End of split 206.53/127.79 | 206.53/127.79 End of proof 206.53/127.79 206.53/127.79 Sub-proof #60 shows that the following formulas are inconsistent: 206.53/127.79 ---------------------------------------------------------------- 206.53/127.79 (1) elts(int, all_103_4) = all_191_3 206.53/127.79 (2) length1(int, all_103_2) = all_170_1 206.53/127.79 (3) elts(int, all_103_4) = all_103_3 206.53/127.79 (4) length1(int, all_103_4) = all_86_13 206.53/127.79 (5) map_eq_sub1(int, all_103_3, all_103_1, $sum(all_86_10, 1), all_86_13) = 0 206.53/127.79 (6) length1(int, all_103_2) = all_193_1 206.53/127.79 (7) length1(int, all_103_4) = all_193_1 206.53/127.79 (8) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.53/127.79 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ 206.53/127.79 (array_eq_sub1(v6, v5, v4, v3, v2) = v1) | ~ (array_eq_sub1(v6, v5, 206.53/127.79 v4, v3, v2) = v0)) 206.53/127.79 (9) elts(int, all_103_2) = all_191_2 206.53/127.79 (10) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 206.53/127.79 | ~ (elts(v3, v2) = v1) | ~ (elts(v3, v2) = v0)) 206.53/127.79 (11) length1(int, all_103_4) = all_171_1 206.53/127.79 (12) map_eq_sub1(int, all_103_3, all_103_1, 0, all_86_11) = 0 206.53/127.79 (13) (all_168_0 = all_168_1 & $lesseq(1, $difference(all_168_1, all_86_8)) & 206.53/127.79 $lesseq(all_86_13, all_168_1) & $lesseq(-1, all_86_8) & $lesseq(0, 206.53/127.79 all_86_13) & length1(int, all_105_4) = all_168_1 & length1(int, 206.53/127.79 all_103_2) = all_168_1) | ( ~ (all_168_1 = 0) & array_eq_sub1(int, 206.53/127.79 all_103_2, all_105_4, $sum(all_86_8, 1), all_86_13) = all_168_1) 206.53/127.79 (14) elts(int, all_103_2) = all_177_4 206.53/127.79 (15) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.53/127.79 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ (map_eq_sub1(v6, 206.53/127.79 v5, v4, v3, v2) = v1) | ~ (map_eq_sub1(v6, v5, v4, v3, v2) = v0)) 206.53/127.79 (16) elts(int, all_103_2) = all_103_1 206.53/127.79 (17) array_eq_sub1(int, all_103_2, all_105_4, $sum(all_86_8, 1), all_86_13) = 206.53/127.79 0 206.53/127.79 (18) length1(int, all_103_2) = all_171_1 206.53/127.79 (19) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 206.53/127.79 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 206.53/127.79 (20) length1(int, all_103_2) = all_177_2 206.53/127.79 (21) elts(int, all_103_2) = all_156_3 206.53/127.79 (22) length1(int, all_103_2) = all_156_0 206.53/127.79 (23) ( ~ (all_191_0 = 0) & map_eq_sub1(int, all_191_3, all_191_2, 206.53/127.79 $sum(all_86_10, 1), all_191_1) = all_191_0 & length1(int, all_103_4) 206.53/127.79 = all_191_1) | ( ~ (all_191_1 = 0) & map_eq_sub1(int, all_191_3, 206.53/127.79 all_191_2, 0, all_86_11) = all_191_1) 206.53/127.79 206.53/127.79 Begin of proof 206.53/127.79 | 206.53/127.79 | BETA: splitting (13) gives: 206.53/127.79 | 206.53/127.79 | Case 1: 206.53/127.79 | | 206.53/127.80 | | (24) all_168_0 = all_168_1 & $lesseq(1, $difference(all_168_1, all_86_8)) 206.53/127.80 | | & $lesseq(all_86_13, all_168_1) & $lesseq(-1, all_86_8) & $lesseq(0, 206.53/127.80 | | all_86_13) & length1(int, all_105_4) = all_168_1 & length1(int, 206.53/127.80 | | all_103_2) = all_168_1 206.53/127.80 | | 206.53/127.80 | | ALPHA: (24) implies: 206.53/127.80 | | (25) length1(int, all_103_2) = all_168_1 206.53/127.80 | | 206.53/127.80 | | GROUND_INST: instantiating (19) with all_177_2, all_170_1, all_103_2, int, 206.53/127.80 | | simplifying with (2), (20) gives: 206.53/127.80 | | (26) all_177_2 = all_170_1 206.53/127.80 | | 206.53/127.80 | | GROUND_INST: instantiating (19) with all_171_1, all_170_1, all_103_2, int, 206.53/127.80 | | simplifying with (2), (18) gives: 206.53/127.80 | | (27) all_171_1 = all_170_1 206.53/127.80 | | 206.53/127.80 | | GROUND_INST: instantiating (19) with all_193_1, all_168_1, all_103_2, int, 206.53/127.80 | | simplifying with (6), (25) gives: 206.53/127.80 | | (28) all_193_1 = all_168_1 206.53/127.80 | | 206.53/127.80 | | GROUND_INST: instantiating (19) with all_177_2, all_156_0, all_103_2, int, 206.53/127.80 | | simplifying with (20), (22) gives: 206.53/127.80 | | (29) all_177_2 = all_156_0 206.53/127.80 | | 206.53/127.80 | | GROUND_INST: instantiating (19) with all_86_13, all_171_1, all_103_4, int, 206.53/127.80 | | simplifying with (4), (11) gives: 206.53/127.80 | | (30) all_171_1 = all_86_13 206.53/127.80 | | 206.53/127.80 | | GROUND_INST: instantiating (19) with all_193_1, all_171_1, all_103_4, int, 206.53/127.80 | | simplifying with (7), (11) gives: 206.53/127.80 | | (31) all_193_1 = all_171_1 206.53/127.80 | | 206.53/127.80 | | GROUND_INST: instantiating (10) with all_103_1, all_177_4, all_103_2, int, 206.53/127.80 | | simplifying with (14), (16) gives: 206.53/127.80 | | (32) all_177_4 = all_103_1 206.53/127.80 | | 206.53/127.80 | | GROUND_INST: instantiating (10) with all_191_2, all_177_4, all_103_2, int, 206.53/127.80 | | simplifying with (9), (14) gives: 206.53/127.80 | | (33) all_191_2 = all_177_4 206.53/127.80 | | 206.53/127.80 | | GROUND_INST: instantiating (10) with all_191_2, all_156_3, all_103_2, int, 206.53/127.80 | | simplifying with (9), (21) gives: 206.53/127.80 | | (34) all_191_2 = all_156_3 206.53/127.80 | | 206.53/127.80 | | GROUND_INST: instantiating (10) with all_103_3, all_191_3, all_103_4, int, 206.53/127.80 | | simplifying with (1), (3) gives: 206.53/127.80 | | (35) all_191_3 = all_103_3 206.53/127.80 | | 206.53/127.80 | | COMBINE_EQS: (28), (31) imply: 206.53/127.80 | | (36) all_171_1 = all_168_1 206.53/127.80 | | 206.53/127.80 | | SIMP: (36) implies: 206.53/127.80 | | (37) all_171_1 = all_168_1 206.53/127.80 | | 206.53/127.80 | | COMBINE_EQS: (33), (34) imply: 206.53/127.80 | | (38) all_177_4 = all_156_3 206.53/127.80 | | 206.53/127.80 | | SIMP: (38) implies: 206.53/127.80 | | (39) all_177_4 = all_156_3 206.53/127.80 | | 206.53/127.80 | | COMBINE_EQS: (26), (29) imply: 206.53/127.80 | | (40) all_170_1 = all_156_0 206.53/127.80 | | 206.53/127.80 | | SIMP: (40) implies: 206.53/127.80 | | (41) all_170_1 = all_156_0 206.53/127.80 | | 206.53/127.80 | | COMBINE_EQS: (32), (39) imply: 206.53/127.80 | | (42) all_156_3 = all_103_1 206.53/127.80 | | 206.53/127.80 | | SIMP: (42) implies: 206.53/127.80 | | (43) all_156_3 = all_103_1 206.53/127.80 | | 206.53/127.80 | | COMBINE_EQS: (27), (37) imply: 206.53/127.80 | | (44) all_170_1 = all_168_1 206.53/127.80 | | 206.53/127.80 | | SIMP: (44) implies: 206.53/127.80 | | (45) all_170_1 = all_168_1 206.53/127.80 | | 206.53/127.80 | | COMBINE_EQS: (30), (37) imply: 206.53/127.80 | | (46) all_168_1 = all_86_13 206.53/127.80 | | 206.53/127.80 | | COMBINE_EQS: (41), (45) imply: 206.53/127.80 | | (47) all_168_1 = all_156_0 206.53/127.80 | | 206.53/127.80 | | SIMP: (47) implies: 206.53/127.80 | | (48) all_168_1 = all_156_0 206.53/127.80 | | 206.53/127.80 | | COMBINE_EQS: (46), (48) imply: 206.53/127.80 | | (49) all_156_0 = all_86_13 206.53/127.80 | | 206.53/127.80 | | COMBINE_EQS: (34), (43) imply: 206.53/127.80 | | (50) all_191_2 = all_103_1 206.53/127.80 | | 206.53/127.80 | | BETA: splitting (23) gives: 206.53/127.80 | | 206.53/127.80 | | Case 1: 206.53/127.80 | | | 206.53/127.80 | | | (51) ~ (all_191_0 = 0) & map_eq_sub1(int, all_191_3, all_191_2, 206.53/127.80 | | | $sum(all_86_10, 1), all_191_1) = all_191_0 & length1(int, 206.53/127.80 | | | all_103_4) = all_191_1 206.53/127.80 | | | 206.53/127.80 | | | ALPHA: (51) implies: 206.53/127.80 | | | (52) ~ (all_191_0 = 0) 206.53/127.80 | | | (53) length1(int, all_103_4) = all_191_1 206.53/127.80 | | | (54) map_eq_sub1(int, all_191_3, all_191_2, $sum(all_86_10, 1), 206.53/127.80 | | | all_191_1) = all_191_0 206.53/127.80 | | | 206.53/127.80 | | | REDUCE: (35), (50), (54) imply: 206.53/127.80 | | | (55) map_eq_sub1(int, all_103_3, all_103_1, $sum(all_86_10, 1), 206.53/127.80 | | | all_191_1) = all_191_0 206.53/127.80 | | | 206.53/127.80 | | | REF_CLOSE: (4), (5), (15), (19), (52), (53), (55) are inconsistent by 206.53/127.80 | | | sub-proof #61. 206.53/127.80 | | | 206.53/127.80 | | Case 2: 206.53/127.80 | | | 206.53/127.80 | | | (56) ~ (all_191_1 = 0) & map_eq_sub1(int, all_191_3, all_191_2, 0, 206.53/127.80 | | | all_86_11) = all_191_1 206.53/127.80 | | | 206.53/127.80 | | | ALPHA: (56) implies: 206.53/127.80 | | | (57) ~ (all_191_1 = 0) 206.53/127.80 | | | (58) map_eq_sub1(int, all_191_3, all_191_2, 0, all_86_11) = all_191_1 206.53/127.80 | | | 206.53/127.80 | | | REDUCE: (35), (50), (58) imply: 206.53/127.80 | | | (59) map_eq_sub1(int, all_103_3, all_103_1, 0, all_86_11) = all_191_1 206.53/127.80 | | | 206.53/127.80 | | | GROUND_INST: instantiating (15) with 0, all_191_1, all_86_11, 0, 206.53/127.80 | | | all_103_1, all_103_3, int, simplifying with (12), (59) gives: 206.53/127.80 | | | (60) all_191_1 = 0 206.53/127.80 | | | 206.53/127.80 | | | REDUCE: (57), (60) imply: 206.53/127.80 | | | (61) ~ (0 = 0) 206.53/127.80 | | | 206.53/127.80 | | | CLOSE: (61) is inconsistent. 206.53/127.80 | | | 206.53/127.80 | | End of split 206.53/127.80 | | 206.53/127.80 | Case 2: 206.53/127.80 | | 206.53/127.80 | | (62) ~ (all_168_1 = 0) & array_eq_sub1(int, all_103_2, all_105_4, 206.53/127.80 | | $sum(all_86_8, 1), all_86_13) = all_168_1 206.53/127.80 | | 206.53/127.80 | | REF_CLOSE: (8), (17), (62) are inconsistent by sub-proof #83. 206.53/127.80 | | 206.53/127.80 | End of split 206.53/127.80 | 206.53/127.80 End of proof 206.53/127.80 206.53/127.80 Sub-proof #61 shows that the following formulas are inconsistent: 206.53/127.80 ---------------------------------------------------------------- 206.53/127.80 (1) length1(int, all_103_4) = all_86_13 206.53/127.80 (2) length1(int, all_103_4) = all_191_1 206.53/127.80 (3) map_eq_sub1(int, all_103_3, all_103_1, $sum(all_86_10, 1), all_86_13) = 0 206.53/127.80 (4) map_eq_sub1(int, all_103_3, all_103_1, $sum(all_86_10, 1), all_191_1) = 206.53/127.80 all_191_0 206.53/127.80 (5) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.53/127.80 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ (map_eq_sub1(v6, 206.53/127.80 v5, v4, v3, v2) = v1) | ~ (map_eq_sub1(v6, v5, v4, v3, v2) = v0)) 206.53/127.80 (6) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 206.53/127.80 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 206.53/127.80 (7) ~ (all_191_0 = 0) 206.53/127.80 206.53/127.80 Begin of proof 206.53/127.80 | 206.53/127.80 | GROUND_INST: instantiating (6) with all_86_13, all_191_1, all_103_4, int, 206.53/127.80 | simplifying with (1), (2) gives: 206.53/127.80 | (8) all_191_1 = all_86_13 206.53/127.80 | 206.53/127.80 | REDUCE: (4), (8) imply: 206.53/127.80 | (9) map_eq_sub1(int, all_103_3, all_103_1, $sum(all_86_10, 1), all_86_13) = 206.53/127.80 | all_191_0 206.53/127.80 | 206.53/127.80 | GROUND_INST: instantiating (5) with 0, all_191_0, all_86_13, $sum(all_86_10, 206.53/127.80 | 1), all_103_1, all_103_3, int, simplifying with (3), (9) gives: 206.53/127.80 | (10) all_191_0 = 0 206.53/127.80 | 206.53/127.80 | REDUCE: (7), (10) imply: 206.53/127.80 | (11) ~ (0 = 0) 206.53/127.80 | 206.53/127.80 | CLOSE: (11) is inconsistent. 206.53/127.80 | 206.53/127.80 End of proof 206.53/127.80 206.53/127.80 Sub-proof #62 shows that the following formulas are inconsistent: 206.53/127.80 ---------------------------------------------------------------- 206.53/127.80 (1) length1(int, all_103_2) = all_86_13 206.53/127.80 (2) length1(int, all_105_4) = all_153_1 206.53/127.80 (3) length1(int, all_103_4) = all_215_1 206.53/127.80 (4) length1(int, all_103_2) = all_193_1 206.53/127.80 (5) length1(int, all_103_2) = all_168_1 206.53/127.80 (6) ~ ($lesseq(all_86_11, all_215_1)) | ~ ($lesseq(0, all_215_1)) | ( ~ 206.53/127.80 (all_215_0 = all_215_1) & length1(int, all_103_2) = all_215_0) 206.53/127.80 (7) length1(int, all_103_4) = all_193_1 206.53/127.80 (8) $lesseq(1, $difference(all_153_1, all_86_10)) 206.53/127.80 (9) $lesseq(all_86_11, all_86_8) 206.53/127.80 (10) $lesseq(all_86_7, all_86_10) 206.53/127.80 (11) $lesseq(1, $difference(all_86_7, all_86_8)) 206.53/127.80 (12) $lesseq(0, all_86_11) 206.53/127.80 (13) length1(int, all_105_4) = all_170_1 206.53/127.80 (14) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 206.53/127.80 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 206.53/127.80 (15) length1(int, all_103_2) = all_177_2 206.53/127.80 (16) length1(int, all_103_2) = all_156_0 206.53/127.80 (17) length1(int, all_105_4) = all_169_1 206.53/127.80 (18) length1(int, all_105_4) = all_168_1 206.53/127.80 206.53/127.80 Begin of proof 206.53/127.80 | 206.53/127.80 | GROUND_INST: instantiating (14) with all_170_1, all_169_1, all_105_4, int, 206.53/127.80 | simplifying with (13), (17) gives: 206.53/127.80 | (19) all_170_1 = all_169_1 206.53/127.80 | 206.53/127.80 | GROUND_INST: instantiating (14) with all_169_1, all_168_1, all_105_4, int, 206.53/127.80 | simplifying with (17), (18) gives: 206.53/127.80 | (20) all_169_1 = all_168_1 206.53/127.80 | 206.53/127.80 | GROUND_INST: instantiating (14) with all_170_1, all_153_1, all_105_4, int, 206.53/127.80 | simplifying with (2), (13) gives: 206.53/127.80 | (21) all_170_1 = all_153_1 206.53/127.80 | 206.53/127.80 | GROUND_INST: instantiating (14) with all_193_1, all_177_2, all_103_2, int, 206.53/127.80 | simplifying with (4), (15) gives: 206.53/127.80 | (22) all_193_1 = all_177_2 206.53/127.80 | 206.53/127.80 | GROUND_INST: instantiating (14) with all_193_1, all_168_1, all_103_2, int, 206.53/127.80 | simplifying with (4), (5) gives: 206.53/127.80 | (23) all_193_1 = all_168_1 206.53/127.80 | 206.53/127.80 | GROUND_INST: instantiating (14) with all_86_13, all_156_0, all_103_2, int, 206.53/127.80 | simplifying with (1), (16) gives: 206.53/127.80 | (24) all_156_0 = all_86_13 206.53/127.80 | 206.53/127.80 | GROUND_INST: instantiating (14) with all_177_2, all_156_0, all_103_2, int, 206.53/127.80 | simplifying with (15), (16) gives: 206.53/127.80 | (25) all_177_2 = all_156_0 206.53/127.80 | 206.53/127.80 | GROUND_INST: instantiating (14) with all_215_1, all_193_1, all_103_4, int, 206.53/127.80 | simplifying with (3), (7) gives: 206.53/127.80 | (26) all_215_1 = all_193_1 206.53/127.80 | 206.53/127.80 | COMBINE_EQS: (22), (23) imply: 206.53/127.80 | (27) all_177_2 = all_168_1 206.53/127.80 | 206.53/127.80 | SIMP: (27) implies: 206.53/127.80 | (28) all_177_2 = all_168_1 206.53/127.80 | 206.53/127.80 | COMBINE_EQS: (25), (28) imply: 206.53/127.80 | (29) all_168_1 = all_156_0 206.53/127.80 | 206.53/127.80 | COMBINE_EQS: (19), (21) imply: 206.53/127.80 | (30) all_169_1 = all_153_1 206.53/127.80 | 206.53/127.80 | SIMP: (30) implies: 206.53/127.80 | (31) all_169_1 = all_153_1 206.53/127.80 | 206.53/127.80 | COMBINE_EQS: (20), (31) imply: 206.53/127.80 | (32) all_168_1 = all_153_1 206.53/127.80 | 206.53/127.80 | COMBINE_EQS: (29), (32) imply: 206.53/127.80 | (33) all_156_0 = all_153_1 206.53/127.80 | 206.53/127.80 | SIMP: (33) implies: 206.53/127.80 | (34) all_156_0 = all_153_1 206.53/127.80 | 206.53/127.80 | COMBINE_EQS: (24), (34) imply: 206.53/127.80 | (35) all_153_1 = all_86_13 206.53/127.80 | 206.53/127.80 | COMBINE_EQS: (32), (35) imply: 206.53/127.80 | (36) all_168_1 = all_86_13 206.53/127.80 | 206.53/127.80 | COMBINE_EQS: (23), (36) imply: 206.53/127.80 | (37) all_193_1 = all_86_13 206.53/127.80 | 206.53/127.80 | COMBINE_EQS: (26), (37) imply: 206.53/127.80 | (38) all_215_1 = all_86_13 206.53/127.80 | 206.53/127.80 | REF_CLOSE: (6), (8), (9), (10), (11), (12), (14), (16), (24), (35), (38) are 206.53/127.80 | inconsistent by sub-proof #72. 206.53/127.80 | 206.53/127.80 End of proof 206.53/127.80 206.53/127.80 Sub-proof #63 shows that the following formulas are inconsistent: 206.53/127.80 ---------------------------------------------------------------- 206.53/127.80 (1) elts(int, all_105_4) = all_177_3 206.53/127.80 (2) length1(int, all_103_2) = all_86_13 206.53/127.80 (3) length1(int, all_103_2) = all_170_1 206.53/127.80 (4) length1(int, all_105_4) = all_153_1 206.53/127.80 (5) (all_219_1 = 0 & array_eq_sub1(int, all_105_4, all_105_2, 0, all_86_7) = 206.53/127.80 0) | (length1(int, all_105_4) = all_219_1 & ( ~ ($lesseq(all_86_7, 206.53/127.80 all_219_1)) | ~ ($lesseq(0, all_219_1)) | ( ~ (all_219_0 = 206.53/127.80 all_219_1) & length1(int, all_105_2) = all_219_0))) 206.53/127.80 (6) length1(int, all_103_2) = all_193_1 206.53/127.80 (7) elts(int, all_105_2) = all_187_2 206.53/127.80 (8) length1(int, all_103_4) = all_193_1 206.53/127.80 (9) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.53/127.80 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ 206.53/127.80 (array_eq_sub1(v6, v5, v4, v3, v2) = v1) | ~ (array_eq_sub1(v6, v5, 206.53/127.80 v4, v3, v2) = v0)) 206.53/127.80 (10) (all_171_0 = all_171_1 & $lesseq(all_86_11, all_171_1) & $lesseq(0, 206.53/127.80 all_171_1) & $lesseq(0, all_86_11) & length1(int, all_103_2) = 206.53/127.80 all_171_1 & length1(int, all_103_4) = all_171_1) | ( ~ (all_171_1 = 0) 206.53/127.80 & array_eq_sub1(int, all_103_4, all_103_2, 0, all_86_11) = all_171_1) 206.53/127.80 (11) elts(int, all_105_4) = all_187_3 206.53/127.80 (12) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 206.53/127.80 | ~ (elts(v3, v2) = v1) | ~ (elts(v3, v2) = v0)) 206.53/127.80 (13) length1(int, all_105_4) = all_86_13 206.53/127.80 (14) elts(int, all_105_4) = all_105_3 206.53/127.80 (15) elts(int, all_105_4) = all_156_1 206.53/127.80 (16) map_eq_sub1(int, all_105_3, all_105_1, 0, all_86_7) = 0 206.53/127.80 (17) (all_169_0 = all_169_1 & $lesseq(all_86_7, all_169_1) & $lesseq(0, 206.53/127.80 all_169_1) & $lesseq(0, all_86_7) & length1(int, all_105_2) = 206.53/127.80 all_169_1 & length1(int, all_105_4) = all_169_1) | ( ~ (all_169_1 = 0) 206.53/127.80 & array_eq_sub1(int, all_105_4, all_105_2, 0, all_86_7) = all_169_1) 206.53/127.80 (18) (all_242_1 = 0 & array_eq_sub1(int, all_103_2, all_105_4, $sum(all_86_8, 206.53/127.80 1), all_86_13) = 0) | (length1(int, all_103_2) = all_242_1 & ( ~ 206.53/127.80 ($lesseq(1, $difference(all_242_1, all_86_8))) | ~ 206.53/127.80 ($lesseq(all_86_13, all_242_1)) | ( ~ (all_242_0 = all_242_1) & 206.53/127.80 length1(int, all_105_4) = all_242_0))) 206.53/127.80 (19) elts(int, all_105_2) = all_105_1 206.53/127.80 (20) array_eq_sub1(int, all_103_4, all_103_2, 0, all_86_11) = 0 206.53/127.80 (21) (all_168_0 = all_168_1 & $lesseq(1, $difference(all_168_1, all_86_8)) & 206.53/127.80 $lesseq(all_86_13, all_168_1) & $lesseq(-1, all_86_8) & $lesseq(0, 206.53/127.80 all_86_13) & length1(int, all_105_4) = all_168_1 & length1(int, 206.53/127.80 all_103_2) = all_168_1) | ( ~ (all_168_1 = 0) & array_eq_sub1(int, 206.53/127.80 all_103_2, all_105_4, $sum(all_86_8, 1), all_86_13) = all_168_1) 206.53/127.81 (22) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.53/127.81 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ (map_eq_sub1(v6, 206.53/127.81 v5, v4, v3, v2) = v1) | ~ (map_eq_sub1(v6, v5, v4, v3, v2) = v0)) 206.53/127.81 (23) length1(int, all_105_4) = all_170_1 206.53/127.81 (24) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 206.53/127.81 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 206.53/127.81 (25) length1(int, all_103_2) = all_177_2 206.53/127.81 (26) ( ~ (all_187_0 = 0) & map_eq_sub1(int, all_187_3, all_187_2, 206.53/127.81 $sum(all_86_10, 1), all_187_1) = all_187_0 & length1(int, all_105_4) 206.53/127.81 = all_187_1) | ( ~ (all_187_1 = 0) & map_eq_sub1(int, all_187_3, 206.53/127.81 all_187_2, 0, all_86_7) = all_187_1) 206.53/127.81 (27) map_eq_sub1(int, all_105_3, all_105_1, $sum(all_86_10, 1), all_86_13) = 206.53/127.81 0 206.53/127.81 (28) length1(int, all_103_2) = all_156_0 206.53/127.81 206.53/127.81 Begin of proof 206.53/127.81 | 206.53/127.81 | BETA: splitting (10) gives: 206.53/127.81 | 206.53/127.81 | Case 1: 206.53/127.81 | | 206.53/127.81 | | (29) all_171_0 = all_171_1 & $lesseq(all_86_11, all_171_1) & $lesseq(0, 206.53/127.81 | | all_171_1) & $lesseq(0, all_86_11) & length1(int, all_103_2) = 206.53/127.81 | | all_171_1 & length1(int, all_103_4) = all_171_1 206.53/127.81 | | 206.53/127.81 | | ALPHA: (29) implies: 206.53/127.81 | | (30) length1(int, all_103_4) = all_171_1 206.53/127.81 | | 206.53/127.81 | | BETA: splitting (5) gives: 206.53/127.81 | | 206.53/127.81 | | Case 1: 206.53/127.81 | | | 206.53/127.81 | | | (31) all_219_1 = 0 & array_eq_sub1(int, all_105_4, all_105_2, 0, 206.53/127.81 | | | all_86_7) = 0 206.53/127.81 | | | 206.53/127.81 | | | ALPHA: (31) implies: 206.53/127.81 | | | (32) array_eq_sub1(int, all_105_4, all_105_2, 0, all_86_7) = 0 206.53/127.81 | | | 206.53/127.81 | | | BETA: splitting (17) gives: 206.53/127.81 | | | 206.53/127.81 | | | Case 1: 206.53/127.81 | | | | 206.53/127.81 | | | | (33) all_169_0 = all_169_1 & $lesseq(all_86_7, all_169_1) & 206.53/127.81 | | | | $lesseq(0, all_169_1) & $lesseq(0, all_86_7) & length1(int, 206.53/127.81 | | | | all_105_2) = all_169_1 & length1(int, all_105_4) = all_169_1 206.53/127.81 | | | | 206.53/127.81 | | | | ALPHA: (33) implies: 206.53/127.81 | | | | (34) length1(int, all_105_4) = all_169_1 206.53/127.81 | | | | 206.53/127.81 | | | | BETA: splitting (18) gives: 206.53/127.81 | | | | 206.53/127.81 | | | | Case 1: 206.53/127.81 | | | | | 206.53/127.81 | | | | | (35) all_242_1 = 0 & array_eq_sub1(int, all_103_2, all_105_4, 206.53/127.81 | | | | | $sum(all_86_8, 1), all_86_13) = 0 206.53/127.81 | | | | | 206.53/127.81 | | | | | ALPHA: (35) implies: 206.53/127.81 | | | | | (36) array_eq_sub1(int, all_103_2, all_105_4, $sum(all_86_8, 1), 206.53/127.81 | | | | | all_86_13) = 0 206.53/127.81 | | | | | 206.53/127.81 | | | | | BETA: splitting (21) gives: 206.53/127.81 | | | | | 206.53/127.81 | | | | | Case 1: 206.53/127.81 | | | | | | 206.53/127.81 | | | | | | (37) all_168_0 = all_168_1 & $lesseq(1, $difference(all_168_1, 206.53/127.81 | | | | | | all_86_8)) & $lesseq(all_86_13, all_168_1) & $lesseq(-1, 206.53/127.81 | | | | | | all_86_8) & $lesseq(0, all_86_13) & length1(int, 206.53/127.81 | | | | | | all_105_4) = all_168_1 & length1(int, all_103_2) = 206.53/127.81 | | | | | | all_168_1 206.53/127.81 | | | | | | 206.53/127.81 | | | | | | ALPHA: (37) implies: 206.53/127.81 | | | | | | (38) length1(int, all_105_4) = all_168_1 206.53/127.81 | | | | | | 206.53/127.81 | | | | | | GROUND_INST: instantiating (24) with all_86_13, all_169_1, 206.53/127.81 | | | | | | all_105_4, int, simplifying with (13), (34) gives: 206.53/127.81 | | | | | | (39) all_169_1 = all_86_13 206.53/127.81 | | | | | | 206.53/127.81 | | | | | | GROUND_INST: instantiating (24) with all_170_1, all_169_1, 206.53/127.81 | | | | | | all_105_4, int, simplifying with (23), (34) gives: 206.53/127.81 | | | | | | (40) all_170_1 = all_169_1 206.53/127.81 | | | | | | 206.53/127.81 | | | | | | GROUND_INST: instantiating (24) with all_169_1, all_168_1, 206.53/127.81 | | | | | | all_105_4, int, simplifying with (34), (38) gives: 206.53/127.81 | | | | | | (41) all_169_1 = all_168_1 206.53/127.81 | | | | | | 206.53/127.81 | | | | | | GROUND_INST: instantiating (24) with all_170_1, all_153_1, 206.53/127.81 | | | | | | all_105_4, int, simplifying with (4), (23) gives: 206.53/127.81 | | | | | | (42) all_170_1 = all_153_1 206.53/127.81 | | | | | | 206.53/127.81 | | | | | | GROUND_INST: instantiating (24) with all_193_1, all_177_2, 206.53/127.81 | | | | | | all_103_2, int, simplifying with (6), (25) gives: 206.53/127.81 | | | | | | (43) all_193_1 = all_177_2 206.53/127.81 | | | | | | 206.53/127.81 | | | | | | GROUND_INST: instantiating (24) with all_177_2, all_170_1, 206.53/127.81 | | | | | | all_103_2, int, simplifying with (3), (25) gives: 206.53/127.81 | | | | | | (44) all_177_2 = all_170_1 206.53/127.81 | | | | | | 206.53/127.81 | | | | | | GROUND_INST: instantiating (24) with all_177_2, all_156_0, 206.53/127.81 | | | | | | all_103_2, int, simplifying with (25), (28) gives: 206.53/127.81 | | | | | | (45) all_177_2 = all_156_0 206.53/127.81 | | | | | | 206.53/127.81 | | | | | | GROUND_INST: instantiating (24) with all_193_1, all_171_1, 206.53/127.81 | | | | | | all_103_4, int, simplifying with (8), (30) gives: 206.53/127.81 | | | | | | (46) all_193_1 = all_171_1 206.53/127.81 | | | | | | 206.53/127.81 | | | | | | GROUND_INST: instantiating (12) with all_105_1, all_187_2, 206.53/127.81 | | | | | | all_105_2, int, simplifying with (7), (19) gives: 206.53/127.81 | | | | | | (47) all_187_2 = all_105_1 206.53/127.81 | | | | | | 206.53/127.81 | | | | | | GROUND_INST: instantiating (12) with all_105_3, all_177_3, 206.53/127.81 | | | | | | all_105_4, int, simplifying with (1), (14) gives: 206.53/127.81 | | | | | | (48) all_177_3 = all_105_3 206.53/127.81 | | | | | | 206.53/127.81 | | | | | | GROUND_INST: instantiating (12) with all_187_3, all_177_3, 206.53/127.81 | | | | | | all_105_4, int, simplifying with (1), (11) gives: 206.53/127.81 | | | | | | (49) all_187_3 = all_177_3 206.53/127.81 | | | | | | 206.53/127.81 | | | | | | GROUND_INST: instantiating (12) with all_187_3, all_156_1, 206.53/127.81 | | | | | | all_105_4, int, simplifying with (11), (15) gives: 206.53/127.81 | | | | | | (50) all_187_3 = all_156_1 206.53/127.81 | | | | | | 206.53/127.81 | | | | | | COMBINE_EQS: (43), (46) imply: 206.53/127.81 | | | | | | (51) all_177_2 = all_171_1 206.53/127.81 | | | | | | 206.53/127.81 | | | | | | SIMP: (51) implies: 206.53/127.81 | | | | | | (52) all_177_2 = all_171_1 206.53/127.81 | | | | | | 206.53/127.81 | | | | | | COMBINE_EQS: (49), (50) imply: 206.53/127.81 | | | | | | (53) all_177_3 = all_156_1 206.53/127.81 | | | | | | 206.53/127.81 | | | | | | SIMP: (53) implies: 206.53/127.81 | | | | | | (54) all_177_3 = all_156_1 206.53/127.81 | | | | | | 206.53/127.81 | | | | | | COMBINE_EQS: (45), (52) imply: 206.53/127.81 | | | | | | (55) all_171_1 = all_156_0 206.53/127.81 | | | | | | 206.53/127.81 | | | | | | COMBINE_EQS: (44), (52) imply: 206.53/127.81 | | | | | | (56) all_171_1 = all_170_1 206.53/127.81 | | | | | | 206.53/127.81 | | | | | | COMBINE_EQS: (48), (54) imply: 206.53/127.81 | | | | | | (57) all_156_1 = all_105_3 206.53/127.81 | | | | | | 206.53/127.81 | | | | | | COMBINE_EQS: (55), (56) imply: 206.53/127.81 | | | | | | (58) all_170_1 = all_156_0 206.53/127.81 | | | | | | 206.53/127.81 | | | | | | COMBINE_EQS: (42), (58) imply: 206.53/127.81 | | | | | | (59) all_156_0 = all_153_1 206.53/127.81 | | | | | | 206.53/127.81 | | | | | | COMBINE_EQS: (40), (58) imply: 206.53/127.81 | | | | | | (60) all_169_1 = all_156_0 206.53/127.81 | | | | | | 206.53/127.81 | | | | | | SIMP: (60) implies: 206.53/127.81 | | | | | | (61) all_169_1 = all_156_0 206.53/127.81 | | | | | | 206.53/127.81 | | | | | | COMBINE_EQS: (39), (41) imply: 206.53/127.81 | | | | | | (62) all_168_1 = all_86_13 206.53/127.81 | | | | | | 206.53/127.81 | | | | | | COMBINE_EQS: (41), (61) imply: 206.53/127.81 | | | | | | (63) all_168_1 = all_156_0 206.53/127.81 | | | | | | 206.53/127.81 | | | | | | COMBINE_EQS: (62), (63) imply: 206.53/127.81 | | | | | | (64) all_156_0 = all_86_13 206.53/127.81 | | | | | | 206.53/127.81 | | | | | | SIMP: (64) implies: 206.53/127.81 | | | | | | (65) all_156_0 = all_86_13 206.53/127.81 | | | | | | 206.53/127.81 | | | | | | COMBINE_EQS: (59), (65) imply: 206.53/127.81 | | | | | | (66) all_153_1 = all_86_13 206.53/127.81 | | | | | | 206.53/127.81 | | | | | | SIMP: (66) implies: 206.53/127.81 | | | | | | (67) all_153_1 = all_86_13 206.53/127.81 | | | | | | 206.53/127.81 | | | | | | COMBINE_EQS: (50), (57) imply: 206.53/127.81 | | | | | | (68) all_187_3 = all_105_3 206.53/127.81 | | | | | | 206.53/127.81 | | | | | | BETA: splitting (26) gives: 206.53/127.81 | | | | | | 206.53/127.81 | | | | | | Case 1: 206.53/127.81 | | | | | | | 206.53/127.81 | | | | | | | (69) ~ (all_187_0 = 0) & map_eq_sub1(int, all_187_3, 206.53/127.81 | | | | | | | all_187_2, $sum(all_86_10, 1), all_187_1) = all_187_0 & 206.53/127.81 | | | | | | | length1(int, all_105_4) = all_187_1 206.53/127.81 | | | | | | | 206.53/127.81 | | | | | | | ALPHA: (69) implies: 206.53/127.81 | | | | | | | (70) ~ (all_187_0 = 0) 206.53/127.81 | | | | | | | (71) length1(int, all_105_4) = all_187_1 206.53/127.81 | | | | | | | (72) map_eq_sub1(int, all_187_3, all_187_2, $sum(all_86_10, 1), 206.53/127.81 | | | | | | | all_187_1) = all_187_0 206.53/127.81 | | | | | | | 206.53/127.81 | | | | | | | REDUCE: (47), (68), (72) imply: 206.53/127.81 | | | | | | | (73) map_eq_sub1(int, all_105_3, all_105_1, $sum(all_86_10, 1), 206.53/127.81 | | | | | | | all_187_1) = all_187_0 206.53/127.81 | | | | | | | 206.53/127.81 | | | | | | | REF_CLOSE: (13), (22), (24), (27), (70), (71), (73) are 206.53/127.81 | | | | | | | inconsistent by sub-proof #67. 206.53/127.81 | | | | | | | 206.53/127.81 | | | | | | Case 2: 206.53/127.81 | | | | | | | 206.53/127.81 | | | | | | | (74) ~ (all_187_1 = 0) & map_eq_sub1(int, all_187_3, 206.53/127.81 | | | | | | | all_187_2, 0, all_86_7) = all_187_1 206.53/127.81 | | | | | | | 206.53/127.81 | | | | | | | ALPHA: (74) implies: 206.53/127.81 | | | | | | | (75) ~ (all_187_1 = 0) 206.53/127.81 | | | | | | | (76) map_eq_sub1(int, all_187_3, all_187_2, 0, all_86_7) = 206.53/127.81 | | | | | | | all_187_1 206.53/127.81 | | | | | | | 206.53/127.81 | | | | | | | REDUCE: (47), (68), (76) imply: 206.53/127.81 | | | | | | | (77) map_eq_sub1(int, all_105_3, all_105_1, 0, all_86_7) = 206.53/127.81 | | | | | | | all_187_1 206.53/127.81 | | | | | | | 206.53/127.81 | | | | | | | GROUND_INST: instantiating (22) with 0, all_187_1, all_86_7, 0, 206.53/127.81 | | | | | | | all_105_1, all_105_3, int, simplifying with (16), 206.53/127.81 | | | | | | | (77) gives: 206.53/127.81 | | | | | | | (78) all_187_1 = 0 206.53/127.81 | | | | | | | 206.53/127.81 | | | | | | | REDUCE: (75), (78) imply: 206.53/127.81 | | | | | | | (79) ~ (0 = 0) 206.53/127.81 | | | | | | | 206.53/127.81 | | | | | | | CLOSE: (79) is inconsistent. 206.53/127.81 | | | | | | | 206.53/127.81 | | | | | | End of split 206.53/127.81 | | | | | | 206.53/127.81 | | | | | Case 2: 206.53/127.81 | | | | | | 206.53/127.81 | | | | | | (80) ~ (all_168_1 = 0) & array_eq_sub1(int, all_103_2, 206.53/127.81 | | | | | | all_105_4, $sum(all_86_8, 1), all_86_13) = all_168_1 206.53/127.81 | | | | | | 206.53/127.81 | | | | | | REF_CLOSE: (9), (36), (80) are inconsistent by sub-proof #83. 206.53/127.81 | | | | | | 206.53/127.81 | | | | | End of split 206.53/127.81 | | | | | 206.53/127.81 | | | | Case 2: 206.53/127.81 | | | | | 206.53/127.81 | | | | | (81) length1(int, all_103_2) = all_242_1 & ( ~ ($lesseq(1, 206.53/127.81 | | | | | $difference(all_242_1, all_86_8))) | ~ 206.53/127.81 | | | | | ($lesseq(all_86_13, all_242_1)) | ( ~ (all_242_0 = 206.53/127.81 | | | | | all_242_1) & length1(int, all_105_4) = all_242_0)) 206.53/127.81 | | | | | 206.53/127.81 | | | | | ALPHA: (81) implies: 206.53/127.81 | | | | | (82) length1(int, all_103_2) = all_242_1 206.53/127.81 | | | | | 206.53/127.81 | | | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (11), (12), (14), (16), 206.53/127.81 | | | | | (19), (22), (23), (24), (25), (26), (27), (28), (30), (82) 206.53/127.81 | | | | | are inconsistent by sub-proof #65. 206.53/127.81 | | | | | 206.53/127.81 | | | | End of split 206.53/127.81 | | | | 206.53/127.81 | | | Case 2: 206.53/127.81 | | | | 206.53/127.81 | | | | (83) ~ (all_169_1 = 0) & array_eq_sub1(int, all_105_4, all_105_2, 0, 206.53/127.81 | | | | all_86_7) = all_169_1 206.53/127.81 | | | | 206.53/127.81 | | | | REF_CLOSE: (9), (32), (83) are inconsistent by sub-proof #75. 206.53/127.81 | | | | 206.53/127.81 | | | End of split 206.53/127.81 | | | 206.53/127.81 | | Case 2: 206.53/127.81 | | | 206.53/127.81 | | | (84) length1(int, all_105_4) = all_219_1 & ( ~ ($lesseq(all_86_7, 206.53/127.81 | | | all_219_1)) | ~ ($lesseq(0, all_219_1)) | ( ~ (all_219_0 = 206.53/127.81 | | | all_219_1) & length1(int, all_105_2) = all_219_0)) 206.53/127.81 | | | 206.53/127.81 | | | ALPHA: (84) implies: 206.53/127.81 | | | (85) length1(int, all_105_4) = all_219_1 206.53/127.81 | | | 206.53/127.81 | | | BETA: splitting (18) gives: 206.53/127.81 | | | 206.53/127.81 | | | Case 1: 206.53/127.81 | | | | 206.53/127.81 | | | | (86) all_242_1 = 0 & array_eq_sub1(int, all_103_2, all_105_4, 206.53/127.81 | | | | $sum(all_86_8, 1), all_86_13) = 0 206.53/127.81 | | | | 206.53/127.81 | | | | ALPHA: (86) implies: 206.53/127.81 | | | | (87) array_eq_sub1(int, all_103_2, all_105_4, $sum(all_86_8, 1), 206.53/127.81 | | | | all_86_13) = 0 206.53/127.81 | | | | 206.53/127.81 | | | | BETA: splitting (21) gives: 206.53/127.81 | | | | 206.53/127.81 | | | | Case 1: 206.53/127.81 | | | | | 206.53/127.81 | | | | | (88) all_168_0 = all_168_1 & $lesseq(1, $difference(all_168_1, 206.53/127.81 | | | | | all_86_8)) & $lesseq(all_86_13, all_168_1) & $lesseq(-1, 206.53/127.81 | | | | | all_86_8) & $lesseq(0, all_86_13) & length1(int, all_105_4) 206.53/127.81 | | | | | = all_168_1 & length1(int, all_103_2) = all_168_1 206.53/127.81 | | | | | 206.53/127.81 | | | | | ALPHA: (88) implies: 206.53/127.81 | | | | | (89) length1(int, all_103_2) = all_168_1 206.53/127.81 | | | | | (90) length1(int, all_105_4) = all_168_1 206.53/127.81 | | | | | 206.53/127.81 | | | | | GROUND_INST: instantiating (24) with all_219_1, all_168_1, all_105_4, 206.53/127.81 | | | | | int, simplifying with (85), (90) gives: 206.53/127.81 | | | | | (91) all_219_1 = all_168_1 206.53/127.81 | | | | | 206.53/127.81 | | | | | GROUND_INST: instantiating (24) with all_219_1, all_153_1, all_105_4, 206.53/127.81 | | | | | int, simplifying with (4), (85) gives: 206.53/127.81 | | | | | (92) all_219_1 = all_153_1 206.53/127.81 | | | | | 206.53/127.81 | | | | | GROUND_INST: instantiating (24) with all_193_1, all_177_2, all_103_2, 206.53/127.81 | | | | | int, simplifying with (6), (25) gives: 206.53/127.81 | | | | | (93) all_193_1 = all_177_2 206.53/127.81 | | | | | 206.53/127.81 | | | | | GROUND_INST: instantiating (24) with all_86_13, all_170_1, all_103_2, 206.53/127.81 | | | | | int, simplifying with (2), (3) gives: 206.53/127.81 | | | | | (94) all_170_1 = all_86_13 206.53/127.81 | | | | | 206.53/127.81 | | | | | GROUND_INST: instantiating (24) with all_177_2, all_170_1, all_103_2, 206.53/127.81 | | | | | int, simplifying with (3), (25) gives: 206.53/127.81 | | | | | (95) all_177_2 = all_170_1 206.53/127.81 | | | | | 206.53/127.81 | | | | | GROUND_INST: instantiating (24) with all_177_2, all_168_1, all_103_2, 206.53/127.81 | | | | | int, simplifying with (25), (89) gives: 206.53/127.81 | | | | | (96) all_177_2 = all_168_1 206.53/127.81 | | | | | 206.53/127.81 | | | | | GROUND_INST: instantiating (24) with all_193_1, all_171_1, all_103_4, 206.53/127.81 | | | | | int, simplifying with (8), (30) gives: 206.53/127.81 | | | | | (97) all_193_1 = all_171_1 206.53/127.81 | | | | | 206.53/127.81 | | | | | GROUND_INST: instantiating (12) with all_105_1, all_187_2, all_105_2, 206.53/127.81 | | | | | int, simplifying with (7), (19) gives: 206.53/127.81 | | | | | (98) all_187_2 = all_105_1 206.53/127.81 | | | | | 206.53/127.81 | | | | | GROUND_INST: instantiating (12) with all_105_3, all_177_3, all_105_4, 206.53/127.81 | | | | | int, simplifying with (1), (14) gives: 206.53/127.81 | | | | | (99) all_177_3 = all_105_3 206.53/127.81 | | | | | 206.53/127.81 | | | | | GROUND_INST: instantiating (12) with all_187_3, all_177_3, all_105_4, 206.53/127.81 | | | | | int, simplifying with (1), (11) gives: 206.53/127.81 | | | | | (100) all_187_3 = all_177_3 206.53/127.81 | | | | | 206.53/127.81 | | | | | GROUND_INST: instantiating (12) with all_187_3, all_156_1, all_105_4, 206.53/127.81 | | | | | int, simplifying with (11), (15) gives: 206.53/127.81 | | | | | (101) all_187_3 = all_156_1 206.53/127.81 | | | | | 206.53/127.81 | | | | | COMBINE_EQS: (91), (92) imply: 206.53/127.81 | | | | | (102) all_168_1 = all_153_1 206.53/127.81 | | | | | 206.53/127.81 | | | | | SIMP: (102) implies: 206.53/127.81 | | | | | (103) all_168_1 = all_153_1 206.53/127.81 | | | | | 206.53/127.81 | | | | | COMBINE_EQS: (93), (97) imply: 206.53/127.81 | | | | | (104) all_177_2 = all_171_1 206.53/127.81 | | | | | 206.53/127.81 | | | | | SIMP: (104) implies: 206.53/127.81 | | | | | (105) all_177_2 = all_171_1 206.53/127.81 | | | | | 206.53/127.81 | | | | | COMBINE_EQS: (100), (101) imply: 206.53/127.81 | | | | | (106) all_177_3 = all_156_1 206.53/127.81 | | | | | 206.53/127.81 | | | | | SIMP: (106) implies: 206.53/127.81 | | | | | (107) all_177_3 = all_156_1 206.53/127.81 | | | | | 206.53/127.81 | | | | | COMBINE_EQS: (96), (105) imply: 206.53/127.81 | | | | | (108) all_171_1 = all_168_1 206.53/127.81 | | | | | 206.53/127.81 | | | | | COMBINE_EQS: (95), (105) imply: 206.53/127.81 | | | | | (109) all_171_1 = all_170_1 206.53/127.81 | | | | | 206.53/127.81 | | | | | COMBINE_EQS: (99), (107) imply: 206.53/127.81 | | | | | (110) all_156_1 = all_105_3 206.53/127.81 | | | | | 206.53/127.81 | | | | | COMBINE_EQS: (108), (109) imply: 206.53/127.81 | | | | | (111) all_170_1 = all_168_1 206.53/127.81 | | | | | 206.53/127.81 | | | | | SIMP: (111) implies: 206.53/127.81 | | | | | (112) all_170_1 = all_168_1 206.53/127.81 | | | | | 206.53/127.81 | | | | | COMBINE_EQS: (94), (112) imply: 206.53/127.81 | | | | | (113) all_168_1 = all_86_13 206.53/127.82 | | | | | 206.53/127.82 | | | | | SIMP: (113) implies: 206.53/127.82 | | | | | (114) all_168_1 = all_86_13 206.69/127.82 | | | | | 206.69/127.82 | | | | | COMBINE_EQS: (103), (114) imply: 206.69/127.82 | | | | | (115) all_153_1 = all_86_13 206.69/127.82 | | | | | 206.69/127.82 | | | | | REF_CLOSE: (4), (16), (22), (24), (26), (27), (98), (101), (110), 206.69/127.82 | | | | | (115) are inconsistent by sub-proof #64. 206.69/127.82 | | | | | 206.69/127.82 | | | | Case 2: 206.69/127.82 | | | | | 206.69/127.82 | | | | | (116) ~ (all_168_1 = 0) & array_eq_sub1(int, all_103_2, all_105_4, 206.69/127.82 | | | | | $sum(all_86_8, 1), all_86_13) = all_168_1 206.69/127.82 | | | | | 206.69/127.82 | | | | | REF_CLOSE: (9), (87), (116) are inconsistent by sub-proof #83. 206.69/127.82 | | | | | 206.69/127.82 | | | | End of split 206.69/127.82 | | | | 206.69/127.82 | | | Case 2: 206.69/127.82 | | | | 206.69/127.82 | | | | (117) length1(int, all_103_2) = all_242_1 & ( ~ ($lesseq(1, 206.69/127.82 | | | | $difference(all_242_1, all_86_8))) | ~ 206.69/127.82 | | | | ($lesseq(all_86_13, all_242_1)) | ( ~ (all_242_0 = all_242_1) 206.69/127.82 | | | | & length1(int, all_105_4) = all_242_0)) 206.69/127.82 | | | | 206.69/127.82 | | | | ALPHA: (117) implies: 206.69/127.82 | | | | (118) length1(int, all_103_2) = all_242_1 206.69/127.82 | | | | 206.69/127.82 | | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (11), (12), (14), (16), 206.69/127.82 | | | | (19), (22), (23), (24), (25), (26), (27), (28), (30), (118) 206.69/127.82 | | | | are inconsistent by sub-proof #65. 206.69/127.82 | | | | 206.69/127.82 | | | End of split 206.69/127.82 | | | 206.69/127.82 | | End of split 206.69/127.82 | | 206.69/127.82 | Case 2: 206.69/127.82 | | 206.69/127.82 | | (119) ~ (all_171_1 = 0) & array_eq_sub1(int, all_103_4, all_103_2, 0, 206.69/127.82 | | all_86_11) = all_171_1 206.69/127.82 | | 206.69/127.82 | | REF_CLOSE: (9), (20), (119) are inconsistent by sub-proof #81. 206.69/127.82 | | 206.69/127.82 | End of split 206.69/127.82 | 206.69/127.82 End of proof 206.69/127.82 206.69/127.82 Sub-proof #64 shows that the following formulas are inconsistent: 206.69/127.82 ---------------------------------------------------------------- 206.69/127.82 (1) all_187_2 = all_105_1 206.69/127.82 (2) all_187_3 = all_156_1 206.69/127.82 (3) length1(int, all_105_4) = all_153_1 206.69/127.82 (4) map_eq_sub1(int, all_105_3, all_105_1, 0, all_86_7) = 0 206.69/127.82 (5) all_156_1 = all_105_3 206.69/127.82 (6) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.69/127.82 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ (map_eq_sub1(v6, 206.69/127.82 v5, v4, v3, v2) = v1) | ~ (map_eq_sub1(v6, v5, v4, v3, v2) = v0)) 206.69/127.82 (7) all_153_1 = all_86_13 206.69/127.82 (8) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 206.69/127.82 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 206.69/127.82 (9) ( ~ (all_187_0 = 0) & map_eq_sub1(int, all_187_3, all_187_2, 206.69/127.82 $sum(all_86_10, 1), all_187_1) = all_187_0 & length1(int, all_105_4) 206.69/127.82 = all_187_1) | ( ~ (all_187_1 = 0) & map_eq_sub1(int, all_187_3, 206.69/127.82 all_187_2, 0, all_86_7) = all_187_1) 206.69/127.82 (10) map_eq_sub1(int, all_105_3, all_105_1, $sum(all_86_10, 1), all_86_13) = 206.69/127.82 0 206.69/127.82 206.69/127.82 Begin of proof 206.69/127.82 | 206.69/127.82 | SIMP: (7) implies: 206.69/127.82 | (11) all_153_1 = all_86_13 206.69/127.82 | 206.69/127.82 | COMBINE_EQS: (2), (5) imply: 206.69/127.82 | (12) all_187_3 = all_105_3 206.69/127.82 | 206.69/127.82 | REDUCE: (3), (11) imply: 206.69/127.82 | (13) length1(int, all_105_4) = all_86_13 206.69/127.82 | 206.69/127.82 | REF_CLOSE: (1), (4), (6), (8), (9), (10), (12), (13) are inconsistent by 206.69/127.82 | sub-proof #66. 206.69/127.82 | 206.69/127.82 End of proof 206.69/127.82 206.69/127.82 Sub-proof #65 shows that the following formulas are inconsistent: 206.69/127.82 ---------------------------------------------------------------- 206.69/127.82 (1) elts(int, all_105_4) = all_177_3 206.69/127.82 (2) length1(int, all_103_2) = all_86_13 206.69/127.82 (3) length1(int, all_103_2) = all_170_1 206.69/127.82 (4) length1(int, all_105_4) = all_153_1 206.69/127.82 (5) length1(int, all_103_2) = all_242_1 206.69/127.82 (6) length1(int, all_103_2) = all_193_1 206.69/127.82 (7) elts(int, all_105_2) = all_187_2 206.69/127.82 (8) length1(int, all_103_4) = all_193_1 206.69/127.82 (9) elts(int, all_105_4) = all_187_3 206.69/127.82 (10) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 206.69/127.82 | ~ (elts(v3, v2) = v1) | ~ (elts(v3, v2) = v0)) 206.69/127.82 (11) elts(int, all_105_4) = all_105_3 206.69/127.82 (12) map_eq_sub1(int, all_105_3, all_105_1, 0, all_86_7) = 0 206.69/127.82 (13) length1(int, all_103_4) = all_171_1 206.69/127.82 (14) elts(int, all_105_2) = all_105_1 206.69/127.82 (15) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.69/127.82 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ (map_eq_sub1(v6, 206.69/127.82 v5, v4, v3, v2) = v1) | ~ (map_eq_sub1(v6, v5, v4, v3, v2) = v0)) 206.69/127.82 (16) length1(int, all_105_4) = all_170_1 206.69/127.82 (17) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 206.69/127.82 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 206.69/127.82 (18) length1(int, all_103_2) = all_177_2 206.69/127.82 (19) ( ~ (all_187_0 = 0) & map_eq_sub1(int, all_187_3, all_187_2, 206.69/127.82 $sum(all_86_10, 1), all_187_1) = all_187_0 & length1(int, all_105_4) 206.69/127.82 = all_187_1) | ( ~ (all_187_1 = 0) & map_eq_sub1(int, all_187_3, 206.69/127.82 all_187_2, 0, all_86_7) = all_187_1) 206.69/127.82 (20) map_eq_sub1(int, all_105_3, all_105_1, $sum(all_86_10, 1), all_86_13) = 206.69/127.82 0 206.69/127.82 (21) length1(int, all_103_2) = all_156_0 206.69/127.82 206.69/127.82 Begin of proof 206.69/127.82 | 206.69/127.82 | GROUND_INST: instantiating (17) with all_170_1, all_153_1, all_105_4, int, 206.69/127.82 | simplifying with (4), (16) gives: 206.69/127.82 | (22) all_170_1 = all_153_1 206.69/127.82 | 206.69/127.82 | GROUND_INST: instantiating (17) with all_86_13, all_177_2, all_103_2, int, 206.69/127.82 | simplifying with (2), (18) gives: 206.69/127.82 | (23) all_177_2 = all_86_13 206.69/127.82 | 206.69/127.82 | GROUND_INST: instantiating (17) with all_242_1, all_177_2, all_103_2, int, 206.69/127.82 | simplifying with (5), (18) gives: 206.69/127.82 | (24) all_242_1 = all_177_2 206.69/127.82 | 206.69/127.82 | GROUND_INST: instantiating (17) with all_193_1, all_177_2, all_103_2, int, 206.69/127.82 | simplifying with (6), (18) gives: 206.69/127.82 | (25) all_193_1 = all_177_2 206.69/127.82 | 206.69/127.82 | GROUND_INST: instantiating (17) with all_242_1, all_170_1, all_103_2, int, 206.69/127.82 | simplifying with (3), (5) gives: 206.69/127.82 | (26) all_242_1 = all_170_1 206.69/127.82 | 206.69/127.82 | GROUND_INST: instantiating (17) with all_177_2, all_156_0, all_103_2, int, 206.69/127.82 | simplifying with (18), (21) gives: 206.69/127.82 | (27) all_177_2 = all_156_0 206.69/127.82 | 206.69/127.82 | GROUND_INST: instantiating (17) with all_193_1, all_171_1, all_103_4, int, 206.69/127.82 | simplifying with (8), (13) gives: 206.69/127.82 | (28) all_193_1 = all_171_1 206.69/127.82 | 206.69/127.82 | GROUND_INST: instantiating (10) with all_105_1, all_187_2, all_105_2, int, 206.69/127.82 | simplifying with (7), (14) gives: 206.69/127.82 | (29) all_187_2 = all_105_1 206.69/127.82 | 206.69/127.82 | GROUND_INST: instantiating (10) with all_105_3, all_187_3, all_105_4, int, 206.69/127.82 | simplifying with (9), (11) gives: 206.69/127.82 | (30) all_187_3 = all_105_3 206.69/127.82 | 206.69/127.82 | GROUND_INST: instantiating (10) with all_187_3, all_177_3, all_105_4, int, 206.69/127.82 | simplifying with (1), (9) gives: 206.69/127.82 | (31) all_187_3 = all_177_3 206.69/127.82 | 206.69/127.82 | COMBINE_EQS: (24), (26) imply: 206.69/127.82 | (32) all_177_2 = all_170_1 206.69/127.82 | 206.69/127.82 | SIMP: (32) implies: 206.69/127.82 | (33) all_177_2 = all_170_1 206.69/127.82 | 206.69/127.82 | COMBINE_EQS: (25), (28) imply: 206.69/127.82 | (34) all_177_2 = all_171_1 206.69/127.82 | 206.69/127.82 | SIMP: (34) implies: 206.69/127.82 | (35) all_177_2 = all_171_1 206.69/127.82 | 206.69/127.82 | COMBINE_EQS: (30), (31) imply: 206.69/127.82 | (36) all_177_3 = all_105_3 206.69/127.82 | 206.69/127.82 | COMBINE_EQS: (23), (35) imply: 206.69/127.82 | (37) all_171_1 = all_86_13 206.69/127.82 | 206.69/127.82 | COMBINE_EQS: (27), (35) imply: 206.69/127.82 | (38) all_171_1 = all_156_0 206.69/127.82 | 206.69/127.83 | COMBINE_EQS: (33), (35) imply: 206.69/127.83 | (39) all_171_1 = all_170_1 206.69/127.83 | 206.69/127.83 | COMBINE_EQS: (37), (38) imply: 206.69/127.83 | (40) all_156_0 = all_86_13 206.69/127.83 | 206.69/127.83 | COMBINE_EQS: (38), (39) imply: 206.69/127.83 | (41) all_170_1 = all_156_0 206.69/127.83 | 206.69/127.83 | SIMP: (41) implies: 206.69/127.83 | (42) all_170_1 = all_156_0 206.69/127.83 | 206.69/127.83 | COMBINE_EQS: (22), (42) imply: 206.69/127.83 | (43) all_156_0 = all_153_1 206.69/127.83 | 206.69/127.83 | SIMP: (43) implies: 206.69/127.83 | (44) all_156_0 = all_153_1 206.69/127.83 | 206.69/127.83 | COMBINE_EQS: (40), (44) imply: 206.69/127.83 | (45) all_153_1 = all_86_13 206.69/127.83 | 206.69/127.83 | REDUCE: (4), (45) imply: 206.69/127.83 | (46) length1(int, all_105_4) = all_86_13 206.69/127.83 | 206.69/127.83 | REF_CLOSE: (12), (15), (17), (19), (20), (29), (30), (46) are inconsistent by 206.69/127.83 | sub-proof #66. 206.69/127.83 | 206.69/127.83 End of proof 206.69/127.83 206.69/127.83 Sub-proof #66 shows that the following formulas are inconsistent: 206.69/127.83 ---------------------------------------------------------------- 206.69/127.83 (1) all_187_2 = all_105_1 206.69/127.83 (2) all_187_3 = all_105_3 206.69/127.83 (3) length1(int, all_105_4) = all_86_13 206.69/127.83 (4) map_eq_sub1(int, all_105_3, all_105_1, 0, all_86_7) = 0 206.69/127.83 (5) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.69/127.83 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ (map_eq_sub1(v6, 206.69/127.83 v5, v4, v3, v2) = v1) | ~ (map_eq_sub1(v6, v5, v4, v3, v2) = v0)) 206.69/127.83 (6) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 206.69/127.83 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 206.69/127.83 (7) ( ~ (all_187_0 = 0) & map_eq_sub1(int, all_187_3, all_187_2, 206.69/127.83 $sum(all_86_10, 1), all_187_1) = all_187_0 & length1(int, all_105_4) 206.69/127.83 = all_187_1) | ( ~ (all_187_1 = 0) & map_eq_sub1(int, all_187_3, 206.69/127.83 all_187_2, 0, all_86_7) = all_187_1) 206.69/127.83 (8) map_eq_sub1(int, all_105_3, all_105_1, $sum(all_86_10, 1), all_86_13) = 0 206.69/127.83 206.69/127.83 Begin of proof 206.69/127.83 | 206.69/127.83 | BETA: splitting (7) gives: 206.69/127.83 | 206.69/127.83 | Case 1: 206.69/127.83 | | 206.69/127.83 | | (9) ~ (all_187_0 = 0) & map_eq_sub1(int, all_187_3, all_187_2, 206.69/127.83 | | $sum(all_86_10, 1), all_187_1) = all_187_0 & length1(int, 206.69/127.83 | | all_105_4) = all_187_1 206.69/127.83 | | 206.69/127.83 | | ALPHA: (9) implies: 206.69/127.83 | | (10) ~ (all_187_0 = 0) 206.69/127.83 | | (11) length1(int, all_105_4) = all_187_1 206.69/127.83 | | (12) map_eq_sub1(int, all_187_3, all_187_2, $sum(all_86_10, 1), 206.69/127.83 | | all_187_1) = all_187_0 206.69/127.83 | | 206.69/127.83 | | REDUCE: (1), (2), (12) imply: 206.69/127.83 | | (13) map_eq_sub1(int, all_105_3, all_105_1, $sum(all_86_10, 1), 206.69/127.83 | | all_187_1) = all_187_0 206.69/127.83 | | 206.69/127.83 | | REF_CLOSE: (3), (5), (6), (8), (10), (11), (13) are inconsistent by 206.69/127.83 | | sub-proof #67. 206.69/127.83 | | 206.69/127.83 | Case 2: 206.69/127.83 | | 206.69/127.83 | | (14) ~ (all_187_1 = 0) & map_eq_sub1(int, all_187_3, all_187_2, 0, 206.69/127.83 | | all_86_7) = all_187_1 206.69/127.83 | | 206.69/127.83 | | ALPHA: (14) implies: 206.69/127.83 | | (15) ~ (all_187_1 = 0) 206.69/127.83 | | (16) map_eq_sub1(int, all_187_3, all_187_2, 0, all_86_7) = all_187_1 206.69/127.83 | | 206.69/127.83 | | REDUCE: (1), (2), (16) imply: 206.69/127.83 | | (17) map_eq_sub1(int, all_105_3, all_105_1, 0, all_86_7) = all_187_1 206.69/127.83 | | 206.69/127.83 | | GROUND_INST: instantiating (5) with 0, all_187_1, all_86_7, 0, all_105_1, 206.69/127.83 | | all_105_3, int, simplifying with (4), (17) gives: 206.69/127.83 | | (18) all_187_1 = 0 206.69/127.83 | | 206.69/127.83 | | REDUCE: (15), (18) imply: 206.69/127.83 | | (19) ~ (0 = 0) 206.69/127.83 | | 206.69/127.83 | | CLOSE: (19) is inconsistent. 206.69/127.83 | | 206.69/127.83 | End of split 206.69/127.83 | 206.69/127.83 End of proof 206.69/127.83 206.69/127.83 Sub-proof #67 shows that the following formulas are inconsistent: 206.69/127.83 ---------------------------------------------------------------- 206.69/127.83 (1) ~ (all_187_0 = 0) 206.69/127.83 (2) map_eq_sub1(int, all_105_3, all_105_1, $sum(all_86_10, 1), all_187_1) = 206.69/127.83 all_187_0 206.69/127.83 (3) length1(int, all_105_4) = all_187_1 206.69/127.83 (4) length1(int, all_105_4) = all_86_13 206.69/127.83 (5) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.69/127.83 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ (map_eq_sub1(v6, 206.69/127.83 v5, v4, v3, v2) = v1) | ~ (map_eq_sub1(v6, v5, v4, v3, v2) = v0)) 206.69/127.83 (6) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 206.69/127.83 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 206.69/127.83 (7) map_eq_sub1(int, all_105_3, all_105_1, $sum(all_86_10, 1), all_86_13) = 0 206.69/127.83 206.69/127.83 Begin of proof 206.69/127.83 | 206.69/127.83 | GROUND_INST: instantiating (6) with all_86_13, all_187_1, all_105_4, int, 206.69/127.83 | simplifying with (3), (4) gives: 206.69/127.83 | (8) all_187_1 = all_86_13 206.69/127.83 | 206.69/127.83 | REDUCE: (2), (8) imply: 206.69/127.83 | (9) map_eq_sub1(int, all_105_3, all_105_1, $sum(all_86_10, 1), all_86_13) = 206.69/127.83 | all_187_0 206.69/127.83 | 206.69/127.83 | GROUND_INST: instantiating (5) with 0, all_187_0, all_86_13, $sum(all_86_10, 206.69/127.83 | 1), all_105_1, all_105_3, int, simplifying with (7), (9) gives: 206.69/127.83 | (10) all_187_0 = 0 206.69/127.83 | 206.69/127.83 | REDUCE: (1), (10) imply: 206.69/127.83 | (11) ~ (0 = 0) 206.69/127.83 | 206.69/127.83 | CLOSE: (11) is inconsistent. 206.69/127.83 | 206.69/127.83 End of proof 206.69/127.83 206.69/127.83 Sub-proof #68 shows that the following formulas are inconsistent: 206.69/127.83 ---------------------------------------------------------------- 206.69/127.83 (1) ~ (all_190_4 = 0) & permut_sub2(int, all_105_4, all_105_2, all_86_7, 206.69/127.83 $sum(all_86_10, 1)) = all_190_4 206.69/127.83 (2) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.69/127.83 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ (permut_sub2(v6, 206.69/127.83 v5, v4, v3, v2) = v1) | ~ (permut_sub2(v6, v5, v4, v3, v2) = v0)) 206.69/127.83 (3) permut_sub2(int, all_105_4, all_105_2, all_86_7, $sum(all_86_10, 1)) = 0 206.69/127.83 206.69/127.83 Begin of proof 206.69/127.83 | 206.69/127.83 | ALPHA: (1) implies: 206.69/127.83 | (4) ~ (all_190_4 = 0) 206.69/127.83 | (5) permut_sub2(int, all_105_4, all_105_2, all_86_7, $sum(all_86_10, 1)) = 206.69/127.83 | all_190_4 206.69/127.83 | 206.69/127.83 | GROUND_INST: instantiating (2) with all_190_4, 0, $sum(all_86_10, 1), 206.69/127.83 | all_86_7, all_105_2, all_105_4, int, simplifying with (3), (5) 206.69/127.83 | gives: 206.69/127.83 | (6) all_190_4 = 0 206.69/127.83 | 206.69/127.83 | REDUCE: (4), (6) imply: 206.69/127.83 | (7) ~ (0 = 0) 206.69/127.83 | 206.69/127.83 | CLOSE: (7) is inconsistent. 206.69/127.83 | 206.69/127.83 End of proof 206.69/127.83 206.69/127.83 Sub-proof #69 shows that the following formulas are inconsistent: 206.69/127.83 ---------------------------------------------------------------- 206.69/127.83 (1) ~ (all_192_4 = 0) & permut_sub2(int, all_103_4, all_103_2, all_86_11, 206.69/127.83 $sum(all_86_10, 1)) = all_192_4 206.69/127.83 (2) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.69/127.83 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ (permut_sub2(v6, 206.69/127.83 v5, v4, v3, v2) = v1) | ~ (permut_sub2(v6, v5, v4, v3, v2) = v0)) 206.69/127.83 (3) permut_sub2(int, all_103_4, all_103_2, all_86_11, $sum(all_86_10, 1)) = 0 206.69/127.83 206.69/127.83 Begin of proof 206.69/127.83 | 206.69/127.83 | ALPHA: (1) implies: 206.69/127.83 | (4) ~ (all_192_4 = 0) 206.69/127.83 | (5) permut_sub2(int, all_103_4, all_103_2, all_86_11, $sum(all_86_10, 1)) = 206.69/127.83 | all_192_4 206.69/127.83 | 206.69/127.83 | GROUND_INST: instantiating (2) with all_192_4, 0, $sum(all_86_10, 1), 206.69/127.83 | all_86_11, all_103_2, all_103_4, int, simplifying with (3), (5) 206.69/127.83 | gives: 206.69/127.83 | (6) all_192_4 = 0 206.69/127.83 | 206.69/127.83 | REDUCE: (4), (6) imply: 206.69/127.83 | (7) ~ (0 = 0) 206.69/127.83 | 206.69/127.83 | CLOSE: (7) is inconsistent. 206.69/127.83 | 206.69/127.83 End of proof 206.69/127.83 206.69/127.83 Sub-proof #70 shows that the following formulas are inconsistent: 206.69/127.83 ---------------------------------------------------------------- 206.69/127.83 (1) length1(int, all_103_2) = all_86_13 206.69/127.83 (2) length1(int, all_103_2) = all_170_1 206.69/127.83 (3) length1(int, all_105_4) = all_153_1 206.69/127.83 (4) length1(int, all_103_4) = all_86_13 206.69/127.83 (5) length1(int, all_103_4) = all_215_1 206.69/127.83 (6) length1(int, all_103_2) = all_193_1 206.69/127.83 (7) length1(int, all_103_4) = all_192_2 206.69/127.83 (8) ~ ($lesseq(all_86_11, all_215_1)) | ~ ($lesseq(0, all_215_1)) | ( ~ 206.69/127.83 (all_215_0 = all_215_1) & length1(int, all_103_2) = all_215_0) 206.69/127.83 (9) length1(int, all_103_4) = all_193_1 206.69/127.83 (10) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.69/127.83 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ 206.69/127.83 (array_eq_sub1(v6, v5, v4, v3, v2) = v1) | ~ (array_eq_sub1(v6, v5, 206.69/127.83 v4, v3, v2) = v0)) 206.69/127.83 (11) (all_242_1 = 0 & array_eq_sub1(int, all_103_2, all_105_4, $sum(all_86_8, 206.69/127.83 1), all_86_13) = 0) | (length1(int, all_103_2) = all_242_1 & ( ~ 206.69/127.83 ($lesseq(1, $difference(all_242_1, all_86_8))) | ~ 206.69/127.83 ($lesseq(all_86_13, all_242_1)) | ( ~ (all_242_0 = all_242_1) & 206.69/127.83 length1(int, all_105_4) = all_242_0))) 206.69/127.83 (12) $lesseq(1, $difference(all_153_1, all_86_10)) 206.69/127.83 (13) $lesseq(all_86_11, all_86_8) 206.69/127.83 (14) $lesseq(all_86_7, all_86_10) 206.69/127.83 (15) (all_168_0 = all_168_1 & $lesseq(1, $difference(all_168_1, all_86_8)) & 206.69/127.83 $lesseq(all_86_13, all_168_1) & $lesseq(-1, all_86_8) & $lesseq(0, 206.69/127.83 all_86_13) & length1(int, all_105_4) = all_168_1 & length1(int, 206.69/127.83 all_103_2) = all_168_1) | ( ~ (all_168_1 = 0) & array_eq_sub1(int, 206.69/127.83 all_103_2, all_105_4, $sum(all_86_8, 1), all_86_13) = all_168_1) 206.69/127.83 (16) $lesseq(1, $difference(all_86_7, all_86_8)) 206.69/127.83 (17) $lesseq(0, all_86_11) 206.69/127.83 (18) length1(int, all_105_4) = all_170_1 206.69/127.83 (19) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 206.69/127.83 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 206.69/127.83 (20) length1(int, all_103_2) = all_177_2 206.69/127.83 (21) length1(int, all_105_4) = all_219_1 206.69/127.83 (22) length1(int, all_103_2) = all_156_0 206.69/127.83 206.69/127.83 Begin of proof 206.69/127.83 | 206.69/127.83 | BETA: splitting (11) gives: 206.69/127.83 | 206.69/127.83 | Case 1: 206.69/127.83 | | 206.69/127.83 | | (23) all_242_1 = 0 & array_eq_sub1(int, all_103_2, all_105_4, 206.69/127.83 | | $sum(all_86_8, 1), all_86_13) = 0 206.69/127.83 | | 206.69/127.83 | | ALPHA: (23) implies: 206.69/127.83 | | (24) array_eq_sub1(int, all_103_2, all_105_4, $sum(all_86_8, 1), 206.69/127.83 | | all_86_13) = 0 206.69/127.83 | | 206.69/127.83 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (10), (12), (13), (14), (15), 206.69/127.83 | | (16), (17), (18), (19), (20), (21), (22), (24) are inconsistent 206.69/127.83 | | by sub-proof #71. 206.69/127.83 | | 206.69/127.83 | Case 2: 206.69/127.83 | | 206.69/127.83 | | (25) length1(int, all_103_2) = all_242_1 & ( ~ ($lesseq(1, 206.69/127.83 | | $difference(all_242_1, all_86_8))) | ~ ($lesseq(all_86_13, 206.69/127.83 | | all_242_1)) | ( ~ (all_242_0 = all_242_1) & length1(int, 206.69/127.83 | | all_105_4) = all_242_0)) 206.69/127.83 | | 206.69/127.83 | | ALPHA: (25) implies: 206.69/127.83 | | (26) length1(int, all_103_2) = all_242_1 206.69/127.83 | | 206.69/127.83 | | GROUND_INST: instantiating (19) with all_219_1, all_170_1, all_105_4, int, 206.69/127.83 | | simplifying with (18), (21) gives: 206.69/127.83 | | (27) all_219_1 = all_170_1 206.69/127.83 | | 206.69/127.83 | | GROUND_INST: instantiating (19) with all_219_1, all_153_1, all_105_4, int, 206.69/127.83 | | simplifying with (3), (21) gives: 206.69/127.83 | | (28) all_219_1 = all_153_1 206.69/127.83 | | 206.69/127.83 | | GROUND_INST: instantiating (19) with all_242_1, all_193_1, all_103_2, int, 206.69/127.83 | | simplifying with (6), (26) gives: 206.69/127.83 | | (29) all_242_1 = all_193_1 206.69/127.83 | | 206.69/127.83 | | GROUND_INST: instantiating (19) with all_193_1, all_177_2, all_103_2, int, 206.69/127.83 | | simplifying with (6), (20) gives: 206.69/127.83 | | (30) all_193_1 = all_177_2 206.69/127.83 | | 206.69/127.83 | | GROUND_INST: instantiating (19) with all_242_1, all_170_1, all_103_2, int, 206.69/127.83 | | simplifying with (2), (26) gives: 206.69/127.83 | | (31) all_242_1 = all_170_1 206.69/127.83 | | 206.69/127.83 | | GROUND_INST: instantiating (19) with all_242_1, all_156_0, all_103_2, int, 206.69/127.83 | | simplifying with (22), (26) gives: 206.69/127.83 | | (32) all_242_1 = all_156_0 206.69/127.83 | | 206.69/127.83 | | GROUND_INST: instantiating (19) with all_86_13, all_215_1, all_103_4, int, 206.69/127.83 | | simplifying with (4), (5) gives: 206.69/127.83 | | (33) all_215_1 = all_86_13 206.69/127.83 | | 206.69/127.83 | | GROUND_INST: instantiating (19) with all_215_1, all_192_2, all_103_4, int, 206.69/127.83 | | simplifying with (5), (7) gives: 206.69/127.83 | | (34) all_215_1 = all_192_2 206.69/127.83 | | 206.69/127.83 | | GROUND_INST: instantiating (19) with all_193_1, all_192_2, all_103_4, int, 206.69/127.83 | | simplifying with (7), (9) gives: 206.69/127.83 | | (35) all_193_1 = all_192_2 206.69/127.83 | | 206.69/127.83 | | COMBINE_EQS: (29), (31) imply: 206.69/127.83 | | (36) all_193_1 = all_170_1 206.69/127.83 | | 206.69/127.83 | | SIMP: (36) implies: 206.69/127.83 | | (37) all_193_1 = all_170_1 206.69/127.83 | | 206.69/127.83 | | COMBINE_EQS: (31), (32) imply: 206.69/127.83 | | (38) all_170_1 = all_156_0 206.69/127.83 | | 206.69/127.83 | | COMBINE_EQS: (27), (28) imply: 206.69/127.83 | | (39) all_170_1 = all_153_1 206.69/127.83 | | 206.69/127.83 | | SIMP: (39) implies: 206.69/127.83 | | (40) all_170_1 = all_153_1 206.69/127.83 | | 206.69/127.83 | | COMBINE_EQS: (33), (34) imply: 206.69/127.83 | | (41) all_192_2 = all_86_13 206.69/127.83 | | 206.69/127.83 | | SIMP: (41) implies: 206.69/127.83 | | (42) all_192_2 = all_86_13 206.69/127.83 | | 206.69/127.83 | | COMBINE_EQS: (30), (37) imply: 206.69/127.83 | | (43) all_177_2 = all_170_1 206.69/127.83 | | 206.69/127.83 | | COMBINE_EQS: (30), (35) imply: 206.69/127.83 | | (44) all_192_2 = all_177_2 206.69/127.83 | | 206.69/127.83 | | SIMP: (44) implies: 206.69/127.83 | | (45) all_192_2 = all_177_2 206.69/127.83 | | 206.69/127.83 | | COMBINE_EQS: (42), (45) imply: 206.69/127.83 | | (46) all_177_2 = all_86_13 206.69/127.83 | | 206.69/127.83 | | SIMP: (46) implies: 206.69/127.83 | | (47) all_177_2 = all_86_13 206.69/127.83 | | 206.69/127.83 | | COMBINE_EQS: (43), (47) imply: 206.69/127.83 | | (48) all_170_1 = all_86_13 206.69/127.83 | | 206.69/127.83 | | SIMP: (48) implies: 206.69/127.83 | | (49) all_170_1 = all_86_13 206.69/127.83 | | 206.69/127.83 | | COMBINE_EQS: (38), (49) imply: 206.69/127.83 | | (50) all_156_0 = all_86_13 206.69/127.83 | | 206.69/127.83 | | SIMP: (50) implies: 206.69/127.83 | | (51) all_156_0 = all_86_13 206.69/127.83 | | 206.69/127.83 | | COMBINE_EQS: (40), (49) imply: 206.69/127.83 | | (52) all_153_1 = all_86_13 206.69/127.83 | | 206.69/127.83 | | SIMP: (52) implies: 206.69/127.83 | | (53) all_153_1 = all_86_13 206.69/127.83 | | 206.69/127.83 | | REF_CLOSE: (8), (12), (13), (14), (16), (17), (19), (22), (33), (51), (53) 206.69/127.83 | | are inconsistent by sub-proof #72. 206.69/127.83 | | 206.69/127.83 | End of split 206.69/127.83 | 206.69/127.83 End of proof 206.69/127.83 206.69/127.83 Sub-proof #71 shows that the following formulas are inconsistent: 206.69/127.83 ---------------------------------------------------------------- 206.69/127.83 (1) length1(int, all_103_2) = all_86_13 206.69/127.83 (2) length1(int, all_103_2) = all_170_1 206.69/127.83 (3) length1(int, all_105_4) = all_153_1 206.69/127.83 (4) length1(int, all_103_4) = all_86_13 206.69/127.83 (5) length1(int, all_103_4) = all_215_1 206.69/127.83 (6) length1(int, all_103_2) = all_193_1 206.69/127.83 (7) ~ ($lesseq(all_86_11, all_215_1)) | ~ ($lesseq(0, all_215_1)) | ( ~ 206.69/127.83 (all_215_0 = all_215_1) & length1(int, all_103_2) = all_215_0) 206.69/127.83 (8) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.69/127.83 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ 206.69/127.83 (array_eq_sub1(v6, v5, v4, v3, v2) = v1) | ~ (array_eq_sub1(v6, v5, 206.69/127.83 v4, v3, v2) = v0)) 206.69/127.83 (9) $lesseq(1, $difference(all_153_1, all_86_10)) 206.69/127.83 (10) $lesseq(all_86_11, all_86_8) 206.69/127.83 (11) $lesseq(all_86_7, all_86_10) 206.69/127.83 (12) (all_168_0 = all_168_1 & $lesseq(1, $difference(all_168_1, all_86_8)) & 206.69/127.83 $lesseq(all_86_13, all_168_1) & $lesseq(-1, all_86_8) & $lesseq(0, 206.69/127.83 all_86_13) & length1(int, all_105_4) = all_168_1 & length1(int, 206.69/127.83 all_103_2) = all_168_1) | ( ~ (all_168_1 = 0) & array_eq_sub1(int, 206.69/127.83 all_103_2, all_105_4, $sum(all_86_8, 1), all_86_13) = all_168_1) 206.69/127.83 (13) $lesseq(1, $difference(all_86_7, all_86_8)) 206.69/127.83 (14) $lesseq(0, all_86_11) 206.69/127.83 (15) length1(int, all_105_4) = all_170_1 206.69/127.83 (16) array_eq_sub1(int, all_103_2, all_105_4, $sum(all_86_8, 1), all_86_13) = 206.69/127.83 0 206.69/127.83 (17) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 206.69/127.83 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 206.69/127.83 (18) length1(int, all_103_2) = all_177_2 206.69/127.83 (19) length1(int, all_105_4) = all_219_1 206.69/127.83 (20) length1(int, all_103_2) = all_156_0 206.69/127.83 206.69/127.83 Begin of proof 206.69/127.83 | 206.69/127.83 | BETA: splitting (12) gives: 206.69/127.83 | 206.69/127.83 | Case 1: 206.69/127.83 | | 206.69/127.83 | | (21) all_168_0 = all_168_1 & $lesseq(1, $difference(all_168_1, all_86_8)) 206.69/127.83 | | & $lesseq(all_86_13, all_168_1) & $lesseq(-1, all_86_8) & $lesseq(0, 206.69/127.83 | | all_86_13) & length1(int, all_105_4) = all_168_1 & length1(int, 206.69/127.83 | | all_103_2) = all_168_1 206.69/127.83 | | 206.69/127.83 | | ALPHA: (21) implies: 206.69/127.83 | | (22) length1(int, all_103_2) = all_168_1 206.69/127.83 | | 206.69/127.83 | | GROUND_INST: instantiating (17) with all_219_1, all_170_1, all_105_4, int, 206.69/127.83 | | simplifying with (15), (19) gives: 206.69/127.83 | | (23) all_219_1 = all_170_1 206.69/127.83 | | 206.69/127.83 | | GROUND_INST: instantiating (17) with all_219_1, all_153_1, all_105_4, int, 206.69/127.83 | | simplifying with (3), (19) gives: 206.69/127.83 | | (24) all_219_1 = all_153_1 206.69/127.83 | | 206.69/127.83 | | GROUND_INST: instantiating (17) with all_86_13, all_177_2, all_103_2, int, 206.69/127.83 | | simplifying with (1), (18) gives: 206.69/127.83 | | (25) all_177_2 = all_86_13 206.69/127.83 | | 206.69/127.83 | | GROUND_INST: instantiating (17) with all_193_1, all_177_2, all_103_2, int, 206.69/127.83 | | simplifying with (6), (18) gives: 206.69/127.83 | | (26) all_193_1 = all_177_2 206.69/127.83 | | 206.69/127.83 | | GROUND_INST: instantiating (17) with all_193_1, all_170_1, all_103_2, int, 206.69/127.83 | | simplifying with (2), (6) gives: 206.69/127.83 | | (27) all_193_1 = all_170_1 206.69/127.83 | | 206.69/127.83 | | GROUND_INST: instantiating (17) with all_193_1, all_168_1, all_103_2, int, 206.69/127.83 | | simplifying with (6), (22) gives: 206.69/127.83 | | (28) all_193_1 = all_168_1 206.69/127.83 | | 206.69/127.83 | | GROUND_INST: instantiating (17) with all_177_2, all_156_0, all_103_2, int, 206.69/127.83 | | simplifying with (18), (20) gives: 206.69/127.83 | | (29) all_177_2 = all_156_0 206.69/127.83 | | 206.69/127.83 | | GROUND_INST: instantiating (17) with all_86_13, all_215_1, all_103_4, int, 206.69/127.83 | | simplifying with (4), (5) gives: 206.69/127.83 | | (30) all_215_1 = all_86_13 206.69/127.83 | | 206.69/127.83 | | COMBINE_EQS: (23), (24) imply: 206.69/127.83 | | (31) all_170_1 = all_153_1 206.69/127.83 | | 206.69/127.83 | | SIMP: (31) implies: 206.69/127.83 | | (32) all_170_1 = all_153_1 206.69/127.83 | | 206.69/127.83 | | COMBINE_EQS: (27), (28) imply: 206.69/127.83 | | (33) all_170_1 = all_168_1 206.69/127.83 | | 206.69/127.83 | | COMBINE_EQS: (26), (27) imply: 206.69/127.83 | | (34) all_177_2 = all_170_1 206.69/127.83 | | 206.69/127.83 | | SIMP: (34) implies: 206.69/127.83 | | (35) all_177_2 = all_170_1 206.69/127.83 | | 206.69/127.83 | | COMBINE_EQS: (29), (35) imply: 206.69/127.83 | | (36) all_170_1 = all_156_0 206.69/127.83 | | 206.69/127.83 | | SIMP: (36) implies: 206.69/127.83 | | (37) all_170_1 = all_156_0 206.69/127.83 | | 206.69/127.83 | | COMBINE_EQS: (25), (29) imply: 206.69/127.83 | | (38) all_156_0 = all_86_13 206.69/127.83 | | 206.69/127.83 | | COMBINE_EQS: (32), (33) imply: 206.69/127.83 | | (39) all_168_1 = all_153_1 206.69/127.83 | | 206.69/127.83 | | COMBINE_EQS: (33), (37) imply: 206.69/127.83 | | (40) all_168_1 = all_156_0 206.69/127.83 | | 206.69/127.83 | | COMBINE_EQS: (39), (40) imply: 206.69/127.83 | | (41) all_156_0 = all_153_1 206.69/127.83 | | 206.69/127.83 | | SIMP: (41) implies: 206.69/127.83 | | (42) all_156_0 = all_153_1 206.69/127.83 | | 206.69/127.83 | | COMBINE_EQS: (38), (42) imply: 206.69/127.83 | | (43) all_153_1 = all_86_13 206.69/127.83 | | 206.69/127.83 | | REF_CLOSE: (7), (9), (10), (11), (13), (14), (17), (20), (30), (38), (43) 206.69/127.83 | | are inconsistent by sub-proof #72. 206.69/127.83 | | 206.69/127.83 | Case 2: 206.69/127.83 | | 206.69/127.83 | | (44) ~ (all_168_1 = 0) & array_eq_sub1(int, all_103_2, all_105_4, 206.69/127.83 | | $sum(all_86_8, 1), all_86_13) = all_168_1 206.69/127.83 | | 206.69/127.83 | | REF_CLOSE: (8), (16), (44) are inconsistent by sub-proof #83. 206.69/127.83 | | 206.69/127.83 | End of split 206.69/127.83 | 206.69/127.83 End of proof 206.69/127.83 206.69/127.83 Sub-proof #72 shows that the following formulas are inconsistent: 206.69/127.83 ---------------------------------------------------------------- 206.69/127.83 (1) all_156_0 = all_86_13 206.69/127.83 (2) all_153_1 = all_86_13 206.69/127.84 (3) ~ ($lesseq(all_86_11, all_215_1)) | ~ ($lesseq(0, all_215_1)) | ( ~ 206.69/127.84 (all_215_0 = all_215_1) & length1(int, all_103_2) = all_215_0) 206.69/127.84 (4) $lesseq(1, $difference(all_153_1, all_86_10)) 206.69/127.84 (5) $lesseq(all_86_11, all_86_8) 206.69/127.84 (6) $lesseq(all_86_7, all_86_10) 206.69/127.84 (7) all_215_1 = all_86_13 206.69/127.84 (8) $lesseq(1, $difference(all_86_7, all_86_8)) 206.69/127.84 (9) $lesseq(0, all_86_11) 206.69/127.84 (10) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 206.69/127.84 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 206.69/127.84 (11) length1(int, all_103_2) = all_156_0 206.69/127.84 206.69/127.84 Begin of proof 206.69/127.84 | 206.69/127.84 | REDUCE: (2), (4) imply: 206.69/127.84 | (12) $lesseq(1, $difference(all_86_13, all_86_10)) 206.69/127.84 | 206.69/127.84 | REDUCE: (1), (11) imply: 206.69/127.84 | (13) length1(int, all_103_2) = all_86_13 206.69/127.84 | 206.69/127.84 | BETA: splitting (3) gives: 206.69/127.84 | 206.69/127.84 | Case 1: 206.69/127.84 | | 206.69/127.84 | | (14) $lesseq(all_215_1, -1) 206.69/127.84 | | 206.69/127.84 | | REDUCE: (7), (14) imply: 206.69/127.84 | | (15) $lesseq(all_86_13, -1) 206.69/127.84 | | 206.69/127.84 | | REF_CLOSE: (5), (6), (8), (9), (12), (15) are inconsistent by sub-proof #80. 206.69/127.84 | | 206.69/127.84 | Case 2: 206.69/127.84 | | 206.69/127.84 | | (16) ~ ($lesseq(all_86_11, all_215_1)) | ( ~ (all_215_0 = all_215_1) & 206.69/127.84 | | length1(int, all_103_2) = all_215_0) 206.69/127.84 | | 206.69/127.84 | | REF_CLOSE: (5), (6), (7), (8), (10), (12), (13), (16) are inconsistent by 206.69/127.84 | | sub-proof #78. 206.69/127.84 | | 206.69/127.84 | End of split 206.69/127.84 | 206.69/127.84 End of proof 206.69/127.84 206.69/127.84 Sub-proof #73 shows that the following formulas are inconsistent: 206.69/127.84 ---------------------------------------------------------------- 206.69/127.84 (1) length1(int, all_103_2) = all_170_1 206.69/127.84 (2) length1(int, all_105_4) = all_153_1 206.69/127.84 (3) length1(int, all_103_4) = all_86_13 206.69/127.84 (4) $lesseq(all_86_7, all_86_13) 206.69/127.84 (5) length1(int, all_103_2) = all_193_1 206.69/127.84 (6) length1(int, all_103_4) = all_193_1 206.69/127.84 (7) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.69/127.84 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ 206.69/127.84 (array_eq_sub1(v6, v5, v4, v3, v2) = v1) | ~ (array_eq_sub1(v6, v5, 206.69/127.84 v4, v3, v2) = v0)) 206.69/127.84 (8) (all_171_0 = all_171_1 & $lesseq(all_86_11, all_171_1) & $lesseq(0, 206.69/127.84 all_171_1) & $lesseq(0, all_86_11) & length1(int, all_103_2) = 206.69/127.84 all_171_1 & length1(int, all_103_4) = all_171_1) | ( ~ (all_171_1 = 0) 206.69/127.84 & array_eq_sub1(int, all_103_4, all_103_2, 0, all_86_11) = all_171_1) 206.69/127.84 (9) $lesseq(1, $difference(all_153_1, all_86_10)) 206.69/127.84 (10) $lesseq(all_86_11, all_86_8) 206.69/127.84 (11) $lesseq(all_86_7, all_86_10) 206.69/127.84 (12) array_eq_sub1(int, all_103_4, all_103_2, 0, all_86_11) = 0 206.69/127.84 (13) (all_168_0 = all_168_1 & $lesseq(1, $difference(all_168_1, all_86_8)) & 206.69/127.84 $lesseq(all_86_13, all_168_1) & $lesseq(-1, all_86_8) & $lesseq(0, 206.69/127.84 all_86_13) & length1(int, all_105_4) = all_168_1 & length1(int, 206.69/127.84 all_103_2) = all_168_1) | ( ~ (all_168_1 = 0) & array_eq_sub1(int, 206.69/127.84 all_103_2, all_105_4, $sum(all_86_8, 1), all_86_13) = all_168_1) 206.69/127.84 (14) ~ ($lesseq(all_86_7, all_219_1)) | ~ ($lesseq(0, all_219_1)) | ( ~ 206.69/127.84 (all_219_0 = all_219_1) & length1(int, all_105_2) = all_219_0) 206.69/127.84 (15) length1(int, all_105_4) = all_190_2 206.69/127.84 (16) $lesseq(1, $difference(all_86_7, all_86_8)) 206.69/127.84 (17) array_eq_sub1(int, all_103_2, all_105_4, $sum(all_86_8, 1), all_86_13) = 206.69/127.84 0 206.69/127.84 (18) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 206.69/127.84 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 206.69/127.84 (19) length1(int, all_103_2) = all_177_2 206.69/127.84 (20) length1(int, all_105_4) = all_219_1 206.69/127.84 (21) length1(int, all_105_2) = all_153_1 206.69/127.84 (22) length1(int, all_103_2) = all_156_0 206.69/127.84 206.69/127.84 Begin of proof 206.69/127.84 | 206.69/127.84 | BETA: splitting (13) gives: 206.69/127.84 | 206.69/127.84 | Case 1: 206.69/127.84 | | 206.69/127.84 | | (23) all_168_0 = all_168_1 & $lesseq(1, $difference(all_168_1, all_86_8)) 206.69/127.84 | | & $lesseq(all_86_13, all_168_1) & $lesseq(-1, all_86_8) & $lesseq(0, 206.69/127.84 | | all_86_13) & length1(int, all_105_4) = all_168_1 & length1(int, 206.69/127.84 | | all_103_2) = all_168_1 206.69/127.84 | | 206.69/127.84 | | ALPHA: (23) implies: 206.69/127.84 | | (24) length1(int, all_103_2) = all_168_1 206.69/127.84 | | (25) length1(int, all_105_4) = all_168_1 206.69/127.84 | | 206.69/127.84 | | BETA: splitting (8) gives: 206.69/127.84 | | 206.69/127.84 | | Case 1: 206.69/127.84 | | | 206.69/127.84 | | | (26) all_171_0 = all_171_1 & $lesseq(all_86_11, all_171_1) & $lesseq(0, 206.69/127.84 | | | all_171_1) & $lesseq(0, all_86_11) & length1(int, all_103_2) = 206.69/127.84 | | | all_171_1 & length1(int, all_103_4) = all_171_1 206.69/127.84 | | | 206.69/127.84 | | | ALPHA: (26) implies: 206.69/127.84 | | | (27) $lesseq(0, all_86_11) 206.69/127.84 | | | (28) length1(int, all_103_2) = all_171_1 206.69/127.84 | | | 206.69/127.84 | | | GROUND_INST: instantiating (18) with all_219_1, all_190_2, all_105_4, int, 206.69/127.84 | | | simplifying with (15), (20) gives: 206.69/127.84 | | | (29) all_219_1 = all_190_2 206.69/127.84 | | | 206.69/127.84 | | | GROUND_INST: instantiating (18) with all_190_2, all_168_1, all_105_4, int, 206.69/127.84 | | | simplifying with (15), (25) gives: 206.69/127.84 | | | (30) all_190_2 = all_168_1 206.69/127.84 | | | 206.69/127.84 | | | GROUND_INST: instantiating (18) with all_219_1, all_153_1, all_105_4, int, 206.69/127.84 | | | simplifying with (2), (20) gives: 206.69/127.84 | | | (31) all_219_1 = all_153_1 206.69/127.84 | | | 206.69/127.84 | | | GROUND_INST: instantiating (18) with all_177_2, all_171_1, all_103_2, int, 206.69/127.84 | | | simplifying with (19), (28) gives: 206.69/127.84 | | | (32) all_177_2 = all_171_1 206.69/127.84 | | | 206.69/127.84 | | | GROUND_INST: instantiating (18) with all_193_1, all_170_1, all_103_2, int, 206.69/127.84 | | | simplifying with (1), (5) gives: 206.69/127.84 | | | (33) all_193_1 = all_170_1 206.69/127.84 | | | 206.69/127.84 | | | GROUND_INST: instantiating (18) with all_171_1, all_170_1, all_103_2, int, 206.69/127.84 | | | simplifying with (1), (28) gives: 206.69/127.84 | | | (34) all_171_1 = all_170_1 206.69/127.84 | | | 206.69/127.84 | | | GROUND_INST: instantiating (18) with all_177_2, all_168_1, all_103_2, int, 206.69/127.84 | | | simplifying with (19), (24) gives: 206.69/127.84 | | | (35) all_177_2 = all_168_1 206.69/127.84 | | | 206.69/127.84 | | | GROUND_INST: instantiating (18) with all_171_1, all_156_0, all_103_2, int, 206.69/127.84 | | | simplifying with (22), (28) gives: 206.69/127.84 | | | (36) all_171_1 = all_156_0 206.69/127.84 | | | 206.69/127.84 | | | GROUND_INST: instantiating (18) with all_86_13, all_193_1, all_103_4, int, 206.69/127.84 | | | simplifying with (3), (6) gives: 206.69/127.84 | | | (37) all_193_1 = all_86_13 206.69/127.84 | | | 206.69/127.84 | | | COMBINE_EQS: (29), (31) imply: 206.69/127.84 | | | (38) all_190_2 = all_153_1 206.69/127.84 | | | 206.69/127.84 | | | SIMP: (38) implies: 206.69/127.84 | | | (39) all_190_2 = all_153_1 206.69/127.84 | | | 206.69/127.84 | | | COMBINE_EQS: (33), (37) imply: 206.69/127.84 | | | (40) all_170_1 = all_86_13 206.69/127.84 | | | 206.69/127.84 | | | SIMP: (40) implies: 206.69/127.84 | | | (41) all_170_1 = all_86_13 206.69/127.84 | | | 206.69/127.84 | | | COMBINE_EQS: (30), (39) imply: 206.69/127.84 | | | (42) all_168_1 = all_153_1 206.69/127.84 | | | 206.69/127.84 | | | COMBINE_EQS: (32), (35) imply: 206.69/127.84 | | | (43) all_171_1 = all_168_1 206.69/127.84 | | | 206.69/127.84 | | | SIMP: (43) implies: 206.69/127.84 | | | (44) all_171_1 = all_168_1 206.69/127.84 | | | 206.69/127.84 | | | COMBINE_EQS: (36), (44) imply: 206.69/127.84 | | | (45) all_168_1 = all_156_0 206.69/127.84 | | | 206.69/127.84 | | | SIMP: (45) implies: 206.69/127.84 | | | (46) all_168_1 = all_156_0 206.69/127.84 | | | 206.69/127.84 | | | COMBINE_EQS: (34), (36) imply: 206.69/127.84 | | | (47) all_170_1 = all_156_0 206.69/127.84 | | | 206.69/127.84 | | | SIMP: (47) implies: 206.69/127.84 | | | (48) all_170_1 = all_156_0 206.69/127.84 | | | 206.69/127.84 | | | COMBINE_EQS: (41), (48) imply: 206.69/127.84 | | | (49) all_156_0 = all_86_13 206.69/127.84 | | | 206.69/127.84 | | | SIMP: (49) implies: 206.69/127.84 | | | (50) all_156_0 = all_86_13 206.69/127.84 | | | 206.69/127.84 | | | COMBINE_EQS: (42), (46) imply: 206.69/127.84 | | | (51) all_156_0 = all_153_1 206.69/127.84 | | | 206.69/127.84 | | | SIMP: (51) implies: 206.69/127.84 | | | (52) all_156_0 = all_153_1 206.69/127.84 | | | 206.69/127.84 | | | COMBINE_EQS: (50), (52) imply: 206.69/127.84 | | | (53) all_153_1 = all_86_13 206.69/127.84 | | | 206.69/127.84 | | | COMBINE_EQS: (31), (53) imply: 206.69/127.84 | | | (54) all_219_1 = all_86_13 206.69/127.84 | | | 206.69/127.84 | | | REDUCE: (9), (53) imply: 206.69/127.84 | | | (55) $lesseq(1, $difference(all_86_13, all_86_10)) 206.69/127.84 | | | 206.69/127.84 | | | REDUCE: (21), (53) imply: 206.69/127.84 | | | (56) length1(int, all_105_2) = all_86_13 206.69/127.84 | | | 206.69/127.84 | | | BETA: splitting (14) gives: 206.69/127.84 | | | 206.69/127.84 | | | Case 1: 206.69/127.84 | | | | 206.69/127.84 | | | | (57) $lesseq(all_219_1, -1) 206.69/127.84 | | | | 206.69/127.84 | | | | REDUCE: (54), (57) imply: 206.69/127.84 | | | | (58) $lesseq(all_86_13, -1) 206.69/127.84 | | | | 206.69/127.84 | | | | REF_CLOSE: (10), (11), (16), (27), (55), (58) are inconsistent by 206.69/127.84 | | | | sub-proof #80. 206.69/127.84 | | | | 206.69/127.84 | | | Case 2: 206.69/127.84 | | | | 206.69/127.84 | | | | (59) ~ ($lesseq(all_86_7, all_219_1)) | ( ~ (all_219_0 = all_219_1) 206.69/127.84 | | | | & length1(int, all_105_2) = all_219_0) 206.69/127.84 | | | | 206.69/127.84 | | | | REF_CLOSE: (4), (18), (54), (56), (59) are inconsistent by sub-proof 206.69/127.84 | | | | #74. 206.69/127.84 | | | | 206.69/127.84 | | | End of split 206.69/127.84 | | | 206.69/127.84 | | Case 2: 206.69/127.84 | | | 206.69/127.84 | | | (60) ~ (all_171_1 = 0) & array_eq_sub1(int, all_103_4, all_103_2, 0, 206.69/127.84 | | | all_86_11) = all_171_1 206.69/127.84 | | | 206.69/127.84 | | | REF_CLOSE: (7), (12), (60) are inconsistent by sub-proof #81. 206.69/127.84 | | | 206.69/127.84 | | End of split 206.69/127.84 | | 206.69/127.84 | Case 2: 206.69/127.84 | | 206.69/127.84 | | (61) ~ (all_168_1 = 0) & array_eq_sub1(int, all_103_2, all_105_4, 206.69/127.84 | | $sum(all_86_8, 1), all_86_13) = all_168_1 206.69/127.84 | | 206.69/127.84 | | REF_CLOSE: (7), (17), (61) are inconsistent by sub-proof #83. 206.69/127.84 | | 206.69/127.84 | End of split 206.69/127.84 | 206.69/127.84 End of proof 206.69/127.84 206.69/127.84 Sub-proof #74 shows that the following formulas are inconsistent: 206.69/127.84 ---------------------------------------------------------------- 206.69/127.84 (1) length1(int, all_105_2) = all_86_13 206.69/127.84 (2) $lesseq(all_86_7, all_86_13) 206.69/127.84 (3) all_219_1 = all_86_13 206.69/127.84 (4) ~ ($lesseq(all_86_7, all_219_1)) | ( ~ (all_219_0 = all_219_1) & 206.69/127.84 length1(int, all_105_2) = all_219_0) 206.69/127.84 (5) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 206.69/127.84 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 206.69/127.84 206.69/127.84 Begin of proof 206.69/127.84 | 206.69/127.84 | BETA: splitting (4) gives: 206.69/127.84 | 206.69/127.84 | Case 1: 206.69/127.84 | | 206.69/127.84 | | (6) $lesseq(1, $difference(all_86_7, all_219_1)) 206.69/127.84 | | 206.69/127.84 | | REDUCE: (3), (6) imply: 206.69/127.84 | | (7) $lesseq(1, $difference(all_86_7, all_86_13)) 206.69/127.84 | | 206.69/127.84 | | COMBINE_INEQS: (2), (7) imply: 206.69/127.84 | | (8) $lesseq(0, -1) 206.69/127.84 | | 206.69/127.84 | | CLOSE: (8) is inconsistent. 206.69/127.84 | | 206.69/127.84 | Case 2: 206.69/127.84 | | 206.69/127.84 | | (9) ~ (all_219_0 = all_219_1) & length1(int, all_105_2) = all_219_0 206.69/127.84 | | 206.69/127.84 | | ALPHA: (9) implies: 206.69/127.84 | | (10) ~ (all_219_0 = all_219_1) 206.69/127.84 | | (11) length1(int, all_105_2) = all_219_0 206.69/127.84 | | 206.69/127.84 | | REDUCE: (3), (10) imply: 206.69/127.84 | | (12) ~ (all_219_0 = all_86_13) 206.69/127.84 | | 206.69/127.84 | | GROUND_INST: instantiating (5) with all_86_13, all_219_0, all_105_2, int, 206.69/127.84 | | simplifying with (1), (11) gives: 206.69/127.84 | | (13) all_219_0 = all_86_13 206.69/127.84 | | 206.69/127.84 | | REDUCE: (12), (13) imply: 206.69/127.84 | | (14) ~ (0 = 0) 206.69/127.84 | | 206.69/127.84 | | CLOSE: (14) is inconsistent. 206.69/127.84 | | 206.69/127.84 | End of split 206.69/127.84 | 206.69/127.84 End of proof 206.69/127.84 206.69/127.84 Sub-proof #75 shows that the following formulas are inconsistent: 206.69/127.84 ---------------------------------------------------------------- 206.69/127.84 (1) ~ (all_169_1 = 0) & array_eq_sub1(int, all_105_4, all_105_2, 0, 206.69/127.85 all_86_7) = all_169_1 206.69/127.85 (2) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.69/127.85 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ 206.69/127.85 (array_eq_sub1(v6, v5, v4, v3, v2) = v1) | ~ (array_eq_sub1(v6, v5, 206.69/127.85 v4, v3, v2) = v0)) 206.69/127.85 (3) array_eq_sub1(int, all_105_4, all_105_2, 0, all_86_7) = 0 206.69/127.85 206.69/127.85 Begin of proof 206.69/127.85 | 206.69/127.85 | ALPHA: (1) implies: 206.69/127.85 | (4) ~ (all_169_1 = 0) 206.69/127.85 | (5) array_eq_sub1(int, all_105_4, all_105_2, 0, all_86_7) = all_169_1 206.69/127.85 | 206.69/127.85 | GROUND_INST: instantiating (2) with all_169_1, 0, all_86_7, 0, all_105_2, 206.69/127.85 | all_105_4, int, simplifying with (3), (5) gives: 206.69/127.85 | (6) all_169_1 = 0 206.69/127.85 | 206.69/127.85 | REDUCE: (4), (6) imply: 206.69/127.85 | (7) ~ (0 = 0) 206.69/127.85 | 206.69/127.85 | CLOSE: (7) is inconsistent. 206.69/127.85 | 206.69/127.85 End of proof 206.69/127.85 206.69/127.85 Sub-proof #76 shows that the following formulas are inconsistent: 206.69/127.85 ---------------------------------------------------------------- 206.69/127.85 (1) length1(int, all_103_2) = all_170_1 206.69/127.85 (2) length1(int, all_105_4) = all_153_1 206.69/127.85 (3) length1(int, all_103_2) = all_242_1 206.69/127.85 (4) length1(int, all_103_2) = all_193_1 206.69/127.85 (5) length1(int, all_105_4) = all_86_13 206.69/127.85 (6) length1(int, all_105_4) = all_190_2 206.69/127.85 (7) $lesseq(1, $difference(all_86_7, all_86_8)) 206.69/127.85 (8) length1(int, all_105_4) = all_170_1 206.69/127.85 (9) ~ ($lesseq(1, $difference(all_242_1, all_86_8))) | ~ 206.69/127.85 ($lesseq(all_86_13, all_242_1)) | ( ~ (all_242_0 = all_242_1) & 206.69/127.85 length1(int, all_105_4) = all_242_0) 206.69/127.85 (10) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 206.69/127.85 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 206.69/127.85 (11) length1(int, all_103_2) = all_177_2 206.69/127.85 (12) $lesseq(all_86_7, all_169_1) 206.69/127.85 (13) length1(int, all_103_2) = all_156_0 206.69/127.85 (14) length1(int, all_105_4) = all_169_1 206.69/127.85 206.69/127.85 Begin of proof 206.69/127.85 | 206.69/127.85 | GROUND_INST: instantiating (10) with all_86_13, all_190_2, all_105_4, int, 206.69/127.85 | simplifying with (5), (6) gives: 206.69/127.85 | (15) all_190_2 = all_86_13 206.69/127.85 | 206.69/127.85 | GROUND_INST: instantiating (10) with all_190_2, all_169_1, all_105_4, int, 206.69/127.85 | simplifying with (6), (14) gives: 206.69/127.85 | (16) all_190_2 = all_169_1 206.69/127.85 | 206.69/127.85 | GROUND_INST: instantiating (10) with all_170_1, all_169_1, all_105_4, int, 206.69/127.85 | simplifying with (8), (14) gives: 206.69/127.85 | (17) all_170_1 = all_169_1 206.69/127.85 | 206.69/127.85 | GROUND_INST: instantiating (10) with all_170_1, all_153_1, all_105_4, int, 206.69/127.85 | simplifying with (2), (8) gives: 206.69/127.85 | (18) all_170_1 = all_153_1 206.69/127.85 | 206.69/127.85 | GROUND_INST: instantiating (10) with all_242_1, all_193_1, all_103_2, int, 206.69/127.85 | simplifying with (3), (4) gives: 206.69/127.85 | (19) all_242_1 = all_193_1 206.69/127.85 | 206.69/127.85 | GROUND_INST: instantiating (10) with all_193_1, all_177_2, all_103_2, int, 206.69/127.85 | simplifying with (4), (11) gives: 206.69/127.85 | (20) all_193_1 = all_177_2 206.69/127.85 | 206.69/127.85 | GROUND_INST: instantiating (10) with all_242_1, all_170_1, all_103_2, int, 206.69/127.85 | simplifying with (1), (3) gives: 206.69/127.85 | (21) all_242_1 = all_170_1 206.69/127.85 | 206.69/127.85 | GROUND_INST: instantiating (10) with all_193_1, all_156_0, all_103_2, int, 206.69/127.85 | simplifying with (4), (13) gives: 206.69/127.85 | (22) all_193_1 = all_156_0 206.69/127.85 | 206.69/127.85 | COMBINE_EQS: (19), (21) imply: 206.69/127.85 | (23) all_193_1 = all_170_1 206.69/127.85 | 206.69/127.85 | SIMP: (23) implies: 206.69/127.85 | (24) all_193_1 = all_170_1 206.69/127.85 | 206.69/127.85 | COMBINE_EQS: (20), (24) imply: 206.69/127.85 | (25) all_177_2 = all_170_1 206.69/127.85 | 206.69/127.85 | COMBINE_EQS: (20), (22) imply: 206.69/127.85 | (26) all_177_2 = all_156_0 206.69/127.85 | 206.69/127.85 | COMBINE_EQS: (15), (16) imply: 206.69/127.85 | (27) all_169_1 = all_86_13 206.69/127.85 | 206.69/127.85 | SIMP: (27) implies: 206.69/127.85 | (28) all_169_1 = all_86_13 206.69/127.85 | 206.69/127.85 | COMBINE_EQS: (25), (26) imply: 206.69/127.85 | (29) all_170_1 = all_156_0 206.69/127.85 | 206.69/127.85 | COMBINE_EQS: (17), (29) imply: 206.69/127.85 | (30) all_169_1 = all_156_0 206.69/127.85 | 206.69/127.85 | SIMP: (30) implies: 206.69/127.85 | (31) all_169_1 = all_156_0 206.69/127.85 | 206.69/127.85 | COMBINE_EQS: (18), (29) imply: 206.69/127.85 | (32) all_156_0 = all_153_1 206.69/127.85 | 206.69/127.85 | COMBINE_EQS: (28), (31) imply: 206.69/127.85 | (33) all_156_0 = all_86_13 206.69/127.85 | 206.69/127.85 | SIMP: (33) implies: 206.69/127.85 | (34) all_156_0 = all_86_13 206.69/127.85 | 206.69/127.85 | COMBINE_EQS: (32), (34) imply: 206.69/127.85 | (35) all_153_1 = all_86_13 206.69/127.85 | 206.69/127.85 | SIMP: (35) implies: 206.69/127.85 | (36) all_153_1 = all_86_13 206.69/127.85 | 206.69/127.85 | COMBINE_EQS: (29), (34) imply: 206.69/127.85 | (37) all_170_1 = all_86_13 206.69/127.85 | 206.69/127.85 | COMBINE_EQS: (21), (37) imply: 206.69/127.85 | (38) all_242_1 = all_86_13 206.69/127.85 | 206.69/127.85 | REDUCE: (12), (28) imply: 206.69/127.85 | (39) $lesseq(all_86_7, all_86_13) 206.69/127.85 | 206.69/127.85 | REF_CLOSE: (5), (7), (9), (10), (38), (39) are inconsistent by sub-proof #77. 206.69/127.85 | 206.69/127.85 End of proof 206.69/127.85 206.69/127.85 Sub-proof #77 shows that the following formulas are inconsistent: 206.69/127.85 ---------------------------------------------------------------- 206.69/127.85 (1) $lesseq(all_86_7, all_86_13) 206.69/127.85 (2) length1(int, all_105_4) = all_86_13 206.69/127.85 (3) all_242_1 = all_86_13 206.69/127.85 (4) $lesseq(1, $difference(all_86_7, all_86_8)) 206.69/127.85 (5) ~ ($lesseq(1, $difference(all_242_1, all_86_8))) | ~ 206.69/127.85 ($lesseq(all_86_13, all_242_1)) | ( ~ (all_242_0 = all_242_1) & 206.69/127.85 length1(int, all_105_4) = all_242_0) 206.69/127.85 (6) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 206.69/127.85 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 206.69/127.85 206.69/127.85 Begin of proof 206.69/127.85 | 206.69/127.85 | BETA: splitting (5) gives: 206.69/127.85 | 206.69/127.85 | Case 1: 206.69/127.85 | | 206.69/127.85 | | (7) $lesseq(1, $difference(all_86_13, all_242_1)) 206.69/127.85 | | 206.69/127.85 | | REDUCE: (3), (7) imply: 206.69/127.85 | | (8) $lesseq(0, -1) 206.69/127.85 | | 206.69/127.85 | | CLOSE: (8) is inconsistent. 206.69/127.85 | | 206.69/127.85 | Case 2: 206.69/127.85 | | 206.69/127.85 | | (9) ~ ($lesseq(1, $difference(all_242_1, all_86_8))) | ( ~ (all_242_0 = 206.69/127.85 | | all_242_1) & length1(int, all_105_4) = all_242_0) 206.69/127.85 | | 206.69/127.85 | | REF_CLOSE: (1), (2), (3), (4), (6), (9) are inconsistent by sub-proof #82. 206.69/127.85 | | 206.69/127.85 | End of split 206.69/127.85 | 206.69/127.85 End of proof 206.69/127.85 206.69/127.85 Sub-proof #78 shows that the following formulas are inconsistent: 206.69/127.85 ---------------------------------------------------------------- 206.69/127.85 (1) length1(int, all_103_2) = all_86_13 206.69/127.85 (2) ~ ($lesseq(all_86_11, all_215_1)) | ( ~ (all_215_0 = all_215_1) & 206.69/127.85 length1(int, all_103_2) = all_215_0) 206.69/127.85 (3) $lesseq(all_86_11, all_86_8) 206.69/127.85 (4) $lesseq(all_86_7, all_86_10) 206.69/127.85 (5) all_215_1 = all_86_13 206.69/127.85 (6) $lesseq(1, $difference(all_86_7, all_86_8)) 206.69/127.85 (7) $lesseq(1, $difference(all_86_13, all_86_10)) 206.69/127.85 (8) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 206.69/127.85 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 206.69/127.85 206.69/127.85 Begin of proof 206.69/127.85 | 206.69/127.85 | BETA: splitting (2) gives: 206.69/127.85 | 206.69/127.85 | Case 1: 206.69/127.85 | | 206.69/127.85 | | (9) $lesseq(1, $difference(all_86_11, all_215_1)) 206.69/127.85 | | 206.69/127.85 | | REDUCE: (5), (9) imply: 206.69/127.85 | | (10) $lesseq(1, $difference(all_86_11, all_86_13)) 206.69/127.85 | | 206.69/127.85 | | REF_CLOSE: (3), (4), (6), (7), (10) are inconsistent by sub-proof #79. 206.69/127.85 | | 206.69/127.85 | Case 2: 206.69/127.85 | | 206.69/127.85 | | (11) ~ (all_215_0 = all_215_1) & length1(int, all_103_2) = all_215_0 206.69/127.85 | | 206.69/127.85 | | ALPHA: (11) implies: 206.69/127.85 | | (12) ~ (all_215_0 = all_215_1) 206.69/127.85 | | (13) length1(int, all_103_2) = all_215_0 206.69/127.85 | | 206.69/127.85 | | REDUCE: (5), (12) imply: 206.69/127.85 | | (14) ~ (all_215_0 = all_86_13) 206.69/127.85 | | 206.69/127.85 | | GROUND_INST: instantiating (8) with all_86_13, all_215_0, all_103_2, int, 206.69/127.85 | | simplifying with (1), (13) gives: 206.69/127.85 | | (15) all_215_0 = all_86_13 206.69/127.85 | | 206.69/127.85 | | REDUCE: (14), (15) imply: 206.69/127.85 | | (16) ~ (0 = 0) 206.69/127.85 | | 206.69/127.85 | | CLOSE: (16) is inconsistent. 206.69/127.85 | | 206.69/127.85 | End of split 206.69/127.85 | 206.69/127.85 End of proof 206.69/127.85 206.69/127.85 Sub-proof #79 shows that the following formulas are inconsistent: 206.69/127.85 ---------------------------------------------------------------- 206.69/127.85 (1) $lesseq(all_86_11, all_86_8) 206.69/127.85 (2) $lesseq(all_86_7, all_86_10) 206.69/127.85 (3) $lesseq(1, $difference(all_86_7, all_86_8)) 206.69/127.85 (4) $lesseq(1, $difference(all_86_13, all_86_10)) 206.69/127.85 (5) $lesseq(1, $difference(all_86_11, all_86_13)) 206.69/127.85 206.69/127.85 Begin of proof 206.69/127.85 | 206.69/127.85 | COMBINE_INEQS: (2), (3) imply: 206.69/127.85 | (6) $lesseq(1, $difference(all_86_10, all_86_8)) 206.69/127.85 | 206.69/127.85 | COMBINE_INEQS: (1), (6) imply: 206.69/127.85 | (7) $lesseq(1, $difference(all_86_10, all_86_11)) 206.69/127.85 | 206.69/127.85 | COMBINE_INEQS: (4), (7) imply: 206.69/127.85 | (8) $lesseq(2, $difference(all_86_13, all_86_11)) 206.69/127.85 | 206.69/127.85 | COMBINE_INEQS: (5), (8) imply: 206.69/127.85 | (9) $lesseq(0, -1) 206.69/127.85 | 206.69/127.85 | CLOSE: (9) is inconsistent. 206.69/127.85 | 206.69/127.85 End of proof 206.69/127.85 206.69/127.85 Sub-proof #80 shows that the following formulas are inconsistent: 206.69/127.85 ---------------------------------------------------------------- 206.69/127.85 (1) $lesseq(all_86_11, all_86_8) 206.69/127.85 (2) $lesseq(all_86_7, all_86_10) 206.69/127.85 (3) $lesseq(1, $difference(all_86_7, all_86_8)) 206.69/127.85 (4) $lesseq(all_86_13, -1) 206.69/127.85 (5) $lesseq(1, $difference(all_86_13, all_86_10)) 206.69/127.85 (6) $lesseq(0, all_86_11) 206.69/127.85 206.69/127.85 Begin of proof 206.69/127.85 | 206.69/127.85 | COMBINE_INEQS: (2), (3) imply: 206.69/127.85 | (7) $lesseq(1, $difference(all_86_10, all_86_8)) 206.69/127.85 | 206.69/127.85 | COMBINE_INEQS: (1), (7) imply: 206.69/127.85 | (8) $lesseq(1, $difference(all_86_10, all_86_11)) 206.69/127.85 | 206.69/127.85 | COMBINE_INEQS: (5), (8) imply: 206.69/127.85 | (9) $lesseq(2, $difference(all_86_13, all_86_11)) 206.69/127.85 | 206.69/127.85 | COMBINE_INEQS: (6), (9) imply: 206.69/127.85 | (10) $lesseq(2, all_86_13) 206.69/127.85 | 206.69/127.85 | COMBINE_INEQS: (4), (10) imply: 206.69/127.85 | (11) $lesseq(0, -1) 206.69/127.85 | 206.69/127.85 | CLOSE: (11) is inconsistent. 206.69/127.85 | 206.69/127.85 End of proof 206.69/127.85 206.69/127.85 Sub-proof #81 shows that the following formulas are inconsistent: 206.69/127.85 ---------------------------------------------------------------- 206.69/127.85 (1) ~ (all_171_1 = 0) & array_eq_sub1(int, all_103_4, all_103_2, 0, 206.69/127.85 all_86_11) = all_171_1 206.69/127.85 (2) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.69/127.85 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ 206.69/127.85 (array_eq_sub1(v6, v5, v4, v3, v2) = v1) | ~ (array_eq_sub1(v6, v5, 206.69/127.85 v4, v3, v2) = v0)) 206.69/127.85 (3) array_eq_sub1(int, all_103_4, all_103_2, 0, all_86_11) = 0 206.69/127.85 206.69/127.85 Begin of proof 206.69/127.85 | 206.69/127.85 | ALPHA: (1) implies: 206.69/127.85 | (4) ~ (all_171_1 = 0) 206.69/127.85 | (5) array_eq_sub1(int, all_103_4, all_103_2, 0, all_86_11) = all_171_1 206.69/127.85 | 206.69/127.85 | GROUND_INST: instantiating (2) with all_171_1, 0, all_86_11, 0, all_103_2, 206.69/127.85 | all_103_4, int, simplifying with (3), (5) gives: 206.69/127.85 | (6) all_171_1 = 0 206.69/127.85 | 206.69/127.85 | REDUCE: (4), (6) imply: 206.69/127.85 | (7) ~ (0 = 0) 206.69/127.85 | 206.69/127.85 | CLOSE: (7) is inconsistent. 206.69/127.85 | 206.69/127.85 End of proof 206.69/127.85 206.69/127.85 Sub-proof #82 shows that the following formulas are inconsistent: 206.69/127.85 ---------------------------------------------------------------- 206.69/127.85 (1) $lesseq(all_86_7, all_86_13) 206.69/127.85 (2) ~ ($lesseq(1, $difference(all_242_1, all_86_8))) | ( ~ (all_242_0 = 206.69/127.85 all_242_1) & length1(int, all_105_4) = all_242_0) 206.69/127.85 (3) length1(int, all_105_4) = all_86_13 206.69/127.85 (4) all_242_1 = all_86_13 206.69/127.85 (5) $lesseq(1, $difference(all_86_7, all_86_8)) 206.69/127.85 (6) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 206.69/127.85 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 206.69/127.85 206.69/127.85 Begin of proof 206.69/127.85 | 206.69/127.85 | BETA: splitting (2) gives: 206.69/127.85 | 206.69/127.85 | Case 1: 206.69/127.85 | | 206.69/127.85 | | (7) $lesseq(all_242_1, all_86_8) 206.69/127.85 | | 206.69/127.85 | | REDUCE: (4), (7) imply: 206.69/127.85 | | (8) $lesseq(all_86_13, all_86_8) 206.69/127.85 | | 206.69/127.85 | | COMBINE_INEQS: (1), (5) imply: 206.69/127.85 | | (9) $lesseq(1, $difference(all_86_13, all_86_8)) 206.69/127.85 | | 206.69/127.85 | | COMBINE_INEQS: (8), (9) imply: 206.69/127.85 | | (10) $lesseq(0, -1) 206.69/127.85 | | 206.69/127.85 | | CLOSE: (10) is inconsistent. 206.69/127.85 | | 206.69/127.85 | Case 2: 206.69/127.85 | | 206.69/127.85 | | (11) ~ (all_242_0 = all_242_1) & length1(int, all_105_4) = all_242_0 206.69/127.85 | | 206.69/127.85 | | ALPHA: (11) implies: 206.69/127.85 | | (12) ~ (all_242_0 = all_242_1) 206.69/127.85 | | (13) length1(int, all_105_4) = all_242_0 206.69/127.85 | | 206.69/127.85 | | REDUCE: (4), (12) imply: 206.69/127.85 | | (14) ~ (all_242_0 = all_86_13) 206.69/127.85 | | 206.69/127.85 | | GROUND_INST: instantiating (6) with all_86_13, all_242_0, all_105_4, int, 206.69/127.85 | | simplifying with (3), (13) gives: 206.69/127.85 | | (15) all_242_0 = all_86_13 206.69/127.85 | | 206.69/127.85 | | REDUCE: (14), (15) imply: 206.69/127.85 | | (16) ~ (0 = 0) 206.69/127.85 | | 206.69/127.85 | | CLOSE: (16) is inconsistent. 206.69/127.85 | | 206.69/127.85 | End of split 206.69/127.85 | 206.69/127.85 End of proof 206.69/127.85 206.69/127.85 Sub-proof #83 shows that the following formulas are inconsistent: 206.69/127.85 ---------------------------------------------------------------- 206.69/127.85 (1) ~ (all_168_1 = 0) & array_eq_sub1(int, all_103_2, all_105_4, 206.69/127.85 $sum(all_86_8, 1), all_86_13) = all_168_1 206.69/127.85 (2) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.69/127.85 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ 206.69/127.85 (array_eq_sub1(v6, v5, v4, v3, v2) = v1) | ~ (array_eq_sub1(v6, v5, 206.69/127.85 v4, v3, v2) = v0)) 206.69/127.85 (3) array_eq_sub1(int, all_103_2, all_105_4, $sum(all_86_8, 1), all_86_13) = 206.69/127.85 0 206.69/127.85 206.69/127.85 Begin of proof 206.69/127.85 | 206.69/127.85 | ALPHA: (1) implies: 206.69/127.85 | (4) ~ (all_168_1 = 0) 206.69/127.85 | (5) array_eq_sub1(int, all_103_2, all_105_4, $sum(all_86_8, 1), all_86_13) 206.69/127.85 | = all_168_1 206.69/127.85 | 206.69/127.85 | GROUND_INST: instantiating (2) with all_168_1, 0, all_86_13, $sum(all_86_8, 206.69/127.85 | 1), all_105_4, all_103_2, int, simplifying with (3), (5) gives: 206.69/127.85 | (6) all_168_1 = 0 206.69/127.85 | 206.69/127.85 | REDUCE: (4), (6) imply: 206.69/127.85 | (7) ~ (0 = 0) 206.69/127.85 | 206.69/127.85 | CLOSE: (7) is inconsistent. 206.69/127.85 | 206.69/127.85 End of proof 206.69/127.85 206.69/127.85 Sub-proof #84 shows that the following formulas are inconsistent: 206.69/127.85 ---------------------------------------------------------------- 206.69/127.85 (1) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ (tb2t1(v2) 206.69/127.85 = v1) | ~ (tb2t1(v2) = v0)) 206.69/127.85 (2) ! [v0: $int] : ! [v1: $int] : ( ~ ($lesseq(43, v1)) | ~ ($lesseq(v0, 206.69/127.85 all_86_8)) | ~ ($lesseq(all_86_11, v0)) | ~ (get3(all_86_6, v0) = 206.69/127.85 v1)) 206.69/127.85 (3) length1(int, all_103_2) = all_86_13 206.69/127.85 (4) in_map_int_int(all_86_6) 206.69/127.85 (5) in_map_int_int(all_86_12) 206.69/127.85 (6) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.69/127.85 $int] : ! [v5: $int] : ! [v6: $int] : ( ~ ($lesseq(0, v4)) | ~ 206.69/127.85 ($lesseq(0, v3)) | ~ (map_eq_sub1(v0, v5, v6, v3, v4) = 0) | ~ 206.69/127.85 (elts(v0, v2) = v6) | ~ (elts(v0, v1) = v5) | ~ in_ty(v0) | ? [v7: 206.69/127.85 $int] : ? [v8: $int] : ((v7 = 0 & array_eq_sub1(v0, v1, v2, v3, v4) 206.69/127.85 = 0) | (length1(v0, v1) = v7 & ( ~ ($lesseq(v4, v7)) | ~ 206.69/127.85 ($lesseq(v3, v7)) | ( ~ (v8 = v7) & length1(v0, v2) = v8))))) 206.69/127.85 (7) length1(int, all_105_2) = all_86_13 206.69/127.85 (8) elts(int, all_103_4) = all_103_3 206.81/127.85 (9) t2tb2(all_86_3) = all_105_4 206.81/127.85 (10) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.81/127.85 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 206.81/127.85 (map_eq_sub1(v0, v5, v6, v3, v4) = v7) | ~ (elts(v0, v2) = v6) | ~ 206.81/127.85 (elts(v0, v1) = v5) | ~ in_ty(v0) | ? [v8: $int] : ? [v9: $int] : 206.81/127.85 ((v9 = v8 & v7 = 0 & $lesseq(v4, v8) & $lesseq(v3, v8) & $lesseq(0, 206.81/127.85 v4) & $lesseq(0, v3) & length1(v0, v2) = v8 & length1(v0, v1) = 206.81/127.85 v8) | ( ~ (v8 = 0) & array_eq_sub1(v0, v1, v2, v3, v4) = v8))) 206.81/127.85 (11) t2tb(all_86_2) = all_105_1 206.81/127.85 (12) in_ty(int) 206.81/127.86 (13) length1(int, all_103_4) = all_86_13 206.81/127.86 (14) $lesseq(2, all_86_13) 206.81/127.86 (15) ( ~ (all_133_0 = 42) & $lesseq(1, $difference(all_86_7, all_133_2)) & 206.81/127.86 $lesseq(1, $difference(all_133_2, all_86_8)) & tb2t1(all_133_1) = 206.81/127.86 all_133_0 & get4(int, all_133_3, all_133_2) = all_133_1 & 206.81/127.86 in_uni(all_133_1)) | ($lesseq(all_133_0, 41) & $lesseq(all_133_2, 206.81/127.86 all_86_10) & $lesseq(all_86_7, all_133_2) & tb2t1(all_133_1) = 206.81/127.86 all_133_0 & get4(int, all_133_3, all_133_2) = all_133_1 & 206.81/127.86 in_uni(all_133_1)) | ($lesseq(43, all_133_0) & $lesseq(all_133_2, 206.81/127.86 all_86_8) & $lesseq(all_86_11, all_133_2) & tb2t1(all_133_1) = 206.81/127.86 all_133_0 & get4(int, all_133_3, all_133_2) = all_133_1 & 206.81/127.86 in_uni(all_133_1)) 206.81/127.86 (16) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.81/127.86 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 206.81/127.86 (permut2(v0, v5, v6, v3, v4) = v7) | ~ (elts(v0, v2) = v6) | ~ 206.81/127.86 (elts(v0, v1) = v5) | ~ in_ty(v0) | ? [v8: $int] : ? [v9: $int] : 206.81/127.86 ((v9 = v8 & v7 = 0 & $lesseq(v4, v8) & $lesseq(v3, v8) & $lesseq(0, 206.81/127.86 v4) & $lesseq(0, v3) & length1(v0, v2) = v8 & length1(v0, v1) = 206.81/127.86 v8) | ( ~ (v8 = 0) & permut3(v0, v1, v2, v3, v4) = v8))) 206.81/127.86 (17) all_125_0 = all_105_4 206.81/127.86 (18) $lesseq(-1, all_86_8) 206.81/127.86 (19) $lesseq(all_86_7, all_86_13) 206.81/127.86 (20) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.81/127.86 $int] : ! [v5: $int] : ( ~ (permut2(v0, v2, v3, v4, v5) = 0) | ~ 206.81/127.86 (permut2(v0, v1, v2, v4, v5) = 0) | ~ in_ty(v0) | permut2(v0, v1, v3, 206.81/127.86 v4, v5) = 0) 206.81/127.86 (21) ! [v0: $int] : ! [v1: $int] : (v1 = 42 | ~ ($lesseq(1, 206.81/127.86 $difference(all_86_7, v0))) | ~ ($lesseq(1, $difference(v0, 206.81/127.86 all_86_8))) | ~ (get3(all_86_6, v0) = v1)) 206.81/127.86 (22) map_eq_sub1(int, all_103_3, all_103_1, $sum(all_86_10, 1), all_86_13) = 206.81/127.86 0 206.81/127.86 (23) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.81/127.86 $int] : ! [v5: $int] : ! [v6: $int] : ( ~ (permut2(v0, v3, v4, 0, 206.81/127.86 v5) = v6) | ~ (length1(v0, v1) = v5) | ~ (elts(v0, v2) = v4) | 206.81/127.86 ~ (elts(v0, v1) = v3) | ~ in_ty(v0) | ? [v7: $int] : ((v7 = v5 & v6 206.81/127.86 = 0 & length1(v0, v2) = v5) | ( ~ (v7 = 0) & permut_all(v0, v1, 206.81/127.86 v2) = v7))) 206.81/127.86 (24) t2tb(all_86_6) = all_103_1 206.81/127.86 (25) map_eq_sub1(int, all_103_1, all_105_3, $sum(all_86_8, 1), all_86_13) = 0 206.81/127.86 (26) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.81/127.86 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ (permut3(v6, v5, 206.81/127.86 v4, v3, v2) = v1) | ~ (permut3(v6, v5, v4, v3, v2) = v0)) 206.81/127.86 (27) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.81/127.86 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ 206.81/127.86 (array_eq_sub1(v6, v5, v4, v3, v2) = v1) | ~ (array_eq_sub1(v6, v5, 206.81/127.86 v4, v3, v2) = v0)) 206.81/127.86 (28) tb2t(all_205_3) = all_205_2 206.81/127.86 (29) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 206.81/127.86 | ~ (elts(v3, v2) = v1) | ~ (elts(v3, v2) = v0)) 206.81/127.86 (30) length1(int, all_105_4) = all_86_13 206.81/127.86 (31) in_array_int(all_86_3) 206.81/127.86 (32) elts(int, all_105_4) = all_105_3 206.81/127.86 (33) map_eq_sub1(int, all_105_3, all_105_1, 0, all_86_7) = 0 206.81/127.86 (34) tb2t(all_105_1) = all_86_2 206.81/127.86 (35) permut2(int, all_103_1, all_105_3, all_86_11, $sum(all_86_8, 1)) = 0 206.81/127.86 (36) elts(int, all_105_2) = all_105_1 206.81/127.86 (37) map_eq_sub1(int, all_103_3, all_103_1, 0, all_86_11) = 0 206.81/127.86 (38) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.81/127.86 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 206.81/127.86 ($lesseq(1, $difference(v4, v5))) | ~ ($lesseq(v3, v5)) | ~ 206.81/127.86 (permut2(v0, v1, v2, v3, v4) = 0) | ~ (t2tb1(v5) = v6) | ~ (get(v0, 206.81/127.86 int, v2, v6) = v7) | ~ in_ty(v0) | ? [v8: $int] : ? [v9: $int] 206.81/127.86 : ($lesseq(1, $difference(v4, v8)) & $lesseq(v3, v8) & t2tb1(v8) = v9 206.81/127.86 & get(v0, int, v1, v9) = v7 & in_uni(v9) & in_uni(v7))) 206.81/127.86 (39) t2tb2(all_86_1) = all_105_2 206.81/127.86 (40) $lesseq(all_86_11, all_86_8) 206.81/127.86 (41) ~ (permut2(int, all_105_3, all_105_1, 0, all_86_13) = 0) | ? [v0: 206.81/127.86 $int] : ((v0 = 0 & permut_all(int, all_105_4, all_105_2) = 0) | ( ~ 206.81/127.86 (v0 = all_86_13) & length1(int, all_105_2) = v0)) 206.81/127.86 (42) $lesseq(all_86_7, all_86_10) 206.81/127.86 (43) permut2(int, all_103_1, all_105_3, all_86_11, $sum(all_86_10, 1)) = 0 206.81/127.86 (44) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.81/127.86 $int] : ! [v5: $int] : ( ~ (elts(v0, v1) = v3) | ~ (t2tb1(v2) = v4) 206.81/127.86 | ~ (get(v0, int, v3, v4) = v5) | ~ in_ty(v0) | (get4(v0, v1, v2) = 206.81/127.86 v5 & in_uni(v5))) 206.81/127.86 (45) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.81/127.86 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 206.81/127.86 ($lesseq(1, $difference(v3, v4))) | ~ ($lesseq(v2, v4)) | ~ 206.81/127.86 (permut2(int, v5, v6, v2, v3) = 0) | ~ (t2tb(v1) = v6) | ~ (t2tb(v0) 206.81/127.86 = v5) | ~ (get3(v1, v4) = v7) | ~ in_map_int_int(v0) | ? [v8: 206.81/127.86 $int] : ($lesseq(1, $difference(v3, v8)) & $lesseq(v2, v8) & 206.81/127.86 get3(v0, v8) = v7)) 206.81/127.86 (46) $lesseq(0, all_86_7) 206.81/127.86 (47) permut2(int, all_105_3, all_105_1, all_86_7, $sum(all_86_10, 1)) = 0 206.81/127.86 (48) permut2(int, all_103_3, all_103_1, all_86_11, $sum(all_86_10, 1)) = 0 206.81/127.86 (49) ~ (permut2(int, all_103_3, all_103_1, 0, all_86_13) = 0) | ? [v0: 206.81/127.86 $int] : ((v0 = 0 & permut_all(int, all_103_4, all_103_2) = 0) | ( ~ 206.81/127.86 (v0 = all_86_13) & length1(int, all_103_2) = v0)) 206.81/127.86 (50) in_array_int(all_86_1) 206.81/127.86 (51) t2tb(all_86_12) = all_103_3 206.81/127.86 (52) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.81/127.86 $int] : ! [v5: $int] : ! [v6: $int] : ( ~ ($lesseq(0, v4)) | ~ 206.81/127.86 ($lesseq(0, v3)) | ~ (permut2(v0, v5, v6, v3, v4) = 0) | ~ (elts(v0, 206.81/127.86 v2) = v6) | ~ (elts(v0, v1) = v5) | ~ in_ty(v0) | ? [v7: $int] 206.81/127.86 : ? [v8: $int] : ((v7 = 0 & permut3(v0, v1, v2, v3, v4) = 0) | 206.81/127.86 (length1(v0, v1) = v7 & ( ~ ($lesseq(v4, v7)) | ~ ($lesseq(v3, v7)) 206.81/127.86 | ( ~ (v8 = v7) & length1(v0, v2) = v8))))) 206.81/127.86 (53) $lesseq(1, $difference(all_86_7, all_86_8)) 206.81/127.86 (54) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.81/127.86 $int] : ! [v5: $int] : ! [v6: $int] : ( ~ ($lesseq(1, 206.81/127.86 $difference(v4, v5))) | ~ ($lesseq(v3, v5)) | ~ (map_eq_sub1(v0, 206.81/127.86 v1, v2, v3, v4) = 0) | ~ (t2tb1(v5) = v6) | ~ in_ty(v0) | ? 206.81/127.86 [v7: $int] : (get(v0, int, v2, v6) = v7 & get(v0, int, v1, v6) = v7 & 206.81/127.86 in_uni(v7))) 206.81/127.86 (55) $lesseq(1, $difference(all_86_13, all_86_10)) 206.81/127.86 (56) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.81/127.86 $int] : ! [v5: $int] : (v5 = 0 | ~ (permut_sub2(v0, v1, v2, v3, v4) 206.81/127.86 = v5) | ~ in_ty(v0) | ? [v6: $int] : ? [v7: $int] : ? [v8: $int] 206.81/127.86 : ? [v9: $int] : (( ~ (v9 = 0) & map_eq_sub1(v0, v6, v7, v4, v8) = v9 206.81/127.86 & length1(v0, v1) = v8 & elts(v0, v2) = v7 & elts(v0, v1) = v6 & 206.81/127.86 in_uni(v7) & in_uni(v6)) | ( ~ (v8 = 0) & map_eq_sub1(v0, v6, v7, 206.81/127.86 0, v3) = v8 & elts(v0, v2) = v7 & elts(v0, v1) = v6 & in_uni(v7) 206.81/127.86 & in_uni(v6)) | ( ~ (v6 = 0) & permut3(v0, v1, v2, v3, v4) = v6))) 206.81/127.86 (57) in_map_int_int(all_86_4) 206.81/127.86 (58) map_eq_sub1(int, all_105_3, all_105_1, 0, all_86_13) = 0 206.81/127.86 (59) $lesseq(0, all_86_11) 206.81/127.86 (60) elts(int, all_103_2) = all_103_1 206.81/127.86 (61) ~ (permut2(int, all_103_1, all_105_3, 0, all_86_13) = 0) | ? [v0: 206.81/127.86 $int] : ((v0 = 0 & permut_all(int, all_103_2, all_105_4) = 0) | ( ~ 206.81/127.86 (v0 = all_86_13) & length1(int, all_105_4) = v0)) 206.81/127.86 (62) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ( ~ 206.81/127.86 (t2tb2(v0) = v2) | ~ (get4(int, v2, v1) = v3) | ~ in_array_int(v0) | 206.81/127.86 ? [v4: $int] : ? [v5: $int] : ? [v6: $int] : (tb2t(v4) = v5 & 206.81/127.86 tb2t1(v3) = v6 & get3(v5, v1) = v6 & elts(int, v2) = v4 & 206.81/127.86 in_map_int_int(v5) & in_uni(v4))) 206.81/127.86 (63) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ (tb2t(v2) 206.81/127.86 = v1) | ~ (tb2t(v2) = v0)) 206.81/127.86 (64) all_133_3 = all_105_2 206.81/127.86 (65) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.81/127.86 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 206.81/127.86 ($lesseq(1, $difference(v3, v6))) | ~ ($lesseq(v2, v6)) | ~ 206.81/127.86 (map_eq_sub1(int, v4, v5, v2, v3) = 0) | ~ (t2tb(v1) = v5) | ~ 206.81/127.86 (t2tb(v0) = v4) | ~ (get3(v1, v6) = v7) | ~ in_map_int_int(v0) | 206.81/127.86 get3(v0, v6) = v7) 206.81/127.86 (66) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 206.81/127.86 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 206.81/127.86 (67) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ( ~ 206.81/127.86 (get4(v0, v1, v2) = v3) | ~ in_ty(v0) | ? [v4: $int] : ? [v5: $int] 206.81/127.86 : (elts(v0, v1) = v4 & t2tb1(v2) = v5 & get(v0, int, v4, v5) = v3 & 206.81/127.86 in_uni(v5) & in_uni(v4) & in_uni(v3))) 206.81/127.86 (68) length1(int, all_105_2) = all_205_1 206.81/127.86 (69) map_eq_sub1(int, all_103_1, all_105_3, 0, all_86_13) = 0 206.81/127.86 (70) ! [v0: $int] : ! [v1: $int] : ( ~ (tb2t1(v0) = v1) | ~ in_uni(v0) | 206.81/127.86 t2tb1(v1) = v0) 206.81/127.86 (71) map_eq_sub1(int, all_105_3, all_105_1, $sum(all_86_10, 1), all_86_13) = 206.81/127.86 0 206.81/127.86 (72) t2tb(all_86_4) = all_105_3 206.81/127.86 (73) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.81/127.86 $int] : ! [v5: $int] : ( ~ (permut3(v0, v1, v2, v3, v4) = v5) | ~ 206.81/127.86 in_ty(v0) | ? [v6: $int] : ? [v7: $int] : ? [v8: $int] : ? [v9: 206.81/127.86 $int] : ? [v10: $int] : ((v10 = 0 & v9 = 0 & v5 = 0 & 206.81/127.86 map_eq_sub1(v0, v6, v7, v4, v8) = 0 & map_eq_sub1(v0, v6, v7, 0, 206.81/127.86 v3) = 0 & length1(v0, v1) = v8 & elts(v0, v2) = v7 & elts(v0, 206.81/127.86 v1) = v6 & in_uni(v7) & in_uni(v6)) | ( ~ (v6 = 0) & 206.81/127.86 permut_sub2(v0, v1, v2, v3, v4) = v6))) 206.81/127.86 (74) elts(int, all_105_2) = all_205_3 206.81/127.86 (75) ! [v0: $int] : ! [v1: $int] : ( ~ ($lesseq(v0, all_86_10)) | ~ 206.81/127.86 ($lesseq(all_86_7, v0)) | ~ (get4(int, all_125_0, v0) = v1) | ? [v2: 206.81/127.86 $int] : ($lesseq(42, v2) & tb2t1(v1) = v2)) 206.81/127.86 206.81/127.86 Begin of proof 206.81/127.86 | 206.81/127.86 | GROUND_INST: instantiating (66) with all_86_13, all_205_1, all_105_2, int, 206.81/127.86 | simplifying with (7), (68) gives: 206.81/127.86 | (76) all_205_1 = all_86_13 206.81/127.86 | 206.81/127.86 | GROUND_INST: instantiating (29) with all_105_1, all_205_3, all_105_2, int, 206.81/127.86 | simplifying with (36), (74) gives: 206.81/127.86 | (77) all_205_3 = all_105_1 206.81/127.86 | 206.81/127.86 | REDUCE: (28), (77) imply: 206.81/127.86 | (78) tb2t(all_105_1) = all_205_2 206.81/127.86 | 206.81/127.86 | GROUND_INST: instantiating (63) with all_86_2, all_205_2, all_105_1, 206.81/127.86 | simplifying with (34), (78) gives: 206.81/127.86 | (79) all_205_2 = all_86_2 206.81/127.86 | 206.81/127.86 | GROUND_INST: instantiating (10) with int, all_105_4, all_105_2, 0, all_86_13, 206.81/127.86 | all_105_3, all_105_1, 0, simplifying with (12), (32), (36), (58) 206.81/127.86 | gives: 206.81/127.86 | (80) ? [v0: $int] : ? [v1: $int] : ((v1 = v0 & $lesseq(all_86_13, v0) & 206.81/127.86 | $lesseq(0, v0) & $lesseq(0, all_86_13) & length1(int, all_105_2) = 206.81/127.86 | v0 & length1(int, all_105_4) = v0) | ( ~ (v0 = 0) & 206.81/127.86 | array_eq_sub1(int, all_105_4, all_105_2, 0, all_86_13) = v0)) 206.81/127.86 | 206.81/127.86 | GROUND_INST: instantiating (6) with int, all_105_4, all_105_2, 0, all_86_13, 206.81/127.86 | all_105_3, all_105_1, simplifying with (12), (32), (36), (58) 206.81/127.86 | gives: 206.81/127.86 | (81) ~ ($lesseq(0, all_86_13)) | ? [v0: $int] : ? [v1: $int] : ((v0 = 0 206.81/127.86 | & array_eq_sub1(int, all_105_4, all_105_2, 0, all_86_13) = 0) | 206.81/127.86 | (length1(int, all_105_4) = v0 & ( ~ ($lesseq(all_86_13, v0)) | ~ 206.81/127.86 | ($lesseq(0, v0)) | ( ~ (v1 = v0) & length1(int, all_105_2) = 206.81/127.86 | v1)))) 206.81/127.86 | 206.81/127.86 | GROUND_INST: instantiating (10) with int, all_103_2, all_105_4, 0, all_86_13, 206.81/127.86 | all_103_1, all_105_3, 0, simplifying with (12), (32), (60), (69) 206.81/127.86 | gives: 206.81/127.86 | (82) ? [v0: $int] : ? [v1: $int] : ((v1 = v0 & $lesseq(all_86_13, v0) & 206.81/127.86 | $lesseq(0, v0) & $lesseq(0, all_86_13) & length1(int, all_105_4) = 206.81/127.86 | v0 & length1(int, all_103_2) = v0) | ( ~ (v0 = 0) & 206.81/127.86 | array_eq_sub1(int, all_103_2, all_105_4, 0, all_86_13) = v0)) 206.81/127.86 | 206.81/127.86 | GROUND_INST: instantiating (6) with int, all_103_2, all_105_4, 0, all_86_13, 206.81/127.86 | all_103_1, all_105_3, simplifying with (12), (32), (60), (69) 206.81/127.86 | gives: 206.81/127.86 | (83) ~ ($lesseq(0, all_86_13)) | ? [v0: $int] : ? [v1: $int] : ((v0 = 0 206.81/127.86 | & array_eq_sub1(int, all_103_2, all_105_4, 0, all_86_13) = 0) | 206.81/127.86 | (length1(int, all_103_2) = v0 & ( ~ ($lesseq(all_86_13, v0)) | ~ 206.81/127.86 | ($lesseq(0, v0)) | ( ~ (v1 = v0) & length1(int, all_105_4) = 206.81/127.86 | v1)))) 206.81/127.86 | 206.81/127.86 | GROUND_INST: instantiating (20) with int, all_103_1, all_105_3, all_105_1, 206.81/127.86 | all_86_11, $sum(all_86_10, 1), simplifying with (12), (43) gives: 206.81/127.86 | (84) ~ (permut2(int, all_105_3, all_105_1, all_86_11, $sum(all_86_10, 1)) 206.81/127.86 | = 0) | permut2(int, all_103_1, all_105_1, all_86_11, $sum(all_86_10, 206.81/127.86 | 1)) = 0 206.81/127.86 | 206.81/127.86 | GROUND_INST: instantiating (20) with int, all_103_3, all_103_1, all_105_3, 206.81/127.86 | all_86_11, $sum(all_86_10, 1), simplifying with (12), (43), (48) 206.81/127.86 | gives: 206.81/127.86 | (85) permut2(int, all_103_3, all_105_3, all_86_11, $sum(all_86_10, 1)) = 0 206.81/127.86 | 206.81/127.86 | DELTA: instantiating (82) with fresh symbols all_600_0, all_600_1 gives: 206.81/127.86 | (86) (all_600_0 = all_600_1 & $lesseq(all_86_13, all_600_1) & $lesseq(0, 206.81/127.86 | all_600_1) & $lesseq(0, all_86_13) & length1(int, all_105_4) = 206.81/127.86 | all_600_1 & length1(int, all_103_2) = all_600_1) | ( ~ (all_600_1 = 206.81/127.86 | 0) & array_eq_sub1(int, all_103_2, all_105_4, 0, all_86_13) = 206.81/127.86 | all_600_1) 206.81/127.86 | 206.81/127.86 | DELTA: instantiating (80) with fresh symbols all_603_0, all_603_1 gives: 206.81/127.86 | (87) (all_603_0 = all_603_1 & $lesseq(all_86_13, all_603_1) & $lesseq(0, 206.81/127.86 | all_603_1) & $lesseq(0, all_86_13) & length1(int, all_105_2) = 206.81/127.86 | all_603_1 & length1(int, all_105_4) = all_603_1) | ( ~ (all_603_1 = 206.81/127.86 | 0) & array_eq_sub1(int, all_105_4, all_105_2, 0, all_86_13) = 206.81/127.86 | all_603_1) 206.81/127.86 | 206.81/127.86 | BETA: splitting (83) gives: 206.81/127.86 | 206.81/127.86 | Case 1: 206.81/127.86 | | 206.81/127.86 | | (88) $lesseq(all_86_13, -1) 206.81/127.86 | | 206.81/127.86 | | COMBINE_INEQS: (14), (88) imply: 206.81/127.86 | | (89) $lesseq(0, -1) 206.81/127.86 | | 206.81/127.86 | | CLOSE: (89) is inconsistent. 206.81/127.86 | | 206.81/127.86 | Case 2: 206.81/127.86 | | 206.81/127.86 | | (90) ? [v0: $int] : ? [v1: $int] : ((v0 = 0 & array_eq_sub1(int, 206.81/127.86 | | all_103_2, all_105_4, 0, all_86_13) = 0) | (length1(int, 206.81/127.86 | | all_103_2) = v0 & ( ~ ($lesseq(all_86_13, v0)) | ~ 206.81/127.86 | | ($lesseq(0, v0)) | ( ~ (v1 = v0) & length1(int, all_105_4) = 206.81/127.86 | | v1)))) 206.81/127.86 | | 206.81/127.86 | | DELTA: instantiating (90) with fresh symbols all_609_0, all_609_1 gives: 206.81/127.86 | | (91) (all_609_1 = 0 & array_eq_sub1(int, all_103_2, all_105_4, 0, 206.81/127.86 | | all_86_13) = 0) | (length1(int, all_103_2) = all_609_1 & ( ~ 206.81/127.86 | | ($lesseq(all_86_13, all_609_1)) | ~ ($lesseq(0, all_609_1)) | ( 206.81/127.86 | | ~ (all_609_0 = all_609_1) & length1(int, all_105_4) = 206.81/127.86 | | all_609_0))) 206.81/127.86 | | 206.81/127.86 | | BETA: splitting (91) gives: 206.81/127.86 | | 206.81/127.86 | | Case 1: 206.81/127.86 | | | 206.81/127.86 | | | (92) all_609_1 = 0 & array_eq_sub1(int, all_103_2, all_105_4, 0, 206.81/127.86 | | | all_86_13) = 0 206.81/127.86 | | | 206.81/127.86 | | | ALPHA: (92) implies: 206.81/127.86 | | | (93) array_eq_sub1(int, all_103_2, all_105_4, 0, all_86_13) = 0 206.81/127.86 | | | 206.81/127.86 | | | BETA: splitting (86) gives: 206.81/127.86 | | | 206.81/127.86 | | | Case 1: 206.81/127.86 | | | | 206.81/127.86 | | | | (94) all_600_0 = all_600_1 & $lesseq(all_86_13, all_600_1) & 206.81/127.86 | | | | $lesseq(0, all_600_1) & $lesseq(0, all_86_13) & length1(int, 206.81/127.86 | | | | all_105_4) = all_600_1 & length1(int, all_103_2) = all_600_1 206.81/127.86 | | | | 206.81/127.86 | | | | ALPHA: (94) implies: 206.81/127.86 | | | | (95) length1(int, all_103_2) = all_600_1 206.81/127.86 | | | | (96) length1(int, all_105_4) = all_600_1 206.81/127.86 | | | | 206.81/127.86 | | | | BETA: splitting (81) gives: 206.81/127.86 | | | | 206.81/127.86 | | | | Case 1: 206.81/127.86 | | | | | 206.81/127.86 | | | | | (97) $lesseq(all_86_13, -1) 206.81/127.86 | | | | | 206.81/127.86 | | | | | COMBINE_INEQS: (14), (97) imply: 206.81/127.86 | | | | | (98) $lesseq(0, -1) 206.81/127.86 | | | | | 206.81/127.86 | | | | | CLOSE: (98) is inconsistent. 206.81/127.86 | | | | | 206.81/127.86 | | | | Case 2: 206.81/127.86 | | | | | 206.81/127.87 | | | | | (99) ? [v0: $int] : ? [v1: $int] : ((v0 = 0 & array_eq_sub1(int, 206.81/127.87 | | | | | all_105_4, all_105_2, 0, all_86_13) = 0) | (length1(int, 206.81/127.87 | | | | | all_105_4) = v0 & ( ~ ($lesseq(all_86_13, v0)) | ~ 206.81/127.87 | | | | | ($lesseq(0, v0)) | ( ~ (v1 = v0) & length1(int, 206.81/127.87 | | | | | all_105_2) = v1)))) 206.81/127.87 | | | | | 206.81/127.87 | | | | | DELTA: instantiating (99) with fresh symbols all_631_0, all_631_1 206.81/127.87 | | | | | gives: 206.81/127.87 | | | | | (100) (all_631_1 = 0 & array_eq_sub1(int, all_105_4, all_105_2, 0, 206.81/127.87 | | | | | all_86_13) = 0) | (length1(int, all_105_4) = all_631_1 & 206.81/127.87 | | | | | ( ~ ($lesseq(all_86_13, all_631_1)) | ~ ($lesseq(0, 206.81/127.87 | | | | | all_631_1)) | ( ~ (all_631_0 = all_631_1) & 206.81/127.87 | | | | | length1(int, all_105_2) = all_631_0))) 206.81/127.87 | | | | | 206.81/127.87 | | | | | GROUND_INST: instantiating (66) with all_86_13, all_600_1, all_103_2, 206.81/127.87 | | | | | int, simplifying with (3), (95) gives: 206.81/127.87 | | | | | (101) all_600_1 = all_86_13 206.81/127.87 | | | | | 206.81/127.87 | | | | | BETA: splitting (100) gives: 206.81/127.87 | | | | | 206.81/127.87 | | | | | Case 1: 206.81/127.87 | | | | | | 206.81/127.87 | | | | | | (102) all_631_1 = 0 & array_eq_sub1(int, all_105_4, all_105_2, 0, 206.81/127.87 | | | | | | all_86_13) = 0 206.81/127.87 | | | | | | 206.81/127.87 | | | | | | ALPHA: (102) implies: 206.81/127.87 | | | | | | (103) array_eq_sub1(int, all_105_4, all_105_2, 0, all_86_13) = 0 206.81/127.87 | | | | | | 206.81/127.87 | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (11), (12), (13), 206.81/127.87 | | | | | | (15), (16), (17), (18), (19), (20), (21), (22), (23), 206.81/127.87 | | | | | | (24), (25), (26), (27), (29), (30), (31), (32), (33), 206.81/127.87 | | | | | | (34), (35), (36), (37), (38), (39), (40), (41), (42), 206.81/127.87 | | | | | | (43), (44), (45), (46), (47), (48), (49), (50), (51), 206.81/127.87 | | | | | | (52), (53), (54), (55), (56), (57), (58), (59), (60), 206.81/127.87 | | | | | | (61), (62), (63), (64), (65), (66), (67), (69), (70), 206.81/127.87 | | | | | | (71), (72), (73), (75), (84), (85), (87), (103) are 206.81/127.87 | | | | | | inconsistent by sub-proof #85. 206.81/127.87 | | | | | | 206.81/127.87 | | | | | Case 2: 206.81/127.87 | | | | | | 206.81/127.87 | | | | | | (104) length1(int, all_105_4) = all_631_1 & ( ~ 206.81/127.87 | | | | | | ($lesseq(all_86_13, all_631_1)) | ~ ($lesseq(0, 206.81/127.87 | | | | | | all_631_1)) | ( ~ (all_631_0 = all_631_1) & 206.81/127.87 | | | | | | length1(int, all_105_2) = all_631_0)) 206.81/127.87 | | | | | | 206.81/127.87 | | | | | | ALPHA: (104) implies: 206.81/127.87 | | | | | | (105) length1(int, all_105_4) = all_631_1 206.81/127.87 | | | | | | (106) ~ ($lesseq(all_86_13, all_631_1)) | ~ ($lesseq(0, 206.81/127.87 | | | | | | all_631_1)) | ( ~ (all_631_0 = all_631_1) & 206.81/127.87 | | | | | | length1(int, all_105_2) = all_631_0) 206.81/127.87 | | | | | | 206.81/127.87 | | | | | | GROUND_INST: instantiating (66) with all_86_13, all_631_1, 206.81/127.87 | | | | | | all_105_4, int, simplifying with (30), (105) gives: 206.81/127.87 | | | | | | (107) all_631_1 = all_86_13 206.81/127.87 | | | | | | 206.81/127.87 | | | | | | BETA: splitting (106) gives: 206.81/127.87 | | | | | | 206.81/127.87 | | | | | | Case 1: 206.81/127.87 | | | | | | | 206.81/127.87 | | | | | | | (108) $lesseq(all_631_1, -1) 206.81/127.87 | | | | | | | 206.81/127.87 | | | | | | | REDUCE: (107), (108) imply: 206.81/127.87 | | | | | | | (109) $lesseq(all_86_13, -1) 206.81/127.87 | | | | | | | 206.81/127.87 | | | | | | | COMBINE_INEQS: (42), (53) imply: 206.81/127.87 | | | | | | | (110) $lesseq(1, $difference(all_86_10, all_86_8)) 206.81/127.87 | | | | | | | 206.81/127.87 | | | | | | | COMBINE_INEQS: (40), (110) imply: 206.81/127.87 | | | | | | | (111) $lesseq(1, $difference(all_86_10, all_86_11)) 206.81/127.87 | | | | | | | 206.81/127.87 | | | | | | | COMBINE_INEQS: (55), (111) imply: 206.81/127.87 | | | | | | | (112) $lesseq(2, $difference(all_86_13, all_86_11)) 206.81/127.87 | | | | | | | 206.81/127.87 | | | | | | | COMBINE_INEQS: (14), (109) imply: 206.81/127.87 | | | | | | | (113) $lesseq(0, -1) 206.81/127.87 | | | | | | | 206.81/127.87 | | | | | | | CLOSE: (113) is inconsistent. 206.81/127.87 | | | | | | | 206.81/127.87 | | | | | | Case 2: 206.81/127.87 | | | | | | | 206.81/127.87 | | | | | | | (114) ~ ($lesseq(all_86_13, all_631_1)) | ( ~ (all_631_0 = 206.81/127.87 | | | | | | | all_631_1) & length1(int, all_105_2) = all_631_0) 206.81/127.87 | | | | | | | 206.81/127.87 | | | | | | | BETA: splitting (114) gives: 206.81/127.87 | | | | | | | 206.81/127.87 | | | | | | | Case 1: 206.81/127.87 | | | | | | | | 206.81/127.87 | | | | | | | | (115) $lesseq(1, $difference(all_86_13, all_631_1)) 206.81/127.87 | | | | | | | | 206.81/127.87 | | | | | | | | REDUCE: (107), (115) imply: 206.81/127.87 | | | | | | | | (116) $lesseq(0, -1) 206.81/127.87 | | | | | | | | 206.81/127.87 | | | | | | | | CLOSE: (116) is inconsistent. 206.81/127.87 | | | | | | | | 206.81/127.87 | | | | | | | Case 2: 206.81/127.87 | | | | | | | | 206.81/127.87 | | | | | | | | (117) ~ (all_631_0 = all_631_1) & length1(int, all_105_2) = 206.81/127.87 | | | | | | | | all_631_0 206.81/127.87 | | | | | | | | 206.81/127.87 | | | | | | | | ALPHA: (117) implies: 206.81/127.87 | | | | | | | | (118) ~ (all_631_0 = all_631_1) 206.81/127.87 | | | | | | | | (119) length1(int, all_105_2) = all_631_0 206.81/127.87 | | | | | | | | 206.81/127.87 | | | | | | | | REDUCE: (107), (118) imply: 206.81/127.87 | | | | | | | | (120) ~ (all_631_0 = all_86_13) 206.81/127.87 | | | | | | | | 206.81/127.87 | | | | | | | | GROUND_INST: instantiating (66) with all_86_13, all_631_0, 206.81/127.87 | | | | | | | | all_105_2, int, simplifying with (7), (119) gives: 206.81/127.87 | | | | | | | | (121) all_631_0 = all_86_13 206.81/127.87 | | | | | | | | 206.81/127.87 | | | | | | | | REDUCE: (120), (121) imply: 206.81/127.87 | | | | | | | | (122) ~ (0 = 0) 206.81/127.87 | | | | | | | | 206.81/127.87 | | | | | | | | CLOSE: (122) is inconsistent. 206.81/127.87 | | | | | | | | 206.81/127.87 | | | | | | | End of split 206.81/127.87 | | | | | | | 206.81/127.87 | | | | | | End of split 206.81/127.87 | | | | | | 206.81/127.87 | | | | | End of split 206.81/127.87 | | | | | 206.81/127.87 | | | | End of split 206.81/127.87 | | | | 206.81/127.87 | | | Case 2: 206.81/127.87 | | | | 206.81/127.87 | | | | (123) ~ (all_600_1 = 0) & array_eq_sub1(int, all_103_2, all_105_4, 206.81/127.87 | | | | 0, all_86_13) = all_600_1 206.81/127.87 | | | | 206.81/127.87 | | | | ALPHA: (123) implies: 206.81/127.87 | | | | (124) ~ (all_600_1 = 0) 206.81/127.87 | | | | (125) array_eq_sub1(int, all_103_2, all_105_4, 0, all_86_13) = 206.81/127.87 | | | | all_600_1 206.81/127.87 | | | | 206.81/127.87 | | | | GROUND_INST: instantiating (27) with 0, all_600_1, all_86_13, 0, 206.81/127.87 | | | | all_105_4, all_103_2, int, simplifying with (93), (125) 206.81/127.87 | | | | gives: 206.81/127.87 | | | | (126) all_600_1 = 0 206.81/127.87 | | | | 206.81/127.87 | | | | REDUCE: (124), (126) imply: 206.81/127.87 | | | | (127) ~ (0 = 0) 206.81/127.87 | | | | 206.81/127.87 | | | | CLOSE: (127) is inconsistent. 206.81/127.87 | | | | 206.81/127.87 | | | End of split 206.81/127.87 | | | 206.81/127.87 | | Case 2: 206.81/127.87 | | | 206.81/127.87 | | | (128) length1(int, all_103_2) = all_609_1 & ( ~ ($lesseq(all_86_13, 206.81/127.87 | | | all_609_1)) | ~ ($lesseq(0, all_609_1)) | ( ~ (all_609_0 = 206.81/127.87 | | | all_609_1) & length1(int, all_105_4) = all_609_0)) 206.81/127.87 | | | 206.81/127.87 | | | ALPHA: (128) implies: 206.81/127.87 | | | (129) length1(int, all_103_2) = all_609_1 206.81/127.87 | | | (130) ~ ($lesseq(all_86_13, all_609_1)) | ~ ($lesseq(0, all_609_1)) | 206.81/127.87 | | | ( ~ (all_609_0 = all_609_1) & length1(int, all_105_4) = 206.81/127.87 | | | all_609_0) 206.81/127.87 | | | 206.81/127.87 | | | BETA: splitting (81) gives: 206.81/127.87 | | | 206.81/127.87 | | | Case 1: 206.81/127.87 | | | | 206.81/127.87 | | | | (131) $lesseq(all_86_13, -1) 206.81/127.87 | | | | 206.81/127.87 | | | | COMBINE_INEQS: (14), (131) imply: 206.81/127.87 | | | | (132) $lesseq(0, -1) 206.81/127.87 | | | | 206.81/127.87 | | | | CLOSE: (132) is inconsistent. 206.81/127.87 | | | | 206.81/127.87 | | | Case 2: 206.81/127.87 | | | | 206.81/127.87 | | | | (133) ? [v0: $int] : ? [v1: $int] : ((v0 = 0 & array_eq_sub1(int, 206.81/127.87 | | | | all_105_4, all_105_2, 0, all_86_13) = 0) | (length1(int, 206.81/127.87 | | | | all_105_4) = v0 & ( ~ ($lesseq(all_86_13, v0)) | ~ 206.81/127.87 | | | | ($lesseq(0, v0)) | ( ~ (v1 = v0) & length1(int, 206.81/127.87 | | | | all_105_2) = v1)))) 206.81/127.87 | | | | 206.81/127.87 | | | | DELTA: instantiating (133) with fresh symbols all_625_0, all_625_1 206.81/127.87 | | | | gives: 206.81/127.87 | | | | (134) (all_625_1 = 0 & array_eq_sub1(int, all_105_4, all_105_2, 0, 206.81/127.87 | | | | all_86_13) = 0) | (length1(int, all_105_4) = all_625_1 & ( 206.81/127.87 | | | | ~ ($lesseq(all_86_13, all_625_1)) | ~ ($lesseq(0, 206.81/127.87 | | | | all_625_1)) | ( ~ (all_625_0 = all_625_1) & 206.81/127.87 | | | | length1(int, all_105_2) = all_625_0))) 206.81/127.87 | | | | 206.81/127.87 | | | | BETA: splitting (134) gives: 206.81/127.87 | | | | 206.81/127.87 | | | | Case 1: 206.81/127.87 | | | | | 206.81/127.87 | | | | | (135) all_625_1 = 0 & array_eq_sub1(int, all_105_4, all_105_2, 0, 206.81/127.87 | | | | | all_86_13) = 0 206.81/127.87 | | | | | 206.81/127.87 | | | | | ALPHA: (135) implies: 206.81/127.87 | | | | | (136) array_eq_sub1(int, all_105_4, all_105_2, 0, all_86_13) = 0 206.81/127.87 | | | | | 206.81/127.87 | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (11), (12), (13), 206.81/127.87 | | | | | (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), 206.81/127.87 | | | | | (25), (26), (27), (29), (30), (31), (32), (33), (34), (35), 206.81/127.87 | | | | | (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), 206.81/127.87 | | | | | (46), (47), (48), (49), (50), (51), (52), (53), (54), (55), 206.81/127.87 | | | | | (56), (57), (58), (59), (60), (61), (62), (63), (64), (65), 206.81/127.87 | | | | | (66), (67), (69), (70), (71), (72), (73), (75), (84), (85), 206.81/127.87 | | | | | (87), (136) are inconsistent by sub-proof #85. 206.81/127.87 | | | | | 206.81/127.87 | | | | Case 2: 206.81/127.87 | | | | | 206.81/127.87 | | | | | (137) length1(int, all_105_4) = all_625_1 & ( ~ ($lesseq(all_86_13, 206.81/127.87 | | | | | all_625_1)) | ~ ($lesseq(0, all_625_1)) | ( ~ 206.81/127.87 | | | | | (all_625_0 = all_625_1) & length1(int, all_105_2) = 206.81/127.87 | | | | | all_625_0)) 206.81/127.87 | | | | | 206.81/127.87 | | | | | ALPHA: (137) implies: 206.81/127.87 | | | | | (138) length1(int, all_105_4) = all_625_1 206.81/127.87 | | | | | 206.81/127.87 | | | | | GROUND_INST: instantiating (66) with all_86_13, all_625_1, all_105_4, 206.81/127.87 | | | | | int, simplifying with (30), (138) gives: 206.81/127.87 | | | | | (139) all_625_1 = all_86_13 206.81/127.87 | | | | | 206.81/127.87 | | | | | GROUND_INST: instantiating (66) with all_86_13, all_609_1, all_103_2, 206.81/127.87 | | | | | int, simplifying with (3), (129) gives: 206.81/127.87 | | | | | (140) all_609_1 = all_86_13 206.81/127.87 | | | | | 206.81/127.87 | | | | | BETA: splitting (130) gives: 206.81/127.87 | | | | | 206.81/127.87 | | | | | Case 1: 206.81/127.87 | | | | | | 206.81/127.87 | | | | | | (141) $lesseq(all_609_1, -1) 206.81/127.87 | | | | | | 206.81/127.87 | | | | | | REDUCE: (140), (141) imply: 206.81/127.87 | | | | | | (142) $lesseq(all_86_13, -1) 206.81/127.87 | | | | | | 206.81/127.87 | | | | | | COMBINE_INEQS: (42), (53) imply: 206.81/127.87 | | | | | | (143) $lesseq(1, $difference(all_86_10, all_86_8)) 206.81/127.87 | | | | | | 206.81/127.87 | | | | | | COMBINE_INEQS: (40), (143) imply: 206.81/127.87 | | | | | | (144) $lesseq(1, $difference(all_86_10, all_86_11)) 206.81/127.87 | | | | | | 206.81/127.87 | | | | | | COMBINE_INEQS: (55), (144) imply: 206.81/127.87 | | | | | | (145) $lesseq(2, $difference(all_86_13, all_86_11)) 206.81/127.87 | | | | | | 206.81/127.87 | | | | | | COMBINE_INEQS: (14), (142) imply: 206.81/127.87 | | | | | | (146) $lesseq(0, -1) 206.81/127.87 | | | | | | 206.81/127.87 | | | | | | CLOSE: (146) is inconsistent. 206.81/127.87 | | | | | | 206.81/127.87 | | | | | Case 2: 206.81/127.87 | | | | | | 206.81/127.87 | | | | | | (147) ~ ($lesseq(all_86_13, all_609_1)) | ( ~ (all_609_0 = 206.81/127.87 | | | | | | all_609_1) & length1(int, all_105_4) = all_609_0) 206.81/127.87 | | | | | | 206.81/127.87 | | | | | | BETA: splitting (147) gives: 206.81/127.87 | | | | | | 206.81/127.87 | | | | | | Case 1: 206.81/127.87 | | | | | | | 206.81/127.87 | | | | | | | (148) $lesseq(1, $difference(all_86_13, all_609_1)) 206.81/127.87 | | | | | | | 206.81/127.87 | | | | | | | REDUCE: (140), (148) imply: 206.81/127.87 | | | | | | | (149) $lesseq(0, -1) 206.81/127.87 | | | | | | | 206.81/127.87 | | | | | | | CLOSE: (149) is inconsistent. 206.81/127.87 | | | | | | | 206.81/127.87 | | | | | | Case 2: 206.81/127.87 | | | | | | | 206.81/127.87 | | | | | | | (150) ~ (all_609_0 = all_609_1) & length1(int, all_105_4) = 206.81/127.87 | | | | | | | all_609_0 206.81/127.87 | | | | | | | 206.81/127.87 | | | | | | | ALPHA: (150) implies: 206.81/127.87 | | | | | | | (151) ~ (all_609_0 = all_609_1) 206.81/127.87 | | | | | | | (152) length1(int, all_105_4) = all_609_0 206.81/127.87 | | | | | | | 206.81/127.87 | | | | | | | REDUCE: (140), (151) imply: 206.81/127.87 | | | | | | | (153) ~ (all_609_0 = all_86_13) 206.81/127.87 | | | | | | | 206.81/127.87 | | | | | | | GROUND_INST: instantiating (66) with all_86_13, all_609_0, 206.81/127.87 | | | | | | | all_105_4, int, simplifying with (30), (152) gives: 206.81/127.87 | | | | | | | (154) all_609_0 = all_86_13 206.81/127.87 | | | | | | | 206.81/127.87 | | | | | | | REDUCE: (153), (154) imply: 206.81/127.87 | | | | | | | (155) ~ (0 = 0) 206.81/127.87 | | | | | | | 206.81/127.87 | | | | | | | CLOSE: (155) is inconsistent. 206.81/127.87 | | | | | | | 206.81/127.87 | | | | | | End of split 206.81/127.87 | | | | | | 206.81/127.87 | | | | | End of split 206.81/127.87 | | | | | 206.81/127.87 | | | | End of split 206.81/127.87 | | | | 206.81/127.87 | | | End of split 206.81/127.87 | | | 206.81/127.87 | | End of split 206.81/127.87 | | 206.81/127.87 | End of split 206.81/127.87 | 206.81/127.87 End of proof 206.81/127.87 206.81/127.87 Sub-proof #85 shows that the following formulas are inconsistent: 206.81/127.87 ---------------------------------------------------------------- 206.81/127.87 (1) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ (tb2t1(v2) 206.81/127.87 = v1) | ~ (tb2t1(v2) = v0)) 206.81/127.87 (2) ! [v0: $int] : ! [v1: $int] : ( ~ ($lesseq(43, v1)) | ~ ($lesseq(v0, 206.81/127.87 all_86_8)) | ~ ($lesseq(all_86_11, v0)) | ~ (get3(all_86_6, v0) = 206.81/127.87 v1)) 206.81/127.87 (3) array_eq_sub1(int, all_105_4, all_105_2, 0, all_86_13) = 0 206.81/127.87 (4) length1(int, all_103_2) = all_86_13 206.81/127.87 (5) in_map_int_int(all_86_6) 206.81/127.87 (6) in_map_int_int(all_86_12) 206.81/127.87 (7) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.81/127.87 $int] : ! [v5: $int] : ! [v6: $int] : ( ~ ($lesseq(0, v4)) | ~ 206.81/127.87 ($lesseq(0, v3)) | ~ (map_eq_sub1(v0, v5, v6, v3, v4) = 0) | ~ 206.81/127.87 (elts(v0, v2) = v6) | ~ (elts(v0, v1) = v5) | ~ in_ty(v0) | ? [v7: 206.81/127.87 $int] : ? [v8: $int] : ((v7 = 0 & array_eq_sub1(v0, v1, v2, v3, v4) 206.81/127.87 = 0) | (length1(v0, v1) = v7 & ( ~ ($lesseq(v4, v7)) | ~ 206.81/127.87 ($lesseq(v3, v7)) | ( ~ (v8 = v7) & length1(v0, v2) = v8))))) 206.81/127.87 (8) elts(int, all_103_4) = all_103_3 206.81/127.87 (9) t2tb2(all_86_3) = all_105_4 206.81/127.87 (10) t2tb(all_86_2) = all_105_1 206.81/127.87 (11) in_ty(int) 206.81/127.87 (12) length1(int, all_103_4) = all_86_13 206.81/127.87 (13) ( ~ (all_133_0 = 42) & $lesseq(1, $difference(all_86_7, all_133_2)) & 206.81/127.87 $lesseq(1, $difference(all_133_2, all_86_8)) & tb2t1(all_133_1) = 206.81/127.87 all_133_0 & get4(int, all_133_3, all_133_2) = all_133_1 & 206.81/127.87 in_uni(all_133_1)) | ($lesseq(all_133_0, 41) & $lesseq(all_133_2, 206.81/127.87 all_86_10) & $lesseq(all_86_7, all_133_2) & tb2t1(all_133_1) = 206.81/127.87 all_133_0 & get4(int, all_133_3, all_133_2) = all_133_1 & 206.81/127.87 in_uni(all_133_1)) | ($lesseq(43, all_133_0) & $lesseq(all_133_2, 206.81/127.87 all_86_8) & $lesseq(all_86_11, all_133_2) & tb2t1(all_133_1) = 206.81/127.87 all_133_0 & get4(int, all_133_3, all_133_2) = all_133_1 & 206.81/127.87 in_uni(all_133_1)) 206.81/127.87 (14) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.81/127.87 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 206.81/127.87 (permut2(v0, v5, v6, v3, v4) = v7) | ~ (elts(v0, v2) = v6) | ~ 206.81/127.87 (elts(v0, v1) = v5) | ~ in_ty(v0) | ? [v8: $int] : ? [v9: $int] : 206.81/127.87 ((v9 = v8 & v7 = 0 & $lesseq(v4, v8) & $lesseq(v3, v8) & $lesseq(0, 206.81/127.87 v4) & $lesseq(0, v3) & length1(v0, v2) = v8 & length1(v0, v1) = 206.81/127.87 v8) | ( ~ (v8 = 0) & permut3(v0, v1, v2, v3, v4) = v8))) 206.81/127.87 (15) all_125_0 = all_105_4 206.81/127.87 (16) $lesseq(-1, all_86_8) 206.81/127.87 (17) $lesseq(all_86_7, all_86_13) 206.81/127.87 (18) ~ (permut2(int, all_105_3, all_105_1, all_86_11, $sum(all_86_10, 1)) = 206.81/127.87 0) | permut2(int, all_103_1, all_105_1, all_86_11, $sum(all_86_10, 1)) 206.81/127.87 = 0 206.81/127.87 (19) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.81/127.87 $int] : ! [v5: $int] : ( ~ (permut2(v0, v2, v3, v4, v5) = 0) | ~ 206.81/127.87 (permut2(v0, v1, v2, v4, v5) = 0) | ~ in_ty(v0) | permut2(v0, v1, v3, 206.81/127.87 v4, v5) = 0) 206.81/127.87 (20) ! [v0: $int] : ! [v1: $int] : (v1 = 42 | ~ ($lesseq(1, 206.81/127.87 $difference(all_86_7, v0))) | ~ ($lesseq(1, $difference(v0, 206.81/127.88 all_86_8))) | ~ (get3(all_86_6, v0) = v1)) 206.81/127.88 (21) map_eq_sub1(int, all_103_3, all_103_1, $sum(all_86_10, 1), all_86_13) = 206.81/127.88 0 206.81/127.88 (22) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.81/127.88 $int] : ! [v5: $int] : ! [v6: $int] : ( ~ (permut2(v0, v3, v4, 0, 206.81/127.88 v5) = v6) | ~ (length1(v0, v1) = v5) | ~ (elts(v0, v2) = v4) | 206.81/127.88 ~ (elts(v0, v1) = v3) | ~ in_ty(v0) | ? [v7: $int] : ((v7 = v5 & v6 206.81/127.88 = 0 & length1(v0, v2) = v5) | ( ~ (v7 = 0) & permut_all(v0, v1, 206.81/127.88 v2) = v7))) 206.81/127.88 (23) t2tb(all_86_6) = all_103_1 206.81/127.88 (24) map_eq_sub1(int, all_103_1, all_105_3, $sum(all_86_8, 1), all_86_13) = 0 206.81/127.88 (25) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.81/127.88 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ (permut3(v6, v5, 206.81/127.88 v4, v3, v2) = v1) | ~ (permut3(v6, v5, v4, v3, v2) = v0)) 206.81/127.88 (26) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.81/127.88 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ 206.81/127.88 (array_eq_sub1(v6, v5, v4, v3, v2) = v1) | ~ (array_eq_sub1(v6, v5, 206.81/127.88 v4, v3, v2) = v0)) 206.81/127.88 (27) permut2(int, all_103_3, all_105_3, all_86_11, $sum(all_86_10, 1)) = 0 206.81/127.88 (28) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 206.81/127.88 | ~ (elts(v3, v2) = v1) | ~ (elts(v3, v2) = v0)) 206.81/127.88 (29) length1(int, all_105_4) = all_86_13 206.81/127.88 (30) in_array_int(all_86_3) 206.81/127.88 (31) (all_603_0 = all_603_1 & $lesseq(all_86_13, all_603_1) & $lesseq(0, 206.81/127.88 all_603_1) & $lesseq(0, all_86_13) & length1(int, all_105_2) = 206.81/127.88 all_603_1 & length1(int, all_105_4) = all_603_1) | ( ~ (all_603_1 = 0) 206.81/127.88 & array_eq_sub1(int, all_105_4, all_105_2, 0, all_86_13) = all_603_1) 206.81/127.88 (32) elts(int, all_105_4) = all_105_3 206.81/127.88 (33) map_eq_sub1(int, all_105_3, all_105_1, 0, all_86_7) = 0 206.81/127.88 (34) tb2t(all_105_1) = all_86_2 206.81/127.88 (35) permut2(int, all_103_1, all_105_3, all_86_11, $sum(all_86_8, 1)) = 0 206.81/127.88 (36) elts(int, all_105_2) = all_105_1 206.81/127.88 (37) map_eq_sub1(int, all_103_3, all_103_1, 0, all_86_11) = 0 206.81/127.88 (38) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.81/127.88 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 206.81/127.88 ($lesseq(1, $difference(v4, v5))) | ~ ($lesseq(v3, v5)) | ~ 206.81/127.88 (permut2(v0, v1, v2, v3, v4) = 0) | ~ (t2tb1(v5) = v6) | ~ (get(v0, 206.81/127.88 int, v2, v6) = v7) | ~ in_ty(v0) | ? [v8: $int] : ? [v9: $int] 206.81/127.88 : ($lesseq(1, $difference(v4, v8)) & $lesseq(v3, v8) & t2tb1(v8) = v9 206.81/127.88 & get(v0, int, v1, v9) = v7 & in_uni(v9) & in_uni(v7))) 206.81/127.88 (39) t2tb2(all_86_1) = all_105_2 206.81/127.88 (40) $lesseq(all_86_11, all_86_8) 206.81/127.88 (41) ~ (permut2(int, all_105_3, all_105_1, 0, all_86_13) = 0) | ? [v0: 206.81/127.88 $int] : ((v0 = 0 & permut_all(int, all_105_4, all_105_2) = 0) | ( ~ 206.81/127.88 (v0 = all_86_13) & length1(int, all_105_2) = v0)) 206.81/127.88 (42) $lesseq(all_86_7, all_86_10) 206.81/127.88 (43) permut2(int, all_103_1, all_105_3, all_86_11, $sum(all_86_10, 1)) = 0 206.81/127.88 (44) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.81/127.88 $int] : ! [v5: $int] : ( ~ (elts(v0, v1) = v3) | ~ (t2tb1(v2) = v4) 206.81/127.88 | ~ (get(v0, int, v3, v4) = v5) | ~ in_ty(v0) | (get4(v0, v1, v2) = 206.81/127.88 v5 & in_uni(v5))) 206.81/127.88 (45) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.81/127.88 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 206.81/127.88 ($lesseq(1, $difference(v3, v4))) | ~ ($lesseq(v2, v4)) | ~ 206.81/127.88 (permut2(int, v5, v6, v2, v3) = 0) | ~ (t2tb(v1) = v6) | ~ (t2tb(v0) 206.81/127.88 = v5) | ~ (get3(v1, v4) = v7) | ~ in_map_int_int(v0) | ? [v8: 206.81/127.88 $int] : ($lesseq(1, $difference(v3, v8)) & $lesseq(v2, v8) & 206.81/127.88 get3(v0, v8) = v7)) 206.81/127.88 (46) $lesseq(0, all_86_7) 206.81/127.88 (47) permut2(int, all_105_3, all_105_1, all_86_7, $sum(all_86_10, 1)) = 0 206.81/127.88 (48) permut2(int, all_103_3, all_103_1, all_86_11, $sum(all_86_10, 1)) = 0 206.81/127.88 (49) ~ (permut2(int, all_103_3, all_103_1, 0, all_86_13) = 0) | ? [v0: 206.81/127.88 $int] : ((v0 = 0 & permut_all(int, all_103_4, all_103_2) = 0) | ( ~ 206.81/127.88 (v0 = all_86_13) & length1(int, all_103_2) = v0)) 206.81/127.88 (50) in_array_int(all_86_1) 206.81/127.88 (51) t2tb(all_86_12) = all_103_3 206.81/127.88 (52) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.81/127.88 $int] : ! [v5: $int] : ! [v6: $int] : ( ~ ($lesseq(0, v4)) | ~ 206.81/127.88 ($lesseq(0, v3)) | ~ (permut2(v0, v5, v6, v3, v4) = 0) | ~ (elts(v0, 206.81/127.88 v2) = v6) | ~ (elts(v0, v1) = v5) | ~ in_ty(v0) | ? [v7: $int] 206.81/127.88 : ? [v8: $int] : ((v7 = 0 & permut3(v0, v1, v2, v3, v4) = 0) | 206.81/127.88 (length1(v0, v1) = v7 & ( ~ ($lesseq(v4, v7)) | ~ ($lesseq(v3, v7)) 206.81/127.88 | ( ~ (v8 = v7) & length1(v0, v2) = v8))))) 206.81/127.88 (53) $lesseq(1, $difference(all_86_7, all_86_8)) 206.81/127.88 (54) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.81/127.88 $int] : ! [v5: $int] : ! [v6: $int] : ( ~ ($lesseq(1, 206.81/127.88 $difference(v4, v5))) | ~ ($lesseq(v3, v5)) | ~ (map_eq_sub1(v0, 206.81/127.88 v1, v2, v3, v4) = 0) | ~ (t2tb1(v5) = v6) | ~ in_ty(v0) | ? 206.81/127.88 [v7: $int] : (get(v0, int, v2, v6) = v7 & get(v0, int, v1, v6) = v7 & 206.81/127.88 in_uni(v7))) 206.81/127.88 (55) $lesseq(1, $difference(all_86_13, all_86_10)) 206.81/127.88 (56) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.81/127.88 $int] : ! [v5: $int] : (v5 = 0 | ~ (permut_sub2(v0, v1, v2, v3, v4) 206.81/127.88 = v5) | ~ in_ty(v0) | ? [v6: $int] : ? [v7: $int] : ? [v8: $int] 206.81/127.88 : ? [v9: $int] : (( ~ (v9 = 0) & map_eq_sub1(v0, v6, v7, v4, v8) = v9 206.81/127.88 & length1(v0, v1) = v8 & elts(v0, v2) = v7 & elts(v0, v1) = v6 & 206.81/127.88 in_uni(v7) & in_uni(v6)) | ( ~ (v8 = 0) & map_eq_sub1(v0, v6, v7, 206.81/127.88 0, v3) = v8 & elts(v0, v2) = v7 & elts(v0, v1) = v6 & in_uni(v7) 206.81/127.88 & in_uni(v6)) | ( ~ (v6 = 0) & permut3(v0, v1, v2, v3, v4) = v6))) 206.81/127.88 (57) in_map_int_int(all_86_4) 206.81/127.88 (58) map_eq_sub1(int, all_105_3, all_105_1, 0, all_86_13) = 0 206.81/127.88 (59) $lesseq(0, all_86_11) 206.81/127.88 (60) elts(int, all_103_2) = all_103_1 206.81/127.88 (61) ~ (permut2(int, all_103_1, all_105_3, 0, all_86_13) = 0) | ? [v0: 206.81/127.88 $int] : ((v0 = 0 & permut_all(int, all_103_2, all_105_4) = 0) | ( ~ 206.81/127.88 (v0 = all_86_13) & length1(int, all_105_4) = v0)) 206.81/127.88 (62) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ( ~ 206.81/127.88 (t2tb2(v0) = v2) | ~ (get4(int, v2, v1) = v3) | ~ in_array_int(v0) | 206.81/127.88 ? [v4: $int] : ? [v5: $int] : ? [v6: $int] : (tb2t(v4) = v5 & 206.81/127.88 tb2t1(v3) = v6 & get3(v5, v1) = v6 & elts(int, v2) = v4 & 206.81/127.88 in_map_int_int(v5) & in_uni(v4))) 206.81/127.88 (63) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ (tb2t(v2) 206.81/127.88 = v1) | ~ (tb2t(v2) = v0)) 206.81/127.88 (64) all_133_3 = all_105_2 206.81/127.88 (65) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.81/127.88 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 206.81/127.88 ($lesseq(1, $difference(v3, v6))) | ~ ($lesseq(v2, v6)) | ~ 206.81/127.88 (map_eq_sub1(int, v4, v5, v2, v3) = 0) | ~ (t2tb(v1) = v5) | ~ 206.81/127.88 (t2tb(v0) = v4) | ~ (get3(v1, v6) = v7) | ~ in_map_int_int(v0) | 206.81/127.88 get3(v0, v6) = v7) 206.81/127.88 (66) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 206.81/127.88 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 206.81/127.88 (67) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ( ~ 206.81/127.88 (get4(v0, v1, v2) = v3) | ~ in_ty(v0) | ? [v4: $int] : ? [v5: $int] 206.81/127.88 : (elts(v0, v1) = v4 & t2tb1(v2) = v5 & get(v0, int, v4, v5) = v3 & 206.81/127.88 in_uni(v5) & in_uni(v4) & in_uni(v3))) 206.81/127.88 (68) map_eq_sub1(int, all_103_1, all_105_3, 0, all_86_13) = 0 206.81/127.88 (69) ! [v0: $int] : ! [v1: $int] : ( ~ (tb2t1(v0) = v1) | ~ in_uni(v0) | 206.81/127.88 t2tb1(v1) = v0) 206.81/127.88 (70) map_eq_sub1(int, all_105_3, all_105_1, $sum(all_86_10, 1), all_86_13) = 206.81/127.88 0 206.81/127.88 (71) t2tb(all_86_4) = all_105_3 206.81/127.88 (72) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.81/127.88 $int] : ! [v5: $int] : ( ~ (permut3(v0, v1, v2, v3, v4) = v5) | ~ 206.81/127.88 in_ty(v0) | ? [v6: $int] : ? [v7: $int] : ? [v8: $int] : ? [v9: 206.81/127.88 $int] : ? [v10: $int] : ((v10 = 0 & v9 = 0 & v5 = 0 & 206.81/127.88 map_eq_sub1(v0, v6, v7, v4, v8) = 0 & map_eq_sub1(v0, v6, v7, 0, 206.81/127.88 v3) = 0 & length1(v0, v1) = v8 & elts(v0, v2) = v7 & elts(v0, 206.81/127.88 v1) = v6 & in_uni(v7) & in_uni(v6)) | ( ~ (v6 = 0) & 206.81/127.88 permut_sub2(v0, v1, v2, v3, v4) = v6))) 206.81/127.88 (73) ! [v0: $int] : ! [v1: $int] : ( ~ ($lesseq(v0, all_86_10)) | ~ 206.81/127.88 ($lesseq(all_86_7, v0)) | ~ (get4(int, all_125_0, v0) = v1) | ? [v2: 206.81/127.88 $int] : ($lesseq(42, v2) & tb2t1(v1) = v2)) 206.81/127.88 206.81/127.88 Begin of proof 206.81/127.88 | 206.81/127.88 | BETA: splitting (31) gives: 206.81/127.88 | 206.81/127.88 | Case 1: 206.81/127.88 | | 206.81/127.88 | | (74) all_603_0 = all_603_1 & $lesseq(all_86_13, all_603_1) & $lesseq(0, 206.81/127.88 | | all_603_1) & $lesseq(0, all_86_13) & length1(int, all_105_2) = 206.81/127.88 | | all_603_1 & length1(int, all_105_4) = all_603_1 206.81/127.88 | | 206.81/127.88 | | ALPHA: (74) implies: 206.81/127.88 | | (75) length1(int, all_105_4) = all_603_1 206.81/127.88 | | (76) length1(int, all_105_2) = all_603_1 206.81/127.88 | | 206.81/127.88 | | GROUND_INST: instantiating (66) with all_86_13, all_603_1, all_105_4, int, 206.81/127.88 | | simplifying with (29), (75) gives: 206.81/127.88 | | (77) all_603_1 = all_86_13 206.81/127.88 | | 206.81/127.88 | | COMBINE_INEQS: (42), (53) imply: 206.81/127.88 | | (78) $lesseq(1, $difference(all_86_10, all_86_8)) 206.81/127.88 | | 206.81/127.88 | | COMBINE_INEQS: (40), (78) imply: 206.81/127.88 | | (79) $lesseq(1, $difference(all_86_10, all_86_11)) 206.81/127.88 | | 206.81/127.88 | | COMBINE_INEQS: (16), (78) imply: 206.81/127.88 | | (80) $lesseq(0, all_86_10) 206.81/127.88 | | 206.81/127.88 | | COMBINE_INEQS: (55), (79) imply: 206.81/127.88 | | (81) $lesseq(2, $difference(all_86_13, all_86_11)) 206.81/127.88 | | 206.81/127.88 | | COMBINE_INEQS: (59), (81) imply: 206.81/127.88 | | (82) $lesseq(2, all_86_13) 206.81/127.88 | | 206.81/127.88 | | REDUCE: (76), (77) imply: 206.81/127.88 | | (83) length1(int, all_105_2) = all_86_13 206.81/127.88 | | 206.81/127.88 | | BETA: splitting (61) gives: 206.81/127.88 | | 206.81/127.88 | | Case 1: 206.81/127.88 | | | 206.81/127.88 | | | (84) ~ (permut2(int, all_103_1, all_105_3, 0, all_86_13) = 0) 206.81/127.88 | | | 206.81/127.88 | | | PRED_UNIFY: (35), (84) imply: 206.81/127.88 | | | (85) ~ ($difference(all_86_8, all_86_13) = -1) | ~ (all_86_11 = 0) 206.81/127.88 | | | 206.81/127.88 | | | REF_CLOSE: (1), (2), (5), (7), (8), (9), (10), (11), (12), (13), (14), 206.81/127.88 | | | (15), (16), (17), (20), (21), (23), (24), (25), (27), (28), 206.81/127.88 | | | (29), (30), (32), (33), (34), (35), (36), (37), (38), (39), 206.81/127.88 | | | (40), (41), (42), (43), (44), (45), (46), (47), (50), (52), 206.81/127.88 | | | (53), (54), (55), (56), (57), (58), (59), (62), (63), (64), 206.81/127.88 | | | (65), (66), (67), (68), (69), (70), (71), (72), (73), (80), 206.81/127.88 | | | (82), (83), (84), (85) are inconsistent by sub-proof #98. 206.81/127.88 | | | 206.81/127.88 | | Case 2: 206.81/127.88 | | | 206.81/127.88 | | | (86) permut2(int, all_103_1, all_105_3, 0, all_86_13) = 0 206.81/127.88 | | | 206.81/127.88 | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13), 206.81/127.88 | | | (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), 206.81/127.88 | | | (24), (25), (27), (28), (29), (30), (32), (33), (34), (35), 206.81/127.88 | | | (36), (37), (38), (39), (40), (41), (42), (44), (45), (46), 206.81/127.88 | | | (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), 206.81/127.88 | | | (57), (58), (59), (60), (62), (63), (64), (65), (66), (67), 206.81/127.88 | | | (68), (69), (70), (71), (72), (73), (80), (81), (82), (83), 206.81/127.88 | | | (86) are inconsistent by sub-proof #86. 206.81/127.88 | | | 206.81/127.88 | | End of split 206.81/127.88 | | 206.81/127.88 | Case 2: 206.81/127.88 | | 206.81/127.88 | | (87) ~ (all_603_1 = 0) & array_eq_sub1(int, all_105_4, all_105_2, 0, 206.81/127.88 | | all_86_13) = all_603_1 206.81/127.88 | | 206.81/127.88 | | ALPHA: (87) implies: 206.81/127.88 | | (88) ~ (all_603_1 = 0) 206.81/127.88 | | (89) array_eq_sub1(int, all_105_4, all_105_2, 0, all_86_13) = all_603_1 206.81/127.88 | | 206.81/127.88 | | GROUND_INST: instantiating (26) with 0, all_603_1, all_86_13, 0, all_105_2, 206.81/127.88 | | all_105_4, int, simplifying with (3), (89) gives: 206.81/127.88 | | (90) all_603_1 = 0 206.81/127.88 | | 206.81/127.88 | | REDUCE: (88), (90) imply: 206.81/127.88 | | (91) ~ (0 = 0) 206.81/127.88 | | 206.81/127.88 | | CLOSE: (91) is inconsistent. 206.81/127.88 | | 206.81/127.88 | End of split 206.81/127.88 | 206.81/127.88 End of proof 206.81/127.88 206.81/127.88 Sub-proof #86 shows that the following formulas are inconsistent: 206.81/127.88 ---------------------------------------------------------------- 206.81/127.88 (1) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ (tb2t1(v2) 206.81/127.88 = v1) | ~ (tb2t1(v2) = v0)) 206.81/127.88 (2) ! [v0: $int] : ! [v1: $int] : ( ~ ($lesseq(43, v1)) | ~ ($lesseq(v0, 206.81/127.88 all_86_8)) | ~ ($lesseq(all_86_11, v0)) | ~ (get3(all_86_6, v0) = 206.81/127.88 v1)) 206.81/127.88 (3) length1(int, all_103_2) = all_86_13 206.81/127.88 (4) in_map_int_int(all_86_6) 206.81/127.88 (5) in_map_int_int(all_86_12) 206.81/127.88 (6) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.81/127.88 $int] : ! [v5: $int] : ! [v6: $int] : ( ~ ($lesseq(0, v4)) | ~ 206.81/127.88 ($lesseq(0, v3)) | ~ (map_eq_sub1(v0, v5, v6, v3, v4) = 0) | ~ 206.81/127.88 (elts(v0, v2) = v6) | ~ (elts(v0, v1) = v5) | ~ in_ty(v0) | ? [v7: 206.81/127.88 $int] : ? [v8: $int] : ((v7 = 0 & array_eq_sub1(v0, v1, v2, v3, v4) 206.81/127.88 = 0) | (length1(v0, v1) = v7 & ( ~ ($lesseq(v4, v7)) | ~ 206.81/127.88 ($lesseq(v3, v7)) | ( ~ (v8 = v7) & length1(v0, v2) = v8))))) 206.81/127.88 (7) length1(int, all_105_2) = all_86_13 206.81/127.88 (8) elts(int, all_103_4) = all_103_3 206.81/127.88 (9) t2tb2(all_86_3) = all_105_4 206.81/127.88 (10) t2tb(all_86_2) = all_105_1 206.81/127.88 (11) in_ty(int) 206.81/127.88 (12) length1(int, all_103_4) = all_86_13 206.81/127.88 (13) $lesseq(2, all_86_13) 206.81/127.88 (14) ( ~ (all_133_0 = 42) & $lesseq(1, $difference(all_86_7, all_133_2)) & 206.81/127.88 $lesseq(1, $difference(all_133_2, all_86_8)) & tb2t1(all_133_1) = 206.81/127.88 all_133_0 & get4(int, all_133_3, all_133_2) = all_133_1 & 206.81/127.88 in_uni(all_133_1)) | ($lesseq(all_133_0, 41) & $lesseq(all_133_2, 206.81/127.88 all_86_10) & $lesseq(all_86_7, all_133_2) & tb2t1(all_133_1) = 206.81/127.88 all_133_0 & get4(int, all_133_3, all_133_2) = all_133_1 & 206.81/127.88 in_uni(all_133_1)) | ($lesseq(43, all_133_0) & $lesseq(all_133_2, 206.81/127.88 all_86_8) & $lesseq(all_86_11, all_133_2) & tb2t1(all_133_1) = 206.81/127.88 all_133_0 & get4(int, all_133_3, all_133_2) = all_133_1 & 206.81/127.88 in_uni(all_133_1)) 206.81/127.88 (15) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.81/127.88 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 206.81/127.88 (permut2(v0, v5, v6, v3, v4) = v7) | ~ (elts(v0, v2) = v6) | ~ 206.81/127.88 (elts(v0, v1) = v5) | ~ in_ty(v0) | ? [v8: $int] : ? [v9: $int] : 206.81/127.88 ((v9 = v8 & v7 = 0 & $lesseq(v4, v8) & $lesseq(v3, v8) & $lesseq(0, 206.81/127.88 v4) & $lesseq(0, v3) & length1(v0, v2) = v8 & length1(v0, v1) = 206.81/127.88 v8) | ( ~ (v8 = 0) & permut3(v0, v1, v2, v3, v4) = v8))) 206.81/127.88 (16) all_125_0 = all_105_4 206.81/127.88 (17) $lesseq(-1, all_86_8) 206.81/127.88 (18) $lesseq(all_86_7, all_86_13) 206.81/127.88 (19) ~ (permut2(int, all_105_3, all_105_1, all_86_11, $sum(all_86_10, 1)) = 206.81/127.88 0) | permut2(int, all_103_1, all_105_1, all_86_11, $sum(all_86_10, 1)) 206.81/127.88 = 0 206.81/127.88 (20) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.81/127.88 $int] : ! [v5: $int] : ( ~ (permut2(v0, v2, v3, v4, v5) = 0) | ~ 206.81/127.88 (permut2(v0, v1, v2, v4, v5) = 0) | ~ in_ty(v0) | permut2(v0, v1, v3, 206.81/127.88 v4, v5) = 0) 206.81/127.89 (21) ! [v0: $int] : ! [v1: $int] : (v1 = 42 | ~ ($lesseq(1, 206.81/127.89 $difference(all_86_7, v0))) | ~ ($lesseq(1, $difference(v0, 206.81/127.89 all_86_8))) | ~ (get3(all_86_6, v0) = v1)) 206.81/127.89 (22) map_eq_sub1(int, all_103_3, all_103_1, $sum(all_86_10, 1), all_86_13) = 206.81/127.89 0 206.81/127.89 (23) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.81/127.89 $int] : ! [v5: $int] : ! [v6: $int] : ( ~ (permut2(v0, v3, v4, 0, 206.81/127.89 v5) = v6) | ~ (length1(v0, v1) = v5) | ~ (elts(v0, v2) = v4) | 206.81/127.89 ~ (elts(v0, v1) = v3) | ~ in_ty(v0) | ? [v7: $int] : ((v7 = v5 & v6 206.81/127.89 = 0 & length1(v0, v2) = v5) | ( ~ (v7 = 0) & permut_all(v0, v1, 206.81/127.89 v2) = v7))) 206.81/127.89 (24) t2tb(all_86_6) = all_103_1 206.81/127.89 (25) $lesseq(2, $difference(all_86_13, all_86_11)) 206.81/127.89 (26) map_eq_sub1(int, all_103_1, all_105_3, $sum(all_86_8, 1), all_86_13) = 0 206.81/127.89 (27) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.81/127.89 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ (permut3(v6, v5, 206.81/127.89 v4, v3, v2) = v1) | ~ (permut3(v6, v5, v4, v3, v2) = v0)) 206.81/127.89 (28) permut2(int, all_103_1, all_105_3, 0, all_86_13) = 0 206.81/127.89 (29) permut2(int, all_103_3, all_105_3, all_86_11, $sum(all_86_10, 1)) = 0 206.81/127.89 (30) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 206.81/127.89 | ~ (elts(v3, v2) = v1) | ~ (elts(v3, v2) = v0)) 206.81/127.89 (31) length1(int, all_105_4) = all_86_13 206.81/127.89 (32) in_array_int(all_86_3) 206.81/127.89 (33) elts(int, all_105_4) = all_105_3 206.81/127.89 (34) map_eq_sub1(int, all_105_3, all_105_1, 0, all_86_7) = 0 206.81/127.89 (35) tb2t(all_105_1) = all_86_2 206.81/127.89 (36) permut2(int, all_103_1, all_105_3, all_86_11, $sum(all_86_8, 1)) = 0 206.81/127.89 (37) elts(int, all_105_2) = all_105_1 206.81/127.89 (38) map_eq_sub1(int, all_103_3, all_103_1, 0, all_86_11) = 0 206.81/127.89 (39) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.81/127.89 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 206.81/127.89 ($lesseq(1, $difference(v4, v5))) | ~ ($lesseq(v3, v5)) | ~ 206.81/127.89 (permut2(v0, v1, v2, v3, v4) = 0) | ~ (t2tb1(v5) = v6) | ~ (get(v0, 206.81/127.89 int, v2, v6) = v7) | ~ in_ty(v0) | ? [v8: $int] : ? [v9: $int] 206.81/127.89 : ($lesseq(1, $difference(v4, v8)) & $lesseq(v3, v8) & t2tb1(v8) = v9 206.81/127.89 & get(v0, int, v1, v9) = v7 & in_uni(v9) & in_uni(v7))) 206.81/127.89 (40) t2tb2(all_86_1) = all_105_2 206.81/127.89 (41) $lesseq(all_86_11, all_86_8) 206.81/127.89 (42) ~ (permut2(int, all_105_3, all_105_1, 0, all_86_13) = 0) | ? [v0: 206.81/127.89 $int] : ((v0 = 0 & permut_all(int, all_105_4, all_105_2) = 0) | ( ~ 206.81/127.89 (v0 = all_86_13) & length1(int, all_105_2) = v0)) 206.81/127.89 (43) $lesseq(all_86_7, all_86_10) 206.81/127.89 (44) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.81/127.89 $int] : ! [v5: $int] : ( ~ (elts(v0, v1) = v3) | ~ (t2tb1(v2) = v4) 206.81/127.89 | ~ (get(v0, int, v3, v4) = v5) | ~ in_ty(v0) | (get4(v0, v1, v2) = 206.81/127.89 v5 & in_uni(v5))) 206.81/127.89 (45) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.81/127.89 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 206.81/127.89 ($lesseq(1, $difference(v3, v4))) | ~ ($lesseq(v2, v4)) | ~ 206.81/127.89 (permut2(int, v5, v6, v2, v3) = 0) | ~ (t2tb(v1) = v6) | ~ (t2tb(v0) 206.81/127.89 = v5) | ~ (get3(v1, v4) = v7) | ~ in_map_int_int(v0) | ? [v8: 206.81/127.89 $int] : ($lesseq(1, $difference(v3, v8)) & $lesseq(v2, v8) & 206.81/127.89 get3(v0, v8) = v7)) 206.81/127.89 (46) $lesseq(0, all_86_7) 206.81/127.89 (47) permut2(int, all_105_3, all_105_1, all_86_7, $sum(all_86_10, 1)) = 0 206.81/127.89 (48) permut2(int, all_103_3, all_103_1, all_86_11, $sum(all_86_10, 1)) = 0 206.81/127.89 (49) ~ (permut2(int, all_103_3, all_103_1, 0, all_86_13) = 0) | ? [v0: 206.81/127.89 $int] : ((v0 = 0 & permut_all(int, all_103_4, all_103_2) = 0) | ( ~ 206.81/127.89 (v0 = all_86_13) & length1(int, all_103_2) = v0)) 206.81/127.89 (50) in_array_int(all_86_1) 206.81/127.89 (51) t2tb(all_86_12) = all_103_3 206.81/127.89 (52) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.81/127.89 $int] : ! [v5: $int] : ! [v6: $int] : ( ~ ($lesseq(0, v4)) | ~ 206.81/127.89 ($lesseq(0, v3)) | ~ (permut2(v0, v5, v6, v3, v4) = 0) | ~ (elts(v0, 206.81/127.89 v2) = v6) | ~ (elts(v0, v1) = v5) | ~ in_ty(v0) | ? [v7: $int] 206.81/127.89 : ? [v8: $int] : ((v7 = 0 & permut3(v0, v1, v2, v3, v4) = 0) | 206.81/127.89 (length1(v0, v1) = v7 & ( ~ ($lesseq(v4, v7)) | ~ ($lesseq(v3, v7)) 206.81/127.89 | ( ~ (v8 = v7) & length1(v0, v2) = v8))))) 206.81/127.89 (53) $lesseq(1, $difference(all_86_7, all_86_8)) 206.81/127.89 (54) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.81/127.89 $int] : ! [v5: $int] : ! [v6: $int] : ( ~ ($lesseq(1, 206.81/127.89 $difference(v4, v5))) | ~ ($lesseq(v3, v5)) | ~ (map_eq_sub1(v0, 206.81/127.89 v1, v2, v3, v4) = 0) | ~ (t2tb1(v5) = v6) | ~ in_ty(v0) | ? 206.81/127.89 [v7: $int] : (get(v0, int, v2, v6) = v7 & get(v0, int, v1, v6) = v7 & 206.81/127.89 in_uni(v7))) 206.81/127.89 (55) $lesseq(1, $difference(all_86_13, all_86_10)) 206.81/127.89 (56) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.81/127.89 $int] : ! [v5: $int] : (v5 = 0 | ~ (permut_sub2(v0, v1, v2, v3, v4) 206.81/127.89 = v5) | ~ in_ty(v0) | ? [v6: $int] : ? [v7: $int] : ? [v8: $int] 206.81/127.89 : ? [v9: $int] : (( ~ (v9 = 0) & map_eq_sub1(v0, v6, v7, v4, v8) = v9 206.81/127.89 & length1(v0, v1) = v8 & elts(v0, v2) = v7 & elts(v0, v1) = v6 & 206.81/127.89 in_uni(v7) & in_uni(v6)) | ( ~ (v8 = 0) & map_eq_sub1(v0, v6, v7, 206.81/127.89 0, v3) = v8 & elts(v0, v2) = v7 & elts(v0, v1) = v6 & in_uni(v7) 206.81/127.89 & in_uni(v6)) | ( ~ (v6 = 0) & permut3(v0, v1, v2, v3, v4) = v6))) 206.81/127.89 (57) in_map_int_int(all_86_4) 206.81/127.89 (58) map_eq_sub1(int, all_105_3, all_105_1, 0, all_86_13) = 0 206.81/127.89 (59) $lesseq(0, all_86_11) 206.81/127.89 (60) elts(int, all_103_2) = all_103_1 206.81/127.89 (61) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ( ~ 206.81/127.89 (t2tb2(v0) = v2) | ~ (get4(int, v2, v1) = v3) | ~ in_array_int(v0) | 206.81/127.89 ? [v4: $int] : ? [v5: $int] : ? [v6: $int] : (tb2t(v4) = v5 & 206.81/127.89 tb2t1(v3) = v6 & get3(v5, v1) = v6 & elts(int, v2) = v4 & 206.81/127.89 in_map_int_int(v5) & in_uni(v4))) 206.81/127.89 (62) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ (tb2t(v2) 206.81/127.89 = v1) | ~ (tb2t(v2) = v0)) 206.81/127.89 (63) all_133_3 = all_105_2 206.81/127.89 (64) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.81/127.89 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 206.81/127.89 ($lesseq(1, $difference(v3, v6))) | ~ ($lesseq(v2, v6)) | ~ 206.81/127.89 (map_eq_sub1(int, v4, v5, v2, v3) = 0) | ~ (t2tb(v1) = v5) | ~ 206.81/127.89 (t2tb(v0) = v4) | ~ (get3(v1, v6) = v7) | ~ in_map_int_int(v0) | 206.81/127.89 get3(v0, v6) = v7) 206.81/127.89 (65) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 206.81/127.89 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 206.81/127.89 (66) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ( ~ 206.81/127.89 (get4(v0, v1, v2) = v3) | ~ in_ty(v0) | ? [v4: $int] : ? [v5: $int] 206.81/127.89 : (elts(v0, v1) = v4 & t2tb1(v2) = v5 & get(v0, int, v4, v5) = v3 & 206.81/127.89 in_uni(v5) & in_uni(v4) & in_uni(v3))) 206.81/127.89 (67) $lesseq(0, all_86_10) 206.81/127.89 (68) map_eq_sub1(int, all_103_1, all_105_3, 0, all_86_13) = 0 206.81/127.89 (69) ! [v0: $int] : ! [v1: $int] : ( ~ (tb2t1(v0) = v1) | ~ in_uni(v0) | 206.81/127.89 t2tb1(v1) = v0) 206.81/127.89 (70) map_eq_sub1(int, all_105_3, all_105_1, $sum(all_86_10, 1), all_86_13) = 206.81/127.89 0 206.81/127.89 (71) t2tb(all_86_4) = all_105_3 206.81/127.89 (72) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 206.81/127.89 $int] : ! [v5: $int] : ( ~ (permut3(v0, v1, v2, v3, v4) = v5) | ~ 206.81/127.89 in_ty(v0) | ? [v6: $int] : ? [v7: $int] : ? [v8: $int] : ? [v9: 206.81/127.89 $int] : ? [v10: $int] : ((v10 = 0 & v9 = 0 & v5 = 0 & 206.81/127.89 map_eq_sub1(v0, v6, v7, v4, v8) = 0 & map_eq_sub1(v0, v6, v7, 0, 206.81/127.89 v3) = 0 & length1(v0, v1) = v8 & elts(v0, v2) = v7 & elts(v0, 206.81/127.89 v1) = v6 & in_uni(v7) & in_uni(v6)) | ( ~ (v6 = 0) & 206.81/127.89 permut_sub2(v0, v1, v2, v3, v4) = v6))) 206.81/127.89 (73) ! [v0: $int] : ! [v1: $int] : ( ~ ($lesseq(v0, all_86_10)) | ~ 206.81/127.89 ($lesseq(all_86_7, v0)) | ~ (get4(int, all_125_0, v0) = v1) | ? [v2: 206.81/127.89 $int] : ($lesseq(42, v2) & tb2t1(v1) = v2)) 206.81/127.89 206.81/127.89 Begin of proof 206.81/127.89 | 206.81/127.89 | BETA: splitting (42) gives: 206.81/127.89 | 206.81/127.89 | Case 1: 206.81/127.89 | | 206.81/127.89 | | (74) ~ (permut2(int, all_105_3, all_105_1, 0, all_86_13) = 0) 206.81/127.89 | | 206.81/127.89 | | PRED_UNIFY: (47), (74) imply: 206.81/127.89 | | (75) ~ (all_86_7 = 0) | ~ ($difference(all_86_10, all_86_13) = -1) 206.81/127.89 | | 206.81/127.89 | | BETA: splitting (49) gives: 206.81/127.89 | | 206.81/127.89 | | Case 1: 206.81/127.89 | | | 206.81/127.89 | | | (76) ~ (permut2(int, all_103_3, all_103_1, 0, all_86_13) = 0) 206.81/127.89 | | | 206.81/127.89 | | | PRED_UNIFY: (48), (76) imply: 206.81/127.89 | | | (77) ~ ($difference(all_86_10, all_86_13) = -1) | ~ (all_86_11 = 0) 206.81/127.89 | | | 206.81/127.89 | | | BETA: splitting (14) gives: 206.81/127.89 | | | 206.81/127.89 | | | Case 1: 206.81/127.89 | | | | 206.81/127.89 | | | | (78) ~ (all_133_0 = 42) & $lesseq(1, $difference(all_86_7, 206.81/127.89 | | | | all_133_2)) & $lesseq(1, $difference(all_133_2, all_86_8)) & 206.81/127.89 | | | | tb2t1(all_133_1) = all_133_0 & get4(int, all_133_3, all_133_2) = 206.81/127.89 | | | | all_133_1 & in_uni(all_133_1) 206.81/127.89 | | | | 206.81/127.89 | | | | ALPHA: (78) implies: 206.81/127.89 | | | | (79) ~ (all_133_0 = 42) 206.81/127.89 | | | | (80) $lesseq(1, $difference(all_133_2, all_86_8)) 206.81/127.89 | | | | (81) $lesseq(1, $difference(all_86_7, all_133_2)) 206.81/127.89 | | | | (82) in_uni(all_133_1) 206.81/127.89 | | | | (83) get4(int, all_133_3, all_133_2) = all_133_1 206.81/127.89 | | | | (84) tb2t1(all_133_1) = all_133_0 206.81/127.89 | | | | 206.81/127.89 | | | | COMBINE_INEQS: (80), (81) imply: 206.81/127.89 | | | | (85) $lesseq(2, $difference(all_86_7, all_86_8)) 206.81/127.89 | | | | 206.81/127.89 | | | | COMBINE_INEQS: (43), (85) imply: 206.81/127.89 | | | | (86) $lesseq(2, $difference(all_86_10, all_86_8)) 206.81/127.89 | | | | 206.81/127.89 | | | | COMBINE_INEQS: (17), (86) imply: 206.81/127.89 | | | | (87) $lesseq(1, all_86_10) 206.81/127.89 | | | | 206.81/127.89 | | | | REDUCE: (63), (83) imply: 206.81/127.89 | | | | (88) get4(int, all_105_2, all_133_2) = all_133_1 206.81/127.89 | | | | 206.81/127.89 | | | | REF_CLOSE: (1), (4), (6), (8), (10), (11), (12), (15), (17), (18), (21), 206.81/127.89 | | | | (22), (24), (26), (27), (29), (30), (31), (33), (34), (35), 206.81/127.89 | | | | (37), (38), (40), (41), (43), (50), (52), (54), (55), (56), 206.81/127.89 | | | | (57), (59), (61), (62), (64), (65), (66), (68), (69), (70), 206.81/127.89 | | | | (71), (72), (77), (79), (80), (81), (82), (84), (87), (88) 206.81/127.89 | | | | are inconsistent by sub-proof #102. 