%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWW590_2 : TPTP v8.1.2. Released v6.1.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n031.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Fri Sep 1 00:50:49 EDT 2023 % Result : Theorem 21.22s 3.90s % Output : Proof 115.54s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.15 % Problem : SWW590_2 : TPTP v8.1.2. Released v6.1.0. % 0.00/0.16 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.16/0.36 % Computer : n031.cluster.edu % 0.16/0.36 % Model : x86_64 x86_64 % 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.36 % Memory : 8042.1875MB % 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.36 % CPULimit : 300 % 0.16/0.36 % WCLimit : 300 % 0.16/0.36 % DateTime : Sun Aug 27 22:24:54 EDT 2023 % 0.16/0.37 % CPUTime : % 0.22/0.64 ________ _____ % 0.22/0.64 ___ __ \_________(_)________________________________ % 0.22/0.64 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.22/0.64 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.22/0.64 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.22/0.64 % 0.22/0.64 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.22/0.64 (2023-06-19) % 0.22/0.64 % 0.22/0.64 (c) Philipp Rümmer, 2009-2023 % 0.22/0.64 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.22/0.64 Amanda Stjerna. % 0.22/0.64 Free software under BSD-3-Clause. % 0.22/0.64 % 0.22/0.64 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.22/0.64 % 0.22/0.64 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.22/0.66 Running up to 7 provers in parallel. % 0.22/0.68 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.22/0.68 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.22/0.68 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.22/0.68 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.22/0.68 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.22/0.68 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.22/0.68 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.17/1.47 Prover 1: Preprocessing ... % 3.17/1.47 Prover 5: Preprocessing ... % 3.17/1.47 Prover 0: Preprocessing ... % 3.17/1.47 Prover 3: Preprocessing ... % 3.17/1.47 Prover 2: Preprocessing ... % 3.17/1.47 Prover 4: Preprocessing ... % 3.17/1.47 Prover 6: Preprocessing ... % 8.91/2.18 Prover 1: Warning: ignoring some quantifiers % 9.53/2.28 Prover 6: Proving ... % 10.05/2.36 Prover 4: Warning: ignoring some quantifiers % 10.05/2.39 Prover 3: Warning: ignoring some quantifiers % 10.05/2.41 Prover 3: Constructing countermodel ... % 10.61/2.43 Prover 1: Constructing countermodel ... % 10.61/2.45 Prover 4: Constructing countermodel ... % 11.02/2.50 Prover 0: Proving ... % 11.61/2.57 Prover 5: Proving ... % 12.15/2.64 Prover 2: Proving ... % 21.22/3.90 Prover 0: proved (3224ms) % 21.22/3.90 % 21.22/3.90 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 21.22/3.90 % 21.22/3.90 Prover 3: stopped % 21.22/3.90 Prover 5: stopped % 21.22/3.90 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 21.22/3.90 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 21.22/3.90 Prover 6: stopped % 21.59/3.93 Prover 2: stopped % 21.59/3.93 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 21.59/3.93 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 21.59/3.93 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 21.85/4.12 Prover 7: Preprocessing ... % 21.85/4.13 Prover 11: Preprocessing ... % 22.62/4.18 Prover 8: Preprocessing ... % 23.60/4.19 Prover 10: Preprocessing ... % 23.60/4.22 Prover 13: Preprocessing ... % 24.16/4.31 Prover 11: Warning: ignoring some quantifiers % 24.54/4.33 Prover 8: Warning: ignoring some quantifiers % 24.54/4.33 Prover 11: Constructing countermodel ... % 24.84/4.36 Prover 8: Constructing countermodel ... % 24.84/4.37 Prover 10: Warning: ignoring some quantifiers % 24.84/4.39 Prover 7: Warning: ignoring some quantifiers % 24.84/4.40 Prover 10: Constructing countermodel ... % 24.84/4.41 Prover 7: Constructing countermodel ... % 25.84/4.55 Prover 13: Warning: ignoring some quantifiers % 26.33/4.60 Prover 13: Constructing countermodel ... % 63.36/9.43 Prover 13: stopped % 63.36/9.45 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 64.46/9.56 Prover 16: Preprocessing ... % 65.75/9.75 Prover 16: Warning: ignoring some quantifiers % 65.75/9.78 Prover 16: Constructing countermodel ... % 107.36/15.31 Prover 16: stopped % 107.36/15.33 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 108.81/15.50 Prover 19: Preprocessing ... % 109.67/15.71 Prover 19: Warning: ignoring some quantifiers % 109.67/15.74 Prover 19: Constructing countermodel ... % 112.69/16.01 Prover 1: stopped % 112.69/16.02 Prover 11: Found proof (size 504) % 112.69/16.02 Prover 11: proved (12091ms) % 112.69/16.02 Prover 19: stopped % 112.69/16.02 Prover 8: stopped % 112.69/16.02 Prover 7: stopped % 112.69/16.02 Prover 10: stopped % 113.29/16.06 Prover 4: stopped % 113.29/16.06 % 113.29/16.06 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 113.29/16.06 % 113.43/16.13 % SZS output start Proof for theBenchmark % 113.60/16.14 Assumptions after simplification: % 113.60/16.14 --------------------------------- % 113.60/16.14 % 113.60/16.14 (closed_formula_0) % 113.63/16.15 p1(0) = 0 % 113.63/16.15 % 113.63/16.15 (closed_formula_aux_def) % 113.63/16.16 ! [v0: int] : ! [v1: int] : ( ~ (closed_formula_aux1(v0) = v1) | ? [v2: % 113.63/16.16 int] : ? [v3: int] : ? [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: % 113.63/16.16 int] : ($sum($difference($difference($product(15, v7), $product(5, v5)), % 113.63/16.16 $product(3, v3)), v1) = 0 & tr1(v6) = v7 & tr1(v4) = v5 & tr1(v2) = v3 % 113.63/16.16 & div1(v0, 15) = v6 & div1(v0, 5) = v4 & div1(v0, 3) = v2)) & ! [v0: int] % 113.63/16.16 : ! [v1: int] : ( ~ (div1(v0, 15) = v1) | ? [v2: int] : ? [v3: int] : ? % 113.63/16.16 [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : % 113.63/16.16 ($sum($difference($difference($product(15, v7), $product(5, v6)), % 113.63/16.16 $product(3, v4)), v2) = 0 & closed_formula_aux1(v0) = v2 & tr1(v5) = % 113.63/16.16 v6 & tr1(v3) = v4 & tr1(v1) = v7 & div1(v0, 5) = v5 & div1(v0, 3) = v3)) & % 113.63/16.16 ! [v0: int] : ! [v1: int] : ( ~ (div1(v0, 5) = v1) | ? [v2: int] : ? [v3: % 113.63/16.16 int] : ? [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : % 113.63/16.16 ($sum($difference($difference($product(15, v7), $product(5, v5)), % 113.63/16.16 $product(3, v4)), v2) = 0 & closed_formula_aux1(v0) = v2 & tr1(v6) = % 113.63/16.16 v7 & tr1(v3) = v4 & tr1(v1) = v5 & div1(v0, 15) = v6 & div1(v0, 3) = v3)) % 113.63/16.16 & ! [v0: int] : ! [v1: int] : ( ~ (div1(v0, 3) = v1) | ? [v2: int] : ? % 113.63/16.16 [v3: int] : ? [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : % 113.63/16.16 ($sum($difference($difference($product(15, v7), $product(5, v5)), % 