206.81/127.89 | | | | 206.81/127.89 | | | Case 2: 206.81/127.89 | | | | 206.81/127.89 | | | | (89) ($lesseq(all_133_0, 41) & $lesseq(all_133_2, all_86_10) & 206.81/127.89 | | | | $lesseq(all_86_7, all_133_2) & tb2t1(all_133_1) = all_133_0 & 206.81/127.89 | | | | get4(int, all_133_3, all_133_2) = all_133_1 & 206.81/127.89 | | | | in_uni(all_133_1)) | ($lesseq(43, all_133_0) & 206.81/127.89 | | | | $lesseq(all_133_2, all_86_8) & $lesseq(all_86_11, all_133_2) & 206.81/127.89 | | | | tb2t1(all_133_1) = all_133_0 & get4(int, all_133_3, all_133_2) 206.81/127.89 | | | | = all_133_1 & in_uni(all_133_1)) 206.81/127.89 | | | | 206.81/127.89 | | | | BETA: splitting (89) gives: 206.81/127.89 | | | | 206.81/127.89 | | | | Case 1: 206.81/127.89 | | | | | 206.81/127.89 | | | | | (90) $lesseq(all_133_0, 41) & $lesseq(all_133_2, all_86_10) & 206.81/127.89 | | | | | $lesseq(all_86_7, all_133_2) & tb2t1(all_133_1) = all_133_0 & 206.81/127.89 | | | | | get4(int, all_133_3, all_133_2) = all_133_1 & 206.81/127.89 | | | | | in_uni(all_133_1) 206.81/127.89 | | | | | 206.81/127.89 | | | | | ALPHA: (90) implies: 206.81/127.89 | | | | | (91) $lesseq(all_86_7, all_133_2) 206.81/127.89 | | | | | (92) $lesseq(all_133_2, all_86_10) 206.81/127.89 | | | | | (93) $lesseq(all_133_0, 41) 206.81/127.89 | | | | | (94) get4(int, all_133_3, all_133_2) = all_133_1 206.81/127.89 | | | | | (95) tb2t1(all_133_1) = all_133_0 206.81/127.89 | | | | | 206.81/127.89 | | | | | REDUCE: (63), (94) imply: 206.81/127.89 | | | | | (96) get4(int, all_105_2, all_133_2) = all_133_1 206.81/127.89 | | | | | 206.81/127.89 | | | | | REF_CLOSE: (1), (8), (9), (10), (11), (16), (29), (30), (32), (33), 206.81/127.89 | | | | | (35), (37), (39), (40), (44), (45), (47), (50), (52), (57), 206.81/127.89 | | | | | (59), (61), (62), (66), (67), (71), (73), (91), (92), (93), 206.81/127.89 | | | | | (95), (96) are inconsistent by sub-proof #126. 206.81/127.89 | | | | | 206.81/127.89 | | | | Case 2: 206.81/127.89 | | | | | 206.81/127.89 | | | | | (97) $lesseq(43, all_133_0) & $lesseq(all_133_2, all_86_8) & 206.81/127.89 | | | | | $lesseq(all_86_11, all_133_2) & tb2t1(all_133_1) = all_133_0 & 206.81/127.89 | | | | | get4(int, all_133_3, all_133_2) = all_133_1 & 206.81/127.89 | | | | | in_uni(all_133_1) 206.81/127.89 | | | | | 206.81/127.89 | | | | | ALPHA: (97) implies: 206.81/127.89 | | | | | (98) $lesseq(all_86_11, all_133_2) 206.81/127.89 | | | | | (99) $lesseq(all_133_2, all_86_8) 206.81/127.89 | | | | | (100) $lesseq(43, all_133_0) 206.81/127.89 | | | | | (101) get4(int, all_133_3, all_133_2) = all_133_1 206.81/127.89 | | | | | (102) tb2t1(all_133_1) = all_133_0 206.81/127.89 | | | | | 206.81/127.89 | | | | | REDUCE: (63), (101) imply: 206.81/127.89 | | | | | (103) get4(int, all_105_2, all_133_2) = all_133_1 206.81/127.89 | | | | | 206.81/127.89 | | | | | BETA: splitting (75) gives: 206.81/127.89 | | | | | 206.81/127.89 | | | | | Case 1: 206.81/127.89 | | | | | | 206.81/127.89 | | | | | | (104) ~ (all_86_7 = 0) 206.81/127.89 | | | | | | 206.81/127.89 | | | | | | STRENGTHEN: (46), (104) imply: 206.81/127.89 | | | | | | (105) $lesseq(1, all_86_7) 206.81/127.89 | | | | | | 206.81/127.89 | | | | | | COMBINE_INEQS: (43), (105) imply: 206.81/127.89 | | | | | | (106) $lesseq(1, all_86_10) 206.81/127.89 | | | | | | 206.81/127.89 | | | | | | REF_CLOSE: (1), (2), (4), (8), (10), (11), (12), (15), (24), (27), 206.81/127.89 | | | | | | (29), (30), (31), (33), (34), (35), (36), (37), (39), 206.81/127.89 | | | | | | (40), (43), (45), (47), (50), (52), (53), (54), (55), 206.81/127.89 | | | | | | (57), (58), (59), (61), (62), (64), (65), (66), (71), 206.81/127.89 | | | | | | (77), (98), (99), (100), (102), (103), (106) are 206.81/127.89 | | | | | | inconsistent by sub-proof #109. 206.81/127.89 | | | | | | 206.81/127.89 | | | | | Case 2: 206.81/127.89 | | | | | | 206.81/127.89 | | | | | | (107) all_86_7 = 0 206.81/127.89 | | | | | | 206.81/127.89 | | | | | | REDUCE: (53), (107) imply: 206.81/127.89 | | | | | | (108) $lesseq(all_86_8, -1) 206.81/127.89 | | | | | | 206.81/127.89 | | | | | | COMBINE_INEQS: (41), (108) imply: 206.81/127.89 | | | | | | (109) $lesseq(all_86_11, -1) 206.81/127.89 | | | | | | 206.81/127.89 | | | | | | COMBINE_INEQS: (59), (109) imply: 206.81/127.89 | | | | | | (110) $lesseq(0, -1) 206.81/127.89 | | | | | | 206.81/127.89 | | | | | | CLOSE: (110) is inconsistent. 206.81/127.89 | | | | | | 206.81/127.89 | | | | | End of split 206.81/127.89 | | | | | 206.81/127.89 | | | | End of split 206.81/127.89 | | | | 206.81/127.89 | | | End of split 206.81/127.89 | | | 206.81/127.89 | | Case 2: 206.81/127.89 | | | 206.81/127.89 | | | (111) permut2(int, all_103_3, all_103_1, 0, all_86_13) = 0 206.81/127.89 | | | 206.81/127.89 | | | BETA: splitting (14) gives: 206.81/127.89 | | | 206.81/127.89 | | | Case 1: 206.81/127.89 | | | | 206.81/127.89 | | | | (112) ~ (all_133_0 = 42) & $lesseq(1, $difference(all_86_7, 206.81/127.89 | | | | all_133_2)) & $lesseq(1, $difference(all_133_2, all_86_8)) 206.81/127.89 | | | | & tb2t1(all_133_1) = all_133_0 & get4(int, all_133_3, 206.81/127.89 | | | | all_133_2) = all_133_1 & in_uni(all_133_1) 206.81/127.89 | | | | 206.81/127.89 | | | | ALPHA: (112) implies: 206.81/127.89 | | | | (113) ~ (all_133_0 = 42) 206.81/127.89 | | | | (114) $lesseq(1, $difference(all_133_2, all_86_8)) 206.81/127.90 | | | | (115) $lesseq(1, $difference(all_86_7, all_133_2)) 206.81/127.90 | | | | (116) in_uni(all_133_1) 206.81/127.90 | | | | (117) get4(int, all_133_3, all_133_2) = all_133_1 206.81/127.90 | | | | (118) tb2t1(all_133_1) = all_133_0 206.81/127.90 | | | | 206.81/127.90 | | | | COMBINE_INEQS: (114), (115) imply: 206.81/127.90 | | | | (119) $lesseq(2, $difference(all_86_7, all_86_8)) 206.81/127.90 | | | | 206.81/127.90 | | | | COMBINE_INEQS: (43), (119) imply: 206.81/127.90 | | | | (120) $lesseq(2, $difference(all_86_10, all_86_8)) 206.81/127.90 | | | | 206.81/127.90 | | | | COMBINE_INEQS: (41), (120) imply: 206.81/127.90 | | | | (121) $lesseq(2, $difference(all_86_10, all_86_11)) 206.81/127.90 | | | | 206.81/127.90 | | | | COMBINE_INEQS: (17), (120) imply: 206.81/127.90 | | | | (122) $lesseq(1, all_86_10) 206.81/127.90 | | | | 206.81/127.90 | | | | COMBINE_INEQS: (55), (121) imply: 206.81/127.90 | | | | (123) $lesseq(3, $difference(all_86_13, all_86_11)) 206.81/127.90 | | | | 206.81/127.90 | | | | COMBINE_INEQS: (59), (123) imply: 206.81/127.90 | | | | (124) $lesseq(3, all_86_13) 206.81/127.90 | | | | 206.81/127.90 | | | | REDUCE: (63), (117) imply: 206.81/127.90 | | | | (125) get4(int, all_105_2, all_133_2) = all_133_1 206.81/127.90 | | | | 206.81/127.90 | | | | REF_CLOSE: (1), (3), (4), (5), (8), (10), (11), (12), (15), (17), (18), 206.81/127.90 | | | | (20), (21), (22), (23), (24), (26), (27), (28), (29), (30), 206.81/127.90 | | | | (31), (33), (34), (35), (37), (38), (40), (41), (43), (45), 206.81/127.90 | | | | (50), (51), (52), (54), (55), (57), (59), (60), (61), (62), 206.81/127.90 | | | | (64), (65), (66), (69), (70), (71), (111), (113), (114), 206.81/127.90 | | | | (115), (116), (118), (122), (123), (124), (125) are 206.81/127.90 | | | | inconsistent by sub-proof #92. 206.81/127.90 | | | | 206.81/127.90 | | | Case 2: 206.81/127.90 | | | | 206.81/127.90 | | | | (126) ($lesseq(all_133_0, 41) & $lesseq(all_133_2, all_86_10) & 206.81/127.90 | | | | $lesseq(all_86_7, all_133_2) & tb2t1(all_133_1) = all_133_0 & 206.81/127.90 | | | | get4(int, all_133_3, all_133_2) = all_133_1 & 206.81/127.90 | | | | in_uni(all_133_1)) | ($lesseq(43, all_133_0) & 206.81/127.90 | | | | $lesseq(all_133_2, all_86_8) & $lesseq(all_86_11, all_133_2) 206.81/127.90 | | | | & tb2t1(all_133_1) = all_133_0 & get4(int, all_133_3, 206.81/127.90 | | | | all_133_2) = all_133_1 & in_uni(all_133_1)) 206.81/127.90 | | | | 206.81/127.90 | | | | BETA: splitting (126) gives: 206.81/127.90 | | | | 206.81/127.90 | | | | Case 1: 206.81/127.90 | | | | | 206.81/127.90 | | | | | (127) $lesseq(all_133_0, 41) & $lesseq(all_133_2, all_86_10) & 206.81/127.90 | | | | | $lesseq(all_86_7, all_133_2) & tb2t1(all_133_1) = all_133_0 & 206.81/127.90 | | | | | get4(int, all_133_3, all_133_2) = all_133_1 & 206.81/127.90 | | | | | in_uni(all_133_1) 206.81/127.90 | | | | | 206.81/127.90 | | | | | ALPHA: (127) implies: 206.81/127.90 | | | | | (128) $lesseq(all_86_7, all_133_2) 206.81/127.90 | | | | | (129) $lesseq(all_133_2, all_86_10) 206.81/127.90 | | | | | (130) $lesseq(all_133_0, 41) 206.81/127.90 | | | | | (131) get4(int, all_133_3, all_133_2) = all_133_1 206.81/127.90 | | | | | (132) tb2t1(all_133_1) = all_133_0 206.81/127.90 | | | | | 206.81/127.90 | | | | | REDUCE: (63), (131) imply: 206.81/127.90 | | | | | (133) get4(int, all_105_2, all_133_2) = all_133_1 206.81/127.90 | | | | | 206.81/127.90 | | | | | REF_CLOSE: (1), (8), (9), (10), (11), (16), (29), (30), (32), (33), 206.81/127.90 | | | | | (35), (37), (39), (40), (44), (45), (47), (50), (52), (57), 206.81/127.90 | | | | | (59), (61), (62), (66), (67), (71), (73), (128), (129), 206.81/127.90 | | | | | (130), (132), (133) are inconsistent by sub-proof #126. 206.81/127.90 | | | | | 206.81/127.90 | | | | Case 2: 206.81/127.90 | | | | | 206.81/127.90 | | | | | (134) $lesseq(43, all_133_0) & $lesseq(all_133_2, all_86_8) & 206.81/127.90 | | | | | $lesseq(all_86_11, all_133_2) & tb2t1(all_133_1) = all_133_0 206.81/127.90 | | | | | & get4(int, all_133_3, all_133_2) = all_133_1 & 206.81/127.90 | | | | | in_uni(all_133_1) 206.81/127.90 | | | | | 206.81/127.90 | | | | | ALPHA: (134) implies: 206.81/127.90 | | | | | (135) $lesseq(all_86_11, all_133_2) 206.81/127.90 | | | | | (136) $lesseq(all_133_2, all_86_8) 206.81/127.90 | | | | | (137) $lesseq(43, all_133_0) 206.81/127.90 | | | | | (138) get4(int, all_133_3, all_133_2) = all_133_1 206.81/127.90 | | | | | (139) tb2t1(all_133_1) = all_133_0 206.81/127.90 | | | | | 206.81/127.90 | | | | | REDUCE: (63), (138) imply: 206.81/127.90 | | | | | (140) get4(int, all_105_2, all_133_2) = all_133_1 206.81/127.90 | | | | | 206.81/127.90 | | | | | REF_CLOSE: (1), (2), (3), (4), (8), (10), (11), (12), (15), (24), 206.81/127.90 | | | | | (27), (28), (29), (30), (31), (33), (34), (35), (36), (37), 206.81/127.90 | | | | | (39), (40), (43), (45), (46), (47), (50), (52), (53), (54), 206.81/127.90 | | | | | (55), (57), (59), (60), (61), (62), (64), (65), (66), (71), 206.81/127.90 | | | | | (75), (111), (135), (136), (137), (139), (140) are 206.81/127.90 | | | | | inconsistent by sub-proof #117. 206.81/127.90 | | | | | 206.81/127.90 | | | | End of split 206.81/127.90 | | | | 206.81/127.90 | | | End of split 206.81/127.90 | | | 206.81/127.90 | | End of split 206.81/127.90 | | 206.81/127.90 | Case 2: 206.81/127.90 | | 206.81/127.90 | | (141) permut2(int, all_105_3, all_105_1, 0, all_86_13) = 0 206.81/127.90 | | 206.81/127.90 | | BETA: splitting (49) gives: 206.81/127.90 | | 206.81/127.90 | | Case 1: 206.81/127.90 | | | 206.81/127.90 | | | (142) ~ (permut2(int, all_103_3, all_103_1, 0, all_86_13) = 0) 206.81/127.90 | | | 206.81/127.90 | | | PRED_UNIFY: (48), (142) imply: 206.81/127.90 | | | (143) ~ ($difference(all_86_10, all_86_13) = -1) | ~ (all_86_11 = 0) 206.81/127.90 | | | 206.81/127.90 | | | BETA: splitting (14) gives: 206.81/127.90 | | | 206.81/127.90 | | | Case 1: 206.81/127.90 | | | | 206.81/127.90 | | | | (144) ~ (all_133_0 = 42) & $lesseq(1, $difference(all_86_7, 206.81/127.90 | | | | all_133_2)) & $lesseq(1, $difference(all_133_2, all_86_8)) 206.81/127.90 | | | | & tb2t1(all_133_1) = all_133_0 & get4(int, all_133_3, 206.81/127.90 | | | | all_133_2) = all_133_1 & in_uni(all_133_1) 206.81/127.90 | | | | 206.81/127.90 | | | | ALPHA: (144) implies: 206.81/127.90 | | | | (145) ~ (all_133_0 = 42) 206.81/127.90 | | | | (146) $lesseq(1, $difference(all_133_2, all_86_8)) 206.81/127.90 | | | | (147) $lesseq(1, $difference(all_86_7, all_133_2)) 206.81/127.90 | | | | (148) in_uni(all_133_1) 206.81/127.90 | | | | (149) get4(int, all_133_3, all_133_2) = all_133_1 206.81/127.90 | | | | (150) tb2t1(all_133_1) = all_133_0 206.81/127.90 | | | | 206.81/127.90 | | | | COMBINE_INEQS: (146), (147) imply: 206.81/127.90 | | | | (151) $lesseq(2, $difference(all_86_7, all_86_8)) 206.81/127.90 | | | | 206.81/127.90 | | | | COMBINE_INEQS: (43), (151) imply: 206.81/127.90 | | | | (152) $lesseq(2, $difference(all_86_10, all_86_8)) 206.81/127.90 | | | | 206.81/127.90 | | | | COMBINE_INEQS: (17), (152) imply: 206.81/127.90 | | | | (153) $lesseq(1, all_86_10) 206.81/127.90 | | | | 206.81/127.90 | | | | REDUCE: (63), (149) imply: 206.81/127.90 | | | | (154) get4(int, all_105_2, all_133_2) = all_133_1 206.81/127.90 | | | | 206.81/127.90 | | | | REF_CLOSE: (1), (4), (6), (8), (10), (11), (12), (15), (17), (18), (21), 206.81/127.90 | | | | (22), (24), (26), (27), (29), (30), (31), (33), (34), (35), 206.81/127.90 | | | | (37), (38), (40), (41), (43), (50), (52), (54), (55), (56), 206.81/127.90 | | | | (57), (59), (61), (62), (64), (65), (66), (68), (69), (70), 206.81/127.90 | | | | (71), (72), (143), (145), (146), (147), (148), (150), (153), 206.81/127.90 | | | | (154) are inconsistent by sub-proof #102. 206.81/127.90 | | | | 206.81/127.90 | | | Case 2: 206.81/127.90 | | | | 206.81/127.90 | | | | (155) ($lesseq(all_133_0, 41) & $lesseq(all_133_2, all_86_10) & 206.81/127.90 | | | | $lesseq(all_86_7, all_133_2) & tb2t1(all_133_1) = all_133_0 & 206.81/127.90 | | | | get4(int, all_133_3, all_133_2) = all_133_1 & 206.81/127.90 | | | | in_uni(all_133_1)) | ($lesseq(43, all_133_0) & 206.81/127.90 | | | | $lesseq(all_133_2, all_86_8) & $lesseq(all_86_11, all_133_2) 206.81/127.90 | | | | & tb2t1(all_133_1) = all_133_0 & get4(int, all_133_3, 206.81/127.90 | | | | all_133_2) = all_133_1 & in_uni(all_133_1)) 206.81/127.90 | | | | 206.81/127.90 | | | | BETA: splitting (155) gives: 206.81/127.90 | | | | 206.81/127.90 | | | | Case 1: 206.81/127.90 | | | | | 206.81/127.90 | | | | | (156) $lesseq(all_133_0, 41) & $lesseq(all_133_2, all_86_10) & 206.81/127.90 | | | | | $lesseq(all_86_7, all_133_2) & tb2t1(all_133_1) = all_133_0 & 206.81/127.90 | | | | | get4(int, all_133_3, all_133_2) = all_133_1 & 206.81/127.90 | | | | | in_uni(all_133_1) 206.81/127.90 | | | | | 206.81/127.90 | | | | | ALPHA: (156) implies: 206.81/127.90 | | | | | (157) $lesseq(all_86_7, all_133_2) 206.81/127.90 | | | | | (158) $lesseq(all_133_2, all_86_10) 206.81/127.90 | | | | | (159) $lesseq(all_133_0, 41) 206.81/127.90 | | | | | (160) get4(int, all_133_3, all_133_2) = all_133_1 206.81/127.90 | | | | | (161) tb2t1(all_133_1) = all_133_0 206.81/127.90 | | | | | 206.81/127.90 | | | | | REDUCE: (63), (160) imply: 206.81/127.90 | | | | | (162) get4(int, all_105_2, all_133_2) = all_133_1 206.81/127.90 | | | | | 206.81/127.90 | | | | | REF_CLOSE: (1), (8), (9), (10), (11), (16), (29), (30), (32), (33), 206.81/127.90 | | | | | (35), (37), (39), (40), (44), (45), (47), (50), (52), (57), 206.81/127.90 | | | | | (59), (61), (62), (66), (67), (71), (73), (157), (158), 206.81/127.90 | | | | | (159), (161), (162) are inconsistent by sub-proof #126. 206.81/127.90 | | | | | 206.81/127.90 | | | | Case 2: 206.81/127.90 | | | | | 206.81/127.90 | | | | | (163) $lesseq(43, all_133_0) & $lesseq(all_133_2, all_86_8) & 206.81/127.90 | | | | | $lesseq(all_86_11, all_133_2) & tb2t1(all_133_1) = all_133_0 206.81/127.90 | | | | | & get4(int, all_133_3, all_133_2) = all_133_1 & 206.81/127.90 | | | | | in_uni(all_133_1) 206.81/127.90 | | | | | 206.81/127.90 | | | | | ALPHA: (163) implies: 206.81/127.90 | | | | | (164) $lesseq(all_86_11, all_133_2) 206.81/127.90 | | | | | (165) $lesseq(all_133_2, all_86_8) 206.81/127.90 | | | | | (166) $lesseq(43, all_133_0) 206.81/127.90 | | | | | (167) get4(int, all_133_3, all_133_2) = all_133_1 206.81/127.90 | | | | | (168) tb2t1(all_133_1) = all_133_0 206.81/127.90 | | | | | 206.81/127.90 | | | | | REDUCE: (63), (167) imply: 206.81/127.90 | | | | | (169) get4(int, all_105_2, all_133_2) = all_133_1 206.81/127.90 | | | | | 206.81/127.90 | | | | | REF_CLOSE: (1), (2), (3), (4), (7), (8), (10), (11), (12), (15), (24), 206.81/127.90 | | | | | (25), (27), (28), (29), (30), (31), (33), (34), (35), (36), 206.81/127.90 | | | | | (37), (39), (40), (43), (45), (47), (50), (52), (53), (54), 206.81/127.90 | | | | | (55), (57), (58), (59), (60), (61), (62), (64), (65), (66), 206.81/127.90 | | | | | (67), (71), (141), (143), (164), (165), (166), (168), (169) 206.81/127.90 | | | | | are inconsistent by sub-proof #89. 206.81/127.90 | | | | | 206.81/127.90 | | | | End of split 206.81/127.90 | | | | 206.81/127.90 | | | End of split 206.81/127.90 | | | 206.81/127.90 | | Case 2: 206.81/127.90 | | | 206.81/127.90 | | | (170) permut2(int, all_103_3, all_103_1, 0, all_86_13) = 0 206.81/127.90 | | | 206.81/127.90 | | | BETA: splitting (14) gives: 206.81/127.90 | | | 206.81/127.90 | | | Case 1: 206.81/127.90 | | | | 206.81/127.90 | | | | (171) ~ (all_133_0 = 42) & $lesseq(1, $difference(all_86_7, 206.81/127.90 | | | | all_133_2)) & $lesseq(1, $difference(all_133_2, all_86_8)) 206.81/127.90 | | | | & tb2t1(all_133_1) = all_133_0 & get4(int, all_133_3, 206.81/127.90 | | | | all_133_2) = all_133_1 & in_uni(all_133_1) 206.81/127.90 | | | | 206.81/127.90 | | | | ALPHA: (171) implies: 206.81/127.90 | | | | (172) ~ (all_133_0 = 42) 206.81/127.90 | | | | (173) $lesseq(1, $difference(all_133_2, all_86_8)) 206.81/127.90 | | | | (174) $lesseq(1, $difference(all_86_7, all_133_2)) 206.81/127.90 | | | | (175) in_uni(all_133_1) 206.81/127.90 | | | | (176) get4(int, all_133_3, all_133_2) = all_133_1 206.81/127.90 | | | | (177) tb2t1(all_133_1) = all_133_0 206.81/127.90 | | | | 206.81/127.90 | | | | COMBINE_INEQS: (173), (174) imply: 206.81/127.90 | | | | (178) $lesseq(2, $difference(all_86_7, all_86_8)) 206.81/127.90 | | | | 206.81/127.90 | | | | COMBINE_INEQS: (43), (178) imply: 206.81/127.90 | | | | (179) $lesseq(2, $difference(all_86_10, all_86_8)) 206.81/127.90 | | | | 206.81/127.90 | | | | COMBINE_INEQS: (41), (179) imply: 206.81/127.90 | | | | (180) $lesseq(2, $difference(all_86_10, all_86_11)) 206.81/127.90 | | | | 206.81/127.90 | | | | COMBINE_INEQS: (17), (179) imply: 206.81/127.90 | | | | (181) $lesseq(1, all_86_10) 206.81/127.90 | | | | 206.81/127.90 | | | | COMBINE_INEQS: (55), (180) imply: 206.81/127.90 | | | | (182) $lesseq(3, $difference(all_86_13, all_86_11)) 206.81/127.90 | | | | 206.81/127.90 | | | | COMBINE_INEQS: (59), (182) imply: 206.81/127.90 | | | | (183) $lesseq(3, all_86_13) 206.81/127.90 | | | | 206.81/127.90 | | | | REDUCE: (63), (176) imply: 206.81/127.90 | | | | (184) get4(int, all_105_2, all_133_2) = all_133_1 206.81/127.90 | | | | 206.81/127.90 | | | | REF_CLOSE: (1), (3), (4), (5), (8), (10), (11), (12), (15), (17), (18), 206.81/127.90 | | | | (20), (21), (22), (23), (24), (26), (27), (28), (29), (30), 206.81/127.90 | | | | (31), (33), (34), (35), (37), (38), (40), (41), (43), (45), 206.81/127.90 | | | | (50), (51), (52), (54), (55), (57), (59), (60), (61), (62), 206.81/127.90 | | | | (64), (65), (66), (69), (70), (71), (170), (172), (173), 206.81/127.90 | | | | (174), (175), (177), (181), (182), (183), (184) are 206.81/127.90 | | | | inconsistent by sub-proof #92. 206.81/127.90 | | | | 206.81/127.90 | | | Case 2: 206.81/127.90 | | | | 206.81/127.90 | | | | (185) ($lesseq(all_133_0, 41) & $lesseq(all_133_2, all_86_10) & 206.81/127.90 | | | | $lesseq(all_86_7, all_133_2) & tb2t1(all_133_1) = all_133_0 & 206.81/127.90 | | | | get4(int, all_133_3, all_133_2) = all_133_1 & 206.81/127.90 | | | | in_uni(all_133_1)) | ($lesseq(43, all_133_0) & 206.81/127.90 | | | | $lesseq(all_133_2, all_86_8) & $lesseq(all_86_11, all_133_2) 206.81/127.90 | | | | & tb2t1(all_133_1) = all_133_0 & get4(int, all_133_3, 206.81/127.90 | | | | all_133_2) = all_133_1 & in_uni(all_133_1)) 206.81/127.90 | | | | 206.81/127.90 | | | | BETA: splitting (185) gives: 206.81/127.90 | | | | 206.81/127.90 | | | | Case 1: 206.81/127.90 | | | | | 206.81/127.90 | | | | | (186) $lesseq(all_133_0, 41) & $lesseq(all_133_2, all_86_10) & 206.81/127.90 | | | | | $lesseq(all_86_7, all_133_2) & tb2t1(all_133_1) = all_133_0 & 206.81/127.90 | | | | | get4(int, all_133_3, all_133_2) = all_133_1 & 206.81/127.90 | | | | | in_uni(all_133_1) 206.81/127.90 | | | | | 206.81/127.90 | | | | | ALPHA: (186) implies: 206.81/127.90 | | | | | (187) $lesseq(all_86_7, all_133_2) 206.81/127.90 | | | | | (188) $lesseq(all_133_2, all_86_10) 206.81/127.90 | | | | | (189) $lesseq(all_133_0, 41) 206.81/127.90 | | | | | (190) get4(int, all_133_3, all_133_2) = all_133_1 206.81/127.90 | | | | | (191) tb2t1(all_133_1) = all_133_0 206.81/127.90 | | | | | 206.81/127.90 | | | | | REDUCE: (63), (190) imply: 206.81/127.90 | | | | | (192) get4(int, all_105_2, all_133_2) = all_133_1 206.81/127.90 | | | | | 206.81/127.90 | | | | | REF_CLOSE: (1), (8), (9), (10), (11), (16), (29), (30), (32), (33), 206.81/127.90 | | | | | (35), (37), (39), (40), (44), (45), (47), (50), (52), (57), 206.81/127.90 | | | | | (59), (61), (62), (66), (67), (71), (73), (187), (188), 206.81/127.90 | | | | | (189), (191), (192) are inconsistent by sub-proof #126. 206.81/127.90 | | | | | 206.81/127.90 | | | | Case 2: 206.81/127.90 | | | | | 206.81/127.90 | | | | | (193) $lesseq(43, all_133_0) & $lesseq(all_133_2, all_86_8) & 206.81/127.90 | | | | | $lesseq(all_86_11, all_133_2) & tb2t1(all_133_1) = all_133_0 206.81/127.90 | | | | | & get4(int, all_133_3, all_133_2) = all_133_1 & 206.81/127.90 | | | | | in_uni(all_133_1) 206.81/127.90 | | | | | 206.81/127.90 | | | | | ALPHA: (193) implies: 206.81/127.90 | | | | | (194) $lesseq(all_86_11, all_133_2) 206.81/127.90 | | | | | (195) $lesseq(all_133_2, all_86_8) 206.81/127.90 | | | | | (196) $lesseq(43, all_133_0) 206.81/127.90 | | | | | (197) get4(int, all_133_3, all_133_2) = all_133_1 206.81/127.90 | | | | | (198) tb2t1(all_133_1) = all_133_0 206.81/127.90 | | | | | 206.81/127.90 | | | | | REDUCE: (63), (197) imply: 206.81/127.90 | | | | | (199) get4(int, all_105_2, all_133_2) = all_133_1 206.81/127.90 | | | | | 206.81/127.90 | | | | | GROUND_INST: instantiating (15) with int, all_105_4, all_105_2, 0, 206.81/127.90 | | | | | all_86_13, all_105_3, all_105_1, 0, simplifying with 206.81/127.90 | | | | | (11), (33), (37), (141) gives: 206.81/127.90 | | | | | (200) ? [v0: $int] : ? [v1: $int] : ((v1 = v0 & 206.81/127.90 | | | | | $lesseq(all_86_13, v0) & $lesseq(0, v0) & $lesseq(0, 206.81/127.90 | | | | | all_86_13) & length1(int, all_105_2) = v0 & 206.81/127.90 | | | | | length1(int, all_105_4) = v0) | ( ~ (v0 = 0) & 206.81/127.90 | | | | | permut3(int, all_105_4, all_105_2, 0, all_86_13) = v0)) 206.81/127.90 | | | | | 206.81/127.91 | | | | | GROUND_INST: instantiating (52) with int, all_105_4, all_105_2, 0, 206.81/127.91 | | | | | all_86_13, all_105_3, all_105_1, simplifying with (11), 206.81/127.91 | | | | | (33), (37), (141) gives: 206.81/127.91 | | | | | (201) ~ ($lesseq(0, all_86_13)) | ? [v0: $int] : ? [v1: $int] : 206.81/127.91 | | | | | ((v0 = 0 & permut3(int, all_105_4, all_105_2, 0, all_86_13) = 206.81/127.91 | | | | | 0) | (length1(int, all_105_4) = v0 & ( ~ 206.81/127.91 | | | | | ($lesseq(all_86_13, v0)) | ~ ($lesseq(0, v0)) | ( ~ 206.81/127.91 | | | | | (v1 = v0) & length1(int, all_105_2) = v1)))) 206.81/127.91 | | | | | 206.81/127.91 | | | | | GROUND_INST: instantiating (15) with int, all_103_2, all_105_4, 0, 206.81/127.91 | | | | | all_86_13, all_103_1, all_105_3, 0, simplifying with 206.81/127.91 | | | | | (11), (28), (33), (60) gives: 206.81/127.91 | | | | | (202) ? [v0: $int] : ? [v1: $int] : ((v1 = v0 & 206.81/127.91 | | | | | $lesseq(all_86_13, v0) & $lesseq(0, v0) & $lesseq(0, 206.81/127.91 | | | | | all_86_13) & length1(int, all_105_4) = v0 & 206.81/127.91 | | | | | length1(int, all_103_2) = v0) | ( ~ (v0 = 0) & 206.81/127.91 | | | | | permut3(int, all_103_2, all_105_4, 0, all_86_13) = v0)) 206.81/127.91 | | | | | 206.81/127.91 | | | | | GROUND_INST: instantiating (52) with int, all_103_2, all_105_4, 0, 206.81/127.91 | | | | | all_86_13, all_103_1, all_105_3, simplifying with (11), 206.81/127.91 | | | | | (28), (33), (60) gives: 206.81/127.91 | | | | | (203) ~ ($lesseq(0, all_86_13)) | ? [v0: $int] : ? [v1: $int] : 206.81/127.91 | | | | | ((v0 = 0 & permut3(int, all_103_2, all_105_4, 0, all_86_13) = 206.81/127.91 | | | | | 0) | (length1(int, all_103_2) = v0 & ( ~ 206.81/127.91 | | | | | ($lesseq(all_86_13, v0)) | ~ ($lesseq(0, v0)) | ( ~ 206.81/127.91 | | | | | (v1 = v0) & length1(int, all_105_4) = v1)))) 206.81/127.91 | | | | | 206.81/127.91 | | | | | GROUND_INST: instantiating (15) with int, all_103_4, all_105_4, 206.81/127.91 | | | | | all_86_11, $sum(all_86_10, 1), all_103_3, all_105_3, 0, 206.81/127.91 | | | | | simplifying with (8), (11), (29), (33) gives: 206.81/127.91 | | | | | (204) ? [v0: $int] : ? [v1: $int] : ((v1 = v0 & $lesseq(1, 206.81/127.91 | | | | | $difference(v0, all_86_10)) & $lesseq(all_86_11, v0) & 206.81/127.91 | | | | | $lesseq(-1, all_86_10) & $lesseq(0, all_86_11) & 206.81/127.91 | | | | | length1(int, all_105_4) = v0 & length1(int, all_103_4) = 206.81/127.91 | | | | | v0) | ( ~ (v0 = 0) & permut3(int, all_103_4, all_105_4, 206.81/127.91 | | | | | all_86_11, $sum(all_86_10, 1)) = v0)) 206.81/127.91 | | | | | 206.81/127.91 | | | | | GROUND_INST: instantiating (20) with int, all_103_3, all_105_3, 206.81/127.91 | | | | | all_105_1, all_86_11, $sum(all_86_10, 1), simplifying 206.81/127.91 | | | | | with (11), (29) gives: 206.81/127.91 | | | | | (205) ~ (permut2(int, all_105_3, all_105_1, all_86_11, 206.81/127.91 | | | | | $sum(all_86_10, 1)) = 0) | permut2(int, all_103_3, 206.81/127.91 | | | | | all_105_1, all_86_11, $sum(all_86_10, 1)) = 0 206.81/127.91 | | | | | 206.81/127.91 | | | | | GROUND_INST: instantiating (52) with int, all_103_4, all_105_4, 206.81/127.91 | | | | | all_86_11, $sum(all_86_10, 1), all_103_3, all_105_3, 206.81/127.91 | | | | | simplifying with (8), (11), (29), (33) gives: 206.81/127.91 | | | | | (206) ~ ($lesseq(-1, all_86_10)) | ~ ($lesseq(0, all_86_11)) | ? 206.81/127.91 | | | | | [v0: $int] : ? [v1: $int] : ((v0 = 0 & permut3(int, 206.81/127.91 | | | | | all_103_4, all_105_4, all_86_11, $sum(all_86_10, 1)) = 206.81/127.91 | | | | | 0) | (length1(int, all_103_4) = v0 & ( ~ ($lesseq(1, 206.81/127.91 | | | | | $difference(v0, all_86_10))) | ~ 206.81/127.91 | | | | | ($lesseq(all_86_11, v0)) | ( ~ (v1 = v0) & length1(int, 206.81/127.91 | | | | | all_105_4) = v1)))) 206.81/127.91 | | | | | 206.81/127.91 | | | | | GROUND_INST: instantiating (15) with int, all_103_4, all_103_2, 0, 206.81/127.91 | | | | | all_86_13, all_103_3, all_103_1, 0, simplifying with (8), 206.81/127.91 | | | | | (11), (60), (170) gives: 206.81/127.91 | | | | | (207) ? [v0: $int] : ? [v1: $int] : ((v1 = v0 & 206.81/127.91 | | | | | $lesseq(all_86_13, v0) & $lesseq(0, v0) & $lesseq(0, 206.81/127.91 | | | | | all_86_13) & length1(int, all_103_2) = v0 & 206.81/127.91 | | | | | length1(int, all_103_4) = v0) | ( ~ (v0 = 0) & 206.81/127.91 | | | | | permut3(int, all_103_4, all_103_2, 0, all_86_13) = v0)) 206.81/127.91 | | | | | 206.81/127.91 | | | | | GROUND_INST: instantiating (52) with int, all_103_4, all_103_2, 0, 206.81/127.91 | | | | | all_86_13, all_103_3, all_103_1, simplifying with (8), 206.81/127.91 | | | | | (11), (60), (170) gives: 206.81/127.91 | | | | | (208) ~ ($lesseq(0, all_86_13)) | ? [v0: $int] : ? [v1: $int] : 206.81/127.91 | | | | | ((v0 = 0 & permut3(int, all_103_4, all_103_2, 0, all_86_13) = 206.81/127.91 | | | | | 0) | (length1(int, all_103_4) = v0 & ( ~ 206.81/127.91 | | | | | ($lesseq(all_86_13, v0)) | ~ ($lesseq(0, v0)) | ( ~ 206.81/127.91 | | | | | (v1 = v0) & length1(int, all_103_2) = v1)))) 206.81/127.91 | | | | | 206.81/127.91 | | | | | GROUND_INST: instantiating (61) with all_86_1, all_133_2, all_105_2, 206.81/127.91 | | | | | all_133_1, simplifying with (40), (50), (199) gives: 206.81/127.91 | | | | | (209) ? [v0: $int] : ? [v1: $int] : ? [v2: $int] : (tb2t(v0) = 206.81/127.91 | | | | | v1 & tb2t1(all_133_1) = v2 & get3(v1, all_133_2) = v2 & 206.81/127.91 | | | | | elts(int, all_105_2) = v0 & in_map_int_int(v1) & 206.81/127.91 | | | | | in_uni(v0)) 206.81/127.91 | | | | | 206.81/127.91 | | | | | GROUND_INST: instantiating (66) with int, all_105_2, all_133_2, 206.81/127.91 | | | | | all_133_1, simplifying with (11), (199) gives: 206.81/127.91 | | | | | (210) ? [v0: $int] : ? [v1: $int] : (elts(int, all_105_2) = v0 & 206.81/127.91 | | | | | t2tb1(all_133_2) = v1 & get(int, int, v0, v1) = all_133_1 & 206.81/127.91 | | | | | in_uni(v1) & in_uni(v0) & in_uni(all_133_1)) 206.81/127.91 | | | | | 206.81/127.91 | | | | | DELTA: instantiating (202) with fresh symbols all_769_0, all_769_1 206.81/127.91 | | | | | gives: 206.81/127.91 | | | | | (211) (all_769_0 = all_769_1 & $lesseq(all_86_13, all_769_1) & 206.81/127.91 | | | | | $lesseq(0, all_769_1) & $lesseq(0, all_86_13) & 206.81/127.91 | | | | | length1(int, all_105_4) = all_769_1 & length1(int, 206.81/127.91 | | | | | all_103_2) = all_769_1) | ( ~ (all_769_1 = 0) & 206.81/127.91 | | | | | permut3(int, all_103_2, all_105_4, 0, all_86_13) = 206.81/127.91 | | | | | all_769_1) 206.81/127.91 | | | | | 206.81/127.91 | | | | | DELTA: instantiating (207) with fresh symbols all_770_0, all_770_1 206.81/127.91 | | | | | gives: 206.81/127.91 | | | | | (212) (all_770_0 = all_770_1 & $lesseq(all_86_13, all_770_1) & 206.81/127.91 | | | | | $lesseq(0, all_770_1) & $lesseq(0, all_86_13) & 206.81/127.91 | | | | | length1(int, all_103_2) = all_770_1 & length1(int, 206.81/127.91 | | | | | all_103_4) = all_770_1) | ( ~ (all_770_1 = 0) & 206.81/127.91 | | | | | permut3(int, all_103_4, all_103_2, 0, all_86_13) = 206.81/127.91 | | | | | all_770_1) 206.81/127.91 | | | | | 206.81/127.91 | | | | | DELTA: instantiating (204) with fresh symbols all_771_0, all_771_1 206.81/127.91 | | | | | gives: 206.81/127.91 | | | | | (213) (all_771_0 = all_771_1 & $lesseq(1, $difference(all_771_1, 206.81/127.91 | | | | | all_86_10)) & $lesseq(all_86_11, all_771_1) & 206.81/127.91 | | | | | $lesseq(-1, all_86_10) & $lesseq(0, all_86_11) & 206.81/127.91 | | | | | length1(int, all_105_4) = all_771_1 & length1(int, 206.81/127.91 | | | | | all_103_4) = all_771_1) | ( ~ (all_771_1 = 0) & 206.81/127.91 | | | | | permut3(int, all_103_4, all_105_4, all_86_11, 206.81/127.91 | | | | | $sum(all_86_10, 1)) = all_771_1) 206.81/127.91 | | | | | 206.81/127.91 | | | | | DELTA: instantiating (200) with fresh symbols all_772_0, all_772_1 206.81/127.91 | | | | | gives: 206.81/127.91 | | | | | (214) (all_772_0 = all_772_1 & $lesseq(all_86_13, all_772_1) & 206.81/127.91 | | | | | $lesseq(0, all_772_1) & $lesseq(0, all_86_13) & 206.81/127.91 | | | | | length1(int, all_105_2) = all_772_1 & length1(int, 206.81/127.91 | | | | | all_105_4) = all_772_1) | ( ~ (all_772_1 = 0) & 206.81/127.91 | | | | | permut3(int, all_105_4, all_105_2, 0, all_86_13) = 206.81/127.91 | | | | | all_772_1) 206.81/127.91 | | | | | 206.81/127.91 | | | | | DELTA: instantiating (210) with fresh symbols all_773_0, all_773_1 206.81/127.91 | | | | | gives: 206.81/127.91 | | | | | (215) elts(int, all_105_2) = all_773_1 & t2tb1(all_133_2) = 206.81/127.91 | | | | | all_773_0 & get(int, int, all_773_1, all_773_0) = all_133_1 & 206.81/127.91 | | | | | in_uni(all_773_0) & in_uni(all_773_1) & in_uni(all_133_1) 206.81/127.91 | | | | | 206.81/127.91 | | | | | ALPHA: (215) implies: 206.81/127.91 | | | | | (216) get(int, int, all_773_1, all_773_0) = all_133_1 206.81/127.91 | | | | | (217) t2tb1(all_133_2) = all_773_0 206.81/127.91 | | | | | (218) elts(int, all_105_2) = all_773_1 206.81/127.91 | | | | | 206.81/127.91 | | | | | DELTA: instantiating (209) with fresh symbols all_775_0, all_775_1, 206.81/127.91 | | | | | all_775_2 gives: 206.81/127.91 | | | | | (219) tb2t(all_775_2) = all_775_1 & tb2t1(all_133_1) = all_775_0 & 206.81/127.91 | | | | | get3(all_775_1, all_133_2) = all_775_0 & elts(int, all_105_2) 206.81/127.91 | | | | | = all_775_2 & in_map_int_int(all_775_1) & in_uni(all_775_2) 206.81/127.91 | | | | | 206.81/127.91 | | | | | ALPHA: (219) implies: 206.81/127.91 | | | | | (220) elts(int, all_105_2) = all_775_2 206.81/127.91 | | | | | (221) get3(all_775_1, all_133_2) = all_775_0 206.81/127.91 | | | | | (222) tb2t1(all_133_1) = all_775_0 206.81/127.91 | | | | | (223) tb2t(all_775_2) = all_775_1 206.81/127.91 | | | | | 206.81/127.91 | | | | | BETA: splitting (201) gives: 206.81/127.91 | | | | | 206.81/127.91 | | | | | Case 1: 206.81/127.91 | | | | | | 206.81/127.91 | | | | | | (224) $lesseq(all_86_13, -1) 206.81/127.91 | | | | | | 206.81/127.91 | | | | | | COMBINE_INEQS: (13), (224) imply: 206.81/127.91 | | | | | | (225) $lesseq(0, -1) 206.81/127.91 | | | | | | 206.81/127.91 | | | | | | CLOSE: (225) is inconsistent. 206.81/127.91 | | | | | | 206.81/127.91 | | | | | Case 2: 206.81/127.91 | | | | | | 206.81/127.91 | | | | | | (226) ? [v0: $int] : ? [v1: $int] : ((v0 = 0 & permut3(int, 206.81/127.91 | | | | | | all_105_4, all_105_2, 0, all_86_13) = 0) | 206.81/127.91 | | | | | | (length1(int, all_105_4) = v0 & ( ~ ($lesseq(all_86_13, 206.81/127.91 | | | | | | v0)) | ~ ($lesseq(0, v0)) | ( ~ (v1 = v0) & 206.81/127.91 | | | | | | length1(int, all_105_2) = v1)))) 206.81/127.91 | | | | | | 206.81/127.91 | | | | | | DELTA: instantiating (226) with fresh symbols all_798_0, all_798_1 206.81/127.91 | | | | | | gives: 206.81/127.91 | | | | | | (227) (all_798_1 = 0 & permut3(int, all_105_4, all_105_2, 0, 206.81/127.91 | | | | | | all_86_13) = 0) | (length1(int, all_105_4) = all_798_1 206.81/127.91 | | | | | | & ( ~ ($lesseq(all_86_13, all_798_1)) | ~ ($lesseq(0, 206.81/127.91 | | | | | | all_798_1)) | ( ~ (all_798_0 = all_798_1) & 206.81/127.91 | | | | | | length1(int, all_105_2) = all_798_0))) 206.81/127.91 | | | | | | 206.81/127.91 | | | | | | BETA: splitting (227) gives: 206.81/127.91 | | | | | | 206.81/127.91 | | | | | | Case 1: 206.81/127.91 | | | | | | | 206.81/127.91 | | | | | | | (228) all_798_1 = 0 & permut3(int, all_105_4, all_105_2, 0, 206.81/127.91 | | | | | | | all_86_13) = 0 206.81/127.91 | | | | | | | 206.81/127.91 | | | | | | | ALPHA: (228) implies: 206.81/127.91 | | | | | | | (229) permut3(int, all_105_4, all_105_2, 0, all_86_13) = 0 206.81/127.91 | | | | | | | 206.81/127.91 | | | | | | | BETA: splitting (214) gives: 206.81/127.91 | | | | | | | 206.81/127.91 | | | | | | | Case 1: 206.81/127.91 | | | | | | | | 206.81/127.91 | | | | | | | | (230) all_772_0 = all_772_1 & $lesseq(all_86_13, all_772_1) & 206.81/127.91 | | | | | | | | $lesseq(0, all_772_1) & $lesseq(0, all_86_13) & 206.81/127.91 | | | | | | | | length1(int, all_105_2) = all_772_1 & length1(int, 206.81/127.91 | | | | | | | | all_105_4) = all_772_1 206.81/127.91 | | | | | | | | 206.81/127.91 | | | | | | | | ALPHA: (230) implies: 206.81/127.91 | | | | | | | | (231) length1(int, all_105_4) = all_772_1 206.81/127.91 | | | | | | | | (232) length1(int, all_105_2) = all_772_1 206.81/127.91 | | | | | | | | 206.81/127.91 | | | | | | | | BETA: splitting (203) gives: 206.81/127.91 | | | | | | | | 206.81/127.91 | | | | | | | | Case 1: 206.81/127.91 | | | | | | | | | 206.81/127.91 | | | | | | | | | (233) $lesseq(all_86_13, -1) 206.81/127.91 | | | | | | | | | 206.81/127.91 | | | | | | | | | COMBINE_INEQS: (13), (233) imply: 206.81/127.91 | | | | | | | | | (234) $lesseq(0, -1) 206.81/127.91 | | | | | | | | | 206.81/127.91 | | | | | | | | | CLOSE: (234) is inconsistent. 206.81/127.91 | | | | | | | | | 206.81/127.91 | | | | | | | | Case 2: 206.81/127.91 | | | | | | | | | 206.81/127.91 | | | | | | | | | (235) ? [v0: $int] : ? [v1: $int] : ((v0 = 0 & 206.81/127.91 | | | | | | | | | permut3(int, all_103_2, all_105_4, 0, all_86_13) 206.81/127.91 | | | | | | | | | = 0) | (length1(int, all_103_2) = v0 & ( ~ 206.81/127.91 | | | | | | | | | ($lesseq(all_86_13, v0)) | ~ ($lesseq(0, v0)) 206.81/127.91 | | | | | | | | | | ( ~ (v1 = v0) & length1(int, all_105_4) = 206.81/127.91 | | | | | | | | | v1)))) 206.81/127.91 | | | | | | | | | 206.81/127.91 | | | | | | | | | DELTA: instantiating (235) with fresh symbols all_822_0, 206.81/127.91 | | | | | | | | | all_822_1 gives: 206.81/127.91 | | | | | | | | | (236) (all_822_1 = 0 & permut3(int, all_103_2, all_105_4, 206.81/127.91 | | | | | | | | | 0, all_86_13) = 0) | (length1(int, all_103_2) = 206.81/127.91 | | | | | | | | | all_822_1 & ( ~ ($lesseq(all_86_13, all_822_1)) | 206.81/127.91 | | | | | | | | | ~ ($lesseq(0, all_822_1)) | ( ~ (all_822_0 = 206.81/127.91 | | | | | | | | | all_822_1) & length1(int, all_105_4) = 206.81/127.91 | | | | | | | | | all_822_0))) 206.81/127.91 | | | | | | | | | 206.81/127.91 | | | | | | | | | BETA: splitting (208) gives: 206.81/127.91 | | | | | | | | | 206.81/127.91 | | | | | | | | | Case 1: 206.81/127.91 | | | | | | | | | | 206.81/127.91 | | | | | | | | | | (237) $lesseq(all_86_13, -1) 206.81/127.91 | | | | | | | | | | 206.81/127.91 | | | | | | | | | | COMBINE_INEQS: (13), (237) imply: 206.81/127.91 | | | | | | | | | | (238) $lesseq(0, -1) 206.81/127.91 | | | | | | | | | | 206.81/127.91 | | | | | | | | | | CLOSE: (238) is inconsistent. 206.81/127.91 | | | | | | | | | | 206.81/127.91 | | | | | | | | | Case 2: 206.81/127.91 | | | | | | | | | | 206.81/127.91 | | | | | | | | | | (239) ? [v0: $int] : ? [v1: $int] : ((v0 = 0 & 206.81/127.91 | | | | | | | | | | permut3(int, all_103_4, all_103_2, 0, 206.81/127.91 | | | | | | | | | | all_86_13) = 0) | (length1(int, all_103_4) = 206.81/127.91 | | | | | | | | | | v0 & ( ~ ($lesseq(all_86_13, v0)) | ~ 206.81/127.91 | | | | | | | | | | ($lesseq(0, v0)) | ( ~ (v1 = v0) & 206.81/127.91 | | | | | | | | | | length1(int, all_103_2) = v1)))) 206.81/127.91 | | | | | | | | | | 206.81/127.91 | | | | | | | | | | DELTA: instantiating (239) with fresh symbols all_828_0, 206.81/127.91 | | | | | | | | | | all_828_1 gives: 206.81/127.91 | | | | | | | | | | (240) (all_828_1 = 0 & permut3(int, all_103_4, all_103_2, 206.81/127.91 | | | | | | | | | | 0, all_86_13) = 0) | (length1(int, all_103_4) = 206.81/127.91 | | | | | | | | | | all_828_1 & ( ~ ($lesseq(all_86_13, all_828_1)) | 206.81/127.91 | | | | | | | | | | ~ ($lesseq(0, all_828_1)) | ( ~ (all_828_0 = 206.81/127.91 | | | | | | | | | | all_828_1) & length1(int, all_103_2) = 206.81/127.91 | | | | | | | | | | all_828_0))) 206.81/127.91 | | | | | | | | | | 206.81/127.91 | | | | | | | | | | BETA: splitting (206) gives: 206.81/127.91 | | | | | | | | | | 206.81/127.91 | | | | | | | | | | Case 1: 206.81/127.91 | | | | | | | | | | | 206.81/127.91 | | | | | | | | | | | (241) $lesseq(all_86_11, -1) 206.81/127.91 | | | | | | | | | | | 206.81/127.91 | | | | | | | | | | | COMBINE_INEQS: (59), (241) imply: 206.81/127.91 | | | | | | | | | | | (242) $lesseq(0, -1) 206.81/127.91 | | | | | | | | | | | 206.81/127.91 | | | | | | | | | | | CLOSE: (242) is inconsistent. 206.81/127.91 | | | | | | | | | | | 206.81/127.91 | | | | | | | | | | Case 2: 206.81/127.91 | | | | | | | | | | | 206.81/127.91 | | | | | | | | | | | (243) ~ ($lesseq(-1, all_86_10)) | ? [v0: $int] : ? 206.81/127.91 | | | | | | | | | | | [v1: $int] : ((v0 = 0 & permut3(int, all_103_4, 206.81/127.91 | | | | | | | | | | | all_105_4, all_86_11, $sum(all_86_10, 1)) = 206.81/127.91 | | | | | | | | | | | 0) | (length1(int, all_103_4) = v0 & ( ~ 206.81/127.91 | | | | | | | | | | | ($lesseq(1, $difference(v0, all_86_10))) | 206.81/127.91 | | | | | | | | | | | ~ ($lesseq(all_86_11, v0)) | ( ~ (v1 = v0) & 206.81/127.91 | | | | | | | | | | | length1(int, all_105_4) = v1)))) 206.81/127.91 | | | | | | | | | | | 206.81/127.91 | | | | | | | | | | | BETA: splitting (240) gives: 206.81/127.91 | | | | | | | | | | | 206.81/127.91 | | | | | | | | | | | Case 1: 206.81/127.91 | | | | | | | | | | | | 206.81/127.91 | | | | | | | | | | | | (244) all_828_1 = 0 & permut3(int, all_103_4, all_103_2, 206.81/127.91 | | | | | | | | | | | | 0, all_86_13) = 0 206.81/127.91 | | | | | | | | | | | | 206.81/127.91 | | | | | | | | | | | | ALPHA: (244) implies: 206.81/127.91 | | | | | | | | | | | | (245) permut3(int, all_103_4, all_103_2, 0, all_86_13) = 206.81/127.91 | | | | | | | | | | | | 0 206.81/127.91 | | | | | | | | | | | | 206.81/127.91 | | | | | | | | | | | | BETA: splitting (212) gives: 206.81/127.91 | | | | | | | | | | | | 206.81/127.91 | | | | | | | | | | | | Case 1: 206.81/127.91 | | | | | | | | | | | | | 206.81/127.91 | | | | | | | | | | | | | (246) all_770_0 = all_770_1 & $lesseq(all_86_13, 206.81/127.91 | | | | | | | | | | | | | all_770_1) & $lesseq(0, all_770_1) & $lesseq(0, 206.81/127.91 | | | | | | | | | | | | | all_86_13) & length1(int, all_103_2) = all_770_1 206.81/127.91 | | | | | | | | | | | | | & length1(int, all_103_4) = all_770_1 206.81/127.91 | | | | | | | | | | | | | 206.81/127.91 | | | | | | | | | | | | | ALPHA: (246) implies: 206.81/127.91 | | | | | | | | | | | | | (247) length1(int, all_103_4) = all_770_1 206.81/127.91 | | | | | | | | | | | | | (248) length1(int, all_103_2) = all_770_1 206.81/127.91 | | | | | | | | | | | | | 206.81/127.91 | | | | | | | | | | | | | BETA: splitting (243) gives: 206.81/127.91 | | | | | | | | | | | | | 206.81/127.91 | | | | | | | | | | | | | Case 1: 206.81/127.91 | | | | | | | | | | | | | | 206.81/127.91 | | | | | | | | | | | | | | (249) $lesseq(all_86_10, -2) 206.81/127.91 | | | | | | | | | | | | | | 206.81/127.91 | | | | | | | | | | | | | | COMBINE_INEQS: (67), (249) imply: 206.81/127.91 | | | | | | | | | | | | | | (250) $lesseq(0, -1) 206.81/127.91 | | | | | | | | | | | | | | 206.81/127.91 | | | | | | | | | | | | | | CLOSE: (250) is inconsistent. 206.81/127.91 | | | | | | | | | | | | | | 206.81/127.91 | | | | | | | | | | | | | Case 2: 206.81/127.91 | | | | | | | | | | | | | | 206.81/127.91 | | | | | | | | | | | | | | (251) ? [v0: $int] : ? [v1: $int] : ((v0 = 0 & 206.81/127.91 | | | | | | | | | | | | | | permut3(int, all_103_4, all_105_4, all_86_11, 206.81/127.91 | | | | | | | | | | | | | | $sum(all_86_10, 1)) = 0) | (length1(int, 206.81/127.91 | | | | | | | | | | | | | | all_103_4) = v0 & ( ~ ($lesseq(1, 206.81/127.91 | | | | | | | | | | | | | | $difference(v0, all_86_10))) | ~ 206.81/127.91 | | | | | | | | | | | | | | ($lesseq(all_86_11, v0)) | ( ~ (v1 = v0) & 206.81/127.91 | | | | | | | | | | | | | | length1(int, all_105_4) = v1)))) 206.81/127.91 | | | | | | | | | | | | | | 206.81/127.91 | | | | | | | | | | | | | | DELTA: instantiating (251) with fresh symbols all_852_0, 206.81/127.91 | | | | | | | | | | | | | | all_852_1 gives: 206.81/127.91 | | | | | | | | | | | | | | (252) (all_852_1 = 0 & permut3(int, all_103_4, 206.81/127.91 | | | | | | | | | | | | | | all_105_4, all_86_11, $sum(all_86_10, 1)) = 0) 206.81/127.91 | | | | | | | | | | | | | | | (length1(int, all_103_4) = all_852_1 & ( ~ 206.81/127.91 | | | | | | | | | | | | | | ($lesseq(1, $difference(all_852_1, 206.81/127.91 | | | | | | | | | | | | | | all_86_10))) | ~ ($lesseq(all_86_11, 206.81/127.91 | | | | | | | | | | | | | | all_852_1)) | ( ~ (all_852_0 = all_852_1) 206.81/127.91 | | | | | | | | | | | | | | & length1(int, all_105_4) = all_852_0))) 206.81/127.91 | | | | | | | | | | | | | | 206.81/127.91 | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_133_0, all_775_0, 206.81/127.91 | | | | | | | | | | | | | | all_133_1, simplifying with (198), (222) gives: 206.81/127.91 | | | | | | | | | | | | | | (253) all_775_0 = all_133_0 206.81/127.91 | | | | | | | | | | | | | | 206.81/127.91 | | | | | | | | | | | | | | GROUND_INST: instantiating (65) with all_86_13, all_772_1, 206.81/127.91 | | | | | | | | | | | | | | all_105_4, int, simplifying with (31), (231) 206.81/127.91 | | | | | | | | | | | | | | gives: 206.81/127.91 | | | | | | | | | | | | | | (254) all_772_1 = all_86_13 206.81/127.91 | | | | | | | | | | | | | | 206.81/127.91 | | | | | | | | | | | | | | GROUND_INST: instantiating (65) with all_86_13, all_770_1, 206.81/127.91 | | | | | | | | | | | | | | all_103_4, int, simplifying with (12), (247) 206.81/127.91 | | | | | | | | | | | | | | gives: 206.81/127.91 | | | | | | | | | | | | | | (255) all_770_1 = all_86_13 206.81/127.91 | | | | | | | | | | | | | | 206.81/127.91 | | | | | | | | | | | | | | GROUND_INST: instantiating (30) with all_105_1, all_775_2, 206.81/127.91 | | | | | | | | | | | | | | all_105_2, int, simplifying with (37), (220) 206.81/127.91 | | | | | | | | | | | | | | gives: 206.81/127.91 | | | | | | | | | | | | | | (256) all_775_2 = all_105_1 206.81/127.91 | | | | | | | | | | | | | | 206.81/127.91 | | | | | | | | | | | | | | GROUND_INST: instantiating (30) with all_775_2, all_773_1, 206.81/127.91 | | | | | | | | | | | | | | all_105_2, int, simplifying with (218), (220) 206.81/127.91 | | | | | | | | | | | | | | gives: 206.81/127.91 | | | | | | | | | | | | | | (257) all_775_2 = all_773_1 206.81/127.91 | | | | | | | | | | | | | | 206.81/127.91 | | | | | | | | | | | | | | COMBINE_EQS: (256), (257) imply: 206.81/127.91 | | | | | | | | | | | | | | (258) all_773_1 = all_105_1 206.81/127.91 | | | | | | | | | | | | | | 206.81/127.91 | | | | | | | | | | | | | | SIMP: (258) implies: 206.81/127.91 | | | | | | | | | | | | | | (259) all_773_1 = all_105_1 206.81/127.91 | | | | | | | | | | | | | | 206.81/127.91 | | | | | | | | | | | | | | REDUCE: (223), (256) imply: 206.81/127.91 | | | | | | | | | | | | | | (260) tb2t(all_105_1) = all_775_1 206.81/127.91 | | | | | | | | | | | | | | 206.81/127.91 | | | | | | | | | | | | | | REDUCE: (221), (253) imply: 206.81/127.91 | | | | | | | | | | | | | | (261) get3(all_775_1, all_133_2) = all_133_0 206.81/127.91 | | | | | | | | | | | | | | 206.81/127.91 | | | | | | | | | | | | | | REDUCE: (216), (259) imply: 206.81/127.91 | | | | | | | | | | | | | | (262) get(int, int, all_105_1, all_773_0) = all_133_1 206.81/127.91 | | | | | | | | | | | | | | 206.81/127.91 | | | | | | | | | | | | | | BETA: splitting (236) gives: 206.81/127.91 | | | | | | | | | | | | | | 206.81/127.91 | | | | | | | | | | | | | | Case 1: 206.81/127.91 | | | | | | | | | | | | | | | 206.81/127.91 | | | | | | | | | | | | | | | (263) all_822_1 = 0 & permut3(int, all_103_2, all_105_4, 206.81/127.91 | | | | | | | | | | | | | | | 0, all_86_13) = 0 206.81/127.91 | | | | | | | | | | | | | | | 206.81/127.91 | | | | | | | | | | | | | | | ALPHA: (263) implies: 206.81/127.91 | | | | | | | | | | | | | | | (264) permut3(int, all_103_2, all_105_4, 0, all_86_13) = 206.81/127.91 | | | | | | | | | | | | | | | 0 206.81/127.91 | | | | | | | | | | | | | | | 206.81/127.91 | | | | | | | | | | | | | | | BETA: splitting (211) gives: 206.81/127.91 | | | | | | | | | | | | | | | 206.81/127.91 | | | | | | | | | | | | | | | Case 1: 206.81/127.91 | | | | | | | | | | | | | | | | 206.81/127.91 | | | | | | | | | | | | | | | | (265) all_769_0 = all_769_1 & $lesseq(all_86_13, 206.81/127.91 | | | | | | | | | | | | | | | | all_769_1) & $lesseq(0, all_769_1) & $lesseq(0, 206.81/127.91 | | | | | | | | | | | | | | | | all_86_13) & length1(int, all_105_4) = all_769_1 206.81/127.91 | | | | | | | | | | | | | | | | & length1(int, all_103_2) = all_769_1 206.81/127.91 | | | | | | | | | | | | | | | | 206.81/127.91 | | | | | | | | | | | | | | | | ALPHA: (265) implies: 206.81/127.91 | | | | | | | | | | | | | | | | (266) length1(int, all_103_2) = all_769_1 206.81/127.91 | | | | | | | | | | | | | | | | (267) length1(int, all_105_4) = all_769_1 206.81/127.91 | | | | | | | | | | | | | | | | 206.81/127.91 | | | | | | | | | | | | | | | | BETA: splitting (252) gives: 206.81/127.91 | | | | | | | | | | | | | | | | 206.81/127.91 | | | | | | | | | | | | | | | | Case 1: 206.81/127.91 | | | | | | | | | | | | | | | | | 206.81/127.91 | | | | | | | | | | | | | | | | | (268) all_852_1 = 0 & permut3(int, all_103_4, all_105_4, 206.81/127.91 | | | | | | | | | | | | | | | | | all_86_11, $sum(all_86_10, 1)) = 0 206.81/127.91 | | | | | | | | | | | | | | | | | 206.81/127.91 | | | | | | | | | | | | | | | | | ALPHA: (268) implies: 206.81/127.92 | | | | | | | | | | | | | | | | | (269) permut3(int, all_103_4, all_105_4, all_86_11, 206.81/127.92 | | | | | | | | | | | | | | | | | $sum(all_86_10, 1)) = 0 206.81/127.92 | | | | | | | | | | | | | | | | | 206.81/127.92 | | | | | | | | | | | | | | | | | BETA: splitting (213) gives: 206.81/127.92 | | | | | | | | | | | | | | | | | 206.81/127.92 | | | | | | | | | | | | | | | | | Case 1: 206.81/127.92 | | | | | | | | | | | | | | | | | | 206.81/127.92 | | | | | | | | | | | | | | | | | | (270) all_771_0 = all_771_1 & $lesseq(1, 206.81/127.92 | | | | | | | | | | | | | | | | | | $difference(all_771_1, all_86_10)) & 206.81/127.92 | | | | | | | | | | | | | | | | | | $lesseq(all_86_11, all_771_1) & $lesseq(-1, 206.81/127.92 | | | | | | | | | | | | | | | | | | all_86_10) & $lesseq(0, all_86_11) & 206.81/127.92 | | | | | | | | | | | | | | | | | | length1(int, all_105_4) = all_771_1 & length1(int, 206.81/127.92 | | | | | | | | | | | | | | | | | | all_103_4) = all_771_1 206.81/127.92 | | | | | | | | | | | | | | | | | | 206.81/127.92 | | | | | | | | | | | | | | | | | | ALPHA: (270) implies: 206.81/127.92 | | | | | | | | | | | | | | | | | | (271) $lesseq(1, $difference(all_771_1, all_86_10)) 206.81/127.92 | | | | | | | | | | | | | | | | | | (272) length1(int, all_103_4) = all_771_1 206.81/127.92 | | | | | | | | | | | | | | | | | | (273) length1(int, all_105_4) = all_771_1 206.81/127.92 | | | | | | | | | | | | | | | | | | 206.81/127.92 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (62) with all_86_2, all_775_1, 206.81/127.92 | | | | | | | | | | | | | | | | | | all_105_1, simplifying with (35), (260) gives: 206.81/127.92 | | | | | | | | | | | | | | | | | | (274) all_775_1 = all_86_2 206.81/127.92 | | | | | | | | | | | | | | | | | | 206.81/127.92 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (65) with all_771_1, all_769_1, 206.81/127.92 | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (267), (273) 206.81/127.92 | | | | | | | | | | | | | | | | | | gives: 206.81/127.92 | | | | | | | | | | | | | | | | | | (275) all_771_1 = all_769_1 206.81/127.92 | | | | | | | | | | | | | | | | | | 206.81/127.92 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (65) with all_86_13, all_771_1, 206.81/127.92 | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (12), (272) 206.81/127.92 | | | | | | | | | | | | | | | | | | gives: 206.81/127.92 | | | | | | | | | | | | | | | | | | (276) all_771_1 = all_86_13 206.81/127.92 | | | | | | | | | | | | | | | | | | 206.81/127.92 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (275), (276) imply: 206.81/127.92 | | | | | | | | | | | | | | | | | | (277) all_769_1 = all_86_13 206.81/127.92 | | | | | | | | | | | | | | | | | | 206.81/127.92 | | | | | | | | | | | | | | | | | | COMBINE_INEQS: (43), (53) imply: 206.81/127.92 | | | | | | | | | | | | | | | | | | (278) $lesseq(1, $difference(all_86_10, all_86_8)) 206.81/127.92 | | | | | | | | | | | | | | | | | | 206.81/127.92 | | | | | | | | | | | | | | | | | | COMBINE_INEQS: (41), (278) imply: 206.81/127.92 | | | | | | | | | | | | | | | | | | (279) $lesseq(1, $difference(all_86_10, all_86_11)) 206.81/127.92 | | | | | | | | | | | | | | | | | | 206.81/127.92 | | | | | | | | | | | | | | | | | | REDUCE: (261), (274) imply: 206.81/127.92 | | | | | | | | | | | | | | | | | | (280) get3(all_86_2, all_133_2) = all_133_0 206.81/127.92 | | | | | | | | | | | | | | | | | | 206.81/127.92 | | | | | | | | | | | | | | | | | | BETA: splitting (19) gives: 206.81/127.92 | | | | | | | | | | | | | | | | | | 206.81/127.92 | | | | | | | | | | | | | | | | | | Case 1: 206.81/127.92 | | | | | | | | | | | | | | | | | | | 206.81/127.92 | | | | | | | | | | | | | | | | | | | (281) ~ (permut2(int, all_105_3, all_105_1, all_86_11, 206.81/127.92 | | | | | | | | | | | | | | | | | | | $sum(all_86_10, 1)) = 0) 206.81/127.92 | | | | | | | | | | | | | | | | | | | 206.81/127.92 | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (141), (281) imply: 206.81/127.92 | | | | | | | | | | | | | | | | | | | (282) ~ ($difference(all_86_10, all_86_13) = -1) | ~ 206.81/127.92 | | | | | | | | | | | | | | | | | | | (all_86_11 = 0) 206.81/127.92 | | | | | | | | | | | | | | | | | | | 206.81/127.92 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (7), (8), (10), (11), (12), 206.81/127.92 | | | | | | | | | | | | | | | | | | | (15), (24), (25), (27), (28), (29), (30), (31), 206.81/127.92 | | | | | | | | | | | | | | | | | | | (33), (34), (35), (36), (37), (39), (40), (43), 206.81/127.92 | | | | | | | | | | | | | | | | | | | (45), (47), (50), (52), (53), (54), (55), (57), 206.81/127.92 | | | | | | | | | | | | | | | | | | | (58), (59), (60), (61), (62), (64), (65), (66), 206.81/127.92 | | | | | | | | | | | | | | | | | | | (67), (71), (141), (194), (195), (196), (198), 206.81/127.92 | | | | | | | | | | | | | | | | | | | (199), (282) are inconsistent by sub-proof #89. 206.81/127.92 | | | | | | | | | | | | | | | | | | | 206.81/127.92 | | | | | | | | | | | | | | | | | | Case 2: 206.81/127.92 | | | | | | | | | | | | | | | | | | | 206.81/127.92 | | | | | | | | | | | | | | | | | | | (283) permut2(int, all_105_3, all_105_1, all_86_11, 206.81/127.92 | | | | | | | | | | | | | | | | | | | $sum(all_86_10, 1)) = 0 206.81/127.92 | | | | | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | | | | | | BETA: splitting (205) gives: 206.81/127.93 | | | | | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | | | | | | Case 1: 206.81/127.93 | | | | | | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | | | | | | | (284) ~ (permut2(int, all_105_3, all_105_1, all_86_11, 206.81/127.93 | | | | | | | | | | | | | | | | | | | | $sum(all_86_10, 1)) = 0) 206.81/127.93 | | | | | | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (283), (284) imply: 206.81/127.93 | | | | | | | | | | | | | | | | | | | | (285) $false 206.81/127.93 | | | | | | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | | | | | | | CLOSE: (285) is inconsistent. 206.81/127.93 | | | | | | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | | | | | | Case 2: 206.81/127.93 | | | | | | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (64) with all_86_4, all_86_2, 0, 206.81/127.93 | | | | | | | | | | | | | | | | | | | | all_86_7, all_105_3, all_105_1, all_133_2, 206.81/127.93 | | | | | | | | | | | | | | | | | | | | all_133_0, simplifying with (10), (34), (57), 206.81/127.93 | | | | | | | | | | | | | | | | | | | | (71), (280) gives: 206.81/127.93 | | | | | | | | | | | | | | | | | | | | (286) ~ ($lesseq(1, $difference(all_86_7, all_133_2))) 206.81/127.93 | | | | | | | | | | | | | | | | | | | | | ~ ($lesseq(0, all_133_2)) | get3(all_86_4, 206.81/127.93 | | | | | | | | | | | | | | | | | | | | all_133_2) = all_133_0 206.81/127.93 | | | | | | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (45) with all_86_4, all_86_2, 206.81/127.93 | | | | | | | | | | | | | | | | | | | | all_86_7, $sum(all_86_10, 1), all_133_2, 206.81/127.93 | | | | | | | | | | | | | | | | | | | | all_105_3, all_105_1, all_133_0, simplifying with 206.81/127.93 | | | | | | | | | | | | | | | | | | | | (10), (47), (57), (71), (280) gives: 206.81/127.93 | | | | | | | | | | | | | | | | | | | | (287) ~ ($lesseq(all_133_2, all_86_10)) | ~ 206.81/127.93 | | | | | | | | | | | | | | | | | | | | ($lesseq(all_86_7, all_133_2)) | ? [v0: $int] : 206.81/127.93 | | | | | | | | | | | | | | | | | | | | ($lesseq(v0, all_86_10) & $lesseq(all_86_7, v0) & 206.81/127.93 | | | | | | | | | | | | | | | | | | | | get3(all_86_4, v0) = all_133_0) 206.81/127.93 | | | | | | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (54) with int, all_105_3, all_105_1, 206.81/127.93 | | | | | | | | | | | | | | | | | | | | 0, all_86_7, all_133_2, all_773_0, simplifying 206.81/127.93 | | | | | | | | | | | | | | | | | | | | with (11), (34), (217) gives: 206.81/127.93 | | | | | | | | | | | | | | | | | | | | (288) ~ ($lesseq(1, $difference(all_86_7, all_133_2))) 206.81/127.93 | | | | | | | | | | | | | | | | | | | | | ~ ($lesseq(0, all_133_2)) | ? [v0: $int] : 206.81/127.93 | | | | | | | | | | | | | | | | | | | | (get(int, int, all_105_1, all_773_0) = v0 & 206.81/127.93 | | | | | | | | | | | | | | | | | | | | get(int, int, all_105_3, all_773_0) = v0 & 206.81/127.93 | | | | | | | | | | | | | | | | | | | | in_uni(v0)) 206.81/127.93 | | | | | | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with int, all_105_3, all_105_1, 206.81/127.93 | | | | | | | | | | | | | | | | | | | | all_86_7, $sum(all_86_10, 1), all_133_2, 206.81/127.93 | | | | | | | | | | | | | | | | | | | | all_773_0, all_133_1, simplifying with (11), (47), 206.81/127.93 | | | | | | | | | | | | | | | | | | | | (217), (262) gives: 206.81/127.93 | | | | | | | | | | | | | | | | | | | | (289) ~ ($lesseq(all_133_2, all_86_10)) | ~ 206.81/127.93 | | | | | | | | | | | | | | | | | | | | ($lesseq(all_86_7, all_133_2)) | ? [v0: $int] : 206.81/127.93 | | | | | | | | | | | | | | | | | | | | ? [v1: $int] : ($lesseq(v0, all_86_10) & 206.81/127.93 | | | | | | | | | | | | | | | | | | | | $lesseq(all_86_7, v0) & t2tb1(v0) = v1 & 206.81/127.93 | | | | | | | | | | | | | | | | | | | | get(int, int, all_105_3, v1) = all_133_1 & 206.81/127.93 | | | | | | | | | | | | | | | | | | | | in_uni(v1) & in_uni(all_133_1)) 206.81/127.93 | | | | | | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | | | | | | | BETA: splitting (288) gives: 206.81/127.93 | | | | | | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | | | | | | | Case 1: 206.81/127.93 | | | | | | | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | | | | | | | | (290) $lesseq(all_133_2, -1) 206.81/127.93 | | | | | | | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | | | | | | | | COMBINE_INEQS: (194), (290) imply: 206.81/127.93 | | | | | | | | | | | | | | | | | | | | | (291) $lesseq(all_86_11, -1) 206.81/127.93 | | | | | | | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | | | | | | | | COMBINE_INEQS: (59), (291) imply: 206.81/127.93 | | | | | | | | | | | | | | | | | | | | | (292) $lesseq(0, -1) 206.81/127.93 | | | | | | | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | | | | | | | | CLOSE: (292) is inconsistent. 206.81/127.93 | | | | | | | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | | | | | | | Case 2: 206.81/127.93 | | | | | | | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | | | | | | | | (293) $lesseq(0, all_133_2) 206.81/127.93 | | | | | | | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (24), (36), (45), (53), (71), (194), 206.81/127.93 | | | | | | | | | | | | | | | | | | | | | (195), (196), (278), (286), (287), (289), (293) 206.81/127.93 | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #144. 206.81/127.93 | | | | | | | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | | | | | | | End of split 206.81/127.93 | | | | | | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | | | | | | End of split 206.81/127.93 | | | | | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | | | | | End of split 206.81/127.93 | | | | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | | | | Case 2: 206.81/127.93 | | | | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | | | | | (294) ~ (all_771_1 = 0) & permut3(int, all_103_4, 206.81/127.93 | | | | | | | | | | | | | | | | | | all_105_4, all_86_11, $sum(all_86_10, 1)) = 206.81/127.93 | | | | | | | | | | | | | | | | | | all_771_1 206.81/127.93 | | | | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | | | | | ALPHA: (294) implies: 206.81/127.93 | | | | | | | | | | | | | | | | | | (295) ~ (all_771_1 = 0) 206.81/127.93 | | | | | | | | | | | | | | | | | | (296) permut3(int, all_103_4, all_105_4, all_86_11, 206.81/127.93 | | | | | | | | | | | | | | | | | | $sum(all_86_10, 1)) = all_771_1 206.81/127.93 | | | | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (27) with all_771_1, 0, 206.81/127.93 | | | | | | | | | | | | | | | | | | $sum(all_86_10, 1), all_86_11, all_105_4, 206.81/127.93 | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (269), (296) 206.81/127.93 | | | | | | | | | | | | | | | | | | gives: 206.81/127.93 | | | | | | | | | | | | | | | | | | (297) all_771_1 = 0 206.81/127.93 | | | | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | | | | | REDUCE: (295), (297) imply: 206.81/127.93 | | | | | | | | | | | | | | | | | | (298) ~ (0 = 0) 206.81/127.93 | | | | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | | | | | CLOSE: (298) is inconsistent. 206.81/127.93 | | | | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | | | | End of split 206.81/127.93 | | | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | | | Case 2: 206.81/127.93 | | | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | | | | (299) length1(int, all_103_4) = all_852_1 & ( ~ 206.81/127.93 | | | | | | | | | | | | | | | | | ($lesseq(1, $difference(all_852_1, all_86_10))) 206.81/127.93 | | | | | | | | | | | | | | | | | | ~ ($lesseq(all_86_11, all_852_1)) | ( ~ 206.81/127.93 | | | | | | | | | | | | | | | | | (all_852_0 = all_852_1) & length1(int, 206.81/127.93 | | | | | | | | | | | | | | | | | all_105_4) = all_852_0)) 206.81/127.93 | | | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | | | | ALPHA: (299) implies: 206.81/127.93 | | | | | | | | | | | | | | | | | (300) length1(int, all_103_4) = all_852_1 206.81/127.93 | | | | | | | | | | | | | | | | | (301) ~ ($lesseq(1, $difference(all_852_1, all_86_10))) 206.81/127.93 | | | | | | | | | | | | | | | | | | ~ ($lesseq(all_86_11, all_852_1)) | ( ~ 206.81/127.93 | | | | | | | | | | | | | | | | | (all_852_0 = all_852_1) & length1(int, 206.81/127.93 | | | | | | | | | | | | | | | | | all_105_4) = all_852_0) 206.81/127.93 | | | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (65) with all_86_13, all_769_1, 206.81/127.93 | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (3), (266) gives: 206.81/127.93 | | | | | | | | | | | | | | | | | (302) all_769_1 = all_86_13 206.81/127.93 | | | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (65) with all_86_13, all_852_1, 206.81/127.93 | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (12), (300) 206.81/127.93 | | | | | | | | | | | | | | | | | gives: 206.81/127.93 | | | | | | | | | | | | | | | | | (303) all_852_1 = all_86_13 206.81/127.93 | | | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | | | | BETA: splitting (301) gives: 206.81/127.93 | | | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | | | | Case 1: 206.81/127.93 | | | | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | | | | | (304) $lesseq(1, $difference(all_86_11, all_852_1)) 206.81/127.93 | | | | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | | | | | REDUCE: (303), (304) imply: 206.81/127.93 | | | | | | | | | | | | | | | | | | (305) $lesseq(1, $difference(all_86_11, all_86_13)) 206.81/127.93 | | | | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | | | | | COMBINE_INEQS: (43), (53) imply: 206.81/127.93 | | | | | | | | | | | | | | | | | | (306) $lesseq(1, $difference(all_86_10, all_86_8)) 206.81/127.93 | | | | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | | | | | COMBINE_INEQS: (41), (306) imply: 206.81/127.93 | | | | | | | | | | | | | | | | | | (307) $lesseq(1, $difference(all_86_10, all_86_11)) 206.81/127.93 | | | | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | | | | | COMBINE_INEQS: (25), (305) imply: 206.81/127.93 | | | | | | | | | | | | | | | | | | (308) $lesseq(0, -1) 206.81/127.93 | | | | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | | | | | CLOSE: (308) is inconsistent. 206.81/127.93 | | | | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | | | | Case 2: 206.81/127.93 | | | | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | | | | | (309) ~ ($lesseq(1, $difference(all_852_1, all_86_10))) 206.81/127.93 | | | | | | | | | | | | | | | | | | | ( ~ (all_852_0 = all_852_1) & length1(int, 206.81/127.93 | | | | | | | | | | | | | | | | | | all_105_4) = all_852_0) 206.81/127.93 | | | | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | | | | | BETA: splitting (309) gives: 206.81/127.93 | | | | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | | | | | Case 1: 206.81/127.93 | | | | | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | | | | | | (310) $lesseq(all_852_1, all_86_10) 206.81/127.93 | | | | | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | | | | | | REDUCE: (303), (310) imply: 206.81/127.93 | | | | | | | | | | | | | | | | | | | (311) $lesseq(all_86_13, all_86_10) 206.81/127.93 | | | | | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | | | | | | COMBINE_INEQS: (55), (311) imply: 206.81/127.93 | | | | | | | | | | | | | | | | | | | (312) $lesseq(0, -1) 206.81/127.93 | | | | | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | | | | | | CLOSE: (312) is inconsistent. 206.81/127.93 | | | | | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | | | | | Case 2: 206.81/127.93 | | | | | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | | | | | | (313) ~ (all_852_0 = all_852_1) & length1(int, 206.81/127.93 | | | | | | | | | | | | | | | | | | | all_105_4) = all_852_0 206.81/127.93 | | | | | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | | | | | | ALPHA: (313) implies: 206.81/127.93 | | | | | | | | | | | | | | | | | | | (314) ~ (all_852_0 = all_852_1) 206.81/127.93 | | | | | | | | | | | | | | | | | | | (315) length1(int, all_105_4) = all_852_0 206.81/127.93 | | | | | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | | | | | | REDUCE: (303), (314) imply: 206.81/127.93 | | | | | | | | | | | | | | | | | | | (316) ~ (all_852_0 = all_86_13) 206.81/127.93 | | | | | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (65) with all_86_13, all_852_0, 206.81/127.93 | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (31), (315) 206.81/127.93 | | | | | | | | | | | | | | | | | | | gives: 206.81/127.93 | | | | | | | | | | | | | | | | | | | (317) all_852_0 = all_86_13 206.81/127.93 | | | | | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | | | | | | REDUCE: (316), (317) imply: 206.81/127.93 | | | | | | | | | | | | | | | | | | | (318) ~ (0 = 0) 206.81/127.93 | | | | | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | | | | | | CLOSE: (318) is inconsistent. 206.81/127.93 | | | | | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | | | | | End of split 206.81/127.93 | | | | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | | | | End of split 206.81/127.93 | | | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | | | End of split 206.81/127.93 | | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | | Case 2: 206.81/127.93 | | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | | | (319) ~ (all_769_1 = 0) & permut3(int, all_103_2, 206.81/127.93 | | | | | | | | | | | | | | | | all_105_4, 0, all_86_13) = all_769_1 206.81/127.93 | | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | | | ALPHA: (319) implies: 206.81/127.93 | | | | | | | | | | | | | | | | (320) ~ (all_769_1 = 0) 206.81/127.93 | | | | | | | | | | | | | | | | (321) permut3(int, all_103_2, all_105_4, 0, all_86_13) = 206.81/127.93 | | | | | | | | | | | | | | | | all_769_1 206.81/127.93 | | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | | | REF_CLOSE: (27), (264), (320), (321) are inconsistent by 206.81/127.93 | | | | | | | | | | | | | | | | sub-proof #88. 206.81/127.93 | | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | | End of split 206.81/127.93 | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | Case 2: 206.81/127.93 | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | | (322) length1(int, all_103_2) = all_822_1 & ( ~ 206.81/127.93 | | | | | | | | | | | | | | | ($lesseq(all_86_13, all_822_1)) | ~ ($lesseq(0, 206.81/127.93 | | | | | | | | | | | | | | | all_822_1)) | ( ~ (all_822_0 = all_822_1) & 206.81/127.93 | | | | | | | | | | | | | | | length1(int, all_105_4) = all_822_0)) 206.81/127.93 | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | | ALPHA: (322) implies: 206.81/127.93 | | | | | | | | | | | | | | | (323) length1(int, all_103_2) = all_822_1 206.81/127.93 | | | | | | | | | | | | | | | (324) ~ ($lesseq(all_86_13, all_822_1)) | ~ 206.81/127.93 | | | | | | | | | | | | | | | ($lesseq(0, all_822_1)) | ( ~ (all_822_0 = 206.81/127.93 | | | | | | | | | | | | | | | all_822_1) & length1(int, all_105_4) = 206.81/127.93 | | | | | | | | | | | | | | | all_822_0) 206.81/127.93 | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | | REF_CLOSE: (3), (31), (43), (53), (55), (59), (65), (194), 206.81/127.93 | | | | | | | | | | | | | | | (195), (323), (324) are inconsistent by sub-proof 206.81/127.93 | | | | | | | | | | | | | | | #87. 206.81/127.93 | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | End of split 206.81/127.93 | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | End of split 206.81/127.93 | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | Case 2: 206.81/127.93 | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | (325) ~ (all_770_1 = 0) & permut3(int, all_103_4, 206.81/127.93 | | | | | | | | | | | | | all_103_2, 0, all_86_13) = all_770_1 206.81/127.93 | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | ALPHA: (325) implies: 206.81/127.93 | | | | | | | | | | | | | (326) ~ (all_770_1 = 0) 206.81/127.93 | | | | | | | | | | | | | (327) permut3(int, all_103_4, all_103_2, 0, all_86_13) = 206.81/127.93 | | | | | | | | | | | | | all_770_1 206.81/127.93 | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | GROUND_INST: instantiating (27) with 0, all_770_1, all_86_13, 206.81/127.93 | | | | | | | | | | | | | 0, all_103_2, all_103_4, int, simplifying with 206.81/127.93 | | | | | | | | | | | | | (245), (327) gives: 206.81/127.93 | | | | | | | | | | | | | (328) all_770_1 = 0 206.81/127.93 | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | REDUCE: (326), (328) imply: 206.81/127.93 | | | | | | | | | | | | | (329) ~ (0 = 0) 206.81/127.93 | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | CLOSE: (329) is inconsistent. 206.81/127.93 | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | End of split 206.81/127.93 | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | Case 2: 206.81/127.93 | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | (330) length1(int, all_103_4) = all_828_1 & ( ~ 206.81/127.93 | | | | | | | | | | | | ($lesseq(all_86_13, all_828_1)) | ~ ($lesseq(0, 206.81/127.93 | | | | | | | | | | | | all_828_1)) | ( ~ (all_828_0 = all_828_1) & 206.81/127.93 | | | | | | | | | | | | length1(int, all_103_2) = all_828_0)) 206.81/127.93 | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | ALPHA: (330) implies: 206.81/127.93 | | | | | | | | | | | | (331) length1(int, all_103_4) = all_828_1 206.81/127.93 | | | | | | | | | | | | (332) ~ ($lesseq(all_86_13, all_828_1)) | ~ 206.81/127.93 | | | | | | | | | | | | ($lesseq(0, all_828_1)) | ( ~ (all_828_0 = 206.81/127.93 | | | | | | | | | | | | all_828_1) & length1(int, all_103_2) = 206.81/127.93 | | | | | | | | | | | | all_828_0) 206.81/127.93 | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | BETA: splitting (243) gives: 206.81/127.93 | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | Case 1: 206.81/127.93 | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | (333) $lesseq(all_86_10, -2) 206.81/127.93 | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | COMBINE_INEQS: (67), (333) imply: 206.81/127.93 | | | | | | | | | | | | | (334) $lesseq(0, -1) 206.81/127.93 | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | CLOSE: (334) is inconsistent. 206.81/127.93 | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | Case 2: 206.81/127.93 | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | GROUND_INST: instantiating (65) with all_86_13, all_772_1, 206.81/127.93 | | | | | | | | | | | | | all_105_4, int, simplifying with (31), (231) 206.81/127.93 | | | | | | | | | | | | | gives: 206.81/127.93 | | | | | | | | | | | | | (335) all_772_1 = all_86_13 206.81/127.93 | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | GROUND_INST: instantiating (65) with all_86_13, all_828_1, 206.81/127.93 | | | | | | | | | | | | | all_103_4, int, simplifying with (12), (331) 206.81/127.93 | | | | | | | | | | | | | gives: 206.81/127.93 | | | | | | | | | | | | | (336) all_828_1 = all_86_13 206.81/127.93 | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | BETA: splitting (236) gives: 206.81/127.93 | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | Case 1: 206.81/127.93 | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | (337) all_822_1 = 0 & permut3(int, all_103_2, all_105_4, 206.81/127.93 | | | | | | | | | | | | | | 0, all_86_13) = 0 206.81/127.93 | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | ALPHA: (337) implies: 206.81/127.93 | | | | | | | | | | | | | | (338) permut3(int, all_103_2, all_105_4, 0, all_86_13) = 206.81/127.93 | | | | | | | | | | | | | | 0 206.81/127.93 | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | BETA: splitting (211) gives: 206.81/127.93 | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | Case 1: 206.81/127.93 | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | | (339) all_769_0 = all_769_1 & $lesseq(all_86_13, 206.81/127.93 | | | | | | | | | | | | | | | all_769_1) & $lesseq(0, all_769_1) & $lesseq(0, 206.81/127.93 | | | | | | | | | | | | | | | all_86_13) & length1(int, all_105_4) = all_769_1 206.81/127.93 | | | | | | | | | | | | | | | & length1(int, all_103_2) = all_769_1 206.81/127.93 | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | | ALPHA: (339) implies: 206.81/127.93 | | | | | | | | | | | | | | | (340) length1(int, all_103_2) = all_769_1 206.81/127.93 | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | | BETA: splitting (332) gives: 206.81/127.93 | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | | Case 1: 206.81/127.93 | | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | | | (341) $lesseq(all_828_1, -1) 206.81/127.93 | | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | | | REDUCE: (336), (341) imply: 206.81/127.93 | | | | | | | | | | | | | | | | (342) $lesseq(all_86_13, -1) 206.81/127.93 | | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | | | COMBINE_INEQS: (43), (53) imply: 206.81/127.93 | | | | | | | | | | | | | | | | (343) $lesseq(1, $difference(all_86_10, all_86_8)) 206.81/127.93 | | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | | | COMBINE_INEQS: (41), (343) imply: 206.81/127.93 | | | | | | | | | | | | | | | | (344) $lesseq(1, $difference(all_86_10, all_86_11)) 206.81/127.93 | | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | | | COMBINE_INEQS: (13), (342) imply: 206.81/127.93 | | | | | | | | | | | | | | | | (345) $lesseq(0, -1) 206.81/127.93 | | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | | | CLOSE: (345) is inconsistent. 206.81/127.93 | | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | | Case 2: 206.81/127.93 | | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | | | (346) ~ ($lesseq(all_86_13, all_828_1)) | ( ~ 206.81/127.93 | | | | | | | | | | | | | | | | (all_828_0 = all_828_1) & length1(int, 206.81/127.93 | | | | | | | | | | | | | | | | all_103_2) = all_828_0) 206.81/127.93 | | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | | | BETA: splitting (346) gives: 206.81/127.93 | | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | | | Case 1: 206.81/127.93 | | | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | | | | (347) $lesseq(1, $difference(all_86_13, all_828_1)) 206.81/127.93 | | | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | | | | REDUCE: (336), (347) imply: 206.81/127.93 | | | | | | | | | | | | | | | | | (348) $lesseq(0, -1) 206.81/127.93 | | | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | | | | CLOSE: (348) is inconsistent. 206.81/127.93 | | | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | | | Case 2: 206.81/127.93 | | | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | | | | (349) ~ (all_828_0 = all_828_1) & length1(int, 206.81/127.93 | | | | | | | | | | | | | | | | | all_103_2) = all_828_0 206.81/127.93 | | | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | | | | ALPHA: (349) implies: 206.81/127.93 | | | | | | | | | | | | | | | | | (350) ~ (all_828_0 = all_828_1) 206.81/127.93 | | | | | | | | | | | | | | | | | (351) length1(int, all_103_2) = all_828_0 206.81/127.93 | | | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | | | | REDUCE: (336), (350) imply: 206.81/127.93 | | | | | | | | | | | | | | | | | (352) ~ (all_828_0 = all_86_13) 206.81/127.93 | | | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (65) with all_86_13, all_828_0, 206.81/127.93 | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (3), (351) gives: 206.81/127.93 | | | | | | | | | | | | | | | | | (353) all_828_0 = all_86_13 206.81/127.93 | | | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (65) with all_828_0, all_769_1, 206.81/127.93 | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (340), (351) 206.81/127.93 | | | | | | | | | | | | | | | | | gives: 206.81/127.93 | | | | | | | | | | | | | | | | | (354) all_828_0 = all_769_1 206.81/127.93 | | | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | | | | COMBINE_EQS: (353), (354) imply: 206.81/127.93 | | | | | | | | | | | | | | | | | (355) all_769_1 = all_86_13 206.81/127.93 | | | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | | | | REDUCE: (352), (353) imply: 206.81/127.93 | | | | | | | | | | | | | | | | | (356) ~ (0 = 0) 206.81/127.93 | | | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | | | | CLOSE: (356) is inconsistent. 206.81/127.93 | | | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | | | End of split 206.81/127.93 | | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | | End of split 206.81/127.93 | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | Case 2: 206.81/127.93 | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | | (357) ~ (all_769_1 = 0) & permut3(int, all_103_2, 206.81/127.93 | | | | | | | | | | | | | | | all_105_4, 0, all_86_13) = all_769_1 206.81/127.93 | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | | ALPHA: (357) implies: 206.81/127.93 | | | | | | | | | | | | | | | (358) ~ (all_769_1 = 0) 206.81/127.93 | | | | | | | | | | | | | | | (359) permut3(int, all_103_2, all_105_4, 0, all_86_13) = 206.81/127.93 | | | | | | | | | | | | | | | all_769_1 206.81/127.93 | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | | REF_CLOSE: (27), (338), (358), (359) are inconsistent by 206.81/127.93 | | | | | | | | | | | | | | | sub-proof #88. 206.81/127.93 | | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | End of split 206.81/127.93 | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | Case 2: 206.81/127.93 | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | (360) length1(int, all_103_2) = all_822_1 & ( ~ 206.81/127.93 | | | | | | | | | | | | | | ($lesseq(all_86_13, all_822_1)) | ~ ($lesseq(0, 206.81/127.93 | | | | | | | | | | | | | | all_822_1)) | ( ~ (all_822_0 = all_822_1) & 206.81/127.93 | | | | | | | | | | | | | | length1(int, all_105_4) = all_822_0)) 206.81/127.93 | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | ALPHA: (360) implies: 206.81/127.93 | | | | | | | | | | | | | | (361) length1(int, all_103_2) = all_822_1 206.81/127.93 | | | | | | | | | | | | | | (362) ~ ($lesseq(all_86_13, all_822_1)) | ~ 206.81/127.93 | | | | | | | | | | | | | | ($lesseq(0, all_822_1)) | ( ~ (all_822_0 = 206.81/127.93 | | | | | | | | | | | | | | all_822_1) & length1(int, all_105_4) = 206.81/127.93 | | | | | | | | | | | | | | all_822_0) 206.81/127.93 | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | | REF_CLOSE: (3), (31), (43), (53), (55), (59), (65), (194), 206.81/127.93 | | | | | | | | | | | | | | (195), (361), (362) are inconsistent by sub-proof 206.81/127.93 | | | | | | | | | | | | | | #87. 206.81/127.93 | | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | | End of split 206.81/127.93 | | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | | End of split 206.81/127.93 | | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | | End of split 206.81/127.93 | | | | | | | | | | | 206.81/127.93 | | | | | | | | | | End of split 206.81/127.93 | | | | | | | | | | 206.81/127.93 | | | | | | | | | End of split 206.81/127.93 | | | | | | | | | 206.81/127.93 | | | | | | | | End of split 206.81/127.93 | | | | | | | | 206.81/127.93 | | | | | | | Case 2: 206.81/127.93 | | | | | | | | 206.81/127.93 | | | | | | | | (363) ~ (all_772_1 = 0) & permut3(int, all_105_4, all_105_2, 206.81/127.93 | | | | | | | | 0, all_86_13) = all_772_1 206.81/127.93 | | | | | | | | 206.81/127.93 | | | | | | | | ALPHA: (363) implies: 206.81/127.93 | | | | | | | | (364) ~ (all_772_1 = 0) 207.07/127.94 | | | | | | | | (365) permut3(int, all_105_4, all_105_2, 0, all_86_13) = 207.07/127.94 | | | | | | | | all_772_1 207.07/127.94 | | | | | | | | 207.07/127.94 | | | | | | | | GROUND_INST: instantiating (27) with 0, all_772_1, all_86_13, 0, 207.07/127.94 | | | | | | | | all_105_2, all_105_4, int, simplifying with (229), 207.07/127.94 | | | | | | | | (365) gives: 207.07/127.94 | | | | | | | | (366) all_772_1 = 0 207.07/127.94 | | | | | | | | 207.07/127.94 | | | | | | | | REDUCE: (364), (366) imply: 207.07/127.94 | | | | | | | | (367) ~ (0 = 0) 207.07/127.94 | | | | | | | | 207.07/127.94 | | | | | | | | CLOSE: (367) is inconsistent. 207.07/127.94 | | | | | | | | 207.07/127.94 | | | | | | | End of split 207.07/127.94 | | | | | | | 207.07/127.94 | | | | | | Case 2: 207.07/127.94 | | | | | | | 207.07/127.94 | | | | | | | (368) length1(int, all_105_4) = all_798_1 & ( ~ 207.07/127.94 | | | | | | | ($lesseq(all_86_13, all_798_1)) | ~ ($lesseq(0, 207.07/127.94 | | | | | | | all_798_1)) | ( ~ (all_798_0 = all_798_1) & 207.07/127.94 | | | | | | | length1(int, all_105_2) = all_798_0)) 207.07/127.94 | | | | | | | 207.07/127.94 | | | | | | | ALPHA: (368) implies: 207.07/127.94 | | | | | | | (369) length1(int, all_105_4) = all_798_1 207.07/127.94 | | | | | | | (370) ~ ($lesseq(all_86_13, all_798_1)) | ~ ($lesseq(0, 207.07/127.94 | | | | | | | all_798_1)) | ( ~ (all_798_0 = all_798_1) & 207.07/127.94 | | | | | | | length1(int, all_105_2) = all_798_0) 207.07/127.94 | | | | | | | 207.07/127.94 | | | | | | | GROUND_INST: instantiating (65) with all_86_13, all_798_1, 207.07/127.94 | | | | | | | all_105_4, int, simplifying with (31), (369) gives: 207.07/127.94 | | | | | | | (371) all_798_1 = all_86_13 207.07/127.94 | | | | | | | 207.07/127.94 | | | | | | | BETA: splitting (370) gives: 207.07/127.94 | | | | | | | 207.07/127.94 | | | | | | | Case 1: 207.07/127.94 | | | | | | | | 207.07/127.94 | | | | | | | | (372) $lesseq(all_798_1, -1) 207.07/127.94 | | | | | | | | 207.07/127.94 | | | | | | | | REDUCE: (371), (372) imply: 207.07/127.94 | | | | | | | | (373) $lesseq(all_86_13, -1) 207.07/127.94 | | | | | | | | 207.07/127.94 | | | | | | | | COMBINE_INEQS: (43), (53) imply: 207.07/127.94 | | | | | | | | (374) $lesseq(1, $difference(all_86_10, all_86_8)) 207.07/127.94 | | | | | | | | 207.07/127.94 | | | | | | | | COMBINE_INEQS: (41), (374) imply: 207.07/127.94 | | | | | | | | (375) $lesseq(1, $difference(all_86_10, all_86_11)) 207.07/127.94 | | | | | | | | 207.07/127.94 | | | | | | | | COMBINE_INEQS: (13), (373) imply: 207.07/127.94 | | | | | | | | (376) $lesseq(0, -1) 207.07/127.94 | | | | | | | | 207.07/127.94 | | | | | | | | CLOSE: (376) is inconsistent. 207.07/127.94 | | | | | | | | 207.07/127.94 | | | | | | | Case 2: 207.07/127.94 | | | | | | | | 207.07/127.94 | | | | | | | | (377) ~ ($lesseq(all_86_13, all_798_1)) | ( ~ (all_798_0 = 207.07/127.94 | | | | | | | | all_798_1) & length1(int, all_105_2) = all_798_0) 207.07/127.94 | | | | | | | | 207.07/127.94 | | | | | | | | BETA: splitting (377) gives: 207.07/127.94 | | | | | | | | 207.07/127.94 | | | | | | | | Case 1: 207.07/127.94 | | | | | | | | | 207.07/127.94 | | | | | | | | | (378) $lesseq(1, $difference(all_86_13, all_798_1)) 207.07/127.94 | | | | | | | | | 207.07/127.94 | | | | | | | | | REDUCE: (371), (378) imply: 207.07/127.94 | | | | | | | | | (379) $lesseq(0, -1) 207.07/127.94 | | | | | | | | | 207.07/127.94 | | | | | | | | | CLOSE: (379) is inconsistent. 207.07/127.94 | | | | | | | | | 207.07/127.94 | | | | | | | | Case 2: 207.07/127.94 | | | | | | | | | 207.07/127.94 | | | | | | | | | (380) ~ (all_798_0 = all_798_1) & length1(int, all_105_2) 207.07/127.94 | | | | | | | | | = all_798_0 207.07/127.94 | | | | | | | | | 207.07/127.94 | | | | | | | | | ALPHA: (380) implies: 207.07/127.94 | | | | | | | | | (381) ~ (all_798_0 = all_798_1) 207.07/127.94 | | | | | | | | | (382) length1(int, all_105_2) = all_798_0 207.07/127.94 | | | | | | | | | 207.07/127.94 | | | | | | | | | REDUCE: (371), (381) imply: 207.07/127.94 | | | | | | | | | (383) ~ (all_798_0 = all_86_13) 207.07/127.94 | | | | | | | | | 207.07/127.94 | | | | | | | | | GROUND_INST: instantiating (65) with all_86_13, all_798_0, 207.07/127.94 | | | | | | | | | all_105_2, int, simplifying with (7), (382) gives: 207.07/127.94 | | | | | | | | | (384) all_798_0 = all_86_13 207.07/127.94 | | | | | | | | | 207.07/127.94 | | | | | | | | | REDUCE: (383), (384) imply: 207.07/127.94 | | | | | | | | | (385) ~ (0 = 0) 207.07/127.94 | | | | | | | | | 207.07/127.94 | | | | | | | | | CLOSE: (385) is inconsistent. 207.07/127.94 | | | | | | | | | 207.07/127.94 | | | | | | | | End of split 207.07/127.94 | | | | | | | | 207.07/127.94 | | | | | | | End of split 207.07/127.94 | | | | | | | 207.07/127.94 | | | | | | End of split 207.07/127.94 | | | | | | 207.07/127.94 | | | | | End of split 207.07/127.94 | | | | | 207.07/127.94 | | | | End of split 207.07/127.94 | | | | 207.07/127.94 | | | End of split 207.07/127.94 | | | 207.07/127.94 | | End of split 207.07/127.94 | | 207.07/127.94 | End of split 207.07/127.94 | 207.07/127.94 End of proof 207.07/127.94 207.07/127.94 Sub-proof #87 shows that the following formulas are inconsistent: 207.07/127.94 ---------------------------------------------------------------- 207.07/127.94 (1) ~ ($lesseq(all_86_13, all_822_1)) | ~ ($lesseq(0, all_822_1)) | ( ~ 207.07/127.94 (all_822_0 = all_822_1) & length1(int, all_105_4) = all_822_0) 207.07/127.94 (2) length1(int, all_103_2) = all_86_13 207.07/127.94 (3) $lesseq(all_133_2, all_86_8) 207.07/127.94 (4) length1(int, all_105_4) = all_86_13 207.07/127.94 (5) $lesseq(all_86_11, all_133_2) 207.07/127.94 (6) $lesseq(all_86_7, all_86_10) 207.07/127.94 (7) length1(int, all_103_2) = all_822_1 207.07/127.94 (8) $lesseq(1, $difference(all_86_7, all_86_8)) 207.07/127.94 (9) $lesseq(1, $difference(all_86_13, all_86_10)) 207.07/127.94 (10) $lesseq(0, all_86_11) 207.07/127.94 (11) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 207.07/127.94 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 207.07/127.94 207.07/127.94 Begin of proof 207.07/127.94 | 207.07/127.94 | GROUND_INST: instantiating (11) with all_86_13, all_822_1, all_103_2, int, 207.07/127.94 | simplifying with (2), (7) gives: 207.07/127.94 | (12) all_822_1 = all_86_13 207.07/127.94 | 207.07/127.94 | BETA: splitting (1) gives: 207.07/127.94 | 207.07/127.94 | Case 1: 207.07/127.94 | | 207.07/127.94 | | (13) $lesseq(all_822_1, -1) 207.07/127.94 | | 207.07/127.94 | | REDUCE: (12), (13) imply: 207.07/127.94 | | (14) $lesseq(all_86_13, -1) 207.07/127.94 | | 207.07/127.94 | | COMBINE_INEQS: (3), (5) imply: 207.07/127.94 | | (15) $lesseq(all_86_11, all_86_8) 207.07/127.94 | | 207.07/127.94 | | COMBINE_INEQS: (6), (8) imply: 207.07/127.94 | | (16) $lesseq(1, $difference(all_86_10, all_86_8)) 207.07/127.94 | | 207.07/127.94 | | COMBINE_INEQS: (15), (16) imply: 207.07/127.94 | | (17) $lesseq(1, $difference(all_86_10, all_86_11)) 207.07/127.94 | | 207.07/127.94 | | COMBINE_INEQS: (9), (17) imply: 207.07/127.94 | | (18) $lesseq(2, $difference(all_86_13, all_86_11)) 207.07/127.94 | | 207.07/127.94 | | COMBINE_INEQS: (10), (18) imply: 207.07/127.94 | | (19) $lesseq(2, all_86_13) 207.07/127.94 | | 207.07/127.94 | | COMBINE_INEQS: (14), (19) imply: 207.07/127.94 | | (20) $lesseq(0, -1) 207.07/127.94 | | 207.07/127.94 | | CLOSE: (20) is inconsistent. 207.07/127.94 | | 207.07/127.94 | Case 2: 207.07/127.94 | | 207.07/127.94 | | (21) ~ ($lesseq(all_86_13, all_822_1)) | ( ~ (all_822_0 = all_822_1) & 207.07/127.94 | | length1(int, all_105_4) = all_822_0) 207.07/127.94 | | 207.07/127.94 | | BETA: splitting (21) gives: 207.07/127.94 | | 207.07/127.94 | | Case 1: 207.07/127.94 | | | 207.07/127.94 | | | (22) $lesseq(1, $difference(all_86_13, all_822_1)) 207.07/127.94 | | | 207.07/127.94 | | | REDUCE: (12), (22) imply: 207.07/127.94 | | | (23) $lesseq(0, -1) 207.07/127.94 | | | 207.07/127.94 | | | CLOSE: (23) is inconsistent. 207.07/127.94 | | | 207.07/127.94 | | Case 2: 207.07/127.94 | | | 207.07/127.94 | | | (24) ~ (all_822_0 = all_822_1) & length1(int, all_105_4) = all_822_0 207.07/127.94 | | | 207.07/127.94 | | | ALPHA: (24) implies: 207.07/127.94 | | | (25) ~ (all_822_0 = all_822_1) 207.07/127.94 | | | (26) length1(int, all_105_4) = all_822_0 207.07/127.94 | | | 207.07/127.94 | | | REDUCE: (12), (25) imply: 207.07/127.94 | | | (27) ~ (all_822_0 = all_86_13) 207.07/127.94 | | | 207.07/127.94 | | | GROUND_INST: instantiating (11) with all_86_13, all_822_0, all_105_4, int, 207.07/127.94 | | | simplifying with (4), (26) gives: 207.07/127.94 | | | (28) all_822_0 = all_86_13 207.07/127.94 | | | 207.07/127.94 | | | REDUCE: (27), (28) imply: 207.07/127.94 | | | (29) ~ (0 = 0) 207.07/127.94 | | | 207.07/127.94 | | | CLOSE: (29) is inconsistent. 207.07/127.94 | | | 207.07/127.94 | | End of split 207.07/127.94 | | 207.07/127.94 | End of split 207.07/127.94 | 207.07/127.94 End of proof 207.07/127.94 207.07/127.94 Sub-proof #88 shows that the following formulas are inconsistent: 207.07/127.94 ---------------------------------------------------------------- 207.07/127.94 (1) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.07/127.94 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ (permut3(v6, v5, 207.07/127.94 v4, v3, v2) = v1) | ~ (permut3(v6, v5, v4, v3, v2) = v0)) 207.07/127.94 (2) permut3(int, all_103_2, all_105_4, 0, all_86_13) = all_769_1 207.07/127.94 (3) permut3(int, all_103_2, all_105_4, 0, all_86_13) = 0 207.07/127.94 (4) ~ (all_769_1 = 0) 207.07/127.94 207.07/127.94 Begin of proof 207.07/127.94 | 207.07/127.94 | GROUND_INST: instantiating (1) with 0, all_769_1, all_86_13, 0, all_105_4, 207.07/127.94 | all_103_2, int, simplifying with (2), (3) gives: 207.07/127.94 | (5) all_769_1 = 0 207.07/127.94 | 207.07/127.94 | REDUCE: (4), (5) imply: 207.07/127.94 | (6) ~ (0 = 0) 207.07/127.94 | 207.07/127.94 | CLOSE: (6) is inconsistent. 207.07/127.94 | 207.07/127.94 End of proof 207.07/127.94 207.07/127.94 Sub-proof #89 shows that the following formulas are inconsistent: 207.07/127.94 ---------------------------------------------------------------- 207.07/127.94 (1) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ (tb2t1(v2) 207.07/127.94 = v1) | ~ (tb2t1(v2) = v0)) 207.07/127.94 (2) ! [v0: $int] : ! [v1: $int] : ( ~ ($lesseq(43, v1)) | ~ ($lesseq(v0, 207.07/127.94 all_86_8)) | ~ ($lesseq(all_86_11, v0)) | ~ (get3(all_86_6, v0) = 207.07/127.94 v1)) 207.07/127.94 (3) length1(int, all_103_2) = all_86_13 207.07/127.94 (4) in_map_int_int(all_86_6) 207.07/127.94 (5) length1(int, all_105_2) = all_86_13 207.07/127.94 (6) elts(int, all_103_4) = all_103_3 207.07/127.94 (7) t2tb(all_86_2) = all_105_1 207.07/127.94 (8) in_ty(int) 207.07/127.94 (9) length1(int, all_103_4) = all_86_13 207.07/127.94 (10) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.07/127.94 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 207.07/127.94 (permut2(v0, v5, v6, v3, v4) = v7) | ~ (elts(v0, v2) = v6) | ~ 207.07/127.94 (elts(v0, v1) = v5) | ~ in_ty(v0) | ? [v8: $int] : ? [v9: $int] : 207.07/127.94 ((v9 = v8 & v7 = 0 & $lesseq(v4, v8) & $lesseq(v3, v8) & $lesseq(0, 207.07/127.94 v4) & $lesseq(0, v3) & length1(v0, v2) = v8 & length1(v0, v1) = 207.07/127.94 v8) | ( ~ (v8 = 0) & permut3(v0, v1, v2, v3, v4) = v8))) 207.07/127.94 (11) t2tb(all_86_6) = all_103_1 207.07/127.94 (12) $lesseq(2, $difference(all_86_13, all_86_11)) 207.07/127.94 (13) $lesseq(all_133_2, all_86_8) 207.07/127.94 (14) tb2t1(all_133_1) = all_133_0 207.07/127.94 (15) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.07/127.94 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ (permut3(v6, v5, 207.07/127.94 v4, v3, v2) = v1) | ~ (permut3(v6, v5, v4, v3, v2) = v0)) 207.07/127.94 (16) permut2(int, all_103_1, all_105_3, 0, all_86_13) = 0 207.07/127.94 (17) permut2(int, all_103_3, all_105_3, all_86_11, $sum(all_86_10, 1)) = 0 207.07/127.94 (18) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 207.07/127.94 | ~ (elts(v3, v2) = v1) | ~ (elts(v3, v2) = v0)) 207.07/127.94 (19) length1(int, all_105_4) = all_86_13 207.07/127.94 (20) elts(int, all_105_4) = all_105_3 207.07/127.94 (21) map_eq_sub1(int, all_105_3, all_105_1, 0, all_86_7) = 0 207.07/127.94 (22) get4(int, all_105_2, all_133_2) = all_133_1 207.07/127.94 (23) tb2t(all_105_1) = all_86_2 207.07/127.94 (24) permut2(int, all_103_1, all_105_3, all_86_11, $sum(all_86_8, 1)) = 0 207.07/127.94 (25) elts(int, all_105_2) = all_105_1 207.07/127.94 (26) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.07/127.94 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 207.07/127.94 ($lesseq(1, $difference(v4, v5))) | ~ ($lesseq(v3, v5)) | ~ 207.07/127.94 (permut2(v0, v1, v2, v3, v4) = 0) | ~ (t2tb1(v5) = v6) | ~ (get(v0, 207.07/127.94 int, v2, v6) = v7) | ~ in_ty(v0) | ? [v8: $int] : ? [v9: $int] 207.07/127.94 : ($lesseq(1, $difference(v4, v8)) & $lesseq(v3, v8) & t2tb1(v8) = v9 207.07/127.94 & get(v0, int, v1, v9) = v7 & in_uni(v9) & in_uni(v7))) 207.07/127.94 (27) t2tb2(all_86_1) = all_105_2 207.07/127.94 (28) $lesseq(all_86_11, all_133_2) 207.07/127.94 (29) ~ ($difference(all_86_10, all_86_13) = -1) | ~ (all_86_11 = 0) 207.07/127.94 (30) $lesseq(all_86_7, all_86_10) 207.07/127.94 (31) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.07/127.94 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 207.07/127.94 ($lesseq(1, $difference(v3, v4))) | ~ ($lesseq(v2, v4)) | ~ 207.07/127.94 (permut2(int, v5, v6, v2, v3) = 0) | ~ (t2tb(v1) = v6) | ~ (t2tb(v0) 207.07/127.94 = v5) | ~ (get3(v1, v4) = v7) | ~ in_map_int_int(v0) | ? [v8: 207.07/127.94 $int] : ($lesseq(1, $difference(v3, v8)) & $lesseq(v2, v8) & 207.07/127.94 get3(v0, v8) = v7)) 207.07/127.94 (32) permut2(int, all_105_3, all_105_1, all_86_7, $sum(all_86_10, 1)) = 0 207.07/127.94 (33) permut2(int, all_105_3, all_105_1, 0, all_86_13) = 0 207.07/127.94 (34) in_array_int(all_86_1) 207.07/127.94 (35) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.07/127.94 $int] : ! [v5: $int] : ! [v6: $int] : ( ~ ($lesseq(0, v4)) | ~ 207.07/127.94 ($lesseq(0, v3)) | ~ (permut2(v0, v5, v6, v3, v4) = 0) | ~ (elts(v0, 207.07/127.94 v2) = v6) | ~ (elts(v0, v1) = v5) | ~ in_ty(v0) | ? [v7: $int] 207.07/127.94 : ? [v8: $int] : ((v7 = 0 & permut3(v0, v1, v2, v3, v4) = 0) | 207.07/127.94 (length1(v0, v1) = v7 & ( ~ ($lesseq(v4, v7)) | ~ ($lesseq(v3, v7)) 207.07/127.94 | ( ~ (v8 = v7) & length1(v0, v2) = v8))))) 207.07/127.94 (36) $lesseq(1, $difference(all_86_7, all_86_8)) 207.07/127.94 (37) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.07/127.94 $int] : ! [v5: $int] : ! [v6: $int] : ( ~ ($lesseq(1, 207.07/127.94 $difference(v4, v5))) | ~ ($lesseq(v3, v5)) | ~ (map_eq_sub1(v0, 207.07/127.94 v1, v2, v3, v4) = 0) | ~ (t2tb1(v5) = v6) | ~ in_ty(v0) | ? 207.07/127.94 [v7: $int] : (get(v0, int, v2, v6) = v7 & get(v0, int, v1, v6) = v7 & 207.07/127.94 in_uni(v7))) 207.07/127.94 (38) $lesseq(1, $difference(all_86_13, all_86_10)) 207.07/127.94 (39) in_map_int_int(all_86_4) 207.07/127.94 (40) map_eq_sub1(int, all_105_3, all_105_1, 0, all_86_13) = 0 207.07/127.94 (41) $lesseq(0, all_86_11) 207.07/127.94 (42) elts(int, all_103_2) = all_103_1 207.07/127.94 (43) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ( ~ 207.07/127.95 (t2tb2(v0) = v2) | ~ (get4(int, v2, v1) = v3) | ~ in_array_int(v0) | 207.07/127.95 ? [v4: $int] : ? [v5: $int] : ? [v6: $int] : (tb2t(v4) = v5 & 207.07/127.95 tb2t1(v3) = v6 & get3(v5, v1) = v6 & elts(int, v2) = v4 & 207.07/127.95 in_map_int_int(v5) & in_uni(v4))) 207.07/127.95 (44) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ (tb2t(v2) 207.07/127.95 = v1) | ~ (tb2t(v2) = v0)) 207.07/127.95 (45) $lesseq(43, all_133_0) 207.07/127.95 (46) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.07/127.95 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 207.07/127.95 ($lesseq(1, $difference(v3, v6))) | ~ ($lesseq(v2, v6)) | ~ 207.07/127.95 (map_eq_sub1(int, v4, v5, v2, v3) = 0) | ~ (t2tb(v1) = v5) | ~ 207.07/127.95 (t2tb(v0) = v4) | ~ (get3(v1, v6) = v7) | ~ in_map_int_int(v0) | 207.07/127.95 get3(v0, v6) = v7) 207.07/127.95 (47) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 207.07/127.95 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 207.07/127.95 (48) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ( ~ 207.07/127.95 (get4(v0, v1, v2) = v3) | ~ in_ty(v0) | ? [v4: $int] : ? [v5: $int] 207.07/127.95 : (elts(v0, v1) = v4 & t2tb1(v2) = v5 & get(v0, int, v4, v5) = v3 & 207.07/127.95 in_uni(v5) & in_uni(v4) & in_uni(v3))) 207.07/127.95 (49) $lesseq(0, all_86_10) 207.07/127.95 (50) t2tb(all_86_4) = all_105_3 207.07/127.95 207.07/127.95 Begin of proof 207.07/127.96 | 207.07/127.96 | GROUND_INST: instantiating (10) with int, all_105_4, all_105_2, 0, all_86_13, 207.07/127.96 | all_105_3, all_105_1, 0, simplifying with (8), (20), (25), (33) 207.07/127.96 | gives: 207.07/127.96 | (51) ? [v0: $int] : ? [v1: $int] : ((v1 = v0 & $lesseq(all_86_13, v0) & 207.07/127.96 | $lesseq(0, v0) & $lesseq(0, all_86_13) & length1(int, all_105_2) = 207.07/127.96 | v0 & length1(int, all_105_4) = v0) | ( ~ (v0 = 0) & permut3(int, 207.07/127.96 | all_105_4, all_105_2, 0, all_86_13) = v0)) 207.07/127.96 | 207.07/127.96 | GROUND_INST: instantiating (35) with int, all_105_4, all_105_2, 0, all_86_13, 207.07/127.96 | all_105_3, all_105_1, simplifying with (8), (20), (25), (33) 207.07/127.96 | gives: 207.07/127.96 | (52) ~ ($lesseq(0, all_86_13)) | ? [v0: $int] : ? [v1: $int] : ((v0 = 0 207.07/127.96 | & permut3(int, all_105_4, all_105_2, 0, all_86_13) = 0) | 207.07/127.96 | (length1(int, all_105_4) = v0 & ( ~ ($lesseq(all_86_13, v0)) | ~ 207.07/127.96 | ($lesseq(0, v0)) | ( ~ (v1 = v0) & length1(int, all_105_2) = 207.07/127.96 | v1)))) 207.07/127.96 | 207.07/127.96 | GROUND_INST: instantiating (10) with int, all_103_2, all_105_4, 0, all_86_13, 207.07/127.96 | all_103_1, all_105_3, 0, simplifying with (8), (16), (20), (42) 207.07/127.96 | gives: 207.07/127.96 | (53) ? [v0: $int] : ? [v1: $int] : ((v1 = v0 & $lesseq(all_86_13, v0) & 207.07/127.96 | $lesseq(0, v0) & $lesseq(0, all_86_13) & length1(int, all_105_4) = 207.07/127.96 | v0 & length1(int, all_103_2) = v0) | ( ~ (v0 = 0) & permut3(int, 207.07/127.96 | all_103_2, all_105_4, 0, all_86_13) = v0)) 207.07/127.96 | 207.07/127.96 | GROUND_INST: instantiating (35) with int, all_103_2, all_105_4, 0, all_86_13, 207.07/127.96 | all_103_1, all_105_3, simplifying with (8), (16), (20), (42) 207.07/127.96 | gives: 207.07/127.96 | (54) ~ ($lesseq(0, all_86_13)) | ? [v0: $int] : ? [v1: $int] : ((v0 = 0 207.07/127.96 | & permut3(int, all_103_2, all_105_4, 0, all_86_13) = 0) | 207.07/127.96 | (length1(int, all_103_2) = v0 & ( ~ ($lesseq(all_86_13, v0)) | ~ 207.07/127.96 | ($lesseq(0, v0)) | ( ~ (v1 = v0) & length1(int, all_105_4) = 207.07/127.96 | v1)))) 207.07/127.96 | 207.07/127.96 | GROUND_INST: instantiating (10) with int, all_103_4, all_105_4, all_86_11, 207.07/127.96 | $sum(all_86_10, 1), all_103_3, all_105_3, 0, simplifying with 207.07/127.96 | (6), (8), (17), (20) gives: 207.07/127.96 | (55) ? [v0: $int] : ? [v1: $int] : ((v1 = v0 & $lesseq(1, $difference(v0, 207.07/127.96 | all_86_10)) & $lesseq(all_86_11, v0) & $lesseq(-1, all_86_10) 207.07/127.96 | & $lesseq(0, all_86_11) & length1(int, all_105_4) = v0 & 207.07/127.96 | length1(int, all_103_4) = v0) | ( ~ (v0 = 0) & permut3(int, 207.07/127.96 | all_103_4, all_105_4, all_86_11, $sum(all_86_10, 1)) = v0)) 207.07/127.96 | 207.07/127.96 | GROUND_INST: instantiating (35) with int, all_103_4, all_105_4, all_86_11, 207.07/127.96 | $sum(all_86_10, 1), all_103_3, all_105_3, simplifying with (6), 207.07/127.96 | (8), (17), (20) gives: 207.07/127.96 | (56) ~ ($lesseq(-1, all_86_10)) | ~ ($lesseq(0, all_86_11)) | ? [v0: 207.07/127.96 | $int] : ? [v1: $int] : ((v0 = 0 & permut3(int, all_103_4, 207.07/127.96 | all_105_4, all_86_11, $sum(all_86_10, 1)) = 0) | (length1(int, 207.07/127.96 | all_103_4) = v0 & ( ~ ($lesseq(1, $difference(v0, all_86_10))) | 207.07/127.96 | ~ ($lesseq(all_86_11, v0)) | ( ~ (v1 = v0) & length1(int, 207.07/127.96 | all_105_4) = v1)))) 207.07/127.96 | 207.07/127.96 | GROUND_INST: instantiating (43) with all_86_1, all_133_2, all_105_2, 207.07/127.96 | all_133_1, simplifying with (22), (27), (34) gives: 207.07/127.96 | (57) ? [v0: $int] : ? [v1: $int] : ? [v2: $int] : (tb2t(v0) = v1 & 207.07/127.96 | tb2t1(all_133_1) = v2 & get3(v1, all_133_2) = v2 & elts(int, 207.07/127.96 | all_105_2) = v0 & in_map_int_int(v1) & in_uni(v0)) 207.07/127.96 | 207.07/127.96 | GROUND_INST: instantiating (48) with int, all_105_2, all_133_2, all_133_1, 207.07/127.96 | simplifying with (8), (22) gives: 207.07/127.96 | (58) ? [v0: $int] : ? [v1: $int] : (elts(int, all_105_2) = v0 & 207.07/127.96 | t2tb1(all_133_2) = v1 & get(int, int, v0, v1) = all_133_1 & 207.07/127.96 | in_uni(v1) & in_uni(v0) & in_uni(all_133_1)) 207.07/127.96 | 207.07/127.96 | DELTA: instantiating (53) with fresh symbols all_754_0, all_754_1 gives: 207.07/127.96 | (59) (all_754_0 = all_754_1 & $lesseq(all_86_13, all_754_1) & $lesseq(0, 207.07/127.96 | all_754_1) & $lesseq(0, all_86_13) & length1(int, all_105_4) = 207.07/127.96 | all_754_1 & length1(int, all_103_2) = all_754_1) | ( ~ (all_754_1 = 207.07/127.96 | 0) & permut3(int, all_103_2, all_105_4, 0, all_86_13) = all_754_1) 207.07/127.96 | 207.07/127.96 | DELTA: instantiating (58) with fresh symbols all_755_0, all_755_1 gives: 207.07/127.96 | (60) elts(int, all_105_2) = all_755_1 & t2tb1(all_133_2) = all_755_0 & 207.07/127.96 | get(int, int, all_755_1, all_755_0) = all_133_1 & in_uni(all_755_0) & 207.07/127.96 | in_uni(all_755_1) & in_uni(all_133_1) 207.07/127.96 | 207.07/127.96 | ALPHA: (60) implies: 207.07/127.96 | (61) get(int, int, all_755_1, all_755_0) = all_133_1 207.07/127.96 | (62) t2tb1(all_133_2) = all_755_0 207.07/127.96 | (63) elts(int, all_105_2) = all_755_1 207.07/127.96 | 207.07/127.96 | DELTA: instantiating (55) with fresh symbols all_759_0, all_759_1 gives: 207.07/127.96 | (64) (all_759_0 = all_759_1 & $lesseq(1, $difference(all_759_1, all_86_10)) 207.07/127.96 | & $lesseq(all_86_11, all_759_1) & $lesseq(-1, all_86_10) & 207.07/127.96 | $lesseq(0, all_86_11) & length1(int, all_105_4) = all_759_1 & 207.07/127.96 | length1(int, all_103_4) = all_759_1) | ( ~ (all_759_1 = 0) & 207.07/127.96 | permut3(int, all_103_4, all_105_4, all_86_11, $sum(all_86_10, 1)) = 207.07/127.96 | all_759_1) 207.07/127.96 | 207.07/127.96 | DELTA: instantiating (57) with fresh symbols all_760_0, all_760_1, all_760_2 207.07/127.96 | gives: 207.07/127.96 | (65) tb2t(all_760_2) = all_760_1 & tb2t1(all_133_1) = all_760_0 & 207.07/127.96 | get3(all_760_1, all_133_2) = all_760_0 & elts(int, all_105_2) = 207.07/127.96 | all_760_2 & in_map_int_int(all_760_1) & in_uni(all_760_2) 207.07/127.96 | 207.07/127.96 | ALPHA: (65) implies: 207.07/127.96 | (66) elts(int, all_105_2) = all_760_2 207.07/127.96 | (67) get3(all_760_1, all_133_2) = all_760_0 207.07/127.96 | (68) tb2t1(all_133_1) = all_760_0 207.07/127.96 | (69) tb2t(all_760_2) = all_760_1 207.07/127.96 | 207.07/127.96 | DELTA: instantiating (51) with fresh symbols all_766_0, all_766_1 gives: 207.07/127.96 | (70) (all_766_0 = all_766_1 & $lesseq(all_86_13, all_766_1) & $lesseq(0, 207.07/127.96 | all_766_1) & $lesseq(0, all_86_13) & length1(int, all_105_2) = 207.07/127.96 | all_766_1 & length1(int, all_105_4) = all_766_1) | ( ~ (all_766_1 = 207.07/127.96 | 0) & permut3(int, all_105_4, all_105_2, 0, all_86_13) = all_766_1) 207.07/127.96 | 207.07/127.96 | BETA: splitting (56) gives: 207.07/127.96 | 207.07/127.96 | Case 1: 207.07/127.96 | | 207.07/127.96 | | (71) $lesseq(all_86_11, -1) 207.07/127.96 | | 207.07/127.96 | | COMBINE_INEQS: (41), (71) imply: 207.07/127.96 | | (72) $lesseq(0, -1) 207.07/127.96 | | 207.07/127.96 | | CLOSE: (72) is inconsistent. 207.07/127.96 | | 207.07/127.96 | Case 2: 207.07/127.96 | | 207.07/127.96 | | (73) ~ ($lesseq(-1, all_86_10)) | ? [v0: $int] : ? [v1: $int] : ((v0 = 207.07/127.96 | | 0 & permut3(int, all_103_4, all_105_4, all_86_11, 207.07/127.96 | | $sum(all_86_10, 1)) = 0) | (length1(int, all_103_4) = v0 & ( ~ 207.07/127.96 | | ($lesseq(1, $difference(v0, all_86_10))) | ~ 207.07/127.96 | | ($lesseq(all_86_11, v0)) | ( ~ (v1 = v0) & length1(int, 207.07/127.96 | | all_105_4) = v1)))) 207.07/127.96 | | 207.07/127.96 | | COMBINE_INEQS: (12), (41) imply: 207.07/127.96 | | (74) $lesseq(2, all_86_13) 207.07/127.96 | | 207.07/127.96 | | BETA: splitting (54) gives: 207.07/127.96 | | 207.07/127.96 | | Case 1: 207.07/127.96 | | | 207.07/127.96 | | | (75) $lesseq(all_86_13, -1) 207.07/127.96 | | | 207.07/127.96 | | | COMBINE_INEQS: (74), (75) imply: 207.07/127.96 | | | (76) $lesseq(0, -1) 207.07/127.96 | | | 207.07/127.96 | | | CLOSE: (76) is inconsistent. 207.07/127.96 | | | 207.07/127.96 | | Case 2: 207.07/127.96 | | | 207.07/127.96 | | | (77) ? [v0: $int] : ? [v1: $int] : ((v0 = 0 & permut3(int, all_103_2, 207.07/127.96 | | | all_105_4, 0, all_86_13) = 0) | (length1(int, all_103_2) = 207.07/127.96 | | | v0 & ( ~ ($lesseq(all_86_13, v0)) | ~ ($lesseq(0, v0)) | ( ~ 207.07/127.96 | | | (v1 = v0) & length1(int, all_105_4) = v1)))) 207.07/127.96 | | | 207.07/127.96 | | | DELTA: instantiating (77) with fresh symbols all_787_0, all_787_1 gives: 207.07/127.96 | | | (78) (all_787_1 = 0 & permut3(int, all_103_2, all_105_4, 0, all_86_13) 207.07/127.96 | | | = 0) | (length1(int, all_103_2) = all_787_1 & ( ~ 207.07/127.96 | | | ($lesseq(all_86_13, all_787_1)) | ~ ($lesseq(0, all_787_1)) | 207.07/127.96 | | | ( ~ (all_787_0 = all_787_1) & length1(int, all_105_4) = 207.07/127.96 | | | all_787_0))) 207.07/127.96 | | | 207.07/127.96 | | | BETA: splitting (78) gives: 207.07/127.96 | | | 207.07/127.96 | | | Case 1: 207.07/127.96 | | | | 207.07/127.96 | | | | (79) all_787_1 = 0 & permut3(int, all_103_2, all_105_4, 0, all_86_13) 207.07/127.96 | | | | = 0 207.07/127.96 | | | | 207.07/127.96 | | | | ALPHA: (79) implies: 207.07/127.96 | | | | (80) permut3(int, all_103_2, all_105_4, 0, all_86_13) = 0 207.07/127.96 | | | | 207.07/127.96 | | | | BETA: splitting (73) gives: 207.07/127.96 | | | | 207.07/127.96 | | | | Case 1: 207.07/127.96 | | | | | 207.07/127.96 | | | | | (81) $lesseq(all_86_10, -2) 207.07/127.96 | | | | | 207.07/127.96 | | | | | COMBINE_INEQS: (49), (81) imply: 207.07/127.96 | | | | | (82) $lesseq(0, -1) 207.07/127.96 | | | | | 207.07/127.96 | | | | | CLOSE: (82) is inconsistent. 207.07/127.96 | | | | | 207.07/127.96 | | | | Case 2: 207.07/127.96 | | | | | 207.07/127.96 | | | | | (83) ? [v0: $int] : ? [v1: $int] : ((v0 = 0 & permut3(int, 207.07/127.96 | | | | | all_103_4, all_105_4, all_86_11, $sum(all_86_10, 1)) = 207.07/127.96 | | | | | 0) | (length1(int, all_103_4) = v0 & ( ~ ($lesseq(1, 207.07/127.96 | | | | | $difference(v0, all_86_10))) | ~ 207.07/127.96 | | | | | ($lesseq(all_86_11, v0)) | ( ~ (v1 = v0) & length1(int, 207.07/127.96 | | | | | all_105_4) = v1)))) 207.07/127.96 | | | | | 207.07/127.96 | | | | | DELTA: instantiating (83) with fresh symbols all_798_0, all_798_1 207.07/127.96 | | | | | gives: 207.07/127.96 | | | | | (84) (all_798_1 = 0 & permut3(int, all_103_4, all_105_4, all_86_11, 207.07/127.96 | | | | | $sum(all_86_10, 1)) = 0) | (length1(int, all_103_4) = 207.07/127.96 | | | | | all_798_1 & ( ~ ($lesseq(1, $difference(all_798_1, 207.07/127.96 | | | | | all_86_10))) | ~ ($lesseq(all_86_11, all_798_1)) | 207.07/127.96 | | | | | ( ~ (all_798_0 = all_798_1) & length1(int, all_105_4) = 207.07/127.96 | | | | | all_798_0))) 207.07/127.96 | | | | | 207.07/127.96 | | | | | BETA: splitting (84) gives: 207.07/127.96 | | | | | 207.07/127.96 | | | | | Case 1: 207.07/127.96 | | | | | | 207.07/127.96 | | | | | | (85) all_798_1 = 0 & permut3(int, all_103_4, all_105_4, 207.07/127.96 | | | | | | all_86_11, $sum(all_86_10, 1)) = 0 207.07/127.96 | | | | | | 207.07/127.96 | | | | | | ALPHA: (85) implies: 207.07/127.96 | | | | | | (86) permut3(int, all_103_4, all_105_4, all_86_11, 207.07/127.96 | | | | | | $sum(all_86_10, 1)) = 0 207.07/127.96 | | | | | | 207.07/127.96 | | | | | | BETA: splitting (52) gives: 207.07/127.96 | | | | | | 207.07/127.96 | | | | | | Case 1: 207.07/127.96 | | | | | | | 207.07/127.96 | | | | | | | (87) $lesseq(all_86_13, -1) 207.07/127.96 | | | | | | | 207.07/127.96 | | | | | | | COMBINE_INEQS: (74), (87) imply: 207.07/127.96 | | | | | | | (88) $lesseq(0, -1) 207.07/127.96 | | | | | | | 207.07/127.96 | | | | | | | CLOSE: (88) is inconsistent. 207.07/127.96 | | | | | | | 207.07/127.96 | | | | | | Case 2: 207.07/127.96 | | | | | | | 207.07/127.96 | | | | | | | (89) ? [v0: $int] : ? [v1: $int] : ((v0 = 0 & permut3(int, 207.07/127.96 | | | | | | | all_105_4, all_105_2, 0, all_86_13) = 0) | 207.07/127.96 | | | | | | | (length1(int, all_105_4) = v0 & ( ~ ($lesseq(all_86_13, 207.07/127.96 | | | | | | | v0)) | ~ ($lesseq(0, v0)) | ( ~ (v1 = v0) & 207.07/127.96 | | | | | | | length1(int, all_105_2) = v1)))) 207.07/127.96 | | | | | | | 207.07/127.96 | | | | | | | DELTA: instantiating (89) with fresh symbols all_809_0, all_809_1 207.07/127.96 | | | | | | | gives: 207.07/127.96 | | | | | | | (90) (all_809_1 = 0 & permut3(int, all_105_4, all_105_2, 0, 207.07/127.96 | | | | | | | all_86_13) = 0) | (length1(int, all_105_4) = all_809_1 207.07/127.96 | | | | | | | & ( ~ ($lesseq(all_86_13, all_809_1)) | ~ ($lesseq(0, 207.07/127.96 | | | | | | | all_809_1)) | ( ~ (all_809_0 = all_809_1) & 207.07/127.96 | | | | | | | length1(int, all_105_2) = all_809_0))) 207.07/127.96 | | | | | | | 207.07/127.96 | | | | | | | BETA: splitting (59) gives: 207.07/127.96 | | | | | | | 207.07/127.96 | | | | | | | Case 1: 207.07/127.96 | | | | | | | | 207.07/127.96 | | | | | | | | (91) all_754_0 = all_754_1 & $lesseq(all_86_13, all_754_1) & 207.07/127.96 | | | | | | | | $lesseq(0, all_754_1) & $lesseq(0, all_86_13) & 207.07/127.96 | | | | | | | | length1(int, all_105_4) = all_754_1 & length1(int, 207.07/127.96 | | | | | | | | all_103_2) = all_754_1 207.07/127.96 | | | | | | | | 207.07/127.96 | | | | | | | | ALPHA: (91) implies: 207.07/127.96 | | | | | | | | (92) length1(int, all_105_4) = all_754_1 207.07/127.96 | | | | | | | | 207.07/127.96 | | | | | | | | BETA: splitting (64) gives: 207.07/127.96 | | | | | | | | 207.07/127.96 | | | | | | | | Case 1: 207.07/127.96 | | | | | | | | | 207.07/127.96 | | | | | | | | | (93) all_759_0 = all_759_1 & $lesseq(1, 207.07/127.96 | | | | | | | | | $difference(all_759_1, all_86_10)) & 207.07/127.96 | | | | | | | | | $lesseq(all_86_11, all_759_1) & $lesseq(-1, all_86_10) 207.07/127.96 | | | | | | | | | & $lesseq(0, all_86_11) & length1(int, all_105_4) = 207.07/127.96 | | | | | | | | | all_759_1 & length1(int, all_103_4) = all_759_1 207.07/127.96 | | | | | | | | | 207.07/127.96 | | | | | | | | | ALPHA: (93) implies: 207.07/127.96 | | | | | | | | | (94) $lesseq(1, $difference(all_759_1, all_86_10)) 207.07/127.96 | | | | | | | | | (95) length1(int, all_103_4) = all_759_1 207.07/127.96 | | | | | | | | | (96) length1(int, all_105_4) = all_759_1 207.07/127.96 | | | | | | | | | 207.07/127.96 | | | | | | | | | GROUND_INST: instantiating (1) with all_133_0, all_760_0, 207.07/127.96 | | | | | | | | | all_133_1, simplifying with (14), (68) gives: 207.07/127.96 | | | | | | | | | (97) all_760_0 = all_133_0 207.07/127.96 | | | | | | | | | 207.07/127.96 | | | | | | | | | GROUND_INST: instantiating (47) with all_759_1, all_754_1, 207.07/127.96 | | | | | | | | | all_105_4, int, simplifying with (92), (96) gives: 207.07/127.96 | | | | | | | | | (98) all_759_1 = all_754_1 207.07/127.96 | | | | | | | | | 207.07/127.96 | | | | | | | | | GROUND_INST: instantiating (47) with all_86_13, all_759_1, 207.07/127.96 | | | | | | | | | all_103_4, int, simplifying with (9), (95) gives: 207.07/127.96 | | | | | | | | | (99) all_759_1 = all_86_13 207.07/127.96 | | | | | | | | | 207.07/127.96 | | | | | | | | | GROUND_INST: instantiating (18) with all_105_1, all_760_2, 207.07/127.96 | | | | | | | | | all_105_2, int, simplifying with (25), (66) gives: 207.07/127.96 | | | | | | | | | (100) all_760_2 = all_105_1 207.07/127.96 | | | | | | | | | 207.07/127.96 | | | | | | | | | GROUND_INST: instantiating (18) with all_760_2, all_755_1, 207.07/127.96 | | | | | | | | | all_105_2, int, simplifying with (63), (66) gives: 207.07/127.96 | | | | | | | | | (101) all_760_2 = all_755_1 207.07/127.96 | | | | | | | | | 207.07/127.96 | | | | | | | | | COMBINE_EQS: (100), (101) imply: 207.07/127.96 | | | | | | | | | (102) all_755_1 = all_105_1 207.07/127.96 | | | | | | | | | 207.07/127.96 | | | | | | | | | SIMP: (102) implies: 207.07/127.96 | | | | | | | | | (103) all_755_1 = all_105_1 207.07/127.96 | | | | | | | | | 207.07/127.96 | | | | | | | | | COMBINE_EQS: (98), (99) imply: 207.07/127.96 | | | | | | | | | (104) all_754_1 = all_86_13 207.07/127.96 | | | | | | | | | 207.07/127.96 | | | | | | | | | REDUCE: (69), (100) imply: 207.07/127.96 | | | | | | | | | (105) tb2t(all_105_1) = all_760_1 207.07/127.96 | | | | | | | | | 207.07/127.96 | | | | | | | | | REDUCE: (67), (97) imply: 207.07/127.96 | | | | | | | | | (106) get3(all_760_1, all_133_2) = all_133_0 207.07/127.96 | | | | | | | | | 207.07/127.96 | | | | | | | | | REDUCE: (61), (103) imply: 207.07/127.96 | | | | | | | | | (107) get(int, int, all_105_1, all_755_0) = all_133_1 207.07/127.96 | | | | | | | | | 207.07/127.96 | | | | | | | | | BETA: splitting (90) gives: 207.07/127.96 | | | | | | | | | 207.07/127.96 | | | | | | | | | Case 1: 207.07/127.96 | | | | | | | | | | 207.07/127.96 | | | | | | | | | | (108) all_809_1 = 0 & permut3(int, all_105_4, all_105_2, 207.07/127.96 | | | | | | | | | | 0, all_86_13) = 0 207.07/127.96 | | | | | | | | | | 207.07/127.96 | | | | | | | | | | ALPHA: (108) implies: 207.07/127.96 | | | | | | | | | | (109) permut3(int, all_105_4, all_105_2, 0, all_86_13) = 207.07/127.96 | | | | | | | | | | 0 207.07/127.96 | | | | | | | | | | 207.07/127.96 | | | | | | | | | | REF_CLOSE: (1), (2), (4), (6), (7), (8), (9), (10), (11), 207.07/127.96 | | | | | | | | | | (13), (14), (15), (17), (18), (19), (20), (21), 207.07/127.96 | | | | | | | | | | (22), (23), (24), (25), (26), (27), (28), (29), 207.07/127.96 | | | | | | | | | | (30), (31), (32), (34), (35), (36), (37), (38), 207.07/127.96 | | | | | | | | | | (39), (40), (41), (43), (44), (45), (46), (47), 207.07/127.96 | | | | | | | | | | (48), (50), (62), (70), (105), (106), (107), (109) 207.07/127.96 | | | | | | | | | | are inconsistent by sub-proof #91. 207.07/127.96 | | | | | | | | | | 207.07/127.96 | | | | | | | | | Case 2: 207.07/127.96 | | | | | | | | | | 207.07/127.96 | | | | | | | | | | (110) length1(int, all_105_4) = all_809_1 & ( ~ 207.07/127.96 | | | | | | | | | | ($lesseq(all_86_13, all_809_1)) | ~ ($lesseq(0, 207.07/127.96 | | | | | | | | | | all_809_1)) | ( ~ (all_809_0 = all_809_1) & 207.07/127.96 | | | | | | | | | | length1(int, all_105_2) = all_809_0)) 207.07/127.96 | | | | | | | | | | 207.07/127.96 | | | | | | | | | | ALPHA: (110) implies: 207.07/127.96 | | | | | | | | | | (111) length1(int, all_105_4) = all_809_1 207.07/127.96 | | | | | | | | | | (112) ~ ($lesseq(all_86_13, all_809_1)) | ~ ($lesseq(0, 207.07/127.96 | | | | | | | | | | all_809_1)) | ( ~ (all_809_0 = all_809_1) & 207.07/127.96 | | | | | | | | | | length1(int, all_105_2) = all_809_0) 207.07/127.96 | | | | | | | | | | 207.07/127.96 | | | | | | | | | | GROUND_INST: instantiating (47) with all_86_13, all_809_1, 207.07/127.96 | | | | | | | | | | all_105_4, int, simplifying with (19), (111) 207.07/127.96 | | | | | | | | | | gives: 207.07/127.96 | | | | | | | | | | (113) all_809_1 = all_86_13 207.07/127.96 | | | | | | | | | | 207.07/127.96 | | | | | | | | | | BETA: splitting (112) gives: 207.07/127.96 | | | | | | | | | | 207.07/127.96 | | | | | | | | | | Case 1: 207.07/127.96 | | | | | | | | | | | 207.07/127.96 | | | | | | | | | | | (114) $lesseq(all_809_1, -1) 207.07/127.96 | | | | | | | | | | | 207.07/127.96 | | | | | | | | | | | REDUCE: (113), (114) imply: 207.07/127.96 | | | | | | | | | | | (115) $lesseq(all_86_13, -1) 207.07/127.96 | | | | | | | | | | | 207.07/127.96 | | | | | | | | | | | COMBINE_INEQS: (13), (28) imply: 207.07/127.96 | | | | | | | | | | | (116) $lesseq(all_86_11, all_86_8) 207.07/127.96 | | | | | | | | | | | 207.07/127.96 | | | | | | | | | | | COMBINE_INEQS: (30), (36) imply: 207.07/127.96 | | | | | | | | | | | (117) $lesseq(1, $difference(all_86_10, all_86_8)) 207.07/127.96 | | | | | | | | | | | 207.07/127.96 | | | | | | | | | | | COMBINE_INEQS: (116), (117) imply: 207.07/127.96 | | | | | | | | | | | (118) $lesseq(1, $difference(all_86_10, all_86_11)) 207.07/127.96 | | | | | | | | | | | 207.07/127.96 | | | | | | | | | | | COMBINE_INEQS: (74), (115) imply: 207.07/127.96 | | | | | | | | | | | (119) $lesseq(0, -1) 207.07/127.96 | | | | | | | | | | | 207.07/127.96 | | | | | | | | | | | CLOSE: (119) is inconsistent. 207.07/127.96 | | | | | | | | | | | 207.07/127.96 | | | | | | | | | | Case 2: 207.07/127.96 | | | | | | | | | | | 207.07/127.96 | | | | | | | | | | | (120) ~ ($lesseq(all_86_13, all_809_1)) | ( ~ 207.07/127.96 | | | | | | | | | | | (all_809_0 = all_809_1) & length1(int, 207.07/127.96 | | | | | | | | | | | all_105_2) = all_809_0) 207.07/127.96 | | | | | | | | | | | 207.07/127.96 | | | | | | | | | | | BETA: splitting (120) gives: 207.07/127.96 | | | | | | | | | | | 207.07/127.96 | | | | | | | | | | | Case 1: 207.07/127.96 | | | | | | | | | | | | 207.07/127.96 | | | | | | | | | | | | (121) $lesseq(1, $difference(all_86_13, all_809_1)) 207.07/127.96 | | | | | | | | | | | | 207.07/127.96 | | | | | | | | | | | | REDUCE: (113), (121) imply: 207.07/127.96 | | | | | | | | | | | | (122) $lesseq(0, -1) 207.07/127.96 | | | | | | | | | | | | 207.07/127.96 | | | | | | | | | | | | CLOSE: (122) is inconsistent. 207.07/127.96 | | | | | | | | | | | | 207.07/127.96 | | | | | | | | | | | Case 2: 207.07/127.96 | | | | | | | | | | | | 207.07/127.96 | | | | | | | | | | | | (123) ~ (all_809_0 = all_809_1) & length1(int, 207.07/127.96 | | | | | | | | | | | | all_105_2) = all_809_0 207.07/127.96 | | | | | | | | | | | | 207.07/127.96 | | | | | | | | | | | | ALPHA: (123) implies: 207.07/127.96 | | | | | | | | | | | | (124) ~ (all_809_0 = all_809_1) 207.07/127.96 | | | | | | | | | | | | (125) length1(int, all_105_2) = all_809_0 207.07/127.96 | | | | | | | | | | | | 207.07/127.96 | | | | | | | | | | | | REDUCE: (113), (124) imply: 207.07/127.96 | | | | | | | | | | | | (126) ~ (all_809_0 = all_86_13) 207.07/127.96 | | | | | | | | | | | | 207.07/127.96 | | | | | | | | | | | | GROUND_INST: instantiating (47) with all_86_13, all_809_0, 207.07/127.96 | | | | | | | | | | | | all_105_2, int, simplifying with (5), (125) gives: 207.07/127.96 | | | | | | | | | | | | (127) all_809_0 = all_86_13 207.07/127.96 | | | | | | | | | | | | 207.07/127.96 | | | | | | | | | | | | REDUCE: (126), (127) imply: 207.07/127.96 | | | | | | | | | | | | (128) ~ (0 = 0) 207.07/127.96 | | | | | | | | | | | | 207.07/127.96 | | | | | | | | | | | | CLOSE: (128) is inconsistent. 207.07/127.96 | | | | | | | | | | | | 207.07/127.96 | | | | | | | | | | | End of split 207.07/127.96 | | | | | | | | | | | 207.07/127.96 | | | | | | | | | | End of split 207.07/127.96 | | | | | | | | | | 207.07/127.96 | | | | | | | | | End of split 207.07/127.96 | | | | | | | | | 207.07/127.96 | | | | | | | | Case 2: 207.07/127.96 | | | | | | | | | 207.07/127.96 | | | | | | | | | (129) ~ (all_759_1 = 0) & permut3(int, all_103_4, 207.07/127.96 | | | | | | | | | all_105_4, all_86_11, $sum(all_86_10, 1)) = 207.07/127.96 | | | | | | | | | all_759_1 207.07/127.96 | | | | | | | | | 207.07/127.96 | | | | | | | | | ALPHA: (129) implies: 207.07/127.96 | | | | | | | | | (130) ~ (all_759_1 = 0) 207.07/127.96 | | | | | | | | | (131) permut3(int, all_103_4, all_105_4, all_86_11, 207.07/127.96 | | | | | | | | | $sum(all_86_10, 1)) = all_759_1 207.07/127.96 | | | | | | | | | 207.07/127.96 | | | | | | | | | GROUND_INST: instantiating (15) with all_759_1, 0, 207.07/127.96 | | | | | | | | | $sum(all_86_10, 1), all_86_11, all_105_4, 207.07/127.96 | | | | | | | | | all_103_4, int, simplifying with (86), (131) 207.07/127.96 | | | | | | | | | gives: 207.07/127.96 | | | | | | | | | (132) all_759_1 = 0 207.07/127.96 | | | | | | | | | 207.07/127.96 | | | | | | | | | REDUCE: (130), (132) imply: 207.07/127.96 | | | | | | | | | (133) ~ (0 = 0) 207.07/127.96 | | | | | | | | | 207.07/127.96 | | | | | | | | | CLOSE: (133) is inconsistent. 207.07/127.96 | | | | | | | | | 207.07/127.96 | | | | | | | | End of split 207.07/127.96 | | | | | | | | 207.07/127.96 | | | | | | | Case 2: 207.07/127.96 | | | | | | | | 207.07/127.96 | | | | | | | | (134) ~ (all_754_1 = 0) & permut3(int, all_103_2, all_105_4, 207.07/127.96 | | | | | | | | 0, all_86_13) = all_754_1 207.07/127.96 | | | | | | | | 207.07/127.96 | | | | | | | | ALPHA: (134) implies: 207.07/127.96 | | | | | | | | (135) ~ (all_754_1 = 0) 207.07/127.96 | | | | | | | | (136) permut3(int, all_103_2, all_105_4, 0, all_86_13) = 207.07/127.96 | | | | | | | | all_754_1 207.07/127.96 | | | | | | | | 207.07/127.96 | | | | | | | | REF_CLOSE: (15), (80), (135), (136) are inconsistent by 207.07/127.96 | | | | | | | | sub-proof #90. 207.07/127.96 | | | | | | | | 207.07/127.96 | | | | | | | End of split 207.07/127.96 | | | | | | | 207.07/127.96 | | | | | | End of split 207.07/127.96 | | | | | | 207.07/127.96 | | | | | Case 2: 207.07/127.96 | | | | | | 207.07/127.96 | | | | | | (137) length1(int, all_103_4) = all_798_1 & ( ~ ($lesseq(1, 207.07/127.96 | | | | | | $difference(all_798_1, all_86_10))) | ~ 207.07/127.96 | | | | | | ($lesseq(all_86_11, all_798_1)) | ( ~ (all_798_0 = 207.07/127.96 | | | | | | all_798_1) & length1(int, all_105_4) = all_798_0)) 207.07/127.96 | | | | | | 207.07/127.96 | | | | | | ALPHA: (137) implies: 207.07/127.96 | | | | | | (138) length1(int, all_103_4) = all_798_1 207.07/127.96 | | | | | | (139) ~ ($lesseq(1, $difference(all_798_1, all_86_10))) | ~ 207.07/127.96 | | | | | | ($lesseq(all_86_11, all_798_1)) | ( ~ (all_798_0 = 207.07/127.96 | | | | | | all_798_1) & length1(int, all_105_4) = all_798_0) 207.07/127.96 | | | | | | 207.07/127.96 | | | | | | BETA: splitting (52) gives: 207.07/127.96 | | | | | | 207.07/127.96 | | | | | | Case 1: 207.07/127.96 | | | | | | | 207.07/127.96 | | | | | | | (140) $lesseq(all_86_13, -1) 207.07/127.96 | | | | | | | 207.07/127.96 | | | | | | | COMBINE_INEQS: (74), (140) imply: 207.07/127.96 | | | | | | | (141) $lesseq(0, -1) 207.07/127.96 | | | | | | | 207.07/127.96 | | | | | | | CLOSE: (141) is inconsistent. 207.07/127.96 | | | | | | | 207.07/127.96 | | | | | | Case 2: 207.07/127.96 | | | | | | | 207.07/127.96 | | | | | | | (142) ? [v0: $int] : ? [v1: $int] : ((v0 = 0 & permut3(int, 207.07/127.96 | | | | | | | all_105_4, all_105_2, 0, all_86_13) = 0) | 207.07/127.96 | | | | | | | (length1(int, all_105_4) = v0 & ( ~ ($lesseq(all_86_13, 207.07/127.96 | | | | | | | v0)) | ~ ($lesseq(0, v0)) | ( ~ (v1 = v0) & 207.07/127.96 | | | | | | | length1(int, all_105_2) = v1)))) 207.07/127.96 | | | | | | | 207.07/127.96 | | | | | | | DELTA: instantiating (142) with fresh symbols all_809_0, all_809_1 207.07/127.96 | | | | | | | gives: 207.07/127.96 | | | | | | | (143) (all_809_1 = 0 & permut3(int, all_105_4, all_105_2, 0, 207.07/127.96 | | | | | | | all_86_13) = 0) | (length1(int, all_105_4) = 207.07/127.96 | | | | | | | all_809_1 & ( ~ ($lesseq(all_86_13, all_809_1)) | ~ 207.07/127.96 | | | | | | | ($lesseq(0, all_809_1)) | ( ~ (all_809_0 = all_809_1) 207.07/127.96 | | | | | | | & length1(int, all_105_2) = all_809_0))) 207.07/127.96 | | | | | | | 207.07/127.96 | | | | | | | BETA: splitting (59) gives: 207.07/127.96 | | | | | | | 207.07/127.96 | | | | | | | Case 1: 207.07/127.96 | | | | | | | | 207.07/127.96 | | | | | | | | (144) all_754_0 = all_754_1 & $lesseq(all_86_13, all_754_1) & 207.07/127.96 | | | | | | | | $lesseq(0, all_754_1) & $lesseq(0, all_86_13) & 207.07/127.96 | | | | | | | | length1(int, all_105_4) = all_754_1 & length1(int, 207.07/127.96 | | | | | | | | all_103_2) = all_754_1 207.07/127.96 | | | | | | | | 207.07/127.96 | | | | | | | | ALPHA: (144) implies: 207.07/127.96 | | | | | | | | (145) length1(int, all_103_2) = all_754_1 207.07/127.96 | | | | | | | | (146) length1(int, all_105_4) = all_754_1 207.07/127.96 | | | | | | | | 207.07/127.96 | | | | | | | | GROUND_INST: instantiating (1) with all_133_0, all_760_0, 207.07/127.96 | | | | | | | | all_133_1, simplifying with (14), (68) gives: 207.07/127.96 | | | | | | | | (147) all_760_0 = all_133_0 207.07/127.96 | | | | | | | | 207.07/127.96 | | | | | | | | GROUND_INST: instantiating (47) with all_86_13, all_754_1, 207.07/127.96 | | | | | | | | all_103_2, int, simplifying with (3), (145) gives: 207.07/127.96 | | | | | | | | (148) all_754_1 = all_86_13 207.07/127.96 | | | | | | | | 207.07/127.96 | | | | | | | | GROUND_INST: instantiating (47) with all_86_13, all_798_1, 207.07/127.96 | | | | | | | | all_103_4, int, simplifying with (9), (138) gives: 207.07/127.96 | | | | | | | | (149) all_798_1 = all_86_13 207.07/127.96 | | | | | | | | 207.07/127.96 | | | | | | | | GROUND_INST: instantiating (18) with all_105_1, all_760_2, 207.07/127.96 | | | | | | | | all_105_2, int, simplifying with (25), (66) gives: 207.07/127.96 | | | | | | | | (150) all_760_2 = all_105_1 207.07/127.96 | | | | | | | | 207.07/127.96 | | | | | | | | GROUND_INST: instantiating (18) with all_760_2, all_755_1, 207.07/127.96 | | | | | | | | all_105_2, int, simplifying with (63), (66) gives: 207.07/127.96 | | | | | | | | (151) all_760_2 = all_755_1 207.07/127.96 | | | | | | | | 207.07/127.96 | | | | | | | | COMBINE_EQS: (150), (151) imply: 207.07/127.96 | | | | | | | | (152) all_755_1 = all_105_1 207.07/127.96 | | | | | | | | 207.07/127.96 | | | | | | | | REDUCE: (69), (150) imply: 207.07/127.96 | | | | | | | | (153) tb2t(all_105_1) = all_760_1 207.07/127.96 | | | | | | | | 207.07/127.96 | | | | | | | | REDUCE: (67), (147) imply: 207.07/127.96 | | | | | | | | (154) get3(all_760_1, all_133_2) = all_133_0 207.07/127.96 | | | | | | | | 207.07/127.96 | | | | | | | | REDUCE: (61), (152) imply: 207.07/127.96 | | | | | | | | (155) get(int, int, all_105_1, all_755_0) = all_133_1 207.07/127.96 | | | | | | | | 207.07/127.96 | | | | | | | | BETA: splitting (143) gives: 207.07/127.96 | | | | | | | | 207.07/127.96 | | | | | | | | Case 1: 207.07/127.96 | | | | | | | | | 207.07/127.96 | | | | | | | | | (156) all_809_1 = 0 & permut3(int, all_105_4, all_105_2, 0, 207.07/127.96 | | | | | | | | | all_86_13) = 0 207.07/127.96 | | | | | | | | | 207.07/127.96 | | | | | | | | | ALPHA: (156) implies: 207.07/127.96 | | | | | | | | | (157) permut3(int, all_105_4, all_105_2, 0, all_86_13) = 0 207.07/127.96 | | | | | | | | | 207.07/127.97 | | | | | | | | | REF_CLOSE: (1), (2), (4), (6), (7), (8), (9), (10), (11), 207.07/127.97 | | | | | | | | | (13), (14), (15), (17), (18), (19), (20), (21), 207.07/127.97 | | | | | | | | | (22), (23), (24), (25), (26), (27), (28), (29), 207.07/127.97 | | | | | | | | | (30), (31), (32), (34), (35), (36), (37), (38), 207.07/127.97 | | | | | | | | | (39), (40), (41), (43), (44), (45), (46), (47), 207.07/127.97 | | | | | | | | | (48), (50), (62), (70), (153), (154), (155), (157) 207.07/127.97 | | | | | | | | | are inconsistent by sub-proof #91. 207.07/127.97 | | | | | | | | | 207.07/127.97 | | | | | | | | Case 2: 207.07/127.97 | | | | | | | | | 207.07/127.97 | | | | | | | | | (158) length1(int, all_105_4) = all_809_1 & ( ~ 207.07/127.97 | | | | | | | | | ($lesseq(all_86_13, all_809_1)) | ~ ($lesseq(0, 207.07/127.97 | | | | | | | | | all_809_1)) | ( ~ (all_809_0 = all_809_1) & 207.07/127.97 | | | | | | | | | length1(int, all_105_2) = all_809_0)) 207.07/127.97 | | | | | | | | | 207.07/127.97 | | | | | | | | | ALPHA: (158) implies: 207.07/127.97 | | | | | | | | | (159) length1(int, all_105_4) = all_809_1 207.07/127.97 | | | | | | | | | 207.07/127.97 | | | | | | | | | BETA: splitting (139) gives: 207.07/127.97 | | | | | | | | | 207.07/127.97 | | | | | | | | | Case 1: 207.07/127.97 | | | | | | | | | | 207.07/127.97 | | | | | | | | | | (160) $lesseq(1, $difference(all_86_11, all_798_1)) 207.07/127.97 | | | | | | | | | | 207.07/127.97 | | | | | | | | | | REDUCE: (149), (160) imply: 207.07/127.97 | | | | | | | | | | (161) $lesseq(1, $difference(all_86_11, all_86_13)) 207.07/127.97 | | | | | | | | | | 207.07/127.97 | | | | | | | | | | COMBINE_INEQS: (13), (28) imply: 207.07/127.97 | | | | | | | | | | (162) $lesseq(all_86_11, all_86_8) 207.07/127.97 | | | | | | | | | | 207.07/127.97 | | | | | | | | | | COMBINE_INEQS: (30), (36) imply: 207.07/127.97 | | | | | | | | | | (163) $lesseq(1, $difference(all_86_10, all_86_8)) 207.07/127.97 | | | | | | | | | | 207.07/127.97 | | | | | | | | | | COMBINE_INEQS: (162), (163) imply: 207.07/127.97 | | | | | | | | | | (164) $lesseq(1, $difference(all_86_10, all_86_11)) 207.07/127.97 | | | | | | | | | | 207.07/127.97 | | | | | | | | | | COMBINE_INEQS: (12), (161) imply: 207.07/127.97 | | | | | | | | | | (165) $lesseq(0, -1) 207.07/127.97 | | | | | | | | | | 207.07/127.97 | | | | | | | | | | CLOSE: (165) is inconsistent. 207.07/127.97 | | | | | | | | | | 207.07/127.97 | | | | | | | | | Case 2: 207.07/127.97 | | | | | | | | | | 207.07/127.97 | | | | | | | | | | (166) ~ ($lesseq(1, $difference(all_798_1, all_86_10))) 207.07/127.97 | | | | | | | | | | | ( ~ (all_798_0 = all_798_1) & length1(int, 207.07/127.97 | | | | | | | | | | all_105_4) = all_798_0) 207.07/127.97 | | | | | | | | | | 207.07/127.97 | | | | | | | | | | BETA: splitting (166) gives: 207.07/127.97 | | | | | | | | | | 207.07/127.97 | | | | | | | | | | Case 1: 207.07/127.97 | | | | | | | | | | | 207.07/127.97 | | | | | | | | | | | (167) $lesseq(all_798_1, all_86_10) 207.07/127.97 | | | | | | | | | | | 207.07/127.97 | | | | | | | | | | | REDUCE: (149), (167) imply: 207.07/127.97 | | | | | | | | | | | (168) $lesseq(all_86_13, all_86_10) 207.07/127.97 | | | | | | | | | | | 207.07/127.97 | | | | | | | | | | | COMBINE_INEQS: (38), (168) imply: 207.07/127.97 | | | | | | | | | | | (169) $lesseq(0, -1) 207.07/127.97 | | | | | | | | | | | 207.07/127.97 | | | | | | | | | | | CLOSE: (169) is inconsistent. 207.07/127.97 | | | | | | | | | | | 207.07/127.97 | | | | | | | | | | Case 2: 207.07/127.97 | | | | | | | | | | | 207.07/127.97 | | | | | | | | | | | (170) ~ (all_798_0 = all_798_1) & length1(int, 207.07/127.97 | | | | | | | | | | | all_105_4) = all_798_0 207.07/127.97 | | | | | | | | | | | 207.07/127.97 | | | | | | | | | | | ALPHA: (170) implies: 207.07/127.97 | | | | | | | | | | | (171) ~ (all_798_0 = all_798_1) 207.07/127.97 | | | | | | | | | | | (172) length1(int, all_105_4) = all_798_0 207.07/127.97 | | | | | | | | | | | 207.07/127.97 | | | | | | | | | | | REDUCE: (149), (171) imply: 207.07/127.97 | | | | | | | | | | | (173) ~ (all_798_0 = all_86_13) 207.07/127.97 | | | | | | | | | | | 207.07/127.97 | | | | | | | | | | | GROUND_INST: instantiating (47) with all_86_13, all_809_1, 207.07/127.97 | | | | | | | | | | | all_105_4, int, simplifying with (19), (159) 207.07/127.97 | | | | | | | | | | | gives: 207.07/127.97 | | | | | | | | | | | (174) all_809_1 = all_86_13 207.07/127.97 | | | | | | | | | | | 207.07/127.97 | | | | | | | | | | | GROUND_INST: instantiating (47) with all_809_1, all_798_0, 207.07/127.97 | | | | | | | | | | | all_105_4, int, simplifying with (159), (172) 207.07/127.97 | | | | | | | | | | | gives: 207.07/127.97 | | | | | | | | | | | (175) all_809_1 = all_798_0 207.07/127.97 | | | | | | | | | | | 207.07/127.97 | | | | | | | | | | | COMBINE_EQS: (174), (175) imply: 207.07/127.97 | | | | | | | | | | | (176) all_798_0 = all_86_13 207.07/127.97 | | | | | | | | | | | 207.07/127.97 | | | | | | | | | | | REDUCE: (173), (176) imply: 207.07/127.97 | | | | | | | | | | | (177) ~ (0 = 0) 207.07/127.97 | | | | | | | | | | | 207.07/127.97 | | | | | | | | | | | CLOSE: (177) is inconsistent. 207.07/127.97 | | | | | | | | | | | 207.07/127.97 | | | | | | | | | | End of split 207.07/127.97 | | | | | | | | | | 207.07/127.97 | | | | | | | | | End of split 207.07/127.97 | | | | | | | | | 207.07/127.97 | | | | | | | | End of split 207.07/127.97 | | | | | | | | 207.07/127.97 | | | | | | | Case 2: 207.07/127.97 | | | | | | | | 207.07/127.97 | | | | | | | | (178) ~ (all_754_1 = 0) & permut3(int, all_103_2, all_105_4, 207.07/127.97 | | | | | | | | 0, all_86_13) = all_754_1 207.07/127.97 | | | | | | | | 207.07/127.97 | | | | | | | | ALPHA: (178) implies: 207.07/127.97 | | | | | | | | (179) ~ (all_754_1 = 0) 207.07/127.97 | | | | | | | | (180) permut3(int, all_103_2, all_105_4, 0, all_86_13) = 207.07/127.97 | | | | | | | | all_754_1 207.07/127.97 | | | | | | | | 207.07/127.97 | | | | | | | | REF_CLOSE: (15), (80), (179), (180) are inconsistent by 207.07/127.97 | | | | | | | | sub-proof #90. 207.07/127.97 | | | | | | | | 207.07/127.97 | | | | | | | End of split 207.07/127.97 | | | | | | | 207.07/127.97 | | | | | | End of split 207.07/127.97 | | | | | | 207.07/127.97 | | | | | End of split 207.07/127.97 | | | | | 207.07/127.97 | | | | End of split 207.07/127.97 | | | | 207.07/127.97 | | | Case 2: 207.07/127.97 | | | | 207.07/127.97 | | | | (181) length1(int, all_103_2) = all_787_1 & ( ~ ($lesseq(all_86_13, 207.07/127.97 | | | | all_787_1)) | ~ ($lesseq(0, all_787_1)) | ( ~ (all_787_0 207.07/127.97 | | | | = all_787_1) & length1(int, all_105_4) = all_787_0)) 207.07/127.97 | | | | 207.07/127.97 | | | | ALPHA: (181) implies: 207.07/127.97 | | | | (182) length1(int, all_103_2) = all_787_1 207.07/127.97 | | | | (183) ~ ($lesseq(all_86_13, all_787_1)) | ~ ($lesseq(0, all_787_1)) 207.07/127.97 | | | | | ( ~ (all_787_0 = all_787_1) & length1(int, all_105_4) = 207.07/127.97 | | | | all_787_0) 207.07/127.97 | | | | 207.07/127.97 | | | | BETA: splitting (73) gives: 207.07/127.97 | | | | 207.07/127.97 | | | | Case 1: 207.07/127.97 | | | | | 207.07/127.97 | | | | | (184) $lesseq(all_86_10, -2) 207.07/127.97 | | | | | 207.07/127.97 | | | | | COMBINE_INEQS: (49), (184) imply: 207.07/127.97 | | | | | (185) $lesseq(0, -1) 207.07/127.97 | | | | | 207.07/127.97 | | | | | CLOSE: (185) is inconsistent. 207.07/127.97 | | | | | 207.07/127.97 | | | | Case 2: 207.07/127.97 | | | | | 207.07/127.97 | | | | | (186) ? [v0: $int] : ? [v1: $int] : ((v0 = 0 & permut3(int, 207.07/127.97 | | | | | all_103_4, all_105_4, all_86_11, $sum(all_86_10, 1)) = 207.07/127.97 | | | | | 0) | (length1(int, all_103_4) = v0 & ( ~ ($lesseq(1, 207.07/127.97 | | | | | $difference(v0, all_86_10))) | ~ 207.07/127.97 | | | | | ($lesseq(all_86_11, v0)) | ( ~ (v1 = v0) & length1(int, 207.07/127.97 | | | | | all_105_4) = v1)))) 207.07/127.97 | | | | | 207.07/127.97 | | | | | DELTA: instantiating (186) with fresh symbols all_798_0, all_798_1 207.07/127.97 | | | | | gives: 207.07/127.97 | | | | | (187) (all_798_1 = 0 & permut3(int, all_103_4, all_105_4, 207.07/127.97 | | | | | all_86_11, $sum(all_86_10, 1)) = 0) | (length1(int, 207.07/127.97 | | | | | all_103_4) = all_798_1 & ( ~ ($lesseq(1, 207.07/127.97 | | | | | $difference(all_798_1, all_86_10))) | ~ 207.07/127.97 | | | | | ($lesseq(all_86_11, all_798_1)) | ( ~ (all_798_0 = 207.07/127.97 | | | | | all_798_1) & length1(int, all_105_4) = all_798_0))) 207.07/127.97 | | | | | 207.07/127.97 | | | | | BETA: splitting (187) gives: 207.07/127.97 | | | | | 207.07/127.97 | | | | | Case 1: 207.07/127.97 | | | | | | 207.07/127.97 | | | | | | (188) all_798_1 = 0 & permut3(int, all_103_4, all_105_4, 207.07/127.97 | | | | | | all_86_11, $sum(all_86_10, 1)) = 0 207.07/127.97 | | | | | | 207.07/127.97 | | | | | | ALPHA: (188) implies: 207.07/127.97 | | | | | | (189) permut3(int, all_103_4, all_105_4, all_86_11, 207.07/127.97 | | | | | | $sum(all_86_10, 1)) = 0 207.07/127.97 | | | | | | 207.07/127.97 | | | | | | BETA: splitting (52) gives: 207.07/127.97 | | | | | | 207.07/127.97 | | | | | | Case 1: 207.07/127.97 | | | | | | | 207.07/127.97 | | | | | | | (190) $lesseq(all_86_13, -1) 207.07/127.97 | | | | | | | 207.07/127.97 | | | | | | | COMBINE_INEQS: (74), (190) imply: 207.07/127.97 | | | | | | | (191) $lesseq(0, -1) 207.07/127.97 | | | | | | | 207.07/127.97 | | | | | | | CLOSE: (191) is inconsistent. 207.07/127.97 | | | | | | | 207.07/127.97 | | | | | | Case 2: 207.07/127.97 | | | | | | | 207.07/127.97 | | | | | | | (192) ? [v0: $int] : ? [v1: $int] : ((v0 = 0 & permut3(int, 207.07/127.97 | | | | | | | all_105_4, all_105_2, 0, all_86_13) = 0) | 207.07/127.97 | | | | | | | (length1(int, all_105_4) = v0 & ( ~ ($lesseq(all_86_13, 207.07/127.97 | | | | | | | v0)) | ~ ($lesseq(0, v0)) | ( ~ (v1 = v0) & 207.07/127.97 | | | | | | | length1(int, all_105_2) = v1)))) 207.07/127.97 | | | | | | | 207.07/127.97 | | | | | | | DELTA: instantiating (192) with fresh symbols all_809_0, all_809_1 207.07/127.97 | | | | | | | gives: 207.07/127.97 | | | | | | | (193) (all_809_1 = 0 & permut3(int, all_105_4, all_105_2, 0, 207.07/127.97 | | | | | | | all_86_13) = 0) | (length1(int, all_105_4) = 207.07/127.97 | | | | | | | all_809_1 & ( ~ ($lesseq(all_86_13, all_809_1)) | ~ 207.07/127.97 | | | | | | | ($lesseq(0, all_809_1)) | ( ~ (all_809_0 = all_809_1) 207.07/127.97 | | | | | | | & length1(int, all_105_2) = all_809_0))) 207.07/127.97 | | | | | | | 207.07/127.97 | | | | | | | BETA: splitting (64) gives: 207.07/127.97 | | | | | | | 207.07/127.97 | | | | | | | Case 1: 207.07/127.97 | | | | | | | | 207.07/127.97 | | | | | | | | (194) all_759_0 = all_759_1 & $lesseq(1, 207.07/127.97 | | | | | | | | $difference(all_759_1, all_86_10)) & 207.07/127.97 | | | | | | | | $lesseq(all_86_11, all_759_1) & $lesseq(-1, all_86_10) 207.07/127.97 | | | | | | | | & $lesseq(0, all_86_11) & length1(int, all_105_4) = 207.07/127.97 | | | | | | | | all_759_1 & length1(int, all_103_4) = all_759_1 207.07/127.97 | | | | | | | | 207.07/127.97 | | | | | | | | ALPHA: (194) implies: 207.07/127.97 | | | | | | | | (195) $lesseq(1, $difference(all_759_1, all_86_10)) 207.07/127.97 | | | | | | | | (196) length1(int, all_103_4) = all_759_1 207.07/127.97 | | | | | | | | (197) length1(int, all_105_4) = all_759_1 207.07/127.97 | | | | | | | | 207.07/127.97 | | | | | | | | GROUND_INST: instantiating (1) with all_133_0, all_760_0, 207.07/127.97 | | | | | | | | all_133_1, simplifying with (14), (68) gives: 207.07/127.97 | | | | | | | | (198) all_760_0 = all_133_0 207.07/127.97 | | | | | | | | 207.07/127.97 | | | | | | | | GROUND_INST: instantiating (47) with all_86_13, all_787_1, 207.07/127.97 | | | | | | | | all_103_2, int, simplifying with (3), (182) gives: 207.07/127.97 | | | | | | | | (199) all_787_1 = all_86_13 207.07/127.97 | | | | | | | | 207.07/127.97 | | | | | | | | GROUND_INST: instantiating (47) with all_86_13, all_759_1, 207.07/127.97 | | | | | | | | all_103_4, int, simplifying with (9), (196) gives: 207.07/127.97 | | | | | | | | (200) all_759_1 = all_86_13 207.07/127.97 | | | | | | | | 207.07/127.97 | | | | | | | | GROUND_INST: instantiating (18) with all_105_1, all_760_2, 207.07/127.97 | | | | | | | | all_105_2, int, simplifying with (25), (66) gives: 207.07/127.97 | | | | | | | | (201) all_760_2 = all_105_1 207.07/127.97 | | | | | | | | 207.07/127.97 | | | | | | | | GROUND_INST: instantiating (18) with all_760_2, all_755_1, 207.07/127.97 | | | | | | | | all_105_2, int, simplifying with (63), (66) gives: 207.07/127.97 | | | | | | | | (202) all_760_2 = all_755_1 207.07/127.97 | | | | | | | | 207.07/127.97 | | | | | | | | COMBINE_EQS: (201), (202) imply: 207.07/127.97 | | | | | | | | (203) all_755_1 = all_105_1 207.07/127.97 | | | | | | | | 207.07/127.97 | | | | | | | | REDUCE: (69), (201) imply: 207.07/127.97 | | | | | | | | (204) tb2t(all_105_1) = all_760_1 207.07/127.97 | | | | | | | | 207.07/127.97 | | | | | | | | REDUCE: (67), (198) imply: 207.07/127.97 | | | | | | | | (205) get3(all_760_1, all_133_2) = all_133_0 207.07/127.97 | | | | | | | | 207.07/127.97 | | | | | | | | REDUCE: (61), (203) imply: 207.07/127.97 | | | | | | | | (206) get(int, int, all_105_1, all_755_0) = all_133_1 207.07/127.97 | | | | | | | | 207.07/127.97 | | | | | | | | BETA: splitting (193) gives: 207.07/127.97 | | | | | | | | 207.07/127.97 | | | | | | | | Case 1: 207.07/127.97 | | | | | | | | | 207.07/127.97 | | | | | | | | | (207) all_809_1 = 0 & permut3(int, all_105_4, all_105_2, 0, 207.07/127.97 | | | | | | | | | all_86_13) = 0 207.07/127.97 | | | | | | | | | 207.07/127.97 | | | | | | | | | ALPHA: (207) implies: 207.07/127.97 | | | | | | | | | (208) permut3(int, all_105_4, all_105_2, 0, all_86_13) = 0 207.07/127.97 | | | | | | | | | 207.07/127.97 | | | | | | | | | REF_CLOSE: (1), (2), (4), (6), (7), (8), (9), (10), (11), 207.07/127.97 | | | | | | | | | (13), (14), (15), (17), (18), (19), (20), (21), 207.07/127.97 | | | | | | | | | (22), (23), (24), (25), (26), (27), (28), (29), 207.07/127.97 | | | | | | | | | (30), (31), (32), (34), (35), (36), (37), (38), 207.07/127.97 | | | | | | | | | (39), (40), (41), (43), (44), (45), (46), (47), 207.07/127.97 | | | | | | | | | (48), (50), (62), (70), (204), (205), (206), (208) 207.07/127.97 | | | | | | | | | are inconsistent by sub-proof #91. 207.07/127.97 | | | | | | | | | 207.07/127.97 | | | | | | | | Case 2: 207.07/127.97 | | | | | | | | | 207.07/127.97 | | | | | | | | | (209) length1(int, all_105_4) = all_809_1 & ( ~ 207.07/127.97 | | | | | | | | | ($lesseq(all_86_13, all_809_1)) | ~ ($lesseq(0, 207.07/127.97 | | | | | | | | | all_809_1)) | ( ~ (all_809_0 = all_809_1) & 207.07/127.97 | | | | | | | | | length1(int, all_105_2) = all_809_0)) 207.07/127.97 | | | | | | | | | 207.07/127.97 | | | | | | | | | ALPHA: (209) implies: 207.07/127.97 | | | | | | | | | (210) length1(int, all_105_4) = all_809_1 207.07/127.97 | | | | | | | | | 207.07/127.97 | | | | | | | | | BETA: splitting (183) gives: 207.07/127.97 | | | | | | | | | 207.07/127.97 | | | | | | | | | Case 1: 207.07/127.97 | | | | | | | | | | 207.07/127.97 | | | | | | | | | | (211) $lesseq(all_787_1, -1) 207.07/127.97 | | | | | | | | | | 207.07/127.97 | | | | | | | | | | REDUCE: (199), (211) imply: 207.07/127.97 | | | | | | | | | | (212) $lesseq(all_86_13, -1) 207.07/127.97 | | | | | | | | | | 207.07/127.97 | | | | | | | | | | COMBINE_INEQS: (13), (28) imply: 207.07/127.97 | | | | | | | | | | (213) $lesseq(all_86_11, all_86_8) 207.07/127.97 | | | | | | | | | | 207.07/127.97 | | | | | | | | | | COMBINE_INEQS: (30), (36) imply: 207.07/127.97 | | | | | | | | | | (214) $lesseq(1, $difference(all_86_10, all_86_8)) 207.07/127.97 | | | | | | | | | | 207.07/127.97 | | | | | | | | | | COMBINE_INEQS: (213), (214) imply: 207.07/127.97 | | | | | | | | | | (215) $lesseq(1, $difference(all_86_10, all_86_11)) 207.07/127.97 | | | | | | | | | | 207.07/127.97 | | | | | | | | | | COMBINE_INEQS: (74), (212) imply: 207.07/127.97 | | | | | | | | | | (216) $lesseq(0, -1) 207.07/127.97 | | | | | | | | | | 207.07/127.97 | | | | | | | | | | CLOSE: (216) is inconsistent. 207.07/127.97 | | | | | | | | | | 207.07/127.97 | | | | | | | | | Case 2: 207.07/127.97 | | | | | | | | | | 207.07/127.97 | | | | | | | | | | (217) ~ ($lesseq(all_86_13, all_787_1)) | ( ~ (all_787_0 207.07/127.97 | | | | | | | | | | = all_787_1) & length1(int, all_105_4) = 207.07/127.97 | | | | | | | | | | all_787_0) 207.07/127.97 | | | | | | | | | | 207.07/127.97 | | | | | | | | | | BETA: splitting (217) gives: 207.07/127.97 | | | | | | | | | | 207.07/127.97 | | | | | | | | | | Case 1: 207.07/127.97 | | | | | | | | | | | 207.07/127.97 | | | | | | | | | | | (218) $lesseq(1, $difference(all_86_13, all_787_1)) 207.07/127.97 | | | | | | | | | | | 207.07/127.97 | | | | | | | | | | | REDUCE: (199), (218) imply: 207.07/127.97 | | | | | | | | | | | (219) $lesseq(0, -1) 207.07/127.97 | | | | | | | | | | | 207.07/127.97 | | | | | | | | | | | CLOSE: (219) is inconsistent. 207.07/127.97 | | | | | | | | | | | 207.07/127.97 | | | | | | | | | | Case 2: 207.07/127.97 | | | | | | | | | | | 207.07/127.97 | | | | | | | | | | | (220) ~ (all_787_0 = all_787_1) & length1(int, 207.07/127.97 | | | | | | | | | | | all_105_4) = all_787_0 207.07/127.97 | | | | | | | | | | | 207.07/127.97 | | | | | | | | | | | ALPHA: (220) implies: 207.07/127.97 | | | | | | | | | | | (221) ~ (all_787_0 = all_787_1) 207.07/127.97 | | | | | | | | | | | (222) length1(int, all_105_4) = all_787_0 207.07/127.97 | | | | | | | | | | | 207.07/127.97 | | | | | | | | | | | REDUCE: (199), (221) imply: 207.07/127.97 | | | | | | | | | | | (223) ~ (all_787_0 = all_86_13) 207.07/127.97 | | | | | | | | | | | 207.07/127.97 | | | | | | | | | | | GROUND_INST: instantiating (47) with all_86_13, all_809_1, 207.07/127.97 | | | | | | | | | | | all_105_4, int, simplifying with (19), (210) 207.07/127.97 | | | | | | | | | | | gives: 207.07/127.97 | | | | | | | | | | | (224) all_809_1 = all_86_13 207.07/127.97 | | | | | | | | | | | 207.07/127.97 | | | | | | | | | | | GROUND_INST: instantiating (47) with all_809_1, all_787_0, 207.07/127.97 | | | | | | | | | | | all_105_4, int, simplifying with (210), (222) 207.07/127.97 | | | | | | | | | | | gives: 207.07/127.97 | | | | | | | | | | | (225) all_809_1 = all_787_0 207.07/127.97 | | | | | | | | | | | 207.07/127.97 | | | | | | | | | | | COMBINE_EQS: (224), (225) imply: 207.07/127.97 | | | | | | | | | | | (226) all_787_0 = all_86_13 207.07/127.97 | | | | | | | | | | | 207.07/127.97 | | | | | | | | | | | REDUCE: (223), (226) imply: 207.07/127.97 | | | | | | | | | | | (227) ~ (0 = 0) 207.07/127.97 | | | | | | | | | | | 207.07/127.97 | | | | | | | | | | | CLOSE: (227) is inconsistent. 207.07/127.97 | | | | | | | | | | | 207.07/127.97 | | | | | | | | | | End of split 207.07/127.97 | | | | | | | | | | 207.07/127.97 | | | | | | | | | End of split 207.07/127.97 | | | | | | | | | 207.07/127.97 | | | | | | | | End of split 207.07/127.97 | | | | | | | | 207.07/127.97 | | | | | | | Case 2: 207.07/127.97 | | | | | | | | 207.07/127.97 | | | | | | | | (228) ~ (all_759_1 = 0) & permut3(int, all_103_4, all_105_4, 207.07/127.97 | | | | | | | | all_86_11, $sum(all_86_10, 1)) = all_759_1 207.07/127.97 | | | | | | | | 207.07/127.97 | | | | | | | | ALPHA: (228) implies: 207.07/127.97 | | | | | | | | (229) ~ (all_759_1 = 0) 207.07/127.97 | | | | | | | | (230) permut3(int, all_103_4, all_105_4, all_86_11, 207.07/127.97 | | | | | | | | $sum(all_86_10, 1)) = all_759_1 207.07/127.97 | | | | | | | | 207.07/127.97 | | | | | | | | GROUND_INST: instantiating (15) with all_759_1, 0, 207.07/127.97 | | | | | | | | $sum(all_86_10, 1), all_86_11, all_105_4, 207.07/127.97 | | | | | | | | all_103_4, int, simplifying with (189), (230) 207.07/127.97 | | | | | | | | gives: 207.07/127.97 | | | | | | | | (231) all_759_1 = 0 207.07/127.97 | | | | | | | | 207.07/127.97 | | | | | | | | REDUCE: (229), (231) imply: 207.07/127.97 | | | | | | | | (232) ~ (0 = 0) 207.07/127.97 | | | | | | | | 207.07/127.97 | | | | | | | | CLOSE: (232) is inconsistent. 207.07/127.97 | | | | | | | | 207.07/127.97 | | | | | | | End of split 207.07/127.97 | | | | | | | 207.07/127.97 | | | | | | End of split 207.07/127.97 | | | | | | 207.07/127.97 | | | | | Case 2: 207.07/127.97 | | | | | | 207.07/127.97 | | | | | | (233) length1(int, all_103_4) = all_798_1 & ( ~ ($lesseq(1, 207.07/127.97 | | | | | | $difference(all_798_1, all_86_10))) | ~ 207.07/127.97 | | | | | | ($lesseq(all_86_11, all_798_1)) | ( ~ (all_798_0 = 207.07/127.97 | | | | | | all_798_1) & length1(int, all_105_4) = all_798_0)) 207.07/127.97 | | | | | | 207.07/127.97 | | | | | | ALPHA: (233) implies: 207.07/127.97 | | | | | | (234) length1(int, all_103_4) = all_798_1 207.07/127.97 | | | | | | (235) ~ ($lesseq(1, $difference(all_798_1, all_86_10))) | ~ 207.07/127.97 | | | | | | ($lesseq(all_86_11, all_798_1)) | ( ~ (all_798_0 = 207.07/127.97 | | | | | | all_798_1) & length1(int, all_105_4) = all_798_0) 207.07/127.97 | | | | | | 207.07/127.97 | | | | | | BETA: splitting (52) gives: 207.07/127.97 | | | | | | 207.07/127.97 | | | | | | Case 1: 207.07/127.97 | | | | | | | 207.07/127.97 | | | | | | | (236) $lesseq(all_86_13, -1) 207.07/127.97 | | | | | | | 207.07/127.97 | | | | | | | COMBINE_INEQS: (74), (236) imply: 207.07/127.97 | | | | | | | (237) $lesseq(0, -1) 207.07/127.97 | | | | | | | 207.07/127.97 | | | | | | | CLOSE: (237) is inconsistent. 207.07/127.97 | | | | | | | 207.07/127.97 | | | | | | Case 2: 207.07/127.97 | | | | | | | 207.07/127.97 | | | | | | | (238) ? [v0: $int] : ? [v1: $int] : ((v0 = 0 & permut3(int, 207.07/127.97 | | | | | | | all_105_4, all_105_2, 0, all_86_13) = 0) | 207.07/127.97 | | | | | | | (length1(int, all_105_4) = v0 & ( ~ ($lesseq(all_86_13, 207.07/127.97 | | | | | | | v0)) | ~ ($lesseq(0, v0)) | ( ~ (v1 = v0) & 207.07/127.97 | | | | | | | length1(int, all_105_2) = v1)))) 207.07/127.97 | | | | | | | 207.07/127.97 | | | | | | | DELTA: instantiating (238) with fresh symbols all_809_0, all_809_1 207.07/127.97 | | | | | | | gives: 207.07/127.98 | | | | | | | (239) (all_809_1 = 0 & permut3(int, all_105_4, all_105_2, 0, 207.07/127.98 | | | | | | | all_86_13) = 0) | (length1(int, all_105_4) = 207.07/127.98 | | | | | | | all_809_1 & ( ~ ($lesseq(all_86_13, all_809_1)) | ~ 207.07/127.98 | | | | | | | ($lesseq(0, all_809_1)) | ( ~ (all_809_0 = all_809_1) 207.07/127.98 | | | | | | | & length1(int, all_105_2) = all_809_0))) 207.07/127.98 | | | | | | | 207.07/127.98 | | | | | | | BETA: splitting (239) gives: 207.07/127.98 | | | | | | | 207.07/127.98 | | | | | | | Case 1: 207.07/127.98 | | | | | | | | 207.07/127.98 | | | | | | | | (240) all_809_1 = 0 & permut3(int, all_105_4, all_105_2, 0, 207.07/127.98 | | | | | | | | all_86_13) = 0 207.07/127.98 | | | | | | | | 207.07/127.98 | | | | | | | | ALPHA: (240) implies: 207.07/127.98 | | | | | | | | (241) permut3(int, all_105_4, all_105_2, 0, all_86_13) = 0 207.07/127.98 | | | | | | | | 207.07/127.98 | | | | | | | | BETA: splitting (70) gives: 207.07/127.98 | | | | | | | | 207.07/127.98 | | | | | | | | Case 1: 207.07/127.98 | | | | | | | | | 207.07/127.98 | | | | | | | | | (242) all_766_0 = all_766_1 & $lesseq(all_86_13, all_766_1) 207.07/127.98 | | | | | | | | | & $lesseq(0, all_766_1) & $lesseq(0, all_86_13) & 207.07/127.98 | | | | | | | | | length1(int, all_105_2) = all_766_1 & length1(int, 207.07/127.98 | | | | | | | | | all_105_4) = all_766_1 207.07/127.98 | | | | | | | | | 207.07/127.98 | | | | | | | | | ALPHA: (242) implies: 207.07/127.98 | | | | | | | | | (243) length1(int, all_105_4) = all_766_1 207.07/127.98 | | | | | | | | | 207.07/127.98 | | | | | | | | | GROUND_INST: instantiating (1) with all_133_0, all_760_0, 207.07/127.98 | | | | | | | | | all_133_1, simplifying with (14), (68) gives: 207.07/127.98 | | | | | | | | | (244) all_760_0 = all_133_0 207.07/127.98 | | | | | | | | | 207.07/127.98 | | | | | | | | | GROUND_INST: instantiating (47) with all_86_13, all_766_1, 207.07/127.98 | | | | | | | | | all_105_4, int, simplifying with (19), (243) 207.07/127.98 | | | | | | | | | gives: 207.07/127.98 | | | | | | | | | (245) all_766_1 = all_86_13 207.07/127.98 | | | | | | | | | 207.07/127.98 | | | | | | | | | GROUND_INST: instantiating (47) with all_86_13, all_798_1, 207.07/127.98 | | | | | | | | | all_103_4, int, simplifying with (9), (234) gives: 207.07/127.98 | | | | | | | | | (246) all_798_1 = all_86_13 207.07/127.98 | | | | | | | | | 207.07/127.98 | | | | | | | | | GROUND_INST: instantiating (18) with all_105_1, all_760_2, 207.07/127.98 | | | | | | | | | all_105_2, int, simplifying with (25), (66) gives: 207.07/127.98 | | | | | | | | | (247) all_760_2 = all_105_1 207.07/127.98 | | | | | | | | | 207.07/127.98 | | | | | | | | | GROUND_INST: instantiating (18) with all_760_2, all_755_1, 207.07/127.98 | | | | | | | | | all_105_2, int, simplifying with (63), (66) gives: 207.07/127.98 | | | | | | | | | (248) all_760_2 = all_755_1 207.07/127.98 | | | | | | | | | 207.07/127.98 | | | | | | | | | COMBINE_EQS: (247), (248) imply: 207.07/127.98 | | | | | | | | | (249) all_755_1 = all_105_1 207.07/127.98 | | | | | | | | | 207.07/127.98 | | | | | | | | | REDUCE: (69), (247) imply: 207.07/127.98 | | | | | | | | | (250) tb2t(all_105_1) = all_760_1 207.07/127.98 | | | | | | | | | 207.07/127.98 | | | | | | | | | REDUCE: (67), (244) imply: 207.07/127.98 | | | | | | | | | (251) get3(all_760_1, all_133_2) = all_133_0 207.07/127.98 | | | | | | | | | 207.07/127.98 | | | | | | | | | REDUCE: (61), (249) imply: 207.07/127.98 | | | | | | | | | (252) get(int, int, all_105_1, all_755_0) = all_133_1 207.07/127.98 | | | | | | | | | 207.07/127.98 | | | | | | | | | REF_CLOSE: (1), (2), (4), (6), (7), (8), (9), (10), (11), 207.07/127.98 | | | | | | | | | (13), (14), (15), (17), (18), (19), (20), (21), 207.07/127.98 | | | | | | | | | (22), (23), (24), (25), (26), (27), (28), (29), 207.07/127.98 | | | | | | | | | (30), (31), (32), (34), (35), (36), (37), (38), 207.07/127.98 | | | | | | | | | (39), (40), (41), (43), (44), (45), (46), (47), 207.07/127.98 | | | | | | | | | (48), (50), (62), (70), (241), (250), (251), (252) 207.07/127.98 | | | | | | | | | are inconsistent by sub-proof #91. 207.07/127.98 | | | | | | | | | 207.07/127.98 | | | | | | | | Case 2: 207.07/127.98 | | | | | | | | | 207.24/127.99 | | | | | | | | | (253) ~ (all_766_1 = 0) & permut3(int, all_105_4, 207.24/127.99 | | | | | | | | | all_105_2, 0, all_86_13) = all_766_1 207.24/127.99 | | | | | | | | | 207.24/127.99 | | | | | | | | | ALPHA: (253) implies: 207.24/127.99 | | | | | | | | | (254) ~ (all_766_1 = 0) 207.24/127.99 | | | | | | | | | (255) permut3(int, all_105_4, all_105_2, 0, all_86_13) = 207.24/127.99 | | | | | | | | | all_766_1 207.24/127.99 | | | | | | | | | 207.24/127.99 | | | | | | | | | GROUND_INST: instantiating (15) with 0, all_766_1, all_86_13, 207.24/127.99 | | | | | | | | | 0, all_105_2, all_105_4, int, simplifying with 207.24/127.99 | | | | | | | | | (241), (255) gives: 207.24/127.99 | | | | | | | | | (256) all_766_1 = 0 207.24/127.99 | | | | | | | | | 207.24/127.99 | | | | | | | | | REDUCE: (254), (256) imply: 207.24/127.99 | | | | | | | | | (257) ~ (0 = 0) 207.24/127.99 | | | | | | | | | 207.24/127.99 | | | | | | | | | CLOSE: (257) is inconsistent. 207.24/127.99 | | | | | | | | | 207.24/127.99 | | | | | | | | End of split 207.24/127.99 | | | | | | | | 207.24/127.99 | | | | | | | Case 2: 207.24/127.99 | | | | | | | | 207.24/127.99 | | | | | | | | (258) length1(int, all_105_4) = all_809_1 & ( ~ 207.24/127.99 | | | | | | | | ($lesseq(all_86_13, all_809_1)) | ~ ($lesseq(0, 207.24/127.99 | | | | | | | | all_809_1)) | ( ~ (all_809_0 = all_809_1) & 207.24/127.99 | | | | | | | | length1(int, all_105_2) = all_809_0)) 207.24/127.99 | | | | | | | | 207.24/127.99 | | | | | | | | ALPHA: (258) implies: 207.24/127.99 | | | | | | | | (259) length1(int, all_105_4) = all_809_1 207.24/127.99 | | | | | | | | 207.24/127.99 | | | | | | | | GROUND_INST: instantiating (47) with all_86_13, all_809_1, 207.24/127.99 | | | | | | | | all_105_4, int, simplifying with (19), (259) gives: 207.24/127.99 | | | | | | | | (260) all_809_1 = all_86_13 207.24/127.99 | | | | | | | | 207.24/127.99 | | | | | | | | GROUND_INST: instantiating (47) with all_86_13, all_787_1, 207.24/127.99 | | | | | | | | all_103_2, int, simplifying with (3), (182) gives: 207.24/127.99 | | | | | | | | (261) all_787_1 = all_86_13 207.24/127.99 | | | | | | | | 207.24/127.99 | | | | | | | | GROUND_INST: instantiating (47) with all_86_13, all_798_1, 207.24/127.99 | | | | | | | | all_103_4, int, simplifying with (9), (234) gives: 207.24/127.99 | | | | | | | | (262) all_798_1 = all_86_13 207.24/127.99 | | | | | | | | 207.24/127.99 | | | | | | | | BETA: splitting (183) gives: 207.24/127.99 | | | | | | | | 207.24/127.99 | | | | | | | | Case 1: 207.24/127.99 | | | | | | | | | 207.24/127.99 | | | | | | | | | (263) $lesseq(all_787_1, -1) 207.24/127.99 | | | | | | | | | 207.24/127.99 | | | | | | | | | REDUCE: (261), (263) imply: 207.24/127.99 | | | | | | | | | (264) $lesseq(all_86_13, -1) 207.24/127.99 | | | | | | | | | 207.24/127.99 | | | | | | | | | COMBINE_INEQS: (13), (28) imply: 207.24/127.99 | | | | | | | | | (265) $lesseq(all_86_11, all_86_8) 207.24/127.99 | | | | | | | | | 207.24/127.99 | | | | | | | | | COMBINE_INEQS: (30), (36) imply: 207.24/127.99 | | | | | | | | | (266) $lesseq(1, $difference(all_86_10, all_86_8)) 207.24/127.99 | | | | | | | | | 207.24/127.99 | | | | | | | | | COMBINE_INEQS: (265), (266) imply: 207.24/127.99 | | | | | | | | | (267) $lesseq(1, $difference(all_86_10, all_86_11)) 207.24/127.99 | | | | | | | | | 207.24/127.99 | | | | | | | | | COMBINE_INEQS: (74), (264) imply: 207.24/127.99 | | | | | | | | | (268) $lesseq(0, -1) 207.24/127.99 | | | | | | | | | 207.24/127.99 | | | | | | | | | CLOSE: (268) is inconsistent. 207.24/127.99 | | | | | | | | | 207.24/127.99 | | | | | | | | Case 2: 207.24/127.99 | | | | | | | | | 207.24/127.99 | | | | | | | | | (269) ~ ($lesseq(all_86_13, all_787_1)) | ( ~ (all_787_0 = 207.24/127.99 | | | | | | | | | all_787_1) & length1(int, all_105_4) = all_787_0) 207.24/127.99 | | | | | | | | | 207.24/127.99 | | | | | | | | | BETA: splitting (235) gives: 207.24/127.99 | | | | | | | | | 207.24/127.99 | | | | | | | | | Case 1: 207.24/127.99 | | | | | | | | | | 207.24/127.99 | | | | | | | | | | (270) $lesseq(1, $difference(all_86_11, all_798_1)) 207.24/127.99 | | | | | | | | | | 207.24/127.99 | | | | | | | | | | REDUCE: (262), (270) imply: 207.24/127.99 | | | | | | | | | | (271) $lesseq(1, $difference(all_86_11, all_86_13)) 207.24/127.99 | | | | | | | | | | 207.24/127.99 | | | | | | | | | | COMBINE_INEQS: (13), (28) imply: 207.24/127.99 | | | | | | | | | | (272) $lesseq(all_86_11, all_86_8) 207.24/127.99 | | | | | | | | | | 207.24/127.99 | | | | | | | | | | COMBINE_INEQS: (30), (36) imply: 207.24/127.99 | | | | | | | | | | (273) $lesseq(1, $difference(all_86_10, all_86_8)) 207.24/127.99 | | | | | | | | | | 207.24/127.99 | | | | | | | | | | COMBINE_INEQS: (272), (273) imply: 207.24/127.99 | | | | | | | | | | (274) $lesseq(1, $difference(all_86_10, all_86_11)) 207.24/127.99 | | | | | | | | | | 207.24/127.99 | | | | | | | | | | COMBINE_INEQS: (12), (271) imply: 207.24/127.99 | | | | | | | | | | (275) $lesseq(0, -1) 207.24/127.99 | | | | | | | | | | 207.24/127.99 | | | | | | | | | | CLOSE: (275) is inconsistent. 207.24/127.99 | | | | | | | | | | 207.24/127.99 | | | | | | | | | Case 2: 207.24/127.99 | | | | | | | | | | 207.24/127.99 | | | | | | | | | | (276) ~ ($lesseq(1, $difference(all_798_1, all_86_10))) 207.24/127.99 | | | | | | | | | | | ( ~ (all_798_0 = all_798_1) & length1(int, 207.24/127.99 | | | | | | | | | | all_105_4) = all_798_0) 207.24/127.99 | | | | | | | | | | 207.24/127.99 | | | | | | | | | | BETA: splitting (276) gives: 207.24/127.99 | | | | | | | | | | 207.24/127.99 | | | | | | | | | | Case 1: 207.24/127.99 | | | | | | | | | | | 207.24/127.99 | | | | | | | | | | | (277) $lesseq(all_798_1, all_86_10) 207.24/127.99 | | | | | | | | | | | 207.24/127.99 | | | | | | | | | | | REDUCE: (262), (277) imply: 207.24/127.99 | | | | | | | | | | | (278) $lesseq(all_86_13, all_86_10) 207.24/127.99 | | | | | | | | | | | 207.24/127.99 | | | | | | | | | | | COMBINE_INEQS: (38), (278) imply: 207.24/127.99 | | | | | | | | | | | (279) $lesseq(0, -1) 207.24/127.99 | | | | | | | | | | | 207.24/127.99 | | | | | | | | | | | CLOSE: (279) is inconsistent. 207.24/127.99 | | | | | | | | | | | 207.24/127.99 | | | | | | | | | | Case 2: 207.24/127.99 | | | | | | | | | | | 207.24/127.99 | | | | | | | | | | | (280) ~ (all_798_0 = all_798_1) & length1(int, 207.24/127.99 | | | | | | | | | | | all_105_4) = all_798_0 207.24/127.99 | | | | | | | | | | | 207.24/127.99 | | | | | | | | | | | ALPHA: (280) implies: 207.24/127.99 | | | | | | | | | | | (281) length1(int, all_105_4) = all_798_0 207.24/127.99 | | | | | | | | | | | 207.24/127.99 | | | | | | | | | | | BETA: splitting (269) gives: 207.24/127.99 | | | | | | | | | | | 207.24/127.99 | | | | | | | | | | | Case 1: 207.24/127.99 | | | | | | | | | | | | 207.24/127.99 | | | | | | | | | | | | (282) $lesseq(1, $difference(all_86_13, all_787_1)) 207.24/127.99 | | | | | | | | | | | | 207.24/127.99 | | | | | | | | | | | | REDUCE: (261), (282) imply: 207.24/127.99 | | | | | | | | | | | | (283) $lesseq(0, -1) 207.24/127.99 | | | | | | | | | | | | 207.24/127.99 | | | | | | | | | | | | CLOSE: (283) is inconsistent. 207.24/127.99 | | | | | | | | | | | | 207.24/127.99 | | | | | | | | | | | Case 2: 207.24/127.99 | | | | | | | | | | | | 207.24/127.99 | | | | | | | | | | | | (284) ~ (all_787_0 = all_787_1) & length1(int, 207.24/127.99 | | | | | | | | | | | | all_105_4) = all_787_0 207.24/127.99 | | | | | | | | | | | | 207.24/127.99 | | | | | | | | | | | | ALPHA: (284) implies: 207.24/127.99 | | | | | | | | | | | | (285) ~ (all_787_0 = all_787_1) 207.24/127.99 | | | | | | | | | | | | (286) length1(int, all_105_4) = all_787_0 207.24/127.99 | | | | | | | | | | | | 207.24/127.99 | | | | | | | | | | | | REDUCE: (261), (285) imply: 207.24/127.99 | | | | | | | | | | | | (287) ~ (all_787_0 = all_86_13) 207.24/127.99 | | | | | | | | | | | | 207.24/127.99 | | | | | | | | | | | | GROUND_INST: instantiating (47) with all_86_13, all_798_0, 207.24/127.99 | | | | | | | | | | | | all_105_4, int, simplifying with (19), (281) 207.24/127.99 | | | | | | | | | | | | gives: 207.24/127.99 | | | | | | | | | | | | (288) all_798_0 = all_86_13 207.24/127.99 | | | | | | | | | | | | 207.24/127.99 | | | | | | | | | | | | GROUND_INST: instantiating (47) with all_798_0, all_787_0, 207.24/127.99 | | | | | | | | | | | | all_105_4, int, simplifying with (281), (286) 207.24/127.99 | | | | | | | | | | | | gives: 207.24/127.99 | | | | | | | | | | | | (289) all_798_0 = all_787_0 207.24/127.99 | | | | | | | | | | | | 207.24/127.99 | | | | | | | | | | | | COMBINE_EQS: (288), (289) imply: 207.24/127.99 | | | | | | | | | | | | (290) all_787_0 = all_86_13 207.24/127.99 | | | | | | | | | | | | 207.24/127.99 | | | | | | | | | | | | REDUCE: (287), (290) imply: 207.24/127.99 | | | | | | | | | | | | (291) ~ (0 = 0) 207.24/127.99 | | | | | | | | | | | | 207.24/127.99 | | | | | | | | | | | | CLOSE: (291) is inconsistent. 207.24/127.99 | | | | | | | | | | | | 207.24/127.99 | | | | | | | | | | | End of split 207.24/127.99 | | | | | | | | | | | 207.24/127.99 | | | | | | | | | | End of split 207.24/127.99 | | | | | | | | | | 207.24/127.99 | | | | | | | | | End of split 207.24/127.99 | | | | | | | | | 207.24/127.99 | | | | | | | | End of split 207.24/127.99 | | | | | | | | 207.24/127.99 | | | | | | | End of split 207.24/127.99 | | | | | | | 207.24/127.99 | | | | | | End of split 207.24/127.99 | | | | | | 207.24/127.99 | | | | | End of split 207.24/127.99 | | | | | 207.24/127.99 | | | | End of split 207.24/127.99 | | | | 207.24/127.99 | | | End of split 207.24/127.99 | | | 207.24/127.99 | | End of split 207.24/127.99 | | 207.24/127.99 | End of split 207.24/127.99 | 207.24/127.99 End of proof 207.24/127.99 207.24/127.99 Sub-proof #90 shows that the following formulas are inconsistent: 207.24/127.99 ---------------------------------------------------------------- 207.24/127.99 (1) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.24/127.99 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ (permut3(v6, v5, 207.24/127.99 v4, v3, v2) = v1) | ~ (permut3(v6, v5, v4, v3, v2) = v0)) 207.24/127.99 (2) permut3(int, all_103_2, all_105_4, 0, all_86_13) = all_754_1 207.24/127.99 (3) permut3(int, all_103_2, all_105_4, 0, all_86_13) = 0 207.24/127.99 (4) ~ (all_754_1 = 0) 207.24/127.99 207.24/127.99 Begin of proof 207.24/127.99 | 207.24/127.99 | GROUND_INST: instantiating (1) with 0, all_754_1, all_86_13, 0, all_105_4, 207.24/127.99 | all_103_2, int, simplifying with (2), (3) gives: 207.24/127.99 | (5) all_754_1 = 0 207.24/127.99 | 207.24/127.99 | REDUCE: (4), (5) imply: 207.24/127.99 | (6) ~ (0 = 0) 207.24/127.99 | 207.24/127.99 | CLOSE: (6) is inconsistent. 207.24/127.99 | 207.24/127.99 End of proof 207.24/127.99 207.24/127.99 Sub-proof #91 shows that the following formulas are inconsistent: 207.24/127.99 ---------------------------------------------------------------- 207.24/127.99 (1) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ (tb2t1(v2) 207.24/127.99 = v1) | ~ (tb2t1(v2) = v0)) 207.24/127.99 (2) ! [v0: $int] : ! [v1: $int] : ( ~ ($lesseq(43, v1)) | ~ ($lesseq(v0, 207.24/127.99 all_86_8)) | ~ ($lesseq(all_86_11, v0)) | ~ (get3(all_86_6, v0) = 207.24/127.99 v1)) 207.24/127.99 (3) in_map_int_int(all_86_6) 207.24/127.99 (4) tb2t(all_105_1) = all_760_1 207.24/127.99 (5) elts(int, all_103_4) = all_103_3 207.24/127.99 (6) t2tb(all_86_2) = all_105_1 207.24/127.99 (7) in_ty(int) 207.24/127.99 (8) length1(int, all_103_4) = all_86_13 207.24/127.99 (9) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.24/127.99 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 207.24/127.99 (permut2(v0, v5, v6, v3, v4) = v7) | ~ (elts(v0, v2) = v6) | ~ 207.24/127.99 (elts(v0, v1) = v5) | ~ in_ty(v0) | ? [v8: $int] : ? [v9: $int] : 207.24/127.99 ((v9 = v8 & v7 = 0 & $lesseq(v4, v8) & $lesseq(v3, v8) & $lesseq(0, v4) 207.24/127.99 & $lesseq(0, v3) & length1(v0, v2) = v8 & length1(v0, v1) = v8) | ( 207.24/127.99 ~ (v8 = 0) & permut3(v0, v1, v2, v3, v4) = v8))) 207.24/127.99 (10) permut3(int, all_105_4, all_105_2, 0, all_86_13) = 0 207.24/127.99 (11) t2tb(all_86_6) = all_103_1 207.24/127.99 (12) $lesseq(all_133_2, all_86_8) 207.24/127.99 (13) tb2t1(all_133_1) = all_133_0 207.24/127.99 (14) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.24/127.99 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ (permut3(v6, v5, 207.24/127.99 v4, v3, v2) = v1) | ~ (permut3(v6, v5, v4, v3, v2) = v0)) 207.24/127.99 (15) permut2(int, all_103_3, all_105_3, all_86_11, $sum(all_86_10, 1)) = 0 207.24/127.99 (16) (all_766_0 = all_766_1 & $lesseq(all_86_13, all_766_1) & $lesseq(0, 207.24/127.99 all_766_1) & $lesseq(0, all_86_13) & length1(int, all_105_2) = 207.24/127.99 all_766_1 & length1(int, all_105_4) = all_766_1) | ( ~ (all_766_1 = 0) 207.24/127.99 & permut3(int, all_105_4, all_105_2, 0, all_86_13) = all_766_1) 207.24/127.99 (17) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 207.24/127.99 | ~ (elts(v3, v2) = v1) | ~ (elts(v3, v2) = v0)) 207.24/127.99 (18) length1(int, all_105_4) = all_86_13 207.24/127.99 (19) elts(int, all_105_4) = all_105_3 207.24/127.99 (20) map_eq_sub1(int, all_105_3, all_105_1, 0, all_86_7) = 0 207.24/127.99 (21) get4(int, all_105_2, all_133_2) = all_133_1 207.24/127.99 (22) tb2t(all_105_1) = all_86_2 207.24/127.99 (23) permut2(int, all_103_1, all_105_3, all_86_11, $sum(all_86_8, 1)) = 0 207.24/127.99 (24) elts(int, all_105_2) = all_105_1 207.24/127.99 (25) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.24/127.99 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 207.24/127.99 ($lesseq(1, $difference(v4, v5))) | ~ ($lesseq(v3, v5)) | ~ 207.24/127.99 (permut2(v0, v1, v2, v3, v4) = 0) | ~ (t2tb1(v5) = v6) | ~ (get(v0, 207.24/127.99 int, v2, v6) = v7) | ~ in_ty(v0) | ? [v8: $int] : ? [v9: $int] 207.24/127.99 : ($lesseq(1, $difference(v4, v8)) & $lesseq(v3, v8) & t2tb1(v8) = v9 207.24/127.99 & get(v0, int, v1, v9) = v7 & in_uni(v9) & in_uni(v7))) 207.24/127.99 (26) t2tb2(all_86_1) = all_105_2 207.24/127.99 (27) $lesseq(all_86_11, all_133_2) 207.24/127.99 (28) ~ ($difference(all_86_10, all_86_13) = -1) | ~ (all_86_11 = 0) 207.24/127.99 (29) $lesseq(all_86_7, all_86_10) 207.24/127.99 (30) get(int, int, all_105_1, all_755_0) = all_133_1 207.24/127.99 (31) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.24/127.99 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 207.24/127.99 ($lesseq(1, $difference(v3, v4))) | ~ ($lesseq(v2, v4)) | ~ 207.24/127.99 (permut2(int, v5, v6, v2, v3) = 0) | ~ (t2tb(v1) = v6) | ~ (t2tb(v0) 207.24/127.99 = v5) | ~ (get3(v1, v4) = v7) | ~ in_map_int_int(v0) | ? [v8: 207.24/127.99 $int] : ($lesseq(1, $difference(v3, v8)) & $lesseq(v2, v8) & 207.24/127.99 get3(v0, v8) = v7)) 207.24/127.99 (32) permut2(int, all_105_3, all_105_1, all_86_7, $sum(all_86_10, 1)) = 0 207.24/127.99 (33) in_array_int(all_86_1) 207.24/127.99 (34) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.24/127.99 $int] : ! [v5: $int] : ! [v6: $int] : ( ~ ($lesseq(0, v4)) | ~ 207.24/127.99 ($lesseq(0, v3)) | ~ (permut2(v0, v5, v6, v3, v4) = 0) | ~ (elts(v0, 207.24/127.99 v2) = v6) | ~ (elts(v0, v1) = v5) | ~ in_ty(v0) | ? [v7: $int] 207.24/127.99 : ? [v8: $int] : ((v7 = 0 & permut3(v0, v1, v2, v3, v4) = 0) | 207.24/127.99 (length1(v0, v1) = v7 & ( ~ ($lesseq(v4, v7)) | ~ ($lesseq(v3, v7)) 207.24/127.99 | ( ~ (v8 = v7) & length1(v0, v2) = v8))))) 207.24/127.99 (35) $lesseq(1, $difference(all_86_7, all_86_8)) 207.24/127.99 (36) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.24/127.99 $int] : ! [v5: $int] : ! [v6: $int] : ( ~ ($lesseq(1, 207.24/127.99 $difference(v4, v5))) | ~ ($lesseq(v3, v5)) | ~ (map_eq_sub1(v0, 207.24/127.99 v1, v2, v3, v4) = 0) | ~ (t2tb1(v5) = v6) | ~ in_ty(v0) | ? 207.24/127.99 [v7: $int] : (get(v0, int, v2, v6) = v7 & get(v0, int, v1, v6) = v7 & 207.24/127.99 in_uni(v7))) 207.24/127.99 (37) $lesseq(1, $difference(all_86_13, all_86_10)) 207.24/127.99 (38) in_map_int_int(all_86_4) 207.24/127.99 (39) map_eq_sub1(int, all_105_3, all_105_1, 0, all_86_13) = 0 207.24/127.99 (40) $lesseq(0, all_86_11) 207.24/127.99 (41) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ( ~ 207.24/127.99 (t2tb2(v0) = v2) | ~ (get4(int, v2, v1) = v3) | ~ in_array_int(v0) | 207.24/127.99 ? [v4: $int] : ? [v5: $int] : ? [v6: $int] : (tb2t(v4) = v5 & 207.24/127.99 tb2t1(v3) = v6 & get3(v5, v1) = v6 & elts(int, v2) = v4 & 207.24/127.99 in_map_int_int(v5) & in_uni(v4))) 207.24/127.99 (42) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ (tb2t(v2) 207.24/127.99 = v1) | ~ (tb2t(v2) = v0)) 207.24/127.99 (43) $lesseq(43, all_133_0) 207.24/127.99 (44) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.24/127.99 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 207.24/127.99 ($lesseq(1, $difference(v3, v6))) | ~ ($lesseq(v2, v6)) | ~ 207.24/127.99 (map_eq_sub1(int, v4, v5, v2, v3) = 0) | ~ (t2tb(v1) = v5) | ~ 207.24/127.99 (t2tb(v0) = v4) | ~ (get3(v1, v6) = v7) | ~ in_map_int_int(v0) | 207.24/127.99 get3(v0, v6) = v7) 207.24/127.99 (45) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 207.24/127.99 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 207.24/127.99 (46) t2tb1(all_133_2) = all_755_0 207.24/127.99 (47) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ( ~ 207.24/127.99 (get4(v0, v1, v2) = v3) | ~ in_ty(v0) | ? [v4: $int] : ? [v5: $int] 207.24/127.99 : (elts(v0, v1) = v4 & t2tb1(v2) = v5 & get(v0, int, v4, v5) = v3 & 207.24/127.99 in_uni(v5) & in_uni(v4) & in_uni(v3))) 207.24/127.99 (48) t2tb(all_86_4) = all_105_3 207.24/127.99 (49) get3(all_760_1, all_133_2) = all_133_0 207.24/127.99 207.24/127.99 Begin of proof 207.24/127.99 | 207.24/127.99 | BETA: splitting (16) gives: 207.24/127.99 | 207.24/127.99 | Case 1: 207.24/127.99 | | 207.24/127.99 | | (50) all_766_0 = all_766_1 & $lesseq(all_86_13, all_766_1) & $lesseq(0, 207.24/127.99 | | all_766_1) & $lesseq(0, all_86_13) & length1(int, all_105_2) = 207.24/127.99 | | all_766_1 & length1(int, all_105_4) = all_766_1 207.24/127.99 | | 207.24/127.99 | | ALPHA: (50) implies: 207.24/127.99 | | (51) length1(int, all_105_4) = all_766_1 207.24/127.99 | | 207.24/127.99 | | GROUND_INST: instantiating (42) with all_86_2, all_760_1, all_105_1, 207.24/127.99 | | simplifying with (4), (22) gives: 207.24/127.99 | | (52) all_760_1 = all_86_2 207.24/127.99 | | 207.24/127.99 | | GROUND_INST: instantiating (45) with all_86_13, all_766_1, all_105_4, int, 207.24/127.99 | | simplifying with (18), (51) gives: 207.24/127.99 | | (53) all_766_1 = all_86_13 207.24/127.99 | | 207.24/127.99 | | REDUCE: (49), (52) imply: 207.24/127.99 | | (54) get3(all_86_2, all_133_2) = all_133_0 207.24/127.99 | | 207.24/127.99 | | GROUND_INST: instantiating (44) with all_86_4, all_86_2, 0, all_86_7, 207.24/127.99 | | all_105_3, all_105_1, all_133_2, all_133_0, simplifying with 207.24/127.99 | | (6), (20), (38), (48), (54) gives: 207.24/127.99 | | (55) ~ ($lesseq(1, $difference(all_86_7, all_133_2))) | ~ ($lesseq(0, 207.24/127.99 | | all_133_2)) | get3(all_86_4, all_133_2) = all_133_0 207.24/127.99 | | 207.24/127.99 | | GROUND_INST: instantiating (31) with all_86_4, all_86_2, all_86_7, 207.24/127.99 | | $sum(all_86_10, 1), all_133_2, all_105_3, all_105_1, all_133_0, 207.24/127.99 | | simplifying with (6), (32), (38), (48), (54) gives: 207.24/127.99 | | (56) ~ ($lesseq(all_133_2, all_86_10)) | ~ ($lesseq(all_86_7, 207.24/127.99 | | all_133_2)) | ? [v0: $int] : ($lesseq(v0, all_86_10) & 207.24/127.99 | | $lesseq(all_86_7, v0) & get3(all_86_4, v0) = all_133_0) 207.24/127.99 | | 207.24/127.99 | | GROUND_INST: instantiating (36) with int, all_105_3, all_105_1, 0, 207.24/127.99 | | all_86_13, all_133_2, all_755_0, simplifying with (7), (39), 207.24/127.99 | | (46) gives: 207.24/127.99 | | (57) ~ ($lesseq(1, $difference(all_86_13, all_133_2))) | ~ ($lesseq(0, 207.24/127.99 | | all_133_2)) | ? [v0: $int] : (get(int, int, all_105_1, 207.24/127.99 | | all_755_0) = v0 & get(int, int, all_105_3, all_755_0) = v0 & 207.24/127.99 | | in_uni(v0)) 207.24/127.99 | | 207.24/127.99 | | GROUND_INST: instantiating (25) with int, all_105_3, all_105_1, all_86_7, 207.24/127.99 | | $sum(all_86_10, 1), all_133_2, all_755_0, all_133_1, 207.24/127.99 | | simplifying with (7), (30), (32), (46) gives: 207.24/127.99 | | (58) ~ ($lesseq(all_133_2, all_86_10)) | ~ ($lesseq(all_86_7, 207.24/127.99 | | all_133_2)) | ? [v0: $int] : ? [v1: $int] : ($lesseq(v0, 207.24/127.99 | | all_86_10) & $lesseq(all_86_7, v0) & t2tb1(v0) = v1 & get(int, 207.24/127.99 | | int, all_105_3, v1) = all_133_1 & in_uni(v1) & 207.24/127.99 | | in_uni(all_133_1)) 207.24/127.99 | | 207.24/127.99 | | BETA: splitting (28) gives: 207.24/127.99 | | 207.24/127.99 | | Case 1: 207.24/127.99 | | | 207.24/127.99 | | | (59) ~ (all_86_11 = 0) 207.24/127.99 | | | 207.24/127.99 | | | STRENGTHEN: (40), (59) imply: 207.24/127.99 | | | (60) $lesseq(1, all_86_11) 207.24/127.99 | | | 207.24/127.99 | | | COMBINE_INEQS: (29), (35) imply: 207.24/127.99 | | | (61) $lesseq(1, $difference(all_86_10, all_86_8)) 207.24/127.99 | | | 207.24/127.99 | | | BETA: splitting (57) gives: 207.24/127.99 | | | 207.24/127.99 | | | Case 1: 207.24/127.99 | | | | 207.24/127.99 | | | | (62) $lesseq(all_133_2, -1) 207.24/127.99 | | | | 207.24/127.99 | | | | COMBINE_INEQS: (27), (62) imply: 207.24/127.99 | | | | (63) $lesseq(all_86_11, -1) 207.24/127.99 | | | | 207.24/127.99 | | | | COMBINE_INEQS: (60), (63) imply: 207.24/127.99 | | | | (64) $lesseq(0, -1) 207.24/127.99 | | | | 207.24/127.99 | | | | CLOSE: (64) is inconsistent. 207.24/127.99 | | | | 207.24/127.99 | | | Case 2: 207.24/127.99 | | | | 207.24/127.99 | | | | (65) $lesseq(0, all_133_2) 207.24/127.99 | | | | 207.24/127.99 | | | | REF_CLOSE: (2), (3), (11), (12), (23), (27), (31), (35), (43), (48), 207.24/127.99 | | | | (55), (56), (58), (61), (65) are inconsistent by sub-proof 207.24/127.99 | | | | #144. 207.24/127.99 | | | | 207.24/127.99 | | | End of split 207.24/127.99 | | | 207.24/127.99 | | Case 2: 207.24/127.99 | | | 207.24/127.99 | | | (66) all_86_11 = 0 207.24/127.99 | | | 207.24/127.99 | | | REDUCE: (27), (66) imply: 207.24/127.99 | | | (67) $lesseq(0, all_133_2) 207.24/127.99 | | | 207.24/127.99 | | | COMBINE_INEQS: (12), (67) imply: 207.24/127.99 | | | (68) $lesseq(0, all_86_8) 207.24/127.99 | | | 207.24/127.99 | | | COMBINE_INEQS: (29), (35) imply: 207.24/127.99 | | | (69) $lesseq(1, $difference(all_86_10, all_86_8)) 207.24/127.99 | | | 207.24/127.99 | | | COMBINE_INEQS: (68), (69) imply: 207.24/127.99 | | | (70) $lesseq(1, all_86_10) 207.24/127.99 | | | 207.24/127.99 | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (11), (12), (13), (14), 207.24/127.99 | | | (15), (17), (18), (19), (20), (21), (22), (23), (24), (25), 207.24/127.99 | | | (26), (27), (28), (29), (31), (32), (33), (34), (35), (36), 207.24/127.99 | | | (37), (38), (39), (40), (41), (42), (43), (44), (45), (47), 207.24/127.99 | | | (48), (70) are inconsistent by sub-proof #109. 207.24/127.99 | | | 207.24/127.99 | | End of split 207.24/127.99 | | 207.24/127.99 | Case 2: 207.24/127.99 | | 207.24/127.99 | | (71) ~ (all_766_1 = 0) & permut3(int, all_105_4, all_105_2, 0, 207.24/127.99 | | all_86_13) = all_766_1 207.24/127.99 | | 207.24/127.99 | | ALPHA: (71) implies: 207.24/127.99 | | (72) ~ (all_766_1 = 0) 207.24/127.99 | | (73) permut3(int, all_105_4, all_105_2, 0, all_86_13) = all_766_1 207.24/127.99 | | 207.24/127.99 | | GROUND_INST: instantiating (14) with 0, all_766_1, all_86_13, 0, all_105_2, 207.24/127.99 | | all_105_4, int, simplifying with (10), (73) gives: 207.24/127.99 | | (74) all_766_1 = 0 207.24/127.99 | | 207.24/127.99 | | REDUCE: (72), (74) imply: 207.24/127.99 | | (75) ~ (0 = 0) 207.24/127.99 | | 207.24/127.99 | | CLOSE: (75) is inconsistent. 207.24/127.99 | | 207.24/127.99 | End of split 207.24/127.99 | 207.24/127.99 End of proof 207.24/127.99 207.24/127.99 Sub-proof #92 shows that the following formulas are inconsistent: 207.24/127.99 ---------------------------------------------------------------- 207.24/127.99 (1) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ (tb2t1(v2) 207.24/127.99 = v1) | ~ (tb2t1(v2) = v0)) 207.24/127.99 (2) length1(int, all_103_2) = all_86_13 207.24/127.99 (3) in_map_int_int(all_86_6) 207.24/127.99 (4) in_map_int_int(all_86_12) 207.24/127.99 (5) elts(int, all_103_4) = all_103_3 207.24/127.99 (6) t2tb(all_86_2) = all_105_1 207.24/127.99 (7) in_ty(int) 207.24/127.99 (8) length1(int, all_103_4) = all_86_13 207.24/127.99 (9) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.24/127.99 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 207.24/127.99 (permut2(v0, v5, v6, v3, v4) = v7) | ~ (elts(v0, v2) = v6) | ~ 207.24/127.99 (elts(v0, v1) = v5) | ~ in_ty(v0) | ? [v8: $int] : ? [v9: $int] : 207.24/127.99 ((v9 = v8 & v7 = 0 & $lesseq(v4, v8) & $lesseq(v3, v8) & $lesseq(0, v4) 207.24/127.99 & $lesseq(0, v3) & length1(v0, v2) = v8 & length1(v0, v1) = v8) | ( 207.24/127.99 ~ (v8 = 0) & permut3(v0, v1, v2, v3, v4) = v8))) 207.24/127.99 (10) $lesseq(-1, all_86_8) 207.24/127.99 (11) $lesseq(all_86_7, all_86_13) 207.24/127.99 (12) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.24/127.99 $int] : ! [v5: $int] : ( ~ (permut2(v0, v2, v3, v4, v5) = 0) | ~ 207.24/127.99 (permut2(v0, v1, v2, v4, v5) = 0) | ~ in_ty(v0) | permut2(v0, v1, v3, 207.24/127.99 v4, v5) = 0) 207.24/127.99 (13) ! [v0: $int] : ! [v1: $int] : (v1 = 42 | ~ ($lesseq(1, 207.24/127.99 $difference(all_86_7, v0))) | ~ ($lesseq(1, $difference(v0, 207.24/127.99 all_86_8))) | ~ (get3(all_86_6, v0) = v1)) 207.24/127.99 (14) map_eq_sub1(int, all_103_3, all_103_1, $sum(all_86_10, 1), all_86_13) = 207.24/127.99 0 207.24/127.99 (15) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.24/127.99 $int] : ! [v5: $int] : ! [v6: $int] : ( ~ (permut2(v0, v3, v4, 0, 207.24/127.99 v5) = v6) | ~ (length1(v0, v1) = v5) | ~ (elts(v0, v2) = v4) | 207.24/127.99 ~ (elts(v0, v1) = v3) | ~ in_ty(v0) | ? [v7: $int] : ((v7 = v5 & v6 207.24/128.00 = 0 & length1(v0, v2) = v5) | ( ~ (v7 = 0) & permut_all(v0, v1, 207.24/128.00 v2) = v7))) 207.24/128.00 (16) t2tb(all_86_6) = all_103_1 207.24/128.00 (17) $lesseq(3, $difference(all_86_13, all_86_11)) 207.24/128.00 (18) $lesseq(1, $difference(all_133_2, all_86_8)) 207.24/128.00 (19) tb2t1(all_133_1) = all_133_0 207.24/128.00 (20) map_eq_sub1(int, all_103_1, all_105_3, $sum(all_86_8, 1), all_86_13) = 0 207.24/128.00 (21) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.24/128.00 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ (permut3(v6, v5, 207.24/128.00 v4, v3, v2) = v1) | ~ (permut3(v6, v5, v4, v3, v2) = v0)) 207.24/128.00 (22) permut2(int, all_103_1, all_105_3, 0, all_86_13) = 0 207.24/128.00 (23) permut2(int, all_103_3, all_105_3, all_86_11, $sum(all_86_10, 1)) = 0 207.24/128.00 (24) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 207.24/128.00 | ~ (elts(v3, v2) = v1) | ~ (elts(v3, v2) = v0)) 207.24/128.00 (25) length1(int, all_105_4) = all_86_13 207.24/128.00 (26) elts(int, all_105_4) = all_105_3 207.24/128.00 (27) $lesseq(1, $difference(all_86_7, all_133_2)) 207.24/128.00 (28) permut2(int, all_103_3, all_103_1, 0, all_86_13) = 0 207.24/128.00 (29) map_eq_sub1(int, all_105_3, all_105_1, 0, all_86_7) = 0 207.24/128.00 (30) get4(int, all_105_2, all_133_2) = all_133_1 207.24/128.00 (31) $lesseq(3, all_86_13) 207.24/128.00 (32) tb2t(all_105_1) = all_86_2 207.24/128.00 (33) elts(int, all_105_2) = all_105_1 207.24/128.00 (34) map_eq_sub1(int, all_103_3, all_103_1, 0, all_86_11) = 0 207.24/128.00 (35) t2tb2(all_86_1) = all_105_2 207.24/128.00 (36) $lesseq(all_86_11, all_86_8) 207.24/128.00 (37) $lesseq(all_86_7, all_86_10) 207.24/128.00 (38) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.24/128.00 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 207.24/128.00 ($lesseq(1, $difference(v3, v4))) | ~ ($lesseq(v2, v4)) | ~ 207.24/128.00 (permut2(int, v5, v6, v2, v3) = 0) | ~ (t2tb(v1) = v6) | ~ (t2tb(v0) 207.24/128.00 = v5) | ~ (get3(v1, v4) = v7) | ~ in_map_int_int(v0) | ? [v8: 207.24/128.00 $int] : ($lesseq(1, $difference(v3, v8)) & $lesseq(v2, v8) & 207.24/128.00 get3(v0, v8) = v7)) 207.24/128.00 (39) ~ (all_133_0 = 42) 207.24/128.00 (40) in_array_int(all_86_1) 207.24/128.00 (41) t2tb(all_86_12) = all_103_3 207.24/128.00 (42) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.24/128.00 $int] : ! [v5: $int] : ! [v6: $int] : ( ~ ($lesseq(0, v4)) | ~ 207.24/128.00 ($lesseq(0, v3)) | ~ (permut2(v0, v5, v6, v3, v4) = 0) | ~ (elts(v0, 207.24/128.00 v2) = v6) | ~ (elts(v0, v1) = v5) | ~ in_ty(v0) | ? [v7: $int] 207.24/128.00 : ? [v8: $int] : ((v7 = 0 & permut3(v0, v1, v2, v3, v4) = 0) | 207.24/128.00 (length1(v0, v1) = v7 & ( ~ ($lesseq(v4, v7)) | ~ ($lesseq(v3, v7)) 207.24/128.00 | ( ~ (v8 = v7) & length1(v0, v2) = v8))))) 207.24/128.00 (43) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.24/128.00 $int] : ! [v5: $int] : ! [v6: $int] : ( ~ ($lesseq(1, 207.24/128.00 $difference(v4, v5))) | ~ ($lesseq(v3, v5)) | ~ (map_eq_sub1(v0, 207.24/128.00 v1, v2, v3, v4) = 0) | ~ (t2tb1(v5) = v6) | ~ in_ty(v0) | ? 207.24/128.00 [v7: $int] : (get(v0, int, v2, v6) = v7 & get(v0, int, v1, v6) = v7 & 207.24/128.00 in_uni(v7))) 207.24/128.00 (44) $lesseq(1, $difference(all_86_13, all_86_10)) 207.24/128.00 (45) in_map_int_int(all_86_4) 207.24/128.00 (46) $lesseq(0, all_86_11) 207.24/128.00 (47) elts(int, all_103_2) = all_103_1 207.24/128.00 (48) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ( ~ 207.24/128.00 (t2tb2(v0) = v2) | ~ (get4(int, v2, v1) = v3) | ~ in_array_int(v0) | 207.24/128.00 ? [v4: $int] : ? [v5: $int] : ? [v6: $int] : (tb2t(v4) = v5 & 207.24/128.00 tb2t1(v3) = v6 & get3(v5, v1) = v6 & elts(int, v2) = v4 & 207.24/128.00 in_map_int_int(v5) & in_uni(v4))) 207.24/128.00 (49) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ (tb2t(v2) 207.24/128.00 = v1) | ~ (tb2t(v2) = v0)) 207.24/128.00 (50) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.24/128.00 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 207.24/128.00 ($lesseq(1, $difference(v3, v6))) | ~ ($lesseq(v2, v6)) | ~ 207.24/128.00 (map_eq_sub1(int, v4, v5, v2, v3) = 0) | ~ (t2tb(v1) = v5) | ~ 207.24/128.00 (t2tb(v0) = v4) | ~ (get3(v1, v6) = v7) | ~ in_map_int_int(v0) | 207.24/128.00 get3(v0, v6) = v7) 207.24/128.00 (51) in_uni(all_133_1) 207.24/128.00 (52) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 207.24/128.00 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 207.24/128.00 (53) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ( ~ 207.24/128.00 (get4(v0, v1, v2) = v3) | ~ in_ty(v0) | ? [v4: $int] : ? [v5: $int] 207.24/128.00 : (elts(v0, v1) = v4 & t2tb1(v2) = v5 & get(v0, int, v4, v5) = v3 & 207.24/128.00 in_uni(v5) & in_uni(v4) & in_uni(v3))) 207.24/128.00 (54) $lesseq(1, all_86_10) 207.24/128.00 (55) ! [v0: $int] : ! [v1: $int] : ( ~ (tb2t1(v0) = v1) | ~ in_uni(v0) | 207.24/128.00 t2tb1(v1) = v0) 207.24/128.00 (56) map_eq_sub1(int, all_105_3, all_105_1, $sum(all_86_10, 1), all_86_13) = 207.24/128.00 0 207.24/128.00 (57) t2tb(all_86_4) = all_105_3 207.24/128.00 207.24/128.00 Begin of proof 207.24/128.00 | 207.24/128.00 | GROUND_INST: instantiating (9) with int, all_103_2, all_105_4, 0, all_86_13, 207.24/128.00 | all_103_1, all_105_3, 0, simplifying with (7), (22), (26), (47) 207.24/128.00 | gives: 207.24/128.00 | (58) ? [v0: $int] : ? [v1: $int] : ((v1 = v0 & $lesseq(all_86_13, v0) & 207.24/128.00 | $lesseq(0, v0) & $lesseq(0, all_86_13) & length1(int, all_105_4) = 207.24/128.00 | v0 & length1(int, all_103_2) = v0) | ( ~ (v0 = 0) & permut3(int, 207.24/128.00 | all_103_2, all_105_4, 0, all_86_13) = v0)) 207.24/128.00 | 207.24/128.00 | GROUND_INST: instantiating (12) with int, all_103_3, all_103_1, all_105_3, 0, 207.24/128.00 | all_86_13, simplifying with (7), (22), (28) gives: 207.24/128.00 | (59) permut2(int, all_103_3, all_105_3, 0, all_86_13) = 0 207.24/128.00 | 207.24/128.00 | GROUND_INST: instantiating (42) with int, all_103_2, all_105_4, 0, all_86_13, 207.24/128.00 | all_103_1, all_105_3, simplifying with (7), (22), (26), (47) 207.24/128.00 | gives: 207.24/128.00 | (60) ~ ($lesseq(0, all_86_13)) | ? [v0: $int] : ? [v1: $int] : ((v0 = 0 207.24/128.00 | & permut3(int, all_103_2, all_105_4, 0, all_86_13) = 0) | 207.24/128.00 | (length1(int, all_103_2) = v0 & ( ~ ($lesseq(all_86_13, v0)) | ~ 207.24/128.00 | ($lesseq(0, v0)) | ( ~ (v1 = v0) & length1(int, all_105_4) = 207.24/128.00 | v1)))) 207.24/128.00 | 207.24/128.00 | GROUND_INST: instantiating (9) with int, all_103_4, all_105_4, all_86_11, 207.24/128.00 | $sum(all_86_10, 1), all_103_3, all_105_3, 0, simplifying with 207.24/128.00 | (5), (7), (23), (26) gives: 207.24/128.00 | (61) ? [v0: $int] : ? [v1: $int] : ((v1 = v0 & $lesseq(1, $difference(v0, 207.24/128.00 | all_86_10)) & $lesseq(all_86_11, v0) & $lesseq(-1, all_86_10) 207.24/128.00 | & $lesseq(0, all_86_11) & length1(int, all_105_4) = v0 & 207.24/128.00 | length1(int, all_103_4) = v0) | ( ~ (v0 = 0) & permut3(int, 207.24/128.00 | all_103_4, all_105_4, all_86_11, $sum(all_86_10, 1)) = v0)) 207.24/128.00 | 207.24/128.00 | GROUND_INST: instantiating (42) with int, all_103_4, all_105_4, all_86_11, 207.24/128.00 | $sum(all_86_10, 1), all_103_3, all_105_3, simplifying with (5), 207.24/128.00 | (7), (23), (26) gives: 207.24/128.00 | (62) ~ ($lesseq(-1, all_86_10)) | ~ ($lesseq(0, all_86_11)) | ? [v0: 207.24/128.00 | $int] : ? [v1: $int] : ((v0 = 0 & permut3(int, all_103_4, 207.24/128.00 | all_105_4, all_86_11, $sum(all_86_10, 1)) = 0) | (length1(int, 207.24/128.00 | all_103_4) = v0 & ( ~ ($lesseq(1, $difference(v0, all_86_10))) | 207.24/128.00 | ~ ($lesseq(all_86_11, v0)) | ( ~ (v1 = v0) & length1(int, 207.24/128.00 | all_105_4) = v1)))) 207.24/128.00 | 207.24/128.00 | GROUND_INST: instantiating (15) with int, all_103_4, all_105_4, all_103_3, 207.24/128.00 | all_105_3, all_86_13, 0, simplifying with (5), (7), (8), (26) 207.24/128.00 | gives: 207.24/128.00 | (63) ~ (permut2(int, all_103_3, all_105_3, 0, all_86_13) = 0) | ? [v0: 207.24/128.00 | $int] : ((v0 = all_86_13 & length1(int, all_105_4) = all_86_13) | ( 207.24/128.00 | ~ (v0 = 0) & permut_all(int, all_103_4, all_105_4) = v0)) 207.24/128.00 | 207.24/128.00 | GROUND_INST: instantiating (9) with int, all_103_4, all_103_2, 0, all_86_13, 207.24/128.00 | all_103_3, all_103_1, 0, simplifying with (5), (7), (28), (47) 207.24/128.00 | gives: 207.24/128.00 | (64) ? [v0: $int] : ? [v1: $int] : ((v1 = v0 & $lesseq(all_86_13, v0) & 207.24/128.00 | $lesseq(0, v0) & $lesseq(0, all_86_13) & length1(int, all_103_2) = 207.24/128.00 | v0 & length1(int, all_103_4) = v0) | ( ~ (v0 = 0) & permut3(int, 207.24/128.00 | all_103_4, all_103_2, 0, all_86_13) = v0)) 207.24/128.00 | 207.24/128.00 | GROUND_INST: instantiating (42) with int, all_103_4, all_103_2, 0, all_86_13, 207.24/128.00 | all_103_3, all_103_1, simplifying with (5), (7), (28), (47) 207.24/128.00 | gives: 207.24/128.00 | (65) ~ ($lesseq(0, all_86_13)) | ? [v0: $int] : ? [v1: $int] : ((v0 = 0 207.24/128.00 | & permut3(int, all_103_4, all_103_2, 0, all_86_13) = 0) | 207.24/128.00 | (length1(int, all_103_4) = v0 & ( ~ ($lesseq(all_86_13, v0)) | ~ 207.24/128.00 | ($lesseq(0, v0)) | ( ~ (v1 = v0) & length1(int, all_103_2) = 207.24/128.00 | v1)))) 207.24/128.00 | 207.24/128.00 | GROUND_INST: instantiating (55) with all_133_1, all_133_0, simplifying with 207.24/128.00 | (19), (51) gives: 207.24/128.00 | (66) t2tb1(all_133_0) = all_133_1 207.24/128.00 | 207.24/128.00 | GROUND_INST: instantiating (48) with all_86_1, all_133_2, all_105_2, 207.24/128.00 | all_133_1, simplifying with (30), (35), (40) gives: 207.24/128.00 | (67) ? [v0: $int] : ? [v1: $int] : ? [v2: $int] : (tb2t(v0) = v1 & 207.24/128.00 | tb2t1(all_133_1) = v2 & get3(v1, all_133_2) = v2 & elts(int, 207.24/128.00 | all_105_2) = v0 & in_map_int_int(v1) & in_uni(v0)) 207.24/128.00 | 207.24/128.00 | GROUND_INST: instantiating (53) with int, all_105_2, all_133_2, all_133_1, 207.24/128.00 | simplifying with (7), (30) gives: 207.24/128.00 | (68) ? [v0: $int] : ? [v1: $int] : (elts(int, all_105_2) = v0 & 207.24/128.00 | t2tb1(all_133_2) = v1 & get(int, int, v0, v1) = all_133_1 & 207.24/128.00 | in_uni(v1) & in_uni(v0) & in_uni(all_133_1)) 207.24/128.00 | 207.24/128.00 | DELTA: instantiating (67) with fresh symbols all_758_0, all_758_1, all_758_2 207.24/128.00 | gives: 207.24/128.00 | (69) tb2t(all_758_2) = all_758_1 & tb2t1(all_133_1) = all_758_0 & 207.24/128.00 | get3(all_758_1, all_133_2) = all_758_0 & elts(int, all_105_2) = 207.24/128.00 | all_758_2 & in_map_int_int(all_758_1) & in_uni(all_758_2) 207.24/128.00 | 207.24/128.00 | ALPHA: (69) implies: 207.24/128.00 | (70) elts(int, all_105_2) = all_758_2 207.24/128.00 | (71) get3(all_758_1, all_133_2) = all_758_0 207.24/128.00 | (72) tb2t1(all_133_1) = all_758_0 207.24/128.00 | (73) tb2t(all_758_2) = all_758_1 207.24/128.00 | 207.24/128.00 | DELTA: instantiating (64) with fresh symbols all_764_0, all_764_1 gives: 207.24/128.00 | (74) (all_764_0 = all_764_1 & $lesseq(all_86_13, all_764_1) & $lesseq(0, 207.24/128.00 | all_764_1) & $lesseq(0, all_86_13) & length1(int, all_103_2) = 207.24/128.00 | all_764_1 & length1(int, all_103_4) = all_764_1) | ( ~ (all_764_1 = 207.24/128.00 | 0) & permut3(int, all_103_4, all_103_2, 0, all_86_13) = all_764_1) 207.24/128.00 | 207.24/128.00 | DELTA: instantiating (61) with fresh symbols all_769_0, all_769_1 gives: 207.24/128.00 | (75) (all_769_0 = all_769_1 & $lesseq(1, $difference(all_769_1, all_86_10)) 207.24/128.00 | & $lesseq(all_86_11, all_769_1) & $lesseq(-1, all_86_10) & 207.24/128.00 | $lesseq(0, all_86_11) & length1(int, all_105_4) = all_769_1 & 207.24/128.00 | length1(int, all_103_4) = all_769_1) | ( ~ (all_769_1 = 0) & 207.24/128.00 | permut3(int, all_103_4, all_105_4, all_86_11, $sum(all_86_10, 1)) = 207.24/128.00 | all_769_1) 207.24/128.00 | 207.24/128.00 | DELTA: instantiating (58) with fresh symbols all_770_0, all_770_1 gives: 207.24/128.00 | (76) (all_770_0 = all_770_1 & $lesseq(all_86_13, all_770_1) & $lesseq(0, 207.24/128.00 | all_770_1) & $lesseq(0, all_86_13) & length1(int, all_105_4) = 207.24/128.00 | all_770_1 & length1(int, all_103_2) = all_770_1) | ( ~ (all_770_1 = 207.24/128.00 | 0) & permut3(int, all_103_2, all_105_4, 0, all_86_13) = all_770_1) 207.24/128.00 | 207.24/128.00 | DELTA: instantiating (68) with fresh symbols all_771_0, all_771_1 gives: 207.24/128.00 | (77) elts(int, all_105_2) = all_771_1 & t2tb1(all_133_2) = all_771_0 & 207.24/128.00 | get(int, int, all_771_1, all_771_0) = all_133_1 & in_uni(all_771_0) & 207.24/128.00 | in_uni(all_771_1) & in_uni(all_133_1) 207.24/128.00 | 207.24/128.00 | ALPHA: (77) implies: 207.24/128.00 | (78) t2tb1(all_133_2) = all_771_0 207.24/128.00 | (79) elts(int, all_105_2) = all_771_1 207.24/128.00 | 207.24/128.00 | BETA: splitting (60) gives: 207.24/128.00 | 207.24/128.00 | Case 1: 207.24/128.00 | | 207.24/128.00 | | (80) $lesseq(all_86_13, -1) 207.24/128.00 | | 207.24/128.00 | | COMBINE_INEQS: (31), (80) imply: 207.24/128.00 | | (81) $lesseq(0, -1) 207.24/128.00 | | 207.24/128.00 | | CLOSE: (81) is inconsistent. 207.24/128.00 | | 207.24/128.00 | Case 2: 207.24/128.00 | | 207.24/128.00 | | (82) ? [v0: $int] : ? [v1: $int] : ((v0 = 0 & permut3(int, all_103_2, 207.24/128.00 | | all_105_4, 0, all_86_13) = 0) | (length1(int, all_103_2) = v0 207.24/128.00 | | & ( ~ ($lesseq(all_86_13, v0)) | ~ ($lesseq(0, v0)) | ( ~ (v1 = 207.24/128.00 | | v0) & length1(int, all_105_4) = v1)))) 207.24/128.00 | | 207.24/128.00 | | DELTA: instantiating (82) with fresh symbols all_782_0, all_782_1 gives: 207.24/128.00 | | (83) (all_782_1 = 0 & permut3(int, all_103_2, all_105_4, 0, all_86_13) = 207.24/128.00 | | 0) | (length1(int, all_103_2) = all_782_1 & ( ~ 207.24/128.00 | | ($lesseq(all_86_13, all_782_1)) | ~ ($lesseq(0, all_782_1)) | ( 207.24/128.00 | | ~ (all_782_0 = all_782_1) & length1(int, all_105_4) = 207.24/128.00 | | all_782_0))) 207.24/128.00 | | 207.24/128.00 | | BETA: splitting (83) gives: 207.24/128.00 | | 207.24/128.00 | | Case 1: 207.24/128.00 | | | 207.24/128.00 | | | (84) all_782_1 = 0 & permut3(int, all_103_2, all_105_4, 0, all_86_13) = 207.24/128.00 | | | 0 207.24/128.00 | | | 207.24/128.00 | | | ALPHA: (84) implies: 207.24/128.00 | | | (85) permut3(int, all_103_2, all_105_4, 0, all_86_13) = 0 207.24/128.00 | | | 207.24/128.00 | | | BETA: splitting (62) gives: 207.24/128.00 | | | 207.24/128.00 | | | Case 1: 207.24/128.00 | | | | 207.24/128.00 | | | | (86) $lesseq(all_86_11, -1) 207.24/128.00 | | | | 207.24/128.00 | | | | COMBINE_INEQS: (46), (86) imply: 207.24/128.00 | | | | (87) $lesseq(0, -1) 207.24/128.00 | | | | 207.24/128.00 | | | | CLOSE: (87) is inconsistent. 207.24/128.00 | | | | 207.24/128.00 | | | Case 2: 207.24/128.00 | | | | 207.24/128.00 | | | | (88) ~ ($lesseq(-1, all_86_10)) | ? [v0: $int] : ? [v1: $int] : 207.24/128.00 | | | | ((v0 = 0 & permut3(int, all_103_4, all_105_4, all_86_11, 207.24/128.00 | | | | $sum(all_86_10, 1)) = 0) | (length1(int, all_103_4) = v0 & 207.24/128.00 | | | | ( ~ ($lesseq(1, $difference(v0, all_86_10))) | ~ 207.24/128.00 | | | | ($lesseq(all_86_11, v0)) | ( ~ (v1 = v0) & length1(int, 207.24/128.00 | | | | all_105_4) = v1)))) 207.24/128.00 | | | | 207.24/128.00 | | | | BETA: splitting (63) gives: 207.24/128.00 | | | | 207.24/128.00 | | | | Case 1: 207.24/128.00 | | | | | 207.24/128.00 | | | | | (89) ~ (permut2(int, all_103_3, all_105_3, 0, all_86_13) = 0) 207.24/128.00 | | | | | 207.24/128.00 | | | | | PRED_UNIFY: (59), (89) imply: 207.24/128.00 | | | | | (90) $false 207.24/128.00 | | | | | 207.24/128.00 | | | | | CLOSE: (90) is inconsistent. 207.24/128.00 | | | | | 207.24/128.00 | | | | Case 2: 207.24/128.00 | | | | | 207.24/128.00 | | | | | (91) ? [v0: $int] : ((v0 = all_86_13 & length1(int, all_105_4) = 207.24/128.00 | | | | | all_86_13) | ( ~ (v0 = 0) & permut_all(int, all_103_4, 207.24/128.00 | | | | | all_105_4) = v0)) 207.24/128.00 | | | | | 207.24/128.00 | | | | | DELTA: instantiating (91) with fresh symbol all_802_0 gives: 207.24/128.00 | | | | | (92) (all_802_0 = all_86_13 & length1(int, all_105_4) = all_86_13) 207.24/128.00 | | | | | | ( ~ (all_802_0 = 0) & permut_all(int, all_103_4, all_105_4) 207.24/128.00 | | | | | = all_802_0) 207.24/128.00 | | | | | 207.24/128.00 | | | | | BETA: splitting (88) gives: 207.24/128.00 | | | | | 207.24/128.00 | | | | | Case 1: 207.24/128.00 | | | | | | 207.24/128.00 | | | | | | (93) $lesseq(all_86_10, -2) 207.24/128.00 | | | | | | 207.24/128.00 | | | | | | COMBINE_INEQS: (54), (93) imply: 207.24/128.00 | | | | | | (94) $lesseq(0, -1) 207.24/128.00 | | | | | | 207.24/128.00 | | | | | | CLOSE: (94) is inconsistent. 207.24/128.00 | | | | | | 207.24/128.00 | | | | | Case 2: 207.24/128.00 | | | | | | 207.24/128.00 | | | | | | (95) ? [v0: $int] : ? [v1: $int] : ((v0 = 0 & permut3(int, 207.24/128.00 | | | | | | all_103_4, all_105_4, all_86_11, $sum(all_86_10, 1)) = 207.24/128.00 | | | | | | 0) | (length1(int, all_103_4) = v0 & ( ~ ($lesseq(1, 207.24/128.00 | | | | | | $difference(v0, all_86_10))) | ~ 207.24/128.00 | | | | | | ($lesseq(all_86_11, v0)) | ( ~ (v1 = v0) & 207.24/128.00 | | | | | | length1(int, all_105_4) = v1)))) 207.24/128.00 | | | | | | 207.24/128.00 | | | | | | DELTA: instantiating (95) with fresh symbols all_808_0, all_808_1 207.24/128.00 | | | | | | gives: 207.24/128.00 | | | | | | (96) (all_808_1 = 0 & permut3(int, all_103_4, all_105_4, 207.24/128.00 | | | | | | all_86_11, $sum(all_86_10, 1)) = 0) | (length1(int, 207.24/128.00 | | | | | | all_103_4) = all_808_1 & ( ~ ($lesseq(1, 207.24/128.00 | | | | | | $difference(all_808_1, all_86_10))) | ~ 207.24/128.00 | | | | | | ($lesseq(all_86_11, all_808_1)) | ( ~ (all_808_0 = 207.24/128.00 | | | | | | all_808_1) & length1(int, all_105_4) = all_808_0))) 207.24/128.00 | | | | | | 207.24/128.00 | | | | | | BETA: splitting (76) gives: 207.24/128.00 | | | | | | 207.24/128.00 | | | | | | Case 1: 207.24/128.00 | | | | | | | 207.24/128.00 | | | | | | | (97) all_770_0 = all_770_1 & $lesseq(all_86_13, all_770_1) & 207.24/128.00 | | | | | | | $lesseq(0, all_770_1) & $lesseq(0, all_86_13) & 207.24/128.00 | | | | | | | length1(int, all_105_4) = all_770_1 & length1(int, 207.24/128.00 | | | | | | | all_103_2) = all_770_1 207.24/128.00 | | | | | | | 207.24/128.00 | | | | | | | ALPHA: (97) implies: 207.24/128.01 | | | | | | | (98) length1(int, all_103_2) = all_770_1 207.24/128.01 | | | | | | | (99) length1(int, all_105_4) = all_770_1 207.24/128.01 | | | | | | | 207.24/128.01 | | | | | | | BETA: splitting (65) gives: 207.24/128.01 | | | | | | | 207.24/128.01 | | | | | | | Case 1: 207.24/128.01 | | | | | | | | 207.24/128.01 | | | | | | | | (100) $lesseq(all_86_13, -1) 207.24/128.01 | | | | | | | | 207.24/128.01 | | | | | | | | COMBINE_INEQS: (31), (100) imply: 207.24/128.01 | | | | | | | | (101) $lesseq(0, -1) 207.24/128.01 | | | | | | | | 207.24/128.01 | | | | | | | | CLOSE: (101) is inconsistent. 207.24/128.01 | | | | | | | | 207.24/128.01 | | | | | | | Case 2: 207.24/128.01 | | | | | | | | 207.24/128.01 | | | | | | | | (102) ? [v0: $int] : ? [v1: $int] : ((v0 = 0 & permut3(int, 207.24/128.01 | | | | | | | | all_103_4, all_103_2, 0, all_86_13) = 0) | 207.24/128.01 | | | | | | | | (length1(int, all_103_4) = v0 & ( ~ 207.24/128.01 | | | | | | | | ($lesseq(all_86_13, v0)) | ~ ($lesseq(0, v0)) | 207.24/128.01 | | | | | | | | ( ~ (v1 = v0) & length1(int, all_103_2) = v1)))) 207.24/128.01 | | | | | | | | 207.24/128.01 | | | | | | | | DELTA: instantiating (102) with fresh symbols all_820_0, 207.24/128.01 | | | | | | | | all_820_1 gives: 207.24/128.01 | | | | | | | | (103) (all_820_1 = 0 & permut3(int, all_103_4, all_103_2, 0, 207.24/128.01 | | | | | | | | all_86_13) = 0) | (length1(int, all_103_4) = 207.24/128.01 | | | | | | | | all_820_1 & ( ~ ($lesseq(all_86_13, all_820_1)) | ~ 207.24/128.01 | | | | | | | | ($lesseq(0, all_820_1)) | ( ~ (all_820_0 = 207.24/128.01 | | | | | | | | all_820_1) & length1(int, all_103_2) = 207.24/128.01 | | | | | | | | all_820_0))) 207.24/128.01 | | | | | | | | 207.24/128.01 | | | | | | | | GROUND_INST: instantiating (1) with all_133_0, all_758_0, 207.24/128.01 | | | | | | | | all_133_1, simplifying with (19), (72) gives: 207.24/128.01 | | | | | | | | (104) all_758_0 = all_133_0 207.24/128.01 | | | | | | | | 207.24/128.01 | | | | | | | | GROUND_INST: instantiating (52) with all_86_13, all_770_1, 207.24/128.01 | | | | | | | | all_103_2, int, simplifying with (2), (98) gives: 207.24/128.01 | | | | | | | | (105) all_770_1 = all_86_13 207.24/128.01 | | | | | | | | 207.24/128.01 | | | | | | | | GROUND_INST: instantiating (24) with all_105_1, all_771_1, 207.24/128.01 | | | | | | | | all_105_2, int, simplifying with (33), (79) gives: 207.24/128.01 | | | | | | | | (106) all_771_1 = all_105_1 207.24/128.01 | | | | | | | | 207.24/128.01 | | | | | | | | GROUND_INST: instantiating (24) with all_771_1, all_758_2, 207.24/128.01 | | | | | | | | all_105_2, int, simplifying with (70), (79) gives: 207.24/128.01 | | | | | | | | (107) all_771_1 = all_758_2 207.24/128.01 | | | | | | | | 207.24/128.01 | | | | | | | | COMBINE_EQS: (106), (107) imply: 207.24/128.01 | | | | | | | | (108) all_758_2 = all_105_1 207.24/128.01 | | | | | | | | 207.24/128.01 | | | | | | | | REDUCE: (73), (108) imply: 207.24/128.01 | | | | | | | | (109) tb2t(all_105_1) = all_758_1 207.24/128.01 | | | | | | | | 207.24/128.01 | | | | | | | | REDUCE: (71), (104) imply: 207.24/128.01 | | | | | | | | (110) get3(all_758_1, all_133_2) = all_133_0 207.24/128.01 | | | | | | | | 207.24/128.01 | | | | | | | | BETA: splitting (96) gives: 207.24/128.01 | | | | | | | | 207.24/128.01 | | | | | | | | Case 1: 207.24/128.01 | | | | | | | | | 207.24/128.01 | | | | | | | | | (111) all_808_1 = 0 & permut3(int, all_103_4, all_105_4, 207.24/128.01 | | | | | | | | | all_86_11, $sum(all_86_10, 1)) = 0 207.24/128.01 | | | | | | | | | 207.24/128.01 | | | | | | | | | ALPHA: (111) implies: 207.24/128.01 | | | | | | | | | (112) permut3(int, all_103_4, all_105_4, all_86_11, 207.24/128.01 | | | | | | | | | $sum(all_86_10, 1)) = 0 207.24/128.01 | | | | | | | | | 207.24/128.01 | | | | | | | | | REF_CLOSE: (3), (4), (6), (7), (8), (10), (11), (13), (14), 207.24/128.01 | | | | | | | | | (16), (18), (20), (21), (27), (29), (32), (34), 207.24/128.01 | | | | | | | | | (36), (37), (38), (39), (41), (43), (45), (49), 207.24/128.01 | | | | | | | | | (50), (52), (56), (57), (59), (66), (75), (78), 207.24/128.01 | | | | | | | | | (109), (110), (112) are inconsistent by sub-proof 207.24/128.01 | | | | | | | | | #96. 207.24/128.01 | | | | | | | | | 207.24/128.01 | | | | | | | | Case 2: 207.24/128.01 | | | | | | | | | 207.24/128.01 | | | | | | | | | (113) length1(int, all_103_4) = all_808_1 & ( ~ ($lesseq(1, 207.24/128.01 | | | | | | | | | $difference(all_808_1, all_86_10))) | ~ 207.24/128.01 | | | | | | | | | ($lesseq(all_86_11, all_808_1)) | ( ~ (all_808_0 = 207.24/128.01 | | | | | | | | | all_808_1) & length1(int, all_105_4) = 207.24/128.01 | | | | | | | | | all_808_0)) 207.24/128.01 | | | | | | | | | 207.24/128.01 | | | | | | | | | ALPHA: (113) implies: 207.24/128.01 | | | | | | | | | (114) length1(int, all_103_4) = all_808_1 207.24/128.01 | | | | | | | | | (115) ~ ($lesseq(1, $difference(all_808_1, all_86_10))) | 207.24/128.01 | | | | | | | | | ~ ($lesseq(all_86_11, all_808_1)) | ( ~ (all_808_0 = 207.24/128.01 | | | | | | | | | all_808_1) & length1(int, all_105_4) = all_808_0) 207.24/128.01 | | | | | | | | | 207.24/128.01 | | | | | | | | | BETA: splitting (103) gives: 207.24/128.01 | | | | | | | | | 207.24/128.01 | | | | | | | | | Case 1: 207.24/128.01 | | | | | | | | | | 207.24/128.01 | | | | | | | | | | (116) all_820_1 = 0 & permut3(int, all_103_4, all_103_2, 207.24/128.01 | | | | | | | | | | 0, all_86_13) = 0 207.24/128.01 | | | | | | | | | | 207.24/128.01 | | | | | | | | | | ALPHA: (116) implies: 207.24/128.01 | | | | | | | | | | (117) permut3(int, all_103_4, all_103_2, 0, all_86_13) = 207.24/128.01 | | | | | | | | | | 0 207.24/128.01 | | | | | | | | | | 207.24/128.01 | | | | | | | | | | BETA: splitting (74) gives: 207.24/128.01 | | | | | | | | | | 207.24/128.01 | | | | | | | | | | Case 1: 207.24/128.01 | | | | | | | | | | | 207.24/128.01 | | | | | | | | | | | (118) all_764_0 = all_764_1 & $lesseq(all_86_13, 207.24/128.01 | | | | | | | | | | | all_764_1) & $lesseq(0, all_764_1) & $lesseq(0, 207.24/128.01 | | | | | | | | | | | all_86_13) & length1(int, all_103_2) = all_764_1 207.24/128.01 | | | | | | | | | | | & length1(int, all_103_4) = all_764_1 207.24/128.01 | | | | | | | | | | | 207.24/128.01 | | | | | | | | | | | ALPHA: (118) implies: 207.24/128.01 | | | | | | | | | | | (119) length1(int, all_103_4) = all_764_1 207.24/128.01 | | | | | | | | | | | 207.24/128.01 | | | | | | | | | | | GROUND_INST: instantiating (52) with all_86_13, all_808_1, 207.24/128.01 | | | | | | | | | | | all_103_4, int, simplifying with (8), (114) gives: 207.24/128.01 | | | | | | | | | | | (120) all_808_1 = all_86_13 207.24/128.01 | | | | | | | | | | | 207.24/128.01 | | | | | | | | | | | GROUND_INST: instantiating (52) with all_808_1, all_764_1, 207.24/128.01 | | | | | | | | | | | all_103_4, int, simplifying with (114), (119) 207.24/128.01 | | | | | | | | | | | gives: 207.24/128.01 | | | | | | | | | | | (121) all_808_1 = all_764_1 207.24/128.01 | | | | | | | | | | | 207.24/128.01 | | | | | | | | | | | COMBINE_EQS: (120), (121) imply: 207.24/128.01 | | | | | | | | | | | (122) all_764_1 = all_86_13 207.24/128.01 | | | | | | | | | | | 207.24/128.01 | | | | | | | | | | | BETA: splitting (115) gives: 207.24/128.01 | | | | | | | | | | | 207.24/128.01 | | | | | | | | | | | Case 1: 207.24/128.01 | | | | | | | | | | | | 207.24/128.01 | | | | | | | | | | | | (123) $lesseq(1, $difference(all_86_11, all_808_1)) 207.24/128.01 | | | | | | | | | | | | 207.24/128.01 | | | | | | | | | | | | REF_CLOSE: (18), (27), (36), (37), (44), (120), (123) are 207.24/128.01 | | | | | | | | | | | | inconsistent by sub-proof #95. 207.24/128.01 | | | | | | | | | | | | 207.24/128.01 | | | | | | | | | | | Case 2: 207.24/128.01 | | | | | | | | | | | | 207.24/128.01 | | | | | | | | | | | | (124) ~ ($lesseq(1, $difference(all_808_1, all_86_10))) 207.24/128.01 | | | | | | | | | | | | | ( ~ (all_808_0 = all_808_1) & length1(int, 207.24/128.01 | | | | | | | | | | | | all_105_4) = all_808_0) 207.24/128.01 | | | | | | | | | | | | 207.24/128.01 | | | | | | | | | | | | REF_CLOSE: (25), (44), (52), (120), (124) are inconsistent by 207.24/128.01 | | | | | | | | | | | | sub-proof #94. 207.24/128.01 | | | | | | | | | | | | 207.24/128.01 | | | | | | | | | | | End of split 207.24/128.01 | | | | | | | | | | | 207.24/128.01 | | | | | | | | | | Case 2: 207.24/128.01 | | | | | | | | | | | 207.24/128.01 | | | | | | | | | | | (125) ~ (all_764_1 = 0) & permut3(int, all_103_4, 207.24/128.01 | | | | | | | | | | | all_103_2, 0, all_86_13) = all_764_1 207.24/128.01 | | | | | | | | | | | 207.24/128.01 | | | | | | | | | | | ALPHA: (125) implies: 207.24/128.01 | | | | | | | | | | | (126) ~ (all_764_1 = 0) 207.24/128.01 | | | | | | | | | | | (127) permut3(int, all_103_4, all_103_2, 0, all_86_13) = 207.24/128.01 | | | | | | | | | | | all_764_1 207.24/128.01 | | | | | | | | | | | 207.24/128.01 | | | | | | | | | | | GROUND_INST: instantiating (21) with 0, all_764_1, all_86_13, 207.24/128.01 | | | | | | | | | | | 0, all_103_2, all_103_4, int, simplifying with 207.24/128.01 | | | | | | | | | | | (117), (127) gives: 207.24/128.01 | | | | | | | | | | | (128) all_764_1 = 0 207.24/128.01 | | | | | | | | | | | 207.24/128.01 | | | | | | | | | | | REDUCE: (126), (128) imply: 207.24/128.01 | | | | | | | | | | | (129) ~ (0 = 0) 207.24/128.01 | | | | | | | | | | | 207.24/128.01 | | | | | | | | | | | CLOSE: (129) is inconsistent. 207.24/128.01 | | | | | | | | | | | 207.24/128.01 | | | | | | | | | | End of split 207.24/128.01 | | | | | | | | | | 207.24/128.01 | | | | | | | | | Case 2: 207.24/128.01 | | | | | | | | | | 207.24/128.01 | | | | | | | | | | (130) length1(int, all_103_4) = all_820_1 & ( ~ 207.24/128.01 | | | | | | | | | | ($lesseq(all_86_13, all_820_1)) | ~ ($lesseq(0, 207.24/128.01 | | | | | | | | | | all_820_1)) | ( ~ (all_820_0 = all_820_1) & 207.24/128.01 | | | | | | | | | | length1(int, all_103_2) = all_820_0)) 207.24/128.01 | | | | | | | | | | 207.24/128.01 | | | | | | | | | | ALPHA: (130) implies: 207.24/128.01 | | | | | | | | | | (131) length1(int, all_103_4) = all_820_1 207.24/128.01 | | | | | | | | | | 207.24/128.01 | | | | | | | | | | BETA: splitting (92) gives: 207.24/128.01 | | | | | | | | | | 207.24/128.01 | | | | | | | | | | Case 1: 207.24/128.01 | | | | | | | | | | | 207.24/128.01 | | | | | | | | | | | (132) all_802_0 = all_86_13 & length1(int, all_105_4) = 207.24/128.01 | | | | | | | | | | | all_86_13 207.24/128.01 | | | | | | | | | | | 207.24/128.01 | | | | | | | | | | | GROUND_INST: instantiating (52) with all_86_13, all_820_1, 207.24/128.01 | | | | | | | | | | | all_103_4, int, simplifying with (8), (131) gives: 207.24/128.01 | | | | | | | | | | | (133) all_820_1 = all_86_13 207.24/128.01 | | | | | | | | | | | 207.24/128.01 | | | | | | | | | | | GROUND_INST: instantiating (52) with all_820_1, all_808_1, 207.24/128.01 | | | | | | | | | | | all_103_4, int, simplifying with (114), (131) 207.24/128.01 | | | | | | | | | | | gives: 207.24/128.01 | | | | | | | | | | | (134) all_820_1 = all_808_1 207.24/128.01 | | | | | | | | | | | 207.24/128.01 | | | | | | | | | | | COMBINE_EQS: (133), (134) imply: 207.24/128.01 | | | | | | | | | | | (135) all_808_1 = all_86_13 207.24/128.01 | | | | | | | | | | | 207.24/128.01 | | | | | | | | | | | REF_CLOSE: (18), (25), (27), (36), (37), (44), (52), (115), 207.24/128.01 | | | | | | | | | | | (135) are inconsistent by sub-proof #93. 207.24/128.01 | | | | | | | | | | | 207.24/128.01 | | | | | | | | | | Case 2: 207.24/128.01 | | | | | | | | | | | 207.24/128.01 | | | | | | | | | | | 207.24/128.01 | | | | | | | | | | | GROUND_INST: instantiating (52) with all_86_13, all_808_1, 207.24/128.01 | | | | | | | | | | | all_103_4, int, simplifying with (8), (114) gives: 207.24/128.01 | | | | | | | | | | | (136) all_808_1 = all_86_13 207.24/128.01 | | | | | | | | | | | 207.24/128.01 | | | | | | | | | | | REF_CLOSE: (18), (25), (27), (36), (37), (44), (52), (115), 207.24/128.01 | | | | | | | | | | | (136) are inconsistent by sub-proof #93. 207.24/128.01 | | | | | | | | | | | 207.24/128.01 | | | | | | | | | | End of split 207.24/128.01 | | | | | | | | | | 207.24/128.01 | | | | | | | | | End of split 207.24/128.01 | | | | | | | | | 207.24/128.01 | | | | | | | | End of split 207.24/128.01 | | | | | | | | 207.24/128.01 | | | | | | | End of split 207.24/128.01 | | | | | | | 207.24/128.01 | | | | | | Case 2: 207.24/128.01 | | | | | | | 207.24/128.01 | | | | | | | (137) ~ (all_770_1 = 0) & permut3(int, all_103_2, all_105_4, 207.24/128.01 | | | | | | | 0, all_86_13) = all_770_1 207.24/128.01 | | | | | | | 207.24/128.01 | | | | | | | ALPHA: (137) implies: 207.24/128.01 | | | | | | | (138) ~ (all_770_1 = 0) 207.24/128.01 | | | | | | | (139) permut3(int, all_103_2, all_105_4, 0, all_86_13) = 207.24/128.01 | | | | | | | all_770_1 207.24/128.01 | | | | | | | 207.24/128.01 | | | | | | | GROUND_INST: instantiating (21) with 0, all_770_1, all_86_13, 0, 207.24/128.01 | | | | | | | all_105_4, all_103_2, int, simplifying with (85), 207.24/128.01 | | | | | | | (139) gives: 207.24/128.01 | | | | | | | (140) all_770_1 = 0 207.24/128.01 | | | | | | | 207.24/128.01 | | | | | | | REDUCE: (138), (140) imply: 207.24/128.01 | | | | | | | (141) ~ (0 = 0) 207.24/128.01 | | | | | | | 207.24/128.01 | | | | | | | CLOSE: (141) is inconsistent. 207.24/128.01 | | | | | | | 207.24/128.01 | | | | | | End of split 207.24/128.01 | | | | | | 207.24/128.01 | | | | | End of split 207.24/128.01 | | | | | 207.24/128.01 | | | | End of split 207.24/128.01 | | | | 207.24/128.01 | | | End of split 207.24/128.01 | | | 207.24/128.01 | | Case 2: 207.24/128.01 | | | 207.24/128.01 | | | (142) length1(int, all_103_2) = all_782_1 & ( ~ ($lesseq(all_86_13, 207.24/128.01 | | | all_782_1)) | ~ ($lesseq(0, all_782_1)) | ( ~ (all_782_0 = 207.24/128.01 | | | all_782_1) & length1(int, all_105_4) = all_782_0)) 207.24/128.01 | | | 207.24/128.01 | | | ALPHA: (142) implies: 207.24/128.01 | | | (143) length1(int, all_103_2) = all_782_1 207.24/128.01 | | | (144) ~ ($lesseq(all_86_13, all_782_1)) | ~ ($lesseq(0, all_782_1)) | 207.24/128.01 | | | ( ~ (all_782_0 = all_782_1) & length1(int, all_105_4) = 207.24/128.01 | | | all_782_0) 207.24/128.01 | | | 207.24/128.01 | | | BETA: splitting (62) gives: 207.24/128.01 | | | 207.24/128.01 | | | Case 1: 207.24/128.01 | | | | 207.24/128.01 | | | | (145) $lesseq(all_86_11, -1) 207.24/128.01 | | | | 207.24/128.01 | | | | COMBINE_INEQS: (46), (145) imply: 207.24/128.01 | | | | (146) $lesseq(0, -1) 207.24/128.01 | | | | 207.24/128.01 | | | | CLOSE: (146) is inconsistent. 207.24/128.01 | | | | 207.24/128.01 | | | Case 2: 207.24/128.01 | | | | 207.24/128.01 | | | | (147) ~ ($lesseq(-1, all_86_10)) | ? [v0: $int] : ? [v1: $int] : 207.24/128.01 | | | | ((v0 = 0 & permut3(int, all_103_4, all_105_4, all_86_11, 207.24/128.01 | | | | $sum(all_86_10, 1)) = 0) | (length1(int, all_103_4) = v0 207.24/128.01 | | | | & ( ~ ($lesseq(1, $difference(v0, all_86_10))) | ~ 207.24/128.01 | | | | ($lesseq(all_86_11, v0)) | ( ~ (v1 = v0) & length1(int, 207.24/128.01 | | | | all_105_4) = v1)))) 207.24/128.01 | | | | 207.24/128.01 | | | | BETA: splitting (147) gives: 207.24/128.01 | | | | 207.24/128.01 | | | | Case 1: 207.24/128.01 | | | | | 207.24/128.01 | | | | | (148) $lesseq(all_86_10, -2) 207.24/128.01 | | | | | 207.24/128.01 | | | | | COMBINE_INEQS: (54), (148) imply: 207.24/128.01 | | | | | (149) $lesseq(0, -1) 207.24/128.01 | | | | | 207.24/128.01 | | | | | CLOSE: (149) is inconsistent. 207.24/128.01 | | | | | 207.24/128.01 | | | | Case 2: 207.24/128.01 | | | | | 207.24/128.01 | | | | | (150) ? [v0: $int] : ? [v1: $int] : ((v0 = 0 & permut3(int, 207.24/128.01 | | | | | all_103_4, all_105_4, all_86_11, $sum(all_86_10, 1)) = 207.24/128.01 | | | | | 0) | (length1(int, all_103_4) = v0 & ( ~ ($lesseq(1, 207.24/128.01 | | | | | $difference(v0, all_86_10))) | ~ 207.24/128.01 | | | | | ($lesseq(all_86_11, v0)) | ( ~ (v1 = v0) & length1(int, 207.24/128.01 | | | | | all_105_4) = v1)))) 207.24/128.01 | | | | | 207.24/128.01 | | | | | DELTA: instantiating (150) with fresh symbols all_822_0, all_822_1 207.24/128.01 | | | | | gives: 207.24/128.01 | | | | | (151) (all_822_1 = 0 & permut3(int, all_103_4, all_105_4, 207.24/128.01 | | | | | all_86_11, $sum(all_86_10, 1)) = 0) | (length1(int, 207.24/128.01 | | | | | all_103_4) = all_822_1 & ( ~ ($lesseq(1, 207.24/128.01 | | | | | $difference(all_822_1, all_86_10))) | ~ 207.24/128.01 | | | | | ($lesseq(all_86_11, all_822_1)) | ( ~ (all_822_0 = 207.24/128.01 | | | | | all_822_1) & length1(int, all_105_4) = all_822_0))) 207.24/128.01 | | | | | 207.24/128.01 | | | | | BETA: splitting (151) gives: 207.24/128.01 | | | | | 207.24/128.01 | | | | | Case 1: 207.24/128.01 | | | | | | 207.24/128.01 | | | | | | (152) all_822_1 = 0 & permut3(int, all_103_4, all_105_4, 207.24/128.01 | | | | | | all_86_11, $sum(all_86_10, 1)) = 0 207.24/128.01 | | | | | | 207.24/128.01 | | | | | | ALPHA: (152) implies: 207.24/128.01 | | | | | | (153) permut3(int, all_103_4, all_105_4, all_86_11, 207.24/128.01 | | | | | | $sum(all_86_10, 1)) = 0 207.24/128.01 | | | | | | 207.24/128.01 | | | | | | BETA: splitting (75) gives: 207.24/128.01 | | | | | | 207.24/128.01 | | | | | | Case 1: 207.24/128.01 | | | | | | | 207.24/128.01 | | | | | | | (154) all_769_0 = all_769_1 & $lesseq(1, $difference(all_769_1, 207.24/128.01 | | | | | | | all_86_10)) & $lesseq(all_86_11, all_769_1) & 207.24/128.01 | | | | | | | $lesseq(-1, all_86_10) & $lesseq(0, all_86_11) & 207.24/128.01 | | | | | | | length1(int, all_105_4) = all_769_1 & length1(int, 207.24/128.01 | | | | | | | all_103_4) = all_769_1 207.24/128.01 | | | | | | | 207.24/128.01 | | | | | | | ALPHA: (154) implies: 207.24/128.01 | | | | | | | (155) length1(int, all_103_4) = all_769_1 207.24/128.01 | | | | | | | 207.24/128.01 | | | | | | | GROUND_INST: instantiating (1) with all_133_0, all_758_0, 207.24/128.01 | | | | | | | all_133_1, simplifying with (19), (72) gives: 207.24/128.01 | | | | | | | (156) all_758_0 = all_133_0 207.24/128.01 | | | | | | | 207.24/128.01 | | | | | | | GROUND_INST: instantiating (52) with all_86_13, all_769_1, 207.24/128.01 | | | | | | | all_103_4, int, simplifying with (8), (155) gives: 207.24/128.01 | | | | | | | (157) all_769_1 = all_86_13 207.24/128.01 | | | | | | | 207.24/128.01 | | | | | | | GROUND_INST: instantiating (24) with all_105_1, all_771_1, 207.24/128.01 | | | | | | | all_105_2, int, simplifying with (33), (79) gives: 207.24/128.01 | | | | | | | (158) all_771_1 = all_105_1 207.24/128.01 | | | | | | | 207.24/128.01 | | | | | | | GROUND_INST: instantiating (24) with all_771_1, all_758_2, 207.24/128.01 | | | | | | | all_105_2, int, simplifying with (70), (79) gives: 207.24/128.01 | | | | | | | (159) all_771_1 = all_758_2 207.24/128.01 | | | | | | | 207.24/128.01 | | | | | | | COMBINE_EQS: (158), (159) imply: 207.24/128.01 | | | | | | | (160) all_758_2 = all_105_1 207.24/128.01 | | | | | | | 207.24/128.01 | | | | | | | REDUCE: (73), (160) imply: 207.24/128.01 | | | | | | | (161) tb2t(all_105_1) = all_758_1 207.24/128.01 | | | | | | | 207.24/128.01 | | | | | | | REDUCE: (71), (156) imply: 207.24/128.01 | | | | | | | (162) get3(all_758_1, all_133_2) = all_133_0 207.24/128.01 | | | | | | | 207.24/128.01 | | | | | | | REF_CLOSE: (3), (4), (6), (7), (8), (10), (11), (13), (14), (16), 207.24/128.01 | | | | | | | (18), (20), (21), (27), (29), (32), (34), (36), (37), 207.24/128.01 | | | | | | | (38), (39), (41), (43), (45), (49), (50), (52), (56), 207.24/128.01 | | | | | | | (57), (59), (66), (75), (78), (153), (161), (162) are 207.24/128.01 | | | | | | | inconsistent by sub-proof #96. 207.24/128.01 | | | | | | | 207.24/128.01 | | | | | | Case 2: 207.24/128.01 | | | | | | | 207.24/128.01 | | | | | | | (163) ~ (all_769_1 = 0) & permut3(int, all_103_4, all_105_4, 207.24/128.01 | | | | | | | all_86_11, $sum(all_86_10, 1)) = all_769_1 207.24/128.01 | | | | | | | 207.24/128.01 | | | | | | | ALPHA: (163) implies: 207.24/128.01 | | | | | | | (164) ~ (all_769_1 = 0) 207.24/128.01 | | | | | | | (165) permut3(int, all_103_4, all_105_4, all_86_11, 207.24/128.01 | | | | | | | $sum(all_86_10, 1)) = all_769_1 207.24/128.01 | | | | | | | 207.24/128.01 | | | | | | | REF_CLOSE: (21), (153), (164), (165) are inconsistent by sub-proof 207.24/128.01 | | | | | | | #97. 207.24/128.01 | | | | | | | 207.24/128.01 | | | | | | End of split 207.24/128.01 | | | | | | 207.24/128.01 | | | | | Case 2: 207.24/128.01 | | | | | | 207.24/128.01 | | | | | | (166) length1(int, all_103_4) = all_822_1 & ( ~ ($lesseq(1, 207.24/128.01 | | | | | | $difference(all_822_1, all_86_10))) | ~ 207.24/128.01 | | | | | | ($lesseq(all_86_11, all_822_1)) | ( ~ (all_822_0 = 207.24/128.01 | | | | | | all_822_1) & length1(int, all_105_4) = all_822_0)) 207.24/128.01 | | | | | | 207.24/128.01 | | | | | | ALPHA: (166) implies: 207.24/128.01 | | | | | | (167) length1(int, all_103_4) = all_822_1 207.24/128.01 | | | | | | (168) ~ ($lesseq(1, $difference(all_822_1, all_86_10))) | ~ 207.24/128.01 | | | | | | ($lesseq(all_86_11, all_822_1)) | ( ~ (all_822_0 = 207.24/128.01 | | | | | | all_822_1) & length1(int, all_105_4) = all_822_0) 207.24/128.01 | | | | | | 207.24/128.01 | | | | | | GROUND_INST: instantiating (52) with all_86_13, all_782_1, 207.24/128.01 | | | | | | all_103_2, int, simplifying with (2), (143) gives: 207.24/128.01 | | | | | | (169) all_782_1 = all_86_13 207.24/128.01 | | | | | | 207.24/128.01 | | | | | | GROUND_INST: instantiating (52) with all_86_13, all_822_1, 207.24/128.01 | | | | | | all_103_4, int, simplifying with (8), (167) gives: 207.24/128.01 | | | | | | (170) all_822_1 = all_86_13 207.24/128.01 | | | | | | 207.24/128.01 | | | | | | BETA: splitting (144) gives: 207.24/128.01 | | | | | | 207.24/128.01 | | | | | | Case 1: 207.24/128.01 | | | | | | | 207.24/128.01 | | | | | | | (171) $lesseq(all_782_1, -1) 207.24/128.01 | | | | | | | 207.24/128.01 | | | | | | | REDUCE: (169), (171) imply: 207.24/128.01 | | | | | | | (172) $lesseq(all_86_13, -1) 207.24/128.01 | | | | | | | 207.24/128.01 | | | | | | | COMBINE_INEQS: (18), (27) imply: 207.24/128.01 | | | | | | | (173) $lesseq(2, $difference(all_86_7, all_86_8)) 207.24/128.01 | | | | | | | 207.24/128.01 | | | | | | | COMBINE_INEQS: (37), (173) imply: 207.24/128.02 | | | | | | | (174) $lesseq(2, $difference(all_86_10, all_86_8)) 207.24/128.02 | | | | | | | 207.24/128.02 | | | | | | | COMBINE_INEQS: (36), (174) imply: 207.24/128.02 | | | | | | | (175) $lesseq(2, $difference(all_86_10, all_86_11)) 207.24/128.02 | | | | | | | 207.24/128.02 | | | | | | | COMBINE_INEQS: (31), (172) imply: 207.24/128.02 | | | | | | | (176) $lesseq(0, -1) 207.24/128.02 | | | | | | | 207.24/128.02 | | | | | | | CLOSE: (176) is inconsistent. 207.24/128.02 | | | | | | | 207.24/128.02 | | | | | | Case 2: 207.24/128.02 | | | | | | | 207.24/128.02 | | | | | | | (177) ~ ($lesseq(all_86_13, all_782_1)) | ( ~ (all_782_0 = 207.24/128.02 | | | | | | | all_782_1) & length1(int, all_105_4) = all_782_0) 207.24/128.02 | | | | | | | 207.24/128.02 | | | | | | | BETA: splitting (168) gives: 207.24/128.02 | | | | | | | 207.24/128.02 | | | | | | | Case 1: 207.24/128.02 | | | | | | | | 207.24/128.02 | | | | | | | | (178) $lesseq(1, $difference(all_86_11, all_822_1)) 207.24/128.02 | | | | | | | | 207.24/128.02 | | | | | | | | REDUCE: (170), (178) imply: 207.24/128.02 | | | | | | | | (179) $lesseq(1, $difference(all_86_11, all_86_13)) 207.24/128.02 | | | | | | | | 207.24/128.02 | | | | | | | | COMBINE_INEQS: (18), (27) imply: 207.24/128.02 | | | | | | | | (180) $lesseq(2, $difference(all_86_7, all_86_8)) 207.24/128.02 | | | | | | | | 207.24/128.02 | | | | | | | | COMBINE_INEQS: (37), (180) imply: 207.24/128.02 | | | | | | | | (181) $lesseq(2, $difference(all_86_10, all_86_8)) 207.24/128.02 | | | | | | | | 207.24/128.02 | | | | | | | | COMBINE_INEQS: (36), (181) imply: 207.24/128.02 | | | | | | | | (182) $lesseq(2, $difference(all_86_10, all_86_11)) 207.24/128.02 | | | | | | | | 207.24/128.02 | | | | | | | | COMBINE_INEQS: (17), (179) imply: 207.24/128.02 | | | | | | | | (183) $lesseq(0, -1) 207.24/128.02 | | | | | | | | 207.24/128.02 | | | | | | | | CLOSE: (183) is inconsistent. 207.24/128.02 | | | | | | | | 207.24/128.02 | | | | | | | Case 2: 207.24/128.02 | | | | | | | | 207.24/128.02 | | | | | | | | (184) ~ ($lesseq(1, $difference(all_822_1, all_86_10))) | ( 207.24/128.02 | | | | | | | | ~ (all_822_0 = all_822_1) & length1(int, all_105_4) = 207.24/128.02 | | | | | | | | all_822_0) 207.24/128.02 | | | | | | | | 207.24/128.02 | | | | | | | | BETA: splitting (177) gives: 207.24/128.02 | | | | | | | | 207.24/128.02 | | | | | | | | Case 1: 207.24/128.02 | | | | | | | | | 207.24/128.02 | | | | | | | | | (185) $lesseq(1, $difference(all_86_13, all_782_1)) 207.24/128.02 | | | | | | | | | 207.24/128.02 | | | | | | | | | REDUCE: (169), (185) imply: 207.24/128.02 | | | | | | | | | (186) $lesseq(0, -1) 207.24/128.02 | | | | | | | | | 207.24/128.02 | | | | | | | | | CLOSE: (186) is inconsistent. 207.24/128.02 | | | | | | | | | 207.24/128.02 | | | | | | | | Case 2: 207.24/128.02 | | | | | | | | | 207.24/128.02 | | | | | | | | | (187) ~ (all_782_0 = all_782_1) & length1(int, all_105_4) 207.24/128.02 | | | | | | | | | = all_782_0 207.24/128.02 | | | | | | | | | 207.24/128.02 | | | | | | | | | ALPHA: (187) implies: 207.24/128.02 | | | | | | | | | (188) ~ (all_782_0 = all_782_1) 207.24/128.02 | | | | | | | | | (189) length1(int, all_105_4) = all_782_0 207.24/128.02 | | | | | | | | | 207.24/128.02 | | | | | | | | | REDUCE: (169), (188) imply: 207.24/128.02 | | | | | | | | | (190) ~ (all_782_0 = all_86_13) 207.24/128.02 | | | | | | | | | 207.24/128.02 | | | | | | | | | BETA: splitting (184) gives: 207.24/128.02 | | | | | | | | | 207.24/128.02 | | | | | | | | | Case 1: 207.24/128.02 | | | | | | | | | | 207.24/128.02 | | | | | | | | | | (191) $lesseq(all_822_1, all_86_10) 207.24/128.02 | | | | | | | | | | 207.24/128.02 | | | | | | | | | | REDUCE: (170), (191) imply: 207.24/128.02 | | | | | | | | | | (192) $lesseq(all_86_13, all_86_10) 207.24/128.02 | | | | | | | | | | 207.24/128.02 | | | | | | | | | | COMBINE_INEQS: (44), (192) imply: 207.24/128.02 | | | | | | | | | | (193) $lesseq(0, -1) 207.24/128.02 | | | | | | | | | | 207.24/128.02 | | | | | | | | | | CLOSE: (193) is inconsistent. 207.24/128.02 | | | | | | | | | | 207.24/128.02 | | | | | | | | | Case 2: 207.24/128.02 | | | | | | | | | | 207.24/128.02 | | | | | | | | | | (194) ~ (all_822_0 = all_822_1) & length1(int, 207.24/128.02 | | | | | | | | | | all_105_4) = all_822_0 207.24/128.02 | | | | | | | | | | 207.24/128.02 | | | | | | | | | | ALPHA: (194) implies: 207.24/128.02 | | | | | | | | | | (195) length1(int, all_105_4) = all_822_0 207.24/128.02 | | | | | | | | | | 207.24/128.02 | | | | | | | | | | GROUND_INST: instantiating (52) with all_86_13, all_822_0, 207.24/128.02 | | | | | | | | | | all_105_4, int, simplifying with (25), (195) 207.24/128.02 | | | | | | | | | | gives: 207.24/128.02 | | | | | | | | | | (196) all_822_0 = all_86_13 207.24/128.02 | | | | | | | | | | 207.24/128.02 | | | | | | | | | | GROUND_INST: instantiating (52) with all_822_0, all_782_0, 207.24/128.02 | | | | | | | | | | all_105_4, int, simplifying with (189), (195) 207.24/128.02 | | | | | | | | | | gives: 207.24/128.02 | | | | | | | | | | (197) all_822_0 = all_782_0 207.24/128.02 | | | | | | | | | | 207.24/128.02 | | | | | | | | | | COMBINE_EQS: (196), (197) imply: 207.24/128.02 | | | | | | | | | | (198) all_782_0 = all_86_13 207.24/128.02 | | | | | | | | | | 207.24/128.02 | | | | | | | | | | REDUCE: (190), (198) imply: 207.24/128.02 | | | | | | | | | | (199) ~ (0 = 0) 207.24/128.02 | | | | | | | | | | 207.24/128.02 | | | | | | | | | | CLOSE: (199) is inconsistent. 207.24/128.02 | | | | | | | | | | 207.24/128.02 | | | | | | | | | End of split 207.24/128.02 | | | | | | | | | 207.24/128.02 | | | | | | | | End of split 207.24/128.02 | | | | | | | | 207.24/128.02 | | | | | | | End of split 207.24/128.02 | | | | | | | 207.24/128.02 | | | | | | End of split 207.24/128.02 | | | | | | 207.24/128.02 | | | | | End of split 207.24/128.02 | | | | | 207.24/128.02 | | | | End of split 207.24/128.02 | | | | 207.24/128.02 | | | End of split 207.24/128.02 | | | 207.24/128.02 | | End of split 207.24/128.02 | | 207.24/128.02 | End of split 207.24/128.02 | 207.24/128.02 End of proof 207.24/128.02 207.24/128.02 Sub-proof #93 shows that the following formulas are inconsistent: 207.24/128.02 ---------------------------------------------------------------- 207.24/128.02 (1) $lesseq(1, $difference(all_133_2, all_86_8)) 207.24/128.02 (2) ~ ($lesseq(1, $difference(all_808_1, all_86_10))) | ~ 207.24/128.02 ($lesseq(all_86_11, all_808_1)) | ( ~ (all_808_0 = all_808_1) & 207.24/128.02 length1(int, all_105_4) = all_808_0) 207.24/128.02 (3) length1(int, all_105_4) = all_86_13 207.24/128.02 (4) $lesseq(1, $difference(all_86_7, all_133_2)) 207.24/128.02 (5) all_808_1 = all_86_13 207.24/128.02 (6) $lesseq(all_86_11, all_86_8) 207.24/128.02 (7) $lesseq(all_86_7, all_86_10) 207.24/128.02 (8) $lesseq(1, $difference(all_86_13, all_86_10)) 207.24/128.02 (9) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 207.24/128.02 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 207.24/128.02 207.24/128.02 Begin of proof 207.24/128.02 | 207.24/128.02 | BETA: splitting (2) gives: 207.24/128.02 | 207.24/128.02 | Case 1: 207.24/128.02 | | 207.24/128.02 | | (10) $lesseq(1, $difference(all_86_11, all_808_1)) 207.24/128.02 | | 207.24/128.02 | | REF_CLOSE: (1), (4), (5), (6), (7), (8), (10) are inconsistent by sub-proof 207.24/128.02 | | #95. 207.24/128.02 | | 207.24/128.02 | Case 2: 207.24/128.02 | | 207.24/128.02 | | (11) ~ ($lesseq(1, $difference(all_808_1, all_86_10))) | ( ~ (all_808_0 207.24/128.02 | | = all_808_1) & length1(int, all_105_4) = all_808_0) 207.24/128.02 | | 207.24/128.02 | | REF_CLOSE: (3), (5), (8), (9), (11) are inconsistent by sub-proof #94. 207.24/128.02 | | 207.24/128.02 | End of split 207.24/128.02 | 207.24/128.02 End of proof 207.24/128.02 207.24/128.02 Sub-proof #94 shows that the following formulas are inconsistent: 207.24/128.02 ---------------------------------------------------------------- 207.24/128.02 (1) ~ ($lesseq(1, $difference(all_808_1, all_86_10))) | ( ~ (all_808_0 = 207.24/128.02 all_808_1) & length1(int, all_105_4) = all_808_0) 207.24/128.02 (2) length1(int, all_105_4) = all_86_13 207.24/128.02 (3) all_808_1 = all_86_13 207.24/128.02 (4) $lesseq(1, $difference(all_86_13, all_86_10)) 207.24/128.02 (5) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 207.24/128.02 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 207.24/128.02 207.24/128.02 Begin of proof 207.24/128.02 | 207.24/128.02 | BETA: splitting (1) gives: 207.24/128.02 | 207.24/128.02 | Case 1: 207.24/128.02 | | 207.24/128.02 | | (6) $lesseq(all_808_1, all_86_10) 207.24/128.02 | | 207.24/128.02 | | REDUCE: (3), (6) imply: 207.24/128.02 | | (7) $lesseq(all_86_13, all_86_10) 207.24/128.02 | | 207.24/128.02 | | COMBINE_INEQS: (4), (7) imply: 207.24/128.02 | | (8) $lesseq(0, -1) 207.24/128.02 | | 207.24/128.02 | | CLOSE: (8) is inconsistent. 207.24/128.02 | | 207.24/128.02 | Case 2: 207.24/128.02 | | 207.24/128.02 | | (9) ~ (all_808_0 = all_808_1) & length1(int, all_105_4) = all_808_0 207.24/128.02 | | 207.24/128.02 | | ALPHA: (9) implies: 207.24/128.02 | | (10) ~ (all_808_0 = all_808_1) 207.24/128.02 | | (11) length1(int, all_105_4) = all_808_0 207.24/128.02 | | 207.24/128.02 | | REDUCE: (3), (10) imply: 207.24/128.02 | | (12) ~ (all_808_0 = all_86_13) 207.24/128.02 | | 207.24/128.02 | | GROUND_INST: instantiating (5) with all_86_13, all_808_0, all_105_4, int, 207.24/128.02 | | simplifying with (2), (11) gives: 207.24/128.02 | | (13) all_808_0 = all_86_13 207.24/128.02 | | 207.24/128.02 | | REDUCE: (12), (13) imply: 207.24/128.02 | | (14) ~ (0 = 0) 207.24/128.02 | | 207.24/128.02 | | CLOSE: (14) is inconsistent. 207.24/128.02 | | 207.24/128.02 | End of split 207.24/128.02 | 207.24/128.02 End of proof 207.24/128.02 207.24/128.02 Sub-proof #95 shows that the following formulas are inconsistent: 207.24/128.02 ---------------------------------------------------------------- 207.24/128.02 (1) $lesseq(1, $difference(all_133_2, all_86_8)) 207.24/128.02 (2) $lesseq(1, $difference(all_86_7, all_133_2)) 207.24/128.02 (3) all_808_1 = all_86_13 207.24/128.02 (4) $lesseq(all_86_11, all_86_8) 207.24/128.02 (5) $lesseq(all_86_7, all_86_10) 207.24/128.02 (6) $lesseq(1, $difference(all_86_11, all_808_1)) 207.24/128.02 (7) $lesseq(1, $difference(all_86_13, all_86_10)) 207.24/128.02 207.24/128.02 Begin of proof 207.24/128.02 | 207.24/128.02 | REDUCE: (3), (6) imply: 207.24/128.02 | (8) $lesseq(1, $difference(all_86_11, all_86_13)) 207.24/128.02 | 207.24/128.02 | COMBINE_INEQS: (1), (2) imply: 207.24/128.02 | (9) $lesseq(2, $difference(all_86_7, all_86_8)) 207.24/128.02 | 207.24/128.02 | COMBINE_INEQS: (5), (9) imply: 207.24/128.02 | (10) $lesseq(2, $difference(all_86_10, all_86_8)) 207.24/128.02 | 207.24/128.02 | COMBINE_INEQS: (4), (10) imply: 207.24/128.02 | (11) $lesseq(2, $difference(all_86_10, all_86_11)) 207.24/128.02 | 207.24/128.02 | COMBINE_INEQS: (7), (11) imply: 207.24/128.02 | (12) $lesseq(3, $difference(all_86_13, all_86_11)) 207.24/128.02 | 207.24/128.02 | COMBINE_INEQS: (8), (12) imply: 207.24/128.02 | (13) $lesseq(0, -1) 207.24/128.02 | 207.24/128.02 | CLOSE: (13) is inconsistent. 207.24/128.02 | 207.24/128.02 End of proof 207.24/128.02 207.24/128.02 Sub-proof #96 shows that the following formulas are inconsistent: 207.24/128.02 ---------------------------------------------------------------- 207.24/128.02 (1) get3(all_758_1, all_133_2) = all_133_0 207.24/128.02 (2) in_map_int_int(all_86_6) 207.24/128.02 (3) in_map_int_int(all_86_12) 207.24/128.02 (4) t2tb(all_86_2) = all_105_1 207.24/128.02 (5) in_ty(int) 207.24/128.02 (6) length1(int, all_103_4) = all_86_13 207.24/128.02 (7) $lesseq(-1, all_86_8) 207.24/128.02 (8) $lesseq(all_86_7, all_86_13) 207.24/128.02 (9) ! [v0: $int] : ! [v1: $int] : (v1 = 42 | ~ ($lesseq(1, 207.24/128.02 $difference(all_86_7, v0))) | ~ ($lesseq(1, $difference(v0, 207.24/128.02 all_86_8))) | ~ (get3(all_86_6, v0) = v1)) 207.24/128.02 (10) map_eq_sub1(int, all_103_3, all_103_1, $sum(all_86_10, 1), all_86_13) = 207.24/128.02 0 207.24/128.02 (11) t2tb1(all_133_2) = all_771_0 207.24/128.02 (12) t2tb(all_86_6) = all_103_1 207.24/128.02 (13) $lesseq(1, $difference(all_133_2, all_86_8)) 207.24/128.02 (14) map_eq_sub1(int, all_103_1, all_105_3, $sum(all_86_8, 1), all_86_13) = 0 207.24/128.02 (15) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.24/128.02 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ (permut3(v6, v5, 207.24/128.02 v4, v3, v2) = v1) | ~ (permut3(v6, v5, v4, v3, v2) = v0)) 207.24/128.02 (16) $lesseq(1, $difference(all_86_7, all_133_2)) 207.24/128.02 (17) map_eq_sub1(int, all_105_3, all_105_1, 0, all_86_7) = 0 207.24/128.02 (18) permut3(int, all_103_4, all_105_4, all_86_11, $sum(all_86_10, 1)) = 0 207.24/128.02 (19) tb2t(all_105_1) = all_86_2 207.24/128.02 (20) tb2t(all_105_1) = all_758_1 207.24/128.02 (21) t2tb1(all_133_0) = all_133_1 207.24/128.02 (22) map_eq_sub1(int, all_103_3, all_103_1, 0, all_86_11) = 0 207.24/128.02 (23) $lesseq(all_86_11, all_86_8) 207.24/128.02 (24) $lesseq(all_86_7, all_86_10) 207.24/128.02 (25) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.24/128.02 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 207.24/128.02 ($lesseq(1, $difference(v3, v4))) | ~ ($lesseq(v2, v4)) | ~ 207.24/128.02 (permut2(int, v5, v6, v2, v3) = 0) | ~ (t2tb(v1) = v6) | ~ (t2tb(v0) 207.24/128.02 = v5) | ~ (get3(v1, v4) = v7) | ~ in_map_int_int(v0) | ? [v8: 207.24/128.02 $int] : ($lesseq(1, $difference(v3, v8)) & $lesseq(v2, v8) & 207.24/128.02 get3(v0, v8) = v7)) 207.24/128.02 (26) ~ (all_133_0 = 42) 207.24/128.02 (27) (all_769_0 = all_769_1 & $lesseq(1, $difference(all_769_1, all_86_10)) & 207.24/128.02 $lesseq(all_86_11, all_769_1) & $lesseq(-1, all_86_10) & $lesseq(0, 207.24/128.02 all_86_11) & length1(int, all_105_4) = all_769_1 & length1(int, 207.24/128.02 all_103_4) = all_769_1) | ( ~ (all_769_1 = 0) & permut3(int, 207.24/128.02 all_103_4, all_105_4, all_86_11, $sum(all_86_10, 1)) = all_769_1) 207.24/128.02 (28) t2tb(all_86_12) = all_103_3 207.24/128.02 (29) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.24/128.02 $int] : ! [v5: $int] : ! [v6: $int] : ( ~ ($lesseq(1, 207.24/128.02 $difference(v4, v5))) | ~ ($lesseq(v3, v5)) | ~ (map_eq_sub1(v0, 207.24/128.02 v1, v2, v3, v4) = 0) | ~ (t2tb1(v5) = v6) | ~ in_ty(v0) | ? 207.24/128.02 [v7: $int] : (get(v0, int, v2, v6) = v7 & get(v0, int, v1, v6) = v7 & 207.24/128.02 in_uni(v7))) 207.24/128.02 (30) in_map_int_int(all_86_4) 207.24/128.02 (31) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ (tb2t(v2) 207.24/128.02 = v1) | ~ (tb2t(v2) = v0)) 207.24/128.02 (32) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.24/128.02 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 207.24/128.02 ($lesseq(1, $difference(v3, v6))) | ~ ($lesseq(v2, v6)) | ~ 207.24/128.02 (map_eq_sub1(int, v4, v5, v2, v3) = 0) | ~ (t2tb(v1) = v5) | ~ 207.24/128.02 (t2tb(v0) = v4) | ~ (get3(v1, v6) = v7) | ~ in_map_int_int(v0) | 207.24/128.02 get3(v0, v6) = v7) 207.24/128.02 (33) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 207.24/128.02 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 207.24/128.02 (34) map_eq_sub1(int, all_105_3, all_105_1, $sum(all_86_10, 1), all_86_13) = 207.24/128.02 0 207.24/128.02 (35) permut2(int, all_103_3, all_105_3, 0, all_86_13) = 0 207.24/128.02 (36) t2tb(all_86_4) = all_105_3 207.24/128.04 207.24/128.04 Begin of proof 207.24/128.04 | 207.24/128.04 | BETA: splitting (27) gives: 207.24/128.04 | 207.24/128.04 | Case 1: 207.24/128.04 | | 207.24/128.04 | | (37) all_769_0 = all_769_1 & $lesseq(1, $difference(all_769_1, 207.24/128.04 | | all_86_10)) & $lesseq(all_86_11, all_769_1) & $lesseq(-1, 207.24/128.04 | | all_86_10) & $lesseq(0, all_86_11) & length1(int, all_105_4) = 207.24/128.04 | | all_769_1 & length1(int, all_103_4) = all_769_1 207.24/128.04 | | 207.24/128.04 | | ALPHA: (37) implies: 207.24/128.04 | | (38) $lesseq(0, all_86_11) 207.24/128.04 | | (39) $lesseq(1, $difference(all_769_1, all_86_10)) 207.24/128.04 | | (40) length1(int, all_103_4) = all_769_1 207.24/128.04 | | 207.24/128.04 | | GROUND_INST: instantiating (31) with all_86_2, all_758_1, all_105_1, 207.24/128.04 | | simplifying with (19), (20) gives: 207.24/128.04 | | (41) all_758_1 = all_86_2 207.24/128.04 | | 207.24/128.04 | | GROUND_INST: instantiating (33) with all_86_13, all_769_1, all_103_4, int, 207.24/128.04 | | simplifying with (6), (40) gives: 207.24/128.04 | | (42) all_769_1 = all_86_13 207.24/128.04 | | 207.24/128.04 | | REDUCE: (39), (42) imply: 207.24/128.04 | | (43) $lesseq(1, $difference(all_86_13, all_86_10)) 207.24/128.04 | | 207.24/128.04 | | COMBINE_INEQS: (13), (16) imply: 207.24/128.04 | | (44) $lesseq(2, $difference(all_86_7, all_86_8)) 207.24/128.04 | | 207.24/128.04 | | COMBINE_INEQS: (24), (44) imply: 207.24/128.04 | | (45) $lesseq(2, $difference(all_86_10, all_86_8)) 207.24/128.04 | | 207.24/128.04 | | COMBINE_INEQS: (23), (45) imply: 207.24/128.04 | | (46) $lesseq(2, $difference(all_86_10, all_86_11)) 207.24/128.04 | | 207.24/128.04 | | COMBINE_INEQS: (43), (46) imply: 207.24/128.04 | | (47) $lesseq(3, $difference(all_86_13, all_86_11)) 207.24/128.04 | | 207.24/128.04 | | COMBINE_INEQS: (38), (47) imply: 207.24/128.04 | | (48) $lesseq(3, all_86_13) 207.24/128.04 | | 207.24/128.04 | | REDUCE: (1), (41) imply: 207.24/128.04 | | (49) get3(all_86_2, all_133_2) = all_133_0 207.24/128.04 | | 207.24/128.04 | | GROUND_INST: instantiating (32) with all_86_4, all_86_2, 0, all_86_7, 207.24/128.04 | | all_105_3, all_105_1, all_133_2, all_133_0, simplifying with 207.24/128.04 | | (4), (17), (30), (36), (49) gives: 207.24/128.04 | | (50) ~ ($lesseq(1, $difference(all_86_7, all_133_2))) | ~ ($lesseq(0, 207.24/128.04 | | all_133_2)) | get3(all_86_4, all_133_2) = all_133_0 207.24/128.04 | | 207.24/128.04 | | GROUND_INST: instantiating (29) with int, all_105_3, all_105_1, 207.24/128.04 | | $sum(all_86_10, 1), all_86_13, all_133_0, all_133_1, 207.24/128.04 | | simplifying with (5), (21), (34) gives: 207.24/128.04 | | (51) ~ ($lesseq(1, $difference(all_86_13, all_133_0))) | ~ ($lesseq(1, 207.24/128.04 | | $difference(all_133_0, all_86_10))) | ? [v0: $int] : (get(int, 207.24/128.04 | | int, all_105_1, all_133_1) = v0 & get(int, int, all_105_3, 207.24/128.04 | | all_133_1) = v0 & in_uni(v0)) 207.24/128.04 | | 207.24/128.04 | | GROUND_INST: instantiating (29) with int, all_103_3, all_103_1, 207.24/128.04 | | $sum(all_86_10, 1), all_86_13, all_133_0, all_133_1, 207.24/128.04 | | simplifying with (5), (10), (21) gives: 207.24/128.04 | | (52) ~ ($lesseq(1, $difference(all_86_13, all_133_0))) | ~ ($lesseq(1, 207.24/128.04 | | $difference(all_133_0, all_86_10))) | ? [v0: $int] : (get(int, 207.24/128.04 | | int, all_103_1, all_133_1) = v0 & get(int, int, all_103_3, 207.24/128.04 | | all_133_1) = v0 & in_uni(v0)) 207.24/128.04 | | 207.24/128.04 | | GROUND_INST: instantiating (29) with int, all_103_3, all_103_1, 0, 207.24/128.04 | | all_86_11, all_133_0, all_133_1, simplifying with (5), (21), 207.24/128.04 | | (22) gives: 207.24/128.04 | | (53) ~ ($lesseq(1, $difference(all_86_11, all_133_0))) | ~ ($lesseq(0, 207.24/128.04 | | all_133_0)) | ? [v0: $int] : (get(int, int, all_103_1, 207.24/128.04 | | all_133_1) = v0 & get(int, int, all_103_3, all_133_1) = v0 & 207.24/128.04 | | in_uni(v0)) 207.24/128.04 | | 207.24/128.04 | | GROUND_INST: instantiating (29) with int, all_105_3, all_105_1, 0, all_86_7, 207.24/128.04 | | all_133_2, all_771_0, simplifying with (5), (11), (17) gives: 207.24/128.04 | | (54) ~ ($lesseq(1, $difference(all_86_7, all_133_2))) | ~ ($lesseq(0, 207.24/128.04 | | all_133_2)) | ? [v0: $int] : (get(int, int, all_105_1, 207.24/128.04 | | all_771_0) = v0 & get(int, int, all_105_3, all_771_0) = v0 & 207.24/128.04 | | in_uni(v0)) 207.24/128.04 | | 207.24/128.04 | | GROUND_INST: instantiating (29) with int, all_103_1, all_105_3, 207.24/128.04 | | $sum(all_86_8, 1), all_86_13, all_133_2, all_771_0, simplifying 207.24/128.04 | | with (5), (11), (14) gives: 207.24/128.04 | | (55) ~ ($lesseq(1, $difference(all_86_13, all_133_2))) | ~ ($lesseq(1, 207.24/128.04 | | $difference(all_133_2, all_86_8))) | ? [v0: $int] : (get(int, 207.24/128.04 | | int, all_105_3, all_771_0) = v0 & get(int, int, all_103_1, 207.24/128.04 | | all_771_0) = v0 & in_uni(v0)) 207.24/128.04 | | 207.24/128.04 | | BETA: splitting (54) gives: 207.24/128.04 | | 207.24/128.04 | | Case 1: 207.24/128.04 | | | 207.24/128.04 | | | (56) $lesseq(all_133_2, -1) 207.24/128.04 | | | 207.24/128.04 | | | COMBINE_INEQS: (13), (56) imply: 207.24/128.04 | | | (57) $lesseq(all_86_8, -2) 207.24/128.04 | | | 207.24/128.04 | | | COMBINE_INEQS: (7), (57) imply: 207.24/128.04 | | | (58) $lesseq(0, -1) 207.24/128.04 | | | 207.24/128.04 | | | CLOSE: (58) is inconsistent. 207.24/128.04 | | | 207.24/128.04 | | Case 2: 207.24/128.04 | | | 207.24/128.04 | | | (59) $lesseq(0, all_133_2) 207.24/128.04 | | | 207.24/128.04 | | | BETA: splitting (50) gives: 207.24/128.04 | | | 207.24/128.04 | | | Case 1: 207.24/128.04 | | | | 207.24/128.04 | | | | (60) get3(all_86_4, all_133_2) = all_133_0 207.24/128.04 | | | | 207.24/128.04 | | | | BETA: splitting (55) gives: 207.24/128.04 | | | | 207.24/128.04 | | | | Case 1: 207.24/128.04 | | | | | 207.24/128.04 | | | | | (61) $lesseq(all_86_13, all_133_2) 207.24/128.04 | | | | | 207.24/128.04 | | | | | COMBINE_INEQS: (16), (61) imply: 207.24/128.04 | | | | | (62) $lesseq(1, $difference(all_86_7, all_86_13)) 207.24/128.04 | | | | | 207.24/128.04 | | | | | COMBINE_INEQS: (8), (62) imply: 207.24/128.04 | | | | | (63) $lesseq(0, -1) 207.24/128.04 | | | | | 207.24/128.04 | | | | | CLOSE: (63) is inconsistent. 207.24/128.04 | | | | | 207.24/128.04 | | | | Case 2: 207.24/128.04 | | | | | 207.24/128.04 | | | | | (64) $lesseq(1, $difference(all_86_13, all_133_2)) 207.24/128.04 | | | | | 207.24/128.04 | | | | | REF_CLOSE: (2), (3), (9), (12), (13), (14), (16), (25), (26), (28), 207.24/128.04 | | | | | (32), (35), (36), (48), (51), (52), (53), (59), (60), (64) 207.24/128.04 | | | | | are inconsistent by sub-proof #124. 207.24/128.04 | | | | | 207.24/128.04 | | | | End of split 207.24/128.04 | | | | 207.24/128.04 | | | Case 2: 207.24/128.04 | | | | 207.24/128.04 | | | | (65) ~ ($lesseq(1, $difference(all_86_7, all_133_2))) | ~ 207.24/128.04 | | | | ($lesseq(0, all_133_2)) 207.24/128.04 | | | | 207.24/128.04 | | | | REF_CLOSE: (16), (59), (65) are inconsistent by sub-proof #151. 207.24/128.04 | | | | 207.24/128.04 | | | End of split 207.24/128.04 | | | 207.24/128.04 | | End of split 207.24/128.04 | | 207.24/128.04 | Case 2: 207.24/128.04 | | 207.24/128.04 | | (66) ~ (all_769_1 = 0) & permut3(int, all_103_4, all_105_4, all_86_11, 207.24/128.04 | | $sum(all_86_10, 1)) = all_769_1 207.24/128.04 | | 207.24/128.04 | | ALPHA: (66) implies: 207.24/128.04 | | (67) ~ (all_769_1 = 0) 207.24/128.04 | | (68) permut3(int, all_103_4, all_105_4, all_86_11, $sum(all_86_10, 1)) = 207.24/128.04 | | all_769_1 207.24/128.04 | | 207.24/128.04 | | REF_CLOSE: (15), (18), (67), (68) are inconsistent by sub-proof #97. 207.24/128.04 | | 207.24/128.04 | End of split 207.24/128.04 | 207.24/128.04 End of proof 207.24/128.04 207.24/128.04 Sub-proof #97 shows that the following formulas are inconsistent: 207.24/128.04 ---------------------------------------------------------------- 207.24/128.04 (1) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.24/128.04 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ (permut3(v6, v5, 207.24/128.04 v4, v3, v2) = v1) | ~ (permut3(v6, v5, v4, v3, v2) = v0)) 207.24/128.04 (2) permut3(int, all_103_4, all_105_4, all_86_11, $sum(all_86_10, 1)) = 207.24/128.04 all_769_1 207.24/128.04 (3) permut3(int, all_103_4, all_105_4, all_86_11, $sum(all_86_10, 1)) = 0 207.24/128.04 (4) ~ (all_769_1 = 0) 207.24/128.04 207.24/128.04 Begin of proof 207.24/128.04 | 207.24/128.04 | GROUND_INST: instantiating (1) with all_769_1, 0, $sum(all_86_10, 1), 207.24/128.04 | all_86_11, all_105_4, all_103_4, int, simplifying with (2), (3) 207.24/128.04 | gives: 207.24/128.04 | (5) all_769_1 = 0 207.24/128.04 | 207.24/128.04 | REDUCE: (4), (5) imply: 207.24/128.04 | (6) ~ (0 = 0) 207.24/128.04 | 207.24/128.04 | CLOSE: (6) is inconsistent. 207.24/128.04 | 207.24/128.04 End of proof 207.24/128.04 207.24/128.04 Sub-proof #98 shows that the following formulas are inconsistent: 207.24/128.04 ---------------------------------------------------------------- 207.24/128.04 (1) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ (tb2t1(v2) 207.24/128.04 = v1) | ~ (tb2t1(v2) = v0)) 207.24/128.04 (2) ! [v0: $int] : ! [v1: $int] : ( ~ ($lesseq(43, v1)) | ~ ($lesseq(v0, 207.24/128.04 all_86_8)) | ~ ($lesseq(all_86_11, v0)) | ~ (get3(all_86_6, v0) = 207.24/128.04 v1)) 207.24/128.04 (3) in_map_int_int(all_86_6) 207.24/128.04 (4) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.24/128.04 $int] : ! [v5: $int] : ! [v6: $int] : ( ~ ($lesseq(0, v4)) | ~ 207.24/128.04 ($lesseq(0, v3)) | ~ (map_eq_sub1(v0, v5, v6, v3, v4) = 0) | ~ 207.24/128.04 (elts(v0, v2) = v6) | ~ (elts(v0, v1) = v5) | ~ in_ty(v0) | ? [v7: 207.24/128.04 $int] : ? [v8: $int] : ((v7 = 0 & array_eq_sub1(v0, v1, v2, v3, v4) 207.24/128.04 = 0) | (length1(v0, v1) = v7 & ( ~ ($lesseq(v4, v7)) | ~ 207.24/128.04 ($lesseq(v3, v7)) | ( ~ (v8 = v7) & length1(v0, v2) = v8))))) 207.24/128.04 (5) length1(int, all_105_2) = all_86_13 207.24/128.04 (6) elts(int, all_103_4) = all_103_3 207.24/128.04 (7) t2tb2(all_86_3) = all_105_4 207.24/128.04 (8) t2tb(all_86_2) = all_105_1 207.24/128.04 (9) in_ty(int) 207.24/128.04 (10) length1(int, all_103_4) = all_86_13 207.24/128.04 (11) $lesseq(2, all_86_13) 207.24/128.04 (12) ( ~ (all_133_0 = 42) & $lesseq(1, $difference(all_86_7, all_133_2)) & 207.24/128.04 $lesseq(1, $difference(all_133_2, all_86_8)) & tb2t1(all_133_1) = 207.24/128.04 all_133_0 & get4(int, all_133_3, all_133_2) = all_133_1 & 207.24/128.04 in_uni(all_133_1)) | ($lesseq(all_133_0, 41) & $lesseq(all_133_2, 207.24/128.04 all_86_10) & $lesseq(all_86_7, all_133_2) & tb2t1(all_133_1) = 207.24/128.04 all_133_0 & get4(int, all_133_3, all_133_2) = all_133_1 & 207.24/128.04 in_uni(all_133_1)) | ($lesseq(43, all_133_0) & $lesseq(all_133_2, 207.24/128.04 all_86_8) & $lesseq(all_86_11, all_133_2) & tb2t1(all_133_1) = 207.24/128.04 all_133_0 & get4(int, all_133_3, all_133_2) = all_133_1 & 207.24/128.04 in_uni(all_133_1)) 207.24/128.04 (13) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.24/128.04 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 207.24/128.04 (permut2(v0, v5, v6, v3, v4) = v7) | ~ (elts(v0, v2) = v6) | ~ 207.24/128.04 (elts(v0, v1) = v5) | ~ in_ty(v0) | ? [v8: $int] : ? [v9: $int] : 207.24/128.04 ((v9 = v8 & v7 = 0 & $lesseq(v4, v8) & $lesseq(v3, v8) & $lesseq(0, 207.24/128.04 v4) & $lesseq(0, v3) & length1(v0, v2) = v8 & length1(v0, v1) = 207.24/128.04 v8) | ( ~ (v8 = 0) & permut3(v0, v1, v2, v3, v4) = v8))) 207.24/128.04 (14) all_125_0 = all_105_4 207.24/128.04 (15) $lesseq(-1, all_86_8) 207.24/128.04 (16) $lesseq(all_86_7, all_86_13) 207.24/128.04 (17) ! [v0: $int] : ! [v1: $int] : (v1 = 42 | ~ ($lesseq(1, 207.24/128.04 $difference(all_86_7, v0))) | ~ ($lesseq(1, $difference(v0, 207.24/128.04 all_86_8))) | ~ (get3(all_86_6, v0) = v1)) 207.24/128.04 (18) map_eq_sub1(int, all_103_3, all_103_1, $sum(all_86_10, 1), all_86_13) = 207.24/128.04 0 207.24/128.04 (19) t2tb(all_86_6) = all_103_1 207.24/128.04 (20) map_eq_sub1(int, all_103_1, all_105_3, $sum(all_86_8, 1), all_86_13) = 0 207.24/128.04 (21) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.24/128.04 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ (permut3(v6, v5, 207.24/128.04 v4, v3, v2) = v1) | ~ (permut3(v6, v5, v4, v3, v2) = v0)) 207.24/128.04 (22) permut2(int, all_103_3, all_105_3, all_86_11, $sum(all_86_10, 1)) = 0 207.24/128.04 (23) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 207.24/128.04 | ~ (elts(v3, v2) = v1) | ~ (elts(v3, v2) = v0)) 207.24/128.04 (24) length1(int, all_105_4) = all_86_13 207.24/128.04 (25) in_array_int(all_86_3) 207.24/128.04 (26) elts(int, all_105_4) = all_105_3 207.24/128.04 (27) map_eq_sub1(int, all_105_3, all_105_1, 0, all_86_7) = 0 207.24/128.04 (28) ~ ($difference(all_86_8, all_86_13) = -1) | ~ (all_86_11 = 0) 207.24/128.04 (29) tb2t(all_105_1) = all_86_2 207.24/128.04 (30) permut2(int, all_103_1, all_105_3, all_86_11, $sum(all_86_8, 1)) = 0 207.24/128.04 (31) elts(int, all_105_2) = all_105_1 207.24/128.04 (32) map_eq_sub1(int, all_103_3, all_103_1, 0, all_86_11) = 0 207.24/128.04 (33) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.24/128.04 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 207.24/128.04 ($lesseq(1, $difference(v4, v5))) | ~ ($lesseq(v3, v5)) | ~ 207.24/128.04 (permut2(v0, v1, v2, v3, v4) = 0) | ~ (t2tb1(v5) = v6) | ~ (get(v0, 207.24/128.04 int, v2, v6) = v7) | ~ in_ty(v0) | ? [v8: $int] : ? [v9: $int] 207.24/128.04 : ($lesseq(1, $difference(v4, v8)) & $lesseq(v3, v8) & t2tb1(v8) = v9 207.24/128.04 & get(v0, int, v1, v9) = v7 & in_uni(v9) & in_uni(v7))) 207.24/128.04 (34) t2tb2(all_86_1) = all_105_2 207.24/128.04 (35) $lesseq(all_86_11, all_86_8) 207.24/128.04 (36) ~ (permut2(int, all_105_3, all_105_1, 0, all_86_13) = 0) | ? [v0: 207.24/128.04 $int] : ((v0 = 0 & permut_all(int, all_105_4, all_105_2) = 0) | ( ~ 207.24/128.04 (v0 = all_86_13) & length1(int, all_105_2) = v0)) 207.24/128.04 (37) $lesseq(all_86_7, all_86_10) 207.24/128.04 (38) permut2(int, all_103_1, all_105_3, all_86_11, $sum(all_86_10, 1)) = 0 207.24/128.04 (39) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.24/128.04 $int] : ! [v5: $int] : ( ~ (elts(v0, v1) = v3) | ~ (t2tb1(v2) = v4) 207.24/128.04 | ~ (get(v0, int, v3, v4) = v5) | ~ in_ty(v0) | (get4(v0, v1, v2) = 207.24/128.04 v5 & in_uni(v5))) 207.24/128.04 (40) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.24/128.04 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 207.24/128.04 ($lesseq(1, $difference(v3, v4))) | ~ ($lesseq(v2, v4)) | ~ 207.24/128.04 (permut2(int, v5, v6, v2, v3) = 0) | ~ (t2tb(v1) = v6) | ~ (t2tb(v0) 207.24/128.04 = v5) | ~ (get3(v1, v4) = v7) | ~ in_map_int_int(v0) | ? [v8: 207.24/128.04 $int] : ($lesseq(1, $difference(v3, v8)) & $lesseq(v2, v8) & 207.24/128.04 get3(v0, v8) = v7)) 207.24/128.04 (41) $lesseq(0, all_86_7) 207.24/128.04 (42) permut2(int, all_105_3, all_105_1, all_86_7, $sum(all_86_10, 1)) = 0 207.24/128.04 (43) in_array_int(all_86_1) 207.24/128.04 (44) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.24/128.04 $int] : ! [v5: $int] : ! [v6: $int] : ( ~ ($lesseq(0, v4)) | ~ 207.24/128.04 ($lesseq(0, v3)) | ~ (permut2(v0, v5, v6, v3, v4) = 0) | ~ (elts(v0, 207.24/128.04 v2) = v6) | ~ (elts(v0, v1) = v5) | ~ in_ty(v0) | ? [v7: $int] 207.24/128.04 : ? [v8: $int] : ((v7 = 0 & permut3(v0, v1, v2, v3, v4) = 0) | 207.24/128.04 (length1(v0, v1) = v7 & ( ~ ($lesseq(v4, v7)) | ~ ($lesseq(v3, v7)) 207.24/128.04 | ( ~ (v8 = v7) & length1(v0, v2) = v8))))) 207.24/128.04 (45) $lesseq(1, $difference(all_86_7, all_86_8)) 207.24/128.04 (46) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.24/128.04 $int] : ! [v5: $int] : ! [v6: $int] : ( ~ ($lesseq(1, 207.24/128.04 $difference(v4, v5))) | ~ ($lesseq(v3, v5)) | ~ (map_eq_sub1(v0, 207.24/128.04 v1, v2, v3, v4) = 0) | ~ (t2tb1(v5) = v6) | ~ in_ty(v0) | ? 207.24/128.04 [v7: $int] : (get(v0, int, v2, v6) = v7 & get(v0, int, v1, v6) = v7 & 207.24/128.04 in_uni(v7))) 207.24/128.04 (47) $lesseq(1, $difference(all_86_13, all_86_10)) 207.24/128.04 (48) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.24/128.04 $int] : ! [v5: $int] : (v5 = 0 | ~ (permut_sub2(v0, v1, v2, v3, v4) 207.24/128.04 = v5) | ~ in_ty(v0) | ? [v6: $int] : ? [v7: $int] : ? [v8: $int] 207.24/128.04 : ? [v9: $int] : (( ~ (v9 = 0) & map_eq_sub1(v0, v6, v7, v4, v8) = v9 207.24/128.04 & length1(v0, v1) = v8 & elts(v0, v2) = v7 & elts(v0, v1) = v6 & 207.24/128.04 in_uni(v7) & in_uni(v6)) | ( ~ (v8 = 0) & map_eq_sub1(v0, v6, v7, 207.24/128.04 0, v3) = v8 & elts(v0, v2) = v7 & elts(v0, v1) = v6 & in_uni(v7) 207.24/128.04 & in_uni(v6)) | ( ~ (v6 = 0) & permut3(v0, v1, v2, v3, v4) = v6))) 207.24/128.04 (49) in_map_int_int(all_86_4) 207.24/128.04 (50) map_eq_sub1(int, all_105_3, all_105_1, 0, all_86_13) = 0 207.24/128.04 (51) $lesseq(0, all_86_11) 207.24/128.04 (52) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ( ~ 207.24/128.04 (t2tb2(v0) = v2) | ~ (get4(int, v2, v1) = v3) | ~ in_array_int(v0) | 207.24/128.04 ? [v4: $int] : ? [v5: $int] : ? [v6: $int] : (tb2t(v4) = v5 & 207.24/128.04 tb2t1(v3) = v6 & get3(v5, v1) = v6 & elts(int, v2) = v4 & 207.24/128.04 in_map_int_int(v5) & in_uni(v4))) 207.24/128.04 (53) ~ (permut2(int, all_103_1, all_105_3, 0, all_86_13) = 0) 207.24/128.04 (54) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ (tb2t(v2) 207.24/128.04 = v1) | ~ (tb2t(v2) = v0)) 207.24/128.04 (55) all_133_3 = all_105_2 207.24/128.04 (56) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.24/128.04 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 207.24/128.04 ($lesseq(1, $difference(v3, v6))) | ~ ($lesseq(v2, v6)) | ~ 207.24/128.04 (map_eq_sub1(int, v4, v5, v2, v3) = 0) | ~ (t2tb(v1) = v5) | ~ 207.24/128.04 (t2tb(v0) = v4) | ~ (get3(v1, v6) = v7) | ~ in_map_int_int(v0) | 207.24/128.04 get3(v0, v6) = v7) 207.24/128.04 (57) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 207.24/128.04 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 207.24/128.04 (58) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ( ~ 207.24/128.04 (get4(v0, v1, v2) = v3) | ~ in_ty(v0) | ? [v4: $int] : ? [v5: $int] 207.24/128.04 : (elts(v0, v1) = v4 & t2tb1(v2) = v5 & get(v0, int, v4, v5) = v3 & 207.24/128.04 in_uni(v5) & in_uni(v4) & in_uni(v3))) 207.24/128.04 (59) $lesseq(0, all_86_10) 207.24/128.04 (60) map_eq_sub1(int, all_103_1, all_105_3, 0, all_86_13) = 0 207.24/128.04 (61) ! [v0: $int] : ! [v1: $int] : ( ~ (tb2t1(v0) = v1) | ~ in_uni(v0) | 207.24/128.04 t2tb1(v1) = v0) 207.24/128.04 (62) map_eq_sub1(int, all_105_3, all_105_1, $sum(all_86_10, 1), all_86_13) = 207.24/128.04 0 207.24/128.04 (63) t2tb(all_86_4) = all_105_3 207.24/128.04 (64) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.24/128.04 $int] : ! [v5: $int] : ( ~ (permut3(v0, v1, v2, v3, v4) = v5) | ~ 207.24/128.04 in_ty(v0) | ? [v6: $int] : ? [v7: $int] : ? [v8: $int] : ? [v9: 207.24/128.04 $int] : ? [v10: $int] : ((v10 = 0 & v9 = 0 & v5 = 0 & 207.24/128.04 map_eq_sub1(v0, v6, v7, v4, v8) = 0 & map_eq_sub1(v0, v6, v7, 0, 207.24/128.04 v3) = 0 & length1(v0, v1) = v8 & elts(v0, v2) = v7 & elts(v0, 207.24/128.04 v1) = v6 & in_uni(v7) & in_uni(v6)) | ( ~ (v6 = 0) & 207.24/128.04 permut_sub2(v0, v1, v2, v3, v4) = v6))) 207.24/128.04 (65) ! [v0: $int] : ! [v1: $int] : ( ~ ($lesseq(v0, all_86_10)) | ~ 207.24/128.04 ($lesseq(all_86_7, v0)) | ~ (get4(int, all_125_0, v0) = v1) | ? [v2: 207.24/128.04 $int] : ($lesseq(42, v2) & tb2t1(v1) = v2)) 207.24/128.04 207.24/128.04 Begin of proof 207.24/128.04 | 207.24/128.04 | PRED_UNIFY: (38), (53) imply: 207.24/128.04 | (66) ~ ($difference(all_86_10, all_86_13) = -1) | ~ (all_86_11 = 0) 207.24/128.04 | 207.24/128.04 | BETA: splitting (36) gives: 207.24/128.04 | 207.24/128.04 | Case 1: 207.24/128.04 | | 207.24/128.04 | | (67) ~ (permut2(int, all_105_3, all_105_1, 0, all_86_13) = 0) 207.24/128.04 | | 207.24/128.04 | | PRED_UNIFY: (42), (67) imply: 207.24/128.04 | | (68) ~ (all_86_7 = 0) | ~ ($difference(all_86_10, all_86_13) = -1) 207.24/128.04 | | 207.24/128.04 | | BETA: splitting (12) gives: 207.24/128.04 | | 207.24/128.04 | | Case 1: 207.24/128.04 | | | 207.24/128.04 | | | (69) ~ (all_133_0 = 42) & $lesseq(1, $difference(all_86_7, all_133_2)) 207.24/128.04 | | | & $lesseq(1, $difference(all_133_2, all_86_8)) & tb2t1(all_133_1) 207.24/128.04 | | | = all_133_0 & get4(int, all_133_3, all_133_2) = all_133_1 & 207.24/128.04 | | | in_uni(all_133_1) 207.24/128.04 | | | 207.24/128.04 | | | ALPHA: (69) implies: 207.24/128.04 | | | (70) ~ (all_133_0 = 42) 207.24/128.04 | | | (71) $lesseq(1, $difference(all_133_2, all_86_8)) 207.24/128.04 | | | (72) $lesseq(1, $difference(all_86_7, all_133_2)) 207.24/128.04 | | | (73) in_uni(all_133_1) 207.24/128.04 | | | (74) get4(int, all_133_3, all_133_2) = all_133_1 207.24/128.04 | | | (75) tb2t1(all_133_1) = all_133_0 207.24/128.04 | | | 207.24/128.04 | | | COMBINE_INEQS: (71), (72) imply: 207.24/128.04 | | | (76) $lesseq(2, $difference(all_86_7, all_86_8)) 207.24/128.04 | | | 207.24/128.04 | | | COMBINE_INEQS: (37), (76) imply: 207.24/128.04 | | | (77) $lesseq(2, $difference(all_86_10, all_86_8)) 207.24/128.04 | | | 207.24/128.04 | | | COMBINE_INEQS: (15), (77) imply: 207.24/128.04 | | | (78) $lesseq(1, all_86_10) 207.24/128.04 | | | 207.24/128.04 | | | REDUCE: (55), (74) imply: 207.24/128.04 | | | (79) get4(int, all_105_2, all_133_2) = all_133_1 207.24/128.04 | | | 207.24/128.04 | | | REF_CLOSE: (1), (3), (4), (6), (8), (9), (10), (13), (15), (16), (17), 207.24/128.04 | | | (18), (19), (20), (21), (22), (23), (24), (26), (27), (29), 207.24/128.04 | | | (31), (32), (34), (35), (37), (43), (44), (46), (47), (48), 207.24/128.04 | | | (49), (51), (52), (54), (56), (57), (58), (60), (61), (62), 207.24/128.04 | | | (63), (64), (66), (70), (71), (72), (73), (75), (78), (79) are 207.24/128.04 | | | inconsistent by sub-proof #102. 207.24/128.04 | | | 207.24/128.04 | | Case 2: 207.24/128.04 | | | 207.24/128.04 | | | (80) ($lesseq(all_133_0, 41) & $lesseq(all_133_2, all_86_10) & 207.24/128.04 | | | $lesseq(all_86_7, all_133_2) & tb2t1(all_133_1) = all_133_0 & 207.24/128.04 | | | get4(int, all_133_3, all_133_2) = all_133_1 & in_uni(all_133_1)) 207.24/128.04 | | | | ($lesseq(43, all_133_0) & $lesseq(all_133_2, all_86_8) & 207.24/128.04 | | | $lesseq(all_86_11, all_133_2) & tb2t1(all_133_1) = all_133_0 & 207.24/128.04 | | | get4(int, all_133_3, all_133_2) = all_133_1 & in_uni(all_133_1)) 207.24/128.04 | | | 207.24/128.04 | | | BETA: splitting (80) gives: 207.24/128.04 | | | 207.24/128.04 | | | Case 1: 207.24/128.04 | | | | 207.24/128.04 | | | | (81) $lesseq(all_133_0, 41) & $lesseq(all_133_2, all_86_10) & 207.24/128.04 | | | | $lesseq(all_86_7, all_133_2) & tb2t1(all_133_1) = all_133_0 & 207.24/128.04 | | | | get4(int, all_133_3, all_133_2) = all_133_1 & in_uni(all_133_1) 207.24/128.04 | | | | 207.24/128.04 | | | | ALPHA: (81) implies: 207.24/128.04 | | | | (82) $lesseq(all_86_7, all_133_2) 207.24/128.04 | | | | (83) $lesseq(all_133_2, all_86_10) 207.24/128.04 | | | | (84) $lesseq(all_133_0, 41) 207.24/128.04 | | | | (85) get4(int, all_133_3, all_133_2) = all_133_1 207.24/128.04 | | | | (86) tb2t1(all_133_1) = all_133_0 207.24/128.04 | | | | 207.24/128.04 | | | | REDUCE: (55), (85) imply: 207.24/128.04 | | | | (87) get4(int, all_105_2, all_133_2) = all_133_1 207.24/128.04 | | | | 207.24/128.04 | | | | REF_CLOSE: (1), (6), (7), (8), (9), (14), (22), (23), (25), (26), (29), 207.24/128.04 | | | | (31), (33), (34), (39), (40), (42), (43), (44), (49), (51), 207.24/128.04 | | | | (52), (54), (58), (59), (63), (65), (82), (83), (84), (86), 207.24/128.04 | | | | (87) are inconsistent by sub-proof #126. 207.24/128.04 | | | | 207.24/128.04 | | | Case 2: 207.24/128.04 | | | | 207.24/128.04 | | | | (88) $lesseq(43, all_133_0) & $lesseq(all_133_2, all_86_8) & 207.24/128.04 | | | | $lesseq(all_86_11, all_133_2) & tb2t1(all_133_1) = all_133_0 & 207.24/128.04 | | | | get4(int, all_133_3, all_133_2) = all_133_1 & in_uni(all_133_1) 207.24/128.04 | | | | 207.24/128.04 | | | | ALPHA: (88) implies: 207.24/128.04 | | | | (89) $lesseq(all_86_11, all_133_2) 207.24/128.04 | | | | (90) $lesseq(all_133_2, all_86_8) 207.24/128.04 | | | | (91) $lesseq(43, all_133_0) 207.24/128.04 | | | | (92) get4(int, all_133_3, all_133_2) = all_133_1 207.24/128.04 | | | | (93) tb2t1(all_133_1) = all_133_0 207.24/128.04 | | | | 207.24/128.04 | | | | REDUCE: (55), (92) imply: 207.24/128.04 | | | | (94) get4(int, all_105_2, all_133_2) = all_133_1 207.24/128.04 | | | | 207.24/128.04 | | | | BETA: splitting (28) gives: 207.24/128.04 | | | | 207.24/128.04 | | | | Case 1: 207.24/128.04 | | | | | 207.24/128.04 | | | | | (95) ~ (all_86_11 = 0) 207.24/128.04 | | | | | 207.24/128.04 | | | | | STRENGTHEN: (51), (95) imply: 207.24/128.04 | | | | | (96) $lesseq(1, all_86_11) 207.24/128.04 | | | | | 207.24/128.04 | | | | | BETA: splitting (68) gives: 207.24/128.04 | | | | | 207.24/128.04 | | | | | Case 1: 207.24/128.04 | | | | | | 207.24/128.04 | | | | | | (97) ~ (all_86_7 = 0) 207.24/128.04 | | | | | | 207.24/128.04 | | | | | | STRENGTHEN: (41), (97) imply: 207.24/128.04 | | | | | | (98) $lesseq(1, all_86_7) 207.24/128.04 | | | | | | 207.24/128.04 | | | | | | COMBINE_INEQS: (37), (98) imply: 207.24/128.04 | | | | | | (99) $lesseq(1, all_86_10) 207.24/128.04 | | | | | | 207.24/128.04 | | | | | | REF_CLOSE: (1), (2), (3), (6), (8), (9), (10), (13), (19), (21), 207.24/128.04 | | | | | | (22), (23), (24), (26), (27), (29), (30), (31), (33), 207.24/128.04 | | | | | | (34), (37), (40), (42), (43), (44), (45), (46), (47), 207.24/128.04 | | | | | | (49), (50), (51), (52), (54), (56), (57), (58), (63), 207.24/128.04 | | | | | | (66), (89), (90), (91), (93), (94), (99) are inconsistent 207.24/128.04 | | | | | | by sub-proof #109. 207.24/128.04 | | | | | | 207.24/128.04 | | | | | Case 2: 207.24/128.04 | | | | | | 207.24/128.04 | | | | | | (100) all_86_7 = 0 207.24/128.04 | | | | | | 207.24/128.04 | | | | | | REDUCE: (45), (100) imply: 207.24/128.04 | | | | | | (101) $lesseq(all_86_8, -1) 207.24/128.04 | | | | | | 207.24/128.04 | | | | | | COMBINE_INEQS: (35), (101) imply: 207.24/128.04 | | | | | | (102) $lesseq(all_86_11, -1) 207.24/128.04 | | | | | | 207.24/128.04 | | | | | | COMBINE_INEQS: (96), (102) imply: 207.24/128.04 | | | | | | (103) $lesseq(0, -1) 207.24/128.04 | | | | | | 207.24/128.04 | | | | | | CLOSE: (103) is inconsistent. 207.24/128.04 | | | | | | 207.24/128.04 | | | | | End of split 207.24/128.04 | | | | | 207.24/128.04 | | | | Case 2: 207.24/128.04 | | | | | 207.24/128.04 | | | | | (104) all_86_11 = 0 207.24/128.04 | | | | | 207.24/128.04 | | | | | REDUCE: (89), (104) imply: 207.24/128.04 | | | | | (105) $lesseq(0, all_133_2) 207.24/128.04 | | | | | 207.24/128.04 | | | | | COMBINE_INEQS: (90), (105) imply: 207.24/128.04 | | | | | (106) $lesseq(0, all_86_8) 207.24/128.04 | | | | | 207.24/128.04 | | | | | COMBINE_INEQS: (37), (45) imply: 207.24/128.04 | | | | | (107) $lesseq(1, $difference(all_86_10, all_86_8)) 207.24/128.04 | | | | | 207.24/128.04 | | | | | COMBINE_INEQS: (106), (107) imply: 207.24/128.04 | | | | | (108) $lesseq(1, all_86_10) 207.24/128.04 | | | | | 207.24/128.04 | | | | | REF_CLOSE: (1), (2), (3), (6), (8), (9), (10), (13), (19), (21), (22), 207.24/128.04 | | | | | (23), (24), (26), (27), (29), (30), (31), (33), (34), (37), 207.24/128.04 | | | | | (40), (42), (43), (44), (45), (46), (47), (49), (50), (51), 207.24/128.04 | | | | | (52), (54), (56), (57), (58), (63), (66), (89), (90), (91), 207.24/128.04 | | | | | (93), (94), (108) are inconsistent by sub-proof #109. 207.24/128.04 | | | | | 207.24/128.04 | | | | End of split 207.24/128.04 | | | | 207.24/128.04 | | | End of split 207.24/128.04 | | | 207.24/128.04 | | End of split 207.24/128.04 | | 207.24/128.04 | Case 2: 207.24/128.04 | | 207.24/128.04 | | (109) permut2(int, all_105_3, all_105_1, 0, all_86_13) = 0 207.24/128.04 | | 207.24/128.04 | | BETA: splitting (12) gives: 207.24/128.04 | | 207.24/128.04 | | Case 1: 207.24/128.04 | | | 207.24/128.04 | | | (110) ~ (all_133_0 = 42) & $lesseq(1, $difference(all_86_7, 207.24/128.04 | | | all_133_2)) & $lesseq(1, $difference(all_133_2, all_86_8)) & 207.24/128.04 | | | tb2t1(all_133_1) = all_133_0 & get4(int, all_133_3, all_133_2) = 207.24/128.04 | | | all_133_1 & in_uni(all_133_1) 207.24/128.04 | | | 207.24/128.04 | | | ALPHA: (110) implies: 207.24/128.04 | | | (111) ~ (all_133_0 = 42) 207.24/128.04 | | | (112) $lesseq(1, $difference(all_133_2, all_86_8)) 207.24/128.04 | | | (113) $lesseq(1, $difference(all_86_7, all_133_2)) 207.24/128.04 | | | (114) in_uni(all_133_1) 207.24/128.04 | | | (115) get4(int, all_133_3, all_133_2) = all_133_1 207.24/128.04 | | | (116) tb2t1(all_133_1) = all_133_0 207.24/128.04 | | | 207.24/128.04 | | | COMBINE_INEQS: (112), (113) imply: 207.24/128.04 | | | (117) $lesseq(2, $difference(all_86_7, all_86_8)) 207.24/128.04 | | | 207.24/128.04 | | | COMBINE_INEQS: (37), (117) imply: 207.24/128.04 | | | (118) $lesseq(2, $difference(all_86_10, all_86_8)) 207.24/128.04 | | | 207.24/128.04 | | | COMBINE_INEQS: (15), (118) imply: 207.24/128.04 | | | (119) $lesseq(1, all_86_10) 207.24/128.04 | | | 207.24/128.04 | | | REDUCE: (55), (115) imply: 207.24/128.04 | | | (120) get4(int, all_105_2, all_133_2) = all_133_1 207.24/128.04 | | | 207.24/128.04 | | | REF_CLOSE: (1), (3), (4), (6), (8), (9), (10), (13), (15), (16), (17), 207.24/128.04 | | | (18), (19), (20), (21), (22), (23), (24), (26), (27), (29), 207.24/128.04 | | | (31), (32), (34), (35), (37), (43), (44), (46), (47), (48), 207.24/128.04 | | | (49), (51), (52), (54), (56), (57), (58), (60), (61), (62), 207.24/128.04 | | | (63), (64), (66), (111), (112), (113), (114), (116), (119), 207.24/128.04 | | | (120) are inconsistent by sub-proof #102. 207.24/128.04 | | | 207.24/128.04 | | Case 2: 207.24/128.04 | | | 207.24/128.04 | | | (121) ($lesseq(all_133_0, 41) & $lesseq(all_133_2, all_86_10) & 207.24/128.04 | | | $lesseq(all_86_7, all_133_2) & tb2t1(all_133_1) = all_133_0 & 207.24/128.04 | | | get4(int, all_133_3, all_133_2) = all_133_1 & 207.24/128.04 | | | in_uni(all_133_1)) | ($lesseq(43, all_133_0) & 207.24/128.04 | | | $lesseq(all_133_2, all_86_8) & $lesseq(all_86_11, all_133_2) & 207.24/128.04 | | | tb2t1(all_133_1) = all_133_0 & get4(int, all_133_3, all_133_2) 207.24/128.04 | | | = all_133_1 & in_uni(all_133_1)) 207.24/128.04 | | | 207.24/128.04 | | | BETA: splitting (121) gives: 207.24/128.04 | | | 207.24/128.04 | | | Case 1: 207.24/128.04 | | | | 207.24/128.04 | | | | (122) $lesseq(all_133_0, 41) & $lesseq(all_133_2, all_86_10) & 207.24/128.04 | | | | $lesseq(all_86_7, all_133_2) & tb2t1(all_133_1) = all_133_0 & 207.24/128.04 | | | | get4(int, all_133_3, all_133_2) = all_133_1 & in_uni(all_133_1) 207.24/128.04 | | | | 207.24/128.04 | | | | ALPHA: (122) implies: 207.24/128.04 | | | | (123) $lesseq(all_86_7, all_133_2) 207.24/128.04 | | | | (124) $lesseq(all_133_2, all_86_10) 207.24/128.04 | | | | (125) $lesseq(all_133_0, 41) 207.24/128.04 | | | | (126) get4(int, all_133_3, all_133_2) = all_133_1 207.24/128.04 | | | | (127) tb2t1(all_133_1) = all_133_0 207.24/128.04 | | | | 207.24/128.04 | | | | REDUCE: (55), (126) imply: 207.24/128.04 | | | | (128) get4(int, all_105_2, all_133_2) = all_133_1 207.24/128.04 | | | | 207.24/128.04 | | | | REF_CLOSE: (1), (6), (7), (8), (9), (14), (22), (23), (25), (26), (29), 207.24/128.04 | | | | (31), (33), (34), (39), (40), (42), (43), (44), (49), (51), 207.24/128.04 | | | | (52), (54), (58), (59), (63), (65), (123), (124), (125), 207.24/128.04 | | | | (127), (128) are inconsistent by sub-proof #126. 207.24/128.04 | | | | 207.24/128.04 | | | Case 2: 207.24/128.04 | | | | 207.24/128.04 | | | | (129) $lesseq(43, all_133_0) & $lesseq(all_133_2, all_86_8) & 207.24/128.04 | | | | $lesseq(all_86_11, all_133_2) & tb2t1(all_133_1) = all_133_0 & 207.24/128.04 | | | | get4(int, all_133_3, all_133_2) = all_133_1 & in_uni(all_133_1) 207.24/128.04 | | | | 207.24/128.04 | | | | ALPHA: (129) implies: 207.24/128.04 | | | | (130) $lesseq(all_86_11, all_133_2) 207.24/128.04 | | | | (131) $lesseq(all_133_2, all_86_8) 207.24/128.04 | | | | (132) $lesseq(43, all_133_0) 207.24/128.04 | | | | (133) get4(int, all_133_3, all_133_2) = all_133_1 207.24/128.04 | | | | (134) tb2t1(all_133_1) = all_133_0 207.24/128.04 | | | | 207.24/128.04 | | | | REDUCE: (55), (133) imply: 207.24/128.04 | | | | (135) get4(int, all_105_2, all_133_2) = all_133_1 207.24/128.04 | | | | 207.24/128.04 | | | | GROUND_INST: instantiating (13) with int, all_105_4, all_105_2, 0, 207.24/128.04 | | | | all_86_13, all_105_3, all_105_1, 0, simplifying with (9), 207.24/128.04 | | | | (26), (31), (109) gives: 207.45/128.05 | | | | (136) ? [v0: $int] : ? [v1: $int] : ((v1 = v0 & $lesseq(all_86_13, 207.45/128.05 | | | | v0) & $lesseq(0, v0) & $lesseq(0, all_86_13) & 207.45/128.05 | | | | length1(int, all_105_2) = v0 & length1(int, all_105_4) = 207.45/128.05 | | | | v0) | ( ~ (v0 = 0) & permut3(int, all_105_4, all_105_2, 0, 207.45/128.05 | | | | all_86_13) = v0)) 207.45/128.05 | | | | 207.45/128.05 | | | | GROUND_INST: instantiating (44) with int, all_105_4, all_105_2, 0, 207.45/128.05 | | | | all_86_13, all_105_3, all_105_1, simplifying with (9), 207.45/128.05 | | | | (26), (31), (109) gives: 207.45/128.05 | | | | (137) ~ ($lesseq(0, all_86_13)) | ? [v0: $int] : ? [v1: $int] : 207.45/128.05 | | | | ((v0 = 0 & permut3(int, all_105_4, all_105_2, 0, all_86_13) = 207.45/128.05 | | | | 0) | (length1(int, all_105_4) = v0 & ( ~ 207.45/128.05 | | | | ($lesseq(all_86_13, v0)) | ~ ($lesseq(0, v0)) | ( ~ (v1 207.45/128.05 | | | | = v0) & length1(int, all_105_2) = v1)))) 207.45/128.05 | | | | 207.45/128.05 | | | | GROUND_INST: instantiating (13) with int, all_103_4, all_105_4, 207.45/128.05 | | | | all_86_11, $sum(all_86_10, 1), all_103_3, all_105_3, 0, 207.45/128.05 | | | | simplifying with (6), (9), (22), (26) gives: 207.45/128.05 | | | | (138) ? [v0: $int] : ? [v1: $int] : ((v1 = v0 & $lesseq(1, 207.45/128.05 | | | | $difference(v0, all_86_10)) & $lesseq(all_86_11, v0) & 207.45/128.05 | | | | $lesseq(-1, all_86_10) & $lesseq(0, all_86_11) & 207.45/128.05 | | | | length1(int, all_105_4) = v0 & length1(int, all_103_4) = 207.45/128.05 | | | | v0) | ( ~ (v0 = 0) & permut3(int, all_103_4, all_105_4, 207.45/128.05 | | | | all_86_11, $sum(all_86_10, 1)) = v0)) 207.45/128.05 | | | | 207.45/128.05 | | | | GROUND_INST: instantiating (44) with int, all_103_4, all_105_4, 207.45/128.05 | | | | all_86_11, $sum(all_86_10, 1), all_103_3, all_105_3, 207.45/128.05 | | | | simplifying with (6), (9), (22), (26) gives: 207.45/128.05 | | | | (139) ~ ($lesseq(-1, all_86_10)) | ~ ($lesseq(0, all_86_11)) | ? 207.45/128.05 | | | | [v0: $int] : ? [v1: $int] : ((v0 = 0 & permut3(int, all_103_4, 207.45/128.05 | | | | all_105_4, all_86_11, $sum(all_86_10, 1)) = 0) | 207.45/128.05 | | | | (length1(int, all_103_4) = v0 & ( ~ ($lesseq(1, 207.45/128.05 | | | | $difference(v0, all_86_10))) | ~ ($lesseq(all_86_11, 207.45/128.05 | | | | v0)) | ( ~ (v1 = v0) & length1(int, all_105_4) = 207.45/128.05 | | | | v1)))) 207.45/128.05 | | | | 207.45/128.05 | | | | GROUND_INST: instantiating (52) with all_86_1, all_133_2, all_105_2, 207.45/128.05 | | | | all_133_1, simplifying with (34), (43), (135) gives: 207.45/128.05 | | | | (140) ? [v0: $int] : ? [v1: $int] : ? [v2: $int] : (tb2t(v0) = v1 207.45/128.05 | | | | & tb2t1(all_133_1) = v2 & get3(v1, all_133_2) = v2 & 207.45/128.05 | | | | elts(int, all_105_2) = v0 & in_map_int_int(v1) & in_uni(v0)) 207.45/128.05 | | | | 207.45/128.05 | | | | GROUND_INST: instantiating (58) with int, all_105_2, all_133_2, 207.45/128.05 | | | | all_133_1, simplifying with (9), (135) gives: 207.45/128.05 | | | | (141) ? [v0: $int] : ? [v1: $int] : (elts(int, all_105_2) = v0 & 207.45/128.05 | | | | t2tb1(all_133_2) = v1 & get(int, int, v0, v1) = all_133_1 & 207.45/128.05 | | | | in_uni(v1) & in_uni(v0) & in_uni(all_133_1)) 207.45/128.05 | | | | 207.45/128.05 | | | | DELTA: instantiating (140) with fresh symbols all_739_0, all_739_1, 207.45/128.05 | | | | all_739_2 gives: 207.45/128.05 | | | | (142) tb2t(all_739_2) = all_739_1 & tb2t1(all_133_1) = all_739_0 & 207.45/128.05 | | | | get3(all_739_1, all_133_2) = all_739_0 & elts(int, all_105_2) = 207.45/128.05 | | | | all_739_2 & in_map_int_int(all_739_1) & in_uni(all_739_2) 207.45/128.05 | | | | 207.45/128.05 | | | | ALPHA: (142) implies: 207.45/128.05 | | | | (143) elts(int, all_105_2) = all_739_2 207.45/128.05 | | | | (144) get3(all_739_1, all_133_2) = all_739_0 207.45/128.05 | | | | (145) tb2t1(all_133_1) = all_739_0 207.45/128.05 | | | | (146) tb2t(all_739_2) = all_739_1 207.45/128.05 | | | | 207.45/128.05 | | | | DELTA: instantiating (141) with fresh symbols all_753_0, all_753_1 207.45/128.05 | | | | gives: 207.45/128.05 | | | | (147) elts(int, all_105_2) = all_753_1 & t2tb1(all_133_2) = all_753_0 207.45/128.05 | | | | & get(int, int, all_753_1, all_753_0) = all_133_1 & 207.45/128.05 | | | | in_uni(all_753_0) & in_uni(all_753_1) & in_uni(all_133_1) 207.45/128.05 | | | | 207.45/128.05 | | | | ALPHA: (147) implies: 207.45/128.05 | | | | (148) get(int, int, all_753_1, all_753_0) = all_133_1 207.45/128.05 | | | | (149) t2tb1(all_133_2) = all_753_0 207.45/128.05 | | | | (150) elts(int, all_105_2) = all_753_1 207.45/128.05 | | | | 207.45/128.05 | | | | DELTA: instantiating (138) with fresh symbols all_759_0, all_759_1 207.45/128.05 | | | | gives: 207.45/128.05 | | | | (151) (all_759_0 = all_759_1 & $lesseq(1, $difference(all_759_1, 207.45/128.05 | | | | all_86_10)) & $lesseq(all_86_11, all_759_1) & $lesseq(-1, 207.45/128.05 | | | | all_86_10) & $lesseq(0, all_86_11) & length1(int, 207.45/128.05 | | | | all_105_4) = all_759_1 & length1(int, all_103_4) = 207.45/128.05 | | | | all_759_1) | ( ~ (all_759_1 = 0) & permut3(int, all_103_4, 207.45/128.05 | | | | all_105_4, all_86_11, $sum(all_86_10, 1)) = all_759_1) 207.45/128.05 | | | | 207.45/128.05 | | | | DELTA: instantiating (136) with fresh symbols all_760_0, all_760_1 207.45/128.05 | | | | gives: 207.45/128.05 | | | | (152) (all_760_0 = all_760_1 & $lesseq(all_86_13, all_760_1) & 207.45/128.05 | | | | $lesseq(0, all_760_1) & $lesseq(0, all_86_13) & length1(int, 207.45/128.05 | | | | all_105_2) = all_760_1 & length1(int, all_105_4) = 207.45/128.05 | | | | all_760_1) | ( ~ (all_760_1 = 0) & permut3(int, all_105_4, 207.45/128.05 | | | | all_105_2, 0, all_86_13) = all_760_1) 207.45/128.05 | | | | 207.45/128.05 | | | | BETA: splitting (137) gives: 207.45/128.05 | | | | 207.45/128.05 | | | | Case 1: 207.45/128.05 | | | | | 207.45/128.05 | | | | | (153) $lesseq(all_86_13, -1) 207.45/128.05 | | | | | 207.45/128.05 | | | | | COMBINE_INEQS: (11), (153) imply: 207.45/128.05 | | | | | (154) $lesseq(0, -1) 207.45/128.05 | | | | | 207.45/128.05 | | | | | CLOSE: (154) is inconsistent. 207.45/128.05 | | | | | 207.45/128.05 | | | | Case 2: 207.45/128.05 | | | | | 207.45/128.05 | | | | | (155) ? [v0: $int] : ? [v1: $int] : ((v0 = 0 & permut3(int, 207.45/128.05 | | | | | all_105_4, all_105_2, 0, all_86_13) = 0) | 207.45/128.05 | | | | | (length1(int, all_105_4) = v0 & ( ~ ($lesseq(all_86_13, 207.45/128.05 | | | | | v0)) | ~ ($lesseq(0, v0)) | ( ~ (v1 = v0) & 207.45/128.05 | | | | | length1(int, all_105_2) = v1)))) 207.45/128.05 | | | | | 207.45/128.05 | | | | | DELTA: instantiating (155) with fresh symbols all_766_0, all_766_1 207.45/128.05 | | | | | gives: 207.45/128.05 | | | | | (156) (all_766_1 = 0 & permut3(int, all_105_4, all_105_2, 0, 207.45/128.05 | | | | | all_86_13) = 0) | (length1(int, all_105_4) = all_766_1 & 207.45/128.05 | | | | | ( ~ ($lesseq(all_86_13, all_766_1)) | ~ ($lesseq(0, 207.45/128.05 | | | | | all_766_1)) | ( ~ (all_766_0 = all_766_1) & 207.45/128.05 | | | | | length1(int, all_105_2) = all_766_0))) 207.45/128.05 | | | | | 207.45/128.05 | | | | | BETA: splitting (139) gives: 207.45/128.05 | | | | | 207.45/128.05 | | | | | Case 1: 207.45/128.05 | | | | | | 207.45/128.05 | | | | | | (157) $lesseq(all_86_11, -1) 207.45/128.05 | | | | | | 207.45/128.05 | | | | | | COMBINE_INEQS: (51), (157) imply: 207.45/128.05 | | | | | | (158) $lesseq(0, -1) 207.45/128.05 | | | | | | 207.45/128.05 | | | | | | CLOSE: (158) is inconsistent. 207.45/128.05 | | | | | | 207.45/128.05 | | | | | Case 2: 207.45/128.05 | | | | | | 207.45/128.05 | | | | | | (159) ~ ($lesseq(-1, all_86_10)) | ? [v0: $int] : ? [v1: $int] 207.45/128.05 | | | | | | : ((v0 = 0 & permut3(int, all_103_4, all_105_4, all_86_11, 207.45/128.05 | | | | | | $sum(all_86_10, 1)) = 0) | (length1(int, all_103_4) = 207.45/128.05 | | | | | | v0 & ( ~ ($lesseq(1, $difference(v0, all_86_10))) | ~ 207.45/128.05 | | | | | | ($lesseq(all_86_11, v0)) | ( ~ (v1 = v0) & 207.45/128.05 | | | | | | length1(int, all_105_4) = v1)))) 207.45/128.05 | | | | | | 207.45/128.05 | | | | | | BETA: splitting (159) gives: 207.45/128.05 | | | | | | 207.45/128.05 | | | | | | Case 1: 207.45/128.05 | | | | | | | 207.45/128.05 | | | | | | | (160) $lesseq(all_86_10, -2) 207.45/128.05 | | | | | | | 207.45/128.05 | | | | | | | COMBINE_INEQS: (59), (160) imply: 207.45/128.05 | | | | | | | (161) $lesseq(0, -1) 207.45/128.05 | | | | | | | 207.45/128.05 | | | | | | | CLOSE: (161) is inconsistent. 207.45/128.05 | | | | | | | 207.45/128.05 | | | | | | Case 2: 207.45/128.05 | | | | | | | 207.45/128.05 | | | | | | | (162) ? [v0: $int] : ? [v1: $int] : ((v0 = 0 & permut3(int, 207.45/128.05 | | | | | | | all_103_4, all_105_4, all_86_11, $sum(all_86_10, 207.45/128.05 | | | | | | | 1)) = 0) | (length1(int, all_103_4) = v0 & ( ~ 207.45/128.05 | | | | | | | ($lesseq(1, $difference(v0, all_86_10))) | ~ 207.45/128.05 | | | | | | | ($lesseq(all_86_11, v0)) | ( ~ (v1 = v0) & 207.45/128.05 | | | | | | | length1(int, all_105_4) = v1)))) 207.45/128.05 | | | | | | | 207.45/128.05 | | | | | | | DELTA: instantiating (162) with fresh symbols all_777_0, all_777_1 207.45/128.05 | | | | | | | gives: 207.45/128.05 | | | | | | | (163) (all_777_1 = 0 & permut3(int, all_103_4, all_105_4, 207.45/128.05 | | | | | | | all_86_11, $sum(all_86_10, 1)) = 0) | (length1(int, 207.45/128.05 | | | | | | | all_103_4) = all_777_1 & ( ~ ($lesseq(1, 207.45/128.05 | | | | | | | $difference(all_777_1, all_86_10))) | ~ 207.45/128.05 | | | | | | | ($lesseq(all_86_11, all_777_1)) | ( ~ (all_777_0 = 207.45/128.05 | | | | | | | all_777_1) & length1(int, all_105_4) = 207.45/128.05 | | | | | | | all_777_0))) 207.45/128.05 | | | | | | | 207.45/128.05 | | | | | | | BETA: splitting (163) gives: 207.45/128.05 | | | | | | | 207.45/128.05 | | | | | | | Case 1: 207.45/128.05 | | | | | | | | 207.45/128.05 | | | | | | | | (164) all_777_1 = 0 & permut3(int, all_103_4, all_105_4, 207.45/128.05 | | | | | | | | all_86_11, $sum(all_86_10, 1)) = 0 207.45/128.05 | | | | | | | | 207.45/128.05 | | | | | | | | ALPHA: (164) implies: 207.45/128.05 | | | | | | | | (165) permut3(int, all_103_4, all_105_4, all_86_11, 207.45/128.05 | | | | | | | | $sum(all_86_10, 1)) = 0 207.45/128.05 | | | | | | | | 207.45/128.05 | | | | | | | | BETA: splitting (156) gives: 207.45/128.05 | | | | | | | | 207.45/128.05 | | | | | | | | Case 1: 207.45/128.05 | | | | | | | | | 207.45/128.05 | | | | | | | | | (166) all_766_1 = 0 & permut3(int, all_105_4, all_105_2, 0, 207.45/128.05 | | | | | | | | | all_86_13) = 0 207.45/128.05 | | | | | | | | | 207.45/128.05 | | | | | | | | | ALPHA: (166) implies: 207.45/128.05 | | | | | | | | | (167) permut3(int, all_105_4, all_105_2, 0, all_86_13) = 0 207.45/128.05 | | | | | | | | | 207.45/128.05 | | | | | | | | | BETA: splitting (152) gives: 207.45/128.05 | | | | | | | | | 207.45/128.05 | | | | | | | | | Case 1: 207.45/128.05 | | | | | | | | | | 207.45/128.05 | | | | | | | | | | (168) all_760_0 = all_760_1 & $lesseq(all_86_13, 207.45/128.05 | | | | | | | | | | all_760_1) & $lesseq(0, all_760_1) & $lesseq(0, 207.45/128.05 | | | | | | | | | | all_86_13) & length1(int, all_105_2) = all_760_1 207.45/128.05 | | | | | | | | | | & length1(int, all_105_4) = all_760_1 207.45/128.05 | | | | | | | | | | 207.45/128.05 | | | | | | | | | | ALPHA: (168) implies: 207.45/128.05 | | | | | | | | | | (169) length1(int, all_105_4) = all_760_1 207.45/128.05 | | | | | | | | | | 207.45/128.05 | | | | | | | | | | BETA: splitting (151) gives: 207.45/128.05 | | | | | | | | | | 207.45/128.05 | | | | | | | | | | Case 1: 207.45/128.05 | | | | | | | | | | | 207.45/128.05 | | | | | | | | | | | (170) all_759_0 = all_759_1 & $lesseq(1, 207.45/128.05 | | | | | | | | | | | $difference(all_759_1, all_86_10)) & 207.45/128.05 | | | | | | | | | | | $lesseq(all_86_11, all_759_1) & $lesseq(-1, 207.45/128.05 | | | | | | | | | | | all_86_10) & $lesseq(0, all_86_11) & 207.45/128.05 | | | | | | | | | | | length1(int, all_105_4) = all_759_1 & length1(int, 207.45/128.05 | | | | | | | | | | | all_103_4) = all_759_1 207.45/128.05 | | | | | | | | | | | 207.45/128.05 | | | | | | | | | | | ALPHA: (170) implies: 207.45/128.05 | | | | | | | | | | | (171) $lesseq(1, $difference(all_759_1, all_86_10)) 207.45/128.05 | | | | | | | | | | | (172) length1(int, all_103_4) = all_759_1 207.45/128.05 | | | | | | | | | | | (173) length1(int, all_105_4) = all_759_1 207.45/128.05 | | | | | | | | | | | 207.45/128.05 | | | | | | | | | | | GROUND_INST: instantiating (1) with all_133_0, all_739_0, 207.45/128.05 | | | | | | | | | | | all_133_1, simplifying with (134), (145) gives: 207.45/128.05 | | | | | | | | | | | (174) all_739_0 = all_133_0 207.45/128.05 | | | | | | | | | | | 207.45/128.05 | | | | | | | | | | | GROUND_INST: instantiating (57) with all_86_13, all_760_1, 207.45/128.05 | | | | | | | | | | | all_105_4, int, simplifying with (24), (169) 207.45/128.05 | | | | | | | | | | | gives: 207.45/128.05 | | | | | | | | | | | (175) all_760_1 = all_86_13 207.45/128.05 | | | | | | | | | | | 207.45/128.06 | | | | | | | | | | | GROUND_INST: instantiating (57) with all_760_1, all_759_1, 207.45/128.06 | | | | | | | | | | | all_105_4, int, simplifying with (169), (173) 207.45/128.06 | | | | | | | | | | | gives: 207.45/128.06 | | | | | | | | | | | (176) all_760_1 = all_759_1 207.45/128.06 | | | | | | | | | | | 207.45/128.06 | | | | | | | | | | | GROUND_INST: instantiating (23) with all_105_1, all_753_1, 207.45/128.06 | | | | | | | | | | | all_105_2, int, simplifying with (31), (150) 207.45/128.06 | | | | | | | | | | | gives: 207.45/128.06 | | | | | | | | | | | (177) all_753_1 = all_105_1 207.45/128.06 | | | | | | | | | | | 207.45/128.06 | | | | | | | | | | | GROUND_INST: instantiating (23) with all_753_1, all_739_2, 207.45/128.06 | | | | | | | | | | | all_105_2, int, simplifying with (143), (150) 207.45/128.06 | | | | | | | | | | | gives: 207.45/128.06 | | | | | | | | | | | (178) all_753_1 = all_739_2 207.45/128.06 | | | | | | | | | | | 207.45/128.06 | | | | | | | | | | | COMBINE_EQS: (175), (176) imply: 207.45/128.06 | | | | | | | | | | | (179) all_759_1 = all_86_13 207.45/128.06 | | | | | | | | | | | 207.45/128.06 | | | | | | | | | | | COMBINE_EQS: (177), (178) imply: 207.45/128.06 | | | | | | | | | | | (180) all_739_2 = all_105_1 207.45/128.06 | | | | | | | | | | | 207.45/128.06 | | | | | | | | | | | REDUCE: (146), (180) imply: 207.45/128.06 | | | | | | | | | | | (181) tb2t(all_105_1) = all_739_1 207.45/128.06 | | | | | | | | | | | 207.45/128.06 | | | | | | | | | | | REDUCE: (144), (174) imply: 207.45/128.06 | | | | | | | | | | | (182) get3(all_739_1, all_133_2) = all_133_0 207.45/128.06 | | | | | | | | | | | 207.45/128.06 | | | | | | | | | | | REDUCE: (148), (177) imply: 207.45/128.06 | | | | | | | | | | | (183) get(int, int, all_105_1, all_753_0) = all_133_1 207.45/128.06 | | | | | | | | | | | 207.45/128.06 | | | | | | | | | | | GROUND_INST: instantiating (54) with all_86_2, all_739_1, 207.45/128.06 | | | | | | | | | | | all_105_1, simplifying with (29), (181) gives: 207.45/128.06 | | | | | | | | | | | (184) all_739_1 = all_86_2 207.45/128.06 | | | | | | | | | | | 207.45/128.06 | | | | | | | | | | | REDUCE: (182), (184) imply: 207.45/128.06 | | | | | | | | | | | (185) get3(all_86_2, all_133_2) = all_133_0 207.45/128.06 | | | | | | | | | | | 207.45/128.06 | | | | | | | | | | | GROUND_INST: instantiating (56) with all_86_4, all_86_2, 0, 207.45/128.06 | | | | | | | | | | | all_86_7, all_105_3, all_105_1, all_133_2, 207.45/128.06 | | | | | | | | | | | all_133_0, simplifying with (8), (27), (49), (63), 207.45/128.06 | | | | | | | | | | | (185) gives: 207.45/128.06 | | | | | | | | | | | (186) ~ ($lesseq(1, $difference(all_86_7, all_133_2))) 207.45/128.06 | | | | | | | | | | | | ~ ($lesseq(0, all_133_2)) | get3(all_86_4, 207.45/128.06 | | | | | | | | | | | all_133_2) = all_133_0 207.45/128.06 | | | | | | | | | | | 207.45/128.06 | | | | | | | | | | | GROUND_INST: instantiating (40) with all_86_4, all_86_2, 207.45/128.06 | | | | | | | | | | | all_86_7, $sum(all_86_10, 1), all_133_2, 207.45/128.06 | | | | | | | | | | | all_105_3, all_105_1, all_133_0, simplifying with 207.45/128.06 | | | | | | | | | | | (8), (42), (49), (63), (185) gives: 207.45/128.06 | | | | | | | | | | | (187) ~ ($lesseq(all_133_2, all_86_10)) | ~ 207.45/128.06 | | | | | | | | | | | ($lesseq(all_86_7, all_133_2)) | ? [v0: $int] : 207.45/128.06 | | | | | | | | | | | ($lesseq(v0, all_86_10) & $lesseq(all_86_7, v0) & 207.45/128.06 | | | | | | | | | | | get3(all_86_4, v0) = all_133_0) 207.45/128.06 | | | | | | | | | | | 207.45/128.06 | | | | | | | | | | | GROUND_INST: instantiating (46) with int, all_105_3, all_105_1, 207.45/128.06 | | | | | | | | | | | 0, all_86_7, all_133_2, all_753_0, simplifying 207.45/128.06 | | | | | | | | | | | with (9), (27), (149) gives: 207.45/128.06 | | | | | | | | | | | (188) ~ ($lesseq(1, $difference(all_86_7, all_133_2))) 207.45/128.06 | | | | | | | | | | | | ~ ($lesseq(0, all_133_2)) | ? [v0: $int] : 207.45/128.06 | | | | | | | | | | | (get(int, int, all_105_1, all_753_0) = v0 & 207.45/128.06 | | | | | | | | | | | get(int, int, all_105_3, all_753_0) = v0 & 207.45/128.06 | | | | | | | | | | | in_uni(v0)) 207.45/128.06 | | | | | | | | | | | 207.45/128.06 | | | | | | | | | | | GROUND_INST: instantiating (33) with int, all_105_3, all_105_1, 207.45/128.06 | | | | | | | | | | | all_86_7, $sum(all_86_10, 1), all_133_2, 207.45/128.06 | | | | | | | | | | | all_753_0, all_133_1, simplifying with (9), (42), 207.45/128.06 | | | | | | | | | | | (149), (183) gives: 207.45/128.06 | | | | | | | | | | | (189) ~ ($lesseq(all_133_2, all_86_10)) | ~ 207.45/128.06 | | | | | | | | | | | ($lesseq(all_86_7, all_133_2)) | ? [v0: $int] : 207.45/128.06 | | | | | | | | | | | ? [v1: $int] : ($lesseq(v0, all_86_10) & 207.45/128.06 | | | | | | | | | | | $lesseq(all_86_7, v0) & t2tb1(v0) = v1 & 207.45/128.06 | | | | | | | | | | | get(int, int, all_105_3, v1) = all_133_1 & 207.45/128.06 | | | | | | | | | | | in_uni(v1) & in_uni(all_133_1)) 207.45/128.06 | | | | | | | | | | | 207.45/128.06 | | | | | | | | | | | BETA: splitting (28) gives: 207.45/128.06 | | | | | | | | | | | 207.45/128.06 | | | | | | | | | | | Case 1: 207.45/128.06 | | | | | | | | | | | | 207.45/128.06 | | | | | | | | | | | | (190) ~ (all_86_11 = 0) 207.45/128.06 | | | | | | | | | | | | 207.45/128.06 | | | | | | | | | | | | STRENGTHEN: (51), (190) imply: 207.45/128.06 | | | | | | | | | | | | (191) $lesseq(1, all_86_11) 207.45/128.06 | | | | | | | | | | | | 207.45/128.06 | | | | | | | | | | | | COMBINE_INEQS: (37), (45) imply: 207.45/128.06 | | | | | | | | | | | | (192) $lesseq(1, $difference(all_86_10, all_86_8)) 207.45/128.06 | | | | | | | | | | | | 207.45/128.06 | | | | | | | | | | | | BETA: splitting (188) gives: 207.45/128.06 | | | | | | | | | | | | 207.45/128.06 | | | | | | | | | | | | Case 1: 207.45/128.06 | | | | | | | | | | | | | 207.45/128.06 | | | | | | | | | | | | | (193) $lesseq(all_133_2, -1) 207.45/128.06 | | | | | | | | | | | | | 207.45/128.06 | | | | | | | | | | | | | COMBINE_INEQS: (130), (193) imply: 207.45/128.06 | | | | | | | | | | | | | (194) $lesseq(all_86_11, -1) 207.45/128.06 | | | | | | | | | | | | | 207.45/128.06 | | | | | | | | | | | | | COMBINE_INEQS: (191), (194) imply: 207.45/128.06 | | | | | | | | | | | | | (195) $lesseq(0, -1) 207.45/128.06 | | | | | | | | | | | | | 207.45/128.06 | | | | | | | | | | | | | CLOSE: (195) is inconsistent. 207.45/128.06 | | | | | | | | | | | | | 207.45/128.06 | | | | | | | | | | | | Case 2: 207.45/128.06 | | | | | | | | | | | | | 207.45/128.06 | | | | | | | | | | | | | (196) $lesseq(0, all_133_2) 207.45/128.06 | | | | | | | | | | | | | 207.45/128.06 | | | | | | | | | | | | | REF_CLOSE: (2), (3), (19), (30), (40), (45), (63), (130), 207.45/128.06 | | | | | | | | | | | | | (131), (132), (186), (187), (189), (192), (196) 207.45/128.06 | | | | | | | | | | | | | are inconsistent by sub-proof #144. 207.45/128.06 | | | | | | | | | | | | | 207.45/128.06 | | | | | | | | | | | | End of split 207.45/128.06 | | | | | | | | | | | | 207.45/128.06 | | | | | | | | | | | Case 2: 207.45/128.06 | | | | | | | | | | | | 207.45/128.06 | | | | | | | | | | | | (197) all_86_11 = 0 207.45/128.06 | | | | | | | | | | | | 207.45/128.06 | | | | | | | | | | | | REDUCE: (130), (197) imply: 207.45/128.06 | | | | | | | | | | | | (198) $lesseq(0, all_133_2) 207.45/128.06 | | | | | | | | | | | | 207.45/128.06 | | | | | | | | | | | | COMBINE_INEQS: (131), (198) imply: 207.45/128.06 | | | | | | | | | | | | (199) $lesseq(0, all_86_8) 207.45/128.06 | | | | | | | | | | | | 207.45/128.06 | | | | | | | | | | | | COMBINE_INEQS: (37), (45) imply: 207.45/128.06 | | | | | | | | | | | | (200) $lesseq(1, $difference(all_86_10, all_86_8)) 207.45/128.06 | | | | | | | | | | | | 207.45/128.06 | | | | | | | | | | | | COMBINE_INEQS: (199), (200) imply: 207.45/128.06 | | | | | | | | | | | | (201) $lesseq(1, all_86_10) 207.45/128.06 | | | | | | | | | | | | 207.45/128.06 | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (6), (8), (9), (10), (13), (19), 207.45/128.06 | | | | | | | | | | | | (21), (22), (23), (24), (26), (27), (29), (30), 207.45/128.06 | | | | | | | | | | | | (31), (33), (34), (37), (40), (42), (43), (44), 207.45/128.06 | | | | | | | | | | | | (45), (46), (47), (49), (50), (51), (52), (54), 207.45/128.06 | | | | | | | | | | | | (56), (57), (58), (63), (66), (130), (131), (132), 207.45/128.06 | | | | | | | | | | | | (134), (135), (201) are inconsistent by sub-proof 207.45/128.06 | | | | | | | | | | | | #109. 207.45/128.06 | | | | | | | | | | | | 207.45/128.06 | | | | | | | | | | | End of split 207.45/128.06 | | | | | | | | | | | 207.45/128.06 | | | | | | | | | | Case 2: 207.45/128.06 | | | | | | | | | | | 207.45/128.06 | | | | | | | | | | | (202) ~ (all_759_1 = 0) & permut3(int, all_103_4, 207.45/128.06 | | | | | | | | | | | all_105_4, all_86_11, $sum(all_86_10, 1)) = 207.45/128.06 | | | | | | | | | | | all_759_1 207.45/128.06 | | | | | | | | | | | 207.45/128.06 | | | | | | | | | | | ALPHA: (202) implies: 207.45/128.06 | | | | | | | | | | | (203) ~ (all_759_1 = 0) 207.45/128.06 | | | | | | | | | | | (204) permut3(int, all_103_4, all_105_4, all_86_11, 207.45/128.06 | | | | | | | | | | | $sum(all_86_10, 1)) = all_759_1 207.45/128.06 | | | | | | | | | | | 207.45/128.06 | | | | | | | | | | | GROUND_INST: instantiating (21) with all_759_1, 0, 207.45/128.06 | | | | | | | | | | | $sum(all_86_10, 1), all_86_11, all_105_4, 207.45/128.06 | | | | | | | | | | | all_103_4, int, simplifying with (165), (204) 207.45/128.06 | | | | | | | | | | | gives: 207.45/128.06 | | | | | | | | | | | (205) all_759_1 = 0 207.45/128.06 | | | | | | | | | | | 207.45/128.06 | | | | | | | | | | | REDUCE: (203), (205) imply: 207.45/128.06 | | | | | | | | | | | (206) ~ (0 = 0) 207.45/128.06 | | | | | | | | | | | 207.45/128.06 | | | | | | | | | | | CLOSE: (206) is inconsistent. 207.45/128.06 | | | | | | | | | | | 207.45/128.06 | | | | | | | | | | End of split 207.45/128.06 | | | | | | | | | | 207.45/128.06 | | | | | | | | | Case 2: 207.45/128.06 | | | | | | | | | | 207.45/128.06 | | | | | | | | | | (207) ~ (all_760_1 = 0) & permut3(int, all_105_4, 207.45/128.06 | | | | | | | | | | all_105_2, 0, all_86_13) = all_760_1 207.45/128.06 | | | | | | | | | | 207.45/128.06 | | | | | | | | | | REF_CLOSE: (21), (167), (207) are inconsistent by sub-proof 207.45/128.06 | | | | | | | | | | #101. 207.45/128.06 | | | | | | | | | | 207.45/128.06 | | | | | | | | | End of split 207.45/128.06 | | | | | | | | | 207.45/128.06 | | | | | | | | Case 2: 207.45/128.06 | | | | | | | | | 207.45/128.06 | | | | | | | | | (208) length1(int, all_105_4) = all_766_1 & ( ~ 207.45/128.06 | | | | | | | | | ($lesseq(all_86_13, all_766_1)) | ~ ($lesseq(0, 207.45/128.06 | | | | | | | | | all_766_1)) | ( ~ (all_766_0 = all_766_1) & 207.45/128.06 | | | | | | | | | length1(int, all_105_2) = all_766_0)) 207.45/128.06 | | | | | | | | | 207.45/128.06 | | | | | | | | | ALPHA: (208) implies: 207.45/128.06 | | | | | | | | | (209) length1(int, all_105_4) = all_766_1 207.45/128.06 | | | | | | | | | (210) ~ ($lesseq(all_86_13, all_766_1)) | ~ ($lesseq(0, 207.45/128.06 | | | | | | | | | all_766_1)) | ( ~ (all_766_0 = all_766_1) & 207.45/128.06 | | | | | | | | | length1(int, all_105_2) = all_766_0) 207.45/128.06 | | | | | | | | | 207.45/128.06 | | | | | | | | | BETA: splitting (151) gives: 207.45/128.06 | | | | | | | | | 207.45/128.06 | | | | | | | | | Case 1: 207.45/128.06 | | | | | | | | | | 207.52/128.07 | | | | | | | | | | (211) all_759_0 = all_759_1 & $lesseq(1, 207.52/128.07 | | | | | | | | | | $difference(all_759_1, all_86_10)) & 207.52/128.07 | | | | | | | | | | $lesseq(all_86_11, all_759_1) & $lesseq(-1, 207.52/128.07 | | | | | | | | | | all_86_10) & $lesseq(0, all_86_11) & length1(int, 207.52/128.07 | | | | | | | | | | all_105_4) = all_759_1 & length1(int, all_103_4) 207.52/128.07 | | | | | | | | | | = all_759_1 207.52/128.07 | | | | | | | | | | 207.52/128.07 | | | | | | | | | | ALPHA: (211) implies: 207.52/128.07 | | | | | | | | | | (212) $lesseq(1, $difference(all_759_1, all_86_10)) 207.52/128.07 | | | | | | | | | | (213) length1(int, all_105_4) = all_759_1 207.52/128.07 | | | | | | | | | | 207.52/128.07 | | | | | | | | | | GROUND_INST: instantiating (57) with all_86_13, all_766_1, 207.52/128.07 | | | | | | | | | | all_105_4, int, simplifying with (24), (209) 207.52/128.07 | | | | | | | | | | gives: 207.52/128.07 | | | | | | | | | | (214) all_766_1 = all_86_13 207.52/128.07 | | | | | | | | | | 207.52/128.07 | | | | | | | | | | GROUND_INST: instantiating (57) with all_766_1, all_759_1, 207.52/128.07 | | | | | | | | | | all_105_4, int, simplifying with (209), (213) 207.52/128.07 | | | | | | | | | | gives: 207.52/128.07 | | | | | | | | | | (215) all_766_1 = all_759_1 207.52/128.07 | | | | | | | | | | 207.52/128.07 | | | | | | | | | | COMBINE_EQS: (214), (215) imply: 207.52/128.07 | | | | | | | | | | (216) all_759_1 = all_86_13 207.52/128.07 | | | | | | | | | | 207.52/128.07 | | | | | | | | | | SIMP: (216) implies: 207.52/128.07 | | | | | | | | | | (217) all_759_1 = all_86_13 207.52/128.07 | | | | | | | | | | 207.52/128.07 | | | | | | | | | | BETA: splitting (210) gives: 207.52/128.07 | | | | | | | | | | 207.52/128.07 | | | | | | | | | | Case 1: 207.52/128.07 | | | | | | | | | | | 207.52/128.07 | | | | | | | | | | | (218) $lesseq(all_766_1, -1) 207.52/128.07 | | | | | | | | | | | 207.52/128.07 | | | | | | | | | | | REDUCE: (214), (218) imply: 207.52/128.07 | | | | | | | | | | | (219) $lesseq(all_86_13, -1) 207.52/128.07 | | | | | | | | | | | 207.52/128.07 | | | | | | | | | | | COMBINE_INEQS: (37), (45) imply: 207.52/128.07 | | | | | | | | | | | (220) $lesseq(1, $difference(all_86_10, all_86_8)) 207.52/128.07 | | | | | | | | | | | 207.52/128.07 | | | | | | | | | | | COMBINE_INEQS: (35), (220) imply: 207.52/128.07 | | | | | | | | | | | (221) $lesseq(1, $difference(all_86_10, all_86_11)) 207.52/128.07 | | | | | | | | | | | 207.52/128.07 | | | | | | | | | | | COMBINE_INEQS: (47), (221) imply: 207.52/128.07 | | | | | | | | | | | (222) $lesseq(2, $difference(all_86_13, all_86_11)) 207.52/128.07 | | | | | | | | | | | 207.52/128.07 | | | | | | | | | | | COMBINE_INEQS: (11), (219) imply: 207.52/128.07 | | | | | | | | | | | (223) $lesseq(0, -1) 207.52/128.07 | | | | | | | | | | | 207.52/128.07 | | | | | | | | | | | CLOSE: (223) is inconsistent. 207.52/128.07 | | | | | | | | | | | 207.52/128.07 | | | | | | | | | | Case 2: 207.52/128.07 | | | | | | | | | | | 207.52/128.07 | | | | | | | | | | | (224) ~ ($lesseq(all_86_13, all_766_1)) | ( ~ 207.52/128.07 | | | | | | | | | | | (all_766_0 = all_766_1) & length1(int, 207.52/128.07 | | | | | | | | | | | all_105_2) = all_766_0) 207.52/128.07 | | | | | | | | | | | 207.52/128.07 | | | | | | | | | | | BETA: splitting (224) gives: 207.52/128.07 | | | | | | | | | | | 207.52/128.07 | | | | | | | | | | | Case 1: 207.52/128.07 | | | | | | | | | | | | 207.52/128.07 | | | | | | | | | | | | (225) $lesseq(1, $difference(all_86_13, all_766_1)) 207.52/128.07 | | | | | | | | | | | | 207.52/128.07 | | | | | | | | | | | | REDUCE: (214), (225) imply: 207.52/128.07 | | | | | | | | | | | | (226) $lesseq(0, -1) 207.52/128.07 | | | | | | | | | | | | 207.52/128.07 | | | | | | | | | | | | CLOSE: (226) is inconsistent. 207.52/128.07 | | | | | | | | | | | | 207.52/128.07 | | | | | | | | | | | Case 2: 207.52/128.07 | | | | | | | | | | | | 207.52/128.07 | | | | | | | | | | | | (227) ~ (all_766_0 = all_766_1) & length1(int, 207.52/128.07 | | | | | | | | | | | | all_105_2) = all_766_0 207.52/128.07 | | | | | | | | | | | | 207.52/128.07 | | | | | | | | | | | | ALPHA: (227) implies: 207.52/128.07 | | | | | | | | | | | | (228) ~ (all_766_0 = all_766_1) 207.52/128.07 | | | | | | | | | | | | (229) length1(int, all_105_2) = all_766_0 207.52/128.07 | | | | | | | | | | | | 207.52/128.07 | | | | | | | | | | | | REDUCE: (214), (228) imply: 207.52/128.07 | | | | | | | | | | | | (230) ~ (all_766_0 = all_86_13) 207.52/128.07 | | | | | | | | | | | | 207.52/128.07 | | | | | | | | | | | | GROUND_INST: instantiating (57) with all_86_13, all_766_0, 207.52/128.07 | | | | | | | | | | | | all_105_2, int, simplifying with (5), (229) gives: 207.52/128.07 | | | | | | | | | | | | (231) all_766_0 = all_86_13 207.52/128.07 | | | | | | | | | | | | 207.52/128.07 | | | | | | | | | | | | REDUCE: (230), (231) imply: 207.52/128.07 | | | | | | | | | | | | (232) ~ (0 = 0) 207.52/128.07 | | | | | | | | | | | | 207.52/128.07 | | | | | | | | | | | | CLOSE: (232) is inconsistent. 207.52/128.07 | | | | | | | | | | | | 207.52/128.07 | | | | | | | | | | | End of split 207.52/128.07 | | | | | | | | | | | 207.52/128.07 | | | | | | | | | | End of split 207.52/128.07 | | | | | | | | | | 207.52/128.07 | | | | | | | | | Case 2: 207.52/128.07 | | | | | | | | | | 207.52/128.07 | | | | | | | | | | (233) ~ (all_759_1 = 0) & permut3(int, all_103_4, 207.52/128.07 | | | | | | | | | | all_105_4, all_86_11, $sum(all_86_10, 1)) = 207.52/128.07 | | | | | | | | | | all_759_1 207.52/128.07 | | | | | | | | | | 207.52/128.07 | | | | | | | | | | ALPHA: (233) implies: 207.52/128.07 | | | | | | | | | | (234) ~ (all_759_1 = 0) 207.52/128.07 | | | | | | | | | | (235) permut3(int, all_103_4, all_105_4, all_86_11, 207.52/128.07 | | | | | | | | | | $sum(all_86_10, 1)) = all_759_1 207.52/128.07 | | | | | | | | | | 207.52/128.07 | | | | | | | | | | GROUND_INST: instantiating (21) with all_759_1, 0, 207.52/128.07 | | | | | | | | | | $sum(all_86_10, 1), all_86_11, all_105_4, 207.52/128.07 | | | | | | | | | | all_103_4, int, simplifying with (165), (235) 207.52/128.07 | | | | | | | | | | gives: 207.52/128.07 | | | | | | | | | | (236) all_759_1 = 0 207.52/128.07 | | | | | | | | | | 207.52/128.07 | | | | | | | | | | REDUCE: (234), (236) imply: 207.52/128.07 | | | | | | | | | | (237) ~ (0 = 0) 207.52/128.07 | | | | | | | | | | 207.52/128.07 | | | | | | | | | | CLOSE: (237) is inconsistent. 207.52/128.07 | | | | | | | | | | 207.52/128.07 | | | | | | | | | End of split 207.52/128.07 | | | | | | | | | 207.52/128.07 | | | | | | | | End of split 207.52/128.07 | | | | | | | | 207.52/128.07 | | | | | | | Case 2: 207.52/128.07 | | | | | | | | 207.52/128.07 | | | | | | | | (238) length1(int, all_103_4) = all_777_1 & ( ~ ($lesseq(1, 207.52/128.07 | | | | | | | | $difference(all_777_1, all_86_10))) | ~ 207.52/128.07 | | | | | | | | ($lesseq(all_86_11, all_777_1)) | ( ~ (all_777_0 = 207.52/128.07 | | | | | | | | all_777_1) & length1(int, all_105_4) = 207.52/128.07 | | | | | | | | all_777_0)) 207.52/128.07 | | | | | | | | 207.52/128.07 | | | | | | | | ALPHA: (238) implies: 207.52/128.07 | | | | | | | | (239) length1(int, all_103_4) = all_777_1 207.52/128.07 | | | | | | | | (240) ~ ($lesseq(1, $difference(all_777_1, all_86_10))) | ~ 207.52/128.07 | | | | | | | | ($lesseq(all_86_11, all_777_1)) | ( ~ (all_777_0 = 207.52/128.07 | | | | | | | | all_777_1) & length1(int, all_105_4) = all_777_0) 207.52/128.07 | | | | | | | | 207.52/128.07 | | | | | | | | BETA: splitting (156) gives: 207.52/128.07 | | | | | | | | 207.52/128.07 | | | | | | | | Case 1: 207.52/128.07 | | | | | | | | | 207.52/128.07 | | | | | | | | | (241) all_766_1 = 0 & permut3(int, all_105_4, all_105_2, 0, 207.52/128.07 | | | | | | | | | all_86_13) = 0 207.52/128.07 | | | | | | | | | 207.52/128.07 | | | | | | | | | ALPHA: (241) implies: 207.52/128.07 | | | | | | | | | (242) permut3(int, all_105_4, all_105_2, 0, all_86_13) = 0 207.52/128.07 | | | | | | | | | 207.52/128.07 | | | | | | | | | BETA: splitting (152) gives: 207.52/128.07 | | | | | | | | | 207.52/128.07 | | | | | | | | | Case 1: 207.52/128.07 | | | | | | | | | | 207.52/128.07 | | | | | | | | | | (243) all_760_0 = all_760_1 & $lesseq(all_86_13, 207.52/128.07 | | | | | | | | | | all_760_1) & $lesseq(0, all_760_1) & $lesseq(0, 207.52/128.07 | | | | | | | | | | all_86_13) & length1(int, all_105_2) = all_760_1 207.52/128.07 | | | | | | | | | | & length1(int, all_105_4) = all_760_1 207.52/128.07 | | | | | | | | | | 207.52/128.07 | | | | | | | | | | ALPHA: (243) implies: 207.52/128.07 | | | | | | | | | | (244) length1(int, all_105_4) = all_760_1 207.52/128.07 | | | | | | | | | | 207.52/128.07 | | | | | | | | | | GROUND_INST: instantiating (57) with all_86_13, all_760_1, 207.52/128.07 | | | | | | | | | | all_105_4, int, simplifying with (24), (244) 207.52/128.07 | | | | | | | | | | gives: 207.52/128.07 | | | | | | | | | | (245) all_760_1 = all_86_13 207.52/128.07 | | | | | | | | | | 207.52/128.07 | | | | | | | | | | GROUND_INST: instantiating (57) with all_86_13, all_777_1, 207.52/128.07 | | | | | | | | | | all_103_4, int, simplifying with (10), (239) 207.52/128.07 | | | | | | | | | | gives: 207.52/128.07 | | | | | | | | | | (246) all_777_1 = all_86_13 207.52/128.07 | | | | | | | | | | 207.52/128.07 | | | | | | | | | | BETA: splitting (240) gives: 207.52/128.07 | | | | | | | | | | 207.52/128.07 | | | | | | | | | | Case 1: 207.52/128.07 | | | | | | | | | | | 207.52/128.07 | | | | | | | | | | | (247) $lesseq(1, $difference(all_86_11, all_777_1)) 207.52/128.07 | | | | | | | | | | | 207.52/128.07 | | | | | | | | | | | REF_CLOSE: (37), (45), (47), (130), (131), (246), (247) are 207.52/128.07 | | | | | | | | | | | inconsistent by sub-proof #100. 207.52/128.07 | | | | | | | | | | | 207.52/128.07 | | | | | | | | | | Case 2: 207.52/128.07 | | | | | | | | | | | 207.52/128.07 | | | | | | | | | | | (248) ~ ($lesseq(1, $difference(all_777_1, all_86_10))) 207.52/128.07 | | | | | | | | | | | | ( ~ (all_777_0 = all_777_1) & length1(int, 207.52/128.07 | | | | | | | | | | | all_105_4) = all_777_0) 207.52/128.07 | | | | | | | | | | | 207.52/128.07 | | | | | | | | | | | REF_CLOSE: (24), (47), (57), (246), (248) are inconsistent by 207.52/128.07 | | | | | | | | | | | sub-proof #99. 207.52/128.07 | | | | | | | | | | | 207.52/128.07 | | | | | | | | | | End of split 207.52/128.07 | | | | | | | | | | 207.52/128.07 | | | | | | | | | Case 2: 207.52/128.07 | | | | | | | | | | 207.52/128.07 | | | | | | | | | | (249) ~ (all_760_1 = 0) & permut3(int, all_105_4, 207.52/128.07 | | | | | | | | | | all_105_2, 0, all_86_13) = all_760_1 207.52/128.07 | | | | | | | | | | 207.52/128.07 | | | | | | | | | | REF_CLOSE: (21), (242), (249) are inconsistent by sub-proof 207.52/128.07 | | | | | | | | | | #101. 207.52/128.07 | | | | | | | | | | 207.52/128.07 | | | | | | | | | End of split 207.52/128.07 | | | | | | | | | 207.52/128.07 | | | | | | | | Case 2: 207.52/128.07 | | | | | | | | | 207.52/128.07 | | | | | | | | | (250) length1(int, all_105_4) = all_766_1 & ( ~ 207.52/128.07 | | | | | | | | | ($lesseq(all_86_13, all_766_1)) | ~ ($lesseq(0, 207.52/128.07 | | | | | | | | | all_766_1)) | ( ~ (all_766_0 = all_766_1) & 207.52/128.07 | | | | | | | | | length1(int, all_105_2) = all_766_0)) 207.52/128.07 | | | | | | | | | 207.52/128.07 | | | | | | | | | ALPHA: (250) implies: 207.52/128.07 | | | | | | | | | (251) length1(int, all_105_4) = all_766_1 207.52/128.07 | | | | | | | | | 207.52/128.07 | | | | | | | | | GROUND_INST: instantiating (57) with all_86_13, all_766_1, 207.52/128.07 | | | | | | | | | all_105_4, int, simplifying with (24), (251) 207.52/128.07 | | | | | | | | | gives: 207.52/128.07 | | | | | | | | | (252) all_766_1 = all_86_13 207.52/128.07 | | | | | | | | | 207.52/128.07 | | | | | | | | | GROUND_INST: instantiating (57) with all_86_13, all_777_1, 207.52/128.07 | | | | | | | | | all_103_4, int, simplifying with (10), (239) 207.52/128.07 | | | | | | | | | gives: 207.52/128.07 | | | | | | | | | (253) all_777_1 = all_86_13 207.52/128.07 | | | | | | | | | 207.52/128.07 | | | | | | | | | BETA: splitting (240) gives: 207.52/128.07 | | | | | | | | | 207.52/128.07 | | | | | | | | | Case 1: 207.52/128.07 | | | | | | | | | | 207.52/128.07 | | | | | | | | | | (254) $lesseq(1, $difference(all_86_11, all_777_1)) 207.52/128.07 | | | | | | | | | | 207.52/128.07 | | | | | | | | | | REF_CLOSE: (37), (45), (47), (130), (131), (253), (254) are 207.52/128.07 | | | | | | | | | | inconsistent by sub-proof #100. 207.52/128.07 | | | | | | | | | | 207.52/128.07 | | | | | | | | | Case 2: 207.52/128.07 | | | | | | | | | | 207.52/128.07 | | | | | | | | | | (255) ~ ($lesseq(1, $difference(all_777_1, all_86_10))) 207.52/128.07 | | | | | | | | | | | ( ~ (all_777_0 = all_777_1) & length1(int, 207.52/128.07 | | | | | | | | | | all_105_4) = all_777_0) 207.52/128.07 | | | | | | | | | | 207.52/128.07 | | | | | | | | | | REF_CLOSE: (24), (47), (57), (253), (255) are inconsistent by 207.52/128.07 | | | | | | | | | | sub-proof #99. 207.52/128.07 | | | | | | | | | | 207.52/128.07 | | | | | | | | | End of split 207.52/128.07 | | | | | | | | | 207.52/128.07 | | | | | | | | End of split 207.52/128.07 | | | | | | | | 207.52/128.07 | | | | | | | End of split 207.52/128.07 | | | | | | | 207.52/128.07 | | | | | | End of split 207.52/128.07 | | | | | | 207.52/128.07 | | | | | End of split 207.52/128.07 | | | | | 207.52/128.07 | | | | End of split 207.52/128.07 | | | | 207.52/128.07 | | | End of split 207.52/128.07 | | | 207.52/128.07 | | End of split 207.52/128.07 | | 207.52/128.07 | End of split 207.52/128.07 | 207.52/128.07 End of proof 207.52/128.07 207.52/128.07 Sub-proof #99 shows that the following formulas are inconsistent: 207.52/128.07 ---------------------------------------------------------------- 207.52/128.07 (1) length1(int, all_105_4) = all_86_13 207.52/128.07 (2) $lesseq(1, $difference(all_86_13, all_86_10)) 207.52/128.07 (3) ~ ($lesseq(1, $difference(all_777_1, all_86_10))) | ( ~ (all_777_0 = 207.52/128.07 all_777_1) & length1(int, all_105_4) = all_777_0) 207.52/128.07 (4) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 207.52/128.07 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 207.52/128.07 (5) all_777_1 = all_86_13 207.52/128.07 207.52/128.07 Begin of proof 207.52/128.07 | 207.52/128.07 | BETA: splitting (3) gives: 207.52/128.07 | 207.52/128.07 | Case 1: 207.52/128.07 | | 207.52/128.07 | | (6) $lesseq(all_777_1, all_86_10) 207.52/128.07 | | 207.52/128.07 | | REDUCE: (5), (6) imply: 207.52/128.07 | | (7) $lesseq(all_86_13, all_86_10) 207.52/128.07 | | 207.52/128.07 | | COMBINE_INEQS: (2), (7) imply: 207.52/128.07 | | (8) $lesseq(0, -1) 207.52/128.07 | | 207.52/128.07 | | CLOSE: (8) is inconsistent. 207.52/128.07 | | 207.52/128.07 | Case 2: 207.52/128.07 | | 207.52/128.07 | | (9) ~ (all_777_0 = all_777_1) & length1(int, all_105_4) = all_777_0 207.52/128.07 | | 207.52/128.07 | | ALPHA: (9) implies: 207.52/128.07 | | (10) ~ (all_777_0 = all_777_1) 207.52/128.07 | | (11) length1(int, all_105_4) = all_777_0 207.52/128.07 | | 207.52/128.07 | | REDUCE: (5), (10) imply: 207.52/128.07 | | (12) ~ (all_777_0 = all_86_13) 207.52/128.07 | | 207.52/128.07 | | GROUND_INST: instantiating (4) with all_86_13, all_777_0, all_105_4, int, 207.52/128.07 | | simplifying with (1), (11) gives: 207.52/128.07 | | (13) all_777_0 = all_86_13 207.52/128.07 | | 207.52/128.07 | | REDUCE: (12), (13) imply: 207.52/128.07 | | (14) ~ (0 = 0) 207.52/128.07 | | 207.52/128.07 | | CLOSE: (14) is inconsistent. 207.52/128.07 | | 207.52/128.07 | End of split 207.52/128.07 | 207.52/128.07 End of proof 207.52/128.07 207.52/128.07 Sub-proof #100 shows that the following formulas are inconsistent: 207.52/128.07 ---------------------------------------------------------------- 207.52/128.07 (1) $lesseq(all_133_2, all_86_8) 207.52/128.07 (2) $lesseq(1, $difference(all_86_11, all_777_1)) 207.52/128.07 (3) $lesseq(all_86_11, all_133_2) 207.52/128.07 (4) $lesseq(all_86_7, all_86_10) 207.52/128.07 (5) $lesseq(1, $difference(all_86_7, all_86_8)) 207.52/128.07 (6) $lesseq(1, $difference(all_86_13, all_86_10)) 207.52/128.07 (7) all_777_1 = all_86_13 207.52/128.07 207.52/128.07 Begin of proof 207.52/128.07 | 207.52/128.07 | REDUCE: (2), (7) imply: 207.52/128.07 | (8) $lesseq(1, $difference(all_86_11, all_86_13)) 207.52/128.07 | 207.52/128.07 | COMBINE_INEQS: (1), (3) imply: 207.52/128.07 | (9) $lesseq(all_86_11, all_86_8) 207.52/128.07 | 207.52/128.07 | COMBINE_INEQS: (4), (5) imply: 207.52/128.07 | (10) $lesseq(1, $difference(all_86_10, all_86_8)) 207.52/128.07 | 207.52/128.07 | COMBINE_INEQS: (9), (10) imply: 207.52/128.07 | (11) $lesseq(1, $difference(all_86_10, all_86_11)) 207.52/128.07 | 207.52/128.07 | COMBINE_INEQS: (6), (11) imply: 207.52/128.07 | (12) $lesseq(2, $difference(all_86_13, all_86_11)) 207.52/128.07 | 207.52/128.07 | COMBINE_INEQS: (8), (12) imply: 207.52/128.07 | (13) $lesseq(0, -1) 207.52/128.07 | 207.52/128.07 | CLOSE: (13) is inconsistent. 207.52/128.07 | 207.52/128.07 End of proof 207.52/128.07 207.52/128.07 Sub-proof #101 shows that the following formulas are inconsistent: 207.52/128.07 ---------------------------------------------------------------- 207.52/128.07 (1) ~ (all_760_1 = 0) & permut3(int, all_105_4, all_105_2, 0, all_86_13) = 207.52/128.07 all_760_1 207.52/128.07 (2) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.52/128.07 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ (permut3(v6, v5, 207.52/128.07 v4, v3, v2) = v1) | ~ (permut3(v6, v5, v4, v3, v2) = v0)) 207.52/128.07 (3) permut3(int, all_105_4, all_105_2, 0, all_86_13) = 0 207.52/128.07 207.52/128.07 Begin of proof 207.52/128.07 | 207.52/128.07 | ALPHA: (1) implies: 207.52/128.07 | (4) ~ (all_760_1 = 0) 207.52/128.07 | (5) permut3(int, all_105_4, all_105_2, 0, all_86_13) = all_760_1 207.52/128.07 | 207.52/128.07 | GROUND_INST: instantiating (2) with 0, all_760_1, all_86_13, 0, all_105_2, 207.52/128.07 | all_105_4, int, simplifying with (3), (5) gives: 207.52/128.07 | (6) all_760_1 = 0 207.52/128.07 | 207.52/128.07 | REDUCE: (4), (6) imply: 207.52/128.07 | (7) ~ (0 = 0) 207.52/128.07 | 207.52/128.07 | CLOSE: (7) is inconsistent. 207.52/128.07 | 207.52/128.07 End of proof 207.52/128.07 207.52/128.07 Sub-proof #102 shows that the following formulas are inconsistent: 207.52/128.07 ---------------------------------------------------------------- 207.52/128.07 (1) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ (tb2t1(v2) 207.52/128.07 = v1) | ~ (tb2t1(v2) = v0)) 207.52/128.07 (2) in_map_int_int(all_86_6) 207.52/128.07 (3) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.52/128.07 $int] : ! [v5: $int] : ! [v6: $int] : ( ~ ($lesseq(0, v4)) | ~ 207.52/128.07 ($lesseq(0, v3)) | ~ (map_eq_sub1(v0, v5, v6, v3, v4) = 0) | ~ 207.52/128.07 (elts(v0, v2) = v6) | ~ (elts(v0, v1) = v5) | ~ in_ty(v0) | ? [v7: 207.52/128.07 $int] : ? [v8: $int] : ((v7 = 0 & array_eq_sub1(v0, v1, v2, v3, v4) 207.52/128.07 = 0) | (length1(v0, v1) = v7 & ( ~ ($lesseq(v4, v7)) | ~ 207.52/128.07 ($lesseq(v3, v7)) | ( ~ (v8 = v7) & length1(v0, v2) = v8))))) 207.52/128.07 (4) elts(int, all_103_4) = all_103_3 207.52/128.07 (5) t2tb(all_86_2) = all_105_1 207.52/128.07 (6) in_ty(int) 207.52/128.07 (7) length1(int, all_103_4) = all_86_13 207.52/128.07 (8) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.52/128.07 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 207.52/128.07 (permut2(v0, v5, v6, v3, v4) = v7) | ~ (elts(v0, v2) = v6) | ~ 207.52/128.07 (elts(v0, v1) = v5) | ~ in_ty(v0) | ? [v8: $int] : ? [v9: $int] : 207.52/128.07 ((v9 = v8 & v7 = 0 & $lesseq(v4, v8) & $lesseq(v3, v8) & $lesseq(0, v4) 207.52/128.07 & $lesseq(0, v3) & length1(v0, v2) = v8 & length1(v0, v1) = v8) | ( 207.52/128.07 ~ (v8 = 0) & permut3(v0, v1, v2, v3, v4) = v8))) 207.52/128.07 (9) $lesseq(-1, all_86_8) 207.52/128.07 (10) $lesseq(all_86_7, all_86_13) 207.52/128.07 (11) ! [v0: $int] : ! [v1: $int] : (v1 = 42 | ~ ($lesseq(1, 207.52/128.07 $difference(all_86_7, v0))) | ~ ($lesseq(1, $difference(v0, 207.52/128.07 all_86_8))) | ~ (get3(all_86_6, v0) = v1)) 207.52/128.07 (12) map_eq_sub1(int, all_103_3, all_103_1, $sum(all_86_10, 1), all_86_13) = 207.52/128.07 0 207.52/128.07 (13) t2tb(all_86_6) = all_103_1 207.52/128.07 (14) $lesseq(1, $difference(all_133_2, all_86_8)) 207.52/128.07 (15) tb2t1(all_133_1) = all_133_0 207.52/128.07 (16) map_eq_sub1(int, all_103_1, all_105_3, $sum(all_86_8, 1), all_86_13) = 0 207.52/128.07 (17) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.52/128.07 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ (permut3(v6, v5, 207.52/128.07 v4, v3, v2) = v1) | ~ (permut3(v6, v5, v4, v3, v2) = v0)) 207.52/128.07 (18) permut2(int, all_103_3, all_105_3, all_86_11, $sum(all_86_10, 1)) = 0 207.52/128.07 (19) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 207.52/128.07 | ~ (elts(v3, v2) = v1) | ~ (elts(v3, v2) = v0)) 207.52/128.07 (20) length1(int, all_105_4) = all_86_13 207.52/128.07 (21) elts(int, all_105_4) = all_105_3 207.52/128.07 (22) $lesseq(1, $difference(all_86_7, all_133_2)) 207.52/128.07 (23) map_eq_sub1(int, all_105_3, all_105_1, 0, all_86_7) = 0 207.52/128.07 (24) get4(int, all_105_2, all_133_2) = all_133_1 207.52/128.07 (25) tb2t(all_105_1) = all_86_2 207.52/128.07 (26) elts(int, all_105_2) = all_105_1 207.52/128.07 (27) map_eq_sub1(int, all_103_3, all_103_1, 0, all_86_11) = 0 207.52/128.07 (28) t2tb2(all_86_1) = all_105_2 207.52/128.07 (29) ~ ($difference(all_86_10, all_86_13) = -1) | ~ (all_86_11 = 0) 207.52/128.07 (30) $lesseq(all_86_11, all_86_8) 207.52/128.07 (31) $lesseq(all_86_7, all_86_10) 207.52/128.07 (32) ~ (all_133_0 = 42) 207.52/128.07 (33) in_array_int(all_86_1) 207.52/128.07 (34) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.52/128.07 $int] : ! [v5: $int] : ! [v6: $int] : ( ~ ($lesseq(0, v4)) | ~ 207.52/128.07 ($lesseq(0, v3)) | ~ (permut2(v0, v5, v6, v3, v4) = 0) | ~ (elts(v0, 207.52/128.07 v2) = v6) | ~ (elts(v0, v1) = v5) | ~ in_ty(v0) | ? [v7: $int] 207.52/128.07 : ? [v8: $int] : ((v7 = 0 & permut3(v0, v1, v2, v3, v4) = 0) | 207.52/128.07 (length1(v0, v1) = v7 & ( ~ ($lesseq(v4, v7)) | ~ ($lesseq(v3, v7)) 207.52/128.07 | ( ~ (v8 = v7) & length1(v0, v2) = v8))))) 207.52/128.07 (35) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.52/128.07 $int] : ! [v5: $int] : ! [v6: $int] : ( ~ ($lesseq(1, 207.52/128.07 $difference(v4, v5))) | ~ ($lesseq(v3, v5)) | ~ (map_eq_sub1(v0, 207.52/128.07 v1, v2, v3, v4) = 0) | ~ (t2tb1(v5) = v6) | ~ in_ty(v0) | ? 207.52/128.07 [v7: $int] : (get(v0, int, v2, v6) = v7 & get(v0, int, v1, v6) = v7 & 207.52/128.07 in_uni(v7))) 207.52/128.07 (36) $lesseq(1, $difference(all_86_13, all_86_10)) 207.52/128.08 (37) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.52/128.08 $int] : ! [v5: $int] : (v5 = 0 | ~ (permut_sub2(v0, v1, v2, v3, v4) 207.52/128.08 = v5) | ~ in_ty(v0) | ? [v6: $int] : ? [v7: $int] : ? [v8: $int] 207.52/128.08 : ? [v9: $int] : (( ~ (v9 = 0) & map_eq_sub1(v0, v6, v7, v4, v8) = v9 207.52/128.08 & length1(v0, v1) = v8 & elts(v0, v2) = v7 & elts(v0, v1) = v6 & 207.52/128.08 in_uni(v7) & in_uni(v6)) | ( ~ (v8 = 0) & map_eq_sub1(v0, v6, v7, 207.52/128.08 0, v3) = v8 & elts(v0, v2) = v7 & elts(v0, v1) = v6 & in_uni(v7) 207.52/128.08 & in_uni(v6)) | ( ~ (v6 = 0) & permut3(v0, v1, v2, v3, v4) = v6))) 207.52/128.08 (38) in_map_int_int(all_86_4) 207.52/128.08 (39) $lesseq(0, all_86_11) 207.52/128.08 (40) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ( ~ 207.52/128.08 (t2tb2(v0) = v2) | ~ (get4(int, v2, v1) = v3) | ~ in_array_int(v0) | 207.52/128.08 ? [v4: $int] : ? [v5: $int] : ? [v6: $int] : (tb2t(v4) = v5 & 207.52/128.08 tb2t1(v3) = v6 & get3(v5, v1) = v6 & elts(int, v2) = v4 & 207.52/128.08 in_map_int_int(v5) & in_uni(v4))) 207.52/128.08 (41) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ (tb2t(v2) 207.52/128.08 = v1) | ~ (tb2t(v2) = v0)) 207.52/128.08 (42) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.52/128.08 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 207.52/128.08 ($lesseq(1, $difference(v3, v6))) | ~ ($lesseq(v2, v6)) | ~ 207.52/128.08 (map_eq_sub1(int, v4, v5, v2, v3) = 0) | ~ (t2tb(v1) = v5) | ~ 207.52/128.08 (t2tb(v0) = v4) | ~ (get3(v1, v6) = v7) | ~ in_map_int_int(v0) | 207.52/128.08 get3(v0, v6) = v7) 207.52/128.08 (43) in_uni(all_133_1) 207.52/128.08 (44) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 207.52/128.08 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 207.52/128.08 (45) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ( ~ 207.52/128.08 (get4(v0, v1, v2) = v3) | ~ in_ty(v0) | ? [v4: $int] : ? [v5: $int] 207.52/128.08 : (elts(v0, v1) = v4 & t2tb1(v2) = v5 & get(v0, int, v4, v5) = v3 & 207.52/128.08 in_uni(v5) & in_uni(v4) & in_uni(v3))) 207.52/128.08 (46) $lesseq(1, all_86_10) 207.52/128.08 (47) map_eq_sub1(int, all_103_1, all_105_3, 0, all_86_13) = 0 207.52/128.08 (48) ! [v0: $int] : ! [v1: $int] : ( ~ (tb2t1(v0) = v1) | ~ in_uni(v0) | 207.52/128.08 t2tb1(v1) = v0) 207.52/128.08 (49) map_eq_sub1(int, all_105_3, all_105_1, $sum(all_86_10, 1), all_86_13) = 207.52/128.08 0 207.52/128.08 (50) t2tb(all_86_4) = all_105_3 207.52/128.08 (51) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.52/128.08 $int] : ! [v5: $int] : ( ~ (permut3(v0, v1, v2, v3, v4) = v5) | ~ 207.52/128.08 in_ty(v0) | ? [v6: $int] : ? [v7: $int] : ? [v8: $int] : ? [v9: 207.52/128.08 $int] : ? [v10: $int] : ((v10 = 0 & v9 = 0 & v5 = 0 & 207.52/128.08 map_eq_sub1(v0, v6, v7, v4, v8) = 0 & map_eq_sub1(v0, v6, v7, 0, 207.52/128.08 v3) = 0 & length1(v0, v1) = v8 & elts(v0, v2) = v7 & elts(v0, 207.52/128.08 v1) = v6 & in_uni(v7) & in_uni(v6)) | ( ~ (v6 = 0) & 207.52/128.08 permut_sub2(v0, v1, v2, v3, v4) = v6))) 207.52/128.08 207.52/128.08 Begin of proof 207.52/128.08 | 207.52/128.08 | GROUND_INST: instantiating (8) with int, all_103_4, all_105_4, all_86_11, 207.52/128.08 | $sum(all_86_10, 1), all_103_3, all_105_3, 0, simplifying with 207.52/128.08 | (4), (6), (18), (21) gives: 207.52/128.08 | (52) ? [v0: $int] : ? [v1: $int] : ((v1 = v0 & $lesseq(1, $difference(v0, 207.52/128.08 | all_86_10)) & $lesseq(all_86_11, v0) & $lesseq(-1, all_86_10) 207.52/128.08 | & $lesseq(0, all_86_11) & length1(int, all_105_4) = v0 & 207.52/128.08 | length1(int, all_103_4) = v0) | ( ~ (v0 = 0) & permut3(int, 207.52/128.08 | all_103_4, all_105_4, all_86_11, $sum(all_86_10, 1)) = v0)) 207.52/128.08 | 207.52/128.08 | GROUND_INST: instantiating (34) with int, all_103_4, all_105_4, all_86_11, 207.52/128.08 | $sum(all_86_10, 1), all_103_3, all_105_3, simplifying with (4), 207.52/128.08 | (6), (18), (21) gives: 207.52/128.08 | (53) ~ ($lesseq(-1, all_86_10)) | ~ ($lesseq(0, all_86_11)) | ? [v0: 207.52/128.08 | $int] : ? [v1: $int] : ((v0 = 0 & permut3(int, all_103_4, 207.52/128.08 | all_105_4, all_86_11, $sum(all_86_10, 1)) = 0) | (length1(int, 207.52/128.08 | all_103_4) = v0 & ( ~ ($lesseq(1, $difference(v0, all_86_10))) | 207.52/128.08 | ~ ($lesseq(all_86_11, v0)) | ( ~ (v1 = v0) & length1(int, 207.52/128.08 | all_105_4) = v1)))) 207.52/128.08 | 207.52/128.08 | GROUND_INST: instantiating (48) with all_133_1, all_133_0, simplifying with 207.52/128.08 | (15), (43) gives: 207.52/128.08 | (54) t2tb1(all_133_0) = all_133_1 207.52/128.08 | 207.52/128.08 | GROUND_INST: instantiating (40) with all_86_1, all_133_2, all_105_2, 207.52/128.08 | all_133_1, simplifying with (24), (28), (33) gives: 207.52/128.08 | (55) ? [v0: $int] : ? [v1: $int] : ? [v2: $int] : (tb2t(v0) = v1 & 207.52/128.08 | tb2t1(all_133_1) = v2 & get3(v1, all_133_2) = v2 & elts(int, 207.52/128.08 | all_105_2) = v0 & in_map_int_int(v1) & in_uni(v0)) 207.52/128.08 | 207.52/128.08 | GROUND_INST: instantiating (45) with int, all_105_2, all_133_2, all_133_1, 207.52/128.08 | simplifying with (6), (24) gives: 207.52/128.08 | (56) ? [v0: $int] : ? [v1: $int] : (elts(int, all_105_2) = v0 & 207.52/128.08 | t2tb1(all_133_2) = v1 & get(int, int, v0, v1) = all_133_1 & 207.52/128.08 | in_uni(v1) & in_uni(v0) & in_uni(all_133_1)) 207.52/128.08 | 207.52/128.08 | DELTA: instantiating (52) with fresh symbols all_726_0, all_726_1 gives: 207.52/128.08 | (57) (all_726_0 = all_726_1 & $lesseq(1, $difference(all_726_1, all_86_10)) 207.52/128.08 | & $lesseq(all_86_11, all_726_1) & $lesseq(-1, all_86_10) & 207.52/128.08 | $lesseq(0, all_86_11) & length1(int, all_105_4) = all_726_1 & 207.52/128.08 | length1(int, all_103_4) = all_726_1) | ( ~ (all_726_1 = 0) & 207.52/128.08 | permut3(int, all_103_4, all_105_4, all_86_11, $sum(all_86_10, 1)) = 207.52/128.08 | all_726_1) 207.52/128.08 | 207.52/128.08 | DELTA: instantiating (56) with fresh symbols all_729_0, all_729_1 gives: 207.52/128.08 | (58) elts(int, all_105_2) = all_729_1 & t2tb1(all_133_2) = all_729_0 & 207.52/128.08 | get(int, int, all_729_1, all_729_0) = all_133_1 & in_uni(all_729_0) & 207.52/128.08 | in_uni(all_729_1) & in_uni(all_133_1) 207.52/128.08 | 207.52/128.08 | ALPHA: (58) implies: 207.52/128.08 | (59) t2tb1(all_133_2) = all_729_0 207.52/128.08 | (60) elts(int, all_105_2) = all_729_1 207.52/128.08 | 207.52/128.08 | DELTA: instantiating (55) with fresh symbols all_739_0, all_739_1, all_739_2 207.52/128.08 | gives: 207.52/128.08 | (61) tb2t(all_739_2) = all_739_1 & tb2t1(all_133_1) = all_739_0 & 207.52/128.08 | get3(all_739_1, all_133_2) = all_739_0 & elts(int, all_105_2) = 207.52/128.08 | all_739_2 & in_map_int_int(all_739_1) & in_uni(all_739_2) 207.52/128.08 | 207.52/128.08 | ALPHA: (61) implies: 207.52/128.08 | (62) elts(int, all_105_2) = all_739_2 207.52/128.08 | (63) get3(all_739_1, all_133_2) = all_739_0 207.52/128.08 | (64) tb2t1(all_133_1) = all_739_0 207.52/128.08 | (65) tb2t(all_739_2) = all_739_1 207.52/128.08 | 207.52/128.08 | BETA: splitting (53) gives: 207.52/128.08 | 207.52/128.08 | Case 1: 207.52/128.08 | | 207.52/128.08 | | (66) $lesseq(all_86_11, -1) 207.52/128.08 | | 207.52/128.08 | | COMBINE_INEQS: (39), (66) imply: 207.52/128.08 | | (67) $lesseq(0, -1) 207.52/128.08 | | 207.52/128.08 | | CLOSE: (67) is inconsistent. 207.52/128.08 | | 207.52/128.08 | Case 2: 207.52/128.08 | | 207.52/128.08 | | (68) ~ ($lesseq(-1, all_86_10)) | ? [v0: $int] : ? [v1: $int] : ((v0 = 207.52/128.08 | | 0 & permut3(int, all_103_4, all_105_4, all_86_11, 207.52/128.08 | | $sum(all_86_10, 1)) = 0) | (length1(int, all_103_4) = v0 & ( ~ 207.52/128.08 | | ($lesseq(1, $difference(v0, all_86_10))) | ~ 207.52/128.08 | | ($lesseq(all_86_11, v0)) | ( ~ (v1 = v0) & length1(int, 207.52/128.08 | | all_105_4) = v1)))) 207.52/128.08 | | 207.52/128.08 | | BETA: splitting (68) gives: 207.52/128.08 | | 207.52/128.08 | | Case 1: 207.52/128.08 | | | 207.52/128.08 | | | (69) $lesseq(all_86_10, -2) 207.52/128.08 | | | 207.52/128.08 | | | COMBINE_INEQS: (46), (69) imply: 207.52/128.08 | | | (70) $lesseq(0, -1) 207.52/128.08 | | | 207.52/128.08 | | | CLOSE: (70) is inconsistent. 207.52/128.08 | | | 207.52/128.08 | | Case 2: 207.52/128.08 | | | 207.52/128.08 | | | (71) ? [v0: $int] : ? [v1: $int] : ((v0 = 0 & permut3(int, all_103_4, 207.52/128.08 | | | all_105_4, all_86_11, $sum(all_86_10, 1)) = 0) | 207.52/128.08 | | | (length1(int, all_103_4) = v0 & ( ~ ($lesseq(1, $difference(v0, 207.52/128.08 | | | all_86_10))) | ~ ($lesseq(all_86_11, v0)) | ( ~ (v1 = 207.52/128.08 | | | v0) & length1(int, all_105_4) = v1)))) 207.52/128.08 | | | 207.52/128.08 | | | DELTA: instantiating (71) with fresh symbols all_755_0, all_755_1 gives: 207.52/128.08 | | | (72) (all_755_1 = 0 & permut3(int, all_103_4, all_105_4, all_86_11, 207.52/128.08 | | | $sum(all_86_10, 1)) = 0) | (length1(int, all_103_4) = 207.52/128.08 | | | all_755_1 & ( ~ ($lesseq(1, $difference(all_755_1, all_86_10))) 207.52/128.08 | | | | ~ ($lesseq(all_86_11, all_755_1)) | ( ~ (all_755_0 = 207.52/128.08 | | | all_755_1) & length1(int, all_105_4) = all_755_0))) 207.52/128.08 | | | 207.52/128.08 | | | BETA: splitting (72) gives: 207.52/128.08 | | | 207.52/128.08 | | | Case 1: 207.52/128.08 | | | | 207.52/128.08 | | | | (73) all_755_1 = 0 & permut3(int, all_103_4, all_105_4, all_86_11, 207.52/128.08 | | | | $sum(all_86_10, 1)) = 0 207.52/128.08 | | | | 207.52/128.08 | | | | ALPHA: (73) implies: 207.52/128.08 | | | | (74) permut3(int, all_103_4, all_105_4, all_86_11, $sum(all_86_10, 207.52/128.08 | | | | 1)) = 0 207.52/128.08 | | | | 207.52/128.08 | | | | BETA: splitting (57) gives: 207.52/128.08 | | | | 207.52/128.08 | | | | Case 1: 207.52/128.08 | | | | | 207.52/128.08 | | | | | (75) all_726_0 = all_726_1 & $lesseq(1, $difference(all_726_1, 207.52/128.08 | | | | | all_86_10)) & $lesseq(all_86_11, all_726_1) & $lesseq(-1, 207.52/128.08 | | | | | all_86_10) & $lesseq(0, all_86_11) & length1(int, all_105_4) 207.52/128.08 | | | | | = all_726_1 & length1(int, all_103_4) = all_726_1 207.52/128.08 | | | | | 207.52/128.08 | | | | | ALPHA: (75) implies: 207.52/128.08 | | | | | (76) $lesseq(1, $difference(all_726_1, all_86_10)) 207.52/128.08 | | | | | (77) length1(int, all_103_4) = all_726_1 207.52/128.08 | | | | | 207.52/128.08 | | | | | GROUND_INST: instantiating (1) with all_133_0, all_739_0, all_133_1, 207.52/128.08 | | | | | simplifying with (15), (64) gives: 207.52/128.08 | | | | | (78) all_739_0 = all_133_0 207.52/128.08 | | | | | 207.52/128.08 | | | | | GROUND_INST: instantiating (44) with all_86_13, all_726_1, all_103_4, 207.52/128.08 | | | | | int, simplifying with (7), (77) gives: 207.52/128.08 | | | | | (79) all_726_1 = all_86_13 207.52/128.08 | | | | | 207.52/128.08 | | | | | GROUND_INST: instantiating (19) with all_105_1, all_739_2, all_105_2, 207.52/128.08 | | | | | int, simplifying with (26), (62) gives: 207.52/128.08 | | | | | (80) all_739_2 = all_105_1 207.52/128.08 | | | | | 207.52/128.08 | | | | | GROUND_INST: instantiating (19) with all_739_2, all_729_1, all_105_2, 207.52/128.08 | | | | | int, simplifying with (60), (62) gives: 207.52/128.08 | | | | | (81) all_739_2 = all_729_1 207.52/128.08 | | | | | 207.52/128.08 | | | | | COMBINE_EQS: (80), (81) imply: 207.52/128.08 | | | | | (82) all_729_1 = all_105_1 207.52/128.08 | | | | | 207.52/128.08 | | | | | REDUCE: (65), (80) imply: 207.52/128.08 | | | | | (83) tb2t(all_105_1) = all_739_1 207.52/128.08 | | | | | 207.52/128.08 | | | | | REDUCE: (63), (78) imply: 207.52/128.08 | | | | | (84) get3(all_739_1, all_133_2) = all_133_0 207.52/128.08 | | | | | 207.52/128.08 | | | | | GROUND_INST: instantiating (41) with all_86_2, all_739_1, all_105_1, 207.52/128.08 | | | | | simplifying with (25), (83) gives: 207.52/128.08 | | | | | (85) all_739_1 = all_86_2 207.52/128.08 | | | | | 207.52/128.08 | | | | | REDUCE: (84), (85) imply: 207.52/128.08 | | | | | (86) get3(all_86_2, all_133_2) = all_133_0 207.52/128.08 | | | | | 207.52/128.08 | | | | | GROUND_INST: instantiating (51) with int, all_103_4, all_105_4, 207.52/128.08 | | | | | all_86_11, $sum(all_86_10, 1), 0, simplifying with (6), 207.52/128.08 | | | | | (74) gives: 207.52/128.08 | | | | | (87) ? [v0: $int] : ? [v1: $int] : ? [v2: $int] : ? [v3: $int] 207.52/128.08 | | | | | : ? [v4: $int] : ((v4 = 0 & v3 = 0 & map_eq_sub1(int, v0, v1, 207.52/128.08 | | | | | $sum(all_86_10, 1), v2) = 0 & map_eq_sub1(int, v0, v1, 207.52/128.08 | | | | | 0, all_86_11) = 0 & length1(int, all_103_4) = v2 & 207.52/128.08 | | | | | elts(int, all_105_4) = v1 & elts(int, all_103_4) = v0 & 207.52/128.08 | | | | | in_uni(v1) & in_uni(v0)) | ( ~ (v0 = 0) & permut_sub2(int, 207.52/128.08 | | | | | all_103_4, all_105_4, all_86_11, $sum(all_86_10, 1)) = 207.52/128.08 | | | | | v0)) 207.52/128.08 | | | | | 207.52/128.08 | | | | | GROUND_INST: instantiating (42) with all_86_4, all_86_2, 0, all_86_7, 207.52/128.08 | | | | | all_105_3, all_105_1, all_133_2, all_133_0, simplifying 207.52/128.08 | | | | | with (5), (23), (38), (50), (86) gives: 207.52/128.08 | | | | | (88) ~ ($lesseq(1, $difference(all_86_7, all_133_2))) | ~ 207.52/128.08 | | | | | ($lesseq(0, all_133_2)) | get3(all_86_4, all_133_2) = 207.52/128.08 | | | | | all_133_0 207.52/128.08 | | | | | 207.52/128.08 | | | | | GROUND_INST: instantiating (35) with int, all_105_3, all_105_1, 207.52/128.08 | | | | | $sum(all_86_10, 1), all_86_13, all_133_0, all_133_1, 207.52/128.08 | | | | | simplifying with (6), (49), (54) gives: 207.52/128.08 | | | | | (89) ~ ($lesseq(1, $difference(all_86_13, all_133_0))) | ~ 207.52/128.08 | | | | | ($lesseq(1, $difference(all_133_0, all_86_10))) | ? [v0: 207.52/128.08 | | | | | $int] : (get(int, int, all_105_1, all_133_1) = v0 & get(int, 207.52/128.08 | | | | | int, all_105_3, all_133_1) = v0 & in_uni(v0)) 207.52/128.08 | | | | | 207.52/128.08 | | | | | GROUND_INST: instantiating (35) with int, all_103_3, all_103_1, 207.52/128.08 | | | | | $sum(all_86_10, 1), all_86_13, all_133_0, all_133_1, 207.52/128.08 | | | | | simplifying with (6), (12), (54) gives: 207.52/128.08 | | | | | (90) ~ ($lesseq(1, $difference(all_86_13, all_133_0))) | ~ 207.52/128.08 | | | | | ($lesseq(1, $difference(all_133_0, all_86_10))) | ? [v0: 207.52/128.08 | | | | | $int] : (get(int, int, all_103_1, all_133_1) = v0 & get(int, 207.52/128.08 | | | | | int, all_103_3, all_133_1) = v0 & in_uni(v0)) 207.52/128.08 | | | | | 207.52/128.08 | | | | | GROUND_INST: instantiating (35) with int, all_103_3, all_103_1, 0, 207.52/128.08 | | | | | all_86_11, all_133_0, all_133_1, simplifying with (6), 207.52/128.08 | | | | | (27), (54) gives: 207.52/128.08 | | | | | (91) ~ ($lesseq(1, $difference(all_86_11, all_133_0))) | ~ 207.52/128.08 | | | | | ($lesseq(0, all_133_0)) | ? [v0: $int] : (get(int, int, 207.52/128.08 | | | | | all_103_1, all_133_1) = v0 & get(int, int, all_103_3, 207.52/128.08 | | | | | all_133_1) = v0 & in_uni(v0)) 207.52/128.08 | | | | | 207.52/128.08 | | | | | GROUND_INST: instantiating (35) with int, all_105_3, all_105_1, 0, 207.52/128.08 | | | | | all_86_7, all_133_2, all_729_0, simplifying with (6), 207.52/128.08 | | | | | (23), (59) gives: 207.52/128.08 | | | | | (92) ~ ($lesseq(1, $difference(all_86_7, all_133_2))) | ~ 207.52/128.08 | | | | | ($lesseq(0, all_133_2)) | ? [v0: $int] : (get(int, int, 207.52/128.08 | | | | | all_105_1, all_729_0) = v0 & get(int, int, all_105_3, 207.52/128.08 | | | | | all_729_0) = v0 & in_uni(v0)) 207.52/128.08 | | | | | 207.52/128.08 | | | | | GROUND_INST: instantiating (35) with int, all_103_1, all_105_3, 207.52/128.08 | | | | | $sum(all_86_8, 1), all_86_13, all_133_2, all_729_0, 207.52/128.08 | | | | | simplifying with (6), (16), (59) gives: 207.52/128.08 | | | | | (93) ~ ($lesseq(1, $difference(all_86_13, all_133_2))) | ~ 207.52/128.08 | | | | | ($lesseq(1, $difference(all_133_2, all_86_8))) | ? [v0: $int] 207.52/128.08 | | | | | : (get(int, int, all_105_3, all_729_0) = v0 & get(int, int, 207.52/128.08 | | | | | all_103_1, all_729_0) = v0 & in_uni(v0)) 207.52/128.08 | | | | | 207.52/128.08 | | | | | DELTA: instantiating (87) with fresh symbols all_806_0, all_806_1, 207.52/128.08 | | | | | all_806_2, all_806_3, all_806_4 gives: 207.52/128.08 | | | | | (94) (all_806_0 = 0 & all_806_1 = 0 & map_eq_sub1(int, all_806_4, 207.52/128.08 | | | | | all_806_3, $sum(all_86_10, 1), all_806_2) = 0 & 207.52/128.08 | | | | | map_eq_sub1(int, all_806_4, all_806_3, 0, all_86_11) = 0 & 207.52/128.08 | | | | | length1(int, all_103_4) = all_806_2 & elts(int, all_105_4) = 207.52/128.08 | | | | | all_806_3 & elts(int, all_103_4) = all_806_4 & 207.52/128.08 | | | | | in_uni(all_806_3) & in_uni(all_806_4)) | ( ~ (all_806_4 = 0) 207.52/128.08 | | | | | & permut_sub2(int, all_103_4, all_105_4, all_86_11, 207.52/128.08 | | | | | $sum(all_86_10, 1)) = all_806_4) 207.52/128.08 | | | | | 207.52/128.08 | | | | | BETA: splitting (29) gives: 207.52/128.08 | | | | | 207.52/128.08 | | | | | Case 1: 207.52/128.08 | | | | | | 207.52/128.08 | | | | | | (95) ~ (all_86_11 = 0) 207.52/128.08 | | | | | | 207.52/128.08 | | | | | | STRENGTHEN: (39), (95) imply: 207.52/128.08 | | | | | | (96) $lesseq(1, all_86_11) 207.52/128.08 | | | | | | 207.52/128.08 | | | | | | COMBINE_INEQS: (14), (22) imply: 207.52/128.08 | | | | | | (97) $lesseq(2, $difference(all_86_7, all_86_8)) 207.52/128.08 | | | | | | 207.52/128.08 | | | | | | COMBINE_INEQS: (31), (97) imply: 207.52/128.08 | | | | | | (98) $lesseq(2, $difference(all_86_10, all_86_8)) 207.52/128.08 | | | | | | 207.52/128.08 | | | | | | COMBINE_INEQS: (30), (98) imply: 207.52/128.08 | | | | | | (99) $lesseq(2, $difference(all_86_10, all_86_11)) 207.52/128.08 | | | | | | 207.52/128.08 | | | | | | COMBINE_INEQS: (36), (99) imply: 207.52/128.08 | | | | | | (100) $lesseq(3, $difference(all_86_13, all_86_11)) 207.52/128.08 | | | | | | 207.52/128.08 | | | | | | COMBINE_INEQS: (96), (100) imply: 207.52/128.08 | | | | | | (101) $lesseq(4, all_86_13) 207.52/128.08 | | | | | | 207.52/128.08 | | | | | | REF_CLOSE: (2), (3), (4), (6), (7), (9), (10), (11), (13), (14), 207.52/128.08 | | | | | | (19), (21), (22), (31), (32), (37), (42), (44), (47), 207.52/128.08 | | | | | | (50), (88), (89), (90), (91), (92), (93), (94), (101) are 207.52/128.08 | | | | | | inconsistent by sub-proof #103. 