113.63/16.17 $product(3, v3)), v2) = 0 & closed_formula_aux1(v0) = v2 & tr1(v6) = % 113.63/16.17 v7 & tr1(v4) = v5 & tr1(v1) = v3 & div1(v0, 15) = v6 & div1(v0, 5) = v4)) % 113.63/16.17 % 113.63/16.17 (closed_formula_n_15) % 113.63/16.17 ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & $lesseq(1, v0) & p1($sum(v0, -1)) % 113.63/16.17 = 0 & p1(v0) = v1 & mod1(v0, 5) = 0 & mod1(v0, 3) = 0) % 113.63/16.17 % 113.63/16.17 (closed_formula_n_5) % 113.63/16.18 ! [v0: int] : ! [v1: int] : (v1 = 0 | ~ ($lesseq(1, v0)) | ~ (p1(v0) = v1) % 113.63/16.18 | ? [v2: int] : ? [v3: int] : ? [v4: int] : ((v3 = 0 & mod1(v0, 3) = 0) | % 113.63/16.18 ( ~ (v4 = 0) & mod1(v0, 5) = v4) | ( ~ (v2 = 0) & p1($sum(v0, -1)) = v2))) % 113.63/16.18 & ! [v0: int] : ! [v1: int] : (v1 = 0 | ~ ($lesseq(1, v0)) | ~ (mod1(v0, % 113.63/16.18 3) = v1) | ? [v2: int] : ? [v3: int] : ? [v4: int] : ((v4 = 0 & % 113.63/16.18 p1(v0) = 0) | ( ~ (v3 = 0) & mod1(v0, 5) = v3) | ( ~ (v2 = 0) & % 113.63/16.18 p1($sum(v0, -1)) = v2))) & ! [v0: int] : ( ~ ($lesseq(1, v0)) | ~ % 113.63/16.18 (p1($sum(v0, -1)) = 0) | ? [v1: int] : ? [v2: int] : ? [v3: int] : ((v3 = % 113.63/16.18 0 & p1(v0) = 0) | (v1 = 0 & mod1(v0, 3) = 0) | ( ~ (v2 = 0) & mod1(v0, % 113.63/16.18 5) = v2))) & ! [v0: int] : ( ~ ($lesseq(1, v0)) | ~ (mod1(v0, 5) = % 113.63/16.18 0) | ? [v1: int] : ? [v2: int] : ? [v3: int] : ((v3 = 0 & p1(v0) = 0) | % 113.63/16.18 (v2 = 0 & mod1(v0, 3) = 0) | ( ~ (v1 = 0) & p1($sum(v0, -1)) = v1))) % 113.63/16.18 % 113.63/16.18 (div_mod) % 113.63/16.18 ! [v0: int] : ! [v1: int] : ! [v2: int] : (v1 = 0 | ~ (div1(v0, v1) = v2) % 113.63/16.18 | ? [v3: int] : (mod1(v0, v1) = $difference(v0, v3) & $product(v1, v2) = % 113.63/16.18 v3)) & ! [v0: int] : ! [v1: int] : ! [v2: int] : (v1 = 0 | ~ (mod1(v0, % 113.63/16.18 v1) = v2) | ? [v3: int] : (div1(v0, v1) = v3 & $product(v1, v3) = % 113.63/16.18 $difference(v0, v2))) % 113.63/16.18 % 113.63/16.18 (div_succ_1) % 113.63/16.19 ! [v0: int] : ! [v1: int] : ! [v2: int] : ( ~ ($lesseq(1, v1)) | ~ % 113.63/16.19 ($lesseq(0, v0)) | ~ (div1($sum(v0, 1), v1) = v2) | ? [v3: int] : ? [v4: % 113.63/16.19 int] : (($difference(v4, v2) = -1 & div1(v0, v1) = $sum(v2, -1)) | ( ~ (v3 % 113.63/16.19 = 0) & mod1($sum(v0, 1), v1) = v3))) & ! [v0: int] : ! [v1: int] : % 113.63/16.19 ! [v2: int] : ( ~ ($lesseq(1, v1)) | ~ ($lesseq(0, v0)) | ~ (div1(v0, v1) = % 113.63/16.19 v2) | ? [v3: int] : ? [v4: int] : (($difference(v4, v2) = 1 & % 113.63/16.19 div1($sum(v0, 1), v1) = $sum(v2, 1)) | ( ~ (v3 = 0) & mod1($sum(v0, 1), % 113.63/16.19 v1) = v3))) & ! [v0: int] : ! [v1: int] : ( ~ ($lesseq(1, v1)) | ~ % 113.63/16.19 ($lesseq(0, v0)) | ~ (mod1($sum(v0, 1), v1) = 0) | ? [v2: int] : % 113.63/16.19 (div1($sum(v0, 1), v1) = v2 & div1(v0, v1) = $sum(v2, -1))) % 113.63/16.19 % 113.63/16.19 (div_succ_2) % 113.63/16.19 ! [v0: int] : ! [v1: int] : ! [v2: int] : (v2 = 0 | ~ ($lesseq(1, v1)) | % 113.63/16.19 ~ ($lesseq(0, v0)) | ~ (mod1($sum(v0, 1), v1) = v2) | ? [v3: int] : % 113.63/16.19 (div1($sum(v0, 1), v1) = v3 & div1(v0, v1) = v3)) & ! [v0: int] : ! [v1: % 113.63/16.20 int] : ! [v2: int] : ( ~ ($lesseq(1, v1)) | ~ ($lesseq(0, v0)) | ~ % 113.63/16.20 (div1($sum(v0, 1), v1) = v2) | ? [v3: int] : ? [v4: int] : ((v4 = v2 & % 113.63/16.20 div1(v0, v1) = v2) | (v3 = 0 & mod1($sum(v0, 1), v1) = 0))) & ! [v0: % 113.63/16.20 int] : ! [v1: int] : ! [v2: int] : ( ~ ($lesseq(1, v1)) | ~ ($lesseq(0, % 113.63/16.20 v0)) | ~ (div1(v0, v1) = v2) | ? [v3: int] : ? [v4: int] : ((v4 = v2 % 113.63/16.20 & div1($sum(v0, 1), v1) = v2) | (v3 = 0 & mod1($sum(v0, 1), v1) = 0))) % 113.63/16.20 % 113.63/16.20 (mod_15) % 113.94/16.20 ! [v0: int] : ! [v1: int] : (v1 = 0 | ~ (mod1(v0, 15) = v1) | ? [v2: int] % 113.94/16.20 : ? [v3: int] : (( ~ (v3 = 0) & mod1(v0, 5) = v3) | ( ~ (v2 = 0) & mod1(v0, % 113.94/16.20 3) = v2))) & ! [v0: int] : ! [v1: int] : ( ~ (mod1(v0, 5) = v1) | ? % 113.94/16.20 [v2: int] : ? [v3: int] : ((v3 = 0 & v1 = 0 & mod1(v0, 3) = 0) | ( ~ (v2 = % 113.94/16.20 0) & mod1(v0, 15) = v2))) & ! [v0: int] : ! [v1: int] : ( ~ % 113.94/16.20 (mod1(v0, 3) = v1) | ? [v2: int] : ? [v3: int] : ((v3 = 0 & v1 = 0 & % 113.94/16.20 mod1(v0, 5) = 0) | ( ~ (v2 = 0) & mod1(v0, 15) = v2))) & ! [v0: int] : % 113.94/16.20 ( ~ (mod1(v0, 15) = 0) | (mod1(v0, 5) = 0 & mod1(v0, 3) = 0)) & ! [v0: int] : % 113.94/16.20 ( ~ (mod1(v0, 5) = 0) | ? [v1: int] : ? [v2: int] : ((v2 = 0 & mod1(v0, 15) % 113.94/16.20 = 0) | ( ~ (v1 = 0) & mod1(v0, 3) = v1))) & ! [v0: int] : ( ~ (mod1(v0, % 113.94/16.20 3) = 0) | ? [v1: int] : ? [v2: int] : ((v2 = 0 & mod1(v0, 15) = 0) | ( % 113.94/16.20 ~ (v1 = 0) & mod1(v0, 5) = v1))) % 113.94/16.20 % 113.94/16.20 (mod_sign_neg) % 113.94/16.21 ! [v0: int] : ! [v1: int] : ! [v2: int] : (v1 = 0 | ~ ($lesseq(1, v2)) | % 113.94/16.21 ~ ($lesseq(v0, 0) | ~ (mod1(v0, v1) = v2)) % 113.94/16.21 % 113.94/16.21 (mod_sign_pos) % 113.94/16.21 ! [v0: int] : ! [v1: int] : ! [v2: int] : (v1 = 0 | ~ ($lesseq(v2, -1)) | % 113.94/16.21 ~ ($lesseq(0, v0)) | ~ (mod1(v0, v1) = v2)) % 113.94/16.21 % 113.94/16.21 (mod_succ_1) % 113.94/16.21 ! [v0: int] : ! [v1: int] : ! [v2: int] : (v2 = 0 | ~ ($lesseq(1, v1)) | % 113.94/16.21 ~ ($lesseq(0, v0)) | ~ (mod1($sum(v0, 1), v1) = v2) | mod1(v0, v1) = % 113.94/16.21 $sum(v2, -1)) & ! [v0: int] : ! [v1: int] : ! [v2: int] : ( ~ ($lesseq(1, % 113.94/16.21 v1)) | ~ ($lesseq(0, v0)) | ~ (mod1(v0, v1) = v2) | ? [v3: int] : % 113.94/16.21 (mod1($sum(v0, 1), v1) = v3 & ($difference(v3, v2) = 1 | v3 = 0))) % 113.94/16.21 % 113.94/16.21 (mod_succ_2) % 113.94/16.21 ! [v0: int] : ! [v1: int] : ! [v2: int] : ($difference(v2, v1) = -1 | ~ % 113.94/16.21 ($lesseq(1, v1)) | ~ ($lesseq(0, v0)) | ~ (mod1(v0, v1) = v2) | ? [v3: % 113.94/16.21 int] : ( ~ (v3 = 0) & mod1($sum(v0, 1), v1) = v3)) & ! [v0: int] : ! % 113.94/16.21 [v1: int] : ( ~ ($lesseq(1, v1)) | ~ ($lesseq(0, v0)) | ~ (mod1($sum(v0, 1), % 113.94/16.21 v1) = 0) | mod1(v0, v1) = $sum(v1, -1)) % 113.94/16.21 % 113.94/16.21 (p_def) % 113.94/16.22 ! [v0: int] : ! [v1: int] : (v1 = 0 | ~ (p1(v0) = v1) | ? [v2: int] : ? % 113.94/16.22 [v3: int] : ( ~ (v3 = v2) & closed_formula_aux1(v0) = v3 & % 113.94/16.22 sum_multiple_3_5_lt1($sum(v0, 1)) = v2)) & ! [v0: int] : ! [v1: int] : ( % 113.94/16.22 ~ (closed_formula_aux1(v0) = v1) | ? [v2: int] : ? [v3: int] : ((v3 = v1 & % 113.94/16.22 sum_multiple_3_5_lt1($sum(v0, 1)) = v1) | ( ~ (v2 = 0) & p1(v0) = v2))) % 113.94/16.22 & ! [v0: int] : ! [v1: int] : ( ~ (closed_formula_aux1(v0) = v1) | ? [v2: % 113.94/16.22 int] : ? [v3: int] : ((v3 = 0 & p1(v0) = 0) | ( ~ (v2 = v1) & % 113.94/16.22 sum_multiple_3_5_lt1($sum(v0, 1)) = v2))) & ! [v0: int] : ! [v1: int] % 113.94/16.22 : ( ~ (sum_multiple_3_5_lt1($sum(v0, 1)) = v1) | ? [v2: int] : ? [v3: int] : % 113.94/16.22 ((v3 = v1 & closed_formula_aux1(v0) = v1) | ( ~ (v2 = 0) & p1(v0) = v2))) & % 