207.52/128.08 | | | | | | 207.52/128.08 | | | | | Case 2: 207.52/128.08 | | | | | | 207.52/128.08 | | | | | | (102) all_86_11 = 0 207.52/128.08 | | | | | | (103) ~ ($difference(all_86_10, all_86_13) = -1) 207.52/128.08 | | | | | | 207.52/128.08 | | | | | | REDUCE: (30), (102) imply: 207.52/128.08 | | | | | | (104) $lesseq(0, all_86_8) 207.52/128.08 | | | | | | 207.52/128.08 | | | | | | STRENGTHEN: (36), (103) imply: 207.52/128.08 | | | | | | (105) $lesseq(2, $difference(all_86_13, all_86_10)) 207.52/128.08 | | | | | | 207.52/128.08 | | | | | | COMBINE_INEQS: (14), (22) imply: 207.52/128.08 | | | | | | (106) $lesseq(2, $difference(all_86_7, all_86_8)) 207.52/128.08 | | | | | | 207.52/128.08 | | | | | | COMBINE_INEQS: (31), (106) imply: 207.52/128.08 | | | | | | (107) $lesseq(2, $difference(all_86_10, all_86_8)) 207.52/128.08 | | | | | | 207.52/128.08 | | | | | | COMBINE_INEQS: (104), (107) imply: 207.52/128.08 | | | | | | (108) $lesseq(2, all_86_10) 207.52/128.08 | | | | | | 207.52/128.08 | | | | | | COMBINE_INEQS: (105), (108) imply: 207.52/128.08 | | | | | | (109) $lesseq(4, all_86_13) 207.52/128.08 | | | | | | 207.52/128.08 | | | | | | REF_CLOSE: (2), (3), (4), (6), (7), (9), (10), (11), (13), (14), 207.52/128.08 | | | | | | (19), (21), (22), (31), (32), (37), (42), (44), (47), 207.52/128.08 | | | | | | (50), (88), (89), (90), (91), (92), (93), (94), (109) are 207.52/128.08 | | | | | | inconsistent by sub-proof #103. 207.52/128.08 | | | | | | 207.52/128.08 | | | | | End of split 207.52/128.08 | | | | | 207.52/128.08 | | | | Case 2: 207.52/128.08 | | | | | 207.52/128.08 | | | | | (110) ~ (all_726_1 = 0) & permut3(int, all_103_4, all_105_4, 207.52/128.08 | | | | | all_86_11, $sum(all_86_10, 1)) = all_726_1 207.52/128.08 | | | | | 207.52/128.08 | | | | | ALPHA: (110) implies: 207.52/128.08 | | | | | (111) ~ (all_726_1 = 0) 207.52/128.08 | | | | | (112) permut3(int, all_103_4, all_105_4, all_86_11, $sum(all_86_10, 207.52/128.09 | | | | | 1)) = all_726_1 207.52/128.09 | | | | | 207.52/128.09 | | | | | GROUND_INST: instantiating (17) with all_726_1, 0, $sum(all_86_10, 1), 207.52/128.09 | | | | | all_86_11, all_105_4, all_103_4, int, simplifying with 207.52/128.09 | | | | | (74), (112) gives: 207.52/128.09 | | | | | (113) all_726_1 = 0 207.52/128.09 | | | | | 207.52/128.09 | | | | | REDUCE: (111), (113) imply: 207.52/128.09 | | | | | (114) ~ (0 = 0) 207.52/128.09 | | | | | 207.52/128.09 | | | | | CLOSE: (114) is inconsistent. 207.52/128.09 | | | | | 207.52/128.09 | | | | End of split 207.52/128.09 | | | | 207.52/128.09 | | | Case 2: 207.52/128.09 | | | | 207.52/128.09 | | | | (115) length1(int, all_103_4) = all_755_1 & ( ~ ($lesseq(1, 207.52/128.09 | | | | $difference(all_755_1, all_86_10))) | ~ 207.52/128.09 | | | | ($lesseq(all_86_11, all_755_1)) | ( ~ (all_755_0 = all_755_1) 207.52/128.09 | | | | & length1(int, all_105_4) = all_755_0)) 207.52/128.09 | | | | 207.52/128.09 | | | | ALPHA: (115) implies: 207.52/128.09 | | | | (116) length1(int, all_103_4) = all_755_1 207.52/128.09 | | | | (117) ~ ($lesseq(1, $difference(all_755_1, all_86_10))) | ~ 207.52/128.09 | | | | ($lesseq(all_86_11, all_755_1)) | ( ~ (all_755_0 = all_755_1) & 207.52/128.09 | | | | length1(int, all_105_4) = all_755_0) 207.52/128.09 | | | | 207.52/128.09 | | | | GROUND_INST: instantiating (44) with all_86_13, all_755_1, all_103_4, 207.52/128.09 | | | | int, simplifying with (7), (116) gives: 207.52/128.09 | | | | (118) all_755_1 = all_86_13 207.52/128.09 | | | | 207.52/128.09 | | | | BETA: splitting (117) gives: 207.52/128.09 | | | | 207.52/128.09 | | | | Case 1: 207.52/128.09 | | | | | 207.52/128.09 | | | | | (119) $lesseq(1, $difference(all_86_11, all_755_1)) 207.52/128.09 | | | | | 207.52/128.09 | | | | | REDUCE: (118), (119) imply: 207.52/128.09 | | | | | (120) $lesseq(1, $difference(all_86_11, all_86_13)) 207.52/128.09 | | | | | 207.52/128.09 | | | | | COMBINE_INEQS: (14), (22) imply: 207.52/128.09 | | | | | (121) $lesseq(2, $difference(all_86_7, all_86_8)) 207.52/128.09 | | | | | 207.52/128.09 | | | | | COMBINE_INEQS: (31), (121) imply: 207.52/128.09 | | | | | (122) $lesseq(2, $difference(all_86_10, all_86_8)) 207.52/128.09 | | | | | 207.52/128.09 | | | | | COMBINE_INEQS: (30), (122) imply: 207.52/128.09 | | | | | (123) $lesseq(2, $difference(all_86_10, all_86_11)) 207.52/128.09 | | | | | 207.52/128.09 | | | | | COMBINE_INEQS: (36), (123) imply: 207.52/128.09 | | | | | (124) $lesseq(3, $difference(all_86_13, all_86_11)) 207.52/128.09 | | | | | 207.52/128.09 | | | | | COMBINE_INEQS: (120), (124) imply: 207.52/128.09 | | | | | (125) $lesseq(0, -1) 207.52/128.09 | | | | | 207.52/128.09 | | | | | CLOSE: (125) is inconsistent. 207.52/128.09 | | | | | 207.52/128.09 | | | | Case 2: 207.52/128.09 | | | | | 207.52/128.09 | | | | | (126) ~ ($lesseq(1, $difference(all_755_1, all_86_10))) | ( ~ 207.52/128.09 | | | | | (all_755_0 = all_755_1) & length1(int, all_105_4) = 207.52/128.09 | | | | | all_755_0) 207.52/128.09 | | | | | 207.52/128.09 | | | | | BETA: splitting (126) gives: 207.52/128.09 | | | | | 207.52/128.09 | | | | | Case 1: 207.52/128.09 | | | | | | 207.52/128.09 | | | | | | (127) $lesseq(all_755_1, all_86_10) 207.52/128.09 | | | | | | 207.52/128.09 | | | | | | REDUCE: (118), (127) imply: 207.52/128.09 | | | | | | (128) $lesseq(all_86_13, all_86_10) 207.52/128.09 | | | | | | 207.52/128.09 | | | | | | COMBINE_INEQS: (36), (128) imply: 207.52/128.09 | | | | | | (129) $lesseq(0, -1) 207.52/128.09 | | | | | | 207.52/128.09 | | | | | | CLOSE: (129) is inconsistent. 207.52/128.09 | | | | | | 207.52/128.09 | | | | | Case 2: 207.52/128.09 | | | | | | 207.52/128.09 | | | | | | (130) ~ (all_755_0 = all_755_1) & length1(int, all_105_4) = 207.52/128.09 | | | | | | all_755_0 207.52/128.09 | | | | | | 207.52/128.09 | | | | | | ALPHA: (130) implies: 207.52/128.09 | | | | | | (131) ~ (all_755_0 = all_755_1) 207.52/128.09 | | | | | | (132) length1(int, all_105_4) = all_755_0 207.52/128.09 | | | | | | 207.52/128.09 | | | | | | REDUCE: (118), (131) imply: 207.52/128.09 | | | | | | (133) ~ (all_755_0 = all_86_13) 207.52/128.09 | | | | | | 207.52/128.09 | | | | | | GROUND_INST: instantiating (44) with all_86_13, all_755_0, 207.52/128.09 | | | | | | all_105_4, int, simplifying with (20), (132) gives: 207.52/128.09 | | | | | | (134) all_755_0 = all_86_13 207.52/128.09 | | | | | | 207.52/128.09 | | | | | | REDUCE: (133), (134) imply: 207.52/128.09 | | | | | | (135) ~ (0 = 0) 207.52/128.09 | | | | | | 207.52/128.09 | | | | | | CLOSE: (135) is inconsistent. 207.52/128.09 | | | | | | 207.52/128.09 | | | | | End of split 207.52/128.09 | | | | | 207.52/128.09 | | | | End of split 207.52/128.09 | | | | 207.52/128.09 | | | End of split 207.52/128.09 | | | 207.52/128.09 | | End of split 207.52/128.09 | | 207.52/128.09 | End of split 207.52/128.09 | 207.52/128.09 End of proof 207.52/128.09 207.52/128.09 Sub-proof #103 shows that the following formulas are inconsistent: 207.52/128.09 ---------------------------------------------------------------- 207.52/128.09 (1) in_map_int_int(all_86_6) 207.52/128.09 (2) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.52/128.09 $int] : ! [v5: $int] : ! [v6: $int] : ( ~ ($lesseq(0, v4)) | ~ 207.52/128.09 ($lesseq(0, v3)) | ~ (map_eq_sub1(v0, v5, v6, v3, v4) = 0) | ~ 207.52/128.09 (elts(v0, v2) = v6) | ~ (elts(v0, v1) = v5) | ~ in_ty(v0) | ? [v7: 207.52/128.09 $int] : ? [v8: $int] : ((v7 = 0 & array_eq_sub1(v0, v1, v2, v3, v4) 207.52/128.09 = 0) | (length1(v0, v1) = v7 & ( ~ ($lesseq(v4, v7)) | ~ 207.52/128.09 ($lesseq(v3, v7)) | ( ~ (v8 = v7) & length1(v0, v2) = v8))))) 207.52/128.09 (3) elts(int, all_103_4) = all_103_3 207.52/128.09 (4) in_ty(int) 207.52/128.09 (5) length1(int, all_103_4) = all_86_13 207.52/128.09 (6) $lesseq(-1, all_86_8) 207.52/128.09 (7) $lesseq(all_86_7, all_86_13) 207.52/128.09 (8) ! [v0: $int] : ! [v1: $int] : (v1 = 42 | ~ ($lesseq(1, 207.52/128.09 $difference(all_86_7, v0))) | ~ ($lesseq(1, $difference(v0, 207.52/128.09 all_86_8))) | ~ (get3(all_86_6, v0) = v1)) 207.52/128.09 (9) t2tb(all_86_6) = all_103_1 207.52/128.09 (10) $lesseq(1, $difference(all_133_2, all_86_8)) 207.52/128.09 (11) ~ ($lesseq(1, $difference(all_86_13, all_133_0))) | ~ ($lesseq(1, 207.52/128.09 $difference(all_133_0, all_86_10))) | ? [v0: $int] : (get(int, int, 207.52/128.09 all_105_1, all_133_1) = v0 & get(int, int, all_105_3, all_133_1) = 207.52/128.09 v0 & in_uni(v0)) 207.52/128.09 (12) (all_806_0 = 0 & all_806_1 = 0 & map_eq_sub1(int, all_806_4, all_806_3, 207.52/128.09 $sum(all_86_10, 1), all_806_2) = 0 & map_eq_sub1(int, all_806_4, 207.52/128.09 all_806_3, 0, all_86_11) = 0 & length1(int, all_103_4) = all_806_2 & 207.52/128.09 elts(int, all_105_4) = all_806_3 & elts(int, all_103_4) = all_806_4 & 207.52/128.09 in_uni(all_806_3) & in_uni(all_806_4)) | ( ~ (all_806_4 = 0) & 207.52/128.09 permut_sub2(int, all_103_4, all_105_4, all_86_11, $sum(all_86_10, 1)) 207.52/128.09 = all_806_4) 207.52/128.09 (13) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 207.52/128.09 | ~ (elts(v3, v2) = v1) | ~ (elts(v3, v2) = v0)) 207.52/128.09 (14) elts(int, all_105_4) = all_105_3 207.52/128.09 (15) $lesseq(1, $difference(all_86_7, all_133_2)) 207.52/128.09 (16) ~ ($lesseq(1, $difference(all_86_11, all_133_0))) | ~ ($lesseq(0, 207.52/128.09 all_133_0)) | ? [v0: $int] : (get(int, int, all_103_1, all_133_1) = 207.52/128.09 v0 & get(int, int, all_103_3, all_133_1) = v0 & in_uni(v0)) 207.52/128.09 (17) $lesseq(all_86_7, all_86_10) 207.52/128.09 (18) $lesseq(4, all_86_13) 207.52/128.09 (19) ~ (all_133_0 = 42) 207.52/128.09 (20) ~ ($lesseq(1, $difference(all_86_13, all_133_2))) | ~ ($lesseq(1, 207.52/128.09 $difference(all_133_2, all_86_8))) | ? [v0: $int] : (get(int, int, 207.52/128.09 all_105_3, all_729_0) = v0 & get(int, int, all_103_1, all_729_0) = 207.52/128.09 v0 & in_uni(v0)) 207.52/128.09 (21) ~ ($lesseq(1, $difference(all_86_7, all_133_2))) | ~ ($lesseq(0, 207.52/128.09 all_133_2)) | get3(all_86_4, all_133_2) = all_133_0 207.52/128.09 (22) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.52/128.09 $int] : ! [v5: $int] : (v5 = 0 | ~ (permut_sub2(v0, v1, v2, v3, v4) 207.52/128.09 = v5) | ~ in_ty(v0) | ? [v6: $int] : ? [v7: $int] : ? [v8: $int] 207.52/128.09 : ? [v9: $int] : (( ~ (v9 = 0) & map_eq_sub1(v0, v6, v7, v4, v8) = v9 207.52/128.09 & length1(v0, v1) = v8 & elts(v0, v2) = v7 & elts(v0, v1) = v6 & 207.52/128.09 in_uni(v7) & in_uni(v6)) | ( ~ (v8 = 0) & map_eq_sub1(v0, v6, v7, 207.52/128.09 0, v3) = v8 & elts(v0, v2) = v7 & elts(v0, v1) = v6 & in_uni(v7) 207.52/128.09 & in_uni(v6)) | ( ~ (v6 = 0) & permut3(v0, v1, v2, v3, v4) = v6))) 207.52/128.09 (23) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.52/128.09 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 207.52/128.09 ($lesseq(1, $difference(v3, v6))) | ~ ($lesseq(v2, v6)) | ~ 207.52/128.09 (map_eq_sub1(int, v4, v5, v2, v3) = 0) | ~ (t2tb(v1) = v5) | ~ 207.52/128.09 (t2tb(v0) = v4) | ~ (get3(v1, v6) = v7) | ~ in_map_int_int(v0) | 207.52/128.09 get3(v0, v6) = v7) 207.52/128.09 (24) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 207.52/128.09 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 207.52/128.09 (25) map_eq_sub1(int, all_103_1, all_105_3, 0, all_86_13) = 0 207.52/128.09 (26) ~ ($lesseq(1, $difference(all_86_7, all_133_2))) | ~ ($lesseq(0, 207.52/128.09 all_133_2)) | ? [v0: $int] : (get(int, int, all_105_1, all_729_0) = 207.52/128.09 v0 & get(int, int, all_105_3, all_729_0) = v0 & in_uni(v0)) 207.52/128.09 (27) ~ ($lesseq(1, $difference(all_86_13, all_133_0))) | ~ ($lesseq(1, 207.52/128.09 $difference(all_133_0, all_86_10))) | ? [v0: $int] : (get(int, int, 207.52/128.09 all_103_1, all_133_1) = v0 & get(int, int, all_103_3, all_133_1) = 207.52/128.09 v0 & in_uni(v0)) 207.52/128.09 (28) t2tb(all_86_4) = all_105_3 207.52/128.09 207.52/128.09 Begin of proof 207.52/128.09 | 207.52/128.09 | BETA: splitting (26) gives: 207.52/128.09 | 207.52/128.09 | Case 1: 207.52/128.09 | | 207.52/128.09 | | (29) $lesseq(all_133_2, -1) 207.52/128.09 | | 207.52/128.09 | | COMBINE_INEQS: (10), (29) imply: 207.52/128.09 | | (30) $lesseq(all_86_8, -2) 207.52/128.09 | | 207.52/128.09 | | COMBINE_INEQS: (6), (30) imply: 207.52/128.09 | | (31) $lesseq(0, -1) 207.52/128.09 | | 207.52/128.09 | | CLOSE: (31) is inconsistent. 207.52/128.09 | | 207.52/128.09 | Case 2: 207.52/128.09 | | 207.52/128.09 | | (32) $lesseq(0, all_133_2) 207.52/128.09 | | 207.52/128.09 | | COMBINE_INEQS: (15), (32) imply: 207.52/128.09 | | (33) $lesseq(1, all_86_7) 207.52/128.09 | | 207.52/128.09 | | COMBINE_INEQS: (17), (33) imply: 207.52/128.09 | | (34) $lesseq(1, all_86_10) 207.52/128.09 | | 207.52/128.09 | | BETA: splitting (21) gives: 207.52/128.09 | | 207.52/128.09 | | Case 1: 207.52/128.09 | | | 207.52/128.09 | | | (35) get3(all_86_4, all_133_2) = all_133_0 207.52/128.09 | | | 207.52/128.09 | | | BETA: splitting (20) gives: 207.52/128.09 | | | 207.52/128.09 | | | Case 1: 207.52/128.09 | | | | 207.52/128.09 | | | | (36) $lesseq(all_86_13, all_133_2) 207.52/128.09 | | | | 207.52/128.09 | | | | COMBINE_INEQS: (15), (36) imply: 207.52/128.09 | | | | (37) $lesseq(1, $difference(all_86_7, all_86_13)) 207.52/128.09 | | | | 207.52/128.09 | | | | COMBINE_INEQS: (7), (37) imply: 207.52/128.09 | | | | (38) $lesseq(0, -1) 207.52/128.09 | | | | 207.52/128.09 | | | | CLOSE: (38) is inconsistent. 207.52/128.09 | | | | 207.52/128.09 | | | Case 2: 207.52/128.09 | | | | 207.52/128.09 | | | | (39) $lesseq(1, $difference(all_86_13, all_133_2)) 207.52/128.09 | | | | 207.52/128.09 | | | | BETA: splitting (12) gives: 207.52/128.09 | | | | 207.52/128.09 | | | | Case 1: 207.52/128.09 | | | | | 207.52/128.09 | | | | | (40) all_806_0 = 0 & all_806_1 = 0 & map_eq_sub1(int, all_806_4, 207.52/128.09 | | | | | all_806_3, $sum(all_86_10, 1), all_806_2) = 0 & 207.52/128.09 | | | | | map_eq_sub1(int, all_806_4, all_806_3, 0, all_86_11) = 0 & 207.52/128.09 | | | | | length1(int, all_103_4) = all_806_2 & elts(int, all_105_4) = 207.52/128.09 | | | | | all_806_3 & elts(int, all_103_4) = all_806_4 & 207.52/128.09 | | | | | in_uni(all_806_3) & in_uni(all_806_4) 207.52/128.09 | | | | | 207.52/128.09 | | | | | ALPHA: (40) implies: 207.52/128.09 | | | | | (41) elts(int, all_103_4) = all_806_4 207.52/128.09 | | | | | (42) map_eq_sub1(int, all_806_4, all_806_3, $sum(all_86_10, 1), 207.52/128.09 | | | | | all_806_2) = 0 207.52/128.09 | | | | | (43) elts(int, all_105_4) = all_806_3 207.52/128.09 | | | | | (44) length1(int, all_103_4) = all_806_2 207.52/128.09 | | | | | 207.52/128.09 | | | | | GROUND_INST: instantiating (24) with all_86_13, all_806_2, all_103_4, 207.52/128.09 | | | | | int, simplifying with (5), (44) gives: 207.52/128.09 | | | | | (45) all_806_2 = all_86_13 207.52/128.09 | | | | | 207.52/128.09 | | | | | GROUND_INST: instantiating (13) with all_105_3, all_806_3, all_105_4, 207.52/128.09 | | | | | int, simplifying with (14), (43) gives: 207.52/128.09 | | | | | (46) all_806_3 = all_105_3 207.52/128.09 | | | | | 207.52/128.09 | | | | | GROUND_INST: instantiating (13) with all_103_3, all_806_4, all_103_4, 207.52/128.09 | | | | | int, simplifying with (3), (41) gives: 207.52/128.09 | | | | | (47) all_806_4 = all_103_3 207.52/128.09 | | | | | 207.52/128.09 | | | | | REDUCE: (42), (45), (46), (47) imply: 207.52/128.09 | | | | | (48) map_eq_sub1(int, all_103_3, all_105_3, $sum(all_86_10, 1), 207.52/128.09 | | | | | all_86_13) = 0 207.52/128.09 | | | | | 207.52/128.09 | | | | | REF_CLOSE: (1), (2), (3), (4), (8), (9), (10), (11), (14), (15), (16), 207.52/128.09 | | | | | (18), (19), (23), (25), (27), (28), (32), (34), (35), (39), 207.52/128.09 | | | | | (48) are inconsistent by sub-proof #129. 207.52/128.09 | | | | | 207.52/128.09 | | | | Case 2: 207.52/128.09 | | | | | 207.52/128.09 | | | | | (49) ~ (all_806_4 = 0) & permut_sub2(int, all_103_4, all_105_4, 207.52/128.09 | | | | | all_86_11, $sum(all_86_10, 1)) = all_806_4 207.52/128.09 | | | | | 207.52/128.09 | | | | | ALPHA: (49) implies: 207.52/128.09 | | | | | (50) ~ (all_806_4 = 0) 207.52/128.09 | | | | | (51) permut_sub2(int, all_103_4, all_105_4, all_86_11, 207.52/128.09 | | | | | $sum(all_86_10, 1)) = all_806_4 207.52/128.09 | | | | | 207.52/128.09 | | | | | GROUND_INST: instantiating (22) with int, all_103_4, all_105_4, 207.52/128.09 | | | | | all_86_11, $sum(all_86_10, 1), all_806_4, simplifying 207.52/128.09 | | | | | with (4), (51) gives: 207.52/128.09 | | | | | (52) all_806_4 = 0 | ? [v0: $int] : ? [v1: $int] : ? [v2: $int] 207.52/128.09 | | | | | : ? [v3: $int] : (( ~ (v3 = 0) & map_eq_sub1(int, v0, v1, 207.52/128.09 | | | | | $sum(all_86_10, 1), v2) = v3 & length1(int, all_103_4) = 207.52/128.09 | | | | | v2 & elts(int, all_105_4) = v1 & elts(int, all_103_4) = v0 207.52/128.09 | | | | | & in_uni(v1) & in_uni(v0)) | ( ~ (v2 = 0) & 207.52/128.09 | | | | | map_eq_sub1(int, v0, v1, 0, all_86_11) = v2 & elts(int, 207.52/128.09 | | | | | all_105_4) = v1 & elts(int, all_103_4) = v0 & in_uni(v1) 207.52/128.09 | | | | | & in_uni(v0)) | ( ~ (v0 = 0) & permut3(int, all_103_4, 207.52/128.09 | | | | | all_105_4, all_86_11, $sum(all_86_10, 1)) = v0)) 207.52/128.09 | | | | | 207.52/128.09 | | | | | GROUND_INST: instantiating (23) with all_86_6, all_86_4, 0, all_86_13, 207.52/128.09 | | | | | all_103_1, all_105_3, all_133_2, all_133_0, simplifying 207.52/128.09 | | | | | with (1), (9), (25), (28), (35) gives: 207.52/128.09 | | | | | (53) ~ ($lesseq(1, $difference(all_86_13, all_133_2))) | ~ 207.52/128.09 | | | | | ($lesseq(0, all_133_2)) | get3(all_86_6, all_133_2) = 207.52/128.09 | | | | | all_133_0 207.52/128.09 | | | | | 207.52/128.09 | | | | | BETA: splitting (53) gives: 207.52/128.09 | | | | | 207.52/128.09 | | | | | Case 1: 207.52/128.09 | | | | | | 207.52/128.09 | | | | | | (54) get3(all_86_6, all_133_2) = all_133_0 207.52/128.09 | | | | | | 207.52/128.09 | | | | | | BETA: splitting (52) gives: 207.52/128.09 | | | | | | 207.52/128.09 | | | | | | Case 1: 207.52/128.09 | | | | | | | 207.52/128.09 | | | | | | | (55) all_806_4 = 0 207.52/128.09 | | | | | | | 207.52/128.09 | | | | | | | REDUCE: (50), (55) imply: 207.52/128.09 | | | | | | | (56) ~ (0 = 0) 207.52/128.09 | | | | | | | 207.52/128.09 | | | | | | | CLOSE: (56) is inconsistent. 207.52/128.09 | | | | | | | 207.52/128.09 | | | | | | Case 2: 207.52/128.09 | | | | | | | 207.52/128.09 | | | | | | | 207.52/128.09 | | | | | | | GROUND_INST: instantiating (8) with all_133_2, all_133_0, 207.52/128.09 | | | | | | | simplifying with (54) gives: 207.52/128.09 | | | | | | | (57) all_133_0 = 42 | ~ ($lesseq(1, $difference(all_86_7, 207.52/128.09 | | | | | | | all_133_2))) | ~ ($lesseq(1, $difference(all_133_2, 207.52/128.09 | | | | | | | all_86_8))) 207.52/128.09 | | | | | | | 207.52/128.09 | | | | | | | REF_CLOSE: (10), (15), (19), (57) are inconsistent by sub-proof 207.52/128.09 | | | | | | | #155. 207.52/128.09 | | | | | | | 207.52/128.09 | | | | | | End of split 207.52/128.09 | | | | | | 207.52/128.09 | | | | | Case 2: 207.52/128.09 | | | | | | 207.52/128.09 | | | | | | (58) ~ ($lesseq(1, $difference(all_86_13, all_133_2))) | ~ 207.52/128.09 | | | | | | ($lesseq(0, all_133_2)) 207.52/128.09 | | | | | | 207.52/128.09 | | | | | | REF_CLOSE: (32), (39), (58) are inconsistent by sub-proof #130. 207.52/128.09 | | | | | | 207.52/128.09 | | | | | End of split 207.52/128.09 | | | | | 207.52/128.09 | | | | End of split 207.52/128.09 | | | | 207.52/128.09 | | | End of split 207.52/128.09 | | | 207.52/128.09 | | Case 2: 207.52/128.09 | | | 207.52/128.09 | | | (59) ~ ($lesseq(1, $difference(all_86_7, all_133_2))) | ~ ($lesseq(0, 207.52/128.09 | | | all_133_2)) 207.52/128.09 | | | 207.52/128.09 | | | REF_CLOSE: (15), (32), (59) are inconsistent by sub-proof #151. 207.52/128.09 | | | 207.52/128.09 | | End of split 207.52/128.09 | | 207.52/128.09 | End of split 207.52/128.09 | 207.52/128.09 End of proof 207.52/128.09 207.52/128.09 Sub-proof #104 shows that the following formulas are inconsistent: 207.52/128.09 ---------------------------------------------------------------- 207.52/128.09 (1) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ (tb2t1(v2) 207.52/128.09 = v1) | ~ (tb2t1(v2) = v0)) 207.52/128.09 (2) ! [v0: $int] : ! [v1: $int] : ( ~ ($lesseq(43, v1)) | ~ ($lesseq(v0, 207.52/128.09 all_86_8)) | ~ ($lesseq(all_86_11, v0)) | ~ (get3(all_86_6, v0) = 207.52/128.09 v1)) 207.52/128.09 (3) length1(int, all_103_2) = all_86_13 207.52/128.09 (4) in_map_int_int(all_86_6) 207.52/128.09 (5) in_map_int_int(all_86_12) 207.52/128.09 (6) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.52/128.09 $int] : ! [v5: $int] : ! [v6: $int] : ( ~ ($lesseq(0, v4)) | ~ 207.52/128.09 ($lesseq(0, v3)) | ~ (map_eq_sub1(v0, v5, v6, v3, v4) = 0) | ~ 207.52/128.09 (elts(v0, v2) = v6) | ~ (elts(v0, v1) = v5) | ~ in_ty(v0) | ? [v7: 207.52/128.09 $int] : ? [v8: $int] : ((v7 = 0 & array_eq_sub1(v0, v1, v2, v3, v4) 207.52/128.09 = 0) | (length1(v0, v1) = v7 & ( ~ ($lesseq(v4, v7)) | ~ 207.52/128.09 ($lesseq(v3, v7)) | ( ~ (v8 = v7) & length1(v0, v2) = v8))))) 207.52/128.09 (7) elts(int, all_103_4) = all_103_3 207.52/128.09 (8) t2tb2(all_86_3) = all_105_4 207.52/128.09 (9) t2tb(all_86_2) = all_105_1 207.52/128.09 (10) in_ty(int) 207.52/128.09 (11) length1(int, all_103_4) = all_86_13 207.52/128.09 (12) $lesseq(2, all_86_13) 207.52/128.09 (13) ( ~ (all_133_0 = 42) & $lesseq(1, $difference(all_86_7, all_133_2)) & 207.52/128.09 $lesseq(1, $difference(all_133_2, all_86_8)) & tb2t1(all_133_1) = 207.52/128.09 all_133_0 & get4(int, all_133_3, all_133_2) = all_133_1 & 207.52/128.09 in_uni(all_133_1)) | ($lesseq(all_133_0, 41) & $lesseq(all_133_2, 207.52/128.09 all_86_10) & $lesseq(all_86_7, all_133_2) & tb2t1(all_133_1) = 207.52/128.09 all_133_0 & get4(int, all_133_3, all_133_2) = all_133_1 & 207.52/128.09 in_uni(all_133_1)) | ($lesseq(43, all_133_0) & $lesseq(all_133_2, 207.52/128.09 all_86_8) & $lesseq(all_86_11, all_133_2) & tb2t1(all_133_1) = 207.52/128.09 all_133_0 & get4(int, all_133_3, all_133_2) = all_133_1 & 207.52/128.09 in_uni(all_133_1)) 207.52/128.09 (14) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.52/128.09 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 207.52/128.09 (permut2(v0, v5, v6, v3, v4) = v7) | ~ (elts(v0, v2) = v6) | ~ 207.52/128.09 (elts(v0, v1) = v5) | ~ in_ty(v0) | ? [v8: $int] : ? [v9: $int] : 207.52/128.09 ((v9 = v8 & v7 = 0 & $lesseq(v4, v8) & $lesseq(v3, v8) & $lesseq(0, 207.52/128.09 v4) & $lesseq(0, v3) & length1(v0, v2) = v8 & length1(v0, v1) = 207.52/128.09 v8) | ( ~ (v8 = 0) & permut3(v0, v1, v2, v3, v4) = v8))) 207.52/128.09 (15) all_125_0 = all_105_4 207.52/128.09 (16) $lesseq(all_86_7, all_86_13) 207.52/128.09 (17) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.52/128.09 $int] : ! [v5: $int] : ( ~ (permut2(v0, v2, v3, v4, v5) = 0) | ~ 207.52/128.09 (permut2(v0, v1, v2, v4, v5) = 0) | ~ in_ty(v0) | permut2(v0, v1, v3, 207.52/128.09 v4, v5) = 0) 207.52/128.09 (18) ! [v0: $int] : ! [v1: $int] : (v1 = 42 | ~ ($lesseq(1, 207.52/128.09 $difference(all_86_7, v0))) | ~ ($lesseq(1, $difference(v0, 207.52/128.09 all_86_8))) | ~ (get3(all_86_6, v0) = v1)) 207.52/128.09 (19) map_eq_sub1(int, all_103_3, all_103_1, $sum(all_86_10, 1), all_86_13) = 207.52/128.09 0 207.52/128.09 (20) t2tb(all_86_6) = all_103_1 207.52/128.09 (21) $lesseq(2, $difference(all_86_13, all_86_11)) 207.52/128.09 (22) map_eq_sub1(int, all_103_1, all_105_3, $sum(all_86_8, 1), all_86_13) = 0 207.52/128.09 (23) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.52/128.09 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ (permut3(v6, v5, 207.52/128.09 v4, v3, v2) = v1) | ~ (permut3(v6, v5, v4, v3, v2) = v0)) 207.52/128.09 (24) permut2(int, all_103_3, all_105_3, all_86_11, $sum(all_86_10, 1)) = 0 207.52/128.09 (25) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 207.52/128.09 | ~ (elts(v3, v2) = v1) | ~ (elts(v3, v2) = v0)) 207.52/128.09 (26) length1(int, all_105_4) = all_86_13 207.52/128.09 (27) in_array_int(all_86_3) 207.52/128.09 (28) elts(int, all_105_4) = all_105_3 207.52/128.09 (29) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.52/128.09 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ (permut_sub2(v6, 207.52/128.09 v5, v4, v3, v2) = v1) | ~ (permut_sub2(v6, v5, v4, v3, v2) = v0)) 207.52/128.09 (30) t2tb2(all_86_9) = all_103_4 207.52/128.09 (31) map_eq_sub1(int, all_105_3, all_105_1, 0, all_86_7) = 0 207.52/128.09 (32) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.52/128.09 $int] : ! [v5: $int] : ( ~ (permut3(int, v4, v5, v2, v3) = 0) | ~ 207.52/128.09 (t2tb2(v1) = v5) | ~ (t2tb2(v0) = v4) | ~ in_array_int(v0) | ? [v6: 207.52/128.09 $int] : ? [v7: $int] : ? [v8: $int] : ? [v9: $int] : ((v6 = 0 & 207.52/128.09 permut_sub3(v0, v1, v2, v3) = 0) | (elts(int, v5) = v7 & elts(int, 207.52/128.09 v4) = v6 & in_uni(v7) & in_uni(v6) & (( ~ (v9 = 0) & 207.52/128.09 map_eq_sub1(int, v6, v7, v3, v8) = v9 & length1(int, v4) = v8) 207.52/128.09 | ( ~ (v8 = 0) & map_eq_sub1(int, v6, v7, 0, v2) = v8))))) 207.52/128.09 (33) tb2t(all_105_1) = all_86_2 207.52/128.09 (34) permut2(int, all_103_1, all_105_3, all_86_11, $sum(all_86_8, 1)) = 0 207.52/128.09 (35) in_array_int(all_86_9) 207.52/128.09 (36) elts(int, all_105_2) = all_105_1 207.52/128.09 (37) map_eq_sub1(int, all_103_3, all_103_1, 0, all_86_11) = 0 207.52/128.09 (38) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.52/128.09 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 207.52/128.09 ($lesseq(1, $difference(v4, v5))) | ~ ($lesseq(v3, v5)) | ~ 207.52/128.09 (permut2(v0, v1, v2, v3, v4) = 0) | ~ (t2tb1(v5) = v6) | ~ (get(v0, 207.52/128.09 int, v2, v6) = v7) | ~ in_ty(v0) | ? [v8: $int] : ? [v9: $int] 207.52/128.09 : ($lesseq(1, $difference(v4, v8)) & $lesseq(v3, v8) & t2tb1(v8) = v9 207.52/128.09 & get(v0, int, v1, v9) = v7 & in_uni(v9) & in_uni(v7))) 207.52/128.09 (39) t2tb2(all_86_1) = all_105_2 207.52/128.09 (40) $lesseq(all_86_11, all_86_8) 207.52/128.09 (41) $lesseq(all_86_7, all_86_10) 207.52/128.09 (42) $lesseq(0, all_86_8) 207.52/128.09 (43) permut2(int, all_103_1, all_105_3, all_86_11, $sum(all_86_10, 1)) = 0 207.52/128.09 (44) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.52/128.09 $int] : ! [v5: $int] : ( ~ (elts(v0, v1) = v3) | ~ (t2tb1(v2) = v4) 207.52/128.09 | ~ (get(v0, int, v3, v4) = v5) | ~ in_ty(v0) | (get4(v0, v1, v2) = 207.52/128.09 v5 & in_uni(v5))) 207.52/128.09 (45) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.52/128.09 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 207.52/128.09 ($lesseq(1, $difference(v3, v4))) | ~ ($lesseq(v2, v4)) | ~ 207.52/128.09 (permut2(int, v5, v6, v2, v3) = 0) | ~ (t2tb(v1) = v6) | ~ (t2tb(v0) 207.52/128.09 = v5) | ~ (get3(v1, v4) = v7) | ~ in_map_int_int(v0) | ? [v8: 207.52/128.09 $int] : ($lesseq(1, $difference(v3, v8)) & $lesseq(v2, v8) & 207.52/128.09 get3(v0, v8) = v7)) 207.52/128.09 (46) permut2(int, all_105_3, all_105_1, all_86_7, $sum(all_86_10, 1)) = 0 207.52/128.09 (47) permut2(int, all_103_3, all_103_1, all_86_11, $sum(all_86_10, 1)) = 0 207.52/128.09 (48) ~ (permut2(int, all_103_3, all_103_1, 0, all_86_13) = 0) | ? [v0: 207.52/128.09 $int] : ((v0 = 0 & permut_all(int, all_103_4, all_103_2) = 0) | ( ~ 207.52/128.09 (v0 = all_86_13) & length1(int, all_103_2) = v0)) 207.52/128.09 (49) in_array_int(all_86_1) 207.52/128.11 (50) t2tb(all_86_12) = all_103_3 207.52/128.11 (51) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.52/128.11 $int] : ! [v5: $int] : ! [v6: $int] : ( ~ ($lesseq(0, v4)) | ~ 207.52/128.11 ($lesseq(0, v3)) | ~ (permut2(v0, v5, v6, v3, v4) = 0) | ~ (elts(v0, 207.52/128.11 v2) = v6) | ~ (elts(v0, v1) = v5) | ~ in_ty(v0) | ? [v7: $int] 207.52/128.11 : ? [v8: $int] : ((v7 = 0 & permut3(v0, v1, v2, v3, v4) = 0) | 207.52/128.11 (length1(v0, v1) = v7 & ( ~ ($lesseq(v4, v7)) | ~ ($lesseq(v3, v7)) 207.52/128.11 | ( ~ (v8 = v7) & length1(v0, v2) = v8))))) 207.52/128.11 (52) $lesseq(1, $difference(all_86_7, all_86_8)) 207.52/128.11 (53) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.52/128.11 $int] : ! [v5: $int] : ! [v6: $int] : ( ~ ($lesseq(1, 207.52/128.11 $difference(v4, v5))) | ~ ($lesseq(v3, v5)) | ~ (map_eq_sub1(v0, 207.52/128.11 v1, v2, v3, v4) = 0) | ~ (t2tb1(v5) = v6) | ~ in_ty(v0) | ? 207.52/128.11 [v7: $int] : (get(v0, int, v2, v6) = v7 & get(v0, int, v1, v6) = v7 & 207.52/128.11 in_uni(v7))) 207.52/128.11 (54) $lesseq(1, $difference(all_86_13, all_86_10)) 207.52/128.11 (55) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.52/128.11 $int] : ! [v5: $int] : (v5 = 0 | ~ (permut_sub2(v0, v1, v2, v3, v4) 207.52/128.11 = v5) | ~ in_ty(v0) | ? [v6: $int] : ? [v7: $int] : ? [v8: $int] 207.52/128.11 : ? [v9: $int] : (( ~ (v9 = 0) & map_eq_sub1(v0, v6, v7, v4, v8) = v9 207.52/128.11 & length1(v0, v1) = v8 & elts(v0, v2) = v7 & elts(v0, v1) = v6 & 207.52/128.11 in_uni(v7) & in_uni(v6)) | ( ~ (v8 = 0) & map_eq_sub1(v0, v6, v7, 207.52/128.11 0, v3) = v8 & elts(v0, v2) = v7 & elts(v0, v1) = v6 & in_uni(v7) 207.52/128.11 & in_uni(v6)) | ( ~ (v6 = 0) & permut3(v0, v1, v2, v3, v4) = v6))) 207.52/128.11 (56) in_map_int_int(all_86_4) 207.52/128.11 (57) map_eq_sub1(int, all_105_3, all_105_1, 0, all_86_13) = 0 207.52/128.11 (58) $lesseq(0, all_86_11) 207.52/128.11 (59) elts(int, all_103_2) = all_103_1 207.52/128.11 (60) ~ (permut2(int, all_103_1, all_105_3, 0, all_86_13) = 0) | ? [v0: 207.52/128.11 $int] : ((v0 = 0 & permut_all(int, all_103_2, all_105_4) = 0) | ( ~ 207.52/128.11 (v0 = all_86_13) & length1(int, all_105_4) = v0)) 207.52/128.11 (61) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ( ~ 207.52/128.11 (t2tb2(v0) = v2) | ~ (get4(int, v2, v1) = v3) | ~ in_array_int(v0) | 207.52/128.11 ? [v4: $int] : ? [v5: $int] : ? [v6: $int] : (tb2t(v4) = v5 & 207.52/128.11 tb2t1(v3) = v6 & get3(v5, v1) = v6 & elts(int, v2) = v4 & 207.52/128.11 in_map_int_int(v5) & in_uni(v4))) 207.52/128.11 (62) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ (tb2t(v2) 207.52/128.11 = v1) | ~ (tb2t(v2) = v0)) 207.52/128.11 (63) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.52/128.11 $int] : ! [v5: $int] : (v1 = v0 | ~ (permut_sub3(v5, v4, v3, v2) = 207.52/128.11 v1) | ~ (permut_sub3(v5, v4, v3, v2) = v0)) 207.52/128.11 (64) all_133_3 = all_105_2 207.52/128.11 (65) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.52/128.11 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 207.52/128.11 ($lesseq(1, $difference(v3, v6))) | ~ ($lesseq(v2, v6)) | ~ 207.52/128.11 (map_eq_sub1(int, v4, v5, v2, v3) = 0) | ~ (t2tb(v1) = v5) | ~ 207.52/128.11 (t2tb(v0) = v4) | ~ (get3(v1, v6) = v7) | ~ in_map_int_int(v0) | 207.52/128.11 get3(v0, v6) = v7) 207.52/128.11 (66) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.52/128.11 $int] : ! [v5: $int] : ! [v6: $int] : ( ~ (permut3(int, v4, v5, v2, 207.52/128.11 v3) = v6) | ~ (t2tb2(v1) = v5) | ~ (t2tb2(v0) = v4) | ~ 207.52/128.11 in_array_int(v0) | ? [v7: $int] : ? [v8: $int] : ? [v9: $int] : ? 207.52/128.11 [v10: $int] : ? [v11: $int] : ((v11 = 0 & v9 = 0 & v6 = 0 & 207.52/128.11 map_eq_sub1(int, v7, v8, v3, v10) = 0 & map_eq_sub1(int, v7, v8, 207.52/128.11 0, v2) = 0 & length1(int, v4) = v10 & elts(int, v5) = v8 & 207.52/128.11 elts(int, v4) = v7 & in_uni(v8) & in_uni(v7)) | ( ~ (v7 = 0) & 207.52/128.11 permut_sub3(v0, v1, v2, v3) = v7))) 207.52/128.11 (67) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 207.52/128.11 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 207.52/128.11 (68) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.52/128.11 $int] : ( ~ (permut3(v0, v1, v2, v3, v4) = 0) | ~ in_ty(v0) | ? [v5: 207.52/128.11 $int] : ? [v6: $int] : ? [v7: $int] : ? [v8: $int] : ((v5 = 0 & 207.52/128.11 permut_sub2(v0, v1, v2, v3, v4) = 0) | (elts(v0, v2) = v6 & 207.52/128.11 elts(v0, v1) = v5 & in_uni(v6) & in_uni(v5) & (( ~ (v8 = 0) & 207.52/128.11 map_eq_sub1(v0, v5, v6, v4, v7) = v8 & length1(v0, v1) = v7) | 207.52/128.11 ( ~ (v7 = 0) & map_eq_sub1(v0, v5, v6, 0, v3) = v7))))) 207.52/128.11 (69) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ( ~ 207.52/128.11 (get4(v0, v1, v2) = v3) | ~ in_ty(v0) | ? [v4: $int] : ? [v5: $int] 207.52/128.11 : (elts(v0, v1) = v4 & t2tb1(v2) = v5 & get(v0, int, v4, v5) = v3 & 207.52/128.11 in_uni(v5) & in_uni(v4) & in_uni(v3))) 207.52/128.11 (70) $lesseq(1, all_86_10) 207.52/128.11 (71) ! [v0: $int] : ! [v1: $int] : ( ~ (tb2t1(v0) = v1) | ~ in_uni(v0) | 207.52/128.11 t2tb1(v1) = v0) 207.52/128.11 (72) map_eq_sub1(int, all_105_3, all_105_1, $sum(all_86_10, 1), all_86_13) = 207.52/128.11 0 207.52/128.11 (73) t2tb(all_86_4) = all_105_3 207.52/128.11 (74) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.52/128.11 $int] : ! [v5: $int] : ( ~ (permut3(v0, v1, v2, v3, v4) = v5) | ~ 207.52/128.11 in_ty(v0) | ? [v6: $int] : ? [v7: $int] : ? [v8: $int] : ? [v9: 207.52/128.11 $int] : ? [v10: $int] : ((v10 = 0 & v9 = 0 & v5 = 0 & 207.52/128.11 map_eq_sub1(v0, v6, v7, v4, v8) = 0 & map_eq_sub1(v0, v6, v7, 0, 207.52/128.11 v3) = 0 & length1(v0, v1) = v8 & elts(v0, v2) = v7 & elts(v0, 207.52/128.11 v1) = v6 & in_uni(v7) & in_uni(v6)) | ( ~ (v6 = 0) & 207.52/128.11 permut_sub2(v0, v1, v2, v3, v4) = v6))) 207.52/128.11 (75) ! [v0: $int] : ! [v1: $int] : ( ~ ($lesseq(v0, all_86_10)) | ~ 207.52/128.11 ($lesseq(all_86_7, v0)) | ~ (get4(int, all_125_0, v0) = v1) | ? [v2: 207.52/128.11 $int] : ($lesseq(42, v2) & tb2t1(v1) = v2)) 207.52/128.11 207.52/128.11 Begin of proof 207.52/128.11 | 207.52/128.11 | BETA: splitting (48) gives: 207.52/128.11 | 207.52/128.11 | Case 1: 207.52/128.11 | | 207.52/128.11 | | (76) ~ (permut2(int, all_103_3, all_103_1, 0, all_86_13) = 0) 207.52/128.11 | | 207.52/128.11 | | PRED_UNIFY: (47), (76) imply: 207.52/128.11 | | (77) ~ ($difference(all_86_10, all_86_13) = -1) | ~ (all_86_11 = 0) 207.52/128.11 | | 207.52/128.11 | | REF_CLOSE: (1), (2), (4), (6), (7), (8), (9), (10), (11), (13), (14), (15), 207.52/128.11 | | (16), (18), (20), (22), (23), (24), (25), (26), (27), (28), (29), 207.52/128.11 | | (30), (31), (32), (33), (34), (35), (36), (38), (39), (40), (41), 207.52/128.11 | | (42), (44), (45), (46), (49), (51), (52), (53), (54), (55), (56), 207.52/128.11 | | (57), (58), (61), (62), (63), (64), (65), (66), (67), (68), (69), 207.52/128.11 | | (70), (73), (74), (75), (77) are inconsistent by sub-proof #108. 207.52/128.11 | | 207.52/128.11 | Case 2: 207.52/128.11 | | 207.52/128.11 | | (78) permut2(int, all_103_3, all_103_1, 0, all_86_13) = 0 207.52/128.11 | | 207.52/128.11 | | BETA: splitting (60) gives: 207.52/128.11 | | 207.52/128.11 | | Case 1: 207.52/128.11 | | | 207.52/128.11 | | | (79) ~ (permut2(int, all_103_1, all_105_3, 0, all_86_13) = 0) 207.52/128.11 | | | 207.52/128.11 | | | PRED_UNIFY: (43), (79) imply: 207.52/128.11 | | | (80) ~ ($difference(all_86_10, all_86_13) = -1) | ~ (all_86_11 = 0) 207.52/128.11 | | | 207.52/128.11 | | | REF_CLOSE: (1), (2), (4), (6), (7), (8), (9), (10), (11), (13), (14), 207.52/128.11 | | | (15), (16), (18), (20), (22), (23), (24), (25), (26), (27), 207.52/128.11 | | | (28), (29), (30), (31), (32), (33), (34), (35), (36), (38), 207.52/128.11 | | | (39), (40), (41), (42), (44), (45), (46), (49), (51), (52), 207.52/128.11 | | | (53), (54), (55), (56), (57), (58), (61), (62), (63), (64), 207.52/128.11 | | | (65), (66), (67), (68), (69), (70), (73), (74), (75), (80) are 207.52/128.11 | | | inconsistent by sub-proof #108. 207.52/128.11 | | | 207.52/128.11 | | Case 2: 207.52/128.11 | | | 207.52/128.11 | | | (81) permut2(int, all_103_1, all_105_3, 0, all_86_13) = 0 207.52/128.11 | | | 207.52/128.11 | | | BETA: splitting (13) gives: 207.52/128.11 | | | 207.52/128.11 | | | Case 1: 207.52/128.11 | | | | 207.52/128.11 | | | | (82) ~ (all_133_0 = 42) & $lesseq(1, $difference(all_86_7, 207.52/128.11 | | | | all_133_2)) & $lesseq(1, $difference(all_133_2, all_86_8)) & 207.52/128.11 | | | | tb2t1(all_133_1) = all_133_0 & get4(int, all_133_3, all_133_2) = 207.52/128.11 | | | | all_133_1 & in_uni(all_133_1) 207.52/128.11 | | | | 207.52/128.11 | | | | ALPHA: (82) implies: 207.52/128.11 | | | | (83) ~ (all_133_0 = 42) 207.52/128.11 | | | | (84) $lesseq(1, $difference(all_133_2, all_86_8)) 207.52/128.11 | | | | (85) $lesseq(1, $difference(all_86_7, all_133_2)) 207.52/128.11 | | | | (86) in_uni(all_133_1) 207.52/128.11 | | | | (87) get4(int, all_133_3, all_133_2) = all_133_1 207.52/128.11 | | | | (88) tb2t1(all_133_1) = all_133_0 207.52/128.11 | | | | 207.52/128.11 | | | | COMBINE_INEQS: (84), (85) imply: 207.52/128.11 | | | | (89) $lesseq(2, $difference(all_86_7, all_86_8)) 207.52/128.11 | | | | 207.52/128.11 | | | | COMBINE_INEQS: (41), (89) imply: 207.52/128.11 | | | | (90) $lesseq(2, $difference(all_86_10, all_86_8)) 207.52/128.11 | | | | 207.52/128.11 | | | | COMBINE_INEQS: (40), (90) imply: 207.52/128.11 | | | | (91) $lesseq(2, $difference(all_86_10, all_86_11)) 207.52/128.11 | | | | 207.52/128.11 | | | | COMBINE_INEQS: (42), (90) imply: 207.52/128.11 | | | | (92) $lesseq(2, all_86_10) 207.52/128.11 | | | | 207.52/128.11 | | | | COMBINE_INEQS: (54), (91) imply: 207.52/128.11 | | | | (93) $lesseq(3, $difference(all_86_13, all_86_11)) 207.52/128.11 | | | | 207.52/128.11 | | | | COMBINE_INEQS: (58), (93) imply: 207.52/128.11 | | | | (94) $lesseq(3, all_86_13) 207.52/128.11 | | | | 207.52/128.11 | | | | REDUCE: (64), (87) imply: 207.52/128.11 | | | | (95) get4(int, all_105_2, all_133_2) = all_133_1 207.52/128.11 | | | | 207.52/128.11 | | | | GROUND_INST: instantiating (14) with int, all_103_2, all_105_4, 0, 207.52/128.11 | | | | all_86_13, all_103_1, all_105_3, 0, simplifying with (10), 207.52/128.11 | | | | (28), (59), (81) gives: 207.52/128.11 | | | | (96) ? [v0: $int] : ? [v1: $int] : ((v1 = v0 & $lesseq(all_86_13, 207.52/128.11 | | | | v0) & $lesseq(0, v0) & $lesseq(0, all_86_13) & 207.52/128.11 | | | | length1(int, all_105_4) = v0 & length1(int, all_103_2) = v0) 207.52/128.11 | | | | | ( ~ (v0 = 0) & permut3(int, all_103_2, all_105_4, 0, 207.52/128.11 | | | | all_86_13) = v0)) 207.52/128.11 | | | | 207.52/128.11 | | | | GROUND_INST: instantiating (17) with int, all_103_3, all_103_1, 207.52/128.11 | | | | all_105_3, 0, all_86_13, simplifying with (10), (78), (81) 207.52/128.11 | | | | gives: 207.52/128.11 | | | | (97) permut2(int, all_103_3, all_105_3, 0, all_86_13) = 0 207.52/128.11 | | | | 207.52/128.11 | | | | GROUND_INST: instantiating (51) with int, all_103_2, all_105_4, 0, 207.52/128.11 | | | | all_86_13, all_103_1, all_105_3, simplifying with (10), 207.52/128.11 | | | | (28), (59), (81) gives: 207.52/128.11 | | | | (98) ~ ($lesseq(0, all_86_13)) | ? [v0: $int] : ? [v1: $int] : 207.52/128.11 | | | | ((v0 = 0 & permut3(int, all_103_2, all_105_4, 0, all_86_13) = 0) 207.52/128.11 | | | | | (length1(int, all_103_2) = v0 & ( ~ ($lesseq(all_86_13, v0)) 207.52/128.11 | | | | | ~ ($lesseq(0, v0)) | ( ~ (v1 = v0) & length1(int, 207.52/128.11 | | | | all_105_4) = v1)))) 207.52/128.11 | | | | 207.52/128.11 | | | | GROUND_INST: instantiating (14) with int, all_103_4, all_105_4, 207.52/128.11 | | | | all_86_11, $sum(all_86_10, 1), all_103_3, all_105_3, 0, 207.52/128.11 | | | | simplifying with (7), (10), (24), (28) gives: 207.70/128.12 | | | | (99) ? [v0: $int] : ? [v1: $int] : ((v1 = v0 & $lesseq(1, 207.70/128.12 | | | | $difference(v0, all_86_10)) & $lesseq(all_86_11, v0) & 207.70/128.12 | | | | $lesseq(-1, all_86_10) & $lesseq(0, all_86_11) & 207.70/128.12 | | | | length1(int, all_105_4) = v0 & length1(int, all_103_4) = v0) 207.70/128.12 | | | | | ( ~ (v0 = 0) & permut3(int, all_103_4, all_105_4, all_86_11, 207.70/128.12 | | | | $sum(all_86_10, 1)) = v0)) 207.70/128.12 | | | | 207.70/128.12 | | | | GROUND_INST: instantiating (51) with int, all_103_4, all_105_4, 207.70/128.12 | | | | all_86_11, $sum(all_86_10, 1), all_103_3, all_105_3, 207.70/128.12 | | | | simplifying with (7), (10), (24), (28) gives: 207.70/128.12 | | | | (100) ~ ($lesseq(-1, all_86_10)) | ~ ($lesseq(0, all_86_11)) | ? 207.70/128.12 | | | | [v0: $int] : ? [v1: $int] : ((v0 = 0 & permut3(int, all_103_4, 207.70/128.12 | | | | all_105_4, all_86_11, $sum(all_86_10, 1)) = 0) | 207.70/128.12 | | | | (length1(int, all_103_4) = v0 & ( ~ ($lesseq(1, 207.70/128.12 | | | | $difference(v0, all_86_10))) | ~ ($lesseq(all_86_11, 207.70/128.12 | | | | v0)) | ( ~ (v1 = v0) & length1(int, all_105_4) = 207.70/128.12 | | | | v1)))) 207.70/128.12 | | | | 207.70/128.12 | | | | GROUND_INST: instantiating (14) with int, all_103_4, all_103_2, 0, 207.70/128.12 | | | | all_86_13, all_103_3, all_103_1, 0, simplifying with (7), 207.70/128.12 | | | | (10), (59), (78) gives: 207.70/128.12 | | | | (101) ? [v0: $int] : ? [v1: $int] : ((v1 = v0 & $lesseq(all_86_13, 207.70/128.12 | | | | v0) & $lesseq(0, v0) & $lesseq(0, all_86_13) & 207.70/128.12 | | | | length1(int, all_103_2) = v0 & length1(int, all_103_4) = 207.70/128.12 | | | | v0) | ( ~ (v0 = 0) & permut3(int, all_103_4, all_103_2, 0, 207.70/128.12 | | | | all_86_13) = v0)) 207.70/128.12 | | | | 207.70/128.12 | | | | GROUND_INST: instantiating (51) with int, all_103_4, all_103_2, 0, 207.70/128.12 | | | | all_86_13, all_103_3, all_103_1, simplifying with (7), 207.70/128.12 | | | | (10), (59), (78) gives: 207.70/128.12 | | | | (102) ~ ($lesseq(0, all_86_13)) | ? [v0: $int] : ? [v1: $int] : 207.70/128.12 | | | | ((v0 = 0 & permut3(int, all_103_4, all_103_2, 0, all_86_13) = 207.70/128.12 | | | | 0) | (length1(int, all_103_4) = v0 & ( ~ 207.70/128.12 | | | | ($lesseq(all_86_13, v0)) | ~ ($lesseq(0, v0)) | ( ~ (v1 207.70/128.12 | | | | = v0) & length1(int, all_103_2) = v1)))) 207.70/128.12 | | | | 207.70/128.12 | | | | GROUND_INST: instantiating (71) with all_133_1, all_133_0, simplifying 207.70/128.12 | | | | with (86), (88) gives: 207.70/128.12 | | | | (103) t2tb1(all_133_0) = all_133_1 207.70/128.12 | | | | 207.70/128.12 | | | | GROUND_INST: instantiating (61) with all_86_1, all_133_2, all_105_2, 207.70/128.12 | | | | all_133_1, simplifying with (39), (49), (95) gives: 207.70/128.12 | | | | (104) ? [v0: $int] : ? [v1: $int] : ? [v2: $int] : (tb2t(v0) = v1 207.70/128.12 | | | | & tb2t1(all_133_1) = v2 & get3(v1, all_133_2) = v2 & 207.70/128.12 | | | | elts(int, all_105_2) = v0 & in_map_int_int(v1) & in_uni(v0)) 207.70/128.12 | | | | 207.70/128.12 | | | | GROUND_INST: instantiating (69) with int, all_105_2, all_133_2, 207.70/128.12 | | | | all_133_1, simplifying with (10), (95) gives: 207.70/128.12 | | | | (105) ? [v0: $int] : ? [v1: $int] : (elts(int, all_105_2) = v0 & 207.70/128.12 | | | | t2tb1(all_133_2) = v1 & get(int, int, v0, v1) = all_133_1 & 207.70/128.12 | | | | in_uni(v1) & in_uni(v0) & in_uni(all_133_1)) 207.70/128.12 | | | | 207.70/128.12 | | | | DELTA: instantiating (104) with fresh symbols all_725_0, all_725_1, 207.70/128.12 | | | | all_725_2 gives: 207.70/128.12 | | | | (106) tb2t(all_725_2) = all_725_1 & tb2t1(all_133_1) = all_725_0 & 207.70/128.12 | | | | get3(all_725_1, all_133_2) = all_725_0 & elts(int, all_105_2) = 207.70/128.12 | | | | all_725_2 & in_map_int_int(all_725_1) & in_uni(all_725_2) 207.70/128.12 | | | | 207.70/128.12 | | | | ALPHA: (106) implies: 207.70/128.12 | | | | (107) elts(int, all_105_2) = all_725_2 207.70/128.12 | | | | (108) get3(all_725_1, all_133_2) = all_725_0 207.70/128.12 | | | | (109) tb2t1(all_133_1) = all_725_0 207.70/128.12 | | | | (110) tb2t(all_725_2) = all_725_1 207.70/128.12 | | | | 207.70/128.12 | | | | DELTA: instantiating (101) with fresh symbols all_731_0, all_731_1 207.70/128.12 | | | | gives: 207.70/128.12 | | | | (111) (all_731_0 = all_731_1 & $lesseq(all_86_13, all_731_1) & 207.70/128.12 | | | | $lesseq(0, all_731_1) & $lesseq(0, all_86_13) & length1(int, 207.70/128.12 | | | | all_103_2) = all_731_1 & length1(int, all_103_4) = 207.70/128.12 | | | | all_731_1) | ( ~ (all_731_1 = 0) & permut3(int, all_103_4, 207.70/128.12 | | | | all_103_2, 0, all_86_13) = all_731_1) 207.70/128.12 | | | | 207.70/128.12 | | | | DELTA: instantiating (99) with fresh symbols all_736_0, all_736_1 gives: 207.70/128.12 | | | | (112) (all_736_0 = all_736_1 & $lesseq(1, $difference(all_736_1, 207.70/128.12 | | | | all_86_10)) & $lesseq(all_86_11, all_736_1) & $lesseq(-1, 207.70/128.12 | | | | all_86_10) & $lesseq(0, all_86_11) & length1(int, 207.70/128.12 | | | | all_105_4) = all_736_1 & length1(int, all_103_4) = 207.70/128.12 | | | | all_736_1) | ( ~ (all_736_1 = 0) & permut3(int, all_103_4, 207.70/128.12 | | | | all_105_4, all_86_11, $sum(all_86_10, 1)) = all_736_1) 207.70/128.12 | | | | 207.70/128.12 | | | | DELTA: instantiating (96) with fresh symbols all_737_0, all_737_1 gives: 207.70/128.12 | | | | (113) (all_737_0 = all_737_1 & $lesseq(all_86_13, all_737_1) & 207.70/128.12 | | | | $lesseq(0, all_737_1) & $lesseq(0, all_86_13) & length1(int, 207.70/128.12 | | | | all_105_4) = all_737_1 & length1(int, all_103_2) = 207.70/128.12 | | | | all_737_1) | ( ~ (all_737_1 = 0) & permut3(int, all_103_2, 207.70/128.12 | | | | all_105_4, 0, all_86_13) = all_737_1) 207.70/128.12 | | | | 207.70/128.12 | | | | DELTA: instantiating (105) with fresh symbols all_738_0, all_738_1 207.70/128.12 | | | | gives: 207.70/128.12 | | | | (114) elts(int, all_105_2) = all_738_1 & t2tb1(all_133_2) = all_738_0 207.70/128.12 | | | | & get(int, int, all_738_1, all_738_0) = all_133_1 & 207.70/128.12 | | | | in_uni(all_738_0) & in_uni(all_738_1) & in_uni(all_133_1) 207.70/128.12 | | | | 207.70/128.12 | | | | ALPHA: (114) implies: 207.70/128.12 | | | | (115) t2tb1(all_133_2) = all_738_0 207.70/128.12 | | | | (116) elts(int, all_105_2) = all_738_1 207.70/128.12 | | | | 207.70/128.12 | | | | BETA: splitting (98) gives: 207.70/128.12 | | | | 207.70/128.12 | | | | Case 1: 207.70/128.12 | | | | | 207.70/128.12 | | | | | (117) $lesseq(all_86_13, -1) 207.70/128.12 | | | | | 207.70/128.12 | | | | | COMBINE_INEQS: (94), (117) imply: 207.70/128.12 | | | | | (118) $lesseq(0, -1) 207.70/128.12 | | | | | 207.70/128.12 | | | | | CLOSE: (118) is inconsistent. 207.70/128.12 | | | | | 207.70/128.12 | | | | Case 2: 207.70/128.12 | | | | | 207.70/128.12 | | | | | (119) ? [v0: $int] : ? [v1: $int] : ((v0 = 0 & permut3(int, 207.70/128.12 | | | | | all_103_2, all_105_4, 0, all_86_13) = 0) | 207.70/128.12 | | | | | (length1(int, all_103_2) = v0 & ( ~ ($lesseq(all_86_13, 207.70/128.12 | | | | | v0)) | ~ ($lesseq(0, v0)) | ( ~ (v1 = v0) & 207.70/128.12 | | | | | length1(int, all_105_4) = v1)))) 207.70/128.12 | | | | | 207.70/128.12 | | | | | DELTA: instantiating (119) with fresh symbols all_749_0, all_749_1 207.70/128.12 | | | | | gives: 207.70/128.12 | | | | | (120) (all_749_1 = 0 & permut3(int, all_103_2, all_105_4, 0, 207.70/128.12 | | | | | all_86_13) = 0) | (length1(int, all_103_2) = all_749_1 & 207.70/128.12 | | | | | ( ~ ($lesseq(all_86_13, all_749_1)) | ~ ($lesseq(0, 207.70/128.12 | | | | | all_749_1)) | ( ~ (all_749_0 = all_749_1) & 207.70/128.12 | | | | | length1(int, all_105_4) = all_749_0))) 207.70/128.12 | | | | | 207.70/128.12 | | | | | BETA: splitting (120) gives: 207.70/128.12 | | | | | 207.70/128.12 | | | | | Case 1: 207.70/128.12 | | | | | | 207.70/128.12 | | | | | | (121) all_749_1 = 0 & permut3(int, all_103_2, all_105_4, 0, 207.70/128.12 | | | | | | all_86_13) = 0 207.70/128.12 | | | | | | 207.70/128.12 | | | | | | ALPHA: (121) implies: 207.70/128.12 | | | | | | (122) permut3(int, all_103_2, all_105_4, 0, all_86_13) = 0 207.70/128.12 | | | | | | 207.70/128.12 | | | | | | BETA: splitting (100) gives: 207.70/128.12 | | | | | | 207.70/128.12 | | | | | | Case 1: 207.70/128.12 | | | | | | | 207.70/128.12 | | | | | | | (123) $lesseq(all_86_11, -1) 207.70/128.12 | | | | | | | 207.70/128.12 | | | | | | | COMBINE_INEQS: (58), (123) imply: 207.70/128.12 | | | | | | | (124) $lesseq(0, -1) 207.70/128.12 | | | | | | | 207.70/128.12 | | | | | | | CLOSE: (124) is inconsistent. 207.70/128.12 | | | | | | | 207.70/128.12 | | | | | | Case 2: 207.70/128.12 | | | | | | | 207.70/128.12 | | | | | | | (125) ~ ($lesseq(-1, all_86_10)) | ? [v0: $int] : ? [v1: 207.70/128.12 | | | | | | | $int] : ((v0 = 0 & permut3(int, all_103_4, all_105_4, 207.70/128.12 | | | | | | | all_86_11, $sum(all_86_10, 1)) = 0) | (length1(int, 207.70/128.12 | | | | | | | all_103_4) = v0 & ( ~ ($lesseq(1, $difference(v0, 207.70/128.12 | | | | | | | all_86_10))) | ~ ($lesseq(all_86_11, v0)) | 207.70/128.12 | | | | | | | ( ~ (v1 = v0) & length1(int, all_105_4) = v1)))) 207.70/128.12 | | | | | | | 207.70/128.12 | | | | | | | BETA: splitting (125) gives: 207.70/128.12 | | | | | | | 207.70/128.12 | | | | | | | Case 1: 207.70/128.12 | | | | | | | | 207.70/128.12 | | | | | | | | (126) $lesseq(all_86_10, -2) 207.70/128.12 | | | | | | | | 207.70/128.12 | | | | | | | | COMBINE_INEQS: (92), (126) imply: 207.70/128.12 | | | | | | | | (127) $lesseq(0, -1) 207.70/128.12 | | | | | | | | 207.70/128.12 | | | | | | | | CLOSE: (127) is inconsistent. 207.70/128.12 | | | | | | | | 207.70/128.12 | | | | | | | Case 2: 207.70/128.12 | | | | | | | | 207.70/128.12 | | | | | | | | (128) ? [v0: $int] : ? [v1: $int] : ((v0 = 0 & permut3(int, 207.70/128.12 | | | | | | | | all_103_4, all_105_4, all_86_11, $sum(all_86_10, 207.70/128.12 | | | | | | | | 1)) = 0) | (length1(int, all_103_4) = v0 & ( ~ 207.70/128.12 | | | | | | | | ($lesseq(1, $difference(v0, all_86_10))) | ~ 207.70/128.12 | | | | | | | | ($lesseq(all_86_11, v0)) | ( ~ (v1 = v0) & 207.70/128.12 | | | | | | | | length1(int, all_105_4) = v1)))) 207.70/128.12 | | | | | | | | 207.70/128.12 | | | | | | | | DELTA: instantiating (128) with fresh symbols all_775_0, 207.70/128.12 | | | | | | | | all_775_1 gives: 207.70/128.12 | | | | | | | | (129) (all_775_1 = 0 & permut3(int, all_103_4, all_105_4, 207.70/128.12 | | | | | | | | all_86_11, $sum(all_86_10, 1)) = 0) | (length1(int, 207.70/128.12 | | | | | | | | all_103_4) = all_775_1 & ( ~ ($lesseq(1, 207.70/128.12 | | | | | | | | $difference(all_775_1, all_86_10))) | ~ 207.70/128.12 | | | | | | | | ($lesseq(all_86_11, all_775_1)) | ( ~ (all_775_0 = 207.70/128.12 | | | | | | | | all_775_1) & length1(int, all_105_4) = 207.70/128.12 | | | | | | | | all_775_0))) 207.70/128.12 | | | | | | | | 207.70/128.12 | | | | | | | | BETA: splitting (113) gives: 207.70/128.12 | | | | | | | | 207.70/128.12 | | | | | | | | Case 1: 207.70/128.12 | | | | | | | | | 207.70/128.12 | | | | | | | | | (130) all_737_0 = all_737_1 & $lesseq(all_86_13, all_737_1) 207.70/128.12 | | | | | | | | | & $lesseq(0, all_737_1) & $lesseq(0, all_86_13) & 207.70/128.12 | | | | | | | | | length1(int, all_105_4) = all_737_1 & length1(int, 207.70/128.12 | | | | | | | | | all_103_2) = all_737_1 207.70/128.12 | | | | | | | | | 207.70/128.12 | | | | | | | | | ALPHA: (130) implies: 207.70/128.12 | | | | | | | | | (131) length1(int, all_103_2) = all_737_1 207.70/128.12 | | | | | | | | | (132) length1(int, all_105_4) = all_737_1 207.70/128.12 | | | | | | | | | 207.70/128.12 | | | | | | | | | BETA: splitting (102) gives: 207.70/128.12 | | | | | | | | | 207.70/128.12 | | | | | | | | | Case 1: 207.70/128.12 | | | | | | | | | | 207.70/128.12 | | | | | | | | | | (133) $lesseq(all_86_13, -1) 207.70/128.12 | | | | | | | | | | 207.70/128.12 | | | | | | | | | | COMBINE_INEQS: (94), (133) imply: 207.70/128.12 | | | | | | | | | | (134) $lesseq(0, -1) 207.70/128.12 | | | | | | | | | | 207.70/128.12 | | | | | | | | | | CLOSE: (134) is inconsistent. 207.70/128.12 | | | | | | | | | | 207.70/128.12 | | | | | | | | | Case 2: 207.70/128.12 | | | | | | | | | | 207.70/128.12 | | | | | | | | | | (135) ? [v0: $int] : ? [v1: $int] : ((v0 = 0 & 207.70/128.12 | | | | | | | | | | permut3(int, all_103_4, all_103_2, 0, 207.70/128.12 | | | | | | | | | | all_86_13) = 0) | (length1(int, all_103_4) = 207.70/128.12 | | | | | | | | | | v0 & ( ~ ($lesseq(all_86_13, v0)) | ~ 207.70/128.12 | | | | | | | | | | ($lesseq(0, v0)) | ( ~ (v1 = v0) & 207.70/128.12 | | | | | | | | | | length1(int, all_103_2) = v1)))) 207.70/128.12 | | | | | | | | | | 207.70/128.12 | | | | | | | | | | DELTA: instantiating (135) with fresh symbols all_787_0, 207.70/128.12 | | | | | | | | | | all_787_1 gives: 207.70/128.12 | | | | | | | | | | (136) (all_787_1 = 0 & permut3(int, all_103_4, all_103_2, 207.70/128.12 | | | | | | | | | | 0, all_86_13) = 0) | (length1(int, all_103_4) = 207.70/128.12 | | | | | | | | | | all_787_1 & ( ~ ($lesseq(all_86_13, all_787_1)) | 207.70/128.12 | | | | | | | | | | ~ ($lesseq(0, all_787_1)) | ( ~ (all_787_0 = 207.70/128.12 | | | | | | | | | | all_787_1) & length1(int, all_103_2) = 207.70/128.12 | | | | | | | | | | all_787_0))) 207.70/128.12 | | | | | | | | | | 207.70/128.12 | | | | | | | | | | GROUND_INST: instantiating (1) with all_133_0, all_725_0, 207.70/128.12 | | | | | | | | | | all_133_1, simplifying with (88), (109) gives: 207.70/128.12 | | | | | | | | | | (137) all_725_0 = all_133_0 207.70/128.12 | | | | | | | | | | 207.70/128.12 | | | | | | | | | | GROUND_INST: instantiating (67) with all_86_13, all_737_1, 207.70/128.12 | | | | | | | | | | all_103_2, int, simplifying with (3), (131) gives: 207.70/128.12 | | | | | | | | | | (138) all_737_1 = all_86_13 207.70/128.12 | | | | | | | | | | 207.70/128.12 | | | | | | | | | | GROUND_INST: instantiating (25) with all_105_1, all_738_1, 207.70/128.12 | | | | | | | | | | all_105_2, int, simplifying with (36), (116) 207.70/128.12 | | | | | | | | | | gives: 207.70/128.12 | | | | | | | | | | (139) all_738_1 = all_105_1 207.70/128.12 | | | | | | | | | | 207.70/128.12 | | | | | | | | | | GROUND_INST: instantiating (25) with all_738_1, all_725_2, 207.70/128.12 | | | | | | | | | | all_105_2, int, simplifying with (107), (116) 207.70/128.12 | | | | | | | | | | gives: 207.70/128.12 | | | | | | | | | | (140) all_738_1 = all_725_2 207.70/128.12 | | | | | | | | | | 207.70/128.12 | | | | | | | | | | COMBINE_EQS: (139), (140) imply: 207.70/128.12 | | | | | | | | | | (141) all_725_2 = all_105_1 207.70/128.12 | | | | | | | | | | 207.70/128.12 | | | | | | | | | | REDUCE: (110), (141) imply: 207.70/128.12 | | | | | | | | | | (142) tb2t(all_105_1) = all_725_1 207.70/128.12 | | | | | | | | | | 207.70/128.12 | | | | | | | | | | REDUCE: (108), (137) imply: 207.70/128.12 | | | | | | | | | | (143) get3(all_725_1, all_133_2) = all_133_0 207.70/128.12 | | | | | | | | | | 207.70/128.12 | | | | | | | | | | BETA: splitting (136) gives: 207.70/128.12 | | | | | | | | | | 207.70/128.12 | | | | | | | | | | Case 1: 207.70/128.12 | | | | | | | | | | | 207.70/128.12 | | | | | | | | | | | (144) all_787_1 = 0 & permut3(int, all_103_4, all_103_2, 207.70/128.12 | | | | | | | | | | | 0, all_86_13) = 0 207.70/128.12 | | | | | | | | | | | 207.70/128.12 | | | | | | | | | | | ALPHA: (144) implies: 207.70/128.12 | | | | | | | | | | | (145) permut3(int, all_103_4, all_103_2, 0, all_86_13) = 207.70/128.12 | | | | | | | | | | | 0 207.70/128.12 | | | | | | | | | | | 207.70/128.12 | | | | | | | | | | | BETA: splitting (111) gives: 207.70/128.12 | | | | | | | | | | | 207.70/128.12 | | | | | | | | | | | Case 1: 207.70/128.12 | | | | | | | | | | | | 207.70/128.12 | | | | | | | | | | | | (146) all_731_0 = all_731_1 & $lesseq(all_86_13, 207.70/128.12 | | | | | | | | | | | | all_731_1) & $lesseq(0, all_731_1) & $lesseq(0, 207.70/128.12 | | | | | | | | | | | | all_86_13) & length1(int, all_103_2) = all_731_1 207.70/128.12 | | | | | | | | | | | | & length1(int, all_103_4) = all_731_1 207.70/128.12 | | | | | | | | | | | | 207.70/128.12 | | | | | | | | | | | | ALPHA: (146) implies: 207.70/128.12 | | | | | | | | | | | | (147) length1(int, all_103_4) = all_731_1 207.70/128.12 | | | | | | | | | | | | 207.70/128.12 | | | | | | | | | | | | BETA: splitting (129) gives: 207.70/128.12 | | | | | | | | | | | | 207.70/128.12 | | | | | | | | | | | | Case 1: 207.70/128.12 | | | | | | | | | | | | | 207.70/128.12 | | | | | | | | | | | | | (148) all_775_1 = 0 & permut3(int, all_103_4, all_105_4, 207.70/128.12 | | | | | | | | | | | | | all_86_11, $sum(all_86_10, 1)) = 0 207.70/128.12 | | | | | | | | | | | | | 207.70/128.12 | | | | | | | | | | | | | ALPHA: (148) implies: 207.70/128.12 | | | | | | | | | | | | | (149) permut3(int, all_103_4, all_105_4, all_86_11, 207.70/128.12 | | | | | | | | | | | | | $sum(all_86_10, 1)) = 0 207.70/128.12 | | | | | | | | | | | | | 207.70/128.12 | | | | | | | | | | | | | REF_CLOSE: (4), (5), (9), (10), (11), (16), (18), (19), (20), 207.70/128.12 | | | | | | | | | | | | | (22), (23), (31), (33), (37), (40), (41), (42), 207.70/128.12 | | | | | | | | | | | | | (45), (50), (53), (56), (62), (65), (67), (72), 207.70/128.12 | | | | | | | | | | | | | (73), (83), (84), (85), (97), (103), (112), (115), 207.70/128.12 | | | | | | | | | | | | | (142), (143), (149) are inconsistent by sub-proof 207.70/128.12 | | | | | | | | | | | | | #107. 207.70/128.12 | | | | | | | | | | | | | 207.70/128.12 | | | | | | | | | | | | Case 2: 207.70/128.12 | | | | | | | | | | | | | 207.70/128.12 | | | | | | | | | | | | | (150) length1(int, all_103_4) = all_775_1 & ( ~ 207.70/128.12 | | | | | | | | | | | | | ($lesseq(1, $difference(all_775_1, all_86_10))) 207.70/128.12 | | | | | | | | | | | | | | ~ ($lesseq(all_86_11, all_775_1)) | ( ~ 207.70/128.12 | | | | | | | | | | | | | (all_775_0 = all_775_1) & length1(int, 207.70/128.12 | | | | | | | | | | | | | all_105_4) = all_775_0)) 207.70/128.12 | | | | | | | | | | | | | 207.70/128.12 | | | | | | | | | | | | | ALPHA: (150) implies: 207.70/128.12 | | | | | | | | | | | | | (151) length1(int, all_103_4) = all_775_1 207.70/128.12 | | | | | | | | | | | | | (152) ~ ($lesseq(1, $difference(all_775_1, all_86_10))) 207.70/128.12 | | | | | | | | | | | | | | ~ ($lesseq(all_86_11, all_775_1)) | ( ~ 207.70/128.12 | | | | | | | | | | | | | (all_775_0 = all_775_1) & length1(int, 207.70/128.12 | | | | | | | | | | | | | all_105_4) = all_775_0) 207.70/128.12 | | | | | | | | | | | | | 207.70/128.12 | | | | | | | | | | | | | GROUND_INST: instantiating (67) with all_86_13, all_775_1, 207.70/128.12 | | | | | | | | | | | | | all_103_4, int, simplifying with (11), (151) 207.70/128.12 | | | | | | | | | | | | | gives: 207.70/128.12 | | | | | | | | | | | | | (153) all_775_1 = all_86_13 207.70/128.12 | | | | | | | | | | | | | 207.70/128.12 | | | | | | | | | | | | | GROUND_INST: instantiating (67) with all_775_1, all_731_1, 207.70/128.12 | | | | | | | | | | | | | all_103_4, int, simplifying with (147), (151) 207.70/128.12 | | | | | | | | | | | | | gives: 207.70/128.12 | | | | | | | | | | | | | (154) all_775_1 = all_731_1 207.70/128.12 | | | | | | | | | | | | | 207.70/128.12 | | | | | | | | | | | | | COMBINE_EQS: (153), (154) imply: 207.70/128.12 | | | | | | | | | | | | | (155) all_731_1 = all_86_13 207.70/128.12 | | | | | | | | | | | | | 207.70/128.12 | | | | | | | | | | | | | BETA: splitting (152) gives: 207.70/128.12 | | | | | | | | | | | | | 207.70/128.12 | | | | | | | | | | | | | Case 1: 207.70/128.12 | | | | | | | | | | | | | | 207.70/128.12 | | | | | | | | | | | | | | (156) $lesseq(1, $difference(all_86_11, all_775_1)) 207.70/128.12 | | | | | | | | | | | | | | 207.70/128.12 | | | | | | | | | | | | | | REF_CLOSE: (40), (41), (54), (84), (85), (153), (156) are 207.70/128.12 | | | | | | | | | | | | | | inconsistent by sub-proof #106. 207.70/128.12 | | | | | | | | | | | | | | 207.70/128.12 | | | | | | | | | | | | | Case 2: 207.70/128.12 | | | | | | | | | | | | | | 207.70/128.12 | | | | | | | | | | | | | | (157) ~ ($lesseq(1, $difference(all_775_1, all_86_10))) 207.70/128.12 | | | | | | | | | | | | | | | ( ~ (all_775_0 = all_775_1) & length1(int, 207.70/128.12 | | | | | | | | | | | | | | all_105_4) = all_775_0) 207.70/128.12 | | | | | | | | | | | | | | 207.70/128.12 | | | | | | | | | | | | | | REF_CLOSE: (26), (54), (67), (153), (157) are inconsistent by 207.70/128.12 | | | | | | | | | | | | | | sub-proof #105. 207.70/128.12 | | | | | | | | | | | | | | 207.70/128.12 | | | | | | | | | | | | | End of split 207.70/128.12 | | | | | | | | | | | | | 207.70/128.12 | | | | | | | | | | | | End of split 207.70/128.12 | | | | | | | | | | | | 207.70/128.12 | | | | | | | | | | | Case 2: 207.70/128.12 | | | | | | | | | | | | 207.70/128.12 | | | | | | | | | | | | (158) ~ (all_731_1 = 0) & permut3(int, all_103_4, 207.70/128.12 | | | | | | | | | | | | all_103_2, 0, all_86_13) = all_731_1 207.70/128.12 | | | | | | | | | | | | 207.70/128.12 | | | | | | | | | | | | ALPHA: (158) implies: 207.70/128.12 | | | | | | | | | | | | (159) ~ (all_731_1 = 0) 207.70/128.12 | | | | | | | | | | | | (160) permut3(int, all_103_4, all_103_2, 0, all_86_13) = 207.70/128.12 | | | | | | | | | | | | all_731_1 207.70/128.12 | | | | | | | | | | | | 207.70/128.12 | | | | | | | | | | | | GROUND_INST: instantiating (23) with 0, all_731_1, all_86_13, 207.70/128.12 | | | | | | | | | | | | 0, all_103_2, all_103_4, int, simplifying with 207.70/128.12 | | | | | | | | | | | | (145), (160) gives: 207.70/128.12 | | | | | | | | | | | | (161) all_731_1 = 0 207.70/128.12 | | | | | | | | | | | | 207.70/128.12 | | | | | | | | | | | | REDUCE: (159), (161) imply: 207.70/128.12 | | | | | | | | | | | | (162) ~ (0 = 0) 207.70/128.12 | | | | | | | | | | | | 207.70/128.12 | | | | | | | | | | | | CLOSE: (162) is inconsistent. 207.70/128.12 | | | | | | | | | | | | 207.70/128.12 | | | | | | | | | | | End of split 207.70/128.12 | | | | | | | | | | | 207.70/128.12 | | | | | | | | | | Case 2: 207.70/128.12 | | | | | | | | | | | 207.70/128.12 | | | | | | | | | | | (163) length1(int, all_103_4) = all_787_1 & ( ~ 207.70/128.12 | | | | | | | | | | | ($lesseq(all_86_13, all_787_1)) | ~ ($lesseq(0, 207.70/128.12 | | | | | | | | | | | all_787_1)) | ( ~ (all_787_0 = all_787_1) & 207.70/128.12 | | | | | | | | | | | length1(int, all_103_2) = all_787_0)) 207.70/128.12 | | | | | | | | | | | 207.70/128.12 | | | | | | | | | | | ALPHA: (163) implies: 207.70/128.12 | | | | | | | | | | | (164) length1(int, all_103_4) = all_787_1 207.70/128.12 | | | | | | | | | | | 207.70/128.12 | | | | | | | | | | | BETA: splitting (129) gives: 207.70/128.12 | | | | | | | | | | | 207.70/128.12 | | | | | | | | | | | Case 1: 207.70/128.12 | | | | | | | | | | | | 207.70/128.12 | | | | | | | | | | | | (165) all_775_1 = 0 & permut3(int, all_103_4, all_105_4, 207.70/128.12 | | | | | | | | | | | | all_86_11, $sum(all_86_10, 1)) = 0 207.70/128.12 | | | | | | | | | | | | 207.70/128.12 | | | | | | | | | | | | ALPHA: (165) implies: 207.70/128.12 | | | | | | | | | | | | (166) permut3(int, all_103_4, all_105_4, all_86_11, 207.70/128.12 | | | | | | | | | | | | $sum(all_86_10, 1)) = 0 207.70/128.12 | | | | | | | | | | | | 207.70/128.12 | | | | | | | | | | | | REF_CLOSE: (4), (5), (9), (10), (11), (16), (18), (19), (20), 207.70/128.12 | | | | | | | | | | | | (22), (23), (31), (33), (37), (40), (41), (42), 207.70/128.12 | | | | | | | | | | | | (45), (50), (53), (56), (62), (65), (67), (72), 207.70/128.12 | | | | | | | | | | | | (73), (83), (84), (85), (97), (103), (112), (115), 207.70/128.12 | | | | | | | | | | | | (142), (143), (166) are inconsistent by sub-proof 207.70/128.12 | | | | | | | | | | | | #107. 207.70/128.12 | | | | | | | | | | | | 207.70/128.12 | | | | | | | | | | | Case 2: 207.70/128.12 | | | | | | | | | | | | 207.70/128.12 | | | | | | | | | | | | (167) length1(int, all_103_4) = all_775_1 & ( ~ 207.70/128.12 | | | | | | | | | | | | ($lesseq(1, $difference(all_775_1, all_86_10))) 207.70/128.12 | | | | | | | | | | | | | ~ ($lesseq(all_86_11, all_775_1)) | ( ~ 207.70/128.12 | | | | | | | | | | | | (all_775_0 = all_775_1) & length1(int, 207.70/128.12 | | | | | | | | | | | | all_105_4) = all_775_0)) 207.70/128.12 | | | | | | | | | | | | 207.70/128.12 | | | | | | | | | | | | ALPHA: (167) implies: 207.70/128.12 | | | | | | | | | | | | (168) length1(int, all_103_4) = all_775_1 207.70/128.12 | | | | | | | | | | | | (169) ~ ($lesseq(1, $difference(all_775_1, all_86_10))) 207.70/128.12 | | | | | | | | | | | | | ~ ($lesseq(all_86_11, all_775_1)) | ( ~ 207.70/128.12 | | | | | | | | | | | | (all_775_0 = all_775_1) & length1(int, 207.70/128.12 | | | | | | | | | | | | all_105_4) = all_775_0) 207.70/128.12 | | | | | | | | | | | | 207.70/128.12 | | | | | | | | | | | | GROUND_INST: instantiating (67) with all_86_13, all_787_1, 207.70/128.12 | | | | | | | | | | | | all_103_4, int, simplifying with (11), (164) 207.70/128.12 | | | | | | | | | | | | gives: 207.70/128.12 | | | | | | | | | | | | (170) all_787_1 = all_86_13 207.70/128.12 | | | | | | | | | | | | 207.70/128.12 | | | | | | | | | | | | GROUND_INST: instantiating (67) with all_787_1, all_775_1, 207.70/128.12 | | | | | | | | | | | | all_103_4, int, simplifying with (164), (168) 207.70/128.12 | | | | | | | | | | | | gives: 207.70/128.12 | | | | | | | | | | | | (171) all_787_1 = all_775_1 207.70/128.12 | | | | | | | | | | | | 207.70/128.12 | | | | | | | | | | | | COMBINE_EQS: (170), (171) imply: 207.70/128.12 | | | | | | | | | | | | (172) all_775_1 = all_86_13 207.70/128.12 | | | | | | | | | | | | 207.70/128.12 | | | | | | | | | | | | BETA: splitting (169) gives: 207.70/128.12 | | | | | | | | | | | | 207.70/128.12 | | | | | | | | | | | | Case 1: 207.70/128.12 | | | | | | | | | | | | | 207.70/128.12 | | | | | | | | | | | | | (173) $lesseq(1, $difference(all_86_11, all_775_1)) 207.70/128.12 | | | | | | | | | | | | | 207.70/128.12 | | | | | | | | | | | | | REF_CLOSE: (40), (41), (54), (84), (85), (172), (173) are 207.70/128.12 | | | | | | | | | | | | | inconsistent by sub-proof #106. 207.70/128.12 | | | | | | | | | | | | | 207.70/128.12 | | | | | | | | | | | | Case 2: 207.70/128.12 | | | | | | | | | | | | | 207.70/128.12 | | | | | | | | | | | | | (174) ~ ($lesseq(1, $difference(all_775_1, all_86_10))) 207.70/128.12 | | | | | | | | | | | | | | ( ~ (all_775_0 = all_775_1) & length1(int, 207.70/128.12 | | | | | | | | | | | | | all_105_4) = all_775_0) 207.70/128.12 | | | | | | | | | | | | | 207.70/128.12 | | | | | | | | | | | | | REF_CLOSE: (26), (54), (67), (172), (174) are inconsistent by 207.70/128.12 | | | | | | | | | | | | | sub-proof #105. 207.70/128.12 | | | | | | | | | | | | | 207.70/128.12 | | | | | | | | | | | | End of split 207.70/128.12 | | | | | | | | | | | | 207.70/128.12 | | | | | | | | | | | End of split 207.70/128.12 | | | | | | | | | | | 207.70/128.12 | | | | | | | | | | End of split 207.70/128.12 | | | | | | | | | | 207.70/128.12 | | | | | | | | | End of split 207.70/128.12 | | | | | | | | | 207.70/128.12 | | | | | | | | Case 2: 207.70/128.12 | | | | | | | | | 207.70/128.12 | | | | | | | | | (175) ~ (all_737_1 = 0) & permut3(int, all_103_2, 207.70/128.12 | | | | | | | | | all_105_4, 0, all_86_13) = all_737_1 207.70/128.12 | | | | | | | | | 207.70/128.12 | | | | | | | | | ALPHA: (175) implies: 207.70/128.12 | | | | | | | | | (176) ~ (all_737_1 = 0) 207.70/128.12 | | | | | | | | | (177) permut3(int, all_103_2, all_105_4, 0, all_86_13) = 207.70/128.12 | | | | | | | | | all_737_1 207.70/128.12 | | | | | | | | | 207.70/128.12 | | | | | | | | | GROUND_INST: instantiating (23) with 0, all_737_1, all_86_13, 207.70/128.12 | | | | | | | | | 0, all_105_4, all_103_2, int, simplifying with 207.70/128.12 | | | | | | | | | (122), (177) gives: 207.70/128.12 | | | | | | | | | (178) all_737_1 = 0 207.70/128.12 | | | | | | | | | 207.70/128.12 | | | | | | | | | REDUCE: (176), (178) imply: 207.70/128.12 | | | | | | | | | (179) ~ (0 = 0) 207.70/128.12 | | | | | | | | | 207.70/128.12 | | | | | | | | | CLOSE: (179) is inconsistent. 207.70/128.12 | | | | | | | | | 207.70/128.12 | | | | | | | | End of split 207.70/128.12 | | | | | | | | 207.70/128.12 | | | | | | | End of split 207.70/128.12 | | | | | | | 207.70/128.12 | | | | | | End of split 207.70/128.12 | | | | | | 207.70/128.12 | | | | | Case 2: 207.70/128.12 | | | | | | 207.70/128.12 | | | | | | (180) length1(int, all_103_2) = all_749_1 & ( ~ 207.70/128.12 | | | | | | ($lesseq(all_86_13, all_749_1)) | ~ ($lesseq(0, 207.70/128.12 | | | | | | all_749_1)) | ( ~ (all_749_0 = all_749_1) & 207.70/128.12 | | | | | | length1(int, all_105_4) = all_749_0)) 207.70/128.12 | | | | | | 207.70/128.12 | | | | | | ALPHA: (180) implies: 207.70/128.12 | | | | | | (181) length1(int, all_103_2) = all_749_1 207.70/128.12 | | | | | | (182) ~ ($lesseq(all_86_13, all_749_1)) | ~ ($lesseq(0, 207.70/128.12 | | | | | | all_749_1)) | ( ~ (all_749_0 = all_749_1) & 207.70/128.12 | | | | | | length1(int, all_105_4) = all_749_0) 207.70/128.12 | | | | | | 207.70/128.12 | | | | | | BETA: splitting (100) gives: 207.70/128.12 | | | | | | 207.70/128.12 | | | | | | Case 1: 207.70/128.12 | | | | | | | 207.70/128.12 | | | | | | | (183) $lesseq(all_86_11, -1) 207.70/128.12 | | | | | | | 207.70/128.12 | | | | | | | COMBINE_INEQS: (58), (183) imply: 207.70/128.12 | | | | | | | (184) $lesseq(0, -1) 207.70/128.12 | | | | | | | 207.70/128.12 | | | | | | | CLOSE: (184) is inconsistent. 207.70/128.12 | | | | | | | 207.70/128.12 | | | | | | Case 2: 207.70/128.12 | | | | | | | 207.70/128.12 | | | | | | | (185) ~ ($lesseq(-1, all_86_10)) | ? [v0: $int] : ? [v1: 207.70/128.12 | | | | | | | $int] : ((v0 = 0 & permut3(int, all_103_4, all_105_4, 207.70/128.12 | | | | | | | all_86_11, $sum(all_86_10, 1)) = 0) | (length1(int, 207.70/128.12 | | | | | | | all_103_4) = v0 & ( ~ ($lesseq(1, $difference(v0, 207.70/128.12 | | | | | | | all_86_10))) | ~ ($lesseq(all_86_11, v0)) | 207.70/128.12 | | | | | | | ( ~ (v1 = v0) & length1(int, all_105_4) = v1)))) 207.70/128.12 | | | | | | | 207.70/128.12 | | | | | | | BETA: splitting (185) gives: 207.70/128.12 | | | | | | | 207.70/128.12 | | | | | | | Case 1: 207.70/128.12 | | | | | | | | 207.70/128.12 | | | | | | | | (186) $lesseq(all_86_10, -2) 207.70/128.12 | | | | | | | | 207.70/128.12 | | | | | | | | COMBINE_INEQS: (92), (186) imply: 207.70/128.12 | | | | | | | | (187) $lesseq(0, -1) 207.70/128.12 | | | | | | | | 207.70/128.12 | | | | | | | | CLOSE: (187) is inconsistent. 207.70/128.12 | | | | | | | | 207.70/128.12 | | | | | | | Case 2: 207.70/128.12 | | | | | | | | 207.70/128.12 | | | | | | | | (188) ? [v0: $int] : ? [v1: $int] : ((v0 = 0 & permut3(int, 207.70/128.12 | | | | | | | | all_103_4, all_105_4, all_86_11, $sum(all_86_10, 207.70/128.12 | | | | | | | | 1)) = 0) | (length1(int, all_103_4) = v0 & ( ~ 207.70/128.12 | | | | | | | | ($lesseq(1, $difference(v0, all_86_10))) | ~ 207.70/128.12 | | | | | | | | ($lesseq(all_86_11, v0)) | ( ~ (v1 = v0) & 207.70/128.12 | | | | | | | | length1(int, all_105_4) = v1)))) 207.70/128.12 | | | | | | | | 207.70/128.12 | | | | | | | | DELTA: instantiating (188) with fresh symbols all_789_0, 207.70/128.12 | | | | | | | | all_789_1 gives: 207.70/128.12 | | | | | | | | (189) (all_789_1 = 0 & permut3(int, all_103_4, all_105_4, 207.70/128.12 | | | | | | | | all_86_11, $sum(all_86_10, 1)) = 0) | (length1(int, 207.70/128.12 | | | | | | | | all_103_4) = all_789_1 & ( ~ ($lesseq(1, 207.70/128.12 | | | | | | | | $difference(all_789_1, all_86_10))) | ~ 207.70/128.12 | | | | | | | | ($lesseq(all_86_11, all_789_1)) | ( ~ (all_789_0 = 207.70/128.12 | | | | | | | | all_789_1) & length1(int, all_105_4) = 207.70/128.12 | | | | | | | | all_789_0))) 207.70/128.12 | | | | | | | | 207.70/128.12 | | | | | | | | BETA: splitting (189) gives: 207.70/128.12 | | | | | | | | 207.70/128.12 | | | | | | | | Case 1: 207.70/128.12 | | | | | | | | | 207.70/128.12 | | | | | | | | | (190) all_789_1 = 0 & permut3(int, all_103_4, all_105_4, 207.70/128.12 | | | | | | | | | all_86_11, $sum(all_86_10, 1)) = 0 207.70/128.12 | | | | | | | | | 207.70/128.12 | | | | | | | | | ALPHA: (190) implies: 207.70/128.12 | | | | | | | | | (191) permut3(int, all_103_4, all_105_4, all_86_11, 207.70/128.12 | | | | | | | | | $sum(all_86_10, 1)) = 0 207.70/128.12 | | | | | | | | | 207.70/128.12 | | | | | | | | | BETA: splitting (112) gives: 207.70/128.12 | | | | | | | | | 207.70/128.12 | | | | | | | | | Case 1: 207.70/128.12 | | | | | | | | | | 207.70/128.12 | | | | | | | | | | (192) all_736_0 = all_736_1 & $lesseq(1, 207.70/128.12 | | | | | | | | | | $difference(all_736_1, all_86_10)) & 207.70/128.12 | | | | | | | | | | $lesseq(all_86_11, all_736_1) & $lesseq(-1, 207.70/128.12 | | | | | | | | | | all_86_10) & $lesseq(0, all_86_11) & length1(int, 207.70/128.12 | | | | | | | | | | all_105_4) = all_736_1 & length1(int, all_103_4) 207.70/128.12 | | | | | | | | | | = all_736_1 207.70/128.12 | | | | | | | | | | 207.70/128.12 | | | | | | | | | | ALPHA: (192) implies: 207.70/128.12 | | | | | | | | | | (193) length1(int, all_103_4) = all_736_1 207.70/128.12 | | | | | | | | | | 207.70/128.12 | | | | | | | | | | GROUND_INST: instantiating (1) with all_133_0, all_725_0, 207.70/128.12 | | | | | | | | | | all_133_1, simplifying with (88), (109) gives: 207.70/128.12 | | | | | | | | | | (194) all_725_0 = all_133_0 207.70/128.12 | | | | | | | | | | 207.70/128.12 | | | | | | | | | | GROUND_INST: instantiating (67) with all_86_13, all_736_1, 207.70/128.12 | | | | | | | | | | all_103_4, int, simplifying with (11), (193) 207.70/128.12 | | | | | | | | | | gives: 207.70/128.12 | | | | | | | | | | (195) all_736_1 = all_86_13 207.70/128.12 | | | | | | | | | | 207.70/128.12 | | | | | | | | | | GROUND_INST: instantiating (25) with all_105_1, all_738_1, 207.70/128.12 | | | | | | | | | | all_105_2, int, simplifying with (36), (116) 207.70/128.12 | | | | | | | | | | gives: 207.70/128.12 | | | | | | | | | | (196) all_738_1 = all_105_1 207.70/128.12 | | | | | | | | | | 207.70/128.13 | | | | | | | | | | GROUND_INST: instantiating (25) with all_738_1, all_725_2, 207.70/128.13 | | | | | | | | | | all_105_2, int, simplifying with (107), (116) 207.70/128.13 | | | | | | | | | | gives: 207.70/128.13 | | | | | | | | | | (197) all_738_1 = all_725_2 207.70/128.13 | | | | | | | | | | 207.70/128.13 | | | | | | | | | | COMBINE_EQS: (196), (197) imply: 207.70/128.13 | | | | | | | | | | (198) all_725_2 = all_105_1 207.70/128.13 | | | | | | | | | | 207.70/128.13 | | | | | | | | | | REDUCE: (110), (198) imply: 207.70/128.13 | | | | | | | | | | (199) tb2t(all_105_1) = all_725_1 207.70/128.13 | | | | | | | | | | 207.70/128.13 | | | | | | | | | | REDUCE: (108), (194) imply: 207.70/128.13 | | | | | | | | | | (200) get3(all_725_1, all_133_2) = all_133_0 207.70/128.13 | | | | | | | | | | 207.70/128.13 | | | | | | | | | | REF_CLOSE: (4), (5), (9), (10), (11), (16), (18), (19), (20), 207.70/128.13 | | | | | | | | | | (22), (23), (31), (33), (37), (40), (41), (42), 207.70/128.13 | | | | | | | | | | (45), (50), (53), (56), (62), (65), (67), (72), 207.70/128.13 | | | | | | | | | | (73), (83), (84), (85), (97), (103), (112), (115), 207.70/128.13 | | | | | | | | | | (191), (199), (200) are inconsistent by sub-proof 207.70/128.13 | | | | | | | | | | #107. 207.70/128.13 | | | | | | | | | | 207.70/128.13 | | | | | | | | | Case 2: 207.70/128.13 | | | | | | | | | | 207.70/128.13 | | | | | | | | | | (201) ~ (all_736_1 = 0) & permut3(int, all_103_4, 207.70/128.13 | | | | | | | | | | all_105_4, all_86_11, $sum(all_86_10, 1)) = 207.70/128.13 | | | | | | | | | | all_736_1 207.70/128.13 | | | | | | | | | | 207.70/128.13 | | | | | | | | | | ALPHA: (201) implies: 207.70/128.13 | | | | | | | | | | (202) ~ (all_736_1 = 0) 207.70/128.13 | | | | | | | | | | (203) permut3(int, all_103_4, all_105_4, all_86_11, 207.70/128.13 | | | | | | | | | | $sum(all_86_10, 1)) = all_736_1 207.70/128.13 | | | | | | | | | | 207.70/128.13 | | | | | | | | | | GROUND_INST: instantiating (23) with all_736_1, 0, 207.70/128.13 | | | | | | | | | | $sum(all_86_10, 1), all_86_11, all_105_4, 207.70/128.13 | | | | | | | | | | all_103_4, int, simplifying with (191), (203) 207.70/128.13 | | | | | | | | | | gives: 207.70/128.13 | | | | | | | | | | (204) all_736_1 = 0 207.70/128.13 | | | | | | | | | | 207.70/128.13 | | | | | | | | | | REDUCE: (202), (204) imply: 207.70/128.13 | | | | | | | | | | (205) ~ (0 = 0) 207.70/128.13 | | | | | | | | | | 207.70/128.13 | | | | | | | | | | CLOSE: (205) is inconsistent. 207.70/128.13 | | | | | | | | | | 207.70/128.13 | | | | | | | | | End of split 207.70/128.13 | | | | | | | | | 207.70/128.13 | | | | | | | | Case 2: 207.70/128.13 | | | | | | | | | 207.70/128.13 | | | | | | | | | (206) length1(int, all_103_4) = all_789_1 & ( ~ ($lesseq(1, 207.70/128.13 | | | | | | | | | $difference(all_789_1, all_86_10))) | ~ 207.70/128.13 | | | | | | | | | ($lesseq(all_86_11, all_789_1)) | ( ~ (all_789_0 = 207.70/128.13 | | | | | | | | | all_789_1) & length1(int, all_105_4) = 207.70/128.13 | | | | | | | | | all_789_0)) 207.70/128.13 | | | | | | | | | 207.70/128.13 | | | | | | | | | ALPHA: (206) implies: 207.70/128.13 | | | | | | | | | (207) length1(int, all_103_4) = all_789_1 207.70/128.13 | | | | | | | | | (208) ~ ($lesseq(1, $difference(all_789_1, all_86_10))) | 207.70/128.13 | | | | | | | | | ~ ($lesseq(all_86_11, all_789_1)) | ( ~ (all_789_0 = 207.70/128.13 | | | | | | | | | all_789_1) & length1(int, all_105_4) = all_789_0) 207.70/128.13 | | | | | | | | | 207.70/128.13 | | | | | | | | | GROUND_INST: instantiating (67) with all_86_13, all_749_1, 207.70/128.13 | | | | | | | | | all_103_2, int, simplifying with (3), (181) gives: 207.70/128.13 | | | | | | | | | (209) all_749_1 = all_86_13 207.70/128.13 | | | | | | | | | 207.70/128.13 | | | | | | | | | GROUND_INST: instantiating (67) with all_86_13, all_789_1, 207.70/128.13 | | | | | | | | | all_103_4, int, simplifying with (11), (207) 207.70/128.13 | | | | | | | | | gives: 207.70/128.13 | | | | | | | | | (210) all_789_1 = all_86_13 207.70/128.13 | | | | | | | | | 207.70/128.13 | | | | | | | | | BETA: splitting (182) gives: 207.70/128.13 | | | | | | | | | 207.70/128.13 | | | | | | | | | Case 1: 207.70/128.13 | | | | | | | | | | 207.70/128.13 | | | | | | | | | | (211) $lesseq(all_749_1, -1) 207.70/128.13 | | | | | | | | | | 207.70/128.13 | | | | | | | | | | REDUCE: (209), (211) imply: 207.70/128.13 | | | | | | | | | | (212) $lesseq(all_86_13, -1) 207.70/128.13 | | | | | | | | | | 207.70/128.13 | | | | | | | | | | COMBINE_INEQS: (94), (212) imply: 207.70/128.13 | | | | | | | | | | (213) $lesseq(0, -1) 207.70/128.13 | | | | | | | | | | 207.70/128.13 | | | | | | | | | | CLOSE: (213) is inconsistent. 207.70/128.13 | | | | | | | | | | 207.70/128.13 | | | | | | | | | Case 2: 207.70/128.13 | | | | | | | | | | 207.70/128.13 | | | | | | | | | | (214) ~ ($lesseq(all_86_13, all_749_1)) | ( ~ (all_749_0 207.70/128.13 | | | | | | | | | | = all_749_1) & length1(int, all_105_4) = 207.70/128.13 | | | | | | | | | | all_749_0) 207.70/128.13 | | | | | | | | | | 207.70/128.13 | | | | | | | | | | BETA: splitting (208) gives: 207.70/128.13 | | | | | | | | | | 207.70/128.13 | | | | | | | | | | Case 1: 207.70/128.13 | | | | | | | | | | | 207.70/128.13 | | | | | | | | | | | (215) $lesseq(1, $difference(all_86_11, all_789_1)) 207.70/128.13 | | | | | | | | | | | 207.70/128.13 | | | | | | | | | | | REDUCE: (210), (215) imply: 207.70/128.13 | | | | | | | | | | | (216) $lesseq(1, $difference(all_86_11, all_86_13)) 207.70/128.13 | | | | | | | | | | | 207.70/128.13 | | | | | | | | | | | COMBINE_INEQS: (93), (216) imply: 207.70/128.13 | | | | | | | | | | | (217) $lesseq(0, -1) 207.70/128.13 | | | | | | | | | | | 207.70/128.13 | | | | | | | | | | | CLOSE: (217) is inconsistent. 207.70/128.13 | | | | | | | | | | | 207.70/128.13 | | | | | | | | | | Case 2: 207.70/128.13 | | | | | | | | | | | 207.70/128.13 | | | | | | | | | | | (218) ~ ($lesseq(1, $difference(all_789_1, all_86_10))) 207.70/128.13 | | | | | | | | | | | | ( ~ (all_789_0 = all_789_1) & length1(int, 207.70/128.13 | | | | | | | | | | | all_105_4) = all_789_0) 207.70/128.13 | | | | | | | | | | | 207.70/128.13 | | | | | | | | | | | BETA: splitting (214) gives: 207.70/128.13 | | | | | | | | | | | 207.70/128.13 | | | | | | | | | | | Case 1: 207.70/128.13 | | | | | | | | | | | | 207.70/128.13 | | | | | | | | | | | | (219) $lesseq(1, $difference(all_86_13, all_749_1)) 207.70/128.13 | | | | | | | | | | | | 207.70/128.13 | | | | | | | | | | | | REDUCE: (209), (219) imply: 207.70/128.13 | | | | | | | | | | | | (220) $lesseq(0, -1) 207.70/128.13 | | | | | | | | | | | | 207.70/128.13 | | | | | | | | | | | | CLOSE: (220) is inconsistent. 207.70/128.13 | | | | | | | | | | | | 207.70/128.13 | | | | | | | | | | | Case 2: 207.70/128.13 | | | | | | | | | | | | 207.70/128.13 | | | | | | | | | | | | (221) ~ (all_749_0 = all_749_1) & length1(int, 207.70/128.13 | | | | | | | | | | | | all_105_4) = all_749_0 207.70/128.13 | | | | | | | | | | | | 207.70/128.13 | | | | | | | | | | | | ALPHA: (221) implies: 207.70/128.13 | | | | | | | | | | | | (222) ~ (all_749_0 = all_749_1) 207.70/128.13 | | | | | | | | | | | | (223) length1(int, all_105_4) = all_749_0 207.70/128.13 | | | | | | | | | | | | 207.70/128.13 | | | | | | | | | | | | REDUCE: (209), (222) imply: 207.70/128.13 | | | | | | | | | | | | (224) ~ (all_749_0 = all_86_13) 207.70/128.13 | | | | | | | | | | | | 207.70/128.13 | | | | | | | | | | | | BETA: splitting (218) gives: 207.70/128.13 | | | | | | | | | | | | 207.70/128.13 | | | | | | | | | | | | Case 1: 207.70/128.13 | | | | | | | | | | | | | 207.70/128.13 | | | | | | | | | | | | | (225) $lesseq(all_789_1, all_86_10) 207.70/128.13 | | | | | | | | | | | | | 207.70/128.13 | | | | | | | | | | | | | REDUCE: (210), (225) imply: 207.70/128.13 | | | | | | | | | | | | | (226) $lesseq(all_86_13, all_86_10) 207.70/128.13 | | | | | | | | | | | | | 207.70/128.13 | | | | | | | | | | | | | COMBINE_INEQS: (54), (226) imply: 207.70/128.13 | | | | | | | | | | | | | (227) $lesseq(0, -1) 207.70/128.13 | | | | | | | | | | | | | 207.70/128.13 | | | | | | | | | | | | | CLOSE: (227) is inconsistent. 207.70/128.13 | | | | | | | | | | | | | 207.70/128.13 | | | | | | | | | | | | Case 2: 207.70/128.13 | | | | | | | | | | | | | 207.70/128.13 | | | | | | | | | | | | | (228) ~ (all_789_0 = all_789_1) & length1(int, 207.70/128.13 | | | | | | | | | | | | | all_105_4) = all_789_0 207.70/128.13 | | | | | | | | | | | | | 207.70/128.13 | | | | | | | | | | | | | ALPHA: (228) implies: 207.70/128.13 | | | | | | | | | | | | | (229) length1(int, all_105_4) = all_789_0 207.70/128.13 | | | | | | | | | | | | | 207.70/128.13 | | | | | | | | | | | | | GROUND_INST: instantiating (67) with all_86_13, all_789_0, 207.70/128.13 | | | | | | | | | | | | | all_105_4, int, simplifying with (26), (229) 207.70/128.13 | | | | | | | | | | | | | gives: 207.70/128.13 | | | | | | | | | | | | | (230) all_789_0 = all_86_13 207.70/128.13 | | | | | | | | | | | | | 207.70/128.13 | | | | | | | | | | | | | GROUND_INST: instantiating (67) with all_789_0, all_749_0, 207.70/128.13 | | | | | | | | | | | | | all_105_4, int, simplifying with (223), (229) 207.70/128.13 | | | | | | | | | | | | | gives: 207.70/128.13 | | | | | | | | | | | | | (231) all_789_0 = all_749_0 207.70/128.13 | | | | | | | | | | | | | 207.70/128.13 | | | | | | | | | | | | | COMBINE_EQS: (230), (231) imply: 207.70/128.13 | | | | | | | | | | | | | (232) all_749_0 = all_86_13 207.70/128.13 | | | | | | | | | | | | | 207.70/128.13 | | | | | | | | | | | | | REDUCE: (224), (232) imply: 207.70/128.13 | | | | | | | | | | | | | (233) ~ (0 = 0) 207.70/128.13 | | | | | | | | | | | | | 207.70/128.13 | | | | | | | | | | | | | CLOSE: (233) is inconsistent. 207.70/128.13 | | | | | | | | | | | | | 207.70/128.13 | | | | | | | | | | | | End of split 207.70/128.13 | | | | | | | | | | | | 207.70/128.13 | | | | | | | | | | | End of split 207.70/128.13 | | | | | | | | | | | 207.70/128.13 | | | | | | | | | | End of split 207.70/128.13 | | | | | | | | | | 207.70/128.13 | | | | | | | | | End of split 207.70/128.13 | | | | | | | | | 207.70/128.13 | | | | | | | | End of split 207.70/128.13 | | | | | | | | 207.70/128.13 | | | | | | | End of split 207.70/128.13 | | | | | | | 207.70/128.13 | | | | | | End of split 207.70/128.13 | | | | | | 207.70/128.13 | | | | | End of split 207.70/128.13 | | | | | 207.70/128.13 | | | | End of split 207.70/128.13 | | | | 207.70/128.13 | | | Case 2: 207.70/128.13 | | | | 207.70/128.13 | | | | (234) ($lesseq(all_133_0, 41) & $lesseq(all_133_2, all_86_10) & 207.70/128.13 | | | | $lesseq(all_86_7, all_133_2) & tb2t1(all_133_1) = all_133_0 & 207.70/128.13 | | | | get4(int, all_133_3, all_133_2) = all_133_1 & 207.70/128.13 | | | | in_uni(all_133_1)) | ($lesseq(43, all_133_0) & 207.70/128.13 | | | | $lesseq(all_133_2, all_86_8) & $lesseq(all_86_11, all_133_2) 207.70/128.13 | | | | & tb2t1(all_133_1) = all_133_0 & get4(int, all_133_3, 207.70/128.13 | | | | all_133_2) = all_133_1 & in_uni(all_133_1)) 207.70/128.13 | | | | 207.70/128.13 | | | | BETA: splitting (234) gives: 207.70/128.13 | | | | 207.70/128.13 | | | | Case 1: 207.70/128.13 | | | | | 207.70/128.13 | | | | | (235) $lesseq(all_133_0, 41) & $lesseq(all_133_2, all_86_10) & 207.70/128.13 | | | | | $lesseq(all_86_7, all_133_2) & tb2t1(all_133_1) = all_133_0 & 207.70/128.13 | | | | | get4(int, all_133_3, all_133_2) = all_133_1 & 207.70/128.13 | | | | | in_uni(all_133_1) 207.70/128.13 | | | | | 207.70/128.13 | | | | | ALPHA: (235) implies: 207.70/128.13 | | | | | (236) $lesseq(all_86_7, all_133_2) 207.70/128.13 | | | | | (237) $lesseq(all_133_2, all_86_10) 207.70/128.13 | | | | | (238) $lesseq(all_133_0, 41) 207.70/128.13 | | | | | (239) get4(int, all_133_3, all_133_2) = all_133_1 207.70/128.13 | | | | | (240) tb2t1(all_133_1) = all_133_0 207.70/128.13 | | | | | 207.70/128.13 | | | | | REDUCE: (64), (239) imply: 207.70/128.13 | | | | | (241) get4(int, all_105_2, all_133_2) = all_133_1 207.70/128.13 | | | | | 207.70/128.13 | | | | | REF_CLOSE: (1), (7), (8), (9), (10), (15), (24), (25), (27), (28), 207.70/128.13 | | | | | (33), (36), (38), (39), (44), (45), (46), (49), (51), (56), 207.70/128.13 | | | | | (58), (61), (62), (69), (70), (73), (75), (236), (237), 207.70/128.13 | | | | | (238), (240), (241) are inconsistent by sub-proof #148. 207.70/128.13 | | | | | 207.70/128.13 | | | | Case 2: 207.70/128.13 | | | | | 207.70/128.13 | | | | | (242) $lesseq(43, all_133_0) & $lesseq(all_133_2, all_86_8) & 207.70/128.13 | | | | | $lesseq(all_86_11, all_133_2) & tb2t1(all_133_1) = all_133_0 207.70/128.13 | | | | | & get4(int, all_133_3, all_133_2) = all_133_1 & 207.70/128.13 | | | | | in_uni(all_133_1) 207.70/128.13 | | | | | 207.70/128.13 | | | | | ALPHA: (242) implies: 207.70/128.13 | | | | | (243) $lesseq(all_86_11, all_133_2) 207.70/128.13 | | | | | (244) $lesseq(all_133_2, all_86_8) 207.70/128.13 | | | | | (245) $lesseq(43, all_133_0) 207.70/128.13 | | | | | (246) get4(int, all_133_3, all_133_2) = all_133_1 207.70/128.13 | | | | | (247) tb2t1(all_133_1) = all_133_0 207.70/128.13 | | | | | 207.70/128.13 | | | | | REDUCE: (64), (246) imply: 207.70/128.13 | | | | | (248) get4(int, all_105_2, all_133_2) = all_133_1 207.70/128.13 | | | | | 207.70/128.13 | | | | | REF_CLOSE: (1), (2), (3), (4), (7), (9), (10), (11), (12), (14), (20), 207.70/128.13 | | | | | (21), (23), (24), (25), (26), (28), (31), (33), (34), (36), 207.70/128.13 | | | | | (38), (39), (41), (45), (46), (49), (51), (52), (53), (54), 207.70/128.13 | | | | | (56), (58), (59), (61), (62), (65), (67), (69), (70), (73), 207.70/128.13 | | | | | (78), (81), (243), (244), (245), (247), (248) are 207.70/128.13 | | | | | inconsistent by sub-proof #133. 207.70/128.13 | | | | | 207.70/128.13 | | | | End of split 207.70/128.13 | | | | 207.70/128.13 | | | End of split 207.70/128.13 | | | 207.70/128.13 | | End of split 207.70/128.13 | | 207.70/128.13 | End of split 207.70/128.13 | 207.70/128.13 End of proof 207.70/128.13 207.70/128.13 Sub-proof #105 shows that the following formulas are inconsistent: 207.70/128.13 ---------------------------------------------------------------- 207.70/128.13 (1) length1(int, all_105_4) = all_86_13 207.70/128.13 (2) $lesseq(1, $difference(all_86_13, all_86_10)) 207.70/128.13 (3) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 207.70/128.13 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 207.70/128.13 (4) all_775_1 = all_86_13 207.70/128.13 (5) ~ ($lesseq(1, $difference(all_775_1, all_86_10))) | ( ~ (all_775_0 = 207.70/128.13 all_775_1) & length1(int, all_105_4) = all_775_0) 207.70/128.13 207.70/128.13 Begin of proof 207.70/128.13 | 207.70/128.13 | BETA: splitting (5) gives: 207.70/128.13 | 207.70/128.13 | Case 1: 207.70/128.13 | | 207.70/128.13 | | (6) $lesseq(all_775_1, all_86_10) 207.70/128.13 | | 207.70/128.13 | | REDUCE: (4), (6) imply: 207.70/128.13 | | (7) $lesseq(all_86_13, all_86_10) 207.70/128.13 | | 207.70/128.13 | | COMBINE_INEQS: (2), (7) imply: 207.70/128.13 | | (8) $lesseq(0, -1) 207.70/128.13 | | 207.70/128.13 | | CLOSE: (8) is inconsistent. 207.70/128.13 | | 207.70/128.13 | Case 2: 207.70/128.13 | | 207.70/128.13 | | (9) ~ (all_775_0 = all_775_1) & length1(int, all_105_4) = all_775_0 207.70/128.13 | | 207.70/128.13 | | ALPHA: (9) implies: 207.70/128.13 | | (10) ~ (all_775_0 = all_775_1) 207.70/128.13 | | (11) length1(int, all_105_4) = all_775_0 207.70/128.13 | | 207.70/128.13 | | REDUCE: (4), (10) imply: 207.70/128.13 | | (12) ~ (all_775_0 = all_86_13) 207.70/128.13 | | 207.70/128.13 | | GROUND_INST: instantiating (3) with all_86_13, all_775_0, all_105_4, int, 207.70/128.13 | | simplifying with (1), (11) gives: 207.70/128.13 | | (13) all_775_0 = all_86_13 207.70/128.13 | | 207.70/128.13 | | REDUCE: (12), (13) imply: 207.70/128.13 | | (14) ~ (0 = 0) 207.70/128.13 | | 207.70/128.13 | | CLOSE: (14) is inconsistent. 207.70/128.13 | | 207.70/128.13 | End of split 207.70/128.13 | 207.70/128.13 End of proof 207.70/128.13 207.70/128.13 Sub-proof #106 shows that the following formulas are inconsistent: 207.70/128.13 ---------------------------------------------------------------- 207.70/128.13 (1) $lesseq(1, $difference(all_133_2, all_86_8)) 207.70/128.13 (2) $lesseq(1, $difference(all_86_7, all_133_2)) 207.70/128.13 (3) $lesseq(all_86_11, all_86_8) 207.70/128.13 (4) $lesseq(all_86_7, all_86_10) 207.70/128.13 (5) $lesseq(1, $difference(all_86_13, all_86_10)) 207.70/128.13 (6) all_775_1 = all_86_13 207.70/128.13 (7) $lesseq(1, $difference(all_86_11, all_775_1)) 207.70/128.13 207.70/128.13 Begin of proof 207.70/128.13 | 207.70/128.13 | REDUCE: (6), (7) imply: 207.70/128.13 | (8) $lesseq(1, $difference(all_86_11, all_86_13)) 207.70/128.13 | 207.70/128.13 | COMBINE_INEQS: (1), (2) imply: 207.70/128.13 | (9) $lesseq(2, $difference(all_86_7, all_86_8)) 207.70/128.13 | 207.70/128.13 | COMBINE_INEQS: (4), (9) imply: 207.70/128.13 | (10) $lesseq(2, $difference(all_86_10, all_86_8)) 207.70/128.13 | 207.70/128.13 | COMBINE_INEQS: (3), (10) imply: 207.70/128.13 | (11) $lesseq(2, $difference(all_86_10, all_86_11)) 207.70/128.13 | 207.70/128.13 | COMBINE_INEQS: (5), (11) imply: 207.70/128.13 | (12) $lesseq(3, $difference(all_86_13, all_86_11)) 207.70/128.13 | 207.70/128.13 | COMBINE_INEQS: (8), (12) imply: 207.70/128.13 | (13) $lesseq(0, -1) 207.70/128.13 | 207.70/128.13 | CLOSE: (13) is inconsistent. 207.70/128.13 | 207.70/128.13 End of proof 207.70/128.13 207.70/128.13 Sub-proof #107 shows that the following formulas are inconsistent: 207.70/128.13 ---------------------------------------------------------------- 207.70/128.13 (1) in_map_int_int(all_86_6) 207.70/128.13 (2) in_map_int_int(all_86_12) 207.70/128.13 (3) t2tb(all_86_2) = all_105_1 207.70/128.13 (4) in_ty(int) 207.70/128.13 (5) get3(all_725_1, all_133_2) = all_133_0 207.70/128.13 (6) length1(int, all_103_4) = all_86_13 207.70/128.13 (7) $lesseq(all_86_7, all_86_13) 207.70/128.13 (8) ! [v0: $int] : ! [v1: $int] : (v1 = 42 | ~ ($lesseq(1, 207.70/128.13 $difference(all_86_7, v0))) | ~ ($lesseq(1, $difference(v0, 207.70/128.13 all_86_8))) | ~ (get3(all_86_6, v0) = v1)) 207.70/128.13 (9) map_eq_sub1(int, all_103_3, all_103_1, $sum(all_86_10, 1), all_86_13) = 0 207.70/128.13 (10) t2tb(all_86_6) = all_103_1 207.70/128.13 (11) $lesseq(1, $difference(all_133_2, all_86_8)) 207.70/128.13 (12) map_eq_sub1(int, all_103_1, all_105_3, $sum(all_86_8, 1), all_86_13) = 0 207.70/128.13 (13) t2tb1(all_133_2) = all_738_0 207.70/128.14 (14) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.70/128.14 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ (permut3(v6, v5, 207.70/128.14 v4, v3, v2) = v1) | ~ (permut3(v6, v5, v4, v3, v2) = v0)) 207.70/128.14 (15) tb2t(all_105_1) = all_725_1 207.70/128.14 (16) $lesseq(1, $difference(all_86_7, all_133_2)) 207.70/128.14 (17) map_eq_sub1(int, all_105_3, all_105_1, 0, all_86_7) = 0 207.70/128.14 (18) permut3(int, all_103_4, all_105_4, all_86_11, $sum(all_86_10, 1)) = 0 207.70/128.14 (19) (all_736_0 = all_736_1 & $lesseq(1, $difference(all_736_1, all_86_10)) & 207.70/128.14 $lesseq(all_86_11, all_736_1) & $lesseq(-1, all_86_10) & $lesseq(0, 207.70/128.14 all_86_11) & length1(int, all_105_4) = all_736_1 & length1(int, 207.70/128.14 all_103_4) = all_736_1) | ( ~ (all_736_1 = 0) & permut3(int, 207.70/128.14 all_103_4, all_105_4, all_86_11, $sum(all_86_10, 1)) = all_736_1) 207.70/128.14 (20) tb2t(all_105_1) = all_86_2 207.70/128.14 (21) t2tb1(all_133_0) = all_133_1 207.70/128.14 (22) map_eq_sub1(int, all_103_3, all_103_1, 0, all_86_11) = 0 207.70/128.14 (23) $lesseq(all_86_11, all_86_8) 207.70/128.14 (24) $lesseq(all_86_7, all_86_10) 207.70/128.14 (25) $lesseq(0, all_86_8) 207.70/128.14 (26) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.70/128.14 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 207.70/128.14 ($lesseq(1, $difference(v3, v4))) | ~ ($lesseq(v2, v4)) | ~ 207.70/128.14 (permut2(int, v5, v6, v2, v3) = 0) | ~ (t2tb(v1) = v6) | ~ (t2tb(v0) 207.70/128.14 = v5) | ~ (get3(v1, v4) = v7) | ~ in_map_int_int(v0) | ? [v8: 207.70/128.14 $int] : ($lesseq(1, $difference(v3, v8)) & $lesseq(v2, v8) & 207.70/128.14 get3(v0, v8) = v7)) 207.70/128.14 (27) ~ (all_133_0 = 42) 207.70/128.14 (28) t2tb(all_86_12) = all_103_3 207.70/128.14 (29) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.70/128.14 $int] : ! [v5: $int] : ! [v6: $int] : ( ~ ($lesseq(1, 207.70/128.14 $difference(v4, v5))) | ~ ($lesseq(v3, v5)) | ~ (map_eq_sub1(v0, 207.70/128.14 v1, v2, v3, v4) = 0) | ~ (t2tb1(v5) = v6) | ~ in_ty(v0) | ? 207.70/128.14 [v7: $int] : (get(v0, int, v2, v6) = v7 & get(v0, int, v1, v6) = v7 & 207.70/128.14 in_uni(v7))) 207.70/128.14 (30) in_map_int_int(all_86_4) 207.70/128.14 (31) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ (tb2t(v2) 207.70/128.14 = v1) | ~ (tb2t(v2) = v0)) 207.70/128.14 (32) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.70/128.14 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 207.70/128.14 ($lesseq(1, $difference(v3, v6))) | ~ ($lesseq(v2, v6)) | ~ 207.70/128.14 (map_eq_sub1(int, v4, v5, v2, v3) = 0) | ~ (t2tb(v1) = v5) | ~ 207.70/128.14 (t2tb(v0) = v4) | ~ (get3(v1, v6) = v7) | ~ in_map_int_int(v0) | 207.70/128.14 get3(v0, v6) = v7) 207.70/128.14 (33) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 207.70/128.14 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 207.70/128.14 (34) map_eq_sub1(int, all_105_3, all_105_1, $sum(all_86_10, 1), all_86_13) = 207.70/128.14 0 207.70/128.14 (35) permut2(int, all_103_3, all_105_3, 0, all_86_13) = 0 207.70/128.14 (36) t2tb(all_86_4) = all_105_3 207.70/128.14 207.70/128.14 Begin of proof 207.70/128.14 | 207.70/128.14 | BETA: splitting (19) gives: 207.70/128.14 | 207.70/128.14 | Case 1: 207.70/128.14 | | 207.70/128.14 | | (37) all_736_0 = all_736_1 & $lesseq(1, $difference(all_736_1, 207.70/128.14 | | all_86_10)) & $lesseq(all_86_11, all_736_1) & $lesseq(-1, 207.70/128.14 | | all_86_10) & $lesseq(0, all_86_11) & length1(int, all_105_4) = 207.70/128.14 | | all_736_1 & length1(int, all_103_4) = all_736_1 207.70/128.14 | | 207.70/128.14 | | ALPHA: (37) implies: 207.70/128.14 | | (38) $lesseq(0, all_86_11) 207.70/128.14 | | (39) $lesseq(1, $difference(all_736_1, all_86_10)) 207.70/128.14 | | (40) length1(int, all_103_4) = all_736_1 207.70/128.14 | | 207.70/128.14 | | GROUND_INST: instantiating (31) with all_86_2, all_725_1, all_105_1, 207.70/128.14 | | simplifying with (15), (20) gives: 207.70/128.14 | | (41) all_725_1 = all_86_2 207.70/128.14 | | 207.70/128.14 | | GROUND_INST: instantiating (33) with all_86_13, all_736_1, all_103_4, int, 207.70/128.14 | | simplifying with (6), (40) gives: 207.70/128.14 | | (42) all_736_1 = all_86_13 207.70/128.14 | | 207.70/128.14 | | REDUCE: (39), (42) imply: 207.70/128.14 | | (43) $lesseq(1, $difference(all_86_13, all_86_10)) 207.70/128.14 | | 207.70/128.14 | | COMBINE_INEQS: (11), (16) imply: 207.70/128.14 | | (44) $lesseq(2, $difference(all_86_7, all_86_8)) 207.70/128.14 | | 207.70/128.14 | | COMBINE_INEQS: (24), (44) imply: 207.70/128.14 | | (45) $lesseq(2, $difference(all_86_10, all_86_8)) 207.70/128.14 | | 207.70/128.14 | | COMBINE_INEQS: (23), (45) imply: 207.70/128.14 | | (46) $lesseq(2, $difference(all_86_10, all_86_11)) 207.70/128.14 | | 207.70/128.14 | | COMBINE_INEQS: (43), (46) imply: 207.70/128.14 | | (47) $lesseq(3, $difference(all_86_13, all_86_11)) 207.70/128.14 | | 207.70/128.14 | | COMBINE_INEQS: (38), (47) imply: 207.70/128.14 | | (48) $lesseq(3, all_86_13) 207.70/128.14 | | 207.70/128.14 | | REDUCE: (5), (41) imply: 207.70/128.14 | | (49) get3(all_86_2, all_133_2) = all_133_0 207.70/128.14 | | 207.70/128.14 | | GROUND_INST: instantiating (32) with all_86_4, all_86_2, 0, all_86_7, 207.70/128.14 | | all_105_3, all_105_1, all_133_2, all_133_0, simplifying with 207.70/128.14 | | (3), (17), (30), (36), (49) gives: 207.70/128.14 | | (50) ~ ($lesseq(1, $difference(all_86_7, all_133_2))) | ~ ($lesseq(0, 207.70/128.14 | | all_133_2)) | get3(all_86_4, all_133_2) = all_133_0 207.70/128.14 | | 207.70/128.14 | | GROUND_INST: instantiating (29) with int, all_105_3, all_105_1, 207.70/128.14 | | $sum(all_86_10, 1), all_86_13, all_133_0, all_133_1, 207.70/128.14 | | simplifying with (4), (21), (34) gives: 207.70/128.14 | | (51) ~ ($lesseq(1, $difference(all_86_13, all_133_0))) | ~ ($lesseq(1, 207.70/128.14 | | $difference(all_133_0, all_86_10))) | ? [v0: $int] : (get(int, 207.70/128.14 | | int, all_105_1, all_133_1) = v0 & get(int, int, all_105_3, 207.70/128.14 | | all_133_1) = v0 & in_uni(v0)) 207.70/128.14 | | 207.70/128.14 | | GROUND_INST: instantiating (29) with int, all_103_3, all_103_1, 207.70/128.14 | | $sum(all_86_10, 1), all_86_13, all_133_0, all_133_1, 207.70/128.14 | | simplifying with (4), (9), (21) gives: 207.70/128.14 | | (52) ~ ($lesseq(1, $difference(all_86_13, all_133_0))) | ~ ($lesseq(1, 207.70/128.14 | | $difference(all_133_0, all_86_10))) | ? [v0: $int] : (get(int, 207.70/128.14 | | int, all_103_1, all_133_1) = v0 & get(int, int, all_103_3, 207.70/128.14 | | all_133_1) = v0 & in_uni(v0)) 207.70/128.14 | | 207.70/128.14 | | GROUND_INST: instantiating (29) with int, all_103_3, all_103_1, 0, 207.70/128.14 | | all_86_11, all_133_0, all_133_1, simplifying with (4), (21), 207.70/128.14 | | (22) gives: 207.70/128.14 | | (53) ~ ($lesseq(1, $difference(all_86_11, all_133_0))) | ~ ($lesseq(0, 207.70/128.14 | | all_133_0)) | ? [v0: $int] : (get(int, int, all_103_1, 207.70/128.14 | | all_133_1) = v0 & get(int, int, all_103_3, all_133_1) = v0 & 207.70/128.14 | | in_uni(v0)) 207.70/128.14 | | 207.70/128.14 | | GROUND_INST: instantiating (29) with int, all_105_3, all_105_1, 0, all_86_7, 207.70/128.14 | | all_133_2, all_738_0, simplifying with (4), (13), (17) gives: 207.70/128.14 | | (54) ~ ($lesseq(1, $difference(all_86_7, all_133_2))) | ~ ($lesseq(0, 207.70/128.14 | | all_133_2)) | ? [v0: $int] : (get(int, int, all_105_1, 207.70/128.14 | | all_738_0) = v0 & get(int, int, all_105_3, all_738_0) = v0 & 207.70/128.14 | | in_uni(v0)) 207.70/128.14 | | 207.70/128.14 | | GROUND_INST: instantiating (29) with int, all_103_1, all_105_3, 207.70/128.14 | | $sum(all_86_8, 1), all_86_13, all_133_2, all_738_0, simplifying 207.70/128.14 | | with (4), (12), (13) gives: 207.70/128.14 | | (55) ~ ($lesseq(1, $difference(all_86_13, all_133_2))) | ~ ($lesseq(1, 207.70/128.14 | | $difference(all_133_2, all_86_8))) | ? [v0: $int] : (get(int, 207.70/128.14 | | int, all_105_3, all_738_0) = v0 & get(int, int, all_103_1, 207.70/128.14 | | all_738_0) = v0 & in_uni(v0)) 207.70/128.14 | | 207.70/128.14 | | BETA: splitting (54) gives: 207.70/128.14 | | 207.70/128.14 | | Case 1: 207.70/128.14 | | | 207.70/128.14 | | | (56) $lesseq(all_133_2, -1) 207.70/128.14 | | | 207.70/128.14 | | | COMBINE_INEQS: (11), (56) imply: 207.70/128.14 | | | (57) $lesseq(all_86_8, -2) 207.70/128.14 | | | 207.70/128.14 | | | COMBINE_INEQS: (25), (57) imply: 207.70/128.14 | | | (58) $lesseq(0, -1) 207.70/128.14 | | | 207.70/128.14 | | | CLOSE: (58) is inconsistent. 207.70/128.14 | | | 207.70/128.14 | | Case 2: 207.70/128.14 | | | 207.70/128.14 | | | (59) $lesseq(0, all_133_2) 207.70/128.14 | | | 207.70/128.14 | | | BETA: splitting (50) gives: 207.70/128.14 | | | 207.70/128.14 | | | Case 1: 207.70/128.14 | | | | 207.70/128.14 | | | | (60) get3(all_86_4, all_133_2) = all_133_0 207.70/128.14 | | | | 207.70/128.14 | | | | BETA: splitting (55) gives: 207.70/128.14 | | | | 207.70/128.14 | | | | Case 1: 207.70/128.14 | | | | | 207.70/128.14 | | | | | (61) $lesseq(all_86_13, all_133_2) 207.70/128.14 | | | | | 207.70/128.14 | | | | | COMBINE_INEQS: (16), (61) imply: 207.70/128.14 | | | | | (62) $lesseq(1, $difference(all_86_7, all_86_13)) 207.70/128.14 | | | | | 207.70/128.14 | | | | | COMBINE_INEQS: (7), (62) imply: 207.70/128.14 | | | | | (63) $lesseq(0, -1) 207.70/128.14 | | | | | 207.70/128.14 | | | | | CLOSE: (63) is inconsistent. 207.70/128.14 | | | | | 207.70/128.14 | | | | Case 2: 207.70/128.14 | | | | | 207.70/128.14 | | | | | (64) $lesseq(1, $difference(all_86_13, all_133_2)) 207.70/128.14 | | | | | 207.70/128.14 | | | | | REF_CLOSE: (1), (2), (8), (10), (11), (12), (16), (26), (27), (28), 207.70/128.14 | | | | | (32), (35), (36), (48), (51), (52), (53), (59), (60), (64) 207.70/128.14 | | | | | are inconsistent by sub-proof #124. 207.70/128.14 | | | | | 207.70/128.14 | | | | End of split 207.70/128.14 | | | | 207.70/128.14 | | | Case 2: 207.70/128.14 | | | | 207.70/128.14 | | | | (65) ~ ($lesseq(1, $difference(all_86_7, all_133_2))) | ~ 207.70/128.14 | | | | ($lesseq(0, all_133_2)) 207.70/128.14 | | | | 207.70/128.14 | | | | REF_CLOSE: (16), (59), (65) are inconsistent by sub-proof #151. 207.70/128.14 | | | | 207.70/128.14 | | | End of split 207.70/128.14 | | | 207.70/128.14 | | End of split 207.70/128.14 | | 207.70/128.14 | Case 2: 207.70/128.14 | | 207.70/128.14 | | (66) ~ (all_736_1 = 0) & permut3(int, all_103_4, all_105_4, all_86_11, 207.70/128.14 | | $sum(all_86_10, 1)) = all_736_1 207.70/128.14 | | 207.70/128.14 | | ALPHA: (66) implies: 207.70/128.14 | | (67) ~ (all_736_1 = 0) 207.70/128.14 | | (68) permut3(int, all_103_4, all_105_4, all_86_11, $sum(all_86_10, 1)) = 207.70/128.14 | | all_736_1 207.70/128.14 | | 207.70/128.14 | | GROUND_INST: instantiating (14) with all_736_1, 0, $sum(all_86_10, 1), 207.70/128.14 | | all_86_11, all_105_4, all_103_4, int, simplifying with (18), 207.70/128.14 | | (68) gives: 207.70/128.14 | | (69) all_736_1 = 0 207.70/128.14 | | 207.70/128.14 | | REDUCE: (67), (69) imply: 207.70/128.14 | | (70) ~ (0 = 0) 207.70/128.14 | | 207.70/128.14 | | CLOSE: (70) is inconsistent. 207.70/128.14 | | 207.70/128.14 | End of split 207.70/128.14 | 207.70/128.14 End of proof 207.70/128.14 207.70/128.14 Sub-proof #108 shows that the following formulas are inconsistent: 207.70/128.14 ---------------------------------------------------------------- 207.70/128.14 (1) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ (tb2t1(v2) 207.70/128.14 = v1) | ~ (tb2t1(v2) = v0)) 207.70/128.14 (2) ! [v0: $int] : ! [v1: $int] : ( ~ ($lesseq(43, v1)) | ~ ($lesseq(v0, 207.70/128.14 all_86_8)) | ~ ($lesseq(all_86_11, v0)) | ~ (get3(all_86_6, v0) = 207.70/128.14 v1)) 207.70/128.14 (3) in_map_int_int(all_86_6) 207.70/128.14 (4) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.70/128.14 $int] : ! [v5: $int] : ! [v6: $int] : ( ~ ($lesseq(0, v4)) | ~ 207.70/128.14 ($lesseq(0, v3)) | ~ (map_eq_sub1(v0, v5, v6, v3, v4) = 0) | ~ 207.70/128.14 (elts(v0, v2) = v6) | ~ (elts(v0, v1) = v5) | ~ in_ty(v0) | ? [v7: 207.70/128.14 $int] : ? [v8: $int] : ((v7 = 0 & array_eq_sub1(v0, v1, v2, v3, v4) 207.70/128.14 = 0) | (length1(v0, v1) = v7 & ( ~ ($lesseq(v4, v7)) | ~ 207.70/128.14 ($lesseq(v3, v7)) | ( ~ (v8 = v7) & length1(v0, v2) = v8))))) 207.70/128.14 (5) elts(int, all_103_4) = all_103_3 207.70/128.14 (6) t2tb2(all_86_3) = all_105_4 207.70/128.14 (7) t2tb(all_86_2) = all_105_1 207.70/128.14 (8) in_ty(int) 207.70/128.14 (9) length1(int, all_103_4) = all_86_13 207.70/128.14 (10) ( ~ (all_133_0 = 42) & $lesseq(1, $difference(all_86_7, all_133_2)) & 207.70/128.14 $lesseq(1, $difference(all_133_2, all_86_8)) & tb2t1(all_133_1) = 207.70/128.14 all_133_0 & get4(int, all_133_3, all_133_2) = all_133_1 & 207.70/128.14 in_uni(all_133_1)) | ($lesseq(all_133_0, 41) & $lesseq(all_133_2, 207.70/128.14 all_86_10) & $lesseq(all_86_7, all_133_2) & tb2t1(all_133_1) = 207.70/128.14 all_133_0 & get4(int, all_133_3, all_133_2) = all_133_1 & 207.70/128.14 in_uni(all_133_1)) | ($lesseq(43, all_133_0) & $lesseq(all_133_2, 207.70/128.14 all_86_8) & $lesseq(all_86_11, all_133_2) & tb2t1(all_133_1) = 207.70/128.14 all_133_0 & get4(int, all_133_3, all_133_2) = all_133_1 & 207.70/128.14 in_uni(all_133_1)) 207.70/128.14 (11) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.70/128.14 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 207.70/128.14 (permut2(v0, v5, v6, v3, v4) = v7) | ~ (elts(v0, v2) = v6) | ~ 207.70/128.14 (elts(v0, v1) = v5) | ~ in_ty(v0) | ? [v8: $int] : ? [v9: $int] : 207.70/128.14 ((v9 = v8 & v7 = 0 & $lesseq(v4, v8) & $lesseq(v3, v8) & $lesseq(0, 207.70/128.14 v4) & $lesseq(0, v3) & length1(v0, v2) = v8 & length1(v0, v1) = 207.70/128.14 v8) | ( ~ (v8 = 0) & permut3(v0, v1, v2, v3, v4) = v8))) 207.70/128.14 (12) all_125_0 = all_105_4 207.70/128.14 (13) $lesseq(all_86_7, all_86_13) 207.70/128.14 (14) ! [v0: $int] : ! [v1: $int] : (v1 = 42 | ~ ($lesseq(1, 207.70/128.14 $difference(all_86_7, v0))) | ~ ($lesseq(1, $difference(v0, 207.70/128.14 all_86_8))) | ~ (get3(all_86_6, v0) = v1)) 207.70/128.14 (15) t2tb(all_86_6) = all_103_1 207.70/128.14 (16) map_eq_sub1(int, all_103_1, all_105_3, $sum(all_86_8, 1), all_86_13) = 0 207.70/128.14 (17) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.70/128.14 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ (permut3(v6, v5, 207.70/128.14 v4, v3, v2) = v1) | ~ (permut3(v6, v5, v4, v3, v2) = v0)) 207.70/128.14 (18) permut2(int, all_103_3, all_105_3, all_86_11, $sum(all_86_10, 1)) = 0 207.70/128.14 (19) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 207.70/128.14 | ~ (elts(v3, v2) = v1) | ~ (elts(v3, v2) = v0)) 207.70/128.14 (20) length1(int, all_105_4) = all_86_13 207.70/128.14 (21) in_array_int(all_86_3) 207.70/128.14 (22) elts(int, all_105_4) = all_105_3 207.70/128.14 (23) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.70/128.14 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ (permut_sub2(v6, 207.70/128.14 v5, v4, v3, v2) = v1) | ~ (permut_sub2(v6, v5, v4, v3, v2) = v0)) 207.70/128.14 (24) t2tb2(all_86_9) = all_103_4 207.70/128.14 (25) map_eq_sub1(int, all_105_3, all_105_1, 0, all_86_7) = 0 207.70/128.14 (26) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.70/128.14 $int] : ! [v5: $int] : ( ~ (permut3(int, v4, v5, v2, v3) = 0) | ~ 207.70/128.14 (t2tb2(v1) = v5) | ~ (t2tb2(v0) = v4) | ~ in_array_int(v0) | ? [v6: 207.70/128.14 $int] : ? [v7: $int] : ? [v8: $int] : ? [v9: $int] : ((v6 = 0 & 207.70/128.14 permut_sub3(v0, v1, v2, v3) = 0) | (elts(int, v5) = v7 & elts(int, 207.70/128.14 v4) = v6 & in_uni(v7) & in_uni(v6) & (( ~ (v9 = 0) & 207.70/128.14 map_eq_sub1(int, v6, v7, v3, v8) = v9 & length1(int, v4) = v8) 207.70/128.14 | ( ~ (v8 = 0) & map_eq_sub1(int, v6, v7, 0, v2) = v8))))) 207.70/128.14 (27) tb2t(all_105_1) = all_86_2 207.70/128.14 (28) permut2(int, all_103_1, all_105_3, all_86_11, $sum(all_86_8, 1)) = 0 207.70/128.14 (29) in_array_int(all_86_9) 207.70/128.14 (30) elts(int, all_105_2) = all_105_1 207.70/128.14 (31) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.70/128.14 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 207.70/128.14 ($lesseq(1, $difference(v4, v5))) | ~ ($lesseq(v3, v5)) | ~ 207.70/128.14 (permut2(v0, v1, v2, v3, v4) = 0) | ~ (t2tb1(v5) = v6) | ~ (get(v0, 207.70/128.14 int, v2, v6) = v7) | ~ in_ty(v0) | ? [v8: $int] : ? [v9: $int] 207.70/128.14 : ($lesseq(1, $difference(v4, v8)) & $lesseq(v3, v8) & t2tb1(v8) = v9 207.70/128.14 & get(v0, int, v1, v9) = v7 & in_uni(v9) & in_uni(v7))) 207.70/128.14 (32) t2tb2(all_86_1) = all_105_2 207.70/128.14 (33) ~ ($difference(all_86_10, all_86_13) = -1) | ~ (all_86_11 = 0) 207.70/128.14 (34) $lesseq(all_86_11, all_86_8) 207.70/128.14 (35) $lesseq(all_86_7, all_86_10) 207.70/128.14 (36) $lesseq(0, all_86_8) 207.70/128.15 (37) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.70/128.15 $int] : ! [v5: $int] : ( ~ (elts(v0, v1) = v3) | ~ (t2tb1(v2) = v4) 207.70/128.15 | ~ (get(v0, int, v3, v4) = v5) | ~ in_ty(v0) | (get4(v0, v1, v2) = 207.70/128.15 v5 & in_uni(v5))) 207.80/128.15 (38) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.80/128.15 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 207.80/128.15 ($lesseq(1, $difference(v3, v4))) | ~ ($lesseq(v2, v4)) | ~ 207.80/128.15 (permut2(int, v5, v6, v2, v3) = 0) | ~ (t2tb(v1) = v6) | ~ (t2tb(v0) 207.80/128.15 = v5) | ~ (get3(v1, v4) = v7) | ~ in_map_int_int(v0) | ? [v8: 207.80/128.15 $int] : ($lesseq(1, $difference(v3, v8)) & $lesseq(v2, v8) & 207.80/128.15 get3(v0, v8) = v7)) 207.80/128.15 (39) permut2(int, all_105_3, all_105_1, all_86_7, $sum(all_86_10, 1)) = 0 207.80/128.15 (40) in_array_int(all_86_1) 207.80/128.15 (41) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.80/128.15 $int] : ! [v5: $int] : ! [v6: $int] : ( ~ ($lesseq(0, v4)) | ~ 207.80/128.15 ($lesseq(0, v3)) | ~ (permut2(v0, v5, v6, v3, v4) = 0) | ~ (elts(v0, 207.80/128.15 v2) = v6) | ~ (elts(v0, v1) = v5) | ~ in_ty(v0) | ? [v7: $int] 207.80/128.15 : ? [v8: $int] : ((v7 = 0 & permut3(v0, v1, v2, v3, v4) = 0) | 207.80/128.15 (length1(v0, v1) = v7 & ( ~ ($lesseq(v4, v7)) | ~ ($lesseq(v3, v7)) 207.80/128.15 | ( ~ (v8 = v7) & length1(v0, v2) = v8))))) 207.80/128.15 (42) $lesseq(1, $difference(all_86_7, all_86_8)) 207.80/128.15 (43) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.80/128.15 $int] : ! [v5: $int] : ! [v6: $int] : ( ~ ($lesseq(1, 207.80/128.15 $difference(v4, v5))) | ~ ($lesseq(v3, v5)) | ~ (map_eq_sub1(v0, 207.80/128.15 v1, v2, v3, v4) = 0) | ~ (t2tb1(v5) = v6) | ~ in_ty(v0) | ? 207.80/128.15 [v7: $int] : (get(v0, int, v2, v6) = v7 & get(v0, int, v1, v6) = v7 & 207.80/128.15 in_uni(v7))) 207.80/128.15 (44) $lesseq(1, $difference(all_86_13, all_86_10)) 207.80/128.15 (45) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.80/128.15 $int] : ! [v5: $int] : (v5 = 0 | ~ (permut_sub2(v0, v1, v2, v3, v4) 207.80/128.15 = v5) | ~ in_ty(v0) | ? [v6: $int] : ? [v7: $int] : ? [v8: $int] 207.80/128.15 : ? [v9: $int] : (( ~ (v9 = 0) & map_eq_sub1(v0, v6, v7, v4, v8) = v9 207.80/128.15 & length1(v0, v1) = v8 & elts(v0, v2) = v7 & elts(v0, v1) = v6 & 207.80/128.15 in_uni(v7) & in_uni(v6)) | ( ~ (v8 = 0) & map_eq_sub1(v0, v6, v7, 207.80/128.15 0, v3) = v8 & elts(v0, v2) = v7 & elts(v0, v1) = v6 & in_uni(v7) 207.80/128.15 & in_uni(v6)) | ( ~ (v6 = 0) & permut3(v0, v1, v2, v3, v4) = v6))) 207.80/128.15 (46) in_map_int_int(all_86_4) 207.80/128.15 (47) map_eq_sub1(int, all_105_3, all_105_1, 0, all_86_13) = 0 207.80/128.15 (48) $lesseq(0, all_86_11) 207.80/128.15 (49) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ( ~ 207.80/128.15 (t2tb2(v0) = v2) | ~ (get4(int, v2, v1) = v3) | ~ in_array_int(v0) | 207.80/128.15 ? [v4: $int] : ? [v5: $int] : ? [v6: $int] : (tb2t(v4) = v5 & 207.80/128.15 tb2t1(v3) = v6 & get3(v5, v1) = v6 & elts(int, v2) = v4 & 207.80/128.15 in_map_int_int(v5) & in_uni(v4))) 207.80/128.15 (50) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ (tb2t(v2) 207.80/128.15 = v1) | ~ (tb2t(v2) = v0)) 207.80/128.15 (51) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.80/128.15 $int] : ! [v5: $int] : (v1 = v0 | ~ (permut_sub3(v5, v4, v3, v2) = 207.80/128.15 v1) | ~ (permut_sub3(v5, v4, v3, v2) = v0)) 207.80/128.15 (52) all_133_3 = all_105_2 207.80/128.15 (53) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.80/128.15 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 207.80/128.15 ($lesseq(1, $difference(v3, v6))) | ~ ($lesseq(v2, v6)) | ~ 207.80/128.15 (map_eq_sub1(int, v4, v5, v2, v3) = 0) | ~ (t2tb(v1) = v5) | ~ 207.80/128.15 (t2tb(v0) = v4) | ~ (get3(v1, v6) = v7) | ~ in_map_int_int(v0) | 207.80/128.15 get3(v0, v6) = v7) 207.80/128.15 (54) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.80/128.15 $int] : ! [v5: $int] : ! [v6: $int] : ( ~ (permut3(int, v4, v5, v2, 207.80/128.15 v3) = v6) | ~ (t2tb2(v1) = v5) | ~ (t2tb2(v0) = v4) | ~ 207.80/128.15 in_array_int(v0) | ? [v7: $int] : ? [v8: $int] : ? [v9: $int] : ? 207.80/128.15 [v10: $int] : ? [v11: $int] : ((v11 = 0 & v9 = 0 & v6 = 0 & 207.80/128.15 map_eq_sub1(int, v7, v8, v3, v10) = 0 & map_eq_sub1(int, v7, v8, 207.80/128.15 0, v2) = 0 & length1(int, v4) = v10 & elts(int, v5) = v8 & 207.80/128.15 elts(int, v4) = v7 & in_uni(v8) & in_uni(v7)) | ( ~ (v7 = 0) & 207.80/128.15 permut_sub3(v0, v1, v2, v3) = v7))) 207.80/128.15 (55) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 207.80/128.15 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 207.80/128.15 (56) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.80/128.15 $int] : ( ~ (permut3(v0, v1, v2, v3, v4) = 0) | ~ in_ty(v0) | ? [v5: 207.80/128.15 $int] : ? [v6: $int] : ? [v7: $int] : ? [v8: $int] : ((v5 = 0 & 207.80/128.15 permut_sub2(v0, v1, v2, v3, v4) = 0) | (elts(v0, v2) = v6 & 207.80/128.15 elts(v0, v1) = v5 & in_uni(v6) & in_uni(v5) & (( ~ (v8 = 0) & 207.80/128.15 map_eq_sub1(v0, v5, v6, v4, v7) = v8 & length1(v0, v1) = v7) | 207.80/128.15 ( ~ (v7 = 0) & map_eq_sub1(v0, v5, v6, 0, v3) = v7))))) 207.80/128.15 (57) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ( ~ 207.80/128.15 (get4(v0, v1, v2) = v3) | ~ in_ty(v0) | ? [v4: $int] : ? [v5: $int] 207.80/128.15 : (elts(v0, v1) = v4 & t2tb1(v2) = v5 & get(v0, int, v4, v5) = v3 & 207.80/128.15 in_uni(v5) & in_uni(v4) & in_uni(v3))) 207.80/128.15 (58) $lesseq(1, all_86_10) 207.80/128.15 (59) t2tb(all_86_4) = all_105_3 207.80/128.15 (60) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.80/128.15 $int] : ! [v5: $int] : ( ~ (permut3(v0, v1, v2, v3, v4) = v5) | ~ 207.80/128.15 in_ty(v0) | ? [v6: $int] : ? [v7: $int] : ? [v8: $int] : ? [v9: 207.80/128.15 $int] : ? [v10: $int] : ((v10 = 0 & v9 = 0 & v5 = 0 & 207.80/128.15 map_eq_sub1(v0, v6, v7, v4, v8) = 0 & map_eq_sub1(v0, v6, v7, 0, 207.80/128.15 v3) = 0 & length1(v0, v1) = v8 & elts(v0, v2) = v7 & elts(v0, 207.80/128.15 v1) = v6 & in_uni(v7) & in_uni(v6)) | ( ~ (v6 = 0) & 207.80/128.15 permut_sub2(v0, v1, v2, v3, v4) = v6))) 207.80/128.15 (61) ! [v0: $int] : ! [v1: $int] : ( ~ ($lesseq(v0, all_86_10)) | ~ 207.80/128.15 ($lesseq(all_86_7, v0)) | ~ (get4(int, all_125_0, v0) = v1) | ? [v2: 207.80/128.15 $int] : ($lesseq(42, v2) & tb2t1(v1) = v2)) 207.80/128.15 207.80/128.15 Begin of proof 207.80/128.15 | 207.80/128.15 | BETA: splitting (10) gives: 207.80/128.15 | 207.80/128.15 | Case 1: 207.80/128.15 | | 207.80/128.15 | | (62) ~ (all_133_0 = 42) & $lesseq(1, $difference(all_86_7, all_133_2)) & 207.80/128.15 | | $lesseq(1, $difference(all_133_2, all_86_8)) & tb2t1(all_133_1) = 207.80/128.15 | | all_133_0 & get4(int, all_133_3, all_133_2) = all_133_1 & 207.80/128.15 | | in_uni(all_133_1) 207.80/128.15 | | 207.80/128.15 | | ALPHA: (62) implies: 207.80/128.15 | | (63) ~ (all_133_0 = 42) 207.80/128.15 | | (64) $lesseq(1, $difference(all_133_2, all_86_8)) 207.80/128.15 | | (65) $lesseq(1, $difference(all_86_7, all_133_2)) 207.80/128.15 | | (66) get4(int, all_133_3, all_133_2) = all_133_1 207.80/128.15 | | (67) tb2t1(all_133_1) = all_133_0 207.80/128.15 | | 207.80/128.15 | | COMBINE_INEQS: (64), (65) imply: 207.80/128.15 | | (68) $lesseq(2, $difference(all_86_7, all_86_8)) 207.80/128.15 | | 207.80/128.15 | | COMBINE_INEQS: (35), (68) imply: 207.80/128.15 | | (69) $lesseq(2, $difference(all_86_10, all_86_8)) 207.80/128.15 | | 207.80/128.15 | | COMBINE_INEQS: (36), (69) imply: 207.80/128.15 | | (70) $lesseq(2, all_86_10) 207.80/128.15 | | 207.80/128.15 | | REDUCE: (52), (66) imply: 207.80/128.15 | | (71) get4(int, all_105_2, all_133_2) = all_133_1 207.80/128.15 | | 207.80/128.15 | | GROUND_INST: instantiating (11) with int, all_103_4, all_105_4, all_86_11, 207.80/128.15 | | $sum(all_86_10, 1), all_103_3, all_105_3, 0, simplifying with 207.80/128.15 | | (5), (8), (18), (22) gives: 207.80/128.15 | | (72) ? [v0: $int] : ? [v1: $int] : ((v1 = v0 & $lesseq(1, 207.80/128.15 | | $difference(v0, all_86_10)) & $lesseq(all_86_11, v0) & 207.80/128.15 | | $lesseq(-1, all_86_10) & $lesseq(0, all_86_11) & length1(int, 207.80/128.15 | | all_105_4) = v0 & length1(int, all_103_4) = v0) | ( ~ (v0 = 0) 207.80/128.15 | | & permut3(int, all_103_4, all_105_4, all_86_11, $sum(all_86_10, 207.80/128.15 | | 1)) = v0)) 207.80/128.15 | | 207.80/128.15 | | GROUND_INST: instantiating (41) with int, all_103_4, all_105_4, all_86_11, 207.80/128.15 | | $sum(all_86_10, 1), all_103_3, all_105_3, simplifying with (5), 207.80/128.15 | | (8), (18), (22) gives: 207.80/128.15 | | (73) ~ ($lesseq(-1, all_86_10)) | ~ ($lesseq(0, all_86_11)) | ? [v0: 207.80/128.15 | | $int] : ? [v1: $int] : ((v0 = 0 & permut3(int, all_103_4, 207.80/128.15 | | all_105_4, all_86_11, $sum(all_86_10, 1)) = 0) | (length1(int, 207.80/128.15 | | all_103_4) = v0 & ( ~ ($lesseq(1, $difference(v0, all_86_10))) 207.80/128.15 | | | ~ ($lesseq(all_86_11, v0)) | ( ~ (v1 = v0) & length1(int, 207.80/128.15 | | all_105_4) = v1)))) 207.80/128.15 | | 207.80/128.15 | | GROUND_INST: instantiating (49) with all_86_1, all_133_2, all_105_2, 207.80/128.15 | | all_133_1, simplifying with (32), (40), (71) gives: 207.80/128.15 | | (74) ? [v0: $int] : ? [v1: $int] : ? [v2: $int] : (tb2t(v0) = v1 & 207.80/128.15 | | tb2t1(all_133_1) = v2 & get3(v1, all_133_2) = v2 & elts(int, 207.80/128.15 | | all_105_2) = v0 & in_map_int_int(v1) & in_uni(v0)) 207.80/128.15 | | 207.80/128.15 | | GROUND_INST: instantiating (57) with int, all_105_2, all_133_2, all_133_1, 207.80/128.15 | | simplifying with (8), (71) gives: 207.80/128.15 | | (75) ? [v0: $int] : ? [v1: $int] : (elts(int, all_105_2) = v0 & 207.80/128.15 | | t2tb1(all_133_2) = v1 & get(int, int, v0, v1) = all_133_1 & 207.80/128.15 | | in_uni(v1) & in_uni(v0) & in_uni(all_133_1)) 207.80/128.15 | | 207.80/128.15 | | DELTA: instantiating (72) with fresh symbols all_693_0, all_693_1 gives: 207.80/128.15 | | (76) (all_693_0 = all_693_1 & $lesseq(1, $difference(all_693_1, 207.80/128.15 | | all_86_10)) & $lesseq(all_86_11, all_693_1) & $lesseq(-1, 207.80/128.15 | | all_86_10) & $lesseq(0, all_86_11) & length1(int, all_105_4) = 207.80/128.15 | | all_693_1 & length1(int, all_103_4) = all_693_1) | ( ~ (all_693_1 207.80/128.15 | | = 0) & permut3(int, all_103_4, all_105_4, all_86_11, 207.80/128.15 | | $sum(all_86_10, 1)) = all_693_1) 207.80/128.15 | | 207.80/128.15 | | DELTA: instantiating (75) with fresh symbols all_696_0, all_696_1 gives: 207.80/128.15 | | (77) elts(int, all_105_2) = all_696_1 & t2tb1(all_133_2) = all_696_0 & 207.80/128.15 | | get(int, int, all_696_1, all_696_0) = all_133_1 & in_uni(all_696_0) 207.80/128.15 | | & in_uni(all_696_1) & in_uni(all_133_1) 207.80/128.15 | | 207.80/128.15 | | ALPHA: (77) implies: 207.80/128.15 | | (78) t2tb1(all_133_2) = all_696_0 207.80/128.15 | | (79) elts(int, all_105_2) = all_696_1 207.80/128.15 | | 207.80/128.15 | | DELTA: instantiating (74) with fresh symbols all_706_0, all_706_1, all_706_2 207.80/128.15 | | gives: 207.80/128.15 | | (80) tb2t(all_706_2) = all_706_1 & tb2t1(all_133_1) = all_706_0 & 207.80/128.15 | | get3(all_706_1, all_133_2) = all_706_0 & elts(int, all_105_2) = 207.80/128.15 | | all_706_2 & in_map_int_int(all_706_1) & in_uni(all_706_2) 207.80/128.15 | | 207.80/128.15 | | ALPHA: (80) implies: 207.80/128.15 | | (81) elts(int, all_105_2) = all_706_2 207.80/128.15 | | (82) get3(all_706_1, all_133_2) = all_706_0 207.80/128.15 | | (83) tb2t1(all_133_1) = all_706_0 207.80/128.15 | | (84) tb2t(all_706_2) = all_706_1 207.80/128.15 | | 207.80/128.15 | | BETA: splitting (73) gives: 207.80/128.15 | | 207.80/128.15 | | Case 1: 207.80/128.15 | | | 207.80/128.15 | | | (85) $lesseq(all_86_11, -1) 207.80/128.15 | | | 207.80/128.15 | | | COMBINE_INEQS: (48), (85) imply: 207.80/128.15 | | | (86) $lesseq(0, -1) 207.80/128.15 | | | 207.80/128.15 | | | CLOSE: (86) is inconsistent. 207.80/128.15 | | | 207.80/128.15 | | Case 2: 207.80/128.15 | | | 207.80/128.15 | | | (87) ~ ($lesseq(-1, all_86_10)) | ? [v0: $int] : ? [v1: $int] : ((v0 207.80/128.15 | | | = 0 & permut3(int, all_103_4, all_105_4, all_86_11, 207.80/128.15 | | | $sum(all_86_10, 1)) = 0) | (length1(int, all_103_4) = v0 & ( 207.80/128.15 | | | ~ ($lesseq(1, $difference(v0, all_86_10))) | ~ 207.80/128.15 | | | ($lesseq(all_86_11, v0)) | ( ~ (v1 = v0) & length1(int, 207.80/128.15 | | | all_105_4) = v1)))) 207.80/128.15 | | | 207.80/128.15 | | | BETA: splitting (87) gives: 207.80/128.15 | | | 207.80/128.15 | | | Case 1: 207.80/128.15 | | | | 207.80/128.15 | | | | (88) $lesseq(all_86_10, -2) 207.80/128.15 | | | | 207.80/128.15 | | | | COMBINE_INEQS: (70), (88) imply: 207.80/128.15 | | | | (89) $lesseq(0, -1) 207.80/128.15 | | | | 207.80/128.15 | | | | CLOSE: (89) is inconsistent. 207.80/128.15 | | | | 207.80/128.15 | | | Case 2: 207.80/128.15 | | | | 207.80/128.15 | | | | (90) ? [v0: $int] : ? [v1: $int] : ((v0 = 0 & permut3(int, 207.80/128.15 | | | | all_103_4, all_105_4, all_86_11, $sum(all_86_10, 1)) = 0) 207.80/128.15 | | | | | (length1(int, all_103_4) = v0 & ( ~ ($lesseq(1, 207.80/128.15 | | | | $difference(v0, all_86_10))) | ~ ($lesseq(all_86_11, 207.80/128.15 | | | | v0)) | ( ~ (v1 = v0) & length1(int, all_105_4) = 207.80/128.15 | | | | v1)))) 207.80/128.15 | | | | 207.80/128.15 | | | | DELTA: instantiating (90) with fresh symbols all_722_0, all_722_1 gives: 207.80/128.15 | | | | (91) (all_722_1 = 0 & permut3(int, all_103_4, all_105_4, all_86_11, 207.80/128.15 | | | | $sum(all_86_10, 1)) = 0) | (length1(int, all_103_4) = 207.80/128.15 | | | | all_722_1 & ( ~ ($lesseq(1, $difference(all_722_1, 207.80/128.15 | | | | all_86_10))) | ~ ($lesseq(all_86_11, all_722_1)) | ( 207.80/128.15 | | | | ~ (all_722_0 = all_722_1) & length1(int, all_105_4) = 207.80/128.15 | | | | all_722_0))) 207.80/128.15 | | | | 207.80/128.15 | | | | BETA: splitting (91) gives: 207.80/128.15 | | | | 207.80/128.15 | | | | Case 1: 207.80/128.15 | | | | | 207.80/128.15 | | | | | (92) all_722_1 = 0 & permut3(int, all_103_4, all_105_4, all_86_11, 207.80/128.15 | | | | | $sum(all_86_10, 1)) = 0 207.80/128.15 | | | | | 207.80/128.15 | | | | | ALPHA: (92) implies: 207.80/128.15 | | | | | (93) permut3(int, all_103_4, all_105_4, all_86_11, $sum(all_86_10, 207.80/128.15 | | | | | 1)) = 0 207.80/128.15 | | | | | 207.80/128.15 | | | | | BETA: splitting (76) gives: 207.80/128.15 | | | | | 207.80/128.15 | | | | | Case 1: 207.80/128.15 | | | | | | 207.80/128.15 | | | | | | (94) all_693_0 = all_693_1 & $lesseq(1, $difference(all_693_1, 207.80/128.15 | | | | | | all_86_10)) & $lesseq(all_86_11, all_693_1) & 207.80/128.15 | | | | | | $lesseq(-1, all_86_10) & $lesseq(0, all_86_11) & 207.80/128.15 | | | | | | length1(int, all_105_4) = all_693_1 & length1(int, 207.80/128.15 | | | | | | all_103_4) = all_693_1 207.80/128.15 | | | | | | 207.80/128.15 | | | | | | ALPHA: (94) implies: 207.80/128.15 | | | | | | (95) $lesseq(1, $difference(all_693_1, all_86_10)) 207.80/128.15 | | | | | | (96) length1(int, all_103_4) = all_693_1 207.80/128.15 | | | | | | 207.80/128.15 | | | | | | GROUND_INST: instantiating (1) with all_133_0, all_706_0, all_133_1, 207.80/128.15 | | | | | | simplifying with (67), (83) gives: 207.80/128.15 | | | | | | (97) all_706_0 = all_133_0 207.80/128.15 | | | | | | 207.80/128.15 | | | | | | GROUND_INST: instantiating (55) with all_86_13, all_693_1, 207.80/128.15 | | | | | | all_103_4, int, simplifying with (9), (96) gives: 207.80/128.15 | | | | | | (98) all_693_1 = all_86_13 207.80/128.15 | | | | | | 207.80/128.15 | | | | | | GROUND_INST: instantiating (19) with all_105_1, all_706_2, 207.80/128.15 | | | | | | all_105_2, int, simplifying with (30), (81) gives: 207.80/128.15 | | | | | | (99) all_706_2 = all_105_1 207.80/128.15 | | | | | | 207.80/128.15 | | | | | | GROUND_INST: instantiating (19) with all_706_2, all_696_1, 207.80/128.15 | | | | | | all_105_2, int, simplifying with (79), (81) gives: 207.80/128.15 | | | | | | (100) all_706_2 = all_696_1 207.80/128.15 | | | | | | 207.80/128.15 | | | | | | COMBINE_EQS: (99), (100) imply: 207.80/128.15 | | | | | | (101) all_696_1 = all_105_1 207.80/128.15 | | | | | | 207.80/128.15 | | | | | | REDUCE: (84), (99) imply: 207.80/128.15 | | | | | | (102) tb2t(all_105_1) = all_706_1 207.80/128.15 | | | | | | 207.80/128.15 | | | | | | REDUCE: (82), (97) imply: 207.80/128.15 | | | | | | (103) get3(all_706_1, all_133_2) = all_133_0 207.80/128.15 | | | | | | 207.80/128.15 | | | | | | GROUND_INST: instantiating (50) with all_86_2, all_706_1, all_105_1, 207.80/128.15 | | | | | | simplifying with (27), (102) gives: 207.80/128.15 | | | | | | (104) all_706_1 = all_86_2 207.80/128.15 | | | | | | 207.80/128.15 | | | | | | REDUCE: (103), (104) imply: 207.80/128.15 | | | | | | (105) get3(all_86_2, all_133_2) = all_133_0 207.80/128.15 | | | | | | 207.80/128.15 | | | | | | GROUND_INST: instantiating (26) with all_86_9, all_86_3, all_86_11, 207.80/128.15 | | | | | | $sum(all_86_10, 1), all_103_4, all_105_4, simplifying 207.80/128.15 | | | | | | with (6), (24), (29), (93) gives: 207.80/128.15 | | | | | | (106) ? [v0: $int] : ? [v1: $int] : ? [v2: $int] : ? [v3: 207.80/128.15 | | | | | | $int] : ((v0 = 0 & permut_sub3(all_86_9, all_86_3, 207.80/128.15 | | | | | | all_86_11, $sum(all_86_10, 1)) = 0) | (elts(int, 207.80/128.15 | | | | | | all_105_4) = v1 & elts(int, all_103_4) = v0 & 207.80/128.15 | | | | | | in_uni(v1) & in_uni(v0) & (( ~ (v3 = 0) & 207.80/128.15 | | | | | | map_eq_sub1(int, v0, v1, $sum(all_86_10, 1), v2) = 207.80/128.15 | | | | | | v3 & length1(int, all_103_4) = v2) | ( ~ (v2 = 0) & 207.80/128.15 | | | | | | map_eq_sub1(int, v0, v1, 0, all_86_11) = v2)))) 207.80/128.15 | | | | | | 207.80/128.15 | | | | | | GROUND_INST: instantiating (56) with int, all_103_4, all_105_4, 207.80/128.15 | | | | | | all_86_11, $sum(all_86_10, 1), simplifying with (8), 207.80/128.15 | | | | | | (93) gives: 207.80/128.16 | | | | | | (107) ? [v0: $int] : ? [v1: $int] : ? [v2: $int] : ? [v3: 207.80/128.16 | | | | | | $int] : ((v0 = 0 & permut_sub2(int, all_103_4, all_105_4, 207.80/128.16 | | | | | | all_86_11, $sum(all_86_10, 1)) = 0) | (elts(int, 207.80/128.16 | | | | | | all_105_4) = v1 & elts(int, all_103_4) = v0 & 207.80/128.16 | | | | | | in_uni(v1) & in_uni(v0) & (( ~ (v3 = 0) & 207.80/128.16 | | | | | | map_eq_sub1(int, v0, v1, $sum(all_86_10, 1), v2) = 207.80/128.16 | | | | | | v3 & length1(int, all_103_4) = v2) | ( ~ (v2 = 0) & 207.80/128.16 | | | | | | map_eq_sub1(int, v0, v1, 0, all_86_11) = v2)))) 207.80/128.16 | | | | | | 207.80/128.16 | | | | | | GROUND_INST: instantiating (54) with all_86_9, all_86_3, all_86_11, 207.80/128.16 | | | | | | $sum(all_86_10, 1), all_103_4, all_105_4, 0, 207.80/128.16 | | | | | | simplifying with (6), (24), (29), (93) gives: 207.80/128.16 | | | | | | (108) ? [v0: $int] : ? [v1: $int] : ? [v2: $int] : ? [v3: 207.80/128.16 | | | | | | $int] : ? [v4: $int] : ((v4 = 0 & v2 = 0 & 207.80/128.16 | | | | | | map_eq_sub1(int, v0, v1, $sum(all_86_10, 1), v3) = 0 & 207.80/128.16 | | | | | | map_eq_sub1(int, v0, v1, 0, all_86_11) = 0 & 207.80/128.16 | | | | | | length1(int, all_103_4) = v3 & elts(int, all_105_4) = 207.80/128.16 | | | | | | v1 & elts(int, all_103_4) = v0 & in_uni(v1) & 207.80/128.16 | | | | | | in_uni(v0)) | ( ~ (v0 = 0) & permut_sub3(all_86_9, 207.80/128.16 | | | | | | all_86_3, all_86_11, $sum(all_86_10, 1)) = v0)) 207.80/128.16 | | | | | | 207.80/128.16 | | | | | | GROUND_INST: instantiating (60) with int, all_103_4, all_105_4, 207.80/128.16 | | | | | | all_86_11, $sum(all_86_10, 1), 0, simplifying with (8), 207.80/128.16 | | | | | | (93) gives: 207.80/128.16 | | | | | | (109) ? [v0: $int] : ? [v1: $int] : ? [v2: $int] : ? [v3: 207.80/128.16 | | | | | | $int] : ? [v4: $int] : ((v4 = 0 & v3 = 0 & 207.80/128.16 | | | | | | map_eq_sub1(int, v0, v1, $sum(all_86_10, 1), v2) = 0 & 207.80/128.16 | | | | | | map_eq_sub1(int, v0, v1, 0, all_86_11) = 0 & 207.80/128.16 | | | | | | length1(int, all_103_4) = v2 & elts(int, all_105_4) = 207.80/128.16 | | | | | | v1 & elts(int, all_103_4) = v0 & in_uni(v1) & 207.80/128.16 | | | | | | in_uni(v0)) | ( ~ (v0 = 0) & permut_sub2(int, 207.80/128.16 | | | | | | all_103_4, all_105_4, all_86_11, $sum(all_86_10, 1)) 207.80/128.16 | | | | | | = v0)) 207.80/128.16 | | | | | | 207.80/128.16 | | | | | | GROUND_INST: instantiating (53) with all_86_4, all_86_2, 0, 207.80/128.16 | | | | | | all_86_7, all_105_3, all_105_1, all_133_2, all_133_0, 207.80/128.16 | | | | | | simplifying with (7), (25), (46), (59), (105) gives: 207.80/128.16 | | | | | | (110) ~ ($lesseq(1, $difference(all_86_7, all_133_2))) | ~ 207.80/128.16 | | | | | | ($lesseq(0, all_133_2)) | get3(all_86_4, all_133_2) = 207.80/128.16 | | | | | | all_133_0 207.80/128.16 | | | | | | 207.80/128.16 | | | | | | GROUND_INST: instantiating (43) with int, all_105_3, all_105_1, 0, 207.80/128.16 | | | | | | all_86_7, all_133_2, all_696_0, simplifying with (8), 207.80/128.16 | | | | | | (25), (78) gives: 207.80/128.16 | | | | | | (111) ~ ($lesseq(1, $difference(all_86_7, all_133_2))) | ~ 207.80/128.16 | | | | | | ($lesseq(0, all_133_2)) | ? [v0: $int] : (get(int, int, 207.80/128.16 | | | | | | all_105_1, all_696_0) = v0 & get(int, int, all_105_3, 207.80/128.16 | | | | | | all_696_0) = v0 & in_uni(v0)) 207.80/128.16 | | | | | | 207.80/128.16 | | | | | | GROUND_INST: instantiating (43) with int, all_103_1, all_105_3, 207.80/128.16 | | | | | | $sum(all_86_8, 1), all_86_13, all_133_2, all_696_0, 207.80/128.16 | | | | | | simplifying with (8), (16), (78) gives: 207.80/128.16 | | | | | | (112) ~ ($lesseq(1, $difference(all_86_13, all_133_2))) | ~ 207.80/128.16 | | | | | | ($lesseq(1, $difference(all_133_2, all_86_8))) | ? [v0: 207.80/128.16 | | | | | | $int] : (get(int, int, all_105_3, all_696_0) = v0 & 207.80/128.16 | | | | | | get(int, int, all_103_1, all_696_0) = v0 & in_uni(v0)) 207.80/128.16 | | | | | | 207.80/128.16 | | | | | | DELTA: instantiating (109) with fresh symbols all_773_0, all_773_1, 207.80/128.16 | | | | | | all_773_2, all_773_3, all_773_4 gives: 207.80/128.16 | | | | | | (113) (all_773_0 = 0 & all_773_1 = 0 & map_eq_sub1(int, 207.80/128.16 | | | | | | all_773_4, all_773_3, $sum(all_86_10, 1), all_773_2) = 207.80/128.16 | | | | | | 0 & map_eq_sub1(int, all_773_4, all_773_3, 0, all_86_11) 207.80/128.16 | | | | | | = 0 & length1(int, all_103_4) = all_773_2 & elts(int, 207.80/128.16 | | | | | | all_105_4) = all_773_3 & elts(int, all_103_4) = 207.80/128.16 | | | | | | all_773_4 & in_uni(all_773_3) & in_uni(all_773_4)) | ( ~ 207.80/128.16 | | | | | | (all_773_4 = 0) & permut_sub2(int, all_103_4, all_105_4, 207.80/128.16 | | | | | | all_86_11, $sum(all_86_10, 1)) = all_773_4) 207.80/128.16 | | | | | | 207.80/128.16 | | | | | | DELTA: instantiating (108) with fresh symbols all_774_0, all_774_1, 207.80/128.16 | | | | | | all_774_2, all_774_3, all_774_4 gives: 207.80/128.16 | | | | | | (114) (all_774_0 = 0 & all_774_2 = 0 & map_eq_sub1(int, 207.80/128.16 | | | | | | all_774_4, all_774_3, $sum(all_86_10, 1), all_774_1) = 207.80/128.16 | | | | | | 0 & map_eq_sub1(int, all_774_4, all_774_3, 0, all_86_11) 207.80/128.16 | | | | | | = 0 & length1(int, all_103_4) = all_774_1 & elts(int, 207.80/128.16 | | | | | | all_105_4) = all_774_3 & elts(int, all_103_4) = 207.80/128.16 | | | | | | all_774_4 & in_uni(all_774_3) & in_uni(all_774_4)) | ( ~ 207.80/128.16 | | | | | | (all_774_4 = 0) & permut_sub3(all_86_9, all_86_3, 207.80/128.16 | | | | | | all_86_11, $sum(all_86_10, 1)) = all_774_4) 207.80/128.16 | | | | | | 207.80/128.16 | | | | | | DELTA: instantiating (107) with fresh symbols all_783_0, all_783_1, 207.80/128.16 | | | | | | all_783_2, all_783_3 gives: 207.80/128.16 | | | | | | (115) (all_783_3 = 0 & permut_sub2(int, all_103_4, all_105_4, 207.80/128.16 | | | | | | all_86_11, $sum(all_86_10, 1)) = 0) | (elts(int, 207.80/128.16 | | | | | | all_105_4) = all_783_2 & elts(int, all_103_4) = 207.80/128.16 | | | | | | all_783_3 & in_uni(all_783_2) & in_uni(all_783_3) & (( ~ 207.80/128.16 | | | | | | (all_783_0 = 0) & map_eq_sub1(int, all_783_3, 207.80/128.16 | | | | | | all_783_2, $sum(all_86_10, 1), all_783_1) = 207.80/128.16 | | | | | | all_783_0 & length1(int, all_103_4) = all_783_1) | ( 207.80/128.16 | | | | | | ~ (all_783_1 = 0) & map_eq_sub1(int, all_783_3, 207.80/128.16 | | | | | | all_783_2, 0, all_86_11) = all_783_1))) 207.80/128.16 | | | | | | 207.80/128.16 | | | | | | DELTA: instantiating (106) with fresh symbols all_790_0, all_790_1, 207.80/128.16 | | | | | | all_790_2, all_790_3 gives: 207.80/128.16 | | | | | | (116) (all_790_3 = 0 & permut_sub3(all_86_9, all_86_3, all_86_11, 207.80/128.16 | | | | | | $sum(all_86_10, 1)) = 0) | (elts(int, all_105_4) = 207.80/128.16 | | | | | | all_790_2 & elts(int, all_103_4) = all_790_3 & 207.80/128.16 | | | | | | in_uni(all_790_2) & in_uni(all_790_3) & (( ~ (all_790_0 = 207.80/128.16 | | | | | | 0) & map_eq_sub1(int, all_790_3, all_790_2, 207.80/128.16 | | | | | | $sum(all_86_10, 1), all_790_1) = all_790_0 & 207.80/128.16 | | | | | | length1(int, all_103_4) = all_790_1) | ( ~ (all_790_1 207.80/128.16 | | | | | | = 0) & map_eq_sub1(int, all_790_3, all_790_2, 0, 207.80/128.16 | | | | | | all_86_11) = all_790_1))) 207.80/128.16 | | | | | | 207.80/128.16 | | | | | | BETA: splitting (33) gives: 207.80/128.16 | | | | | | 207.80/128.16 | | | | | | Case 1: 207.80/128.16 | | | | | | | 207.80/128.16 | | | | | | | (117) ~ (all_86_11 = 0) 207.80/128.16 | | | | | | | 207.80/128.16 | | | | | | | STRENGTHEN: (48), (117) imply: 207.80/128.16 | | | | | | | (118) $lesseq(1, all_86_11) 207.80/128.16 | | | | | | | 207.80/128.16 | | | | | | | COMBINE_INEQS: (34), (69) imply: 207.80/128.16 | | | | | | | (119) $lesseq(2, $difference(all_86_10, all_86_11)) 207.80/128.16 | | | | | | | 207.80/128.16 | | | | | | | COMBINE_INEQS: (44), (119) imply: 207.80/128.16 | | | | | | | (120) $lesseq(3, $difference(all_86_13, all_86_11)) 207.80/128.16 | | | | | | | 207.80/128.16 | | | | | | | COMBINE_INEQS: (118), (120) imply: 207.80/128.16 | | | | | | | (121) $lesseq(4, all_86_13) 207.80/128.16 | | | | | | | 207.80/128.16 | | | | | | | REF_CLOSE: (3), (4), (5), (8), (9), (13), (14), (15), (16), (19), 207.80/128.16 | | | | | | | (22), (23), (36), (45), (51), (53), (55), (59), (63), 207.80/128.16 | | | | | | | (64), (65), (70), (110), (111), (112), (113), (114), 207.80/128.16 | | | | | | | (115), (116), (121) are inconsistent by sub-proof #110. 207.80/128.16 | | | | | | | 207.80/128.16 | | | | | | Case 2: 207.80/128.16 | | | | | | | 207.80/128.16 | | | | | | | (122) all_86_11 = 0 207.80/128.16 | | | | | | | (123) ~ ($difference(all_86_10, all_86_13) = -1) 207.80/128.16 | | | | | | | 207.80/128.16 | | | | | | | STRENGTHEN: (44), (123) imply: 207.80/128.16 | | | | | | | (124) $lesseq(2, $difference(all_86_13, all_86_10)) 207.80/128.16 | | | | | | | 207.80/128.16 | | | | | | | COMBINE_INEQS: (70), (124) imply: 207.80/128.16 | | | | | | | (125) $lesseq(4, all_86_13) 207.80/128.16 | | | | | | | 207.80/128.16 | | | | | | | REF_CLOSE: (3), (4), (5), (8), (9), (13), (14), (15), (16), (19), 207.80/128.16 | | | | | | | (22), (23), (36), (45), (51), (53), (55), (59), (63), 207.80/128.16 | | | | | | | (64), (65), (70), (110), (111), (112), (113), (114), 207.80/128.16 | | | | | | | (115), (116), (125) are inconsistent by sub-proof #110. 207.80/128.16 | | | | | | | 207.80/128.16 | | | | | | End of split 207.80/128.16 | | | | | | 207.80/128.16 | | | | | Case 2: 207.80/128.16 | | | | | | 207.80/128.16 | | | | | | (126) ~ (all_693_1 = 0) & permut3(int, all_103_4, all_105_4, 207.80/128.16 | | | | | | all_86_11, $sum(all_86_10, 1)) = all_693_1 207.80/128.16 | | | | | | 207.80/128.16 | | | | | | ALPHA: (126) implies: 207.80/128.16 | | | | | | (127) ~ (all_693_1 = 0) 207.80/128.16 | | | | | | (128) permut3(int, all_103_4, all_105_4, all_86_11, 207.80/128.16 | | | | | | $sum(all_86_10, 1)) = all_693_1 207.80/128.16 | | | | | | 207.80/128.16 | | | | | | GROUND_INST: instantiating (17) with all_693_1, 0, $sum(all_86_10, 207.80/128.16 | | | | | | 1), all_86_11, all_105_4, all_103_4, int, simplifying 207.80/128.16 | | | | | | with (93), (128) gives: 207.80/128.16 | | | | | | (129) all_693_1 = 0 207.80/128.16 | | | | | | 207.80/128.16 | | | | | | REDUCE: (127), (129) imply: 207.80/128.16 | | | | | | (130) ~ (0 = 0) 207.80/128.16 | | | | | | 207.80/128.16 | | | | | | CLOSE: (130) is inconsistent. 207.80/128.16 | | | | | | 207.80/128.16 | | | | | End of split 207.80/128.16 | | | | | 207.80/128.16 | | | | Case 2: 207.80/128.16 | | | | | 207.80/128.16 | | | | | (131) length1(int, all_103_4) = all_722_1 & ( ~ ($lesseq(1, 207.80/128.16 | | | | | $difference(all_722_1, all_86_10))) | ~ 207.80/128.16 | | | | | ($lesseq(all_86_11, all_722_1)) | ( ~ (all_722_0 = 207.80/128.16 | | | | | all_722_1) & length1(int, all_105_4) = all_722_0)) 207.80/128.16 | | | | | 207.80/128.16 | | | | | ALPHA: (131) implies: 207.80/128.16 | | | | | (132) length1(int, all_103_4) = all_722_1 207.80/128.16 | | | | | (133) ~ ($lesseq(1, $difference(all_722_1, all_86_10))) | ~ 207.80/128.16 | | | | | ($lesseq(all_86_11, all_722_1)) | ( ~ (all_722_0 = all_722_1) 207.80/128.16 | | | | | & length1(int, all_105_4) = all_722_0) 207.80/128.16 | | | | | 207.80/128.16 | | | | | GROUND_INST: instantiating (55) with all_86_13, all_722_1, all_103_4, 207.80/128.16 | | | | | int, simplifying with (9), (132) gives: 207.80/128.16 | | | | | (134) all_722_1 = all_86_13 207.80/128.16 | | | | | 207.80/128.16 | | | | | BETA: splitting (133) gives: 207.80/128.16 | | | | | 207.80/128.16 | | | | | Case 1: 207.80/128.16 | | | | | | 207.80/128.16 | | | | | | (135) $lesseq(1, $difference(all_86_11, all_722_1)) 207.80/128.16 | | | | | | 207.80/128.16 | | | | | | REDUCE: (134), (135) imply: 207.80/128.16 | | | | | | (136) $lesseq(1, $difference(all_86_11, all_86_13)) 207.80/128.16 | | | | | | 207.80/128.16 | | | | | | COMBINE_INEQS: (34), (69) imply: 207.80/128.16 | | | | | | (137) $lesseq(2, $difference(all_86_10, all_86_11)) 207.80/128.16 | | | | | | 207.80/128.16 | | | | | | COMBINE_INEQS: (44), (137) imply: 207.80/128.16 | | | | | | (138) $lesseq(3, $difference(all_86_13, all_86_11)) 207.80/128.16 | | | | | | 207.80/128.16 | | | | | | COMBINE_INEQS: (136), (138) imply: 207.80/128.16 | | | | | | (139) $lesseq(0, -1) 207.80/128.16 | | | | | | 207.80/128.16 | | | | | | CLOSE: (139) is inconsistent. 207.80/128.16 | | | | | | 207.80/128.16 | | | | | Case 2: 207.80/128.16 | | | | | | 207.80/128.16 | | | | | | (140) ~ ($lesseq(1, $difference(all_722_1, all_86_10))) | ( ~ 207.80/128.16 | | | | | | (all_722_0 = all_722_1) & length1(int, all_105_4) = 207.80/128.16 | | | | | | all_722_0) 207.80/128.16 | | | | | | 207.80/128.16 | | | | | | BETA: splitting (140) gives: 207.80/128.16 | | | | | | 207.80/128.16 | | | | | | Case 1: 207.80/128.16 | | | | | | | 207.80/128.16 | | | | | | | (141) $lesseq(all_722_1, all_86_10) 207.80/128.16 | | | | | | | 207.80/128.16 | | | | | | | REDUCE: (134), (141) imply: 207.80/128.16 | | | | | | | (142) $lesseq(all_86_13, all_86_10) 207.80/128.16 | | | | | | | 207.80/128.16 | | | | | | | COMBINE_INEQS: (44), (142) imply: 207.80/128.16 | | | | | | | (143) $lesseq(0, -1) 207.80/128.16 | | | | | | | 207.80/128.16 | | | | | | | CLOSE: (143) is inconsistent. 207.80/128.16 | | | | | | | 207.80/128.16 | | | | | | Case 2: 207.80/128.16 | | | | | | | 207.80/128.16 | | | | | | | (144) ~ (all_722_0 = all_722_1) & length1(int, all_105_4) = 207.80/128.16 | | | | | | | all_722_0 207.80/128.16 | | | | | | | 207.80/128.16 | | | | | | | ALPHA: (144) implies: 207.80/128.16 | | | | | | | (145) ~ (all_722_0 = all_722_1) 207.80/128.16 | | | | | | | (146) length1(int, all_105_4) = all_722_0 207.80/128.16 | | | | | | | 207.80/128.16 | | | | | | | REDUCE: (134), (145) imply: 207.80/128.16 | | | | | | | (147) ~ (all_722_0 = all_86_13) 207.80/128.16 | | | | | | | 207.80/128.16 | | | | | | | GROUND_INST: instantiating (55) with all_86_13, all_722_0, 207.80/128.16 | | | | | | | all_105_4, int, simplifying with (20), (146) gives: 207.80/128.16 | | | | | | | (148) all_722_0 = all_86_13 207.80/128.16 | | | | | | | 207.80/128.16 | | | | | | | REDUCE: (147), (148) imply: 207.80/128.16 | | | | | | | (149) ~ (0 = 0) 207.80/128.16 | | | | | | | 207.80/128.16 | | | | | | | CLOSE: (149) is inconsistent. 207.80/128.16 | | | | | | | 207.80/128.16 | | | | | | End of split 207.80/128.16 | | | | | | 207.80/128.16 | | | | | End of split 207.80/128.16 | | | | | 207.80/128.16 | | | | End of split 207.80/128.16 | | | | 207.80/128.16 | | | End of split 207.80/128.16 | | | 207.80/128.16 | | End of split 207.80/128.16 | | 207.80/128.16 | Case 2: 207.80/128.16 | | 207.80/128.16 | | (150) ($lesseq(all_133_0, 41) & $lesseq(all_133_2, all_86_10) & 207.80/128.16 | | $lesseq(all_86_7, all_133_2) & tb2t1(all_133_1) = all_133_0 & 207.80/128.16 | | get4(int, all_133_3, all_133_2) = all_133_1 & in_uni(all_133_1)) 207.80/128.16 | | | ($lesseq(43, all_133_0) & $lesseq(all_133_2, all_86_8) & 207.80/128.16 | | $lesseq(all_86_11, all_133_2) & tb2t1(all_133_1) = all_133_0 & 207.80/128.16 | | get4(int, all_133_3, all_133_2) = all_133_1 & in_uni(all_133_1)) 207.80/128.16 | | 207.80/128.16 | | BETA: splitting (150) gives: 207.80/128.16 | | 207.80/128.16 | | Case 1: 207.80/128.16 | | | 207.80/128.16 | | | (151) $lesseq(all_133_0, 41) & $lesseq(all_133_2, all_86_10) & 207.80/128.16 | | | $lesseq(all_86_7, all_133_2) & tb2t1(all_133_1) = all_133_0 & 207.80/128.16 | | | get4(int, all_133_3, all_133_2) = all_133_1 & in_uni(all_133_1) 207.80/128.16 | | | 207.80/128.16 | | | ALPHA: (151) implies: 207.80/128.16 | | | (152) $lesseq(all_86_7, all_133_2) 207.80/128.16 | | | (153) $lesseq(all_133_2, all_86_10) 207.80/128.16 | | | (154) $lesseq(all_133_0, 41) 207.80/128.16 | | | (155) get4(int, all_133_3, all_133_2) = all_133_1 207.80/128.16 | | | (156) tb2t1(all_133_1) = all_133_0 207.80/128.16 | | | 207.80/128.16 | | | REDUCE: (52), (155) imply: 207.80/128.16 | | | (157) get4(int, all_105_2, all_133_2) = all_133_1 207.80/128.16 | | | 207.80/128.16 | | | REF_CLOSE: (1), (5), (6), (7), (8), (12), (18), (19), (21), (22), (27), 207.80/128.16 | | | (30), (31), (32), (37), (38), (39), (40), (41), (46), (48), 207.80/128.16 | | | (49), (50), (57), (58), (59), (61), (152), (153), (154), (156), 207.80/128.16 | | | (157) are inconsistent by sub-proof #148. 207.80/128.16 | | | 207.80/128.16 | | Case 2: 207.80/128.16 | | | 207.80/128.16 | | | (158) $lesseq(43, all_133_0) & $lesseq(all_133_2, all_86_8) & 207.80/128.16 | | | $lesseq(all_86_11, all_133_2) & tb2t1(all_133_1) = all_133_0 & 207.80/128.16 | | | get4(int, all_133_3, all_133_2) = all_133_1 & in_uni(all_133_1) 207.80/128.16 | | | 207.80/128.16 | | | ALPHA: (158) implies: 207.80/128.16 | | | (159) $lesseq(all_86_11, all_133_2) 207.80/128.16 | | | (160) $lesseq(all_133_2, all_86_8) 207.80/128.16 | | | (161) $lesseq(43, all_133_0) 207.80/128.16 | | | (162) get4(int, all_133_3, all_133_2) = all_133_1 207.80/128.16 | | | (163) tb2t1(all_133_1) = all_133_0 207.80/128.16 | | | 207.80/128.16 | | | REDUCE: (52), (162) imply: 207.80/128.16 | | | (164) get4(int, all_105_2, all_133_2) = all_133_1 207.80/128.16 | | | 207.80/128.16 | | | REF_CLOSE: (1), (2), (3), (5), (7), (8), (9), (11), (15), (17), (18), 207.80/128.16 | | | (19), (20), (22), (25), (27), (28), (30), (31), (32), (33), 207.80/128.16 | | | (35), (38), (39), (40), (41), (42), (43), (44), (46), (47), 207.80/128.16 | | | (48), (49), (50), (53), (55), (57), (58), (59), (159), (160), 207.80/128.16 | | | (161), (163), (164) are inconsistent by sub-proof #109. 207.80/128.16 | | | 207.80/128.16 | | End of split 207.80/128.16 | | 207.80/128.16 | End of split 207.80/128.16 | 207.80/128.16 End of proof 207.80/128.16 207.80/128.16 Sub-proof #109 shows that the following formulas are inconsistent: 207.80/128.16 ---------------------------------------------------------------- 207.80/128.16 (1) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ (tb2t1(v2) 207.80/128.16 = v1) | ~ (tb2t1(v2) = v0)) 207.80/128.16 (2) ! [v0: $int] : ! [v1: $int] : ( ~ ($lesseq(43, v1)) | ~ ($lesseq(v0, 207.80/128.16 all_86_8)) | ~ ($lesseq(all_86_11, v0)) | ~ (get3(all_86_6, v0) = 207.80/128.16 v1)) 207.80/128.16 (3) in_map_int_int(all_86_6) 207.80/128.16 (4) elts(int, all_103_4) = all_103_3 207.80/128.16 (5) t2tb(all_86_2) = all_105_1 207.80/128.16 (6) in_ty(int) 207.80/128.16 (7) length1(int, all_103_4) = all_86_13 207.80/128.16 (8) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.80/128.16 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 207.80/128.16 (permut2(v0, v5, v6, v3, v4) = v7) | ~ (elts(v0, v2) = v6) | ~ 207.80/128.16 (elts(v0, v1) = v5) | ~ in_ty(v0) | ? [v8: $int] : ? [v9: $int] : 207.80/128.16 ((v9 = v8 & v7 = 0 & $lesseq(v4, v8) & $lesseq(v3, v8) & $lesseq(0, v4) 207.80/128.16 & $lesseq(0, v3) & length1(v0, v2) = v8 & length1(v0, v1) = v8) | ( 207.80/128.16 ~ (v8 = 0) & permut3(v0, v1, v2, v3, v4) = v8))) 207.80/128.16 (9) t2tb(all_86_6) = all_103_1 207.80/128.16 (10) $lesseq(all_133_2, all_86_8) 207.80/128.16 (11) tb2t1(all_133_1) = all_133_0 207.80/128.16 (12) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.80/128.16 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ (permut3(v6, v5, 207.80/128.16 v4, v3, v2) = v1) | ~ (permut3(v6, v5, v4, v3, v2) = v0)) 207.80/128.16 (13) permut2(int, all_103_3, all_105_3, all_86_11, $sum(all_86_10, 1)) = 0 207.80/128.16 (14) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 207.80/128.16 | ~ (elts(v3, v2) = v1) | ~ (elts(v3, v2) = v0)) 207.80/128.16 (15) length1(int, all_105_4) = all_86_13 207.80/128.16 (16) elts(int, all_105_4) = all_105_3 207.80/128.17 (17) map_eq_sub1(int, all_105_3, all_105_1, 0, all_86_7) = 0 207.80/128.17 (18) get4(int, all_105_2, all_133_2) = all_133_1 207.80/128.17 (19) tb2t(all_105_1) = all_86_2 207.80/128.17 (20) permut2(int, all_103_1, all_105_3, all_86_11, $sum(all_86_8, 1)) = 0 207.80/128.17 (21) elts(int, all_105_2) = all_105_1 207.80/128.17 (22) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.80/128.17 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 207.80/128.17 ($lesseq(1, $difference(v4, v5))) | ~ ($lesseq(v3, v5)) | ~ 207.80/128.17 (permut2(v0, v1, v2, v3, v4) = 0) | ~ (t2tb1(v5) = v6) | ~ (get(v0, 207.80/128.17 int, v2, v6) = v7) | ~ in_ty(v0) | ? [v8: $int] : ? [v9: $int] 207.80/128.17 : ($lesseq(1, $difference(v4, v8)) & $lesseq(v3, v8) & t2tb1(v8) = v9 207.80/128.17 & get(v0, int, v1, v9) = v7 & in_uni(v9) & in_uni(v7))) 207.80/128.17 (23) t2tb2(all_86_1) = all_105_2 207.80/128.17 (24) $lesseq(all_86_11, all_133_2) 207.80/128.17 (25) ~ ($difference(all_86_10, all_86_13) = -1) | ~ (all_86_11 = 0) 207.80/128.17 (26) $lesseq(all_86_7, all_86_10) 207.80/128.17 (27) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.80/128.17 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 207.80/128.17 ($lesseq(1, $difference(v3, v4))) | ~ ($lesseq(v2, v4)) | ~ 207.80/128.17 (permut2(int, v5, v6, v2, v3) = 0) | ~ (t2tb(v1) = v6) | ~ (t2tb(v0) 207.80/128.17 = v5) | ~ (get3(v1, v4) = v7) | ~ in_map_int_int(v0) | ? [v8: 207.80/128.17 $int] : ($lesseq(1, $difference(v3, v8)) & $lesseq(v2, v8) & 207.80/128.17 get3(v0, v8) = v7)) 207.80/128.17 (28) permut2(int, all_105_3, all_105_1, all_86_7, $sum(all_86_10, 1)) = 0 207.80/128.17 (29) in_array_int(all_86_1) 207.80/128.17 (30) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.80/128.17 $int] : ! [v5: $int] : ! [v6: $int] : ( ~ ($lesseq(0, v4)) | ~ 207.80/128.17 ($lesseq(0, v3)) | ~ (permut2(v0, v5, v6, v3, v4) = 0) | ~ (elts(v0, 207.80/128.17 v2) = v6) | ~ (elts(v0, v1) = v5) | ~ in_ty(v0) | ? [v7: $int] 207.80/128.17 : ? [v8: $int] : ((v7 = 0 & permut3(v0, v1, v2, v3, v4) = 0) | 207.80/128.17 (length1(v0, v1) = v7 & ( ~ ($lesseq(v4, v7)) | ~ ($lesseq(v3, v7)) 207.80/128.17 | ( ~ (v8 = v7) & length1(v0, v2) = v8))))) 207.80/128.17 (31) $lesseq(1, $difference(all_86_7, all_86_8)) 207.80/128.17 (32) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.80/128.17 $int] : ! [v5: $int] : ! [v6: $int] : ( ~ ($lesseq(1, 207.80/128.17 $difference(v4, v5))) | ~ ($lesseq(v3, v5)) | ~ (map_eq_sub1(v0, 207.80/128.17 v1, v2, v3, v4) = 0) | ~ (t2tb1(v5) = v6) | ~ in_ty(v0) | ? 207.80/128.17 [v7: $int] : (get(v0, int, v2, v6) = v7 & get(v0, int, v1, v6) = v7 & 207.80/128.17 in_uni(v7))) 207.80/128.17 (33) $lesseq(1, $difference(all_86_13, all_86_10)) 207.80/128.17 (34) in_map_int_int(all_86_4) 207.80/128.17 (35) map_eq_sub1(int, all_105_3, all_105_1, 0, all_86_13) = 0 207.80/128.17 (36) $lesseq(0, all_86_11) 207.80/128.17 (37) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ( ~ 207.80/128.17 (t2tb2(v0) = v2) | ~ (get4(int, v2, v1) = v3) | ~ in_array_int(v0) | 207.80/128.17 ? [v4: $int] : ? [v5: $int] : ? [v6: $int] : (tb2t(v4) = v5 & 207.80/128.17 tb2t1(v3) = v6 & get3(v5, v1) = v6 & elts(int, v2) = v4 & 207.80/128.17 in_map_int_int(v5) & in_uni(v4))) 207.80/128.17 (38) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ (tb2t(v2) 207.80/128.17 = v1) | ~ (tb2t(v2) = v0)) 207.80/128.17 (39) $lesseq(43, all_133_0) 207.80/128.17 (40) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.80/128.17 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 207.80/128.17 ($lesseq(1, $difference(v3, v6))) | ~ ($lesseq(v2, v6)) | ~ 207.80/128.17 (map_eq_sub1(int, v4, v5, v2, v3) = 0) | ~ (t2tb(v1) = v5) | ~ 207.80/128.17 (t2tb(v0) = v4) | ~ (get3(v1, v6) = v7) | ~ in_map_int_int(v0) | 207.80/128.17 get3(v0, v6) = v7) 207.80/128.17 (41) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 207.80/128.17 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 207.80/128.17 (42) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ( ~ 207.80/128.17 (get4(v0, v1, v2) = v3) | ~ in_ty(v0) | ? [v4: $int] : ? [v5: $int] 207.80/128.17 : (elts(v0, v1) = v4 & t2tb1(v2) = v5 & get(v0, int, v4, v5) = v3 & 207.80/128.17 in_uni(v5) & in_uni(v4) & in_uni(v3))) 207.80/128.17 (43) $lesseq(1, all_86_10) 207.80/128.17 (44) t2tb(all_86_4) = all_105_3 207.80/128.17 207.80/128.17 Begin of proof 207.80/128.17 | 207.80/128.17 | GROUND_INST: instantiating (8) with int, all_103_4, all_105_4, all_86_11, 207.80/128.17 | $sum(all_86_10, 1), all_103_3, all_105_3, 0, simplifying with 207.80/128.17 | (4), (6), (13), (16) gives: 207.80/128.17 | (45) ? [v0: $int] : ? [v1: $int] : ((v1 = v0 & $lesseq(1, $difference(v0, 207.80/128.17 | all_86_10)) & $lesseq(all_86_11, v0) & $lesseq(-1, all_86_10) 207.80/128.17 | & $lesseq(0, all_86_11) & length1(int, all_105_4) = v0 & 207.80/128.17 | length1(int, all_103_4) = v0) | ( ~ (v0 = 0) & permut3(int, 207.80/128.17 | all_103_4, all_105_4, all_86_11, $sum(all_86_10, 1)) = v0)) 207.80/128.17 | 207.80/128.17 | GROUND_INST: instantiating (30) with int, all_103_4, all_105_4, all_86_11, 207.80/128.17 | $sum(all_86_10, 1), all_103_3, all_105_3, simplifying with (4), 207.80/128.17 | (6), (13), (16) gives: 207.80/128.17 | (46) ~ ($lesseq(-1, all_86_10)) | ~ ($lesseq(0, all_86_11)) | ? [v0: 207.80/128.17 | $int] : ? [v1: $int] : ((v0 = 0 & permut3(int, all_103_4, 207.80/128.17 | all_105_4, all_86_11, $sum(all_86_10, 1)) = 0) | (length1(int, 207.80/128.17 | all_103_4) = v0 & ( ~ ($lesseq(1, $difference(v0, all_86_10))) | 207.80/128.17 | ~ ($lesseq(all_86_11, v0)) | ( ~ (v1 = v0) & length1(int, 207.80/128.17 | all_105_4) = v1)))) 207.80/128.17 | 207.80/128.17 | GROUND_INST: instantiating (37) with all_86_1, all_133_2, all_105_2, 207.80/128.17 | all_133_1, simplifying with (18), (23), (29) gives: 207.80/128.17 | (47) ? [v0: $int] : ? [v1: $int] : ? [v2: $int] : (tb2t(v0) = v1 & 207.80/128.17 | tb2t1(all_133_1) = v2 & get3(v1, all_133_2) = v2 & elts(int, 207.80/128.17 | all_105_2) = v0 & in_map_int_int(v1) & in_uni(v0)) 207.80/128.17 | 207.80/128.17 | GROUND_INST: instantiating (42) with int, all_105_2, all_133_2, all_133_1, 207.80/128.17 | simplifying with (6), (18) gives: 207.80/128.17 | (48) ? [v0: $int] : ? [v1: $int] : (elts(int, all_105_2) = v0 & 207.80/128.17 | t2tb1(all_133_2) = v1 & get(int, int, v0, v1) = all_133_1 & 207.80/128.17 | in_uni(v1) & in_uni(v0) & in_uni(all_133_1)) 207.80/128.17 | 207.80/128.17 | DELTA: instantiating (45) with fresh symbols all_693_0, all_693_1 gives: 207.80/128.17 | (49) (all_693_0 = all_693_1 & $lesseq(1, $difference(all_693_1, all_86_10)) 207.80/128.17 | & $lesseq(all_86_11, all_693_1) & $lesseq(-1, all_86_10) & 207.80/128.17 | $lesseq(0, all_86_11) & length1(int, all_105_4) = all_693_1 & 207.80/128.17 | length1(int, all_103_4) = all_693_1) | ( ~ (all_693_1 = 0) & 207.80/128.17 | permut3(int, all_103_4, all_105_4, all_86_11, $sum(all_86_10, 1)) = 207.80/128.17 | all_693_1) 207.80/128.17 | 207.80/128.17 | DELTA: instantiating (48) with fresh symbols all_696_0, all_696_1 gives: 207.80/128.17 | (50) elts(int, all_105_2) = all_696_1 & t2tb1(all_133_2) = all_696_0 & 207.80/128.17 | get(int, int, all_696_1, all_696_0) = all_133_1 & in_uni(all_696_0) & 207.80/128.17 | in_uni(all_696_1) & in_uni(all_133_1) 207.80/128.17 | 207.80/128.17 | ALPHA: (50) implies: 207.80/128.17 | (51) get(int, int, all_696_1, all_696_0) = all_133_1 207.80/128.17 | (52) t2tb1(all_133_2) = all_696_0 207.80/128.17 | (53) elts(int, all_105_2) = all_696_1 207.80/128.17 | 207.80/128.17 | DELTA: instantiating (47) with fresh symbols all_706_0, all_706_1, all_706_2 207.80/128.17 | gives: 207.80/128.17 | (54) tb2t(all_706_2) = all_706_1 & tb2t1(all_133_1) = all_706_0 & 207.80/128.17 | get3(all_706_1, all_133_2) = all_706_0 & elts(int, all_105_2) = 207.80/128.17 | all_706_2 & in_map_int_int(all_706_1) & in_uni(all_706_2) 207.80/128.17 | 207.80/128.17 | ALPHA: (54) implies: 207.80/128.17 | (55) elts(int, all_105_2) = all_706_2 207.80/128.17 | (56) get3(all_706_1, all_133_2) = all_706_0 207.80/128.17 | (57) tb2t1(all_133_1) = all_706_0 207.80/128.17 | (58) tb2t(all_706_2) = all_706_1 207.80/128.17 | 207.80/128.17 | BETA: splitting (46) gives: 207.80/128.17 | 207.80/128.17 | Case 1: 207.80/128.17 | | 207.80/128.17 | | (59) $lesseq(all_86_11, -1) 207.80/128.17 | | 207.80/128.17 | | COMBINE_INEQS: (36), (59) imply: 207.80/128.17 | | (60) $lesseq(0, -1) 207.80/128.17 | | 207.80/128.17 | | CLOSE: (60) is inconsistent. 207.80/128.17 | | 207.80/128.17 | Case 2: 207.80/128.17 | | 207.80/128.17 | | (61) ~ ($lesseq(-1, all_86_10)) | ? [v0: $int] : ? [v1: $int] : ((v0 = 207.80/128.17 | | 0 & permut3(int, all_103_4, all_105_4, all_86_11, 207.80/128.17 | | $sum(all_86_10, 1)) = 0) | (length1(int, all_103_4) = v0 & ( ~ 207.80/128.17 | | ($lesseq(1, $difference(v0, all_86_10))) | ~ 207.80/128.17 | | ($lesseq(all_86_11, v0)) | ( ~ (v1 = v0) & length1(int, 207.80/128.17 | | all_105_4) = v1)))) 207.80/128.17 | | 207.80/128.17 | | BETA: splitting (61) gives: 207.80/128.17 | | 207.80/128.17 | | Case 1: 207.80/128.17 | | | 207.80/128.17 | | | (62) $lesseq(all_86_10, -2) 207.80/128.17 | | | 207.80/128.17 | | | COMBINE_INEQS: (43), (62) imply: 207.80/128.17 | | | (63) $lesseq(0, -1) 207.80/128.17 | | | 207.80/128.17 | | | CLOSE: (63) is inconsistent. 207.80/128.17 | | | 207.80/128.17 | | Case 2: 207.80/128.17 | | | 207.80/128.17 | | | (64) ? [v0: $int] : ? [v1: $int] : ((v0 = 0 & permut3(int, all_103_4, 207.80/128.17 | | | all_105_4, all_86_11, $sum(all_86_10, 1)) = 0) | 207.80/128.17 | | | (length1(int, all_103_4) = v0 & ( ~ ($lesseq(1, $difference(v0, 207.80/128.17 | | | all_86_10))) | ~ ($lesseq(all_86_11, v0)) | ( ~ (v1 = 207.80/128.17 | | | v0) & length1(int, all_105_4) = v1)))) 207.80/128.17 | | | 207.80/128.17 | | | DELTA: instantiating (64) with fresh symbols all_722_0, all_722_1 gives: 207.80/128.17 | | | (65) (all_722_1 = 0 & permut3(int, all_103_4, all_105_4, all_86_11, 207.80/128.17 | | | $sum(all_86_10, 1)) = 0) | (length1(int, all_103_4) = 207.80/128.17 | | | all_722_1 & ( ~ ($lesseq(1, $difference(all_722_1, all_86_10))) 207.80/128.17 | | | | ~ ($lesseq(all_86_11, all_722_1)) | ( ~ (all_722_0 = 207.80/128.17 | | | all_722_1) & length1(int, all_105_4) = all_722_0))) 207.80/128.17 | | | 207.80/128.17 | | | BETA: splitting (65) gives: 207.80/128.17 | | | 207.80/128.17 | | | Case 1: 207.80/128.17 | | | | 207.80/128.17 | | | | (66) all_722_1 = 0 & permut3(int, all_103_4, all_105_4, all_86_11, 207.80/128.17 | | | | $sum(all_86_10, 1)) = 0 207.80/128.17 | | | | 207.80/128.17 | | | | ALPHA: (66) implies: 207.80/128.17 | | | | (67) permut3(int, all_103_4, all_105_4, all_86_11, $sum(all_86_10, 207.80/128.17 | | | | 1)) = 0 207.80/128.17 | | | | 207.80/128.17 | | | | BETA: splitting (49) gives: 207.80/128.17 | | | | 207.80/128.17 | | | | Case 1: 207.80/128.17 | | | | | 207.80/128.17 | | | | | (68) all_693_0 = all_693_1 & $lesseq(1, $difference(all_693_1, 207.80/128.17 | | | | | all_86_10)) & $lesseq(all_86_11, all_693_1) & $lesseq(-1, 207.80/128.17 | | | | | all_86_10) & $lesseq(0, all_86_11) & length1(int, all_105_4) 207.80/128.17 | | | | | = all_693_1 & length1(int, all_103_4) = all_693_1 207.80/128.17 | | | | | 207.80/128.17 | | | | | GROUND_INST: instantiating (1) with all_133_0, all_706_0, all_133_1, 207.80/128.17 | | | | | simplifying with (11), (57) gives: 207.80/128.17 | | | | | (69) all_706_0 = all_133_0 207.80/128.17 | | | | | 207.80/128.17 | | | | | GROUND_INST: instantiating (14) with all_105_1, all_706_2, all_105_2, 207.80/128.17 | | | | | int, simplifying with (21), (55) gives: 207.80/128.17 | | | | | (70) all_706_2 = all_105_1 207.80/128.17 | | | | | 207.80/128.17 | | | | | GROUND_INST: instantiating (14) with all_706_2, all_696_1, all_105_2, 207.80/128.17 | | | | | int, simplifying with (53), (55) gives: 207.80/128.17 | | | | | (71) all_706_2 = all_696_1 207.80/128.17 | | | | | 207.80/128.17 | | | | | COMBINE_EQS: (70), (71) imply: 207.80/128.17 | | | | | (72) all_696_1 = all_105_1 207.80/128.17 | | | | | 207.80/128.17 | | | | | REDUCE: (58), (70) imply: 207.80/128.17 | | | | | (73) tb2t(all_105_1) = all_706_1 207.80/128.17 | | | | | 207.80/128.17 | | | | | REDUCE: (56), (69) imply: 207.80/128.17 | | | | | (74) get3(all_706_1, all_133_2) = all_133_0 207.80/128.17 | | | | | 207.80/128.17 | | | | | REDUCE: (51), (72) imply: 207.80/128.17 | | | | | (75) get(int, int, all_105_1, all_696_0) = all_133_1 207.80/128.17 | | | | | 207.80/128.17 | | | | | GROUND_INST: instantiating (38) with all_86_2, all_706_1, all_105_1, 207.80/128.17 | | | | | simplifying with (19), (73) gives: 207.80/128.17 | | | | | (76) all_706_1 = all_86_2 207.80/128.17 | | | | | 207.80/128.17 | | | | | REDUCE: (74), (76) imply: 207.80/128.17 | | | | | (77) get3(all_86_2, all_133_2) = all_133_0 207.80/128.17 | | | | | 207.80/128.17 | | | | | GROUND_INST: instantiating (40) with all_86_4, all_86_2, 0, all_86_7, 207.80/128.17 | | | | | all_105_3, all_105_1, all_133_2, all_133_0, simplifying 207.80/128.17 | | | | | with (5), (17), (34), (44), (77) gives: 207.80/128.17 | | | | | (78) ~ ($lesseq(1, $difference(all_86_7, all_133_2))) | ~ 207.80/128.17 | | | | | ($lesseq(0, all_133_2)) | get3(all_86_4, all_133_2) = 207.80/128.17 | | | | | all_133_0 207.80/128.17 | | | | | 207.80/128.17 | | | | | GROUND_INST: instantiating (27) with all_86_4, all_86_2, all_86_7, 207.80/128.17 | | | | | $sum(all_86_10, 1), all_133_2, all_105_3, all_105_1, 207.80/128.17 | | | | | all_133_0, simplifying with (5), (28), (34), (44), (77) 207.80/128.17 | | | | | gives: 207.80/128.17 | | | | | (79) ~ ($lesseq(all_133_2, all_86_10)) | ~ ($lesseq(all_86_7, 207.80/128.17 | | | | | all_133_2)) | ? [v0: $int] : ($lesseq(v0, all_86_10) & 207.80/128.17 | | | | | $lesseq(all_86_7, v0) & get3(all_86_4, v0) = all_133_0) 207.80/128.17 | | | | | 207.80/128.17 | | | | | GROUND_INST: instantiating (32) with int, all_105_3, all_105_1, 0, 207.80/128.17 | | | | | all_86_13, all_133_2, all_696_0, simplifying with (6), 207.80/128.17 | | | | | (35), (52) gives: 207.80/128.17 | | | | | (80) ~ ($lesseq(1, $difference(all_86_13, all_133_2))) | ~ 207.80/128.17 | | | | | ($lesseq(0, all_133_2)) | ? [v0: $int] : (get(int, int, 207.80/128.17 | | | | | all_105_1, all_696_0) = v0 & get(int, int, all_105_3, 207.80/128.17 | | | | | all_696_0) = v0 & in_uni(v0)) 207.80/128.17 | | | | | 207.80/128.17 | | | | | GROUND_INST: instantiating (22) with int, all_105_3, all_105_1, 207.80/128.17 | | | | | all_86_7, $sum(all_86_10, 1), all_133_2, all_696_0, 207.80/128.17 | | | | | all_133_1, simplifying with (6), (28), (52), (75) gives: 207.80/128.17 | | | | | (81) ~ ($lesseq(all_133_2, all_86_10)) | ~ ($lesseq(all_86_7, 207.80/128.17 | | | | | all_133_2)) | ? [v0: $int] : ? [v1: $int] : ($lesseq(v0, 207.80/128.17 | | | | | all_86_10) & $lesseq(all_86_7, v0) & t2tb1(v0) = v1 & 207.80/128.17 | | | | | get(int, int, all_105_3, v1) = all_133_1 & in_uni(v1) & 207.80/128.17 | | | | | in_uni(all_133_1)) 207.80/128.17 | | | | | 207.80/128.17 | | | | | BETA: splitting (25) gives: 207.80/128.17 | | | | | 207.80/128.17 | | | | | Case 1: 207.80/128.17 | | | | | | 207.80/128.17 | | | | | | (82) ~ (all_86_11 = 0) 207.80/128.17 | | | | | | 207.80/128.17 | | | | | | STRENGTHEN: (36), (82) imply: 207.80/128.17 | | | | | | (83) $lesseq(1, all_86_11) 207.80/128.17 | | | | | | 207.80/128.17 | | | | | | COMBINE_INEQS: (26), (31) imply: 207.80/128.17 | | | | | | (84) $lesseq(1, $difference(all_86_10, all_86_8)) 207.80/128.17 | | | | | | 207.80/128.17 | | | | | | BETA: splitting (80) gives: 207.80/128.17 | | | | | | 207.80/128.17 | | | | | | Case 1: 207.80/128.17 | | | | | | | 207.80/128.17 | | | | | | | (85) $lesseq(all_133_2, -1) 207.80/128.17 | | | | | | | 207.80/128.17 | | | | | | | COMBINE_INEQS: (24), (85) imply: 207.80/128.17 | | | | | | | (86) $lesseq(all_86_11, -1) 207.80/128.17 | | | | | | | 207.80/128.17 | | | | | | | COMBINE_INEQS: (83), (86) imply: 207.80/128.17 | | | | | | | (87) $lesseq(0, -1) 207.80/128.17 | | | | | | | 207.80/128.17 | | | | | | | CLOSE: (87) is inconsistent. 207.80/128.17 | | | | | | | 207.80/128.17 | | | | | | Case 2: 207.80/128.17 | | | | | | | 207.80/128.17 | | | | | | | (88) $lesseq(0, all_133_2) 207.80/128.17 | | | | | | | 207.80/128.17 | | | | | | | REF_CLOSE: (2), (3), (9), (10), (20), (24), (27), (31), (39), 207.80/128.17 | | | | | | | (44), (78), (79), (81), (84), (88) are inconsistent by 207.80/128.17 | | | | | | | sub-proof #144. 207.80/128.17 | | | | | | | 207.80/128.17 | | | | | | End of split 207.80/128.17 | | | | | | 207.80/128.17 | | | | | Case 2: 207.80/128.17 | | | | | | 207.80/128.17 | | | | | | (89) all_86_11 = 0 207.80/128.17 | | | | | | 207.80/128.17 | | | | | | REDUCE: (24), (89) imply: 207.80/128.17 | | | | | | (90) $lesseq(0, all_133_2) 207.80/128.17 | | | | | | 207.80/128.17 | | | | | | COMBINE_INEQS: (26), (31) imply: 207.80/128.17 | | | | | | (91) $lesseq(1, $difference(all_86_10, all_86_8)) 207.80/128.17 | | | | | | 207.80/128.17 | | | | | | REF_CLOSE: (2), (3), (9), (10), (20), (24), (27), (31), (39), (44), 207.80/128.17 | | | | | | (78), (79), (81), (90), (91) are inconsistent by 207.80/128.17 | | | | | | sub-proof #144. 207.80/128.17 | | | | | | 207.80/128.17 | | | | | End of split 207.80/128.17 | | | | | 207.80/128.17 | | | | Case 2: 207.80/128.17 | | | | | 207.80/128.17 | | | | | (92) ~ (all_693_1 = 0) & permut3(int, all_103_4, all_105_4, 207.80/128.17 | | | | | all_86_11, $sum(all_86_10, 1)) = all_693_1 207.80/128.17 | | | | | 207.80/128.17 | | | | | ALPHA: (92) implies: 207.80/128.17 | | | | | (93) ~ (all_693_1 = 0) 207.80/128.17 | | | | | (94) permut3(int, all_103_4, all_105_4, all_86_11, $sum(all_86_10, 207.80/128.17 | | | | | 1)) = all_693_1 207.80/128.17 | | | | | 207.80/128.18 | | | | | GROUND_INST: instantiating (12) with all_693_1, 0, $sum(all_86_10, 1), 207.80/128.18 | | | | | all_86_11, all_105_4, all_103_4, int, simplifying with 207.80/128.18 | | | | | (67), (94) gives: 207.80/128.18 | | | | | (95) all_693_1 = 0 207.80/128.18 | | | | | 207.80/128.18 | | | | | REDUCE: (93), (95) imply: 207.80/128.18 | | | | | (96) ~ (0 = 0) 207.80/128.18 | | | | | 207.80/128.18 | | | | | CLOSE: (96) is inconsistent. 207.80/128.18 | | | | | 207.80/128.18 | | | | End of split 207.80/128.18 | | | | 207.80/128.18 | | | Case 2: 207.80/128.18 | | | | 207.80/128.18 | | | | (97) length1(int, all_103_4) = all_722_1 & ( ~ ($lesseq(1, 207.80/128.18 | | | | $difference(all_722_1, all_86_10))) | ~ 207.80/128.18 | | | | ($lesseq(all_86_11, all_722_1)) | ( ~ (all_722_0 = all_722_1) 207.80/128.18 | | | | & length1(int, all_105_4) = all_722_0)) 207.80/128.18 | | | | 207.80/128.18 | | | | ALPHA: (97) implies: 207.80/128.18 | | | | (98) length1(int, all_103_4) = all_722_1 207.80/128.18 | | | | (99) ~ ($lesseq(1, $difference(all_722_1, all_86_10))) | ~ 207.80/128.18 | | | | ($lesseq(all_86_11, all_722_1)) | ( ~ (all_722_0 = all_722_1) & 207.80/128.18 | | | | length1(int, all_105_4) = all_722_0) 207.80/128.18 | | | | 207.80/128.18 | | | | GROUND_INST: instantiating (41) with all_86_13, all_722_1, all_103_4, 207.80/128.18 | | | | int, simplifying with (7), (98) gives: 207.80/128.18 | | | | (100) all_722_1 = all_86_13 207.80/128.18 | | | | 207.80/128.18 | | | | BETA: splitting (99) gives: 207.80/128.18 | | | | 207.80/128.18 | | | | Case 1: 207.80/128.18 | | | | | 207.80/128.18 | | | | | (101) $lesseq(1, $difference(all_86_11, all_722_1)) 207.80/128.18 | | | | | 207.80/128.18 | | | | | REDUCE: (100), (101) imply: 207.80/128.18 | | | | | (102) $lesseq(1, $difference(all_86_11, all_86_13)) 207.80/128.18 | | | | | 207.80/128.18 | | | | | COMBINE_INEQS: (10), (24) imply: 207.80/128.18 | | | | | (103) $lesseq(all_86_11, all_86_8) 207.80/128.18 | | | | | 207.80/128.18 | | | | | COMBINE_INEQS: (26), (31) imply: 207.80/128.18 | | | | | (104) $lesseq(1, $difference(all_86_10, all_86_8)) 207.80/128.18 | | | | | 207.80/128.18 | | | | | COMBINE_INEQS: (103), (104) imply: 207.80/128.18 | | | | | (105) $lesseq(1, $difference(all_86_10, all_86_11)) 207.80/128.18 | | | | | 207.80/128.18 | | | | | COMBINE_INEQS: (33), (105) imply: 207.80/128.18 | | | | | (106) $lesseq(2, $difference(all_86_13, all_86_11)) 207.80/128.18 | | | | | 207.80/128.18 | | | | | COMBINE_INEQS: (102), (106) imply: 207.80/128.18 | | | | | (107) $lesseq(0, -1) 207.80/128.18 | | | | | 207.80/128.18 | | | | | CLOSE: (107) is inconsistent. 207.80/128.18 | | | | | 207.80/128.18 | | | | Case 2: 207.80/128.18 | | | | | 207.80/128.18 | | | | | (108) ~ ($lesseq(1, $difference(all_722_1, all_86_10))) | ( ~ 207.80/128.18 | | | | | (all_722_0 = all_722_1) & length1(int, all_105_4) = 207.80/128.18 | | | | | all_722_0) 207.80/128.18 | | | | | 207.80/128.18 | | | | | BETA: splitting (108) gives: 207.80/128.18 | | | | | 207.80/128.18 | | | | | Case 1: 207.80/128.18 | | | | | | 207.80/128.18 | | | | | | (109) $lesseq(all_722_1, all_86_10) 207.80/128.18 | | | | | | 207.80/128.18 | | | | | | REDUCE: (100), (109) imply: 207.80/128.18 | | | | | | (110) $lesseq(all_86_13, all_86_10) 207.80/128.18 | | | | | | 207.80/128.18 | | | | | | COMBINE_INEQS: (33), (110) imply: 207.80/128.18 | | | | | | (111) $lesseq(0, -1) 207.80/128.18 | | | | | | 207.80/128.18 | | | | | | CLOSE: (111) is inconsistent. 207.80/128.18 | | | | | | 207.80/128.18 | | | | | Case 2: 207.80/128.18 | | | | | | 207.80/128.18 | | | | | | (112) ~ (all_722_0 = all_722_1) & length1(int, all_105_4) = 207.80/128.18 | | | | | | all_722_0 207.80/128.18 | | | | | | 207.80/128.18 | | | | | | ALPHA: (112) implies: 207.80/128.18 | | | | | | (113) ~ (all_722_0 = all_722_1) 207.80/128.18 | | | | | | (114) length1(int, all_105_4) = all_722_0 207.80/128.18 | | | | | | 207.80/128.18 | | | | | | REDUCE: (100), (113) imply: 207.80/128.18 | | | | | | (115) ~ (all_722_0 = all_86_13) 207.80/128.18 | | | | | | 207.80/128.18 | | | | | | GROUND_INST: instantiating (41) with all_86_13, all_722_0, 207.80/128.18 | | | | | | all_105_4, int, simplifying with (15), (114) gives: 207.80/128.18 | | | | | | (116) all_722_0 = all_86_13 207.80/128.18 | | | | | | 207.80/128.18 | | | | | | REDUCE: (115), (116) imply: 207.80/128.18 | | | | | | (117) ~ (0 = 0) 207.80/128.18 | | | | | | 207.80/128.18 | | | | | | CLOSE: (117) is inconsistent. 207.80/128.18 | | | | | | 207.80/128.18 | | | | | End of split 207.80/128.18 | | | | | 207.80/128.18 | | | | End of split 207.80/128.18 | | | | 207.80/128.18 | | | End of split 207.80/128.18 | | | 207.80/128.18 | | End of split 207.80/128.18 | | 207.80/128.18 | End of split 207.80/128.18 | 207.80/128.18 End of proof 207.80/128.18 207.80/128.18 Sub-proof #110 shows that the following formulas are inconsistent: 207.80/128.18 ---------------------------------------------------------------- 207.80/128.18 (1) in_map_int_int(all_86_6) 207.80/128.18 (2) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.80/128.18 $int] : ! [v5: $int] : ! [v6: $int] : ( ~ ($lesseq(0, v4)) | ~ 207.80/128.18 ($lesseq(0, v3)) | ~ (map_eq_sub1(v0, v5, v6, v3, v4) = 0) | ~ 207.80/128.18 (elts(v0, v2) = v6) | ~ (elts(v0, v1) = v5) | ~ in_ty(v0) | ? [v7: 207.80/128.18 $int] : ? [v8: $int] : ((v7 = 0 & array_eq_sub1(v0, v1, v2, v3, v4) 207.80/128.18 = 0) | (length1(v0, v1) = v7 & ( ~ ($lesseq(v4, v7)) | ~ 207.80/128.18 ($lesseq(v3, v7)) | ( ~ (v8 = v7) & length1(v0, v2) = v8))))) 207.80/128.18 (3) elts(int, all_103_4) = all_103_3 207.80/128.18 (4) in_ty(int) 207.80/128.18 (5) length1(int, all_103_4) = all_86_13 207.80/128.18 (6) $lesseq(all_86_7, all_86_13) 207.80/128.18 (7) ! [v0: $int] : ! [v1: $int] : (v1 = 42 | ~ ($lesseq(1, 207.80/128.18 $difference(all_86_7, v0))) | ~ ($lesseq(1, $difference(v0, 207.80/128.18 all_86_8))) | ~ (get3(all_86_6, v0) = v1)) 207.80/128.18 (8) t2tb(all_86_6) = all_103_1 207.80/128.18 (9) $lesseq(1, $difference(all_133_2, all_86_8)) 207.80/128.18 (10) map_eq_sub1(int, all_103_1, all_105_3, $sum(all_86_8, 1), all_86_13) = 0 207.80/128.18 (11) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 207.80/128.18 | ~ (elts(v3, v2) = v1) | ~ (elts(v3, v2) = v0)) 207.80/128.18 (12) elts(int, all_105_4) = all_105_3 207.80/128.18 (13) $lesseq(1, $difference(all_86_7, all_133_2)) 207.80/128.18 (14) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.80/128.18 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ (permut_sub2(v6, 207.80/128.18 v5, v4, v3, v2) = v1) | ~ (permut_sub2(v6, v5, v4, v3, v2) = v0)) 207.80/128.18 (15) (all_774_0 = 0 & all_774_2 = 0 & map_eq_sub1(int, all_774_4, all_774_3, 207.80/128.18 $sum(all_86_10, 1), all_774_1) = 0 & map_eq_sub1(int, all_774_4, 207.80/128.18 all_774_3, 0, all_86_11) = 0 & length1(int, all_103_4) = all_774_1 & 207.80/128.18 elts(int, all_105_4) = all_774_3 & elts(int, all_103_4) = all_774_4 & 207.80/128.18 in_uni(all_774_3) & in_uni(all_774_4)) | ( ~ (all_774_4 = 0) & 207.80/128.18 permut_sub3(all_86_9, all_86_3, all_86_11, $sum(all_86_10, 1)) = 207.80/128.18 all_774_4) 207.80/128.18 (16) ~ ($lesseq(1, $difference(all_86_13, all_133_2))) | ~ ($lesseq(1, 207.80/128.18 $difference(all_133_2, all_86_8))) | ? [v0: $int] : (get(int, int, 207.80/128.18 all_105_3, all_696_0) = v0 & get(int, int, all_103_1, all_696_0) = 207.80/128.18 v0 & in_uni(v0)) 207.80/128.18 (17) $lesseq(0, all_86_8) 207.80/128.18 (18) (all_790_3 = 0 & permut_sub3(all_86_9, all_86_3, all_86_11, 207.80/128.18 $sum(all_86_10, 1)) = 0) | (elts(int, all_105_4) = all_790_2 & 207.80/128.18 elts(int, all_103_4) = all_790_3 & in_uni(all_790_2) & 207.80/128.18 in_uni(all_790_3) & (( ~ (all_790_0 = 0) & map_eq_sub1(int, all_790_3, 207.80/128.18 all_790_2, $sum(all_86_10, 1), all_790_1) = all_790_0 & 207.80/128.18 length1(int, all_103_4) = all_790_1) | ( ~ (all_790_1 = 0) & 207.80/128.18 map_eq_sub1(int, all_790_3, all_790_2, 0, all_86_11) = 207.80/128.18 all_790_1))) 207.80/128.18 (19) $lesseq(4, all_86_13) 207.80/128.18 (20) ~ (all_133_0 = 42) 207.80/128.18 (21) (all_773_0 = 0 & all_773_1 = 0 & map_eq_sub1(int, all_773_4, all_773_3, 207.80/128.18 $sum(all_86_10, 1), all_773_2) = 0 & map_eq_sub1(int, all_773_4, 207.80/128.18 all_773_3, 0, all_86_11) = 0 & length1(int, all_103_4) = all_773_2 & 207.80/128.18 elts(int, all_105_4) = all_773_3 & elts(int, all_103_4) = all_773_4 & 207.80/128.18 in_uni(all_773_3) & in_uni(all_773_4)) | ( ~ (all_773_4 = 0) & 207.80/128.18 permut_sub2(int, all_103_4, all_105_4, all_86_11, $sum(all_86_10, 1)) 207.80/128.18 = all_773_4) 207.80/128.18 (22) ~ ($lesseq(1, $difference(all_86_7, all_133_2))) | ~ ($lesseq(0, 207.80/128.18 all_133_2)) | get3(all_86_4, all_133_2) = all_133_0 207.80/128.18 (23) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.80/128.18 $int] : ! [v5: $int] : (v5 = 0 | ~ (permut_sub2(v0, v1, v2, v3, v4) 207.80/128.18 = v5) | ~ in_ty(v0) | ? [v6: $int] : ? [v7: $int] : ? [v8: $int] 207.80/128.18 : ? [v9: $int] : (( ~ (v9 = 0) & map_eq_sub1(v0, v6, v7, v4, v8) = v9 207.80/128.18 & length1(v0, v1) = v8 & elts(v0, v2) = v7 & elts(v0, v1) = v6 & 207.80/128.18 in_uni(v7) & in_uni(v6)) | ( ~ (v8 = 0) & map_eq_sub1(v0, v6, v7, 207.80/128.18 0, v3) = v8 & elts(v0, v2) = v7 & elts(v0, v1) = v6 & in_uni(v7) 207.80/128.18 & in_uni(v6)) | ( ~ (v6 = 0) & permut3(v0, v1, v2, v3, v4) = v6))) 207.80/128.18 (24) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.80/128.18 $int] : ! [v5: $int] : (v1 = v0 | ~ (permut_sub3(v5, v4, v3, v2) = 207.80/128.18 v1) | ~ (permut_sub3(v5, v4, v3, v2) = v0)) 207.80/128.18 (25) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.80/128.18 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 207.80/128.18 ($lesseq(1, $difference(v3, v6))) | ~ ($lesseq(v2, v6)) | ~ 207.80/128.18 (map_eq_sub1(int, v4, v5, v2, v3) = 0) | ~ (t2tb(v1) = v5) | ~ 207.80/128.18 (t2tb(v0) = v4) | ~ (get3(v1, v6) = v7) | ~ in_map_int_int(v0) | 207.80/128.18 get3(v0, v6) = v7) 207.80/128.18 (26) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 207.80/128.18 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 207.80/128.18 (27) (all_783_3 = 0 & permut_sub2(int, all_103_4, all_105_4, all_86_11, 207.80/128.18 $sum(all_86_10, 1)) = 0) | (elts(int, all_105_4) = all_783_2 & 207.80/128.18 elts(int, all_103_4) = all_783_3 & in_uni(all_783_2) & 207.80/128.18 in_uni(all_783_3) & (( ~ (all_783_0 = 0) & map_eq_sub1(int, all_783_3, 207.80/128.18 all_783_2, $sum(all_86_10, 1), all_783_1) = all_783_0 & 207.80/128.18 length1(int, all_103_4) = all_783_1) | ( ~ (all_783_1 = 0) & 207.80/128.18 map_eq_sub1(int, all_783_3, all_783_2, 0, all_86_11) = 207.80/128.18 all_783_1))) 207.80/128.18 (28) t2tb(all_86_4) = all_105_3 207.80/128.18 (29) $lesseq(2, all_86_10) 207.80/128.18 (30) ~ ($lesseq(1, $difference(all_86_7, all_133_2))) | ~ ($lesseq(0, 207.80/128.18 all_133_2)) | ? [v0: $int] : (get(int, int, all_105_1, all_696_0) = 207.80/128.18 v0 & get(int, int, all_105_3, all_696_0) = v0 & in_uni(v0)) 207.80/128.18 207.80/128.18 Begin of proof 207.80/128.18 | 207.80/128.18 | BETA: splitting (30) gives: 207.80/128.18 | 207.80/128.18 | Case 1: 207.80/128.18 | | 207.80/128.18 | | (31) $lesseq(all_133_2, -1) 207.80/128.18 | | 207.80/128.18 | | COMBINE_INEQS: (9), (31) imply: 207.80/128.18 | | (32) $lesseq(all_86_8, -2) 207.80/128.18 | | 207.80/128.18 | | COMBINE_INEQS: (17), (32) imply: 207.80/128.18 | | (33) $lesseq(0, -1) 207.80/128.18 | | 207.80/128.18 | | CLOSE: (33) is inconsistent. 207.80/128.18 | | 207.80/128.18 | Case 2: 207.80/128.18 | | 207.80/128.18 | | (34) $lesseq(0, all_133_2) 207.80/128.18 | | 207.80/128.18 | | BETA: splitting (22) gives: 207.80/128.18 | | 207.80/128.18 | | Case 1: 207.80/128.18 | | | 207.80/128.18 | | | (35) get3(all_86_4, all_133_2) = all_133_0 207.80/128.18 | | | 207.80/128.18 | | | BETA: splitting (16) gives: 207.80/128.18 | | | 207.80/128.18 | | | Case 1: 207.80/128.18 | | | | 207.80/128.18 | | | | (36) $lesseq(all_86_13, all_133_2) 207.80/128.18 | | | | 207.80/128.18 | | | | COMBINE_INEQS: (13), (36) imply: 207.80/128.18 | | | | (37) $lesseq(1, $difference(all_86_7, all_86_13)) 207.80/128.18 | | | | 207.80/128.18 | | | | COMBINE_INEQS: (6), (37) imply: 207.80/128.18 | | | | (38) $lesseq(0, -1) 207.80/128.18 | | | | 207.80/128.18 | | | | CLOSE: (38) is inconsistent. 207.80/128.18 | | | | 207.80/128.18 | | | Case 2: 207.80/128.18 | | | | 207.80/128.18 | | | | (39) $lesseq(1, $difference(all_86_13, all_133_2)) 207.80/128.18 | | | | 207.80/128.18 | | | | BETA: splitting (21) gives: 207.80/128.18 | | | | 207.80/128.18 | | | | Case 1: 207.80/128.18 | | | | | 207.80/128.18 | | | | | (40) all_773_0 = 0 & all_773_1 = 0 & map_eq_sub1(int, all_773_4, 207.80/128.18 | | | | | all_773_3, $sum(all_86_10, 1), all_773_2) = 0 & 207.80/128.18 | | | | | map_eq_sub1(int, all_773_4, all_773_3, 0, all_86_11) = 0 & 207.80/128.18 | | | | | length1(int, all_103_4) = all_773_2 & elts(int, all_105_4) = 207.80/128.18 | | | | | all_773_3 & elts(int, all_103_4) = all_773_4 & 207.80/128.18 | | | | | in_uni(all_773_3) & in_uni(all_773_4) 207.80/128.18 | | | | | 207.80/128.18 | | | | | ALPHA: (40) implies: 207.80/128.18 | | | | | (41) length1(int, all_103_4) = all_773_2 207.80/128.18 | | | | | (42) elts(int, all_103_4) = all_773_4 207.80/128.18 | | | | | (43) map_eq_sub1(int, all_773_4, all_773_3, $sum(all_86_10, 1), 207.80/128.18 | | | | | all_773_2) = 0 207.80/128.18 | | | | | (44) elts(int, all_105_4) = all_773_3 207.80/128.18 | | | | | 207.80/128.18 | | | | | GROUND_INST: instantiating (26) with all_86_13, all_773_2, all_103_4, 207.80/128.18 | | | | | int, simplifying with (5), (41) gives: 207.80/128.18 | | | | | (45) all_773_2 = all_86_13 207.80/128.18 | | | | | 207.80/128.18 | | | | | GROUND_INST: instantiating (11) with all_105_3, all_773_3, all_105_4, 207.80/128.18 | | | | | int, simplifying with (12), (44) gives: 207.80/128.18 | | | | | (46) all_773_3 = all_105_3 207.80/128.18 | | | | | 207.80/128.18 | | | | | GROUND_INST: instantiating (11) with all_103_3, all_773_4, all_103_4, 207.80/128.18 | | | | | int, simplifying with (3), (42) gives: 207.80/128.18 | | | | | (47) all_773_4 = all_103_3 207.80/128.18 | | | | | 207.80/128.18 | | | | | REDUCE: (43), (45), (46), (47) imply: 207.80/128.18 | | | | | (48) map_eq_sub1(int, all_103_3, all_105_3, $sum(all_86_10, 1), 207.80/128.18 | | | | | all_86_13) = 0 207.80/128.18 | | | | | 207.80/128.18 | | | | | REF_CLOSE: (1), (2), (3), (4), (7), (8), (9), (10), (12), (13), (19), 207.80/128.18 | | | | | (20), (25), (28), (29), (35), (39), (48) are inconsistent 207.80/128.18 | | | | | by sub-proof #152. 207.80/128.18 | | | | | 207.80/128.18 | | | | Case 2: 207.80/128.18 | | | | | 207.80/128.18 | | | | | (49) ~ (all_773_4 = 0) & permut_sub2(int, all_103_4, all_105_4, 207.80/128.18 | | | | | all_86_11, $sum(all_86_10, 1)) = all_773_4 207.80/128.18 | | | | | 207.80/128.18 | | | | | ALPHA: (49) implies: 207.80/128.18 | | | | | (50) ~ (all_773_4 = 0) 207.80/128.18 | | | | | (51) permut_sub2(int, all_103_4, all_105_4, all_86_11, 207.80/128.18 | | | | | $sum(all_86_10, 1)) = all_773_4 207.80/128.18 | | | | | 207.80/128.18 | | | | | BETA: splitting (27) gives: 207.80/128.18 | | | | | 207.80/128.18 | | | | | Case 1: 207.80/128.18 | | | | | | 207.80/128.18 | | | | | | (52) all_783_3 = 0 & permut_sub2(int, all_103_4, all_105_4, 207.80/128.18 | | | | | | all_86_11, $sum(all_86_10, 1)) = 0 207.80/128.18 | | | | | | 207.80/128.18 | | | | | | ALPHA: (52) implies: 207.80/128.18 | | | | | | (53) permut_sub2(int, all_103_4, all_105_4, all_86_11, 207.80/128.18 | | | | | | $sum(all_86_10, 1)) = 0 207.80/128.18 | | | | | | 207.80/128.18 | | | | | | GROUND_INST: instantiating (14) with all_773_4, 0, $sum(all_86_10, 207.80/128.18 | | | | | | 1), all_86_11, all_105_4, all_103_4, int, simplifying 207.80/128.18 | | | | | | with (51), (53) gives: 207.80/128.18 | | | | | | (54) all_773_4 = 0 207.80/128.18 | | | | | | 207.80/128.18 | | | | | | REDUCE: (50), (54) imply: 207.80/128.18 | | | | | | (55) ~ (0 = 0) 207.80/128.18 | | | | | | 207.80/128.18 | | | | | | CLOSE: (55) is inconsistent. 207.80/128.18 | | | | | | 207.80/128.18 | | | | | Case 2: 207.80/128.18 | | | | | | 207.80/128.18 | | | | | | (56) elts(int, all_105_4) = all_783_2 & elts(int, all_103_4) = 207.80/128.18 | | | | | | all_783_3 & in_uni(all_783_2) & in_uni(all_783_3) & (( ~ 207.80/128.18 | | | | | | (all_783_0 = 0) & map_eq_sub1(int, all_783_3, all_783_2, 207.80/128.18 | | | | | | $sum(all_86_10, 1), all_783_1) = all_783_0 & 207.80/128.18 | | | | | | length1(int, all_103_4) = all_783_1) | ( ~ (all_783_1 = 207.80/128.18 | | | | | | 0) & map_eq_sub1(int, all_783_3, all_783_2, 0, 207.80/128.18 | | | | | | all_86_11) = all_783_1)) 207.80/128.18 | | | | | | 207.80/128.18 | | | | | | ALPHA: (56) implies: 207.80/128.18 | | | | | | (57) elts(int, all_103_4) = all_783_3 207.80/128.18 | | | | | | (58) elts(int, all_105_4) = all_783_2 207.80/128.18 | | | | | | 207.80/128.18 | | | | | | GROUND_INST: instantiating (11) with all_105_3, all_783_2, 207.80/128.18 | | | | | | all_105_4, int, simplifying with (12), (58) gives: 207.80/128.18 | | | | | | (59) all_783_2 = all_105_3 207.80/128.18 | | | | | | 207.80/128.18 | | | | | | GROUND_INST: instantiating (11) with all_103_3, all_783_3, 207.80/128.18 | | | | | | all_103_4, int, simplifying with (3), (57) gives: 207.80/128.18 | | | | | | (60) all_783_3 = all_103_3 207.80/128.18 | | | | | | 207.80/128.18 | | | | | | BETA: splitting (15) gives: 207.80/128.18 | | | | | | 207.80/128.18 | | | | | | Case 1: 207.80/128.18 | | | | | | | 207.80/128.18 | | | | | | | (61) all_774_0 = 0 & all_774_2 = 0 & map_eq_sub1(int, 207.80/128.18 | | | | | | | all_774_4, all_774_3, $sum(all_86_10, 1), all_774_1) = 0 207.80/128.18 | | | | | | | & map_eq_sub1(int, all_774_4, all_774_3, 0, all_86_11) = 0 207.80/128.18 | | | | | | | & length1(int, all_103_4) = all_774_1 & elts(int, 207.80/128.18 | | | | | | | all_105_4) = all_774_3 & elts(int, all_103_4) = 207.80/128.18 | | | | | | | all_774_4 & in_uni(all_774_3) & in_uni(all_774_4) 207.80/128.18 | | | | | | | 207.80/128.18 | | | | | | | ALPHA: (61) implies: 207.80/128.18 | | | | | | | (62) elts(int, all_105_4) = all_774_3 207.80/128.18 | | | | | | | (63) elts(int, all_103_4) = all_774_4 207.80/128.18 | | | | | | | (64) map_eq_sub1(int, all_774_4, all_774_3, $sum(all_86_10, 1), 207.80/128.18 | | | | | | | all_774_1) = 0 207.80/128.18 | | | | | | | (65) length1(int, all_103_4) = all_774_1 207.80/128.18 | | | | | | | 207.80/128.18 | | | | | | | GROUND_INST: instantiating (26) with all_86_13, all_774_1, 207.80/128.18 | | | | | | | all_103_4, int, simplifying with (5), (65) gives: 207.80/128.18 | | | | | | | (66) all_774_1 = all_86_13 207.80/128.18 | | | | | | | 207.80/128.18 | | | | | | | GROUND_INST: instantiating (11) with all_105_3, all_774_3, 207.80/128.18 | | | | | | | all_105_4, int, simplifying with (12), (62) gives: 207.80/128.19 | | | | | | | (67) all_774_3 = all_105_3 207.80/128.19 | | | | | | | 207.80/128.19 | | | | | | | GROUND_INST: instantiating (11) with all_103_3, all_774_4, 207.80/128.19 | | | | | | | all_103_4, int, simplifying with (3), (63) gives: 207.80/128.19 | | | | | | | (68) all_774_4 = all_103_3 207.80/128.19 | | | | | | | 207.80/128.19 | | | | | | | REDUCE: (64), (66), (67), (68) imply: 207.80/128.19 | | | | | | | (69) map_eq_sub1(int, all_103_3, all_105_3, $sum(all_86_10, 1), 207.80/128.19 | | | | | | | all_86_13) = 0 207.80/128.19 | | | | | | | 207.80/128.19 | | | | | | | REF_CLOSE: (1), (2), (3), (4), (7), (8), (9), (10), (12), (13), 207.80/128.19 | | | | | | | (19), (20), (25), (28), (29), (35), (39), (69) are 207.80/128.19 | | | | | | | inconsistent by sub-proof #152. 207.80/128.19 | | | | | | | 207.80/128.19 | | | | | | Case 2: 207.80/128.19 | | | | | | | 207.80/128.19 | | | | | | | (70) ~ (all_774_4 = 0) & permut_sub3(all_86_9, all_86_3, 207.80/128.19 | | | | | | | all_86_11, $sum(all_86_10, 1)) = all_774_4 207.80/128.19 | | | | | | | 207.80/128.19 | | | | | | | ALPHA: (70) implies: 207.80/128.19 | | | | | | | (71) ~ (all_774_4 = 0) 207.80/128.19 | | | | | | | (72) permut_sub3(all_86_9, all_86_3, all_86_11, $sum(all_86_10, 207.80/128.19 | | | | | | | 1)) = all_774_4 207.80/128.19 | | | | | | | 207.80/128.19 | | | | | | | BETA: splitting (18) gives: 207.80/128.19 | | | | | | | 207.80/128.19 | | | | | | | Case 1: 207.80/128.19 | | | | | | | | 207.80/128.19 | | | | | | | | (73) all_790_3 = 0 & permut_sub3(all_86_9, all_86_3, 207.80/128.19 | | | | | | | | all_86_11, $sum(all_86_10, 1)) = 0 207.80/128.19 | | | | | | | | 207.80/128.19 | | | | | | | | ALPHA: (73) implies: 207.80/128.19 | | | | | | | | (74) permut_sub3(all_86_9, all_86_3, all_86_11, 207.80/128.19 | | | | | | | | $sum(all_86_10, 1)) = 0 207.80/128.19 | | | | | | | | 207.80/128.19 | | | | | | | | GROUND_INST: instantiating (24) with all_774_4, 0, 207.80/128.19 | | | | | | | | $sum(all_86_10, 1), all_86_11, all_86_3, all_86_9, 207.80/128.19 | | | | | | | | simplifying with (72), (74) gives: 207.80/128.19 | | | | | | | | (75) all_774_4 = 0 207.80/128.19 | | | | | | | | 207.80/128.19 | | | | | | | | REDUCE: (71), (75) imply: 207.80/128.19 | | | | | | | | (76) ~ (0 = 0) 207.80/128.19 | | | | | | | | 207.80/128.19 | | | | | | | | CLOSE: (76) is inconsistent. 207.80/128.19 | | | | | | | | 207.80/128.19 | | | | | | | Case 2: 207.80/128.19 | | | | | | | | 207.80/128.19 | | | | | | | | 207.80/128.19 | | | | | | | | GROUND_INST: instantiating (23) with int, all_103_4, all_105_4, 207.80/128.19 | | | | | | | | all_86_11, $sum(all_86_10, 1), all_773_4, 207.80/128.19 | | | | | | | | simplifying with (4), (51) gives: 207.80/128.19 | | | | | | | | (77) all_773_4 = 0 | ? [v0: $int] : ? [v1: $int] : ? [v2: 207.80/128.19 | | | | | | | | $int] : ? [v3: $int] : (( ~ (v3 = 0) & 207.80/128.19 | | | | | | | | map_eq_sub1(int, v0, v1, $sum(all_86_10, 1), v2) = 207.80/128.19 | | | | | | | | v3 & length1(int, all_103_4) = v2 & elts(int, 207.80/128.19 | | | | | | | | all_105_4) = v1 & elts(int, all_103_4) = v0 & 207.80/128.19 | | | | | | | | in_uni(v1) & in_uni(v0)) | ( ~ (v2 = 0) & 207.80/128.19 | | | | | | | | map_eq_sub1(int, v0, v1, 0, all_86_11) = v2 & 207.80/128.19 | | | | | | | | elts(int, all_105_4) = v1 & elts(int, all_103_4) = 207.80/128.19 | | | | | | | | v0 & in_uni(v1) & in_uni(v0)) | ( ~ (v0 = 0) & 207.80/128.19 | | | | | | | | permut3(int, all_103_4, all_105_4, all_86_11, 207.80/128.19 | | | | | | | | $sum(all_86_10, 1)) = v0)) 207.80/128.19 | | | | | | | | 207.80/128.19 | | | | | | | | GROUND_INST: instantiating (25) with all_86_6, all_86_4, 207.80/128.19 | | | | | | | | $sum(all_86_8, 1), all_86_13, all_103_1, all_105_3, 207.80/128.19 | | | | | | | | all_133_2, all_133_0, simplifying with (1), (8), 207.80/128.19 | | | | | | | | (10), (28), (35) gives: 207.80/128.19 | | | | | | | | (78) ~ ($lesseq(1, $difference(all_86_13, all_133_2))) | ~ 207.80/128.19 | | | | | | | | ($lesseq(1, $difference(all_133_2, all_86_8))) | 207.80/128.19 | | | | | | | | get3(all_86_6, all_133_2) = all_133_0 207.80/128.19 | | | | | | | | 207.80/128.19 | | | | | | | | BETA: splitting (78) gives: 207.80/128.19 | | | | | | | | 207.80/128.19 | | | | | | | | Case 1: 207.80/128.19 | | | | | | | | | 207.80/128.19 | | | | | | | | | (79) get3(all_86_6, all_133_2) = all_133_0 207.80/128.19 | | | | | | | | | 207.80/128.19 | | | | | | | | | BETA: splitting (77) gives: 207.80/128.19 | | | | | | | | | 207.80/128.19 | | | | | | | | | Case 1: 207.80/128.19 | | | | | | | | | | 207.80/128.19 | | | | | | | | | | (80) all_773_4 = 0 207.80/128.19 | | | | | | | | | | 207.80/128.19 | | | | | | | | | | REDUCE: (50), (80) imply: 207.80/128.19 | | | | | | | | | | (81) ~ (0 = 0) 207.80/128.19 | | | | | | | | | | 207.80/128.19 | | | | | | | | | | CLOSE: (81) is inconsistent. 207.80/128.19 | | | | | | | | | | 207.80/128.19 | | | | | | | | | Case 2: 207.80/128.19 | | | | | | | | | | 207.80/128.19 | | | | | | | | | | 207.80/128.19 | | | | | | | | | | GROUND_INST: instantiating (7) with all_133_2, all_133_0, 207.80/128.19 | | | | | | | | | | simplifying with (79) gives: 207.80/128.19 | | | | | | | | | | (82) all_133_0 = 42 | ~ ($lesseq(1, 207.80/128.19 | | | | | | | | | | $difference(all_86_7, all_133_2))) | ~ 207.80/128.19 | | | | | | | | | | ($lesseq(1, $difference(all_133_2, all_86_8))) 207.80/128.19 | | | | | | | | | | 207.80/128.19 | | | | | | | | | | REF_CLOSE: (9), (13), (20), (82) are inconsistent by 207.80/128.19 | | | | | | | | | | sub-proof #155. 207.80/128.19 | | | | | | | | | | 207.80/128.19 | | | | | | | | | End of split 207.80/128.19 | | | | | | | | | 207.80/128.19 | | | | | | | | Case 2: 207.80/128.19 | | | | | | | | | 207.80/128.19 | | | | | | | | | (83) ~ ($lesseq(1, $difference(all_86_13, all_133_2))) | 207.80/128.19 | | | | | | | | | ~ ($lesseq(1, $difference(all_133_2, all_86_8))) 207.80/128.19 | | | | | | | | | 207.80/128.19 | | | | | | | | | REF_CLOSE: (9), (39), (83) are inconsistent by sub-proof #153. 207.80/128.19 | | | | | | | | | 207.80/128.19 | | | | | | | | End of split 207.80/128.19 | | | | | | | | 207.80/128.19 | | | | | | | End of split 207.80/128.19 | | | | | | | 207.80/128.19 | | | | | | End of split 207.80/128.19 | | | | | | 207.80/128.19 | | | | | End of split 207.80/128.19 | | | | | 207.80/128.19 | | | | End of split 207.80/128.19 | | | | 207.80/128.19 | | | End of split 207.80/128.19 | | | 207.80/128.19 | | Case 2: 207.80/128.19 | | | 207.80/128.19 | | | (84) ~ ($lesseq(1, $difference(all_86_7, all_133_2))) | ~ ($lesseq(0, 207.80/128.19 | | | all_133_2)) 207.80/128.19 | | | 207.80/128.19 | | | REF_CLOSE: (13), (34), (84) are inconsistent by sub-proof #151. 207.80/128.19 | | | 207.80/128.19 | | End of split 207.80/128.19 | | 207.80/128.19 | End of split 207.80/128.19 | 207.80/128.19 End of proof 207.80/128.19 207.80/128.19 Sub-proof #111 shows that the following formulas are inconsistent: 207.80/128.19 ---------------------------------------------------------------- 207.80/128.19 (1) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ 207.80/128.19 (sorted1(v2) = v1) | ~ (sorted1(v2) = v0)) 207.80/128.19 (2) sorted1(all_86_1) = all_205_3 207.80/128.19 (3) sorted1(all_86_1) = 0 207.80/128.19 (4) ~ (all_205_3 = 0) 207.80/128.19 207.80/128.19 Begin of proof 207.80/128.19 | 207.80/128.19 | GROUND_INST: instantiating (1) with all_205_3, 0, all_86_1, simplifying with 207.80/128.19 | (2), (3) gives: 207.80/128.19 | (5) all_205_3 = 0 207.80/128.19 | 207.80/128.19 | REDUCE: (4), (5) imply: 207.80/128.19 | (6) ~ (0 = 0) 207.80/128.19 | 207.80/128.19 | CLOSE: (6) is inconsistent. 207.80/128.19 | 207.80/128.19 End of proof 207.80/128.19 207.80/128.19 Sub-proof #112 shows that the following formulas are inconsistent: 207.80/128.19 ---------------------------------------------------------------- 207.80/128.19 (1) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ (tb2t1(v2) 207.80/128.19 = v1) | ~ (tb2t1(v2) = v0)) 207.80/128.19 (2) ! [v0: $int] : ! [v1: $int] : ( ~ ($lesseq(43, v1)) | ~ ($lesseq(v0, 207.80/128.19 all_86_8)) | ~ ($lesseq(all_86_11, v0)) | ~ (get3(all_86_6, v0) = 207.80/128.19 v1)) 207.80/128.19 (3) length1(int, all_103_2) = all_86_13 207.80/128.19 (4) in_map_int_int(all_86_6) 207.80/128.19 (5) in_map_int_int(all_86_12) 207.80/128.19 (6) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.80/128.19 $int] : ! [v5: $int] : ! [v6: $int] : ( ~ ($lesseq(0, v4)) | ~ 207.80/128.19 ($lesseq(0, v3)) | ~ (map_eq_sub1(v0, v5, v6, v3, v4) = 0) | ~ 207.80/128.19 (elts(v0, v2) = v6) | ~ (elts(v0, v1) = v5) | ~ in_ty(v0) | ? [v7: 207.80/128.19 $int] : ? [v8: $int] : ((v7 = 0 & array_eq_sub1(v0, v1, v2, v3, v4) 207.80/128.19 = 0) | (length1(v0, v1) = v7 & ( ~ ($lesseq(v4, v7)) | ~ 207.80/128.19 ($lesseq(v3, v7)) | ( ~ (v8 = v7) & length1(v0, v2) = v8))))) 207.80/128.19 (7) length1(int, all_105_2) = all_86_13 207.80/128.19 (8) elts(int, all_103_4) = all_103_3 207.80/128.19 (9) t2tb2(all_86_3) = all_105_4 207.80/128.19 (10) t2tb(all_86_2) = all_105_1 207.80/128.19 (11) in_ty(int) 207.80/128.19 (12) length1(int, all_103_4) = all_86_13 207.80/128.19 (13) $lesseq(2, all_86_13) 207.80/128.19 (14) ( ~ (all_133_0 = 42) & $lesseq(1, $difference(all_86_7, all_133_2)) & 207.80/128.19 $lesseq(1, $difference(all_133_2, all_86_8)) & tb2t1(all_133_1) = 207.80/128.19 all_133_0 & get4(int, all_133_3, all_133_2) = all_133_1 & 207.80/128.19 in_uni(all_133_1)) | ($lesseq(all_133_0, 41) & $lesseq(all_133_2, 207.80/128.19 all_86_10) & $lesseq(all_86_7, all_133_2) & tb2t1(all_133_1) = 207.80/128.19 all_133_0 & get4(int, all_133_3, all_133_2) = all_133_1 & 207.80/128.19 in_uni(all_133_1)) | ($lesseq(43, all_133_0) & $lesseq(all_133_2, 207.80/128.19 all_86_8) & $lesseq(all_86_11, all_133_2) & tb2t1(all_133_1) = 207.80/128.19 all_133_0 & get4(int, all_133_3, all_133_2) = all_133_1 & 207.80/128.19 in_uni(all_133_1)) 207.80/128.19 (15) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.80/128.19 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 207.80/128.19 (permut2(v0, v5, v6, v3, v4) = v7) | ~ (elts(v0, v2) = v6) | ~ 207.80/128.19 (elts(v0, v1) = v5) | ~ in_ty(v0) | ? [v8: $int] : ? [v9: $int] : 207.80/128.19 ((v9 = v8 & v7 = 0 & $lesseq(v4, v8) & $lesseq(v3, v8) & $lesseq(0, 207.80/128.19 v4) & $lesseq(0, v3) & length1(v0, v2) = v8 & length1(v0, v1) = 207.80/128.19 v8) | ( ~ (v8 = 0) & permut3(v0, v1, v2, v3, v4) = v8))) 207.80/128.19 (16) all_125_0 = all_105_4 207.80/128.19 (17) $lesseq(-1, all_86_8) 207.80/128.19 (18) $lesseq(1, $difference(all_86_13, all_86_7)) 207.80/128.19 (19) ~ (permut2(int, all_105_3, all_105_1, all_86_11, $sum(all_86_10, 1)) = 207.80/128.19 0) | permut2(int, all_103_1, all_105_1, all_86_11, $sum(all_86_10, 1)) 207.80/128.19 = 0 207.80/128.19 (20) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.80/128.19 $int] : ! [v5: $int] : ( ~ (permut2(v0, v2, v3, v4, v5) = 0) | ~ 207.80/128.19 (permut2(v0, v1, v2, v4, v5) = 0) | ~ in_ty(v0) | permut2(v0, v1, v3, 207.80/128.19 v4, v5) = 0) 207.80/128.19 (21) ! [v0: $int] : ! [v1: $int] : (v1 = 42 | ~ ($lesseq(1, 207.80/128.19 $difference(all_86_7, v0))) | ~ ($lesseq(1, $difference(v0, 207.80/128.19 all_86_8))) | ~ (get3(all_86_6, v0) = v1)) 207.80/128.19 (22) map_eq_sub1(int, all_103_3, all_103_1, $sum(all_86_10, 1), all_86_13) = 207.80/128.19 0 207.80/128.19 (23) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.80/128.19 $int] : ! [v5: $int] : ! [v6: $int] : ( ~ (permut2(v0, v3, v4, 0, 207.80/128.19 v5) = v6) | ~ (length1(v0, v1) = v5) | ~ (elts(v0, v2) = v4) | 207.80/128.19 ~ (elts(v0, v1) = v3) | ~ in_ty(v0) | ? [v7: $int] : ((v7 = v5 & v6 207.80/128.19 = 0 & length1(v0, v2) = v5) | ( ~ (v7 = 0) & permut_all(v0, v1, 207.80/128.19 v2) = v7))) 207.80/128.19 (24) t2tb(all_86_6) = all_103_1 207.80/128.19 (25) map_eq_sub1(int, all_103_1, all_105_3, $sum(all_86_8, 1), all_86_13) = 0 207.80/128.19 (26) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.80/128.19 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ (permut3(v6, v5, 207.80/128.19 v4, v3, v2) = v1) | ~ (permut3(v6, v5, v4, v3, v2) = v0)) 207.80/128.19 (27) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 207.80/128.19 | ~ (elts(v3, v2) = v1) | ~ (elts(v3, v2) = v0)) 207.80/128.19 (28) length1(int, all_105_4) = all_86_13 207.80/128.19 (29) in_array_int(all_86_3) 207.80/128.19 (30) elts(int, all_105_4) = all_105_3 207.80/128.19 (31) map_eq_sub1(int, all_105_3, all_105_1, 0, all_86_7) = 0 207.80/128.19 (32) tb2t(all_105_1) = all_86_2 207.80/128.19 (33) permut2(int, all_103_1, all_105_3, all_86_11, $sum(all_86_8, 1)) = 0 207.80/128.19 (34) elts(int, all_105_2) = all_105_1 207.80/128.19 (35) map_eq_sub1(int, all_103_3, all_103_1, 0, all_86_11) = 0 207.80/128.19 (36) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.80/128.19 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 207.80/128.19 ($lesseq(1, $difference(v4, v5))) | ~ ($lesseq(v3, v5)) | ~ 207.80/128.19 (permut2(v0, v1, v2, v3, v4) = 0) | ~ (t2tb1(v5) = v6) | ~ (get(v0, 207.80/128.19 int, v2, v6) = v7) | ~ in_ty(v0) | ? [v8: $int] : ? [v9: $int] 207.80/128.19 : ($lesseq(1, $difference(v4, v8)) & $lesseq(v3, v8) & t2tb1(v8) = v9 207.80/128.19 & get(v0, int, v1, v9) = v7 & in_uni(v9) & in_uni(v7))) 207.80/128.19 (37) t2tb2(all_86_1) = all_105_2 207.80/128.19 (38) $lesseq(all_86_11, all_86_8) 207.80/128.19 (39) ~ (permut2(int, all_105_3, all_105_1, 0, all_86_13) = 0) | ? [v0: 207.80/128.19 $int] : ((v0 = 0 & permut_all(int, all_105_4, all_105_2) = 0) | ( ~ 207.80/128.19 (v0 = all_86_13) & length1(int, all_105_2) = v0)) 207.80/128.19 (40) $lesseq(all_86_7, all_86_10) 207.80/128.19 (41) permut2(int, all_103_1, all_105_3, all_86_11, $sum(all_86_10, 1)) = 0 207.80/128.19 (42) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.80/128.19 $int] : ! [v5: $int] : ( ~ (elts(v0, v1) = v3) | ~ (t2tb1(v2) = v4) 207.80/128.19 | ~ (get(v0, int, v3, v4) = v5) | ~ in_ty(v0) | (get4(v0, v1, v2) = 207.80/128.19 v5 & in_uni(v5))) 207.80/128.19 (43) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.80/128.19 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 207.80/128.19 ($lesseq(1, $difference(v3, v4))) | ~ ($lesseq(v2, v4)) | ~ 207.80/128.19 (permut2(int, v5, v6, v2, v3) = 0) | ~ (t2tb(v1) = v6) | ~ (t2tb(v0) 207.80/128.19 = v5) | ~ (get3(v1, v4) = v7) | ~ in_map_int_int(v0) | ? [v8: 207.80/128.19 $int] : ($lesseq(1, $difference(v3, v8)) & $lesseq(v2, v8) & 207.80/128.19 get3(v0, v8) = v7)) 207.80/128.19 (44) $lesseq(0, all_86_7) 207.80/128.19 (45) permut2(int, all_105_3, all_105_1, all_86_7, $sum(all_86_10, 1)) = 0 207.80/128.19 (46) permut2(int, all_103_3, all_103_1, all_86_11, $sum(all_86_10, 1)) = 0 207.80/128.19 (47) ~ (permut2(int, all_103_3, all_103_1, 0, all_86_13) = 0) | ? [v0: 207.80/128.19 $int] : ((v0 = 0 & permut_all(int, all_103_4, all_103_2) = 0) | ( ~ 207.80/128.19 (v0 = all_86_13) & length1(int, all_103_2) = v0)) 207.80/128.19 (48) in_array_int(all_86_1) 207.80/128.19 (49) t2tb(all_86_12) = all_103_3 207.80/128.19 (50) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.80/128.19 $int] : ! [v5: $int] : ! [v6: $int] : ( ~ ($lesseq(0, v4)) | ~ 207.80/128.19 ($lesseq(0, v3)) | ~ (permut2(v0, v5, v6, v3, v4) = 0) | ~ (elts(v0, 207.80/128.19 v2) = v6) | ~ (elts(v0, v1) = v5) | ~ in_ty(v0) | ? [v7: $int] 207.80/128.19 : ? [v8: $int] : ((v7 = 0 & permut3(v0, v1, v2, v3, v4) = 0) | 207.80/128.19 (length1(v0, v1) = v7 & ( ~ ($lesseq(v4, v7)) | ~ ($lesseq(v3, v7)) 207.80/128.19 | ( ~ (v8 = v7) & length1(v0, v2) = v8))))) 207.80/128.19 (51) $lesseq(1, $difference(all_86_7, all_86_8)) 207.80/128.19 (52) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.80/128.19 $int] : ! [v5: $int] : ! [v6: $int] : ( ~ ($lesseq(1, 207.80/128.19 $difference(v4, v5))) | ~ ($lesseq(v3, v5)) | ~ (map_eq_sub1(v0, 207.80/128.19 v1, v2, v3, v4) = 0) | ~ (t2tb1(v5) = v6) | ~ in_ty(v0) | ? 207.80/128.19 [v7: $int] : (get(v0, int, v2, v6) = v7 & get(v0, int, v1, v6) = v7 & 207.80/128.19 in_uni(v7))) 207.80/128.19 (53) $lesseq(1, $difference(all_86_13, all_86_10)) 207.80/128.19 (54) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.80/128.19 $int] : ! [v5: $int] : (v5 = 0 | ~ (permut_sub2(v0, v1, v2, v3, v4) 207.80/128.19 = v5) | ~ in_ty(v0) | ? [v6: $int] : ? [v7: $int] : ? [v8: $int] 207.80/128.19 : ? [v9: $int] : (( ~ (v9 = 0) & map_eq_sub1(v0, v6, v7, v4, v8) = v9 207.80/128.19 & length1(v0, v1) = v8 & elts(v0, v2) = v7 & elts(v0, v1) = v6 & 207.80/128.19 in_uni(v7) & in_uni(v6)) | ( ~ (v8 = 0) & map_eq_sub1(v0, v6, v7, 207.80/128.19 0, v3) = v8 & elts(v0, v2) = v7 & elts(v0, v1) = v6 & in_uni(v7) 207.80/128.19 & in_uni(v6)) | ( ~ (v6 = 0) & permut3(v0, v1, v2, v3, v4) = v6))) 207.80/128.19 (55) in_map_int_int(all_86_4) 207.80/128.19 (56) $lesseq(0, all_86_11) 207.80/128.19 (57) elts(int, all_103_2) = all_103_1 207.80/128.19 (58) ~ (permut2(int, all_103_1, all_105_3, 0, all_86_13) = 0) | ? [v0: 207.80/128.19 $int] : ((v0 = 0 & permut_all(int, all_103_2, all_105_4) = 0) | ( ~ 207.80/128.19 (v0 = all_86_13) & length1(int, all_105_4) = v0)) 207.80/128.19 (59) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ( ~ 207.80/128.19 (t2tb2(v0) = v2) | ~ (get4(int, v2, v1) = v3) | ~ in_array_int(v0) | 207.80/128.19 ? [v4: $int] : ? [v5: $int] : ? [v6: $int] : (tb2t(v4) = v5 & 207.80/128.19 tb2t1(v3) = v6 & get3(v5, v1) = v6 & elts(int, v2) = v4 & 207.80/128.19 in_map_int_int(v5) & in_uni(v4))) 207.80/128.19 (60) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ (tb2t(v2) 207.80/128.19 = v1) | ~ (tb2t(v2) = v0)) 207.80/128.19 (61) all_133_3 = all_105_2 207.80/128.19 (62) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.80/128.19 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 207.80/128.19 ($lesseq(1, $difference(v3, v6))) | ~ ($lesseq(v2, v6)) | ~ 207.80/128.19 (map_eq_sub1(int, v4, v5, v2, v3) = 0) | ~ (t2tb(v1) = v5) | ~ 207.80/128.19 (t2tb(v0) = v4) | ~ (get3(v1, v6) = v7) | ~ in_map_int_int(v0) | 207.80/128.19 get3(v0, v6) = v7) 207.80/128.19 (63) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 207.80/128.19 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 207.80/128.19 (64) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ( ~ 207.80/128.19 (get4(v0, v1, v2) = v3) | ~ in_ty(v0) | ? [v4: $int] : ? [v5: $int] 207.80/128.19 : (elts(v0, v1) = v4 & t2tb1(v2) = v5 & get(v0, int, v4, v5) = v3 & 207.80/128.19 in_uni(v5) & in_uni(v4) & in_uni(v3))) 207.80/128.19 (65) $lesseq(0, all_86_10) 207.80/128.19 (66) map_eq_sub1(int, all_103_1, all_105_3, 0, all_86_13) = 0 207.80/128.19 (67) ! [v0: $int] : ! [v1: $int] : ( ~ (tb2t1(v0) = v1) | ~ in_uni(v0) | 207.80/128.19 t2tb1(v1) = v0) 207.80/128.19 (68) map_eq_sub1(int, all_105_3, all_105_1, $sum(all_86_10, 1), all_86_13) = 207.80/128.19 0 207.80/128.19 (69) t2tb(all_86_4) = all_105_3 207.80/128.20 (70) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 207.80/128.20 $int] : ! [v5: $int] : ( ~ (permut3(v0, v1, v2, v3, v4) = v5) | ~ 207.80/128.20 in_ty(v0) | ? [v6: $int] : ? [v7: $int] : ? [v8: $int] : ? [v9: 207.80/128.20 $int] : ? [v10: $int] : ((v10 = 0 & v9 = 0 & v5 = 0 & 207.80/128.20 map_eq_sub1(v0, v6, v7, v4, v8) = 0 & map_eq_sub1(v0, v6, v7, 0, 207.80/128.20 v3) = 0 & length1(v0, v1) = v8 & elts(v0, v2) = v7 & elts(v0, 207.80/128.20 v1) = v6 & in_uni(v7) & in_uni(v6)) | ( ~ (v6 = 0) & 207.80/128.20 permut_sub2(v0, v1, v2, v3, v4) = v6))) 207.80/128.20 (71) ! [v0: $int] : ! [v1: $int] : ( ~ ($lesseq(v0, all_86_10)) | ~ 207.80/128.20 ($lesseq(all_86_7, v0)) | ~ (get4(int, all_125_0, v0) = v1) | ? [v2: 207.80/128.20 $int] : ($lesseq(42, v2) & tb2t1(v1) = v2)) 207.80/128.20 207.80/128.20 Begin of proof 207.80/128.20 | 207.80/128.20 | GROUND_INST: instantiating (20) with int, all_103_3, all_103_1, all_105_3, 207.80/128.20 | all_86_11, $sum(all_86_10, 1), simplifying with (11), (41), (46) 207.80/128.20 | gives: 207.80/128.20 | (72) permut2(int, all_103_3, all_105_3, all_86_11, $sum(all_86_10, 1)) = 0 207.80/128.20 | 207.80/128.20 | BETA: splitting (39) gives: 207.80/128.20 | 207.80/128.20 | Case 1: 207.80/128.20 | | 207.80/128.20 | | (73) ~ (permut2(int, all_105_3, all_105_1, 0, all_86_13) = 0) 207.80/128.20 | | 207.80/128.20 | | PRED_UNIFY: (45), (73) imply: 207.80/128.20 | | (74) ~ (all_86_7 = 0) | ~ ($difference(all_86_10, all_86_13) = -1) 207.80/128.20 | | 207.80/128.20 | | BETA: splitting (58) gives: 207.80/128.20 | | 207.80/128.20 | | Case 1: 207.80/128.20 | | | 207.80/128.20 | | | (75) ~ (permut2(int, all_103_1, all_105_3, 0, all_86_13) = 0) 207.80/128.20 | | | 207.80/128.20 | | | PRED_UNIFY: (41), (75) imply: 207.80/128.20 | | | (76) ~ ($difference(all_86_10, all_86_13) = -1) | ~ (all_86_11 = 0) 207.80/128.20 | | | 207.80/128.20 | | | REF_CLOSE: (1), (2), (4), (6), (8), (9), (10), (11), (12), (14), (15), 207.80/128.20 | | | (16), (17), (18), (21), (22), (24), (25), (26), (27), (28), 207.80/128.20 | | | (29), (30), (31), (32), (33), (34), (35), (36), (37), (38), 207.80/128.20 | | | (40), (42), (43), (44), (45), (48), (50), (51), (52), (53), 207.80/128.20 | | | (54), (55), (56), (59), (60), (61), (62), (63), (64), (66), 207.80/128.20 | | | (67), (68), (69), (70), (71), (72), (74), (76) are inconsistent 207.80/128.20 | | | by sub-proof #125. 207.80/128.20 | | | 207.80/128.20 | | Case 2: 207.80/128.20 | | | 207.80/128.20 | | | (77) permut2(int, all_103_1, all_105_3, 0, all_86_13) = 0 207.80/128.20 | | | 207.80/128.20 | | | BETA: splitting (47) gives: 207.80/128.20 | | | 207.80/128.20 | | | Case 1: 207.80/128.20 | | | | 207.80/128.20 | | | | (78) ~ (permut2(int, all_103_3, all_103_1, 0, all_86_13) = 0) 207.80/128.20 | | | | 207.80/128.20 | | | | PRED_UNIFY: (46), (78) imply: 207.80/128.20 | | | | (79) ~ ($difference(all_86_10, all_86_13) = -1) | ~ (all_86_11 = 0) 207.80/128.20 | | | | 207.80/128.20 | | | | REF_CLOSE: (1), (2), (4), (6), (8), (9), (10), (11), (12), (14), (15), 207.80/128.20 | | | | (16), (17), (18), (21), (22), (24), (25), (26), (27), (28), 207.80/128.20 | | | | (29), (30), (31), (32), (33), (34), (35), (36), (37), (38), 207.80/128.20 | | | | (40), (42), (43), (44), (45), (48), (50), (51), (52), (53), 207.80/128.20 | | | | (54), (55), (56), (59), (60), (61), (62), (63), (64), (66), 207.80/128.20 | | | | (67), (68), (69), (70), (71), (72), (74), (79) are 207.80/128.20 | | | | inconsistent by sub-proof #125. 207.80/128.20 | | | | 207.80/128.20 | | | Case 2: 207.80/128.20 | | | | 207.80/128.20 | | | | (80) permut2(int, all_103_3, all_103_1, 0, all_86_13) = 0 207.80/128.20 | | | | 207.80/128.20 | | | | BETA: splitting (14) gives: 207.80/128.20 | | | | 207.80/128.20 | | | | Case 1: 207.80/128.20 | | | | | 207.80/128.20 | | | | | (81) ~ (all_133_0 = 42) & $lesseq(1, $difference(all_86_7, 207.80/128.20 | | | | | all_133_2)) & $lesseq(1, $difference(all_133_2, all_86_8)) 207.80/128.20 | | | | | & tb2t1(all_133_1) = all_133_0 & get4(int, all_133_3, 207.80/128.20 | | | | | all_133_2) = all_133_1 & in_uni(all_133_1) 207.80/128.20 | | | | | 207.80/128.20 | | | | | ALPHA: (81) implies: 207.80/128.20 | | | | | (82) ~ (all_133_0 = 42) 207.80/128.20 | | | | | (83) $lesseq(1, $difference(all_133_2, all_86_8)) 207.80/128.20 | | | | | (84) $lesseq(1, $difference(all_86_7, all_133_2)) 207.80/128.20 | | | | | (85) in_uni(all_133_1) 207.80/128.20 | | | | | (86) get4(int, all_133_3, all_133_2) = all_133_1 207.80/128.20 | | | | | (87) tb2t1(all_133_1) = all_133_0 207.80/128.20 | | | | | 207.80/128.20 | | | | | COMBINE_INEQS: (83), (84) imply: 207.80/128.20 | | | | | (88) $lesseq(2, $difference(all_86_7, all_86_8)) 207.80/128.20 | | | | | 207.80/128.20 | | | | | COMBINE_INEQS: (40), (88) imply: 207.80/128.20 | | | | | (89) $lesseq(2, $difference(all_86_10, all_86_8)) 207.80/128.20 | | | | | 207.80/128.20 | | | | | COMBINE_INEQS: (38), (89) imply: 207.80/128.20 | | | | | (90) $lesseq(2, $difference(all_86_10, all_86_11)) 207.80/128.20 | | | | | 207.80/128.20 | | | | | COMBINE_INEQS: (17), (89) imply: 207.80/128.20 | | | | | (91) $lesseq(1, all_86_10) 207.80/128.20 | | | | | 207.80/128.20 | | | | | COMBINE_INEQS: (53), (90) imply: 207.80/128.20 | | | | | (92) $lesseq(3, $difference(all_86_13, all_86_11)) 207.80/128.20 | | | | | 207.80/128.20 | | | | | COMBINE_INEQS: (56), (92) imply: 207.80/128.20 | | | | | (93) $lesseq(3, all_86_13) 207.80/128.20 | | | | | 207.80/128.20 | | | | | REDUCE: (61), (86) imply: 207.80/128.20 | | | | | (94) get4(int, all_105_2, all_133_2) = all_133_1 207.80/128.20 | | | | | 207.80/128.20 | | | | | REF_CLOSE: (1), (3), (4), (5), (8), (10), (11), (12), (15), (17), 207.80/128.20 | | | | | (18), (20), (21), (22), (23), (24), (25), (26), (27), (28), 207.80/128.20 | | | | | (30), (31), (32), (34), (35), (37), (38), (40), (43), (48), 207.80/128.20 | | | | | (49), (50), (52), (53), (55), (56), (57), (59), (60), (62), 207.80/128.20 | | | | | (63), (64), (67), (68), (69), (72), (77), (80), (82), (83), 207.80/128.20 | | | | | (84), (85), (87), (91), (92), (93), (94) are inconsistent 207.80/128.20 | | | | | by sub-proof #118. 207.80/128.20 | | | | | 207.80/128.20 | | | | Case 2: 207.80/128.20 | | | | | 207.80/128.20 | | | | | (95) ($lesseq(all_133_0, 41) & $lesseq(all_133_2, all_86_10) & 207.80/128.20 | | | | | $lesseq(all_86_7, all_133_2) & tb2t1(all_133_1) = all_133_0 207.80/128.20 | | | | | & get4(int, all_133_3, all_133_2) = all_133_1 & 207.80/128.20 | | | | | in_uni(all_133_1)) | ($lesseq(43, all_133_0) & 207.80/128.20 | | | | | $lesseq(all_133_2, all_86_8) & $lesseq(all_86_11, all_133_2) 207.80/128.20 | | | | | & tb2t1(all_133_1) = all_133_0 & get4(int, all_133_3, 207.80/128.20 | | | | | all_133_2) = all_133_1 & in_uni(all_133_1)) 207.80/128.20 | | | | | 207.80/128.20 | | | | | BETA: splitting (95) gives: 207.80/128.20 | | | | | 207.80/128.20 | | | | | Case 1: 207.80/128.20 | | | | | | 207.80/128.20 | | | | | | (96) $lesseq(all_133_0, 41) & $lesseq(all_133_2, all_86_10) & 207.80/128.20 | | | | | | $lesseq(all_86_7, all_133_2) & tb2t1(all_133_1) = all_133_0 207.80/128.20 | | | | | | & get4(int, all_133_3, all_133_2) = all_133_1 & 207.80/128.20 | | | | | | in_uni(all_133_1) 207.80/128.20 | | | | | | 207.80/128.20 | | | | | | ALPHA: (96) implies: 207.80/128.20 | | | | | | (97) $lesseq(all_86_7, all_133_2) 207.80/128.20 | | | | | | (98) $lesseq(all_133_2, all_86_10) 207.80/128.20 | | | | | | (99) $lesseq(all_133_0, 41) 207.80/128.20 | | | | | | (100) get4(int, all_133_3, all_133_2) = all_133_1 207.80/128.20 | | | | | | (101) tb2t1(all_133_1) = all_133_0 207.80/128.20 | | | | | | 207.80/128.20 | | | | | | REDUCE: (61), (100) imply: 207.80/128.20 | | | | | | (102) get4(int, all_105_2, all_133_2) = all_133_1 207.80/128.20 | | | | | | 207.80/128.20 | | | | | | REF_CLOSE: (1), (8), (9), (10), (11), (16), (27), (29), (30), (32), 207.80/128.20 | | | | | | (34), (36), (37), (42), (43), (45), (48), (50), (55), 207.80/128.20 | | | | | | (56), (59), (60), (64), (65), (69), (71), (72), (97), 207.80/128.20 | | | | | | (98), (99), (101), (102) are inconsistent by sub-proof 207.80/128.20 | | | | | | #126. 207.80/128.20 | | | | | | 207.80/128.20 | | | | | Case 2: 207.80/128.20 | | | | | | 207.80/128.20 | | | | | | (103) $lesseq(43, all_133_0) & $lesseq(all_133_2, all_86_8) & 207.80/128.20 | | | | | | $lesseq(all_86_11, all_133_2) & tb2t1(all_133_1) = 207.80/128.20 | | | | | | all_133_0 & get4(int, all_133_3, all_133_2) = all_133_1 & 207.80/128.20 | | | | | | in_uni(all_133_1) 207.80/128.20 | | | | | | 207.80/128.20 | | | | | | ALPHA: (103) implies: 207.80/128.20 | | | | | | (104) $lesseq(all_86_11, all_133_2) 207.80/128.20 | | | | | | (105) $lesseq(all_133_2, all_86_8) 207.80/128.20 | | | | | | (106) $lesseq(43, all_133_0) 207.80/128.20 | | | | | | (107) get4(int, all_133_3, all_133_2) = all_133_1 207.80/128.20 | | | | | | (108) tb2t1(all_133_1) = all_133_0 207.80/128.20 | | | | | | 207.80/128.20 | | | | | | REDUCE: (61), (107) imply: 207.80/128.20 | | | | | | (109) get4(int, all_105_2, all_133_2) = all_133_1 207.80/128.20 | | | | | | 207.80/128.20 | | | | | | REF_CLOSE: (1), (2), (3), (4), (8), (10), (11), (12), (15), (24), 207.80/128.20 | | | | | | (26), (27), (28), (30), (31), (32), (33), (34), (36), 207.80/128.20 | | | | | | (37), (40), (43), (44), (45), (48), (50), (51), (52), 207.80/128.20 | | | | | | (53), (55), (56), (57), (59), (60), (62), (63), (64), 207.80/128.20 | | | | | | (69), (72), (74), (77), (80), (104), (105), (106), (108), 207.80/128.20 | | | | | | (109) are inconsistent by sub-proof #117. 207.80/128.20 | | | | | | 207.80/128.20 | | | | | End of split 207.80/128.20 | | | | | 207.80/128.20 | | | | End of split 207.80/128.20 | | | | 207.80/128.20 | | | End of split 207.80/128.20 | | | 207.80/128.20 | | End of split 207.80/128.20 | | 207.80/128.20 | Case 2: 207.80/128.20 | | 207.80/128.20 | | (110) permut2(int, all_105_3, all_105_1, 0, all_86_13) = 0 207.80/128.20 | | 207.80/128.20 | | BETA: splitting (58) gives: 207.80/128.20 | | 207.80/128.20 | | Case 1: 207.80/128.20 | | | 207.80/128.20 | | | (111) ~ (permut2(int, all_103_1, all_105_3, 0, all_86_13) = 0) 207.80/128.20 | | | 207.80/128.20 | | | PRED_UNIFY: (41), (111) imply: 207.80/128.20 | | | (112) ~ ($difference(all_86_10, all_86_13) = -1) | ~ (all_86_11 = 0) 207.80/128.20 | | | 207.80/128.20 | | | REF_CLOSE: (1), (2), (4), (6), (7), (8), (9), (10), (11), (12), (13), 207.80/128.20 | | | (14), (15), (16), (17), (18), (21), (22), (24), (25), (26), 207.80/128.20 | | | (27), (28), (29), (30), (31), (32), (33), (34), (35), (36), 207.80/128.20 | | | (37), (38), (40), (42), (43), (44), (45), (48), (50), (51), 207.80/128.20 | | | (52), (53), (54), (55), (56), (59), (60), (61), (62), (63), 207.80/128.20 | | | (64), (65), (66), (67), (68), (69), (70), (71), (72), (110), 207.80/128.20 | | | (112) are inconsistent by sub-proof #115. 207.80/128.20 | | | 207.80/128.20 | | Case 2: 207.80/128.20 | | | 207.80/128.20 | | | (113) permut2(int, all_103_1, all_105_3, 0, all_86_13) = 0 207.80/128.20 | | | 207.80/128.20 | | | BETA: splitting (47) gives: 207.80/128.20 | | | 207.80/128.20 | | | Case 1: 207.80/128.20 | | | | 207.80/128.20 | | | | (114) ~ (permut2(int, all_103_3, all_103_1, 0, all_86_13) = 0) 207.80/128.20 | | | | 207.80/128.20 | | | | PRED_UNIFY: (46), (114) imply: 207.80/128.20 | | | | (115) ~ ($difference(all_86_10, all_86_13) = -1) | ~ (all_86_11 = 207.80/128.20 | | | | 0) 207.80/128.20 | | | | 207.80/128.20 | | | | REF_CLOSE: (1), (2), (4), (6), (7), (8), (9), (10), (11), (12), (13), 207.80/128.20 | | | | (14), (15), (16), (17), (18), (21), (22), (24), (25), (26), 207.80/128.20 | | | | (27), (28), (29), (30), (31), (32), (33), (34), (35), (36), 207.80/128.20 | | | | (37), (38), (40), (42), (43), (44), (45), (48), (50), (51), 207.80/128.20 | | | | (52), (53), (54), (55), (56), (59), (60), (61), (62), (63), 207.80/128.20 | | | | (64), (65), (66), (67), (68), (69), (70), (71), (72), (110), 207.80/128.20 | | | | (115) are inconsistent by sub-proof #115. 207.80/128.20 | | | | 207.80/128.20 | | | Case 2: 207.80/128.20 | | | | 207.80/128.20 | | | | (116) permut2(int, all_103_3, all_103_1, 0, all_86_13) = 0 207.80/128.20 | | | | 207.80/128.20 | | | | BETA: splitting (14) gives: 207.80/128.20 | | | | 207.80/128.20 | | | | Case 1: 207.80/128.20 | | | | | 207.80/128.20 | | | | | (117) ~ (all_133_0 = 42) & $lesseq(1, $difference(all_86_7, 207.80/128.20 | | | | | all_133_2)) & $lesseq(1, $difference(all_133_2, 207.80/128.20 | | | | | all_86_8)) & tb2t1(all_133_1) = all_133_0 & get4(int, 207.80/128.20 | | | | | all_133_3, all_133_2) = all_133_1 & in_uni(all_133_1) 207.80/128.20 | | | | | 207.80/128.20 | | | | | ALPHA: (117) implies: 207.80/128.20 | | | | | (118) ~ (all_133_0 = 42) 207.80/128.20 | | | | | (119) $lesseq(1, $difference(all_133_2, all_86_8)) 207.80/128.20 | | | | | (120) $lesseq(1, $difference(all_86_7, all_133_2)) 207.80/128.20 | | | | | (121) in_uni(all_133_1) 207.80/128.20 | | | | | (122) get4(int, all_133_3, all_133_2) = all_133_1 207.80/128.20 | | | | | (123) tb2t1(all_133_1) = all_133_0 207.80/128.20 | | | | | 207.80/128.20 | | | | | COMBINE_INEQS: (119), (120) imply: 207.80/128.20 | | | | | (124) $lesseq(2, $difference(all_86_7, all_86_8)) 207.80/128.20 | | | | | 207.80/128.20 | | | | | COMBINE_INEQS: (40), (124) imply: 207.80/128.20 | | | | | (125) $lesseq(2, $difference(all_86_10, all_86_8)) 207.80/128.20 | | | | | 207.80/128.20 | | | | | COMBINE_INEQS: (38), (125) imply: 207.80/128.20 | | | | | (126) $lesseq(2, $difference(all_86_10, all_86_11)) 207.80/128.20 | | | | | 207.80/128.20 | | | | | COMBINE_INEQS: (17), (125) imply: 207.80/128.20 | | | | | (127) $lesseq(1, all_86_10) 207.80/128.20 | | | | | 207.80/128.20 | | | | | COMBINE_INEQS: (53), (126) imply: 207.80/128.20 | | | | | (128) $lesseq(3, $difference(all_86_13, all_86_11)) 207.80/128.20 | | | | | 207.80/128.20 | | | | | COMBINE_INEQS: (56), (128) imply: 207.80/128.20 | | | | | (129) $lesseq(3, all_86_13) 207.80/128.20 | | | | | 207.80/128.20 | | | | | REDUCE: (61), (122) imply: 207.80/128.20 | | | | | (130) get4(int, all_105_2, all_133_2) = all_133_1 207.80/128.20 | | | | | 207.80/128.20 | | | | | REF_CLOSE: (1), (3), (4), (5), (8), (10), (11), (12), (15), (17), 207.80/128.20 | | | | | (18), (20), (21), (22), (23), (24), (25), (26), (27), (28), 207.80/128.20 | | | | | (30), (31), (32), (34), (35), (37), (38), (40), (43), (48), 207.80/128.20 | | | | | (49), (50), (52), (53), (55), (56), (57), (59), (60), (62), 207.80/128.20 | | | | | (63), (64), (67), (68), (69), (72), (113), (116), (118), 207.80/128.20 | | | | | (119), (120), (121), (123), (127), (128), (129), (130) are 207.80/128.20 | | | | | inconsistent by sub-proof #118. 207.80/128.20 | | | | | 207.80/128.20 | | | | Case 2: 207.80/128.20 | | | | | 207.80/128.20 | | | | | (131) ($lesseq(all_133_0, 41) & $lesseq(all_133_2, all_86_10) & 207.80/128.20 | | | | | $lesseq(all_86_7, all_133_2) & tb2t1(all_133_1) = all_133_0 207.80/128.20 | | | | | & get4(int, all_133_3, all_133_2) = all_133_1 & 207.80/128.20 | | | | | in_uni(all_133_1)) | ($lesseq(43, all_133_0) & 207.80/128.20 | | | | | $lesseq(all_133_2, all_86_8) & $lesseq(all_86_11, 207.80/128.20 | | | | | all_133_2) & tb2t1(all_133_1) = all_133_0 & get4(int, 207.80/128.20 | | | | | all_133_3, all_133_2) = all_133_1 & in_uni(all_133_1)) 207.80/128.20 | | | | | 207.80/128.20 | | | | | BETA: splitting (131) gives: 207.80/128.20 | | | | | 207.80/128.20 | | | | | Case 1: 207.80/128.20 | | | | | | 207.80/128.20 | | | | | | (132) $lesseq(all_133_0, 41) & $lesseq(all_133_2, all_86_10) & 207.80/128.20 | | | | | | $lesseq(all_86_7, all_133_2) & tb2t1(all_133_1) = all_133_0 207.80/128.20 | | | | | | & get4(int, all_133_3, all_133_2) = all_133_1 & 207.80/128.20 | | | | | | in_uni(all_133_1) 207.80/128.20 | | | | | | 207.80/128.20 | | | | | | ALPHA: (132) implies: 207.80/128.20 | | | | | | (133) $lesseq(all_86_7, all_133_2) 207.80/128.20 | | | | | | (134) $lesseq(all_133_2, all_86_10) 207.80/128.20 | | | | | | (135) $lesseq(all_133_0, 41) 207.80/128.20 | | | | | | (136) get4(int, all_133_3, all_133_2) = all_133_1 207.80/128.20 | | | | | | (137) tb2t1(all_133_1) = all_133_0 207.80/128.20 | | | | | | 207.80/128.20 | | | | | | REDUCE: (61), (136) imply: 207.80/128.20 | | | | | | (138) get4(int, all_105_2, all_133_2) = all_133_1 207.80/128.20 | | | | | | 207.80/128.20 | | | | | | REF_CLOSE: (1), (8), (9), (10), (11), (16), (27), (29), (30), (32), 207.80/128.20 | | | | | | (34), (36), (37), (42), (43), (45), (48), (50), (55), 207.80/128.20 | | | | | | (56), (59), (60), (64), (65), (69), (71), (72), (133), 207.80/128.20 | | | | | | (134), (135), (137), (138) are inconsistent by sub-proof 207.80/128.20 | | | | | | #126. 207.80/128.20 | | | | | | 207.80/128.20 | | | | | Case 2: 207.80/128.20 | | | | | | 207.80/128.20 | | | | | | (139) $lesseq(43, all_133_0) & $lesseq(all_133_2, all_86_8) & 207.80/128.20 | | | | | | $lesseq(all_86_11, all_133_2) & tb2t1(all_133_1) = 207.80/128.20 | | | | | | all_133_0 & get4(int, all_133_3, all_133_2) = all_133_1 & 207.80/128.20 | | | | | | in_uni(all_133_1) 207.80/128.21 | | | | | | 207.80/128.21 | | | | | | ALPHA: (139) implies: 207.80/128.21 | | | | | | (140) $lesseq(all_86_11, all_133_2) 207.80/128.21 | | | | | | (141) $lesseq(all_133_2, all_86_8) 207.80/128.21 | | | | | | (142) $lesseq(43, all_133_0) 207.80/128.21 | | | | | | (143) get4(int, all_133_3, all_133_2) = all_133_1 207.80/128.21 | | | | | | (144) tb2t1(all_133_1) = all_133_0 207.80/128.21 | | | | | | 207.80/128.21 | | | | | | REDUCE: (61), (143) imply: 207.80/128.21 | | | | | | (145) get4(int, all_105_2, all_133_2) = all_133_1 207.80/128.21 | | | | | | 207.80/128.21 | | | | | | GROUND_INST: instantiating (15) with int, all_105_4, all_105_2, 0, 207.80/128.21 | | | | | | all_86_13, all_105_3, all_105_1, 0, simplifying with 207.80/128.21 | | | | | | (11), (30), (34), (110) gives: 207.80/128.21 | | | | | | (146) ? [v0: $int] : ? [v1: $int] : ((v1 = v0 & 207.80/128.21 | | | | | | $lesseq(all_86_13, v0) & $lesseq(0, v0) & $lesseq(0, 207.80/128.21 | | | | | | all_86_13) & length1(int, all_105_2) = v0 & 207.80/128.21 | | | | | | length1(int, all_105_4) = v0) | ( ~ (v0 = 0) & 207.80/128.21 | | | | | | permut3(int, all_105_4, all_105_2, 0, all_86_13) = v0)) 207.80/128.21 | | | | | | 207.80/128.21 | | | | | | GROUND_INST: instantiating (50) with int, all_105_4, all_105_2, 0, 207.80/128.21 | | | | | | all_86_13, all_105_3, all_105_1, simplifying with (11), 207.80/128.21 | | | | | | (30), (34), (110) gives: 207.80/128.21 | | | | | | (147) ~ ($lesseq(0, all_86_13)) | ? [v0: $int] : ? [v1: $int] 207.80/128.21 | | | | | | : ((v0 = 0 & permut3(int, all_105_4, all_105_2, 0, 207.80/128.21 | | | | | | all_86_13) = 0) | (length1(int, all_105_4) = v0 & ( ~ 207.80/128.21 | | | | | | ($lesseq(all_86_13, v0)) | ~ ($lesseq(0, v0)) | ( ~ 207.80/128.21 | | | | | | (v1 = v0) & length1(int, all_105_2) = v1)))) 207.80/128.21 | | | | | | 207.80/128.21 | | | | | | GROUND_INST: instantiating (15) with int, all_103_2, all_105_4, 0, 207.80/128.21 | | | | | | all_86_13, all_103_1, all_105_3, 0, simplifying with 207.80/128.21 | | | | | | (11), (30), (57), (113) gives: 207.80/128.21 | | | | | | (148) ? [v0: $int] : ? [v1: $int] : ((v1 = v0 & 207.80/128.21 | | | | | | $lesseq(all_86_13, v0) & $lesseq(0, v0) & $lesseq(0, 207.80/128.21 | | | | | | all_86_13) & length1(int, all_105_4) = v0 & 207.80/128.21 | | | | | | length1(int, all_103_2) = v0) | ( ~ (v0 = 0) & 207.80/128.21 | | | | | | permut3(int, all_103_2, all_105_4, 0, all_86_13) = v0)) 207.80/128.21 | | | | | | 207.80/128.21 | | | | | | GROUND_INST: instantiating (50) with int, all_103_2, all_105_4, 0, 207.80/128.21 | | | | | | all_86_13, all_103_1, all_105_3, simplifying with (11), 207.80/128.21 | | | | | | (30), (57), (113) gives: 207.80/128.21 | | | | | | (149) ~ ($lesseq(0, all_86_13)) | ? [v0: $int] : ? [v1: $int] 207.80/128.21 | | | | | | : ((v0 = 0 & permut3(int, all_103_2, all_105_4, 0, 207.80/128.21 | | | | | | all_86_13) = 0) | (length1(int, all_103_2) = v0 & ( ~ 207.80/128.21 | | | | | | ($lesseq(all_86_13, v0)) | ~ ($lesseq(0, v0)) | ( ~ 207.80/128.21 | | | | | | (v1 = v0) & length1(int, all_105_4) = v1)))) 207.80/128.21 | | | | | | 207.80/128.21 | | | | | | GROUND_INST: instantiating (15) with int, all_103_4, all_105_4, 207.80/128.21 | | | | | | all_86_11, $sum(all_86_10, 1), all_103_3, all_105_3, 0, 207.80/128.21 | | | | | | simplifying with (8), (11), (30), (72) gives: 207.80/128.21 | | | | | | (150) ? [v0: $int] : ? [v1: $int] : ((v1 = v0 & $lesseq(1, 207.80/128.21 | | | | | | $difference(v0, all_86_10)) & $lesseq(all_86_11, v0) 207.80/128.21 | | | | | | & $lesseq(-1, all_86_10) & $lesseq(0, all_86_11) & 207.80/128.21 | | | | | | length1(int, all_105_4) = v0 & length1(int, all_103_4) 207.80/128.21 | | | | | | = v0) | ( ~ (v0 = 0) & permut3(int, all_103_4, 207.80/128.21 | | | | | | all_105_4, all_86_11, $sum(all_86_10, 1)) = v0)) 207.80/128.21 | | | | | | 207.80/128.21 | | | | | | GROUND_INST: instantiating (20) with int, all_103_3, all_105_3, 207.80/128.21 | | | | | | all_105_1, all_86_11, $sum(all_86_10, 1), simplifying 207.80/128.21 | | | | | | with (11), (72) gives: 207.80/128.21 | | | | | | (151) ~ (permut2(int, all_105_3, all_105_1, all_86_11, 207.80/128.21 | | | | | | $sum(all_86_10, 1)) = 0) | permut2(int, all_103_3, 207.80/128.21 | | | | | | all_105_1, all_86_11, $sum(all_86_10, 1)) = 0 207.80/128.21 | | | | | | 207.80/128.21 | | | | | | GROUND_INST: instantiating (50) with int, all_103_4, all_105_4, 207.80/128.21 | | | | | | all_86_11, $sum(all_86_10, 1), all_103_3, all_105_3, 207.80/128.21 | | | | | | simplifying with (8), (11), (30), (72) gives: 207.80/128.21 | | | | | | (152) ~ ($lesseq(-1, all_86_10)) | ~ ($lesseq(0, all_86_11)) | 207.80/128.21 | | | | | | ? [v0: $int] : ? [v1: $int] : ((v0 = 0 & permut3(int, 207.80/128.21 | | | | | | all_103_4, all_105_4, all_86_11, $sum(all_86_10, 1)) 207.80/128.21 | | | | | | = 0) | (length1(int, all_103_4) = v0 & ( ~ ($lesseq(1, 207.80/128.21 | | | | | | $difference(v0, all_86_10))) | ~ 207.80/128.21 | | | | | | ($lesseq(all_86_11, v0)) | ( ~ (v1 = v0) & 207.80/128.21 | | | | | | length1(int, all_105_4) = v1)))) 207.80/128.21 | | | | | | 207.80/128.21 | | | | | | GROUND_INST: instantiating (15) with int, all_103_4, all_103_2, 0, 207.80/128.21 | | | | | | all_86_13, all_103_3, all_103_1, 0, simplifying with 207.80/128.21 | | | | | | (8), (11), (57), (116) gives: 207.80/128.21 | | | | | | (153) ? [v0: $int] : ? [v1: $int] : ((v1 = v0 & 207.80/128.21 | | | | | | $lesseq(all_86_13, v0) & $lesseq(0, v0) & $lesseq(0, 207.80/128.21 | | | | | | all_86_13) & length1(int, all_103_2) = v0 & 207.80/128.21 | | | | | | length1(int, all_103_4) = v0) | ( ~ (v0 = 0) & 207.80/128.21 | | | | | | permut3(int, all_103_4, all_103_2, 0, all_86_13) = v0)) 207.80/128.21 | | | | | | 207.80/128.21 | | | | | | GROUND_INST: instantiating (50) with int, all_103_4, all_103_2, 0, 207.80/128.21 | | | | | | all_86_13, all_103_3, all_103_1, simplifying with (8), 207.80/128.21 | | | | | | (11), (57), (116) gives: 207.80/128.21 | | | | | | (154) ~ ($lesseq(0, all_86_13)) | ? [v0: $int] : ? [v1: $int] 207.80/128.21 | | | | | | : ((v0 = 0 & permut3(int, all_103_4, all_103_2, 0, 207.80/128.21 | | | | | | all_86_13) = 0) | (length1(int, all_103_4) = v0 & ( ~ 207.80/128.21 | | | | | | ($lesseq(all_86_13, v0)) | ~ ($lesseq(0, v0)) | ( ~ 207.80/128.21 | | | | | | (v1 = v0) & length1(int, all_103_2) = v1)))) 207.80/128.21 | | | | | | 207.80/128.21 | | | | | | GROUND_INST: instantiating (59) with all_86_1, all_133_2, all_105_2, 207.80/128.21 | | | | | | all_133_1, simplifying with (37), (48), (145) gives: 207.80/128.21 | | | | | | (155) ? [v0: $int] : ? [v1: $int] : ? [v2: $int] : (tb2t(v0) = 207.80/128.21 | | | | | | v1 & tb2t1(all_133_1) = v2 & get3(v1, all_133_2) = v2 & 207.80/128.21 | | | | | | elts(int, all_105_2) = v0 & in_map_int_int(v1) & 207.80/128.21 | | | | | | in_uni(v0)) 207.80/128.21 | | | | | | 207.80/128.21 | | | | | | GROUND_INST: instantiating (64) with int, all_105_2, all_133_2, 207.80/128.21 | | | | | | all_133_1, simplifying with (11), (145) gives: 207.80/128.21 | | | | | | (156) ? [v0: $int] : ? [v1: $int] : (elts(int, all_105_2) = v0 207.80/128.21 | | | | | | & t2tb1(all_133_2) = v1 & get(int, int, v0, v1) = 207.80/128.21 | | | | | | all_133_1 & in_uni(v1) & in_uni(v0) & in_uni(all_133_1)) 207.80/128.21 | | | | | | 207.80/128.21 | | | | | | DELTA: instantiating (148) with fresh symbols all_736_0, all_736_1 207.80/128.21 | | | | | | gives: 207.80/128.21 | | | | | | (157) (all_736_0 = all_736_1 & $lesseq(all_86_13, all_736_1) & 207.80/128.21 | | | | | | $lesseq(0, all_736_1) & $lesseq(0, all_86_13) & 207.80/128.21 | | | | | | length1(int, all_105_4) = all_736_1 & length1(int, 207.80/128.21 | | | | | | all_103_2) = all_736_1) | ( ~ (all_736_1 = 0) & 207.80/128.21 | | | | | | permut3(int, all_103_2, all_105_4, 0, all_86_13) = 207.80/128.21 | | | | | | all_736_1) 207.80/128.21 | | | | | | 207.80/128.21 | | | | | | DELTA: instantiating (153) with fresh symbols all_737_0, all_737_1 207.80/128.21 | | | | | | gives: 207.80/128.21 | | | | | | (158) (all_737_0 = all_737_1 & $lesseq(all_86_13, all_737_1) & 207.80/128.21 | | | | | | $lesseq(0, all_737_1) & $lesseq(0, all_86_13) & 207.80/128.21 | | | | | | length1(int, all_103_2) = all_737_1 & length1(int, 207.80/128.21 | | | | | | all_103_4) = all_737_1) | ( ~ (all_737_1 = 0) & 207.80/128.21 | | | | | | permut3(int, all_103_4, all_103_2, 0, all_86_13) = 207.80/128.21 | | | | | | all_737_1) 207.80/128.21 | | | | | | 207.80/128.21 | | | | | | DELTA: instantiating (150) with fresh symbols all_738_0, all_738_1 207.80/128.21 | | | | | | gives: 207.80/128.21 | | | | | | (159) (all_738_0 = all_738_1 & $lesseq(1, $difference(all_738_1, 207.80/128.21 | | | | | | all_86_10)) & $lesseq(all_86_11, all_738_1) & 207.80/128.21 | | | | | | $lesseq(-1, all_86_10) & $lesseq(0, all_86_11) & 207.80/128.21 | | | | | | length1(int, all_105_4) = all_738_1 & length1(int, 207.80/128.21 | | | | | | all_103_4) = all_738_1) | ( ~ (all_738_1 = 0) & 207.80/128.21 | | | | | | permut3(int, all_103_4, all_105_4, all_86_11, 207.80/128.21 | | | | | | $sum(all_86_10, 1)) = all_738_1) 207.80/128.21 | | | | | | 207.80/128.21 | | | | | | DELTA: instantiating (146) with fresh symbols all_739_0, all_739_1 207.80/128.21 | | | | | | gives: 207.80/128.21 | | | | | | (160) (all_739_0 = all_739_1 & $lesseq(all_86_13, all_739_1) & 207.80/128.21 | | | | | | $lesseq(0, all_739_1) & $lesseq(0, all_86_13) & 207.80/128.21 | | | | | | length1(int, all_105_2) = all_739_1 & length1(int, 207.80/128.21 | | | | | | all_105_4) = all_739_1) | ( ~ (all_739_1 = 0) & 207.80/128.21 | | | | | | permut3(int, all_105_4, all_105_2, 0, all_86_13) = 207.80/128.21 | | | | | | all_739_1) 207.80/128.21 | | | | | | 207.80/128.21 | | | | | | DELTA: instantiating (156) with fresh symbols all_740_0, all_740_1 207.80/128.21 | | | | | | gives: 207.80/128.21 | | | | | | (161) elts(int, all_105_2) = all_740_1 & t2tb1(all_133_2) = 207.80/128.21 | | | | | | all_740_0 & get(int, int, all_740_1, all_740_0) = all_133_1 207.80/128.21 | | | | | | & in_uni(all_740_0) & in_uni(all_740_1) & in_uni(all_133_1) 207.80/128.21 | | | | | | 207.80/128.21 | | | | | | ALPHA: (161) implies: 207.80/128.21 | | | | | | (162) get(int, int, all_740_1, all_740_0) = all_133_1 207.80/128.21 | | | | | | (163) t2tb1(all_133_2) = all_740_0 207.80/128.21 | | | | | | (164) elts(int, all_105_2) = all_740_1 207.80/128.21 | | | | | | 207.80/128.21 | | | | | | DELTA: instantiating (155) with fresh symbols all_742_0, all_742_1, 207.80/128.21 | | | | | | all_742_2 gives: 207.80/128.21 | | | | | | (165) tb2t(all_742_2) = all_742_1 & tb2t1(all_133_1) = all_742_0 207.80/128.21 | | | | | | & get3(all_742_1, all_133_2) = all_742_0 & elts(int, 207.80/128.21 | | | | | | all_105_2) = all_742_2 & in_map_int_int(all_742_1) & 207.80/128.21 | | | | | | in_uni(all_742_2) 207.80/128.21 | | | | | | 207.80/128.21 | | | | | | ALPHA: (165) implies: 207.80/128.21 | | | | | | (166) elts(int, all_105_2) = all_742_2 207.80/128.21 | | | | | | (167) get3(all_742_1, all_133_2) = all_742_0 207.80/128.21 | | | | | | (168) tb2t1(all_133_1) = all_742_0 207.80/128.21 | | | | | | (169) tb2t(all_742_2) = all_742_1 207.80/128.21 | | | | | | 207.80/128.21 | | | | | | BETA: splitting (147) gives: 207.80/128.21 | | | | | | 207.80/128.21 | | | | | | Case 1: 207.80/128.21 | | | | | | | 207.80/128.21 | | | | | | | (170) $lesseq(all_86_13, -1) 207.80/128.21 | | | | | | | 207.80/128.21 | | | | | | | COMBINE_INEQS: (13), (170) imply: 207.80/128.21 | | | | | | | (171) $lesseq(0, -1) 207.80/128.21 | | | | | | | 207.80/128.21 | | | | | | | CLOSE: (171) is inconsistent. 207.80/128.21 | | | | | | | 207.80/128.21 | | | | | | Case 2: 207.80/128.21 | | | | | | | 207.80/128.21 | | | | | | | (172) ? [v0: $int] : ? [v1: $int] : ((v0 = 0 & permut3(int, 207.80/128.21 | | | | | | | all_105_4, all_105_2, 0, all_86_13) = 0) | 207.80/128.21 | | | | | | | (length1(int, all_105_4) = v0 & ( ~ ($lesseq(all_86_13, 207.80/128.21 | | | | | | | v0)) | ~ ($lesseq(0, v0)) | ( ~ (v1 = v0) & 207.80/128.21 | | | | | | | length1(int, all_105_2) = v1)))) 207.80/128.21 | | | | | | | 207.80/128.21 | | | | | | | DELTA: instantiating (172) with fresh symbols all_765_0, all_765_1 207.80/128.21 | | | | | | | gives: 207.80/128.21 | | | | | | | (173) (all_765_1 = 0 & permut3(int, all_105_4, all_105_2, 0, 207.80/128.21 | | | | | | | all_86_13) = 0) | (length1(int, all_105_4) = 207.80/128.21 | | | | | | | all_765_1 & ( ~ ($lesseq(all_86_13, all_765_1)) | ~ 207.80/128.21 | | | | | | | ($lesseq(0, all_765_1)) | ( ~ (all_765_0 = all_765_1) 207.80/128.21 | | | | | | | & length1(int, all_105_2) = all_765_0))) 207.80/128.21 | | | | | | | 207.80/128.21 | | | | | | | BETA: splitting (173) gives: 207.80/128.21 | | | | | | | 207.80/128.21 | | | | | | | Case 1: 207.80/128.21 | | | | | | | | 207.80/128.21 | | | | | | | | (174) all_765_1 = 0 & permut3(int, all_105_4, all_105_2, 0, 207.80/128.21 | | | | | | | | all_86_13) = 0 207.80/128.21 | | | | | | | | 207.80/128.21 | | | | | | | | ALPHA: (174) implies: 207.80/128.21 | | | | | | | | (175) permut3(int, all_105_4, all_105_2, 0, all_86_13) = 0 207.80/128.21 | | | | | | | | 207.80/128.21 | | | | | | | | BETA: splitting (160) gives: 207.80/128.21 | | | | | | | | 207.80/128.21 | | | | | | | | Case 1: 207.80/128.21 | | | | | | | | | 207.80/128.21 | | | | | | | | | (176) all_739_0 = all_739_1 & $lesseq(all_86_13, all_739_1) 207.80/128.21 | | | | | | | | | & $lesseq(0, all_739_1) & $lesseq(0, all_86_13) & 207.80/128.21 | | | | | | | | | length1(int, all_105_2) = all_739_1 & length1(int, 207.80/128.21 | | | | | | | | | all_105_4) = all_739_1 207.80/128.21 | | | | | | | | | 207.80/128.21 | | | | | | | | | ALPHA: (176) implies: 207.80/128.21 | | | | | | | | | (177) length1(int, all_105_4) = all_739_1 207.80/128.21 | | | | | | | | | (178) length1(int, all_105_2) = all_739_1 207.80/128.21 | | | | | | | | | 207.80/128.21 | | | | | | | | | BETA: splitting (149) gives: 207.80/128.21 | | | | | | | | | 207.80/128.21 | | | | | | | | | Case 1: 207.80/128.21 | | | | | | | | | | 207.80/128.21 | | | | | | | | | | (179) $lesseq(all_86_13, -1) 207.80/128.21 | | | | | | | | | | 207.80/128.21 | | | | | | | | | | COMBINE_INEQS: (13), (179) imply: 207.80/128.21 | | | | | | | | | | (180) $lesseq(0, -1) 207.80/128.21 | | | | | | | | | | 207.80/128.21 | | | | | | | | | | CLOSE: (180) is inconsistent. 207.80/128.21 | | | | | | | | | | 207.80/128.21 | | | | | | | | | Case 2: 207.80/128.21 | | | | | | | | | | 207.80/128.21 | | | | | | | | | | (181) ? [v0: $int] : ? [v1: $int] : ((v0 = 0 & 207.80/128.21 | | | | | | | | | | permut3(int, all_103_2, all_105_4, 0, 207.80/128.21 | | | | | | | | | | all_86_13) = 0) | (length1(int, all_103_2) = 207.80/128.21 | | | | | | | | | | v0 & ( ~ ($lesseq(all_86_13, v0)) | ~ 207.80/128.21 | | | | | | | | | | ($lesseq(0, v0)) | ( ~ (v1 = v0) & 207.80/128.21 | | | | | | | | | | length1(int, all_105_4) = v1)))) 207.80/128.21 | | | | | | | | | | 207.80/128.21 | | | | | | | | | | DELTA: instantiating (181) with fresh symbols all_789_0, 207.80/128.21 | | | | | | | | | | all_789_1 gives: 207.80/128.21 | | | | | | | | | | (182) (all_789_1 = 0 & permut3(int, all_103_2, all_105_4, 207.80/128.21 | | | | | | | | | | 0, all_86_13) = 0) | (length1(int, all_103_2) = 207.80/128.21 | | | | | | | | | | all_789_1 & ( ~ ($lesseq(all_86_13, all_789_1)) | 207.80/128.21 | | | | | | | | | | ~ ($lesseq(0, all_789_1)) | ( ~ (all_789_0 = 207.80/128.21 | | | | | | | | | | all_789_1) & length1(int, all_105_4) = 207.80/128.21 | | | | | | | | | | all_789_0))) 207.80/128.21 | | | | | | | | | | 207.80/128.21 | | | | | | | | | | BETA: splitting (154) gives: 207.80/128.21 | | | | | | | | | | 207.80/128.21 | | | | | | | | | | Case 1: 207.80/128.21 | | | | | | | | | | | 207.80/128.21 | | | | | | | | | | | (183) $lesseq(all_86_13, -1) 207.80/128.21 | | | | | | | | | | | 207.80/128.21 | | | | | | | | | | | COMBINE_INEQS: (13), (183) imply: 207.80/128.21 | | | | | | | | | | | (184) $lesseq(0, -1) 207.80/128.21 | | | | | | | | | | | 207.80/128.21 | | | | | | | | | | | CLOSE: (184) is inconsistent. 207.80/128.21 | | | | | | | | | | | 207.80/128.21 | | | | | | | | | | Case 2: 207.80/128.21 | | | | | | | | | | | 207.80/128.21 | | | | | | | | | | | (185) ? [v0: $int] : ? [v1: $int] : ((v0 = 0 & 207.80/128.21 | | | | | | | | | | | permut3(int, all_103_4, all_103_2, 0, 207.80/128.21 | | | | | | | | | | | all_86_13) = 0) | (length1(int, all_103_4) = 207.80/128.21 | | | | | | | | | | | v0 & ( ~ ($lesseq(all_86_13, v0)) | ~ 207.80/128.21 | | | | | | | | | | | ($lesseq(0, v0)) | ( ~ (v1 = v0) & 207.80/128.21 | | | | | | | | | | | length1(int, all_103_2) = v1)))) 207.80/128.21 | | | | | | | | | | | 207.80/128.21 | | | | | | | | | | | DELTA: instantiating (185) with fresh symbols all_795_0, 207.80/128.21 | | | | | | | | | | | all_795_1 gives: 207.80/128.21 | | | | | | | | | | | (186) (all_795_1 = 0 & permut3(int, all_103_4, 207.80/128.21 | | | | | | | | | | | all_103_2, 0, all_86_13) = 0) | (length1(int, 207.80/128.21 | | | | | | | | | | | all_103_4) = all_795_1 & ( ~ 207.80/128.21 | | | | | | | | | | | ($lesseq(all_86_13, all_795_1)) | ~ 207.80/128.21 | | | | | | | | | | | ($lesseq(0, all_795_1)) | ( ~ (all_795_0 = 207.80/128.21 | | | | | | | | | | | all_795_1) & length1(int, all_103_2) = 207.80/128.21 | | | | | | | | | | | all_795_0))) 207.80/128.21 | | | | | | | | | | | 207.80/128.21 | | | | | | | | | | | BETA: splitting (152) gives: 207.80/128.21 | | | | | | | | | | | 207.80/128.21 | | | | | | | | | | | Case 1: 207.80/128.21 | | | | | | | | | | | | 207.80/128.21 | | | | | | | | | | | | (187) $lesseq(all_86_11, -1) 207.80/128.21 | | | | | | | | | | | | 207.80/128.21 | | | | | | | | | | | | COMBINE_INEQS: (56), (187) imply: 207.80/128.21 | | | | | | | | | | | | (188) $lesseq(0, -1) 207.80/128.21 | | | | | | | | | | | | 207.80/128.21 | | | | | | | | | | | | CLOSE: (188) is inconsistent. 207.80/128.21 | | | | | | | | | | | | 207.80/128.21 | | | | | | | | | | | Case 2: 207.80/128.21 | | | | | | | | | | | | 207.80/128.21 | | | | | | | | | | | | (189) ~ ($lesseq(-1, all_86_10)) | ? [v0: $int] : ? 207.80/128.21 | | | | | | | | | | | | [v1: $int] : ((v0 = 0 & permut3(int, all_103_4, 207.80/128.21 | | | | | | | | | | | | all_105_4, all_86_11, $sum(all_86_10, 1)) = 207.80/128.21 | | | | | | | | | | | | 0) | (length1(int, all_103_4) = v0 & ( ~ 207.80/128.21 | | | | | | | | | | | | ($lesseq(1, $difference(v0, all_86_10))) | 207.80/128.21 | | | | | | | | | | | | ~ ($lesseq(all_86_11, v0)) | ( ~ (v1 = v0) & 207.80/128.21 | | | | | | | | | | | | length1(int, all_105_4) = v1)))) 207.80/128.21 | | | | | | | | | | | | 207.80/128.21 | | | | | | | | | | | | BETA: splitting (186) gives: 207.80/128.21 | | | | | | | | | | | | 207.80/128.21 | | | | | | | | | | | | Case 1: 207.80/128.21 | | | | | | | | | | | | | 207.80/128.21 | | | | | | | | | | | | | (190) all_795_1 = 0 & permut3(int, all_103_4, all_103_2, 207.80/128.21 | | | | | | | | | | | | | 0, all_86_13) = 0 207.80/128.21 | | | | | | | | | | | | | 207.80/128.21 | | | | | | | | | | | | | ALPHA: (190) implies: 207.80/128.21 | | | | | | | | | | | | | (191) permut3(int, all_103_4, all_103_2, 0, all_86_13) = 207.80/128.21 | | | | | | | | | | | | | 0 207.80/128.21 | | | | | | | | | | | | | 207.80/128.21 | | | | | | | | | | | | | BETA: splitting (158) gives: 207.80/128.21 | | | | | | | | | | | | | 207.80/128.21 | | | | | | | | | | | | | Case 1: 207.80/128.21 | | | | | | | | | | | | | | 207.80/128.21 | | | | | | | | | | | | | | (192) all_737_0 = all_737_1 & $lesseq(all_86_13, 207.80/128.21 | | | | | | | | | | | | | | all_737_1) & $lesseq(0, all_737_1) & $lesseq(0, 207.80/128.21 | | | | | | | | | | | | | | all_86_13) & length1(int, all_103_2) = all_737_1 207.80/128.21 | | | | | | | | | | | | | | & length1(int, all_103_4) = all_737_1 207.80/128.21 | | | | | | | | | | | | | | 207.80/128.21 | | | | | | | | | | | | | | ALPHA: (192) implies: 207.80/128.21 | | | | | | | | | | | | | | (193) length1(int, all_103_4) = all_737_1 207.80/128.21 | | | | | | | | | | | | | | (194) length1(int, all_103_2) = all_737_1 207.80/128.21 | | | | | | | | | | | | | | 207.80/128.21 | | | | | | | | | | | | | | BETA: splitting (189) gives: 207.80/128.21 | | | | | | | | | | | | | | 207.80/128.21 | | | | | | | | | | | | | | Case 1: 207.80/128.21 | | | | | | | | | | | | | | | 207.80/128.21 | | | | | | | | | | | | | | | (195) $lesseq(all_86_10, -2) 207.80/128.21 | | | | | | | | | | | | | | | 207.80/128.21 | | | | | | | | | | | | | | | COMBINE_INEQS: (65), (195) imply: 207.80/128.21 | | | | | | | | | | | | | | | (196) $lesseq(0, -1) 207.80/128.21 | | | | | | | | | | | | | | | 207.80/128.21 | | | | | | | | | | | | | | | CLOSE: (196) is inconsistent. 207.80/128.21 | | | | | | | | | | | | | | | 207.80/128.21 | | | | | | | | | | | | | | Case 2: 207.80/128.21 | | | | | | | | | | | | | | | 207.80/128.21 | | | | | | | | | | | | | | | (197) ? [v0: $int] : ? [v1: $int] : ((v0 = 0 & 207.80/128.21 | | | | | | | | | | | | | | | permut3(int, all_103_4, all_105_4, all_86_11, 207.80/128.21 | | | | | | | | | | | | | | | $sum(all_86_10, 1)) = 0) | (length1(int, 207.80/128.21 | | | | | | | | | | | | | | | all_103_4) = v0 & ( ~ ($lesseq(1, 207.80/128.21 | | | | | | | | | | | | | | | $difference(v0, all_86_10))) | ~ 207.80/128.21 | | | | | | | | | | | | | | | ($lesseq(all_86_11, v0)) | ( ~ (v1 = v0) & 207.80/128.21 | | | | | | | | | | | | | | | length1(int, all_105_4) = v1)))) 207.80/128.21 | | | | | | | | | | | | | | | 207.80/128.21 | | | | | | | | | | | | | | | DELTA: instantiating (197) with fresh symbols all_819_0, 207.80/128.21 | | | | | | | | | | | | | | | all_819_1 gives: 207.80/128.21 | | | | | | | | | | | | | | | (198) (all_819_1 = 0 & permut3(int, all_103_4, 207.80/128.21 | | | | | | | | | | | | | | | all_105_4, all_86_11, $sum(all_86_10, 1)) = 0) 207.80/128.21 | | | | | | | | | | | | | | | | (length1(int, all_103_4) = all_819_1 & ( ~ 207.80/128.21 | | | | | | | | | | | | | | | ($lesseq(1, $difference(all_819_1, 207.80/128.21 | | | | | | | | | | | | | | | all_86_10))) | ~ ($lesseq(all_86_11, 207.80/128.21 | | | | | | | | | | | | | | | all_819_1)) | ( ~ (all_819_0 = all_819_1) 207.80/128.21 | | | | | | | | | | | | | | | & length1(int, all_105_4) = all_819_0))) 207.80/128.21 | | | | | | | | | | | | | | | 207.80/128.21 | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_133_0, all_742_0, 207.80/128.21 | | | | | | | | | | | | | | | all_133_1, simplifying with (144), (168) gives: 207.80/128.21 | | | | | | | | | | | | | | | (199) all_742_0 = all_133_0 207.80/128.21 | | | | | | | | | | | | | | | 207.80/128.21 | | | | | | | | | | | | | | | GROUND_INST: instantiating (63) with all_86_13, all_739_1, 207.80/128.21 | | | | | | | | | | | | | | | all_105_4, int, simplifying with (28), (177) 207.80/128.21 | | | | | | | | | | | | | | | gives: 207.80/128.21 | | | | | | | | | | | | | | | (200) all_739_1 = all_86_13 207.80/128.21 | | | | | | | | | | | | | | | 207.80/128.21 | | | | | | | | | | | | | | | GROUND_INST: instantiating (63) with all_86_13, all_737_1, 207.80/128.21 | | | | | | | | | | | | | | | all_103_4, int, simplifying with (12), (193) 207.80/128.21 | | | | | | | | | | | | | | | gives: 207.80/128.21 | | | | | | | | | | | | | | | (201) all_737_1 = all_86_13 207.80/128.21 | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | GROUND_INST: instantiating (27) with all_105_1, all_742_2, 207.80/128.22 | | | | | | | | | | | | | | | all_105_2, int, simplifying with (34), (166) 207.80/128.22 | | | | | | | | | | | | | | | gives: 207.80/128.22 | | | | | | | | | | | | | | | (202) all_742_2 = all_105_1 207.80/128.22 | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | GROUND_INST: instantiating (27) with all_742_2, all_740_1, 207.80/128.22 | | | | | | | | | | | | | | | all_105_2, int, simplifying with (164), (166) 207.80/128.22 | | | | | | | | | | | | | | | gives: 207.80/128.22 | | | | | | | | | | | | | | | (203) all_742_2 = all_740_1 207.80/128.22 | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | COMBINE_EQS: (202), (203) imply: 207.80/128.22 | | | | | | | | | | | | | | | (204) all_740_1 = all_105_1 207.80/128.22 | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | SIMP: (204) implies: 207.80/128.22 | | | | | | | | | | | | | | | (205) all_740_1 = all_105_1 207.80/128.22 | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | REDUCE: (169), (202) imply: 207.80/128.22 | | | | | | | | | | | | | | | (206) tb2t(all_105_1) = all_742_1 207.80/128.22 | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | REDUCE: (167), (199) imply: 207.80/128.22 | | | | | | | | | | | | | | | (207) get3(all_742_1, all_133_2) = all_133_0 207.80/128.22 | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | REDUCE: (162), (205) imply: 207.80/128.22 | | | | | | | | | | | | | | | (208) get(int, int, all_105_1, all_740_0) = all_133_1 207.80/128.22 | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | BETA: splitting (182) gives: 207.80/128.22 | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | Case 1: 207.80/128.22 | | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | | (209) all_789_1 = 0 & permut3(int, all_103_2, all_105_4, 207.80/128.22 | | | | | | | | | | | | | | | | 0, all_86_13) = 0 207.80/128.22 | | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | | ALPHA: (209) implies: 207.80/128.22 | | | | | | | | | | | | | | | | (210) permut3(int, all_103_2, all_105_4, 0, all_86_13) = 207.80/128.22 | | | | | | | | | | | | | | | | 0 207.80/128.22 | | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | | BETA: splitting (157) gives: 207.80/128.22 | | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | | Case 1: 207.80/128.22 | | | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | | | (211) all_736_0 = all_736_1 & $lesseq(all_86_13, 207.80/128.22 | | | | | | | | | | | | | | | | | all_736_1) & $lesseq(0, all_736_1) & $lesseq(0, 207.80/128.22 | | | | | | | | | | | | | | | | | all_86_13) & length1(int, all_105_4) = all_736_1 207.80/128.22 | | | | | | | | | | | | | | | | | & length1(int, all_103_2) = all_736_1 207.80/128.22 | | | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | | | ALPHA: (211) implies: 207.80/128.22 | | | | | | | | | | | | | | | | | (212) length1(int, all_103_2) = all_736_1 207.80/128.22 | | | | | | | | | | | | | | | | | (213) length1(int, all_105_4) = all_736_1 207.80/128.22 | | | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | | | BETA: splitting (198) gives: 207.80/128.22 | | | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | | | Case 1: 207.80/128.22 | | | | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | | | | (214) all_819_1 = 0 & permut3(int, all_103_4, all_105_4, 207.80/128.22 | | | | | | | | | | | | | | | | | | all_86_11, $sum(all_86_10, 1)) = 0 207.80/128.22 | | | | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | | | | ALPHA: (214) implies: 207.80/128.22 | | | | | | | | | | | | | | | | | | (215) permut3(int, all_103_4, all_105_4, all_86_11, 207.80/128.22 | | | | | | | | | | | | | | | | | | $sum(all_86_10, 1)) = 0 207.80/128.22 | | | | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | | | | BETA: splitting (159) gives: 207.80/128.22 | | | | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | | | | Case 1: 207.80/128.22 | | | | | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | | | | | (216) all_738_0 = all_738_1 & $lesseq(1, 207.80/128.22 | | | | | | | | | | | | | | | | | | | $difference(all_738_1, all_86_10)) & 207.80/128.22 | | | | | | | | | | | | | | | | | | | $lesseq(all_86_11, all_738_1) & $lesseq(-1, 207.80/128.22 | | | | | | | | | | | | | | | | | | | all_86_10) & $lesseq(0, all_86_11) & 207.80/128.22 | | | | | | | | | | | | | | | | | | | length1(int, all_105_4) = all_738_1 & length1(int, 207.80/128.22 | | | | | | | | | | | | | | | | | | | all_103_4) = all_738_1 207.80/128.22 | | | | | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | | | | | ALPHA: (216) implies: 207.80/128.22 | | | | | | | | | | | | | | | | | | | (217) $lesseq(1, $difference(all_738_1, all_86_10)) 207.80/128.22 | | | | | | | | | | | | | | | | | | | (218) length1(int, all_103_4) = all_738_1 207.80/128.22 | | | | | | | | | | | | | | | | | | | (219) length1(int, all_105_4) = all_738_1 207.80/128.22 | | | | | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (60) with all_86_2, all_742_1, 207.80/128.22 | | | | | | | | | | | | | | | | | | | all_105_1, simplifying with (32), (206) gives: 207.80/128.22 | | | | | | | | | | | | | | | | | | | (220) all_742_1 = all_86_2 207.80/128.22 | | | | | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (63) with all_738_1, all_736_1, 207.80/128.22 | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (213), (219) 207.80/128.22 | | | | | | | | | | | | | | | | | | | gives: 207.80/128.22 | | | | | | | | | | | | | | | | | | | (221) all_738_1 = all_736_1 207.80/128.22 | | | | | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (63) with all_86_13, all_738_1, 207.80/128.22 | | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (12), (218) 207.80/128.22 | | | | | | | | | | | | | | | | | | | gives: 207.80/128.22 | | | | | | | | | | | | | | | | | | | (222) all_738_1 = all_86_13 207.80/128.22 | | | | | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (221), (222) imply: 207.80/128.22 | | | | | | | | | | | | | | | | | | | (223) all_736_1 = all_86_13 207.80/128.22 | | | | | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | | | | | COMBINE_INEQS: (40), (51) imply: 207.80/128.22 | | | | | | | | | | | | | | | | | | | (224) $lesseq(1, $difference(all_86_10, all_86_8)) 207.80/128.22 | | | | | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | | | | | COMBINE_INEQS: (38), (224) imply: 207.80/128.22 | | | | | | | | | | | | | | | | | | | (225) $lesseq(1, $difference(all_86_10, all_86_11)) 207.80/128.22 | | | | | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | | | | | COMBINE_INEQS: (53), (225) imply: 207.80/128.22 | | | | | | | | | | | | | | | | | | | (226) $lesseq(2, $difference(all_86_13, all_86_11)) 207.80/128.22 | | | | | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | | | | | REDUCE: (207), (220) imply: 207.80/128.22 | | | | | | | | | | | | | | | | | | | (227) get3(all_86_2, all_133_2) = all_133_0 207.80/128.22 | | | | | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | | | | | BETA: splitting (19) gives: 207.80/128.22 | | | | | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | | | | | Case 1: 207.80/128.22 | | | | | | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | | | | | | (228) ~ (permut2(int, all_105_3, all_105_1, all_86_11, 207.80/128.22 | | | | | | | | | | | | | | | | | | | | $sum(all_86_10, 1)) = 0) 207.80/128.22 | | | | | | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (110), (228) imply: 207.80/128.22 | | | | | | | | | | | | | | | | | | | | (229) ~ ($difference(all_86_10, all_86_13) = -1) | ~ 207.80/128.22 | | | | | | | | | | | | | | | | | | | | (all_86_11 = 0) 207.80/128.22 | | | | | | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (4), (7), (8), (10), (11), (12), (13), 207.80/128.22 | | | | | | | | | | | | | | | | | | | | (15), (18), (24), (26), (27), (28), (30), (31), 207.80/128.22 | | | | | | | | | | | | | | | | | | | | (32), (33), (34), (36), (37), (40), (43), (45), 207.80/128.22 | | | | | | | | | | | | | | | | | | | | (48), (50), (51), (52), (53), (55), (56), (59), 207.80/128.22 | | | | | | | | | | | | | | | | | | | | (60), (62), (63), (64), (65), (68), (69), (72), 207.80/128.22 | | | | | | | | | | | | | | | | | | | | (110), (140), (141), (142), (144), (145), (229) 207.80/128.22 | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #116. 207.80/128.22 | | | | | | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | | | | | Case 2: 207.80/128.22 | | | | | | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | | | | | | (230) permut2(int, all_105_3, all_105_1, all_86_11, 207.80/128.22 | | | | | | | | | | | | | | | | | | | | $sum(all_86_10, 1)) = 0 207.80/128.22 | | | | | | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | | | | | | BETA: splitting (151) gives: 207.80/128.22 | | | | | | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | | | | | | Case 1: 207.80/128.22 | | | | | | | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | | | | | | | (231) ~ (permut2(int, all_105_3, all_105_1, all_86_11, 207.80/128.22 | | | | | | | | | | | | | | | | | | | | | $sum(all_86_10, 1)) = 0) 207.80/128.22 | | | | | | | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (230), (231) imply: 207.80/128.22 | | | | | | | | | | | | | | | | | | | | | (232) $false 207.80/128.22 | | | | | | | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | | | | | | | CLOSE: (232) is inconsistent. 207.80/128.22 | | | | | | | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | | | | | | Case 2: 207.80/128.22 | | | | | | | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (62) with all_86_4, all_86_2, 0, 207.80/128.22 | | | | | | | | | | | | | | | | | | | | | all_86_7, all_105_3, all_105_1, all_133_2, 207.80/128.22 | | | | | | | | | | | | | | | | | | | | | all_133_0, simplifying with (10), (31), (55), 207.80/128.22 | | | | | | | | | | | | | | | | | | | | | (69), (227) gives: 207.80/128.22 | | | | | | | | | | | | | | | | | | | | | (233) ~ ($lesseq(1, $difference(all_86_7, all_133_2))) 207.80/128.22 | | | | | | | | | | | | | | | | | | | | | | ~ ($lesseq(0, all_133_2)) | get3(all_86_4, 207.80/128.22 | | | | | | | | | | | | | | | | | | | | | all_133_2) = all_133_0 207.80/128.22 | | | | | | | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (43) with all_86_4, all_86_2, 207.80/128.22 | | | | | | | | | | | | | | | | | | | | | all_86_7, $sum(all_86_10, 1), all_133_2, 207.80/128.22 | | | | | | | | | | | | | | | | | | | | | all_105_3, all_105_1, all_133_0, simplifying with 207.80/128.22 | | | | | | | | | | | | | | | | | | | | | (10), (45), (55), (69), (227) gives: 207.80/128.22 | | | | | | | | | | | | | | | | | | | | | (234) ~ ($lesseq(all_133_2, all_86_10)) | ~ 207.80/128.22 | | | | | | | | | | | | | | | | | | | | | ($lesseq(all_86_7, all_133_2)) | ? [v0: $int] : 207.80/128.22 | | | | | | | | | | | | | | | | | | | | | ($lesseq(v0, all_86_10) & $lesseq(all_86_7, v0) & 207.80/128.22 | | | | | | | | | | | | | | | | | | | | | get3(all_86_4, v0) = all_133_0) 207.80/128.22 | | | | | | | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (52) with int, all_105_3, all_105_1, 207.80/128.22 | | | | | | | | | | | | | | | | | | | | | 0, all_86_7, all_133_2, all_740_0, simplifying 207.80/128.22 | | | | | | | | | | | | | | | | | | | | | with (11), (31), (163) gives: 207.80/128.22 | | | | | | | | | | | | | | | | | | | | | (235) ~ ($lesseq(1, $difference(all_86_7, all_133_2))) 207.80/128.22 | | | | | | | | | | | | | | | | | | | | | | ~ ($lesseq(0, all_133_2)) | ? [v0: $int] : 207.80/128.22 | | | | | | | | | | | | | | | | | | | | | (get(int, int, all_105_1, all_740_0) = v0 & 207.80/128.22 | | | | | | | | | | | | | | | | | | | | | get(int, int, all_105_3, all_740_0) = v0 & 207.80/128.22 | | | | | | | | | | | | | | | | | | | | | in_uni(v0)) 207.80/128.22 | | | | | | | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (36) with int, all_105_3, all_105_1, 207.80/128.22 | | | | | | | | | | | | | | | | | | | | | all_86_7, $sum(all_86_10, 1), all_133_2, 207.80/128.22 | | | | | | | | | | | | | | | | | | | | | all_740_0, all_133_1, simplifying with (11), (45), 207.80/128.22 | | | | | | | | | | | | | | | | | | | | | (163), (208) gives: 207.80/128.22 | | | | | | | | | | | | | | | | | | | | | (236) ~ ($lesseq(all_133_2, all_86_10)) | ~ 207.80/128.22 | | | | | | | | | | | | | | | | | | | | | ($lesseq(all_86_7, all_133_2)) | ? [v0: $int] : 207.80/128.22 | | | | | | | | | | | | | | | | | | | | | ? [v1: $int] : ($lesseq(v0, all_86_10) & 207.80/128.22 | | | | | | | | | | | | | | | | | | | | | $lesseq(all_86_7, v0) & t2tb1(v0) = v1 & 207.80/128.22 | | | | | | | | | | | | | | | | | | | | | get(int, int, all_105_3, v1) = all_133_1 & 207.80/128.22 | | | | | | | | | | | | | | | | | | | | | in_uni(v1) & in_uni(all_133_1)) 207.80/128.22 | | | | | | | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives: 207.80/128.22 | | | | | | | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | | | | | | | Case 1: 207.80/128.22 | | | | | | | | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | | | | | | | | (237) $lesseq(all_133_2, -1) 207.80/128.22 | | | | | | | | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | | | | | | | | COMBINE_INEQS: (140), (237) imply: 207.80/128.22 | | | | | | | | | | | | | | | | | | | | | | (238) $lesseq(all_86_11, -1) 207.80/128.22 | | | | | | | | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | | | | | | | | COMBINE_INEQS: (56), (238) imply: 207.80/128.22 | | | | | | | | | | | | | | | | | | | | | | (239) $lesseq(0, -1) 207.80/128.22 | | | | | | | | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (239) is inconsistent. 207.80/128.22 | | | | | | | | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | | | | | | | Case 2: 207.80/128.22 | | | | | | | | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | | | | | | | | (240) $lesseq(0, all_133_2) 207.80/128.22 | | | | | | | | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (24), (33), (43), (51), (69), (140), 207.80/128.22 | | | | | | | | | | | | | | | | | | | | | | (141), (142), (224), (233), (234), (236), (240) 207.80/128.22 | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #144. 207.80/128.22 | | | | | | | | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | | | | | | | End of split 207.80/128.22 | | | | | | | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | | | | | | End of split 207.80/128.22 | | | | | | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | | | | | End of split 207.80/128.22 | | | | | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | | | | Case 2: 207.80/128.22 | | | | | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | | | | | (241) ~ (all_738_1 = 0) & permut3(int, all_103_4, 207.80/128.22 | | | | | | | | | | | | | | | | | | | all_105_4, all_86_11, $sum(all_86_10, 1)) = 207.80/128.22 | | | | | | | | | | | | | | | | | | | all_738_1 207.80/128.22 | | | | | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | | | | | ALPHA: (241) implies: 207.80/128.22 | | | | | | | | | | | | | | | | | | | (242) ~ (all_738_1 = 0) 207.80/128.22 | | | | | | | | | | | | | | | | | | | (243) permut3(int, all_103_4, all_105_4, all_86_11, 207.80/128.22 | | | | | | | | | | | | | | | | | | | $sum(all_86_10, 1)) = all_738_1 207.80/128.22 | | | | | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (26) with all_738_1, 0, 207.80/128.22 | | | | | | | | | | | | | | | | | | | $sum(all_86_10, 1), all_86_11, all_105_4, 207.80/128.22 | | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (215), (243) 207.80/128.22 | | | | | | | | | | | | | | | | | | | gives: 207.80/128.22 | | | | | | | | | | | | | | | | | | | (244) all_738_1 = 0 207.80/128.22 | | | | | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | | | | | REDUCE: (242), (244) imply: 207.80/128.22 | | | | | | | | | | | | | | | | | | | (245) ~ (0 = 0) 207.80/128.22 | | | | | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | | | | | CLOSE: (245) is inconsistent. 207.80/128.22 | | | | | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | | | | End of split 207.80/128.22 | | | | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | | | Case 2: 207.80/128.22 | | | | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | | | | (246) length1(int, all_103_4) = all_819_1 & ( ~ 207.80/128.22 | | | | | | | | | | | | | | | | | | ($lesseq(1, $difference(all_819_1, all_86_10))) 207.80/128.22 | | | | | | | | | | | | | | | | | | | ~ ($lesseq(all_86_11, all_819_1)) | ( ~ 207.80/128.22 | | | | | | | | | | | | | | | | | | (all_819_0 = all_819_1) & length1(int, 207.80/128.22 | | | | | | | | | | | | | | | | | | all_105_4) = all_819_0)) 207.80/128.22 | | | | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | | | | ALPHA: (246) implies: 207.80/128.22 | | | | | | | | | | | | | | | | | | (247) length1(int, all_103_4) = all_819_1 207.80/128.22 | | | | | | | | | | | | | | | | | | (248) ~ ($lesseq(1, $difference(all_819_1, all_86_10))) 207.80/128.22 | | | | | | | | | | | | | | | | | | | ~ ($lesseq(all_86_11, all_819_1)) | ( ~ 207.80/128.22 | | | | | | | | | | | | | | | | | | (all_819_0 = all_819_1) & length1(int, 207.80/128.22 | | | | | | | | | | | | | | | | | | all_105_4) = all_819_0) 207.80/128.22 | | | | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (63) with all_86_13, all_736_1, 207.80/128.22 | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (3), (212) gives: 207.80/128.22 | | | | | | | | | | | | | | | | | | (249) all_736_1 = all_86_13 207.80/128.22 | | | | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (63) with all_86_13, all_819_1, 207.80/128.22 | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (12), (247) 207.80/128.22 | | | | | | | | | | | | | | | | | | gives: 207.80/128.22 | | | | | | | | | | | | | | | | | | (250) all_819_1 = all_86_13 207.80/128.22 | | | | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | | | | BETA: splitting (248) gives: 207.80/128.22 | | | | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | | | | Case 1: 207.80/128.22 | | | | | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | | | | | (251) $lesseq(1, $difference(all_86_11, all_819_1)) 207.80/128.22 | | | | | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | | | | | REDUCE: (250), (251) imply: 207.80/128.22 | | | | | | | | | | | | | | | | | | | (252) $lesseq(1, $difference(all_86_11, all_86_13)) 207.80/128.22 | | | | | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | | | | | COMBINE_INEQS: (40), (51) imply: 207.80/128.22 | | | | | | | | | | | | | | | | | | | (253) $lesseq(1, $difference(all_86_10, all_86_8)) 207.80/128.22 | | | | | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | | | | | COMBINE_INEQS: (38), (253) imply: 207.80/128.22 | | | | | | | | | | | | | | | | | | | (254) $lesseq(1, $difference(all_86_10, all_86_11)) 207.80/128.22 | | | | | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | | | | | COMBINE_INEQS: (53), (254) imply: 207.80/128.22 | | | | | | | | | | | | | | | | | | | (255) $lesseq(2, $difference(all_86_13, all_86_11)) 207.80/128.22 | | | | | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | | | | | COMBINE_INEQS: (252), (255) imply: 207.80/128.22 | | | | | | | | | | | | | | | | | | | (256) $lesseq(0, -1) 207.80/128.22 | | | | | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | | | | | CLOSE: (256) is inconsistent. 207.80/128.22 | | | | | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | | | | Case 2: 207.80/128.22 | | | | | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | | | | | (257) ~ ($lesseq(1, $difference(all_819_1, all_86_10))) 207.80/128.22 | | | | | | | | | | | | | | | | | | | | ( ~ (all_819_0 = all_819_1) & length1(int, 207.80/128.22 | | | | | | | | | | | | | | | | | | | all_105_4) = all_819_0) 207.80/128.22 | | | | | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | | | | | BETA: splitting (257) gives: 207.80/128.22 | | | | | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | | | | | Case 1: 207.80/128.22 | | | | | | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | | | | | | (258) $lesseq(all_819_1, all_86_10) 207.80/128.22 | | | | | | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | | | | | | REDUCE: (250), (258) imply: 207.80/128.22 | | | | | | | | | | | | | | | | | | | | (259) $lesseq(all_86_13, all_86_10) 207.80/128.22 | | | | | | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | | | | | | COMBINE_INEQS: (53), (259) imply: 207.80/128.22 | | | | | | | | | | | | | | | | | | | | (260) $lesseq(0, -1) 207.80/128.22 | | | | | | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | | | | | | CLOSE: (260) is inconsistent. 207.80/128.22 | | | | | | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | | | | | Case 2: 207.80/128.22 | | | | | | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | | | | | | (261) ~ (all_819_0 = all_819_1) & length1(int, 207.80/128.22 | | | | | | | | | | | | | | | | | | | | all_105_4) = all_819_0 207.80/128.22 | | | | | | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | | | | | | ALPHA: (261) implies: 207.80/128.22 | | | | | | | | | | | | | | | | | | | | (262) ~ (all_819_0 = all_819_1) 207.80/128.22 | | | | | | | | | | | | | | | | | | | | (263) length1(int, all_105_4) = all_819_0 207.80/128.22 | | | | | | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | | | | | | REDUCE: (250), (262) imply: 207.80/128.22 | | | | | | | | | | | | | | | | | | | | (264) ~ (all_819_0 = all_86_13) 207.80/128.22 | | | | | | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (63) with all_86_13, all_819_0, 207.80/128.22 | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (28), (263) 207.80/128.22 | | | | | | | | | | | | | | | | | | | | gives: 207.80/128.22 | | | | | | | | | | | | | | | | | | | | (265) all_819_0 = all_86_13 207.80/128.22 | | | | | | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | | | | | | REDUCE: (264), (265) imply: 207.80/128.22 | | | | | | | | | | | | | | | | | | | | (266) ~ (0 = 0) 207.80/128.22 | | | | | | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | | | | | | CLOSE: (266) is inconsistent. 207.80/128.22 | | | | | | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | | | | | End of split 207.80/128.22 | | | | | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | | | | End of split 207.80/128.22 | | | | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | | | End of split 207.80/128.22 | | | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | | Case 2: 207.80/128.22 | | | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | | | (267) ~ (all_736_1 = 0) & permut3(int, all_103_2, 207.80/128.22 | | | | | | | | | | | | | | | | | all_105_4, 0, all_86_13) = all_736_1 207.80/128.22 | | | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | | | ALPHA: (267) implies: 207.80/128.22 | | | | | | | | | | | | | | | | | (268) ~ (all_736_1 = 0) 207.80/128.22 | | | | | | | | | | | | | | | | | (269) permut3(int, all_103_2, all_105_4, 0, all_86_13) = 207.80/128.22 | | | | | | | | | | | | | | | | | all_736_1 207.80/128.22 | | | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | | | REF_CLOSE: (26), (210), (268), (269) are inconsistent by 207.80/128.22 | | | | | | | | | | | | | | | | | sub-proof #114. 207.80/128.22 | | | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | | End of split 207.80/128.22 | | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | Case 2: 207.80/128.22 | | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | | (270) length1(int, all_103_2) = all_789_1 & ( ~ 207.80/128.22 | | | | | | | | | | | | | | | | ($lesseq(all_86_13, all_789_1)) | ~ ($lesseq(0, 207.80/128.22 | | | | | | | | | | | | | | | | all_789_1)) | ( ~ (all_789_0 = all_789_1) & 207.80/128.22 | | | | | | | | | | | | | | | | length1(int, all_105_4) = all_789_0)) 207.80/128.22 | | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | | ALPHA: (270) implies: 207.80/128.22 | | | | | | | | | | | | | | | | (271) length1(int, all_103_2) = all_789_1 207.80/128.22 | | | | | | | | | | | | | | | | (272) ~ ($lesseq(all_86_13, all_789_1)) | ~ 207.80/128.22 | | | | | | | | | | | | | | | | ($lesseq(0, all_789_1)) | ( ~ (all_789_0 = 207.80/128.22 | | | | | | | | | | | | | | | | all_789_1) & length1(int, all_105_4) = 207.80/128.22 | | | | | | | | | | | | | | | | all_789_0) 207.80/128.22 | | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | | REF_CLOSE: (3), (28), (40), (51), (53), (56), (63), (140), 207.80/128.22 | | | | | | | | | | | | | | | | (141), (271), (272) are inconsistent by sub-proof 207.80/128.22 | | | | | | | | | | | | | | | | #113. 207.80/128.22 | | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | | End of split 207.80/128.22 | | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | End of split 207.80/128.22 | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | Case 2: 207.80/128.22 | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | (273) ~ (all_737_1 = 0) & permut3(int, all_103_4, 207.80/128.22 | | | | | | | | | | | | | | all_103_2, 0, all_86_13) = all_737_1 207.80/128.22 | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | ALPHA: (273) implies: 207.80/128.22 | | | | | | | | | | | | | | (274) ~ (all_737_1 = 0) 207.80/128.22 | | | | | | | | | | | | | | (275) permut3(int, all_103_4, all_103_2, 0, all_86_13) = 207.80/128.22 | | | | | | | | | | | | | | all_737_1 207.80/128.22 | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | GROUND_INST: instantiating (26) with 0, all_737_1, all_86_13, 207.80/128.22 | | | | | | | | | | | | | | 0, all_103_2, all_103_4, int, simplifying with 207.80/128.22 | | | | | | | | | | | | | | (191), (275) gives: 207.80/128.22 | | | | | | | | | | | | | | (276) all_737_1 = 0 207.80/128.22 | | | | | | | | | | | | | | 207.80/128.22 | | | | | | | | | | | | | | REDUCE: (274), (276) imply: 207.80/128.23 | | | | | | | | | | | | | | (277) ~ (0 = 0) 207.80/128.23 | | | | | | | | | | | | | | 207.80/128.23 | | | | | | | | | | | | | | CLOSE: (277) is inconsistent. 207.80/128.23 | | | | | | | | | | | | | | 207.80/128.23 | | | | | | | | | | | | | End of split 207.80/128.23 | | | | | | | | | | | | | 207.80/128.23 | | | | | | | | | | | | Case 2: 207.80/128.23 | | | | | | | | | | | | | 207.80/128.23 | | | | | | | | | | | | | (278) length1(int, all_103_4) = all_795_1 & ( ~ 207.80/128.23 | | | | | | | | | | | | | ($lesseq(all_86_13, all_795_1)) | ~ ($lesseq(0, 207.80/128.23 | | | | | | | | | | | | | all_795_1)) | ( ~ (all_795_0 = all_795_1) & 207.80/128.23 | | | | | | | | | | | | | length1(int, all_103_2) = all_795_0)) 207.80/128.23 | | | | | | | | | | | | | 207.80/128.23 | | | | | | | | | | | | | ALPHA: (278) implies: 207.80/128.23 | | | | | | | | | | | | | (279) length1(int, all_103_4) = all_795_1 207.80/128.23 | | | | | | | | | | | | | (280) ~ ($lesseq(all_86_13, all_795_1)) | ~ 207.80/128.23 | | | | | | | | | | | | | ($lesseq(0, all_795_1)) | ( ~ (all_795_0 = 207.80/128.23 | | | | | | | | | | | | | all_795_1) & length1(int, all_103_2) = 207.80/128.23 | | | | | | | | | | | | | all_795_0) 207.80/128.23 | | | | | | | | | | | | | 207.80/128.23 | | | | | | | | | | | | | BETA: splitting (189) gives: 207.80/128.23 | | | | | | | | | | | | | 207.80/128.23 | | | | | | | | | | | | | Case 1: 207.80/128.23 | | | | | | | | | | | | | | 207.80/128.23 | | | | | | | | | | | | | | (281) $lesseq(all_86_10, -2) 207.80/128.23 | | | | | | | | | | | | | | 207.80/128.23 | | | | | | | | | | | | | | COMBINE_INEQS: (65), (281) imply: 207.80/128.23 | | | | | | | | | | | | | | (282) $lesseq(0, -1) 207.80/128.23 | | | | | | | | | | | | | | 207.80/128.23 | | | | | | | | | | | | | | CLOSE: (282) is inconsistent. 207.80/128.23 | | | | | | | | | | | | | | 207.80/128.23 | | | | | | | | | | | | | Case 2: 207.80/128.23 | | | | | | | | | | | | | | 207.80/128.23 | | | | | | | | | | | | | | 207.80/128.23 | | | | | | | | | | | | | | GROUND_INST: instantiating (63) with all_86_13, all_739_1, 207.80/128.23 | | | | | | | | | | | | | | all_105_4, int, simplifying with (28), (177) 207.80/128.23 | | | | | | | | | | | | | | gives: 207.80/128.23 | | | | | | | | | | | | | | (283) all_739_1 = all_86_13 207.80/128.23 | | | | | | | | | | | | | | 207.80/128.23 | | | | | | | | | | | | | | GROUND_INST: instantiating (63) with all_86_13, all_795_1, 207.80/128.23 | | | | | | | | | | | | | | all_103_4, int, simplifying with (12), (279) 207.80/128.23 | | | | | | | | | | | | | | gives: 207.80/128.23 | | | | | | | | | | | | | | (284) all_795_1 = all_86_13 207.80/128.23 | | | | | | | | | | | | | | 207.80/128.23 | | | | | | | | | | | | | | BETA: splitting (182) gives: 207.80/128.23 | | | | | | | | | | | | | | 207.80/128.23 | | | | | | | | | | | | | | Case 1: 207.80/128.23 | | | | | | | | | | | | | | | 207.80/128.23 | | | | | | | | | | | | | | | (285) all_789_1 = 0 & permut3(int, all_103_2, all_105_4, 207.80/128.23 | | | | | | | | | | | | | | | 0, all_86_13) = 0 207.80/128.23 | | | | | | | | | | | | | | | 207.80/128.23 | | | | | | | | | | | | | | | ALPHA: (285) implies: 207.80/128.23 | | | | | | | | | | | | | | | (286) permut3(int, all_103_2, all_105_4, 0, all_86_13) = 207.80/128.23 | | | | | | | | | | | | | | | 0 207.80/128.23 | | | | | | | | | | | | | | | 208.04/128.23 | | | | | | | | | | | | | | | BETA: splitting (157) gives: 208.04/128.23 | | | | | | | | | | | | | | | 208.04/128.23 | | | | | | | | | | | | | | | Case 1: 208.04/128.23 | | | | | | | | | | | | | | | | 208.04/128.23 | | | | | | | | | | | | | | | | (287) all_736_0 = all_736_1 & $lesseq(all_86_13, 208.04/128.23 | | | | | | | | | | | | | | | | all_736_1) & $lesseq(0, all_736_1) & $lesseq(0, 208.04/128.23 | | | | | | | | | | | | | | | | all_86_13) & length1(int, all_105_4) = all_736_1 208.04/128.23 | | | | | | | | | | | | | | | | & length1(int, all_103_2) = all_736_1 208.04/128.23 | | | | | | | | | | | | | | | | 208.04/128.23 | | | | | | | | | | | | | | | | ALPHA: (287) implies: 208.04/128.23 | | | | | | | | | | | | | | | | (288) length1(int, all_103_2) = all_736_1 208.04/128.23 | | | | | | | | | | | | | | | | 208.04/128.23 | | | | | | | | | | | | | | | | BETA: splitting (280) gives: 208.04/128.23 | | | | | | | | | | | | | | | | 208.04/128.23 | | | | | | | | | | | | | | | | Case 1: 208.04/128.23 | | | | | | | | | | | | | | | | | 208.04/128.23 | | | | | | | | | | | | | | | | | (289) $lesseq(all_795_1, -1) 208.04/128.23 | | | | | | | | | | | | | | | | | 208.04/128.23 | | | | | | | | | | | | | | | | | REDUCE: (284), (289) imply: 208.04/128.23 | | | | | | | | | | | | | | | | | (290) $lesseq(all_86_13, -1) 208.04/128.23 | | | | | | | | | | | | | | | | | 208.04/128.23 | | | | | | | | | | | | | | | | | COMBINE_INEQS: (40), (51) imply: 208.04/128.23 | | | | | | | | | | | | | | | | | (291) $lesseq(1, $difference(all_86_10, all_86_8)) 208.04/128.23 | | | | | | | | | | | | | | | | | 208.04/128.23 | | | | | | | | | | | | | | | | | COMBINE_INEQS: (38), (291) imply: 208.04/128.23 | | | | | | | | | | | | | | | | | (292) $lesseq(1, $difference(all_86_10, all_86_11)) 208.04/128.23 | | | | | | | | | | | | | | | | | 208.04/128.23 | | | | | | | | | | | | | | | | | COMBINE_INEQS: (53), (292) imply: 208.04/128.23 | | | | | | | | | | | | | | | | | (293) $lesseq(2, $difference(all_86_13, all_86_11)) 208.04/128.23 | | | | | | | | | | | | | | | | | 208.04/128.23 | | | | | | | | | | | | | | | | | COMBINE_INEQS: (13), (290) imply: 208.04/128.23 | | | | | | | | | | | | | | | | | (294) $lesseq(0, -1) 208.04/128.23 | | | | | | | | | | | | | | | | | 208.04/128.23 | | | | | | | | | | | | | | | | | CLOSE: (294) is inconsistent. 208.04/128.23 | | | | | | | | | | | | | | | | | 208.04/128.23 | | | | | | | | | | | | | | | | Case 2: 208.04/128.23 | | | | | | | | | | | | | | | | | 208.04/128.23 | | | | | | | | | | | | | | | | | (295) ~ ($lesseq(all_86_13, all_795_1)) | ( ~ 208.04/128.23 | | | | | | | | | | | | | | | | | (all_795_0 = all_795_1) & length1(int, 208.04/128.23 | | | | | | | | | | | | | | | | | all_103_2) = all_795_0) 208.04/128.23 | | | | | | | | | | | | | | | | | 208.04/128.23 | | | | | | | | | | | | | | | | | BETA: splitting (295) gives: 208.04/128.23 | | | | | | | | | | | | | | | | | 208.04/128.23 | | | | | | | | | | | | | | | | | Case 1: 208.04/128.23 | | | | | | | | | | | | | | | | | | 208.04/128.23 | | | | | | | | | | | | | | | | | | (296) $lesseq(1, $difference(all_86_13, all_795_1)) 208.04/128.23 | | | | | | | | | | | | | | | | | | 208.04/128.23 | | | | | | | | | | | | | | | | | | REDUCE: (284), (296) imply: 208.04/128.23 | | | | | | | | | | | | | | | | | | (297) $lesseq(0, -1) 208.04/128.23 | | | | | | | | | | | | | | | | | | 208.04/128.23 | | | | | | | | | | | | | | | | | | CLOSE: (297) is inconsistent. 208.04/128.23 | | | | | | | | | | | | | | | | | | 208.04/128.23 | | | | | | | | | | | | | | | | | Case 2: 208.04/128.23 | | | | | | | | | | | | | | | | | | 208.04/128.23 | | | | | | | | | | | | | | | | | | (298) ~ (all_795_0 = all_795_1) & length1(int, 208.04/128.23 | | | | | | | | | | | | | | | | | | all_103_2) = all_795_0 208.04/128.23 | | | | | | | | | | | | | | | | | | 208.04/128.23 | | | | | | | | | | | | | | | | | | ALPHA: (298) implies: 208.04/128.23 | | | | | | | | | | | | | | | | | | (299) ~ (all_795_0 = all_795_1) 208.04/128.23 | | | | | | | | | | | | | | | | | | (300) length1(int, all_103_2) = all_795_0 208.04/128.23 | | | | | | | | | | | | | | | | | | 208.04/128.23 | | | | | | | | | | | | | | | | | | REDUCE: (284), (299) imply: 208.04/128.23 | | | | | | | | | | | | | | | | | | (301) ~ (all_795_0 = all_86_13) 208.04/128.23 | | | | | | | | | | | | | | | | | | 208.04/128.23 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (63) with all_86_13, all_795_0, 208.04/128.23 | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (3), (300) gives: 208.04/128.23 | | | | | | | | | | | | | | | | | | (302) all_795_0 = all_86_13 208.04/128.23 | | | | | | | | | | | | | | | | | | 208.04/128.23 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (63) with all_795_0, all_736_1, 208.04/128.23 | | | | | | | | | | | | | | | | | | all_103_2, int, simplifying with (288), (300) 208.04/128.23 | | | | | | | | | | | | | | | | | | gives: 208.04/128.23 | | | | | | | | | | | | | | | | | | (303) all_795_0 = all_736_1 208.04/128.23 | | | | | | | | | | | | | | | | | | 208.04/128.23 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (302), (303) imply: 208.04/128.23 | | | | | | | | | | | | | | | | | | (304) all_736_1 = all_86_13 208.04/128.23 | | | | | | | | | | | | | | | | | | 208.04/128.23 | | | | | | | | | | | | | | | | | | REDUCE: (301), (302) imply: 208.04/128.23 | | | | | | | | | | | | | | | | | | (305) ~ (0 = 0) 208.04/128.23 | | | | | | | | | | | | | | | | | | 208.04/128.23 | | | | | | | | | | | | | | | | | | CLOSE: (305) is inconsistent. 208.04/128.23 | | | | | | | | | | | | | | | | | | 208.04/128.23 | | | | | | | | | | | | | | | | | End of split 208.04/128.23 | | | | | | | | | | | | | | | | | 208.04/128.23 | | | | | | | | | | | | | | | | End of split 208.04/128.23 | | | | | | | | | | | | | | | | 208.04/128.23 | | | | | | | | | | | | | | | Case 2: 208.04/128.23 | | | | | | | | | | | | | | | | 208.04/128.23 | | | | | | | | | | | | | | | | (306) ~ (all_736_1 = 0) & permut3(int, all_103_2, 208.04/128.23 | | | | | | | | | | | | | | | | all_105_4, 0, all_86_13) = all_736_1 208.04/128.23 | | | | | | | | | | | | | | | | 208.04/128.23 | | | | | | | | | | | | | | | | ALPHA: (306) implies: 208.04/128.23 | | | | | | | | | | | | | | | | (307) ~ (all_736_1 = 0) 208.04/128.23 | | | | | | | | | | | | | | | | (308) permut3(int, all_103_2, all_105_4, 0, all_86_13) = 208.04/128.23 | | | | | | | | | | | | | | | | all_736_1 208.04/128.23 | | | | | | | | | | | | | | | | 208.04/128.23 | | | | | | | | | | | | | | | | REF_CLOSE: (26), (286), (307), (308) are inconsistent by 208.04/128.23 | | | | | | | | | | | | | | | | sub-proof #114. 208.04/128.23 | | | | | | | | | | | | | | | | 208.04/128.23 | | | | | | | | | | | | | | | End of split 208.04/128.23 | | | | | | | | | | | | | | | 208.04/128.23 | | | | | | | | | | | | | | Case 2: 208.04/128.23 | | | | | | | | | | | | | | | 208.04/128.23 | | | | | | | | | | | | | | | (309) length1(int, all_103_2) = all_789_1 & ( ~ 208.04/128.23 | | | | | | | | | | | | | | | ($lesseq(all_86_13, all_789_1)) | ~ ($lesseq(0, 208.04/128.23 | | | | | | | | | | | | | | | all_789_1)) | ( ~ (all_789_0 = all_789_1) & 208.04/128.23 | | | | | | | | | | | | | | | length1(int, all_105_4) = all_789_0)) 208.04/128.23 | | | | | | | | | | | | | | | 208.04/128.23 | | | | | | | | | | | | | | | ALPHA: (309) implies: 208.04/128.23 | | | | | | | | | | | | | | | (310) length1(int, all_103_2) = all_789_1 208.04/128.23 | | | | | | | | | | | | | | | (311) ~ ($lesseq(all_86_13, all_789_1)) | ~ 208.04/128.23 | | | | | | | | | | | | | | | ($lesseq(0, all_789_1)) | ( ~ (all_789_0 = 208.04/128.23 | | | | | | | | | | | | | | | all_789_1) & length1(int, all_105_4) = 208.04/128.23 | | | | | | | | | | | | | | | all_789_0) 208.04/128.23 | | | | | | | | | | | | | | | 208.04/128.23 | | | | | | | | | | | | | | | REF_CLOSE: (3), (28), (40), (51), (53), (56), (63), (140), 208.04/128.23 | | | | | | | | | | | | | | | (141), (310), (311) are inconsistent by sub-proof 208.04/128.23 | | | | | | | | | | | | | | | #113. 208.04/128.23 | | | | | | | | | | | | | | | 208.04/128.23 | | | | | | | | | | | | | | End of split 208.04/128.23 | | | | | | | | | | | | | | 208.04/128.23 | | | | | | | | | | | | | End of split 208.04/128.23 | | | | | | | | | | | | | 208.04/128.23 | | | | | | | | | | | | End of split 208.04/128.23 | | | | | | | | | | | | 208.04/128.23 | | | | | | | | | | | End of split 208.04/128.23 | | | | | | | | | | | 208.04/128.23 | | | | | | | | | | End of split 208.04/128.23 | | | | | | | | | | 208.04/128.23 | | | | | | | | | End of split 208.04/128.23 | | | | | | | | | 208.04/128.23 | | | | | | | | Case 2: 208.04/128.23 | | | | | | | | | 208.04/128.23 | | | | | | | | | (312) ~ (all_739_1 = 0) & permut3(int, all_105_4, 208.04/128.23 | | | | | | | | | all_105_2, 0, all_86_13) = all_739_1 208.04/128.23 | | | | | | | | | 208.04/128.23 | | | | | | | | | ALPHA: (312) implies: 208.04/128.23 | | | | | | | | | (313) ~ (all_739_1 = 0) 208.04/128.23 | | | | | | | | | (314) permut3(int, all_105_4, all_105_2, 0, all_86_13) = 208.04/128.23 | | | | | | | | | all_739_1 208.04/128.23 | | | | | | | | | 208.04/128.23 | | | | | | | | | GROUND_INST: instantiating (26) with 0, all_739_1, all_86_13, 208.04/128.23 | | | | | | | | | 0, all_105_2, all_105_4, int, simplifying with 208.04/128.23 | | | | | | | | | (175), (314) gives: 208.04/128.23 | | | | | | | | | (315) all_739_1 = 0 208.04/128.23 | | | | | | | | | 208.04/128.23 | | | | | | | | | REDUCE: (313), (315) imply: 208.04/128.23 | | | | | | | | | (316) ~ (0 = 0) 208.04/128.23 | | | | | | | | | 208.04/128.23 | | | | | | | | | CLOSE: (316) is inconsistent. 208.04/128.23 | | | | | | | | | 208.04/128.23 | | | | | | | | End of split 208.04/128.23 | | | | | | | | 208.04/128.23 | | | | | | | Case 2: 208.04/128.23 | | | | | | | | 208.04/128.23 | | | | | | | | (317) length1(int, all_105_4) = all_765_1 & ( ~ 208.04/128.23 | | | | | | | | ($lesseq(all_86_13, all_765_1)) | ~ ($lesseq(0, 208.04/128.23 | | | | | | | | all_765_1)) | ( ~ (all_765_0 = all_765_1) & 208.04/128.23 | | | | | | | | length1(int, all_105_2) = all_765_0)) 208.04/128.23 | | | | | | | | 208.04/128.23 | | | | | | | | ALPHA: (317) implies: 208.04/128.23 | | | | | | | | (318) length1(int, all_105_4) = all_765_1 208.04/128.23 | | | | | | | | (319) ~ ($lesseq(all_86_13, all_765_1)) | ~ ($lesseq(0, 208.04/128.23 | | | | | | | | all_765_1)) | ( ~ (all_765_0 = all_765_1) & 208.04/128.23 | | | | | | | | length1(int, all_105_2) = all_765_0) 208.04/128.23 | | | | | | | | 208.04/128.23 | | | | | | | | GROUND_INST: instantiating (63) with all_86_13, all_765_1, 208.04/128.23 | | | | | | | | all_105_4, int, simplifying with (28), (318) gives: 208.04/128.23 | | | | | | | | (320) all_765_1 = all_86_13 208.04/128.23 | | | | | | | | 208.04/128.23 | | | | | | | | BETA: splitting (319) gives: 208.04/128.23 | | | | | | | | 208.04/128.23 | | | | | | | | Case 1: 208.04/128.23 | | | | | | | | | 208.04/128.23 | | | | | | | | | (321) $lesseq(all_765_1, -1) 208.04/128.23 | | | | | | | | | 208.04/128.23 | | | | | | | | | REDUCE: (320), (321) imply: 208.04/128.23 | | | | | | | | | (322) $lesseq(all_86_13, -1) 208.04/128.23 | | | | | | | | | 208.04/128.23 | | | | | | | | | COMBINE_INEQS: (40), (51) imply: 208.04/128.23 | | | | | | | | | (323) $lesseq(1, $difference(all_86_10, all_86_8)) 208.04/128.23 | | | | | | | | | 208.04/128.23 | | | | | | | | | COMBINE_INEQS: (38), (323) imply: 208.04/128.23 | | | | | | | | | (324) $lesseq(1, $difference(all_86_10, all_86_11)) 208.04/128.23 | | | | | | | | | 208.04/128.23 | | | | | | | | | COMBINE_INEQS: (53), (324) imply: 208.04/128.23 | | | | | | | | | (325) $lesseq(2, $difference(all_86_13, all_86_11)) 208.04/128.23 | | | | | | | | | 208.04/128.23 | | | | | | | | | COMBINE_INEQS: (13), (322) imply: 208.04/128.23 | | | | | | | | | (326) $lesseq(0, -1) 208.04/128.23 | | | | | | | | | 208.04/128.23 | | | | | | | | | CLOSE: (326) is inconsistent. 208.04/128.23 | | | | | | | | | 208.04/128.23 | | | | | | | | Case 2: 208.04/128.23 | | | | | | | | | 208.04/128.23 | | | | | | | | | (327) ~ ($lesseq(all_86_13, all_765_1)) | ( ~ (all_765_0 = 208.04/128.23 | | | | | | | | | all_765_1) & length1(int, all_105_2) = all_765_0) 208.04/128.23 | | | | | | | | | 208.04/128.23 | | | | | | | | | BETA: splitting (327) gives: 208.04/128.23 | | | | | | | | | 208.04/128.23 | | | | | | | | | Case 1: 208.04/128.23 | | | | | | | | | | 208.04/128.23 | | | | | | | | | | (328) $lesseq(1, $difference(all_86_13, all_765_1)) 208.04/128.23 | | | | | | | | | | 208.04/128.23 | | | | | | | | | | REDUCE: (320), (328) imply: 208.04/128.23 | | | | | | | | | | (329) $lesseq(0, -1) 208.04/128.23 | | | | | | | | | | 208.04/128.23 | | | | | | | | | | CLOSE: (329) is inconsistent. 208.04/128.23 | | | | | | | | | | 208.04/128.23 | | | | | | | | | Case 2: 208.04/128.23 | | | | | | | | | | 208.04/128.23 | | | | | | | | | | (330) ~ (all_765_0 = all_765_1) & length1(int, 208.04/128.23 | | | | | | | | | | all_105_2) = all_765_0 208.04/128.23 | | | | | | | | | | 208.04/128.23 | | | | | | | | | | ALPHA: (330) implies: 208.04/128.23 | | | | | | | | | | (331) ~ (all_765_0 = all_765_1) 208.04/128.23 | | | | | | | | | | (332) length1(int, all_105_2) = all_765_0 208.04/128.23 | | | | | | | | | | 208.04/128.23 | | | | | | | | | | REDUCE: (320), (331) imply: 208.04/128.23 | | | | | | | | | | (333) ~ (all_765_0 = all_86_13) 208.04/128.23 | | | | | | | | | | 208.04/128.23 | | | | | | | | | | GROUND_INST: instantiating (63) with all_86_13, all_765_0, 208.04/128.23 | | | | | | | | | | all_105_2, int, simplifying with (7), (332) gives: 208.04/128.23 | | | | | | | | | | (334) all_765_0 = all_86_13 208.04/128.23 | | | | | | | | | | 208.04/128.23 | | | | | | | | | | REDUCE: (333), (334) imply: 208.04/128.23 | | | | | | | | | | (335) ~ (0 = 0) 208.04/128.23 | | | | | | | | | | 208.04/128.23 | | | | | | | | | | CLOSE: (335) is inconsistent. 208.04/128.23 | | | | | | | | | | 208.04/128.23 | | | | | | | | | End of split 208.04/128.23 | | | | | | | | | 208.04/128.23 | | | | | | | | End of split 208.04/128.23 | | | | | | | | 208.04/128.23 | | | | | | | End of split 208.04/128.23 | | | | | | | 208.04/128.23 | | | | | | End of split 208.04/128.23 | | | | | | 208.04/128.23 | | | | | End of split 208.04/128.23 | | | | | 208.04/128.23 | | | | End of split 208.04/128.23 | | | | 208.04/128.23 | | | End of split 208.04/128.23 | | | 208.04/128.23 | | End of split 208.04/128.23 | | 208.04/128.23 | End of split 208.04/128.23 | 208.04/128.23 End of proof 208.04/128.23 208.04/128.23 Sub-proof #113 shows that the following formulas are inconsistent: 208.04/128.23 ---------------------------------------------------------------- 208.04/128.23 (1) length1(int, all_103_2) = all_86_13 208.04/128.23 (2) length1(int, all_103_2) = all_789_1 208.04/128.23 (3) $lesseq(all_133_2, all_86_8) 208.04/128.23 (4) length1(int, all_105_4) = all_86_13 208.04/128.23 (5) $lesseq(all_86_11, all_133_2) 208.04/128.23 (6) $lesseq(all_86_7, all_86_10) 208.04/128.23 (7) $lesseq(1, $difference(all_86_7, all_86_8)) 208.04/128.23 (8) $lesseq(1, $difference(all_86_13, all_86_10)) 208.04/128.23 (9) $lesseq(0, all_86_11) 208.04/128.23 (10) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 208.04/128.23 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 208.04/128.23 (11) ~ ($lesseq(all_86_13, all_789_1)) | ~ ($lesseq(0, all_789_1)) | ( ~ 208.04/128.23 (all_789_0 = all_789_1) & length1(int, all_105_4) = all_789_0) 208.04/128.23 208.04/128.23 Begin of proof 208.04/128.23 | 208.04/128.23 | GROUND_INST: instantiating (10) with all_86_13, all_789_1, all_103_2, int, 208.04/128.23 | simplifying with (1), (2) gives: 208.04/128.23 | (12) all_789_1 = all_86_13 208.04/128.23 | 208.04/128.23 | BETA: splitting (11) gives: 208.04/128.23 | 208.04/128.23 | Case 1: 208.04/128.23 | | 208.04/128.23 | | (13) $lesseq(all_789_1, -1) 208.04/128.23 | | 208.04/128.23 | | REDUCE: (12), (13) imply: 208.04/128.23 | | (14) $lesseq(all_86_13, -1) 208.04/128.23 | | 208.04/128.23 | | COMBINE_INEQS: (3), (5) imply: 208.04/128.23 | | (15) $lesseq(all_86_11, all_86_8) 208.04/128.23 | | 208.04/128.23 | | COMBINE_INEQS: (6), (7) imply: 208.04/128.23 | | (16) $lesseq(1, $difference(all_86_10, all_86_8)) 208.04/128.23 | | 208.04/128.23 | | COMBINE_INEQS: (15), (16) imply: 208.04/128.23 | | (17) $lesseq(1, $difference(all_86_10, all_86_11)) 208.04/128.23 | | 208.04/128.23 | | COMBINE_INEQS: (8), (17) imply: 208.04/128.23 | | (18) $lesseq(2, $difference(all_86_13, all_86_11)) 208.04/128.23 | | 208.04/128.23 | | COMBINE_INEQS: (9), (18) imply: 208.04/128.23 | | (19) $lesseq(2, all_86_13) 208.04/128.23 | | 208.04/128.23 | | COMBINE_INEQS: (14), (19) imply: 208.04/128.23 | | (20) $lesseq(0, -1) 208.04/128.23 | | 208.04/128.23 | | CLOSE: (20) is inconsistent. 208.04/128.23 | | 208.04/128.23 | Case 2: 208.04/128.23 | | 208.04/128.23 | | (21) ~ ($lesseq(all_86_13, all_789_1)) | ( ~ (all_789_0 = all_789_1) & 208.04/128.23 | | length1(int, all_105_4) = all_789_0) 208.04/128.23 | | 208.04/128.23 | | BETA: splitting (21) gives: 208.04/128.23 | | 208.04/128.23 | | Case 1: 208.04/128.23 | | | 208.04/128.23 | | | (22) $lesseq(1, $difference(all_86_13, all_789_1)) 208.04/128.23 | | | 208.04/128.23 | | | REDUCE: (12), (22) imply: 208.04/128.23 | | | (23) $lesseq(0, -1) 208.04/128.23 | | | 208.04/128.23 | | | CLOSE: (23) is inconsistent. 208.04/128.23 | | | 208.04/128.23 | | Case 2: 208.04/128.23 | | | 208.04/128.23 | | | (24) ~ (all_789_0 = all_789_1) & length1(int, all_105_4) = all_789_0 208.04/128.23 | | | 208.04/128.23 | | | ALPHA: (24) implies: 208.04/128.23 | | | (25) ~ (all_789_0 = all_789_1) 208.04/128.23 | | | (26) length1(int, all_105_4) = all_789_0 208.04/128.23 | | | 208.04/128.23 | | | REDUCE: (12), (25) imply: 208.04/128.23 | | | (27) ~ (all_789_0 = all_86_13) 208.04/128.23 | | | 208.04/128.23 | | | GROUND_INST: instantiating (10) with all_86_13, all_789_0, all_105_4, int, 208.04/128.23 | | | simplifying with (4), (26) gives: 208.04/128.23 | | | (28) all_789_0 = all_86_13 208.04/128.23 | | | 208.04/128.23 | | | REDUCE: (27), (28) imply: 208.04/128.23 | | | (29) ~ (0 = 0) 208.04/128.23 | | | 208.04/128.23 | | | CLOSE: (29) is inconsistent. 208.04/128.23 | | | 208.04/128.23 | | End of split 208.04/128.23 | | 208.04/128.23 | End of split 208.04/128.23 | 208.04/128.23 End of proof 208.04/128.23 208.04/128.23 Sub-proof #114 shows that the following formulas are inconsistent: 208.04/128.23 ---------------------------------------------------------------- 208.04/128.23 (1) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.04/128.23 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ (permut3(v6, v5, 208.04/128.23 v4, v3, v2) = v1) | ~ (permut3(v6, v5, v4, v3, v2) = v0)) 208.04/128.23 (2) permut3(int, all_103_2, all_105_4, 0, all_86_13) = all_736_1 208.04/128.23 (3) permut3(int, all_103_2, all_105_4, 0, all_86_13) = 0 208.04/128.23 (4) ~ (all_736_1 = 0) 208.04/128.24 208.04/128.24 Begin of proof 208.04/128.24 | 208.04/128.24 | GROUND_INST: instantiating (1) with 0, all_736_1, all_86_13, 0, all_105_4, 208.04/128.24 | all_103_2, int, simplifying with (2), (3) gives: 208.04/128.24 | (5) all_736_1 = 0 208.04/128.24 | 208.04/128.24 | REDUCE: (4), (5) imply: 208.04/128.24 | (6) ~ (0 = 0) 208.04/128.24 | 208.04/128.24 | CLOSE: (6) is inconsistent. 208.04/128.24 | 208.04/128.24 End of proof 208.04/128.24 208.04/128.24 Sub-proof #115 shows that the following formulas are inconsistent: 208.04/128.24 ---------------------------------------------------------------- 208.04/128.24 (1) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ (tb2t1(v2) 208.04/128.24 = v1) | ~ (tb2t1(v2) = v0)) 208.04/128.24 (2) ! [v0: $int] : ! [v1: $int] : ( ~ ($lesseq(43, v1)) | ~ ($lesseq(v0, 208.04/128.24 all_86_8)) | ~ ($lesseq(all_86_11, v0)) | ~ (get3(all_86_6, v0) = 208.04/128.24 v1)) 208.04/128.24 (3) in_map_int_int(all_86_6) 208.04/128.24 (4) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.04/128.24 $int] : ! [v5: $int] : ! [v6: $int] : ( ~ ($lesseq(0, v4)) | ~ 208.04/128.24 ($lesseq(0, v3)) | ~ (map_eq_sub1(v0, v5, v6, v3, v4) = 0) | ~ 208.04/128.24 (elts(v0, v2) = v6) | ~ (elts(v0, v1) = v5) | ~ in_ty(v0) | ? [v7: 208.04/128.24 $int] : ? [v8: $int] : ((v7 = 0 & array_eq_sub1(v0, v1, v2, v3, v4) 208.04/128.24 = 0) | (length1(v0, v1) = v7 & ( ~ ($lesseq(v4, v7)) | ~ 208.04/128.24 ($lesseq(v3, v7)) | ( ~ (v8 = v7) & length1(v0, v2) = v8))))) 208.04/128.24 (5) length1(int, all_105_2) = all_86_13 208.04/128.24 (6) elts(int, all_103_4) = all_103_3 208.04/128.24 (7) t2tb2(all_86_3) = all_105_4 208.04/128.24 (8) t2tb(all_86_2) = all_105_1 208.04/128.24 (9) in_ty(int) 208.04/128.24 (10) length1(int, all_103_4) = all_86_13 208.04/128.24 (11) $lesseq(2, all_86_13) 208.04/128.24 (12) ( ~ (all_133_0 = 42) & $lesseq(1, $difference(all_86_7, all_133_2)) & 208.04/128.24 $lesseq(1, $difference(all_133_2, all_86_8)) & tb2t1(all_133_1) = 208.04/128.24 all_133_0 & get4(int, all_133_3, all_133_2) = all_133_1 & 208.04/128.24 in_uni(all_133_1)) | ($lesseq(all_133_0, 41) & $lesseq(all_133_2, 208.04/128.24 all_86_10) & $lesseq(all_86_7, all_133_2) & tb2t1(all_133_1) = 208.04/128.24 all_133_0 & get4(int, all_133_3, all_133_2) = all_133_1 & 208.04/128.24 in_uni(all_133_1)) | ($lesseq(43, all_133_0) & $lesseq(all_133_2, 208.04/128.24 all_86_8) & $lesseq(all_86_11, all_133_2) & tb2t1(all_133_1) = 208.04/128.24 all_133_0 & get4(int, all_133_3, all_133_2) = all_133_1 & 208.04/128.24 in_uni(all_133_1)) 208.04/128.24 (13) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.04/128.24 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 208.04/128.24 (permut2(v0, v5, v6, v3, v4) = v7) | ~ (elts(v0, v2) = v6) | ~ 208.04/128.24 (elts(v0, v1) = v5) | ~ in_ty(v0) | ? [v8: $int] : ? [v9: $int] : 208.04/128.24 ((v9 = v8 & v7 = 0 & $lesseq(v4, v8) & $lesseq(v3, v8) & $lesseq(0, 208.04/128.24 v4) & $lesseq(0, v3) & length1(v0, v2) = v8 & length1(v0, v1) = 208.04/128.24 v8) | ( ~ (v8 = 0) & permut3(v0, v1, v2, v3, v4) = v8))) 208.04/128.24 (14) all_125_0 = all_105_4 208.04/128.24 (15) $lesseq(-1, all_86_8) 208.04/128.24 (16) $lesseq(1, $difference(all_86_13, all_86_7)) 208.04/128.24 (17) ! [v0: $int] : ! [v1: $int] : (v1 = 42 | ~ ($lesseq(1, 208.04/128.24 $difference(all_86_7, v0))) | ~ ($lesseq(1, $difference(v0, 208.04/128.24 all_86_8))) | ~ (get3(all_86_6, v0) = v1)) 208.04/128.24 (18) map_eq_sub1(int, all_103_3, all_103_1, $sum(all_86_10, 1), all_86_13) = 208.04/128.24 0 208.04/128.24 (19) t2tb(all_86_6) = all_103_1 208.04/128.24 (20) map_eq_sub1(int, all_103_1, all_105_3, $sum(all_86_8, 1), all_86_13) = 0 208.04/128.24 (21) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.04/128.24 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ (permut3(v6, v5, 208.04/128.24 v4, v3, v2) = v1) | ~ (permut3(v6, v5, v4, v3, v2) = v0)) 208.04/128.24 (22) permut2(int, all_103_3, all_105_3, all_86_11, $sum(all_86_10, 1)) = 0 208.04/128.24 (23) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 208.04/128.24 | ~ (elts(v3, v2) = v1) | ~ (elts(v3, v2) = v0)) 208.04/128.24 (24) length1(int, all_105_4) = all_86_13 208.04/128.24 (25) in_array_int(all_86_3) 208.04/128.24 (26) elts(int, all_105_4) = all_105_3 208.04/128.24 (27) map_eq_sub1(int, all_105_3, all_105_1, 0, all_86_7) = 0 208.04/128.24 (28) tb2t(all_105_1) = all_86_2 208.04/128.24 (29) permut2(int, all_103_1, all_105_3, all_86_11, $sum(all_86_8, 1)) = 0 208.04/128.24 (30) elts(int, all_105_2) = all_105_1 208.04/128.24 (31) map_eq_sub1(int, all_103_3, all_103_1, 0, all_86_11) = 0 208.04/128.24 (32) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.04/128.24 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 208.04/128.24 ($lesseq(1, $difference(v4, v5))) | ~ ($lesseq(v3, v5)) | ~ 208.04/128.24 (permut2(v0, v1, v2, v3, v4) = 0) | ~ (t2tb1(v5) = v6) | ~ (get(v0, 208.04/128.24 int, v2, v6) = v7) | ~ in_ty(v0) | ? [v8: $int] : ? [v9: $int] 208.04/128.24 : ($lesseq(1, $difference(v4, v8)) & $lesseq(v3, v8) & t2tb1(v8) = v9 208.04/128.24 & get(v0, int, v1, v9) = v7 & in_uni(v9) & in_uni(v7))) 208.04/128.24 (33) t2tb2(all_86_1) = all_105_2 208.04/128.24 (34) ~ ($difference(all_86_10, all_86_13) = -1) | ~ (all_86_11 = 0) 208.04/128.24 (35) $lesseq(all_86_11, all_86_8) 208.04/128.24 (36) $lesseq(all_86_7, all_86_10) 208.04/128.24 (37) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.04/128.24 $int] : ! [v5: $int] : ( ~ (elts(v0, v1) = v3) | ~ (t2tb1(v2) = v4) 208.04/128.24 | ~ (get(v0, int, v3, v4) = v5) | ~ in_ty(v0) | (get4(v0, v1, v2) = 208.04/128.24 v5 & in_uni(v5))) 208.04/128.24 (38) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.04/128.24 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 208.04/128.24 ($lesseq(1, $difference(v3, v4))) | ~ ($lesseq(v2, v4)) | ~ 208.04/128.24 (permut2(int, v5, v6, v2, v3) = 0) | ~ (t2tb(v1) = v6) | ~ (t2tb(v0) 208.04/128.24 = v5) | ~ (get3(v1, v4) = v7) | ~ in_map_int_int(v0) | ? [v8: 208.04/128.24 $int] : ($lesseq(1, $difference(v3, v8)) & $lesseq(v2, v8) & 208.04/128.24 get3(v0, v8) = v7)) 208.04/128.24 (39) $lesseq(0, all_86_7) 208.04/128.24 (40) permut2(int, all_105_3, all_105_1, all_86_7, $sum(all_86_10, 1)) = 0 208.04/128.24 (41) permut2(int, all_105_3, all_105_1, 0, all_86_13) = 0 208.04/128.24 (42) in_array_int(all_86_1) 208.04/128.24 (43) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.04/128.24 $int] : ! [v5: $int] : ! [v6: $int] : ( ~ ($lesseq(0, v4)) | ~ 208.04/128.24 ($lesseq(0, v3)) | ~ (permut2(v0, v5, v6, v3, v4) = 0) | ~ (elts(v0, 208.04/128.24 v2) = v6) | ~ (elts(v0, v1) = v5) | ~ in_ty(v0) | ? [v7: $int] 208.04/128.24 : ? [v8: $int] : ((v7 = 0 & permut3(v0, v1, v2, v3, v4) = 0) | 208.04/128.24 (length1(v0, v1) = v7 & ( ~ ($lesseq(v4, v7)) | ~ ($lesseq(v3, v7)) 208.04/128.24 | ( ~ (v8 = v7) & length1(v0, v2) = v8))))) 208.04/128.24 (44) $lesseq(1, $difference(all_86_7, all_86_8)) 208.04/128.24 (45) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.04/128.24 $int] : ! [v5: $int] : ! [v6: $int] : ( ~ ($lesseq(1, 208.04/128.24 $difference(v4, v5))) | ~ ($lesseq(v3, v5)) | ~ (map_eq_sub1(v0, 208.04/128.24 v1, v2, v3, v4) = 0) | ~ (t2tb1(v5) = v6) | ~ in_ty(v0) | ? 208.04/128.24 [v7: $int] : (get(v0, int, v2, v6) = v7 & get(v0, int, v1, v6) = v7 & 208.04/128.24 in_uni(v7))) 208.04/128.24 (46) $lesseq(1, $difference(all_86_13, all_86_10)) 208.04/128.24 (47) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.04/128.24 $int] : ! [v5: $int] : (v5 = 0 | ~ (permut_sub2(v0, v1, v2, v3, v4) 208.04/128.24 = v5) | ~ in_ty(v0) | ? [v6: $int] : ? [v7: $int] : ? [v8: $int] 208.04/128.24 : ? [v9: $int] : (( ~ (v9 = 0) & map_eq_sub1(v0, v6, v7, v4, v8) = v9 208.04/128.24 & length1(v0, v1) = v8 & elts(v0, v2) = v7 & elts(v0, v1) = v6 & 208.04/128.24 in_uni(v7) & in_uni(v6)) | ( ~ (v8 = 0) & map_eq_sub1(v0, v6, v7, 208.04/128.24 0, v3) = v8 & elts(v0, v2) = v7 & elts(v0, v1) = v6 & in_uni(v7) 208.04/128.24 & in_uni(v6)) | ( ~ (v6 = 0) & permut3(v0, v1, v2, v3, v4) = v6))) 208.04/128.24 (48) in_map_int_int(all_86_4) 208.04/128.24 (49) $lesseq(0, all_86_11) 208.04/128.24 (50) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ( ~ 208.04/128.24 (t2tb2(v0) = v2) | ~ (get4(int, v2, v1) = v3) | ~ in_array_int(v0) | 208.04/128.24 ? [v4: $int] : ? [v5: $int] : ? [v6: $int] : (tb2t(v4) = v5 & 208.04/128.24 tb2t1(v3) = v6 & get3(v5, v1) = v6 & elts(int, v2) = v4 & 208.04/128.24 in_map_int_int(v5) & in_uni(v4))) 208.04/128.24 (51) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ (tb2t(v2) 208.04/128.24 = v1) | ~ (tb2t(v2) = v0)) 208.04/128.24 (52) all_133_3 = all_105_2 208.04/128.24 (53) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.04/128.24 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 208.04/128.24 ($lesseq(1, $difference(v3, v6))) | ~ ($lesseq(v2, v6)) | ~ 208.04/128.24 (map_eq_sub1(int, v4, v5, v2, v3) = 0) | ~ (t2tb(v1) = v5) | ~ 208.04/128.24 (t2tb(v0) = v4) | ~ (get3(v1, v6) = v7) | ~ in_map_int_int(v0) | 208.04/128.24 get3(v0, v6) = v7) 208.04/128.24 (54) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 208.04/128.24 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 208.04/128.24 (55) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ( ~ 208.04/128.24 (get4(v0, v1, v2) = v3) | ~ in_ty(v0) | ? [v4: $int] : ? [v5: $int] 208.04/128.24 : (elts(v0, v1) = v4 & t2tb1(v2) = v5 & get(v0, int, v4, v5) = v3 & 208.04/128.24 in_uni(v5) & in_uni(v4) & in_uni(v3))) 208.04/128.24 (56) $lesseq(0, all_86_10) 208.04/128.24 (57) map_eq_sub1(int, all_103_1, all_105_3, 0, all_86_13) = 0 208.04/128.24 (58) ! [v0: $int] : ! [v1: $int] : ( ~ (tb2t1(v0) = v1) | ~ in_uni(v0) | 208.04/128.24 t2tb1(v1) = v0) 208.04/128.24 (59) map_eq_sub1(int, all_105_3, all_105_1, $sum(all_86_10, 1), all_86_13) = 208.04/128.24 0 208.04/128.24 (60) t2tb(all_86_4) = all_105_3 208.04/128.24 (61) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.04/128.24 $int] : ! [v5: $int] : ( ~ (permut3(v0, v1, v2, v3, v4) = v5) | ~ 208.04/128.24 in_ty(v0) | ? [v6: $int] : ? [v7: $int] : ? [v8: $int] : ? [v9: 208.04/128.24 $int] : ? [v10: $int] : ((v10 = 0 & v9 = 0 & v5 = 0 & 208.04/128.24 map_eq_sub1(v0, v6, v7, v4, v8) = 0 & map_eq_sub1(v0, v6, v7, 0, 208.04/128.24 v3) = 0 & length1(v0, v1) = v8 & elts(v0, v2) = v7 & elts(v0, 208.04/128.24 v1) = v6 & in_uni(v7) & in_uni(v6)) | ( ~ (v6 = 0) & 208.04/128.24 permut_sub2(v0, v1, v2, v3, v4) = v6))) 208.04/128.24 (62) ! [v0: $int] : ! [v1: $int] : ( ~ ($lesseq(v0, all_86_10)) | ~ 208.04/128.24 ($lesseq(all_86_7, v0)) | ~ (get4(int, all_125_0, v0) = v1) | ? [v2: 208.04/128.24 $int] : ($lesseq(42, v2) & tb2t1(v1) = v2)) 208.04/128.24 208.04/128.24 Begin of proof 208.04/128.24 | 208.04/128.24 | BETA: splitting (12) gives: 208.04/128.24 | 208.04/128.24 | Case 1: 208.04/128.24 | | 208.04/128.24 | | (63) ~ (all_133_0 = 42) & $lesseq(1, $difference(all_86_7, all_133_2)) & 208.04/128.24 | | $lesseq(1, $difference(all_133_2, all_86_8)) & tb2t1(all_133_1) = 208.04/128.24 | | all_133_0 & get4(int, all_133_3, all_133_2) = all_133_1 & 208.04/128.24 | | in_uni(all_133_1) 208.04/128.24 | | 208.04/128.24 | | ALPHA: (63) implies: 208.04/128.24 | | (64) ~ (all_133_0 = 42) 208.04/128.24 | | (65) $lesseq(1, $difference(all_133_2, all_86_8)) 208.04/128.24 | | (66) $lesseq(1, $difference(all_86_7, all_133_2)) 208.04/128.24 | | (67) in_uni(all_133_1) 208.04/128.24 | | (68) get4(int, all_133_3, all_133_2) = all_133_1 208.04/128.24 | | (69) tb2t1(all_133_1) = all_133_0 208.04/128.24 | | 208.04/128.24 | | COMBINE_INEQS: (65), (66) imply: 208.04/128.24 | | (70) $lesseq(2, $difference(all_86_7, all_86_8)) 208.04/128.24 | | 208.04/128.24 | | COMBINE_INEQS: (36), (70) imply: 208.04/128.24 | | (71) $lesseq(2, $difference(all_86_10, all_86_8)) 208.04/128.24 | | 208.04/128.24 | | COMBINE_INEQS: (15), (71) imply: 208.04/128.24 | | (72) $lesseq(1, all_86_10) 208.04/128.24 | | 208.04/128.24 | | REDUCE: (52), (68) imply: 208.04/128.24 | | (73) get4(int, all_105_2, all_133_2) = all_133_1 208.04/128.24 | | 208.04/128.24 | | REF_CLOSE: (1), (3), (4), (6), (8), (9), (10), (13), (15), (16), (17), (18), 208.04/128.24 | | (19), (20), (21), (22), (23), (24), (26), (27), (28), (30), (31), 208.04/128.24 | | (33), (34), (35), (36), (42), (43), (45), (46), (47), (48), (49), 208.04/128.24 | | (50), (51), (53), (54), (55), (57), (58), (59), (60), (61), (64), 208.04/128.24 | | (65), (66), (67), (69), (72), (73) are inconsistent by sub-proof 208.04/128.24 | | #127. 208.04/128.24 | | 208.04/128.24 | Case 2: 208.04/128.24 | | 208.04/128.24 | | (74) ($lesseq(all_133_0, 41) & $lesseq(all_133_2, all_86_10) & 208.04/128.24 | | $lesseq(all_86_7, all_133_2) & tb2t1(all_133_1) = all_133_0 & 208.04/128.24 | | get4(int, all_133_3, all_133_2) = all_133_1 & in_uni(all_133_1)) | 208.04/128.24 | | ($lesseq(43, all_133_0) & $lesseq(all_133_2, all_86_8) & 208.04/128.24 | | $lesseq(all_86_11, all_133_2) & tb2t1(all_133_1) = all_133_0 & 208.04/128.24 | | get4(int, all_133_3, all_133_2) = all_133_1 & in_uni(all_133_1)) 208.04/128.24 | | 208.04/128.24 | | BETA: splitting (74) gives: 208.04/128.24 | | 208.04/128.24 | | Case 1: 208.04/128.24 | | | 208.04/128.24 | | | (75) $lesseq(all_133_0, 41) & $lesseq(all_133_2, all_86_10) & 208.04/128.24 | | | $lesseq(all_86_7, all_133_2) & tb2t1(all_133_1) = all_133_0 & 208.04/128.24 | | | get4(int, all_133_3, all_133_2) = all_133_1 & in_uni(all_133_1) 208.04/128.24 | | | 208.04/128.24 | | | ALPHA: (75) implies: 208.04/128.24 | | | (76) $lesseq(all_86_7, all_133_2) 208.04/128.24 | | | (77) $lesseq(all_133_2, all_86_10) 208.04/128.24 | | | (78) $lesseq(all_133_0, 41) 208.04/128.24 | | | (79) get4(int, all_133_3, all_133_2) = all_133_1 208.04/128.24 | | | (80) tb2t1(all_133_1) = all_133_0 208.04/128.24 | | | 208.04/128.24 | | | REDUCE: (52), (79) imply: 208.04/128.24 | | | (81) get4(int, all_105_2, all_133_2) = all_133_1 208.04/128.24 | | | 208.04/128.24 | | | REF_CLOSE: (1), (6), (7), (8), (9), (14), (22), (23), (25), (26), (28), 208.04/128.24 | | | (30), (32), (33), (37), (38), (40), (42), (43), (48), (49), 208.04/128.24 | | | (50), (51), (55), (56), (60), (62), (76), (77), (78), (80), 208.04/128.24 | | | (81) are inconsistent by sub-proof #126. 208.04/128.24 | | | 208.04/128.24 | | Case 2: 208.04/128.24 | | | 208.04/128.24 | | | (82) $lesseq(43, all_133_0) & $lesseq(all_133_2, all_86_8) & 208.04/128.24 | | | $lesseq(all_86_11, all_133_2) & tb2t1(all_133_1) = all_133_0 & 208.04/128.24 | | | get4(int, all_133_3, all_133_2) = all_133_1 & in_uni(all_133_1) 208.04/128.24 | | | 208.04/128.24 | | | ALPHA: (82) implies: 208.04/128.24 | | | (83) $lesseq(all_86_11, all_133_2) 208.04/128.24 | | | (84) $lesseq(all_133_2, all_86_8) 208.04/128.24 | | | (85) $lesseq(43, all_133_0) 208.04/128.24 | | | (86) get4(int, all_133_3, all_133_2) = all_133_1 208.04/128.24 | | | (87) tb2t1(all_133_1) = all_133_0 208.04/128.24 | | | 208.04/128.24 | | | REDUCE: (52), (86) imply: 208.04/128.24 | | | (88) get4(int, all_105_2, all_133_2) = all_133_1 208.04/128.24 | | | 208.04/128.24 | | | REF_CLOSE: (1), (2), (3), (5), (6), (8), (9), (10), (11), (13), (16), 208.04/128.24 | | | (19), (21), (22), (23), (24), (26), (27), (28), (29), (30), 208.04/128.24 | | | (32), (33), (34), (36), (38), (40), (41), (42), (43), (44), 208.04/128.24 | | | (45), (46), (48), (49), (50), (51), (53), (54), (55), (56), 208.04/128.24 | | | (59), (60), (83), (84), (85), (87), (88) are inconsistent by 208.04/128.24 | | | sub-proof #116. 208.04/128.24 | | | 208.04/128.24 | | End of split 208.04/128.24 | | 208.04/128.24 | End of split 208.04/128.24 | 208.04/128.24 End of proof 208.04/128.24 208.04/128.24 Sub-proof #116 shows that the following formulas are inconsistent: 208.04/128.24 ---------------------------------------------------------------- 208.04/128.24 (1) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ (tb2t1(v2) 208.04/128.24 = v1) | ~ (tb2t1(v2) = v0)) 208.04/128.24 (2) ! [v0: $int] : ! [v1: $int] : ( ~ ($lesseq(43, v1)) | ~ ($lesseq(v0, 208.04/128.24 all_86_8)) | ~ ($lesseq(all_86_11, v0)) | ~ (get3(all_86_6, v0) = 208.04/128.24 v1)) 208.04/128.24 (3) in_map_int_int(all_86_6) 208.04/128.24 (4) length1(int, all_105_2) = all_86_13 208.04/128.24 (5) elts(int, all_103_4) = all_103_3 208.04/128.24 (6) t2tb(all_86_2) = all_105_1 208.04/128.24 (7) in_ty(int) 208.04/128.24 (8) length1(int, all_103_4) = all_86_13 208.04/128.24 (9) $lesseq(2, all_86_13) 208.04/128.24 (10) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.04/128.24 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 208.04/128.24 (permut2(v0, v5, v6, v3, v4) = v7) | ~ (elts(v0, v2) = v6) | ~ 208.04/128.24 (elts(v0, v1) = v5) | ~ in_ty(v0) | ? [v8: $int] : ? [v9: $int] : 208.04/128.24 ((v9 = v8 & v7 = 0 & $lesseq(v4, v8) & $lesseq(v3, v8) & $lesseq(0, 208.04/128.24 v4) & $lesseq(0, v3) & length1(v0, v2) = v8 & length1(v0, v1) = 208.04/128.24 v8) | ( ~ (v8 = 0) & permut3(v0, v1, v2, v3, v4) = v8))) 208.04/128.24 (11) $lesseq(1, $difference(all_86_13, all_86_7)) 208.04/128.24 (12) t2tb(all_86_6) = all_103_1 208.04/128.24 (13) $lesseq(all_133_2, all_86_8) 208.04/128.24 (14) tb2t1(all_133_1) = all_133_0 208.04/128.24 (15) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.04/128.24 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ (permut3(v6, v5, 208.04/128.24 v4, v3, v2) = v1) | ~ (permut3(v6, v5, v4, v3, v2) = v0)) 208.04/128.25 (16) permut2(int, all_103_3, all_105_3, all_86_11, $sum(all_86_10, 1)) = 0 208.04/128.25 (17) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 208.04/128.25 | ~ (elts(v3, v2) = v1) | ~ (elts(v3, v2) = v0)) 208.04/128.25 (18) length1(int, all_105_4) = all_86_13 208.04/128.25 (19) elts(int, all_105_4) = all_105_3 208.04/128.25 (20) map_eq_sub1(int, all_105_3, all_105_1, 0, all_86_7) = 0 208.04/128.25 (21) get4(int, all_105_2, all_133_2) = all_133_1 208.04/128.25 (22) tb2t(all_105_1) = all_86_2 208.04/128.25 (23) permut2(int, all_103_1, all_105_3, all_86_11, $sum(all_86_8, 1)) = 0 208.04/128.25 (24) elts(int, all_105_2) = all_105_1 208.04/128.25 (25) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.04/128.25 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 208.04/128.25 ($lesseq(1, $difference(v4, v5))) | ~ ($lesseq(v3, v5)) | ~ 208.04/128.25 (permut2(v0, v1, v2, v3, v4) = 0) | ~ (t2tb1(v5) = v6) | ~ (get(v0, 208.04/128.25 int, v2, v6) = v7) | ~ in_ty(v0) | ? [v8: $int] : ? [v9: $int] 208.04/128.25 : ($lesseq(1, $difference(v4, v8)) & $lesseq(v3, v8) & t2tb1(v8) = v9 208.04/128.25 & get(v0, int, v1, v9) = v7 & in_uni(v9) & in_uni(v7))) 208.04/128.25 (26) t2tb2(all_86_1) = all_105_2 208.04/128.25 (27) $lesseq(all_86_11, all_133_2) 208.04/128.25 (28) ~ ($difference(all_86_10, all_86_13) = -1) | ~ (all_86_11 = 0) 208.04/128.25 (29) $lesseq(all_86_7, all_86_10) 208.04/128.25 (30) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.04/128.25 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 208.04/128.25 ($lesseq(1, $difference(v3, v4))) | ~ ($lesseq(v2, v4)) | ~ 208.04/128.25 (permut2(int, v5, v6, v2, v3) = 0) | ~ (t2tb(v1) = v6) | ~ (t2tb(v0) 208.04/128.25 = v5) | ~ (get3(v1, v4) = v7) | ~ in_map_int_int(v0) | ? [v8: 208.04/128.25 $int] : ($lesseq(1, $difference(v3, v8)) & $lesseq(v2, v8) & 208.04/128.25 get3(v0, v8) = v7)) 208.04/128.25 (31) permut2(int, all_105_3, all_105_1, all_86_7, $sum(all_86_10, 1)) = 0 208.04/128.25 (32) permut2(int, all_105_3, all_105_1, 0, all_86_13) = 0 208.04/128.25 (33) in_array_int(all_86_1) 208.04/128.25 (34) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.04/128.25 $int] : ! [v5: $int] : ! [v6: $int] : ( ~ ($lesseq(0, v4)) | ~ 208.04/128.25 ($lesseq(0, v3)) | ~ (permut2(v0, v5, v6, v3, v4) = 0) | ~ (elts(v0, 208.04/128.25 v2) = v6) | ~ (elts(v0, v1) = v5) | ~ in_ty(v0) | ? [v7: $int] 208.04/128.25 : ? [v8: $int] : ((v7 = 0 & permut3(v0, v1, v2, v3, v4) = 0) | 208.04/128.25 (length1(v0, v1) = v7 & ( ~ ($lesseq(v4, v7)) | ~ ($lesseq(v3, v7)) 208.04/128.25 | ( ~ (v8 = v7) & length1(v0, v2) = v8))))) 208.04/128.25 (35) $lesseq(1, $difference(all_86_7, all_86_8)) 208.04/128.25 (36) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.04/128.25 $int] : ! [v5: $int] : ! [v6: $int] : ( ~ ($lesseq(1, 208.04/128.25 $difference(v4, v5))) | ~ ($lesseq(v3, v5)) | ~ (map_eq_sub1(v0, 208.04/128.25 v1, v2, v3, v4) = 0) | ~ (t2tb1(v5) = v6) | ~ in_ty(v0) | ? 208.04/128.25 [v7: $int] : (get(v0, int, v2, v6) = v7 & get(v0, int, v1, v6) = v7 & 208.04/128.25 in_uni(v7))) 208.04/128.25 (37) $lesseq(1, $difference(all_86_13, all_86_10)) 208.04/128.25 (38) in_map_int_int(all_86_4) 208.04/128.25 (39) $lesseq(0, all_86_11) 208.04/128.25 (40) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ( ~ 208.04/128.25 (t2tb2(v0) = v2) | ~ (get4(int, v2, v1) = v3) | ~ in_array_int(v0) | 208.04/128.25 ? [v4: $int] : ? [v5: $int] : ? [v6: $int] : (tb2t(v4) = v5 & 208.04/128.25 tb2t1(v3) = v6 & get3(v5, v1) = v6 & elts(int, v2) = v4 & 208.04/128.25 in_map_int_int(v5) & in_uni(v4))) 208.04/128.25 (41) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ (tb2t(v2) 208.04/128.25 = v1) | ~ (tb2t(v2) = v0)) 208.04/128.25 (42) $lesseq(43, all_133_0) 208.04/128.25 (43) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.04/128.25 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 208.04/128.25 ($lesseq(1, $difference(v3, v6))) | ~ ($lesseq(v2, v6)) | ~ 208.04/128.25 (map_eq_sub1(int, v4, v5, v2, v3) = 0) | ~ (t2tb(v1) = v5) | ~ 208.04/128.25 (t2tb(v0) = v4) | ~ (get3(v1, v6) = v7) | ~ in_map_int_int(v0) | 208.04/128.25 get3(v0, v6) = v7) 208.04/128.25 (44) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 208.04/128.25 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 208.04/128.25 (45) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ( ~ 208.04/128.25 (get4(v0, v1, v2) = v3) | ~ in_ty(v0) | ? [v4: $int] : ? [v5: $int] 208.04/128.25 : (elts(v0, v1) = v4 & t2tb1(v2) = v5 & get(v0, int, v4, v5) = v3 & 208.04/128.25 in_uni(v5) & in_uni(v4) & in_uni(v3))) 208.04/128.25 (46) $lesseq(0, all_86_10) 208.04/128.25 (47) map_eq_sub1(int, all_105_3, all_105_1, $sum(all_86_10, 1), all_86_13) = 208.04/128.25 0 208.04/128.25 (48) t2tb(all_86_4) = all_105_3 208.04/128.25 208.04/128.25 Begin of proof 208.04/128.25 | 208.04/128.25 | GROUND_INST: instantiating (10) with int, all_105_4, all_105_2, 0, all_86_13, 208.04/128.25 | all_105_3, all_105_1, 0, simplifying with (7), (19), (24), (32) 208.04/128.25 | gives: 208.04/128.25 | (49) ? [v0: $int] : ? [v1: $int] : ((v1 = v0 & $lesseq(all_86_13, v0) & 208.04/128.25 | $lesseq(0, v0) & $lesseq(0, all_86_13) & length1(int, all_105_2) = 208.04/128.25 | v0 & length1(int, all_105_4) = v0) | ( ~ (v0 = 0) & permut3(int, 208.04/128.25 | all_105_4, all_105_2, 0, all_86_13) = v0)) 208.04/128.25 | 208.04/128.25 | GROUND_INST: instantiating (34) with int, all_105_4, all_105_2, 0, all_86_13, 208.04/128.25 | all_105_3, all_105_1, simplifying with (7), (19), (24), (32) 208.04/128.25 | gives: 208.04/128.25 | (50) ~ ($lesseq(0, all_86_13)) | ? [v0: $int] : ? [v1: $int] : ((v0 = 0 208.04/128.25 | & permut3(int, all_105_4, all_105_2, 0, all_86_13) = 0) | 208.04/128.25 | (length1(int, all_105_4) = v0 & ( ~ ($lesseq(all_86_13, v0)) | ~ 208.04/128.25 | ($lesseq(0, v0)) | ( ~ (v1 = v0) & length1(int, all_105_2) = 208.04/128.25 | v1)))) 208.04/128.25 | 208.04/128.25 | GROUND_INST: instantiating (10) with int, all_103_4, all_105_4, all_86_11, 208.04/128.25 | $sum(all_86_10, 1), all_103_3, all_105_3, 0, simplifying with 208.04/128.25 | (5), (7), (16), (19) gives: 208.04/128.25 | (51) ? [v0: $int] : ? [v1: $int] : ((v1 = v0 & $lesseq(1, $difference(v0, 208.04/128.25 | all_86_10)) & $lesseq(all_86_11, v0) & $lesseq(-1, all_86_10) 208.04/128.25 | & $lesseq(0, all_86_11) & length1(int, all_105_4) = v0 & 208.04/128.25 | length1(int, all_103_4) = v0) | ( ~ (v0 = 0) & permut3(int, 208.04/128.25 | all_103_4, all_105_4, all_86_11, $sum(all_86_10, 1)) = v0)) 208.04/128.25 | 208.04/128.25 | GROUND_INST: instantiating (34) with int, all_103_4, all_105_4, all_86_11, 208.04/128.25 | $sum(all_86_10, 1), all_103_3, all_105_3, simplifying with (5), 208.04/128.25 | (7), (16), (19) gives: 208.04/128.25 | (52) ~ ($lesseq(-1, all_86_10)) | ~ ($lesseq(0, all_86_11)) | ? [v0: 208.04/128.25 | $int] : ? [v1: $int] : ((v0 = 0 & permut3(int, all_103_4, 208.04/128.25 | all_105_4, all_86_11, $sum(all_86_10, 1)) = 0) | (length1(int, 208.04/128.25 | all_103_4) = v0 & ( ~ ($lesseq(1, $difference(v0, all_86_10))) | 208.04/128.25 | ~ ($lesseq(all_86_11, v0)) | ( ~ (v1 = v0) & length1(int, 208.04/128.25 | all_105_4) = v1)))) 208.04/128.25 | 208.04/128.25 | GROUND_INST: instantiating (40) with all_86_1, all_133_2, all_105_2, 208.04/128.25 | all_133_1, simplifying with (21), (26), (33) gives: 208.04/128.25 | (53) ? [v0: $int] : ? [v1: $int] : ? [v2: $int] : (tb2t(v0) = v1 & 208.04/128.25 | tb2t1(all_133_1) = v2 & get3(v1, all_133_2) = v2 & elts(int, 208.04/128.25 | all_105_2) = v0 & in_map_int_int(v1) & in_uni(v0)) 208.04/128.25 | 208.04/128.25 | GROUND_INST: instantiating (45) with int, all_105_2, all_133_2, all_133_1, 208.04/128.25 | simplifying with (7), (21) gives: 208.04/128.25 | (54) ? [v0: $int] : ? [v1: $int] : (elts(int, all_105_2) = v0 & 208.04/128.25 | t2tb1(all_133_2) = v1 & get(int, int, v0, v1) = all_133_1 & 208.04/128.25 | in_uni(v1) & in_uni(v0) & in_uni(all_133_1)) 208.04/128.25 | 208.04/128.25 | DELTA: instantiating (51) with fresh symbols all_706_0, all_706_1 gives: 208.04/128.25 | (55) (all_706_0 = all_706_1 & $lesseq(1, $difference(all_706_1, all_86_10)) 208.04/128.25 | & $lesseq(all_86_11, all_706_1) & $lesseq(-1, all_86_10) & 208.04/128.25 | $lesseq(0, all_86_11) & length1(int, all_105_4) = all_706_1 & 208.04/128.25 | length1(int, all_103_4) = all_706_1) | ( ~ (all_706_1 = 0) & 208.04/128.25 | permut3(int, all_103_4, all_105_4, all_86_11, $sum(all_86_10, 1)) = 208.04/128.25 | all_706_1) 208.04/128.25 | 208.04/128.25 | DELTA: instantiating (49) with fresh symbols all_707_0, all_707_1 gives: 208.04/128.25 | (56) (all_707_0 = all_707_1 & $lesseq(all_86_13, all_707_1) & $lesseq(0, 208.04/128.25 | all_707_1) & $lesseq(0, all_86_13) & length1(int, all_105_2) = 208.04/128.25 | all_707_1 & length1(int, all_105_4) = all_707_1) | ( ~ (all_707_1 = 208.04/128.25 | 0) & permut3(int, all_105_4, all_105_2, 0, all_86_13) = all_707_1) 208.04/128.25 | 208.04/128.25 | DELTA: instantiating (54) with fresh symbols all_708_0, all_708_1 gives: 208.04/128.25 | (57) elts(int, all_105_2) = all_708_1 & t2tb1(all_133_2) = all_708_0 & 208.04/128.25 | get(int, int, all_708_1, all_708_0) = all_133_1 & in_uni(all_708_0) & 208.04/128.25 | in_uni(all_708_1) & in_uni(all_133_1) 208.04/128.25 | 208.04/128.25 | ALPHA: (57) implies: 208.04/128.25 | (58) get(int, int, all_708_1, all_708_0) = all_133_1 208.04/128.25 | (59) t2tb1(all_133_2) = all_708_0 208.04/128.25 | (60) elts(int, all_105_2) = all_708_1 208.04/128.25 | 208.04/128.25 | DELTA: instantiating (53) with fresh symbols all_710_0, all_710_1, all_710_2 208.04/128.25 | gives: 208.04/128.25 | (61) tb2t(all_710_2) = all_710_1 & tb2t1(all_133_1) = all_710_0 & 208.04/128.25 | get3(all_710_1, all_133_2) = all_710_0 & elts(int, all_105_2) = 208.04/128.25 | all_710_2 & in_map_int_int(all_710_1) & in_uni(all_710_2) 208.04/128.25 | 208.04/128.25 | ALPHA: (61) implies: 208.04/128.25 | (62) elts(int, all_105_2) = all_710_2 208.04/128.25 | (63) get3(all_710_1, all_133_2) = all_710_0 208.04/128.25 | (64) tb2t1(all_133_1) = all_710_0 208.04/128.25 | (65) tb2t(all_710_2) = all_710_1 208.04/128.25 | 208.04/128.25 | BETA: splitting (50) gives: 208.04/128.25 | 208.04/128.25 | Case 1: 208.04/128.25 | | 208.04/128.25 | | (66) $lesseq(all_86_13, -1) 208.04/128.25 | | 208.04/128.25 | | COMBINE_INEQS: (9), (66) imply: 208.04/128.25 | | (67) $lesseq(0, -1) 208.04/128.25 | | 208.04/128.25 | | CLOSE: (67) is inconsistent. 208.04/128.25 | | 208.04/128.25 | Case 2: 208.04/128.25 | | 208.04/128.25 | | (68) ? [v0: $int] : ? [v1: $int] : ((v0 = 0 & permut3(int, all_105_4, 208.04/128.25 | | all_105_2, 0, all_86_13) = 0) | (length1(int, all_105_4) = v0 208.04/128.25 | | & ( ~ ($lesseq(all_86_13, v0)) | ~ ($lesseq(0, v0)) | ( ~ (v1 = 208.04/128.25 | | v0) & length1(int, all_105_2) = v1)))) 208.04/128.25 | | 208.04/128.25 | | DELTA: instantiating (68) with fresh symbols all_733_0, all_733_1 gives: 208.04/128.25 | | (69) (all_733_1 = 0 & permut3(int, all_105_4, all_105_2, 0, all_86_13) = 208.04/128.25 | | 0) | (length1(int, all_105_4) = all_733_1 & ( ~ 208.04/128.25 | | ($lesseq(all_86_13, all_733_1)) | ~ ($lesseq(0, all_733_1)) | ( 208.04/128.25 | | ~ (all_733_0 = all_733_1) & length1(int, all_105_2) = 208.04/128.25 | | all_733_0))) 208.04/128.25 | | 208.04/128.25 | | BETA: splitting (52) gives: 208.04/128.25 | | 208.04/128.25 | | Case 1: 208.04/128.25 | | | 208.04/128.25 | | | (70) $lesseq(all_86_11, -1) 208.04/128.25 | | | 208.04/128.25 | | | COMBINE_INEQS: (39), (70) imply: 208.04/128.25 | | | (71) $lesseq(0, -1) 208.04/128.25 | | | 208.04/128.25 | | | CLOSE: (71) is inconsistent. 208.04/128.25 | | | 208.04/128.25 | | Case 2: 208.04/128.25 | | | 208.04/128.25 | | | (72) ~ ($lesseq(-1, all_86_10)) | ? [v0: $int] : ? [v1: $int] : ((v0 208.04/128.25 | | | = 0 & permut3(int, all_103_4, all_105_4, all_86_11, 208.04/128.25 | | | $sum(all_86_10, 1)) = 0) | (length1(int, all_103_4) = v0 & ( 208.04/128.25 | | | ~ ($lesseq(1, $difference(v0, all_86_10))) | ~ 208.04/128.25 | | | ($lesseq(all_86_11, v0)) | ( ~ (v1 = v0) & length1(int, 208.04/128.25 | | | all_105_4) = v1)))) 208.04/128.25 | | | 208.04/128.25 | | | BETA: splitting (69) gives: 208.04/128.25 | | | 208.04/128.25 | | | Case 1: 208.04/128.25 | | | | 208.04/128.25 | | | | (73) all_733_1 = 0 & permut3(int, all_105_4, all_105_2, 0, all_86_13) 208.04/128.25 | | | | = 0 208.04/128.25 | | | | 208.04/128.25 | | | | ALPHA: (73) implies: 208.04/128.25 | | | | (74) permut3(int, all_105_4, all_105_2, 0, all_86_13) = 0 208.04/128.25 | | | | 208.04/128.25 | | | | BETA: splitting (56) gives: 208.04/128.25 | | | | 208.04/128.25 | | | | Case 1: 208.04/128.25 | | | | | 208.04/128.25 | | | | | (75) all_707_0 = all_707_1 & $lesseq(all_86_13, all_707_1) & 208.04/128.25 | | | | | $lesseq(0, all_707_1) & $lesseq(0, all_86_13) & length1(int, 208.04/128.25 | | | | | all_105_2) = all_707_1 & length1(int, all_105_4) = all_707_1 208.04/128.25 | | | | | 208.04/128.25 | | | | | ALPHA: (75) implies: 208.04/128.25 | | | | | (76) length1(int, all_105_4) = all_707_1 208.04/128.25 | | | | | 208.04/128.25 | | | | | BETA: splitting (72) gives: 208.04/128.25 | | | | | 208.04/128.25 | | | | | Case 1: 208.04/128.25 | | | | | | 208.04/128.25 | | | | | | (77) $lesseq(all_86_10, -2) 208.04/128.25 | | | | | | 208.04/128.25 | | | | | | COMBINE_INEQS: (46), (77) imply: 208.04/128.25 | | | | | | (78) $lesseq(0, -1) 208.04/128.25 | | | | | | 208.04/128.25 | | | | | | CLOSE: (78) is inconsistent. 208.04/128.25 | | | | | | 208.04/128.25 | | | | | Case 2: 208.04/128.25 | | | | | | 208.04/128.25 | | | | | | (79) ? [v0: $int] : ? [v1: $int] : ((v0 = 0 & permut3(int, 208.04/128.25 | | | | | | all_103_4, all_105_4, all_86_11, $sum(all_86_10, 1)) = 208.04/128.25 | | | | | | 0) | (length1(int, all_103_4) = v0 & ( ~ ($lesseq(1, 208.04/128.25 | | | | | | $difference(v0, all_86_10))) | ~ 208.04/128.25 | | | | | | ($lesseq(all_86_11, v0)) | ( ~ (v1 = v0) & 208.04/128.25 | | | | | | length1(int, all_105_4) = v1)))) 208.04/128.25 | | | | | | 208.04/128.25 | | | | | | DELTA: instantiating (79) with fresh symbols all_755_0, all_755_1 208.04/128.25 | | | | | | gives: 208.04/128.25 | | | | | | (80) (all_755_1 = 0 & permut3(int, all_103_4, all_105_4, 208.04/128.25 | | | | | | all_86_11, $sum(all_86_10, 1)) = 0) | (length1(int, 208.04/128.25 | | | | | | all_103_4) = all_755_1 & ( ~ ($lesseq(1, 208.04/128.25 | | | | | | $difference(all_755_1, all_86_10))) | ~ 208.04/128.25 | | | | | | ($lesseq(all_86_11, all_755_1)) | ( ~ (all_755_0 = 208.04/128.25 | | | | | | all_755_1) & length1(int, all_105_4) = all_755_0))) 208.04/128.25 | | | | | | 208.04/128.25 | | | | | | GROUND_INST: instantiating (1) with all_133_0, all_710_0, all_133_1, 208.04/128.25 | | | | | | simplifying with (14), (64) gives: 208.04/128.25 | | | | | | (81) all_710_0 = all_133_0 208.04/128.25 | | | | | | 208.04/128.25 | | | | | | GROUND_INST: instantiating (44) with all_86_13, all_707_1, 208.04/128.25 | | | | | | all_105_4, int, simplifying with (18), (76) gives: 208.04/128.25 | | | | | | (82) all_707_1 = all_86_13 208.04/128.25 | | | | | | 208.04/128.25 | | | | | | GROUND_INST: instantiating (17) with all_105_1, all_710_2, 208.04/128.25 | | | | | | all_105_2, int, simplifying with (24), (62) gives: 208.04/128.25 | | | | | | (83) all_710_2 = all_105_1 208.04/128.25 | | | | | | 208.04/128.25 | | | | | | GROUND_INST: instantiating (17) with all_710_2, all_708_1, 208.04/128.25 | | | | | | all_105_2, int, simplifying with (60), (62) gives: 208.04/128.25 | | | | | | (84) all_710_2 = all_708_1 208.04/128.25 | | | | | | 208.04/128.25 | | | | | | COMBINE_EQS: (83), (84) imply: 208.04/128.25 | | | | | | (85) all_708_1 = all_105_1 208.04/128.25 | | | | | | 208.04/128.25 | | | | | | REDUCE: (65), (83) imply: 208.04/128.25 | | | | | | (86) tb2t(all_105_1) = all_710_1 208.04/128.25 | | | | | | 208.04/128.25 | | | | | | REDUCE: (63), (81) imply: 208.04/128.25 | | | | | | (87) get3(all_710_1, all_133_2) = all_133_0 208.04/128.25 | | | | | | 208.04/128.25 | | | | | | REDUCE: (58), (85) imply: 208.04/128.25 | | | | | | (88) get(int, int, all_105_1, all_708_0) = all_133_1 208.04/128.25 | | | | | | 208.04/128.25 | | | | | | BETA: splitting (80) gives: 208.04/128.25 | | | | | | 208.04/128.25 | | | | | | Case 1: 208.04/128.25 | | | | | | | 208.04/128.25 | | | | | | | (89) all_755_1 = 0 & permut3(int, all_103_4, all_105_4, 208.04/128.25 | | | | | | | all_86_11, $sum(all_86_10, 1)) = 0 208.04/128.25 | | | | | | | 208.04/128.25 | | | | | | | ALPHA: (89) implies: 208.04/128.25 | | | | | | | (90) permut3(int, all_103_4, all_105_4, all_86_11, 208.04/128.25 | | | | | | | $sum(all_86_10, 1)) = 0 208.04/128.25 | | | | | | | 208.04/128.25 | | | | | | | BETA: splitting (55) gives: 208.04/128.25 | | | | | | | 208.04/128.25 | | | | | | | Case 1: 208.04/128.25 | | | | | | | | 208.04/128.25 | | | | | | | | (91) all_706_0 = all_706_1 & $lesseq(1, 208.04/128.25 | | | | | | | | $difference(all_706_1, all_86_10)) & 208.04/128.25 | | | | | | | | $lesseq(all_86_11, all_706_1) & $lesseq(-1, all_86_10) & 208.04/128.25 | | | | | | | | $lesseq(0, all_86_11) & length1(int, all_105_4) = 208.04/128.25 | | | | | | | | all_706_1 & length1(int, all_103_4) = all_706_1 208.04/128.25 | | | | | | | | 208.04/128.25 | | | | | | | | ALPHA: (91) implies: 208.04/128.25 | | | | | | | | (92) $lesseq(1, $difference(all_706_1, all_86_10)) 208.04/128.25 | | | | | | | | (93) length1(int, all_103_4) = all_706_1 208.04/128.25 | | | | | | | | (94) length1(int, all_105_4) = all_706_1 208.04/128.25 | | | | | | | | 208.04/128.25 | | | | | | | | GROUND_INST: instantiating (41) with all_86_2, all_710_1, 208.04/128.25 | | | | | | | | all_105_1, simplifying with (22), (86) gives: 208.04/128.25 | | | | | | | | (95) all_710_1 = all_86_2 208.04/128.25 | | | | | | | | 208.04/128.25 | | | | | | | | GROUND_INST: instantiating (44) with all_86_13, all_706_1, 208.04/128.25 | | | | | | | | all_103_4, int, simplifying with (8), (93) gives: 208.04/128.25 | | | | | | | | (96) all_706_1 = all_86_13 208.04/128.25 | | | | | | | | 208.04/128.25 | | | | | | | | REDUCE: (87), (95) imply: 208.04/128.25 | | | | | | | | (97) get3(all_86_2, all_133_2) = all_133_0 208.04/128.25 | | | | | | | | 208.04/128.26 | | | | | | | | GROUND_INST: instantiating (43) with all_86_4, all_86_2, 0, 208.04/128.26 | | | | | | | | all_86_7, all_105_3, all_105_1, all_133_2, 208.04/128.26 | | | | | | | | all_133_0, simplifying with (6), (20), (38), (48), 208.04/128.26 | | | | | | | | (97) gives: 208.04/128.26 | | | | | | | | (98) ~ ($lesseq(1, $difference(all_86_7, all_133_2))) | ~ 208.04/128.26 | | | | | | | | ($lesseq(0, all_133_2)) | get3(all_86_4, all_133_2) = 208.04/128.26 | | | | | | | | all_133_0 208.04/128.26 | | | | | | | | 208.04/128.26 | | | | | | | | GROUND_INST: instantiating (30) with all_86_4, all_86_2, 208.04/128.26 | | | | | | | | all_86_7, $sum(all_86_10, 1), all_133_2, all_105_3, 208.04/128.26 | | | | | | | | all_105_1, all_133_0, simplifying with (6), (31), 208.04/128.26 | | | | | | | | (38), (48), (97) gives: 208.04/128.26 | | | | | | | | (99) ~ ($lesseq(all_133_2, all_86_10)) | ~ 208.04/128.26 | | | | | | | | ($lesseq(all_86_7, all_133_2)) | ? [v0: $int] : 208.04/128.26 | | | | | | | | ($lesseq(v0, all_86_10) & $lesseq(all_86_7, v0) & 208.04/128.26 | | | | | | | | get3(all_86_4, v0) = all_133_0) 208.04/128.26 | | | | | | | | 208.04/128.26 | | | | | | | | GROUND_INST: instantiating (36) with int, all_105_3, all_105_1, 208.04/128.26 | | | | | | | | 0, all_86_7, all_133_2, all_708_0, simplifying with 208.04/128.26 | | | | | | | | (7), (20), (59) gives: 208.04/128.26 | | | | | | | | (100) ~ ($lesseq(1, $difference(all_86_7, all_133_2))) | ~ 208.04/128.26 | | | | | | | | ($lesseq(0, all_133_2)) | ? [v0: $int] : (get(int, 208.04/128.26 | | | | | | | | int, all_105_1, all_708_0) = v0 & get(int, int, 208.04/128.26 | | | | | | | | all_105_3, all_708_0) = v0 & in_uni(v0)) 208.04/128.26 | | | | | | | | 208.04/128.26 | | | | | | | | GROUND_INST: instantiating (25) with int, all_105_3, all_105_1, 208.04/128.26 | | | | | | | | all_86_7, $sum(all_86_10, 1), all_133_2, all_708_0, 208.04/128.26 | | | | | | | | all_133_1, simplifying with (7), (31), (59), (88) 208.04/128.26 | | | | | | | | gives: 208.04/128.26 | | | | | | | | (101) ~ ($lesseq(all_133_2, all_86_10)) | ~ 208.04/128.26 | | | | | | | | ($lesseq(all_86_7, all_133_2)) | ? [v0: $int] : ? 