113.94/16.22 ! [v0: int] : ! [v1: int] : ( ~ (sum_multiple_3_5_lt1($sum(v0, 1)) = v1) | ? % 113.94/16.22 [v2: int] : ? [v3: int] : ((v3 = 0 & p1(v0) = 0) | ( ~ (v2 = v1) & % 113.94/16.22 closed_formula_aux1(v0) = v2))) & ! [v0: int] : ( ~ (p1(v0) = 0) | ? % 113.94/16.22 [v1: int] : (closed_formula_aux1(v0) = v1 & sum_multiple_3_5_lt1($sum(v0, % 113.94/16.22 1)) = v1)) % 113.94/16.22 % 113.94/16.22 (rounds_toward_zero) % 113.94/16.22 ! [v0: int] : ! [v1: int] : ! [v2: int] : (v1 = 0 | ~ (div1(v0, v1) = v2) % 113.94/16.22 | ? [v3: int] : ? [v4: int] : ? [v5: int] : ($lesseq(v5, v3) & abs1(v4) = % 113.94/16.22 v5 & abs1(v0) = v3 & $product(v2, v1) = v4)) % 113.94/16.22 % 113.94/16.22 (sumNo) % 113.94/16.23 ! [v0: int] : ! [v1: int] : (v1 = 0 | ~ ($lesseq(0, v0)) | ~ (mod1(v0, 5) % 113.94/16.23 = v1) | ? [v2: int] : ? [v3: int] : ? [v4: int] : ((v4 = v3 & % 113.94/16.23 sum_multiple_3_5_lt1($sum(v0, 1)) = v3 & sum_multiple_3_5_lt1(v0) = v3) % 113.94/16.23 | (v2 = 0 & mod1(v0, 3) = 0))) & ! [v0: int] : ! [v1: int] : (v1 = 0 | % 113.94/16.23 ~ ($lesseq(0, v0)) | ~ (mod1(v0, 3) = v1) | ? [v2: int] : ? [v3: int] : % 113.94/16.23 ? [v4: int] : ((v4 = v3 & sum_multiple_3_5_lt1($sum(v0, 1)) = v3 & % 113.94/16.23 sum_multiple_3_5_lt1(v0) = v3) | (v2 = 0 & mod1(v0, 5) = 0))) & ! [v0: % 113.94/16.23 int] : ! [v1: int] : ( ~ ($lesseq(0, v0)) | ~ % 113.94/16.23 (sum_multiple_3_5_lt1($sum(v0, 1)) = v1) | ? [v2: int] : ? [v3: int] : ? % 113.94/16.23 [v4: int] : ((v4 = v1 & sum_multiple_3_5_lt1(v0) = v1) | (v3 = 0 & mod1(v0, % 113.94/16.23 5) = 0) | (v2 = 0 & mod1(v0, 3) = 0))) & ! [v0: int] : ! [v1: int] : % 113.94/16.23 ( ~ ($lesseq(0, v0)) | ~ (sum_multiple_3_5_lt1(v0) = v1) | ? [v2: int] : ? % 113.94/16.23 [v3: int] : ? [v4: int] : ((v4 = v1 & sum_multiple_3_5_lt1($sum(v0, 1)) = % 113.94/16.23 v1) | (v3 = 0 & mod1(v0, 5) = 0) | (v2 = 0 & mod1(v0, 3) = 0))) % 113.94/16.23 % 113.94/16.23 (sumYes) % 113.94/16.24 ! [v0: int] : ! [v1: int] : ( ~ ($lesseq(0, v0)) | ~ % 113.94/16.24 (sum_multiple_3_5_lt1($sum(v0, 1)) = v1) | ? [v2: int] : ? [v3: int] : ? % 113.94/16.24 [v4: int] : (($sum($difference(v4, v1), v0) = 0 & sum_multiple_3_5_lt1(v0) = % 113.94/16.24 $difference(v1, v0)) | ( ~ (v3 = 0) & ~ (v2 = 0) & mod1(v0, 5) = v3 & % 113.94/16.24 mod1(v0, 3) = v2))) & ! [v0: int] : ! [v1: int] : ( ~ ($lesseq(0, v0)) % 113.94/16.24 | ~ (sum_multiple_3_5_lt1(v0) = v1) | ? [v2: int] : ? [v3: int] : ? [v4: % 113.94/16.24 int] : (($difference(v4, v1) = v0 & sum_multiple_3_5_lt1($sum(v0, 1)) = % 113.94/16.24 $sum(v1, v0)) | ( ~ (v3 = 0) & ~ (v2 = 0) & mod1(v0, 5) = v3 & mod1(v0, % 113.94/16.24 3) = v2))) & ! [v0: int] : ! [v1: int] : ( ~ ($lesseq(0, v0)) | ~ % 113.94/16.24 (mod1(v0, 5) = v1) | ? [v2: int] : ? [v3: int] : ? [v4: int] : % 113.94/16.24 (($sum($difference(v4, v3), v0) = 0 & sum_multiple_3_5_lt1($sum(v0, 1)) = v3 % 113.94/16.24 & sum_multiple_3_5_lt1(v0) = $difference(v3, v0)) | ( ~ (v2 = 0) & ~ % 113.94/16.24 (v1 = 0) & mod1(v0, 3) = v2))) & ! [v0: int] : ! [v1: int] : ( ~ % 113.94/16.24 ($lesseq(0, v0)) | ~ (mod1(v0, 3) = v1) | ? [v2: int] : ? [v3: int] : ? % 113.94/16.24 [v4: int] : (($sum($difference(v4, v3), v0) = 0 & % 113.94/16.24 sum_multiple_3_5_lt1($sum(v0, 1)) = v3 & sum_multiple_3_5_lt1(v0) = % 113.94/16.24 $difference(v3, v0)) | ( ~ (v2 = 0) & ~ (v1 = 0) & mod1(v0, 5) = v2))) % 113.94/16.24 % 113.94/16.24 (tr_def) % 113.94/16.24 ! [v0: int] : ! [v1: int] : ( ~ (tr1(v0) = v1) | ? [v2: int] : (div1(v2, 2) % 113.94/16.24 = v1 & $product(v0, $sum(v0, 1)) = v2)) % 113.94/16.24 % 113.94/16.24 (tr_repr) % 113.94/16.24 ! [v0: int] : ! [v1: int] : ( ~ ($lesseq(0, v0)) | ~ (tr1(v0) = v1) | % 113.94/16.24 $product(v0, $sum(v0, 1)) = $product(2, v1)) % 113.94/16.24 % 113.94/16.24 (function-axioms) % 113.94/16.25 ! [v0: int] : ! [v1: int] : ! [v2: int] : ! [v3: int] : (v1 = v0 | ~ % 113.94/16.25 (div1(v3, v2) = v1) | ~ (div1(v3, v2) = v0)) & ! [v0: int] : ! [v1: int] % 113.94/16.25 : ! [v2: int] : ! [v3: int] : (v1 = v0 | ~ (mod1(v3, v2) = v1) | ~ % 113.94/16.25 (mod1(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 113.94/16.25 MultipleValueBool] : ! [v2: uni] : ! [v3: ty] : (v1 = v0 | ~ (sort1(v3, % 113.94/16.25 v2) = v1) | ~ (sort1(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 113.94/16.25 [v1: MultipleValueBool] : ! [v2: int] : (v1 = v0 | ~ (p1(v2) = v1) | ~ % 113.94/16.25 (p1(v2) = v0)) & ! [v0: int] : ! [v1: int] : ! [v2: int] : (v1 = v0 | ~ % 113.94/16.25 (closed_formula_aux1(v2) = v1) | ~ (closed_formula_aux1(v2) = v0)) & ! % 113.94/16.25 [v0: int] : ! [v1: int] : ! [v2: int] : (v1 = v0 | ~ (tr1(v2) = v1) | ~ % 113.94/16.25 (tr1(v2) = v0)) & ! [v0: int] : ! [v1: int] : ! [v2: int] : (v1 = v0 | ~ % 113.94/16.25 (sum_multiple_3_5_lt1(v2) = v1) | ~ (sum_multiple_3_5_lt1(v2) = v0)) & ! % 113.94/16.25 [v0: int] : ! [v1: int] : ! [v2: int] : (v1 = v0 | ~ (abs1(v2) = v1) | ~ % 113.94/16.25 (abs1(v2) = v0)) & ! [v0: uni] : ! [v1: uni] : ! [v2: ty] : (v1 = v0 | ~ % 113.94/16.25 (witness1(v2) = v1) | ~ (witness1(v2) = v0)) % 113.94/16.25 % 113.94/16.25 Further assumptions not needed in the proof: % 113.94/16.25 -------------------------------------------- % 113.94/16.25 abs_def, abs_le, abs_pos, closed_formula_n, closed_formula_n_3, compatOrderMult, % 113.94/16.25 div2, div2_add, div2_mul2, div2_mul2_aux, div2_sub, div_1, div_bound, div_inf, % 113.94/16.25 div_mult, div_sign_neg, div_sign_pos, mod2_mul2, mod2_mul2_aux, mod2_mul2_aux2, % 113.94/16.25 mod_1, mod_bound, mod_div_unique, mod_inf, mod_mult, sumEmpty, tr_mod_2, % 113.94/16.25 tr_succ, witness_sort1 % 113.94/16.25 % 113.94/16.25 Those formulas are unsatisfiable: % 113.94/16.25 --------------------------------- % 113.94/16.25 % 113.94/16.25 Begin of proof % 113.94/16.25 | % 113.94/16.25 | ALPHA: (div_mod) implies: % 113.94/16.25 | (1) ! [v0: int] : ! [v1: int] : ! [v2: int] : (v1 = 0 | ~ (mod1(v0, v1) % 113.94/16.25 | = v2) | ? [v3: int] : (div1(v0, v1) = v3 & $product(v1, v3) = % 113.94/16.25 | $difference(v0, v2))) % 113.94/16.25 | % 113.94/16.25 | ALPHA: (sumNo) implies: % 113.94/16.25 | (2) ! [v0: int] : ! [v1: int] : ( ~ ($lesseq(0, v0)) | ~ % 113.94/16.25 | (sum_multiple_3_5_lt1($sum(v0, 1)) = v1) | ? [v2: int] : ? [v3: % 113.94/16.25 | int] : ? [v4: int] : ((v4 = v1 & sum_multiple_3_5_lt1(v0) = v1) | % 113.94/16.25 | (v3 = 0 & mod1(v0, 5) = 0) | (v2 = 0 & mod1(v0, 3) = 0))) % 113.94/16.26 | % 113.94/16.26 | ALPHA: (sumYes) implies: % 113.94/16.26 | (3) ! [v0: int] : ! [v1: int] : ( ~ ($lesseq(0, v0)) | ~ (mod1(v0, 5) = % 113.94/16.26 | v1) | ? [v2: int] : ? [v3: int] : ? [v4: int] : % 113.94/16.26 | (($sum($difference(v4, v3), v0) = 0 & sum_multiple_3_5_lt1($sum(v0, % 113.94/16.26 | 1)) = v3 & sum_multiple_3_5_lt1(v0) = $difference(v3, v0)) | % 113.94/16.26 | ( ~ (v2 = 0) & ~ (v1 = 0) & mod1(v0, 3) = v2))) % 113.94/16.26 | (4) ! [v0: int] : ! [v1: int] : ( ~ ($lesseq(0, v0)) | ~ % 113.94/16.26 | (sum_multiple_3_5_lt1($sum(v0, 1)) = v1) | ? [v2: int] : ? [v3: % 113.94/16.26 | int] : ? [v4: int] : (($sum($difference(v4, v1), v0) = 0 & % 113.94/16.26 | sum_multiple_3_5_lt1(v0) = $difference(v1, v0)) | ( ~ (v3 = 0) & % 113.94/16.26 | ~ (v2 = 0) & mod1(v0, 5) = v3 & mod1(v0, 3) = v2))) % 113.94/16.26 | % 113.94/16.26 | ALPHA: (mod_succ_1) implies: % 113.94/16.26 | (5) ! [v0: int] : ! [v1: int] : ! [v2: int] : ( ~ ($lesseq(1, v1)) | ~ % 113.94/16.26 | ($lesseq(0, v0)) | ~ (mod1(v0, v1) = v2) | ? [v3: int] : % 113.94/16.26 | (mod1($sum(v0, 1), v1) = v3 & ($difference(v3, v2) = 1 | v3 = 0))) % 113.94/16.26 | (6) ! [v0: int] : ! [v1: int] : ! [v2: int] : (v2 = 0 | ~ ($lesseq(1, % 113.94/16.26 | v1)) | ~ ($lesseq(0, v0)) | ~ (mod1($sum(v0, 1), v1) = v2) | % 113.94/16.26 | mod1(v0, v1) = $sum(v2, -1)) % 113.94/16.26 | % 113.94/16.26 | ALPHA: (mod_succ_2) implies: % 113.94/16.27 | (7) ! [v0: int] : ! [v1: int] : ( ~ ($lesseq(1, v1)) | ~ ($lesseq(0, % 113.94/16.27 | v0)) | ~ (mod1($sum(v0, 1), v1) = 0) | mod1(v0, v1) = $sum(v1, % 113.94/16.27 | -1)) % 113.94/16.27 | (8) ! [v0: int] : ! [v1: int] : ! [v2: int] : ($difference(v2, v1) = -1 % 113.94/16.27 | | ~ ($lesseq(1, v1)) | ~ ($lesseq(0, v0)) | ~ (mod1(v0, v1) = v2) % 113.94/16.27 | | ? [v3: int] : ( ~ (v3 = 0) & mod1($sum(v0, 1), v1) = v3)) % 113.94/16.27 | % 113.94/16.27 | ALPHA: (div_succ_1) implies: % 113.94/16.27 | (9) ! [v0: int] : ! [v1: int] : ( ~ ($lesseq(1, v1)) | ~ ($lesseq(0, % 113.94/16.27 | v0)) | ~ (mod1($sum(v0, 1), v1) = 0) | ? [v2: int] : % 113.94/16.27 | (div1($sum(v0, 1), v1) = v2 & div1(v0, v1) = $sum(v2, -1))) % 113.94/16.27 | % 113.94/16.27 | ALPHA: (div_succ_2) implies: % 113.94/16.27 | (10) ! [v0: int] : ! [v1: int] : ! [v2: int] : (v2 = 0 | ~ ($lesseq(1, % 113.94/16.27 | v1)) | ~ ($lesseq(0, v0)) | ~ (mod1($sum(v0, 1), v1) = v2) | % 113.94/16.27 | ? [v3: int] : (div1($sum(v0, 1), v1) = v3 & div1(v0, v1) = v3)) % 113.94/16.27 | % 113.94/16.27 | ALPHA: (closed_formula_aux_def) implies: % 113.94/16.27 | (11) ! [v0: int] : ! [v1: int] : ( ~ (div1(v0, 3) = v1) | ? [v2: int] : % 113.94/16.27 | ? [v3: int] : ? [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: % 113.94/16.27 | int] : ($sum($difference($difference($product(15, v7), $product(5, % 113.94/16.27 | v5)), $product(3, v3)), v2) = 0 & closed_formula_aux1(v0) % 113.94/16.27 | = v2 & tr1(v6) = v7 & tr1(v4) = v5 & tr1(v1) = v3 & div1(v0, 15) = % 113.94/16.27 | v6 & div1(v0, 5) = v4)) % 113.94/16.28 | (12) ! [v0: int] : ! [v1: int] : ( ~ (div1(v0, 5) = v1) | ? [v2: int] : % 113.94/16.28 | ? [v3: int] : ? [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: % 113.94/16.28 | int] : ($sum($difference($difference($product(15, v7), $product(5, % 113.94/16.28 | v5)), $product(3, v4)), v2) = 0 & closed_formula_aux1(v0) % 113.94/16.28 | = v2 & tr1(v6) = v7 & tr1(v3) = v4 & tr1(v1) = v5 & div1(v0, 15) = % 113.94/16.28 | v6 & div1(v0, 3) = v3)) % 113.94/16.28 | (13) ! [v0: int] : ! [v1: int] : ( ~ (closed_formula_aux1(v0) = v1) | ? % 113.94/16.28 | [v2: int] : ? [v3: int] : ? [v4: int] : ? [v5: int] : ? [v6: % 113.94/16.28 | int] : ? [v7: int] : ($sum($difference($difference($product(15, % 113.94/16.28 | v7), $product(5, v5)), $product(3, v3)), v1) = 0 & tr1(v6) % 113.94/16.28 | = v7 & tr1(v4) = v5 & tr1(v2) = v3 & div1(v0, 15) = v6 & div1(v0, % 113.94/16.28 | 5) = v4 & div1(v0, 3) = v2)) % 113.94/16.28 | % 113.94/16.28 | ALPHA: (p_def) implies: % 113.94/16.28 | (14) ! [v0: int] : ( ~ (p1(v0) = 0) | ? [v1: int] : % 113.94/16.28 | (closed_formula_aux1(v0) = v1 & sum_multiple_3_5_lt1($sum(v0, 1)) = % 113.94/16.28 | v1)) % 113.94/16.28 | (15) ! [v0: int] : ! [v1: int] : (v1 = 0 | ~ (p1(v0) = v1) | ? [v2: % 113.94/16.28 | int] : ? [v3: int] : ( ~ (v3 = v2) & closed_formula_aux1(v0) = v3 % 113.94/16.28 | & sum_multiple_3_5_lt1($sum(v0, 1)) = v2)) % 113.94/16.28 | % 113.94/16.28 | ALPHA: (mod_15) implies: % 113.94/16.28 | (16) ! [v0: int] : ( ~ (mod1(v0, 5) = 0) | ? [v1: int] : ? [v2: int] : % 113.94/16.28 | ((v2 = 0 & mod1(v0, 15) = 0) | ( ~ (v1 = 0) & mod1(v0, 3) = v1))) % 113.94/16.28 | % 113.94/16.28 | ALPHA: (closed_formula_n_5) implies: % 113.94/16.29 | (17) ! [v0: int] : ! [v1: int] : (v1 = 0 | ~ ($lesseq(1, v0)) | ~ % 113.94/16.29 | (mod1(v0, 3) = v1) | ? [v2: int] : ? [v3: int] : ? [v4: int] : % 113.94/16.29 | ((v4 = 0 & p1(v0) = 0) | ( ~ (v3 = 0) & mod1(v0, 5) = v3) | ( ~ (v2 % 113.94/16.29 | = 0) & p1($sum(v0, -1)) = v2))) % 113.94/16.29 | % 113.94/16.29 | ALPHA: (function-axioms) implies: % 113.94/16.29 | (18) ! [v0: int] : ! [v1: int] : ! [v2: int] : (v1 = v0 | ~ % 113.94/16.29 | (sum_multiple_3_5_lt1(v2) = v1) | ~ (sum_multiple_3_5_lt1(v2) = % 113.94/16.29 | v0)) % 113.94/16.29 | (19) ! [v0: int] : ! [v1: int] : ! [v2: int] : ! [v3: int] : (v1 = v0 | % 113.94/16.29 | ~ (mod1(v3, v2) = v1) | ~ (mod1(v3, v2) = v0)) % 113.94/16.29 | (20) ! [v0: int] : ! [v1: int] : ! [v2: int] : ! [v3: int] : (v1 = v0 | % 113.94/16.29 | ~ (div1(v3, v2) = v1) | ~ (div1(v3, v2) = v0)) % 113.94/16.29 | % 113.94/16.29 | DELTA: instantiating (closed_formula_n_15) with fresh symbols all_55_0, % 113.94/16.29 | all_55_1 gives: % 113.94/16.29 | (21) ~ (all_55_0 = 0) & $lesseq(1, all_55_1) & p1($sum(all_55_1, -1)) = 0 % 113.94/16.29 | & p1(all_55_1) = all_55_0 & mod1(all_55_1, 5) = 0 & mod1(all_55_1, 3) % 113.94/16.29 | = 0 % 113.94/16.29 | % 113.94/16.29 | ALPHA: (21) implies: % 113.94/16.29 | (22) ~ (all_55_0 = 0) % 113.94/16.29 | (23) $lesseq(1, all_55_1) % 113.94/16.29 | (24) mod1(all_55_1, 3) = 0 % 113.94/16.29 | (25) mod1(all_55_1, 5) = 0 % 113.94/16.29 | (26) p1(all_55_1) = all_55_0 % 113.94/16.29 | (27) p1($sum(all_55_1, -1)) = 0 % 113.94/16.29 | % 113.94/16.30 | GROUND_INST: instantiating (7) with $sum(all_55_1, -1), 3, simplifying with % 113.94/16.30 | (24) gives: % 113.94/16.30 | (28) ~ ($lesseq(1, all_55_1)) | mod1($sum(all_55_1, -1), 3) = 2 % 113.94/16.30 | % 113.94/16.30 | GROUND_INST: instantiating (9) with $sum(all_55_1, -1), 3, simplifying with % 113.94/16.30 | (24) gives: % 113.94/16.30 | (29) ~ ($lesseq(1, all_55_1)) | ? [v0: int] : (div1($sum(all_55_1, -1), % 113.94/16.30 | 3) = $sum(v0, -1) & div1(all_55_1, 3) = v0) % 113.94/16.30 | % 113.94/16.30 | GROUND_INST: instantiating (8) with all_55_1, 3, 0, simplifying with (24) % 113.94/16.30 | gives: % 113.94/16.30 | (30) ~ ($lesseq(0, all_55_1)) | ? [v0: int] : ( ~ (v0 = 0) & % 113.94/16.30 | mod1($sum(all_55_1, 1), 3) = v0) % 113.94/16.30 | % 113.94/16.30 | GROUND_INST: instantiating (1) with all_55_1, 3, 0, simplifying with (24) % 113.94/16.30 | gives: % 113.94/16.30 | (31) ? [v0: int] : (div1(all_55_1, 3) = v0 & $product(3, v0) = all_55_1) % 113.94/16.30 | % 113.94/16.30 | GROUND_INST: instantiating (5) with all_55_1, 3, 0, simplifying with (24) % 113.94/16.30 | gives: % 113.94/16.30 | (32) ~ ($lesseq(0, all_55_1)) | ? [v0: int] : (mod1($sum(all_55_1, 1), 3) % 113.94/16.30 | = v0 & (v0 = 1 | v0 = 0)) % 113.94/16.30 | % 113.94/16.30 | GROUND_INST: instantiating (16) with all_55_1, simplifying with (25) gives: % 113.94/16.30 | (33) ? [v0: int] : ? [v1: int] : ((v1 = 0 & mod1(all_55_1, 15) = 0) | ( ~ % 113.94/16.30 | (v0 = 0) & mod1(all_55_1, 3) = v0)) % 113.94/16.30 | % 113.94/16.30 | GROUND_INST: instantiating (3) with all_55_1, 0, simplifying with (25) gives: % 113.94/16.30 | (34) ~ ($lesseq(0, all_55_1)) | ? [v0: int] : % 113.94/16.30 | (sum_multiple_3_5_lt1($sum(all_55_1, 1)) = v0 & % 113.94/16.31 | sum_multiple_3_5_lt1(all_55_1) = $difference(v0, all_55_1)) % 113.94/16.31 | % 113.94/16.31 | GROUND_INST: instantiating (7) with $sum(all_55_1, -1), 5, simplifying with % 113.94/16.31 | (25) gives: % 113.94/16.31 | (35) ~ ($lesseq(1, all_55_1)) | mod1($sum(all_55_1, -1), 5) = 4 % 113.94/16.31 | % 113.94/16.31 | GROUND_INST: instantiating (9) with $sum(all_55_1, -1), 5, simplifying with % 113.94/16.31 | (25) gives: % 113.94/16.31 | (36) ~ ($lesseq(1, all_55_1)) | ? [v0: int] : (div1($sum(all_55_1, -1), % 113.94/16.31 | 5) = $sum(v0, -1) & div1(all_55_1, 5) = v0) % 113.94/16.31 | % 113.94/16.31 | GROUND_INST: instantiating (8) with all_55_1, 5, 0, simplifying with (25) % 113.94/16.31 | gives: % 113.94/16.31 | (37) ~ ($lesseq(0, all_55_1)) | ? [v0: int] : ( ~ (v0 = 0) & % 113.94/16.31 | mod1($sum(all_55_1, 1), 5) = v0) % 113.94/16.31 | % 113.94/16.31 | GROUND_INST: instantiating (1) with all_55_1, 5, 0, simplifying with (25) % 113.94/16.31 | gives: % 113.94/16.31 | (38) ? [v0: int] : (div1(all_55_1, 5) = v0 & $product(5, v0) = all_55_1) % 113.94/16.31 | % 113.94/16.31 | GROUND_INST: instantiating (5) with all_55_1, 5, 0, simplifying with (25) % 113.94/16.31 | gives: % 113.94/16.31 | (39) ~ ($lesseq(0, all_55_1)) | ? [v0: int] : (mod1($sum(all_55_1, 1), 5) % 113.94/16.31 | = v0 & (v0 = 1 | v0 = 0)) % 113.94/16.31 | % 113.94/16.31 | GROUND_INST: instantiating (14) with 0, simplifying with (closed_formula_0) % 113.94/16.31 | gives: % 113.94/16.31 | (40) ? [v0: int] : (closed_formula_aux1(0) = v0 & sum_multiple_3_5_lt1(1) % 113.94/16.31 | = v0) % 113.94/16.31 | % 113.94/16.31 | GROUND_INST: instantiating (15) with all_55_1, all_55_0, simplifying with (26) % 113.94/16.31 | gives: % 113.94/16.31 | (41) all_55_0 = 0 | ? [v0: int] : ? [v1: int] : ( ~ (v1 = v0) & % 113.94/16.31 | closed_formula_aux1(all_55_1) = v1 & % 113.94/16.31 | sum_multiple_3_5_lt1($sum(all_55_1, 1)) = v0) % 113.94/16.31 | % 113.94/16.31 | GROUND_INST: instantiating (14) with $sum(all_55_1, -1), simplifying with (27) % 113.94/16.32 | gives: % 113.94/16.32 | (42) ? [v0: int] : (closed_formula_aux1($sum(all_55_1, -1)) = v0 & % 113.94/16.32 | sum_multiple_3_5_lt1(all_55_1) = v0) % 113.94/16.32 | % 113.94/16.32 | DELTA: instantiating (42) with fresh symbol all_76_0 gives: % 113.94/16.32 | (43) closed_formula_aux1($sum(all_55_1, -1)) = all_76_0 & % 113.94/16.32 | sum_multiple_3_5_lt1(all_55_1) = all_76_0 % 113.94/16.32 | % 113.94/16.32 | ALPHA: (43) implies: % 113.94/16.32 | (44) sum_multiple_3_5_lt1(all_55_1) = all_76_0 % 113.94/16.32 | (45) closed_formula_aux1($sum(all_55_1, -1)) = all_76_0 % 113.94/16.32 | % 113.94/16.32 | DELTA: instantiating (40) with fresh symbol all_78_0 gives: % 113.94/16.32 | (46) closed_formula_aux1(0) = all_78_0 & sum_multiple_3_5_lt1(1) = all_78_0 % 113.94/16.32 | % 113.94/16.32 | ALPHA: (46) implies: % 113.94/16.32 | (47) sum_multiple_3_5_lt1(1) = all_78_0 % 113.94/16.32 | % 113.94/16.32 | DELTA: instantiating (31) with fresh symbol all_80_0 gives: % 113.94/16.32 | (48) div1(all_55_1, 3) = all_80_0 & $product(3, all_80_0) = all_55_1 % 113.94/16.32 | % 113.94/16.32 | ALPHA: (48) implies: % 113.94/16.32 | (49) $product(3, all_80_0) = all_55_1 % 113.94/16.32 | (50) div1(all_55_1, 3) = all_80_0 % 113.94/16.32 | % 113.94/16.32 | DELTA: instantiating (38) with fresh symbol all_94_0 gives: % 113.94/16.32 | (51) div1(all_55_1, 5) = all_94_0 & $product(5, all_94_0) = all_55_1 % 113.94/16.32 | % 113.94/16.32 | ALPHA: (51) implies: % 113.94/16.32 | (52) $product(5, all_94_0) = all_55_1 % 113.94/16.32 | (53) div1(all_55_1, 5) = all_94_0 % 113.94/16.32 | % 113.94/16.32 | DELTA: instantiating (33) with fresh symbols all_103_0, all_103_1 gives: % 113.94/16.32 | (54) (all_103_0 = 0 & mod1(all_55_1, 15) = 0) | ( ~ (all_103_1 = 0) & % 113.94/16.32 | mod1(all_55_1, 3) = all_103_1) % 113.94/16.32 | % 113.94/16.32 | THEORY_AXIOM GroebnerMultiplication: % 113.94/16.33 | (55) ! [v0: int] : ! [v1: int] : ! [v2: int] : ($product(5, v2) = v0 | % 113.94/16.33 | ~ ($product(5, v2) = v0) | ~ ($product(3, v1) = v0)) % 113.94/16.33 | % 113.94/16.33 | GROUND_INST: instantiating (55) with all_55_1, all_80_0, all_94_0, simplifying % 113.94/16.33 | with (49), (52) gives: % 113.94/16.33 | (56) $product(5, all_94_0) = all_55_1 % 113.94/16.33 | % 113.94/16.33 | THEORY_AXIOM GroebnerMultiplication: % 113.94/16.33 | (57) ! [v0: int] : ! [v1: int] : ($product(3, v1) = v0 | ~ ($product(3, % 113.94/16.33 | v1) = v0)) % 113.94/16.33 | % 113.94/16.33 | GROUND_INST: instantiating (57) with all_55_1, all_80_0, simplifying with (49) % 113.94/16.33 | gives: % 113.94/16.33 | (58) $product(3, all_80_0) = all_55_1 % 113.94/16.33 | % 113.94/16.33 | COL_REDUCE: introducing fresh symbol sc_118_0_0 defined by: % 113.94/16.33 | (59) all_94_0 = sc_118_0_0 % 113.94/16.33 | % 113.94/16.33 | COMBINE_EQS: (56), (59) imply: % 113.94/16.33 | (60) all_55_1 = $product(5, sc_118_0_0) % 113.94/16.33 | % 113.94/16.33 | SIMP: (60) implies: % 113.94/16.33 | (61) all_55_1 = $product(5, sc_118_0_0) % 113.94/16.33 | % 113.94/16.33 | COMBINE_EQS: (58), (61) imply: % 113.94/16.33 | (62) $product(3, all_80_0) = $product(5, sc_118_0_0) % 113.94/16.33 | % 113.94/16.33 | COL_REDUCE: introducing fresh symbol sc_118_0_3 defined by: % 113.94/16.33 | (63) $difference(all_80_0, $product(2, sc_118_0_0)) = sc_118_0_3 % 113.94/16.33 | % 113.94/16.33 | COMBINE_EQS: (62), (63) imply: % 113.94/16.33 | (64) $sum(sc_118_0_0, $product(3, sc_118_0_3)) = 0 % 113.94/16.33 | % 113.94/16.33 | COMBINE_EQS: (61), (64) imply: % 113.94/16.33 | (65) $sum(all_55_1, $product(15, sc_118_0_3)) = 0 % 113.94/16.33 | % 113.94/16.33 | COMBINE_EQS: (63), (64) imply: % 113.94/16.34 | (66) $sum(all_80_0, $product(5, sc_118_0_3)) = 0 % 113.94/16.34 | % 113.94/16.34 | COMBINE_EQS: (59), (64) imply: % 113.94/16.34 | (67) $sum(all_94_0, $product(3, sc_118_0_3)) = 0 % 113.94/16.34 | % 113.94/16.34 | REDUCE: (23), (65) imply: % 113.94/16.34 | (68) $lesseq(sc_118_0_3, -1) % 113.94/16.34 | % 113.94/16.34 | SIMP: (68) implies: % 113.94/16.34 | (69) $lesseq(sc_118_0_3, -1) % 113.94/16.34 | % 113.94/16.34 | REDUCE: (45), (65) imply: % 113.94/16.34 | (70) closed_formula_aux1($difference(-1, $product(15, sc_118_0_3))) = % 