208.04/128.26 | | | | | | | | [v1: $int] : ($lesseq(v0, all_86_10) & 208.04/128.26 | | | | | | | | $lesseq(all_86_7, v0) & t2tb1(v0) = v1 & get(int, 208.04/128.26 | | | | | | | | int, all_105_3, v1) = all_133_1 & in_uni(v1) & 208.04/128.26 | | | | | | | | in_uni(all_133_1)) 208.04/128.26 | | | | | | | | 208.04/128.26 | | | | | | | | BETA: splitting (28) gives: 208.04/128.26 | | | | | | | | 208.04/128.26 | | | | | | | | Case 1: 208.04/128.26 | | | | | | | | | 208.04/128.26 | | | | | | | | | (102) ~ (all_86_11 = 0) 208.04/128.26 | | | | | | | | | 208.04/128.26 | | | | | | | | | STRENGTHEN: (39), (102) imply: 208.04/128.26 | | | | | | | | | (103) $lesseq(1, all_86_11) 208.04/128.26 | | | | | | | | | 208.04/128.26 | | | | | | | | | COMBINE_INEQS: (29), (35) imply: 208.04/128.26 | | | | | | | | | (104) $lesseq(1, $difference(all_86_10, all_86_8)) 208.04/128.26 | | | | | | | | | 208.04/128.26 | | | | | | | | | BETA: splitting (100) gives: 208.04/128.26 | | | | | | | | | 208.04/128.26 | | | | | | | | | Case 1: 208.04/128.26 | | | | | | | | | | 208.04/128.26 | | | | | | | | | | (105) $lesseq(all_133_2, -1) 208.04/128.26 | | | | | | | | | | 208.04/128.26 | | | | | | | | | | COMBINE_INEQS: (27), (105) imply: 208.04/128.26 | | | | | | | | | | (106) $lesseq(all_86_11, -1) 208.04/128.26 | | | | | | | | | | 208.04/128.26 | | | | | | | | | | COMBINE_INEQS: (103), (106) imply: 208.04/128.26 | | | | | | | | | | (107) $lesseq(0, -1) 208.04/128.26 | | | | | | | | | | 208.04/128.26 | | | | | | | | | | CLOSE: (107) is inconsistent. 208.04/128.26 | | | | | | | | | | 208.04/128.26 | | | | | | | | | Case 2: 208.04/128.26 | | | | | | | | | | 208.04/128.26 | | | | | | | | | | (108) $lesseq(0, all_133_2) 208.04/128.26 | | | | | | | | | | 208.04/128.26 | | | | | | | | | | REF_CLOSE: (2), (3), (12), (13), (23), (27), (30), (35), 208.04/128.26 | | | | | | | | | | (42), (48), (98), (99), (101), (104), (108) are 208.04/128.26 | | | | | | | | | | inconsistent by sub-proof #144. 208.04/128.26 | | | | | | | | | | 208.04/128.26 | | | | | | | | | End of split 208.04/128.26 | | | | | | | | | 208.04/128.26 | | | | | | | | Case 2: 208.04/128.26 | | | | | | | | | 208.04/128.26 | | | | | | | | | (109) all_86_11 = 0 208.04/128.26 | | | | | | | | | 208.04/128.26 | | | | | | | | | REDUCE: (27), (109) imply: 208.04/128.26 | | | | | | | | | (110) $lesseq(0, all_133_2) 208.04/128.26 | | | | | | | | | 208.04/128.26 | | | | | | | | | COMBINE_INEQS: (13), (110) imply: 208.04/128.26 | | | | | | | | | (111) $lesseq(0, all_86_8) 208.04/128.26 | | | | | | | | | 208.04/128.26 | | | | | | | | | COMBINE_INEQS: (29), (35) imply: 208.04/128.26 | | | | | | | | | (112) $lesseq(1, $difference(all_86_10, all_86_8)) 208.04/128.26 | | | | | | | | | 208.04/128.26 | | | | | | | | | COMBINE_INEQS: (111), (112) imply: 208.04/128.26 | | | | | | | | | (113) $lesseq(1, all_86_10) 208.04/128.26 | | | | | | | | | 208.04/128.26 | | | | | | | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (10), (11), 208.04/128.26 | | | | | | | | | (12), (13), (14), (15), (16), (17), (18), (19), 208.04/128.26 | | | | | | | | | (20), (21), (22), (23), (24), (25), (26), (27), 208.04/128.26 | | | | | | | | | (28), (29), (30), (31), (33), (34), (35), (36), 208.04/128.26 | | | | | | | | | (37), (38), (39), (40), (41), (42), (43), (44), 208.04/128.26 | | | | | | | | | (45), (47), (48), (113) are inconsistent by 208.04/128.26 | | | | | | | | | sub-proof #143. 208.04/128.26 | | | | | | | | | 208.04/128.26 | | | | | | | | End of split 208.04/128.26 | | | | | | | | 208.04/128.26 | | | | | | | Case 2: 208.04/128.26 | | | | | | | | 208.04/128.26 | | | | | | | | (114) ~ (all_706_1 = 0) & permut3(int, all_103_4, all_105_4, 208.04/128.26 | | | | | | | | all_86_11, $sum(all_86_10, 1)) = all_706_1 208.04/128.26 | | | | | | | | 208.04/128.26 | | | | | | | | ALPHA: (114) implies: 208.04/128.26 | | | | | | | | (115) ~ (all_706_1 = 0) 208.04/128.26 | | | | | | | | (116) permut3(int, all_103_4, all_105_4, all_86_11, 208.04/128.26 | | | | | | | | $sum(all_86_10, 1)) = all_706_1 208.04/128.26 | | | | | | | | 208.04/128.26 | | | | | | | | GROUND_INST: instantiating (15) with all_706_1, 0, 208.04/128.26 | | | | | | | | $sum(all_86_10, 1), all_86_11, all_105_4, 208.04/128.26 | | | | | | | | all_103_4, int, simplifying with (90), (116) gives: 208.04/128.26 | | | | | | | | (117) all_706_1 = 0 208.04/128.26 | | | | | | | | 208.04/128.26 | | | | | | | | REDUCE: (115), (117) imply: 208.04/128.26 | | | | | | | | (118) ~ (0 = 0) 208.04/128.26 | | | | | | | | 208.04/128.26 | | | | | | | | CLOSE: (118) is inconsistent. 208.04/128.26 | | | | | | | | 208.04/128.26 | | | | | | | End of split 208.04/128.26 | | | | | | | 208.04/128.26 | | | | | | Case 2: 208.04/128.26 | | | | | | | 208.04/128.26 | | | | | | | (119) length1(int, all_103_4) = all_755_1 & ( ~ ($lesseq(1, 208.04/128.26 | | | | | | | $difference(all_755_1, all_86_10))) | ~ 208.04/128.26 | | | | | | | ($lesseq(all_86_11, all_755_1)) | ( ~ (all_755_0 = 208.04/128.26 | | | | | | | all_755_1) & length1(int, all_105_4) = all_755_0)) 208.04/128.26 | | | | | | | 208.04/128.26 | | | | | | | ALPHA: (119) implies: 208.04/128.26 | | | | | | | (120) length1(int, all_103_4) = all_755_1 208.04/128.26 | | | | | | | (121) ~ ($lesseq(1, $difference(all_755_1, all_86_10))) | ~ 208.04/128.26 | | | | | | | ($lesseq(all_86_11, all_755_1)) | ( ~ (all_755_0 = 208.04/128.26 | | | | | | | all_755_1) & length1(int, all_105_4) = all_755_0) 208.04/128.26 | | | | | | | 208.04/128.26 | | | | | | | GROUND_INST: instantiating (44) with all_86_13, all_755_1, 208.04/128.26 | | | | | | | all_103_4, int, simplifying with (8), (120) gives: 208.04/128.26 | | | | | | | (122) all_755_1 = all_86_13 208.04/128.26 | | | | | | | 208.04/128.26 | | | | | | | BETA: splitting (121) gives: 208.04/128.26 | | | | | | | 208.04/128.26 | | | | | | | Case 1: 208.04/128.26 | | | | | | | | 208.04/128.26 | | | | | | | | (123) $lesseq(1, $difference(all_86_11, all_755_1)) 208.04/128.26 | | | | | | | | 208.04/128.26 | | | | | | | | REDUCE: (122), (123) imply: 208.04/128.26 | | | | | | | | (124) $lesseq(1, $difference(all_86_11, all_86_13)) 208.04/128.26 | | | | | | | | 208.04/128.26 | | | | | | | | COMBINE_INEQS: (13), (27) imply: 208.04/128.26 | | | | | | | | (125) $lesseq(all_86_11, all_86_8) 208.04/128.26 | | | | | | | | 208.04/128.26 | | | | | | | | COMBINE_INEQS: (29), (35) imply: 208.04/128.26 | | | | | | | | (126) $lesseq(1, $difference(all_86_10, all_86_8)) 208.04/128.26 | | | | | | | | 208.04/128.26 | | | | | | | | COMBINE_INEQS: (125), (126) imply: 208.04/128.26 | | | | | | | | (127) $lesseq(1, $difference(all_86_10, all_86_11)) 208.04/128.26 | | | | | | | | 208.04/128.26 | | | | | | | | COMBINE_INEQS: (37), (127) imply: 208.04/128.26 | | | | | | | | (128) $lesseq(2, $difference(all_86_13, all_86_11)) 208.04/128.26 | | | | | | | | 208.04/128.26 | | | | | | | | COMBINE_INEQS: (124), (128) imply: 208.04/128.26 | | | | | | | | (129) $lesseq(0, -1) 208.04/128.26 | | | | | | | | 208.04/128.26 | | | | | | | | CLOSE: (129) is inconsistent. 208.04/128.26 | | | | | | | | 208.04/128.26 | | | | | | | Case 2: 208.04/128.26 | | | | | | | | 208.04/128.26 | | | | | | | | (130) ~ ($lesseq(1, $difference(all_755_1, all_86_10))) | ( 208.04/128.26 | | | | | | | | ~ (all_755_0 = all_755_1) & length1(int, all_105_4) = 208.04/128.26 | | | | | | | | all_755_0) 208.04/128.26 | | | | | | | | 208.04/128.26 | | | | | | | | BETA: splitting (130) gives: 208.04/128.26 | | | | | | | | 208.04/128.26 | | | | | | | | Case 1: 208.04/128.26 | | | | | | | | | 208.04/128.26 | | | | | | | | | (131) $lesseq(all_755_1, all_86_10) 208.04/128.26 | | | | | | | | | 208.04/128.26 | | | | | | | | | REDUCE: (122), (131) imply: 208.04/128.26 | | | | | | | | | (132) $lesseq(all_86_13, all_86_10) 208.04/128.26 | | | | | | | | | 208.04/128.26 | | | | | | | | | COMBINE_INEQS: (37), (132) imply: 208.04/128.26 | | | | | | | | | (133) $lesseq(0, -1) 208.04/128.26 | | | | | | | | | 208.04/128.26 | | | | | | | | | CLOSE: (133) is inconsistent. 208.04/128.26 | | | | | | | | | 208.04/128.26 | | | | | | | | Case 2: 208.04/128.26 | | | | | | | | | 208.04/128.26 | | | | | | | | | (134) ~ (all_755_0 = all_755_1) & length1(int, all_105_4) 208.04/128.26 | | | | | | | | | = all_755_0 208.04/128.26 | | | | | | | | | 208.04/128.26 | | | | | | | | | ALPHA: (134) implies: 208.04/128.26 | | | | | | | | | (135) ~ (all_755_0 = all_755_1) 208.04/128.26 | | | | | | | | | (136) length1(int, all_105_4) = all_755_0 208.04/128.26 | | | | | | | | | 208.04/128.26 | | | | | | | | | REDUCE: (122), (135) imply: 208.04/128.26 | | | | | | | | | (137) ~ (all_755_0 = all_86_13) 208.04/128.26 | | | | | | | | | 208.04/128.26 | | | | | | | | | GROUND_INST: instantiating (44) with all_86_13, all_755_0, 208.04/128.26 | | | | | | | | | all_105_4, int, simplifying with (18), (136) 208.04/128.26 | | | | | | | | | gives: 208.04/128.26 | | | | | | | | | (138) all_755_0 = all_86_13 208.04/128.26 | | | | | | | | | 208.04/128.26 | | | | | | | | | REDUCE: (137), (138) imply: 208.04/128.27 | | | | | | | | | (139) ~ (0 = 0) 208.04/128.27 | | | | | | | | | 208.04/128.27 | | | | | | | | | CLOSE: (139) is inconsistent. 208.04/128.27 | | | | | | | | | 208.04/128.27 | | | | | | | | End of split 208.04/128.27 | | | | | | | | 208.04/128.27 | | | | | | | End of split 208.04/128.27 | | | | | | | 208.04/128.27 | | | | | | End of split 208.04/128.27 | | | | | | 208.04/128.27 | | | | | End of split 208.04/128.27 | | | | | 208.04/128.27 | | | | Case 2: 208.04/128.27 | | | | | 208.04/128.27 | | | | | (140) ~ (all_707_1 = 0) & permut3(int, all_105_4, all_105_2, 0, 208.04/128.27 | | | | | all_86_13) = all_707_1 208.04/128.27 | | | | | 208.04/128.27 | | | | | ALPHA: (140) implies: 208.04/128.27 | | | | | (141) ~ (all_707_1 = 0) 208.04/128.27 | | | | | (142) permut3(int, all_105_4, all_105_2, 0, all_86_13) = all_707_1 208.04/128.27 | | | | | 208.04/128.27 | | | | | GROUND_INST: instantiating (15) with 0, all_707_1, all_86_13, 0, 208.04/128.27 | | | | | all_105_2, all_105_4, int, simplifying with (74), (142) 208.04/128.27 | | | | | gives: 208.04/128.27 | | | | | (143) all_707_1 = 0 208.04/128.27 | | | | | 208.04/128.27 | | | | | REDUCE: (141), (143) imply: 208.04/128.27 | | | | | (144) ~ (0 = 0) 208.04/128.27 | | | | | 208.04/128.27 | | | | | CLOSE: (144) is inconsistent. 208.04/128.27 | | | | | 208.04/128.27 | | | | End of split 208.04/128.27 | | | | 208.04/128.27 | | | Case 2: 208.04/128.27 | | | | 208.04/128.27 | | | | (145) length1(int, all_105_4) = all_733_1 & ( ~ ($lesseq(all_86_13, 208.04/128.27 | | | | all_733_1)) | ~ ($lesseq(0, all_733_1)) | ( ~ (all_733_0 208.04/128.27 | | | | = all_733_1) & length1(int, all_105_2) = all_733_0)) 208.04/128.27 | | | | 208.04/128.27 | | | | ALPHA: (145) implies: 208.04/128.27 | | | | (146) length1(int, all_105_4) = all_733_1 208.04/128.27 | | | | (147) ~ ($lesseq(all_86_13, all_733_1)) | ~ ($lesseq(0, all_733_1)) 208.04/128.27 | | | | | ( ~ (all_733_0 = all_733_1) & length1(int, all_105_2) = 208.04/128.27 | | | | all_733_0) 208.04/128.27 | | | | 208.04/128.27 | | | | BETA: splitting (72) gives: 208.04/128.27 | | | | 208.04/128.27 | | | | Case 1: 208.04/128.27 | | | | | 208.04/128.27 | | | | | (148) $lesseq(all_86_10, -2) 208.04/128.27 | | | | | 208.04/128.27 | | | | | COMBINE_INEQS: (46), (148) imply: 208.04/128.27 | | | | | (149) $lesseq(0, -1) 208.04/128.27 | | | | | 208.04/128.27 | | | | | CLOSE: (149) is inconsistent. 208.04/128.27 | | | | | 208.04/128.27 | | | | Case 2: 208.04/128.27 | | | | | 208.04/128.27 | | | | | 208.04/128.27 | | | | | GROUND_INST: instantiating (44) with all_86_13, all_733_1, all_105_4, 208.04/128.27 | | | | | int, simplifying with (18), (146) gives: 208.04/128.27 | | | | | (150) all_733_1 = all_86_13 208.04/128.27 | | | | | 208.04/128.27 | | | | | BETA: splitting (147) gives: 208.04/128.27 | | | | | 208.04/128.27 | | | | | Case 1: 208.04/128.27 | | | | | | 208.04/128.27 | | | | | | (151) $lesseq(all_733_1, -1) 208.04/128.27 | | | | | | 208.04/128.27 | | | | | | REDUCE: (150), (151) imply: 208.04/128.27 | | | | | | (152) $lesseq(all_86_13, -1) 208.04/128.27 | | | | | | 208.04/128.27 | | | | | | COMBINE_INEQS: (13), (27) imply: 208.04/128.27 | | | | | | (153) $lesseq(all_86_11, all_86_8) 208.04/128.27 | | | | | | 208.04/128.27 | | | | | | COMBINE_INEQS: (29), (35) imply: 208.04/128.27 | | | | | | (154) $lesseq(1, $difference(all_86_10, all_86_8)) 208.04/128.27 | | | | | | 208.04/128.27 | | | | | | COMBINE_INEQS: (153), (154) imply: 208.04/128.27 | | | | | | (155) $lesseq(1, $difference(all_86_10, all_86_11)) 208.04/128.27 | | | | | | 208.04/128.27 | | | | | | COMBINE_INEQS: (37), (155) imply: 208.04/128.27 | | | | | | (156) $lesseq(2, $difference(all_86_13, all_86_11)) 208.04/128.27 | | | | | | 208.04/128.27 | | | | | | COMBINE_INEQS: (9), (152) imply: 208.04/128.27 | | | | | | (157) $lesseq(0, -1) 208.04/128.27 | | | | | | 208.04/128.27 | | | | | | CLOSE: (157) is inconsistent. 208.04/128.27 | | | | | | 208.04/128.27 | | | | | Case 2: 208.04/128.27 | | | | | | 208.04/128.27 | | | | | | (158) ~ ($lesseq(all_86_13, all_733_1)) | ( ~ (all_733_0 = 208.04/128.27 | | | | | | all_733_1) & length1(int, all_105_2) = all_733_0) 208.04/128.27 | | | | | | 208.04/128.27 | | | | | | BETA: splitting (158) gives: 208.04/128.27 | | | | | | 208.04/128.27 | | | | | | Case 1: 208.04/128.27 | | | | | | | 208.04/128.27 | | | | | | | (159) $lesseq(1, $difference(all_86_13, all_733_1)) 208.04/128.27 | | | | | | | 208.04/128.27 | | | | | | | REDUCE: (150), (159) imply: 208.04/128.27 | | | | | | | (160) $lesseq(0, -1) 208.04/128.27 | | | | | | | 208.04/128.27 | | | | | | | CLOSE: (160) is inconsistent. 208.04/128.27 | | | | | | | 208.04/128.27 | | | | | | Case 2: 208.04/128.27 | | | | | | | 208.04/128.27 | | | | | | | (161) ~ (all_733_0 = all_733_1) & length1(int, all_105_2) = 208.04/128.27 | | | | | | | all_733_0 208.04/128.27 | | | | | | | 208.04/128.27 | | | | | | | ALPHA: (161) implies: 208.04/128.27 | | | | | | | (162) ~ (all_733_0 = all_733_1) 208.04/128.27 | | | | | | | (163) length1(int, all_105_2) = all_733_0 208.04/128.27 | | | | | | | 208.04/128.27 | | | | | | | REDUCE: (150), (162) imply: 208.04/128.27 | | | | | | | (164) ~ (all_733_0 = all_86_13) 208.04/128.27 | | | | | | | 208.04/128.27 | | | | | | | GROUND_INST: instantiating (44) with all_86_13, all_733_0, 208.04/128.27 | | | | | | | all_105_2, int, simplifying with (4), (163) gives: 208.04/128.27 | | | | | | | (165) all_733_0 = all_86_13 208.04/128.27 | | | | | | | 208.04/128.27 | | | | | | | REDUCE: (164), (165) imply: 208.04/128.27 | | | | | | | (166) ~ (0 = 0) 208.04/128.27 | | | | | | | 208.04/128.27 | | | | | | | CLOSE: (166) is inconsistent. 208.04/128.27 | | | | | | | 208.04/128.27 | | | | | | End of split 208.04/128.27 | | | | | | 208.04/128.27 | | | | | End of split 208.04/128.27 | | | | | 208.04/128.27 | | | | End of split 208.04/128.27 | | | | 208.04/128.27 | | | End of split 208.04/128.27 | | | 208.04/128.27 | | End of split 208.04/128.27 | | 208.04/128.27 | End of split 208.04/128.27 | 208.04/128.27 End of proof 208.04/128.27 208.04/128.27 Sub-proof #117 shows that the following formulas are inconsistent: 208.04/128.27 ---------------------------------------------------------------- 208.04/128.27 (1) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ (tb2t1(v2) 208.04/128.27 = v1) | ~ (tb2t1(v2) = v0)) 208.04/128.27 (2) ! [v0: $int] : ! [v1: $int] : ( ~ ($lesseq(43, v1)) | ~ ($lesseq(v0, 208.04/128.27 all_86_8)) | ~ ($lesseq(all_86_11, v0)) | ~ (get3(all_86_6, v0) = 208.04/128.27 v1)) 208.04/128.27 (3) length1(int, all_103_2) = all_86_13 208.04/128.27 (4) in_map_int_int(all_86_6) 208.04/128.27 (5) elts(int, all_103_4) = all_103_3 208.04/128.27 (6) t2tb(all_86_2) = all_105_1 208.04/128.27 (7) in_ty(int) 208.04/128.27 (8) length1(int, all_103_4) = all_86_13 208.04/128.27 (9) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.04/128.27 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 208.04/128.27 (permut2(v0, v5, v6, v3, v4) = v7) | ~ (elts(v0, v2) = v6) | ~ 208.04/128.27 (elts(v0, v1) = v5) | ~ in_ty(v0) | ? [v8: $int] : ? [v9: $int] : 208.04/128.27 ((v9 = v8 & v7 = 0 & $lesseq(v4, v8) & $lesseq(v3, v8) & $lesseq(0, v4) 208.04/128.27 & $lesseq(0, v3) & length1(v0, v2) = v8 & length1(v0, v1) = v8) | ( 208.04/128.27 ~ (v8 = 0) & permut3(v0, v1, v2, v3, v4) = v8))) 208.04/128.27 (10) t2tb(all_86_6) = all_103_1 208.04/128.27 (11) $lesseq(all_133_2, all_86_8) 208.04/128.27 (12) tb2t1(all_133_1) = all_133_0 208.04/128.27 (13) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.04/128.27 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ (permut3(v6, v5, 208.04/128.27 v4, v3, v2) = v1) | ~ (permut3(v6, v5, v4, v3, v2) = v0)) 208.04/128.27 (14) permut2(int, all_103_1, all_105_3, 0, all_86_13) = 0 208.04/128.27 (15) permut2(int, all_103_3, all_105_3, all_86_11, $sum(all_86_10, 1)) = 0 208.04/128.27 (16) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 208.04/128.27 | ~ (elts(v3, v2) = v1) | ~ (elts(v3, v2) = v0)) 208.04/128.27 (17) length1(int, all_105_4) = all_86_13 208.04/128.27 (18) elts(int, all_105_4) = all_105_3 208.04/128.27 (19) permut2(int, all_103_3, all_103_1, 0, all_86_13) = 0 208.04/128.27 (20) map_eq_sub1(int, all_105_3, all_105_1, 0, all_86_7) = 0 208.04/128.27 (21) ~ (all_86_7 = 0) | ~ ($difference(all_86_10, all_86_13) = -1) 208.04/128.27 (22) get4(int, all_105_2, all_133_2) = all_133_1 208.04/128.27 (23) tb2t(all_105_1) = all_86_2 208.04/128.27 (24) permut2(int, all_103_1, all_105_3, all_86_11, $sum(all_86_8, 1)) = 0 208.04/128.27 (25) elts(int, all_105_2) = all_105_1 208.04/128.27 (26) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.04/128.27 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 208.04/128.27 ($lesseq(1, $difference(v4, v5))) | ~ ($lesseq(v3, v5)) | ~ 208.04/128.27 (permut2(v0, v1, v2, v3, v4) = 0) | ~ (t2tb1(v5) = v6) | ~ (get(v0, 208.04/128.27 int, v2, v6) = v7) | ~ in_ty(v0) | ? [v8: $int] : ? [v9: $int] 208.04/128.27 : ($lesseq(1, $difference(v4, v8)) & $lesseq(v3, v8) & t2tb1(v8) = v9 208.04/128.27 & get(v0, int, v1, v9) = v7 & in_uni(v9) & in_uni(v7))) 208.04/128.27 (27) t2tb2(all_86_1) = all_105_2 208.04/128.27 (28) $lesseq(all_86_11, all_133_2) 208.04/128.27 (29) $lesseq(all_86_7, all_86_10) 208.04/128.27 (30) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.04/128.27 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 208.04/128.27 ($lesseq(1, $difference(v3, v4))) | ~ ($lesseq(v2, v4)) | ~ 208.04/128.27 (permut2(int, v5, v6, v2, v3) = 0) | ~ (t2tb(v1) = v6) | ~ (t2tb(v0) 208.04/128.27 = v5) | ~ (get3(v1, v4) = v7) | ~ in_map_int_int(v0) | ? [v8: 208.04/128.27 $int] : ($lesseq(1, $difference(v3, v8)) & $lesseq(v2, v8) & 208.04/128.27 get3(v0, v8) = v7)) 208.04/128.27 (31) $lesseq(0, all_86_7) 208.04/128.27 (32) permut2(int, all_105_3, all_105_1, all_86_7, $sum(all_86_10, 1)) = 0 208.04/128.27 (33) in_array_int(all_86_1) 208.04/128.27 (34) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.04/128.27 $int] : ! [v5: $int] : ! [v6: $int] : ( ~ ($lesseq(0, v4)) | ~ 208.04/128.27 ($lesseq(0, v3)) | ~ (permut2(v0, v5, v6, v3, v4) = 0) | ~ (elts(v0, 208.04/128.27 v2) = v6) | ~ (elts(v0, v1) = v5) | ~ in_ty(v0) | ? [v7: $int] 208.04/128.27 : ? [v8: $int] : ((v7 = 0 & permut3(v0, v1, v2, v3, v4) = 0) | 208.04/128.27 (length1(v0, v1) = v7 & ( ~ ($lesseq(v4, v7)) | ~ ($lesseq(v3, v7)) 208.04/128.27 | ( ~ (v8 = v7) & length1(v0, v2) = v8))))) 208.04/128.27 (35) $lesseq(1, $difference(all_86_7, all_86_8)) 208.04/128.27 (36) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.04/128.27 $int] : ! [v5: $int] : ! [v6: $int] : ( ~ ($lesseq(1, 208.04/128.27 $difference(v4, v5))) | ~ ($lesseq(v3, v5)) | ~ (map_eq_sub1(v0, 208.04/128.27 v1, v2, v3, v4) = 0) | ~ (t2tb1(v5) = v6) | ~ in_ty(v0) | ? 208.04/128.27 [v7: $int] : (get(v0, int, v2, v6) = v7 & get(v0, int, v1, v6) = v7 & 208.04/128.27 in_uni(v7))) 208.04/128.27 (37) $lesseq(1, $difference(all_86_13, all_86_10)) 208.04/128.27 (38) in_map_int_int(all_86_4) 208.04/128.27 (39) $lesseq(0, all_86_11) 208.04/128.27 (40) elts(int, all_103_2) = all_103_1 208.04/128.27 (41) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ( ~ 208.04/128.27 (t2tb2(v0) = v2) | ~ (get4(int, v2, v1) = v3) | ~ in_array_int(v0) | 208.04/128.27 ? [v4: $int] : ? [v5: $int] : ? [v6: $int] : (tb2t(v4) = v5 & 208.04/128.27 tb2t1(v3) = v6 & get3(v5, v1) = v6 & elts(int, v2) = v4 & 208.04/128.27 in_map_int_int(v5) & in_uni(v4))) 208.04/128.27 (42) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ (tb2t(v2) 208.04/128.27 = v1) | ~ (tb2t(v2) = v0)) 208.04/128.27 (43) $lesseq(43, all_133_0) 208.04/128.27 (44) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.04/128.27 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 208.04/128.27 ($lesseq(1, $difference(v3, v6))) | ~ ($lesseq(v2, v6)) | ~ 208.04/128.27 (map_eq_sub1(int, v4, v5, v2, v3) = 0) | ~ (t2tb(v1) = v5) | ~ 208.04/128.27 (t2tb(v0) = v4) | ~ (get3(v1, v6) = v7) | ~ in_map_int_int(v0) | 208.04/128.27 get3(v0, v6) = v7) 208.04/128.27 (45) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 208.04/128.27 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 208.04/128.27 (46) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ( ~ 208.04/128.27 (get4(v0, v1, v2) = v3) | ~ in_ty(v0) | ? [v4: $int] : ? [v5: $int] 208.04/128.27 : (elts(v0, v1) = v4 & t2tb1(v2) = v5 & get(v0, int, v4, v5) = v3 & 208.04/128.27 in_uni(v5) & in_uni(v4) & in_uni(v3))) 208.04/128.27 (47) t2tb(all_86_4) = all_105_3 208.04/128.27 208.04/128.27 Begin of proof 208.04/128.27 | 208.04/128.27 | BETA: splitting (21) gives: 208.04/128.27 | 208.04/128.27 | Case 1: 208.04/128.27 | | 208.04/128.27 | | (48) ~ (all_86_7 = 0) 208.04/128.27 | | 208.04/128.27 | | STRENGTHEN: (31), (48) imply: 208.04/128.27 | | (49) $lesseq(1, all_86_7) 208.04/128.27 | | 208.04/128.27 | | COMBINE_INEQS: (11), (28) imply: 208.04/128.27 | | (50) $lesseq(all_86_11, all_86_8) 208.04/128.27 | | 208.04/128.27 | | COMBINE_INEQS: (29), (35) imply: 208.04/128.27 | | (51) $lesseq(1, $difference(all_86_10, all_86_8)) 208.04/128.27 | | 208.04/128.27 | | COMBINE_INEQS: (29), (49) imply: 208.04/128.27 | | (52) $lesseq(1, all_86_10) 208.04/128.27 | | 208.04/128.27 | | COMBINE_INEQS: (50), (51) imply: 208.04/128.27 | | (53) $lesseq(1, $difference(all_86_10, all_86_11)) 208.04/128.27 | | 208.04/128.27 | | COMBINE_INEQS: (37), (53) imply: 208.04/128.27 | | (54) $lesseq(2, $difference(all_86_13, all_86_11)) 208.04/128.27 | | 208.04/128.27 | | COMBINE_INEQS: (39), (54) imply: 208.04/128.27 | | (55) $lesseq(2, all_86_13) 208.04/128.27 | | 208.04/128.27 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), 208.04/128.27 | | (13), (14), (15), (16), (17), (18), (19), (20), (22), (23), (24), 208.04/128.27 | | (25), (26), (27), (28), (29), (30), (32), (33), (34), (35), (36), 208.04/128.27 | | (37), (38), (39), (40), (41), (42), (43), (44), (45), (46), (47), 208.04/128.27 | | (52), (54), (55) are inconsistent by sub-proof #133. 208.04/128.27 | | 208.04/128.27 | Case 2: 208.04/128.27 | | 208.04/128.27 | | (56) all_86_7 = 0 208.04/128.27 | | 208.04/128.27 | | REDUCE: (35), (56) imply: 208.04/128.27 | | (57) $lesseq(all_86_8, -1) 208.04/128.27 | | 208.04/128.27 | | COMBINE_INEQS: (11), (28) imply: 208.04/128.27 | | (58) $lesseq(all_86_11, all_86_8) 208.04/128.27 | | 208.04/128.27 | | COMBINE_INEQS: (57), (58) imply: 208.04/128.27 | | (59) $lesseq(all_86_11, -1) 208.04/128.27 | | 208.04/128.27 | | COMBINE_INEQS: (39), (59) imply: 208.04/128.27 | | (60) $lesseq(0, -1) 208.04/128.27 | | 208.04/128.27 | | CLOSE: (60) is inconsistent. 208.04/128.27 | | 208.04/128.27 | End of split 208.04/128.27 | 208.04/128.27 End of proof 208.04/128.27 208.04/128.27 Sub-proof #118 shows that the following formulas are inconsistent: 208.04/128.27 ---------------------------------------------------------------- 208.04/128.27 (1) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ (tb2t1(v2) 208.04/128.27 = v1) | ~ (tb2t1(v2) = v0)) 208.04/128.27 (2) length1(int, all_103_2) = all_86_13 208.04/128.27 (3) in_map_int_int(all_86_6) 208.04/128.27 (4) in_map_int_int(all_86_12) 208.04/128.27 (5) elts(int, all_103_4) = all_103_3 208.04/128.27 (6) t2tb(all_86_2) = all_105_1 208.04/128.27 (7) in_ty(int) 208.04/128.27 (8) length1(int, all_103_4) = all_86_13 208.04/128.27 (9) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.04/128.27 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 208.04/128.27 (permut2(v0, v5, v6, v3, v4) = v7) | ~ (elts(v0, v2) = v6) | ~ 208.04/128.27 (elts(v0, v1) = v5) | ~ in_ty(v0) | ? [v8: $int] : ? [v9: $int] : 208.04/128.27 ((v9 = v8 & v7 = 0 & $lesseq(v4, v8) & $lesseq(v3, v8) & $lesseq(0, v4) 208.04/128.27 & $lesseq(0, v3) & length1(v0, v2) = v8 & length1(v0, v1) = v8) | ( 208.04/128.27 ~ (v8 = 0) & permut3(v0, v1, v2, v3, v4) = v8))) 208.04/128.27 (10) $lesseq(-1, all_86_8) 208.04/128.27 (11) $lesseq(1, $difference(all_86_13, all_86_7)) 208.04/128.27 (12) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.04/128.27 $int] : ! [v5: $int] : ( ~ (permut2(v0, v2, v3, v4, v5) = 0) | ~ 208.04/128.27 (permut2(v0, v1, v2, v4, v5) = 0) | ~ in_ty(v0) | permut2(v0, v1, v3, 208.04/128.27 v4, v5) = 0) 208.04/128.27 (13) ! [v0: $int] : ! [v1: $int] : (v1 = 42 | ~ ($lesseq(1, 208.04/128.27 $difference(all_86_7, v0))) | ~ ($lesseq(1, $difference(v0, 208.04/128.27 all_86_8))) | ~ (get3(all_86_6, v0) = v1)) 208.04/128.27 (14) map_eq_sub1(int, all_103_3, all_103_1, $sum(all_86_10, 1), all_86_13) = 208.04/128.27 0 208.04/128.27 (15) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.04/128.27 $int] : ! [v5: $int] : ! [v6: $int] : ( ~ (permut2(v0, v3, v4, 0, 208.04/128.27 v5) = v6) | ~ (length1(v0, v1) = v5) | ~ (elts(v0, v2) = v4) | 208.04/128.27 ~ (elts(v0, v1) = v3) | ~ in_ty(v0) | ? [v7: $int] : ((v7 = v5 & v6 208.04/128.27 = 0 & length1(v0, v2) = v5) | ( ~ (v7 = 0) & permut_all(v0, v1, 208.04/128.27 v2) = v7))) 208.04/128.27 (16) t2tb(all_86_6) = all_103_1 208.04/128.27 (17) $lesseq(3, $difference(all_86_13, all_86_11)) 208.04/128.27 (18) $lesseq(1, $difference(all_133_2, all_86_8)) 208.04/128.27 (19) tb2t1(all_133_1) = all_133_0 208.04/128.27 (20) map_eq_sub1(int, all_103_1, all_105_3, $sum(all_86_8, 1), all_86_13) = 0 208.04/128.27 (21) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.04/128.27 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ (permut3(v6, v5, 208.04/128.27 v4, v3, v2) = v1) | ~ (permut3(v6, v5, v4, v3, v2) = v0)) 208.04/128.27 (22) permut2(int, all_103_1, all_105_3, 0, all_86_13) = 0 208.04/128.27 (23) permut2(int, all_103_3, all_105_3, all_86_11, $sum(all_86_10, 1)) = 0 208.04/128.27 (24) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 208.04/128.27 | ~ (elts(v3, v2) = v1) | ~ (elts(v3, v2) = v0)) 208.04/128.27 (25) length1(int, all_105_4) = all_86_13 208.04/128.27 (26) elts(int, all_105_4) = all_105_3 208.04/128.27 (27) $lesseq(1, $difference(all_86_7, all_133_2)) 208.04/128.27 (28) permut2(int, all_103_3, all_103_1, 0, all_86_13) = 0 208.04/128.27 (29) map_eq_sub1(int, all_105_3, all_105_1, 0, all_86_7) = 0 208.04/128.27 (30) get4(int, all_105_2, all_133_2) = all_133_1 208.04/128.27 (31) $lesseq(3, all_86_13) 208.04/128.27 (32) tb2t(all_105_1) = all_86_2 208.04/128.27 (33) elts(int, all_105_2) = all_105_1 208.04/128.27 (34) map_eq_sub1(int, all_103_3, all_103_1, 0, all_86_11) = 0 208.04/128.27 (35) t2tb2(all_86_1) = all_105_2 208.04/128.27 (36) $lesseq(all_86_11, all_86_8) 208.04/128.27 (37) $lesseq(all_86_7, all_86_10) 208.04/128.27 (38) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.04/128.27 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 208.04/128.27 ($lesseq(1, $difference(v3, v4))) | ~ ($lesseq(v2, v4)) | ~ 208.04/128.27 (permut2(int, v5, v6, v2, v3) = 0) | ~ (t2tb(v1) = v6) | ~ (t2tb(v0) 208.04/128.27 = v5) | ~ (get3(v1, v4) = v7) | ~ in_map_int_int(v0) | ? [v8: 208.04/128.27 $int] : ($lesseq(1, $difference(v3, v8)) & $lesseq(v2, v8) & 208.04/128.27 get3(v0, v8) = v7)) 208.04/128.27 (39) ~ (all_133_0 = 42) 208.04/128.27 (40) in_array_int(all_86_1) 208.04/128.27 (41) t2tb(all_86_12) = all_103_3 208.04/128.27 (42) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.04/128.27 $int] : ! [v5: $int] : ! [v6: $int] : ( ~ ($lesseq(0, v4)) | ~ 208.04/128.27 ($lesseq(0, v3)) | ~ (permut2(v0, v5, v6, v3, v4) = 0) | ~ (elts(v0, 208.04/128.27 v2) = v6) | ~ (elts(v0, v1) = v5) | ~ in_ty(v0) | ? [v7: $int] 208.04/128.27 : ? [v8: $int] : ((v7 = 0 & permut3(v0, v1, v2, v3, v4) = 0) | 208.04/128.27 (length1(v0, v1) = v7 & ( ~ ($lesseq(v4, v7)) | ~ ($lesseq(v3, v7)) 208.04/128.27 | ( ~ (v8 = v7) & length1(v0, v2) = v8))))) 208.04/128.27 (43) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.04/128.27 $int] : ! [v5: $int] : ! [v6: $int] : ( ~ ($lesseq(1, 208.04/128.27 $difference(v4, v5))) | ~ ($lesseq(v3, v5)) | ~ (map_eq_sub1(v0, 208.04/128.27 v1, v2, v3, v4) = 0) | ~ (t2tb1(v5) = v6) | ~ in_ty(v0) | ? 208.04/128.27 [v7: $int] : (get(v0, int, v2, v6) = v7 & get(v0, int, v1, v6) = v7 & 208.04/128.27 in_uni(v7))) 208.04/128.27 (44) $lesseq(1, $difference(all_86_13, all_86_10)) 208.04/128.27 (45) in_map_int_int(all_86_4) 208.04/128.27 (46) $lesseq(0, all_86_11) 208.04/128.27 (47) elts(int, all_103_2) = all_103_1 208.04/128.27 (48) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ( ~ 208.04/128.27 (t2tb2(v0) = v2) | ~ (get4(int, v2, v1) = v3) | ~ in_array_int(v0) | 208.04/128.27 ? [v4: $int] : ? [v5: $int] : ? [v6: $int] : (tb2t(v4) = v5 & 208.04/128.27 tb2t1(v3) = v6 & get3(v5, v1) = v6 & elts(int, v2) = v4 & 208.04/128.27 in_map_int_int(v5) & in_uni(v4))) 208.04/128.27 (49) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ (tb2t(v2) 208.04/128.27 = v1) | ~ (tb2t(v2) = v0)) 208.04/128.27 (50) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.04/128.27 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 208.04/128.27 ($lesseq(1, $difference(v3, v6))) | ~ ($lesseq(v2, v6)) | ~ 208.04/128.27 (map_eq_sub1(int, v4, v5, v2, v3) = 0) | ~ (t2tb(v1) = v5) | ~ 208.04/128.27 (t2tb(v0) = v4) | ~ (get3(v1, v6) = v7) | ~ in_map_int_int(v0) | 208.04/128.27 get3(v0, v6) = v7) 208.04/128.27 (51) in_uni(all_133_1) 208.04/128.27 (52) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 208.04/128.27 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 208.04/128.27 (53) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ( ~ 208.04/128.27 (get4(v0, v1, v2) = v3) | ~ in_ty(v0) | ? [v4: $int] : ? [v5: $int] 208.04/128.27 : (elts(v0, v1) = v4 & t2tb1(v2) = v5 & get(v0, int, v4, v5) = v3 & 208.04/128.27 in_uni(v5) & in_uni(v4) & in_uni(v3))) 208.04/128.27 (54) $lesseq(1, all_86_10) 208.04/128.27 (55) ! [v0: $int] : ! [v1: $int] : ( ~ (tb2t1(v0) = v1) | ~ in_uni(v0) | 208.04/128.27 t2tb1(v1) = v0) 208.04/128.27 (56) map_eq_sub1(int, all_105_3, all_105_1, $sum(all_86_10, 1), all_86_13) = 208.04/128.27 0 208.04/128.27 (57) t2tb(all_86_4) = all_105_3 208.04/128.27 208.04/128.27 Begin of proof 208.04/128.27 | 208.04/128.27 | GROUND_INST: instantiating (9) with int, all_103_2, all_105_4, 0, all_86_13, 208.04/128.27 | all_103_1, all_105_3, 0, simplifying with (7), (22), (26), (47) 208.04/128.27 | gives: 208.04/128.27 | (58) ? [v0: $int] : ? [v1: $int] : ((v1 = v0 & $lesseq(all_86_13, v0) & 208.04/128.27 | $lesseq(0, v0) & $lesseq(0, all_86_13) & length1(int, all_105_4) = 208.04/128.27 | v0 & length1(int, all_103_2) = v0) | ( ~ (v0 = 0) & permut3(int, 208.04/128.27 | all_103_2, all_105_4, 0, all_86_13) = v0)) 208.04/128.27 | 208.04/128.27 | GROUND_INST: instantiating (12) with int, all_103_3, all_103_1, all_105_3, 0, 208.04/128.27 | all_86_13, simplifying with (7), (22), (28) gives: 208.04/128.27 | (59) permut2(int, all_103_3, all_105_3, 0, all_86_13) = 0 208.04/128.27 | 208.04/128.27 | GROUND_INST: instantiating (42) with int, all_103_2, all_105_4, 0, all_86_13, 208.04/128.27 | all_103_1, all_105_3, simplifying with (7), (22), (26), (47) 208.04/128.27 | gives: 208.04/128.27 | (60) ~ ($lesseq(0, all_86_13)) | ? [v0: $int] : ? [v1: $int] : ((v0 = 0 208.04/128.27 | & permut3(int, all_103_2, all_105_4, 0, all_86_13) = 0) | 208.04/128.27 | (length1(int, all_103_2) = v0 & ( ~ ($lesseq(all_86_13, v0)) | ~ 208.04/128.27 | ($lesseq(0, v0)) | ( ~ (v1 = v0) & length1(int, all_105_4) = 208.04/128.27 | v1)))) 208.04/128.27 | 208.04/128.27 | GROUND_INST: instantiating (9) with int, all_103_4, all_105_4, all_86_11, 208.04/128.27 | $sum(all_86_10, 1), all_103_3, all_105_3, 0, simplifying with 208.04/128.27 | (5), (7), (23), (26) gives: 208.04/128.27 | (61) ? [v0: $int] : ? [v1: $int] : ((v1 = v0 & $lesseq(1, $difference(v0, 208.04/128.27 | all_86_10)) & $lesseq(all_86_11, v0) & $lesseq(-1, all_86_10) 208.04/128.27 | & $lesseq(0, all_86_11) & length1(int, all_105_4) = v0 & 208.04/128.27 | length1(int, all_103_4) = v0) | ( ~ (v0 = 0) & permut3(int, 208.04/128.27 | all_103_4, all_105_4, all_86_11, $sum(all_86_10, 1)) = v0)) 208.04/128.27 | 208.04/128.27 | GROUND_INST: instantiating (42) with int, all_103_4, all_105_4, all_86_11, 208.04/128.27 | $sum(all_86_10, 1), all_103_3, all_105_3, simplifying with (5), 208.04/128.27 | (7), (23), (26) gives: 208.04/128.27 | (62) ~ ($lesseq(-1, all_86_10)) | ~ ($lesseq(0, all_86_11)) | ? [v0: 208.04/128.27 | $int] : ? [v1: $int] : ((v0 = 0 & permut3(int, all_103_4, 208.04/128.27 | all_105_4, all_86_11, $sum(all_86_10, 1)) = 0) | (length1(int, 208.04/128.27 | all_103_4) = v0 & ( ~ ($lesseq(1, $difference(v0, all_86_10))) | 208.04/128.27 | ~ ($lesseq(all_86_11, v0)) | ( ~ (v1 = v0) & length1(int, 208.04/128.27 | all_105_4) = v1)))) 208.04/128.27 | 208.04/128.27 | GROUND_INST: instantiating (15) with int, all_103_4, all_105_4, all_103_3, 208.04/128.27 | all_105_3, all_86_13, 0, simplifying with (5), (7), (8), (26) 208.04/128.27 | gives: 208.04/128.27 | (63) ~ (permut2(int, all_103_3, all_105_3, 0, all_86_13) = 0) | ? [v0: 208.04/128.27 | $int] : ((v0 = all_86_13 & length1(int, all_105_4) = all_86_13) | ( 208.04/128.27 | ~ (v0 = 0) & permut_all(int, all_103_4, all_105_4) = v0)) 208.04/128.27 | 208.04/128.27 | GROUND_INST: instantiating (9) with int, all_103_4, all_103_2, 0, all_86_13, 208.04/128.27 | all_103_3, all_103_1, 0, simplifying with (5), (7), (28), (47) 208.04/128.27 | gives: 208.04/128.27 | (64) ? [v0: $int] : ? [v1: $int] : ((v1 = v0 & $lesseq(all_86_13, v0) & 208.04/128.27 | $lesseq(0, v0) & $lesseq(0, all_86_13) & length1(int, all_103_2) = 208.04/128.27 | v0 & length1(int, all_103_4) = v0) | ( ~ (v0 = 0) & permut3(int, 208.04/128.27 | all_103_4, all_103_2, 0, all_86_13) = v0)) 208.04/128.27 | 208.04/128.28 | GROUND_INST: instantiating (42) with int, all_103_4, all_103_2, 0, all_86_13, 208.04/128.28 | all_103_3, all_103_1, simplifying with (5), (7), (28), (47) 208.04/128.28 | gives: 208.04/128.28 | (65) ~ ($lesseq(0, all_86_13)) | ? [v0: $int] : ? [v1: $int] : ((v0 = 0 208.04/128.28 | & permut3(int, all_103_4, all_103_2, 0, all_86_13) = 0) | 208.04/128.28 | (length1(int, all_103_4) = v0 & ( ~ ($lesseq(all_86_13, v0)) | ~ 208.04/128.28 | ($lesseq(0, v0)) | ( ~ (v1 = v0) & length1(int, all_103_2) = 208.04/128.28 | v1)))) 208.04/128.28 | 208.04/128.28 | GROUND_INST: instantiating (55) with all_133_1, all_133_0, simplifying with 208.04/128.28 | (19), (51) gives: 208.04/128.28 | (66) t2tb1(all_133_0) = all_133_1 208.04/128.28 | 208.04/128.28 | GROUND_INST: instantiating (48) with all_86_1, all_133_2, all_105_2, 208.04/128.28 | all_133_1, simplifying with (30), (35), (40) gives: 208.04/128.28 | (67) ? [v0: $int] : ? [v1: $int] : ? [v2: $int] : (tb2t(v0) = v1 & 208.04/128.28 | tb2t1(all_133_1) = v2 & get3(v1, all_133_2) = v2 & elts(int, 208.04/128.28 | all_105_2) = v0 & in_map_int_int(v1) & in_uni(v0)) 208.04/128.28 | 208.04/128.28 | GROUND_INST: instantiating (53) with int, all_105_2, all_133_2, all_133_1, 208.04/128.28 | simplifying with (7), (30) gives: 208.04/128.28 | (68) ? [v0: $int] : ? [v1: $int] : (elts(int, all_105_2) = v0 & 208.04/128.28 | t2tb1(all_133_2) = v1 & get(int, int, v0, v1) = all_133_1 & 208.04/128.28 | in_uni(v1) & in_uni(v0) & in_uni(all_133_1)) 208.04/128.28 | 208.04/128.28 | DELTA: instantiating (67) with fresh symbols all_725_0, all_725_1, all_725_2 208.04/128.28 | gives: 208.04/128.28 | (69) tb2t(all_725_2) = all_725_1 & tb2t1(all_133_1) = all_725_0 & 208.04/128.28 | get3(all_725_1, all_133_2) = all_725_0 & elts(int, all_105_2) = 208.04/128.28 | all_725_2 & in_map_int_int(all_725_1) & in_uni(all_725_2) 208.04/128.28 | 208.04/128.28 | ALPHA: (69) implies: 208.04/128.28 | (70) elts(int, all_105_2) = all_725_2 208.04/128.28 | (71) get3(all_725_1, all_133_2) = all_725_0 208.04/128.28 | (72) tb2t1(all_133_1) = all_725_0 208.04/128.28 | (73) tb2t(all_725_2) = all_725_1 208.04/128.28 | 208.04/128.28 | DELTA: instantiating (64) with fresh symbols all_731_0, all_731_1 gives: 208.04/128.28 | (74) (all_731_0 = all_731_1 & $lesseq(all_86_13, all_731_1) & $lesseq(0, 208.04/128.28 | all_731_1) & $lesseq(0, all_86_13) & length1(int, all_103_2) = 208.04/128.28 | all_731_1 & length1(int, all_103_4) = all_731_1) | ( ~ (all_731_1 = 208.04/128.28 | 0) & permut3(int, all_103_4, all_103_2, 0, all_86_13) = all_731_1) 208.04/128.28 | 208.04/128.28 | DELTA: instantiating (61) with fresh symbols all_736_0, all_736_1 gives: 208.04/128.28 | (75) (all_736_0 = all_736_1 & $lesseq(1, $difference(all_736_1, all_86_10)) 208.04/128.28 | & $lesseq(all_86_11, all_736_1) & $lesseq(-1, all_86_10) & 208.04/128.28 | $lesseq(0, all_86_11) & length1(int, all_105_4) = all_736_1 & 208.04/128.28 | length1(int, all_103_4) = all_736_1) | ( ~ (all_736_1 = 0) & 208.04/128.28 | permut3(int, all_103_4, all_105_4, all_86_11, $sum(all_86_10, 1)) = 208.04/128.28 | all_736_1) 208.04/128.28 | 208.04/128.28 | DELTA: instantiating (58) with fresh symbols all_737_0, all_737_1 gives: 208.04/128.28 | (76) (all_737_0 = all_737_1 & $lesseq(all_86_13, all_737_1) & $lesseq(0, 208.04/128.28 | all_737_1) & $lesseq(0, all_86_13) & length1(int, all_105_4) = 208.04/128.28 | all_737_1 & length1(int, all_103_2) = all_737_1) | ( ~ (all_737_1 = 208.04/128.28 | 0) & permut3(int, all_103_2, all_105_4, 0, all_86_13) = all_737_1) 208.04/128.28 | 208.04/128.28 | DELTA: instantiating (68) with fresh symbols all_738_0, all_738_1 gives: 208.04/128.28 | (77) elts(int, all_105_2) = all_738_1 & t2tb1(all_133_2) = all_738_0 & 208.04/128.28 | get(int, int, all_738_1, all_738_0) = all_133_1 & in_uni(all_738_0) & 208.04/128.28 | in_uni(all_738_1) & in_uni(all_133_1) 208.20/128.28 | 208.20/128.28 | ALPHA: (77) implies: 208.20/128.28 | (78) t2tb1(all_133_2) = all_738_0 208.20/128.28 | (79) elts(int, all_105_2) = all_738_1 208.20/128.28 | 208.20/128.28 | BETA: splitting (60) gives: 208.20/128.28 | 208.20/128.28 | Case 1: 208.20/128.28 | | 208.20/128.28 | | (80) $lesseq(all_86_13, -1) 208.20/128.28 | | 208.20/128.28 | | COMBINE_INEQS: (31), (80) imply: 208.20/128.28 | | (81) $lesseq(0, -1) 208.20/128.28 | | 208.20/128.28 | | CLOSE: (81) is inconsistent. 208.20/128.28 | | 208.20/128.28 | Case 2: 208.20/128.28 | | 208.20/128.28 | | (82) ? [v0: $int] : ? [v1: $int] : ((v0 = 0 & permut3(int, all_103_2, 208.20/128.28 | | all_105_4, 0, all_86_13) = 0) | (length1(int, all_103_2) = v0 208.20/128.28 | | & ( ~ ($lesseq(all_86_13, v0)) | ~ ($lesseq(0, v0)) | ( ~ (v1 = 208.20/128.28 | | v0) & length1(int, all_105_4) = v1)))) 208.20/128.28 | | 208.20/128.28 | | DELTA: instantiating (82) with fresh symbols all_749_0, all_749_1 gives: 208.20/128.28 | | (83) (all_749_1 = 0 & permut3(int, all_103_2, all_105_4, 0, all_86_13) = 208.20/128.28 | | 0) | (length1(int, all_103_2) = all_749_1 & ( ~ 208.20/128.28 | | ($lesseq(all_86_13, all_749_1)) | ~ ($lesseq(0, all_749_1)) | ( 208.20/128.28 | | ~ (all_749_0 = all_749_1) & length1(int, all_105_4) = 208.20/128.28 | | all_749_0))) 208.20/128.28 | | 208.20/128.28 | | BETA: splitting (83) gives: 208.20/128.28 | | 208.20/128.28 | | Case 1: 208.20/128.28 | | | 208.20/128.28 | | | (84) all_749_1 = 0 & permut3(int, all_103_2, all_105_4, 0, all_86_13) = 208.20/128.28 | | | 0 208.20/128.28 | | | 208.20/128.28 | | | ALPHA: (84) implies: 208.20/128.28 | | | (85) permut3(int, all_103_2, all_105_4, 0, all_86_13) = 0 208.20/128.28 | | | 208.20/128.28 | | | BETA: splitting (62) gives: 208.20/128.28 | | | 208.20/128.28 | | | Case 1: 208.20/128.28 | | | | 208.20/128.28 | | | | (86) $lesseq(all_86_11, -1) 208.20/128.28 | | | | 208.20/128.28 | | | | COMBINE_INEQS: (46), (86) imply: 208.20/128.28 | | | | (87) $lesseq(0, -1) 208.20/128.28 | | | | 208.20/128.28 | | | | CLOSE: (87) is inconsistent. 208.20/128.28 | | | | 208.20/128.28 | | | Case 2: 208.20/128.28 | | | | 208.20/128.28 | | | | (88) ~ ($lesseq(-1, all_86_10)) | ? [v0: $int] : ? [v1: $int] : 208.20/128.28 | | | | ((v0 = 0 & permut3(int, all_103_4, all_105_4, all_86_11, 208.20/128.28 | | | | $sum(all_86_10, 1)) = 0) | (length1(int, all_103_4) = v0 & 208.20/128.28 | | | | ( ~ ($lesseq(1, $difference(v0, all_86_10))) | ~ 208.20/128.28 | | | | ($lesseq(all_86_11, v0)) | ( ~ (v1 = v0) & length1(int, 208.20/128.28 | | | | all_105_4) = v1)))) 208.20/128.28 | | | | 208.20/128.28 | | | | BETA: splitting (63) gives: 208.20/128.28 | | | | 208.20/128.28 | | | | Case 1: 208.20/128.28 | | | | | 208.20/128.28 | | | | | (89) ~ (permut2(int, all_103_3, all_105_3, 0, all_86_13) = 0) 208.20/128.28 | | | | | 208.20/128.28 | | | | | PRED_UNIFY: (59), (89) imply: 208.20/128.28 | | | | | (90) $false 208.20/128.28 | | | | | 208.20/128.28 | | | | | CLOSE: (90) is inconsistent. 208.20/128.28 | | | | | 208.20/128.28 | | | | Case 2: 208.20/128.28 | | | | | 208.20/128.28 | | | | | (91) ? [v0: $int] : ((v0 = all_86_13 & length1(int, all_105_4) = 208.20/128.28 | | | | | all_86_13) | ( ~ (v0 = 0) & permut_all(int, all_103_4, 208.20/128.28 | | | | | all_105_4) = v0)) 208.20/128.28 | | | | | 208.20/128.28 | | | | | DELTA: instantiating (91) with fresh symbol all_769_0 gives: 208.20/128.28 | | | | | (92) (all_769_0 = all_86_13 & length1(int, all_105_4) = all_86_13) 208.20/128.28 | | | | | | ( ~ (all_769_0 = 0) & permut_all(int, all_103_4, all_105_4) 208.20/128.28 | | | | | = all_769_0) 208.20/128.28 | | | | | 208.20/128.28 | | | | | BETA: splitting (88) gives: 208.20/128.28 | | | | | 208.20/128.28 | | | | | Case 1: 208.20/128.28 | | | | | | 208.20/128.28 | | | | | | (93) $lesseq(all_86_10, -2) 208.20/128.28 | | | | | | 208.20/128.28 | | | | | | COMBINE_INEQS: (54), (93) imply: 208.20/128.28 | | | | | | (94) $lesseq(0, -1) 208.20/128.28 | | | | | | 208.20/128.28 | | | | | | CLOSE: (94) is inconsistent. 208.20/128.28 | | | | | | 208.20/128.28 | | | | | Case 2: 208.20/128.28 | | | | | | 208.20/128.28 | | | | | | (95) ? [v0: $int] : ? [v1: $int] : ((v0 = 0 & permut3(int, 208.20/128.28 | | | | | | all_103_4, all_105_4, all_86_11, $sum(all_86_10, 1)) = 208.20/128.28 | | | | | | 0) | (length1(int, all_103_4) = v0 & ( ~ ($lesseq(1, 208.20/128.28 | | | | | | $difference(v0, all_86_10))) | ~ 208.20/128.28 | | | | | | ($lesseq(all_86_11, v0)) | ( ~ (v1 = v0) & 208.20/128.28 | | | | | | length1(int, all_105_4) = v1)))) 208.20/128.28 | | | | | | 208.20/128.28 | | | | | | DELTA: instantiating (95) with fresh symbols all_775_0, all_775_1 208.20/128.28 | | | | | | gives: 208.20/128.28 | | | | | | (96) (all_775_1 = 0 & permut3(int, all_103_4, all_105_4, 208.20/128.28 | | | | | | all_86_11, $sum(all_86_10, 1)) = 0) | (length1(int, 208.20/128.28 | | | | | | all_103_4) = all_775_1 & ( ~ ($lesseq(1, 208.20/128.28 | | | | | | $difference(all_775_1, all_86_10))) | ~ 208.20/128.28 | | | | | | ($lesseq(all_86_11, all_775_1)) | ( ~ (all_775_0 = 208.20/128.28 | | | | | | all_775_1) & length1(int, all_105_4) = all_775_0))) 208.20/128.28 | | | | | | 208.20/128.28 | | | | | | BETA: splitting (76) gives: 208.20/128.28 | | | | | | 208.20/128.28 | | | | | | Case 1: 208.20/128.28 | | | | | | | 208.20/128.28 | | | | | | | (97) all_737_0 = all_737_1 & $lesseq(all_86_13, all_737_1) & 208.20/128.28 | | | | | | | $lesseq(0, all_737_1) & $lesseq(0, all_86_13) & 208.20/128.28 | | | | | | | length1(int, all_105_4) = all_737_1 & length1(int, 208.20/128.28 | | | | | | | all_103_2) = all_737_1 208.20/128.28 | | | | | | | 208.20/128.28 | | | | | | | ALPHA: (97) implies: 208.20/128.28 | | | | | | | (98) length1(int, all_103_2) = all_737_1 208.20/128.28 | | | | | | | (99) length1(int, all_105_4) = all_737_1 208.20/128.28 | | | | | | | 208.20/128.28 | | | | | | | BETA: splitting (65) gives: 208.20/128.28 | | | | | | | 208.20/128.28 | | | | | | | Case 1: 208.20/128.28 | | | | | | | | 208.20/128.28 | | | | | | | | (100) $lesseq(all_86_13, -1) 208.20/128.28 | | | | | | | | 208.20/128.28 | | | | | | | | COMBINE_INEQS: (31), (100) imply: 208.20/128.28 | | | | | | | | (101) $lesseq(0, -1) 208.20/128.28 | | | | | | | | 208.20/128.28 | | | | | | | | CLOSE: (101) is inconsistent. 208.20/128.28 | | | | | | | | 208.20/128.28 | | | | | | | Case 2: 208.20/128.28 | | | | | | | | 208.20/128.28 | | | | | | | | (102) ? [v0: $int] : ? [v1: $int] : ((v0 = 0 & permut3(int, 208.20/128.28 | | | | | | | | all_103_4, all_103_2, 0, all_86_13) = 0) | 208.20/128.28 | | | | | | | | (length1(int, all_103_4) = v0 & ( ~ 208.20/128.28 | | | | | | | | ($lesseq(all_86_13, v0)) | ~ ($lesseq(0, v0)) | 208.20/128.28 | | | | | | | | ( ~ (v1 = v0) & length1(int, all_103_2) = v1)))) 208.20/128.28 | | | | | | | | 208.20/128.28 | | | | | | | | DELTA: instantiating (102) with fresh symbols all_787_0, 208.20/128.28 | | | | | | | | all_787_1 gives: 208.20/128.28 | | | | | | | | (103) (all_787_1 = 0 & permut3(int, all_103_4, all_103_2, 0, 208.20/128.28 | | | | | | | | all_86_13) = 0) | (length1(int, all_103_4) = 208.20/128.28 | | | | | | | | all_787_1 & ( ~ ($lesseq(all_86_13, all_787_1)) | ~ 208.20/128.28 | | | | | | | | ($lesseq(0, all_787_1)) | ( ~ (all_787_0 = 208.20/128.28 | | | | | | | | all_787_1) & length1(int, all_103_2) = 208.20/128.28 | | | | | | | | all_787_0))) 208.20/128.28 | | | | | | | | 208.20/128.28 | | | | | | | | GROUND_INST: instantiating (1) with all_133_0, all_725_0, 208.20/128.28 | | | | | | | | all_133_1, simplifying with (19), (72) gives: 208.20/128.28 | | | | | | | | (104) all_725_0 = all_133_0 208.20/128.28 | | | | | | | | 208.20/128.28 | | | | | | | | GROUND_INST: instantiating (52) with all_86_13, all_737_1, 208.20/128.28 | | | | | | | | all_103_2, int, simplifying with (2), (98) gives: 208.20/128.28 | | | | | | | | (105) all_737_1 = all_86_13 208.20/128.28 | | | | | | | | 208.20/128.28 | | | | | | | | GROUND_INST: instantiating (24) with all_105_1, all_738_1, 208.20/128.28 | | | | | | | | all_105_2, int, simplifying with (33), (79) gives: 208.20/128.28 | | | | | | | | (106) all_738_1 = all_105_1 208.20/128.28 | | | | | | | | 208.20/128.28 | | | | | | | | GROUND_INST: instantiating (24) with all_738_1, all_725_2, 208.20/128.28 | | | | | | | | all_105_2, int, simplifying with (70), (79) gives: 208.20/128.28 | | | | | | | | (107) all_738_1 = all_725_2 208.20/128.28 | | | | | | | | 208.20/128.28 | | | | | | | | COMBINE_EQS: (106), (107) imply: 208.20/128.28 | | | | | | | | (108) all_725_2 = all_105_1 208.20/128.28 | | | | | | | | 208.20/128.28 | | | | | | | | REDUCE: (73), (108) imply: 208.20/128.28 | | | | | | | | (109) tb2t(all_105_1) = all_725_1 208.20/128.28 | | | | | | | | 208.20/128.28 | | | | | | | | REDUCE: (71), (104) imply: 208.20/128.28 | | | | | | | | (110) get3(all_725_1, all_133_2) = all_133_0 208.20/128.28 | | | | | | | | 208.20/128.28 | | | | | | | | BETA: splitting (96) gives: 208.20/128.28 | | | | | | | | 208.20/128.28 | | | | | | | | Case 1: 208.20/128.28 | | | | | | | | | 208.20/128.28 | | | | | | | | | (111) all_775_1 = 0 & permut3(int, all_103_4, all_105_4, 208.20/128.28 | | | | | | | | | all_86_11, $sum(all_86_10, 1)) = 0 208.20/128.28 | | | | | | | | | 208.20/128.28 | | | | | | | | | ALPHA: (111) implies: 208.20/128.28 | | | | | | | | | (112) permut3(int, all_103_4, all_105_4, all_86_11, 208.20/128.28 | | | | | | | | | $sum(all_86_10, 1)) = 0 208.20/128.28 | | | | | | | | | 208.20/128.28 | | | | | | | | | REF_CLOSE: (3), (4), (6), (7), (8), (10), (11), (13), (14), 208.20/128.28 | | | | | | | | | (16), (18), (20), (21), (27), (29), (32), (34), 208.20/128.28 | | | | | | | | | (36), (37), (38), (39), (41), (43), (45), (49), 208.20/128.28 | | | | | | | | | (50), (52), (56), (57), (59), (66), (75), (78), 208.20/128.28 | | | | | | | | | (109), (110), (112) are inconsistent by sub-proof 208.20/128.28 | | | | | | | | | #122. 208.20/128.28 | | | | | | | | | 208.20/128.28 | | | | | | | | Case 2: 208.20/128.28 | | | | | | | | | 208.20/128.28 | | | | | | | | | (113) length1(int, all_103_4) = all_775_1 & ( ~ ($lesseq(1, 208.20/128.28 | | | | | | | | | $difference(all_775_1, all_86_10))) | ~ 208.20/128.28 | | | | | | | | | ($lesseq(all_86_11, all_775_1)) | ( ~ (all_775_0 = 208.20/128.28 | | | | | | | | | all_775_1) & length1(int, all_105_4) = 208.20/128.28 | | | | | | | | | all_775_0)) 208.20/128.28 | | | | | | | | | 208.20/128.28 | | | | | | | | | ALPHA: (113) implies: 208.20/128.28 | | | | | | | | | (114) length1(int, all_103_4) = all_775_1 208.20/128.28 | | | | | | | | | (115) ~ ($lesseq(1, $difference(all_775_1, all_86_10))) | 208.20/128.28 | | | | | | | | | ~ ($lesseq(all_86_11, all_775_1)) | ( ~ (all_775_0 = 208.20/128.28 | | | | | | | | | all_775_1) & length1(int, all_105_4) = all_775_0) 208.20/128.28 | | | | | | | | | 208.20/128.28 | | | | | | | | | BETA: splitting (103) gives: 208.20/128.28 | | | | | | | | | 208.20/128.28 | | | | | | | | | Case 1: 208.20/128.28 | | | | | | | | | | 208.20/128.28 | | | | | | | | | | (116) all_787_1 = 0 & permut3(int, all_103_4, all_103_2, 208.20/128.28 | | | | | | | | | | 0, all_86_13) = 0 208.20/128.28 | | | | | | | | | | 208.20/128.28 | | | | | | | | | | ALPHA: (116) implies: 208.20/128.28 | | | | | | | | | | (117) permut3(int, all_103_4, all_103_2, 0, all_86_13) = 208.20/128.28 | | | | | | | | | | 0 208.20/128.28 | | | | | | | | | | 208.20/128.28 | | | | | | | | | | BETA: splitting (74) gives: 208.20/128.28 | | | | | | | | | | 208.20/128.28 | | | | | | | | | | Case 1: 208.20/128.28 | | | | | | | | | | | 208.20/128.28 | | | | | | | | | | | (118) all_731_0 = all_731_1 & $lesseq(all_86_13, 208.20/128.28 | | | | | | | | | | | all_731_1) & $lesseq(0, all_731_1) & $lesseq(0, 208.20/128.28 | | | | | | | | | | | all_86_13) & length1(int, all_103_2) = all_731_1 208.20/128.28 | | | | | | | | | | | & length1(int, all_103_4) = all_731_1 208.20/128.28 | | | | | | | | | | | 208.20/128.28 | | | | | | | | | | | ALPHA: (118) implies: 208.20/128.28 | | | | | | | | | | | (119) length1(int, all_103_4) = all_731_1 208.20/128.28 | | | | | | | | | | | 208.20/128.28 | | | | | | | | | | | GROUND_INST: instantiating (52) with all_86_13, all_775_1, 208.20/128.28 | | | | | | | | | | | all_103_4, int, simplifying with (8), (114) gives: 208.20/128.28 | | | | | | | | | | | (120) all_775_1 = all_86_13 208.20/128.28 | | | | | | | | | | | 208.20/128.28 | | | | | | | | | | | GROUND_INST: instantiating (52) with all_775_1, all_731_1, 208.20/128.28 | | | | | | | | | | | all_103_4, int, simplifying with (114), (119) 208.20/128.28 | | | | | | | | | | | gives: 208.20/128.28 | | | | | | | | | | | (121) all_775_1 = all_731_1 208.20/128.28 | | | | | | | | | | | 208.20/128.28 | | | | | | | | | | | COMBINE_EQS: (120), (121) imply: 208.20/128.28 | | | | | | | | | | | (122) all_731_1 = all_86_13 208.20/128.28 | | | | | | | | | | | 208.20/128.28 | | | | | | | | | | | BETA: splitting (115) gives: 208.20/128.28 | | | | | | | | | | | 208.20/128.28 | | | | | | | | | | | Case 1: 208.20/128.28 | | | | | | | | | | | | 208.20/128.28 | | | | | | | | | | | | (123) $lesseq(1, $difference(all_86_11, all_775_1)) 208.20/128.28 | | | | | | | | | | | | 208.20/128.28 | | | | | | | | | | | | REF_CLOSE: (18), (27), (36), (37), (44), (120), (123) are 208.20/128.28 | | | | | | | | | | | | inconsistent by sub-proof #121. 208.20/128.28 | | | | | | | | | | | | 208.20/128.28 | | | | | | | | | | | Case 2: 208.20/128.28 | | | | | | | | | | | | 208.20/128.28 | | | | | | | | | | | | (124) ~ ($lesseq(1, $difference(all_775_1, all_86_10))) 208.20/128.28 | | | | | | | | | | | | | ( ~ (all_775_0 = all_775_1) & length1(int, 208.20/128.28 | | | | | | | | | | | | all_105_4) = all_775_0) 208.20/128.28 | | | | | | | | | | | | 208.20/128.28 | | | | | | | | | | | | REF_CLOSE: (25), (44), (52), (120), (124) are inconsistent by 208.20/128.28 | | | | | | | | | | | | sub-proof #120. 208.20/128.28 | | | | | | | | | | | | 208.20/128.28 | | | | | | | | | | | End of split 208.20/128.28 | | | | | | | | | | | 208.20/128.28 | | | | | | | | | | Case 2: 208.20/128.28 | | | | | | | | | | | 208.20/128.28 | | | | | | | | | | | (125) ~ (all_731_1 = 0) & permut3(int, all_103_4, 208.20/128.28 | | | | | | | | | | | all_103_2, 0, all_86_13) = all_731_1 208.20/128.28 | | | | | | | | | | | 208.20/128.28 | | | | | | | | | | | ALPHA: (125) implies: 208.20/128.28 | | | | | | | | | | | (126) ~ (all_731_1 = 0) 208.20/128.28 | | | | | | | | | | | (127) permut3(int, all_103_4, all_103_2, 0, all_86_13) = 208.20/128.28 | | | | | | | | | | | all_731_1 208.20/128.28 | | | | | | | | | | | 208.20/128.28 | | | | | | | | | | | GROUND_INST: instantiating (21) with 0, all_731_1, all_86_13, 208.20/128.28 | | | | | | | | | | | 0, all_103_2, all_103_4, int, simplifying with 208.20/128.28 | | | | | | | | | | | (117), (127) gives: 208.20/128.28 | | | | | | | | | | | (128) all_731_1 = 0 208.20/128.28 | | | | | | | | | | | 208.20/128.28 | | | | | | | | | | | REDUCE: (126), (128) imply: 208.20/128.28 | | | | | | | | | | | (129) ~ (0 = 0) 208.20/128.28 | | | | | | | | | | | 208.20/128.28 | | | | | | | | | | | CLOSE: (129) is inconsistent. 208.20/128.28 | | | | | | | | | | | 208.20/128.28 | | | | | | | | | | End of split 208.20/128.28 | | | | | | | | | | 208.20/128.28 | | | | | | | | | Case 2: 208.20/128.28 | | | | | | | | | | 208.20/128.28 | | | | | | | | | | (130) length1(int, all_103_4) = all_787_1 & ( ~ 208.20/128.28 | | | | | | | | | | ($lesseq(all_86_13, all_787_1)) | ~ ($lesseq(0, 208.20/128.28 | | | | | | | | | | all_787_1)) | ( ~ (all_787_0 = all_787_1) & 208.20/128.28 | | | | | | | | | | length1(int, all_103_2) = all_787_0)) 208.20/128.28 | | | | | | | | | | 208.20/128.28 | | | | | | | | | | ALPHA: (130) implies: 208.20/128.28 | | | | | | | | | | (131) length1(int, all_103_4) = all_787_1 208.20/128.28 | | | | | | | | | | 208.20/128.28 | | | | | | | | | | BETA: splitting (92) gives: 208.20/128.28 | | | | | | | | | | 208.20/128.28 | | | | | | | | | | Case 1: 208.20/128.28 | | | | | | | | | | | 208.20/128.28 | | | | | | | | | | | (132) all_769_0 = all_86_13 & length1(int, all_105_4) = 208.20/128.28 | | | | | | | | | | | all_86_13 208.20/128.28 | | | | | | | | | | | 208.20/128.28 | | | | | | | | | | | GROUND_INST: instantiating (52) with all_86_13, all_787_1, 208.20/128.28 | | | | | | | | | | | all_103_4, int, simplifying with (8), (131) gives: 208.20/128.28 | | | | | | | | | | | (133) all_787_1 = all_86_13 208.20/128.28 | | | | | | | | | | | 208.20/128.28 | | | | | | | | | | | GROUND_INST: instantiating (52) with all_787_1, all_775_1, 208.20/128.28 | | | | | | | | | | | all_103_4, int, simplifying with (114), (131) 208.20/128.28 | | | | | | | | | | | gives: 208.20/128.28 | | | | | | | | | | | (134) all_787_1 = all_775_1 208.20/128.28 | | | | | | | | | | | 208.20/128.28 | | | | | | | | | | | COMBINE_EQS: (133), (134) imply: 208.20/128.28 | | | | | | | | | | | (135) all_775_1 = all_86_13 208.20/128.28 | | | | | | | | | | | 208.20/128.28 | | | | | | | | | | | REF_CLOSE: (18), (25), (27), (36), (37), (44), (52), (115), 208.20/128.28 | | | | | | | | | | | (135) are inconsistent by sub-proof #119. 208.20/128.28 | | | | | | | | | | | 208.20/128.28 | | | | | | | | | | Case 2: 208.20/128.28 | | | | | | | | | | | 208.20/128.28 | | | | | | | | | | | 208.20/128.28 | | | | | | | | | | | GROUND_INST: instantiating (52) with all_86_13, all_775_1, 208.20/128.28 | | | | | | | | | | | all_103_4, int, simplifying with (8), (114) gives: 208.20/128.28 | | | | | | | | | | | (136) all_775_1 = all_86_13 208.20/128.28 | | | | | | | | | | | 208.20/128.29 | | | | | | | | | | | REF_CLOSE: (18), (25), (27), (36), (37), (44), (52), (115), 208.20/128.29 | | | | | | | | | | | (136) are inconsistent by sub-proof #119. 208.20/128.29 | | | | | | | | | | | 208.20/128.29 | | | | | | | | | | End of split 208.20/128.29 | | | | | | | | | | 208.20/128.29 | | | | | | | | | End of split 208.20/128.29 | | | | | | | | | 208.20/128.29 | | | | | | | | End of split 208.20/128.29 | | | | | | | | 208.20/128.29 | | | | | | | End of split 208.20/128.29 | | | | | | | 208.20/128.29 | | | | | | Case 2: 208.20/128.29 | | | | | | | 208.20/128.29 | | | | | | | (137) ~ (all_737_1 = 0) & permut3(int, all_103_2, all_105_4, 208.20/128.29 | | | | | | | 0, all_86_13) = all_737_1 208.20/128.29 | | | | | | | 208.20/128.29 | | | | | | | ALPHA: (137) implies: 208.20/128.29 | | | | | | | (138) ~ (all_737_1 = 0) 208.20/128.29 | | | | | | | (139) permut3(int, all_103_2, all_105_4, 0, all_86_13) = 208.20/128.29 | | | | | | | all_737_1 208.20/128.29 | | | | | | | 208.20/128.29 | | | | | | | GROUND_INST: instantiating (21) with 0, all_737_1, all_86_13, 0, 208.20/128.29 | | | | | | | all_105_4, all_103_2, int, simplifying with (85), 208.20/128.29 | | | | | | | (139) gives: 208.20/128.29 | | | | | | | (140) all_737_1 = 0 208.20/128.29 | | | | | | | 208.20/128.29 | | | | | | | REDUCE: (138), (140) imply: 208.20/128.29 | | | | | | | (141) ~ (0 = 0) 208.20/128.29 | | | | | | | 208.20/128.29 | | | | | | | CLOSE: (141) is inconsistent. 208.20/128.29 | | | | | | | 208.20/128.29 | | | | | | End of split 208.20/128.29 | | | | | | 208.20/128.29 | | | | | End of split 208.20/128.29 | | | | | 208.20/128.29 | | | | End of split 208.20/128.29 | | | | 208.20/128.29 | | | End of split 208.20/128.29 | | | 208.20/128.29 | | Case 2: 208.20/128.29 | | | 208.20/128.29 | | | (142) length1(int, all_103_2) = all_749_1 & ( ~ ($lesseq(all_86_13, 208.20/128.29 | | | all_749_1)) | ~ ($lesseq(0, all_749_1)) | ( ~ (all_749_0 = 208.20/128.29 | | | all_749_1) & length1(int, all_105_4) = all_749_0)) 208.20/128.29 | | | 208.20/128.29 | | | ALPHA: (142) implies: 208.20/128.29 | | | (143) length1(int, all_103_2) = all_749_1 208.20/128.29 | | | (144) ~ ($lesseq(all_86_13, all_749_1)) | ~ ($lesseq(0, all_749_1)) | 208.20/128.29 | | | ( ~ (all_749_0 = all_749_1) & length1(int, all_105_4) = 208.20/128.29 | | | all_749_0) 208.20/128.29 | | | 208.20/128.29 | | | BETA: splitting (62) gives: 208.20/128.29 | | | 208.20/128.29 | | | Case 1: 208.20/128.29 | | | | 208.20/128.29 | | | | (145) $lesseq(all_86_11, -1) 208.20/128.29 | | | | 208.20/128.29 | | | | COMBINE_INEQS: (46), (145) imply: 208.20/128.29 | | | | (146) $lesseq(0, -1) 208.20/128.29 | | | | 208.20/128.29 | | | | CLOSE: (146) is inconsistent. 208.20/128.29 | | | | 208.20/128.29 | | | Case 2: 208.20/128.29 | | | | 208.20/128.29 | | | | (147) ~ ($lesseq(-1, all_86_10)) | ? [v0: $int] : ? [v1: $int] : 208.20/128.29 | | | | ((v0 = 0 & permut3(int, all_103_4, all_105_4, all_86_11, 208.20/128.29 | | | | $sum(all_86_10, 1)) = 0) | (length1(int, all_103_4) = v0 208.20/128.29 | | | | & ( ~ ($lesseq(1, $difference(v0, all_86_10))) | ~ 208.20/128.29 | | | | ($lesseq(all_86_11, v0)) | ( ~ (v1 = v0) & length1(int, 208.20/128.29 | | | | all_105_4) = v1)))) 208.20/128.29 | | | | 208.20/128.29 | | | | BETA: splitting (147) gives: 208.20/128.29 | | | | 208.20/128.29 | | | | Case 1: 208.20/128.29 | | | | | 208.20/128.29 | | | | | (148) $lesseq(all_86_10, -2) 208.20/128.29 | | | | | 208.20/128.29 | | | | | COMBINE_INEQS: (54), (148) imply: 208.20/128.29 | | | | | (149) $lesseq(0, -1) 208.20/128.29 | | | | | 208.20/128.29 | | | | | CLOSE: (149) is inconsistent. 208.20/128.29 | | | | | 208.20/128.29 | | | | Case 2: 208.20/128.29 | | | | | 208.20/128.29 | | | | | (150) ? [v0: $int] : ? [v1: $int] : ((v0 = 0 & permut3(int, 208.20/128.29 | | | | | all_103_4, all_105_4, all_86_11, $sum(all_86_10, 1)) = 208.20/128.29 | | | | | 0) | (length1(int, all_103_4) = v0 & ( ~ ($lesseq(1, 208.20/128.29 | | | | | $difference(v0, all_86_10))) | ~ 208.20/128.29 | | | | | ($lesseq(all_86_11, v0)) | ( ~ (v1 = v0) & length1(int, 208.20/128.29 | | | | | all_105_4) = v1)))) 208.20/128.29 | | | | | 208.20/128.29 | | | | | DELTA: instantiating (150) with fresh symbols all_789_0, all_789_1 208.20/128.29 | | | | | gives: 208.20/128.29 | | | | | (151) (all_789_1 = 0 & permut3(int, all_103_4, all_105_4, 208.20/128.29 | | | | | all_86_11, $sum(all_86_10, 1)) = 0) | (length1(int, 208.20/128.29 | | | | | all_103_4) = all_789_1 & ( ~ ($lesseq(1, 208.20/128.29 | | | | | $difference(all_789_1, all_86_10))) | ~ 208.20/128.29 | | | | | ($lesseq(all_86_11, all_789_1)) | ( ~ (all_789_0 = 208.20/128.29 | | | | | all_789_1) & length1(int, all_105_4) = all_789_0))) 208.20/128.29 | | | | | 208.20/128.29 | | | | | BETA: splitting (151) gives: 208.20/128.29 | | | | | 208.20/128.29 | | | | | Case 1: 208.20/128.29 | | | | | | 208.20/128.29 | | | | | | (152) all_789_1 = 0 & permut3(int, all_103_4, all_105_4, 208.20/128.29 | | | | | | all_86_11, $sum(all_86_10, 1)) = 0 208.20/128.29 | | | | | | 208.20/128.29 | | | | | | ALPHA: (152) implies: 208.20/128.29 | | | | | | (153) permut3(int, all_103_4, all_105_4, all_86_11, 208.20/128.29 | | | | | | $sum(all_86_10, 1)) = 0 208.20/128.29 | | | | | | 208.20/128.29 | | | | | | BETA: splitting (75) gives: 208.20/128.29 | | | | | | 208.20/128.29 | | | | | | Case 1: 208.20/128.29 | | | | | | | 208.20/128.29 | | | | | | | (154) all_736_0 = all_736_1 & $lesseq(1, $difference(all_736_1, 208.20/128.29 | | | | | | | all_86_10)) & $lesseq(all_86_11, all_736_1) & 208.20/128.29 | | | | | | | $lesseq(-1, all_86_10) & $lesseq(0, all_86_11) & 208.20/128.29 | | | | | | | length1(int, all_105_4) = all_736_1 & length1(int, 208.20/128.29 | | | | | | | all_103_4) = all_736_1 208.20/128.29 | | | | | | | 208.20/128.29 | | | | | | | ALPHA: (154) implies: 208.20/128.29 | | | | | | | (155) length1(int, all_103_4) = all_736_1 208.20/128.29 | | | | | | | 208.20/128.29 | | | | | | | GROUND_INST: instantiating (1) with all_133_0, all_725_0, 208.20/128.29 | | | | | | | all_133_1, simplifying with (19), (72) gives: 208.20/128.29 | | | | | | | (156) all_725_0 = all_133_0 208.20/128.29 | | | | | | | 208.20/128.29 | | | | | | | GROUND_INST: instantiating (52) with all_86_13, all_736_1, 208.20/128.29 | | | | | | | all_103_4, int, simplifying with (8), (155) gives: 208.20/128.29 | | | | | | | (157) all_736_1 = all_86_13 208.20/128.29 | | | | | | | 208.20/128.29 | | | | | | | GROUND_INST: instantiating (24) with all_105_1, all_738_1, 208.20/128.29 | | | | | | | all_105_2, int, simplifying with (33), (79) gives: 208.20/128.29 | | | | | | | (158) all_738_1 = all_105_1 208.20/128.29 | | | | | | | 208.20/128.29 | | | | | | | GROUND_INST: instantiating (24) with all_738_1, all_725_2, 208.20/128.29 | | | | | | | all_105_2, int, simplifying with (70), (79) gives: 208.20/128.29 | | | | | | | (159) all_738_1 = all_725_2 208.20/128.29 | | | | | | | 208.20/128.29 | | | | | | | COMBINE_EQS: (158), (159) imply: 208.20/128.29 | | | | | | | (160) all_725_2 = all_105_1 208.20/128.29 | | | | | | | 208.20/128.29 | | | | | | | REDUCE: (73), (160) imply: 208.20/128.29 | | | | | | | (161) tb2t(all_105_1) = all_725_1 208.20/128.29 | | | | | | | 208.20/128.29 | | | | | | | REDUCE: (71), (156) imply: 208.20/128.29 | | | | | | | (162) get3(all_725_1, all_133_2) = all_133_0 208.20/128.29 | | | | | | | 208.20/128.29 | | | | | | | REF_CLOSE: (3), (4), (6), (7), (8), (10), (11), (13), (14), (16), 208.20/128.29 | | | | | | | (18), (20), (21), (27), (29), (32), (34), (36), (37), 208.20/128.29 | | | | | | | (38), (39), (41), (43), (45), (49), (50), (52), (56), 208.20/128.29 | | | | | | | (57), (59), (66), (75), (78), (153), (161), (162) are 208.20/128.29 | | | | | | | inconsistent by sub-proof #122. 208.20/128.29 | | | | | | | 208.20/128.29 | | | | | | Case 2: 208.20/128.29 | | | | | | | 208.20/128.29 | | | | | | | (163) ~ (all_736_1 = 0) & permut3(int, all_103_4, all_105_4, 208.20/128.29 | | | | | | | all_86_11, $sum(all_86_10, 1)) = all_736_1 208.20/128.29 | | | | | | | 208.20/128.29 | | | | | | | ALPHA: (163) implies: 208.20/128.29 | | | | | | | (164) ~ (all_736_1 = 0) 208.20/128.29 | | | | | | | (165) permut3(int, all_103_4, all_105_4, all_86_11, 208.20/128.29 | | | | | | | $sum(all_86_10, 1)) = all_736_1 208.20/128.29 | | | | | | | 208.20/128.29 | | | | | | | REF_CLOSE: (21), (153), (164), (165) are inconsistent by sub-proof 208.20/128.29 | | | | | | | #123. 208.20/128.29 | | | | | | | 208.20/128.29 | | | | | | End of split 208.20/128.29 | | | | | | 208.20/128.29 | | | | | Case 2: 208.20/128.29 | | | | | | 208.20/128.29 | | | | | | (166) length1(int, all_103_4) = all_789_1 & ( ~ ($lesseq(1, 208.20/128.29 | | | | | | $difference(all_789_1, all_86_10))) | ~ 208.20/128.29 | | | | | | ($lesseq(all_86_11, all_789_1)) | ( ~ (all_789_0 = 208.20/128.29 | | | | | | all_789_1) & length1(int, all_105_4) = all_789_0)) 208.20/128.29 | | | | | | 208.20/128.29 | | | | | | ALPHA: (166) implies: 208.20/128.29 | | | | | | (167) length1(int, all_103_4) = all_789_1 208.20/128.29 | | | | | | (168) ~ ($lesseq(1, $difference(all_789_1, all_86_10))) | ~ 208.20/128.29 | | | | | | ($lesseq(all_86_11, all_789_1)) | ( ~ (all_789_0 = 208.20/128.29 | | | | | | all_789_1) & length1(int, all_105_4) = all_789_0) 208.20/128.29 | | | | | | 208.20/128.29 | | | | | | GROUND_INST: instantiating (52) with all_86_13, all_749_1, 208.20/128.29 | | | | | | all_103_2, int, simplifying with (2), (143) gives: 208.20/128.29 | | | | | | (169) all_749_1 = all_86_13 208.20/128.29 | | | | | | 208.20/128.29 | | | | | | GROUND_INST: instantiating (52) with all_86_13, all_789_1, 208.20/128.29 | | | | | | all_103_4, int, simplifying with (8), (167) gives: 208.20/128.29 | | | | | | (170) all_789_1 = all_86_13 208.20/128.29 | | | | | | 208.20/128.29 | | | | | | BETA: splitting (144) gives: 208.20/128.29 | | | | | | 208.20/128.29 | | | | | | Case 1: 208.20/128.29 | | | | | | | 208.20/128.29 | | | | | | | (171) $lesseq(all_749_1, -1) 208.20/128.29 | | | | | | | 208.20/128.29 | | | | | | | REDUCE: (169), (171) imply: 208.20/128.29 | | | | | | | (172) $lesseq(all_86_13, -1) 208.20/128.29 | | | | | | | 208.20/128.29 | | | | | | | COMBINE_INEQS: (18), (27) imply: 208.20/128.29 | | | | | | | (173) $lesseq(2, $difference(all_86_7, all_86_8)) 208.20/128.29 | | | | | | | 208.20/128.29 | | | | | | | COMBINE_INEQS: (37), (173) imply: 208.20/128.29 | | | | | | | (174) $lesseq(2, $difference(all_86_10, all_86_8)) 208.20/128.29 | | | | | | | 208.20/128.29 | | | | | | | COMBINE_INEQS: (36), (174) imply: 208.20/128.29 | | | | | | | (175) $lesseq(2, $difference(all_86_10, all_86_11)) 208.20/128.29 | | | | | | | 208.20/128.29 | | | | | | | COMBINE_INEQS: (31), (172) imply: 208.20/128.29 | | | | | | | (176) $lesseq(0, -1) 208.20/128.29 | | | | | | | 208.20/128.29 | | | | | | | CLOSE: (176) is inconsistent. 208.20/128.29 | | | | | | | 208.20/128.29 | | | | | | Case 2: 208.20/128.29 | | | | | | | 208.20/128.29 | | | | | | | (177) ~ ($lesseq(all_86_13, all_749_1)) | ( ~ (all_749_0 = 208.20/128.29 | | | | | | | all_749_1) & length1(int, all_105_4) = all_749_0) 208.20/128.29 | | | | | | | 208.20/128.29 | | | | | | | BETA: splitting (168) gives: 208.20/128.29 | | | | | | | 208.20/128.29 | | | | | | | Case 1: 208.20/128.29 | | | | | | | | 208.20/128.29 | | | | | | | | (178) $lesseq(1, $difference(all_86_11, all_789_1)) 208.20/128.29 | | | | | | | | 208.20/128.29 | | | | | | | | REDUCE: (170), (178) imply: 208.20/128.29 | | | | | | | | (179) $lesseq(1, $difference(all_86_11, all_86_13)) 208.20/128.29 | | | | | | | | 208.20/128.29 | | | | | | | | COMBINE_INEQS: (18), (27) imply: 208.20/128.29 | | | | | | | | (180) $lesseq(2, $difference(all_86_7, all_86_8)) 208.20/128.29 | | | | | | | | 208.20/128.29 | | | | | | | | COMBINE_INEQS: (37), (180) imply: 208.20/128.29 | | | | | | | | (181) $lesseq(2, $difference(all_86_10, all_86_8)) 208.20/128.29 | | | | | | | | 208.20/128.29 | | | | | | | | COMBINE_INEQS: (36), (181) imply: 208.20/128.29 | | | | | | | | (182) $lesseq(2, $difference(all_86_10, all_86_11)) 208.20/128.29 | | | | | | | | 208.20/128.29 | | | | | | | | COMBINE_INEQS: (17), (179) imply: 208.20/128.29 | | | | | | | | (183) $lesseq(0, -1) 208.20/128.29 | | | | | | | | 208.20/128.29 | | | | | | | | CLOSE: (183) is inconsistent. 208.20/128.29 | | | | | | | | 208.20/128.29 | | | | | | | Case 2: 208.20/128.29 | | | | | | | | 208.20/128.29 | | | | | | | | (184) ~ ($lesseq(1, $difference(all_789_1, all_86_10))) | ( 208.20/128.29 | | | | | | | | ~ (all_789_0 = all_789_1) & length1(int, all_105_4) = 208.20/128.29 | | | | | | | | all_789_0) 208.20/128.29 | | | | | | | | 208.20/128.29 | | | | | | | | BETA: splitting (177) gives: 208.20/128.29 | | | | | | | | 208.20/128.29 | | | | | | | | Case 1: 208.20/128.29 | | | | | | | | | 208.20/128.29 | | | | | | | | | (185) $lesseq(1, $difference(all_86_13, all_749_1)) 208.20/128.29 | | | | | | | | | 208.20/128.29 | | | | | | | | | REDUCE: (169), (185) imply: 208.20/128.29 | | | | | | | | | (186) $lesseq(0, -1) 208.20/128.29 | | | | | | | | | 208.20/128.29 | | | | | | | | | CLOSE: (186) is inconsistent. 208.20/128.29 | | | | | | | | | 208.20/128.29 | | | | | | | | Case 2: 208.20/128.29 | | | | | | | | | 208.20/128.29 | | | | | | | | | (187) ~ (all_749_0 = all_749_1) & length1(int, all_105_4) 208.20/128.29 | | | | | | | | | = all_749_0 208.20/128.29 | | | | | | | | | 208.20/128.29 | | | | | | | | | ALPHA: (187) implies: 208.20/128.29 | | | | | | | | | (188) ~ (all_749_0 = all_749_1) 208.20/128.29 | | | | | | | | | (189) length1(int, all_105_4) = all_749_0 208.20/128.29 | | | | | | | | | 208.20/128.29 | | | | | | | | | REDUCE: (169), (188) imply: 208.20/128.29 | | | | | | | | | (190) ~ (all_749_0 = all_86_13) 208.20/128.29 | | | | | | | | | 208.20/128.29 | | | | | | | | | BETA: splitting (184) gives: 208.20/128.29 | | | | | | | | | 208.20/128.29 | | | | | | | | | Case 1: 208.20/128.29 | | | | | | | | | | 208.20/128.29 | | | | | | | | | | (191) $lesseq(all_789_1, all_86_10) 208.20/128.29 | | | | | | | | | | 208.20/128.29 | | | | | | | | | | REDUCE: (170), (191) imply: 208.20/128.29 | | | | | | | | | | (192) $lesseq(all_86_13, all_86_10) 208.20/128.29 | | | | | | | | | | 208.20/128.29 | | | | | | | | | | COMBINE_INEQS: (44), (192) imply: 208.20/128.29 | | | | | | | | | | (193) $lesseq(0, -1) 208.20/128.29 | | | | | | | | | | 208.20/128.29 | | | | | | | | | | CLOSE: (193) is inconsistent. 208.20/128.29 | | | | | | | | | | 208.20/128.29 | | | | | | | | | Case 2: 208.20/128.29 | | | | | | | | | | 208.20/128.29 | | | | | | | | | | (194) ~ (all_789_0 = all_789_1) & length1(int, 208.20/128.29 | | | | | | | | | | all_105_4) = all_789_0 208.20/128.29 | | | | | | | | | | 208.20/128.29 | | | | | | | | | | ALPHA: (194) implies: 208.20/128.29 | | | | | | | | | | (195) length1(int, all_105_4) = all_789_0 208.20/128.29 | | | | | | | | | | 208.20/128.29 | | | | | | | | | | GROUND_INST: instantiating (52) with all_86_13, all_789_0, 208.20/128.29 | | | | | | | | | | all_105_4, int, simplifying with (25), (195) 208.20/128.29 | | | | | | | | | | gives: 208.20/128.29 | | | | | | | | | | (196) all_789_0 = all_86_13 208.20/128.29 | | | | | | | | | | 208.20/128.29 | | | | | | | | | | GROUND_INST: instantiating (52) with all_789_0, all_749_0, 208.20/128.29 | | | | | | | | | | all_105_4, int, simplifying with (189), (195) 208.20/128.29 | | | | | | | | | | gives: 208.20/128.29 | | | | | | | | | | (197) all_789_0 = all_749_0 208.20/128.29 | | | | | | | | | | 208.20/128.29 | | | | | | | | | | COMBINE_EQS: (196), (197) imply: 208.20/128.29 | | | | | | | | | | (198) all_749_0 = all_86_13 208.20/128.29 | | | | | | | | | | 208.20/128.29 | | | | | | | | | | REDUCE: (190), (198) imply: 208.20/128.29 | | | | | | | | | | (199) ~ (0 = 0) 208.20/128.29 | | | | | | | | | | 208.20/128.29 | | | | | | | | | | CLOSE: (199) is inconsistent. 208.20/128.29 | | | | | | | | | | 208.20/128.29 | | | | | | | | | End of split 208.20/128.29 | | | | | | | | | 208.20/128.29 | | | | | | | | End of split 208.20/128.29 | | | | | | | | 208.20/128.29 | | | | | | | End of split 208.20/128.29 | | | | | | | 208.20/128.29 | | | | | | End of split 208.20/128.29 | | | | | | 208.20/128.29 | | | | | End of split 208.20/128.29 | | | | | 208.20/128.29 | | | | End of split 208.20/128.29 | | | | 208.20/128.29 | | | End of split 208.20/128.29 | | | 208.20/128.29 | | End of split 208.20/128.29 | | 208.20/128.29 | End of split 208.20/128.29 | 208.20/128.29 End of proof 208.20/128.29 208.20/128.29 Sub-proof #119 shows that the following formulas are inconsistent: 208.20/128.29 ---------------------------------------------------------------- 208.20/128.29 (1) $lesseq(1, $difference(all_133_2, all_86_8)) 208.20/128.29 (2) all_775_1 = all_86_13 208.20/128.29 (3) length1(int, all_105_4) = all_86_13 208.20/128.29 (4) $lesseq(1, $difference(all_86_7, all_133_2)) 208.20/128.29 (5) $lesseq(all_86_11, all_86_8) 208.20/128.29 (6) $lesseq(all_86_7, all_86_10) 208.20/128.29 (7) $lesseq(1, $difference(all_86_13, all_86_10)) 208.20/128.29 (8) ~ ($lesseq(1, $difference(all_775_1, all_86_10))) | ~ 208.20/128.29 ($lesseq(all_86_11, all_775_1)) | ( ~ (all_775_0 = all_775_1) & 208.20/128.29 length1(int, all_105_4) = all_775_0) 208.20/128.29 (9) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 208.20/128.29 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 208.20/128.29 208.20/128.29 Begin of proof 208.20/128.29 | 208.20/128.29 | BETA: splitting (8) gives: 208.20/128.29 | 208.20/128.29 | Case 1: 208.20/128.29 | | 208.20/128.29 | | (10) $lesseq(1, $difference(all_86_11, all_775_1)) 208.20/128.29 | | 208.20/128.29 | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (10) are inconsistent by sub-proof 208.20/128.29 | | #121. 208.20/128.29 | | 208.20/128.29 | Case 2: 208.20/128.29 | | 208.20/128.29 | | (11) ~ ($lesseq(1, $difference(all_775_1, all_86_10))) | ( ~ (all_775_0 208.20/128.29 | | = all_775_1) & length1(int, all_105_4) = all_775_0) 208.20/128.29 | | 208.20/128.29 | | REF_CLOSE: (2), (3), (7), (9), (11) are inconsistent by sub-proof #120. 208.20/128.29 | | 208.20/128.29 | End of split 208.20/128.29 | 208.20/128.29 End of proof 208.20/128.29 208.20/128.29 Sub-proof #120 shows that the following formulas are inconsistent: 208.20/128.29 ---------------------------------------------------------------- 208.20/128.29 (1) all_775_1 = all_86_13 208.20/128.29 (2) length1(int, all_105_4) = all_86_13 208.20/128.29 (3) $lesseq(1, $difference(all_86_13, all_86_10)) 208.20/128.29 (4) ~ ($lesseq(1, $difference(all_775_1, all_86_10))) | ( ~ (all_775_0 = 208.20/128.29 all_775_1) & length1(int, all_105_4) = all_775_0) 208.20/128.29 (5) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 208.20/128.29 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 208.20/128.29 208.20/128.29 Begin of proof 208.20/128.29 | 208.20/128.29 | BETA: splitting (4) gives: 208.20/128.29 | 208.20/128.29 | Case 1: 208.20/128.29 | | 208.20/128.29 | | (6) $lesseq(all_775_1, all_86_10) 208.20/128.29 | | 208.20/128.29 | | REDUCE: (1), (6) imply: 208.20/128.29 | | (7) $lesseq(all_86_13, all_86_10) 208.20/128.29 | | 208.20/128.29 | | COMBINE_INEQS: (3), (7) imply: 208.20/128.29 | | (8) $lesseq(0, -1) 208.20/128.29 | | 208.20/128.29 | | CLOSE: (8) is inconsistent. 208.20/128.29 | | 208.20/128.29 | Case 2: 208.20/128.29 | | 208.20/128.29 | | (9) ~ (all_775_0 = all_775_1) & length1(int, all_105_4) = all_775_0 208.20/128.29 | | 208.20/128.29 | | ALPHA: (9) implies: 208.20/128.29 | | (10) ~ (all_775_0 = all_775_1) 208.20/128.29 | | (11) length1(int, all_105_4) = all_775_0 208.20/128.29 | | 208.20/128.29 | | REDUCE: (1), (10) imply: 208.20/128.29 | | (12) ~ (all_775_0 = all_86_13) 208.20/128.29 | | 208.20/128.29 | | GROUND_INST: instantiating (5) with all_86_13, all_775_0, all_105_4, int, 208.20/128.29 | | simplifying with (2), (11) gives: 208.20/128.29 | | (13) all_775_0 = all_86_13 208.20/128.29 | | 208.20/128.29 | | REDUCE: (12), (13) imply: 208.20/128.29 | | (14) ~ (0 = 0) 208.20/128.29 | | 208.20/128.29 | | CLOSE: (14) is inconsistent. 208.20/128.29 | | 208.20/128.29 | End of split 208.20/128.29 | 208.20/128.29 End of proof 208.20/128.29 208.20/128.29 Sub-proof #121 shows that the following formulas are inconsistent: 208.20/128.29 ---------------------------------------------------------------- 208.20/128.29 (1) $lesseq(1, $difference(all_133_2, all_86_8)) 208.20/128.29 (2) all_775_1 = all_86_13 208.20/128.29 (3) $lesseq(1, $difference(all_86_7, all_133_2)) 208.20/128.29 (4) $lesseq(1, $difference(all_86_11, all_775_1)) 208.20/128.29 (5) $lesseq(all_86_11, all_86_8) 208.20/128.29 (6) $lesseq(all_86_7, all_86_10) 208.20/128.29 (7) $lesseq(1, $difference(all_86_13, all_86_10)) 208.20/128.29 208.20/128.29 Begin of proof 208.20/128.29 | 208.20/128.29 | REDUCE: (2), (4) imply: 208.20/128.29 | (8) $lesseq(1, $difference(all_86_11, all_86_13)) 208.20/128.29 | 208.20/128.29 | COMBINE_INEQS: (1), (3) imply: 208.20/128.29 | (9) $lesseq(2, $difference(all_86_7, all_86_8)) 208.20/128.29 | 208.20/128.30 | COMBINE_INEQS: (6), (9) imply: 208.20/128.30 | (10) $lesseq(2, $difference(all_86_10, all_86_8)) 208.20/128.30 | 208.20/128.30 | COMBINE_INEQS: (5), (10) imply: 208.20/128.30 | (11) $lesseq(2, $difference(all_86_10, all_86_11)) 208.20/128.30 | 208.20/128.30 | COMBINE_INEQS: (7), (11) imply: 208.20/128.30 | (12) $lesseq(3, $difference(all_86_13, all_86_11)) 208.20/128.30 | 208.20/128.30 | COMBINE_INEQS: (8), (12) imply: 208.20/128.30 | (13) $lesseq(0, -1) 208.20/128.30 | 208.20/128.30 | CLOSE: (13) is inconsistent. 208.20/128.30 | 208.20/128.30 End of proof 208.20/128.30 208.20/128.30 Sub-proof #122 shows that the following formulas are inconsistent: 208.20/128.30 ---------------------------------------------------------------- 208.20/128.30 (1) in_map_int_int(all_86_6) 208.20/128.30 (2) in_map_int_int(all_86_12) 208.20/128.30 (3) t2tb(all_86_2) = all_105_1 208.20/128.30 (4) in_ty(int) 208.20/128.30 (5) length1(int, all_103_4) = all_86_13 208.20/128.30 (6) t2tb1(all_133_2) = all_738_0 208.20/128.30 (7) $lesseq(-1, all_86_8) 208.20/128.30 (8) $lesseq(1, $difference(all_86_13, all_86_7)) 208.20/128.30 (9) ! [v0: $int] : ! [v1: $int] : (v1 = 42 | ~ ($lesseq(1, 208.20/128.30 $difference(all_86_7, v0))) | ~ ($lesseq(1, $difference(v0, 208.20/128.30 all_86_8))) | ~ (get3(all_86_6, v0) = v1)) 208.20/128.30 (10) map_eq_sub1(int, all_103_3, all_103_1, $sum(all_86_10, 1), all_86_13) = 208.20/128.30 0 208.20/128.30 (11) t2tb(all_86_6) = all_103_1 208.20/128.30 (12) $lesseq(1, $difference(all_133_2, all_86_8)) 208.20/128.30 (13) map_eq_sub1(int, all_103_1, all_105_3, $sum(all_86_8, 1), all_86_13) = 0 208.20/128.30 (14) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.20/128.30 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ (permut3(v6, v5, 208.20/128.30 v4, v3, v2) = v1) | ~ (permut3(v6, v5, v4, v3, v2) = v0)) 208.20/128.30 (15) $lesseq(1, $difference(all_86_7, all_133_2)) 208.20/128.30 (16) map_eq_sub1(int, all_105_3, all_105_1, 0, all_86_7) = 0 208.20/128.30 (17) permut3(int, all_103_4, all_105_4, all_86_11, $sum(all_86_10, 1)) = 0 208.20/128.30 (18) tb2t(all_105_1) = all_86_2 208.20/128.30 (19) t2tb1(all_133_0) = all_133_1 208.20/128.30 (20) map_eq_sub1(int, all_103_3, all_103_1, 0, all_86_11) = 0 208.20/128.30 (21) $lesseq(all_86_11, all_86_8) 208.20/128.30 (22) $lesseq(all_86_7, all_86_10) 208.20/128.30 (23) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.20/128.30 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 208.20/128.30 ($lesseq(1, $difference(v3, v4))) | ~ ($lesseq(v2, v4)) | ~ 208.20/128.30 (permut2(int, v5, v6, v2, v3) = 0) | ~ (t2tb(v1) = v6) | ~ (t2tb(v0) 208.20/128.30 = v5) | ~ (get3(v1, v4) = v7) | ~ in_map_int_int(v0) | ? [v8: 208.20/128.30 $int] : ($lesseq(1, $difference(v3, v8)) & $lesseq(v2, v8) & 208.20/128.30 get3(v0, v8) = v7)) 208.20/128.30 (24) ~ (all_133_0 = 42) 208.20/128.30 (25) t2tb(all_86_12) = all_103_3 208.20/128.30 (26) tb2t(all_105_1) = all_725_1 208.20/128.30 (27) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.20/128.30 $int] : ! [v5: $int] : ! [v6: $int] : ( ~ ($lesseq(1, 208.20/128.30 $difference(v4, v5))) | ~ ($lesseq(v3, v5)) | ~ (map_eq_sub1(v0, 208.20/128.30 v1, v2, v3, v4) = 0) | ~ (t2tb1(v5) = v6) | ~ in_ty(v0) | ? 208.20/128.30 [v7: $int] : (get(v0, int, v2, v6) = v7 & get(v0, int, v1, v6) = v7 & 208.20/128.30 in_uni(v7))) 208.20/128.30 (28) in_map_int_int(all_86_4) 208.20/128.30 (29) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ (tb2t(v2) 208.20/128.30 = v1) | ~ (tb2t(v2) = v0)) 208.20/128.30 (30) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.20/128.30 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 208.20/128.30 ($lesseq(1, $difference(v3, v6))) | ~ ($lesseq(v2, v6)) | ~ 208.20/128.30 (map_eq_sub1(int, v4, v5, v2, v3) = 0) | ~ (t2tb(v1) = v5) | ~ 208.20/128.30 (t2tb(v0) = v4) | ~ (get3(v1, v6) = v7) | ~ in_map_int_int(v0) | 208.20/128.30 get3(v0, v6) = v7) 208.20/128.30 (31) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 208.20/128.30 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 208.20/128.30 (32) (all_736_0 = all_736_1 & $lesseq(1, $difference(all_736_1, all_86_10)) & 208.20/128.30 $lesseq(all_86_11, all_736_1) & $lesseq(-1, all_86_10) & $lesseq(0, 208.20/128.30 all_86_11) & length1(int, all_105_4) = all_736_1 & length1(int, 208.20/128.30 all_103_4) = all_736_1) | ( ~ (all_736_1 = 0) & permut3(int, 208.20/128.30 all_103_4, all_105_4, all_86_11, $sum(all_86_10, 1)) = all_736_1) 208.20/128.30 (33) map_eq_sub1(int, all_105_3, all_105_1, $sum(all_86_10, 1), all_86_13) = 208.20/128.30 0 208.20/128.30 (34) permut2(int, all_103_3, all_105_3, 0, all_86_13) = 0 208.20/128.30 (35) t2tb(all_86_4) = all_105_3 208.20/128.30 (36) get3(all_725_1, all_133_2) = all_133_0 208.20/128.30 208.20/128.30 Begin of proof 208.20/128.30 | 208.20/128.30 | BETA: splitting (32) gives: 208.20/128.30 | 208.20/128.30 | Case 1: 208.20/128.30 | | 208.20/128.30 | | (37) all_736_0 = all_736_1 & $lesseq(1, $difference(all_736_1, 208.20/128.30 | | all_86_10)) & $lesseq(all_86_11, all_736_1) & $lesseq(-1, 208.20/128.30 | | all_86_10) & $lesseq(0, all_86_11) & length1(int, all_105_4) = 208.20/128.30 | | all_736_1 & length1(int, all_103_4) = all_736_1 208.20/128.30 | | 208.20/128.30 | | ALPHA: (37) implies: 208.20/128.30 | | (38) $lesseq(0, all_86_11) 208.20/128.30 | | (39) $lesseq(1, $difference(all_736_1, all_86_10)) 208.20/128.30 | | (40) length1(int, all_103_4) = all_736_1 208.20/128.30 | | 208.20/128.30 | | GROUND_INST: instantiating (29) with all_86_2, all_725_1, all_105_1, 208.20/128.30 | | simplifying with (18), (26) gives: 208.20/128.30 | | (41) all_725_1 = all_86_2 208.20/128.30 | | 208.20/128.30 | | GROUND_INST: instantiating (31) with all_86_13, all_736_1, all_103_4, int, 208.20/128.30 | | simplifying with (5), (40) gives: 208.20/128.30 | | (42) all_736_1 = all_86_13 208.20/128.30 | | 208.20/128.30 | | REDUCE: (39), (42) imply: 208.20/128.30 | | (43) $lesseq(1, $difference(all_86_13, all_86_10)) 208.20/128.30 | | 208.20/128.30 | | COMBINE_INEQS: (12), (15) imply: 208.20/128.30 | | (44) $lesseq(2, $difference(all_86_7, all_86_8)) 208.20/128.30 | | 208.20/128.30 | | COMBINE_INEQS: (22), (44) imply: 208.20/128.30 | | (45) $lesseq(2, $difference(all_86_10, all_86_8)) 208.20/128.30 | | 208.20/128.30 | | COMBINE_INEQS: (21), (45) imply: 208.20/128.30 | | (46) $lesseq(2, $difference(all_86_10, all_86_11)) 208.20/128.30 | | 208.20/128.30 | | COMBINE_INEQS: (43), (46) imply: 208.20/128.30 | | (47) $lesseq(3, $difference(all_86_13, all_86_11)) 208.20/128.30 | | 208.20/128.30 | | COMBINE_INEQS: (38), (47) imply: 208.20/128.30 | | (48) $lesseq(3, all_86_13) 208.20/128.30 | | 208.20/128.30 | | REDUCE: (36), (41) imply: 208.20/128.30 | | (49) get3(all_86_2, all_133_2) = all_133_0 208.20/128.30 | | 208.20/128.30 | | GROUND_INST: instantiating (30) with all_86_4, all_86_2, 0, all_86_7, 208.20/128.30 | | all_105_3, all_105_1, all_133_2, all_133_0, simplifying with 208.20/128.30 | | (3), (16), (28), (35), (49) gives: 208.20/128.30 | | (50) ~ ($lesseq(1, $difference(all_86_7, all_133_2))) | ~ ($lesseq(0, 208.20/128.30 | | all_133_2)) | get3(all_86_4, all_133_2) = all_133_0 208.20/128.30 | | 208.20/128.30 | | GROUND_INST: instantiating (27) with int, all_105_3, all_105_1, 208.20/128.30 | | $sum(all_86_10, 1), all_86_13, all_133_0, all_133_1, 208.20/128.30 | | simplifying with (4), (19), (33) gives: 208.20/128.30 | | (51) ~ ($lesseq(1, $difference(all_86_13, all_133_0))) | ~ ($lesseq(1, 208.20/128.30 | | $difference(all_133_0, all_86_10))) | ? [v0: $int] : (get(int, 208.20/128.30 | | int, all_105_1, all_133_1) = v0 & get(int, int, all_105_3, 208.20/128.30 | | all_133_1) = v0 & in_uni(v0)) 208.20/128.30 | | 208.20/128.30 | | GROUND_INST: instantiating (27) with int, all_103_3, all_103_1, 208.20/128.30 | | $sum(all_86_10, 1), all_86_13, all_133_0, all_133_1, 208.20/128.30 | | simplifying with (4), (10), (19) gives: 208.20/128.30 | | (52) ~ ($lesseq(1, $difference(all_86_13, all_133_0))) | ~ ($lesseq(1, 208.20/128.30 | | $difference(all_133_0, all_86_10))) | ? [v0: $int] : (get(int, 208.20/128.30 | | int, all_103_1, all_133_1) = v0 & get(int, int, all_103_3, 208.20/128.30 | | all_133_1) = v0 & in_uni(v0)) 208.20/128.30 | | 208.20/128.30 | | GROUND_INST: instantiating (27) with int, all_103_3, all_103_1, 0, 208.20/128.30 | | all_86_11, all_133_0, all_133_1, simplifying with (4), (19), 208.20/128.30 | | (20) gives: 208.20/128.30 | | (53) ~ ($lesseq(1, $difference(all_86_11, all_133_0))) | ~ ($lesseq(0, 208.20/128.30 | | all_133_0)) | ? [v0: $int] : (get(int, int, all_103_1, 208.20/128.30 | | all_133_1) = v0 & get(int, int, all_103_3, all_133_1) = v0 & 208.20/128.30 | | in_uni(v0)) 208.20/128.30 | | 208.20/128.30 | | GROUND_INST: instantiating (27) with int, all_105_3, all_105_1, 0, all_86_7, 208.20/128.30 | | all_133_2, all_738_0, simplifying with (4), (6), (16) gives: 208.20/128.30 | | (54) ~ ($lesseq(1, $difference(all_86_7, all_133_2))) | ~ ($lesseq(0, 208.20/128.30 | | all_133_2)) | ? [v0: $int] : (get(int, int, all_105_1, 208.20/128.30 | | all_738_0) = v0 & get(int, int, all_105_3, all_738_0) = v0 & 208.20/128.30 | | in_uni(v0)) 208.20/128.30 | | 208.20/128.30 | | GROUND_INST: instantiating (27) with int, all_103_1, all_105_3, 208.20/128.30 | | $sum(all_86_8, 1), all_86_13, all_133_2, all_738_0, simplifying 208.20/128.30 | | with (4), (6), (13) gives: 208.20/128.30 | | (55) ~ ($lesseq(1, $difference(all_86_13, all_133_2))) | ~ ($lesseq(1, 208.20/128.30 | | $difference(all_133_2, all_86_8))) | ? [v0: $int] : (get(int, 208.20/128.30 | | int, all_105_3, all_738_0) = v0 & get(int, int, all_103_1, 208.20/128.30 | | all_738_0) = v0 & in_uni(v0)) 208.20/128.30 | | 208.20/128.30 | | BETA: splitting (54) gives: 208.20/128.30 | | 208.20/128.30 | | Case 1: 208.20/128.30 | | | 208.20/128.30 | | | (56) $lesseq(all_133_2, -1) 208.20/128.30 | | | 208.20/128.30 | | | COMBINE_INEQS: (12), (56) imply: 208.20/128.30 | | | (57) $lesseq(all_86_8, -2) 208.20/128.30 | | | 208.20/128.30 | | | COMBINE_INEQS: (7), (57) imply: 208.20/128.30 | | | (58) $lesseq(0, -1) 208.20/128.30 | | | 208.20/128.30 | | | CLOSE: (58) is inconsistent. 208.20/128.30 | | | 208.20/128.30 | | Case 2: 208.20/128.30 | | | 208.20/128.30 | | | (59) $lesseq(0, all_133_2) 208.20/128.30 | | | 208.20/128.30 | | | BETA: splitting (50) gives: 208.20/128.30 | | | 208.20/128.30 | | | Case 1: 208.20/128.30 | | | | 208.20/128.30 | | | | (60) get3(all_86_4, all_133_2) = all_133_0 208.20/128.30 | | | | 208.20/128.30 | | | | BETA: splitting (55) gives: 208.20/128.30 | | | | 208.20/128.30 | | | | Case 1: 208.20/128.30 | | | | | 208.20/128.30 | | | | | (61) $lesseq(all_86_13, all_133_2) 208.20/128.30 | | | | | 208.20/128.30 | | | | | COMBINE_INEQS: (15), (61) imply: 208.20/128.30 | | | | | (62) $lesseq(1, $difference(all_86_7, all_86_13)) 208.20/128.30 | | | | | 208.20/128.30 | | | | | COMBINE_INEQS: (8), (62) imply: 208.20/128.30 | | | | | (63) $lesseq(0, -1) 208.20/128.30 | | | | | 208.20/128.30 | | | | | CLOSE: (63) is inconsistent. 208.20/128.30 | | | | | 208.20/128.30 | | | | Case 2: 208.20/128.30 | | | | | 208.20/128.30 | | | | | (64) $lesseq(1, $difference(all_86_13, all_133_2)) 208.20/128.30 | | | | | 208.20/128.30 | | | | | REF_CLOSE: (1), (2), (9), (11), (12), (13), (15), (23), (24), (25), 208.20/128.30 | | | | | (30), (34), (35), (48), (51), (52), (53), (59), (60), (64) 208.20/128.30 | | | | | are inconsistent by sub-proof #124. 208.20/128.30 | | | | | 208.20/128.30 | | | | End of split 208.20/128.30 | | | | 208.20/128.30 | | | Case 2: 208.20/128.30 | | | | 208.20/128.30 | | | | (65) ~ ($lesseq(1, $difference(all_86_7, all_133_2))) | ~ 208.20/128.30 | | | | ($lesseq(0, all_133_2)) 208.20/128.30 | | | | 208.20/128.30 | | | | REF_CLOSE: (15), (59), (65) are inconsistent by sub-proof #151. 208.20/128.30 | | | | 208.20/128.30 | | | End of split 208.20/128.30 | | | 208.20/128.30 | | End of split 208.20/128.30 | | 208.20/128.30 | Case 2: 208.20/128.30 | | 208.20/128.30 | | (66) ~ (all_736_1 = 0) & permut3(int, all_103_4, all_105_4, all_86_11, 208.20/128.30 | | $sum(all_86_10, 1)) = all_736_1 208.20/128.30 | | 208.20/128.30 | | ALPHA: (66) implies: 208.20/128.30 | | (67) ~ (all_736_1 = 0) 208.20/128.30 | | (68) permut3(int, all_103_4, all_105_4, all_86_11, $sum(all_86_10, 1)) = 208.20/128.30 | | all_736_1 208.20/128.30 | | 208.20/128.30 | | REF_CLOSE: (14), (17), (67), (68) are inconsistent by sub-proof #123. 208.20/128.30 | | 208.20/128.30 | End of split 208.20/128.30 | 208.20/128.30 End of proof 208.20/128.30 208.20/128.30 Sub-proof #123 shows that the following formulas are inconsistent: 208.20/128.30 ---------------------------------------------------------------- 208.20/128.30 (1) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.20/128.30 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ (permut3(v6, v5, 208.20/128.30 v4, v3, v2) = v1) | ~ (permut3(v6, v5, v4, v3, v2) = v0)) 208.20/128.30 (2) permut3(int, all_103_4, all_105_4, all_86_11, $sum(all_86_10, 1)) = 208.20/128.30 all_736_1 208.20/128.30 (3) permut3(int, all_103_4, all_105_4, all_86_11, $sum(all_86_10, 1)) = 0 208.20/128.30 (4) ~ (all_736_1 = 0) 208.20/128.30 208.20/128.30 Begin of proof 208.20/128.30 | 208.20/128.30 | GROUND_INST: instantiating (1) with all_736_1, 0, $sum(all_86_10, 1), 208.20/128.30 | all_86_11, all_105_4, all_103_4, int, simplifying with (2), (3) 208.20/128.30 | gives: 208.20/128.30 | (5) all_736_1 = 0 208.20/128.30 | 208.20/128.30 | REDUCE: (4), (5) imply: 208.20/128.30 | (6) ~ (0 = 0) 208.20/128.30 | 208.20/128.30 | CLOSE: (6) is inconsistent. 208.20/128.30 | 208.20/128.30 End of proof 208.20/128.30 208.20/128.30 Sub-proof #124 shows that the following formulas are inconsistent: 208.20/128.30 ---------------------------------------------------------------- 208.20/128.30 (1) in_map_int_int(all_86_6) 208.20/128.30 (2) in_map_int_int(all_86_12) 208.20/128.30 (3) $lesseq(0, all_133_2) 208.20/128.30 (4) ! [v0: $int] : ! [v1: $int] : (v1 = 42 | ~ ($lesseq(1, 208.20/128.30 $difference(all_86_7, v0))) | ~ ($lesseq(1, $difference(v0, 208.20/128.30 all_86_8))) | ~ (get3(all_86_6, v0) = v1)) 208.20/128.30 (5) t2tb(all_86_6) = all_103_1 208.20/128.30 (6) $lesseq(1, $difference(all_133_2, all_86_8)) 208.20/128.30 (7) ~ ($lesseq(1, $difference(all_86_13, all_133_0))) | ~ ($lesseq(1, 208.20/128.30 $difference(all_133_0, all_86_10))) | ? [v0: $int] : (get(int, int, 208.20/128.30 all_105_1, all_133_1) = v0 & get(int, int, all_105_3, all_133_1) = v0 208.20/128.30 & in_uni(v0)) 208.20/128.30 (8) map_eq_sub1(int, all_103_1, all_105_3, $sum(all_86_8, 1), all_86_13) = 0 208.20/128.30 (9) $lesseq(1, $difference(all_86_7, all_133_2)) 208.20/128.30 (10) $lesseq(3, all_86_13) 208.20/128.30 (11) ~ ($lesseq(1, $difference(all_86_11, all_133_0))) | ~ ($lesseq(0, 208.20/128.30 all_133_0)) | ? [v0: $int] : (get(int, int, all_103_1, all_133_1) = 208.20/128.30 v0 & get(int, int, all_103_3, all_133_1) = v0 & in_uni(v0)) 208.20/128.30 (12) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.20/128.30 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 208.20/128.30 ($lesseq(1, $difference(v3, v4))) | ~ ($lesseq(v2, v4)) | ~ 208.20/128.30 (permut2(int, v5, v6, v2, v3) = 0) | ~ (t2tb(v1) = v6) | ~ (t2tb(v0) 208.20/128.30 = v5) | ~ (get3(v1, v4) = v7) | ~ in_map_int_int(v0) | ? [v8: 208.20/128.30 $int] : ($lesseq(1, $difference(v3, v8)) & $lesseq(v2, v8) & 208.20/128.30 get3(v0, v8) = v7)) 208.20/128.30 (13) ~ (all_133_0 = 42) 208.20/128.30 (14) get3(all_86_4, all_133_2) = all_133_0 208.20/128.30 (15) t2tb(all_86_12) = all_103_3 208.20/128.30 (16) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.20/128.30 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 208.20/128.30 ($lesseq(1, $difference(v3, v6))) | ~ ($lesseq(v2, v6)) | ~ 208.20/128.30 (map_eq_sub1(int, v4, v5, v2, v3) = 0) | ~ (t2tb(v1) = v5) | ~ 208.20/128.30 (t2tb(v0) = v4) | ~ (get3(v1, v6) = v7) | ~ in_map_int_int(v0) | 208.20/128.30 get3(v0, v6) = v7) 208.20/128.30 (17) $lesseq(1, $difference(all_86_13, all_133_2)) 208.20/128.30 (18) ~ ($lesseq(1, $difference(all_86_13, all_133_0))) | ~ ($lesseq(1, 208.20/128.30 $difference(all_133_0, all_86_10))) | ? [v0: $int] : (get(int, int, 208.20/128.30 all_103_1, all_133_1) = v0 & get(int, int, all_103_3, all_133_1) = 208.20/128.30 v0 & in_uni(v0)) 208.20/128.30 (19) permut2(int, all_103_3, all_105_3, 0, all_86_13) = 0 208.20/128.30 (20) t2tb(all_86_4) = all_105_3 208.20/128.30 208.20/128.30 Begin of proof 208.20/128.30 | 208.20/128.30 | BETA: splitting (11) gives: 208.20/128.30 | 208.20/128.30 | Case 1: 208.20/128.30 | | 208.20/128.30 | | (21) $lesseq(all_133_0, -1) 208.20/128.30 | | 208.20/128.30 | | BETA: splitting (7) gives: 208.20/128.30 | | 208.20/128.30 | | Case 1: 208.20/128.30 | | | 208.20/128.30 | | | (22) $lesseq(all_86_13, all_133_0) 208.20/128.30 | | | 208.20/128.30 | | | COMBINE_INEQS: (21), (22) imply: 208.20/128.30 | | | (23) $lesseq(all_86_13, -1) 208.20/128.30 | | | 208.20/128.30 | | | COMBINE_INEQS: (10), (23) imply: 208.20/128.30 | | | (24) $lesseq(0, -1) 208.20/128.30 | | | 208.20/128.30 | | | CLOSE: (24) is inconsistent. 208.20/128.30 | | | 208.20/128.30 | | Case 2: 208.20/128.30 | | | 208.20/128.30 | | | (25) $lesseq(1, $difference(all_86_13, all_133_0)) 208.20/128.30 | | | 208.20/128.30 | | | BETA: splitting (18) gives: 208.20/128.30 | | | 208.20/128.30 | | | Case 1: 208.20/128.30 | | | | 208.20/128.30 | | | | (26) $lesseq(all_86_13, all_133_0) 208.20/128.30 | | | | 208.20/128.30 | | | | COMBINE_INEQS: (25), (26) imply: 208.20/128.30 | | | | (27) $lesseq(0, -1) 208.20/128.30 | | | | 208.20/128.30 | | | | CLOSE: (27) is inconsistent. 208.20/128.30 | | | | 208.20/128.30 | | | Case 2: 208.20/128.30 | | | | 208.20/128.30 | | | | 208.20/128.30 | | | | GROUND_INST: instantiating (16) with all_86_6, all_86_4, $sum(all_86_8, 208.20/128.30 | | | | 1), all_86_13, all_103_1, all_105_3, all_133_2, 208.20/128.30 | | | | all_133_0, simplifying with (1), (5), (8), (14), (20) 208.20/128.30 | | | | gives: 208.20/128.31 | | | | (28) ~ ($lesseq(1, $difference(all_86_13, all_133_2))) | ~ 208.20/128.31 | | | | ($lesseq(1, $difference(all_133_2, all_86_8))) | get3(all_86_6, 208.20/128.31 | | | | all_133_2) = all_133_0 208.20/128.31 | | | | 208.20/128.31 | | | | GROUND_INST: instantiating (12) with all_86_12, all_86_4, 0, all_86_13, 208.20/128.31 | | | | all_133_2, all_103_3, all_105_3, all_133_0, simplifying 208.20/128.31 | | | | with (2), (14), (15), (19), (20) gives: 208.20/128.31 | | | | (29) ~ ($lesseq(1, $difference(all_86_13, all_133_2))) | ~ 208.20/128.31 | | | | ($lesseq(0, all_133_2)) | ? [v0: $int] : ($lesseq(1, 208.20/128.31 | | | | $difference(all_86_13, v0)) & $lesseq(0, v0) & 208.20/128.31 | | | | get3(all_86_12, v0) = all_133_0) 208.20/128.31 | | | | 208.20/128.31 | | | | REF_CLOSE: (3), (4), (6), (9), (13), (17), (28), (29) are inconsistent 208.20/128.31 | | | | by sub-proof #141. 208.20/128.31 | | | | 208.20/128.31 | | | End of split 208.20/128.31 | | | 208.20/128.31 | | End of split 208.20/128.31 | | 208.20/128.31 | Case 2: 208.20/128.31 | | 208.20/128.31 | | 208.20/128.31 | | GROUND_INST: instantiating (16) with all_86_6, all_86_4, $sum(all_86_8, 1), 208.20/128.31 | | all_86_13, all_103_1, all_105_3, all_133_2, all_133_0, 208.20/128.31 | | simplifying with (1), (5), (8), (14), (20) gives: 208.20/128.31 | | (30) ~ ($lesseq(1, $difference(all_86_13, all_133_2))) | ~ ($lesseq(1, 208.20/128.31 | | $difference(all_133_2, all_86_8))) | get3(all_86_6, all_133_2) = 208.20/128.31 | | all_133_0 208.20/128.31 | | 208.20/128.31 | | GROUND_INST: instantiating (12) with all_86_12, all_86_4, 0, all_86_13, 208.20/128.31 | | all_133_2, all_103_3, all_105_3, all_133_0, simplifying with 208.20/128.31 | | (2), (14), (15), (19), (20) gives: 208.20/128.31 | | (31) ~ ($lesseq(1, $difference(all_86_13, all_133_2))) | ~ ($lesseq(0, 208.20/128.31 | | all_133_2)) | ? [v0: $int] : ($lesseq(1, $difference(all_86_13, 208.20/128.31 | | v0)) & $lesseq(0, v0) & get3(all_86_12, v0) = all_133_0) 208.20/128.31 | | 208.20/128.31 | | REF_CLOSE: (3), (4), (6), (9), (13), (17), (30), (31) are inconsistent by 208.20/128.31 | | sub-proof #141. 208.20/128.31 | | 208.20/128.31 | End of split 208.20/128.31 | 208.20/128.31 End of proof 208.20/128.31 208.20/128.31 Sub-proof #125 shows that the following formulas are inconsistent: 208.20/128.31 ---------------------------------------------------------------- 208.20/128.31 (1) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ (tb2t1(v2) 208.20/128.31 = v1) | ~ (tb2t1(v2) = v0)) 208.20/128.31 (2) ! [v0: $int] : ! [v1: $int] : ( ~ ($lesseq(43, v1)) | ~ ($lesseq(v0, 208.20/128.31 all_86_8)) | ~ ($lesseq(all_86_11, v0)) | ~ (get3(all_86_6, v0) = 208.20/128.31 v1)) 208.20/128.31 (3) in_map_int_int(all_86_6) 208.20/128.31 (4) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.20/128.31 $int] : ! [v5: $int] : ! [v6: $int] : ( ~ ($lesseq(0, v4)) | ~ 208.20/128.31 ($lesseq(0, v3)) | ~ (map_eq_sub1(v0, v5, v6, v3, v4) = 0) | ~ 208.20/128.31 (elts(v0, v2) = v6) | ~ (elts(v0, v1) = v5) | ~ in_ty(v0) | ? [v7: 208.20/128.31 $int] : ? [v8: $int] : ((v7 = 0 & array_eq_sub1(v0, v1, v2, v3, v4) 208.20/128.31 = 0) | (length1(v0, v1) = v7 & ( ~ ($lesseq(v4, v7)) | ~ 208.20/128.31 ($lesseq(v3, v7)) | ( ~ (v8 = v7) & length1(v0, v2) = v8))))) 208.20/128.31 (5) elts(int, all_103_4) = all_103_3 208.20/128.31 (6) t2tb2(all_86_3) = all_105_4 208.20/128.31 (7) t2tb(all_86_2) = all_105_1 208.20/128.31 (8) in_ty(int) 208.20/128.31 (9) length1(int, all_103_4) = all_86_13 208.20/128.31 (10) ( ~ (all_133_0 = 42) & $lesseq(1, $difference(all_86_7, all_133_2)) & 208.20/128.31 $lesseq(1, $difference(all_133_2, all_86_8)) & tb2t1(all_133_1) = 208.20/128.31 all_133_0 & get4(int, all_133_3, all_133_2) = all_133_1 & 208.20/128.31 in_uni(all_133_1)) | ($lesseq(all_133_0, 41) & $lesseq(all_133_2, 208.20/128.31 all_86_10) & $lesseq(all_86_7, all_133_2) & tb2t1(all_133_1) = 208.20/128.31 all_133_0 & get4(int, all_133_3, all_133_2) = all_133_1 & 208.20/128.31 in_uni(all_133_1)) | ($lesseq(43, all_133_0) & $lesseq(all_133_2, 208.20/128.31 all_86_8) & $lesseq(all_86_11, all_133_2) & tb2t1(all_133_1) = 208.20/128.31 all_133_0 & get4(int, all_133_3, all_133_2) = all_133_1 & 208.20/128.31 in_uni(all_133_1)) 208.20/128.31 (11) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.20/128.31 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 208.20/128.31 (permut2(v0, v5, v6, v3, v4) = v7) | ~ (elts(v0, v2) = v6) | ~ 208.20/128.31 (elts(v0, v1) = v5) | ~ in_ty(v0) | ? [v8: $int] : ? [v9: $int] : 208.20/128.31 ((v9 = v8 & v7 = 0 & $lesseq(v4, v8) & $lesseq(v3, v8) & $lesseq(0, 208.20/128.31 v4) & $lesseq(0, v3) & length1(v0, v2) = v8 & length1(v0, v1) = 208.20/128.31 v8) | ( ~ (v8 = 0) & permut3(v0, v1, v2, v3, v4) = v8))) 208.20/128.31 (12) all_125_0 = all_105_4 208.20/128.31 (13) $lesseq(-1, all_86_8) 208.20/128.31 (14) $lesseq(1, $difference(all_86_13, all_86_7)) 208.20/128.31 (15) ! [v0: $int] : ! [v1: $int] : (v1 = 42 | ~ ($lesseq(1, 208.20/128.31 $difference(all_86_7, v0))) | ~ ($lesseq(1, $difference(v0, 208.20/128.31 all_86_8))) | ~ (get3(all_86_6, v0) = v1)) 208.20/128.31 (16) map_eq_sub1(int, all_103_3, all_103_1, $sum(all_86_10, 1), all_86_13) = 208.20/128.31 0 208.20/128.31 (17) t2tb(all_86_6) = all_103_1 208.20/128.31 (18) map_eq_sub1(int, all_103_1, all_105_3, $sum(all_86_8, 1), all_86_13) = 0 208.20/128.31 (19) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.20/128.31 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ (permut3(v6, v5, 208.20/128.31 v4, v3, v2) = v1) | ~ (permut3(v6, v5, v4, v3, v2) = v0)) 208.20/128.31 (20) permut2(int, all_103_3, all_105_3, all_86_11, $sum(all_86_10, 1)) = 0 208.20/128.31 (21) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 208.20/128.31 | ~ (elts(v3, v2) = v1) | ~ (elts(v3, v2) = v0)) 208.20/128.31 (22) length1(int, all_105_4) = all_86_13 208.20/128.31 (23) in_array_int(all_86_3) 208.20/128.31 (24) elts(int, all_105_4) = all_105_3 208.20/128.31 (25) map_eq_sub1(int, all_105_3, all_105_1, 0, all_86_7) = 0 208.20/128.31 (26) ~ (all_86_7 = 0) | ~ ($difference(all_86_10, all_86_13) = -1) 208.20/128.31 (27) tb2t(all_105_1) = all_86_2 208.20/128.31 (28) permut2(int, all_103_1, all_105_3, all_86_11, $sum(all_86_8, 1)) = 0 208.20/128.31 (29) elts(int, all_105_2) = all_105_1 208.20/128.31 (30) map_eq_sub1(int, all_103_3, all_103_1, 0, all_86_11) = 0 208.20/128.31 (31) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.20/128.31 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 208.20/128.31 ($lesseq(1, $difference(v4, v5))) | ~ ($lesseq(v3, v5)) | ~ 208.20/128.31 (permut2(v0, v1, v2, v3, v4) = 0) | ~ (t2tb1(v5) = v6) | ~ (get(v0, 208.20/128.31 int, v2, v6) = v7) | ~ in_ty(v0) | ? [v8: $int] : ? [v9: $int] 208.20/128.31 : ($lesseq(1, $difference(v4, v8)) & $lesseq(v3, v8) & t2tb1(v8) = v9 208.20/128.31 & get(v0, int, v1, v9) = v7 & in_uni(v9) & in_uni(v7))) 208.20/128.31 (32) t2tb2(all_86_1) = all_105_2 208.20/128.31 (33) ~ ($difference(all_86_10, all_86_13) = -1) | ~ (all_86_11 = 0) 208.20/128.31 (34) $lesseq(all_86_11, all_86_8) 208.20/128.31 (35) $lesseq(all_86_7, all_86_10) 208.20/128.31 (36) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.20/128.31 $int] : ! [v5: $int] : ( ~ (elts(v0, v1) = v3) | ~ (t2tb1(v2) = v4) 208.20/128.31 | ~ (get(v0, int, v3, v4) = v5) | ~ in_ty(v0) | (get4(v0, v1, v2) = 208.20/128.31 v5 & in_uni(v5))) 208.20/128.31 (37) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.20/128.31 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 208.20/128.31 ($lesseq(1, $difference(v3, v4))) | ~ ($lesseq(v2, v4)) | ~ 208.20/128.31 (permut2(int, v5, v6, v2, v3) = 0) | ~ (t2tb(v1) = v6) | ~ (t2tb(v0) 208.20/128.31 = v5) | ~ (get3(v1, v4) = v7) | ~ in_map_int_int(v0) | ? [v8: 208.20/128.31 $int] : ($lesseq(1, $difference(v3, v8)) & $lesseq(v2, v8) & 208.20/128.31 get3(v0, v8) = v7)) 208.20/128.31 (38) $lesseq(0, all_86_7) 208.20/128.31 (39) permut2(int, all_105_3, all_105_1, all_86_7, $sum(all_86_10, 1)) = 0 208.20/128.31 (40) in_array_int(all_86_1) 208.20/128.31 (41) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.20/128.31 $int] : ! [v5: $int] : ! [v6: $int] : ( ~ ($lesseq(0, v4)) | ~ 208.20/128.31 ($lesseq(0, v3)) | ~ (permut2(v0, v5, v6, v3, v4) = 0) | ~ (elts(v0, 208.20/128.31 v2) = v6) | ~ (elts(v0, v1) = v5) | ~ in_ty(v0) | ? [v7: $int] 208.20/128.31 : ? [v8: $int] : ((v7 = 0 & permut3(v0, v1, v2, v3, v4) = 0) | 208.20/128.31 (length1(v0, v1) = v7 & ( ~ ($lesseq(v4, v7)) | ~ ($lesseq(v3, v7)) 208.20/128.31 | ( ~ (v8 = v7) & length1(v0, v2) = v8))))) 208.20/128.31 (42) $lesseq(1, $difference(all_86_7, all_86_8)) 208.20/128.31 (43) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.20/128.31 $int] : ! [v5: $int] : ! [v6: $int] : ( ~ ($lesseq(1, 208.20/128.31 $difference(v4, v5))) | ~ ($lesseq(v3, v5)) | ~ (map_eq_sub1(v0, 208.20/128.31 v1, v2, v3, v4) = 0) | ~ (t2tb1(v5) = v6) | ~ in_ty(v0) | ? 208.20/128.31 [v7: $int] : (get(v0, int, v2, v6) = v7 & get(v0, int, v1, v6) = v7 & 208.20/128.31 in_uni(v7))) 208.20/128.31 (44) $lesseq(1, $difference(all_86_13, all_86_10)) 208.20/128.31 (45) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.20/128.31 $int] : ! [v5: $int] : (v5 = 0 | ~ (permut_sub2(v0, v1, v2, v3, v4) 208.20/128.31 = v5) | ~ in_ty(v0) | ? [v6: $int] : ? [v7: $int] : ? [v8: $int] 208.20/128.31 : ? [v9: $int] : (( ~ (v9 = 0) & map_eq_sub1(v0, v6, v7, v4, v8) = v9 208.20/128.31 & length1(v0, v1) = v8 & elts(v0, v2) = v7 & elts(v0, v1) = v6 & 208.20/128.31 in_uni(v7) & in_uni(v6)) | ( ~ (v8 = 0) & map_eq_sub1(v0, v6, v7, 208.20/128.31 0, v3) = v8 & elts(v0, v2) = v7 & elts(v0, v1) = v6 & in_uni(v7) 208.20/128.31 & in_uni(v6)) | ( ~ (v6 = 0) & permut3(v0, v1, v2, v3, v4) = v6))) 208.20/128.31 (46) in_map_int_int(all_86_4) 208.20/128.31 (47) $lesseq(0, all_86_11) 208.20/128.31 (48) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ( ~ 208.20/128.31 (t2tb2(v0) = v2) | ~ (get4(int, v2, v1) = v3) | ~ in_array_int(v0) | 208.20/128.31 ? [v4: $int] : ? [v5: $int] : ? [v6: $int] : (tb2t(v4) = v5 & 208.20/128.31 tb2t1(v3) = v6 & get3(v5, v1) = v6 & elts(int, v2) = v4 & 208.20/128.31 in_map_int_int(v5) & in_uni(v4))) 208.20/128.31 (49) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ (tb2t(v2) 208.20/128.31 = v1) | ~ (tb2t(v2) = v0)) 208.20/128.31 (50) all_133_3 = all_105_2 208.20/128.31 (51) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.20/128.31 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 208.20/128.31 ($lesseq(1, $difference(v3, v6))) | ~ ($lesseq(v2, v6)) | ~ 208.20/128.31 (map_eq_sub1(int, v4, v5, v2, v3) = 0) | ~ (t2tb(v1) = v5) | ~ 208.20/128.31 (t2tb(v0) = v4) | ~ (get3(v1, v6) = v7) | ~ in_map_int_int(v0) | 208.20/128.31 get3(v0, v6) = v7) 208.20/128.31 (52) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 208.20/128.31 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 208.20/128.31 (53) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ( ~ 208.20/128.31 (get4(v0, v1, v2) = v3) | ~ in_ty(v0) | ? [v4: $int] : ? [v5: $int] 208.20/128.31 : (elts(v0, v1) = v4 & t2tb1(v2) = v5 & get(v0, int, v4, v5) = v3 & 208.20/128.31 in_uni(v5) & in_uni(v4) & in_uni(v3))) 208.20/128.31 (54) map_eq_sub1(int, all_103_1, all_105_3, 0, all_86_13) = 0 208.20/128.31 (55) ! [v0: $int] : ! [v1: $int] : ( ~ (tb2t1(v0) = v1) | ~ in_uni(v0) | 208.20/128.31 t2tb1(v1) = v0) 208.20/128.31 (56) map_eq_sub1(int, all_105_3, all_105_1, $sum(all_86_10, 1), all_86_13) = 208.20/128.31 0 208.20/128.31 (57) t2tb(all_86_4) = all_105_3 208.20/128.31 (58) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.20/128.31 $int] : ! [v5: $int] : ( ~ (permut3(v0, v1, v2, v3, v4) = v5) | ~ 208.20/128.31 in_ty(v0) | ? [v6: $int] : ? [v7: $int] : ? [v8: $int] : ? [v9: 208.20/128.31 $int] : ? [v10: $int] : ((v10 = 0 & v9 = 0 & v5 = 0 & 208.20/128.31 map_eq_sub1(v0, v6, v7, v4, v8) = 0 & map_eq_sub1(v0, v6, v7, 0, 208.20/128.31 v3) = 0 & length1(v0, v1) = v8 & elts(v0, v2) = v7 & elts(v0, 208.20/128.31 v1) = v6 & in_uni(v7) & in_uni(v6)) | ( ~ (v6 = 0) & 208.20/128.31 permut_sub2(v0, v1, v2, v3, v4) = v6))) 208.20/128.31 (59) ! [v0: $int] : ! [v1: $int] : ( ~ ($lesseq(v0, all_86_10)) | ~ 208.20/128.31 ($lesseq(all_86_7, v0)) | ~ (get4(int, all_125_0, v0) = v1) | ? [v2: 208.20/128.31 $int] : ($lesseq(42, v2) & tb2t1(v1) = v2)) 208.20/128.31 208.20/128.31 Begin of proof 208.20/128.31 | 208.20/128.31 | BETA: splitting (10) gives: 208.20/128.31 | 208.20/128.31 | Case 1: 208.20/128.31 | | 208.20/128.31 | | (60) ~ (all_133_0 = 42) & $lesseq(1, $difference(all_86_7, all_133_2)) & 208.20/128.31 | | $lesseq(1, $difference(all_133_2, all_86_8)) & tb2t1(all_133_1) = 208.20/128.31 | | all_133_0 & get4(int, all_133_3, all_133_2) = all_133_1 & 208.20/128.31 | | in_uni(all_133_1) 208.20/128.31 | | 208.20/128.31 | | ALPHA: (60) implies: 208.20/128.31 | | (61) ~ (all_133_0 = 42) 208.20/128.31 | | (62) $lesseq(1, $difference(all_133_2, all_86_8)) 208.20/128.31 | | (63) $lesseq(1, $difference(all_86_7, all_133_2)) 208.20/128.31 | | (64) in_uni(all_133_1) 208.20/128.31 | | (65) get4(int, all_133_3, all_133_2) = all_133_1 208.20/128.31 | | (66) tb2t1(all_133_1) = all_133_0 208.20/128.31 | | 208.20/128.31 | | COMBINE_INEQS: (62), (63) imply: 208.20/128.31 | | (67) $lesseq(2, $difference(all_86_7, all_86_8)) 208.20/128.31 | | 208.20/128.31 | | COMBINE_INEQS: (35), (67) imply: 208.20/128.31 | | (68) $lesseq(2, $difference(all_86_10, all_86_8)) 208.20/128.31 | | 208.20/128.31 | | COMBINE_INEQS: (13), (68) imply: 208.20/128.31 | | (69) $lesseq(1, all_86_10) 208.20/128.31 | | 208.20/128.31 | | REDUCE: (50), (65) imply: 208.20/128.31 | | (70) get4(int, all_105_2, all_133_2) = all_133_1 208.20/128.31 | | 208.20/128.31 | | REF_CLOSE: (1), (3), (4), (5), (7), (8), (9), (11), (13), (14), (15), (16), 208.20/128.31 | | (17), (18), (19), (20), (21), (22), (24), (25), (27), (29), (30), 208.20/128.31 | | (32), (33), (34), (35), (40), (41), (43), (44), (45), (46), (47), 208.20/128.31 | | (48), (49), (51), (52), (53), (54), (55), (56), (57), (58), (61), 208.20/128.31 | | (62), (63), (64), (66), (69), (70) are inconsistent by sub-proof 208.20/128.31 | | #127. 208.20/128.31 | | 208.20/128.31 | Case 2: 208.20/128.31 | | 208.20/128.31 | | (71) ($lesseq(all_133_0, 41) & $lesseq(all_133_2, all_86_10) & 208.20/128.31 | | $lesseq(all_86_7, all_133_2) & tb2t1(all_133_1) = all_133_0 & 208.20/128.31 | | get4(int, all_133_3, all_133_2) = all_133_1 & in_uni(all_133_1)) | 208.20/128.31 | | ($lesseq(43, all_133_0) & $lesseq(all_133_2, all_86_8) & 208.20/128.31 | | $lesseq(all_86_11, all_133_2) & tb2t1(all_133_1) = all_133_0 & 208.20/128.31 | | get4(int, all_133_3, all_133_2) = all_133_1 & in_uni(all_133_1)) 208.20/128.31 | | 208.20/128.31 | | BETA: splitting (71) gives: 208.20/128.31 | | 208.20/128.31 | | Case 1: 208.20/128.31 | | | 208.20/128.31 | | | (72) $lesseq(all_133_0, 41) & $lesseq(all_133_2, all_86_10) & 208.20/128.31 | | | $lesseq(all_86_7, all_133_2) & tb2t1(all_133_1) = all_133_0 & 208.20/128.31 | | | get4(int, all_133_3, all_133_2) = all_133_1 & in_uni(all_133_1) 208.20/128.31 | | | 208.20/128.31 | | | ALPHA: (72) implies: 208.20/128.31 | | | (73) $lesseq(all_86_7, all_133_2) 208.20/128.31 | | | (74) $lesseq(all_133_2, all_86_10) 208.20/128.31 | | | (75) $lesseq(all_133_0, 41) 208.20/128.31 | | | (76) get4(int, all_133_3, all_133_2) = all_133_1 208.20/128.31 | | | (77) tb2t1(all_133_1) = all_133_0 208.20/128.31 | | | 208.20/128.31 | | | COMBINE_INEQS: (35), (38) imply: 208.20/128.31 | | | (78) $lesseq(0, all_86_10) 208.20/128.31 | | | 208.20/128.31 | | | REDUCE: (50), (76) imply: 208.20/128.31 | | | (79) get4(int, all_105_2, all_133_2) = all_133_1 208.20/128.31 | | | 208.20/128.31 | | | REF_CLOSE: (1), (5), (6), (7), (8), (12), (20), (21), (23), (24), (27), 208.20/128.31 | | | (29), (31), (32), (36), (37), (39), (40), (41), (46), (47), 208.20/128.31 | | | (48), (49), (53), (57), (59), (73), (74), (75), (77), (78), 208.20/128.31 | | | (79) are inconsistent by sub-proof #126. 208.20/128.31 | | | 208.20/128.31 | | Case 2: 208.20/128.31 | | | 208.20/128.31 | | | (80) $lesseq(43, all_133_0) & $lesseq(all_133_2, all_86_8) & 208.20/128.31 | | | $lesseq(all_86_11, all_133_2) & tb2t1(all_133_1) = all_133_0 & 208.20/128.31 | | | get4(int, all_133_3, all_133_2) = all_133_1 & in_uni(all_133_1) 208.20/128.31 | | | 208.20/128.31 | | | ALPHA: (80) implies: 208.20/128.31 | | | (81) $lesseq(all_86_11, all_133_2) 208.20/128.31 | | | (82) $lesseq(all_133_2, all_86_8) 208.20/128.31 | | | (83) $lesseq(43, all_133_0) 208.20/128.31 | | | (84) get4(int, all_133_3, all_133_2) = all_133_1 208.20/128.31 | | | (85) tb2t1(all_133_1) = all_133_0 208.20/128.31 | | | 208.20/128.31 | | | REDUCE: (50), (84) imply: 208.20/128.31 | | | (86) get4(int, all_105_2, all_133_2) = all_133_1 208.20/128.31 | | | 208.20/128.31 | | | BETA: splitting (26) gives: 208.20/128.31 | | | 208.20/128.31 | | | Case 1: 208.20/128.31 | | | | 208.20/128.31 | | | | (87) ~ (all_86_7 = 0) 208.20/128.31 | | | | 208.20/128.31 | | | | STRENGTHEN: (38), (87) imply: 208.20/128.31 | | | | (88) $lesseq(1, all_86_7) 208.20/128.31 | | | | 208.20/128.31 | | | | COMBINE_INEQS: (35), (88) imply: 208.20/128.31 | | | | (89) $lesseq(1, all_86_10) 208.20/128.31 | | | | 208.20/128.31 | | | | REF_CLOSE: (1), (2), (3), (5), (7), (8), (9), (11), (14), (17), (19), 208.20/128.31 | | | | (20), (21), (22), (24), (25), (27), (28), (29), (31), (32), 208.20/128.31 | | | | (33), (35), (37), (39), (40), (41), (42), (43), (44), (46), 208.20/128.31 | | | | (47), (48), (49), (51), (52), (53), (56), (57), (81), (82), 208.20/128.31 | | | | (83), (85), (86), (89) are inconsistent by sub-proof #143. 208.20/128.31 | | | | 208.20/128.31 | | | Case 2: 208.20/128.31 | | | | 208.20/128.31 | | | | (90) all_86_7 = 0 208.20/128.32 | | | | 208.20/128.32 | | | | REDUCE: (42), (90) imply: 208.20/128.32 | | | | (91) $lesseq(all_86_8, -1) 208.20/128.32 | | | | 208.20/128.32 | | | | COMBINE_INEQS: (34), (91) imply: 208.20/128.32 | | | | (92) $lesseq(all_86_11, -1) 208.20/128.32 | | | | 208.20/128.32 | | | | COMBINE_INEQS: (47), (92) imply: 208.20/128.32 | | | | (93) $lesseq(0, -1) 208.20/128.32 | | | | 208.20/128.32 | | | | CLOSE: (93) is inconsistent. 208.20/128.32 | | | | 208.20/128.32 | | | End of split 208.20/128.32 | | | 208.20/128.32 | | End of split 208.20/128.32 | | 208.20/128.32 | End of split 208.20/128.32 | 208.20/128.32 End of proof 208.20/128.32 208.20/128.32 Sub-proof #126 shows that the following formulas are inconsistent: 208.20/128.32 ---------------------------------------------------------------- 208.20/128.32 (1) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ (tb2t1(v2) 208.20/128.32 = v1) | ~ (tb2t1(v2) = v0)) 208.20/128.32 (2) elts(int, all_103_4) = all_103_3 208.20/128.32 (3) t2tb2(all_86_3) = all_105_4 208.20/128.32 (4) t2tb(all_86_2) = all_105_1 208.20/128.32 (5) in_ty(int) 208.20/128.32 (6) all_125_0 = all_105_4 208.20/128.32 (7) $lesseq(all_133_2, all_86_10) 208.20/128.32 (8) $lesseq(all_133_0, 41) 208.20/128.32 (9) tb2t1(all_133_1) = all_133_0 208.20/128.32 (10) permut2(int, all_103_3, all_105_3, all_86_11, $sum(all_86_10, 1)) = 0 208.20/128.32 (11) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 208.20/128.32 | ~ (elts(v3, v2) = v1) | ~ (elts(v3, v2) = v0)) 208.20/128.32 (12) in_array_int(all_86_3) 208.20/128.32 (13) elts(int, all_105_4) = all_105_3 208.20/128.32 (14) $lesseq(all_86_7, all_133_2) 208.20/128.32 (15) get4(int, all_105_2, all_133_2) = all_133_1 208.20/128.32 (16) tb2t(all_105_1) = all_86_2 208.20/128.32 (17) elts(int, all_105_2) = all_105_1 208.20/128.32 (18) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.20/128.32 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 208.20/128.32 ($lesseq(1, $difference(v4, v5))) | ~ ($lesseq(v3, v5)) | ~ 208.20/128.32 (permut2(v0, v1, v2, v3, v4) = 0) | ~ (t2tb1(v5) = v6) | ~ (get(v0, 208.20/128.32 int, v2, v6) = v7) | ~ in_ty(v0) | ? [v8: $int] : ? [v9: $int] 208.20/128.32 : ($lesseq(1, $difference(v4, v8)) & $lesseq(v3, v8) & t2tb1(v8) = v9 208.20/128.32 & get(v0, int, v1, v9) = v7 & in_uni(v9) & in_uni(v7))) 208.20/128.32 (19) t2tb2(all_86_1) = all_105_2 208.20/128.32 (20) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.20/128.32 $int] : ! [v5: $int] : ( ~ (elts(v0, v1) = v3) | ~ (t2tb1(v2) = v4) 208.20/128.32 | ~ (get(v0, int, v3, v4) = v5) | ~ in_ty(v0) | (get4(v0, v1, v2) = 208.20/128.32 v5 & in_uni(v5))) 208.20/128.32 (21) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.20/128.32 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 208.20/128.32 ($lesseq(1, $difference(v3, v4))) | ~ ($lesseq(v2, v4)) | ~ 208.20/128.32 (permut2(int, v5, v6, v2, v3) = 0) | ~ (t2tb(v1) = v6) | ~ (t2tb(v0) 208.20/128.32 = v5) | ~ (get3(v1, v4) = v7) | ~ in_map_int_int(v0) | ? [v8: 208.20/128.32 $int] : ($lesseq(1, $difference(v3, v8)) & $lesseq(v2, v8) & 208.20/128.32 get3(v0, v8) = v7)) 208.20/128.32 (22) permut2(int, all_105_3, all_105_1, all_86_7, $sum(all_86_10, 1)) = 0 208.20/128.32 (23) in_array_int(all_86_1) 208.20/128.32 (24) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.20/128.32 $int] : ! [v5: $int] : ! [v6: $int] : ( ~ ($lesseq(0, v4)) | ~ 208.20/128.32 ($lesseq(0, v3)) | ~ (permut2(v0, v5, v6, v3, v4) = 0) | ~ (elts(v0, 208.20/128.32 v2) = v6) | ~ (elts(v0, v1) = v5) | ~ in_ty(v0) | ? [v7: $int] 208.20/128.32 : ? [v8: $int] : ((v7 = 0 & permut3(v0, v1, v2, v3, v4) = 0) | 208.20/128.32 (length1(v0, v1) = v7 & ( ~ ($lesseq(v4, v7)) | ~ ($lesseq(v3, v7)) 208.20/128.32 | ( ~ (v8 = v7) & length1(v0, v2) = v8))))) 208.20/128.32 (25) in_map_int_int(all_86_4) 208.20/128.32 (26) $lesseq(0, all_86_11) 208.20/128.32 (27) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ( ~ 208.20/128.32 (t2tb2(v0) = v2) | ~ (get4(int, v2, v1) = v3) | ~ in_array_int(v0) | 208.20/128.32 ? [v4: $int] : ? [v5: $int] : ? [v6: $int] : (tb2t(v4) = v5 & 208.20/128.32 tb2t1(v3) = v6 & get3(v5, v1) = v6 & elts(int, v2) = v4 & 208.20/128.32 in_map_int_int(v5) & in_uni(v4))) 208.20/128.32 (28) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ (tb2t(v2) 208.20/128.32 = v1) | ~ (tb2t(v2) = v0)) 208.20/128.32 (29) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ( ~ 208.20/128.32 (get4(v0, v1, v2) = v3) | ~ in_ty(v0) | ? [v4: $int] : ? [v5: $int] 208.20/128.32 : (elts(v0, v1) = v4 & t2tb1(v2) = v5 & get(v0, int, v4, v5) = v3 & 208.20/128.32 in_uni(v5) & in_uni(v4) & in_uni(v3))) 208.20/128.32 (30) $lesseq(0, all_86_10) 208.20/128.32 (31) t2tb(all_86_4) = all_105_3 208.20/128.32 (32) ! [v0: $int] : ! [v1: $int] : ( ~ ($lesseq(v0, all_86_10)) | ~ 208.20/128.32 ($lesseq(all_86_7, v0)) | ~ (get4(int, all_125_0, v0) = v1) | ? [v2: 208.20/128.32 $int] : ($lesseq(42, v2) & tb2t1(v1) = v2)) 208.20/128.32 208.20/128.32 Begin of proof 208.20/128.32 | 208.20/128.32 | GROUND_INST: instantiating (24) with int, all_103_4, all_105_4, all_86_11, 208.20/128.32 | $sum(all_86_10, 1), all_103_3, all_105_3, simplifying with (2), 208.20/128.32 | (5), (10), (13) gives: 208.20/128.32 | (33) ~ ($lesseq(-1, all_86_10)) | ~ ($lesseq(0, all_86_11)) | ? [v0: 208.20/128.32 | $int] : ? [v1: $int] : ((v0 = 0 & permut3(int, all_103_4, 208.20/128.32 | all_105_4, all_86_11, $sum(all_86_10, 1)) = 0) | (length1(int, 208.20/128.32 | all_103_4) = v0 & ( ~ ($lesseq(1, $difference(v0, all_86_10))) | 208.20/128.32 | ~ ($lesseq(all_86_11, v0)) | ( ~ (v1 = v0) & length1(int, 208.20/128.32 | all_105_4) = v1)))) 208.20/128.32 | 208.20/128.32 | GROUND_INST: instantiating (27) with all_86_1, all_133_2, all_105_2, 208.20/128.32 | all_133_1, simplifying with (15), (19), (23) gives: 208.20/128.32 | (34) ? [v0: $int] : ? [v1: $int] : ? [v2: $int] : (tb2t(v0) = v1 & 208.20/128.32 | tb2t1(all_133_1) = v2 & get3(v1, all_133_2) = v2 & elts(int, 208.20/128.32 | all_105_2) = v0 & in_map_int_int(v1) & in_uni(v0)) 208.20/128.32 | 208.20/128.32 | GROUND_INST: instantiating (29) with int, all_105_2, all_133_2, all_133_1, 208.20/128.32 | simplifying with (5), (15) gives: 208.20/128.32 | (35) ? [v0: $int] : ? [v1: $int] : (elts(int, all_105_2) = v0 & 208.20/128.32 | t2tb1(all_133_2) = v1 & get(int, int, v0, v1) = all_133_1 & 208.20/128.32 | in_uni(v1) & in_uni(v0) & in_uni(all_133_1)) 208.20/128.32 | 208.20/128.32 | DELTA: instantiating (35) with fresh symbols all_696_0, all_696_1 gives: 208.20/128.32 | (36) elts(int, all_105_2) = all_696_1 & t2tb1(all_133_2) = all_696_0 & 208.20/128.32 | get(int, int, all_696_1, all_696_0) = all_133_1 & in_uni(all_696_0) & 208.20/128.32 | in_uni(all_696_1) & in_uni(all_133_1) 208.20/128.32 | 208.20/128.32 | ALPHA: (36) implies: 208.20/128.32 | (37) get(int, int, all_696_1, all_696_0) = all_133_1 208.20/128.32 | (38) t2tb1(all_133_2) = all_696_0 208.20/128.32 | (39) elts(int, all_105_2) = all_696_1 208.20/128.32 | 208.20/128.32 | DELTA: instantiating (34) with fresh symbols all_706_0, all_706_1, all_706_2 208.20/128.32 | gives: 208.20/128.32 | (40) tb2t(all_706_2) = all_706_1 & tb2t1(all_133_1) = all_706_0 & 208.20/128.32 | get3(all_706_1, all_133_2) = all_706_0 & elts(int, all_105_2) = 208.20/128.32 | all_706_2 & in_map_int_int(all_706_1) & in_uni(all_706_2) 208.20/128.32 | 208.20/128.32 | ALPHA: (40) implies: 208.20/128.32 | (41) elts(int, all_105_2) = all_706_2 208.20/128.32 | (42) get3(all_706_1, all_133_2) = all_706_0 208.20/128.32 | (43) tb2t1(all_133_1) = all_706_0 208.20/128.32 | (44) tb2t(all_706_2) = all_706_1 208.20/128.32 | 208.20/128.32 | BETA: splitting (33) gives: 208.20/128.32 | 208.20/128.32 | Case 1: 208.20/128.32 | | 208.20/128.32 | | (45) $lesseq(all_86_11, -1) 208.20/128.32 | | 208.20/128.32 | | COMBINE_INEQS: (26), (45) imply: 208.20/128.32 | | (46) $lesseq(0, -1) 208.20/128.32 | | 208.20/128.32 | | CLOSE: (46) is inconsistent. 208.20/128.32 | | 208.20/128.32 | Case 2: 208.20/128.32 | | 208.20/128.32 | | (47) ~ ($lesseq(-1, all_86_10)) | ? [v0: $int] : ? [v1: $int] : ((v0 = 208.20/128.32 | | 0 & permut3(int, all_103_4, all_105_4, all_86_11, 208.20/128.32 | | $sum(all_86_10, 1)) = 0) | (length1(int, all_103_4) = v0 & ( ~ 208.20/128.32 | | ($lesseq(1, $difference(v0, all_86_10))) | ~ 208.20/128.32 | | ($lesseq(all_86_11, v0)) | ( ~ (v1 = v0) & length1(int, 208.20/128.32 | | all_105_4) = v1)))) 208.20/128.32 | | 208.20/128.32 | | BETA: splitting (47) gives: 208.20/128.32 | | 208.20/128.32 | | Case 1: 208.20/128.32 | | | 208.20/128.32 | | | (48) $lesseq(all_86_10, -2) 208.20/128.32 | | | 208.20/128.32 | | | COMBINE_INEQS: (30), (48) imply: 208.20/128.32 | | | (49) $lesseq(0, -1) 208.20/128.32 | | | 208.20/128.32 | | | CLOSE: (49) is inconsistent. 208.20/128.32 | | | 208.20/128.32 | | Case 2: 208.20/128.32 | | | 208.20/128.32 | | | 208.20/128.32 | | | GROUND_INST: instantiating (1) with all_133_0, all_706_0, all_133_1, 208.20/128.32 | | | simplifying with (9), (43) gives: 208.20/128.32 | | | (50) all_706_0 = all_133_0 208.20/128.32 | | | 208.20/128.32 | | | GROUND_INST: instantiating (11) with all_105_1, all_706_2, all_105_2, int, 208.20/128.32 | | | simplifying with (17), (41) gives: 208.20/128.32 | | | (51) all_706_2 = all_105_1 208.20/128.32 | | | 208.20/128.32 | | | GROUND_INST: instantiating (11) with all_706_2, all_696_1, all_105_2, int, 208.20/128.32 | | | simplifying with (39), (41) gives: 208.20/128.32 | | | (52) all_706_2 = all_696_1 208.20/128.32 | | | 208.20/128.32 | | | COMBINE_EQS: (51), (52) imply: 208.20/128.32 | | | (53) all_696_1 = all_105_1 208.20/128.32 | | | 208.20/128.32 | | | REDUCE: (44), (51) imply: 208.20/128.32 | | | (54) tb2t(all_105_1) = all_706_1 208.20/128.32 | | | 208.20/128.32 | | | REDUCE: (42), (50) imply: 208.20/128.32 | | | (55) get3(all_706_1, all_133_2) = all_133_0 208.20/128.32 | | | 208.20/128.32 | | | REDUCE: (37), (53) imply: 208.20/128.32 | | | (56) get(int, int, all_105_1, all_696_0) = all_133_1 208.20/128.32 | | | 208.20/128.32 | | | GROUND_INST: instantiating (28) with all_86_2, all_706_1, all_105_1, 208.20/128.32 | | | simplifying with (16), (54) gives: 208.20/128.32 | | | (57) all_706_1 = all_86_2 208.20/128.32 | | | 208.20/128.32 | | | REDUCE: (55), (57) imply: 208.20/128.32 | | | (58) get3(all_86_2, all_133_2) = all_133_0 208.20/128.32 | | | 208.20/128.32 | | | GROUND_INST: instantiating (21) with all_86_4, all_86_2, all_86_7, 208.20/128.32 | | | $sum(all_86_10, 1), all_133_2, all_105_3, all_105_1, 208.20/128.32 | | | all_133_0, simplifying with (4), (22), (25), (31), (58) 208.20/128.32 | | | gives: 208.20/128.32 | | | (59) ~ ($lesseq(all_133_2, all_86_10)) | ~ ($lesseq(all_86_7, 208.20/128.32 | | | all_133_2)) | ? [v0: $int] : ($lesseq(v0, all_86_10) & 208.20/128.32 | | | $lesseq(all_86_7, v0) & get3(all_86_4, v0) = all_133_0) 208.20/128.32 | | | 208.20/128.32 | | | GROUND_INST: instantiating (18) with int, all_105_3, all_105_1, all_86_7, 208.20/128.32 | | | $sum(all_86_10, 1), all_133_2, all_696_0, all_133_1, 208.20/128.32 | | | simplifying with (5), (22), (38), (56) gives: 208.20/128.32 | | | (60) ~ ($lesseq(all_133_2, all_86_10)) | ~ ($lesseq(all_86_7, 208.20/128.32 | | | all_133_2)) | ? [v0: $int] : ? [v1: $int] : ($lesseq(v0, 208.20/128.32 | | | all_86_10) & $lesseq(all_86_7, v0) & t2tb1(v0) = v1 & get(int, 208.20/128.32 | | | int, all_105_3, v1) = all_133_1 & in_uni(v1) & 208.20/128.32 | | | in_uni(all_133_1)) 208.20/128.32 | | | 208.20/128.32 | | | REF_CLOSE: (1), (3), (5), (6), (7), (8), (9), (12), (13), (14), (20), 208.20/128.32 | | | (27), (32), (59), (60) are inconsistent by sub-proof #149. 208.20/128.32 | | | 208.20/128.32 | | End of split 208.20/128.32 | | 208.20/128.32 | End of split 208.20/128.32 | 208.20/128.32 End of proof 208.20/128.32 208.20/128.32 Sub-proof #127 shows that the following formulas are inconsistent: 208.20/128.32 ---------------------------------------------------------------- 208.20/128.32 (1) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ (tb2t1(v2) 208.20/128.32 = v1) | ~ (tb2t1(v2) = v0)) 208.20/128.32 (2) in_map_int_int(all_86_6) 208.20/128.32 (3) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.20/128.32 $int] : ! [v5: $int] : ! [v6: $int] : ( ~ ($lesseq(0, v4)) | ~ 208.20/128.32 ($lesseq(0, v3)) | ~ (map_eq_sub1(v0, v5, v6, v3, v4) = 0) | ~ 208.20/128.32 (elts(v0, v2) = v6) | ~ (elts(v0, v1) = v5) | ~ in_ty(v0) | ? [v7: 208.20/128.32 $int] : ? [v8: $int] : ((v7 = 0 & array_eq_sub1(v0, v1, v2, v3, v4) 208.20/128.32 = 0) | (length1(v0, v1) = v7 & ( ~ ($lesseq(v4, v7)) | ~ 208.20/128.32 ($lesseq(v3, v7)) | ( ~ (v8 = v7) & length1(v0, v2) = v8))))) 208.20/128.32 (4) elts(int, all_103_4) = all_103_3 208.20/128.32 (5) t2tb(all_86_2) = all_105_1 208.20/128.32 (6) in_ty(int) 208.20/128.32 (7) length1(int, all_103_4) = all_86_13 208.20/128.32 (8) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.20/128.32 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 208.20/128.32 (permut2(v0, v5, v6, v3, v4) = v7) | ~ (elts(v0, v2) = v6) | ~ 208.20/128.32 (elts(v0, v1) = v5) | ~ in_ty(v0) | ? [v8: $int] : ? [v9: $int] : 208.20/128.32 ((v9 = v8 & v7 = 0 & $lesseq(v4, v8) & $lesseq(v3, v8) & $lesseq(0, v4) 208.20/128.32 & $lesseq(0, v3) & length1(v0, v2) = v8 & length1(v0, v1) = v8) | ( 208.20/128.32 ~ (v8 = 0) & permut3(v0, v1, v2, v3, v4) = v8))) 208.20/128.32 (9) $lesseq(-1, all_86_8) 208.20/128.32 (10) $lesseq(1, $difference(all_86_13, all_86_7)) 208.20/128.32 (11) ! [v0: $int] : ! [v1: $int] : (v1 = 42 | ~ ($lesseq(1, 208.20/128.32 $difference(all_86_7, v0))) | ~ ($lesseq(1, $difference(v0, 208.20/128.32 all_86_8))) | ~ (get3(all_86_6, v0) = v1)) 208.20/128.32 (12) map_eq_sub1(int, all_103_3, all_103_1, $sum(all_86_10, 1), all_86_13) = 208.20/128.32 0 208.20/128.32 (13) t2tb(all_86_6) = all_103_1 208.20/128.32 (14) $lesseq(1, $difference(all_133_2, all_86_8)) 208.20/128.32 (15) tb2t1(all_133_1) = all_133_0 208.20/128.32 (16) map_eq_sub1(int, all_103_1, all_105_3, $sum(all_86_8, 1), all_86_13) = 0 208.20/128.32 (17) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.20/128.32 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ (permut3(v6, v5, 208.20/128.32 v4, v3, v2) = v1) | ~ (permut3(v6, v5, v4, v3, v2) = v0)) 208.20/128.32 (18) permut2(int, all_103_3, all_105_3, all_86_11, $sum(all_86_10, 1)) = 0 208.20/128.32 (19) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 208.20/128.32 | ~ (elts(v3, v2) = v1) | ~ (elts(v3, v2) = v0)) 208.20/128.32 (20) length1(int, all_105_4) = all_86_13 208.20/128.32 (21) elts(int, all_105_4) = all_105_3 208.20/128.32 (22) $lesseq(1, $difference(all_86_7, all_133_2)) 208.20/128.32 (23) map_eq_sub1(int, all_105_3, all_105_1, 0, all_86_7) = 0 208.20/128.32 (24) get4(int, all_105_2, all_133_2) = all_133_1 208.20/128.32 (25) tb2t(all_105_1) = all_86_2 208.20/128.32 (26) elts(int, all_105_2) = all_105_1 208.20/128.32 (27) map_eq_sub1(int, all_103_3, all_103_1, 0, all_86_11) = 0 208.20/128.32 (28) t2tb2(all_86_1) = all_105_2 208.20/128.32 (29) ~ ($difference(all_86_10, all_86_13) = -1) | ~ (all_86_11 = 0) 208.20/128.32 (30) $lesseq(all_86_11, all_86_8) 208.20/128.32 (31) $lesseq(all_86_7, all_86_10) 208.20/128.32 (32) ~ (all_133_0 = 42) 208.20/128.32 (33) in_array_int(all_86_1) 208.20/128.32 (34) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.20/128.32 $int] : ! [v5: $int] : ! [v6: $int] : ( ~ ($lesseq(0, v4)) | ~ 208.20/128.32 ($lesseq(0, v3)) | ~ (permut2(v0, v5, v6, v3, v4) = 0) | ~ (elts(v0, 208.20/128.32 v2) = v6) | ~ (elts(v0, v1) = v5) | ~ in_ty(v0) | ? [v7: $int] 208.20/128.32 : ? [v8: $int] : ((v7 = 0 & permut3(v0, v1, v2, v3, v4) = 0) | 208.20/128.32 (length1(v0, v1) = v7 & ( ~ ($lesseq(v4, v7)) | ~ ($lesseq(v3, v7)) 208.20/128.32 | ( ~ (v8 = v7) & length1(v0, v2) = v8))))) 208.20/128.32 (35) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.20/128.32 $int] : ! [v5: $int] : ! [v6: $int] : ( ~ ($lesseq(1, 208.20/128.32 $difference(v4, v5))) | ~ ($lesseq(v3, v5)) | ~ (map_eq_sub1(v0, 208.20/128.32 v1, v2, v3, v4) = 0) | ~ (t2tb1(v5) = v6) | ~ in_ty(v0) | ? 208.20/128.32 [v7: $int] : (get(v0, int, v2, v6) = v7 & get(v0, int, v1, v6) = v7 & 208.20/128.32 in_uni(v7))) 208.20/128.32 (36) $lesseq(1, $difference(all_86_13, all_86_10)) 208.20/128.32 (37) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.20/128.32 $int] : ! [v5: $int] : (v5 = 0 | ~ (permut_sub2(v0, v1, v2, v3, v4) 208.20/128.32 = v5) | ~ in_ty(v0) | ? [v6: $int] : ? [v7: $int] : ? [v8: $int] 208.20/128.32 : ? [v9: $int] : (( ~ (v9 = 0) & map_eq_sub1(v0, v6, v7, v4, v8) = v9 208.20/128.32 & length1(v0, v1) = v8 & elts(v0, v2) = v7 & elts(v0, v1) = v6 & 208.20/128.32 in_uni(v7) & in_uni(v6)) | ( ~ (v8 = 0) & map_eq_sub1(v0, v6, v7, 208.20/128.32 0, v3) = v8 & elts(v0, v2) = v7 & elts(v0, v1) = v6 & in_uni(v7) 208.20/128.32 & in_uni(v6)) | ( ~ (v6 = 0) & permut3(v0, v1, v2, v3, v4) = v6))) 208.20/128.32 (38) in_map_int_int(all_86_4) 208.20/128.32 (39) $lesseq(0, all_86_11) 208.20/128.33 (40) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ( ~ 208.20/128.33 (t2tb2(v0) = v2) | ~ (get4(int, v2, v1) = v3) | ~ in_array_int(v0) | 208.20/128.33 ? [v4: $int] : ? [v5: $int] : ? [v6: $int] : (tb2t(v4) = v5 & 208.20/128.33 tb2t1(v3) = v6 & get3(v5, v1) = v6 & elts(int, v2) = v4 & 208.20/128.33 in_map_int_int(v5) & in_uni(v4))) 208.20/128.33 (41) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ (tb2t(v2) 208.20/128.33 = v1) | ~ (tb2t(v2) = v0)) 208.20/128.33 (42) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.20/128.33 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 208.20/128.33 ($lesseq(1, $difference(v3, v6))) | ~ ($lesseq(v2, v6)) | ~ 208.20/128.33 (map_eq_sub1(int, v4, v5, v2, v3) = 0) | ~ (t2tb(v1) = v5) | ~ 208.20/128.33 (t2tb(v0) = v4) | ~ (get3(v1, v6) = v7) | ~ in_map_int_int(v0) | 208.20/128.33 get3(v0, v6) = v7) 208.20/128.33 (43) in_uni(all_133_1) 208.20/128.33 (44) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 208.20/128.33 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 208.20/128.33 (45) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ( ~ 208.20/128.33 (get4(v0, v1, v2) = v3) | ~ in_ty(v0) | ? [v4: $int] : ? [v5: $int] 208.20/128.33 : (elts(v0, v1) = v4 & t2tb1(v2) = v5 & get(v0, int, v4, v5) = v3 & 208.20/128.33 in_uni(v5) & in_uni(v4) & in_uni(v3))) 208.20/128.33 (46) $lesseq(1, all_86_10) 208.20/128.33 (47) map_eq_sub1(int, all_103_1, all_105_3, 0, all_86_13) = 0 208.20/128.33 (48) ! [v0: $int] : ! [v1: $int] : ( ~ (tb2t1(v0) = v1) | ~ in_uni(v0) | 208.20/128.33 t2tb1(v1) = v0) 208.20/128.33 (49) map_eq_sub1(int, all_105_3, all_105_1, $sum(all_86_10, 1), all_86_13) = 208.20/128.33 0 208.20/128.33 (50) t2tb(all_86_4) = all_105_3 208.20/128.33 (51) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.20/128.33 $int] : ! [v5: $int] : ( ~ (permut3(v0, v1, v2, v3, v4) = v5) | ~ 208.20/128.33 in_ty(v0) | ? [v6: $int] : ? [v7: $int] : ? [v8: $int] : ? [v9: 208.20/128.33 $int] : ? [v10: $int] : ((v10 = 0 & v9 = 0 & v5 = 0 & 208.20/128.33 map_eq_sub1(v0, v6, v7, v4, v8) = 0 & map_eq_sub1(v0, v6, v7, 0, 208.20/128.33 v3) = 0 & length1(v0, v1) = v8 & elts(v0, v2) = v7 & elts(v0, 208.20/128.33 v1) = v6 & in_uni(v7) & in_uni(v6)) | ( ~ (v6 = 0) & 208.20/128.33 permut_sub2(v0, v1, v2, v3, v4) = v6))) 208.20/128.33 208.20/128.33 Begin of proof 208.20/128.33 | 208.20/128.33 | GROUND_INST: instantiating (8) with int, all_103_4, all_105_4, all_86_11, 208.20/128.33 | $sum(all_86_10, 1), all_103_3, all_105_3, 0, simplifying with 208.20/128.33 | (4), (6), (18), (21) gives: 208.20/128.33 | (52) ? [v0: $int] : ? [v1: $int] : ((v1 = v0 & $lesseq(1, $difference(v0, 208.20/128.33 | all_86_10)) & $lesseq(all_86_11, v0) & $lesseq(-1, all_86_10) 208.20/128.33 | & $lesseq(0, all_86_11) & length1(int, all_105_4) = v0 & 208.20/128.33 | length1(int, all_103_4) = v0) | ( ~ (v0 = 0) & permut3(int, 208.20/128.33 | all_103_4, all_105_4, all_86_11, $sum(all_86_10, 1)) = v0)) 208.20/128.33 | 208.20/128.33 | GROUND_INST: instantiating (34) with int, all_103_4, all_105_4, all_86_11, 208.20/128.33 | $sum(all_86_10, 1), all_103_3, all_105_3, simplifying with (4), 208.20/128.33 | (6), (18), (21) gives: 208.20/128.33 | (53) ~ ($lesseq(-1, all_86_10)) | ~ ($lesseq(0, all_86_11)) | ? [v0: 208.20/128.33 | $int] : ? [v1: $int] : ((v0 = 0 & permut3(int, all_103_4, 208.20/128.33 | all_105_4, all_86_11, $sum(all_86_10, 1)) = 0) | (length1(int, 208.20/128.33 | all_103_4) = v0 & ( ~ ($lesseq(1, $difference(v0, all_86_10))) | 208.20/128.33 | ~ ($lesseq(all_86_11, v0)) | ( ~ (v1 = v0) & length1(int, 208.20/128.33 | all_105_4) = v1)))) 208.20/128.33 | 208.20/128.33 | GROUND_INST: instantiating (48) with all_133_1, all_133_0, simplifying with 208.20/128.33 | (15), (43) gives: 208.20/128.33 | (54) t2tb1(all_133_0) = all_133_1 208.20/128.33 | 208.20/128.33 | GROUND_INST: instantiating (40) with all_86_1, all_133_2, all_105_2, 208.20/128.33 | all_133_1, simplifying with (24), (28), (33) gives: 208.20/128.33 | (55) ? [v0: $int] : ? [v1: $int] : ? [v2: $int] : (tb2t(v0) = v1 & 208.20/128.33 | tb2t1(all_133_1) = v2 & get3(v1, all_133_2) = v2 & elts(int, 208.20/128.33 | all_105_2) = v0 & in_map_int_int(v1) & in_uni(v0)) 208.20/128.33 | 208.20/128.33 | GROUND_INST: instantiating (45) with int, all_105_2, all_133_2, all_133_1, 208.20/128.33 | simplifying with (6), (24) gives: 208.20/128.33 | (56) ? [v0: $int] : ? [v1: $int] : (elts(int, all_105_2) = v0 & 208.20/128.33 | t2tb1(all_133_2) = v1 & get(int, int, v0, v1) = all_133_1 & 208.20/128.33 | in_uni(v1) & in_uni(v0) & in_uni(all_133_1)) 208.20/128.33 | 208.20/128.33 | DELTA: instantiating (52) with fresh symbols all_693_0, all_693_1 gives: 208.20/128.33 | (57) (all_693_0 = all_693_1 & $lesseq(1, $difference(all_693_1, all_86_10)) 208.20/128.33 | & $lesseq(all_86_11, all_693_1) & $lesseq(-1, all_86_10) & 208.20/128.33 | $lesseq(0, all_86_11) & length1(int, all_105_4) = all_693_1 & 208.20/128.33 | length1(int, all_103_4) = all_693_1) | ( ~ (all_693_1 = 0) & 208.20/128.33 | permut3(int, all_103_4, all_105_4, all_86_11, $sum(all_86_10, 1)) = 208.20/128.33 | all_693_1) 208.20/128.33 | 208.20/128.33 | DELTA: instantiating (56) with fresh symbols all_696_0, all_696_1 gives: 208.20/128.33 | (58) elts(int, all_105_2) = all_696_1 & t2tb1(all_133_2) = all_696_0 & 208.20/128.33 | get(int, int, all_696_1, all_696_0) = all_133_1 & in_uni(all_696_0) & 208.20/128.33 | in_uni(all_696_1) & in_uni(all_133_1) 208.20/128.33 | 208.20/128.33 | ALPHA: (58) implies: 208.20/128.33 | (59) t2tb1(all_133_2) = all_696_0 208.20/128.33 | (60) elts(int, all_105_2) = all_696_1 208.20/128.33 | 208.20/128.33 | DELTA: instantiating (55) with fresh symbols all_706_0, all_706_1, all_706_2 208.20/128.33 | gives: 208.20/128.33 | (61) tb2t(all_706_2) = all_706_1 & tb2t1(all_133_1) = all_706_0 & 208.20/128.33 | get3(all_706_1, all_133_2) = all_706_0 & elts(int, all_105_2) = 208.20/128.33 | all_706_2 & in_map_int_int(all_706_1) & in_uni(all_706_2) 208.20/128.33 | 208.20/128.33 | ALPHA: (61) implies: 208.20/128.33 | (62) elts(int, all_105_2) = all_706_2 208.20/128.33 | (63) get3(all_706_1, all_133_2) = all_706_0 208.20/128.33 | (64) tb2t1(all_133_1) = all_706_0 208.20/128.33 | (65) tb2t(all_706_2) = all_706_1 208.20/128.33 | 208.20/128.33 | BETA: splitting (53) gives: 208.20/128.33 | 208.20/128.33 | Case 1: 208.20/128.33 | | 208.20/128.33 | | (66) $lesseq(all_86_11, -1) 208.20/128.33 | | 208.20/128.33 | | COMBINE_INEQS: (39), (66) imply: 208.20/128.33 | | (67) $lesseq(0, -1) 208.20/128.33 | | 208.20/128.33 | | CLOSE: (67) is inconsistent. 208.20/128.33 | | 208.20/128.33 | Case 2: 208.20/128.33 | | 208.20/128.33 | | (68) ~ ($lesseq(-1, all_86_10)) | ? [v0: $int] : ? [v1: $int] : ((v0 = 208.20/128.33 | | 0 & permut3(int, all_103_4, all_105_4, all_86_11, 208.20/128.33 | | $sum(all_86_10, 1)) = 0) | (length1(int, all_103_4) = v0 & ( ~ 208.20/128.33 | | ($lesseq(1, $difference(v0, all_86_10))) | ~ 208.20/128.33 | | ($lesseq(all_86_11, v0)) | ( ~ (v1 = v0) & length1(int, 208.20/128.33 | | all_105_4) = v1)))) 208.20/128.33 | | 208.20/128.33 | | BETA: splitting (68) gives: 208.20/128.33 | | 208.20/128.33 | | Case 1: 208.20/128.33 | | | 208.20/128.33 | | | (69) $lesseq(all_86_10, -2) 208.20/128.33 | | | 208.20/128.33 | | | COMBINE_INEQS: (46), (69) imply: 208.20/128.33 | | | (70) $lesseq(0, -1) 208.20/128.33 | | | 208.20/128.33 | | | CLOSE: (70) is inconsistent. 208.20/128.33 | | | 208.20/128.33 | | Case 2: 208.20/128.33 | | | 208.20/128.33 | | | (71) ? [v0: $int] : ? [v1: $int] : ((v0 = 0 & permut3(int, all_103_4, 208.20/128.33 | | | all_105_4, all_86_11, $sum(all_86_10, 1)) = 0) | 208.20/128.33 | | | (length1(int, all_103_4) = v0 & ( ~ ($lesseq(1, $difference(v0, 208.20/128.33 | | | all_86_10))) | ~ ($lesseq(all_86_11, v0)) | ( ~ (v1 = 208.20/128.33 | | | v0) & length1(int, all_105_4) = v1)))) 208.20/128.33 | | | 208.20/128.33 | | | DELTA: instantiating (71) with fresh symbols all_722_0, all_722_1 gives: 208.20/128.33 | | | (72) (all_722_1 = 0 & permut3(int, all_103_4, all_105_4, all_86_11, 208.20/128.33 | | | $sum(all_86_10, 1)) = 0) | (length1(int, all_103_4) = 208.20/128.33 | | | all_722_1 & ( ~ ($lesseq(1, $difference(all_722_1, all_86_10))) 208.20/128.33 | | | | ~ ($lesseq(all_86_11, all_722_1)) | ( ~ (all_722_0 = 208.20/128.33 | | | all_722_1) & length1(int, all_105_4) = all_722_0))) 208.20/128.33 | | | 208.20/128.33 | | | BETA: splitting (72) gives: 208.20/128.33 | | | 208.20/128.33 | | | Case 1: 208.20/128.33 | | | | 208.20/128.33 | | | | (73) all_722_1 = 0 & permut3(int, all_103_4, all_105_4, all_86_11, 208.20/128.33 | | | | $sum(all_86_10, 1)) = 0 208.20/128.33 | | | | 208.20/128.33 | | | | ALPHA: (73) implies: 208.20/128.33 | | | | (74) permut3(int, all_103_4, all_105_4, all_86_11, $sum(all_86_10, 208.20/128.33 | | | | 1)) = 0 208.20/128.33 | | | | 208.20/128.33 | | | | BETA: splitting (57) gives: 208.20/128.33 | | | | 208.20/128.33 | | | | Case 1: 208.20/128.33 | | | | | 208.20/128.33 | | | | | (75) all_693_0 = all_693_1 & $lesseq(1, $difference(all_693_1, 208.20/128.33 | | | | | all_86_10)) & $lesseq(all_86_11, all_693_1) & $lesseq(-1, 208.20/128.33 | | | | | all_86_10) & $lesseq(0, all_86_11) & length1(int, all_105_4) 208.20/128.33 | | | | | = all_693_1 & length1(int, all_103_4) = all_693_1 208.20/128.33 | | | | | 208.20/128.33 | | | | | ALPHA: (75) implies: 208.20/128.33 | | | | | (76) $lesseq(1, $difference(all_693_1, all_86_10)) 208.20/128.33 | | | | | (77) length1(int, all_103_4) = all_693_1 208.20/128.33 | | | | | 208.20/128.33 | | | | | GROUND_INST: instantiating (1) with all_133_0, all_706_0, all_133_1, 208.20/128.33 | | | | | simplifying with (15), (64) gives: 208.20/128.33 | | | | | (78) all_706_0 = all_133_0 208.20/128.33 | | | | | 208.20/128.33 | | | | | GROUND_INST: instantiating (44) with all_86_13, all_693_1, all_103_4, 208.20/128.33 | | | | | int, simplifying with (7), (77) gives: 208.20/128.33 | | | | | (79) all_693_1 = all_86_13 208.20/128.33 | | | | | 208.20/128.33 | | | | | GROUND_INST: instantiating (19) with all_105_1, all_706_2, all_105_2, 208.20/128.33 | | | | | int, simplifying with (26), (62) gives: 208.20/128.33 | | | | | (80) all_706_2 = all_105_1 208.20/128.33 | | | | | 208.20/128.33 | | | | | GROUND_INST: instantiating (19) with all_706_2, all_696_1, all_105_2, 208.20/128.33 | | | | | int, simplifying with (60), (62) gives: 208.20/128.33 | | | | | (81) all_706_2 = all_696_1 208.20/128.33 | | | | | 208.20/128.33 | | | | | COMBINE_EQS: (80), (81) imply: 208.20/128.33 | | | | | (82) all_696_1 = all_105_1 208.20/128.33 | | | | | 208.20/128.33 | | | | | REDUCE: (65), (80) imply: 208.20/128.33 | | | | | (83) tb2t(all_105_1) = all_706_1 208.20/128.33 | | | | | 208.20/128.33 | | | | | REDUCE: (63), (78) imply: 208.20/128.33 | | | | | (84) get3(all_706_1, all_133_2) = all_133_0 208.20/128.33 | | | | | 208.20/128.33 | | | | | GROUND_INST: instantiating (41) with all_86_2, all_706_1, all_105_1, 208.20/128.33 | | | | | simplifying with (25), (83) gives: 208.20/128.33 | | | | | (85) all_706_1 = all_86_2 208.20/128.33 | | | | | 208.20/128.33 | | | | | REDUCE: (84), (85) imply: 208.20/128.33 | | | | | (86) get3(all_86_2, all_133_2) = all_133_0 208.20/128.33 | | | | | 208.20/128.33 | | | | | GROUND_INST: instantiating (51) with int, all_103_4, all_105_4, 208.20/128.33 | | | | | all_86_11, $sum(all_86_10, 1), 0, simplifying with (6), 208.20/128.33 | | | | | (74) gives: 208.20/128.33 | | | | | (87) ? [v0: $int] : ? [v1: $int] : ? [v2: $int] : ? [v3: $int] 208.20/128.33 | | | | | : ? [v4: $int] : ((v4 = 0 & v3 = 0 & map_eq_sub1(int, v0, v1, 208.20/128.33 | | | | | $sum(all_86_10, 1), v2) = 0 & map_eq_sub1(int, v0, v1, 208.20/128.33 | | | | | 0, all_86_11) = 0 & length1(int, all_103_4) = v2 & 208.20/128.33 | | | | | elts(int, all_105_4) = v1 & elts(int, all_103_4) = v0 & 208.20/128.33 | | | | | in_uni(v1) & in_uni(v0)) | ( ~ (v0 = 0) & permut_sub2(int, 208.20/128.33 | | | | | all_103_4, all_105_4, all_86_11, $sum(all_86_10, 1)) = 208.20/128.33 | | | | | v0)) 208.20/128.33 | | | | | 208.20/128.33 | | | | | GROUND_INST: instantiating (42) with all_86_4, all_86_2, 0, all_86_7, 208.20/128.33 | | | | | all_105_3, all_105_1, all_133_2, all_133_0, simplifying 208.20/128.33 | | | | | with (5), (23), (38), (50), (86) gives: 208.20/128.33 | | | | | (88) ~ ($lesseq(1, $difference(all_86_7, all_133_2))) | ~ 208.20/128.33 | | | | | ($lesseq(0, all_133_2)) | get3(all_86_4, all_133_2) = 208.20/128.33 | | | | | all_133_0 208.20/128.33 | | | | | 208.20/128.33 | | | | | GROUND_INST: instantiating (35) with int, all_105_3, all_105_1, 208.20/128.33 | | | | | $sum(all_86_10, 1), all_86_13, all_133_0, all_133_1, 208.20/128.33 | | | | | simplifying with (6), (49), (54) gives: 208.20/128.33 | | | | | (89) ~ ($lesseq(1, $difference(all_86_13, all_133_0))) | ~ 208.20/128.33 | | | | | ($lesseq(1, $difference(all_133_0, all_86_10))) | ? [v0: 208.20/128.33 | | | | | $int] : (get(int, int, all_105_1, all_133_1) = v0 & get(int, 208.20/128.33 | | | | | int, all_105_3, all_133_1) = v0 & in_uni(v0)) 208.20/128.33 | | | | | 208.20/128.33 | | | | | GROUND_INST: instantiating (35) with int, all_103_3, all_103_1, 208.20/128.33 | | | | | $sum(all_86_10, 1), all_86_13, all_133_0, all_133_1, 208.20/128.33 | | | | | simplifying with (6), (12), (54) gives: 208.20/128.33 | | | | | (90) ~ ($lesseq(1, $difference(all_86_13, all_133_0))) | ~ 208.20/128.33 | | | | | ($lesseq(1, $difference(all_133_0, all_86_10))) | ? [v0: 208.20/128.33 | | | | | $int] : (get(int, int, all_103_1, all_133_1) = v0 & get(int, 208.20/128.33 | | | | | int, all_103_3, all_133_1) = v0 & in_uni(v0)) 208.20/128.33 | | | | | 208.20/128.33 | | | | | GROUND_INST: instantiating (35) with int, all_103_3, all_103_1, 0, 208.20/128.33 | | | | | all_86_11, all_133_0, all_133_1, simplifying with (6), 208.20/128.33 | | | | | (27), (54) gives: 208.20/128.33 | | | | | (91) ~ ($lesseq(1, $difference(all_86_11, all_133_0))) | ~ 208.20/128.33 | | | | | ($lesseq(0, all_133_0)) | ? [v0: $int] : (get(int, int, 208.20/128.33 | | | | | all_103_1, all_133_1) = v0 & get(int, int, all_103_3, 208.20/128.33 | | | | | all_133_1) = v0 & in_uni(v0)) 208.20/128.33 | | | | | 208.20/128.33 | | | | | GROUND_INST: instantiating (35) with int, all_105_3, all_105_1, 0, 208.20/128.33 | | | | | all_86_7, all_133_2, all_696_0, simplifying with (6), 208.20/128.33 | | | | | (23), (59) gives: 208.20/128.33 | | | | | (92) ~ ($lesseq(1, $difference(all_86_7, all_133_2))) | ~ 208.20/128.33 | | | | | ($lesseq(0, all_133_2)) | ? [v0: $int] : (get(int, int, 208.20/128.33 | | | | | all_105_1, all_696_0) = v0 & get(int, int, all_105_3, 208.20/128.33 | | | | | all_696_0) = v0 & in_uni(v0)) 208.20/128.33 | | | | | 208.20/128.33 | | | | | GROUND_INST: instantiating (35) with int, all_103_1, all_105_3, 208.20/128.33 | | | | | $sum(all_86_8, 1), all_86_13, all_133_2, all_696_0, 208.20/128.33 | | | | | simplifying with (6), (16), (59) gives: 208.20/128.33 | | | | | (93) ~ ($lesseq(1, $difference(all_86_13, all_133_2))) | ~ 208.20/128.33 | | | | | ($lesseq(1, $difference(all_133_2, all_86_8))) | ? [v0: $int] 208.20/128.33 | | | | | : (get(int, int, all_105_3, all_696_0) = v0 & get(int, int, 208.20/128.33 | | | | | all_103_1, all_696_0) = v0 & in_uni(v0)) 208.20/128.33 | | | | | 208.20/128.33 | | | | | DELTA: instantiating (87) with fresh symbols all_765_0, all_765_1, 208.20/128.33 | | | | | all_765_2, all_765_3, all_765_4 gives: 208.20/128.33 | | | | | (94) (all_765_0 = 0 & all_765_1 = 0 & map_eq_sub1(int, all_765_4, 208.20/128.33 | | | | | all_765_3, $sum(all_86_10, 1), all_765_2) = 0 & 208.20/128.33 | | | | | map_eq_sub1(int, all_765_4, all_765_3, 0, all_86_11) = 0 & 208.20/128.33 | | | | | length1(int, all_103_4) = all_765_2 & elts(int, all_105_4) = 208.20/128.33 | | | | | all_765_3 & elts(int, all_103_4) = all_765_4 & 208.20/128.33 | | | | | in_uni(all_765_3) & in_uni(all_765_4)) | ( ~ (all_765_4 = 0) 208.20/128.33 | | | | | & permut_sub2(int, all_103_4, all_105_4, all_86_11, 208.20/128.33 | | | | | $sum(all_86_10, 1)) = all_765_4) 208.20/128.33 | | | | | 208.20/128.33 | | | | | BETA: splitting (29) gives: 208.20/128.33 | | | | | 208.20/128.33 | | | | | Case 1: 208.20/128.33 | | | | | | 208.20/128.33 | | | | | | (95) ~ (all_86_11 = 0) 208.20/128.33 | | | | | | 208.20/128.33 | | | | | | STRENGTHEN: (39), (95) imply: 208.20/128.33 | | | | | | (96) $lesseq(1, all_86_11) 208.20/128.33 | | | | | | 208.20/128.33 | | | | | | COMBINE_INEQS: (14), (22) imply: 208.20/128.33 | | | | | | (97) $lesseq(2, $difference(all_86_7, all_86_8)) 208.20/128.33 | | | | | | 208.20/128.33 | | | | | | COMBINE_INEQS: (31), (97) imply: 208.20/128.33 | | | | | | (98) $lesseq(2, $difference(all_86_10, all_86_8)) 208.20/128.33 | | | | | | 208.20/128.33 | | | | | | COMBINE_INEQS: (30), (98) imply: 208.20/128.33 | | | | | | (99) $lesseq(2, $difference(all_86_10, all_86_11)) 208.20/128.33 | | | | | | 208.20/128.33 | | | | | | COMBINE_INEQS: (36), (99) imply: 208.20/128.33 | | | | | | (100) $lesseq(3, $difference(all_86_13, all_86_11)) 208.20/128.33 | | | | | | 208.20/128.33 | | | | | | COMBINE_INEQS: (96), (100) imply: 208.20/128.33 | | | | | | (101) $lesseq(4, all_86_13) 208.20/128.33 | | | | | | 208.20/128.33 | | | | | | REF_CLOSE: (2), (3), (4), (6), (7), (9), (10), (11), (13), (14), 208.20/128.33 | | | | | | (19), (21), (22), (31), (32), (37), (42), (44), (47), 208.20/128.33 | | | | | | (50), (88), (89), (90), (91), (92), (93), (94), (101) are 208.20/128.33 | | | | | | inconsistent by sub-proof #128. 208.20/128.33 | | | | | | 208.20/128.33 | | | | | Case 2: 208.20/128.33 | | | | | | 208.20/128.33 | | | | | | (102) all_86_11 = 0 208.20/128.33 | | | | | | (103) ~ ($difference(all_86_10, all_86_13) = -1) 208.20/128.33 | | | | | | 208.20/128.33 | | | | | | REDUCE: (30), (102) imply: 208.20/128.33 | | | | | | (104) $lesseq(0, all_86_8) 208.20/128.33 | | | | | | 208.20/128.34 | | | | | | STRENGTHEN: (36), (103) imply: 208.20/128.34 | | | | | | (105) $lesseq(2, $difference(all_86_13, all_86_10)) 208.20/128.34 | | | | | | 208.20/128.34 | | | | | | COMBINE_INEQS: (14), (22) imply: 208.20/128.34 | | | | | | (106) $lesseq(2, $difference(all_86_7, all_86_8)) 208.20/128.34 | | | | | | 208.20/128.34 | | | | | | COMBINE_INEQS: (31), (106) imply: 208.20/128.34 | | | | | | (107) $lesseq(2, $difference(all_86_10, all_86_8)) 208.20/128.34 | | | | | | 208.20/128.34 | | | | | | COMBINE_INEQS: (104), (107) imply: 208.20/128.34 | | | | | | (108) $lesseq(2, all_86_10) 208.20/128.34 | | | | | | 208.20/128.34 | | | | | | COMBINE_INEQS: (105), (108) imply: 208.20/128.34 | | | | | | (109) $lesseq(4, all_86_13) 208.20/128.34 | | | | | | 208.20/128.34 | | | | | | REF_CLOSE: (2), (3), (4), (6), (7), (9), (10), (11), (13), (14), 208.20/128.34 | | | | | | (19), (21), (22), (31), (32), (37), (42), (44), (47), 208.20/128.34 | | | | | | (50), (88), (89), (90), (91), (92), (93), (94), (109) are 208.20/128.34 | | | | | | inconsistent by sub-proof #128. 208.20/128.34 | | | | | | 208.20/128.34 | | | | | End of split 208.20/128.34 | | | | | 208.20/128.34 | | | | Case 2: 208.20/128.34 | | | | | 208.20/128.34 | | | | | (110) ~ (all_693_1 = 0) & permut3(int, all_103_4, all_105_4, 208.20/128.34 | | | | | all_86_11, $sum(all_86_10, 1)) = all_693_1 208.20/128.34 | | | | | 208.20/128.34 | | | | | ALPHA: (110) implies: 208.20/128.34 | | | | | (111) ~ (all_693_1 = 0) 208.20/128.34 | | | | | (112) permut3(int, all_103_4, all_105_4, all_86_11, $sum(all_86_10, 208.20/128.34 | | | | | 1)) = all_693_1 208.20/128.34 | | | | | 208.20/128.34 | | | | | GROUND_INST: instantiating (17) with all_693_1, 0, $sum(all_86_10, 1), 208.20/128.34 | | | | | all_86_11, all_105_4, all_103_4, int, simplifying with 208.20/128.34 | | | | | (74), (112) gives: 208.20/128.34 | | | | | (113) all_693_1 = 0 208.20/128.34 | | | | | 208.20/128.34 | | | | | REDUCE: (111), (113) imply: 208.20/128.34 | | | | | (114) ~ (0 = 0) 208.20/128.34 | | | | | 208.20/128.34 | | | | | CLOSE: (114) is inconsistent. 208.20/128.34 | | | | | 208.20/128.34 | | | | End of split 208.20/128.34 | | | | 208.20/128.34 | | | Case 2: 208.20/128.34 | | | | 208.20/128.34 | | | | (115) length1(int, all_103_4) = all_722_1 & ( ~ ($lesseq(1, 208.20/128.34 | | | | $difference(all_722_1, all_86_10))) | ~ 208.20/128.34 | | | | ($lesseq(all_86_11, all_722_1)) | ( ~ (all_722_0 = all_722_1) 208.20/128.34 | | | | & length1(int, all_105_4) = all_722_0)) 208.20/128.34 | | | | 208.20/128.34 | | | | ALPHA: (115) implies: 208.20/128.34 | | | | (116) length1(int, all_103_4) = all_722_1 208.20/128.34 | | | | (117) ~ ($lesseq(1, $difference(all_722_1, all_86_10))) | ~ 208.20/128.34 | | | | ($lesseq(all_86_11, all_722_1)) | ( ~ (all_722_0 = all_722_1) & 208.20/128.34 | | | | length1(int, all_105_4) = all_722_0) 208.20/128.34 | | | | 208.20/128.34 | | | | GROUND_INST: instantiating (44) with all_86_13, all_722_1, all_103_4, 208.20/128.34 | | | | int, simplifying with (7), (116) gives: 208.20/128.34 | | | | (118) all_722_1 = all_86_13 208.20/128.34 | | | | 208.20/128.34 | | | | BETA: splitting (117) gives: 208.20/128.34 | | | | 208.20/128.34 | | | | Case 1: 208.20/128.34 | | | | | 208.20/128.34 | | | | | (119) $lesseq(1, $difference(all_86_11, all_722_1)) 208.20/128.34 | | | | | 208.20/128.34 | | | | | REDUCE: (118), (119) imply: 208.20/128.34 | | | | | (120) $lesseq(1, $difference(all_86_11, all_86_13)) 208.20/128.34 | | | | | 208.20/128.34 | | | | | COMBINE_INEQS: (14), (22) imply: 208.20/128.34 | | | | | (121) $lesseq(2, $difference(all_86_7, all_86_8)) 208.20/128.34 | | | | | 208.20/128.34 | | | | | COMBINE_INEQS: (31), (121) imply: 208.20/128.34 | | | | | (122) $lesseq(2, $difference(all_86_10, all_86_8)) 208.20/128.34 | | | | | 208.20/128.34 | | | | | COMBINE_INEQS: (30), (122) imply: 208.20/128.34 | | | | | (123) $lesseq(2, $difference(all_86_10, all_86_11)) 208.20/128.34 | | | | | 208.20/128.34 | | | | | COMBINE_INEQS: (36), (123) imply: 208.20/128.34 | | | | | (124) $lesseq(3, $difference(all_86_13, all_86_11)) 208.20/128.34 | | | | | 208.20/128.34 | | | | | COMBINE_INEQS: (120), (124) imply: 208.20/128.34 | | | | | (125) $lesseq(0, -1) 208.20/128.34 | | | | | 208.20/128.34 | | | | | CLOSE: (125) is inconsistent. 208.20/128.34 | | | | | 208.20/128.34 | | | | Case 2: 208.20/128.34 | | | | | 208.20/128.34 | | | | | (126) ~ ($lesseq(1, $difference(all_722_1, all_86_10))) | ( ~ 208.20/128.34 | | | | | (all_722_0 = all_722_1) & length1(int, all_105_4) = 208.20/128.34 | | | | | all_722_0) 208.20/128.34 | | | | | 208.20/128.34 | | | | | BETA: splitting (126) gives: 208.20/128.34 | | | | | 208.20/128.34 | | | | | Case 1: 208.20/128.34 | | | | | | 208.20/128.34 | | | | | | (127) $lesseq(all_722_1, all_86_10) 208.20/128.34 | | | | | | 208.20/128.34 | | | | | | REDUCE: (118), (127) imply: 208.20/128.34 | | | | | | (128) $lesseq(all_86_13, all_86_10) 208.20/128.34 | | | | | | 208.20/128.34 | | | | | | COMBINE_INEQS: (36), (128) imply: 208.20/128.34 | | | | | | (129) $lesseq(0, -1) 208.20/128.34 | | | | | | 208.20/128.34 | | | | | | CLOSE: (129) is inconsistent. 208.20/128.34 | | | | | | 208.20/128.34 | | | | | Case 2: 208.20/128.34 | | | | | | 208.20/128.34 | | | | | | (130) ~ (all_722_0 = all_722_1) & length1(int, all_105_4) = 208.20/128.34 | | | | | | all_722_0 208.20/128.34 | | | | | | 208.20/128.34 | | | | | | ALPHA: (130) implies: 208.20/128.34 | | | | | | (131) ~ (all_722_0 = all_722_1) 208.20/128.34 | | | | | | (132) length1(int, all_105_4) = all_722_0 208.20/128.34 | | | | | | 208.20/128.34 | | | | | | REDUCE: (118), (131) imply: 208.20/128.34 | | | | | | (133) ~ (all_722_0 = all_86_13) 208.20/128.34 | | | | | | 208.20/128.34 | | | | | | GROUND_INST: instantiating (44) with all_86_13, all_722_0, 208.20/128.34 | | | | | | all_105_4, int, simplifying with (20), (132) gives: 208.20/128.34 | | | | | | (134) all_722_0 = all_86_13 208.20/128.34 | | | | | | 208.20/128.34 | | | | | | REDUCE: (133), (134) imply: 208.20/128.34 | | | | | | (135) ~ (0 = 0) 208.20/128.34 | | | | | | 208.20/128.34 | | | | | | CLOSE: (135) is inconsistent. 208.20/128.34 | | | | | | 208.20/128.34 | | | | | End of split 208.20/128.34 | | | | | 208.20/128.34 | | | | End of split 208.20/128.34 | | | | 208.20/128.34 | | | End of split 208.20/128.34 | | | 208.20/128.34 | | End of split 208.20/128.34 | | 208.20/128.34 | End of split 208.20/128.34 | 208.20/128.34 End of proof 208.20/128.34 208.20/128.34 Sub-proof #128 shows that the following formulas are inconsistent: 208.20/128.34 ---------------------------------------------------------------- 208.20/128.34 (1) in_map_int_int(all_86_6) 208.20/128.34 (2) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.20/128.34 $int] : ! [v5: $int] : ! [v6: $int] : ( ~ ($lesseq(0, v4)) | ~ 208.20/128.34 ($lesseq(0, v3)) | ~ (map_eq_sub1(v0, v5, v6, v3, v4) = 0) | ~ 208.20/128.34 (elts(v0, v2) = v6) | ~ (elts(v0, v1) = v5) | ~ in_ty(v0) | ? [v7: 208.20/128.34 $int] : ? [v8: $int] : ((v7 = 0 & array_eq_sub1(v0, v1, v2, v3, v4) 208.20/128.34 = 0) | (length1(v0, v1) = v7 & ( ~ ($lesseq(v4, v7)) | ~ 208.20/128.34 ($lesseq(v3, v7)) | ( ~ (v8 = v7) & length1(v0, v2) = v8))))) 208.20/128.34 (3) elts(int, all_103_4) = all_103_3 208.20/128.34 (4) in_ty(int) 208.20/128.34 (5) length1(int, all_103_4) = all_86_13 208.20/128.34 (6) $lesseq(-1, all_86_8) 208.20/128.34 (7) $lesseq(1, $difference(all_86_13, all_86_7)) 208.20/128.34 (8) ! [v0: $int] : ! [v1: $int] : (v1 = 42 | ~ ($lesseq(1, 208.20/128.34 $difference(all_86_7, v0))) | ~ ($lesseq(1, $difference(v0, 208.20/128.34 all_86_8))) | ~ (get3(all_86_6, v0) = v1)) 208.20/128.34 (9) t2tb(all_86_6) = all_103_1 208.20/128.34 (10) $lesseq(1, $difference(all_133_2, all_86_8)) 208.20/128.34 (11) ~ ($lesseq(1, $difference(all_86_13, all_133_0))) | ~ ($lesseq(1, 208.20/128.34 $difference(all_133_0, all_86_10))) | ? [v0: $int] : (get(int, int, 208.20/128.34 all_105_1, all_133_1) = v0 & get(int, int, all_105_3, all_133_1) = 208.20/128.34 v0 & in_uni(v0)) 208.20/128.34 (12) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 208.20/128.34 | ~ (elts(v3, v2) = v1) | ~ (elts(v3, v2) = v0)) 208.20/128.34 (13) ~ ($lesseq(1, $difference(all_86_13, all_133_2))) | ~ ($lesseq(1, 208.20/128.34 $difference(all_133_2, all_86_8))) | ? [v0: $int] : (get(int, int, 208.20/128.34 all_105_3, all_696_0) = v0 & get(int, int, all_103_1, all_696_0) = 208.20/128.34 v0 & in_uni(v0)) 208.20/128.34 (14) elts(int, all_105_4) = all_105_3 208.20/128.34 (15) $lesseq(1, $difference(all_86_7, all_133_2)) 208.20/128.34 (16) ~ ($lesseq(1, $difference(all_86_11, all_133_0))) | ~ ($lesseq(0, 208.20/128.34 all_133_0)) | ? [v0: $int] : (get(int, int, all_103_1, all_133_1) = 208.20/128.34 v0 & get(int, int, all_103_3, all_133_1) = v0 & in_uni(v0)) 208.20/128.34 (17) $lesseq(all_86_7, all_86_10) 208.20/128.34 (18) ~ ($lesseq(1, $difference(all_86_7, all_133_2))) | ~ ($lesseq(0, 208.20/128.34 all_133_2)) | ? [v0: $int] : (get(int, int, all_105_1, all_696_0) = 208.20/128.34 v0 & get(int, int, all_105_3, all_696_0) = v0 & in_uni(v0)) 208.20/128.34 (19) $lesseq(4, all_86_13) 208.20/128.34 (20) ~ (all_133_0 = 42) 208.20/128.34 (21) ~ ($lesseq(1, $difference(all_86_7, all_133_2))) | ~ ($lesseq(0, 208.20/128.34 all_133_2)) | get3(all_86_4, all_133_2) = all_133_0 208.20/128.34 (22) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.20/128.34 $int] : ! [v5: $int] : (v5 = 0 | ~ (permut_sub2(v0, v1, v2, v3, v4) 208.20/128.34 = v5) | ~ in_ty(v0) | ? [v6: $int] : ? [v7: $int] : ? [v8: $int] 208.20/128.34 : ? [v9: $int] : (( ~ (v9 = 0) & map_eq_sub1(v0, v6, v7, v4, v8) = v9 208.20/128.34 & length1(v0, v1) = v8 & elts(v0, v2) = v7 & elts(v0, v1) = v6 & 208.20/128.34 in_uni(v7) & in_uni(v6)) | ( ~ (v8 = 0) & map_eq_sub1(v0, v6, v7, 208.20/128.34 0, v3) = v8 & elts(v0, v2) = v7 & elts(v0, v1) = v6 & in_uni(v7) 208.20/128.34 & in_uni(v6)) | ( ~ (v6 = 0) & permut3(v0, v1, v2, v3, v4) = v6))) 208.20/128.34 (23) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.20/128.34 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 208.20/128.34 ($lesseq(1, $difference(v3, v6))) | ~ ($lesseq(v2, v6)) | ~ 208.20/128.34 (map_eq_sub1(int, v4, v5, v2, v3) = 0) | ~ (t2tb(v1) = v5) | ~ 208.20/128.34 (t2tb(v0) = v4) | ~ (get3(v1, v6) = v7) | ~ in_map_int_int(v0) | 208.20/128.34 get3(v0, v6) = v7) 208.20/128.34 (24) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 208.20/128.34 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 208.20/128.34 (25) map_eq_sub1(int, all_103_1, all_105_3, 0, all_86_13) = 0 208.20/128.34 (26) ~ ($lesseq(1, $difference(all_86_13, all_133_0))) | ~ ($lesseq(1, 208.20/128.34 $difference(all_133_0, all_86_10))) | ? [v0: $int] : (get(int, int, 208.20/128.34 all_103_1, all_133_1) = v0 & get(int, int, all_103_3, all_133_1) = 208.20/128.34 v0 & in_uni(v0)) 208.20/128.34 (27) t2tb(all_86_4) = all_105_3 208.20/128.34 (28) (all_765_0 = 0 & all_765_1 = 0 & map_eq_sub1(int, all_765_4, all_765_3, 208.20/128.34 $sum(all_86_10, 1), all_765_2) = 0 & map_eq_sub1(int, all_765_4, 208.20/128.34 all_765_3, 0, all_86_11) = 0 & length1(int, all_103_4) = all_765_2 & 208.20/128.34 elts(int, all_105_4) = all_765_3 & elts(int, all_103_4) = all_765_4 & 208.20/128.34 in_uni(all_765_3) & in_uni(all_765_4)) | ( ~ (all_765_4 = 0) & 208.20/128.34 permut_sub2(int, all_103_4, all_105_4, all_86_11, $sum(all_86_10, 1)) 208.20/128.34 = all_765_4) 208.20/128.34 208.20/128.34 Begin of proof 208.20/128.34 | 208.20/128.34 | BETA: splitting (18) gives: 208.20/128.34 | 208.20/128.34 | Case 1: 208.20/128.34 | | 208.20/128.34 | | (29) $lesseq(all_133_2, -1) 208.20/128.34 | | 208.20/128.34 | | COMBINE_INEQS: (10), (29) imply: 208.20/128.34 | | (30) $lesseq(all_86_8, -2) 208.20/128.34 | | 208.20/128.34 | | COMBINE_INEQS: (6), (30) imply: 208.20/128.34 | | (31) $lesseq(0, -1) 208.20/128.34 | | 208.20/128.34 | | CLOSE: (31) is inconsistent. 208.20/128.34 | | 208.20/128.34 | Case 2: 208.20/128.34 | | 208.20/128.34 | | (32) $lesseq(0, all_133_2) 208.20/128.34 | | 208.20/128.34 | | COMBINE_INEQS: (15), (32) imply: 208.20/128.34 | | (33) $lesseq(1, all_86_7) 208.20/128.34 | | 208.20/128.34 | | COMBINE_INEQS: (17), (33) imply: 208.20/128.34 | | (34) $lesseq(1, all_86_10) 208.20/128.34 | | 208.20/128.34 | | BETA: splitting (21) gives: 208.20/128.34 | | 208.20/128.34 | | Case 1: 208.20/128.34 | | | 208.20/128.34 | | | (35) get3(all_86_4, all_133_2) = all_133_0 208.20/128.34 | | | 208.20/128.34 | | | BETA: splitting (13) gives: 208.20/128.34 | | | 208.20/128.34 | | | Case 1: 208.20/128.34 | | | | 208.20/128.34 | | | | (36) $lesseq(all_86_13, all_133_2) 208.20/128.34 | | | | 208.20/128.34 | | | | COMBINE_INEQS: (15), (36) imply: 208.20/128.34 | | | | (37) $lesseq(1, $difference(all_86_7, all_86_13)) 208.20/128.34 | | | | 208.20/128.34 | | | | COMBINE_INEQS: (7), (37) imply: 208.20/128.34 | | | | (38) $lesseq(0, -1) 208.20/128.34 | | | | 208.20/128.34 | | | | CLOSE: (38) is inconsistent. 208.20/128.34 | | | | 208.20/128.34 | | | Case 2: 208.20/128.34 | | | | 208.20/128.34 | | | | (39) $lesseq(1, $difference(all_86_13, all_133_2)) 208.20/128.34 | | | | 208.20/128.34 | | | | BETA: splitting (28) gives: 208.20/128.34 | | | | 208.20/128.34 | | | | Case 1: 208.20/128.34 | | | | | 208.20/128.34 | | | | | (40) all_765_0 = 0 & all_765_1 = 0 & map_eq_sub1(int, all_765_4, 208.20/128.34 | | | | | all_765_3, $sum(all_86_10, 1), all_765_2) = 0 & 208.20/128.34 | | | | | map_eq_sub1(int, all_765_4, all_765_3, 0, all_86_11) = 0 & 208.20/128.34 | | | | | length1(int, all_103_4) = all_765_2 & elts(int, all_105_4) = 208.20/128.34 | | | | | all_765_3 & elts(int, all_103_4) = all_765_4 & 208.20/128.34 | | | | | in_uni(all_765_3) & in_uni(all_765_4) 208.20/128.34 | | | | | 208.20/128.34 | | | | | ALPHA: (40) implies: 208.20/128.34 | | | | | (41) elts(int, all_103_4) = all_765_4 208.20/128.34 | | | | | (42) elts(int, all_105_4) = all_765_3 208.20/128.34 | | | | | (43) length1(int, all_103_4) = all_765_2 208.20/128.34 | | | | | (44) map_eq_sub1(int, all_765_4, all_765_3, $sum(all_86_10, 1), 208.20/128.34 | | | | | all_765_2) = 0 208.20/128.34 | | | | | 208.20/128.34 | | | | | GROUND_INST: instantiating (24) with all_86_13, all_765_2, all_103_4, 208.20/128.34 | | | | | int, simplifying with (5), (43) gives: 208.20/128.34 | | | | | (45) all_765_2 = all_86_13 208.20/128.34 | | | | | 208.20/128.34 | | | | | GROUND_INST: instantiating (12) with all_105_3, all_765_3, all_105_4, 208.20/128.34 | | | | | int, simplifying with (14), (42) gives: 208.20/128.34 | | | | | (46) all_765_3 = all_105_3 208.20/128.34 | | | | | 208.20/128.34 | | | | | GROUND_INST: instantiating (12) with all_103_3, all_765_4, all_103_4, 208.20/128.34 | | | | | int, simplifying with (3), (41) gives: 208.20/128.34 | | | | | (47) all_765_4 = all_103_3 208.20/128.34 | | | | | 208.20/128.34 | | | | | REDUCE: (44), (45), (46), (47) imply: 208.20/128.34 | | | | | (48) map_eq_sub1(int, all_103_3, all_105_3, $sum(all_86_10, 1), 208.20/128.34 | | | | | all_86_13) = 0 208.20/128.34 | | | | | 208.20/128.34 | | | | | REF_CLOSE: (1), (2), (3), (4), (8), (9), (10), (11), (14), (15), (16), 208.20/128.34 | | | | | (19), (20), (23), (25), (26), (27), (32), (34), (35), (39), 208.20/128.34 | | | | | (48) are inconsistent by sub-proof #129. 208.20/128.34 | | | | | 208.20/128.34 | | | | Case 2: 208.20/128.34 | | | | | 208.20/128.34 | | | | | (49) ~ (all_765_4 = 0) & permut_sub2(int, all_103_4, all_105_4, 208.20/128.34 | | | | | all_86_11, $sum(all_86_10, 1)) = all_765_4 208.20/128.34 | | | | | 208.20/128.34 | | | | | ALPHA: (49) implies: 208.20/128.34 | | | | | (50) ~ (all_765_4 = 0) 208.20/128.34 | | | | | (51) permut_sub2(int, all_103_4, all_105_4, all_86_11, 208.20/128.34 | | | | | $sum(all_86_10, 1)) = all_765_4 208.20/128.34 | | | | | 208.20/128.34 | | | | | GROUND_INST: instantiating (22) with int, all_103_4, all_105_4, 208.20/128.34 | | | | | all_86_11, $sum(all_86_10, 1), all_765_4, simplifying 208.20/128.34 | | | | | with (4), (51) gives: 208.20/128.34 | | | | | (52) all_765_4 = 0 | ? [v0: $int] : ? [v1: $int] : ? [v2: $int] 208.20/128.34 | | | | | : ? [v3: $int] : (( ~ (v3 = 0) & map_eq_sub1(int, v0, v1, 208.20/128.34 | | | | | $sum(all_86_10, 1), v2) = v3 & length1(int, all_103_4) = 208.20/128.34 | | | | | v2 & elts(int, all_105_4) = v1 & elts(int, all_103_4) = v0 208.20/128.34 | | | | | & in_uni(v1) & in_uni(v0)) | ( ~ (v2 = 0) & 208.20/128.34 | | | | | map_eq_sub1(int, v0, v1, 0, all_86_11) = v2 & elts(int, 208.20/128.34 | | | | | all_105_4) = v1 & elts(int, all_103_4) = v0 & in_uni(v1) 208.20/128.34 | | | | | & in_uni(v0)) | ( ~ (v0 = 0) & permut3(int, all_103_4, 208.20/128.34 | | | | | all_105_4, all_86_11, $sum(all_86_10, 1)) = v0)) 208.20/128.34 | | | | | 208.20/128.34 | | | | | GROUND_INST: instantiating (23) with all_86_6, all_86_4, 0, all_86_13, 208.20/128.34 | | | | | all_103_1, all_105_3, all_133_2, all_133_0, simplifying 208.20/128.34 | | | | | with (1), (9), (25), (27), (35) gives: 208.20/128.34 | | | | | (53) ~ ($lesseq(1, $difference(all_86_13, all_133_2))) | ~ 208.20/128.34 | | | | | ($lesseq(0, all_133_2)) | get3(all_86_6, all_133_2) = 208.20/128.34 | | | | | all_133_0 208.20/128.34 | | | | | 208.20/128.34 | | | | | BETA: splitting (53) gives: 208.20/128.34 | | | | | 208.20/128.34 | | | | | Case 1: 208.20/128.34 | | | | | | 208.20/128.34 | | | | | | (54) get3(all_86_6, all_133_2) = all_133_0 208.20/128.34 | | | | | | 208.20/128.34 | | | | | | BETA: splitting (52) gives: 208.20/128.34 | | | | | | 208.20/128.34 | | | | | | Case 1: 208.20/128.34 | | | | | | | 208.20/128.34 | | | | | | | (55) all_765_4 = 0 208.20/128.34 | | | | | | | 208.20/128.34 | | | | | | | REDUCE: (50), (55) imply: 208.20/128.34 | | | | | | | (56) ~ (0 = 0) 208.20/128.34 | | | | | | | 208.20/128.34 | | | | | | | CLOSE: (56) is inconsistent. 208.20/128.34 | | | | | | | 208.20/128.34 | | | | | | Case 2: 208.20/128.34 | | | | | | | 208.20/128.34 | | | | | | | 208.20/128.34 | | | | | | | GROUND_INST: instantiating (8) with all_133_2, all_133_0, 208.20/128.34 | | | | | | | simplifying with (54) gives: 208.20/128.34 | | | | | | | (57) all_133_0 = 42 | ~ ($lesseq(1, $difference(all_86_7, 208.20/128.34 | | | | | | | all_133_2))) | ~ ($lesseq(1, $difference(all_133_2, 208.20/128.34 | | | | | | | all_86_8))) 208.20/128.34 | | | | | | | 208.20/128.34 | | | | | | | REF_CLOSE: (10), (15), (20), (57) are inconsistent by sub-proof 208.20/128.34 | | | | | | | #155. 208.20/128.34 | | | | | | | 208.20/128.34 | | | | | | End of split 208.20/128.34 | | | | | | 208.20/128.34 | | | | | Case 2: 208.20/128.34 | | | | | | 208.20/128.34 | | | | | | (58) ~ ($lesseq(1, $difference(all_86_13, all_133_2))) | ~ 208.20/128.34 | | | | | | ($lesseq(0, all_133_2)) 208.20/128.34 | | | | | | 208.20/128.34 | | | | | | REF_CLOSE: (32), (39), (58) are inconsistent by sub-proof #130. 208.20/128.34 | | | | | | 208.20/128.34 | | | | | End of split 208.20/128.34 | | | | | 208.20/128.34 | | | | End of split 208.20/128.34 | | | | 208.20/128.34 | | | End of split 208.20/128.34 | | | 208.20/128.34 | | Case 2: 208.20/128.34 | | | 208.20/128.34 | | | (59) ~ ($lesseq(1, $difference(all_86_7, all_133_2))) | ~ ($lesseq(0, 208.20/128.34 | | | all_133_2)) 208.20/128.34 | | | 208.20/128.34 | | | REF_CLOSE: (15), (32), (59) are inconsistent by sub-proof #151. 208.20/128.34 | | | 208.20/128.34 | | End of split 208.20/128.34 | | 208.20/128.34 | End of split 208.20/128.34 | 208.20/128.34 End of proof 208.20/128.34 208.20/128.34 Sub-proof #129 shows that the following formulas are inconsistent: 208.20/128.34 ---------------------------------------------------------------- 208.20/128.34 (1) in_map_int_int(all_86_6) 208.20/128.34 (2) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.20/128.34 $int] : ! [v5: $int] : ! [v6: $int] : ( ~ ($lesseq(0, v4)) | ~ 208.20/128.34 ($lesseq(0, v3)) | ~ (map_eq_sub1(v0, v5, v6, v3, v4) = 0) | ~ 208.20/128.34 (elts(v0, v2) = v6) | ~ (elts(v0, v1) = v5) | ~ in_ty(v0) | ? [v7: 208.20/128.34 $int] : ? [v8: $int] : ((v7 = 0 & array_eq_sub1(v0, v1, v2, v3, v4) 208.20/128.34 = 0) | (length1(v0, v1) = v7 & ( ~ ($lesseq(v4, v7)) | ~ 208.20/128.34 ($lesseq(v3, v7)) | ( ~ (v8 = v7) & length1(v0, v2) = v8))))) 208.20/128.34 (3) elts(int, all_103_4) = all_103_3 208.20/128.34 (4) map_eq_sub1(int, all_103_3, all_105_3, $sum(all_86_10, 1), all_86_13) = 0 208.20/128.34 (5) in_ty(int) 208.20/128.34 (6) $lesseq(0, all_133_2) 208.20/128.34 (7) ! [v0: $int] : ! [v1: $int] : (v1 = 42 | ~ ($lesseq(1, 208.20/128.34 $difference(all_86_7, v0))) | ~ ($lesseq(1, $difference(v0, 208.20/128.34 all_86_8))) | ~ (get3(all_86_6, v0) = v1)) 208.20/128.34 (8) t2tb(all_86_6) = all_103_1 208.20/128.34 (9) $lesseq(1, $difference(all_133_2, all_86_8)) 208.20/128.34 (10) ~ ($lesseq(1, $difference(all_86_13, all_133_0))) | ~ ($lesseq(1, 208.20/128.34 $difference(all_133_0, all_86_10))) | ? [v0: $int] : (get(int, int, 208.20/128.34 all_105_1, all_133_1) = v0 & get(int, int, all_105_3, all_133_1) = 208.20/128.34 v0 & in_uni(v0)) 208.20/128.35 (11) elts(int, all_105_4) = all_105_3 208.20/128.35 (12) $lesseq(1, $difference(all_86_7, all_133_2)) 208.20/128.35 (13) ~ ($lesseq(1, $difference(all_86_11, all_133_0))) | ~ ($lesseq(0, 208.20/128.35 all_133_0)) | ? [v0: $int] : (get(int, int, all_103_1, all_133_1) = 208.20/128.35 v0 & get(int, int, all_103_3, all_133_1) = v0 & in_uni(v0)) 208.20/128.35 (14) $lesseq(4, all_86_13) 208.20/128.35 (15) ~ (all_133_0 = 42) 208.20/128.35 (16) get3(all_86_4, all_133_2) = all_133_0 208.20/128.35 (17) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.20/128.35 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 208.20/128.35 ($lesseq(1, $difference(v3, v6))) | ~ ($lesseq(v2, v6)) | ~ 208.20/128.35 (map_eq_sub1(int, v4, v5, v2, v3) = 0) | ~ (t2tb(v1) = v5) | ~ 208.20/128.35 (t2tb(v0) = v4) | ~ (get3(v1, v6) = v7) | ~ in_map_int_int(v0) | 208.20/128.35 get3(v0, v6) = v7) 208.20/128.35 (18) $lesseq(1, $difference(all_86_13, all_133_2)) 208.20/128.35 (19) $lesseq(1, all_86_10) 208.20/128.35 (20) map_eq_sub1(int, all_103_1, all_105_3, 0, all_86_13) = 0 208.20/128.35 (21) ~ ($lesseq(1, $difference(all_86_13, all_133_0))) | ~ ($lesseq(1, 208.20/128.35 $difference(all_133_0, all_86_10))) | ? [v0: $int] : (get(int, int, 208.20/128.35 all_103_1, all_133_1) = v0 & get(int, int, all_103_3, all_133_1) = 208.20/128.35 v0 & in_uni(v0)) 208.20/128.35 (22) t2tb(all_86_4) = all_105_3 208.20/128.35 208.20/128.35 Begin of proof 208.20/128.35 | 208.20/128.35 | BETA: splitting (13) gives: 208.20/128.35 | 208.20/128.35 | Case 1: 208.20/128.35 | | 208.20/128.35 | | (23) $lesseq(all_133_0, -1) 208.20/128.35 | | 208.20/128.35 | | BETA: splitting (21) gives: 208.20/128.35 | | 208.20/128.35 | | Case 1: 208.20/128.35 | | | 208.20/128.35 | | | (24) $lesseq(all_86_13, all_133_0) 208.20/128.35 | | | 208.20/128.35 | | | COMBINE_INEQS: (23), (24) imply: 208.41/128.35 | | | (25) $lesseq(all_86_13, -1) 208.41/128.35 | | | 208.41/128.35 | | | COMBINE_INEQS: (14), (25) imply: 208.41/128.35 | | | (26) $lesseq(0, -1) 208.41/128.35 | | | 208.41/128.35 | | | CLOSE: (26) is inconsistent. 208.41/128.35 | | | 208.41/128.35 | | Case 2: 208.41/128.35 | | | 208.41/128.35 | | | (27) $lesseq(1, $difference(all_86_13, all_133_0)) 208.41/128.35 | | | 208.41/128.35 | | | BETA: splitting (10) gives: 208.41/128.35 | | | 208.41/128.35 | | | Case 1: 208.41/128.35 | | | | 208.41/128.35 | | | | (28) $lesseq(all_86_13, all_133_0) 208.41/128.35 | | | | 208.41/128.35 | | | | COMBINE_INEQS: (27), (28) imply: 208.41/128.35 | | | | (29) $lesseq(0, -1) 208.41/128.35 | | | | 208.41/128.35 | | | | CLOSE: (29) is inconsistent. 208.41/128.35 | | | | 208.41/128.35 | | | Case 2: 208.41/128.35 | | | | 208.41/128.35 | | | | 208.41/128.35 | | | | GROUND_INST: instantiating (2) with int, all_103_4, all_105_4, 208.41/128.35 | | | | $sum(all_86_10, 1), all_86_13, all_103_3, all_105_3, 208.41/128.35 | | | | simplifying with (3), (4), (5), (11) gives: 208.41/128.35 | | | | (30) ~ ($lesseq(-1, all_86_10)) | ~ ($lesseq(0, all_86_13)) | ? 208.41/128.35 | | | | [v0: $int] : ? [v1: $int] : ((v0 = 0 & array_eq_sub1(int, 208.41/128.35 | | | | all_103_4, all_105_4, $sum(all_86_10, 1), all_86_13) = 0) 208.41/128.35 | | | | | (length1(int, all_103_4) = v0 & ( ~ ($lesseq(1, 208.41/128.35 | | | | $difference(v0, all_86_10))) | ~ ($lesseq(all_86_13, 208.41/128.35 | | | | v0)) | ( ~ (v1 = v0) & length1(int, all_105_4) = 208.41/128.35 | | | | v1)))) 208.41/128.35 | | | | 208.41/128.35 | | | | GROUND_INST: instantiating (17) with all_86_6, all_86_4, 0, all_86_13, 208.41/128.35 | | | | all_103_1, all_105_3, all_133_2, all_133_0, simplifying 208.41/128.35 | | | | with (1), (8), (16), (20), (22) gives: 208.41/128.35 | | | | (31) ~ ($lesseq(1, $difference(all_86_13, all_133_2))) | ~ 208.41/128.35 | | | | ($lesseq(0, all_133_2)) | get3(all_86_6, all_133_2) = all_133_0 208.41/128.35 | | | | 208.41/128.35 | | | | BETA: splitting (31) gives: 208.41/128.35 | | | | 208.41/128.35 | | | | Case 1: 208.41/128.35 | | | | | 208.41/128.35 | | | | | (32) get3(all_86_6, all_133_2) = all_133_0 208.41/128.35 | | | | | 208.41/128.35 | | | | | BETA: splitting (30) gives: 208.41/128.35 | | | | | 208.41/128.35 | | | | | Case 1: 208.41/128.35 | | | | | | 208.41/128.35 | | | | | | (33) $lesseq(all_86_13, -1) 208.41/128.35 | | | | | | 208.41/128.35 | | | | | | COMBINE_INEQS: (14), (33) imply: 208.41/128.35 | | | | | | (34) $lesseq(0, -1) 208.41/128.35 | | | | | | 208.41/128.35 | | | | | | CLOSE: (34) is inconsistent. 208.41/128.35 | | | | | | 208.41/128.35 | | | | | Case 2: 208.41/128.35 | | | | | | 208.41/128.35 | | | | | | (35) ~ ($lesseq(-1, all_86_10)) | ? [v0: $int] : ? [v1: $int] 208.41/128.35 | | | | | | : ((v0 = 0 & array_eq_sub1(int, all_103_4, all_105_4, 208.41/128.35 | | | | | | $sum(all_86_10, 1), all_86_13) = 0) | (length1(int, 208.41/128.35 | | | | | | all_103_4) = v0 & ( ~ ($lesseq(1, $difference(v0, 208.41/128.35 | | | | | | all_86_10))) | ~ ($lesseq(all_86_13, v0)) | ( ~ 208.41/128.35 | | | | | | (v1 = v0) & length1(int, all_105_4) = v1)))) 208.41/128.35 | | | | | | 208.41/128.35 | | | | | | BETA: splitting (35) gives: 208.41/128.35 | | | | | | 208.41/128.35 | | | | | | Case 1: 208.41/128.35 | | | | | | | 208.41/128.35 | | | | | | | (36) $lesseq(all_86_10, -2) 208.41/128.35 | | | | | | | 208.41/128.35 | | | | | | | COMBINE_INEQS: (19), (36) imply: 208.41/128.35 | | | | | | | (37) $lesseq(0, -1) 208.41/128.35 | | | | | | | 208.41/128.35 | | | | | | | CLOSE: (37) is inconsistent. 208.41/128.35 | | | | | | | 208.41/128.35 | | | | | | Case 2: 208.41/128.35 | | | | | | | 208.41/128.35 | | | | | | | 208.41/128.35 | | | | | | | GROUND_INST: instantiating (7) with all_133_2, all_133_0, 208.41/128.35 | | | | | | | simplifying with (32) gives: 208.41/128.35 | | | | | | | (38) all_133_0 = 42 | ~ ($lesseq(1, $difference(all_86_7, 208.41/128.35 | | | | | | | all_133_2))) | ~ ($lesseq(1, $difference(all_133_2, 208.41/128.35 | | | | | | | all_86_8))) 208.41/128.35 | | | | | | | 208.41/128.35 | | | | | | | BETA: splitting (38) gives: 208.41/128.35 | | | | | | | 208.41/128.35 | | | | | | | Case 1: 208.41/128.35 | | | | | | | | 208.41/128.35 | | | | | | | | (39) $lesseq(all_86_7, all_133_2) 208.41/128.35 | | | | | | | | 208.41/128.35 | | | | | | | | COMBINE_INEQS: (12), (39) imply: 208.41/128.35 | | | | | | | | (40) $lesseq(0, -1) 208.41/128.35 | | | | | | | | 208.41/128.35 | | | | | | | | CLOSE: (40) is inconsistent. 208.41/128.35 | | | | | | | | 208.41/128.35 | | | | | | | Case 2: 208.41/128.35 | | | | | | | | 208.41/128.35 | | | | | | | | (41) all_133_0 = 42 | ~ ($lesseq(1, $difference(all_133_2, 208.41/128.35 | | | | | | | | all_86_8))) 208.41/128.35 | | | | | | | | 208.41/128.35 | | | | | | | | BETA: splitting (41) gives: 208.41/128.35 | | | | | | | | 208.41/128.35 | | | | | | | | Case 1: 208.41/128.35 | | | | | | | | | 208.41/128.35 | | | | | | | | | (42) $lesseq(all_133_2, all_86_8) 208.41/128.35 | | | | | | | | | 208.41/128.35 | | | | | | | | | COMBINE_INEQS: (9), (42) imply: 208.41/128.35 | | | | | | | | | (43) $lesseq(0, -1) 208.41/128.35 | | | | | | | | | 208.41/128.35 | | | | | | | | | CLOSE: (43) is inconsistent. 208.41/128.35 | | | | | | | | | 208.41/128.35 | | | | | | | | Case 2: 208.41/128.35 | | | | | | | | | 208.41/128.35 | | | | | | | | | (44) all_133_0 = 42 208.41/128.35 | | | | | | | | | 208.41/128.35 | | | | | | | | | REDUCE: (23), (44) imply: 208.41/128.35 | | | | | | | | | (45) $lesseq(0, -1) 208.41/128.35 | | | | | | | | | 208.41/128.35 | | | | | | | | | CLOSE: (45) is inconsistent. 208.41/128.35 | | | | | | | | | 208.41/128.35 | | | | | | | | End of split 208.41/128.35 | | | | | | | | 208.41/128.35 | | | | | | | End of split 208.41/128.35 | | | | | | | 208.41/128.35 | | | | | | End of split 208.41/128.35 | | | | | | 208.41/128.35 | | | | | End of split 208.41/128.35 | | | | | 208.41/128.35 | | | | Case 2: 208.41/128.35 | | | | | 208.41/128.35 | | | | | (46) ~ ($lesseq(1, $difference(all_86_13, all_133_2))) | ~ 208.41/128.35 | | | | | ($lesseq(0, all_133_2)) 208.41/128.35 | | | | | 208.41/128.35 | | | | | REF_CLOSE: (6), (18), (46) are inconsistent by sub-proof #130. 208.41/128.35 | | | | | 208.41/128.35 | | | | End of split 208.41/128.35 | | | | 208.41/128.35 | | | End of split 208.41/128.35 | | | 208.41/128.35 | | End of split 208.41/128.35 | | 208.41/128.35 | Case 2: 208.41/128.35 | | 208.41/128.35 | | 208.41/128.35 | | GROUND_INST: instantiating (2) with int, all_103_4, all_105_4, 208.41/128.35 | | $sum(all_86_10, 1), all_86_13, all_103_3, all_105_3, 208.41/128.35 | | simplifying with (3), (4), (5), (11) gives: 208.41/128.35 | | (47) ~ ($lesseq(-1, all_86_10)) | ~ ($lesseq(0, all_86_13)) | ? [v0: 208.41/128.35 | | $int] : ? [v1: $int] : ((v0 = 0 & array_eq_sub1(int, all_103_4, 208.41/128.35 | | all_105_4, $sum(all_86_10, 1), all_86_13) = 0) | (length1(int, 208.41/128.35 | | all_103_4) = v0 & ( ~ ($lesseq(1, $difference(v0, all_86_10))) 208.41/128.35 | | | ~ ($lesseq(all_86_13, v0)) | ( ~ (v1 = v0) & length1(int, 208.41/128.35 | | all_105_4) = v1)))) 208.41/128.35 | | 208.41/128.35 | | GROUND_INST: instantiating (17) with all_86_6, all_86_4, 0, all_86_13, 208.41/128.35 | | all_103_1, all_105_3, all_133_2, all_133_0, simplifying with 208.41/128.35 | | (1), (8), (16), (20), (22) gives: 208.41/128.35 | | (48) ~ ($lesseq(1, $difference(all_86_13, all_133_2))) | ~ ($lesseq(0, 208.41/128.35 | | all_133_2)) | get3(all_86_6, all_133_2) = all_133_0 208.41/128.35 | | 208.41/128.35 | | BETA: splitting (47) gives: 208.41/128.35 | | 208.41/128.35 | | Case 1: 208.41/128.35 | | | 208.41/128.35 | | | (49) $lesseq(all_86_13, -1) 208.41/128.35 | | | 208.41/128.35 | | | COMBINE_INEQS: (14), (49) imply: 208.41/128.35 | | | (50) $lesseq(0, -1) 208.41/128.35 | | | 208.41/128.35 | | | CLOSE: (50) is inconsistent. 208.41/128.35 | | | 208.41/128.35 | | Case 2: 208.41/128.35 | | | 208.41/128.35 | | | (51) ~ ($lesseq(-1, all_86_10)) | ? [v0: $int] : ? [v1: $int] : ((v0 208.41/128.35 | | | = 0 & array_eq_sub1(int, all_103_4, all_105_4, $sum(all_86_10, 208.41/128.35 | | | 1), all_86_13) = 0) | (length1(int, all_103_4) = v0 & ( ~ 208.41/128.35 | | | ($lesseq(1, $difference(v0, all_86_10))) | ~ 208.41/128.35 | | | ($lesseq(all_86_13, v0)) | ( ~ (v1 = v0) & length1(int, 208.41/128.35 | | | all_105_4) = v1)))) 208.41/128.35 | | | 208.41/128.35 | | | BETA: splitting (48) gives: 208.41/128.35 | | | 208.41/128.35 | | | Case 1: 208.41/128.35 | | | | 208.41/128.35 | | | | (52) get3(all_86_6, all_133_2) = all_133_0 208.41/128.35 | | | | 208.41/128.35 | | | | BETA: splitting (51) gives: 208.41/128.35 | | | | 208.41/128.35 | | | | Case 1: 208.41/128.35 | | | | | 208.41/128.35 | | | | | (53) $lesseq(all_86_10, -2) 208.41/128.35 | | | | | 208.41/128.35 | | | | | COMBINE_INEQS: (19), (53) imply: 208.41/128.35 | | | | | (54) $lesseq(0, -1) 208.41/128.35 | | | | | 208.41/128.35 | | | | | CLOSE: (54) is inconsistent. 208.41/128.35 | | | | | 208.41/128.35 | | | | Case 2: 208.41/128.35 | | | | | 208.41/128.35 | | | | | 208.41/128.35 | | | | | GROUND_INST: instantiating (7) with all_133_2, all_133_0, simplifying 208.41/128.35 | | | | | with (52) gives: 208.41/128.35 | | | | | (55) all_133_0 = 42 | ~ ($lesseq(1, $difference(all_86_7, 208.41/128.35 | | | | | all_133_2))) | ~ ($lesseq(1, $difference(all_133_2, 208.41/128.35 | | | | | all_86_8))) 208.41/128.35 | | | | | 208.41/128.35 | | | | | REF_CLOSE: (9), (12), (15), (55) are inconsistent by sub-proof #155. 208.41/128.35 | | | | | 208.41/128.35 | | | | End of split 208.41/128.35 | | | | 208.41/128.35 | | | Case 2: 208.41/128.35 | | | | 208.41/128.35 | | | | (56) ~ ($lesseq(1, $difference(all_86_13, all_133_2))) | ~ 208.41/128.35 | | | | ($lesseq(0, all_133_2)) 208.41/128.35 | | | | 208.41/128.35 | | | | REF_CLOSE: (6), (18), (56) are inconsistent by sub-proof #130. 208.41/128.35 | | | | 208.41/128.35 | | | End of split 208.41/128.35 | | | 208.41/128.35 | | End of split 208.41/128.35 | | 208.41/128.35 | End of split 208.41/128.35 | 208.41/128.35 End of proof 208.41/128.35 208.41/128.35 Sub-proof #130 shows that the following formulas are inconsistent: 208.41/128.35 ---------------------------------------------------------------- 208.41/128.35 (1) ~ ($lesseq(1, $difference(all_86_13, all_133_2))) | ~ ($lesseq(0, 208.41/128.35 all_133_2)) 208.41/128.35 (2) $lesseq(0, all_133_2) 208.41/128.35 (3) $lesseq(1, $difference(all_86_13, all_133_2)) 208.41/128.35 208.41/128.35 Begin of proof 208.41/128.35 | 208.41/128.35 | BETA: splitting (1) gives: 208.41/128.35 | 208.41/128.35 | Case 1: 208.41/128.35 | | 208.41/128.35 | | (4) $lesseq(all_133_2, -1) 208.41/128.35 | | 208.41/128.35 | | COMBINE_INEQS: (2), (4) imply: 208.41/128.35 | | (5) $lesseq(0, -1) 208.41/128.35 | | 208.41/128.35 | | CLOSE: (5) is inconsistent. 208.41/128.35 | | 208.41/128.35 | Case 2: 208.41/128.35 | | 208.41/128.35 | | (6) $lesseq(all_86_13, all_133_2) 208.41/128.35 | | 208.41/128.35 | | COMBINE_INEQS: (3), (6) imply: 208.41/128.35 | | (7) $lesseq(0, -1) 208.41/128.35 | | 208.41/128.35 | | CLOSE: (7) is inconsistent. 208.41/128.35 | | 208.41/128.35 | End of split 208.41/128.35 | 208.41/128.35 End of proof 208.41/128.35 208.41/128.35 Sub-proof #131 shows that the following formulas are inconsistent: 208.41/128.35 ---------------------------------------------------------------- 208.41/128.35 (1) length1(int, all_105_2) = all_86_13 208.41/128.35 (2) sorted_sub2(all_205_2, 0, all_205_1) = 0 208.41/128.35 (3) sorted_sub2(all_86_2, 0, all_86_13) = all_200_0 208.41/128.35 (4) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.41/128.35 $int] : (v1 = v0 | ~ (sorted_sub2(v4, v3, v2) = v1) | ~ 208.41/128.35 (sorted_sub2(v4, v3, v2) = v0)) 208.41/128.35 (5) tb2t(all_205_3) = all_205_2 208.41/128.35 (6) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 208.41/128.35 | ~ (elts(v3, v2) = v1) | ~ (elts(v3, v2) = v0)) 208.41/128.35 (7) tb2t(all_105_1) = all_86_2 208.41/128.35 (8) elts(int, all_105_2) = all_105_1 208.41/128.35 (9) ~ (all_200_0 = 0) 208.41/128.35 (10) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ (tb2t(v2) 208.41/128.35 = v1) | ~ (tb2t(v2) = v0)) 208.41/128.35 (11) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 208.41/128.35 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 208.41/128.35 (12) length1(int, all_105_2) = all_205_1 208.41/128.35 (13) elts(int, all_105_2) = all_205_3 208.41/128.35 208.41/128.35 Begin of proof 208.41/128.35 | 208.41/128.35 | GROUND_INST: instantiating (4) with 0, all_200_0, all_86_13, 0, all_86_2, 208.41/128.35 | simplifying with (3) gives: 208.41/128.35 | (14) all_200_0 = 0 | ~ (sorted_sub2(all_86_2, 0, all_86_13) = 0) 208.41/128.35 | 208.41/128.35 | GROUND_INST: instantiating (11) with all_86_13, all_205_1, all_105_2, int, 208.41/128.35 | simplifying with (1), (12) gives: 208.41/128.35 | (15) all_205_1 = all_86_13 208.41/128.35 | 208.41/128.35 | GROUND_INST: instantiating (6) with all_105_1, all_205_3, all_105_2, int, 208.41/128.35 | simplifying with (8), (13) gives: 208.41/128.35 | (16) all_205_3 = all_105_1 208.41/128.35 | 208.41/128.35 | REDUCE: (2), (15) imply: 208.41/128.35 | (17) sorted_sub2(all_205_2, 0, all_86_13) = 0 208.41/128.35 | 208.41/128.35 | REDUCE: (5), (16) imply: 208.41/128.35 | (18) tb2t(all_105_1) = all_205_2 208.41/128.35 | 208.41/128.35 | GROUND_INST: instantiating (10) with all_86_2, all_205_2, all_105_1, 208.41/128.35 | simplifying with (7), (18) gives: 208.41/128.35 | (19) all_205_2 = all_86_2 208.41/128.35 | 208.41/128.35 | REDUCE: (17), (19) imply: 208.41/128.35 | (20) sorted_sub2(all_86_2, 0, all_86_13) = 0 208.41/128.35 | 208.41/128.35 | BETA: splitting (14) gives: 208.41/128.35 | 208.41/128.35 | Case 1: 208.41/128.35 | | 208.41/128.35 | | (21) ~ (sorted_sub2(all_86_2, 0, all_86_13) = 0) 208.41/128.35 | | 208.41/128.35 | | PRED_UNIFY: (20), (21) imply: 208.41/128.35 | | (22) $false 208.41/128.35 | | 208.41/128.35 | | CLOSE: (22) is inconsistent. 208.41/128.35 | | 208.41/128.35 | Case 2: 208.41/128.35 | | 208.41/128.35 | | (23) all_200_0 = 0 208.41/128.35 | | 208.41/128.35 | | REDUCE: (9), (23) imply: 208.41/128.35 | | (24) ~ (0 = 0) 208.41/128.35 | | 208.41/128.35 | | CLOSE: (24) is inconsistent. 208.41/128.35 | | 208.41/128.35 | End of split 208.41/128.35 | 208.41/128.35 End of proof 208.41/128.35 208.41/128.35 Sub-proof #132 shows that the following formulas are inconsistent: 208.41/128.35 ---------------------------------------------------------------- 208.41/128.35 (1) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ (tb2t1(v2) 208.41/128.35 = v1) | ~ (tb2t1(v2) = v0)) 208.41/128.35 (2) ! [v0: $int] : ! [v1: $int] : ( ~ ($lesseq(43, v1)) | ~ ($lesseq(v0, 208.41/128.35 all_86_8)) | ~ ($lesseq(all_86_11, v0)) | ~ (get3(all_86_6, v0) = 208.41/128.35 v1)) 208.41/128.35 (3) length1(int, all_103_2) = all_86_13 208.41/128.35 (4) in_map_int_int(all_86_6) 208.41/128.35 (5) in_map_int_int(all_86_12) 208.41/128.35 (6) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.41/128.35 $int] : ! [v5: $int] : ! [v6: $int] : ( ~ ($lesseq(0, v4)) | ~ 208.41/128.35 ($lesseq(0, v3)) | ~ (map_eq_sub1(v0, v5, v6, v3, v4) = 0) | ~ 208.41/128.35 (elts(v0, v2) = v6) | ~ (elts(v0, v1) = v5) | ~ in_ty(v0) | ? [v7: 208.41/128.35 $int] : ? [v8: $int] : ((v7 = 0 & array_eq_sub1(v0, v1, v2, v3, v4) 208.41/128.35 = 0) | (length1(v0, v1) = v7 & ( ~ ($lesseq(v4, v7)) | ~ 208.41/128.35 ($lesseq(v3, v7)) | ( ~ (v8 = v7) & length1(v0, v2) = v8))))) 208.41/128.35 (7) elts(int, all_103_4) = all_103_3 208.41/128.35 (8) t2tb2(all_86_3) = all_105_4 208.41/128.35 (9) t2tb(all_86_2) = all_105_1 208.41/128.35 (10) in_ty(int) 208.41/128.35 (11) length1(int, all_103_4) = all_86_13 208.41/128.35 (12) $lesseq(2, all_86_13) 208.41/128.35 (13) ( ~ (all_133_0 = 42) & $lesseq(1, $difference(all_86_7, all_133_2)) & 208.41/128.35 $lesseq(1, $difference(all_133_2, all_86_8)) & tb2t1(all_133_1) = 208.41/128.35 all_133_0 & get4(int, all_133_3, all_133_2) = all_133_1 & 208.41/128.35 in_uni(all_133_1)) | ($lesseq(all_133_0, 41) & $lesseq(all_133_2, 208.41/128.35 all_86_10) & $lesseq(all_86_7, all_133_2) & tb2t1(all_133_1) = 208.41/128.35 all_133_0 & get4(int, all_133_3, all_133_2) = all_133_1 & 208.41/128.35 in_uni(all_133_1)) | ($lesseq(43, all_133_0) & $lesseq(all_133_2, 208.41/128.35 all_86_8) & $lesseq(all_86_11, all_133_2) & tb2t1(all_133_1) = 208.41/128.35 all_133_0 & get4(int, all_133_3, all_133_2) = all_133_1 & 208.41/128.35 in_uni(all_133_1)) 208.41/128.35 (14) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.41/128.35 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 208.41/128.35 (permut2(v0, v5, v6, v3, v4) = v7) | ~ (elts(v0, v2) = v6) | ~ 208.41/128.35 (elts(v0, v1) = v5) | ~ in_ty(v0) | ? [v8: $int] : ? [v9: $int] : 208.41/128.35 ((v9 = v8 & v7 = 0 & $lesseq(v4, v8) & $lesseq(v3, v8) & $lesseq(0, 208.41/128.35 v4) & $lesseq(0, v3) & length1(v0, v2) = v8 & length1(v0, v1) = 208.41/128.35 v8) | ( ~ (v8 = 0) & permut3(v0, v1, v2, v3, v4) = v8))) 208.41/128.35 (15) $lesseq(2, $difference(all_86_13, all_86_8)) 208.41/128.35 (16) all_125_0 = all_105_4 208.41/128.35 (17) $lesseq(1, $difference(all_86_13, all_86_7)) 208.41/128.35 (18) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.41/128.35 $int] : ! [v5: $int] : ( ~ (permut2(v0, v2, v3, v4, v5) = 0) | ~ 208.41/128.35 (permut2(v0, v1, v2, v4, v5) = 0) | ~ in_ty(v0) | permut2(v0, v1, v3, 208.41/128.35 v4, v5) = 0) 208.41/128.35 (19) ! [v0: $int] : ! [v1: $int] : (v1 = 42 | ~ ($lesseq(1, 208.41/128.35 $difference(all_86_7, v0))) | ~ ($lesseq(1, $difference(v0, 208.41/128.35 all_86_8))) | ~ (get3(all_86_6, v0) = v1)) 208.41/128.35 (20) t2tb(all_86_6) = all_103_1 208.41/128.35 (21) map_eq_sub1(int, all_103_1, all_105_3, $sum(all_86_8, 1), all_86_13) = 0 208.41/128.35 (22) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.41/128.35 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ (permut3(v6, v5, 208.41/128.35 v4, v3, v2) = v1) | ~ (permut3(v6, v5, v4, v3, v2) = v0)) 208.41/128.36 (23) permut2(int, all_103_3, all_105_3, all_86_11, $sum(all_86_10, 1)) = 0 208.41/128.36 (24) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 208.41/128.36 | ~ (elts(v3, v2) = v1) | ~ (elts(v3, v2) = v0)) 208.41/128.36 (25) length1(int, all_105_4) = all_86_13 208.41/128.36 (26) in_array_int(all_86_3) 208.41/128.36 (27) elts(int, all_105_4) = all_105_3 208.41/128.36 (28) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.41/128.36 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ (permut_sub2(v6, 208.41/128.36 v5, v4, v3, v2) = v1) | ~ (permut_sub2(v6, v5, v4, v3, v2) = v0)) 208.41/128.36 (29) t2tb2(all_86_9) = all_103_4 208.41/128.36 (30) map_eq_sub1(int, all_105_3, all_105_1, 0, all_86_7) = 0 208.41/128.36 (31) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.41/128.36 $int] : ! [v5: $int] : ( ~ (permut3(int, v4, v5, v2, v3) = 0) | ~ 208.41/128.36 (t2tb2(v1) = v5) | ~ (t2tb2(v0) = v4) | ~ in_array_int(v0) | ? [v6: 208.41/128.36 $int] : ? [v7: $int] : ? [v8: $int] : ? [v9: $int] : ((v6 = 0 & 208.41/128.36 permut_sub3(v0, v1, v2, v3) = 0) | (elts(int, v5) = v7 & elts(int, 208.41/128.36 v4) = v6 & in_uni(v7) & in_uni(v6) & (( ~ (v9 = 0) & 208.41/128.36 map_eq_sub1(int, v6, v7, v3, v8) = v9 & length1(int, v4) = v8) 208.41/128.36 | ( ~ (v8 = 0) & map_eq_sub1(int, v6, v7, 0, v2) = v8))))) 208.41/128.36 (32) tb2t(all_105_1) = all_86_2 208.41/128.36 (33) permut2(int, all_103_1, all_105_3, all_86_11, $sum(all_86_8, 1)) = 0 208.41/128.36 (34) in_array_int(all_86_9) 208.41/128.36 (35) elts(int, all_105_2) = all_105_1 208.41/128.36 (36) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.41/128.36 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 208.41/128.36 ($lesseq(1, $difference(v4, v5))) | ~ ($lesseq(v3, v5)) | ~ 208.41/128.36 (permut2(v0, v1, v2, v3, v4) = 0) | ~ (t2tb1(v5) = v6) | ~ (get(v0, 208.41/128.36 int, v2, v6) = v7) | ~ in_ty(v0) | ? [v8: $int] : ? [v9: $int] 208.41/128.36 : ($lesseq(1, $difference(v4, v8)) & $lesseq(v3, v8) & t2tb1(v8) = v9 208.41/128.36 & get(v0, int, v1, v9) = v7 & in_uni(v9) & in_uni(v7))) 208.41/128.36 (37) t2tb2(all_86_1) = all_105_2 208.41/128.36 (38) $lesseq(all_86_11, all_86_8) 208.41/128.36 (39) $lesseq(all_86_7, all_86_10) 208.41/128.36 (40) $lesseq(0, all_86_8) 208.41/128.36 (41) permut2(int, all_103_1, all_105_3, all_86_11, $sum(all_86_10, 1)) = 0 208.41/128.36 (42) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.41/128.36 $int] : ! [v5: $int] : ( ~ (elts(v0, v1) = v3) | ~ (t2tb1(v2) = v4) 208.41/128.36 | ~ (get(v0, int, v3, v4) = v5) | ~ in_ty(v0) | (get4(v0, v1, v2) = 208.41/128.36 v5 & in_uni(v5))) 208.41/128.36 (43) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.41/128.36 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 208.41/128.36 ($lesseq(1, $difference(v3, v4))) | ~ ($lesseq(v2, v4)) | ~ 208.41/128.36 (permut2(int, v5, v6, v2, v3) = 0) | ~ (t2tb(v1) = v6) | ~ (t2tb(v0) 208.41/128.36 = v5) | ~ (get3(v1, v4) = v7) | ~ in_map_int_int(v0) | ? [v8: 208.41/128.36 $int] : ($lesseq(1, $difference(v3, v8)) & $lesseq(v2, v8) & 208.41/128.36 get3(v0, v8) = v7)) 208.41/128.36 (44) permut2(int, all_105_3, all_105_1, all_86_7, $sum(all_86_10, 1)) = 0 208.41/128.36 (45) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.41/128.36 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ (map_eq_sub1(v6, 208.41/128.36 v5, v4, v3, v2) = v1) | ~ (map_eq_sub1(v6, v5, v4, v3, v2) = v0)) 208.41/128.36 (46) permut2(int, all_103_3, all_103_1, all_86_11, $sum(all_86_10, 1)) = 0 208.41/128.36 (47) ~ (permut2(int, all_103_3, all_103_1, 0, all_86_13) = 0) | ? [v0: 208.41/128.36 $int] : ((v0 = 0 & permut_all(int, all_103_4, all_103_2) = 0) | ( ~ 208.41/128.36 (v0 = all_86_13) & length1(int, all_103_2) = v0)) 208.41/128.36 (48) in_array_int(all_86_1) 208.41/128.36 (49) t2tb(all_86_12) = all_103_3 208.41/128.36 (50) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.41/128.36 $int] : ! [v5: $int] : ! [v6: $int] : ( ~ ($lesseq(0, v4)) | ~ 208.41/128.36 ($lesseq(0, v3)) | ~ (permut2(v0, v5, v6, v3, v4) = 0) | ~ (elts(v0, 208.41/128.36 v2) = v6) | ~ (elts(v0, v1) = v5) | ~ in_ty(v0) | ? [v7: $int] 208.41/128.36 : ? [v8: $int] : ((v7 = 0 & permut3(v0, v1, v2, v3, v4) = 0) | 208.41/128.36 (length1(v0, v1) = v7 & ( ~ ($lesseq(v4, v7)) | ~ ($lesseq(v3, v7)) 208.41/128.36 | ( ~ (v8 = v7) & length1(v0, v2) = v8))))) 208.41/128.36 (51) $lesseq(1, $difference(all_86_7, all_86_8)) 208.41/128.36 (52) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.41/128.36 $int] : ! [v5: $int] : ! [v6: $int] : ( ~ ($lesseq(1, 208.41/128.36 $difference(v4, v5))) | ~ ($lesseq(v3, v5)) | ~ (map_eq_sub1(v0, 208.41/128.36 v1, v2, v3, v4) = 0) | ~ (t2tb1(v5) = v6) | ~ in_ty(v0) | ? 208.41/128.36 [v7: $int] : (get(v0, int, v2, v6) = v7 & get(v0, int, v1, v6) = v7 & 208.41/128.36 in_uni(v7))) 208.41/128.36 (53) $lesseq(1, $difference(all_86_13, all_86_10)) 208.41/128.36 (54) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.41/128.36 $int] : ! [v5: $int] : (v5 = 0 | ~ (permut_sub2(v0, v1, v2, v3, v4) 208.41/128.36 = v5) | ~ in_ty(v0) | ? [v6: $int] : ? [v7: $int] : ? [v8: $int] 208.41/128.36 : ? [v9: $int] : (( ~ (v9 = 0) & map_eq_sub1(v0, v6, v7, v4, v8) = v9 208.41/128.36 & length1(v0, v1) = v8 & elts(v0, v2) = v7 & elts(v0, v1) = v6 & 208.41/128.36 in_uni(v7) & in_uni(v6)) | ( ~ (v8 = 0) & map_eq_sub1(v0, v6, v7, 208.41/128.36 0, v3) = v8 & elts(v0, v2) = v7 & elts(v0, v1) = v6 & in_uni(v7) 208.41/128.36 & in_uni(v6)) | ( ~ (v6 = 0) & permut3(v0, v1, v2, v3, v4) = v6))) 208.41/128.36 (55) in_map_int_int(all_86_4) 208.41/128.36 (56) $lesseq(0, all_86_11) 208.41/128.36 (57) elts(int, all_103_2) = all_103_1 208.41/128.36 (58) ~ (permut2(int, all_103_1, all_105_3, 0, all_86_13) = 0) | ? [v0: 208.41/128.36 $int] : ((v0 = 0 & permut_all(int, all_103_2, all_105_4) = 0) | ( ~ 208.41/128.36 (v0 = all_86_13) & length1(int, all_105_4) = v0)) 208.41/128.36 (59) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ( ~ 208.41/128.36 (t2tb2(v0) = v2) | ~ (get4(int, v2, v1) = v3) | ~ in_array_int(v0) | 208.41/128.36 ? [v4: $int] : ? [v5: $int] : ? [v6: $int] : (tb2t(v4) = v5 & 208.41/128.36 tb2t1(v3) = v6 & get3(v5, v1) = v6 & elts(int, v2) = v4 & 208.41/128.36 in_map_int_int(v5) & in_uni(v4))) 208.41/128.36 (60) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ (tb2t(v2) 208.41/128.36 = v1) | ~ (tb2t(v2) = v0)) 208.41/128.36 (61) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.41/128.36 $int] : ! [v5: $int] : (v1 = v0 | ~ (permut_sub3(v5, v4, v3, v2) = 208.41/128.36 v1) | ~ (permut_sub3(v5, v4, v3, v2) = v0)) 208.41/128.36 (62) all_133_3 = all_105_2 208.41/128.36 (63) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.41/128.36 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 208.41/128.36 ($lesseq(1, $difference(v3, v6))) | ~ ($lesseq(v2, v6)) | ~ 208.41/128.36 (map_eq_sub1(int, v4, v5, v2, v3) = 0) | ~ (t2tb(v1) = v5) | ~ 208.41/128.36 (t2tb(v0) = v4) | ~ (get3(v1, v6) = v7) | ~ in_map_int_int(v0) | 208.41/128.36 get3(v0, v6) = v7) 208.41/128.36 (64) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.41/128.36 $int] : ! [v5: $int] : ! [v6: $int] : ( ~ (permut3(int, v4, v5, v2, 208.41/128.36 v3) = v6) | ~ (t2tb2(v1) = v5) | ~ (t2tb2(v0) = v4) | ~ 208.41/128.36 in_array_int(v0) | ? [v7: $int] : ? [v8: $int] : ? [v9: $int] : ? 208.41/128.36 [v10: $int] : ? [v11: $int] : ((v11 = 0 & v9 = 0 & v6 = 0 & 208.41/128.36 map_eq_sub1(int, v7, v8, v3, v10) = 0 & map_eq_sub1(int, v7, v8, 208.41/128.36 0, v2) = 0 & length1(int, v4) = v10 & elts(int, v5) = v8 & 208.41/128.36 elts(int, v4) = v7 & in_uni(v8) & in_uni(v7)) | ( ~ (v7 = 0) & 208.41/128.36 permut_sub3(v0, v1, v2, v3) = v7))) 208.41/128.36 (65) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 208.41/128.36 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 208.41/128.36 (66) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.41/128.36 $int] : ( ~ (permut3(v0, v1, v2, v3, v4) = 0) | ~ in_ty(v0) | ? [v5: 208.41/128.36 $int] : ? [v6: $int] : ? [v7: $int] : ? [v8: $int] : ((v5 = 0 & 208.41/128.36 permut_sub2(v0, v1, v2, v3, v4) = 0) | (elts(v0, v2) = v6 & 208.41/128.36 elts(v0, v1) = v5 & in_uni(v6) & in_uni(v5) & (( ~ (v8 = 0) & 208.41/128.36 map_eq_sub1(v0, v5, v6, v4, v7) = v8 & length1(v0, v1) = v7) | 208.41/128.36 ( ~ (v7 = 0) & map_eq_sub1(v0, v5, v6, 0, v3) = v7))))) 208.41/128.36 (67) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ( ~ 208.41/128.36 (get4(v0, v1, v2) = v3) | ~ in_ty(v0) | ? [v4: $int] : ? [v5: $int] 208.41/128.36 : (elts(v0, v1) = v4 & t2tb1(v2) = v5 & get(v0, int, v4, v5) = v3 & 208.41/128.36 in_uni(v5) & in_uni(v4) & in_uni(v3))) 208.41/128.36 (68) $lesseq(1, all_86_10) 208.41/128.36 (69) map_eq_sub1(int, all_105_3, all_105_1, $sum(all_86_10, 1), all_86_13) = 208.41/128.36 0 208.41/128.36 (70) t2tb(all_86_4) = all_105_3 208.41/128.36 (71) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.41/128.36 $int] : ! [v5: $int] : ( ~ (permut3(v0, v1, v2, v3, v4) = v5) | ~ 208.41/128.36 in_ty(v0) | ? [v6: $int] : ? [v7: $int] : ? [v8: $int] : ? [v9: 208.41/128.36 $int] : ? [v10: $int] : ((v10 = 0 & v9 = 0 & v5 = 0 & 208.41/128.36 map_eq_sub1(v0, v6, v7, v4, v8) = 0 & map_eq_sub1(v0, v6, v7, 0, 208.41/128.36 v3) = 0 & length1(v0, v1) = v8 & elts(v0, v2) = v7 & elts(v0, 208.41/128.36 v1) = v6 & in_uni(v7) & in_uni(v6)) | ( ~ (v6 = 0) & 208.41/128.36 permut_sub2(v0, v1, v2, v3, v4) = v6))) 208.41/128.36 (72) ! [v0: $int] : ! [v1: $int] : ( ~ ($lesseq(v0, all_86_10)) | ~ 208.41/128.36 ($lesseq(all_86_7, v0)) | ~ (get4(int, all_125_0, v0) = v1) | ? [v2: 208.41/128.36 $int] : ($lesseq(42, v2) & tb2t1(v1) = v2)) 208.41/128.36 208.41/128.36 Begin of proof 208.41/128.36 | 208.41/128.36 | BETA: splitting (47) gives: 208.41/128.36 | 208.41/128.36 | Case 1: 208.41/128.36 | | 208.41/128.36 | | (73) ~ (permut2(int, all_103_3, all_103_1, 0, all_86_13) = 0) 208.41/128.36 | | 208.41/128.36 | | PRED_UNIFY: (46), (73) imply: 208.41/128.36 | | (74) ~ ($difference(all_86_10, all_86_13) = -1) | ~ (all_86_11 = 0) 208.41/128.36 | | 208.41/128.36 | | REF_CLOSE: (1), (2), (4), (6), (7), (8), (9), (10), (11), (13), (14), (16), 208.41/128.36 | | (17), (19), (20), (21), (22), (23), (24), (25), (26), (27), (28), 208.41/128.36 | | (29), (30), (31), (32), (33), (34), (35), (36), (37), (38), (39), 208.41/128.36 | | (40), (42), (43), (44), (48), (50), (51), (52), (53), (54), (55), 208.41/128.36 | | (56), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68), 208.41/128.36 | | (69), (70), (71), (72), (74) are inconsistent by sub-proof #142. 208.41/128.36 | | 208.41/128.36 | Case 2: 208.41/128.36 | | 208.41/128.36 | | (75) permut2(int, all_103_3, all_103_1, 0, all_86_13) = 0 208.41/128.36 | | 208.41/128.36 | | BETA: splitting (58) gives: 208.41/128.36 | | 208.41/128.36 | | Case 1: 208.41/128.36 | | | 208.41/128.36 | | | (76) ~ (permut2(int, all_103_1, all_105_3, 0, all_86_13) = 0) 208.41/128.36 | | | 208.41/128.36 | | | PRED_UNIFY: (41), (76) imply: 208.41/128.36 | | | (77) ~ ($difference(all_86_10, all_86_13) = -1) | ~ (all_86_11 = 0) 208.41/128.36 | | | 208.41/128.36 | | | REF_CLOSE: (1), (2), (4), (6), (7), (8), (9), (10), (11), (13), (14), 208.41/128.36 | | | (16), (17), (19), (20), (21), (22), (23), (24), (25), (26), 208.41/128.36 | | | (27), (28), (29), (30), (31), (32), (33), (34), (35), (36), 208.41/128.36 | | | (37), (38), (39), (40), (42), (43), (44), (48), (50), (51), 208.41/128.36 | | | (52), (53), (54), (55), (56), (59), (60), (61), (62), (63), 208.41/128.36 | | | (64), (65), (66), (67), (68), (69), (70), (71), (72), (77) are 208.41/128.36 | | | inconsistent by sub-proof #142. 208.41/128.36 | | | 208.41/128.36 | | Case 2: 208.41/128.36 | | | 208.41/128.36 | | | (78) permut2(int, all_103_1, all_105_3, 0, all_86_13) = 0 208.41/128.36 | | | 208.41/128.36 | | | BETA: splitting (13) gives: 208.41/128.36 | | | 208.41/128.36 | | | Case 1: 208.41/128.36 | | | | 208.41/128.36 | | | | (79) ~ (all_133_0 = 42) & $lesseq(1, $difference(all_86_7, 208.41/128.36 | | | | all_133_2)) & $lesseq(1, $difference(all_133_2, all_86_8)) & 208.41/128.36 | | | | tb2t1(all_133_1) = all_133_0 & get4(int, all_133_3, all_133_2) = 208.41/128.36 | | | | all_133_1 & in_uni(all_133_1) 208.41/128.36 | | | | 208.41/128.36 | | | | ALPHA: (79) implies: 208.41/128.36 | | | | (80) ~ (all_133_0 = 42) 208.41/128.36 | | | | (81) $lesseq(1, $difference(all_133_2, all_86_8)) 208.41/128.36 | | | | (82) $lesseq(1, $difference(all_86_7, all_133_2)) 208.41/128.36 | | | | (83) get4(int, all_133_3, all_133_2) = all_133_1 208.41/128.36 | | | | (84) tb2t1(all_133_1) = all_133_0 208.41/128.36 | | | | 208.41/128.36 | | | | COMBINE_INEQS: (81), (82) imply: 208.41/128.36 | | | | (85) $lesseq(2, $difference(all_86_7, all_86_8)) 208.41/128.36 | | | | 208.41/128.36 | | | | COMBINE_INEQS: (39), (85) imply: 208.41/128.36 | | | | (86) $lesseq(2, $difference(all_86_10, all_86_8)) 208.41/128.36 | | | | 208.41/128.36 | | | | COMBINE_INEQS: (38), (86) imply: 208.41/128.36 | | | | (87) $lesseq(2, $difference(all_86_10, all_86_11)) 208.41/128.36 | | | | 208.41/128.36 | | | | COMBINE_INEQS: (40), (86) imply: 208.41/128.36 | | | | (88) $lesseq(2, all_86_10) 208.41/128.36 | | | | 208.41/128.36 | | | | COMBINE_INEQS: (53), (87) imply: 208.41/128.36 | | | | (89) $lesseq(3, $difference(all_86_13, all_86_11)) 208.41/128.36 | | | | 208.41/128.36 | | | | COMBINE_INEQS: (56), (89) imply: 208.41/128.36 | | | | (90) $lesseq(3, all_86_13) 208.41/128.36 | | | | 208.41/128.36 | | | | REDUCE: (62), (83) imply: 208.41/128.36 | | | | (91) get4(int, all_105_2, all_133_2) = all_133_1 208.41/128.36 | | | | 208.41/128.36 | | | | GROUND_INST: instantiating (14) with int, all_103_2, all_105_4, 0, 208.41/128.36 | | | | all_86_13, all_103_1, all_105_3, 0, simplifying with (10), 208.41/128.36 | | | | (27), (57), (78) gives: 208.41/128.36 | | | | (92) ? [v0: $int] : ? [v1: $int] : ((v1 = v0 & $lesseq(all_86_13, 208.41/128.36 | | | | v0) & $lesseq(0, v0) & $lesseq(0, all_86_13) & 208.41/128.36 | | | | length1(int, all_105_4) = v0 & length1(int, all_103_2) = v0) 208.41/128.36 | | | | | ( ~ (v0 = 0) & permut3(int, all_103_2, all_105_4, 0, 208.41/128.36 | | | | all_86_13) = v0)) 208.41/128.36 | | | | 208.41/128.36 | | | | GROUND_INST: instantiating (18) with int, all_103_3, all_103_1, 208.41/128.36 | | | | all_105_3, 0, all_86_13, simplifying with (10), (75), (78) 208.41/128.36 | | | | gives: 208.41/128.36 | | | | (93) permut2(int, all_103_3, all_105_3, 0, all_86_13) = 0 208.41/128.36 | | | | 208.41/128.36 | | | | GROUND_INST: instantiating (50) with int, all_103_2, all_105_4, 0, 208.41/128.36 | | | | all_86_13, all_103_1, all_105_3, simplifying with (10), 208.41/128.36 | | | | (27), (57), (78) gives: 208.41/128.36 | | | | (94) ~ ($lesseq(0, all_86_13)) | ? [v0: $int] : ? [v1: $int] : 208.41/128.36 | | | | ((v0 = 0 & permut3(int, all_103_2, all_105_4, 0, all_86_13) = 0) 208.41/128.36 | | | | | (length1(int, all_103_2) = v0 & ( ~ ($lesseq(all_86_13, v0)) 208.41/128.36 | | | | | ~ ($lesseq(0, v0)) | ( ~ (v1 = v0) & length1(int, 208.41/128.36 | | | | all_105_4) = v1)))) 208.41/128.36 | | | | 208.41/128.36 | | | | GROUND_INST: instantiating (14) with int, all_103_4, all_105_4, 208.41/128.36 | | | | all_86_11, $sum(all_86_10, 1), all_103_3, all_105_3, 0, 208.41/128.36 | | | | simplifying with (7), (10), (23), (27) gives: 208.41/128.36 | | | | (95) ? [v0: $int] : ? [v1: $int] : ((v1 = v0 & $lesseq(1, 208.41/128.36 | | | | $difference(v0, all_86_10)) & $lesseq(all_86_11, v0) & 208.41/128.36 | | | | $lesseq(-1, all_86_10) & $lesseq(0, all_86_11) & 208.41/128.36 | | | | length1(int, all_105_4) = v0 & length1(int, all_103_4) = v0) 208.41/128.36 | | | | | ( ~ (v0 = 0) & permut3(int, all_103_4, all_105_4, all_86_11, 208.41/128.36 | | | | $sum(all_86_10, 1)) = v0)) 208.41/128.36 | | | | 208.41/128.36 | | | | GROUND_INST: instantiating (50) with int, all_103_4, all_105_4, 208.41/128.36 | | | | all_86_11, $sum(all_86_10, 1), all_103_3, all_105_3, 208.41/128.36 | | | | simplifying with (7), (10), (23), (27) gives: 208.41/128.36 | | | | (96) ~ ($lesseq(-1, all_86_10)) | ~ ($lesseq(0, all_86_11)) | ? 208.41/128.36 | | | | [v0: $int] : ? [v1: $int] : ((v0 = 0 & permut3(int, all_103_4, 208.41/128.36 | | | | all_105_4, all_86_11, $sum(all_86_10, 1)) = 0) | 208.41/128.36 | | | | (length1(int, all_103_4) = v0 & ( ~ ($lesseq(1, 208.41/128.36 | | | | $difference(v0, all_86_10))) | ~ ($lesseq(all_86_11, 208.41/128.36 | | | | v0)) | ( ~ (v1 = v0) & length1(int, all_105_4) = 208.41/128.36 | | | | v1)))) 208.41/128.36 | | | | 208.41/128.36 | | | | GROUND_INST: instantiating (14) with int, all_103_4, all_103_2, 0, 208.41/128.36 | | | | all_86_13, all_103_3, all_103_1, 0, simplifying with (7), 208.41/128.36 | | | | (10), (57), (75) gives: 208.41/128.36 | | | | (97) ? [v0: $int] : ? [v1: $int] : ((v1 = v0 & $lesseq(all_86_13, 208.41/128.36 | | | | v0) & $lesseq(0, v0) & $lesseq(0, all_86_13) & 208.41/128.36 | | | | length1(int, all_103_2) = v0 & length1(int, all_103_4) = v0) 208.41/128.36 | | | | | ( ~ (v0 = 0) & permut3(int, all_103_4, all_103_2, 0, 208.41/128.36 | | | | all_86_13) = v0)) 208.41/128.36 | | | | 208.41/128.36 | | | | GROUND_INST: instantiating (50) with int, all_103_4, all_103_2, 0, 208.41/128.36 | | | | all_86_13, all_103_3, all_103_1, simplifying with (7), 208.41/128.36 | | | | (10), (57), (75) gives: 208.41/128.36 | | | | (98) ~ ($lesseq(0, all_86_13)) | ? [v0: $int] : ? [v1: $int] : 208.41/128.36 | | | | ((v0 = 0 & permut3(int, all_103_4, all_103_2, 0, all_86_13) = 0) 208.41/128.36 | | | | | (length1(int, all_103_4) = v0 & ( ~ ($lesseq(all_86_13, v0)) 208.41/128.36 | | | | | ~ ($lesseq(0, v0)) | ( ~ (v1 = v0) & length1(int, 208.41/128.36 | | | | all_103_2) = v1)))) 208.41/128.36 | | | | 208.41/128.36 | | | | GROUND_INST: instantiating (59) with all_86_1, all_133_2, all_105_2, 208.41/128.36 | | | | all_133_1, simplifying with (37), (48), (91) gives: 208.41/128.36 | | | | (99) ? [v0: $int] : ? [v1: $int] : ? [v2: $int] : (tb2t(v0) = v1 & 208.41/128.36 | | | | tb2t1(all_133_1) = v2 & get3(v1, all_133_2) = v2 & elts(int, 208.41/128.36 | | | | all_105_2) = v0 & in_map_int_int(v1) & in_uni(v0)) 208.41/128.36 | | | | 208.41/128.36 | | | | GROUND_INST: instantiating (67) with int, all_105_2, all_133_2, 208.41/128.36 | | | | all_133_1, simplifying with (10), (91) gives: 208.41/128.36 | | | | (100) ? [v0: $int] : ? [v1: $int] : (elts(int, all_105_2) = v0 & 208.41/128.36 | | | | t2tb1(all_133_2) = v1 & get(int, int, v0, v1) = all_133_1 & 208.41/128.36 | | | | in_uni(v1) & in_uni(v0) & in_uni(all_133_1)) 208.41/128.36 | | | | 208.41/128.36 | | | | DELTA: instantiating (99) with fresh symbols all_697_0, all_697_1, 208.41/128.36 | | | | all_697_2 gives: 208.41/128.36 | | | | (101) tb2t(all_697_2) = all_697_1 & tb2t1(all_133_1) = all_697_0 & 208.41/128.36 | | | | get3(all_697_1, all_133_2) = all_697_0 & elts(int, all_105_2) = 208.41/128.36 | | | | all_697_2 & in_map_int_int(all_697_1) & in_uni(all_697_2) 208.41/128.36 | | | | 208.41/128.37 | | | | ALPHA: (101) implies: 208.46/128.37 | | | | (102) elts(int, all_105_2) = all_697_2 208.46/128.37 | | | | (103) get3(all_697_1, all_133_2) = all_697_0 208.46/128.37 | | | | (104) tb2t1(all_133_1) = all_697_0 208.46/128.37 | | | | (105) tb2t(all_697_2) = all_697_1 208.46/128.37 | | | | 208.46/128.37 | | | | DELTA: instantiating (97) with fresh symbols all_703_0, all_703_1 gives: 208.46/128.37 | | | | (106) (all_703_0 = all_703_1 & $lesseq(all_86_13, all_703_1) & 208.46/128.37 | | | | $lesseq(0, all_703_1) & $lesseq(0, all_86_13) & length1(int, 208.46/128.37 | | | | all_103_2) = all_703_1 & length1(int, all_103_4) = 208.46/128.37 | | | | all_703_1) | ( ~ (all_703_1 = 0) & permut3(int, all_103_4, 208.46/128.37 | | | | all_103_2, 0, all_86_13) = all_703_1) 208.46/128.37 | | | | 208.46/128.37 | | | | DELTA: instantiating (95) with fresh symbols all_708_0, all_708_1 gives: 208.46/128.37 | | | | (107) (all_708_0 = all_708_1 & $lesseq(1, $difference(all_708_1, 208.46/128.37 | | | | all_86_10)) & $lesseq(all_86_11, all_708_1) & $lesseq(-1, 208.46/128.37 | | | | all_86_10) & $lesseq(0, all_86_11) & length1(int, 208.46/128.37 | | | | all_105_4) = all_708_1 & length1(int, all_103_4) = 208.46/128.37 | | | | all_708_1) | ( ~ (all_708_1 = 0) & permut3(int, all_103_4, 208.46/128.37 | | | | all_105_4, all_86_11, $sum(all_86_10, 1)) = all_708_1) 208.46/128.37 | | | | 208.46/128.37 | | | | DELTA: instantiating (92) with fresh symbols all_709_0, all_709_1 gives: 208.46/128.37 | | | | (108) (all_709_0 = all_709_1 & $lesseq(all_86_13, all_709_1) & 208.46/128.37 | | | | $lesseq(0, all_709_1) & $lesseq(0, all_86_13) & length1(int, 208.46/128.37 | | | | all_105_4) = all_709_1 & length1(int, all_103_2) = 208.46/128.37 | | | | all_709_1) | ( ~ (all_709_1 = 0) & permut3(int, all_103_2, 208.46/128.37 | | | | all_105_4, 0, all_86_13) = all_709_1) 208.46/128.37 | | | | 208.46/128.37 | | | | DELTA: instantiating (100) with fresh symbols all_710_0, all_710_1 208.46/128.37 | | | | gives: 208.46/128.37 | | | | (109) elts(int, all_105_2) = all_710_1 & t2tb1(all_133_2) = all_710_0 208.46/128.37 | | | | & get(int, int, all_710_1, all_710_0) = all_133_1 & 208.46/128.37 | | | | in_uni(all_710_0) & in_uni(all_710_1) & in_uni(all_133_1) 208.46/128.37 | | | | 208.46/128.37 | | | | ALPHA: (109) implies: 208.46/128.37 | | | | (110) t2tb1(all_133_2) = all_710_0 208.46/128.37 | | | | (111) elts(int, all_105_2) = all_710_1 208.46/128.37 | | | | 208.46/128.37 | | | | BETA: splitting (94) gives: 208.46/128.37 | | | | 208.46/128.37 | | | | Case 1: 208.46/128.37 | | | | | 208.46/128.37 | | | | | (112) $lesseq(all_86_13, -1) 208.46/128.37 | | | | | 208.46/128.37 | | | | | COMBINE_INEQS: (90), (112) imply: 208.46/128.37 | | | | | (113) $lesseq(0, -1) 208.46/128.37 | | | | | 208.46/128.37 | | | | | CLOSE: (113) is inconsistent. 208.46/128.37 | | | | | 208.46/128.37 | | | | Case 2: 208.46/128.37 | | | | | 208.46/128.37 | | | | | (114) ? [v0: $int] : ? [v1: $int] : ((v0 = 0 & permut3(int, 208.46/128.37 | | | | | all_103_2, all_105_4, 0, all_86_13) = 0) | 208.46/128.37 | | | | | (length1(int, all_103_2) = v0 & ( ~ ($lesseq(all_86_13, 208.46/128.37 | | | | | v0)) | ~ ($lesseq(0, v0)) | ( ~ (v1 = v0) & 208.46/128.37 | | | | | length1(int, all_105_4) = v1)))) 208.46/128.37 | | | | | 208.46/128.37 | | | | | DELTA: instantiating (114) with fresh symbols all_721_0, all_721_1 208.46/128.37 | | | | | gives: 208.46/128.37 | | | | | (115) (all_721_1 = 0 & permut3(int, all_103_2, all_105_4, 0, 208.46/128.37 | | | | | all_86_13) = 0) | (length1(int, all_103_2) = all_721_1 & 208.46/128.37 | | | | | ( ~ ($lesseq(all_86_13, all_721_1)) | ~ ($lesseq(0, 208.46/128.37 | | | | | all_721_1)) | ( ~ (all_721_0 = all_721_1) & 208.46/128.37 | | | | | length1(int, all_105_4) = all_721_0))) 208.46/128.37 | | | | | 208.46/128.37 | | | | | BETA: splitting (115) gives: 208.46/128.37 | | | | | 208.46/128.37 | | | | | Case 1: 208.46/128.37 | | | | | | 208.46/128.37 | | | | | | (116) all_721_1 = 0 & permut3(int, all_103_2, all_105_4, 0, 208.46/128.37 | | | | | | all_86_13) = 0 208.46/128.37 | | | | | | 208.46/128.37 | | | | | | ALPHA: (116) implies: 208.46/128.37 | | | | | | (117) permut3(int, all_103_2, all_105_4, 0, all_86_13) = 0 208.46/128.37 | | | | | | 208.46/128.37 | | | | | | BETA: splitting (96) gives: 208.46/128.37 | | | | | | 208.46/128.37 | | | | | | Case 1: 208.46/128.37 | | | | | | | 208.46/128.37 | | | | | | | (118) $lesseq(all_86_11, -1) 208.46/128.37 | | | | | | | 208.46/128.37 | | | | | | | COMBINE_INEQS: (56), (118) imply: 208.46/128.37 | | | | | | | (119) $lesseq(0, -1) 208.46/128.37 | | | | | | | 208.46/128.37 | | | | | | | CLOSE: (119) is inconsistent. 208.46/128.37 | | | | | | | 208.46/128.37 | | | | | | Case 2: 208.46/128.37 | | | | | | | 208.46/128.37 | | | | | | | (120) ~ ($lesseq(-1, all_86_10)) | ? [v0: $int] : ? [v1: 208.46/128.37 | | | | | | | $int] : ((v0 = 0 & permut3(int, all_103_4, all_105_4, 208.46/128.37 | | | | | | | all_86_11, $sum(all_86_10, 1)) = 0) | (length1(int, 208.46/128.37 | | | | | | | all_103_4) = v0 & ( ~ ($lesseq(1, $difference(v0, 208.46/128.37 | | | | | | | all_86_10))) | ~ ($lesseq(all_86_11, v0)) | 208.46/128.37 | | | | | | | ( ~ (v1 = v0) & length1(int, all_105_4) = v1)))) 208.46/128.37 | | | | | | | 208.46/128.37 | | | | | | | BETA: splitting (120) gives: 208.46/128.37 | | | | | | | 208.46/128.37 | | | | | | | Case 1: 208.46/128.37 | | | | | | | | 208.46/128.37 | | | | | | | | (121) $lesseq(all_86_10, -2) 208.46/128.37 | | | | | | | | 208.46/128.37 | | | | | | | | COMBINE_INEQS: (88), (121) imply: 208.46/128.37 | | | | | | | | (122) $lesseq(0, -1) 208.46/128.37 | | | | | | | | 208.46/128.37 | | | | | | | | CLOSE: (122) is inconsistent. 208.46/128.37 | | | | | | | | 208.46/128.37 | | | | | | | Case 2: 208.46/128.37 | | | | | | | | 208.46/128.37 | | | | | | | | (123) ? [v0: $int] : ? [v1: $int] : ((v0 = 0 & permut3(int, 208.46/128.37 | | | | | | | | all_103_4, all_105_4, all_86_11, $sum(all_86_10, 208.46/128.37 | | | | | | | | 1)) = 0) | (length1(int, all_103_4) = v0 & ( ~ 208.46/128.37 | | | | | | | | ($lesseq(1, $difference(v0, all_86_10))) | ~ 208.46/128.37 | | | | | | | | ($lesseq(all_86_11, v0)) | ( ~ (v1 = v0) & 208.46/128.37 | | | | | | | | length1(int, all_105_4) = v1)))) 208.46/128.37 | | | | | | | | 208.46/128.37 | | | | | | | | DELTA: instantiating (123) with fresh symbols all_747_0, 208.46/128.37 | | | | | | | | all_747_1 gives: 208.46/128.37 | | | | | | | | (124) (all_747_1 = 0 & permut3(int, all_103_4, all_105_4, 208.46/128.37 | | | | | | | | all_86_11, $sum(all_86_10, 1)) = 0) | (length1(int, 208.46/128.37 | | | | | | | | all_103_4) = all_747_1 & ( ~ ($lesseq(1, 208.46/128.37 | | | | | | | | $difference(all_747_1, all_86_10))) | ~ 208.46/128.37 | | | | | | | | ($lesseq(all_86_11, all_747_1)) | ( ~ (all_747_0 = 208.46/128.37 | | | | | | | | all_747_1) & length1(int, all_105_4) = 208.46/128.37 | | | | | | | | all_747_0))) 208.46/128.37 | | | | | | | | 208.46/128.37 | | | | | | | | BETA: splitting (108) gives: 208.46/128.37 | | | | | | | | 208.46/128.37 | | | | | | | | Case 1: 208.46/128.37 | | | | | | | | | 208.46/128.37 | | | | | | | | | (125) all_709_0 = all_709_1 & $lesseq(all_86_13, all_709_1) 208.46/128.37 | | | | | | | | | & $lesseq(0, all_709_1) & $lesseq(0, all_86_13) & 208.46/128.37 | | | | | | | | | length1(int, all_105_4) = all_709_1 & length1(int, 208.46/128.37 | | | | | | | | | all_103_2) = all_709_1 208.46/128.37 | | | | | | | | | 208.46/128.37 | | | | | | | | | ALPHA: (125) implies: 208.46/128.37 | | | | | | | | | (126) length1(int, all_103_2) = all_709_1 208.46/128.37 | | | | | | | | | (127) length1(int, all_105_4) = all_709_1 208.46/128.37 | | | | | | | | | 208.46/128.37 | | | | | | | | | BETA: splitting (98) gives: 208.46/128.37 | | | | | | | | | 208.46/128.37 | | | | | | | | | Case 1: 208.46/128.37 | | | | | | | | | | 208.46/128.37 | | | | | | | | | | (128) $lesseq(all_86_13, -1) 208.46/128.37 | | | | | | | | | | 208.46/128.37 | | | | | | | | | | COMBINE_INEQS: (90), (128) imply: 208.46/128.37 | | | | | | | | | | (129) $lesseq(0, -1) 208.46/128.37 | | | | | | | | | | 208.46/128.37 | | | | | | | | | | CLOSE: (129) is inconsistent. 208.46/128.37 | | | | | | | | | | 208.46/128.37 | | | | | | | | | Case 2: 208.46/128.37 | | | | | | | | | | 208.46/128.37 | | | | | | | | | | (130) ? [v0: $int] : ? [v1: $int] : ((v0 = 0 & 208.46/128.37 | | | | | | | | | | permut3(int, all_103_4, all_103_2, 0, 208.46/128.37 | | | | | | | | | | all_86_13) = 0) | (length1(int, all_103_4) = 208.46/128.37 | | | | | | | | | | v0 & ( ~ ($lesseq(all_86_13, v0)) | ~ 208.46/128.37 | | | | | | | | | | ($lesseq(0, v0)) | ( ~ (v1 = v0) & 208.46/128.37 | | | | | | | | | | length1(int, all_103_2) = v1)))) 208.46/128.37 | | | | | | | | | | 208.46/128.37 | | | | | | | | | | DELTA: instantiating (130) with fresh symbols all_759_0, 208.46/128.37 | | | | | | | | | | all_759_1 gives: 208.46/128.37 | | | | | | | | | | (131) (all_759_1 = 0 & permut3(int, all_103_4, all_103_2, 208.46/128.37 | | | | | | | | | | 0, all_86_13) = 0) | (length1(int, all_103_4) = 208.46/128.37 | | | | | | | | | | all_759_1 & ( ~ ($lesseq(all_86_13, all_759_1)) | 208.46/128.37 | | | | | | | | | | ~ ($lesseq(0, all_759_1)) | ( ~ (all_759_0 = 208.46/128.37 | | | | | | | | | | all_759_1) & length1(int, all_103_2) = 208.46/128.37 | | | | | | | | | | all_759_0))) 208.46/128.37 | | | | | | | | | | 208.46/128.37 | | | | | | | | | | GROUND_INST: instantiating (1) with all_133_0, all_697_0, 208.46/128.37 | | | | | | | | | | all_133_1, simplifying with (84), (104) gives: 208.46/128.37 | | | | | | | | | | (132) all_697_0 = all_133_0 208.46/128.37 | | | | | | | | | | 208.46/128.37 | | | | | | | | | | GROUND_INST: instantiating (65) with all_86_13, all_709_1, 208.46/128.37 | | | | | | | | | | all_103_2, int, simplifying with (3), (126) gives: 208.46/128.37 | | | | | | | | | | (133) all_709_1 = all_86_13 208.46/128.37 | | | | | | | | | | 208.46/128.37 | | | | | | | | | | GROUND_INST: instantiating (24) with all_105_1, all_710_1, 208.46/128.37 | | | | | | | | | | all_105_2, int, simplifying with (35), (111) 208.46/128.37 | | | | | | | | | | gives: 208.46/128.37 | | | | | | | | | | (134) all_710_1 = all_105_1 208.46/128.37 | | | | | | | | | | 208.46/128.37 | | | | | | | | | | GROUND_INST: instantiating (24) with all_710_1, all_697_2, 208.46/128.37 | | | | | | | | | | all_105_2, int, simplifying with (102), (111) 208.46/128.37 | | | | | | | | | | gives: 208.46/128.37 | | | | | | | | | | (135) all_710_1 = all_697_2 208.46/128.37 | | | | | | | | | | 208.46/128.37 | | | | | | | | | | COMBINE_EQS: (134), (135) imply: 208.46/128.37 | | | | | | | | | | (136) all_697_2 = all_105_1 208.46/128.37 | | | | | | | | | | 208.46/128.37 | | | | | | | | | | REDUCE: (105), (136) imply: 208.46/128.37 | | | | | | | | | | (137) tb2t(all_105_1) = all_697_1 208.46/128.37 | | | | | | | | | | 208.46/128.37 | | | | | | | | | | REDUCE: (103), (132) imply: 208.46/128.37 | | | | | | | | | | (138) get3(all_697_1, all_133_2) = all_133_0 208.46/128.37 | | | | | | | | | | 208.46/128.37 | | | | | | | | | | BETA: splitting (124) gives: 208.46/128.37 | | | | | | | | | | 208.46/128.37 | | | | | | | | | | Case 1: 208.46/128.37 | | | | | | | | | | | 208.46/128.37 | | | | | | | | | | | (139) all_747_1 = 0 & permut3(int, all_103_4, all_105_4, 208.46/128.37 | | | | | | | | | | | all_86_11, $sum(all_86_10, 1)) = 0 208.46/128.37 | | | | | | | | | | | 208.46/128.37 | | | | | | | | | | | ALPHA: (139) implies: 208.46/128.37 | | | | | | | | | | | (140) permut3(int, all_103_4, all_105_4, all_86_11, 208.46/128.37 | | | | | | | | | | | $sum(all_86_10, 1)) = 0 208.46/128.37 | | | | | | | | | | | 208.46/128.37 | | | | | | | | | | | BETA: splitting (131) gives: 208.46/128.37 | | | | | | | | | | | 208.46/128.37 | | | | | | | | | | | Case 1: 208.46/128.37 | | | | | | | | | | | | 208.46/128.37 | | | | | | | | | | | | (141) all_759_1 = 0 & permut3(int, all_103_4, all_103_2, 208.46/128.37 | | | | | | | | | | | | 0, all_86_13) = 0 208.46/128.37 | | | | | | | | | | | | 208.46/128.37 | | | | | | | | | | | | ALPHA: (141) implies: 208.46/128.37 | | | | | | | | | | | | (142) permut3(int, all_103_4, all_103_2, 0, all_86_13) = 208.46/128.37 | | | | | | | | | | | | 0 208.46/128.37 | | | | | | | | | | | | 208.46/128.37 | | | | | | | | | | | | BETA: splitting (106) gives: 208.46/128.37 | | | | | | | | | | | | 208.46/128.37 | | | | | | | | | | | | Case 1: 208.46/128.37 | | | | | | | | | | | | | 208.46/128.37 | | | | | | | | | | | | | (143) all_703_0 = all_703_1 & $lesseq(all_86_13, 208.46/128.37 | | | | | | | | | | | | | all_703_1) & $lesseq(0, all_703_1) & $lesseq(0, 208.46/128.37 | | | | | | | | | | | | | all_86_13) & length1(int, all_103_2) = all_703_1 208.46/128.37 | | | | | | | | | | | | | & length1(int, all_103_4) = all_703_1 208.46/128.37 | | | | | | | | | | | | | 208.46/128.37 | | | | | | | | | | | | | ALPHA: (143) implies: 208.46/128.37 | | | | | | | | | | | | | (144) length1(int, all_103_4) = all_703_1 208.46/128.37 | | | | | | | | | | | | | 208.46/128.37 | | | | | | | | | | | | | BETA: splitting (107) gives: 208.46/128.37 | | | | | | | | | | | | | 208.46/128.37 | | | | | | | | | | | | | Case 1: 208.46/128.37 | | | | | | | | | | | | | | 208.46/128.37 | | | | | | | | | | | | | | (145) all_708_0 = all_708_1 & $lesseq(1, 208.46/128.37 | | | | | | | | | | | | | | $difference(all_708_1, all_86_10)) & 208.46/128.37 | | | | | | | | | | | | | | $lesseq(all_86_11, all_708_1) & $lesseq(-1, 208.46/128.37 | | | | | | | | | | | | | | all_86_10) & $lesseq(0, all_86_11) & 208.46/128.37 | | | | | | | | | | | | | | length1(int, all_105_4) = all_708_1 & length1(int, 208.46/128.37 | | | | | | | | | | | | | | all_103_4) = all_708_1 208.46/128.37 | | | | | | | | | | | | | | 208.46/128.37 | | | | | | | | | | | | | | ALPHA: (145) implies: 208.46/128.37 | | | | | | | | | | | | | | (146) $lesseq(1, $difference(all_708_1, all_86_10)) 208.46/128.37 | | | | | | | | | | | | | | (147) length1(int, all_103_4) = all_708_1 208.46/128.37 | | | | | | | | | | | | | | 208.46/128.37 | | | | | | | | | | | | | | GROUND_INST: instantiating (60) with all_86_2, all_697_1, 208.46/128.37 | | | | | | | | | | | | | | all_105_1, simplifying with (32), (137) gives: 208.46/128.37 | | | | | | | | | | | | | | (148) all_697_1 = all_86_2 208.46/128.37 | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | GROUND_INST: instantiating (65) with all_86_13, all_708_1, 208.46/128.38 | | | | | | | | | | | | | | all_103_4, int, simplifying with (11), (147) 208.46/128.38 | | | | | | | | | | | | | | gives: 208.46/128.38 | | | | | | | | | | | | | | (149) all_708_1 = all_86_13 208.46/128.38 | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | GROUND_INST: instantiating (65) with all_708_1, all_703_1, 208.46/128.38 | | | | | | | | | | | | | | all_103_4, int, simplifying with (144), (147) 208.46/128.38 | | | | | | | | | | | | | | gives: 208.46/128.38 | | | | | | | | | | | | | | (150) all_708_1 = all_703_1 208.46/128.38 | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | COMBINE_EQS: (149), (150) imply: 208.46/128.38 | | | | | | | | | | | | | | (151) all_703_1 = all_86_13 208.46/128.38 | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | SIMP: (151) implies: 208.46/128.38 | | | | | | | | | | | | | | (152) all_703_1 = all_86_13 208.46/128.38 | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | REDUCE: (138), (148) imply: 208.46/128.38 | | | | | | | | | | | | | | (153) get3(all_86_2, all_133_2) = all_133_0 208.46/128.38 | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | GROUND_INST: instantiating (31) with all_86_9, all_86_3, 208.46/128.38 | | | | | | | | | | | | | | all_86_11, $sum(all_86_10, 1), all_103_4, 208.46/128.38 | | | | | | | | | | | | | | all_105_4, simplifying with (8), (29), (34), (140) 208.46/128.38 | | | | | | | | | | | | | | gives: 208.46/128.38 | | | | | | | | | | | | | | (154) ? [v0: $int] : ? [v1: $int] : ? [v2: $int] : ? 208.46/128.38 | | | | | | | | | | | | | | [v3: $int] : ((v0 = 0 & permut_sub3(all_86_9, 208.46/128.38 | | | | | | | | | | | | | | all_86_3, all_86_11, $sum(all_86_10, 1)) = 208.46/128.38 | | | | | | | | | | | | | | 0) | (elts(int, all_105_4) = v1 & elts(int, 208.46/128.38 | | | | | | | | | | | | | | all_103_4) = v0 & in_uni(v1) & in_uni(v0) & 208.46/128.38 | | | | | | | | | | | | | | (( ~ (v3 = 0) & map_eq_sub1(int, v0, v1, 208.46/128.38 | | | | | | | | | | | | | | $sum(all_86_10, 1), v2) = v3 & 208.46/128.38 | | | | | | | | | | | | | | length1(int, all_103_4) = v2) | ( ~ (v2 = 208.46/128.38 | | | | | | | | | | | | | | 0) & map_eq_sub1(int, v0, v1, 0, 208.46/128.38 | | | | | | | | | | | | | | all_86_11) = v2)))) 208.46/128.38 | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | GROUND_INST: instantiating (66) with int, all_103_4, all_105_4, 208.46/128.38 | | | | | | | | | | | | | | all_86_11, $sum(all_86_10, 1), simplifying with 208.46/128.38 | | | | | | | | | | | | | | (10), (140) gives: 208.46/128.38 | | | | | | | | | | | | | | (155) ? [v0: $int] : ? [v1: $int] : ? [v2: $int] : ? 208.46/128.38 | | | | | | | | | | | | | | [v3: $int] : ((v0 = 0 & permut_sub2(int, 208.46/128.38 | | | | | | | | | | | | | | all_103_4, all_105_4, all_86_11, 208.46/128.38 | | | | | | | | | | | | | | $sum(all_86_10, 1)) = 0) | (elts(int, 208.46/128.38 | | | | | | | | | | | | | | all_105_4) = v1 & elts(int, all_103_4) = v0 208.46/128.38 | | | | | | | | | | | | | | & in_uni(v1) & in_uni(v0) & (( ~ (v3 = 0) & 208.46/128.38 | | | | | | | | | | | | | | map_eq_sub1(int, v0, v1, $sum(all_86_10, 208.46/128.38 | | | | | | | | | | | | | | 1), v2) = v3 & length1(int, all_103_4) 208.46/128.38 | | | | | | | | | | | | | | = v2) | ( ~ (v2 = 0) & map_eq_sub1(int, 208.46/128.38 | | | | | | | | | | | | | | v0, v1, 0, all_86_11) = v2)))) 208.46/128.38 | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | GROUND_INST: instantiating (64) with all_86_9, all_86_3, 208.46/128.38 | | | | | | | | | | | | | | all_86_11, $sum(all_86_10, 1), all_103_4, 208.46/128.38 | | | | | | | | | | | | | | all_105_4, 0, simplifying with (8), (29), (34), 208.46/128.38 | | | | | | | | | | | | | | (140) gives: 208.46/128.38 | | | | | | | | | | | | | | (156) ? [v0: $int] : ? [v1: $int] : ? [v2: $int] : ? 208.46/128.38 | | | | | | | | | | | | | | [v3: $int] : ? [v4: $int] : ((v4 = 0 & v2 = 0 & 208.46/128.38 | | | | | | | | | | | | | | map_eq_sub1(int, v0, v1, $sum(all_86_10, 1), 208.46/128.38 | | | | | | | | | | | | | | v3) = 0 & map_eq_sub1(int, v0, v1, 0, 208.46/128.38 | | | | | | | | | | | | | | all_86_11) = 0 & length1(int, all_103_4) = 208.46/128.38 | | | | | | | | | | | | | | v3 & elts(int, all_105_4) = v1 & elts(int, 208.46/128.38 | | | | | | | | | | | | | | all_103_4) = v0 & in_uni(v1) & in_uni(v0)) | 208.46/128.38 | | | | | | | | | | | | | | ( ~ (v0 = 0) & permut_sub3(all_86_9, all_86_3, 208.46/128.38 | | | | | | | | | | | | | | all_86_11, $sum(all_86_10, 1)) = v0)) 208.46/128.38 | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | GROUND_INST: instantiating (71) with int, all_103_4, all_105_4, 208.46/128.38 | | | | | | | | | | | | | | all_86_11, $sum(all_86_10, 1), 0, simplifying with 208.46/128.38 | | | | | | | | | | | | | | (10), (140) gives: 208.46/128.38 | | | | | | | | | | | | | | (157) ? [v0: $int] : ? [v1: $int] : ? [v2: $int] : ? 208.46/128.38 | | | | | | | | | | | | | | [v3: $int] : ? [v4: $int] : ((v4 = 0 & v3 = 0 & 208.46/128.38 | | | | | | | | | | | | | | map_eq_sub1(int, v0, v1, $sum(all_86_10, 1), 208.46/128.38 | | | | | | | | | | | | | | v2) = 0 & map_eq_sub1(int, v0, v1, 0, 208.46/128.38 | | | | | | | | | | | | | | all_86_11) = 0 & length1(int, all_103_4) = 208.46/128.38 | | | | | | | | | | | | | | v2 & elts(int, all_105_4) = v1 & elts(int, 208.46/128.38 | | | | | | | | | | | | | | all_103_4) = v0 & in_uni(v1) & in_uni(v0)) | 208.46/128.38 | | | | | | | | | | | | | | ( ~ (v0 = 0) & permut_sub2(int, all_103_4, 208.46/128.38 | | | | | | | | | | | | | | all_105_4, all_86_11, $sum(all_86_10, 1)) = 208.46/128.38 | | | | | | | | | | | | | | v0)) 208.46/128.38 | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | GROUND_INST: instantiating (63) with all_86_4, all_86_2, 0, 208.46/128.38 | | | | | | | | | | | | | | all_86_7, all_105_3, all_105_1, all_133_2, 208.46/128.38 | | | | | | | | | | | | | | all_133_0, simplifying with (9), (30), (55), (70), 208.46/128.38 | | | | | | | | | | | | | | (153) gives: 208.46/128.38 | | | | | | | | | | | | | | (158) ~ ($lesseq(1, $difference(all_86_7, all_133_2))) 208.46/128.38 | | | | | | | | | | | | | | | ~ ($lesseq(0, all_133_2)) | get3(all_86_4, 208.46/128.38 | | | | | | | | | | | | | | all_133_2) = all_133_0 208.46/128.38 | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | GROUND_INST: instantiating (52) with int, all_105_3, all_105_1, 208.46/128.38 | | | | | | | | | | | | | | 0, all_86_7, all_133_2, all_710_0, simplifying 208.46/128.38 | | | | | | | | | | | | | | with (10), (30), (110) gives: 208.46/128.38 | | | | | | | | | | | | | | (159) ~ ($lesseq(1, $difference(all_86_7, all_133_2))) 208.46/128.38 | | | | | | | | | | | | | | | ~ ($lesseq(0, all_133_2)) | ? [v0: $int] : 208.46/128.38 | | | | | | | | | | | | | | (get(int, int, all_105_1, all_710_0) = v0 & 208.46/128.38 | | | | | | | | | | | | | | get(int, int, all_105_3, all_710_0) = v0 & 208.46/128.38 | | | | | | | | | | | | | | in_uni(v0)) 208.46/128.38 | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | GROUND_INST: instantiating (52) with int, all_103_1, all_105_3, 208.46/128.38 | | | | | | | | | | | | | | $sum(all_86_8, 1), all_86_13, all_133_2, 208.46/128.38 | | | | | | | | | | | | | | all_710_0, simplifying with (10), (21), (110) 208.46/128.38 | | | | | | | | | | | | | | gives: 208.46/128.38 | | | | | | | | | | | | | | (160) ~ ($lesseq(1, $difference(all_86_13, all_133_2))) 208.46/128.38 | | | | | | | | | | | | | | | ~ ($lesseq(1, $difference(all_133_2, 208.46/128.38 | | | | | | | | | | | | | | all_86_8))) | ? [v0: $int] : (get(int, int, 208.46/128.38 | | | | | | | | | | | | | | all_105_3, all_710_0) = v0 & get(int, int, 208.46/128.38 | | | | | | | | | | | | | | all_103_1, all_710_0) = v0 & in_uni(v0)) 208.46/128.38 | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | DELTA: instantiating (157) with fresh symbols all_835_0, 208.46/128.38 | | | | | | | | | | | | | | all_835_1, all_835_2, all_835_3, all_835_4 gives: 208.46/128.38 | | | | | | | | | | | | | | (161) (all_835_0 = 0 & all_835_1 = 0 & map_eq_sub1(int, 208.46/128.38 | | | | | | | | | | | | | | all_835_4, all_835_3, $sum(all_86_10, 1), 208.46/128.38 | | | | | | | | | | | | | | all_835_2) = 0 & map_eq_sub1(int, all_835_4, 208.46/128.38 | | | | | | | | | | | | | | all_835_3, 0, all_86_11) = 0 & length1(int, 208.46/128.38 | | | | | | | | | | | | | | all_103_4) = all_835_2 & elts(int, all_105_4) 208.46/128.38 | | | | | | | | | | | | | | = all_835_3 & elts(int, all_103_4) = all_835_4 & 208.46/128.38 | | | | | | | | | | | | | | in_uni(all_835_3) & in_uni(all_835_4)) | ( ~ 208.46/128.38 | | | | | | | | | | | | | | (all_835_4 = 0) & permut_sub2(int, all_103_4, 208.46/128.38 | | | | | | | | | | | | | | all_105_4, all_86_11, $sum(all_86_10, 1)) = 208.46/128.38 | | | | | | | | | | | | | | all_835_4) 208.46/128.38 | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | DELTA: instantiating (156) with fresh symbols all_851_0, 208.46/128.38 | | | | | | | | | | | | | | all_851_1, all_851_2, all_851_3, all_851_4 gives: 208.46/128.38 | | | | | | | | | | | | | | (162) (all_851_0 = 0 & all_851_2 = 0 & map_eq_sub1(int, 208.46/128.38 | | | | | | | | | | | | | | all_851_4, all_851_3, $sum(all_86_10, 1), 208.46/128.38 | | | | | | | | | | | | | | all_851_1) = 0 & map_eq_sub1(int, all_851_4, 208.46/128.38 | | | | | | | | | | | | | | all_851_3, 0, all_86_11) = 0 & length1(int, 208.46/128.38 | | | | | | | | | | | | | | all_103_4) = all_851_1 & elts(int, all_105_4) 208.46/128.38 | | | | | | | | | | | | | | = all_851_3 & elts(int, all_103_4) = all_851_4 & 208.46/128.38 | | | | | | | | | | | | | | in_uni(all_851_3) & in_uni(all_851_4)) | ( ~ 208.46/128.38 | | | | | | | | | | | | | | (all_851_4 = 0) & permut_sub3(all_86_9, 208.46/128.38 | | | | | | | | | | | | | | all_86_3, all_86_11, $sum(all_86_10, 1)) = 208.46/128.38 | | | | | | | | | | | | | | all_851_4) 208.46/128.38 | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | DELTA: instantiating (154) with fresh symbols all_852_0, 208.46/128.38 | | | | | | | | | | | | | | all_852_1, all_852_2, all_852_3 gives: 208.46/128.38 | | | | | | | | | | | | | | (163) (all_852_3 = 0 & permut_sub3(all_86_9, all_86_3, 208.46/128.38 | | | | | | | | | | | | | | all_86_11, $sum(all_86_10, 1)) = 0) | 208.46/128.38 | | | | | | | | | | | | | | (elts(int, all_105_4) = all_852_2 & elts(int, 208.46/128.38 | | | | | | | | | | | | | | all_103_4) = all_852_3 & in_uni(all_852_2) & 208.46/128.38 | | | | | | | | | | | | | | in_uni(all_852_3) & (( ~ (all_852_0 = 0) & 208.46/128.38 | | | | | | | | | | | | | | map_eq_sub1(int, all_852_3, all_852_2, 208.46/128.38 | | | | | | | | | | | | | | $sum(all_86_10, 1), all_852_1) = all_852_0 208.46/128.38 | | | | | | | | | | | | | | & length1(int, all_103_4) = all_852_1) | ( ~ 208.46/128.38 | | | | | | | | | | | | | | (all_852_1 = 0) & map_eq_sub1(int, 208.46/128.38 | | | | | | | | | | | | | | all_852_3, all_852_2, 0, all_86_11) = 208.46/128.38 | | | | | | | | | | | | | | all_852_1))) 208.46/128.38 | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | DELTA: instantiating (155) with fresh symbols all_854_0, 208.46/128.38 | | | | | | | | | | | | | | all_854_1, all_854_2, all_854_3 gives: 208.46/128.38 | | | | | | | | | | | | | | (164) (all_854_3 = 0 & permut_sub2(int, all_103_4, 208.46/128.38 | | | | | | | | | | | | | | all_105_4, all_86_11, $sum(all_86_10, 1)) = 0) 208.46/128.38 | | | | | | | | | | | | | | | (elts(int, all_105_4) = all_854_2 & elts(int, 208.46/128.38 | | | | | | | | | | | | | | all_103_4) = all_854_3 & in_uni(all_854_2) & 208.46/128.38 | | | | | | | | | | | | | | in_uni(all_854_3) & (( ~ (all_854_0 = 0) & 208.46/128.38 | | | | | | | | | | | | | | map_eq_sub1(int, all_854_3, all_854_2, 208.46/128.38 | | | | | | | | | | | | | | $sum(all_86_10, 1), all_854_1) = all_854_0 208.46/128.38 | | | | | | | | | | | | | | & length1(int, all_103_4) = all_854_1) | ( ~ 208.46/128.38 | | | | | | | | | | | | | | (all_854_1 = 0) & map_eq_sub1(int, 208.46/128.38 | | | | | | | | | | | | | | all_854_3, all_854_2, 0, all_86_11) = 208.46/128.38 | | | | | | | | | | | | | | all_854_1))) 208.46/128.38 | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | BETA: splitting (159) gives: 208.46/128.38 | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | Case 1: 208.46/128.38 | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | (165) $lesseq(all_133_2, -1) 208.46/128.38 | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | COMBINE_INEQS: (81), (165) imply: 208.46/128.38 | | | | | | | | | | | | | | | (166) $lesseq(all_86_8, -2) 208.46/128.38 | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | COMBINE_INEQS: (40), (166) imply: 208.46/128.38 | | | | | | | | | | | | | | | (167) $lesseq(0, -1) 208.46/128.38 | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | CLOSE: (167) is inconsistent. 208.46/128.38 | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | Case 2: 208.46/128.38 | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | (168) $lesseq(0, all_133_2) 208.46/128.38 | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | BETA: splitting (158) gives: 208.46/128.38 | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | Case 1: 208.46/128.38 | | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | | (169) get3(all_86_4, all_133_2) = all_133_0 208.46/128.38 | | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | | BETA: splitting (160) gives: 208.46/128.38 | | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | | Case 1: 208.46/128.38 | | | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | | | (170) $lesseq(all_86_13, all_133_2) 208.46/128.38 | | | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | | | COMBINE_INEQS: (82), (170) imply: 208.46/128.38 | | | | | | | | | | | | | | | | | (171) $lesseq(1, $difference(all_86_7, all_86_13)) 208.46/128.38 | | | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | | | COMBINE_INEQS: (17), (171) imply: 208.46/128.38 | | | | | | | | | | | | | | | | | (172) $lesseq(0, -1) 208.46/128.38 | | | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | | | CLOSE: (172) is inconsistent. 208.46/128.38 | | | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | | Case 2: 208.46/128.38 | | | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | | | (173) $lesseq(1, $difference(all_86_13, all_133_2)) 208.46/128.38 | | | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | | | BETA: splitting (161) gives: 208.46/128.38 | | | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | | | Case 1: 208.46/128.38 | | | | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | | | | (174) all_835_0 = 0 & all_835_1 = 0 & map_eq_sub1(int, 208.46/128.38 | | | | | | | | | | | | | | | | | | all_835_4, all_835_3, $sum(all_86_10, 1), 208.46/128.38 | | | | | | | | | | | | | | | | | | all_835_2) = 0 & map_eq_sub1(int, all_835_4, 208.46/128.38 | | | | | | | | | | | | | | | | | | all_835_3, 0, all_86_11) = 0 & length1(int, 208.46/128.38 | | | | | | | | | | | | | | | | | | all_103_4) = all_835_2 & elts(int, all_105_4) = 208.46/128.38 | | | | | | | | | | | | | | | | | | all_835_3 & elts(int, all_103_4) = all_835_4 & 208.46/128.38 | | | | | | | | | | | | | | | | | | in_uni(all_835_3) & in_uni(all_835_4) 208.46/128.38 | | | | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | | | | ALPHA: (174) implies: 208.46/128.38 | | | | | | | | | | | | | | | | | | (175) elts(int, all_103_4) = all_835_4 208.46/128.38 | | | | | | | | | | | | | | | | | | (176) elts(int, all_105_4) = all_835_3 208.46/128.38 | | | | | | | | | | | | | | | | | | (177) length1(int, all_103_4) = all_835_2 208.46/128.38 | | | | | | | | | | | | | | | | | | (178) map_eq_sub1(int, all_835_4, all_835_3, 0, 208.46/128.38 | | | | | | | | | | | | | | | | | | all_86_11) = 0 208.46/128.38 | | | | | | | | | | | | | | | | | | (179) map_eq_sub1(int, all_835_4, all_835_3, 208.46/128.38 | | | | | | | | | | | | | | | | | | $sum(all_86_10, 1), all_835_2) = 0 208.46/128.38 | | | | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (65) with all_86_13, all_835_2, 208.46/128.38 | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (11), (177) 208.46/128.38 | | | | | | | | | | | | | | | | | | gives: 208.46/128.38 | | | | | | | | | | | | | | | | | | (180) all_835_2 = all_86_13 208.46/128.38 | | | | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (24) with all_105_3, all_835_3, 208.46/128.38 | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (27), (176) 208.46/128.38 | | | | | | | | | | | | | | | | | | gives: 208.46/128.38 | | | | | | | | | | | | | | | | | | (181) all_835_3 = all_105_3 208.46/128.38 | | | | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (24) with all_103_3, all_835_4, 208.46/128.38 | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (7), (175) gives: 208.46/128.38 | | | | | | | | | | | | | | | | | | (182) all_835_4 = all_103_3 208.46/128.38 | | | | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | | | | REDUCE: (179), (180), (181), (182) imply: 208.46/128.38 | | | | | | | | | | | | | | | | | | (183) map_eq_sub1(int, all_103_3, all_105_3, 208.46/128.38 | | | | | | | | | | | | | | | | | | $sum(all_86_10, 1), all_86_13) = 0 208.46/128.38 | | | | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | | | | REDUCE: (178), (181), (182) imply: 208.46/128.38 | | | | | | | | | | | | | | | | | | (184) map_eq_sub1(int, all_103_3, all_105_3, 0, 208.46/128.38 | | | | | | | | | | | | | | | | | | all_86_11) = 0 208.46/128.38 | | | | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | | | | BETA: splitting (163) gives: 208.46/128.38 | | | | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | | | | Case 1: 208.46/128.38 | | | | | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | | | | | (185) all_852_3 = 0 & permut_sub3(all_86_9, all_86_3, 208.46/128.38 | | | | | | | | | | | | | | | | | | | all_86_11, $sum(all_86_10, 1)) = 0 208.46/128.38 | | | | | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | | | | | ALPHA: (185) implies: 208.46/128.38 | | | | | | | | | | | | | | | | | | | (186) permut_sub3(all_86_9, all_86_3, all_86_11, 208.46/128.38 | | | | | | | | | | | | | | | | | | | $sum(all_86_10, 1)) = 0 208.46/128.38 | | | | | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | | | | | BETA: splitting (162) gives: 208.46/128.38 | | | | | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | | | | | Case 1: 208.46/128.38 | | | | | | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | | | | | | (187) all_851_0 = 0 & all_851_2 = 0 & map_eq_sub1(int, 208.46/128.38 | | | | | | | | | | | | | | | | | | | | all_851_4, all_851_3, $sum(all_86_10, 1), 208.46/128.38 | | | | | | | | | | | | | | | | | | | | all_851_1) = 0 & map_eq_sub1(int, all_851_4, 208.46/128.38 | | | | | | | | | | | | | | | | | | | | all_851_3, 0, all_86_11) = 0 & length1(int, 208.46/128.38 | | | | | | | | | | | | | | | | | | | | all_103_4) = all_851_1 & elts(int, all_105_4) = 208.46/128.38 | | | | | | | | | | | | | | | | | | | | all_851_3 & elts(int, all_103_4) = all_851_4 & 208.46/128.38 | | | | | | | | | | | | | | | | | | | | in_uni(all_851_3) & in_uni(all_851_4) 208.46/128.38 | | | | | | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | | | | | | ALPHA: (187) implies: 208.46/128.38 | | | | | | | | | | | | | | | | | | | | (188) elts(int, all_103_4) = all_851_4 208.46/128.38 | | | | | | | | | | | | | | | | | | | | (189) elts(int, all_105_4) = all_851_3 208.46/128.38 | | | | | | | | | | | | | | | | | | | | (190) length1(int, all_103_4) = all_851_1 208.46/128.38 | | | | | | | | | | | | | | | | | | | | (191) map_eq_sub1(int, all_851_4, all_851_3, 208.46/128.38 | | | | | | | | | | | | | | | | | | | | $sum(all_86_10, 1), all_851_1) = 0 208.46/128.38 | | | | | | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (65) with all_86_13, all_851_1, 208.46/128.38 | | | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (11), (190) 208.46/128.38 | | | | | | | | | | | | | | | | | | | | gives: 208.46/128.38 | | | | | | | | | | | | | | | | | | | | (192) all_851_1 = all_86_13 208.46/128.38 | | | | | | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (24) with all_105_3, all_851_3, 208.46/128.38 | | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (27), (189) 208.46/128.38 | | | | | | | | | | | | | | | | | | | | gives: 208.46/128.38 | | | | | | | | | | | | | | | | | | | | (193) all_851_3 = all_105_3 208.46/128.38 | | | | | | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (24) with all_103_3, all_851_4, 208.46/128.38 | | | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (7), (188) gives: 208.46/128.38 | | | | | | | | | | | | | | | | | | | | (194) all_851_4 = all_103_3 208.46/128.38 | | | | | | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with int, all_103_4, all_105_4, 208.46/128.38 | | | | | | | | | | | | | | | | | | | | $sum(all_86_10, 1), all_86_13, all_103_3, 208.46/128.38 | | | | | | | | | | | | | | | | | | | | all_105_3, simplifying with (7), (10), (27), (183) 208.46/128.38 | | | | | | | | | | | | | | | | | | | | gives: 208.46/128.38 | | | | | | | | | | | | | | | | | | | | (195) ~ ($lesseq(-1, all_86_10)) | ~ ($lesseq(0, 208.46/128.38 | | | | | | | | | | | | | | | | | | | | all_86_13)) | ? [v0: $int] : ? [v1: $int] : 208.46/128.38 | | | | | | | | | | | | | | | | | | | | ((v0 = 0 & array_eq_sub1(int, all_103_4, 208.46/128.38 | | | | | | | | | | | | | | | | | | | | all_105_4, $sum(all_86_10, 1), all_86_13) = 208.46/128.38 | | | | | | | | | | | | | | | | | | | | 0) | (length1(int, all_103_4) = v0 & ( ~ 208.46/128.38 | | | | | | | | | | | | | | | | | | | | ($lesseq(1, $difference(v0, all_86_10))) | 208.46/128.38 | | | | | | | | | | | | | | | | | | | | ~ ($lesseq(all_86_13, v0)) | ( ~ (v1 = v0) & 208.46/128.38 | | | | | | | | | | | | | | | | | | | | length1(int, all_105_4) = v1)))) 208.46/128.38 | | | | | | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (63) with all_86_6, all_86_4, 208.46/128.38 | | | | | | | | | | | | | | | | | | | | $sum(all_86_8, 1), all_86_13, all_103_1, 208.46/128.38 | | | | | | | | | | | | | | | | | | | | all_105_3, all_133_2, all_133_0, simplifying with 208.46/128.38 | | | | | | | | | | | | | | | | | | | | (4), (20), (21), (70), (169) gives: 208.46/128.38 | | | | | | | | | | | | | | | | | | | | (196) ~ ($lesseq(1, $difference(all_86_13, all_133_2))) 208.46/128.38 | | | | | | | | | | | | | | | | | | | | | ~ ($lesseq(1, $difference(all_133_2, 208.46/128.38 | | | | | | | | | | | | | | | | | | | | all_86_8))) | get3(all_86_6, all_133_2) = 208.46/128.38 | | | | | | | | | | | | | | | | | | | | all_133_0 208.46/128.38 | | | | | | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives: 208.46/128.38 | | | | | | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | | | | | | Case 1: 208.46/128.38 | | | | | | | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | | | | | | | (197) get3(all_86_6, all_133_2) = all_133_0 208.46/128.38 | | | | | | | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives: 208.46/128.38 | | | | | | | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | | | | | | | Case 1: 208.46/128.38 | | | | | | | | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | | | | | | | | (198) $lesseq(all_86_13, -1) 208.46/128.38 | | | | | | | | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | | | | | | | | COMBINE_INEQS: (90), (198) imply: 208.46/128.38 | | | | | | | | | | | | | | | | | | | | | | (199) $lesseq(0, -1) 208.46/128.38 | | | | | | | | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (199) is inconsistent. 208.46/128.38 | | | | | | | | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | | | | | | | Case 2: 208.46/128.38 | | | | | | | | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | | | | | | | | (200) ~ ($lesseq(-1, all_86_10)) | ? [v0: $int] : ? 208.46/128.38 | | | | | | | | | | | | | | | | | | | | | | [v1: $int] : ((v0 = 0 & array_eq_sub1(int, 208.46/128.38 | | | | | | | | | | | | | | | | | | | | | | all_103_4, all_105_4, $sum(all_86_10, 1), 208.46/128.38 | | | | | | | | | | | | | | | | | | | | | | all_86_13) = 0) | (length1(int, all_103_4) = 208.46/128.38 | | | | | | | | | | | | | | | | | | | | | | v0 & ( ~ ($lesseq(1, $difference(v0, 208.46/128.38 | | | | | | | | | | | | | | | | | | | | | | all_86_10))) | ~ ($lesseq(all_86_13, 208.46/128.38 | | | | | | | | | | | | | | | | | | | | | | v0)) | ( ~ (v1 = v0) & length1(int, 208.46/128.38 | | | | | | | | | | | | | | | | | | | | | | all_105_4) = v1)))) 208.46/128.38 | | | | | | | | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (80), (81), (82), (88), (197), (200) are 208.46/128.38 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #154. 208.46/128.38 | | | | | | | | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | | | | | | | End of split 208.46/128.38 | | | | | | | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | | | | | | Case 2: 208.46/128.38 | | | | | | | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | | | | | | | (201) ~ ($lesseq(1, $difference(all_86_13, all_133_2))) 208.46/128.38 | | | | | | | | | | | | | | | | | | | | | | ~ ($lesseq(1, $difference(all_133_2, 208.46/128.38 | | | | | | | | | | | | | | | | | | | | | all_86_8))) 208.46/128.38 | | | | | | | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (81), (173), (201) are inconsistent by sub-proof 208.46/128.38 | | | | | | | | | | | | | | | | | | | | | #153. 208.46/128.38 | | | | | | | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | | | | | | End of split 208.46/128.38 | | | | | | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | | | | | Case 2: 208.46/128.38 | | | | | | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | | | | | | (202) ~ (all_851_4 = 0) & permut_sub3(all_86_9, 208.46/128.38 | | | | | | | | | | | | | | | | | | | | all_86_3, all_86_11, $sum(all_86_10, 1)) = 208.46/128.38 | | | | | | | | | | | | | | | | | | | | all_851_4 208.46/128.38 | | | | | | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | | | | | | ALPHA: (202) implies: 208.46/128.38 | | | | | | | | | | | | | | | | | | | | (203) ~ (all_851_4 = 0) 208.46/128.38 | | | | | | | | | | | | | | | | | | | | (204) permut_sub3(all_86_9, all_86_3, all_86_11, 208.46/128.38 | | | | | | | | | | | | | | | | | | | | $sum(all_86_10, 1)) = all_851_4 208.46/128.38 | | | | | | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (61) with all_851_4, 0, 208.46/128.38 | | | | | | | | | | | | | | | | | | | | $sum(all_86_10, 1), all_86_11, all_86_3, all_86_9, 208.46/128.38 | | | | | | | | | | | | | | | | | | | | simplifying with (186), (204) gives: 208.46/128.38 | | | | | | | | | | | | | | | | | | | | (205) all_851_4 = 0 208.46/128.38 | | | | | | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | | | | | | REDUCE: (203), (205) imply: 208.46/128.38 | | | | | | | | | | | | | | | | | | | | (206) ~ (0 = 0) 208.46/128.38 | | | | | | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | | | | | | CLOSE: (206) is inconsistent. 208.46/128.38 | | | | | | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | | | | | End of split 208.46/128.38 | | | | | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | | | | Case 2: 208.46/128.38 | | | | | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | | | | | (207) elts(int, all_105_4) = all_852_2 & elts(int, 208.46/128.38 | | | | | | | | | | | | | | | | | | | all_103_4) = all_852_3 & in_uni(all_852_2) & 208.46/128.38 | | | | | | | | | | | | | | | | | | | in_uni(all_852_3) & (( ~ (all_852_0 = 0) & 208.46/128.38 | | | | | | | | | | | | | | | | | | | map_eq_sub1(int, all_852_3, all_852_2, 208.46/128.38 | | | | | | | | | | | | | | | | | | | $sum(all_86_10, 1), all_852_1) = all_852_0 & 208.46/128.38 | | | | | | | | | | | | | | | | | | | length1(int, all_103_4) = all_852_1) | ( ~ 208.46/128.38 | | | | | | | | | | | | | | | | | | | (all_852_1 = 0) & map_eq_sub1(int, all_852_3, 208.46/128.38 | | | | | | | | | | | | | | | | | | | all_852_2, 0, all_86_11) = all_852_1)) 208.46/128.38 | | | | | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | | | | | ALPHA: (207) implies: 208.46/128.38 | | | | | | | | | | | | | | | | | | | (208) elts(int, all_103_4) = all_852_3 208.46/128.38 | | | | | | | | | | | | | | | | | | | (209) elts(int, all_105_4) = all_852_2 208.46/128.38 | | | | | | | | | | | | | | | | | | | (210) ( ~ (all_852_0 = 0) & map_eq_sub1(int, all_852_3, 208.46/128.38 | | | | | | | | | | | | | | | | | | | all_852_2, $sum(all_86_10, 1), all_852_1) = 208.46/128.38 | | | | | | | | | | | | | | | | | | | all_852_0 & length1(int, all_103_4) = all_852_1) 208.46/128.38 | | | | | | | | | | | | | | | | | | | | ( ~ (all_852_1 = 0) & map_eq_sub1(int, 208.46/128.38 | | | | | | | | | | | | | | | | | | | all_852_3, all_852_2, 0, all_86_11) = 208.46/128.38 | | | | | | | | | | | | | | | | | | | all_852_1) 208.46/128.38 | | | | | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (24) with all_105_3, all_852_2, 208.46/128.38 | | | | | | | | | | | | | | | | | | | all_105_4, int, simplifying with (27), (209) 208.46/128.38 | | | | | | | | | | | | | | | | | | | gives: 208.46/128.38 | | | | | | | | | | | | | | | | | | | (211) all_852_2 = all_105_3 208.46/128.38 | | | | | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (24) with all_103_3, all_852_3, 208.46/128.38 | | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (7), (208) gives: 208.46/128.38 | | | | | | | | | | | | | | | | | | | (212) all_852_3 = all_103_3 208.46/128.38 | | | | | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives: 208.46/128.38 | | | | | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | | | | | Case 1: 208.46/128.38 | | | | | | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | | | | | | (213) ~ (all_852_0 = 0) & map_eq_sub1(int, all_852_3, 208.46/128.38 | | | | | | | | | | | | | | | | | | | | all_852_2, $sum(all_86_10, 1), all_852_1) = 208.46/128.38 | | | | | | | | | | | | | | | | | | | | all_852_0 & length1(int, all_103_4) = all_852_1 208.46/128.38 | | | | | | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | | | | | | ALPHA: (213) implies: 208.46/128.38 | | | | | | | | | | | | | | | | | | | | (214) ~ (all_852_0 = 0) 208.46/128.38 | | | | | | | | | | | | | | | | | | | | (215) length1(int, all_103_4) = all_852_1 208.46/128.38 | | | | | | | | | | | | | | | | | | | | (216) map_eq_sub1(int, all_852_3, all_852_2, 208.46/128.38 | | | | | | | | | | | | | | | | | | | | $sum(all_86_10, 1), all_852_1) = all_852_0 208.46/128.38 | | | | | | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | | | | | | REDUCE: (211), (212), (216) imply: 208.46/128.38 | | | | | | | | | | | | | | | | | | | | (217) map_eq_sub1(int, all_103_3, all_105_3, 208.46/128.38 | | | | | | | | | | | | | | | | | | | | $sum(all_86_10, 1), all_852_1) = all_852_0 208.46/128.38 | | | | | | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (65) with all_86_13, all_852_1, 208.46/128.38 | | | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (11), (215) 208.46/128.38 | | | | | | | | | | | | | | | | | | | | gives: 208.46/128.38 | | | | | | | | | | | | | | | | | | | | (218) all_852_1 = all_86_13 208.46/128.38 | | | | | | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | | | | | | REDUCE: (217), (218) imply: 208.46/128.38 | | | | | | | | | | | | | | | | | | | | (219) map_eq_sub1(int, all_103_3, all_105_3, 208.46/128.38 | | | | | | | | | | | | | | | | | | | | $sum(all_86_10, 1), all_86_13) = all_852_0 208.46/128.38 | | | | | | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (45) with 0, all_852_0, all_86_13, 208.46/128.38 | | | | | | | | | | | | | | | | | | | | $sum(all_86_10, 1), all_105_3, all_103_3, int, 208.46/128.38 | | | | | | | | | | | | | | | | | | | | simplifying with (183), (219) gives: 208.46/128.38 | | | | | | | | | | | | | | | | | | | | (220) all_852_0 = 0 208.46/128.38 | | | | | | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | | | | | | REDUCE: (214), (220) imply: 208.46/128.38 | | | | | | | | | | | | | | | | | | | | (221) ~ (0 = 0) 208.46/128.38 | | | | | | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | | | | | | CLOSE: (221) is inconsistent. 208.46/128.38 | | | | | | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | | | | | Case 2: 208.46/128.38 | | | | | | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | | | | | | (222) ~ (all_852_1 = 0) & map_eq_sub1(int, all_852_3, 208.46/128.38 | | | | | | | | | | | | | | | | | | | | all_852_2, 0, all_86_11) = all_852_1 208.46/128.38 | | | | | | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | | | | | | ALPHA: (222) implies: 208.46/128.38 | | | | | | | | | | | | | | | | | | | | (223) ~ (all_852_1 = 0) 208.46/128.38 | | | | | | | | | | | | | | | | | | | | (224) map_eq_sub1(int, all_852_3, all_852_2, 0, 208.46/128.38 | | | | | | | | | | | | | | | | | | | | all_86_11) = all_852_1 208.46/128.38 | | | | | | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | | | | | | REDUCE: (211), (212), (224) imply: 208.46/128.38 | | | | | | | | | | | | | | | | | | | | (225) map_eq_sub1(int, all_103_3, all_105_3, 0, 208.46/128.38 | | | | | | | | | | | | | | | | | | | | all_86_11) = all_852_1 208.46/128.38 | | | | | | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (45) with 0, all_852_1, all_86_11, 208.46/128.38 | | | | | | | | | | | | | | | | | | | | 0, all_105_3, all_103_3, int, simplifying with 208.46/128.38 | | | | | | | | | | | | | | | | | | | | (184), (225) gives: 208.46/128.38 | | | | | | | | | | | | | | | | | | | | (226) all_852_1 = 0 208.46/128.38 | | | | | | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | | | | | | REDUCE: (223), (226) imply: 208.46/128.38 | | | | | | | | | | | | | | | | | | | | (227) ~ (0 = 0) 208.46/128.38 | | | | | | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | | | | | | CLOSE: (227) is inconsistent. 208.46/128.38 | | | | | | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | | | | | End of split 208.46/128.38 | | | | | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | | | | End of split 208.46/128.38 | | | | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | | | Case 2: 208.46/128.38 | | | | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | | | | (228) ~ (all_835_4 = 0) & permut_sub2(int, all_103_4, 208.46/128.38 | | | | | | | | | | | | | | | | | | all_105_4, all_86_11, $sum(all_86_10, 1)) = 208.46/128.38 | | | | | | | | | | | | | | | | | | all_835_4 208.46/128.38 | | | | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | | | | ALPHA: (228) implies: 208.46/128.38 | | | | | | | | | | | | | | | | | | (229) ~ (all_835_4 = 0) 208.46/128.38 | | | | | | | | | | | | | | | | | | (230) permut_sub2(int, all_103_4, all_105_4, all_86_11, 208.46/128.38 | | | | | | | | | | | | | | | | | | $sum(all_86_10, 1)) = all_835_4 208.46/128.38 | | | | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | | | | BETA: splitting (164) gives: 208.46/128.38 | | | | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | | | | Case 1: 208.46/128.38 | | | | | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | | | | | (231) all_854_3 = 0 & permut_sub2(int, all_103_4, 208.46/128.38 | | | | | | | | | | | | | | | | | | | all_105_4, all_86_11, $sum(all_86_10, 1)) = 0 208.46/128.38 | | | | | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | | | | | ALPHA: (231) implies: 208.46/128.38 | | | | | | | | | | | | | | | | | | | (232) permut_sub2(int, all_103_4, all_105_4, all_86_11, 208.46/128.38 | | | | | | | | | | | | | | | | | | | $sum(all_86_10, 1)) = 0 208.46/128.38 | | | | | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (28) with all_835_4, 0, 208.46/128.38 | | | | | | | | | | | | | | | | | | | $sum(all_86_10, 1), all_86_11, all_105_4, 208.46/128.38 | | | | | | | | | | | | | | | | | | | all_103_4, int, simplifying with (230), (232) 208.46/128.38 | | | | | | | | | | | | | | | | | | | gives: 208.46/128.38 | | | | | | | | | | | | | | | | | | | (233) all_835_4 = 0 208.46/128.38 | | | | | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | | | | | REDUCE: (229), (233) imply: 208.46/128.38 | | | | | | | | | | | | | | | | | | | (234) ~ (0 = 0) 208.46/128.38 | | | | | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | | | | | CLOSE: (234) is inconsistent. 208.46/128.38 | | | | | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | | | | Case 2: 208.46/128.38 | | | | | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (63) with all_86_6, all_86_4, 208.46/128.38 | | | | | | | | | | | | | | | | | | | $sum(all_86_8, 1), all_86_13, all_103_1, 208.46/128.38 | | | | | | | | | | | | | | | | | | | all_105_3, all_133_2, all_133_0, simplifying with 208.46/128.38 | | | | | | | | | | | | | | | | | | | (4), (20), (21), (70), (169) gives: 208.46/128.38 | | | | | | | | | | | | | | | | | | | (235) ~ ($lesseq(1, $difference(all_86_13, all_133_2))) 208.46/128.38 | | | | | | | | | | | | | | | | | | | | ~ ($lesseq(1, $difference(all_133_2, 208.46/128.38 | | | | | | | | | | | | | | | | | | | all_86_8))) | get3(all_86_6, all_133_2) = 208.46/128.38 | | | | | | | | | | | | | | | | | | | all_133_0 208.46/128.38 | | | | | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (43) with all_86_12, all_86_4, 0, 208.46/128.38 | | | | | | | | | | | | | | | | | | | all_86_13, all_133_2, all_103_3, all_105_3, 208.46/128.38 | | | | | | | | | | | | | | | | | | | all_133_0, simplifying with (5), (49), (70), (93), 208.46/128.38 | | | | | | | | | | | | | | | | | | | (169) gives: 208.46/128.38 | | | | | | | | | | | | | | | | | | | (236) ~ ($lesseq(1, $difference(all_86_13, all_133_2))) 208.46/128.38 | | | | | | | | | | | | | | | | | | | | ~ ($lesseq(0, all_133_2)) | ? [v0: $int] : 208.46/128.38 | | | | | | | | | | | | | | | | | | | ($lesseq(1, $difference(all_86_13, v0)) & 208.46/128.38 | | | | | | | | | | | | | | | | | | | $lesseq(0, v0) & get3(all_86_12, v0) = 208.46/128.38 | | | | | | | | | | | | | | | | | | | all_133_0) 208.46/128.38 | | | | | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (80), (81), (82), (168), (173), (235), (236) 208.46/128.38 | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #141. 208.46/128.38 | | | | | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | | | | End of split 208.46/128.38 | | | | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | | | End of split 208.46/128.38 | | | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | | End of split 208.46/128.38 | | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | Case 2: 208.46/128.38 | | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | | (237) ~ ($lesseq(1, $difference(all_86_7, all_133_2))) 208.46/128.38 | | | | | | | | | | | | | | | | | ~ ($lesseq(0, all_133_2)) 208.46/128.38 | | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | | REF_CLOSE: (82), (168), (237) are inconsistent by sub-proof 208.46/128.38 | | | | | | | | | | | | | | | | #151. 208.46/128.38 | | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | | End of split 208.46/128.38 | | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | End of split 208.46/128.38 | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | Case 2: 208.46/128.38 | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | (238) ~ (all_708_1 = 0) & permut3(int, all_103_4, 208.46/128.38 | | | | | | | | | | | | | | all_105_4, all_86_11, $sum(all_86_10, 1)) = 208.46/128.38 | | | | | | | | | | | | | | all_708_1 208.46/128.38 | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | | REF_CLOSE: (22), (140), (238) are inconsistent by sub-proof 208.46/128.38 | | | | | | | | | | | | | | #140. 208.46/128.38 | | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | End of split 208.46/128.38 | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | Case 2: 208.46/128.38 | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | (239) ~ (all_703_1 = 0) & permut3(int, all_103_4, 208.46/128.38 | | | | | | | | | | | | | all_103_2, 0, all_86_13) = all_703_1 208.46/128.38 | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | REF_CLOSE: (22), (142), (239) are inconsistent by sub-proof 208.46/128.38 | | | | | | | | | | | | | #139. 208.46/128.38 | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | End of split 208.46/128.38 | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | Case 2: 208.46/128.38 | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | (240) length1(int, all_103_4) = all_759_1 & ( ~ 208.46/128.38 | | | | | | | | | | | | ($lesseq(all_86_13, all_759_1)) | ~ ($lesseq(0, 208.46/128.38 | | | | | | | | | | | | all_759_1)) | ( ~ (all_759_0 = all_759_1) & 208.46/128.38 | | | | | | | | | | | | length1(int, all_103_2) = all_759_0)) 208.46/128.38 | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | ALPHA: (240) implies: 208.46/128.38 | | | | | | | | | | | | (241) length1(int, all_103_4) = all_759_1 208.46/128.38 | | | | | | | | | | | | (242) ~ ($lesseq(all_86_13, all_759_1)) | ~ 208.46/128.38 | | | | | | | | | | | | ($lesseq(0, all_759_1)) | ( ~ (all_759_0 = 208.46/128.38 | | | | | | | | | | | | all_759_1) & length1(int, all_103_2) = 208.46/128.38 | | | | | | | | | | | | all_759_0) 208.46/128.38 | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | BETA: splitting (107) gives: 208.46/128.38 | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | Case 1: 208.46/128.38 | | | | | | | | | | | | | 208.46/128.38 | | | | | | | | | | | | | (243) all_708_0 = all_708_1 & $lesseq(1, 208.46/128.38 | | | | | | | | | | | | | $difference(all_708_1, all_86_10)) & 208.46/128.38 | | | | | | | | | | | | | $lesseq(all_86_11, all_708_1) & $lesseq(-1, 208.46/128.38 | | | | | | | | | | | | | all_86_10) & $lesseq(0, all_86_11) & 208.46/128.38 | | | | | | | | | | | | | length1(int, all_105_4) = all_708_1 & length1(int, 208.46/128.38 | | | | | | | | | | | | | all_103_4) = all_708_1 208.46/128.39 | | | | | | | | | | | | | 208.46/128.39 | | | | | | | | | | | | | ALPHA: (243) implies: 208.46/128.39 | | | | | | | | | | | | | (244) $lesseq(1, $difference(all_708_1, all_86_10)) 208.46/128.39 | | | | | | | | | | | | | (245) length1(int, all_103_4) = all_708_1 208.46/128.39 | | | | | | | | | | | | | 208.46/128.39 | | | | | | | | | | | | | GROUND_INST: instantiating (65) with all_86_13, all_759_1, 208.46/128.39 | | | | | | | | | | | | | all_103_4, int, simplifying with (11), (241) 208.46/128.39 | | | | | | | | | | | | | gives: 208.46/128.39 | | | | | | | | | | | | | (246) all_759_1 = all_86_13 208.46/128.39 | | | | | | | | | | | | | 208.46/128.39 | | | | | | | | | | | | | GROUND_INST: instantiating (65) with all_759_1, all_708_1, 208.46/128.39 | | | | | | | | | | | | | all_103_4, int, simplifying with (241), (245) 208.46/128.39 | | | | | | | | | | | | | gives: 208.46/128.39 | | | | | | | | | | | | | (247) all_759_1 = all_708_1 208.46/128.39 | | | | | | | | | | | | | 208.46/128.39 | | | | | | | | | | | | | COMBINE_EQS: (246), (247) imply: 208.46/128.39 | | | | | | | | | | | | | (248) all_708_1 = all_86_13 208.46/128.39 | | | | | | | | | | | | | 208.46/128.39 | | | | | | | | | | | | | BETA: splitting (242) gives: 208.46/128.39 | | | | | | | | | | | | | 208.46/128.39 | | | | | | | | | | | | | Case 1: 208.46/128.39 | | | | | | | | | | | | | | 208.46/128.39 | | | | | | | | | | | | | | (249) $lesseq(all_759_1, -1) 208.46/128.39 | | | | | | | | | | | | | | 208.46/128.39 | | | | | | | | | | | | | | REF_CLOSE: (38), (39), (53), (56), (81), (82), (246), (249) 208.46/128.39 | | | | | | | | | | | | | | are inconsistent by sub-proof #138. 208.46/128.39 | | | | | | | | | | | | | | 208.46/128.39 | | | | | | | | | | | | | Case 2: 208.46/128.39 | | | | | | | | | | | | | | 208.46/128.39 | | | | | | | | | | | | | | (250) ~ ($lesseq(all_86_13, all_759_1)) | ( ~ 208.46/128.39 | | | | | | | | | | | | | | (all_759_0 = all_759_1) & length1(int, 208.46/128.39 | | | | | | | | | | | | | | all_103_2) = all_759_0) 208.46/128.39 | | | | | | | | | | | | | | 208.46/128.39 | | | | | | | | | | | | | | REF_CLOSE: (3), (65), (246), (250) are inconsistent by 208.46/128.39 | | | | | | | | | | | | | | sub-proof #137. 208.46/128.39 | | | | | | | | | | | | | | 208.46/128.39 | | | | | | | | | | | | | End of split 208.46/128.39 | | | | | | | | | | | | | 208.46/128.39 | | | | | | | | | | | | Case 2: 208.46/128.39 | | | | | | | | | | | | | 208.46/128.39 | | | | | | | | | | | | | (251) ~ (all_708_1 = 0) & permut3(int, all_103_4, 208.46/128.39 | | | | | | | | | | | | | all_105_4, all_86_11, $sum(all_86_10, 1)) = 208.46/128.39 | | | | | | | | | | | | | all_708_1 208.46/128.39 | | | | | | | | | | | | | 208.46/128.39 | | | | | | | | | | | | | REF_CLOSE: (22), (140), (251) are inconsistent by sub-proof 208.46/128.39 | | | | | | | | | | | | | #140. 208.46/128.39 | | | | | | | | | | | | | 208.46/128.39 | | | | | | | | | | | | End of split 208.46/128.39 | | | | | | | | | | | | 208.46/128.39 | | | | | | | | | | | End of split 208.46/128.39 | | | | | | | | | | | 208.46/128.39 | | | | | | | | | | Case 2: 208.46/128.39 | | | | | | | | | | | 208.46/128.39 | | | | | | | | | | | (252) length1(int, all_103_4) = all_747_1 & ( ~ 208.46/128.39 | | | | | | | | | | | ($lesseq(1, $difference(all_747_1, all_86_10))) 208.46/128.39 | | | | | | | | | | | | ~ ($lesseq(all_86_11, all_747_1)) | ( ~ 208.46/128.39 | | | | | | | | | | | (all_747_0 = all_747_1) & length1(int, 208.46/128.39 | | | | | | | | | | | all_105_4) = all_747_0)) 208.46/128.39 | | | | | | | | | | | 208.46/128.39 | | | | | | | | | | | ALPHA: (252) implies: 208.46/128.39 | | | | | | | | | | | (253) length1(int, all_103_4) = all_747_1 208.46/128.39 | | | | | | | | | | | (254) ~ ($lesseq(1, $difference(all_747_1, all_86_10))) 208.46/128.39 | | | | | | | | | | | | ~ ($lesseq(all_86_11, all_747_1)) | ( ~ 208.46/128.39 | | | | | | | | | | | (all_747_0 = all_747_1) & length1(int, 208.46/128.39 | | | | | | | | | | | all_105_4) = all_747_0) 208.46/128.39 | | | | | | | | | | | 208.46/128.39 | | | | | | | | | | | BETA: splitting (131) gives: 208.46/128.39 | | | | | | | | | | | 208.46/128.39 | | | | | | | | | | | Case 1: 208.46/128.39 | | | | | | | | | | | | 208.46/128.39 | | | | | | | | | | | | (255) all_759_1 = 0 & permut3(int, all_103_4, all_103_2, 208.46/128.39 | | | | | | | | | | | | 0, all_86_13) = 0 208.46/128.39 | | | | | | | | | | | | 208.46/128.39 | | | | | | | | | | | | ALPHA: (255) implies: 208.46/128.39 | | | | | | | | | | | | (256) permut3(int, all_103_4, all_103_2, 0, all_86_13) = 208.46/128.39 | | | | | | | | | | | | 0 208.46/128.39 | | | | | | | | | | | | 208.46/128.39 | | | | | | | | | | | | BETA: splitting (106) gives: 208.46/128.39 | | | | | | | | | | | | 208.46/128.39 | | | | | | | | | | | | Case 1: 208.46/128.39 | | | | | | | | | | | | | 208.46/128.39 | | | | | | | | | | | | | (257) all_703_0 = all_703_1 & $lesseq(all_86_13, 208.46/128.39 | | | | | | | | | | | | | all_703_1) & $lesseq(0, all_703_1) & $lesseq(0, 208.46/128.39 | | | | | | | | | | | | | all_86_13) & length1(int, all_103_2) = all_703_1 208.46/128.39 | | | | | | | | | | | | | & length1(int, all_103_4) = all_703_1 208.46/128.39 | | | | | | | | | | | | | 208.46/128.39 | | | | | | | | | | | | | ALPHA: (257) implies: 208.46/128.39 | | | | | | | | | | | | | (258) length1(int, all_103_4) = all_703_1 208.46/128.39 | | | | | | | | | | | | | 208.46/128.39 | | | | | | | | | | | | | GROUND_INST: instantiating (65) with all_86_13, all_747_1, 208.46/128.39 | | | | | | | | | | | | | all_103_4, int, simplifying with (11), (253) 208.46/128.39 | | | | | | | | | | | | | gives: 208.46/128.39 | | | | | | | | | | | | | (259) all_747_1 = all_86_13 208.46/128.39 | | | | | | | | | | | | | 208.46/128.39 | | | | | | | | | | | | | GROUND_INST: instantiating (65) with all_747_1, all_703_1, 208.46/128.39 | | | | | | | | | | | | | all_103_4, int, simplifying with (253), (258) 208.46/128.39 | | | | | | | | | | | | | gives: 208.46/128.39 | | | | | | | | | | | | | (260) all_747_1 = all_703_1 208.46/128.39 | | | | | | | | | | | | | 208.46/128.39 | | | | | | | | | | | | | COMBINE_EQS: (259), (260) imply: 208.46/128.39 | | | | | | | | | | | | | (261) all_703_1 = all_86_13 208.46/128.39 | | | | | | | | | | | | | 208.46/128.39 | | | | | | | | | | | | | BETA: splitting (254) gives: 208.46/128.39 | | | | | | | | | | | | | 208.46/128.39 | | | | | | | | | | | | | Case 1: 208.46/128.39 | | | | | | | | | | | | | | 208.46/128.39 | | | | | | | | | | | | | | (262) $lesseq(1, $difference(all_86_11, all_747_1)) 208.46/128.39 | | | | | | | | | | | | | | 208.46/128.39 | | | | | | | | | | | | | | REDUCE: (259), (262) imply: 208.46/128.39 | | | | | | | | | | | | | | (263) $lesseq(1, $difference(all_86_11, all_86_13)) 208.46/128.39 | | | | | | | | | | | | | | 208.46/128.39 | | | | | | | | | | | | | | COMBINE_INEQS: (89), (263) imply: 208.46/128.39 | | | | | | | | | | | | | | (264) $lesseq(0, -1) 208.46/128.39 | | | | | | | | | | | | | | 208.46/128.39 | | | | | | | | | | | | | | CLOSE: (264) is inconsistent. 208.46/128.39 | | | | | | | | | | | | | | 208.46/128.39 | | | | | | | | | | | | | Case 2: 208.46/128.39 | | | | | | | | | | | | | | 208.46/128.39 | | | | | | | | | | | | | | (265) ~ ($lesseq(1, $difference(all_747_1, all_86_10))) 208.46/128.39 | | | | | | | | | | | | | | | ( ~ (all_747_0 = all_747_1) & length1(int, 208.46/128.39 | | | | | | | | | | | | | | all_105_4) = all_747_0) 208.46/128.39 | | | | | | | | | | | | | | 208.46/128.39 | | | | | | | | | | | | | | BETA: splitting (265) gives: 208.46/128.39 | | | | | | | | | | | | | | 208.46/128.39 | | | | | | | | | | | | | | Case 1: 208.46/128.39 | | | | | | | | | | | | | | | 208.46/128.39 | | | | | | | | | | | | | | | (266) $lesseq(all_747_1, all_86_10) 208.46/128.39 | | | | | | | | | | | | | | | 208.46/128.39 | | | | | | | | | | | | | | | REDUCE: (259), (266) imply: 208.46/128.39 | | | | | | | | | | | | | | | (267) $lesseq(all_86_13, all_86_10) 208.46/128.39 | | | | | | | | | | | | | | | 208.46/128.39 | | | | | | | | | | | | | | | COMBINE_INEQS: (53), (267) imply: 208.46/128.39 | | | | | | | | | | | | | | | (268) $lesseq(0, -1) 208.46/128.39 | | | | | | | | | | | | | | | 208.46/128.39 | | | | | | | | | | | | | | | CLOSE: (268) is inconsistent. 208.46/128.39 | | | | | | | | | | | | | | | 208.46/128.39 | | | | | | | | | | | | | | Case 2: 208.46/128.39 | | | | | | | | | | | | | | | 208.46/128.39 | | | | | | | | | | | | | | | (269) ~ (all_747_0 = all_747_1) & length1(int, 208.46/128.39 | | | | | | | | | | | | | | | all_105_4) = all_747_0 208.46/128.39 | | | | | | | | | | | | | | | 208.46/128.39 | | | | | | | | | | | | | | | ALPHA: (269) implies: 208.46/128.39 | | | | | | | | | | | | | | | (270) ~ (all_747_0 = all_747_1) 208.46/128.39 | | | | | | | | | | | | | | | (271) length1(int, all_105_4) = all_747_0 208.46/128.39 | | | | | | | | | | | | | | | 208.46/128.39 | | | | | | | | | | | | | | | REDUCE: (259), (270) imply: 208.46/128.39 | | | | | | | | | | | | | | | (272) ~ (all_747_0 = all_86_13) 208.46/128.39 | | | | | | | | | | | | | | | 208.46/128.39 | | | | | | | | | | | | | | | GROUND_INST: instantiating (65) with all_86_13, all_747_0, 208.46/128.39 | | | | | | | | | | | | | | | all_105_4, int, simplifying with (25), (271) 208.46/128.39 | | | | | | | | | | | | | | | gives: 208.46/128.39 | | | | | | | | | | | | | | | (273) all_747_0 = all_86_13 208.46/128.39 | | | | | | | | | | | | | | | 208.46/128.39 | | | | | | | | | | | | | | | REDUCE: (272), (273) imply: 208.46/128.39 | | | | | | | | | | | | | | | (274) ~ (0 = 0) 208.46/128.39 | | | | | | | | | | | | | | | 208.46/128.39 | | | | | | | | | | | | | | | CLOSE: (274) is inconsistent. 208.46/128.39 | | | | | | | | | | | | | | | 208.46/128.39 | | | | | | | | | | | | | | End of split 208.46/128.39 | | | | | | | | | | | | | | 208.46/128.39 | | | | | | | | | | | | | End of split 208.46/128.39 | | | | | | | | | | | | | 208.46/128.39 | | | | | | | | | | | | Case 2: 208.46/128.39 | | | | | | | | | | | | | 208.46/128.39 | | | | | | | | | | | | | (275) ~ (all_703_1 = 0) & permut3(int, all_103_4, 208.46/128.39 | | | | | | | | | | | | | all_103_2, 0, all_86_13) = all_703_1 208.46/128.39 | | | | | | | | | | | | | 208.46/128.39 | | | | | | | | | | | | | REF_CLOSE: (22), (256), (275) are inconsistent by sub-proof 208.46/128.39 | | | | | | | | | | | | | #139. 208.46/128.39 | | | | | | | | | | | | | 208.46/128.39 | | | | | | | | | | | | End of split 208.46/128.39 | | | | | | | | | | | | 208.46/128.39 | | | | | | | | | | | Case 2: 208.46/128.39 | | | | | | | | | | | | 208.46/128.39 | | | | | | | | | | | | (276) length1(int, all_103_4) = all_759_1 & ( ~ 208.46/128.39 | | | | | | | | | | | | ($lesseq(all_86_13, all_759_1)) | ~ ($lesseq(0, 208.46/128.39 | | | | | | | | | | | | all_759_1)) | ( ~ (all_759_0 = all_759_1) & 208.46/128.39 | | | | | | | | | | | | length1(int, all_103_2) = all_759_0)) 208.46/128.39 | | | | | | | | | | | | 208.46/128.39 | | | | | | | | | | | | ALPHA: (276) implies: 208.46/128.39 | | | | | | | | | | | | (277) length1(int, all_103_4) = all_759_1 208.46/128.39 | | | | | | | | | | | | (278) ~ ($lesseq(all_86_13, all_759_1)) | ~ 208.46/128.39 | | | | | | | | | | | | ($lesseq(0, all_759_1)) | ( ~ (all_759_0 = 208.46/128.39 | | | | | | | | | | | | all_759_1) & length1(int, all_103_2) = 208.46/128.39 | | | | | | | | | | | | all_759_0) 208.46/128.39 | | | | | | | | | | | | 208.46/128.39 | | | | | | | | | | | | GROUND_INST: instantiating (65) with all_86_13, all_759_1, 208.46/128.39 | | | | | | | | | | | | all_103_4, int, simplifying with (11), (277) 208.46/128.39 | | | | | | | | | | | | gives: 208.46/128.39 | | | | | | | | | | | | (279) all_759_1 = all_86_13 208.46/128.39 | | | | | | | | | | | | 208.46/128.39 | | | | | | | | | | | | GROUND_INST: instantiating (65) with all_759_1, all_747_1, 208.46/128.39 | | | | | | | | | | | | all_103_4, int, simplifying with (253), (277) 208.46/128.39 | | | | | | | | | | | | gives: 208.46/128.39 | | | | | | | | | | | | (280) all_759_1 = all_747_1 208.46/128.39 | | | | | | | | | | | | 208.46/128.39 | | | | | | | | | | | | COMBINE_EQS: (279), (280) imply: 208.46/128.39 | | | | | | | | | | | | (281) all_747_1 = all_86_13 208.46/128.39 | | | | | | | | | | | | 208.46/128.39 | | | | | | | | | | | | BETA: splitting (278) gives: 208.46/128.39 | | | | | | | | | | | | 208.46/128.39 | | | | | | | | | | | | Case 1: 208.46/128.39 | | | | | | | | | | | | | 208.46/128.39 | | | | | | | | | | | | | (282) $lesseq(all_759_1, -1) 208.46/128.39 | | | | | | | | | | | | | 208.46/128.39 | | | | | | | | | | | | | REF_CLOSE: (38), (39), (53), (56), (81), (82), (279), (282) 208.46/128.39 | | | | | | | | | | | | | are inconsistent by sub-proof #138. 208.46/128.39 | | | | | | | | | | | | | 208.46/128.39 | | | | | | | | | | | | Case 2: 208.46/128.39 | | | | | | | | | | | | | 208.46/128.39 | | | | | | | | | | | | | (283) ~ ($lesseq(all_86_13, all_759_1)) | ( ~ 208.46/128.39 | | | | | | | | | | | | | (all_759_0 = all_759_1) & length1(int, 208.46/128.39 | | | | | | | | | | | | | all_103_2) = all_759_0) 208.46/128.39 | | | | | | | | | | | | | 208.46/128.39 | | | | | | | | | | | | | REF_CLOSE: (3), (65), (279), (283) are inconsistent by 208.46/128.39 | | | | | | | | | | | | | sub-proof #137. 208.46/128.39 | | | | | | | | | | | | | 208.46/128.39 | | | | | | | | | | | | End of split 208.46/128.39 | | | | | | | | | | | | 208.46/128.39 | | | | | | | | | | | End of split 208.46/128.39 | | | | | | | | | | | 208.46/128.39 | | | | | | | | | | End of split 208.46/128.39 | | | | | | | | | | 208.46/128.39 | | | | | | | | | End of split 208.46/128.39 | | | | | | | | | 208.46/128.39 | | | | | | | | Case 2: 208.46/128.39 | | | | | | | | | 208.46/128.39 | | | | | | | | | (284) ~ (all_709_1 = 0) & permut3(int, all_103_2, 208.46/128.39 | | | | | | | | | all_105_4, 0, all_86_13) = all_709_1 208.46/128.39 | | | | | | | | | 208.46/128.39 | | | | | | | | | ALPHA: (284) implies: 208.46/128.39 | | | | | | | | | (285) ~ (all_709_1 = 0) 208.46/128.39 | | | | | | | | | (286) permut3(int, all_103_2, all_105_4, 0, all_86_13) = 208.46/128.39 | | | | | | | | | all_709_1 208.46/128.39 | | | | | | | | | 208.46/128.39 | | | | | | | | | GROUND_INST: instantiating (22) with 0, all_709_1, all_86_13, 208.46/128.39 | | | | | | | | | 0, all_105_4, all_103_2, int, simplifying with 208.46/128.39 | | | | | | | | | (117), (286) gives: 208.46/128.39 | | | | | | | | | (287) all_709_1 = 0 208.46/128.39 | | | | | | | | | 208.46/128.39 | | | | | | | | | REDUCE: (285), (287) imply: 208.46/128.39 | | | | | | | | | (288) ~ (0 = 0) 208.46/128.39 | | | | | | | | | 208.46/128.39 | | | | | | | | | CLOSE: (288) is inconsistent. 208.46/128.39 | | | | | | | | | 208.46/128.39 | | | | | | | | End of split 208.46/128.39 | | | | | | | | 208.46/128.39 | | | | | | | End of split 208.46/128.39 | | | | | | | 208.46/128.39 | | | | | | End of split 208.46/128.39 | | | | | | 208.46/128.39 | | | | | Case 2: 208.46/128.39 | | | | | | 208.46/128.39 | | | | | | (289) length1(int, all_103_2) = all_721_1 & ( ~ 208.46/128.39 | | | | | | ($lesseq(all_86_13, all_721_1)) | ~ ($lesseq(0, 208.46/128.39 | | | | | | all_721_1)) | ( ~ (all_721_0 = all_721_1) & 208.46/128.39 | | | | | | length1(int, all_105_4) = all_721_0)) 208.46/128.39 | | | | | | 208.46/128.39 | | | | | | ALPHA: (289) implies: 208.46/128.39 | | | | | | (290) length1(int, all_103_2) = all_721_1 208.46/128.39 | | | | | | (291) ~ ($lesseq(all_86_13, all_721_1)) | ~ ($lesseq(0, 208.46/128.39 | | | | | | all_721_1)) | ( ~ (all_721_0 = all_721_1) & 208.46/128.39 | | | | | | length1(int, all_105_4) = all_721_0) 208.46/128.39 | | | | | | 208.46/128.39 | | | | | | GROUND_INST: instantiating (65) with all_86_13, all_721_1, 208.46/128.39 | | | | | | all_103_2, int, simplifying with (3), (290) gives: 208.46/128.39 | | | | | | (292) all_721_1 = all_86_13 208.46/128.39 | | | | | | 208.46/128.39 | | | | | | BETA: splitting (291) gives: 208.46/128.39 | | | | | | 208.46/128.39 | | | | | | Case 1: 208.46/128.39 | | | | | | | 208.46/128.39 | | | | | | | (293) $lesseq(all_721_1, -1) 208.46/128.39 | | | | | | | 208.46/128.39 | | | | | | | REDUCE: (292), (293) imply: 208.46/128.39 | | | | | | | (294) $lesseq(all_86_13, -1) 208.46/128.39 | | | | | | | 208.46/128.39 | | | | | | | COMBINE_INEQS: (90), (294) imply: 208.46/128.39 | | | | | | | (295) $lesseq(0, -1) 208.46/128.39 | | | | | | | 208.46/128.39 | | | | | | | CLOSE: (295) is inconsistent. 208.46/128.39 | | | | | | | 208.46/128.39 | | | | | | Case 2: 208.46/128.39 | | | | | | | 208.46/128.39 | | | | | | | (296) ~ ($lesseq(all_86_13, all_721_1)) | ( ~ (all_721_0 = 208.46/128.39 | | | | | | | all_721_1) & length1(int, all_105_4) = all_721_0) 208.46/128.39 | | | | | | | 208.46/128.39 | | | | | | | BETA: splitting (296) gives: 208.46/128.39 | | | | | | | 208.46/128.39 | | | | | | | Case 1: 208.46/128.39 | | | | | | | | 208.46/128.39 | | | | | | | | (297) $lesseq(1, $difference(all_86_13, all_721_1)) 208.46/128.39 | | | | | | | | 208.46/128.39 | | | | | | | | REDUCE: (292), (297) imply: 208.46/128.39 | | | | | | | | (298) $lesseq(0, -1) 208.46/128.39 | | | | | | | | 208.46/128.39 | | | | | | | | CLOSE: (298) is inconsistent. 208.46/128.39 | | | | | | | | 208.46/128.39 | | | | | | | Case 2: 208.46/128.39 | | | | | | | | 208.46/128.39 | | | | | | | | (299) ~ (all_721_0 = all_721_1) & length1(int, all_105_4) = 208.46/128.39 | | | | | | | | all_721_0 208.46/128.39 | | | | | | | | 208.46/128.39 | | | | | | | | ALPHA: (299) implies: 208.46/128.39 | | | | | | | | (300) ~ (all_721_0 = all_721_1) 208.46/128.39 | | | | | | | | (301) length1(int, all_105_4) = all_721_0 208.46/128.39 | | | | | | | | 208.46/128.39 | | | | | | | | REDUCE: (292), (300) imply: 208.46/128.39 | | | | | | | | (302) ~ (all_721_0 = all_86_13) 208.46/128.39 | | | | | | | | 208.46/128.39 | | | | | | | | GROUND_INST: instantiating (65) with all_86_13, all_721_0, 208.46/128.39 | | | | | | | | all_105_4, int, simplifying with (25), (301) gives: 208.46/128.39 | | | | | | | | (303) all_721_0 = all_86_13 208.46/128.39 | | | | | | | | 208.46/128.39 | | | | | | | | REDUCE: (302), (303) imply: 208.46/128.39 | | | | | | | | (304) ~ (0 = 0) 208.46/128.39 | | | | | | | | 208.46/128.39 | | | | | | | | CLOSE: (304) is inconsistent. 208.46/128.39 | | | | | | | | 208.46/128.39 | | | | | | | End of split 208.46/128.39 | | | | | | | 208.46/128.39 | | | | | | End of split 208.46/128.39 | | | | | | 208.46/128.39 | | | | | End of split 208.46/128.39 | | | | | 208.46/128.39 | | | | End of split 208.46/128.39 | | | | 208.46/128.39 | | | Case 2: 208.46/128.39 | | | | 208.46/128.39 | | | | (305) ($lesseq(all_133_0, 41) & $lesseq(all_133_2, all_86_10) & 208.46/128.39 | | | | $lesseq(all_86_7, all_133_2) & tb2t1(all_133_1) = all_133_0 & 208.46/128.39 | | | | get4(int, all_133_3, all_133_2) = all_133_1 & 208.46/128.39 | | | | in_uni(all_133_1)) | ($lesseq(43, all_133_0) & 208.46/128.39 | | | | $lesseq(all_133_2, all_86_8) & $lesseq(all_86_11, all_133_2) 208.46/128.39 | | | | & tb2t1(all_133_1) = all_133_0 & get4(int, all_133_3, 208.46/128.39 | | | | all_133_2) = all_133_1 & in_uni(all_133_1)) 208.46/128.39 | | | | 208.46/128.39 | | | | BETA: splitting (305) gives: 208.46/128.39 | | | | 208.46/128.39 | | | | Case 1: 208.46/128.39 | | | | | 208.46/128.39 | | | | | (306) $lesseq(all_133_0, 41) & $lesseq(all_133_2, all_86_10) & 208.46/128.39 | | | | | $lesseq(all_86_7, all_133_2) & tb2t1(all_133_1) = all_133_0 & 208.46/128.39 | | | | | get4(int, all_133_3, all_133_2) = all_133_1 & 208.46/128.39 | | | | | in_uni(all_133_1) 208.46/128.39 | | | | | 208.46/128.39 | | | | | ALPHA: (306) implies: 208.46/128.39 | | | | | (307) $lesseq(all_86_7, all_133_2) 208.46/128.39 | | | | | (308) $lesseq(all_133_2, all_86_10) 208.46/128.39 | | | | | (309) $lesseq(all_133_0, 41) 208.46/128.39 | | | | | (310) get4(int, all_133_3, all_133_2) = all_133_1 208.46/128.39 | | | | | (311) tb2t1(all_133_1) = all_133_0 208.46/128.39 | | | | | 208.46/128.39 | | | | | REDUCE: (62), (310) imply: 208.46/128.39 | | | | | (312) get4(int, all_105_2, all_133_2) = all_133_1 208.46/128.39 | | | | | 208.46/128.39 | | | | | REF_CLOSE: (1), (7), (8), (9), (10), (16), (23), (24), (26), (27), 208.46/128.39 | | | | | (32), (35), (36), (37), (42), (43), (44), (48), (50), (55), 208.46/128.39 | | | | | (56), (59), (60), (67), (68), (70), (72), (307), (308), 208.46/128.39 | | | | | (309), (311), (312) are inconsistent by sub-proof #148. 208.46/128.39 | | | | | 208.46/128.39 | | | | Case 2: 208.46/128.39 | | | | | 208.46/128.39 | | | | | (313) $lesseq(43, all_133_0) & $lesseq(all_133_2, all_86_8) & 208.46/128.39 | | | | | $lesseq(all_86_11, all_133_2) & tb2t1(all_133_1) = all_133_0 208.46/128.39 | | | | | & get4(int, all_133_3, all_133_2) = all_133_1 & 208.46/128.39 | | | | | in_uni(all_133_1) 208.46/128.39 | | | | | 208.46/128.39 | | | | | ALPHA: (313) implies: 208.46/128.39 | | | | | (314) $lesseq(all_86_11, all_133_2) 208.46/128.39 | | | | | (315) $lesseq(all_133_2, all_86_8) 208.46/128.39 | | | | | (316) $lesseq(43, all_133_0) 208.46/128.39 | | | | | (317) get4(int, all_133_3, all_133_2) = all_133_1 208.46/128.39 | | | | | (318) tb2t1(all_133_1) = all_133_0 208.46/128.39 | | | | | 208.46/128.39 | | | | | COMBINE_INEQS: (15), (38) imply: 208.46/128.39 | | | | | (319) $lesseq(2, $difference(all_86_13, all_86_11)) 208.46/128.39 | | | | | 208.46/128.39 | | | | | REDUCE: (62), (317) imply: 208.46/128.39 | | | | | (320) get4(int, all_105_2, all_133_2) = all_133_1 208.46/128.39 | | | | | 208.46/128.39 | | | | | REF_CLOSE: (1), (2), (3), (4), (7), (9), (10), (11), (12), (14), (20), 208.46/128.39 | | | | | (22), (23), (24), (25), (27), (30), (32), (33), (35), (36), 208.46/128.39 | | | | | (37), (39), (43), (44), (48), (50), (51), (52), (53), (55), 208.46/128.39 | | | | | (56), (57), (59), (60), (63), (65), (67), (68), (70), (75), 208.46/128.39 | | | | | (78), (314), (315), (316), (318), (319), (320) are 208.46/128.39 | | | | | inconsistent by sub-proof #133. 208.46/128.39 | | | | | 208.46/128.39 | | | | End of split 208.46/128.39 | | | | 208.46/128.39 | | | End of split 208.46/128.39 | | | 208.46/128.39 | | End of split 208.46/128.39 | | 208.46/128.39 | End of split 208.46/128.39 | 208.46/128.39 End of proof 208.46/128.39 208.46/128.39 Sub-proof #133 shows that the following formulas are inconsistent: 208.46/128.39 ---------------------------------------------------------------- 208.46/128.39 (1) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ (tb2t1(v2) 208.46/128.39 = v1) | ~ (tb2t1(v2) = v0)) 208.46/128.39 (2) ! [v0: $int] : ! [v1: $int] : ( ~ ($lesseq(43, v1)) | ~ ($lesseq(v0, 208.46/128.39 all_86_8)) | ~ ($lesseq(all_86_11, v0)) | ~ (get3(all_86_6, v0) = 208.46/128.39 v1)) 208.46/128.39 (3) length1(int, all_103_2) = all_86_13 208.46/128.39 (4) in_map_int_int(all_86_6) 208.46/128.39 (5) elts(int, all_103_4) = all_103_3 208.46/128.39 (6) t2tb(all_86_2) = all_105_1 208.46/128.39 (7) in_ty(int) 208.46/128.39 (8) length1(int, all_103_4) = all_86_13 208.46/128.39 (9) $lesseq(2, all_86_13) 208.46/128.39 (10) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.46/128.39 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 208.46/128.39 (permut2(v0, v5, v6, v3, v4) = v7) | ~ (elts(v0, v2) = v6) | ~ 208.46/128.39 (elts(v0, v1) = v5) | ~ in_ty(v0) | ? [v8: $int] : ? [v9: $int] : 208.46/128.39 ((v9 = v8 & v7 = 0 & $lesseq(v4, v8) & $lesseq(v3, v8) & $lesseq(0, 208.46/128.39 v4) & $lesseq(0, v3) & length1(v0, v2) = v8 & length1(v0, v1) = 208.46/128.39 v8) | ( ~ (v8 = 0) & permut3(v0, v1, v2, v3, v4) = v8))) 208.46/128.39 (11) t2tb(all_86_6) = all_103_1 208.46/128.39 (12) $lesseq(2, $difference(all_86_13, all_86_11)) 208.46/128.39 (13) $lesseq(all_133_2, all_86_8) 208.46/128.39 (14) tb2t1(all_133_1) = all_133_0 208.46/128.40 (15) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.46/128.40 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ (permut3(v6, v5, 208.46/128.40 v4, v3, v2) = v1) | ~ (permut3(v6, v5, v4, v3, v2) = v0)) 208.46/128.40 (16) permut2(int, all_103_1, all_105_3, 0, all_86_13) = 0 208.46/128.40 (17) permut2(int, all_103_3, all_105_3, all_86_11, $sum(all_86_10, 1)) = 0 208.46/128.40 (18) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 208.46/128.40 | ~ (elts(v3, v2) = v1) | ~ (elts(v3, v2) = v0)) 208.46/128.40 (19) length1(int, all_105_4) = all_86_13 208.46/128.40 (20) elts(int, all_105_4) = all_105_3 208.46/128.40 (21) permut2(int, all_103_3, all_103_1, 0, all_86_13) = 0 208.46/128.40 (22) map_eq_sub1(int, all_105_3, all_105_1, 0, all_86_7) = 0 208.46/128.40 (23) get4(int, all_105_2, all_133_2) = all_133_1 208.46/128.40 (24) tb2t(all_105_1) = all_86_2 208.46/128.40 (25) permut2(int, all_103_1, all_105_3, all_86_11, $sum(all_86_8, 1)) = 0 208.46/128.40 (26) elts(int, all_105_2) = all_105_1 208.46/128.40 (27) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.46/128.40 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 208.46/128.40 ($lesseq(1, $difference(v4, v5))) | ~ ($lesseq(v3, v5)) | ~ 208.46/128.40 (permut2(v0, v1, v2, v3, v4) = 0) | ~ (t2tb1(v5) = v6) | ~ (get(v0, 208.46/128.40 int, v2, v6) = v7) | ~ in_ty(v0) | ? [v8: $int] : ? [v9: $int] 208.46/128.40 : ($lesseq(1, $difference(v4, v8)) & $lesseq(v3, v8) & t2tb1(v8) = v9 208.46/128.40 & get(v0, int, v1, v9) = v7 & in_uni(v9) & in_uni(v7))) 208.46/128.40 (28) t2tb2(all_86_1) = all_105_2 208.46/128.40 (29) $lesseq(all_86_11, all_133_2) 208.46/128.40 (30) $lesseq(all_86_7, all_86_10) 208.46/128.40 (31) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.46/128.40 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 208.46/128.40 ($lesseq(1, $difference(v3, v4))) | ~ ($lesseq(v2, v4)) | ~ 208.46/128.40 (permut2(int, v5, v6, v2, v3) = 0) | ~ (t2tb(v1) = v6) | ~ (t2tb(v0) 208.46/128.40 = v5) | ~ (get3(v1, v4) = v7) | ~ in_map_int_int(v0) | ? [v8: 208.46/128.40 $int] : ($lesseq(1, $difference(v3, v8)) & $lesseq(v2, v8) & 208.46/128.40 get3(v0, v8) = v7)) 208.46/128.40 (32) permut2(int, all_105_3, all_105_1, all_86_7, $sum(all_86_10, 1)) = 0 208.46/128.40 (33) in_array_int(all_86_1) 208.46/128.40 (34) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.46/128.40 $int] : ! [v5: $int] : ! [v6: $int] : ( ~ ($lesseq(0, v4)) | ~ 208.46/128.40 ($lesseq(0, v3)) | ~ (permut2(v0, v5, v6, v3, v4) = 0) | ~ (elts(v0, 208.46/128.40 v2) = v6) | ~ (elts(v0, v1) = v5) | ~ in_ty(v0) | ? [v7: $int] 208.46/128.40 : ? [v8: $int] : ((v7 = 0 & permut3(v0, v1, v2, v3, v4) = 0) | 208.46/128.40 (length1(v0, v1) = v7 & ( ~ ($lesseq(v4, v7)) | ~ ($lesseq(v3, v7)) 208.46/128.40 | ( ~ (v8 = v7) & length1(v0, v2) = v8))))) 208.46/128.40 (35) $lesseq(1, $difference(all_86_7, all_86_8)) 208.46/128.40 (36) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.46/128.40 $int] : ! [v5: $int] : ! [v6: $int] : ( ~ ($lesseq(1, 208.46/128.40 $difference(v4, v5))) | ~ ($lesseq(v3, v5)) | ~ (map_eq_sub1(v0, 208.46/128.40 v1, v2, v3, v4) = 0) | ~ (t2tb1(v5) = v6) | ~ in_ty(v0) | ? 208.46/128.40 [v7: $int] : (get(v0, int, v2, v6) = v7 & get(v0, int, v1, v6) = v7 & 208.46/128.40 in_uni(v7))) 208.46/128.40 (37) $lesseq(1, $difference(all_86_13, all_86_10)) 208.46/128.40 (38) in_map_int_int(all_86_4) 208.46/128.40 (39) $lesseq(0, all_86_11) 208.46/128.40 (40) elts(int, all_103_2) = all_103_1 208.46/128.40 (41) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ( ~ 208.46/128.40 (t2tb2(v0) = v2) | ~ (get4(int, v2, v1) = v3) | ~ in_array_int(v0) | 208.46/128.40 ? [v4: $int] : ? [v5: $int] : ? [v6: $int] : (tb2t(v4) = v5 & 208.46/128.40 tb2t1(v3) = v6 & get3(v5, v1) = v6 & elts(int, v2) = v4 & 208.46/128.40 in_map_int_int(v5) & in_uni(v4))) 208.46/128.40 (42) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ (tb2t(v2) 208.46/128.40 = v1) | ~ (tb2t(v2) = v0)) 208.46/128.40 (43) $lesseq(43, all_133_0) 208.46/128.40 (44) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.46/128.40 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 208.46/128.40 ($lesseq(1, $difference(v3, v6))) | ~ ($lesseq(v2, v6)) | ~ 208.46/128.40 (map_eq_sub1(int, v4, v5, v2, v3) = 0) | ~ (t2tb(v1) = v5) | ~ 208.46/128.40 (t2tb(v0) = v4) | ~ (get3(v1, v6) = v7) | ~ in_map_int_int(v0) | 208.46/128.40 get3(v0, v6) = v7) 208.46/128.40 (45) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 208.46/128.40 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 208.46/128.40 (46) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ( ~ 208.46/128.40 (get4(v0, v1, v2) = v3) | ~ in_ty(v0) | ? [v4: $int] : ? [v5: $int] 208.46/128.40 : (elts(v0, v1) = v4 & t2tb1(v2) = v5 & get(v0, int, v4, v5) = v3 & 208.46/128.40 in_uni(v5) & in_uni(v4) & in_uni(v3))) 208.46/128.40 (47) $lesseq(1, all_86_10) 208.46/128.40 (48) t2tb(all_86_4) = all_105_3 208.46/128.40 208.46/128.40 Begin of proof 208.46/128.40 | 208.46/128.40 | GROUND_INST: instantiating (10) with int, all_103_2, all_105_4, 0, all_86_13, 208.46/128.40 | all_103_1, all_105_3, 0, simplifying with (7), (16), (20), (40) 208.46/128.40 | gives: 208.46/128.40 | (49) ? [v0: $int] : ? [v1: $int] : ((v1 = v0 & $lesseq(all_86_13, v0) & 208.46/128.40 | $lesseq(0, v0) & $lesseq(0, all_86_13) & length1(int, all_105_4) = 208.46/128.40 | v0 & length1(int, all_103_2) = v0) | ( ~ (v0 = 0) & permut3(int, 208.46/128.40 | all_103_2, all_105_4, 0, all_86_13) = v0)) 208.46/128.40 | 208.46/128.40 | GROUND_INST: instantiating (34) with int, all_103_2, all_105_4, 0, all_86_13, 208.46/128.40 | all_103_1, all_105_3, simplifying with (7), (16), (20), (40) 208.46/128.40 | gives: 208.46/128.40 | (50) ~ ($lesseq(0, all_86_13)) | ? [v0: $int] : ? [v1: $int] : ((v0 = 0 208.46/128.40 | & permut3(int, all_103_2, all_105_4, 0, all_86_13) = 0) | 208.46/128.40 | (length1(int, all_103_2) = v0 & ( ~ ($lesseq(all_86_13, v0)) | ~ 208.46/128.40 | ($lesseq(0, v0)) | ( ~ (v1 = v0) & length1(int, all_105_4) = 208.46/128.40 | v1)))) 208.46/128.40 | 208.46/128.40 | GROUND_INST: instantiating (10) with int, all_103_4, all_105_4, all_86_11, 208.46/128.40 | $sum(all_86_10, 1), all_103_3, all_105_3, 0, simplifying with 208.46/128.40 | (5), (7), (17), (20) gives: 208.46/128.40 | (51) ? [v0: $int] : ? [v1: $int] : ((v1 = v0 & $lesseq(1, $difference(v0, 208.46/128.40 | all_86_10)) & $lesseq(all_86_11, v0) & $lesseq(-1, all_86_10) 208.46/128.40 | & $lesseq(0, all_86_11) & length1(int, all_105_4) = v0 & 208.46/128.40 | length1(int, all_103_4) = v0) | ( ~ (v0 = 0) & permut3(int, 208.46/128.40 | all_103_4, all_105_4, all_86_11, $sum(all_86_10, 1)) = v0)) 208.46/128.40 | 208.46/128.40 | GROUND_INST: instantiating (34) with int, all_103_4, all_105_4, all_86_11, 208.46/128.40 | $sum(all_86_10, 1), all_103_3, all_105_3, simplifying with (5), 208.46/128.40 | (7), (17), (20) gives: 208.46/128.40 | (52) ~ ($lesseq(-1, all_86_10)) | ~ ($lesseq(0, all_86_11)) | ? [v0: 208.46/128.40 | $int] : ? [v1: $int] : ((v0 = 0 & permut3(int, all_103_4, 208.46/128.40 | all_105_4, all_86_11, $sum(all_86_10, 1)) = 0) | (length1(int, 208.46/128.40 | all_103_4) = v0 & ( ~ ($lesseq(1, $difference(v0, all_86_10))) | 208.46/128.40 | ~ ($lesseq(all_86_11, v0)) | ( ~ (v1 = v0) & length1(int, 208.46/128.40 | all_105_4) = v1)))) 208.46/128.40 | 208.46/128.40 | GROUND_INST: instantiating (10) with int, all_103_4, all_103_2, 0, all_86_13, 208.46/128.40 | all_103_3, all_103_1, 0, simplifying with (5), (7), (21), (40) 208.46/128.40 | gives: 208.46/128.40 | (53) ? [v0: $int] : ? [v1: $int] : ((v1 = v0 & $lesseq(all_86_13, v0) & 208.46/128.40 | $lesseq(0, v0) & $lesseq(0, all_86_13) & length1(int, all_103_2) = 208.46/128.40 | v0 & length1(int, all_103_4) = v0) | ( ~ (v0 = 0) & permut3(int, 208.46/128.40 | all_103_4, all_103_2, 0, all_86_13) = v0)) 208.46/128.40 | 208.46/128.40 | GROUND_INST: instantiating (34) with int, all_103_4, all_103_2, 0, all_86_13, 208.46/128.40 | all_103_3, all_103_1, simplifying with (5), (7), (21), (40) 208.46/128.40 | gives: 208.46/128.40 | (54) ~ ($lesseq(0, all_86_13)) | ? [v0: $int] : ? [v1: $int] : ((v0 = 0 208.46/128.40 | & permut3(int, all_103_4, all_103_2, 0, all_86_13) = 0) | 208.46/128.40 | (length1(int, all_103_4) = v0 & ( ~ ($lesseq(all_86_13, v0)) | ~ 208.46/128.40 | ($lesseq(0, v0)) | ( ~ (v1 = v0) & length1(int, all_103_2) = 208.46/128.40 | v1)))) 208.46/128.40 | 208.46/128.40 | GROUND_INST: instantiating (41) with all_86_1, all_133_2, all_105_2, 208.46/128.40 | all_133_1, simplifying with (23), (28), (33) gives: 208.46/128.40 | (55) ? [v0: $int] : ? [v1: $int] : ? [v2: $int] : (tb2t(v0) = v1 & 208.46/128.40 | tb2t1(all_133_1) = v2 & get3(v1, all_133_2) = v2 & elts(int, 208.46/128.40 | all_105_2) = v0 & in_map_int_int(v1) & in_uni(v0)) 208.46/128.40 | 208.46/128.40 | GROUND_INST: instantiating (46) with int, all_105_2, all_133_2, all_133_1, 208.46/128.40 | simplifying with (7), (23) gives: 208.46/128.40 | (56) ? [v0: $int] : ? [v1: $int] : (elts(int, all_105_2) = v0 & 208.46/128.40 | t2tb1(all_133_2) = v1 & get(int, int, v0, v1) = all_133_1 & 208.46/128.40 | in_uni(v1) & in_uni(v0) & in_uni(all_133_1)) 208.46/128.40 | 208.46/128.40 | DELTA: instantiating (55) with fresh symbols all_697_0, all_697_1, all_697_2 208.46/128.40 | gives: 208.46/128.40 | (57) tb2t(all_697_2) = all_697_1 & tb2t1(all_133_1) = all_697_0 & 208.46/128.40 | get3(all_697_1, all_133_2) = all_697_0 & elts(int, all_105_2) = 208.46/128.40 | all_697_2 & in_map_int_int(all_697_1) & in_uni(all_697_2) 208.46/128.40 | 208.46/128.40 | ALPHA: (57) implies: 208.46/128.40 | (58) elts(int, all_105_2) = all_697_2 208.46/128.40 | (59) get3(all_697_1, all_133_2) = all_697_0 208.46/128.40 | (60) tb2t1(all_133_1) = all_697_0 208.46/128.40 | (61) tb2t(all_697_2) = all_697_1 208.46/128.40 | 208.46/128.40 | DELTA: instantiating (53) with fresh symbols all_703_0, all_703_1 gives: 208.46/128.40 | (62) (all_703_0 = all_703_1 & $lesseq(all_86_13, all_703_1) & $lesseq(0, 208.46/128.40 | all_703_1) & $lesseq(0, all_86_13) & length1(int, all_103_2) = 208.46/128.40 | all_703_1 & length1(int, all_103_4) = all_703_1) | ( ~ (all_703_1 = 208.46/128.40 | 0) & permut3(int, all_103_4, all_103_2, 0, all_86_13) = all_703_1) 208.46/128.40 | 208.46/128.40 | DELTA: instantiating (51) with fresh symbols all_708_0, all_708_1 gives: 208.46/128.40 | (63) (all_708_0 = all_708_1 & $lesseq(1, $difference(all_708_1, all_86_10)) 208.46/128.40 | & $lesseq(all_86_11, all_708_1) & $lesseq(-1, all_86_10) & 208.46/128.40 | $lesseq(0, all_86_11) & length1(int, all_105_4) = all_708_1 & 208.46/128.40 | length1(int, all_103_4) = all_708_1) | ( ~ (all_708_1 = 0) & 208.46/128.40 | permut3(int, all_103_4, all_105_4, all_86_11, $sum(all_86_10, 1)) = 208.46/128.40 | all_708_1) 208.46/128.40 | 208.46/128.40 | DELTA: instantiating (49) with fresh symbols all_709_0, all_709_1 gives: 208.46/128.40 | (64) (all_709_0 = all_709_1 & $lesseq(all_86_13, all_709_1) & $lesseq(0, 208.46/128.40 | all_709_1) & $lesseq(0, all_86_13) & length1(int, all_105_4) = 208.46/128.40 | all_709_1 & length1(int, all_103_2) = all_709_1) | ( ~ (all_709_1 = 208.46/128.40 | 0) & permut3(int, all_103_2, all_105_4, 0, all_86_13) = all_709_1) 208.46/128.40 | 208.46/128.40 | DELTA: instantiating (56) with fresh symbols all_710_0, all_710_1 gives: 208.46/128.40 | (65) elts(int, all_105_2) = all_710_1 & t2tb1(all_133_2) = all_710_0 & 208.46/128.40 | get(int, int, all_710_1, all_710_0) = all_133_1 & in_uni(all_710_0) & 208.46/128.40 | in_uni(all_710_1) & in_uni(all_133_1) 208.46/128.40 | 208.46/128.40 | ALPHA: (65) implies: 208.46/128.40 | (66) get(int, int, all_710_1, all_710_0) = all_133_1 208.46/128.40 | (67) t2tb1(all_133_2) = all_710_0 208.46/128.40 | (68) elts(int, all_105_2) = all_710_1 208.46/128.40 | 208.46/128.40 | BETA: splitting (50) gives: 208.46/128.40 | 208.46/128.40 | Case 1: 208.46/128.40 | | 208.46/128.40 | | (69) $lesseq(all_86_13, -1) 208.46/128.40 | | 208.46/128.40 | | COMBINE_INEQS: (9), (69) imply: 208.46/128.40 | | (70) $lesseq(0, -1) 208.46/128.40 | | 208.46/128.40 | | CLOSE: (70) is inconsistent. 208.46/128.40 | | 208.46/128.40 | Case 2: 208.46/128.40 | | 208.46/128.40 | | (71) ? [v0: $int] : ? [v1: $int] : ((v0 = 0 & permut3(int, all_103_2, 208.46/128.40 | | all_105_4, 0, all_86_13) = 0) | (length1(int, all_103_2) = v0 208.46/128.40 | | & ( ~ ($lesseq(all_86_13, v0)) | ~ ($lesseq(0, v0)) | ( ~ (v1 = 208.46/128.40 | | v0) & length1(int, all_105_4) = v1)))) 208.46/128.40 | | 208.46/128.40 | | DELTA: instantiating (71) with fresh symbols all_721_0, all_721_1 gives: 208.46/128.40 | | (72) (all_721_1 = 0 & permut3(int, all_103_2, all_105_4, 0, all_86_13) = 208.46/128.40 | | 0) | (length1(int, all_103_2) = all_721_1 & ( ~ 208.46/128.40 | | ($lesseq(all_86_13, all_721_1)) | ~ ($lesseq(0, all_721_1)) | ( 208.46/128.40 | | ~ (all_721_0 = all_721_1) & length1(int, all_105_4) = 208.46/128.40 | | all_721_0))) 208.46/128.40 | | 208.46/128.40 | | BETA: splitting (72) gives: 208.46/128.40 | | 208.46/128.40 | | Case 1: 208.46/128.40 | | | 208.46/128.40 | | | (73) all_721_1 = 0 & permut3(int, all_103_2, all_105_4, 0, all_86_13) = 208.46/128.40 | | | 0 208.46/128.40 | | | 208.46/128.40 | | | ALPHA: (73) implies: 208.46/128.40 | | | (74) permut3(int, all_103_2, all_105_4, 0, all_86_13) = 0 208.46/128.40 | | | 208.46/128.40 | | | BETA: splitting (52) gives: 208.46/128.40 | | | 208.46/128.40 | | | Case 1: 208.46/128.40 | | | | 208.46/128.40 | | | | (75) $lesseq(all_86_11, -1) 208.46/128.40 | | | | 208.46/128.40 | | | | COMBINE_INEQS: (39), (75) imply: 208.46/128.40 | | | | (76) $lesseq(0, -1) 208.46/128.40 | | | | 208.46/128.40 | | | | CLOSE: (76) is inconsistent. 208.46/128.40 | | | | 208.46/128.40 | | | Case 2: 208.46/128.40 | | | | 208.46/128.40 | | | | (77) ~ ($lesseq(-1, all_86_10)) | ? [v0: $int] : ? [v1: $int] : 208.46/128.40 | | | | ((v0 = 0 & permut3(int, all_103_4, all_105_4, all_86_11, 208.46/128.40 | | | | $sum(all_86_10, 1)) = 0) | (length1(int, all_103_4) = v0 & 208.46/128.40 | | | | ( ~ ($lesseq(1, $difference(v0, all_86_10))) | ~ 208.46/128.40 | | | | ($lesseq(all_86_11, v0)) | ( ~ (v1 = v0) & length1(int, 208.46/128.40 | | | | all_105_4) = v1)))) 208.46/128.40 | | | | 208.46/128.40 | | | | BETA: splitting (77) gives: 208.46/128.40 | | | | 208.46/128.40 | | | | Case 1: 208.46/128.40 | | | | | 208.46/128.40 | | | | | (78) $lesseq(all_86_10, -2) 208.46/128.40 | | | | | 208.46/128.40 | | | | | COMBINE_INEQS: (47), (78) imply: 208.46/128.40 | | | | | (79) $lesseq(0, -1) 208.46/128.40 | | | | | 208.46/128.40 | | | | | CLOSE: (79) is inconsistent. 208.46/128.40 | | | | | 208.46/128.40 | | | | Case 2: 208.46/128.40 | | | | | 208.46/128.40 | | | | | (80) ? [v0: $int] : ? [v1: $int] : ((v0 = 0 & permut3(int, 208.46/128.40 | | | | | all_103_4, all_105_4, all_86_11, $sum(all_86_10, 1)) = 208.46/128.40 | | | | | 0) | (length1(int, all_103_4) = v0 & ( ~ ($lesseq(1, 208.46/128.40 | | | | | $difference(v0, all_86_10))) | ~ 208.46/128.40 | | | | | ($lesseq(all_86_11, v0)) | ( ~ (v1 = v0) & length1(int, 208.46/128.40 | | | | | all_105_4) = v1)))) 208.46/128.40 | | | | | 208.46/128.40 | | | | | DELTA: instantiating (80) with fresh symbols all_747_0, all_747_1 208.46/128.40 | | | | | gives: 208.46/128.40 | | | | | (81) (all_747_1 = 0 & permut3(int, all_103_4, all_105_4, all_86_11, 208.46/128.40 | | | | | $sum(all_86_10, 1)) = 0) | (length1(int, all_103_4) = 208.46/128.40 | | | | | all_747_1 & ( ~ ($lesseq(1, $difference(all_747_1, 208.46/128.40 | | | | | all_86_10))) | ~ ($lesseq(all_86_11, all_747_1)) | 208.46/128.40 | | | | | ( ~ (all_747_0 = all_747_1) & length1(int, all_105_4) = 208.46/128.40 | | | | | all_747_0))) 208.46/128.40 | | | | | 208.46/128.40 | | | | | BETA: splitting (64) gives: 208.46/128.40 | | | | | 208.46/128.40 | | | | | Case 1: 208.46/128.40 | | | | | | 208.46/128.40 | | | | | | (82) all_709_0 = all_709_1 & $lesseq(all_86_13, all_709_1) & 208.46/128.40 | | | | | | $lesseq(0, all_709_1) & $lesseq(0, all_86_13) & length1(int, 208.46/128.40 | | | | | | all_105_4) = all_709_1 & length1(int, all_103_2) = 208.46/128.40 | | | | | | all_709_1 208.46/128.40 | | | | | | 208.46/128.40 | | | | | | ALPHA: (82) implies: 208.46/128.40 | | | | | | (83) length1(int, all_103_2) = all_709_1 208.46/128.40 | | | | | | (84) length1(int, all_105_4) = all_709_1 208.46/128.40 | | | | | | 208.46/128.40 | | | | | | BETA: splitting (54) gives: 208.46/128.40 | | | | | | 208.46/128.40 | | | | | | Case 1: 208.46/128.40 | | | | | | | 208.46/128.40 | | | | | | | (85) $lesseq(all_86_13, -1) 208.46/128.40 | | | | | | | 208.46/128.40 | | | | | | | COMBINE_INEQS: (9), (85) imply: 208.46/128.40 | | | | | | | (86) $lesseq(0, -1) 208.46/128.40 | | | | | | | 208.46/128.40 | | | | | | | CLOSE: (86) is inconsistent. 208.46/128.40 | | | | | | | 208.46/128.40 | | | | | | Case 2: 208.46/128.40 | | | | | | | 208.46/128.40 | | | | | | | (87) ? [v0: $int] : ? [v1: $int] : ((v0 = 0 & permut3(int, 208.46/128.40 | | | | | | | all_103_4, all_103_2, 0, all_86_13) = 0) | 208.46/128.40 | | | | | | | (length1(int, all_103_4) = v0 & ( ~ ($lesseq(all_86_13, 208.46/128.40 | | | | | | | v0)) | ~ ($lesseq(0, v0)) | ( ~ (v1 = v0) & 208.46/128.40 | | | | | | | length1(int, all_103_2) = v1)))) 208.46/128.40 | | | | | | | 208.46/128.40 | | | | | | | DELTA: instantiating (87) with fresh symbols all_759_0, all_759_1 208.46/128.40 | | | | | | | gives: 208.46/128.40 | | | | | | | (88) (all_759_1 = 0 & permut3(int, all_103_4, all_103_2, 0, 208.46/128.40 | | | | | | | all_86_13) = 0) | (length1(int, all_103_4) = all_759_1 208.46/128.40 | | | | | | | & ( ~ ($lesseq(all_86_13, all_759_1)) | ~ ($lesseq(0, 208.46/128.40 | | | | | | | all_759_1)) | ( ~ (all_759_0 = all_759_1) & 208.46/128.40 | | | | | | | length1(int, all_103_2) = all_759_0))) 208.46/128.40 | | | | | | | 208.46/128.40 | | | | | | | GROUND_INST: instantiating (1) with all_133_0, all_697_0, 208.46/128.40 | | | | | | | all_133_1, simplifying with (14), (60) gives: 208.46/128.40 | | | | | | | (89) all_697_0 = all_133_0 208.46/128.40 | | | | | | | 208.46/128.40 | | | | | | | GROUND_INST: instantiating (45) with all_86_13, all_709_1, 208.46/128.40 | | | | | | | all_103_2, int, simplifying with (3), (83) gives: 208.46/128.40 | | | | | | | (90) all_709_1 = all_86_13 208.46/128.40 | | | | | | | 208.46/128.40 | | | | | | | GROUND_INST: instantiating (18) with all_105_1, all_710_1, 208.46/128.40 | | | | | | | all_105_2, int, simplifying with (26), (68) gives: 208.46/128.40 | | | | | | | (91) all_710_1 = all_105_1 208.46/128.40 | | | | | | | 208.46/128.40 | | | | | | | GROUND_INST: instantiating (18) with all_710_1, all_697_2, 208.46/128.40 | | | | | | | all_105_2, int, simplifying with (58), (68) gives: 208.46/128.40 | | | | | | | (92) all_710_1 = all_697_2 208.46/128.40 | | | | | | | 208.46/128.40 | | | | | | | COMBINE_EQS: (91), (92) imply: 208.46/128.40 | | | | | | | (93) all_697_2 = all_105_1 208.46/128.40 | | | | | | | 208.46/128.40 | | | | | | | REDUCE: (61), (93) imply: 208.46/128.40 | | | | | | | (94) tb2t(all_105_1) = all_697_1 208.46/128.40 | | | | | | | 208.46/128.40 | | | | | | | REDUCE: (59), (89) imply: 208.46/128.40 | | | | | | | (95) get3(all_697_1, all_133_2) = all_133_0 208.46/128.40 | | | | | | | 208.46/128.40 | | | | | | | REDUCE: (66), (91) imply: 208.46/128.41 | | | | | | | (96) get(int, int, all_105_1, all_710_0) = all_133_1 208.46/128.41 | | | | | | | 208.46/128.41 | | | | | | | BETA: splitting (81) gives: 208.46/128.41 | | | | | | | 208.46/128.41 | | | | | | | Case 1: 208.46/128.41 | | | | | | | | 208.46/128.41 | | | | | | | | (97) all_747_1 = 0 & permut3(int, all_103_4, all_105_4, 208.46/128.41 | | | | | | | | all_86_11, $sum(all_86_10, 1)) = 0 208.46/128.41 | | | | | | | | 208.46/128.41 | | | | | | | | ALPHA: (97) implies: 208.46/128.41 | | | | | | | | (98) permut3(int, all_103_4, all_105_4, all_86_11, 208.46/128.41 | | | | | | | | $sum(all_86_10, 1)) = 0 208.46/128.41 | | | | | | | | 208.46/128.41 | | | | | | | | REF_CLOSE: (2), (4), (6), (7), (11), (13), (15), (22), (24), 208.46/128.41 | | | | | | | | (25), (27), (29), (30), (31), (32), (35), (36), (38), 208.46/128.41 | | | | | | | | (42), (43), (44), (48), (63), (67), (94), (95), (96), 208.46/128.41 | | | | | | | | (98) are inconsistent by sub-proof #136. 208.46/128.41 | | | | | | | | 208.46/128.41 | | | | | | | Case 2: 208.46/128.41 | | | | | | | | 208.46/128.41 | | | | | | | | (99) length1(int, all_103_4) = all_747_1 & ( ~ ($lesseq(1, 208.46/128.41 | | | | | | | | $difference(all_747_1, all_86_10))) | ~ 208.46/128.41 | | | | | | | | ($lesseq(all_86_11, all_747_1)) | ( ~ (all_747_0 = 208.46/128.41 | | | | | | | | all_747_1) & length1(int, all_105_4) = all_747_0)) 208.46/128.41 | | | | | | | | 208.46/128.41 | | | | | | | | ALPHA: (99) implies: 208.46/128.41 | | | | | | | | (100) length1(int, all_103_4) = all_747_1 208.46/128.41 | | | | | | | | (101) ~ ($lesseq(1, $difference(all_747_1, all_86_10))) | ~ 208.46/128.41 | | | | | | | | ($lesseq(all_86_11, all_747_1)) | ( ~ (all_747_0 = 208.46/128.41 | | | | | | | | all_747_1) & length1(int, all_105_4) = all_747_0) 208.46/128.41 | | | | | | | | 208.46/128.41 | | | | | | | | BETA: splitting (88) gives: 208.46/128.41 | | | | | | | | 208.46/128.41 | | | | | | | | Case 1: 208.46/128.41 | | | | | | | | | 208.46/128.41 | | | | | | | | | (102) all_759_1 = 0 & permut3(int, all_103_4, all_103_2, 0, 208.46/128.41 | | | | | | | | | all_86_13) = 0 208.46/128.41 | | | | | | | | | 208.46/128.41 | | | | | | | | | ALPHA: (102) implies: 208.46/128.41 | | | | | | | | | (103) permut3(int, all_103_4, all_103_2, 0, all_86_13) = 0 208.46/128.41 | | | | | | | | | 208.46/128.41 | | | | | | | | | BETA: splitting (62) gives: 208.46/128.41 | | | | | | | | | 208.46/128.41 | | | | | | | | | Case 1: 208.46/128.41 | | | | | | | | | | 208.46/128.41 | | | | | | | | | | (104) all_703_0 = all_703_1 & $lesseq(all_86_13, 208.46/128.41 | | | | | | | | | | all_703_1) & $lesseq(0, all_703_1) & $lesseq(0, 208.46/128.41 | | | | | | | | | | all_86_13) & length1(int, all_103_2) = all_703_1 208.46/128.41 | | | | | | | | | | & length1(int, all_103_4) = all_703_1 208.46/128.41 | | | | | | | | | | 208.46/128.41 | | | | | | | | | | ALPHA: (104) implies: 208.46/128.41 | | | | | | | | | | (105) length1(int, all_103_4) = all_703_1 208.46/128.41 | | | | | | | | | | 208.46/128.41 | | | | | | | | | | GROUND_INST: instantiating (45) with all_86_13, all_747_1, 208.46/128.41 | | | | | | | | | | all_103_4, int, simplifying with (8), (100) gives: 208.46/128.41 | | | | | | | | | | (106) all_747_1 = all_86_13 208.46/128.41 | | | | | | | | | | 208.46/128.41 | | | | | | | | | | GROUND_INST: instantiating (45) with all_747_1, all_703_1, 208.46/128.41 | | | | | | | | | | all_103_4, int, simplifying with (100), (105) 208.46/128.41 | | | | | | | | | | gives: 208.46/128.41 | | | | | | | | | | (107) all_747_1 = all_703_1 208.46/128.41 | | | | | | | | | | 208.46/128.41 | | | | | | | | | | COMBINE_EQS: (106), (107) imply: 208.46/128.41 | | | | | | | | | | (108) all_703_1 = all_86_13 208.46/128.41 | | | | | | | | | | 208.46/128.41 | | | | | | | | | | BETA: splitting (101) gives: 208.46/128.41 | | | | | | | | | | 208.46/128.41 | | | | | | | | | | Case 1: 208.46/128.41 | | | | | | | | | | | 208.46/128.41 | | | | | | | | | | | (109) $lesseq(1, $difference(all_86_11, all_747_1)) 208.46/128.41 | | | | | | | | | | | 208.46/128.41 | | | | | | | | | | | REF_CLOSE: (13), (29), (30), (35), (37), (106), (109) are 208.46/128.41 | | | | | | | | | | | inconsistent by sub-proof #135. 208.46/128.41 | | | | | | | | | | | 208.46/128.41 | | | | | | | | | | Case 2: 208.46/128.41 | | | | | | | | | | | 208.46/128.41 | | | | | | | | | | | (110) ~ ($lesseq(1, $difference(all_747_1, all_86_10))) 208.46/128.41 | | | | | | | | | | | | ( ~ (all_747_0 = all_747_1) & length1(int, 208.46/128.41 | | | | | | | | | | | all_105_4) = all_747_0) 208.46/128.41 | | | | | | | | | | | 208.46/128.41 | | | | | | | | | | | REF_CLOSE: (19), (37), (45), (106), (110) are inconsistent by 208.46/128.41 | | | | | | | | | | | sub-proof #134. 208.46/128.41 | | | | | | | | | | | 208.46/128.41 | | | | | | | | | | End of split 208.46/128.41 | | | | | | | | | | 208.46/128.41 | | | | | | | | | Case 2: 208.46/128.41 | | | | | | | | | | 208.46/128.41 | | | | | | | | | | (111) ~ (all_703_1 = 0) & permut3(int, all_103_4, 208.46/128.41 | | | | | | | | | | all_103_2, 0, all_86_13) = all_703_1 208.46/128.41 | | | | | | | | | | 208.46/128.41 | | | | | | | | | | ALPHA: (111) implies: 208.46/128.41 | | | | | | | | | | (112) ~ (all_703_1 = 0) 208.46/128.41 | | | | | | | | | | (113) permut3(int, all_103_4, all_103_2, 0, all_86_13) = 208.46/128.41 | | | | | | | | | | all_703_1 208.46/128.41 | | | | | | | | | | 208.46/128.41 | | | | | | | | | | GROUND_INST: instantiating (15) with 0, all_703_1, all_86_13, 208.46/128.41 | | | | | | | | | | 0, all_103_2, all_103_4, int, simplifying with 208.46/128.41 | | | | | | | | | | (103), (113) gives: 208.46/128.41 | | | | | | | | | | (114) all_703_1 = 0 208.46/128.41 | | | | | | | | | | 208.46/128.41 | | | | | | | | | | REDUCE: (112), (114) imply: 208.46/128.41 | | | | | | | | | | (115) ~ (0 = 0) 208.46/128.41 | | | | | | | | | | 208.46/128.41 | | | | | | | | | | CLOSE: (115) is inconsistent. 208.46/128.41 | | | | | | | | | | 208.46/128.41 | | | | | | | | | End of split 208.46/128.41 | | | | | | | | | 208.46/128.41 | | | | | | | | Case 2: 208.46/128.41 | | | | | | | | | 208.46/128.41 | | | | | | | | | (116) length1(int, all_103_4) = all_759_1 & ( ~ 208.46/128.41 | | | | | | | | | ($lesseq(all_86_13, all_759_1)) | ~ ($lesseq(0, 208.46/128.41 | | | | | | | | | all_759_1)) | ( ~ (all_759_0 = all_759_1) & 208.46/128.41 | | | | | | | | | length1(int, all_103_2) = all_759_0)) 208.46/128.41 | | | | | | | | | 208.46/128.41 | | | | | | | | | ALPHA: (116) implies: 208.46/128.41 | | | | | | | | | (117) length1(int, all_103_4) = all_759_1 208.46/128.41 | | | | | | | | | 208.46/128.41 | | | | | | | | | GROUND_INST: instantiating (45) with all_86_13, all_759_1, 208.46/128.41 | | | | | | | | | all_103_4, int, simplifying with (8), (117) gives: 208.46/128.41 | | | | | | | | | (118) all_759_1 = all_86_13 208.46/128.41 | | | | | | | | | 208.46/128.41 | | | | | | | | | GROUND_INST: instantiating (45) with all_759_1, all_747_1, 208.46/128.41 | | | | | | | | | all_103_4, int, simplifying with (100), (117) 208.46/128.41 | | | | | | | | | gives: 208.46/128.41 | | | | | | | | | (119) all_759_1 = all_747_1 208.46/128.41 | | | | | | | | | 208.46/128.41 | | | | | | | | | COMBINE_EQS: (118), (119) imply: 208.46/128.41 | | | | | | | | | (120) all_747_1 = all_86_13 208.46/128.41 | | | | | | | | | 208.46/128.41 | | | | | | | | | BETA: splitting (101) gives: 208.46/128.41 | | | | | | | | | 208.46/128.41 | | | | | | | | | Case 1: 208.46/128.41 | | | | | | | | | | 208.46/128.41 | | | | | | | | | | (121) $lesseq(1, $difference(all_86_11, all_747_1)) 208.46/128.41 | | | | | | | | | | 208.46/128.41 | | | | | | | | | | REF_CLOSE: (13), (29), (30), (35), (37), (120), (121) are 208.46/128.41 | | | | | | | | | | inconsistent by sub-proof #135. 208.46/128.41 | | | | | | | | | | 208.46/128.41 | | | | | | | | | Case 2: 208.46/128.41 | | | | | | | | | | 208.46/128.41 | | | | | | | | | | (122) ~ ($lesseq(1, $difference(all_747_1, all_86_10))) 208.46/128.41 | | | | | | | | | | | ( ~ (all_747_0 = all_747_1) & length1(int, 208.46/128.41 | | | | | | | | | | all_105_4) = all_747_0) 208.46/128.41 | | | | | | | | | | 208.46/128.41 | | | | | | | | | | REF_CLOSE: (19), (37), (45), (120), (122) are inconsistent by 208.46/128.41 | | | | | | | | | | sub-proof #134. 208.46/128.41 | | | | | | | | | | 208.46/128.41 | | | | | | | | | End of split 208.46/128.41 | | | | | | | | | 208.46/128.41 | | | | | | | | End of split 208.46/128.41 | | | | | | | | 208.46/128.41 | | | | | | | End of split 208.46/128.41 | | | | | | | 208.46/128.41 | | | | | | End of split 208.46/128.41 | | | | | | 208.46/128.41 | | | | | Case 2: 208.46/128.41 | | | | | | 208.46/128.41 | | | | | | (123) ~ (all_709_1 = 0) & permut3(int, all_103_2, all_105_4, 0, 208.46/128.41 | | | | | | all_86_13) = all_709_1 208.46/128.41 | | | | | | 208.46/128.41 | | | | | | ALPHA: (123) implies: 208.46/128.41 | | | | | | (124) ~ (all_709_1 = 0) 208.46/128.41 | | | | | | (125) permut3(int, all_103_2, all_105_4, 0, all_86_13) = 208.46/128.41 | | | | | | all_709_1 208.46/128.41 | | | | | | 208.46/128.41 | | | | | | GROUND_INST: instantiating (15) with 0, all_709_1, all_86_13, 0, 208.46/128.41 | | | | | | all_105_4, all_103_2, int, simplifying with (74), (125) 208.46/128.41 | | | | | | gives: 208.46/128.41 | | | | | | (126) all_709_1 = 0 208.46/128.41 | | | | | | 208.46/128.41 | | | | | | REDUCE: (124), (126) imply: 208.46/128.41 | | | | | | (127) ~ (0 = 0) 208.46/128.41 | | | | | | 208.46/128.41 | | | | | | CLOSE: (127) is inconsistent. 208.46/128.41 | | | | | | 208.46/128.41 | | | | | End of split 208.46/128.41 | | | | | 208.46/128.41 | | | | End of split 208.46/128.41 | | | | 208.46/128.41 | | | End of split 208.46/128.41 | | | 208.46/128.41 | | Case 2: 208.46/128.41 | | | 208.46/128.41 | | | (128) length1(int, all_103_2) = all_721_1 & ( ~ ($lesseq(all_86_13, 208.46/128.41 | | | all_721_1)) | ~ ($lesseq(0, all_721_1)) | ( ~ (all_721_0 = 208.46/128.41 | | | all_721_1) & length1(int, all_105_4) = all_721_0)) 208.46/128.41 | | | 208.46/128.41 | | | ALPHA: (128) implies: 208.46/128.41 | | | (129) length1(int, all_103_2) = all_721_1 208.46/128.41 | | | (130) ~ ($lesseq(all_86_13, all_721_1)) | ~ ($lesseq(0, all_721_1)) | 208.46/128.41 | | | ( ~ (all_721_0 = all_721_1) & length1(int, all_105_4) = 208.46/128.41 | | | all_721_0) 208.46/128.41 | | | 208.46/128.41 | | | BETA: splitting (52) gives: 208.46/128.41 | | | 208.46/128.41 | | | Case 1: 208.46/128.41 | | | | 208.46/128.41 | | | | (131) $lesseq(all_86_11, -1) 208.46/128.41 | | | | 208.46/128.41 | | | | COMBINE_INEQS: (39), (131) imply: 208.46/128.41 | | | | (132) $lesseq(0, -1) 208.46/128.41 | | | | 208.46/128.41 | | | | CLOSE: (132) is inconsistent. 208.46/128.41 | | | | 208.46/128.41 | | | Case 2: 208.46/128.41 | | | | 208.46/128.41 | | | | (133) ~ ($lesseq(-1, all_86_10)) | ? [v0: $int] : ? [v1: $int] : 208.46/128.41 | | | | ((v0 = 0 & permut3(int, all_103_4, all_105_4, all_86_11, 208.46/128.41 | | | | $sum(all_86_10, 1)) = 0) | (length1(int, all_103_4) = v0 208.46/128.41 | | | | & ( ~ ($lesseq(1, $difference(v0, all_86_10))) | ~ 208.46/128.41 | | | | ($lesseq(all_86_11, v0)) | ( ~ (v1 = v0) & length1(int, 208.46/128.41 | | | | all_105_4) = v1)))) 208.46/128.41 | | | | 208.46/128.41 | | | | BETA: splitting (133) gives: 208.46/128.41 | | | | 208.46/128.41 | | | | Case 1: 208.46/128.41 | | | | | 208.46/128.41 | | | | | (134) $lesseq(all_86_10, -2) 208.46/128.41 | | | | | 208.46/128.41 | | | | | COMBINE_INEQS: (47), (134) imply: 208.46/128.41 | | | | | (135) $lesseq(0, -1) 208.46/128.41 | | | | | 208.46/128.41 | | | | | CLOSE: (135) is inconsistent. 208.46/128.41 | | | | | 208.46/128.41 | | | | Case 2: 208.46/128.41 | | | | | 208.46/128.41 | | | | | (136) ? [v0: $int] : ? [v1: $int] : ((v0 = 0 & permut3(int, 208.46/128.41 | | | | | all_103_4, all_105_4, all_86_11, $sum(all_86_10, 1)) = 208.46/128.41 | | | | | 0) | (length1(int, all_103_4) = v0 & ( ~ ($lesseq(1, 208.46/128.41 | | | | | $difference(v0, all_86_10))) | ~ 208.46/128.41 | | | | | ($lesseq(all_86_11, v0)) | ( ~ (v1 = v0) & length1(int, 208.46/128.41 | | | | | all_105_4) = v1)))) 208.46/128.41 | | | | | 208.46/128.41 | | | | | DELTA: instantiating (136) with fresh symbols all_761_0, all_761_1 208.46/128.41 | | | | | gives: 208.46/128.41 | | | | | (137) (all_761_1 = 0 & permut3(int, all_103_4, all_105_4, 208.46/128.41 | | | | | all_86_11, $sum(all_86_10, 1)) = 0) | (length1(int, 208.46/128.41 | | | | | all_103_4) = all_761_1 & ( ~ ($lesseq(1, 208.46/128.41 | | | | | $difference(all_761_1, all_86_10))) | ~ 208.46/128.41 | | | | | ($lesseq(all_86_11, all_761_1)) | ( ~ (all_761_0 = 208.46/128.41 | | | | | all_761_1) & length1(int, all_105_4) = all_761_0))) 208.46/128.41 | | | | | 208.46/128.41 | | | | | BETA: splitting (137) gives: 208.46/128.41 | | | | | 208.46/128.41 | | | | | Case 1: 208.46/128.41 | | | | | | 208.46/128.41 | | | | | | (138) all_761_1 = 0 & permut3(int, all_103_4, all_105_4, 208.46/128.41 | | | | | | all_86_11, $sum(all_86_10, 1)) = 0 208.46/128.41 | | | | | | 208.46/128.41 | | | | | | ALPHA: (138) implies: 208.46/128.41 | | | | | | (139) permut3(int, all_103_4, all_105_4, all_86_11, 208.46/128.41 | | | | | | $sum(all_86_10, 1)) = 0 208.46/128.41 | | | | | | 208.46/128.41 | | | | | | GROUND_INST: instantiating (1) with all_133_0, all_697_0, all_133_1, 208.46/128.41 | | | | | | simplifying with (14), (60) gives: 208.46/128.41 | | | | | | (140) all_697_0 = all_133_0 208.46/128.41 | | | | | | 208.46/128.41 | | | | | | GROUND_INST: instantiating (18) with all_105_1, all_710_1, 208.46/128.41 | | | | | | all_105_2, int, simplifying with (26), (68) gives: 208.46/128.41 | | | | | | (141) all_710_1 = all_105_1 208.46/128.41 | | | | | | 208.46/128.41 | | | | | | GROUND_INST: instantiating (18) with all_710_1, all_697_2, 208.46/128.41 | | | | | | all_105_2, int, simplifying with (58), (68) gives: 208.46/128.41 | | | | | | (142) all_710_1 = all_697_2 208.46/128.41 | | | | | | 208.46/128.41 | | | | | | COMBINE_EQS: (141), (142) imply: 208.46/128.41 | | | | | | (143) all_697_2 = all_105_1 208.46/128.41 | | | | | | 208.46/128.41 | | | | | | SIMP: (143) implies: 208.46/128.41 | | | | | | (144) all_697_2 = all_105_1 208.46/128.41 | | | | | | 208.46/128.41 | | | | | | REDUCE: (61), (144) imply: 208.46/128.41 | | | | | | (145) tb2t(all_105_1) = all_697_1 208.46/128.41 | | | | | | 208.46/128.41 | | | | | | REDUCE: (59), (140) imply: 208.46/128.41 | | | | | | (146) get3(all_697_1, all_133_2) = all_133_0 208.46/128.41 | | | | | | 208.46/128.41 | | | | | | REDUCE: (66), (141) imply: 208.46/128.41 | | | | | | (147) get(int, int, all_105_1, all_710_0) = all_133_1 208.46/128.41 | | | | | | 208.46/128.41 | | | | | | REF_CLOSE: (2), (4), (6), (7), (11), (13), (15), (22), (24), (25), 208.46/128.41 | | | | | | (27), (29), (30), (31), (32), (35), (36), (38), (42), 208.46/128.41 | | | | | | (43), (44), (48), (63), (67), (139), (145), (146), (147) 208.46/128.41 | | | | | | are inconsistent by sub-proof #136. 208.46/128.41 | | | | | | 208.46/128.41 | | | | | Case 2: 208.46/128.41 | | | | | | 208.46/128.41 | | | | | | (148) length1(int, all_103_4) = all_761_1 & ( ~ ($lesseq(1, 208.46/128.41 | | | | | | $difference(all_761_1, all_86_10))) | ~ 208.46/128.41 | | | | | | ($lesseq(all_86_11, all_761_1)) | ( ~ (all_761_0 = 208.46/128.41 | | | | | | all_761_1) & length1(int, all_105_4) = all_761_0)) 208.46/128.41 | | | | | | 208.46/128.41 | | | | | | ALPHA: (148) implies: 208.46/128.41 | | | | | | (149) length1(int, all_103_4) = all_761_1 208.46/128.41 | | | | | | (150) ~ ($lesseq(1, $difference(all_761_1, all_86_10))) | ~ 208.46/128.41 | | | | | | ($lesseq(all_86_11, all_761_1)) | ( ~ (all_761_0 = 208.46/128.41 | | | | | | all_761_1) & length1(int, all_105_4) = all_761_0) 208.46/128.41 | | | | | | 208.46/128.41 | | | | | | GROUND_INST: instantiating (45) with all_86_13, all_721_1, 208.46/128.41 | | | | | | all_103_2, int, simplifying with (3), (129) gives: 208.46/128.41 | | | | | | (151) all_721_1 = all_86_13 208.46/128.41 | | | | | | 208.46/128.41 | | | | | | GROUND_INST: instantiating (45) with all_86_13, all_761_1, 208.46/128.41 | | | | | | all_103_4, int, simplifying with (8), (149) gives: 208.46/128.41 | | | | | | (152) all_761_1 = all_86_13 208.46/128.41 | | | | | | 208.46/128.41 | | | | | | BETA: splitting (150) gives: 208.46/128.41 | | | | | | 208.46/128.41 | | | | | | Case 1: 208.46/128.41 | | | | | | | 208.46/128.41 | | | | | | | (153) $lesseq(1, $difference(all_86_11, all_761_1)) 208.46/128.41 | | | | | | | 208.46/128.41 | | | | | | | REDUCE: (152), (153) imply: 208.46/128.41 | | | | | | | (154) $lesseq(1, $difference(all_86_11, all_86_13)) 208.46/128.41 | | | | | | | 208.46/128.41 | | | | | | | COMBINE_INEQS: (13), (29) imply: 208.46/128.41 | | | | | | | (155) $lesseq(all_86_11, all_86_8) 208.46/128.41 | | | | | | | 208.46/128.41 | | | | | | | COMBINE_INEQS: (30), (35) imply: 208.46/128.41 | | | | | | | (156) $lesseq(1, $difference(all_86_10, all_86_8)) 208.46/128.41 | | | | | | | 208.46/128.41 | | | | | | | COMBINE_INEQS: (155), (156) imply: 208.46/128.41 | | | | | | | (157) $lesseq(1, $difference(all_86_10, all_86_11)) 208.46/128.41 | | | | | | | 208.46/128.41 | | | | | | | COMBINE_INEQS: (12), (154) imply: 208.46/128.41 | | | | | | | (158) $lesseq(0, -1) 208.46/128.41 | | | | | | | 208.46/128.41 | | | | | | | CLOSE: (158) is inconsistent. 208.46/128.41 | | | | | | | 208.46/128.41 | | | | | | Case 2: 208.46/128.41 | | | | | | | 208.46/128.41 | | | | | | | (159) ~ ($lesseq(1, $difference(all_761_1, all_86_10))) | ( ~ 208.46/128.41 | | | | | | | (all_761_0 = all_761_1) & length1(int, all_105_4) = 208.46/128.41 | | | | | | | all_761_0) 208.46/128.41 | | | | | | | 208.46/128.41 | | | | | | | BETA: splitting (130) gives: 208.46/128.41 | | | | | | | 208.46/128.41 | | | | | | | Case 1: 208.46/128.41 | | | | | | | | 208.46/128.41 | | | | | | | | (160) $lesseq(all_721_1, -1) 208.46/128.41 | | | | | | | | 208.46/128.41 | | | | | | | | REDUCE: (151), (160) imply: 208.46/128.41 | | | | | | | | (161) $lesseq(all_86_13, -1) 208.46/128.41 | | | | | | | | 208.46/128.41 | | | | | | | | COMBINE_INEQS: (13), (29) imply: 208.46/128.41 | | | | | | | | (162) $lesseq(all_86_11, all_86_8) 208.46/128.41 | | | | | | | | 208.46/128.41 | | | | | | | | COMBINE_INEQS: (30), (35) imply: 208.46/128.41 | | | | | | | | (163) $lesseq(1, $difference(all_86_10, all_86_8)) 208.46/128.41 | | | | | | | | 208.46/128.41 | | | | | | | | COMBINE_INEQS: (162), (163) imply: 208.46/128.41 | | | | | | | | (164) $lesseq(1, $difference(all_86_10, all_86_11)) 208.46/128.41 | | | | | | | | 208.46/128.41 | | | | | | | | COMBINE_INEQS: (9), (161) imply: 208.46/128.41 | | | | | | | | (165) $lesseq(0, -1) 208.46/128.41 | | | | | | | | 208.46/128.41 | | | | | | | | CLOSE: (165) is inconsistent. 208.46/128.41 | | | | | | | | 208.46/128.41 | | | | | | | Case 2: 208.46/128.41 | | | | | | | | 208.46/128.41 | | | | | | | | (166) ~ ($lesseq(all_86_13, all_721_1)) | ( ~ (all_721_0 = 208.46/128.41 | | | | | | | | all_721_1) & length1(int, all_105_4) = all_721_0) 208.46/128.41 | | | | | | | | 208.46/128.41 | | | | | | | | BETA: splitting (159) gives: 208.46/128.41 | | | | | | | | 208.46/128.41 | | | | | | | | Case 1: 208.46/128.41 | | | | | | | | | 208.46/128.41 | | | | | | | | | (167) $lesseq(all_761_1, all_86_10) 208.46/128.41 | | | | | | | | | 208.46/128.41 | | | | | | | | | REDUCE: (152), (167) imply: 208.46/128.41 | | | | | | | | | (168) $lesseq(all_86_13, all_86_10) 208.46/128.41 | | | | | | | | | 208.46/128.41 | | | | | | | | | COMBINE_INEQS: (37), (168) imply: 208.46/128.41 | | | | | | | | | (169) $lesseq(0, -1) 208.46/128.41 | | | | | | | | | 208.46/128.41 | | | | | | | | | CLOSE: (169) is inconsistent. 208.46/128.41 | | | | | | | | | 208.46/128.41 | | | | | | | | Case 2: 208.46/128.41 | | | | | | | | | 208.46/128.41 | | | | | | | | | (170) ~ (all_761_0 = all_761_1) & length1(int, all_105_4) 208.46/128.41 | | | | | | | | | = all_761_0 208.46/128.41 | | | | | | | | | 208.46/128.41 | | | | | | | | | ALPHA: (170) implies: 208.46/128.41 | | | | | | | | | (171) length1(int, all_105_4) = all_761_0 208.46/128.41 | | | | | | | | | 208.46/128.41 | | | | | | | | | BETA: splitting (166) gives: 208.46/128.41 | | | | | | | | | 208.46/128.41 | | | | | | | | | Case 1: 208.46/128.41 | | | | | | | | | | 208.46/128.41 | | | | | | | | | | (172) $lesseq(1, $difference(all_86_13, all_721_1)) 208.46/128.41 | | | | | | | | | | 208.46/128.41 | | | | | | | | | | REDUCE: (151), (172) imply: 208.46/128.41 | | | | | | | | | | (173) $lesseq(0, -1) 208.46/128.41 | | | | | | | | | | 208.46/128.41 | | | | | | | | | | CLOSE: (173) is inconsistent. 208.46/128.41 | | | | | | | | | | 208.46/128.41 | | | | | | | | | Case 2: 208.46/128.41 | | | | | | | | | | 208.46/128.41 | | | | | | | | | | (174) ~ (all_721_0 = all_721_1) & length1(int, 208.46/128.41 | | | | | | | | | | all_105_4) = all_721_0 208.46/128.41 | | | | | | | | | | 208.46/128.41 | | | | | | | | | | ALPHA: (174) implies: 208.46/128.41 | | | | | | | | | | (175) ~ (all_721_0 = all_721_1) 208.46/128.41 | | | | | | | | | | (176) length1(int, all_105_4) = all_721_0 208.46/128.41 | | | | | | | | | | 208.46/128.41 | | | | | | | | | | REDUCE: (151), (175) imply: 208.46/128.41 | | | | | | | | | | (177) ~ (all_721_0 = all_86_13) 208.46/128.41 | | | | | | | | | | 208.46/128.42 | | | | | | | | | | GROUND_INST: instantiating (45) with all_86_13, all_761_0, 208.46/128.42 | | | | | | | | | | all_105_4, int, simplifying with (19), (171) 208.46/128.42 | | | | | | | | | | gives: 208.46/128.42 | | | | | | | | | | (178) all_761_0 = all_86_13 208.46/128.42 | | | | | | | | | | 208.46/128.42 | | | | | | | | | | GROUND_INST: instantiating (45) with all_761_0, all_721_0, 208.46/128.42 | | | | | | | | | | all_105_4, int, simplifying with (171), (176) 208.46/128.42 | | | | | | | | | | gives: 208.46/128.42 | | | | | | | | | | (179) all_761_0 = all_721_0 208.46/128.42 | | | | | | | | | | 208.46/128.42 | | | | | | | | | | COMBINE_EQS: (178), (179) imply: 208.46/128.42 | | | | | | | | | | (180) all_721_0 = all_86_13 208.46/128.42 | | | | | | | | | | 208.46/128.42 | | | | | | | | | | REDUCE: (177), (180) imply: 208.46/128.42 | | | | | | | | | | (181) ~ (0 = 0) 208.46/128.42 | | | | | | | | | | 208.46/128.42 | | | | | | | | | | CLOSE: (181) is inconsistent. 208.46/128.42 | | | | | | | | | | 208.46/128.42 | | | | | | | | | End of split 208.46/128.42 | | | | | | | | | 208.46/128.42 | | | | | | | | End of split 208.46/128.42 | | | | | | | | 208.46/128.42 | | | | | | | End of split 208.46/128.42 | | | | | | | 208.46/128.42 | | | | | | End of split 208.46/128.42 | | | | | | 208.61/128.42 | | | | | End of split 208.61/128.42 | | | | | 208.61/128.42 | | | | End of split 208.61/128.42 | | | | 208.61/128.42 | | | End of split 208.61/128.42 | | | 208.61/128.42 | | End of split 208.61/128.42 | | 208.61/128.42 | End of split 208.61/128.42 | 208.61/128.42 End of proof 208.61/128.42 208.61/128.42 Sub-proof #134 shows that the following formulas are inconsistent: 208.61/128.42 ---------------------------------------------------------------- 208.61/128.42 (1) all_747_1 = all_86_13 208.61/128.42 (2) length1(int, all_105_4) = all_86_13 208.61/128.42 (3) ~ ($lesseq(1, $difference(all_747_1, all_86_10))) | ( ~ (all_747_0 = 208.61/128.42 all_747_1) & length1(int, all_105_4) = all_747_0) 208.61/128.42 (4) $lesseq(1, $difference(all_86_13, all_86_10)) 208.61/128.42 (5) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 208.61/128.42 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 208.61/128.42 208.61/128.42 Begin of proof 208.61/128.42 | 208.61/128.42 | BETA: splitting (3) gives: 208.61/128.42 | 208.61/128.42 | Case 1: 208.61/128.42 | | 208.61/128.42 | | (6) $lesseq(all_747_1, all_86_10) 208.61/128.42 | | 208.61/128.42 | | REDUCE: (1), (6) imply: 208.61/128.42 | | (7) $lesseq(all_86_13, all_86_10) 208.61/128.42 | | 208.61/128.42 | | COMBINE_INEQS: (4), (7) imply: 208.61/128.42 | | (8) $lesseq(0, -1) 208.61/128.42 | | 208.61/128.42 | | CLOSE: (8) is inconsistent. 208.61/128.42 | | 208.61/128.42 | Case 2: 208.61/128.42 | | 208.61/128.42 | | (9) ~ (all_747_0 = all_747_1) & length1(int, all_105_4) = all_747_0 208.61/128.42 | | 208.61/128.42 | | ALPHA: (9) implies: 208.61/128.42 | | (10) ~ (all_747_0 = all_747_1) 208.61/128.42 | | (11) length1(int, all_105_4) = all_747_0 208.61/128.42 | | 208.61/128.42 | | REDUCE: (1), (10) imply: 208.61/128.42 | | (12) ~ (all_747_0 = all_86_13) 208.61/128.42 | | 208.61/128.42 | | GROUND_INST: instantiating (5) with all_86_13, all_747_0, all_105_4, int, 208.61/128.42 | | simplifying with (2), (11) gives: 208.61/128.42 | | (13) all_747_0 = all_86_13 208.61/128.42 | | 208.61/128.42 | | REDUCE: (12), (13) imply: 208.61/128.42 | | (14) ~ (0 = 0) 208.61/128.42 | | 208.61/128.42 | | CLOSE: (14) is inconsistent. 208.61/128.42 | | 208.61/128.42 | End of split 208.61/128.42 | 208.61/128.42 End of proof 208.61/128.42 208.61/128.42 Sub-proof #135 shows that the following formulas are inconsistent: 208.61/128.42 ---------------------------------------------------------------- 208.61/128.42 (1) all_747_1 = all_86_13 208.61/128.42 (2) $lesseq(all_133_2, all_86_8) 208.61/128.42 (3) $lesseq(1, $difference(all_86_11, all_747_1)) 208.61/128.42 (4) $lesseq(all_86_11, all_133_2) 208.61/128.42 (5) $lesseq(all_86_7, all_86_10) 208.61/128.42 (6) $lesseq(1, $difference(all_86_7, all_86_8)) 208.61/128.42 (7) $lesseq(1, $difference(all_86_13, all_86_10)) 208.61/128.42 208.61/128.42 Begin of proof 208.61/128.42 | 208.61/128.42 | REDUCE: (1), (3) imply: 208.61/128.42 | (8) $lesseq(1, $difference(all_86_11, all_86_13)) 208.61/128.42 | 208.61/128.42 | COMBINE_INEQS: (2), (4) imply: 208.61/128.42 | (9) $lesseq(all_86_11, all_86_8) 208.61/128.42 | 208.61/128.42 | COMBINE_INEQS: (5), (6) imply: 208.61/128.42 | (10) $lesseq(1, $difference(all_86_10, all_86_8)) 208.61/128.42 | 208.61/128.42 | COMBINE_INEQS: (9), (10) imply: 208.61/128.42 | (11) $lesseq(1, $difference(all_86_10, all_86_11)) 208.61/128.42 | 208.61/128.42 | COMBINE_INEQS: (7), (11) imply: 208.61/128.42 | (12) $lesseq(2, $difference(all_86_13, all_86_11)) 208.61/128.42 | 208.61/128.42 | COMBINE_INEQS: (8), (12) imply: 208.61/128.42 | (13) $lesseq(0, -1) 208.61/128.42 | 208.61/128.42 | CLOSE: (13) is inconsistent. 208.61/128.42 | 208.61/128.42 End of proof 208.61/128.42 208.61/128.42 Sub-proof #136 shows that the following formulas are inconsistent: 208.61/128.42 ---------------------------------------------------------------- 208.61/128.42 (1) ! [v0: $int] : ! [v1: $int] : ( ~ ($lesseq(43, v1)) | ~ ($lesseq(v0, 208.61/128.42 all_86_8)) | ~ ($lesseq(all_86_11, v0)) | ~ (get3(all_86_6, v0) = 208.61/128.42 v1)) 208.61/128.42 (2) (all_708_0 = all_708_1 & $lesseq(1, $difference(all_708_1, all_86_10)) & 208.61/128.42 $lesseq(all_86_11, all_708_1) & $lesseq(-1, all_86_10) & $lesseq(0, 208.61/128.42 all_86_11) & length1(int, all_105_4) = all_708_1 & length1(int, 208.61/128.42 all_103_4) = all_708_1) | ( ~ (all_708_1 = 0) & permut3(int, 208.61/128.42 all_103_4, all_105_4, all_86_11, $sum(all_86_10, 1)) = all_708_1) 208.61/128.42 (3) in_map_int_int(all_86_6) 208.61/128.42 (4) get3(all_697_1, all_133_2) = all_133_0 208.61/128.42 (5) t2tb(all_86_2) = all_105_1 208.61/128.42 (6) in_ty(int) 208.61/128.42 (7) t2tb(all_86_6) = all_103_1 208.61/128.42 (8) $lesseq(all_133_2, all_86_8) 208.61/128.42 (9) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.61/128.42 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ (permut3(v6, v5, 208.61/128.42 v4, v3, v2) = v1) | ~ (permut3(v6, v5, v4, v3, v2) = v0)) 208.61/128.42 (10) t2tb1(all_133_2) = all_710_0 208.61/128.42 (11) map_eq_sub1(int, all_105_3, all_105_1, 0, all_86_7) = 0 208.61/128.42 (12) permut3(int, all_103_4, all_105_4, all_86_11, $sum(all_86_10, 1)) = 0 208.61/128.42 (13) tb2t(all_105_1) = all_86_2 208.61/128.42 (14) permut2(int, all_103_1, all_105_3, all_86_11, $sum(all_86_8, 1)) = 0 208.61/128.42 (15) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.61/128.42 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 208.61/128.42 ($lesseq(1, $difference(v4, v5))) | ~ ($lesseq(v3, v5)) | ~ 208.61/128.42 (permut2(v0, v1, v2, v3, v4) = 0) | ~ (t2tb1(v5) = v6) | ~ (get(v0, 208.61/128.42 int, v2, v6) = v7) | ~ in_ty(v0) | ? [v8: $int] : ? [v9: $int] 208.61/128.42 : ($lesseq(1, $difference(v4, v8)) & $lesseq(v3, v8) & t2tb1(v8) = v9 208.61/128.42 & get(v0, int, v1, v9) = v7 & in_uni(v9) & in_uni(v7))) 208.61/128.42 (16) $lesseq(all_86_11, all_133_2) 208.61/128.42 (17) $lesseq(all_86_7, all_86_10) 208.61/128.42 (18) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.61/128.42 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 208.61/128.42 ($lesseq(1, $difference(v3, v4))) | ~ ($lesseq(v2, v4)) | ~ 208.61/128.42 (permut2(int, v5, v6, v2, v3) = 0) | ~ (t2tb(v1) = v6) | ~ (t2tb(v0) 208.61/128.42 = v5) | ~ (get3(v1, v4) = v7) | ~ in_map_int_int(v0) | ? [v8: 208.61/128.42 $int] : ($lesseq(1, $difference(v3, v8)) & $lesseq(v2, v8) & 208.61/128.42 get3(v0, v8) = v7)) 208.61/128.42 (19) permut2(int, all_105_3, all_105_1, all_86_7, $sum(all_86_10, 1)) = 0 208.61/128.42 (20) $lesseq(1, $difference(all_86_7, all_86_8)) 208.61/128.42 (21) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.61/128.42 $int] : ! [v5: $int] : ! [v6: $int] : ( ~ ($lesseq(1, 208.61/128.42 $difference(v4, v5))) | ~ ($lesseq(v3, v5)) | ~ (map_eq_sub1(v0, 208.61/128.42 v1, v2, v3, v4) = 0) | ~ (t2tb1(v5) = v6) | ~ in_ty(v0) | ? 208.61/128.42 [v7: $int] : (get(v0, int, v2, v6) = v7 & get(v0, int, v1, v6) = v7 & 208.61/128.42 in_uni(v7))) 208.61/128.42 (22) in_map_int_int(all_86_4) 208.61/128.42 (23) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ (tb2t(v2) 208.61/128.42 = v1) | ~ (tb2t(v2) = v0)) 208.61/128.42 (24) $lesseq(43, all_133_0) 208.61/128.42 (25) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.61/128.42 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 208.61/128.42 ($lesseq(1, $difference(v3, v6))) | ~ ($lesseq(v2, v6)) | ~ 208.61/128.42 (map_eq_sub1(int, v4, v5, v2, v3) = 0) | ~ (t2tb(v1) = v5) | ~ 208.61/128.42 (t2tb(v0) = v4) | ~ (get3(v1, v6) = v7) | ~ in_map_int_int(v0) | 208.61/128.42 get3(v0, v6) = v7) 208.61/128.42 (26) get(int, int, all_105_1, all_710_0) = all_133_1 208.61/128.42 (27) tb2t(all_105_1) = all_697_1 208.61/128.42 (28) t2tb(all_86_4) = all_105_3 208.61/128.42 208.61/128.42 Begin of proof 208.61/128.42 | 208.61/128.42 | BETA: splitting (2) gives: 208.61/128.42 | 208.61/128.42 | Case 1: 208.61/128.42 | | 208.61/128.42 | | (29) all_708_0 = all_708_1 & $lesseq(1, $difference(all_708_1, 208.61/128.42 | | all_86_10)) & $lesseq(all_86_11, all_708_1) & $lesseq(-1, 208.61/128.42 | | all_86_10) & $lesseq(0, all_86_11) & length1(int, all_105_4) = 208.61/128.42 | | all_708_1 & length1(int, all_103_4) = all_708_1 208.61/128.42 | | 208.61/128.42 | | ALPHA: (29) implies: 208.61/128.42 | | (30) $lesseq(0, all_86_11) 208.61/128.42 | | 208.61/128.42 | | GROUND_INST: instantiating (23) with all_86_2, all_697_1, all_105_1, 208.61/128.42 | | simplifying with (13), (27) gives: 208.61/128.42 | | (31) all_697_1 = all_86_2 208.61/128.42 | | 208.61/128.42 | | COMBINE_INEQS: (17), (20) imply: 208.61/128.42 | | (32) $lesseq(1, $difference(all_86_10, all_86_8)) 208.61/128.42 | | 208.61/128.42 | | REDUCE: (4), (31) imply: 208.61/128.42 | | (33) get3(all_86_2, all_133_2) = all_133_0 208.61/128.42 | | 208.61/128.42 | | GROUND_INST: instantiating (25) with all_86_4, all_86_2, 0, all_86_7, 208.61/128.42 | | all_105_3, all_105_1, all_133_2, all_133_0, simplifying with 208.61/128.42 | | (5), (11), (22), (28), (33) gives: 208.61/128.42 | | (34) ~ ($lesseq(1, $difference(all_86_7, all_133_2))) | ~ ($lesseq(0, 208.61/128.42 | | all_133_2)) | get3(all_86_4, all_133_2) = all_133_0 208.61/128.42 | | 208.61/128.42 | | GROUND_INST: instantiating (18) with all_86_4, all_86_2, all_86_7, 208.61/128.42 | | $sum(all_86_10, 1), all_133_2, all_105_3, all_105_1, all_133_0, 208.61/128.42 | | simplifying with (5), (19), (22), (28), (33) gives: 208.61/128.42 | | (35) ~ ($lesseq(all_133_2, all_86_10)) | ~ ($lesseq(all_86_7, 208.61/128.42 | | all_133_2)) | ? [v0: $int] : ($lesseq(v0, all_86_10) & 208.61/128.42 | | $lesseq(all_86_7, v0) & get3(all_86_4, v0) = all_133_0) 208.61/128.42 | | 208.61/128.42 | | GROUND_INST: instantiating (21) with int, all_105_3, all_105_1, 0, all_86_7, 208.61/128.42 | | all_133_2, all_710_0, simplifying with (6), (10), (11) gives: 208.61/128.42 | | (36) ~ ($lesseq(1, $difference(all_86_7, all_133_2))) | ~ ($lesseq(0, 208.61/128.42 | | all_133_2)) | ? [v0: $int] : (get(int, int, all_105_1, 208.61/128.42 | | all_710_0) = v0 & get(int, int, all_105_3, all_710_0) = v0 & 208.61/128.42 | | in_uni(v0)) 208.61/128.42 | | 208.61/128.42 | | GROUND_INST: instantiating (15) with int, all_105_3, all_105_1, all_86_7, 208.61/128.42 | | $sum(all_86_10, 1), all_133_2, all_710_0, all_133_1, 208.61/128.42 | | simplifying with (6), (10), (19), (26) gives: 208.61/128.42 | | (37) ~ ($lesseq(all_133_2, all_86_10)) | ~ ($lesseq(all_86_7, 208.61/128.42 | | all_133_2)) | ? [v0: $int] : ? [v1: $int] : ($lesseq(v0, 208.61/128.42 | | all_86_10) & $lesseq(all_86_7, v0) & t2tb1(v0) = v1 & get(int, 208.61/128.42 | | int, all_105_3, v1) = all_133_1 & in_uni(v1) & 208.61/128.42 | | in_uni(all_133_1)) 208.61/128.42 | | 208.61/128.42 | | BETA: splitting (36) gives: 208.61/128.42 | | 208.61/128.42 | | Case 1: 208.61/128.42 | | | 208.61/128.42 | | | (38) $lesseq(all_133_2, -1) 208.61/128.42 | | | 208.61/128.42 | | | COMBINE_INEQS: (16), (38) imply: 208.61/128.42 | | | (39) $lesseq(all_86_11, -1) 208.61/128.42 | | | 208.61/128.42 | | | COMBINE_INEQS: (30), (39) imply: 208.61/128.42 | | | (40) $lesseq(0, -1) 208.61/128.42 | | | 208.61/128.42 | | | CLOSE: (40) is inconsistent. 208.61/128.42 | | | 208.61/128.42 | | Case 2: 208.61/128.42 | | | 208.61/128.42 | | | (41) $lesseq(0, all_133_2) 208.61/128.42 | | | 208.61/128.42 | | | REF_CLOSE: (1), (3), (7), (8), (14), (16), (18), (20), (24), (28), (32), 208.61/128.42 | | | (34), (35), (37), (41) are inconsistent by sub-proof #144. 208.61/128.42 | | | 208.61/128.42 | | End of split 208.61/128.42 | | 208.61/128.42 | Case 2: 208.61/128.42 | | 208.61/128.42 | | (42) ~ (all_708_1 = 0) & permut3(int, all_103_4, all_105_4, all_86_11, 208.61/128.42 | | $sum(all_86_10, 1)) = all_708_1 208.61/128.42 | | 208.61/128.42 | | ALPHA: (42) implies: 208.61/128.42 | | (43) ~ (all_708_1 = 0) 208.61/128.42 | | (44) permut3(int, all_103_4, all_105_4, all_86_11, $sum(all_86_10, 1)) = 208.61/128.42 | | all_708_1 208.61/128.42 | | 208.61/128.42 | | GROUND_INST: instantiating (9) with all_708_1, 0, $sum(all_86_10, 1), 208.61/128.42 | | all_86_11, all_105_4, all_103_4, int, simplifying with (12), 208.61/128.42 | | (44) gives: 208.61/128.42 | | (45) all_708_1 = 0 208.61/128.42 | | 208.61/128.42 | | REDUCE: (43), (45) imply: 208.61/128.42 | | (46) ~ (0 = 0) 208.61/128.42 | | 208.61/128.42 | | CLOSE: (46) is inconsistent. 208.61/128.42 | | 208.61/128.42 | End of split 208.61/128.42 | 208.61/128.42 End of proof 208.61/128.42 208.61/128.42 Sub-proof #137 shows that the following formulas are inconsistent: 208.61/128.42 ---------------------------------------------------------------- 208.61/128.42 (1) ~ ($lesseq(all_86_13, all_759_1)) | ( ~ (all_759_0 = all_759_1) & 208.61/128.42 length1(int, all_103_2) = all_759_0) 208.61/128.42 (2) all_759_1 = all_86_13 208.61/128.42 (3) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 208.61/128.42 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 208.61/128.42 (4) length1(int, all_103_2) = all_86_13 208.61/128.42 208.61/128.42 Begin of proof 208.61/128.42 | 208.61/128.42 | BETA: splitting (1) gives: 208.61/128.42 | 208.61/128.42 | Case 1: 208.61/128.42 | | 208.61/128.42 | | (5) $lesseq(1, $difference(all_86_13, all_759_1)) 208.61/128.42 | | 208.61/128.42 | | REDUCE: (2), (5) imply: 208.61/128.42 | | (6) $lesseq(0, -1) 208.61/128.42 | | 208.61/128.42 | | CLOSE: (6) is inconsistent. 208.61/128.42 | | 208.61/128.42 | Case 2: 208.61/128.42 | | 208.61/128.42 | | (7) ~ (all_759_0 = all_759_1) & length1(int, all_103_2) = all_759_0 208.61/128.42 | | 208.61/128.42 | | ALPHA: (7) implies: 208.61/128.42 | | (8) ~ (all_759_0 = all_759_1) 208.61/128.42 | | (9) length1(int, all_103_2) = all_759_0 208.61/128.42 | | 208.61/128.42 | | REDUCE: (2), (8) imply: 208.61/128.42 | | (10) ~ (all_759_0 = all_86_13) 208.61/128.42 | | 208.61/128.42 | | GROUND_INST: instantiating (3) with all_86_13, all_759_0, all_103_2, int, 208.61/128.42 | | simplifying with (4), (9) gives: 208.61/128.42 | | (11) all_759_0 = all_86_13 208.61/128.42 | | 208.61/128.42 | | REDUCE: (10), (11) imply: 208.61/128.42 | | (12) ~ (0 = 0) 208.61/128.42 | | 208.61/128.42 | | CLOSE: (12) is inconsistent. 208.61/128.42 | | 208.61/128.42 | End of split 208.61/128.42 | 208.61/128.42 End of proof 208.61/128.42 208.61/128.42 Sub-proof #138 shows that the following formulas are inconsistent: 208.61/128.42 ---------------------------------------------------------------- 208.61/128.42 (1) $lesseq(all_759_1, -1) 208.61/128.42 (2) $lesseq(1, $difference(all_133_2, all_86_8)) 208.61/128.42 (3) $lesseq(1, $difference(all_86_7, all_133_2)) 208.61/128.42 (4) $lesseq(all_86_11, all_86_8) 208.61/128.42 (5) $lesseq(all_86_7, all_86_10) 208.61/128.42 (6) all_759_1 = all_86_13 208.61/128.42 (7) $lesseq(1, $difference(all_86_13, all_86_10)) 208.61/128.42 (8) $lesseq(0, all_86_11) 208.61/128.42 208.61/128.42 Begin of proof 208.61/128.42 | 208.61/128.42 | REDUCE: (1), (6) imply: 208.61/128.42 | (9) $lesseq(all_86_13, -1) 208.61/128.42 | 208.61/128.42 | COMBINE_INEQS: (2), (3) imply: 208.61/128.42 | (10) $lesseq(2, $difference(all_86_7, all_86_8)) 208.61/128.42 | 208.61/128.42 | COMBINE_INEQS: (5), (10) imply: 208.61/128.42 | (11) $lesseq(2, $difference(all_86_10, all_86_8)) 208.61/128.42 | 208.61/128.42 | COMBINE_INEQS: (4), (11) imply: 208.61/128.42 | (12) $lesseq(2, $difference(all_86_10, all_86_11)) 208.61/128.42 | 208.61/128.42 | COMBINE_INEQS: (7), (12) imply: 208.61/128.42 | (13) $lesseq(3, $difference(all_86_13, all_86_11)) 208.61/128.42 | 208.61/128.42 | COMBINE_INEQS: (8), (13) imply: 208.61/128.42 | (14) $lesseq(3, all_86_13) 208.61/128.42 | 208.61/128.42 | COMBINE_INEQS: (9), (14) imply: 208.61/128.42 | (15) $lesseq(0, -1) 208.61/128.42 | 208.61/128.42 | CLOSE: (15) is inconsistent. 208.61/128.42 | 208.61/128.42 End of proof 208.61/128.42 208.61/128.42 Sub-proof #139 shows that the following formulas are inconsistent: 208.61/128.42 ---------------------------------------------------------------- 208.61/128.42 (1) ~ (all_703_1 = 0) & permut3(int, all_103_4, all_103_2, 0, all_86_13) = 208.61/128.42 all_703_1 208.61/128.42 (2) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.61/128.42 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ (permut3(v6, v5, 208.61/128.42 v4, v3, v2) = v1) | ~ (permut3(v6, v5, v4, v3, v2) = v0)) 208.61/128.42 (3) permut3(int, all_103_4, all_103_2, 0, all_86_13) = 0 208.61/128.42 208.61/128.42 Begin of proof 208.61/128.42 | 208.61/128.42 | ALPHA: (1) implies: 208.61/128.42 | (4) ~ (all_703_1 = 0) 208.61/128.42 | (5) permut3(int, all_103_4, all_103_2, 0, all_86_13) = all_703_1 208.61/128.42 | 208.61/128.42 | GROUND_INST: instantiating (2) with 0, all_703_1, all_86_13, 0, all_103_2, 208.61/128.42 | all_103_4, int, simplifying with (3), (5) gives: 208.61/128.42 | (6) all_703_1 = 0 208.61/128.42 | 208.61/128.42 | REDUCE: (4), (6) imply: 208.61/128.42 | (7) ~ (0 = 0) 208.61/128.42 | 208.61/128.42 | CLOSE: (7) is inconsistent. 208.61/128.42 | 208.61/128.42 End of proof 208.61/128.42 208.61/128.42 Sub-proof #140 shows that the following formulas are inconsistent: 208.61/128.42 ---------------------------------------------------------------- 208.61/128.42 (1) ~ (all_708_1 = 0) & permut3(int, all_103_4, all_105_4, all_86_11, 208.61/128.42 $sum(all_86_10, 1)) = all_708_1 208.61/128.42 (2) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.61/128.42 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ (permut3(v6, v5, 208.61/128.42 v4, v3, v2) = v1) | ~ (permut3(v6, v5, v4, v3, v2) = v0)) 208.61/128.42 (3) permut3(int, all_103_4, all_105_4, all_86_11, $sum(all_86_10, 1)) = 0 208.61/128.42 208.61/128.42 Begin of proof 208.61/128.42 | 208.61/128.42 | ALPHA: (1) implies: 208.61/128.42 | (4) ~ (all_708_1 = 0) 208.61/128.43 | (5) permut3(int, all_103_4, all_105_4, all_86_11, $sum(all_86_10, 1)) = 208.61/128.43 | all_708_1 208.61/128.43 | 208.61/128.43 | GROUND_INST: instantiating (2) with all_708_1, 0, $sum(all_86_10, 1), 208.61/128.43 | all_86_11, all_105_4, all_103_4, int, simplifying with (3), (5) 208.61/128.43 | gives: 208.61/128.43 | (6) all_708_1 = 0 208.61/128.43 | 208.61/128.43 | REDUCE: (4), (6) imply: 208.61/128.43 | (7) ~ (0 = 0) 208.61/128.43 | 208.61/128.43 | CLOSE: (7) is inconsistent. 208.61/128.43 | 208.61/128.43 End of proof 208.61/128.43 208.61/128.43 Sub-proof #141 shows that the following formulas are inconsistent: 208.61/128.43 ---------------------------------------------------------------- 208.61/128.43 (1) ~ ($lesseq(1, $difference(all_86_13, all_133_2))) | ~ ($lesseq(0, 208.61/128.43 all_133_2)) | ? [v0: $int] : ($lesseq(1, $difference(all_86_13, v0)) 208.61/128.43 & $lesseq(0, v0) & get3(all_86_12, v0) = all_133_0) 208.61/128.43 (2) $lesseq(0, all_133_2) 208.61/128.43 (3) ! [v0: $int] : ! [v1: $int] : (v1 = 42 | ~ ($lesseq(1, 208.61/128.43 $difference(all_86_7, v0))) | ~ ($lesseq(1, $difference(v0, 208.61/128.43 all_86_8))) | ~ (get3(all_86_6, v0) = v1)) 208.61/128.43 (4) $lesseq(1, $difference(all_133_2, all_86_8)) 208.61/128.43 (5) $lesseq(1, $difference(all_86_7, all_133_2)) 208.61/128.43 (6) ~ (all_133_0 = 42) 208.61/128.43 (7) $lesseq(1, $difference(all_86_13, all_133_2)) 208.61/128.43 (8) ~ ($lesseq(1, $difference(all_86_13, all_133_2))) | ~ ($lesseq(1, 208.61/128.43 $difference(all_133_2, all_86_8))) | get3(all_86_6, all_133_2) = 208.61/128.43 all_133_0 208.61/128.43 208.61/128.43 Begin of proof 208.61/128.43 | 208.61/128.43 | BETA: splitting (8) gives: 208.61/128.43 | 208.61/128.43 | Case 1: 208.61/128.43 | | 208.61/128.43 | | (9) get3(all_86_6, all_133_2) = all_133_0 208.61/128.43 | | 208.61/128.43 | | BETA: splitting (1) gives: 208.61/128.43 | | 208.61/128.43 | | Case 1: 208.61/128.43 | | | 208.61/128.43 | | | (10) $lesseq(all_133_2, -1) 208.61/128.43 | | | 208.61/128.43 | | | COMBINE_INEQS: (2), (10) imply: 208.61/128.43 | | | (11) $lesseq(0, -1) 208.61/128.43 | | | 208.61/128.43 | | | CLOSE: (11) is inconsistent. 208.61/128.43 | | | 208.61/128.43 | | Case 2: 208.61/128.43 | | | 208.61/128.43 | | | (12) ~ ($lesseq(1, $difference(all_86_13, all_133_2))) | ? [v0: $int] 208.61/128.43 | | | : ($lesseq(1, $difference(all_86_13, v0)) & $lesseq(0, v0) & 208.61/128.43 | | | get3(all_86_12, v0) = all_133_0) 208.61/128.43 | | | 208.61/128.43 | | | BETA: splitting (12) gives: 208.61/128.43 | | | 208.61/128.43 | | | Case 1: 208.61/128.43 | | | | 208.61/128.43 | | | | (13) $lesseq(all_86_13, all_133_2) 208.61/128.43 | | | | 208.61/128.43 | | | | COMBINE_INEQS: (7), (13) imply: 208.61/128.43 | | | | (14) $lesseq(0, -1) 208.61/128.43 | | | | 208.61/128.43 | | | | CLOSE: (14) is inconsistent. 208.61/128.43 | | | | 208.61/128.43 | | | Case 2: 208.61/128.43 | | | | 208.61/128.43 | | | | 208.61/128.43 | | | | GROUND_INST: instantiating (3) with all_133_2, all_133_0, simplifying 208.61/128.43 | | | | with (9) gives: 208.61/128.43 | | | | (15) all_133_0 = 42 | ~ ($lesseq(1, $difference(all_86_7, 208.61/128.43 | | | | all_133_2))) | ~ ($lesseq(1, $difference(all_133_2, 208.61/128.43 | | | | all_86_8))) 208.61/128.43 | | | | 208.61/128.43 | | | | REF_CLOSE: (4), (5), (6), (15) are inconsistent by sub-proof #155. 208.61/128.43 | | | | 208.61/128.43 | | | End of split 208.61/128.43 | | | 208.61/128.43 | | End of split 208.61/128.43 | | 208.61/128.43 | Case 2: 208.61/128.43 | | 208.61/128.43 | | (16) ~ ($lesseq(1, $difference(all_86_13, all_133_2))) | ~ ($lesseq(1, 208.61/128.43 | | $difference(all_133_2, all_86_8))) 208.61/128.43 | | 208.61/128.43 | | REF_CLOSE: (4), (7), (16) are inconsistent by sub-proof #153. 208.61/128.43 | | 208.61/128.43 | End of split 208.61/128.43 | 208.61/128.43 End of proof 208.61/128.43 208.61/128.43 Sub-proof #142 shows that the following formulas are inconsistent: 208.61/128.43 ---------------------------------------------------------------- 208.61/128.43 (1) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ (tb2t1(v2) 208.61/128.43 = v1) | ~ (tb2t1(v2) = v0)) 208.61/128.43 (2) ! [v0: $int] : ! [v1: $int] : ( ~ ($lesseq(43, v1)) | ~ ($lesseq(v0, 208.61/128.43 all_86_8)) | ~ ($lesseq(all_86_11, v0)) | ~ (get3(all_86_6, v0) = 208.61/128.43 v1)) 208.61/128.43 (3) in_map_int_int(all_86_6) 208.61/128.43 (4) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.61/128.43 $int] : ! [v5: $int] : ! [v6: $int] : ( ~ ($lesseq(0, v4)) | ~ 208.61/128.43 ($lesseq(0, v3)) | ~ (map_eq_sub1(v0, v5, v6, v3, v4) = 0) | ~ 208.61/128.43 (elts(v0, v2) = v6) | ~ (elts(v0, v1) = v5) | ~ in_ty(v0) | ? [v7: 208.61/128.43 $int] : ? [v8: $int] : ((v7 = 0 & array_eq_sub1(v0, v1, v2, v3, v4) 208.61/128.43 = 0) | (length1(v0, v1) = v7 & ( ~ ($lesseq(v4, v7)) | ~ 208.61/128.43 ($lesseq(v3, v7)) | ( ~ (v8 = v7) & length1(v0, v2) = v8))))) 208.61/128.43 (5) elts(int, all_103_4) = all_103_3 208.61/128.43 (6) t2tb2(all_86_3) = all_105_4 208.61/128.43 (7) t2tb(all_86_2) = all_105_1 208.61/128.43 (8) in_ty(int) 208.61/128.43 (9) length1(int, all_103_4) = all_86_13 208.61/128.43 (10) ( ~ (all_133_0 = 42) & $lesseq(1, $difference(all_86_7, all_133_2)) & 208.61/128.43 $lesseq(1, $difference(all_133_2, all_86_8)) & tb2t1(all_133_1) = 208.61/128.43 all_133_0 & get4(int, all_133_3, all_133_2) = all_133_1 & 208.61/128.43 in_uni(all_133_1)) | ($lesseq(all_133_0, 41) & $lesseq(all_133_2, 208.61/128.43 all_86_10) & $lesseq(all_86_7, all_133_2) & tb2t1(all_133_1) = 208.61/128.43 all_133_0 & get4(int, all_133_3, all_133_2) = all_133_1 & 208.61/128.43 in_uni(all_133_1)) | ($lesseq(43, all_133_0) & $lesseq(all_133_2, 208.61/128.43 all_86_8) & $lesseq(all_86_11, all_133_2) & tb2t1(all_133_1) = 208.61/128.43 all_133_0 & get4(int, all_133_3, all_133_2) = all_133_1 & 208.61/128.43 in_uni(all_133_1)) 208.61/128.43 (11) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.61/128.43 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 208.61/128.43 (permut2(v0, v5, v6, v3, v4) = v7) | ~ (elts(v0, v2) = v6) | ~ 208.61/128.43 (elts(v0, v1) = v5) | ~ in_ty(v0) | ? [v8: $int] : ? [v9: $int] : 208.61/128.43 ((v9 = v8 & v7 = 0 & $lesseq(v4, v8) & $lesseq(v3, v8) & $lesseq(0, 208.61/128.43 v4) & $lesseq(0, v3) & length1(v0, v2) = v8 & length1(v0, v1) = 208.61/128.43 v8) | ( ~ (v8 = 0) & permut3(v0, v1, v2, v3, v4) = v8))) 208.61/128.43 (12) all_125_0 = all_105_4 208.61/128.43 (13) $lesseq(1, $difference(all_86_13, all_86_7)) 208.61/128.43 (14) ! [v0: $int] : ! [v1: $int] : (v1 = 42 | ~ ($lesseq(1, 208.61/128.43 $difference(all_86_7, v0))) | ~ ($lesseq(1, $difference(v0, 208.61/128.43 all_86_8))) | ~ (get3(all_86_6, v0) = v1)) 208.61/128.43 (15) t2tb(all_86_6) = all_103_1 208.61/128.43 (16) map_eq_sub1(int, all_103_1, all_105_3, $sum(all_86_8, 1), all_86_13) = 0 208.61/128.43 (17) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.61/128.43 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ (permut3(v6, v5, 208.61/128.43 v4, v3, v2) = v1) | ~ (permut3(v6, v5, v4, v3, v2) = v0)) 208.61/128.43 (18) permut2(int, all_103_3, all_105_3, all_86_11, $sum(all_86_10, 1)) = 0 208.61/128.43 (19) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 208.61/128.43 | ~ (elts(v3, v2) = v1) | ~ (elts(v3, v2) = v0)) 208.61/128.43 (20) length1(int, all_105_4) = all_86_13 208.61/128.43 (21) in_array_int(all_86_3) 208.61/128.43 (22) elts(int, all_105_4) = all_105_3 208.61/128.43 (23) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.61/128.43 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ (permut_sub2(v6, 208.61/128.43 v5, v4, v3, v2) = v1) | ~ (permut_sub2(v6, v5, v4, v3, v2) = v0)) 208.61/128.43 (24) t2tb2(all_86_9) = all_103_4 208.61/128.43 (25) map_eq_sub1(int, all_105_3, all_105_1, 0, all_86_7) = 0 208.61/128.43 (26) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.61/128.43 $int] : ! [v5: $int] : ( ~ (permut3(int, v4, v5, v2, v3) = 0) | ~ 208.61/128.43 (t2tb2(v1) = v5) | ~ (t2tb2(v0) = v4) | ~ in_array_int(v0) | ? [v6: 208.61/128.43 $int] : ? [v7: $int] : ? [v8: $int] : ? [v9: $int] : ((v6 = 0 & 208.61/128.43 permut_sub3(v0, v1, v2, v3) = 0) | (elts(int, v5) = v7 & elts(int, 208.61/128.43 v4) = v6 & in_uni(v7) & in_uni(v6) & (( ~ (v9 = 0) & 208.61/128.43 map_eq_sub1(int, v6, v7, v3, v8) = v9 & length1(int, v4) = v8) 208.61/128.43 | ( ~ (v8 = 0) & map_eq_sub1(int, v6, v7, 0, v2) = v8))))) 208.61/128.43 (27) tb2t(all_105_1) = all_86_2 208.61/128.43 (28) permut2(int, all_103_1, all_105_3, all_86_11, $sum(all_86_8, 1)) = 0 208.61/128.43 (29) in_array_int(all_86_9) 208.61/128.43 (30) elts(int, all_105_2) = all_105_1 208.61/128.43 (31) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.61/128.43 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 208.61/128.43 ($lesseq(1, $difference(v4, v5))) | ~ ($lesseq(v3, v5)) | ~ 208.61/128.43 (permut2(v0, v1, v2, v3, v4) = 0) | ~ (t2tb1(v5) = v6) | ~ (get(v0, 208.61/128.43 int, v2, v6) = v7) | ~ in_ty(v0) | ? [v8: $int] : ? [v9: $int] 208.61/128.43 : ($lesseq(1, $difference(v4, v8)) & $lesseq(v3, v8) & t2tb1(v8) = v9 208.61/128.43 & get(v0, int, v1, v9) = v7 & in_uni(v9) & in_uni(v7))) 208.61/128.43 (32) t2tb2(all_86_1) = all_105_2 208.61/128.43 (33) ~ ($difference(all_86_10, all_86_13) = -1) | ~ (all_86_11 = 0) 208.61/128.43 (34) $lesseq(all_86_11, all_86_8) 208.61/128.43 (35) $lesseq(all_86_7, all_86_10) 208.61/128.43 (36) $lesseq(0, all_86_8) 208.61/128.43 (37) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.61/128.43 $int] : ! [v5: $int] : ( ~ (elts(v0, v1) = v3) | ~ (t2tb1(v2) = v4) 208.61/128.43 | ~ (get(v0, int, v3, v4) = v5) | ~ in_ty(v0) | (get4(v0, v1, v2) = 208.61/128.43 v5 & in_uni(v5))) 208.61/128.43 (38) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.61/128.43 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 208.61/128.43 ($lesseq(1, $difference(v3, v4))) | ~ ($lesseq(v2, v4)) | ~ 208.61/128.43 (permut2(int, v5, v6, v2, v3) = 0) | ~ (t2tb(v1) = v6) | ~ (t2tb(v0) 208.61/128.43 = v5) | ~ (get3(v1, v4) = v7) | ~ in_map_int_int(v0) | ? [v8: 208.61/128.43 $int] : ($lesseq(1, $difference(v3, v8)) & $lesseq(v2, v8) & 208.61/128.43 get3(v0, v8) = v7)) 208.61/128.43 (39) permut2(int, all_105_3, all_105_1, all_86_7, $sum(all_86_10, 1)) = 0 208.61/128.43 (40) in_array_int(all_86_1) 208.61/128.43 (41) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.61/128.43 $int] : ! [v5: $int] : ! [v6: $int] : ( ~ ($lesseq(0, v4)) | ~ 208.61/128.43 ($lesseq(0, v3)) | ~ (permut2(v0, v5, v6, v3, v4) = 0) | ~ (elts(v0, 208.61/128.43 v2) = v6) | ~ (elts(v0, v1) = v5) | ~ in_ty(v0) | ? [v7: $int] 208.61/128.43 : ? [v8: $int] : ((v7 = 0 & permut3(v0, v1, v2, v3, v4) = 0) | 208.61/128.43 (length1(v0, v1) = v7 & ( ~ ($lesseq(v4, v7)) | ~ ($lesseq(v3, v7)) 208.61/128.43 | ( ~ (v8 = v7) & length1(v0, v2) = v8))))) 208.61/128.43 (42) $lesseq(1, $difference(all_86_7, all_86_8)) 208.61/128.43 (43) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.61/128.43 $int] : ! [v5: $int] : ! [v6: $int] : ( ~ ($lesseq(1, 208.61/128.43 $difference(v4, v5))) | ~ ($lesseq(v3, v5)) | ~ (map_eq_sub1(v0, 208.61/128.43 v1, v2, v3, v4) = 0) | ~ (t2tb1(v5) = v6) | ~ in_ty(v0) | ? 208.61/128.43 [v7: $int] : (get(v0, int, v2, v6) = v7 & get(v0, int, v1, v6) = v7 & 208.61/128.43 in_uni(v7))) 208.61/128.43 (44) $lesseq(1, $difference(all_86_13, all_86_10)) 208.61/128.43 (45) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.61/128.43 $int] : ! [v5: $int] : (v5 = 0 | ~ (permut_sub2(v0, v1, v2, v3, v4) 208.61/128.43 = v5) | ~ in_ty(v0) | ? [v6: $int] : ? [v7: $int] : ? [v8: $int] 208.61/128.43 : ? [v9: $int] : (( ~ (v9 = 0) & map_eq_sub1(v0, v6, v7, v4, v8) = v9 208.61/128.43 & length1(v0, v1) = v8 & elts(v0, v2) = v7 & elts(v0, v1) = v6 & 208.61/128.43 in_uni(v7) & in_uni(v6)) | ( ~ (v8 = 0) & map_eq_sub1(v0, v6, v7, 208.61/128.43 0, v3) = v8 & elts(v0, v2) = v7 & elts(v0, v1) = v6 & in_uni(v7) 208.61/128.43 & in_uni(v6)) | ( ~ (v6 = 0) & permut3(v0, v1, v2, v3, v4) = v6))) 208.61/128.43 (46) in_map_int_int(all_86_4) 208.61/128.43 (47) $lesseq(0, all_86_11) 208.61/128.43 (48) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ( ~ 208.61/128.43 (t2tb2(v0) = v2) | ~ (get4(int, v2, v1) = v3) | ~ in_array_int(v0) | 208.61/128.43 ? [v4: $int] : ? [v5: $int] : ? [v6: $int] : (tb2t(v4) = v5 & 208.61/128.43 tb2t1(v3) = v6 & get3(v5, v1) = v6 & elts(int, v2) = v4 & 208.61/128.43 in_map_int_int(v5) & in_uni(v4))) 208.61/128.43 (49) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ (tb2t(v2) 208.61/128.43 = v1) | ~ (tb2t(v2) = v0)) 208.61/128.43 (50) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.61/128.43 $int] : ! [v5: $int] : (v1 = v0 | ~ (permut_sub3(v5, v4, v3, v2) = 208.61/128.43 v1) | ~ (permut_sub3(v5, v4, v3, v2) = v0)) 208.61/128.43 (51) all_133_3 = all_105_2 208.61/128.43 (52) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.61/128.43 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 208.61/128.43 ($lesseq(1, $difference(v3, v6))) | ~ ($lesseq(v2, v6)) | ~ 208.61/128.43 (map_eq_sub1(int, v4, v5, v2, v3) = 0) | ~ (t2tb(v1) = v5) | ~ 208.61/128.43 (t2tb(v0) = v4) | ~ (get3(v1, v6) = v7) | ~ in_map_int_int(v0) | 208.61/128.43 get3(v0, v6) = v7) 208.61/128.43 (53) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.61/128.43 $int] : ! [v5: $int] : ! [v6: $int] : ( ~ (permut3(int, v4, v5, v2, 208.61/128.43 v3) = v6) | ~ (t2tb2(v1) = v5) | ~ (t2tb2(v0) = v4) | ~ 208.61/128.43 in_array_int(v0) | ? [v7: $int] : ? [v8: $int] : ? [v9: $int] : ? 208.61/128.43 [v10: $int] : ? [v11: $int] : ((v11 = 0 & v9 = 0 & v6 = 0 & 208.61/128.43 map_eq_sub1(int, v7, v8, v3, v10) = 0 & map_eq_sub1(int, v7, v8, 208.61/128.43 0, v2) = 0 & length1(int, v4) = v10 & elts(int, v5) = v8 & 208.61/128.43 elts(int, v4) = v7 & in_uni(v8) & in_uni(v7)) | ( ~ (v7 = 0) & 208.61/128.43 permut_sub3(v0, v1, v2, v3) = v7))) 208.61/128.43 (54) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 208.61/128.43 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 208.61/128.43 (55) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.61/128.43 $int] : ( ~ (permut3(v0, v1, v2, v3, v4) = 0) | ~ in_ty(v0) | ? [v5: 208.61/128.43 $int] : ? [v6: $int] : ? [v7: $int] : ? [v8: $int] : ((v5 = 0 & 208.61/128.43 permut_sub2(v0, v1, v2, v3, v4) = 0) | (elts(v0, v2) = v6 & 208.61/128.43 elts(v0, v1) = v5 & in_uni(v6) & in_uni(v5) & (( ~ (v8 = 0) & 208.61/128.43 map_eq_sub1(v0, v5, v6, v4, v7) = v8 & length1(v0, v1) = v7) | 208.61/128.43 ( ~ (v7 = 0) & map_eq_sub1(v0, v5, v6, 0, v3) = v7))))) 208.61/128.43 (56) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ( ~ 208.61/128.43 (get4(v0, v1, v2) = v3) | ~ in_ty(v0) | ? [v4: $int] : ? [v5: $int] 208.61/128.43 : (elts(v0, v1) = v4 & t2tb1(v2) = v5 & get(v0, int, v4, v5) = v3 & 208.61/128.43 in_uni(v5) & in_uni(v4) & in_uni(v3))) 208.61/128.43 (57) $lesseq(1, all_86_10) 208.61/128.43 (58) map_eq_sub1(int, all_105_3, all_105_1, $sum(all_86_10, 1), all_86_13) = 208.61/128.43 0 208.61/128.43 (59) t2tb(all_86_4) = all_105_3 208.61/128.43 (60) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.61/128.43 $int] : ! [v5: $int] : ( ~ (permut3(v0, v1, v2, v3, v4) = v5) | ~ 208.61/128.43 in_ty(v0) | ? [v6: $int] : ? [v7: $int] : ? [v8: $int] : ? [v9: 208.61/128.43 $int] : ? [v10: $int] : ((v10 = 0 & v9 = 0 & v5 = 0 & 208.61/128.43 map_eq_sub1(v0, v6, v7, v4, v8) = 0 & map_eq_sub1(v0, v6, v7, 0, 208.61/128.43 v3) = 0 & length1(v0, v1) = v8 & elts(v0, v2) = v7 & elts(v0, 208.61/128.43 v1) = v6 & in_uni(v7) & in_uni(v6)) | ( ~ (v6 = 0) & 208.61/128.43 permut_sub2(v0, v1, v2, v3, v4) = v6))) 208.61/128.43 (61) ! [v0: $int] : ! [v1: $int] : ( ~ ($lesseq(v0, all_86_10)) | ~ 208.61/128.43 ($lesseq(all_86_7, v0)) | ~ (get4(int, all_125_0, v0) = v1) | ? [v2: 208.61/128.43 $int] : ($lesseq(42, v2) & tb2t1(v1) = v2)) 208.61/128.43 208.61/128.43 Begin of proof 208.61/128.43 | 208.61/128.43 | BETA: splitting (10) gives: 208.61/128.43 | 208.61/128.43 | Case 1: 208.61/128.43 | | 208.61/128.43 | | (62) ~ (all_133_0 = 42) & $lesseq(1, $difference(all_86_7, all_133_2)) & 208.61/128.43 | | $lesseq(1, $difference(all_133_2, all_86_8)) & tb2t1(all_133_1) = 208.61/128.43 | | all_133_0 & get4(int, all_133_3, all_133_2) = all_133_1 & 208.61/128.43 | | in_uni(all_133_1) 208.61/128.43 | | 208.61/128.43 | | ALPHA: (62) implies: 208.61/128.43 | | (63) ~ (all_133_0 = 42) 208.61/128.43 | | (64) $lesseq(1, $difference(all_133_2, all_86_8)) 208.61/128.43 | | (65) $lesseq(1, $difference(all_86_7, all_133_2)) 208.61/128.43 | | (66) get4(int, all_133_3, all_133_2) = all_133_1 208.61/128.43 | | (67) tb2t1(all_133_1) = all_133_0 208.61/128.43 | | 208.61/128.43 | | COMBINE_INEQS: (64), (65) imply: 208.61/128.43 | | (68) $lesseq(2, $difference(all_86_7, all_86_8)) 208.61/128.43 | | 208.61/128.43 | | COMBINE_INEQS: (35), (68) imply: 208.61/128.43 | | (69) $lesseq(2, $difference(all_86_10, all_86_8)) 208.61/128.43 | | 208.61/128.43 | | COMBINE_INEQS: (36), (69) imply: 208.61/128.43 | | (70) $lesseq(2, all_86_10) 208.61/128.43 | | 208.61/128.43 | | REDUCE: (51), (66) imply: 208.61/128.43 | | (71) get4(int, all_105_2, all_133_2) = all_133_1 208.61/128.43 | | 208.61/128.43 | | GROUND_INST: instantiating (11) with int, all_103_4, all_105_4, all_86_11, 208.61/128.43 | | $sum(all_86_10, 1), all_103_3, all_105_3, 0, simplifying with 208.61/128.43 | | (5), (8), (18), (22) gives: 208.61/128.43 | | (72) ? [v0: $int] : ? [v1: $int] : ((v1 = v0 & $lesseq(1, 208.61/128.43 | | $difference(v0, all_86_10)) & $lesseq(all_86_11, v0) & 208.61/128.43 | | $lesseq(-1, all_86_10) & $lesseq(0, all_86_11) & length1(int, 208.61/128.43 | | all_105_4) = v0 & length1(int, all_103_4) = v0) | ( ~ (v0 = 0) 208.61/128.43 | | & permut3(int, all_103_4, all_105_4, all_86_11, $sum(all_86_10, 208.61/128.43 | | 1)) = v0)) 208.61/128.43 | | 208.61/128.43 | | GROUND_INST: instantiating (41) with int, all_103_4, all_105_4, all_86_11, 208.61/128.43 | | $sum(all_86_10, 1), all_103_3, all_105_3, simplifying with (5), 208.61/128.43 | | (8), (18), (22) gives: 208.61/128.43 | | (73) ~ ($lesseq(-1, all_86_10)) | ~ ($lesseq(0, all_86_11)) | ? [v0: 208.61/128.43 | | $int] : ? [v1: $int] : ((v0 = 0 & permut3(int, all_103_4, 208.61/128.43 | | all_105_4, all_86_11, $sum(all_86_10, 1)) = 0) | (length1(int, 208.61/128.43 | | all_103_4) = v0 & ( ~ ($lesseq(1, $difference(v0, all_86_10))) 208.61/128.43 | | | ~ ($lesseq(all_86_11, v0)) | ( ~ (v1 = v0) & length1(int, 208.61/128.43 | | all_105_4) = v1)))) 208.61/128.43 | | 208.61/128.43 | | GROUND_INST: instantiating (48) with all_86_1, all_133_2, all_105_2, 208.61/128.43 | | all_133_1, simplifying with (32), (40), (71) gives: 208.61/128.43 | | (74) ? [v0: $int] : ? [v1: $int] : ? [v2: $int] : (tb2t(v0) = v1 & 208.61/128.43 | | tb2t1(all_133_1) = v2 & get3(v1, all_133_2) = v2 & elts(int, 208.61/128.43 | | all_105_2) = v0 & in_map_int_int(v1) & in_uni(v0)) 208.61/128.43 | | 208.61/128.44 | | GROUND_INST: instantiating (56) with int, all_105_2, all_133_2, all_133_1, 208.61/128.44 | | simplifying with (8), (71) gives: 208.61/128.44 | | (75) ? [v0: $int] : ? [v1: $int] : (elts(int, all_105_2) = v0 & 208.61/128.44 | | t2tb1(all_133_2) = v1 & get(int, int, v0, v1) = all_133_1 & 208.61/128.44 | | in_uni(v1) & in_uni(v0) & in_uni(all_133_1)) 208.61/128.44 | | 208.61/128.44 | | DELTA: instantiating (72) with fresh symbols all_665_0, all_665_1 gives: 208.61/128.44 | | (76) (all_665_0 = all_665_1 & $lesseq(1, $difference(all_665_1, 208.61/128.44 | | all_86_10)) & $lesseq(all_86_11, all_665_1) & $lesseq(-1, 208.61/128.44 | | all_86_10) & $lesseq(0, all_86_11) & length1(int, all_105_4) = 208.61/128.44 | | all_665_1 & length1(int, all_103_4) = all_665_1) | ( ~ (all_665_1 208.61/128.44 | | = 0) & permut3(int, all_103_4, all_105_4, all_86_11, 208.61/128.44 | | $sum(all_86_10, 1)) = all_665_1) 208.61/128.44 | | 208.61/128.44 | | DELTA: instantiating (75) with fresh symbols all_668_0, all_668_1 gives: 208.61/128.44 | | (77) elts(int, all_105_2) = all_668_1 & t2tb1(all_133_2) = all_668_0 & 208.61/128.44 | | get(int, int, all_668_1, all_668_0) = all_133_1 & in_uni(all_668_0) 208.61/128.44 | | & in_uni(all_668_1) & in_uni(all_133_1) 208.61/128.44 | | 208.61/128.44 | | ALPHA: (77) implies: 208.61/128.44 | | (78) t2tb1(all_133_2) = all_668_0 208.61/128.44 | | (79) elts(int, all_105_2) = all_668_1 208.61/128.44 | | 208.61/128.44 | | DELTA: instantiating (74) with fresh symbols all_678_0, all_678_1, all_678_2 208.61/128.44 | | gives: 208.61/128.44 | | (80) tb2t(all_678_2) = all_678_1 & tb2t1(all_133_1) = all_678_0 & 208.61/128.44 | | get3(all_678_1, all_133_2) = all_678_0 & elts(int, all_105_2) = 208.61/128.44 | | all_678_2 & in_map_int_int(all_678_1) & in_uni(all_678_2) 208.61/128.44 | | 208.61/128.44 | | ALPHA: (80) implies: 208.61/128.44 | | (81) elts(int, all_105_2) = all_678_2 208.61/128.44 | | (82) get3(all_678_1, all_133_2) = all_678_0 208.61/128.44 | | (83) tb2t1(all_133_1) = all_678_0 208.61/128.44 | | (84) tb2t(all_678_2) = all_678_1 208.61/128.44 | | 208.61/128.44 | | BETA: splitting (73) gives: 208.61/128.44 | | 208.61/128.44 | | Case 1: 208.61/128.44 | | | 208.61/128.44 | | | (85) $lesseq(all_86_11, -1) 208.61/128.44 | | | 208.61/128.44 | | | COMBINE_INEQS: (47), (85) imply: 208.61/128.44 | | | (86) $lesseq(0, -1) 208.61/128.44 | | | 208.61/128.44 | | | CLOSE: (86) is inconsistent. 208.61/128.44 | | | 208.61/128.44 | | Case 2: 208.61/128.44 | | | 208.61/128.44 | | | (87) ~ ($lesseq(-1, all_86_10)) | ? [v0: $int] : ? [v1: $int] : ((v0 208.61/128.44 | | | = 0 & permut3(int, all_103_4, all_105_4, all_86_11, 208.61/128.44 | | | $sum(all_86_10, 1)) = 0) | (length1(int, all_103_4) = v0 & ( 208.61/128.44 | | | ~ ($lesseq(1, $difference(v0, all_86_10))) | ~ 208.61/128.44 | | | ($lesseq(all_86_11, v0)) | ( ~ (v1 = v0) & length1(int, 208.61/128.44 | | | all_105_4) = v1)))) 208.61/128.44 | | | 208.61/128.44 | | | BETA: splitting (87) gives: 208.61/128.44 | | | 208.61/128.44 | | | Case 1: 208.61/128.44 | | | | 208.61/128.44 | | | | (88) $lesseq(all_86_10, -2) 208.61/128.44 | | | | 208.61/128.44 | | | | COMBINE_INEQS: (70), (88) imply: 208.61/128.44 | | | | (89) $lesseq(0, -1) 208.61/128.44 | | | | 208.61/128.44 | | | | CLOSE: (89) is inconsistent. 208.61/128.44 | | | | 208.61/128.44 | | | Case 2: 208.61/128.44 | | | | 208.61/128.44 | | | | (90) ? [v0: $int] : ? [v1: $int] : ((v0 = 0 & permut3(int, 208.61/128.44 | | | | all_103_4, all_105_4, all_86_11, $sum(all_86_10, 1)) = 0) 208.61/128.44 | | | | | (length1(int, all_103_4) = v0 & ( ~ ($lesseq(1, 208.61/128.44 | | | | $difference(v0, all_86_10))) | ~ ($lesseq(all_86_11, 208.61/128.44 | | | | v0)) | ( ~ (v1 = v0) & length1(int, all_105_4) = 208.61/128.44 | | | | v1)))) 208.61/128.44 | | | | 208.61/128.44 | | | | DELTA: instantiating (90) with fresh symbols all_694_0, all_694_1 gives: 208.61/128.44 | | | | (91) (all_694_1 = 0 & permut3(int, all_103_4, all_105_4, all_86_11, 208.61/128.44 | | | | $sum(all_86_10, 1)) = 0) | (length1(int, all_103_4) = 208.61/128.44 | | | | all_694_1 & ( ~ ($lesseq(1, $difference(all_694_1, 208.61/128.44 | | | | all_86_10))) | ~ ($lesseq(all_86_11, all_694_1)) | ( 208.61/128.44 | | | | ~ (all_694_0 = all_694_1) & length1(int, all_105_4) = 208.61/128.44 | | | | all_694_0))) 208.61/128.44 | | | | 208.61/128.44 | | | | BETA: splitting (91) gives: 208.61/128.44 | | | | 208.61/128.44 | | | | Case 1: 208.61/128.44 | | | | | 208.61/128.44 | | | | | (92) all_694_1 = 0 & permut3(int, all_103_4, all_105_4, all_86_11, 208.61/128.44 | | | | | $sum(all_86_10, 1)) = 0 208.61/128.44 | | | | | 208.61/128.44 | | | | | ALPHA: (92) implies: 208.61/128.44 | | | | | (93) permut3(int, all_103_4, all_105_4, all_86_11, $sum(all_86_10, 208.61/128.44 | | | | | 1)) = 0 208.61/128.44 | | | | | 208.61/128.44 | | | | | BETA: splitting (76) gives: 208.61/128.44 | | | | | 208.61/128.44 | | | | | Case 1: 208.61/128.44 | | | | | | 208.61/128.44 | | | | | | (94) all_665_0 = all_665_1 & $lesseq(1, $difference(all_665_1, 208.61/128.44 | | | | | | all_86_10)) & $lesseq(all_86_11, all_665_1) & 208.61/128.44 | | | | | | $lesseq(-1, all_86_10) & $lesseq(0, all_86_11) & 208.61/128.44 | | | | | | length1(int, all_105_4) = all_665_1 & length1(int, 208.61/128.44 | | | | | | all_103_4) = all_665_1 208.61/128.44 | | | | | | 208.61/128.44 | | | | | | ALPHA: (94) implies: 208.61/128.44 | | | | | | (95) $lesseq(1, $difference(all_665_1, all_86_10)) 208.61/128.44 | | | | | | (96) length1(int, all_103_4) = all_665_1 208.61/128.44 | | | | | | 208.61/128.44 | | | | | | GROUND_INST: instantiating (1) with all_133_0, all_678_0, all_133_1, 208.61/128.44 | | | | | | simplifying with (67), (83) gives: 208.61/128.44 | | | | | | (97) all_678_0 = all_133_0 208.61/128.44 | | | | | | 208.61/128.44 | | | | | | GROUND_INST: instantiating (54) with all_86_13, all_665_1, 208.61/128.44 | | | | | | all_103_4, int, simplifying with (9), (96) gives: 208.61/128.44 | | | | | | (98) all_665_1 = all_86_13 208.61/128.44 | | | | | | 208.61/128.44 | | | | | | GROUND_INST: instantiating (19) with all_105_1, all_678_2, 208.61/128.44 | | | | | | all_105_2, int, simplifying with (30), (81) gives: 208.61/128.44 | | | | | | (99) all_678_2 = all_105_1 208.61/128.44 | | | | | | 208.61/128.44 | | | | | | GROUND_INST: instantiating (19) with all_678_2, all_668_1, 208.61/128.44 | | | | | | all_105_2, int, simplifying with (79), (81) gives: 208.61/128.44 | | | | | | (100) all_678_2 = all_668_1 208.61/128.44 | | | | | | 208.61/128.44 | | | | | | COMBINE_EQS: (99), (100) imply: 208.61/128.44 | | | | | | (101) all_668_1 = all_105_1 208.61/128.44 | | | | | | 208.61/128.44 | | | | | | REDUCE: (84), (99) imply: 208.61/128.44 | | | | | | (102) tb2t(all_105_1) = all_678_1 208.61/128.44 | | | | | | 208.61/128.44 | | | | | | REDUCE: (82), (97) imply: 208.61/128.44 | | | | | | (103) get3(all_678_1, all_133_2) = all_133_0 208.61/128.44 | | | | | | 208.61/128.44 | | | | | | GROUND_INST: instantiating (49) with all_86_2, all_678_1, all_105_1, 208.61/128.44 | | | | | | simplifying with (27), (102) gives: 208.61/128.44 | | | | | | (104) all_678_1 = all_86_2 208.61/128.44 | | | | | | 208.61/128.44 | | | | | | REDUCE: (103), (104) imply: 208.61/128.44 | | | | | | (105) get3(all_86_2, all_133_2) = all_133_0 208.61/128.44 | | | | | | 208.61/128.44 | | | | | | GROUND_INST: instantiating (26) with all_86_9, all_86_3, all_86_11, 208.61/128.44 | | | | | | $sum(all_86_10, 1), all_103_4, all_105_4, simplifying 208.61/128.44 | | | | | | with (6), (24), (29), (93) gives: 208.61/128.44 | | | | | | (106) ? [v0: $int] : ? [v1: $int] : ? [v2: $int] : ? [v3: 208.61/128.44 | | | | | | $int] : ((v0 = 0 & permut_sub3(all_86_9, all_86_3, 208.61/128.44 | | | | | | all_86_11, $sum(all_86_10, 1)) = 0) | (elts(int, 208.61/128.44 | | | | | | all_105_4) = v1 & elts(int, all_103_4) = v0 & 208.61/128.44 | | | | | | in_uni(v1) & in_uni(v0) & (( ~ (v3 = 0) & 208.61/128.44 | | | | | | map_eq_sub1(int, v0, v1, $sum(all_86_10, 1), v2) = 208.61/128.44 | | | | | | v3 & length1(int, all_103_4) = v2) | ( ~ (v2 = 0) & 208.61/128.44 | | | | | | map_eq_sub1(int, v0, v1, 0, all_86_11) = v2)))) 208.61/128.44 | | | | | | 208.61/128.44 | | | | | | GROUND_INST: instantiating (55) with int, all_103_4, all_105_4, 208.61/128.44 | | | | | | all_86_11, $sum(all_86_10, 1), simplifying with (8), 208.61/128.44 | | | | | | (93) gives: 208.61/128.44 | | | | | | (107) ? [v0: $int] : ? [v1: $int] : ? [v2: $int] : ? [v3: 208.61/128.44 | | | | | | $int] : ((v0 = 0 & permut_sub2(int, all_103_4, all_105_4, 208.61/128.44 | | | | | | all_86_11, $sum(all_86_10, 1)) = 0) | (elts(int, 208.61/128.44 | | | | | | all_105_4) = v1 & elts(int, all_103_4) = v0 & 208.61/128.44 | | | | | | in_uni(v1) & in_uni(v0) & (( ~ (v3 = 0) & 208.61/128.44 | | | | | | map_eq_sub1(int, v0, v1, $sum(all_86_10, 1), v2) = 208.61/128.44 | | | | | | v3 & length1(int, all_103_4) = v2) | ( ~ (v2 = 0) & 208.61/128.44 | | | | | | map_eq_sub1(int, v0, v1, 0, all_86_11) = v2)))) 208.61/128.44 | | | | | | 208.61/128.44 | | | | | | GROUND_INST: instantiating (53) with all_86_9, all_86_3, all_86_11, 208.61/128.44 | | | | | | $sum(all_86_10, 1), all_103_4, all_105_4, 0, 208.61/128.44 | | | | | | simplifying with (6), (24), (29), (93) gives: 208.61/128.44 | | | | | | (108) ? [v0: $int] : ? [v1: $int] : ? [v2: $int] : ? [v3: 208.61/128.44 | | | | | | $int] : ? [v4: $int] : ((v4 = 0 & v2 = 0 & 208.61/128.44 | | | | | | map_eq_sub1(int, v0, v1, $sum(all_86_10, 1), v3) = 0 & 208.61/128.44 | | | | | | map_eq_sub1(int, v0, v1, 0, all_86_11) = 0 & 208.61/128.44 | | | | | | length1(int, all_103_4) = v3 & elts(int, all_105_4) = 208.61/128.44 | | | | | | v1 & elts(int, all_103_4) = v0 & in_uni(v1) & 208.61/128.44 | | | | | | in_uni(v0)) | ( ~ (v0 = 0) & permut_sub3(all_86_9, 208.61/128.44 | | | | | | all_86_3, all_86_11, $sum(all_86_10, 1)) = v0)) 208.61/128.44 | | | | | | 208.61/128.44 | | | | | | GROUND_INST: instantiating (60) with int, all_103_4, all_105_4, 208.61/128.44 | | | | | | all_86_11, $sum(all_86_10, 1), 0, simplifying with (8), 208.61/128.44 | | | | | | (93) gives: 208.61/128.44 | | | | | | (109) ? [v0: $int] : ? [v1: $int] : ? [v2: $int] : ? [v3: 208.61/128.44 | | | | | | $int] : ? [v4: $int] : ((v4 = 0 & v3 = 0 & 208.61/128.44 | | | | | | map_eq_sub1(int, v0, v1, $sum(all_86_10, 1), v2) = 0 & 208.61/128.44 | | | | | | map_eq_sub1(int, v0, v1, 0, all_86_11) = 0 & 208.61/128.44 | | | | | | length1(int, all_103_4) = v2 & elts(int, all_105_4) = 208.61/128.44 | | | | | | v1 & elts(int, all_103_4) = v0 & in_uni(v1) & 208.61/128.44 | | | | | | in_uni(v0)) | ( ~ (v0 = 0) & permut_sub2(int, 208.61/128.44 | | | | | | all_103_4, all_105_4, all_86_11, $sum(all_86_10, 1)) 208.61/128.44 | | | | | | = v0)) 208.61/128.44 | | | | | | 208.61/128.44 | | | | | | GROUND_INST: instantiating (52) with all_86_4, all_86_2, 0, 208.61/128.44 | | | | | | all_86_7, all_105_3, all_105_1, all_133_2, all_133_0, 208.61/128.44 | | | | | | simplifying with (7), (25), (46), (59), (105) gives: 208.61/128.44 | | | | | | (110) ~ ($lesseq(1, $difference(all_86_7, all_133_2))) | ~ 208.61/128.44 | | | | | | ($lesseq(0, all_133_2)) | get3(all_86_4, all_133_2) = 208.61/128.44 | | | | | | all_133_0 208.61/128.44 | | | | | | 208.61/128.44 | | | | | | GROUND_INST: instantiating (43) with int, all_105_3, all_105_1, 0, 208.61/128.44 | | | | | | all_86_7, all_133_2, all_668_0, simplifying with (8), 208.61/128.44 | | | | | | (25), (78) gives: 208.61/128.44 | | | | | | (111) ~ ($lesseq(1, $difference(all_86_7, all_133_2))) | ~ 208.61/128.44 | | | | | | ($lesseq(0, all_133_2)) | ? [v0: $int] : (get(int, int, 208.61/128.44 | | | | | | all_105_1, all_668_0) = v0 & get(int, int, all_105_3, 208.61/128.44 | | | | | | all_668_0) = v0 & in_uni(v0)) 208.61/128.44 | | | | | | 208.61/128.44 | | | | | | GROUND_INST: instantiating (43) with int, all_103_1, all_105_3, 208.61/128.44 | | | | | | $sum(all_86_8, 1), all_86_13, all_133_2, all_668_0, 208.61/128.44 | | | | | | simplifying with (8), (16), (78) gives: 208.61/128.44 | | | | | | (112) ~ ($lesseq(1, $difference(all_86_13, all_133_2))) | ~ 208.61/128.44 | | | | | | ($lesseq(1, $difference(all_133_2, all_86_8))) | ? [v0: 208.61/128.44 | | | | | | $int] : (get(int, int, all_105_3, all_668_0) = v0 & 208.61/128.44 | | | | | | get(int, int, all_103_1, all_668_0) = v0 & in_uni(v0)) 208.61/128.44 | | | | | | 208.61/128.44 | | | | | | DELTA: instantiating (109) with fresh symbols all_745_0, all_745_1, 208.61/128.44 | | | | | | all_745_2, all_745_3, all_745_4 gives: 208.61/128.44 | | | | | | (113) (all_745_0 = 0 & all_745_1 = 0 & map_eq_sub1(int, 208.61/128.44 | | | | | | all_745_4, all_745_3, $sum(all_86_10, 1), all_745_2) = 208.61/128.44 | | | | | | 0 & map_eq_sub1(int, all_745_4, all_745_3, 0, all_86_11) 208.61/128.44 | | | | | | = 0 & length1(int, all_103_4) = all_745_2 & elts(int, 208.61/128.44 | | | | | | all_105_4) = all_745_3 & elts(int, all_103_4) = 208.61/128.44 | | | | | | all_745_4 & in_uni(all_745_3) & in_uni(all_745_4)) | ( ~ 208.61/128.44 | | | | | | (all_745_4 = 0) & permut_sub2(int, all_103_4, all_105_4, 208.61/128.44 | | | | | | all_86_11, $sum(all_86_10, 1)) = all_745_4) 208.61/128.44 | | | | | | 208.61/128.44 | | | | | | DELTA: instantiating (108) with fresh symbols all_746_0, all_746_1, 208.61/128.44 | | | | | | all_746_2, all_746_3, all_746_4 gives: 208.61/128.44 | | | | | | (114) (all_746_0 = 0 & all_746_2 = 0 & map_eq_sub1(int, 208.61/128.44 | | | | | | all_746_4, all_746_3, $sum(all_86_10, 1), all_746_1) = 208.61/128.44 | | | | | | 0 & map_eq_sub1(int, all_746_4, all_746_3, 0, all_86_11) 208.61/128.44 | | | | | | = 0 & length1(int, all_103_4) = all_746_1 & elts(int, 208.61/128.44 | | | | | | all_105_4) = all_746_3 & elts(int, all_103_4) = 208.61/128.44 | | | | | | all_746_4 & in_uni(all_746_3) & in_uni(all_746_4)) | ( ~ 208.61/128.44 | | | | | | (all_746_4 = 0) & permut_sub3(all_86_9, all_86_3, 208.61/128.44 | | | | | | all_86_11, $sum(all_86_10, 1)) = all_746_4) 208.61/128.44 | | | | | | 208.61/128.44 | | | | | | DELTA: instantiating (107) with fresh symbols all_757_0, all_757_1, 208.61/128.44 | | | | | | all_757_2, all_757_3 gives: 208.61/128.44 | | | | | | (115) (all_757_3 = 0 & permut_sub2(int, all_103_4, all_105_4, 208.61/128.44 | | | | | | all_86_11, $sum(all_86_10, 1)) = 0) | (elts(int, 208.61/128.44 | | | | | | all_105_4) = all_757_2 & elts(int, all_103_4) = 208.61/128.44 | | | | | | all_757_3 & in_uni(all_757_2) & in_uni(all_757_3) & (( ~ 208.61/128.44 | | | | | | (all_757_0 = 0) & map_eq_sub1(int, all_757_3, 208.61/128.44 | | | | | | all_757_2, $sum(all_86_10, 1), all_757_1) = 208.61/128.44 | | | | | | all_757_0 & length1(int, all_103_4) = all_757_1) | ( 208.61/128.44 | | | | | | ~ (all_757_1 = 0) & map_eq_sub1(int, all_757_3, 208.61/128.44 | | | | | | all_757_2, 0, all_86_11) = all_757_1))) 208.61/128.44 | | | | | | 208.61/128.44 | | | | | | DELTA: instantiating (106) with fresh symbols all_758_0, all_758_1, 208.61/128.44 | | | | | | all_758_2, all_758_3 gives: 208.61/128.44 | | | | | | (116) (all_758_3 = 0 & permut_sub3(all_86_9, all_86_3, all_86_11, 208.61/128.44 | | | | | | $sum(all_86_10, 1)) = 0) | (elts(int, all_105_4) = 208.61/128.44 | | | | | | all_758_2 & elts(int, all_103_4) = all_758_3 & 208.61/128.44 | | | | | | in_uni(all_758_2) & in_uni(all_758_3) & (( ~ (all_758_0 = 208.61/128.44 | | | | | | 0) & map_eq_sub1(int, all_758_3, all_758_2, 208.61/128.44 | | | | | | $sum(all_86_10, 1), all_758_1) = all_758_0 & 208.61/128.44 | | | | | | length1(int, all_103_4) = all_758_1) | ( ~ (all_758_1 208.61/128.44 | | | | | | = 0) & map_eq_sub1(int, all_758_3, all_758_2, 0, 208.61/128.44 | | | | | | all_86_11) = all_758_1))) 208.61/128.44 | | | | | | 208.61/128.44 | | | | | | BETA: splitting (33) gives: 208.61/128.44 | | | | | | 208.61/128.44 | | | | | | Case 1: 208.61/128.44 | | | | | | | 208.61/128.44 | | | | | | | (117) ~ (all_86_11 = 0) 208.61/128.44 | | | | | | | 208.61/128.44 | | | | | | | STRENGTHEN: (47), (117) imply: 208.61/128.44 | | | | | | | (118) $lesseq(1, all_86_11) 208.61/128.44 | | | | | | | 208.61/128.44 | | | | | | | COMBINE_INEQS: (34), (69) imply: 208.61/128.44 | | | | | | | (119) $lesseq(2, $difference(all_86_10, all_86_11)) 208.61/128.44 | | | | | | | 208.61/128.44 | | | | | | | COMBINE_INEQS: (44), (119) imply: 208.61/128.44 | | | | | | | (120) $lesseq(3, $difference(all_86_13, all_86_11)) 208.61/128.44 | | | | | | | 208.61/128.44 | | | | | | | COMBINE_INEQS: (118), (120) imply: 208.61/128.44 | | | | | | | (121) $lesseq(4, all_86_13) 208.61/128.44 | | | | | | | 208.61/128.44 | | | | | | | REF_CLOSE: (3), (4), (5), (8), (9), (13), (14), (15), (16), (19), 208.61/128.44 | | | | | | | (22), (23), (36), (45), (50), (52), (54), (59), (63), 208.61/128.44 | | | | | | | (64), (65), (70), (110), (111), (112), (113), (114), 208.61/128.44 | | | | | | | (115), (116), (121) are inconsistent by sub-proof #150. 208.61/128.44 | | | | | | | 208.61/128.44 | | | | | | Case 2: 208.61/128.44 | | | | | | | 208.61/128.44 | | | | | | | (122) all_86_11 = 0 208.61/128.44 | | | | | | | (123) ~ ($difference(all_86_10, all_86_13) = -1) 208.61/128.44 | | | | | | | 208.61/128.44 | | | | | | | STRENGTHEN: (44), (123) imply: 208.61/128.44 | | | | | | | (124) $lesseq(2, $difference(all_86_13, all_86_10)) 208.61/128.44 | | | | | | | 208.61/128.44 | | | | | | | COMBINE_INEQS: (70), (124) imply: 208.61/128.44 | | | | | | | (125) $lesseq(4, all_86_13) 208.61/128.44 | | | | | | | 208.61/128.44 | | | | | | | REF_CLOSE: (3), (4), (5), (8), (9), (13), (14), (15), (16), (19), 208.61/128.44 | | | | | | | (22), (23), (36), (45), (50), (52), (54), (59), (63), 208.61/128.44 | | | | | | | (64), (65), (70), (110), (111), (112), (113), (114), 208.61/128.44 | | | | | | | (115), (116), (125) are inconsistent by sub-proof #150. 208.61/128.44 | | | | | | | 208.61/128.44 | | | | | | End of split 208.61/128.44 | | | | | | 208.61/128.44 | | | | | Case 2: 208.61/128.44 | | | | | | 208.61/128.44 | | | | | | (126) ~ (all_665_1 = 0) & permut3(int, all_103_4, all_105_4, 208.61/128.44 | | | | | | all_86_11, $sum(all_86_10, 1)) = all_665_1 208.61/128.44 | | | | | | 208.61/128.44 | | | | | | ALPHA: (126) implies: 208.61/128.44 | | | | | | (127) ~ (all_665_1 = 0) 208.61/128.44 | | | | | | (128) permut3(int, all_103_4, all_105_4, all_86_11, 208.61/128.44 | | | | | | $sum(all_86_10, 1)) = all_665_1 208.61/128.44 | | | | | | 208.61/128.44 | | | | | | GROUND_INST: instantiating (17) with all_665_1, 0, $sum(all_86_10, 208.61/128.44 | | | | | | 1), all_86_11, all_105_4, all_103_4, int, simplifying 208.61/128.44 | | | | | | with (93), (128) gives: 208.61/128.44 | | | | | | (129) all_665_1 = 0 208.61/128.44 | | | | | | 208.61/128.44 | | | | | | REDUCE: (127), (129) imply: 208.61/128.44 | | | | | | (130) ~ (0 = 0) 208.61/128.44 | | | | | | 208.61/128.44 | | | | | | CLOSE: (130) is inconsistent. 208.61/128.44 | | | | | | 208.61/128.44 | | | | | End of split 208.61/128.44 | | | | | 208.61/128.44 | | | | Case 2: 208.61/128.44 | | | | | 208.61/128.44 | | | | | (131) length1(int, all_103_4) = all_694_1 & ( ~ ($lesseq(1, 208.61/128.44 | | | | | $difference(all_694_1, all_86_10))) | ~ 208.61/128.44 | | | | | ($lesseq(all_86_11, all_694_1)) | ( ~ (all_694_0 = 208.61/128.44 | | | | | all_694_1) & length1(int, all_105_4) = all_694_0)) 208.61/128.44 | | | | | 208.61/128.44 | | | | | ALPHA: (131) implies: 208.61/128.44 | | | | | (132) length1(int, all_103_4) = all_694_1 208.61/128.44 | | | | | (133) ~ ($lesseq(1, $difference(all_694_1, all_86_10))) | ~ 208.61/128.44 | | | | | ($lesseq(all_86_11, all_694_1)) | ( ~ (all_694_0 = all_694_1) 208.61/128.44 | | | | | & length1(int, all_105_4) = all_694_0) 208.61/128.44 | | | | | 208.61/128.44 | | | | | GROUND_INST: instantiating (54) with all_86_13, all_694_1, all_103_4, 208.61/128.44 | | | | | int, simplifying with (9), (132) gives: 208.61/128.44 | | | | | (134) all_694_1 = all_86_13 208.61/128.44 | | | | | 208.61/128.44 | | | | | BETA: splitting (133) gives: 208.61/128.44 | | | | | 208.61/128.44 | | | | | Case 1: 208.61/128.44 | | | | | | 208.61/128.44 | | | | | | (135) $lesseq(1, $difference(all_86_11, all_694_1)) 208.61/128.44 | | | | | | 208.61/128.44 | | | | | | REDUCE: (134), (135) imply: 208.61/128.44 | | | | | | (136) $lesseq(1, $difference(all_86_11, all_86_13)) 208.61/128.44 | | | | | | 208.61/128.44 | | | | | | COMBINE_INEQS: (34), (69) imply: 208.61/128.44 | | | | | | (137) $lesseq(2, $difference(all_86_10, all_86_11)) 208.61/128.44 | | | | | | 208.61/128.44 | | | | | | COMBINE_INEQS: (44), (137) imply: 208.61/128.44 | | | | | | (138) $lesseq(3, $difference(all_86_13, all_86_11)) 208.61/128.44 | | | | | | 208.61/128.44 | | | | | | COMBINE_INEQS: (136), (138) imply: 208.61/128.44 | | | | | | (139) $lesseq(0, -1) 208.61/128.44 | | | | | | 208.61/128.44 | | | | | | CLOSE: (139) is inconsistent. 208.61/128.44 | | | | | | 208.61/128.44 | | | | | Case 2: 208.61/128.44 | | | | | | 208.61/128.44 | | | | | | (140) ~ ($lesseq(1, $difference(all_694_1, all_86_10))) | ( ~ 208.61/128.44 | | | | | | (all_694_0 = all_694_1) & length1(int, all_105_4) = 208.61/128.44 | | | | | | all_694_0) 208.61/128.44 | | | | | | 208.61/128.44 | | | | | | BETA: splitting (140) gives: 208.61/128.44 | | | | | | 208.61/128.44 | | | | | | Case 1: 208.61/128.44 | | | | | | | 208.61/128.44 | | | | | | | (141) $lesseq(all_694_1, all_86_10) 208.61/128.44 | | | | | | | 208.61/128.44 | | | | | | | REDUCE: (134), (141) imply: 208.61/128.45 | | | | | | | (142) $lesseq(all_86_13, all_86_10) 208.61/128.45 | | | | | | | 208.61/128.45 | | | | | | | COMBINE_INEQS: (44), (142) imply: 208.61/128.45 | | | | | | | (143) $lesseq(0, -1) 208.61/128.45 | | | | | | | 208.61/128.45 | | | | | | | CLOSE: (143) is inconsistent. 208.61/128.45 | | | | | | | 208.61/128.45 | | | | | | Case 2: 208.61/128.45 | | | | | | | 208.70/128.45 | | | | | | | (144) ~ (all_694_0 = all_694_1) & length1(int, all_105_4) = 208.70/128.45 | | | | | | | all_694_0 208.70/128.45 | | | | | | | 208.70/128.45 | | | | | | | ALPHA: (144) implies: 208.70/128.45 | | | | | | | (145) ~ (all_694_0 = all_694_1) 208.70/128.45 | | | | | | | (146) length1(int, all_105_4) = all_694_0 208.70/128.45 | | | | | | | 208.70/128.45 | | | | | | | REDUCE: (134), (145) imply: 208.70/128.45 | | | | | | | (147) ~ (all_694_0 = all_86_13) 208.70/128.45 | | | | | | | 208.70/128.45 | | | | | | | GROUND_INST: instantiating (54) with all_86_13, all_694_0, 208.70/128.45 | | | | | | | all_105_4, int, simplifying with (20), (146) gives: 208.70/128.45 | | | | | | | (148) all_694_0 = all_86_13 208.70/128.45 | | | | | | | 208.70/128.45 | | | | | | | REDUCE: (147), (148) imply: 208.70/128.45 | | | | | | | (149) ~ (0 = 0) 208.70/128.45 | | | | | | | 208.70/128.45 | | | | | | | CLOSE: (149) is inconsistent. 208.70/128.45 | | | | | | | 208.70/128.45 | | | | | | End of split 208.70/128.45 | | | | | | 208.70/128.45 | | | | | End of split 208.70/128.45 | | | | | 208.70/128.45 | | | | End of split 208.70/128.45 | | | | 208.70/128.45 | | | End of split 208.70/128.45 | | | 208.70/128.45 | | End of split 208.70/128.45 | | 208.70/128.45 | Case 2: 208.70/128.45 | | 208.70/128.45 | | (150) ($lesseq(all_133_0, 41) & $lesseq(all_133_2, all_86_10) & 208.70/128.45 | | $lesseq(all_86_7, all_133_2) & tb2t1(all_133_1) = all_133_0 & 208.70/128.45 | | get4(int, all_133_3, all_133_2) = all_133_1 & in_uni(all_133_1)) 208.70/128.45 | | | ($lesseq(43, all_133_0) & $lesseq(all_133_2, all_86_8) & 208.70/128.45 | | $lesseq(all_86_11, all_133_2) & tb2t1(all_133_1) = all_133_0 & 208.70/128.45 | | get4(int, all_133_3, all_133_2) = all_133_1 & in_uni(all_133_1)) 208.70/128.45 | | 208.70/128.45 | | BETA: splitting (150) gives: 208.70/128.45 | | 208.70/128.45 | | Case 1: 208.70/128.45 | | | 208.70/128.45 | | | (151) $lesseq(all_133_0, 41) & $lesseq(all_133_2, all_86_10) & 208.70/128.45 | | | $lesseq(all_86_7, all_133_2) & tb2t1(all_133_1) = all_133_0 & 208.70/128.45 | | | get4(int, all_133_3, all_133_2) = all_133_1 & in_uni(all_133_1) 208.70/128.45 | | | 208.70/128.45 | | | ALPHA: (151) implies: 208.70/128.45 | | | (152) $lesseq(all_86_7, all_133_2) 208.70/128.45 | | | (153) $lesseq(all_133_2, all_86_10) 208.70/128.45 | | | (154) $lesseq(all_133_0, 41) 208.70/128.45 | | | (155) get4(int, all_133_3, all_133_2) = all_133_1 208.70/128.45 | | | (156) tb2t1(all_133_1) = all_133_0 208.70/128.45 | | | 208.70/128.45 | | | REDUCE: (51), (155) imply: 208.70/128.45 | | | (157) get4(int, all_105_2, all_133_2) = all_133_1 208.70/128.45 | | | 208.70/128.45 | | | REF_CLOSE: (1), (5), (6), (7), (8), (12), (18), (19), (21), (22), (27), 208.70/128.45 | | | (30), (31), (32), (37), (38), (39), (40), (41), (46), (47), 208.70/128.45 | | | (48), (49), (56), (57), (59), (61), (152), (153), (154), (156), 208.70/128.45 | | | (157) are inconsistent by sub-proof #148. 208.70/128.45 | | | 208.70/128.45 | | Case 2: 208.70/128.45 | | | 208.70/128.45 | | | (158) $lesseq(43, all_133_0) & $lesseq(all_133_2, all_86_8) & 208.70/128.45 | | | $lesseq(all_86_11, all_133_2) & tb2t1(all_133_1) = all_133_0 & 208.70/128.45 | | | get4(int, all_133_3, all_133_2) = all_133_1 & in_uni(all_133_1) 208.70/128.45 | | | 208.70/128.45 | | | ALPHA: (158) implies: 208.70/128.45 | | | (159) $lesseq(all_86_11, all_133_2) 208.70/128.45 | | | (160) $lesseq(all_133_2, all_86_8) 208.70/128.45 | | | (161) $lesseq(43, all_133_0) 208.70/128.45 | | | (162) get4(int, all_133_3, all_133_2) = all_133_1 208.70/128.45 | | | (163) tb2t1(all_133_1) = all_133_0 208.70/128.45 | | | 208.70/128.45 | | | REDUCE: (51), (162) imply: 208.70/128.45 | | | (164) get4(int, all_105_2, all_133_2) = all_133_1 208.70/128.45 | | | 208.70/128.45 | | | REF_CLOSE: (1), (2), (3), (5), (7), (8), (9), (11), (13), (15), (17), 208.70/128.45 | | | (18), (19), (20), (22), (25), (27), (28), (30), (31), (32), 208.70/128.45 | | | (33), (35), (38), (39), (40), (41), (42), (43), (44), (46), 208.70/128.45 | | | (47), (48), (49), (52), (54), (56), (57), (58), (59), (159), 208.70/128.45 | | | (160), (161), (163), (164) are inconsistent by sub-proof #143. 208.70/128.45 | | | 208.70/128.45 | | End of split 208.70/128.45 | | 208.70/128.45 | End of split 208.70/128.45 | 208.70/128.45 End of proof 208.70/128.45 208.70/128.45 Sub-proof #143 shows that the following formulas are inconsistent: 208.70/128.45 ---------------------------------------------------------------- 208.70/128.45 (1) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ (tb2t1(v2) 208.70/128.45 = v1) | ~ (tb2t1(v2) = v0)) 208.70/128.45 (2) ! [v0: $int] : ! [v1: $int] : ( ~ ($lesseq(43, v1)) | ~ ($lesseq(v0, 208.70/128.45 all_86_8)) | ~ ($lesseq(all_86_11, v0)) | ~ (get3(all_86_6, v0) = 208.70/128.45 v1)) 208.70/128.45 (3) in_map_int_int(all_86_6) 208.70/128.45 (4) elts(int, all_103_4) = all_103_3 208.70/128.45 (5) t2tb(all_86_2) = all_105_1 208.70/128.45 (6) in_ty(int) 208.70/128.45 (7) length1(int, all_103_4) = all_86_13 208.70/128.45 (8) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.70/128.45 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 208.70/128.45 (permut2(v0, v5, v6, v3, v4) = v7) | ~ (elts(v0, v2) = v6) | ~ 208.70/128.45 (elts(v0, v1) = v5) | ~ in_ty(v0) | ? [v8: $int] : ? [v9: $int] : 208.70/128.45 ((v9 = v8 & v7 = 0 & $lesseq(v4, v8) & $lesseq(v3, v8) & $lesseq(0, v4) 208.70/128.45 & $lesseq(0, v3) & length1(v0, v2) = v8 & length1(v0, v1) = v8) | ( 208.70/128.45 ~ (v8 = 0) & permut3(v0, v1, v2, v3, v4) = v8))) 208.70/128.45 (9) $lesseq(1, $difference(all_86_13, all_86_7)) 208.70/128.45 (10) t2tb(all_86_6) = all_103_1 208.70/128.45 (11) $lesseq(all_133_2, all_86_8) 208.70/128.45 (12) tb2t1(all_133_1) = all_133_0 208.70/128.45 (13) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.70/128.45 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ (permut3(v6, v5, 208.70/128.45 v4, v3, v2) = v1) | ~ (permut3(v6, v5, v4, v3, v2) = v0)) 208.70/128.45 (14) permut2(int, all_103_3, all_105_3, all_86_11, $sum(all_86_10, 1)) = 0 208.70/128.45 (15) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 208.70/128.45 | ~ (elts(v3, v2) = v1) | ~ (elts(v3, v2) = v0)) 208.70/128.45 (16) length1(int, all_105_4) = all_86_13 208.70/128.45 (17) elts(int, all_105_4) = all_105_3 208.70/128.45 (18) map_eq_sub1(int, all_105_3, all_105_1, 0, all_86_7) = 0 208.70/128.45 (19) get4(int, all_105_2, all_133_2) = all_133_1 208.70/128.45 (20) tb2t(all_105_1) = all_86_2 208.70/128.45 (21) permut2(int, all_103_1, all_105_3, all_86_11, $sum(all_86_8, 1)) = 0 208.70/128.45 (22) elts(int, all_105_2) = all_105_1 208.70/128.45 (23) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.70/128.45 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 208.70/128.45 ($lesseq(1, $difference(v4, v5))) | ~ ($lesseq(v3, v5)) | ~ 208.70/128.45 (permut2(v0, v1, v2, v3, v4) = 0) | ~ (t2tb1(v5) = v6) | ~ (get(v0, 208.70/128.45 int, v2, v6) = v7) | ~ in_ty(v0) | ? [v8: $int] : ? [v9: $int] 208.70/128.45 : ($lesseq(1, $difference(v4, v8)) & $lesseq(v3, v8) & t2tb1(v8) = v9 208.70/128.45 & get(v0, int, v1, v9) = v7 & in_uni(v9) & in_uni(v7))) 208.70/128.45 (24) t2tb2(all_86_1) = all_105_2 208.70/128.45 (25) $lesseq(all_86_11, all_133_2) 208.70/128.45 (26) ~ ($difference(all_86_10, all_86_13) = -1) | ~ (all_86_11 = 0) 208.70/128.45 (27) $lesseq(all_86_7, all_86_10) 208.70/128.45 (28) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.70/128.45 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 208.70/128.45 ($lesseq(1, $difference(v3, v4))) | ~ ($lesseq(v2, v4)) | ~ 208.70/128.45 (permut2(int, v5, v6, v2, v3) = 0) | ~ (t2tb(v1) = v6) | ~ (t2tb(v0) 208.70/128.45 = v5) | ~ (get3(v1, v4) = v7) | ~ in_map_int_int(v0) | ? [v8: 208.70/128.45 $int] : ($lesseq(1, $difference(v3, v8)) & $lesseq(v2, v8) & 208.70/128.45 get3(v0, v8) = v7)) 208.70/128.45 (29) permut2(int, all_105_3, all_105_1, all_86_7, $sum(all_86_10, 1)) = 0 208.70/128.45 (30) in_array_int(all_86_1) 208.70/128.45 (31) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.70/128.45 $int] : ! [v5: $int] : ! [v6: $int] : ( ~ ($lesseq(0, v4)) | ~ 208.70/128.45 ($lesseq(0, v3)) | ~ (permut2(v0, v5, v6, v3, v4) = 0) | ~ (elts(v0, 208.70/128.45 v2) = v6) | ~ (elts(v0, v1) = v5) | ~ in_ty(v0) | ? [v7: $int] 208.70/128.45 : ? [v8: $int] : ((v7 = 0 & permut3(v0, v1, v2, v3, v4) = 0) | 208.70/128.45 (length1(v0, v1) = v7 & ( ~ ($lesseq(v4, v7)) | ~ ($lesseq(v3, v7)) 208.70/128.45 | ( ~ (v8 = v7) & length1(v0, v2) = v8))))) 208.70/128.45 (32) $lesseq(1, $difference(all_86_7, all_86_8)) 208.70/128.45 (33) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.70/128.45 $int] : ! [v5: $int] : ! [v6: $int] : ( ~ ($lesseq(1, 208.70/128.45 $difference(v4, v5))) | ~ ($lesseq(v3, v5)) | ~ (map_eq_sub1(v0, 208.70/128.45 v1, v2, v3, v4) = 0) | ~ (t2tb1(v5) = v6) | ~ in_ty(v0) | ? 208.70/128.45 [v7: $int] : (get(v0, int, v2, v6) = v7 & get(v0, int, v1, v6) = v7 & 208.70/128.45 in_uni(v7))) 208.70/128.45 (34) $lesseq(1, $difference(all_86_13, all_86_10)) 208.70/128.45 (35) in_map_int_int(all_86_4) 208.70/128.45 (36) $lesseq(0, all_86_11) 208.70/128.45 (37) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ( ~ 208.70/128.45 (t2tb2(v0) = v2) | ~ (get4(int, v2, v1) = v3) | ~ in_array_int(v0) | 208.70/128.45 ? [v4: $int] : ? [v5: $int] : ? [v6: $int] : (tb2t(v4) = v5 & 208.70/128.45 tb2t1(v3) = v6 & get3(v5, v1) = v6 & elts(int, v2) = v4 & 208.70/128.45 in_map_int_int(v5) & in_uni(v4))) 208.70/128.45 (38) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ (tb2t(v2) 208.70/128.45 = v1) | ~ (tb2t(v2) = v0)) 208.70/128.45 (39) $lesseq(43, all_133_0) 208.70/128.45 (40) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.70/128.45 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 208.70/128.45 ($lesseq(1, $difference(v3, v6))) | ~ ($lesseq(v2, v6)) | ~ 208.70/128.45 (map_eq_sub1(int, v4, v5, v2, v3) = 0) | ~ (t2tb(v1) = v5) | ~ 208.70/128.45 (t2tb(v0) = v4) | ~ (get3(v1, v6) = v7) | ~ in_map_int_int(v0) | 208.70/128.45 get3(v0, v6) = v7) 208.70/128.45 (41) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 208.70/128.45 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 208.70/128.45 (42) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ( ~ 208.70/128.45 (get4(v0, v1, v2) = v3) | ~ in_ty(v0) | ? [v4: $int] : ? [v5: $int] 208.70/128.45 : (elts(v0, v1) = v4 & t2tb1(v2) = v5 & get(v0, int, v4, v5) = v3 & 208.70/128.45 in_uni(v5) & in_uni(v4) & in_uni(v3))) 208.70/128.45 (43) $lesseq(1, all_86_10) 208.70/128.45 (44) map_eq_sub1(int, all_105_3, all_105_1, $sum(all_86_10, 1), all_86_13) = 208.70/128.45 0 208.70/128.45 (45) t2tb(all_86_4) = all_105_3 208.70/128.45 208.70/128.45 Begin of proof 208.70/128.45 | 208.70/128.45 | GROUND_INST: instantiating (8) with int, all_103_4, all_105_4, all_86_11, 208.70/128.45 | $sum(all_86_10, 1), all_103_3, all_105_3, 0, simplifying with 208.70/128.45 | (4), (6), (14), (17) gives: 208.70/128.45 | (46) ? [v0: $int] : ? [v1: $int] : ((v1 = v0 & $lesseq(1, $difference(v0, 208.70/128.45 | all_86_10)) & $lesseq(all_86_11, v0) & $lesseq(-1, all_86_10) 208.70/128.45 | & $lesseq(0, all_86_11) & length1(int, all_105_4) = v0 & 208.70/128.45 | length1(int, all_103_4) = v0) | ( ~ (v0 = 0) & permut3(int, 208.70/128.45 | all_103_4, all_105_4, all_86_11, $sum(all_86_10, 1)) = v0)) 208.70/128.45 | 208.70/128.45 | GROUND_INST: instantiating (31) with int, all_103_4, all_105_4, all_86_11, 208.70/128.45 | $sum(all_86_10, 1), all_103_3, all_105_3, simplifying with (4), 208.70/128.45 | (6), (14), (17) gives: 208.70/128.45 | (47) ~ ($lesseq(-1, all_86_10)) | ~ ($lesseq(0, all_86_11)) | ? [v0: 208.70/128.45 | $int] : ? [v1: $int] : ((v0 = 0 & permut3(int, all_103_4, 208.70/128.45 | all_105_4, all_86_11, $sum(all_86_10, 1)) = 0) | (length1(int, 208.70/128.45 | all_103_4) = v0 & ( ~ ($lesseq(1, $difference(v0, all_86_10))) | 208.70/128.45 | ~ ($lesseq(all_86_11, v0)) | ( ~ (v1 = v0) & length1(int, 208.70/128.45 | all_105_4) = v1)))) 208.70/128.45 | 208.70/128.45 | GROUND_INST: instantiating (37) with all_86_1, all_133_2, all_105_2, 208.70/128.45 | all_133_1, simplifying with (19), (24), (30) gives: 208.70/128.45 | (48) ? [v0: $int] : ? [v1: $int] : ? [v2: $int] : (tb2t(v0) = v1 & 208.70/128.45 | tb2t1(all_133_1) = v2 & get3(v1, all_133_2) = v2 & elts(int, 208.70/128.45 | all_105_2) = v0 & in_map_int_int(v1) & in_uni(v0)) 208.70/128.45 | 208.70/128.45 | GROUND_INST: instantiating (42) with int, all_105_2, all_133_2, all_133_1, 208.70/128.45 | simplifying with (6), (19) gives: 208.70/128.45 | (49) ? [v0: $int] : ? [v1: $int] : (elts(int, all_105_2) = v0 & 208.70/128.45 | t2tb1(all_133_2) = v1 & get(int, int, v0, v1) = all_133_1 & 208.70/128.45 | in_uni(v1) & in_uni(v0) & in_uni(all_133_1)) 208.70/128.45 | 208.70/128.45 | DELTA: instantiating (46) with fresh symbols all_665_0, all_665_1 gives: 208.70/128.45 | (50) (all_665_0 = all_665_1 & $lesseq(1, $difference(all_665_1, all_86_10)) 208.70/128.45 | & $lesseq(all_86_11, all_665_1) & $lesseq(-1, all_86_10) & 208.70/128.45 | $lesseq(0, all_86_11) & length1(int, all_105_4) = all_665_1 & 208.70/128.45 | length1(int, all_103_4) = all_665_1) | ( ~ (all_665_1 = 0) & 208.70/128.45 | permut3(int, all_103_4, all_105_4, all_86_11, $sum(all_86_10, 1)) = 208.70/128.45 | all_665_1) 208.70/128.45 | 208.70/128.45 | DELTA: instantiating (49) with fresh symbols all_668_0, all_668_1 gives: 208.70/128.45 | (51) elts(int, all_105_2) = all_668_1 & t2tb1(all_133_2) = all_668_0 & 208.70/128.45 | get(int, int, all_668_1, all_668_0) = all_133_1 & in_uni(all_668_0) & 208.70/128.45 | in_uni(all_668_1) & in_uni(all_133_1) 208.70/128.45 | 208.70/128.45 | ALPHA: (51) implies: 208.70/128.45 | (52) get(int, int, all_668_1, all_668_0) = all_133_1 208.70/128.45 | (53) t2tb1(all_133_2) = all_668_0 208.70/128.45 | (54) elts(int, all_105_2) = all_668_1 208.70/128.45 | 208.70/128.45 | DELTA: instantiating (48) with fresh symbols all_678_0, all_678_1, all_678_2 208.70/128.45 | gives: 208.70/128.45 | (55) tb2t(all_678_2) = all_678_1 & tb2t1(all_133_1) = all_678_0 & 208.70/128.45 | get3(all_678_1, all_133_2) = all_678_0 & elts(int, all_105_2) = 208.70/128.45 | all_678_2 & in_map_int_int(all_678_1) & in_uni(all_678_2) 208.70/128.45 | 208.70/128.45 | ALPHA: (55) implies: 208.70/128.45 | (56) elts(int, all_105_2) = all_678_2 208.70/128.45 | (57) get3(all_678_1, all_133_2) = all_678_0 208.70/128.45 | (58) tb2t1(all_133_1) = all_678_0 208.70/128.45 | (59) tb2t(all_678_2) = all_678_1 208.70/128.45 | 208.70/128.45 | BETA: splitting (47) gives: 208.70/128.45 | 208.70/128.45 | Case 1: 208.70/128.45 | | 208.70/128.45 | | (60) $lesseq(all_86_11, -1) 208.70/128.45 | | 208.70/128.45 | | COMBINE_INEQS: (36), (60) imply: 208.70/128.45 | | (61) $lesseq(0, -1) 208.70/128.45 | | 208.70/128.45 | | CLOSE: (61) is inconsistent. 208.70/128.45 | | 208.70/128.45 | Case 2: 208.70/128.45 | | 208.70/128.45 | | (62) ~ ($lesseq(-1, all_86_10)) | ? [v0: $int] : ? [v1: $int] : ((v0 = 208.70/128.45 | | 0 & permut3(int, all_103_4, all_105_4, all_86_11, 208.70/128.45 | | $sum(all_86_10, 1)) = 0) | (length1(int, all_103_4) = v0 & ( ~ 208.70/128.45 | | ($lesseq(1, $difference(v0, all_86_10))) | ~ 208.70/128.45 | | ($lesseq(all_86_11, v0)) | ( ~ (v1 = v0) & length1(int, 208.70/128.45 | | all_105_4) = v1)))) 208.70/128.45 | | 208.70/128.45 | | BETA: splitting (62) gives: 208.70/128.45 | | 208.70/128.45 | | Case 1: 208.70/128.45 | | | 208.70/128.45 | | | (63) $lesseq(all_86_10, -2) 208.70/128.45 | | | 208.70/128.45 | | | COMBINE_INEQS: (43), (63) imply: 208.70/128.45 | | | (64) $lesseq(0, -1) 208.70/128.45 | | | 208.70/128.45 | | | CLOSE: (64) is inconsistent. 208.70/128.45 | | | 208.70/128.45 | | Case 2: 208.70/128.45 | | | 208.70/128.45 | | | (65) ? [v0: $int] : ? [v1: $int] : ((v0 = 0 & permut3(int, all_103_4, 208.70/128.45 | | | all_105_4, all_86_11, $sum(all_86_10, 1)) = 0) | 208.70/128.45 | | | (length1(int, all_103_4) = v0 & ( ~ ($lesseq(1, $difference(v0, 208.70/128.45 | | | all_86_10))) | ~ ($lesseq(all_86_11, v0)) | ( ~ (v1 = 208.70/128.45 | | | v0) & length1(int, all_105_4) = v1)))) 208.70/128.45 | | | 208.70/128.45 | | | DELTA: instantiating (65) with fresh symbols all_694_0, all_694_1 gives: 208.70/128.45 | | | (66) (all_694_1 = 0 & permut3(int, all_103_4, all_105_4, all_86_11, 208.70/128.45 | | | $sum(all_86_10, 1)) = 0) | (length1(int, all_103_4) = 208.70/128.45 | | | all_694_1 & ( ~ ($lesseq(1, $difference(all_694_1, all_86_10))) 208.70/128.45 | | | | ~ ($lesseq(all_86_11, all_694_1)) | ( ~ (all_694_0 = 208.70/128.45 | | | all_694_1) & length1(int, all_105_4) = all_694_0))) 208.70/128.45 | | | 208.70/128.45 | | | BETA: splitting (66) gives: 208.70/128.45 | | | 208.70/128.45 | | | Case 1: 208.70/128.45 | | | | 208.70/128.45 | | | | (67) all_694_1 = 0 & permut3(int, all_103_4, all_105_4, all_86_11, 208.70/128.45 | | | | $sum(all_86_10, 1)) = 0 208.70/128.45 | | | | 208.70/128.45 | | | | ALPHA: (67) implies: 208.70/128.45 | | | | (68) permut3(int, all_103_4, all_105_4, all_86_11, $sum(all_86_10, 208.70/128.45 | | | | 1)) = 0 208.70/128.45 | | | | 208.70/128.45 | | | | BETA: splitting (50) gives: 208.70/128.45 | | | | 208.70/128.45 | | | | Case 1: 208.70/128.45 | | | | | 208.70/128.46 | | | | | (69) all_665_0 = all_665_1 & $lesseq(1, $difference(all_665_1, 208.70/128.46 | | | | | all_86_10)) & $lesseq(all_86_11, all_665_1) & $lesseq(-1, 208.70/128.46 | | | | | all_86_10) & $lesseq(0, all_86_11) & length1(int, all_105_4) 208.70/128.46 | | | | | = all_665_1 & length1(int, all_103_4) = all_665_1 208.70/128.46 | | | | | 208.70/128.46 | | | | | GROUND_INST: instantiating (1) with all_133_0, all_678_0, all_133_1, 208.70/128.46 | | | | | simplifying with (12), (58) gives: 208.70/128.46 | | | | | (70) all_678_0 = all_133_0 208.70/128.46 | | | | | 208.70/128.46 | | | | | GROUND_INST: instantiating (15) with all_105_1, all_678_2, all_105_2, 208.70/128.46 | | | | | int, simplifying with (22), (56) gives: 208.70/128.46 | | | | | (71) all_678_2 = all_105_1 208.70/128.46 | | | | | 208.70/128.46 | | | | | GROUND_INST: instantiating (15) with all_678_2, all_668_1, all_105_2, 208.70/128.46 | | | | | int, simplifying with (54), (56) gives: 208.70/128.46 | | | | | (72) all_678_2 = all_668_1 208.70/128.46 | | | | | 208.70/128.46 | | | | | COMBINE_EQS: (71), (72) imply: 208.70/128.46 | | | | | (73) all_668_1 = all_105_1 208.70/128.46 | | | | | 208.70/128.46 | | | | | REDUCE: (59), (71) imply: 208.70/128.46 | | | | | (74) tb2t(all_105_1) = all_678_1 208.70/128.46 | | | | | 208.70/128.46 | | | | | REDUCE: (57), (70) imply: 208.70/128.46 | | | | | (75) get3(all_678_1, all_133_2) = all_133_0 208.70/128.46 | | | | | 208.70/128.46 | | | | | REDUCE: (52), (73) imply: 208.70/128.46 | | | | | (76) get(int, int, all_105_1, all_668_0) = all_133_1 208.70/128.46 | | | | | 208.70/128.46 | | | | | GROUND_INST: instantiating (38) with all_86_2, all_678_1, all_105_1, 208.70/128.46 | | | | | simplifying with (20), (74) gives: 208.70/128.46 | | | | | (77) all_678_1 = all_86_2 208.70/128.46 | | | | | 208.70/128.46 | | | | | REDUCE: (75), (77) imply: 208.70/128.46 | | | | | (78) get3(all_86_2, all_133_2) = all_133_0 208.70/128.46 | | | | | 208.70/128.46 | | | | | GROUND_INST: instantiating (40) with all_86_4, all_86_2, 208.70/128.46 | | | | | $sum(all_86_10, 1), all_86_13, all_105_3, all_105_1, 208.70/128.46 | | | | | all_133_2, all_133_0, simplifying with (5), (35), (44), 208.70/128.46 | | | | | (45), (78) gives: 208.70/128.46 | | | | | (79) ~ ($lesseq(1, $difference(all_86_13, all_133_2))) | ~ 208.70/128.46 | | | | | ($lesseq(1, $difference(all_133_2, all_86_10))) | 208.70/128.46 | | | | | get3(all_86_4, all_133_2) = all_133_0 208.70/128.46 | | | | | 208.70/128.46 | | | | | GROUND_INST: instantiating (40) with all_86_4, all_86_2, 0, all_86_7, 208.70/128.46 | | | | | all_105_3, all_105_1, all_133_2, all_133_0, simplifying 208.70/128.46 | | | | | with (5), (18), (35), (45), (78) gives: 208.70/128.46 | | | | | (80) ~ ($lesseq(1, $difference(all_86_7, all_133_2))) | ~ 208.70/128.46 | | | | | ($lesseq(0, all_133_2)) | get3(all_86_4, all_133_2) = 208.70/128.46 | | | | | all_133_0 208.70/128.46 | | | | | 208.70/128.46 | | | | | GROUND_INST: instantiating (28) with all_86_4, all_86_2, all_86_7, 208.70/128.46 | | | | | $sum(all_86_10, 1), all_133_2, all_105_3, all_105_1, 208.70/128.46 | | | | | all_133_0, simplifying with (5), (29), (35), (45), (78) 208.70/128.46 | | | | | gives: 208.70/128.46 | | | | | (81) ~ ($lesseq(all_133_2, all_86_10)) | ~ ($lesseq(all_86_7, 208.70/128.46 | | | | | all_133_2)) | ? [v0: $int] : ($lesseq(v0, all_86_10) & 208.70/128.46 | | | | | $lesseq(all_86_7, v0) & get3(all_86_4, v0) = all_133_0) 208.70/128.46 | | | | | 208.70/128.46 | | | | | GROUND_INST: instantiating (33) with int, all_105_3, all_105_1, 208.70/128.46 | | | | | $sum(all_86_10, 1), all_86_13, all_133_2, all_668_0, 208.70/128.46 | | | | | simplifying with (6), (44), (53) gives: 208.70/128.46 | | | | | (82) ~ ($lesseq(1, $difference(all_86_13, all_133_2))) | ~ 208.70/128.46 | | | | | ($lesseq(1, $difference(all_133_2, all_86_10))) | ? [v0: 208.70/128.46 | | | | | $int] : (get(int, int, all_105_1, all_668_0) = v0 & get(int, 208.70/128.46 | | | | | int, all_105_3, all_668_0) = v0 & in_uni(v0)) 208.70/128.46 | | | | | 208.70/128.46 | | | | | GROUND_INST: instantiating (33) with int, all_105_3, all_105_1, 0, 208.70/128.46 | | | | | all_86_7, all_133_2, all_668_0, simplifying with (6), 208.70/128.46 | | | | | (18), (53) gives: 208.70/128.46 | | | | | (83) ~ ($lesseq(1, $difference(all_86_7, all_133_2))) | ~ 208.70/128.46 | | | | | ($lesseq(0, all_133_2)) | ? [v0: $int] : (get(int, int, 208.70/128.46 | | | | | all_105_1, all_668_0) = v0 & get(int, int, all_105_3, 208.70/128.46 | | | | | all_668_0) = v0 & in_uni(v0)) 208.70/128.46 | | | | | 208.70/128.46 | | | | | GROUND_INST: instantiating (23) with int, all_105_3, all_105_1, 208.70/128.46 | | | | | all_86_7, $sum(all_86_10, 1), all_133_2, all_668_0, 208.70/128.46 | | | | | all_133_1, simplifying with (6), (29), (53), (76) gives: 208.70/128.46 | | | | | (84) ~ ($lesseq(all_133_2, all_86_10)) | ~ ($lesseq(all_86_7, 208.70/128.46 | | | | | all_133_2)) | ? [v0: $int] : ? [v1: $int] : ($lesseq(v0, 208.70/128.46 | | | | | all_86_10) & $lesseq(all_86_7, v0) & t2tb1(v0) = v1 & 208.70/128.46 | | | | | get(int, int, all_105_3, v1) = all_133_1 & in_uni(v1) & 208.70/128.46 | | | | | in_uni(all_133_1)) 208.70/128.46 | | | | | 208.70/128.46 | | | | | BETA: splitting (26) gives: 208.70/128.46 | | | | | 208.70/128.46 | | | | | Case 1: 208.70/128.46 | | | | | | 208.70/128.46 | | | | | | (85) ~ (all_86_11 = 0) 208.70/128.46 | | | | | | 208.70/128.46 | | | | | | STRENGTHEN: (36), (85) imply: 208.70/128.46 | | | | | | (86) $lesseq(1, all_86_11) 208.70/128.46 | | | | | | 208.70/128.46 | | | | | | COMBINE_INEQS: (27), (32) imply: 208.70/128.46 | | | | | | (87) $lesseq(1, $difference(all_86_10, all_86_8)) 208.70/128.46 | | | | | | 208.70/128.46 | | | | | | COMBINE_INEQS: (9), (32) imply: 208.70/128.46 | | | | | | (88) $lesseq(2, $difference(all_86_13, all_86_8)) 208.70/128.46 | | | | | | 208.70/128.46 | | | | | | BETA: splitting (82) gives: 208.70/128.46 | | | | | | 208.70/128.46 | | | | | | Case 1: 208.70/128.46 | | | | | | | 208.70/128.46 | | | | | | | (89) $lesseq(all_86_13, all_133_2) 208.70/128.46 | | | | | | | 208.70/128.46 | | | | | | | COMBINE_INEQS: (11), (89) imply: 208.70/128.46 | | | | | | | (90) $lesseq(all_86_13, all_86_8) 208.70/128.46 | | | | | | | 208.70/128.46 | | | | | | | COMBINE_INEQS: (88), (90) imply: 208.70/128.46 | | | | | | | (91) $lesseq(0, -1) 208.70/128.46 | | | | | | | 208.70/128.46 | | | | | | | CLOSE: (91) is inconsistent. 208.70/128.46 | | | | | | | 208.70/128.46 | | | | | | Case 2: 208.70/128.46 | | | | | | | 208.70/128.46 | | | | | | | (92) $lesseq(1, $difference(all_86_13, all_133_2)) 208.70/128.46 | | | | | | | 208.70/128.46 | | | | | | | BETA: splitting (79) gives: 208.70/128.46 | | | | | | | 208.70/128.46 | | | | | | | Case 1: 208.70/128.46 | | | | | | | | 208.70/128.46 | | | | | | | | (93) get3(all_86_4, all_133_2) = all_133_0 208.70/128.46 | | | | | | | | 208.70/128.46 | | | | | | | | REF_CLOSE: (2), (3), (10), (11), (21), (25), (28), (39), (45), 208.70/128.46 | | | | | | | | (81), (84), (87), (93) are inconsistent by sub-proof 208.70/128.46 | | | | | | | | #146. 208.70/128.46 | | | | | | | | 208.70/128.46 | | | | | | | Case 2: 208.70/128.46 | | | | | | | | 208.70/128.46 | | | | | | | | (94) ~ ($lesseq(1, $difference(all_86_13, all_133_2))) | ~ 208.70/128.46 | | | | | | | | ($lesseq(1, $difference(all_133_2, all_86_10))) 208.70/128.46 | | | | | | | | 208.70/128.46 | | | | | | | | BETA: splitting (94) gives: 208.70/128.46 | | | | | | | | 208.70/128.46 | | | | | | | | Case 1: 208.70/128.46 | | | | | | | | | 208.70/128.46 | | | | | | | | | (95) $lesseq(all_86_13, all_133_2) 208.70/128.46 | | | | | | | | | 208.70/128.46 | | | | | | | | | COMBINE_INEQS: (92), (95) imply: 208.70/128.46 | | | | | | | | | (96) $lesseq(0, -1) 208.70/128.46 | | | | | | | | | 208.70/128.46 | | | | | | | | | CLOSE: (96) is inconsistent. 208.70/128.46 | | | | | | | | | 208.70/128.46 | | | | | | | | Case 2: 208.70/128.46 | | | | | | | | | 208.70/128.46 | | | | | | | | | (97) $lesseq(all_133_2, all_86_10) 208.70/128.46 | | | | | | | | | 208.70/128.46 | | | | | | | | | BETA: splitting (83) gives: 208.70/128.46 | | | | | | | | | 208.70/128.46 | | | | | | | | | Case 1: 208.70/128.46 | | | | | | | | | | 208.70/128.46 | | | | | | | | | | (98) $lesseq(all_133_2, -1) 208.70/128.46 | | | | | | | | | | 208.70/128.46 | | | | | | | | | | COMBINE_INEQS: (25), (98) imply: 208.70/128.46 | | | | | | | | | | (99) $lesseq(all_86_11, -1) 208.70/128.46 | | | | | | | | | | 208.70/128.46 | | | | | | | | | | COMBINE_INEQS: (86), (99) imply: 208.70/128.46 | | | | | | | | | | (100) $lesseq(0, -1) 208.70/128.46 | | | | | | | | | | 208.70/128.46 | | | | | | | | | | CLOSE: (100) is inconsistent. 208.70/128.46 | | | | | | | | | | 208.70/128.46 | | | | | | | | | Case 2: 208.70/128.46 | | | | | | | | | | 208.70/128.46 | | | | | | | | | | (101) $lesseq(0, all_133_2) 208.70/128.46 | | | | | | | | | | 208.70/128.46 | | | | | | | | | | BETA: splitting (80) gives: 208.70/128.46 | | | | | | | | | | 208.70/128.46 | | | | | | | | | | Case 1: 208.70/128.46 | | | | | | | | | | | 208.70/128.46 | | | | | | | | | | | (102) get3(all_86_4, all_133_2) = all_133_0 208.70/128.46 | | | | | | | | | | | 208.70/128.46 | | | | | | | | | | | REF_CLOSE: (2), (3), (10), (11), (21), (25), (28), (39), 208.70/128.46 | | | | | | | | | | | (45), (81), (97), (102) are inconsistent by 208.70/128.46 | | | | | | | | | | | sub-proof #147. 208.70/128.46 | | | | | | | | | | | 208.70/128.46 | | | | | | | | | | Case 2: 208.70/128.46 | | | | | | | | | | | 208.70/128.46 | | | | | | | | | | | (103) ~ ($lesseq(1, $difference(all_86_7, all_133_2))) 208.70/128.46 | | | | | | | | | | | | ~ ($lesseq(0, all_133_2)) 208.70/128.46 | | | | | | | | | | | 208.70/128.46 | | | | | | | | | | | REF_CLOSE: (11), (32), (101), (103) are inconsistent by 208.70/128.46 | | | | | | | | | | | sub-proof #145. 208.70/128.46 | | | | | | | | | | | 208.70/128.46 | | | | | | | | | | End of split 208.70/128.46 | | | | | | | | | | 208.70/128.46 | | | | | | | | | End of split 208.70/128.46 | | | | | | | | | 208.70/128.46 | | | | | | | | End of split 208.70/128.46 | | | | | | | | 208.70/128.46 | | | | | | | End of split 208.70/128.46 | | | | | | | 208.70/128.46 | | | | | | End of split 208.70/128.46 | | | | | | 208.70/128.46 | | | | | Case 2: 208.70/128.46 | | | | | | 208.70/128.46 | | | | | | (104) all_86_11 = 0 208.70/128.46 | | | | | | 208.70/128.46 | | | | | | REDUCE: (25), (104) imply: 208.70/128.46 | | | | | | (105) $lesseq(0, all_133_2) 208.70/128.46 | | | | | | 208.70/128.46 | | | | | | COMBINE_INEQS: (27), (32) imply: 208.70/128.46 | | | | | | (106) $lesseq(1, $difference(all_86_10, all_86_8)) 208.70/128.46 | | | | | | 208.70/128.46 | | | | | | REF_CLOSE: (2), (3), (10), (11), (21), (25), (28), (32), (39), (45), 208.70/128.46 | | | | | | (80), (81), (84), (105), (106) are inconsistent by 208.70/128.46 | | | | | | sub-proof #144. 208.70/128.46 | | | | | | 208.70/128.46 | | | | | End of split 208.70/128.46 | | | | | 208.70/128.46 | | | | Case 2: 208.70/128.46 | | | | | 208.70/128.46 | | | | | (107) ~ (all_665_1 = 0) & permut3(int, all_103_4, all_105_4, 208.70/128.46 | | | | | all_86_11, $sum(all_86_10, 1)) = all_665_1 208.70/128.46 | | | | | 208.70/128.46 | | | | | ALPHA: (107) implies: 208.70/128.46 | | | | | (108) ~ (all_665_1 = 0) 208.70/128.46 | | | | | (109) permut3(int, all_103_4, all_105_4, all_86_11, $sum(all_86_10, 208.70/128.46 | | | | | 1)) = all_665_1 208.70/128.46 | | | | | 208.70/128.46 | | | | | GROUND_INST: instantiating (13) with all_665_1, 0, $sum(all_86_10, 1), 208.70/128.46 | | | | | all_86_11, all_105_4, all_103_4, int, simplifying with 208.70/128.46 | | | | | (68), (109) gives: 208.70/128.46 | | | | | (110) all_665_1 = 0 208.70/128.46 | | | | | 208.70/128.46 | | | | | REDUCE: (108), (110) imply: 208.70/128.46 | | | | | (111) ~ (0 = 0) 208.70/128.46 | | | | | 208.70/128.46 | | | | | CLOSE: (111) is inconsistent. 208.70/128.46 | | | | | 208.70/128.46 | | | | End of split 208.70/128.46 | | | | 208.70/128.46 | | | Case 2: 208.70/128.46 | | | | 208.70/128.46 | | | | (112) length1(int, all_103_4) = all_694_1 & ( ~ ($lesseq(1, 208.70/128.46 | | | | $difference(all_694_1, all_86_10))) | ~ 208.70/128.46 | | | | ($lesseq(all_86_11, all_694_1)) | ( ~ (all_694_0 = all_694_1) 208.70/128.46 | | | | & length1(int, all_105_4) = all_694_0)) 208.70/128.46 | | | | 208.70/128.46 | | | | ALPHA: (112) implies: 208.70/128.46 | | | | (113) length1(int, all_103_4) = all_694_1 208.70/128.46 | | | | (114) ~ ($lesseq(1, $difference(all_694_1, all_86_10))) | ~ 208.70/128.46 | | | | ($lesseq(all_86_11, all_694_1)) | ( ~ (all_694_0 = all_694_1) & 208.70/128.46 | | | | length1(int, all_105_4) = all_694_0) 208.70/128.46 | | | | 208.70/128.46 | | | | GROUND_INST: instantiating (41) with all_86_13, all_694_1, all_103_4, 208.70/128.46 | | | | int, simplifying with (7), (113) gives: 208.70/128.46 | | | | (115) all_694_1 = all_86_13 208.70/128.46 | | | | 208.70/128.46 | | | | BETA: splitting (114) gives: 208.70/128.46 | | | | 208.70/128.46 | | | | Case 1: 208.70/128.46 | | | | | 208.70/128.46 | | | | | (116) $lesseq(1, $difference(all_86_11, all_694_1)) 208.70/128.46 | | | | | 208.70/128.46 | | | | | REDUCE: (115), (116) imply: 208.70/128.46 | | | | | (117) $lesseq(1, $difference(all_86_11, all_86_13)) 208.70/128.46 | | | | | 208.70/128.46 | | | | | COMBINE_INEQS: (11), (25) imply: 208.70/128.46 | | | | | (118) $lesseq(all_86_11, all_86_8) 208.70/128.46 | | | | | 208.70/128.46 | | | | | COMBINE_INEQS: (27), (32) imply: 208.70/128.46 | | | | | (119) $lesseq(1, $difference(all_86_10, all_86_8)) 208.70/128.46 | | | | | 208.70/128.46 | | | | | COMBINE_INEQS: (118), (119) imply: 208.70/128.46 | | | | | (120) $lesseq(1, $difference(all_86_10, all_86_11)) 208.70/128.46 | | | | | 208.70/128.46 | | | | | COMBINE_INEQS: (34), (120) imply: 208.70/128.46 | | | | | (121) $lesseq(2, $difference(all_86_13, all_86_11)) 208.70/128.46 | | | | | 208.70/128.46 | | | | | COMBINE_INEQS: (117), (121) imply: 208.70/128.46 | | | | | (122) $lesseq(0, -1) 208.70/128.46 | | | | | 208.70/128.46 | | | | | CLOSE: (122) is inconsistent. 208.70/128.46 | | | | | 208.70/128.46 | | | | Case 2: 208.70/128.46 | | | | | 208.70/128.46 | | | | | (123) ~ ($lesseq(1, $difference(all_694_1, all_86_10))) | ( ~ 208.70/128.46 | | | | | (all_694_0 = all_694_1) & length1(int, all_105_4) = 208.70/128.46 | | | | | all_694_0) 208.70/128.46 | | | | | 208.70/128.46 | | | | | BETA: splitting (123) gives: 208.70/128.46 | | | | | 208.70/128.46 | | | | | Case 1: 208.70/128.46 | | | | | | 208.70/128.46 | | | | | | (124) $lesseq(all_694_1, all_86_10) 208.70/128.46 | | | | | | 208.70/128.46 | | | | | | REDUCE: (115), (124) imply: 208.70/128.46 | | | | | | (125) $lesseq(all_86_13, all_86_10) 208.70/128.46 | | | | | | 208.70/128.46 | | | | | | COMBINE_INEQS: (34), (125) imply: 208.70/128.46 | | | | | | (126) $lesseq(0, -1) 208.70/128.46 | | | | | | 208.70/128.46 | | | | | | CLOSE: (126) is inconsistent. 208.70/128.46 | | | | | | 208.70/128.46 | | | | | Case 2: 208.70/128.46 | | | | | | 208.70/128.46 | | | | | | (127) ~ (all_694_0 = all_694_1) & length1(int, all_105_4) = 208.70/128.46 | | | | | | all_694_0 208.70/128.46 | | | | | | 208.70/128.46 | | | | | | ALPHA: (127) implies: 208.70/128.46 | | | | | | (128) ~ (all_694_0 = all_694_1) 208.70/128.46 | | | | | | (129) length1(int, all_105_4) = all_694_0 208.70/128.46 | | | | | | 208.70/128.46 | | | | | | REDUCE: (115), (128) imply: 208.70/128.46 | | | | | | (130) ~ (all_694_0 = all_86_13) 208.70/128.46 | | | | | | 208.70/128.46 | | | | | | GROUND_INST: instantiating (41) with all_86_13, all_694_0, 208.70/128.46 | | | | | | all_105_4, int, simplifying with (16), (129) gives: 208.70/128.46 | | | | | | (131) all_694_0 = all_86_13 208.70/128.46 | | | | | | 208.70/128.46 | | | | | | REDUCE: (130), (131) imply: 208.70/128.46 | | | | | | (132) ~ (0 = 0) 208.70/128.46 | | | | | | 208.70/128.46 | | | | | | CLOSE: (132) is inconsistent. 208.70/128.46 | | | | | | 208.70/128.46 | | | | | End of split 208.70/128.46 | | | | | 208.70/128.46 | | | | End of split 208.70/128.46 | | | | 208.70/128.46 | | | End of split 208.70/128.46 | | | 208.70/128.46 | | End of split 208.70/128.46 | | 208.70/128.46 | End of split 208.70/128.46 | 208.70/128.46 End of proof 208.70/128.46 208.70/128.46 Sub-proof #144 shows that the following formulas are inconsistent: 208.70/128.46 ---------------------------------------------------------------- 208.70/128.46 (1) ! [v0: $int] : ! [v1: $int] : ( ~ ($lesseq(43, v1)) | ~ ($lesseq(v0, 208.70/128.46 all_86_8)) | ~ ($lesseq(all_86_11, v0)) | ~ (get3(all_86_6, v0) = 208.70/128.46 v1)) 208.70/128.46 (2) in_map_int_int(all_86_6) 208.70/128.46 (3) ~ ($lesseq(all_133_2, all_86_10)) | ~ ($lesseq(all_86_7, all_133_2)) | 208.70/128.46 ? [v0: $int] : ($lesseq(v0, all_86_10) & $lesseq(all_86_7, v0) & 208.70/128.46 get3(all_86_4, v0) = all_133_0) 208.70/128.46 (4) $lesseq(0, all_133_2) 208.70/128.46 (5) t2tb(all_86_6) = all_103_1 208.70/128.46 (6) $lesseq(all_133_2, all_86_8) 208.70/128.46 (7) ~ ($lesseq(all_133_2, all_86_10)) | ~ ($lesseq(all_86_7, all_133_2)) | 208.70/128.46 ? [v0: $int] : ? [v1: $int] : ($lesseq(v0, all_86_10) & 208.70/128.46 $lesseq(all_86_7, v0) & t2tb1(v0) = v1 & get(int, int, all_105_3, v1) = 208.70/128.46 all_133_1 & in_uni(v1) & in_uni(all_133_1)) 208.70/128.46 (8) permut2(int, all_103_1, all_105_3, all_86_11, $sum(all_86_8, 1)) = 0 208.70/128.46 (9) $lesseq(all_86_11, all_133_2) 208.70/128.46 (10) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.70/128.46 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 208.70/128.46 ($lesseq(1, $difference(v3, v4))) | ~ ($lesseq(v2, v4)) | ~ 208.70/128.46 (permut2(int, v5, v6, v2, v3) = 0) | ~ (t2tb(v1) = v6) | ~ (t2tb(v0) 208.70/128.46 = v5) | ~ (get3(v1, v4) = v7) | ~ in_map_int_int(v0) | ? [v8: 208.70/128.46 $int] : ($lesseq(1, $difference(v3, v8)) & $lesseq(v2, v8) & 208.70/128.46 get3(v0, v8) = v7)) 208.70/128.46 (11) $lesseq(1, $difference(all_86_7, all_86_8)) 208.70/128.46 (12) ~ ($lesseq(1, $difference(all_86_7, all_133_2))) | ~ ($lesseq(0, 208.70/128.46 all_133_2)) | get3(all_86_4, all_133_2) = all_133_0 208.70/128.46 (13) $lesseq(1, $difference(all_86_10, all_86_8)) 208.70/128.46 (14) $lesseq(43, all_133_0) 208.70/128.46 (15) t2tb(all_86_4) = all_105_3 208.70/128.46 208.70/128.46 Begin of proof 208.70/128.46 | 208.70/128.46 | BETA: splitting (12) gives: 208.70/128.46 | 208.70/128.46 | Case 1: 208.70/128.46 | | 208.70/128.46 | | (16) get3(all_86_4, all_133_2) = all_133_0 208.70/128.46 | | 208.70/128.46 | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (13), (14), (15), 208.70/128.46 | | (16) are inconsistent by sub-proof #146. 208.70/128.46 | | 208.70/128.46 | Case 2: 208.70/128.46 | | 208.70/128.46 | | (17) ~ ($lesseq(1, $difference(all_86_7, all_133_2))) | ~ ($lesseq(0, 208.70/128.46 | | all_133_2)) 208.70/128.46 | | 208.70/128.46 | | REF_CLOSE: (4), (6), (11), (17) are inconsistent by sub-proof #145. 208.70/128.46 | | 208.70/128.46 | End of split 208.70/128.46 | 208.70/128.46 End of proof 208.70/128.46 208.70/128.46 Sub-proof #145 shows that the following formulas are inconsistent: 208.70/128.46 ---------------------------------------------------------------- 208.70/128.46 (1) ~ ($lesseq(1, $difference(all_86_7, all_133_2))) | ~ ($lesseq(0, 208.70/128.46 all_133_2)) 208.70/128.46 (2) $lesseq(0, all_133_2) 208.70/128.46 (3) $lesseq(all_133_2, all_86_8) 208.70/128.46 (4) $lesseq(1, $difference(all_86_7, all_86_8)) 208.70/128.46 208.70/128.46 Begin of proof 208.70/128.46 | 208.70/128.46 | BETA: splitting (1) gives: 208.70/128.46 | 208.70/128.46 | Case 1: 208.70/128.46 | | 208.70/128.46 | | (5) $lesseq(all_133_2, -1) 208.70/128.46 | | 208.70/128.46 | | COMBINE_INEQS: (2), (5) imply: 208.70/128.46 | | (6) $lesseq(0, -1) 208.70/128.46 | | 208.70/128.46 | | CLOSE: (6) is inconsistent. 208.70/128.46 | | 208.70/128.46 | Case 2: 208.70/128.46 | | 208.70/128.46 | | (7) $lesseq(all_86_7, all_133_2) 208.70/128.46 | | 208.70/128.46 | | COMBINE_INEQS: (3), (7) imply: 208.70/128.46 | | (8) $lesseq(all_86_7, all_86_8) 208.70/128.46 | | 208.70/128.46 | | COMBINE_INEQS: (4), (8) imply: 208.70/128.46 | | (9) $lesseq(0, -1) 208.70/128.46 | | 208.70/128.46 | | CLOSE: (9) is inconsistent. 208.70/128.46 | | 208.70/128.46 | End of split 208.70/128.46 | 208.70/128.47 End of proof 208.70/128.47 208.70/128.47 Sub-proof #146 shows that the following formulas are inconsistent: 208.70/128.47 ---------------------------------------------------------------- 208.70/128.47 (1) ! [v0: $int] : ! [v1: $int] : ( ~ ($lesseq(43, v1)) | ~ ($lesseq(v0, 208.70/128.47 all_86_8)) | ~ ($lesseq(all_86_11, v0)) | ~ (get3(all_86_6, v0) = 208.70/128.47 v1)) 208.70/128.47 (2) in_map_int_int(all_86_6) 208.70/128.47 (3) ~ ($lesseq(all_133_2, all_86_10)) | ~ ($lesseq(all_86_7, all_133_2)) | 208.70/128.47 ? [v0: $int] : ($lesseq(v0, all_86_10) & $lesseq(all_86_7, v0) & 208.70/128.47 get3(all_86_4, v0) = all_133_0) 208.70/128.47 (4) t2tb(all_86_6) = all_103_1 208.70/128.47 (5) $lesseq(all_133_2, all_86_8) 208.70/128.47 (6) ~ ($lesseq(all_133_2, all_86_10)) | ~ ($lesseq(all_86_7, all_133_2)) | 208.70/128.47 ? [v0: $int] : ? [v1: $int] : ($lesseq(v0, all_86_10) & 208.70/128.47 $lesseq(all_86_7, v0) & t2tb1(v0) = v1 & get(int, int, all_105_3, v1) = 208.70/128.47 all_133_1 & in_uni(v1) & in_uni(all_133_1)) 208.70/128.47 (7) permut2(int, all_103_1, all_105_3, all_86_11, $sum(all_86_8, 1)) = 0 208.70/128.47 (8) $lesseq(all_86_11, all_133_2) 208.70/128.47 (9) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.70/128.47 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ ($lesseq(1, 208.70/128.47 $difference(v3, v4))) | ~ ($lesseq(v2, v4)) | ~ (permut2(int, v5, 208.70/128.47 v6, v2, v3) = 0) | ~ (t2tb(v1) = v6) | ~ (t2tb(v0) = v5) | ~ 208.70/128.47 (get3(v1, v4) = v7) | ~ in_map_int_int(v0) | ? [v8: $int] : 208.70/128.47 ($lesseq(1, $difference(v3, v8)) & $lesseq(v2, v8) & get3(v0, v8) = 208.70/128.47 v7)) 208.70/128.47 (10) get3(all_86_4, all_133_2) = all_133_0 208.70/128.47 (11) $lesseq(1, $difference(all_86_10, all_86_8)) 208.70/128.47 (12) $lesseq(43, all_133_0) 208.70/128.47 (13) t2tb(all_86_4) = all_105_3 208.70/128.47 208.70/128.47 Begin of proof 208.70/128.47 | 208.70/128.47 | BETA: splitting (6) gives: 208.70/128.47 | 208.70/128.47 | Case 1: 208.70/128.47 | | 208.70/128.47 | | (14) $lesseq(1, $difference(all_133_2, all_86_10)) 208.70/128.47 | | 208.70/128.47 | | COMBINE_INEQS: (5), (14) imply: 208.70/128.47 | | (15) $lesseq(1, $difference(all_86_8, all_86_10)) 208.70/128.47 | | 208.70/128.47 | | COMBINE_INEQS: (11), (15) imply: 208.70/128.47 | | (16) $lesseq(0, -1) 208.70/128.47 | | 208.70/128.47 | | CLOSE: (16) is inconsistent. 208.70/128.47 | | 208.70/128.47 | Case 2: 208.70/128.47 | | 208.70/128.47 | | (17) $lesseq(all_133_2, all_86_10) 208.70/128.47 | | 208.70/128.47 | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (12), (13), (17) 208.70/128.47 | | are inconsistent by sub-proof #147. 208.70/128.47 | | 208.70/128.47 | End of split 208.70/128.47 | 208.70/128.47 End of proof 208.70/128.47 208.70/128.47 Sub-proof #147 shows that the following formulas are inconsistent: 208.70/128.47 ---------------------------------------------------------------- 208.70/128.47 (1) ! [v0: $int] : ! [v1: $int] : ( ~ ($lesseq(43, v1)) | ~ ($lesseq(v0, 208.70/128.47 all_86_8)) | ~ ($lesseq(all_86_11, v0)) | ~ (get3(all_86_6, v0) = 208.70/128.47 v1)) 208.70/128.47 (2) in_map_int_int(all_86_6) 208.70/128.47 (3) ~ ($lesseq(all_133_2, all_86_10)) | ~ ($lesseq(all_86_7, all_133_2)) | 208.70/128.47 ? [v0: $int] : ($lesseq(v0, all_86_10) & $lesseq(all_86_7, v0) & 208.70/128.47 get3(all_86_4, v0) = all_133_0) 208.70/128.47 (4) $lesseq(all_133_2, all_86_10) 208.70/128.47 (5) t2tb(all_86_6) = all_103_1 208.70/128.47 (6) $lesseq(all_133_2, all_86_8) 208.70/128.47 (7) permut2(int, all_103_1, all_105_3, all_86_11, $sum(all_86_8, 1)) = 0 208.70/128.47 (8) $lesseq(all_86_11, all_133_2) 208.70/128.47 (9) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.70/128.47 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ ($lesseq(1, 208.70/128.47 $difference(v3, v4))) | ~ ($lesseq(v2, v4)) | ~ (permut2(int, v5, 208.70/128.47 v6, v2, v3) = 0) | ~ (t2tb(v1) = v6) | ~ (t2tb(v0) = v5) | ~ 208.70/128.47 (get3(v1, v4) = v7) | ~ in_map_int_int(v0) | ? [v8: $int] : 208.70/128.47 ($lesseq(1, $difference(v3, v8)) & $lesseq(v2, v8) & get3(v0, v8) = 208.70/128.47 v7)) 208.70/128.47 (10) get3(all_86_4, all_133_2) = all_133_0 208.70/128.47 (11) $lesseq(43, all_133_0) 208.70/128.47 (12) t2tb(all_86_4) = all_105_3 208.70/128.47 208.70/128.47 Begin of proof 208.70/128.47 | 208.70/128.47 | BETA: splitting (3) gives: 208.70/128.47 | 208.70/128.47 | Case 1: 208.70/128.47 | | 208.70/128.47 | | (13) $lesseq(1, $difference(all_133_2, all_86_10)) 208.70/128.47 | | 208.70/128.47 | | COMBINE_INEQS: (4), (13) imply: 208.70/128.47 | | (14) $lesseq(0, -1) 208.70/128.47 | | 208.70/128.47 | | CLOSE: (14) is inconsistent. 208.70/128.47 | | 208.70/128.47 | Case 2: 208.70/128.47 | | 208.70/128.47 | | 208.70/128.47 | | GROUND_INST: instantiating (9) with all_86_6, all_86_4, all_86_11, 208.70/128.47 | | $sum(all_86_8, 1), all_133_2, all_103_1, all_105_3, all_133_0, 208.70/128.47 | | simplifying with (2), (5), (7), (10), (12) gives: 208.70/128.47 | | (15) ~ ($lesseq(all_133_2, all_86_8)) | ~ ($lesseq(all_86_11, 208.70/128.47 | | all_133_2)) | ? [v0: $int] : ($lesseq(v0, all_86_8) & 208.70/128.47 | | $lesseq(all_86_11, v0) & get3(all_86_6, v0) = all_133_0) 208.70/128.47 | | 208.70/128.47 | | BETA: splitting (15) gives: 208.70/128.47 | | 208.70/128.47 | | Case 1: 208.70/128.47 | | | 208.70/128.47 | | | (16) $lesseq(1, $difference(all_133_2, all_86_8)) 208.70/128.47 | | | 208.70/128.47 | | | COMBINE_INEQS: (6), (16) imply: 208.70/128.47 | | | (17) $lesseq(0, -1) 208.70/128.47 | | | 208.70/128.47 | | | CLOSE: (17) is inconsistent. 208.70/128.47 | | | 208.70/128.47 | | Case 2: 208.70/128.47 | | | 208.70/128.47 | | | (18) ~ ($lesseq(all_86_11, all_133_2)) | ? [v0: $int] : ($lesseq(v0, 208.70/128.47 | | | all_86_8) & $lesseq(all_86_11, v0) & get3(all_86_6, v0) = 208.70/128.47 | | | all_133_0) 208.70/128.47 | | | 208.70/128.47 | | | BETA: splitting (18) gives: 208.70/128.47 | | | 208.70/128.47 | | | Case 1: 208.70/128.47 | | | | 208.70/128.47 | | | | (19) $lesseq(1, $difference(all_86_11, all_133_2)) 208.70/128.47 | | | | 208.70/128.47 | | | | COMBINE_INEQS: (8), (19) imply: 208.70/128.47 | | | | (20) $lesseq(0, -1) 208.70/128.47 | | | | 208.70/128.47 | | | | CLOSE: (20) is inconsistent. 208.70/128.47 | | | | 208.70/128.47 | | | Case 2: 208.70/128.47 | | | | 208.70/128.47 | | | | (21) ? [v0: $int] : ($lesseq(v0, all_86_8) & $lesseq(all_86_11, v0) 208.70/128.47 | | | | & get3(all_86_6, v0) = all_133_0) 208.70/128.47 | | | | 208.70/128.47 | | | | DELTA: instantiating (21) with fresh symbol all_1113_0 gives: 208.70/128.47 | | | | (22) $lesseq(all_1113_0, all_86_8) & $lesseq(all_86_11, all_1113_0) & 208.70/128.47 | | | | get3(all_86_6, all_1113_0) = all_133_0 208.70/128.47 | | | | 208.70/128.47 | | | | ALPHA: (22) implies: 208.70/128.47 | | | | (23) $lesseq(all_86_11, all_1113_0) 208.70/128.47 | | | | (24) $lesseq(all_1113_0, all_86_8) 208.70/128.47 | | | | (25) get3(all_86_6, all_1113_0) = all_133_0 208.70/128.47 | | | | 208.70/128.47 | | | | GROUND_INST: instantiating (1) with all_1113_0, all_133_0, simplifying 208.70/128.47 | | | | with (25) gives: 208.70/128.47 | | | | (26) ~ ($lesseq(all_1113_0, all_86_8)) | ~ ($lesseq(all_86_11, 208.70/128.47 | | | | all_1113_0)) | ~ ($lesseq(43, all_133_0)) 208.70/128.47 | | | | 208.70/128.47 | | | | BETA: splitting (26) gives: 208.70/128.47 | | | | 208.70/128.47 | | | | Case 1: 208.70/128.47 | | | | | 208.70/128.47 | | | | | (27) $lesseq(1, $difference(all_1113_0, all_86_8)) 208.70/128.47 | | | | | 208.70/128.47 | | | | | COMBINE_INEQS: (24), (27) imply: 208.70/128.47 | | | | | (28) $lesseq(0, -1) 208.70/128.47 | | | | | 208.70/128.47 | | | | | CLOSE: (28) is inconsistent. 208.70/128.47 | | | | | 208.70/128.47 | | | | Case 2: 208.70/128.47 | | | | | 208.70/128.47 | | | | | (29) ~ ($lesseq(all_86_11, all_1113_0)) | ~ ($lesseq(43, 208.70/128.47 | | | | | all_133_0)) 208.70/128.47 | | | | | 208.70/128.47 | | | | | BETA: splitting (29) gives: 208.70/128.47 | | | | | 208.70/128.47 | | | | | Case 1: 208.70/128.47 | | | | | | 208.70/128.47 | | | | | | (30) $lesseq(1, $difference(all_86_11, all_1113_0)) 208.70/128.47 | | | | | | 208.70/128.47 | | | | | | COMBINE_INEQS: (23), (30) imply: 208.70/128.47 | | | | | | (31) $lesseq(0, -1) 208.70/128.47 | | | | | | 208.70/128.47 | | | | | | CLOSE: (31) is inconsistent. 208.70/128.47 | | | | | | 208.70/128.47 | | | | | Case 2: 208.70/128.47 | | | | | | 208.70/128.47 | | | | | | (32) $lesseq(all_133_0, 42) 208.70/128.47 | | | | | | 208.70/128.47 | | | | | | COMBINE_INEQS: (11), (32) imply: 208.70/128.47 | | | | | | (33) $lesseq(0, -1) 208.70/128.47 | | | | | | 208.70/128.47 | | | | | | CLOSE: (33) is inconsistent. 208.70/128.47 | | | | | | 208.70/128.47 | | | | | End of split 208.70/128.47 | | | | | 208.70/128.47 | | | | End of split 208.70/128.47 | | | | 208.70/128.47 | | | End of split 208.70/128.47 | | | 208.70/128.47 | | End of split 208.70/128.47 | | 208.70/128.47 | End of split 208.70/128.47 | 208.70/128.47 End of proof 208.70/128.47 208.70/128.47 Sub-proof #148 shows that the following formulas are inconsistent: 208.70/128.47 ---------------------------------------------------------------- 208.70/128.47 (1) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ (tb2t1(v2) 208.70/128.47 = v1) | ~ (tb2t1(v2) = v0)) 208.70/128.47 (2) elts(int, all_103_4) = all_103_3 208.70/128.47 (3) t2tb2(all_86_3) = all_105_4 208.70/128.47 (4) t2tb(all_86_2) = all_105_1 208.70/128.47 (5) in_ty(int) 208.70/128.47 (6) all_125_0 = all_105_4 208.70/128.47 (7) $lesseq(all_133_2, all_86_10) 208.70/128.47 (8) $lesseq(all_133_0, 41) 208.70/128.47 (9) tb2t1(all_133_1) = all_133_0 208.70/128.47 (10) permut2(int, all_103_3, all_105_3, all_86_11, $sum(all_86_10, 1)) = 0 208.70/128.47 (11) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 208.70/128.47 | ~ (elts(v3, v2) = v1) | ~ (elts(v3, v2) = v0)) 208.70/128.47 (12) in_array_int(all_86_3) 208.70/128.47 (13) elts(int, all_105_4) = all_105_3 208.70/128.47 (14) $lesseq(all_86_7, all_133_2) 208.70/128.47 (15) get4(int, all_105_2, all_133_2) = all_133_1 208.70/128.47 (16) tb2t(all_105_1) = all_86_2 208.70/128.47 (17) elts(int, all_105_2) = all_105_1 208.70/128.47 (18) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.70/128.47 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 208.70/128.47 ($lesseq(1, $difference(v4, v5))) | ~ ($lesseq(v3, v5)) | ~ 208.70/128.47 (permut2(v0, v1, v2, v3, v4) = 0) | ~ (t2tb1(v5) = v6) | ~ (get(v0, 208.70/128.47 int, v2, v6) = v7) | ~ in_ty(v0) | ? [v8: $int] : ? [v9: $int] 208.70/128.47 : ($lesseq(1, $difference(v4, v8)) & $lesseq(v3, v8) & t2tb1(v8) = v9 208.70/128.47 & get(v0, int, v1, v9) = v7 & in_uni(v9) & in_uni(v7))) 208.70/128.47 (19) t2tb2(all_86_1) = all_105_2 208.70/128.47 (20) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.70/128.47 $int] : ! [v5: $int] : ( ~ (elts(v0, v1) = v3) | ~ (t2tb1(v2) = v4) 208.70/128.47 | ~ (get(v0, int, v3, v4) = v5) | ~ in_ty(v0) | (get4(v0, v1, v2) = 208.70/128.47 v5 & in_uni(v5))) 208.70/128.47 (21) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.70/128.47 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 208.70/128.47 ($lesseq(1, $difference(v3, v4))) | ~ ($lesseq(v2, v4)) | ~ 208.70/128.47 (permut2(int, v5, v6, v2, v3) = 0) | ~ (t2tb(v1) = v6) | ~ (t2tb(v0) 208.70/128.47 = v5) | ~ (get3(v1, v4) = v7) | ~ in_map_int_int(v0) | ? [v8: 208.70/128.47 $int] : ($lesseq(1, $difference(v3, v8)) & $lesseq(v2, v8) & 208.70/128.47 get3(v0, v8) = v7)) 208.70/128.47 (22) permut2(int, all_105_3, all_105_1, all_86_7, $sum(all_86_10, 1)) = 0 208.70/128.47 (23) in_array_int(all_86_1) 208.70/128.47 (24) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.70/128.47 $int] : ! [v5: $int] : ! [v6: $int] : ( ~ ($lesseq(0, v4)) | ~ 208.70/128.47 ($lesseq(0, v3)) | ~ (permut2(v0, v5, v6, v3, v4) = 0) | ~ (elts(v0, 208.70/128.47 v2) = v6) | ~ (elts(v0, v1) = v5) | ~ in_ty(v0) | ? [v7: $int] 208.70/128.47 : ? [v8: $int] : ((v7 = 0 & permut3(v0, v1, v2, v3, v4) = 0) | 208.70/128.47 (length1(v0, v1) = v7 & ( ~ ($lesseq(v4, v7)) | ~ ($lesseq(v3, v7)) 208.70/128.47 | ( ~ (v8 = v7) & length1(v0, v2) = v8))))) 208.70/128.47 (25) in_map_int_int(all_86_4) 208.70/128.47 (26) $lesseq(0, all_86_11) 208.70/128.47 (27) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ( ~ 208.70/128.47 (t2tb2(v0) = v2) | ~ (get4(int, v2, v1) = v3) | ~ in_array_int(v0) | 208.70/128.47 ? [v4: $int] : ? [v5: $int] : ? [v6: $int] : (tb2t(v4) = v5 & 208.70/128.47 tb2t1(v3) = v6 & get3(v5, v1) = v6 & elts(int, v2) = v4 & 208.70/128.47 in_map_int_int(v5) & in_uni(v4))) 208.70/128.47 (28) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ (tb2t(v2) 208.70/128.47 = v1) | ~ (tb2t(v2) = v0)) 208.70/128.47 (29) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ( ~ 208.70/128.47 (get4(v0, v1, v2) = v3) | ~ in_ty(v0) | ? [v4: $int] : ? [v5: $int] 208.70/128.47 : (elts(v0, v1) = v4 & t2tb1(v2) = v5 & get(v0, int, v4, v5) = v3 & 208.70/128.47 in_uni(v5) & in_uni(v4) & in_uni(v3))) 208.70/128.47 (30) $lesseq(1, all_86_10) 208.70/128.47 (31) t2tb(all_86_4) = all_105_3 208.70/128.47 (32) ! [v0: $int] : ! [v1: $int] : ( ~ ($lesseq(v0, all_86_10)) | ~ 208.70/128.47 ($lesseq(all_86_7, v0)) | ~ (get4(int, all_125_0, v0) = v1) | ? [v2: 208.70/128.47 $int] : ($lesseq(42, v2) & tb2t1(v1) = v2)) 208.70/128.47 208.70/128.47 Begin of proof 208.70/128.47 | 208.70/128.47 | GROUND_INST: instantiating (24) with int, all_103_4, all_105_4, all_86_11, 208.70/128.47 | $sum(all_86_10, 1), all_103_3, all_105_3, simplifying with (2), 208.70/128.47 | (5), (10), (13) gives: 208.70/128.47 | (33) ~ ($lesseq(-1, all_86_10)) | ~ ($lesseq(0, all_86_11)) | ? [v0: 208.70/128.47 | $int] : ? [v1: $int] : ((v0 = 0 & permut3(int, all_103_4, 208.70/128.47 | all_105_4, all_86_11, $sum(all_86_10, 1)) = 0) | (length1(int, 208.70/128.47 | all_103_4) = v0 & ( ~ ($lesseq(1, $difference(v0, all_86_10))) | 208.70/128.47 | ~ ($lesseq(all_86_11, v0)) | ( ~ (v1 = v0) & length1(int, 208.70/128.47 | all_105_4) = v1)))) 208.70/128.47 | 208.70/128.47 | GROUND_INST: instantiating (27) with all_86_1, all_133_2, all_105_2, 208.70/128.47 | all_133_1, simplifying with (15), (19), (23) gives: 208.70/128.47 | (34) ? [v0: $int] : ? [v1: $int] : ? [v2: $int] : (tb2t(v0) = v1 & 208.70/128.47 | tb2t1(all_133_1) = v2 & get3(v1, all_133_2) = v2 & elts(int, 208.70/128.47 | all_105_2) = v0 & in_map_int_int(v1) & in_uni(v0)) 208.70/128.47 | 208.70/128.47 | GROUND_INST: instantiating (29) with int, all_105_2, all_133_2, all_133_1, 208.70/128.47 | simplifying with (5), (15) gives: 208.70/128.47 | (35) ? [v0: $int] : ? [v1: $int] : (elts(int, all_105_2) = v0 & 208.70/128.47 | t2tb1(all_133_2) = v1 & get(int, int, v0, v1) = all_133_1 & 208.70/128.47 | in_uni(v1) & in_uni(v0) & in_uni(all_133_1)) 208.70/128.47 | 208.70/128.47 | DELTA: instantiating (35) with fresh symbols all_668_0, all_668_1 gives: 208.70/128.47 | (36) elts(int, all_105_2) = all_668_1 & t2tb1(all_133_2) = all_668_0 & 208.70/128.47 | get(int, int, all_668_1, all_668_0) = all_133_1 & in_uni(all_668_0) & 208.70/128.47 | in_uni(all_668_1) & in_uni(all_133_1) 208.70/128.47 | 208.70/128.47 | ALPHA: (36) implies: 208.70/128.47 | (37) get(int, int, all_668_1, all_668_0) = all_133_1 208.70/128.47 | (38) t2tb1(all_133_2) = all_668_0 208.70/128.47 | (39) elts(int, all_105_2) = all_668_1 208.70/128.47 | 208.70/128.47 | DELTA: instantiating (34) with fresh symbols all_678_0, all_678_1, all_678_2 208.70/128.47 | gives: 208.70/128.47 | (40) tb2t(all_678_2) = all_678_1 & tb2t1(all_133_1) = all_678_0 & 208.70/128.47 | get3(all_678_1, all_133_2) = all_678_0 & elts(int, all_105_2) = 208.70/128.47 | all_678_2 & in_map_int_int(all_678_1) & in_uni(all_678_2) 208.70/128.47 | 208.70/128.47 | ALPHA: (40) implies: 208.70/128.47 | (41) elts(int, all_105_2) = all_678_2 208.70/128.47 | (42) get3(all_678_1, all_133_2) = all_678_0 208.70/128.47 | (43) tb2t1(all_133_1) = all_678_0 208.70/128.47 | (44) tb2t(all_678_2) = all_678_1 208.70/128.47 | 208.70/128.47 | BETA: splitting (33) gives: 208.70/128.47 | 208.70/128.47 | Case 1: 208.70/128.47 | | 208.70/128.47 | | (45) $lesseq(all_86_11, -1) 208.70/128.47 | | 208.70/128.47 | | COMBINE_INEQS: (26), (45) imply: 208.70/128.47 | | (46) $lesseq(0, -1) 208.70/128.47 | | 208.70/128.47 | | CLOSE: (46) is inconsistent. 208.70/128.47 | | 208.70/128.47 | Case 2: 208.70/128.47 | | 208.70/128.47 | | (47) ~ ($lesseq(-1, all_86_10)) | ? [v0: $int] : ? [v1: $int] : ((v0 = 208.70/128.47 | | 0 & permut3(int, all_103_4, all_105_4, all_86_11, 208.70/128.47 | | $sum(all_86_10, 1)) = 0) | (length1(int, all_103_4) = v0 & ( ~ 208.70/128.47 | | ($lesseq(1, $difference(v0, all_86_10))) | ~ 208.70/128.47 | | ($lesseq(all_86_11, v0)) | ( ~ (v1 = v0) & length1(int, 208.70/128.47 | | all_105_4) = v1)))) 208.70/128.47 | | 208.70/128.47 | | BETA: splitting (47) gives: 208.70/128.47 | | 208.70/128.47 | | Case 1: 208.70/128.47 | | | 208.70/128.47 | | | (48) $lesseq(all_86_10, -2) 208.70/128.47 | | | 208.70/128.47 | | | COMBINE_INEQS: (30), (48) imply: 208.70/128.47 | | | (49) $lesseq(0, -1) 208.70/128.47 | | | 208.70/128.47 | | | CLOSE: (49) is inconsistent. 208.70/128.47 | | | 208.70/128.47 | | Case 2: 208.70/128.47 | | | 208.70/128.47 | | | 208.70/128.47 | | | GROUND_INST: instantiating (1) with all_133_0, all_678_0, all_133_1, 208.70/128.47 | | | simplifying with (9), (43) gives: 208.70/128.47 | | | (50) all_678_0 = all_133_0 208.70/128.47 | | | 208.70/128.47 | | | GROUND_INST: instantiating (11) with all_105_1, all_678_2, all_105_2, int, 208.70/128.47 | | | simplifying with (17), (41) gives: 208.70/128.47 | | | (51) all_678_2 = all_105_1 208.70/128.47 | | | 208.70/128.47 | | | GROUND_INST: instantiating (11) with all_678_2, all_668_1, all_105_2, int, 208.70/128.47 | | | simplifying with (39), (41) gives: 208.70/128.47 | | | (52) all_678_2 = all_668_1 208.70/128.47 | | | 208.70/128.47 | | | COMBINE_EQS: (51), (52) imply: 208.70/128.47 | | | (53) all_668_1 = all_105_1 208.70/128.47 | | | 208.70/128.47 | | | REDUCE: (44), (51) imply: 208.70/128.47 | | | (54) tb2t(all_105_1) = all_678_1 208.70/128.47 | | | 208.70/128.47 | | | REDUCE: (42), (50) imply: 208.70/128.47 | | | (55) get3(all_678_1, all_133_2) = all_133_0 208.70/128.47 | | | 208.70/128.47 | | | REDUCE: (37), (53) imply: 208.70/128.47 | | | (56) get(int, int, all_105_1, all_668_0) = all_133_1 208.70/128.47 | | | 208.70/128.47 | | | GROUND_INST: instantiating (28) with all_86_2, all_678_1, all_105_1, 208.70/128.47 | | | simplifying with (16), (54) gives: 208.70/128.47 | | | (57) all_678_1 = all_86_2 208.70/128.47 | | | 208.70/128.47 | | | REDUCE: (55), (57) imply: 208.70/128.48 | | | (58) get3(all_86_2, all_133_2) = all_133_0 208.70/128.48 | | | 208.70/128.48 | | | GROUND_INST: instantiating (21) with all_86_4, all_86_2, all_86_7, 208.70/128.48 | | | $sum(all_86_10, 1), all_133_2, all_105_3, all_105_1, 208.70/128.48 | | | all_133_0, simplifying with (4), (22), (25), (31), (58) 208.70/128.48 | | | gives: 208.70/128.48 | | | (59) ~ ($lesseq(all_133_2, all_86_10)) | ~ ($lesseq(all_86_7, 208.70/128.48 | | | all_133_2)) | ? [v0: $int] : ($lesseq(v0, all_86_10) & 208.70/128.48 | | | $lesseq(all_86_7, v0) & get3(all_86_4, v0) = all_133_0) 208.70/128.48 | | | 208.70/128.48 | | | GROUND_INST: instantiating (18) with int, all_105_3, all_105_1, all_86_7, 208.70/128.48 | | | $sum(all_86_10, 1), all_133_2, all_668_0, all_133_1, 208.70/128.48 | | | simplifying with (5), (22), (38), (56) gives: 208.70/128.48 | | | (60) ~ ($lesseq(all_133_2, all_86_10)) | ~ ($lesseq(all_86_7, 208.70/128.48 | | | all_133_2)) | ? [v0: $int] : ? [v1: $int] : ($lesseq(v0, 208.70/128.48 | | | all_86_10) & $lesseq(all_86_7, v0) & t2tb1(v0) = v1 & get(int, 208.70/128.48 | | | int, all_105_3, v1) = all_133_1 & in_uni(v1) & 208.70/128.48 | | | in_uni(all_133_1)) 208.70/128.48 | | | 208.70/128.48 | | | REF_CLOSE: (1), (3), (5), (6), (7), (8), (9), (12), (13), (14), (20), 208.70/128.48 | | | (27), (32), (59), (60) are inconsistent by sub-proof #149. 208.70/128.48 | | | 208.70/128.48 | | End of split 208.70/128.48 | | 208.70/128.48 | End of split 208.70/128.48 | 208.70/128.48 End of proof 208.70/128.48 208.70/128.48 Sub-proof #149 shows that the following formulas are inconsistent: 208.70/128.48 ---------------------------------------------------------------- 208.70/128.48 (1) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ (tb2t1(v2) 208.70/128.48 = v1) | ~ (tb2t1(v2) = v0)) 208.70/128.48 (2) ~ ($lesseq(all_133_2, all_86_10)) | ~ ($lesseq(all_86_7, all_133_2)) | 208.70/128.48 ? [v0: $int] : ($lesseq(v0, all_86_10) & $lesseq(all_86_7, v0) & 208.70/128.48 get3(all_86_4, v0) = all_133_0) 208.70/128.48 (3) t2tb2(all_86_3) = all_105_4 208.70/128.48 (4) in_ty(int) 208.70/128.48 (5) all_125_0 = all_105_4 208.70/128.48 (6) $lesseq(all_133_2, all_86_10) 208.70/128.48 (7) $lesseq(all_133_0, 41) 208.70/128.48 (8) tb2t1(all_133_1) = all_133_0 208.70/128.48 (9) in_array_int(all_86_3) 208.70/128.48 (10) elts(int, all_105_4) = all_105_3 208.70/128.48 (11) ~ ($lesseq(all_133_2, all_86_10)) | ~ ($lesseq(all_86_7, all_133_2)) | 208.70/128.48 ? [v0: $int] : ? [v1: $int] : ($lesseq(v0, all_86_10) & 208.70/128.48 $lesseq(all_86_7, v0) & t2tb1(v0) = v1 & get(int, int, all_105_3, v1) 208.70/128.48 = all_133_1 & in_uni(v1) & in_uni(all_133_1)) 208.70/128.48 (12) $lesseq(all_86_7, all_133_2) 208.70/128.48 (13) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.70/128.48 $int] : ! [v5: $int] : ( ~ (elts(v0, v1) = v3) | ~ (t2tb1(v2) = v4) 208.70/128.48 | ~ (get(v0, int, v3, v4) = v5) | ~ in_ty(v0) | (get4(v0, v1, v2) = 208.70/128.48 v5 & in_uni(v5))) 208.70/128.48 (14) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ( ~ 208.70/128.48 (t2tb2(v0) = v2) | ~ (get4(int, v2, v1) = v3) | ~ in_array_int(v0) | 208.70/128.48 ? [v4: $int] : ? [v5: $int] : ? [v6: $int] : (tb2t(v4) = v5 & 208.70/128.48 tb2t1(v3) = v6 & get3(v5, v1) = v6 & elts(int, v2) = v4 & 208.70/128.48 in_map_int_int(v5) & in_uni(v4))) 208.70/128.48 (15) ! [v0: $int] : ! [v1: $int] : ( ~ ($lesseq(v0, all_86_10)) | ~ 208.70/128.48 ($lesseq(all_86_7, v0)) | ~ (get4(int, all_125_0, v0) = v1) | ? [v2: 208.70/128.48 $int] : ($lesseq(42, v2) & tb2t1(v1) = v2)) 208.70/128.48 208.70/128.48 Begin of proof 208.70/128.48 | 208.70/128.48 | BETA: splitting (11) gives: 208.70/128.48 | 208.70/128.48 | Case 1: 208.70/128.48 | | 208.70/128.48 | | (16) $lesseq(1, $difference(all_133_2, all_86_10)) 208.70/128.48 | | 208.70/128.48 | | COMBINE_INEQS: (6), (16) imply: 208.70/128.48 | | (17) $lesseq(0, -1) 208.70/128.48 | | 208.70/128.48 | | CLOSE: (17) is inconsistent. 208.70/128.48 | | 208.70/128.48 | Case 2: 208.70/128.48 | | 208.70/128.48 | | (18) ~ ($lesseq(all_86_7, all_133_2)) | ? [v0: $int] : ? [v1: $int] : 208.70/128.48 | | ($lesseq(v0, all_86_10) & $lesseq(all_86_7, v0) & t2tb1(v0) = v1 & 208.70/128.48 | | get(int, int, all_105_3, v1) = all_133_1 & in_uni(v1) & 208.70/128.48 | | in_uni(all_133_1)) 208.70/128.48 | | 208.70/128.48 | | BETA: splitting (2) gives: 208.70/128.48 | | 208.70/128.48 | | Case 1: 208.70/128.48 | | | 208.70/128.48 | | | (19) $lesseq(1, $difference(all_133_2, all_86_10)) 208.70/128.48 | | | 208.70/128.48 | | | COMBINE_INEQS: (6), (19) imply: 208.70/128.48 | | | (20) $lesseq(0, -1) 208.70/128.48 | | | 208.70/128.48 | | | CLOSE: (20) is inconsistent. 208.70/128.48 | | | 208.70/128.48 | | Case 2: 208.70/128.48 | | | 208.70/128.48 | | | (21) ~ ($lesseq(all_86_7, all_133_2)) | ? [v0: $int] : ($lesseq(v0, 208.70/128.48 | | | all_86_10) & $lesseq(all_86_7, v0) & get3(all_86_4, v0) = 208.70/128.48 | | | all_133_0) 208.70/128.48 | | | 208.70/128.48 | | | BETA: splitting (18) gives: 208.70/128.48 | | | 208.70/128.48 | | | Case 1: 208.70/128.48 | | | | 208.70/128.48 | | | | (22) $lesseq(1, $difference(all_86_7, all_133_2)) 208.70/128.48 | | | | 208.70/128.48 | | | | COMBINE_INEQS: (12), (22) imply: 208.70/128.48 | | | | (23) $lesseq(0, -1) 208.70/128.48 | | | | 208.70/128.48 | | | | CLOSE: (23) is inconsistent. 208.70/128.48 | | | | 208.70/128.48 | | | Case 2: 208.70/128.48 | | | | 208.70/128.48 | | | | (24) ? [v0: $int] : ? [v1: $int] : ($lesseq(v0, all_86_10) & 208.70/128.48 | | | | $lesseq(all_86_7, v0) & t2tb1(v0) = v1 & get(int, int, 208.70/128.48 | | | | all_105_3, v1) = all_133_1 & in_uni(v1) & in_uni(all_133_1)) 208.70/128.48 | | | | 208.70/128.48 | | | | DELTA: instantiating (24) with fresh symbols all_781_0, all_781_1 gives: 208.70/128.48 | | | | (25) $lesseq(all_781_1, all_86_10) & $lesseq(all_86_7, all_781_1) & 208.70/128.48 | | | | t2tb1(all_781_1) = all_781_0 & get(int, int, all_105_3, 208.70/128.48 | | | | all_781_0) = all_133_1 & in_uni(all_781_0) & in_uni(all_133_1) 208.70/128.48 | | | | 208.70/128.48 | | | | ALPHA: (25) implies: 208.70/128.48 | | | | (26) $lesseq(all_86_7, all_781_1) 208.70/128.48 | | | | (27) $lesseq(all_781_1, all_86_10) 208.70/128.48 | | | | (28) get(int, int, all_105_3, all_781_0) = all_133_1 208.70/128.48 | | | | (29) t2tb1(all_781_1) = all_781_0 208.70/128.48 | | | | 208.70/128.48 | | | | BETA: splitting (21) gives: 208.70/128.48 | | | | 208.70/128.48 | | | | Case 1: 208.70/128.48 | | | | | 208.70/128.48 | | | | | (30) $lesseq(1, $difference(all_86_7, all_133_2)) 208.70/128.48 | | | | | 208.70/128.48 | | | | | COMBINE_INEQS: (12), (30) imply: 208.70/128.48 | | | | | (31) $lesseq(0, -1) 208.70/128.48 | | | | | 208.70/128.48 | | | | | CLOSE: (31) is inconsistent. 208.70/128.48 | | | | | 208.70/128.48 | | | | Case 2: 208.70/128.48 | | | | | 208.70/128.48 | | | | | 208.70/128.48 | | | | | GROUND_INST: instantiating (13) with int, all_105_4, all_781_1, 208.70/128.48 | | | | | all_105_3, all_781_0, all_133_1, simplifying with (4), 208.70/128.48 | | | | | (10), (28), (29) gives: 208.70/128.48 | | | | | (32) get4(int, all_105_4, all_781_1) = all_133_1 & 208.70/128.48 | | | | | in_uni(all_133_1) 208.70/128.48 | | | | | 208.70/128.48 | | | | | ALPHA: (32) implies: 208.70/128.48 | | | | | (33) get4(int, all_105_4, all_781_1) = all_133_1 208.70/128.48 | | | | | 208.70/128.48 | | | | | GROUND_INST: instantiating (14) with all_86_3, all_781_1, all_105_4, 208.70/128.48 | | | | | all_133_1, simplifying with (3), (9), (33) gives: 208.70/128.48 | | | | | (34) ? [v0: $int] : ? [v1: $int] : ? [v2: $int] : (tb2t(v0) = v1 208.70/128.48 | | | | | & tb2t1(all_133_1) = v2 & get3(v1, all_781_1) = v2 & 208.70/128.48 | | | | | elts(int, all_105_4) = v0 & in_map_int_int(v1) & in_uni(v0)) 208.70/128.48 | | | | | 208.70/128.48 | | | | | GROUND_INST: instantiating (15) with all_781_1, all_133_1 gives: 208.70/128.48 | | | | | (35) ~ ($lesseq(all_781_1, all_86_10)) | ~ ($lesseq(all_86_7, 208.70/128.48 | | | | | all_781_1)) | ~ (get4(int, all_125_0, all_781_1) = 208.70/128.48 | | | | | all_133_1) | ? [v0: $int] : ($lesseq(42, v0) & 208.70/128.48 | | | | | tb2t1(all_133_1) = v0) 208.70/128.48 | | | | | 208.70/128.48 | | | | | DELTA: instantiating (34) with fresh symbols all_914_0, all_914_1, 208.70/128.48 | | | | | all_914_2 gives: 208.70/128.48 | | | | | (36) tb2t(all_914_2) = all_914_1 & tb2t1(all_133_1) = all_914_0 & 208.70/128.48 | | | | | get3(all_914_1, all_781_1) = all_914_0 & elts(int, all_105_4) 208.70/128.48 | | | | | = all_914_2 & in_map_int_int(all_914_1) & in_uni(all_914_2) 208.70/128.48 | | | | | 208.70/128.48 | | | | | ALPHA: (36) implies: 208.70/128.48 | | | | | (37) tb2t1(all_133_1) = all_914_0 208.70/128.48 | | | | | 208.70/128.48 | | | | | BETA: splitting (35) gives: 208.70/128.48 | | | | | 208.70/128.48 | | | | | Case 1: 208.70/128.48 | | | | | | 208.70/128.48 | | | | | | (38) ~ (get4(int, all_125_0, all_781_1) = all_133_1) 208.70/128.48 | | | | | | 208.70/128.48 | | | | | | REDUCE: (5), (38) imply: 208.70/128.48 | | | | | | (39) ~ (get4(int, all_105_4, all_781_1) = all_133_1) 208.70/128.48 | | | | | | 208.70/128.48 | | | | | | PRED_UNIFY: (33), (39) imply: 208.70/128.48 | | | | | | (40) $false 208.70/128.48 | | | | | | 208.70/128.48 | | | | | | CLOSE: (40) is inconsistent. 208.70/128.48 | | | | | | 208.70/128.48 | | | | | Case 2: 208.70/128.48 | | | | | | 208.70/128.48 | | | | | | (41) ~ ($lesseq(all_781_1, all_86_10)) | ~ ($lesseq(all_86_7, 208.70/128.48 | | | | | | all_781_1)) | ? [v0: $int] : ($lesseq(42, v0) & 208.70/128.48 | | | | | | tb2t1(all_133_1) = v0) 208.70/128.48 | | | | | | 208.70/128.48 | | | | | | BETA: splitting (41) gives: 208.70/128.48 | | | | | | 208.70/128.48 | | | | | | Case 1: 208.70/128.48 | | | | | | | 208.70/128.48 | | | | | | | (42) $lesseq(1, $difference(all_781_1, all_86_10)) 208.70/128.48 | | | | | | | 208.70/128.48 | | | | | | | COMBINE_INEQS: (27), (42) imply: 208.70/128.48 | | | | | | | (43) $lesseq(0, -1) 208.70/128.48 | | | | | | | 208.70/128.48 | | | | | | | CLOSE: (43) is inconsistent. 208.70/128.48 | | | | | | | 208.70/128.48 | | | | | | Case 2: 208.70/128.48 | | | | | | | 208.70/128.48 | | | | | | | (44) ~ ($lesseq(all_86_7, all_781_1)) | ? [v0: $int] : 208.70/128.48 | | | | | | | ($lesseq(42, v0) & tb2t1(all_133_1) = v0) 208.70/128.48 | | | | | | | 208.70/128.48 | | | | | | | BETA: splitting (44) gives: 208.70/128.48 | | | | | | | 208.70/128.48 | | | | | | | Case 1: 208.70/128.48 | | | | | | | | 208.70/128.48 | | | | | | | | (45) $lesseq(1, $difference(all_86_7, all_781_1)) 208.70/128.48 | | | | | | | | 208.70/128.48 | | | | | | | | COMBINE_INEQS: (26), (45) imply: 208.70/128.48 | | | | | | | | (46) $lesseq(0, -1) 208.70/128.48 | | | | | | | | 208.70/128.48 | | | | | | | | CLOSE: (46) is inconsistent. 208.70/128.48 | | | | | | | | 208.70/128.48 | | | | | | | Case 2: 208.70/128.48 | | | | | | | | 208.70/128.48 | | | | | | | | (47) ? [v0: $int] : ($lesseq(42, v0) & tb2t1(all_133_1) = 208.70/128.48 | | | | | | | | v0) 208.70/128.48 | | | | | | | | 208.70/128.48 | | | | | | | | DELTA: instantiating (47) with fresh symbol all_969_0 gives: 208.70/128.48 | | | | | | | | (48) $lesseq(42, all_969_0) & tb2t1(all_133_1) = all_969_0 208.70/128.48 | | | | | | | | 208.70/128.48 | | | | | | | | ALPHA: (48) implies: 208.70/128.48 | | | | | | | | (49) $lesseq(42, all_969_0) 208.70/128.48 | | | | | | | | (50) tb2t1(all_133_1) = all_969_0 208.70/128.48 | | | | | | | | 208.70/128.48 | | | | | | | | GROUND_INST: instantiating (1) with all_133_0, all_969_0, 208.70/128.48 | | | | | | | | all_133_1, simplifying with (8), (50) gives: 208.70/128.48 | | | | | | | | (51) all_969_0 = all_133_0 208.70/128.48 | | | | | | | | 208.70/128.48 | | | | | | | | GROUND_INST: instantiating (1) with all_969_0, all_914_0, 208.70/128.48 | | | | | | | | all_133_1, simplifying with (37), (50) gives: 208.70/128.48 | | | | | | | | (52) all_969_0 = all_914_0 208.70/128.48 | | | | | | | | 208.70/128.48 | | | | | | | | COMBINE_EQS: (51), (52) imply: 208.70/128.48 | | | | | | | | (53) all_914_0 = all_133_0 208.70/128.48 | | | | | | | | 208.70/128.48 | | | | | | | | REDUCE: (49), (51) imply: 208.70/128.48 | | | | | | | | (54) $lesseq(42, all_133_0) 208.70/128.48 | | | | | | | | 208.70/128.48 | | | | | | | | COMBINE_INEQS: (7), (54) imply: 208.70/128.48 | | | | | | | | (55) $lesseq(0, -1) 208.70/128.48 | | | | | | | | 208.70/128.48 | | | | | | | | CLOSE: (55) is inconsistent. 208.70/128.48 | | | | | | | | 208.70/128.48 | | | | | | | End of split 208.70/128.48 | | | | | | | 208.70/128.48 | | | | | | End of split 208.70/128.48 | | | | | | 208.70/128.48 | | | | | End of split 208.70/128.48 | | | | | 208.70/128.48 | | | | End of split 208.70/128.48 | | | | 208.70/128.48 | | | End of split 208.70/128.48 | | | 208.70/128.48 | | End of split 208.70/128.48 | | 208.70/128.48 | End of split 208.70/128.48 | 208.70/128.48 End of proof 208.70/128.48 208.70/128.48 Sub-proof #150 shows that the following formulas are inconsistent: 208.70/128.48 ---------------------------------------------------------------- 208.70/128.48 (1) in_map_int_int(all_86_6) 208.70/128.48 (2) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.70/128.48 $int] : ! [v5: $int] : ! [v6: $int] : ( ~ ($lesseq(0, v4)) | ~ 208.70/128.48 ($lesseq(0, v3)) | ~ (map_eq_sub1(v0, v5, v6, v3, v4) = 0) | ~ 208.70/128.48 (elts(v0, v2) = v6) | ~ (elts(v0, v1) = v5) | ~ in_ty(v0) | ? [v7: 208.70/128.48 $int] : ? [v8: $int] : ((v7 = 0 & array_eq_sub1(v0, v1, v2, v3, v4) 208.70/128.48 = 0) | (length1(v0, v1) = v7 & ( ~ ($lesseq(v4, v7)) | ~ 208.70/128.48 ($lesseq(v3, v7)) | ( ~ (v8 = v7) & length1(v0, v2) = v8))))) 208.70/128.48 (3) elts(int, all_103_4) = all_103_3 208.70/128.48 (4) in_ty(int) 208.70/128.48 (5) length1(int, all_103_4) = all_86_13 208.70/128.48 (6) $lesseq(1, $difference(all_86_13, all_86_7)) 208.70/128.48 (7) ~ ($lesseq(1, $difference(all_86_7, all_133_2))) | ~ ($lesseq(0, 208.70/128.48 all_133_2)) | ? [v0: $int] : (get(int, int, all_105_1, all_668_0) = 208.70/128.48 v0 & get(int, int, all_105_3, all_668_0) = v0 & in_uni(v0)) 208.70/128.48 (8) ! [v0: $int] : ! [v1: $int] : (v1 = 42 | ~ ($lesseq(1, 208.70/128.48 $difference(all_86_7, v0))) | ~ ($lesseq(1, $difference(v0, 208.70/128.48 all_86_8))) | ~ (get3(all_86_6, v0) = v1)) 208.70/128.48 (9) t2tb(all_86_6) = all_103_1 208.70/128.48 (10) $lesseq(1, $difference(all_133_2, all_86_8)) 208.70/128.48 (11) map_eq_sub1(int, all_103_1, all_105_3, $sum(all_86_8, 1), all_86_13) = 0 208.70/128.48 (12) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 208.70/128.48 | ~ (elts(v3, v2) = v1) | ~ (elts(v3, v2) = v0)) 208.70/128.48 (13) (all_745_0 = 0 & all_745_1 = 0 & map_eq_sub1(int, all_745_4, all_745_3, 208.70/128.48 $sum(all_86_10, 1), all_745_2) = 0 & map_eq_sub1(int, all_745_4, 208.70/128.48 all_745_3, 0, all_86_11) = 0 & length1(int, all_103_4) = all_745_2 & 208.70/128.48 elts(int, all_105_4) = all_745_3 & elts(int, all_103_4) = all_745_4 & 208.70/128.48 in_uni(all_745_3) & in_uni(all_745_4)) | ( ~ (all_745_4 = 0) & 208.70/128.48 permut_sub2(int, all_103_4, all_105_4, all_86_11, $sum(all_86_10, 1)) 208.70/128.48 = all_745_4) 208.70/128.48 (14) elts(int, all_105_4) = all_105_3 208.70/128.48 (15) $lesseq(1, $difference(all_86_7, all_133_2)) 208.70/128.48 (16) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.70/128.48 $int] : ! [v5: $int] : ! [v6: $int] : (v1 = v0 | ~ (permut_sub2(v6, 208.70/128.48 v5, v4, v3, v2) = v1) | ~ (permut_sub2(v6, v5, v4, v3, v2) = v0)) 208.70/128.48 (17) (all_758_3 = 0 & permut_sub3(all_86_9, all_86_3, all_86_11, 208.70/128.48 $sum(all_86_10, 1)) = 0) | (elts(int, all_105_4) = all_758_2 & 208.70/128.48 elts(int, all_103_4) = all_758_3 & in_uni(all_758_2) & 208.70/128.48 in_uni(all_758_3) & (( ~ (all_758_0 = 0) & map_eq_sub1(int, all_758_3, 208.70/128.48 all_758_2, $sum(all_86_10, 1), all_758_1) = all_758_0 & 208.70/128.48 length1(int, all_103_4) = all_758_1) | ( ~ (all_758_1 = 0) & 208.70/128.48 map_eq_sub1(int, all_758_3, all_758_2, 0, all_86_11) = 208.70/128.48 all_758_1))) 208.70/128.48 (18) ~ ($lesseq(1, $difference(all_86_13, all_133_2))) | ~ ($lesseq(1, 208.70/128.48 $difference(all_133_2, all_86_8))) | ? [v0: $int] : (get(int, int, 208.70/128.48 all_105_3, all_668_0) = v0 & get(int, int, all_103_1, all_668_0) = 208.70/128.48 v0 & in_uni(v0)) 208.70/128.48 (19) $lesseq(0, all_86_8) 208.70/128.48 (20) $lesseq(4, all_86_13) 208.70/128.48 (21) ~ (all_133_0 = 42) 208.70/128.48 (22) ~ ($lesseq(1, $difference(all_86_7, all_133_2))) | ~ ($lesseq(0, 208.70/128.48 all_133_2)) | get3(all_86_4, all_133_2) = all_133_0 208.70/128.48 (23) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.70/128.48 $int] : ! [v5: $int] : (v5 = 0 | ~ (permut_sub2(v0, v1, v2, v3, v4) 208.70/128.48 = v5) | ~ in_ty(v0) | ? [v6: $int] : ? [v7: $int] : ? [v8: $int] 208.70/128.48 : ? [v9: $int] : (( ~ (v9 = 0) & map_eq_sub1(v0, v6, v7, v4, v8) = v9 208.70/128.48 & length1(v0, v1) = v8 & elts(v0, v2) = v7 & elts(v0, v1) = v6 & 208.70/128.48 in_uni(v7) & in_uni(v6)) | ( ~ (v8 = 0) & map_eq_sub1(v0, v6, v7, 208.70/128.48 0, v3) = v8 & elts(v0, v2) = v7 & elts(v0, v1) = v6 & in_uni(v7) 208.70/128.48 & in_uni(v6)) | ( ~ (v6 = 0) & permut3(v0, v1, v2, v3, v4) = v6))) 208.70/128.48 (24) (all_757_3 = 0 & permut_sub2(int, all_103_4, all_105_4, all_86_11, 208.70/128.48 $sum(all_86_10, 1)) = 0) | (elts(int, all_105_4) = all_757_2 & 208.70/128.48 elts(int, all_103_4) = all_757_3 & in_uni(all_757_2) & 208.70/128.48 in_uni(all_757_3) & (( ~ (all_757_0 = 0) & map_eq_sub1(int, all_757_3, 208.70/128.48 all_757_2, $sum(all_86_10, 1), all_757_1) = all_757_0 & 208.70/128.48 length1(int, all_103_4) = all_757_1) | ( ~ (all_757_1 = 0) & 208.70/128.48 map_eq_sub1(int, all_757_3, all_757_2, 0, all_86_11) = 208.70/128.48 all_757_1))) 208.70/128.48 (25) (all_746_0 = 0 & all_746_2 = 0 & map_eq_sub1(int, all_746_4, all_746_3, 208.70/128.48 $sum(all_86_10, 1), all_746_1) = 0 & map_eq_sub1(int, all_746_4, 208.70/128.48 all_746_3, 0, all_86_11) = 0 & length1(int, all_103_4) = all_746_1 & 208.70/128.48 elts(int, all_105_4) = all_746_3 & elts(int, all_103_4) = all_746_4 & 208.70/128.48 in_uni(all_746_3) & in_uni(all_746_4)) | ( ~ (all_746_4 = 0) & 208.70/128.48 permut_sub3(all_86_9, all_86_3, all_86_11, $sum(all_86_10, 1)) = 208.70/128.48 all_746_4) 208.70/128.48 (26) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.70/128.48 $int] : ! [v5: $int] : (v1 = v0 | ~ (permut_sub3(v5, v4, v3, v2) = 208.70/128.48 v1) | ~ (permut_sub3(v5, v4, v3, v2) = v0)) 208.70/128.48 (27) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.70/128.48 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 208.70/128.48 ($lesseq(1, $difference(v3, v6))) | ~ ($lesseq(v2, v6)) | ~ 208.70/128.48 (map_eq_sub1(int, v4, v5, v2, v3) = 0) | ~ (t2tb(v1) = v5) | ~ 208.70/128.48 (t2tb(v0) = v4) | ~ (get3(v1, v6) = v7) | ~ in_map_int_int(v0) | 208.70/128.48 get3(v0, v6) = v7) 208.70/128.48 (28) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 208.70/128.48 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0)) 208.70/128.48 (29) t2tb(all_86_4) = all_105_3 208.70/128.48 (30) $lesseq(2, all_86_10) 208.70/128.48 208.70/128.48 Begin of proof 208.70/128.48 | 208.70/128.48 | BETA: splitting (7) gives: 208.70/128.48 | 208.70/128.48 | Case 1: 208.70/128.48 | | 208.70/128.48 | | (31) $lesseq(all_133_2, -1) 208.70/128.48 | | 208.70/128.48 | | COMBINE_INEQS: (10), (31) imply: 208.70/128.48 | | (32) $lesseq(all_86_8, -2) 208.70/128.48 | | 208.70/128.48 | | COMBINE_INEQS: (19), (32) imply: 208.70/128.48 | | (33) $lesseq(0, -1) 208.70/128.48 | | 208.70/128.48 | | CLOSE: (33) is inconsistent. 208.70/128.49 | | 208.70/128.49 | Case 2: 208.70/128.49 | | 208.70/128.49 | | (34) $lesseq(0, all_133_2) 208.70/128.49 | | 208.70/128.49 | | BETA: splitting (22) gives: 208.70/128.49 | | 208.70/128.49 | | Case 1: 208.70/128.49 | | | 208.70/128.49 | | | (35) get3(all_86_4, all_133_2) = all_133_0 208.70/128.49 | | | 208.70/128.49 | | | BETA: splitting (18) gives: 208.70/128.49 | | | 208.70/128.49 | | | Case 1: 208.70/128.49 | | | | 208.70/128.49 | | | | (36) $lesseq(all_86_13, all_133_2) 208.70/128.49 | | | | 208.70/128.49 | | | | COMBINE_INEQS: (15), (36) imply: 208.70/128.49 | | | | (37) $lesseq(1, $difference(all_86_7, all_86_13)) 208.70/128.49 | | | | 208.70/128.49 | | | | COMBINE_INEQS: (6), (37) imply: 208.70/128.49 | | | | (38) $lesseq(0, -1) 208.70/128.49 | | | | 208.70/128.49 | | | | CLOSE: (38) is inconsistent. 208.70/128.49 | | | | 208.70/128.49 | | | Case 2: 208.70/128.49 | | | | 208.70/128.49 | | | | (39) $lesseq(1, $difference(all_86_13, all_133_2)) 208.70/128.49 | | | | 208.70/128.49 | | | | BETA: splitting (13) gives: 208.70/128.49 | | | | 208.70/128.49 | | | | Case 1: 208.70/128.49 | | | | | 208.70/128.49 | | | | | (40) all_745_0 = 0 & all_745_1 = 0 & map_eq_sub1(int, all_745_4, 208.70/128.49 | | | | | all_745_3, $sum(all_86_10, 1), all_745_2) = 0 & 208.70/128.49 | | | | | map_eq_sub1(int, all_745_4, all_745_3, 0, all_86_11) = 0 & 208.70/128.49 | | | | | length1(int, all_103_4) = all_745_2 & elts(int, all_105_4) = 208.70/128.49 | | | | | all_745_3 & elts(int, all_103_4) = all_745_4 & 208.70/128.49 | | | | | in_uni(all_745_3) & in_uni(all_745_4) 208.70/128.49 | | | | | 208.70/128.49 | | | | | ALPHA: (40) implies: 208.70/128.49 | | | | | (41) elts(int, all_103_4) = all_745_4 208.70/128.49 | | | | | (42) elts(int, all_105_4) = all_745_3 208.70/128.49 | | | | | (43) length1(int, all_103_4) = all_745_2 208.70/128.49 | | | | | (44) map_eq_sub1(int, all_745_4, all_745_3, $sum(all_86_10, 1), 208.70/128.49 | | | | | all_745_2) = 0 208.70/128.49 | | | | | 208.70/128.49 | | | | | GROUND_INST: instantiating (28) with all_86_13, all_745_2, all_103_4, 208.70/128.49 | | | | | int, simplifying with (5), (43) gives: 208.70/128.49 | | | | | (45) all_745_2 = all_86_13 208.70/128.49 | | | | | 208.70/128.49 | | | | | GROUND_INST: instantiating (12) with all_105_3, all_745_3, all_105_4, 208.70/128.49 | | | | | int, simplifying with (14), (42) gives: 208.70/128.49 | | | | | (46) all_745_3 = all_105_3 208.70/128.49 | | | | | 208.70/128.49 | | | | | GROUND_INST: instantiating (12) with all_103_3, all_745_4, all_103_4, 208.70/128.49 | | | | | int, simplifying with (3), (41) gives: 208.70/128.49 | | | | | (47) all_745_4 = all_103_3 208.70/128.49 | | | | | 208.70/128.49 | | | | | REDUCE: (44), (45), (46), (47) imply: 208.70/128.49 | | | | | (48) map_eq_sub1(int, all_103_3, all_105_3, $sum(all_86_10, 1), 208.70/128.49 | | | | | all_86_13) = 0 208.70/128.49 | | | | | 208.70/128.49 | | | | | REF_CLOSE: (1), (2), (3), (4), (8), (9), (10), (11), (14), (15), (20), 208.70/128.49 | | | | | (21), (27), (29), (30), (35), (39), (48) are inconsistent 208.70/128.49 | | | | | by sub-proof #152. 208.70/128.49 | | | | | 208.70/128.49 | | | | Case 2: 208.70/128.49 | | | | | 208.70/128.49 | | | | | (49) ~ (all_745_4 = 0) & permut_sub2(int, all_103_4, all_105_4, 208.70/128.49 | | | | | all_86_11, $sum(all_86_10, 1)) = all_745_4 208.70/128.49 | | | | | 208.70/128.49 | | | | | ALPHA: (49) implies: 208.70/128.49 | | | | | (50) ~ (all_745_4 = 0) 208.70/128.49 | | | | | (51) permut_sub2(int, all_103_4, all_105_4, all_86_11, 208.70/128.49 | | | | | $sum(all_86_10, 1)) = all_745_4 208.70/128.49 | | | | | 208.70/128.49 | | | | | BETA: splitting (24) gives: 208.70/128.49 | | | | | 208.70/128.49 | | | | | Case 1: 208.70/128.49 | | | | | | 208.70/128.49 | | | | | | (52) all_757_3 = 0 & permut_sub2(int, all_103_4, all_105_4, 208.70/128.49 | | | | | | all_86_11, $sum(all_86_10, 1)) = 0 208.70/128.49 | | | | | | 208.70/128.49 | | | | | | ALPHA: (52) implies: 208.70/128.49 | | | | | | (53) permut_sub2(int, all_103_4, all_105_4, all_86_11, 208.70/128.49 | | | | | | $sum(all_86_10, 1)) = 0 208.70/128.49 | | | | | | 208.70/128.49 | | | | | | GROUND_INST: instantiating (16) with all_745_4, 0, $sum(all_86_10, 208.70/128.49 | | | | | | 1), all_86_11, all_105_4, all_103_4, int, simplifying 208.70/128.49 | | | | | | with (51), (53) gives: 208.70/128.49 | | | | | | (54) all_745_4 = 0 208.70/128.49 | | | | | | 208.70/128.49 | | | | | | REDUCE: (50), (54) imply: 208.70/128.49 | | | | | | (55) ~ (0 = 0) 208.70/128.49 | | | | | | 208.70/128.49 | | | | | | CLOSE: (55) is inconsistent. 208.70/128.49 | | | | | | 208.70/128.49 | | | | | Case 2: 208.70/128.49 | | | | | | 208.70/128.49 | | | | | | (56) elts(int, all_105_4) = all_757_2 & elts(int, all_103_4) = 208.70/128.49 | | | | | | all_757_3 & in_uni(all_757_2) & in_uni(all_757_3) & (( ~ 208.70/128.49 | | | | | | (all_757_0 = 0) & map_eq_sub1(int, all_757_3, all_757_2, 208.70/128.49 | | | | | | $sum(all_86_10, 1), all_757_1) = all_757_0 & 208.70/128.49 | | | | | | length1(int, all_103_4) = all_757_1) | ( ~ (all_757_1 = 208.70/128.49 | | | | | | 0) & map_eq_sub1(int, all_757_3, all_757_2, 0, 208.70/128.49 | | | | | | all_86_11) = all_757_1)) 208.70/128.49 | | | | | | 208.70/128.49 | | | | | | ALPHA: (56) implies: 208.70/128.49 | | | | | | (57) elts(int, all_103_4) = all_757_3 208.70/128.49 | | | | | | (58) elts(int, all_105_4) = all_757_2 208.70/128.49 | | | | | | 208.70/128.49 | | | | | | GROUND_INST: instantiating (12) with all_105_3, all_757_2, 208.70/128.49 | | | | | | all_105_4, int, simplifying with (14), (58) gives: 208.70/128.49 | | | | | | (59) all_757_2 = all_105_3 208.70/128.49 | | | | | | 208.70/128.49 | | | | | | GROUND_INST: instantiating (12) with all_103_3, all_757_3, 208.70/128.49 | | | | | | all_103_4, int, simplifying with (3), (57) gives: 208.70/128.49 | | | | | | (60) all_757_3 = all_103_3 208.70/128.49 | | | | | | 208.70/128.49 | | | | | | BETA: splitting (25) gives: 208.70/128.49 | | | | | | 208.70/128.49 | | | | | | Case 1: 208.70/128.49 | | | | | | | 208.70/128.49 | | | | | | | (61) all_746_0 = 0 & all_746_2 = 0 & map_eq_sub1(int, 208.70/128.49 | | | | | | | all_746_4, all_746_3, $sum(all_86_10, 1), all_746_1) = 0 208.70/128.49 | | | | | | | & map_eq_sub1(int, all_746_4, all_746_3, 0, all_86_11) = 0 208.70/128.49 | | | | | | | & length1(int, all_103_4) = all_746_1 & elts(int, 208.70/128.49 | | | | | | | all_105_4) = all_746_3 & elts(int, all_103_4) = 208.70/128.49 | | | | | | | all_746_4 & in_uni(all_746_3) & in_uni(all_746_4) 208.70/128.49 | | | | | | | 208.70/128.49 | | | | | | | ALPHA: (61) implies: 208.70/128.49 | | | | | | | (62) elts(int, all_103_4) = all_746_4 208.70/128.49 | | | | | | | (63) elts(int, all_105_4) = all_746_3 208.70/128.49 | | | | | | | (64) length1(int, all_103_4) = all_746_1 208.70/128.49 | | | | | | | (65) map_eq_sub1(int, all_746_4, all_746_3, $sum(all_86_10, 1), 208.70/128.49 | | | | | | | all_746_1) = 0 208.70/128.49 | | | | | | | 208.70/128.49 | | | | | | | GROUND_INST: instantiating (28) with all_86_13, all_746_1, 208.70/128.49 | | | | | | | all_103_4, int, simplifying with (5), (64) gives: 208.70/128.49 | | | | | | | (66) all_746_1 = all_86_13 208.70/128.49 | | | | | | | 208.70/128.49 | | | | | | | GROUND_INST: instantiating (12) with all_105_3, all_746_3, 208.70/128.49 | | | | | | | all_105_4, int, simplifying with (14), (63) gives: 208.70/128.49 | | | | | | | (67) all_746_3 = all_105_3 208.70/128.49 | | | | | | | 208.70/128.49 | | | | | | | GROUND_INST: instantiating (12) with all_103_3, all_746_4, 208.70/128.49 | | | | | | | all_103_4, int, simplifying with (3), (62) gives: 208.70/128.49 | | | | | | | (68) all_746_4 = all_103_3 208.70/128.49 | | | | | | | 208.70/128.49 | | | | | | | REDUCE: (65), (66), (67), (68) imply: 208.70/128.49 | | | | | | | (69) map_eq_sub1(int, all_103_3, all_105_3, $sum(all_86_10, 1), 208.70/128.49 | | | | | | | all_86_13) = 0 208.70/128.49 | | | | | | | 208.70/128.49 | | | | | | | REF_CLOSE: (1), (2), (3), (4), (8), (9), (10), (11), (14), (15), 208.70/128.49 | | | | | | | (20), (21), (27), (29), (30), (35), (39), (69) are 208.70/128.49 | | | | | | | inconsistent by sub-proof #152. 208.70/128.49 | | | | | | | 208.70/128.49 | | | | | | Case 2: 208.70/128.49 | | | | | | | 208.70/128.49 | | | | | | | (70) ~ (all_746_4 = 0) & permut_sub3(all_86_9, all_86_3, 208.70/128.49 | | | | | | | all_86_11, $sum(all_86_10, 1)) = all_746_4 208.70/128.49 | | | | | | | 208.70/128.49 | | | | | | | ALPHA: (70) implies: 208.70/128.49 | | | | | | | (71) ~ (all_746_4 = 0) 208.70/128.49 | | | | | | | (72) permut_sub3(all_86_9, all_86_3, all_86_11, $sum(all_86_10, 208.70/128.49 | | | | | | | 1)) = all_746_4 208.70/128.49 | | | | | | | 208.70/128.49 | | | | | | | BETA: splitting (17) gives: 208.70/128.49 | | | | | | | 208.70/128.49 | | | | | | | Case 1: 208.70/128.49 | | | | | | | | 208.70/128.49 | | | | | | | | (73) all_758_3 = 0 & permut_sub3(all_86_9, all_86_3, 208.70/128.49 | | | | | | | | all_86_11, $sum(all_86_10, 1)) = 0 208.70/128.49 | | | | | | | | 208.70/128.49 | | | | | | | | ALPHA: (73) implies: 208.70/128.49 | | | | | | | | (74) permut_sub3(all_86_9, all_86_3, all_86_11, 208.70/128.49 | | | | | | | | $sum(all_86_10, 1)) = 0 208.70/128.49 | | | | | | | | 208.70/128.49 | | | | | | | | GROUND_INST: instantiating (26) with all_746_4, 0, 208.70/128.49 | | | | | | | | $sum(all_86_10, 1), all_86_11, all_86_3, all_86_9, 208.70/128.49 | | | | | | | | simplifying with (72), (74) gives: 208.70/128.49 | | | | | | | | (75) all_746_4 = 0 208.70/128.49 | | | | | | | | 208.70/128.49 | | | | | | | | REDUCE: (71), (75) imply: 208.70/128.49 | | | | | | | | (76) ~ (0 = 0) 208.70/128.49 | | | | | | | | 208.70/128.49 | | | | | | | | CLOSE: (76) is inconsistent. 208.70/128.49 | | | | | | | | 208.70/128.49 | | | | | | | Case 2: 208.70/128.49 | | | | | | | | 208.70/128.49 | | | | | | | | 208.70/128.49 | | | | | | | | GROUND_INST: instantiating (23) with int, all_103_4, all_105_4, 208.70/128.49 | | | | | | | | all_86_11, $sum(all_86_10, 1), all_745_4, 208.70/128.49 | | | | | | | | simplifying with (4), (51) gives: 208.70/128.49 | | | | | | | | (77) all_745_4 = 0 | ? [v0: $int] : ? [v1: $int] : ? [v2: 208.70/128.49 | | | | | | | | $int] : ? [v3: $int] : (( ~ (v3 = 0) & 208.70/128.49 | | | | | | | | map_eq_sub1(int, v0, v1, $sum(all_86_10, 1), v2) = 208.70/128.49 | | | | | | | | v3 & length1(int, all_103_4) = v2 & elts(int, 208.70/128.49 | | | | | | | | all_105_4) = v1 & elts(int, all_103_4) = v0 & 208.70/128.49 | | | | | | | | in_uni(v1) & in_uni(v0)) | ( ~ (v2 = 0) & 208.70/128.49 | | | | | | | | map_eq_sub1(int, v0, v1, 0, all_86_11) = v2 & 208.70/128.49 | | | | | | | | elts(int, all_105_4) = v1 & elts(int, all_103_4) = 208.70/128.49 | | | | | | | | v0 & in_uni(v1) & in_uni(v0)) | ( ~ (v0 = 0) & 208.70/128.49 | | | | | | | | permut3(int, all_103_4, all_105_4, all_86_11, 208.70/128.49 | | | | | | | | $sum(all_86_10, 1)) = v0)) 208.70/128.49 | | | | | | | | 208.70/128.49 | | | | | | | | GROUND_INST: instantiating (27) with all_86_6, all_86_4, 208.70/128.49 | | | | | | | | $sum(all_86_8, 1), all_86_13, all_103_1, all_105_3, 208.70/128.49 | | | | | | | | all_133_2, all_133_0, simplifying with (1), (9), 208.70/128.49 | | | | | | | | (11), (29), (35) gives: 208.70/128.49 | | | | | | | | (78) ~ ($lesseq(1, $difference(all_86_13, all_133_2))) | ~ 208.70/128.49 | | | | | | | | ($lesseq(1, $difference(all_133_2, all_86_8))) | 208.70/128.49 | | | | | | | | get3(all_86_6, all_133_2) = all_133_0 208.70/128.49 | | | | | | | | 208.70/128.49 | | | | | | | | BETA: splitting (78) gives: 208.70/128.49 | | | | | | | | 208.70/128.49 | | | | | | | | Case 1: 208.70/128.49 | | | | | | | | | 208.70/128.49 | | | | | | | | | (79) get3(all_86_6, all_133_2) = all_133_0 208.70/128.49 | | | | | | | | | 208.70/128.49 | | | | | | | | | BETA: splitting (77) gives: 208.70/128.49 | | | | | | | | | 208.70/128.49 | | | | | | | | | Case 1: 208.70/128.49 | | | | | | | | | | 208.70/128.49 | | | | | | | | | | (80) all_745_4 = 0 208.70/128.49 | | | | | | | | | | 208.70/128.49 | | | | | | | | | | REDUCE: (50), (80) imply: 208.70/128.49 | | | | | | | | | | (81) ~ (0 = 0) 208.70/128.49 | | | | | | | | | | 208.70/128.49 | | | | | | | | | | CLOSE: (81) is inconsistent. 208.70/128.49 | | | | | | | | | | 208.70/128.49 | | | | | | | | | Case 2: 208.70/128.49 | | | | | | | | | | 208.70/128.49 | | | | | | | | | | 208.70/128.49 | | | | | | | | | | GROUND_INST: instantiating (8) with all_133_2, all_133_0, 208.70/128.49 | | | | | | | | | | simplifying with (79) gives: 208.70/128.49 | | | | | | | | | | (82) all_133_0 = 42 | ~ ($lesseq(1, 208.70/128.49 | | | | | | | | | | $difference(all_86_7, all_133_2))) | ~ 208.70/128.49 | | | | | | | | | | ($lesseq(1, $difference(all_133_2, all_86_8))) 208.70/128.49 | | | | | | | | | | 208.70/128.49 | | | | | | | | | | REF_CLOSE: (10), (15), (21), (82) are inconsistent by 208.70/128.49 | | | | | | | | | | sub-proof #155. 208.70/128.49 | | | | | | | | | | 208.70/128.49 | | | | | | | | | End of split 208.70/128.49 | | | | | | | | | 208.70/128.49 | | | | | | | | Case 2: 208.70/128.49 | | | | | | | | | 208.70/128.49 | | | | | | | | | (83) ~ ($lesseq(1, $difference(all_86_13, all_133_2))) | 208.70/128.49 | | | | | | | | | ~ ($lesseq(1, $difference(all_133_2, all_86_8))) 208.70/128.49 | | | | | | | | | 208.70/128.49 | | | | | | | | | REF_CLOSE: (10), (39), (83) are inconsistent by sub-proof 208.70/128.49 | | | | | | | | | #153. 208.70/128.49 | | | | | | | | | 208.70/128.49 | | | | | | | | End of split 208.70/128.49 | | | | | | | | 208.70/128.49 | | | | | | | End of split 208.70/128.49 | | | | | | | 208.70/128.49 | | | | | | End of split 208.70/128.49 | | | | | | 208.70/128.49 | | | | | End of split 208.70/128.49 | | | | | 208.70/128.49 | | | | End of split 208.70/128.49 | | | | 208.70/128.49 | | | End of split 208.70/128.49 | | | 208.70/128.49 | | Case 2: 208.70/128.49 | | | 208.70/128.49 | | | (84) ~ ($lesseq(1, $difference(all_86_7, all_133_2))) | ~ ($lesseq(0, 208.70/128.49 | | | all_133_2)) 208.70/128.49 | | | 208.70/128.49 | | | REF_CLOSE: (15), (34), (84) are inconsistent by sub-proof #151. 208.70/128.49 | | | 208.70/128.49 | | End of split 208.70/128.49 | | 208.70/128.49 | End of split 208.70/128.49 | 208.70/128.49 End of proof 208.70/128.49 208.70/128.49 Sub-proof #151 shows that the following formulas are inconsistent: 208.70/128.49 ---------------------------------------------------------------- 208.70/128.49 (1) ~ ($lesseq(1, $difference(all_86_7, all_133_2))) | ~ ($lesseq(0, 208.70/128.49 all_133_2)) 208.70/128.49 (2) $lesseq(0, all_133_2) 208.70/128.49 (3) $lesseq(1, $difference(all_86_7, all_133_2)) 208.70/128.49 208.70/128.49 Begin of proof 208.70/128.49 | 208.70/128.49 | BETA: splitting (1) gives: 208.70/128.49 | 208.70/128.49 | Case 1: 208.70/128.49 | | 208.70/128.49 | | (4) $lesseq(all_133_2, -1) 208.70/128.49 | | 208.70/128.49 | | COMBINE_INEQS: (2), (4) imply: 208.70/128.49 | | (5) $lesseq(0, -1) 208.70/128.49 | | 208.70/128.49 | | CLOSE: (5) is inconsistent. 208.70/128.49 | | 208.70/128.49 | Case 2: 208.70/128.49 | | 208.70/128.49 | | (6) $lesseq(all_86_7, all_133_2) 208.70/128.49 | | 208.70/128.49 | | COMBINE_INEQS: (3), (6) imply: 208.70/128.49 | | (7) $lesseq(0, -1) 208.70/128.49 | | 208.70/128.49 | | CLOSE: (7) is inconsistent. 208.70/128.49 | | 208.70/128.49 | End of split 208.70/128.49 | 208.70/128.49 End of proof 208.70/128.49 208.70/128.49 Sub-proof #152 shows that the following formulas are inconsistent: 208.70/128.49 ---------------------------------------------------------------- 208.70/128.49 (1) in_map_int_int(all_86_6) 208.70/128.49 (2) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.70/128.49 $int] : ! [v5: $int] : ! [v6: $int] : ( ~ ($lesseq(0, v4)) | ~ 208.70/128.49 ($lesseq(0, v3)) | ~ (map_eq_sub1(v0, v5, v6, v3, v4) = 0) | ~ 208.70/128.49 (elts(v0, v2) = v6) | ~ (elts(v0, v1) = v5) | ~ in_ty(v0) | ? [v7: 208.70/128.49 $int] : ? [v8: $int] : ((v7 = 0 & array_eq_sub1(v0, v1, v2, v3, v4) 208.70/128.49 = 0) | (length1(v0, v1) = v7 & ( ~ ($lesseq(v4, v7)) | ~ 208.70/128.49 ($lesseq(v3, v7)) | ( ~ (v8 = v7) & length1(v0, v2) = v8))))) 208.70/128.49 (3) elts(int, all_103_4) = all_103_3 208.70/128.49 (4) map_eq_sub1(int, all_103_3, all_105_3, $sum(all_86_10, 1), all_86_13) = 0 208.70/128.49 (5) in_ty(int) 208.70/128.49 (6) ! [v0: $int] : ! [v1: $int] : (v1 = 42 | ~ ($lesseq(1, 208.70/128.49 $difference(all_86_7, v0))) | ~ ($lesseq(1, $difference(v0, 208.70/128.49 all_86_8))) | ~ (get3(all_86_6, v0) = v1)) 208.70/128.49 (7) t2tb(all_86_6) = all_103_1 208.70/128.49 (8) $lesseq(1, $difference(all_133_2, all_86_8)) 208.70/128.49 (9) map_eq_sub1(int, all_103_1, all_105_3, $sum(all_86_8, 1), all_86_13) = 0 208.70/128.49 (10) elts(int, all_105_4) = all_105_3 208.70/128.49 (11) $lesseq(1, $difference(all_86_7, all_133_2)) 208.70/128.49 (12) $lesseq(4, all_86_13) 208.70/128.49 (13) ~ (all_133_0 = 42) 208.70/128.49 (14) get3(all_86_4, all_133_2) = all_133_0 208.70/128.49 (15) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 208.70/128.49 $int] : ! [v5: $int] : ! [v6: $int] : ! [v7: $int] : ( ~ 208.70/128.49 ($lesseq(1, $difference(v3, v6))) | ~ ($lesseq(v2, v6)) | ~ 208.70/128.49 (map_eq_sub1(int, v4, v5, v2, v3) = 0) | ~ (t2tb(v1) = v5) | ~ 208.70/128.49 (t2tb(v0) = v4) | ~ (get3(v1, v6) = v7) | ~ in_map_int_int(v0) | 208.70/128.49 get3(v0, v6) = v7) 208.70/128.49 (16) $lesseq(1, $difference(all_86_13, all_133_2)) 208.70/128.49 (17) t2tb(all_86_4) = all_105_3 208.70/128.49 (18) $lesseq(2, all_86_10) 208.70/128.49 208.70/128.49 Begin of proof 208.70/128.49 | 208.70/128.49 | GROUND_INST: instantiating (2) with int, all_103_4, all_105_4, $sum(all_86_10, 208.70/128.49 | 1), all_86_13, all_103_3, all_105_3, simplifying with (3), (4), 208.70/128.49 | (5), (10) gives: 208.70/128.49 | (19) ~ ($lesseq(-1, all_86_10)) | ~ ($lesseq(0, all_86_13)) | ? [v0: 208.70/128.49 | $int] : ? [v1: $int] : ((v0 = 0 & array_eq_sub1(int, all_103_4, 208.70/128.49 | all_105_4, $sum(all_86_10, 1), all_86_13) = 0) | (length1(int, 208.70/128.49 | all_103_4) = v0 & ( ~ ($lesseq(1, $difference(v0, all_86_10))) | 208.70/128.49 | ~ ($lesseq(all_86_13, v0)) | ( ~ (v1 = v0) & length1(int, 208.70/128.49 | all_105_4) = v1)))) 208.70/128.49 | 208.70/128.49 | GROUND_INST: instantiating (15) with all_86_6, all_86_4, $sum(all_86_8, 1), 208.70/128.49 | all_86_13, all_103_1, all_105_3, all_133_2, all_133_0, 208.70/128.49 | simplifying with (1), (7), (9), (14), (17) gives: 208.70/128.49 | (20) ~ ($lesseq(1, $difference(all_86_13, all_133_2))) | ~ ($lesseq(1, 208.70/128.49 | $difference(all_133_2, all_86_8))) | get3(all_86_6, all_133_2) = 208.70/128.49 | all_133_0 208.70/128.49 | 208.70/128.49 | BETA: splitting (20) gives: 208.70/128.49 | 208.70/128.49 | Case 1: 208.70/128.49 | | 208.70/128.49 | | (21) get3(all_86_6, all_133_2) = all_133_0 208.70/128.49 | | 208.70/128.49 | | BETA: splitting (19) gives: 208.70/128.49 | | 208.70/128.49 | | Case 1: 208.70/128.49 | | | 208.70/128.49 | | | (22) $lesseq(all_86_13, -1) 208.70/128.49 | | | 208.70/128.49 | | | COMBINE_INEQS: (12), (22) imply: 208.70/128.49 | | | (23) $lesseq(0, -1) 208.70/128.49 | | | 208.70/128.49 | | | CLOSE: (23) is inconsistent. 208.70/128.49 | | | 208.70/128.49 | | Case 2: 208.70/128.49 | | | 208.70/128.49 | | | (24) ~ ($lesseq(-1, all_86_10)) | ? [v0: $int] : ? [v1: $int] : ((v0 208.70/128.49 | | | = 0 & array_eq_sub1(int, all_103_4, all_105_4, $sum(all_86_10, 208.70/128.49 | | | 1), all_86_13) = 0) | (length1(int, all_103_4) = v0 & ( ~ 208.70/128.49 | | | ($lesseq(1, $difference(v0, all_86_10))) | ~ 208.70/128.49 | | | ($lesseq(all_86_13, v0)) | ( ~ (v1 = v0) & length1(int, 208.70/128.49 | | | all_105_4) = v1)))) 208.70/128.49 | | | 208.70/128.50 | | | REF_CLOSE: (6), (8), (11), (13), (18), (21), (24) are inconsistent by 208.70/128.50 | | | sub-proof #154. 208.70/128.50 | | | 208.70/128.50 | | End of split 208.70/128.50 | | 208.70/128.50 | Case 2: 208.70/128.50 | | 208.70/128.50 | | (25) ~ ($lesseq(1, $difference(all_86_13, all_133_2))) | ~ ($lesseq(1, 208.70/128.50 | | $difference(all_133_2, all_86_8))) 208.70/128.50 | | 208.70/128.50 | | REF_CLOSE: (8), (16), (25) are inconsistent by sub-proof #153. 208.70/128.50 | | 208.70/128.50 | End of split 208.70/128.50 | 208.70/128.50 End of proof 208.70/128.50 208.70/128.50 Sub-proof #153 shows that the following formulas are inconsistent: 208.70/128.50 ---------------------------------------------------------------- 208.70/128.50 (1) ~ ($lesseq(1, $difference(all_86_13, all_133_2))) | ~ ($lesseq(1, 208.70/128.50 $difference(all_133_2, all_86_8))) 208.70/128.50 (2) $lesseq(1, $difference(all_86_13, all_133_2)) 208.70/128.50 (3) $lesseq(1, $difference(all_133_2, all_86_8)) 208.70/128.50 208.70/128.50 Begin of proof 208.70/128.50 | 208.70/128.50 | BETA: splitting (1) gives: 208.70/128.50 | 208.70/128.50 | Case 1: 208.70/128.50 | | 208.70/128.50 | | (4) $lesseq(all_86_13, all_133_2) 208.70/128.50 | | 208.70/128.50 | | COMBINE_INEQS: (2), (4) imply: 208.70/128.50 | | (5) $lesseq(0, -1) 208.70/128.50 | | 208.70/128.50 | | CLOSE: (5) is inconsistent. 208.70/128.50 | | 208.70/128.50 | Case 2: 208.70/128.50 | | 208.70/128.50 | | (6) $lesseq(all_133_2, all_86_8) 208.70/128.50 | | 208.70/128.50 | | COMBINE_INEQS: (3), (6) imply: 208.70/128.50 | | (7) $lesseq(0, -1) 208.70/128.50 | | 208.70/128.50 | | CLOSE: (7) is inconsistent. 208.70/128.50 | | 208.70/128.50 | End of split 208.70/128.50 | 208.70/128.50 End of proof 208.70/128.50 208.70/128.50 Sub-proof #154 shows that the following formulas are inconsistent: 208.70/128.50 ---------------------------------------------------------------- 208.70/128.50 (1) get3(all_86_6, all_133_2) = all_133_0 208.70/128.50 (2) ! [v0: $int] : ! [v1: $int] : (v1 = 42 | ~ ($lesseq(1, 208.70/128.50 $difference(all_86_7, v0))) | ~ ($lesseq(1, $difference(v0, 208.70/128.50 all_86_8))) | ~ (get3(all_86_6, v0) = v1)) 208.70/128.50 (3) $lesseq(1, $difference(all_133_2, all_86_8)) 208.70/128.50 (4) $lesseq(1, $difference(all_86_7, all_133_2)) 208.70/128.50 (5) ~ ($lesseq(-1, all_86_10)) | ? [v0: $int] : ? [v1: $int] : ((v0 = 0 & 208.70/128.50 array_eq_sub1(int, all_103_4, all_105_4, $sum(all_86_10, 1), 208.70/128.50 all_86_13) = 0) | (length1(int, all_103_4) = v0 & ( ~ ($lesseq(1, 208.70/128.50 $difference(v0, all_86_10))) | ~ ($lesseq(all_86_13, v0)) | ( 208.70/128.50 ~ (v1 = v0) & length1(int, all_105_4) = v1)))) 208.70/128.50 (6) ~ (all_133_0 = 42) 208.70/128.50 (7) $lesseq(2, all_86_10) 208.70/128.50 208.70/128.50 Begin of proof 208.70/128.50 | 208.70/128.50 | BETA: splitting (5) gives: 208.70/128.50 | 208.70/128.50 | Case 1: 208.70/128.50 | | 208.70/128.50 | | (8) $lesseq(all_86_10, -2) 208.70/128.50 | | 208.70/128.50 | | COMBINE_INEQS: (7), (8) imply: 208.70/128.50 | | (9) $lesseq(0, -1) 208.70/128.50 | | 208.70/128.50 | | CLOSE: (9) is inconsistent. 208.70/128.50 | | 208.70/128.50 | Case 2: 208.70/128.50 | | 208.70/128.50 | | 208.70/128.50 | | GROUND_INST: instantiating (2) with all_133_2, all_133_0, simplifying with 208.70/128.50 | | (1) gives: 208.70/128.50 | | (10) all_133_0 = 42 | ~ ($lesseq(1, $difference(all_86_7, all_133_2))) | 208.70/128.50 | | ~ ($lesseq(1, $difference(all_133_2, all_86_8))) 208.70/128.50 | | 208.70/128.50 | | REF_CLOSE: (3), (4), (6), (10) are inconsistent by sub-proof #155. 208.70/128.50 | | 208.70/128.50 | End of split 208.70/128.50 | 208.70/128.50 End of proof 208.70/128.50 208.70/128.50 Sub-proof #155 shows that the following formulas are inconsistent: 208.70/128.50 ---------------------------------------------------------------- 208.70/128.50 (1) all_133_0 = 42 | ~ ($lesseq(1, $difference(all_86_7, all_133_2))) | ~ 208.70/128.50 ($lesseq(1, $difference(all_133_2, all_86_8))) 208.70/128.50 (2) $lesseq(1, $difference(all_86_7, all_133_2)) 208.70/128.50 (3) $lesseq(1, $difference(all_133_2, all_86_8)) 208.70/128.50 (4) ~ (all_133_0 = 42) 208.70/128.50 208.70/128.50 Begin of proof 208.70/128.50 | 208.70/128.50 | BETA: splitting (1) gives: 208.70/128.50 | 208.70/128.50 | Case 1: 208.70/128.50 | | 208.70/128.50 | | (5) $lesseq(all_86_7, all_133_2) 208.70/128.50 | | 208.70/128.50 | | COMBINE_INEQS: (2), (5) imply: 208.70/128.50 | | (6) $lesseq(0, -1) 208.70/128.50 | | 208.70/128.50 | | CLOSE: (6) is inconsistent. 208.70/128.50 | | 208.70/128.50 | Case 2: 208.70/128.50 | | 208.70/128.50 | | (7) all_133_0 = 42 | ~ ($lesseq(1, $difference(all_133_2, all_86_8))) 208.70/128.50 | | 208.70/128.50 | | BETA: splitting (7) gives: 208.70/128.50 | | 208.70/128.50 | | Case 1: 208.70/128.50 | | | 208.70/128.50 | | | (8) $lesseq(all_133_2, all_86_8) 208.70/128.50 | | | 208.70/128.50 | | | COMBINE_INEQS: (3), (8) imply: 208.70/128.50 | | | (9) $lesseq(0, -1) 208.70/128.50 | | | 208.70/128.50 | | | CLOSE: (9) is inconsistent. 208.70/128.50 | | | 208.70/128.50 | | Case 2: 208.70/128.50 | | | 208.70/128.50 | | | (10) all_133_0 = 42 208.70/128.50 | | | 208.70/128.50 | | | REDUCE: (4), (10) imply: 208.70/128.50 | | | (11) ~ (0 = 0) 208.70/128.50 | | | 208.70/128.50 | | | CLOSE: (11) is inconsistent. 208.70/128.50 | | | 208.70/128.50 | | End of split 208.70/128.50 | | 208.70/128.50 | End of split 208.70/128.50 | 208.70/128.50 End of proof 208.70/128.50 % SZS output end Proof for theBenchmark 208.70/128.50 208.70/128.50 128013ms 210.12/129.77 EOF