113.94/16.34 | all_76_0 % 113.94/16.34 | % 113.94/16.34 | REDUCE: (44), (65) imply: % 113.94/16.34 | (71) sum_multiple_3_5_lt1($product(-15, sc_118_0_3)) = all_76_0 % 113.94/16.34 | % 113.94/16.34 | REDUCE: (53), (65), (67) imply: % 114.27/16.34 | (72) div1($product(-15, sc_118_0_3), 5) = $product(-3, sc_118_0_3) % 114.27/16.34 | % 114.27/16.34 | REDUCE: (50), (65), (66) imply: % 114.27/16.34 | (73) div1($product(-15, sc_118_0_3), 3) = $product(-5, sc_118_0_3) % 114.27/16.34 | % 114.27/16.34 | REDUCE: (24), (65) imply: % 114.27/16.34 | (74) mod1($product(-15, sc_118_0_3), 3) = 0 % 114.27/16.34 | % 114.27/16.34 | BETA: splitting (54) gives: % 114.27/16.34 | % 114.27/16.34 | Case 1: % 114.27/16.34 | | % 114.27/16.34 | | (75) all_103_0 = 0 & mod1(all_55_1, 15) = 0 % 114.27/16.34 | | % 114.27/16.34 | | ALPHA: (75) implies: % 114.27/16.34 | | (76) mod1(all_55_1, 15) = 0 % 114.27/16.34 | | % 114.27/16.34 | | REDUCE: (65), (76) imply: % 114.27/16.34 | | (77) mod1($product(-15, sc_118_0_3), 15) = 0 % 114.27/16.34 | | % 114.27/16.34 | | BETA: splitting (35) gives: % 114.27/16.34 | | % 114.27/16.34 | | Case 1: % 114.27/16.34 | | | % 114.27/16.34 | | | (78) mod1($sum(all_55_1, -1), 5) = 4 % 114.27/16.34 | | | % 114.27/16.34 | | | REDUCE: (65), (78) imply: % 114.27/16.34 | | | (79) mod1($difference(-1, $product(15, sc_118_0_3)), 5) = 4 % 114.27/16.34 | | | % 114.27/16.34 | | | BETA: splitting (41) gives: % 114.27/16.34 | | | % 114.27/16.34 | | | Case 1: % 114.27/16.34 | | | | % 114.27/16.34 | | | | (80) all_55_0 = 0 % 114.27/16.34 | | | | % 114.27/16.34 | | | | REDUCE: (22), (80) imply: % 114.27/16.34 | | | | (81) $false % 114.27/16.35 | | | | % 114.27/16.35 | | | | CLOSE: (81) is inconsistent. % 114.27/16.35 | | | | % 114.27/16.35 | | | Case 2: % 114.27/16.35 | | | | % 114.27/16.35 | | | | (82) ? [v0: int] : ? [v1: int] : ( ~ (v1 = v0) & % 114.27/16.35 | | | | closed_formula_aux1(all_55_1) = v1 & % 114.27/16.35 | | | | sum_multiple_3_5_lt1($sum(all_55_1, 1)) = v0) % 114.27/16.35 | | | | % 114.27/16.35 | | | | DELTA: instantiating (82) with fresh symbols all_135_0, all_135_1 gives: % 114.27/16.35 | | | | (83) ~ (all_135_0 = all_135_1) & closed_formula_aux1(all_55_1) = % 114.27/16.35 | | | | all_135_0 & sum_multiple_3_5_lt1($sum(all_55_1, 1)) = all_135_1 % 114.27/16.35 | | | | % 114.27/16.35 | | | | ALPHA: (83) implies: % 114.27/16.35 | | | | (84) ~ (all_135_0 = all_135_1) % 114.27/16.35 | | | | (85) sum_multiple_3_5_lt1($sum(all_55_1, 1)) = all_135_1 % 114.27/16.35 | | | | (86) closed_formula_aux1(all_55_1) = all_135_0 % 114.27/16.35 | | | | % 114.27/16.35 | | | | REDUCE: (65), (86) imply: % 114.27/16.35 | | | | (87) closed_formula_aux1($product(-15, sc_118_0_3)) = all_135_0 % 114.27/16.35 | | | | % 114.27/16.35 | | | | REDUCE: (65), (85) imply: % 114.27/16.35 | | | | (88) sum_multiple_3_5_lt1($difference(1, $product(15, sc_118_0_3))) = % 114.27/16.35 | | | | all_135_1 % 114.27/16.35 | | | | % 114.27/16.35 | | | | BETA: splitting (32) gives: % 114.27/16.35 | | | | % 114.27/16.35 | | | | Case 1: % 114.27/16.35 | | | | | % 114.27/16.35 | | | | | (89) $lesseq(all_55_1, -1) % 114.27/16.35 | | | | | % 114.27/16.35 | | | | | REDUCE: (65), (89) imply: % 114.27/16.35 | | | | | (90) $lesseq(1, sc_118_0_3) % 114.27/16.35 | | | | | % 114.27/16.35 | | | | | SIMP: (90) implies: % 114.27/16.35 | | | | | (91) $lesseq(1, sc_118_0_3) % 114.27/16.35 | | | | | % 114.27/16.35 | | | | | COMBINE_INEQS: (69), (91) imply: % 114.27/16.35 | | | | | (92) $false % 114.27/16.35 | | | | | % 114.27/16.35 | | | | | CLOSE: (92) is inconsistent. % 114.27/16.35 | | | | | % 114.27/16.35 | | | | Case 2: % 114.27/16.35 | | | | | % 114.27/16.35 | | | | | (93) ? [v0: int] : (mod1($sum(all_55_1, 1), 3) = v0 & (v0 = 1 | v0 % 114.27/16.35 | | | | | = 0)) % 114.27/16.35 | | | | | % 114.27/16.35 | | | | | DELTA: instantiating (93) with fresh symbol all_157_0 gives: % 114.27/16.35 | | | | | (94) mod1($sum(all_55_1, 1), 3) = all_157_0 & (all_157_0 = 1 | % 114.27/16.35 | | | | | all_157_0 = 0) % 114.27/16.35 | | | | | % 114.27/16.35 | | | | | ALPHA: (94) implies: % 114.27/16.35 | | | | | (95) mod1($sum(all_55_1, 1), 3) = all_157_0 % 114.27/16.35 | | | | | (96) all_157_0 = 1 | all_157_0 = 0 % 114.27/16.35 | | | | | % 114.27/16.35 | | | | | REDUCE: (65), (95) imply: % 114.27/16.35 | | | | | (97) mod1($difference(1, $product(15, sc_118_0_3)), 3) = all_157_0 % 114.27/16.35 | | | | | % 114.27/16.35 | | | | | BETA: splitting (30) gives: % 114.27/16.35 | | | | | % 114.27/16.35 | | | | | Case 1: % 114.27/16.35 | | | | | | % 114.27/16.35 | | | | | | (98) $lesseq(all_55_1, -1) % 114.27/16.35 | | | | | | % 114.27/16.35 | | | | | | REDUCE: (65), (98) imply: % 114.27/16.35 | | | | | | (99) $lesseq(1, sc_118_0_3) % 114.27/16.35 | | | | | | % 114.27/16.35 | | | | | | SIMP: (99) implies: % 114.27/16.35 | | | | | | (100) $lesseq(1, sc_118_0_3) % 114.27/16.35 | | | | | | % 114.27/16.36 | | | | | | COMBINE_INEQS: (69), (100) imply: % 114.27/16.36 | | | | | | (101) $false % 114.27/16.36 | | | | | | % 114.27/16.36 | | | | | | CLOSE: (101) is inconsistent. % 114.27/16.36 | | | | | | % 114.27/16.36 | | | | | Case 2: % 114.27/16.36 | | | | | | % 114.27/16.36 | | | | | | (102) ? [v0: int] : ( ~ (v0 = 0) & mod1($sum(all_55_1, 1), 3) = % 114.27/16.36 | | | | | | v0) % 114.27/16.36 | | | | | | % 114.27/16.36 | | | | | | DELTA: instantiating (102) with fresh symbol all_164_0 gives: % 114.27/16.36 | | | | | | (103) ~ (all_164_0 = 0) & mod1($sum(all_55_1, 1), 3) = all_164_0 % 114.27/16.36 | | | | | | % 114.27/16.36 | | | | | | ALPHA: (103) implies: % 114.27/16.36 | | | | | | (104) ~ (all_164_0 = 0) % 114.27/16.36 | | | | | | (105) mod1($sum(all_55_1, 1), 3) = all_164_0 % 114.27/16.36 | | | | | | % 114.27/16.36 | | | | | | REDUCE: (65), (105) imply: % 114.27/16.36 | | | | | | (106) mod1($difference(1, $product(15, sc_118_0_3)), 3) = % 114.27/16.36 | | | | | | all_164_0 % 114.27/16.36 | | | | | | % 114.27/16.36 | | | | | | BETA: splitting (39) gives: % 114.27/16.36 | | | | | | % 114.27/16.36 | | | | | | Case 1: % 114.27/16.36 | | | | | | | % 114.27/16.36 | | | | | | | (107) $lesseq(all_55_1, -1) % 114.27/16.36 | | | | | | | % 114.27/16.36 | | | | | | | REDUCE: (65), (107) imply: % 114.27/16.36 | | | | | | | (108) $lesseq(1, sc_118_0_3) % 114.27/16.36 | | | | | | | % 114.27/16.36 | | | | | | | SIMP: (108) implies: % 114.27/16.36 | | | | | | | (109) $lesseq(1, sc_118_0_3) % 114.27/16.36 | | | | | | | % 114.27/16.36 | | | | | | | COMBINE_INEQS: (69), (109) imply: % 114.27/16.36 | | | | | | | (110) $false % 114.27/16.36 | | | | | | | % 114.27/16.36 | | | | | | | CLOSE: (110) is inconsistent. % 114.27/16.36 | | | | | | | % 114.27/16.36 | | | | | | Case 2: % 114.27/16.36 | | | | | | | % 114.27/16.36 | | | | | | | (111) ? [v0: int] : (mod1($sum(all_55_1, 1), 5) = v0 & (v0 = 1 % 114.27/16.36 | | | | | | | | v0 = 0)) % 114.27/16.36 | | | | | | | % 114.27/16.36 | | | | | | | DELTA: instantiating (111) with fresh symbol all_169_0 gives: % 114.27/16.36 | | | | | | | (112) mod1($sum(all_55_1, 1), 5) = all_169_0 & (all_169_0 = 1 | % 114.27/16.36 | | | | | | | all_169_0 = 0) % 114.27/16.36 | | | | | | | % 114.27/16.36 | | | | | | | ALPHA: (112) implies: % 114.27/16.36 | | | | | | | (113) mod1($sum(all_55_1, 1), 5) = all_169_0 % 114.27/16.36 | | | | | | | (114) all_169_0 = 1 | all_169_0 = 0 % 114.27/16.36 | | | | | | | % 114.27/16.36 | | | | | | | REDUCE: (65), (113) imply: % 114.27/16.36 | | | | | | | (115) mod1($difference(1, $product(15, sc_118_0_3)), 5) = % 114.27/16.36 | | | | | | | all_169_0 % 114.27/16.36 | | | | | | | % 114.27/16.36 | | | | | | | BETA: splitting (28) gives: % 114.27/16.36 | | | | | | | % 114.27/16.36 | | | | | | | Case 1: % 114.27/16.36 | | | | | | | | % 114.27/16.36 | | | | | | | | (116) mod1($sum(all_55_1, -1), 3) = 2 % 114.27/16.36 | | | | | | | | % 114.27/16.36 | | | | | | | | REDUCE: (65), (116) imply: % 114.27/16.36 | | | | | | | | (117) mod1($difference(-1, $product(15, sc_118_0_3)), 3) = 2 % 114.27/16.36 | | | | | | | | % 114.27/16.36 | | | | | | | | BETA: splitting (36) gives: % 114.27/16.36 | | | | | | | | % 114.27/16.36 | | | | | | | | Case 1: % 114.27/16.36 | | | | | | | | | % 114.27/16.36 | | | | | | | | | (118) $lesseq(all_55_1, 0) % 114.27/16.36 | | | | | | | | | % 114.27/16.36 | | | | | | | | | REF_CLOSE: (65), (69), (118) are inconsistent by sub-proof #1. % 114.27/16.36 | | | | | | | | | % 114.27/16.36 | | | | | | | | Case 2: % 114.27/16.36 | | | | | | | | | % 114.27/16.36 | | | | | | | | | (119) ? [v0: int] : (div1($sum(all_55_1, -1), 5) = % 114.27/16.36 | | | | | | | | | $sum(v0, -1) & div1(all_55_1, 5) = v0) % 114.27/16.36 | | | | | | | | | % 114.27/16.36 | | | | | | | | | DELTA: instantiating (119) with fresh symbol all_181_0 gives: % 114.27/16.36 | | | | | | | | | (120) div1($sum(all_55_1, -1), 5) = $sum(all_181_0, -1) & % 114.27/16.36 | | | | | | | | | div1(all_55_1, 5) = all_181_0 % 114.27/16.36 | | | | | | | | | % 114.27/16.37 | | | | | | | | | ALPHA: (120) implies: % 114.27/16.37 | | | | | | | | | (121) div1(all_55_1, 5) = all_181_0 % 114.27/16.37 | | | | | | | | | (122) div1($sum(all_55_1, -1), 5) = $sum(all_181_0, -1) % 114.27/16.37 | | | | | | | | | % 114.27/16.37 | | | | | | | | | REDUCE: (65), (122) imply: % 114.27/16.37 | | | | | | | | | (123) div1($difference(-1, $product(15, sc_118_0_3)), 5) = % 114.27/16.37 | | | | | | | | | $sum(all_181_0, -1) % 114.27/16.37 | | | | | | | | | % 114.27/16.37 | | | | | | | | | REDUCE: (65), (121) imply: % 114.27/16.37 | | | | | | | | | (124) div1($product(-15, sc_118_0_3), 5) = all_181_0 % 114.27/16.37 | | | | | | | | | % 114.27/16.37 | | | | | | | | | BETA: splitting (34) gives: % 114.27/16.37 | | | | | | | | | % 114.27/16.37 | | | | | | | | | Case 1: % 114.27/16.37 | | | | | | | | | | % 114.27/16.37 | | | | | | | | | | (125) $lesseq(all_55_1, -1) % 114.27/16.37 | | | | | | | | | | % 114.27/16.37 | | | | | | | | | | REDUCE: (65), (125) imply: % 114.27/16.37 | | | | | | | | | | (126) $lesseq(1, sc_118_0_3) % 114.27/16.37 | | | | | | | | | | % 114.27/16.37 | | | | | | | | | | SIMP: (126) implies: % 114.27/16.37 | | | | | | | | | | (127) $lesseq(1, sc_118_0_3) % 114.27/16.37 | | | | | | | | | | % 114.27/16.37 | | | | | | | | | | COMBINE_INEQS: (69), (127) imply: % 114.27/16.37 | | | | | | | | | | (128) $false % 114.27/16.37 | | | | | | | | | | % 114.27/16.37 | | | | | | | | | | CLOSE: (128) is inconsistent. % 114.27/16.37 | | | | | | | | | | % 114.27/16.37 | | | | | | | | | Case 2: % 114.27/16.37 | | | | | | | | | | % 114.27/16.37 | | | | | | | | | | (129) ? [v0: int] : (sum_multiple_3_5_lt1($sum(all_55_1, % 114.27/16.37 | | | | | | | | | | 1)) = v0 & sum_multiple_3_5_lt1(all_55_1) = % 114.27/16.37 | | | | | | | | | | $difference(v0, all_55_1)) % 114.27/16.37 | | | | | | | | | | % 114.27/16.37 | | | | | | | | | | DELTA: instantiating (129) with fresh symbol all_188_0 % 114.27/16.37 | | | | | | | | | | gives: % 114.27/16.37 | | | | | | | | | | (130) sum_multiple_3_5_lt1($sum(all_55_1, 1)) = all_188_0 % 114.27/16.37 | | | | | | | | | | & sum_multiple_3_5_lt1(all_55_1) = % 114.27/16.37 | | | | | | | | | | $difference(all_188_0, all_55_1) % 114.27/16.37 | | | | | | | | | | % 114.27/16.37 | | | | | | | | | | ALPHA: (130) implies: % 114.27/16.37 | | | | | | | | | | (131) sum_multiple_3_5_lt1(all_55_1) = % 114.27/16.37 | | | | | | | | | | $difference(all_188_0, all_55_1) % 114.27/16.37 | | | | | | | | | | (132) sum_multiple_3_5_lt1($sum(all_55_1, 1)) = all_188_0 % 114.27/16.37 | | | | | | | | | | % 114.27/16.37 | | | | | | | | | | REDUCE: (65), (132) imply: % 114.27/16.37 | | | | | | | | | | (133) sum_multiple_3_5_lt1($difference(1, $product(15, % 114.27/16.37 | | | | | | | | | | sc_118_0_3))) = all_188_0 % 114.27/16.37 | | | | | | | | | | % 114.27/16.37 | | | | | | | | | | REDUCE: (65), (131) imply: % 114.27/16.37 | | | | | | | | | | (134) sum_multiple_3_5_lt1($product(-15, sc_118_0_3)) = % 114.27/16.37 | | | | | | | | | | $sum(all_188_0, $product(15, sc_118_0_3)) % 114.27/16.37 | | | | | | | | | | % 114.27/16.37 | | | | | | | | | | BETA: splitting (29) gives: % 114.27/16.37 | | | | | | | | | | % 114.27/16.37 | | | | | | | | | | Case 1: % 114.27/16.37 | | | | | | | | | | | % 114.27/16.37 | | | | | | | | | | | (135) $lesseq(all_55_1, 0) % 114.27/16.37 | | | | | | | | | | | % 114.27/16.37 | | | | | | | | | | | REDUCE: (65), (135) imply: % 114.27/16.37 | | | | | | | | | | | (136) $lesseq(0, sc_118_0_3) % 114.27/16.37 | | | | | | | | | | | % 114.27/16.37 | | | | | | | | | | | SIMP: (136) implies: % 114.27/16.38 | | | | | | | | | | | (137) $lesseq(0, sc_118_0_3) % 114.27/16.38 | | | | | | | | | | | % 114.27/16.38 | | | | | | | | | | | COMBINE_INEQS: (69), (137) imply: % 114.27/16.38 | | | | | | | | | | | (138) $false % 114.27/16.38 | | | | | | | | | | | % 114.27/16.38 | | | | | | | | | | | CLOSE: (138) is inconsistent. % 114.27/16.38 | | | | | | | | | | | % 114.27/16.38 | | | | | | | | | | Case 2: % 114.27/16.38 | | | | | | | | | | | % 114.27/16.38 | | | | | | | | | | | (139) ? [v0: int] : (div1($sum(all_55_1, -1), 3) = % 114.27/16.38 | | | | | | | | | | | $sum(v0, -1) & div1(all_55_1, 3) = v0) % 114.27/16.38 | | | | | | | | | | | % 114.27/16.38 | | | | | | | | | | | DELTA: instantiating (139) with fresh symbol all_195_0 % 114.27/16.38 | | | | | | | | | | | gives: % 114.27/16.38 | | | | | | | | | | | (140) div1($sum(all_55_1, -1), 3) = $sum(all_195_0, -1) % 114.27/16.38 | | | | | | | | | | | & div1(all_55_1, 3) = all_195_0 % 114.27/16.38 | | | | | | | | | | | % 114.27/16.38 | | | | | | | | | | | ALPHA: (140) implies: % 114.27/16.38 | | | | | | | | | | | (141) div1(all_55_1, 3) = all_195_0 % 114.27/16.38 | | | | | | | | | | | (142) div1($sum(all_55_1, -1), 3) = $sum(all_195_0, -1) % 114.27/16.38 | | | | | | | | | | | % 114.27/16.38 | | | | | | | | | | | REDUCE: (65), (142) imply: % 114.27/16.38 | | | | | | | | | | | (143) div1($difference(-1, $product(15, sc_118_0_3)), 3) % 114.27/16.38 | | | | | | | | | | | = $sum(all_195_0, -1) % 114.27/16.38 | | | | | | | | | | | % 114.27/16.38 | | | | | | | | | | | REDUCE: (65), (141) imply: % 114.27/16.38 | | | | | | | | | | | (144) div1($product(-15, sc_118_0_3), 3) = all_195_0 % 114.27/16.38 | | | | | | | | | | | % 114.27/16.38 | | | | | | | | | | | BETA: splitting (37) gives: % 114.27/16.38 | | | | | | | | | | | % 114.27/16.38 | | | | | | | | | | | Case 1: % 114.27/16.38 | | | | | | | | | | | | % 114.27/16.38 | | | | | | | | | | | | (145) $lesseq(all_55_1, -1) % 114.27/16.38 | | | | | | | | | | | | % 114.27/16.38 | | | | | | | | | | | | REDUCE: (65), (145) imply: % 114.27/16.38 | | | | | | | | | | | | (146) $lesseq(1, sc_118_0_3) % 114.27/16.38 | | | | | | | | | | | | % 114.27/16.38 | | | | | | | | | | | | SIMP: (146) implies: % 114.27/16.38 | | | | | | | | | | | | (147) $lesseq(1, sc_118_0_3) % 114.27/16.38 | | | | | | | | | | | | % 114.27/16.38 | | | | | | | | | | | | COMBINE_INEQS: (69), (147) imply: % 114.27/16.38 | | | | | | | | | | | | (148) $false % 114.27/16.38 | | | | | | | | | | | | % 114.27/16.38 | | | | | | | | | | | | CLOSE: (148) is inconsistent. % 114.27/16.38 | | | | | | | | | | | | % 114.27/16.38 | | | | | | | | | | | Case 2: % 114.27/16.38 | | | | | | | | | | | | % 114.27/16.38 | | | | | | | | | | | | (149) ? [v0: int] : ( ~ (v0 = 0) & mod1($sum(all_55_1, % 114.27/16.38 | | | | | | | | | | | | 1), 5) = v0) % 114.27/16.38 | | | | | | | | | | | | % 114.27/16.38 | | | | | | | | | | | | DELTA: instantiating (149) with fresh symbol all_206_0 % 114.27/16.38 | | | | | | | | | | | | gives: % 114.27/16.39 | | | | | | | | | | | | (150) ~ (all_206_0 = 0) & mod1($sum(all_55_1, 1), 5) = % 114.27/16.39 | | | | | | | | | | | | all_206_0 % 114.27/16.39 | | | | | | | | | | | | % 114.27/16.39 | | | | | | | | | | | | ALPHA: (150) implies: % 114.27/16.39 | | | | | | | | | | | | (151) ~ (all_206_0 = 0) % 114.27/16.39 | | | | | | | | | | | | (152) mod1($sum(all_55_1, 1), 5) = all_206_0 % 114.27/16.39 | | | | | | | | | | | | % 114.27/16.39 | | | | | | | | | | | | REDUCE: (65), (152) imply: % 114.27/16.39 | | | | | | | | | | | | (153) mod1($difference(1, $product(15, sc_118_0_3)), 5) % 114.27/16.39 | | | | | | | | | | | | = all_206_0 % 114.27/16.39 | | | | | | | | | | | | % 114.27/16.39 | | | | | | | | | | | | GROUND_INST: instantiating (mod_sign_pos) with $difference(1, % 114.27/16.39 | | | | | | | | | | | | $product(15, sc_118_0_3)), 3, all_157_0, % 114.27/16.39 | | | | | | | | | | | | simplifying with (97) gives: % 114.27/16.39 | | | | | | | | | | | | (154) ~ ($lesseq(all_157_0, -1)) | ~ % 114.27/16.39 | | | | | | | | | | | | ($lesseq(sc_118_0_3, 0) % 114.27/16.39 | | | | | | | | | | | | % 114.27/16.39 | | | | | | | | | | | | GROUND_INST: instantiating (19) with all_157_0, all_164_0, 3, % 114.27/16.39 | | | | | | | | | | | | $difference(1, $product(15, sc_118_0_3)), % 114.27/16.39 | | | | | | | | | | | | simplifying with (97), (106) gives: % 114.27/16.39 | | | | | | | | | | | | (155) all_164_0 = all_157_0 % 114.27/16.39 | | | | | | | | | | | | % 114.27/16.39 | | | | | | | | | | | | GROUND_INST: instantiating (19) with all_169_0, all_206_0, 5, % 114.27/16.39 | | | | | | | | | | | | $difference(1, $product(15, sc_118_0_3)), % 114.27/16.39 | | | | | | | | | | | | simplifying with (115), (153) gives: % 114.27/16.39 | | | | | | | | | | | | (156) all_206_0 = all_169_0 % 114.27/16.39 | | | | | | | | | | | | % 114.27/16.39 | | | | | | | | | | | | GROUND_INST: instantiating (20) with $product(-5, sc_118_0_3), % 114.27/16.39 | | | | | | | | | | | | all_195_0, 3, $product(-15, sc_118_0_3), % 114.27/16.39 | | | | | | | | | | | | simplifying with (73), (144) gives: % 114.27/16.39 | | | | | | | | | | | | (157) $sum(all_195_0, $product(5, sc_118_0_3)) = 0 % 114.27/16.39 | | | | | | | | | | | | % 114.27/16.39 | | | | | | | | | | | | GROUND_INST: instantiating (20) with $product(-3, sc_118_0_3), % 114.27/16.39 | | | | | | | | | | | | all_181_0, 5, $product(-15, sc_118_0_3), % 114.27/16.39 | | | | | | | | | | | | simplifying with (72), (124) gives: % 114.27/16.39 | | | | | | | | | | | | (158) $sum(all_181_0, $product(3, sc_118_0_3)) = 0 % 114.27/16.39 | | | | | | | | | | | | % 114.27/16.39 | | | | | | | | | | | | GROUND_INST: instantiating (18) with all_76_0, $sum(all_188_0, % 114.27/16.39 | | | | | | | | | | | | $product(15, sc_118_0_3)), $product(-15, % 114.27/16.39 | | | | | | | | | | | | sc_118_0_3), simplifying with (71), (134) gives: % 114.27/16.39 | | | | | | | | | | | | (159) $sum($difference(all_188_0, all_76_0), % 114.27/16.39 | | | | | | | | | | | | $product(15, sc_118_0_3)) = 0 % 114.27/16.39 | | | | | | | | | | | | % 114.27/16.39 | | | | | | | | | | | | GROUND_INST: instantiating (18) with all_135_1, all_188_0, % 114.27/16.39 | | | | | | | | | | | | $difference(1, $product(15, sc_118_0_3)), % 114.27/16.39 | | | | | | | | | | | | simplifying with (88), (133) gives: % 114.27/16.39 | | | | | | | | | | | | (160) all_188_0 = all_135_1 % 114.27/16.39 | | | | | | | | | | | | % 114.27/16.39 | | | | | | | | | | | | COMBINE_EQS: (159), (160) imply: % 114.27/16.39 | | | | | | | | | | | | (161) $sum($difference(all_135_1, all_76_0), % 114.27/16.39 | | | | | | | | | | | | $product(15, sc_118_0_3)) = 0 % 114.27/16.39 | | | | | | | | | | | | % 114.27/16.39 | | | | | | | | | | | | REDUCE: (151), (156) imply: % 114.27/16.39 | | | | | | | | | | | | (162) ~ (all_169_0 = 0) % 114.27/16.39 | | | | | | | | | | | | % 114.27/16.39 | | | | | | | | | | | | REDUCE: (104), (155) imply: % 114.27/16.39 | | | | | | | | | | | | (163) ~ (all_157_0 = 0) % 114.27/16.39 | | | | | | | | | | | | % 114.27/16.39 | | | | | | | | | | | | REDUCE: (84), (161) imply: % 114.27/16.39 | | | | | | | | | | | | (164) ~ ($sum($difference(all_135_0, all_76_0), % 114.27/16.39 | | | | | | | | | | | | $product(15, sc_118_0_3)) = 0) % 114.27/16.39 | | | | | | | | | | | | % 114.27/16.39 | | | | | | | | | | | | REDUCE: (88), (161) imply: % 114.27/16.39 | | | | | | | | | | | | (165) sum_multiple_3_5_lt1($difference(1, $product(15, % 114.27/16.39 | | | | | | | | | | | | sc_118_0_3))) = $difference(all_76_0, % 114.27/16.39 | | | | | | | | | | | | $product(15, sc_118_0_3)) % 114.27/16.39 | | | | | | | | | | | | % 114.27/16.39 | | | | | | | | | | | | REDUCE: (123), (158) imply: % 114.27/16.39 | | | | | | | | | | | | (166) div1($difference(-1, $product(15, sc_118_0_3)), 5) % 114.27/16.39 | | | | | | | | | | | | = $difference(-1, $product(3, sc_118_0_3)) % 114.27/16.39 | | | | | | | | | | | | % 114.27/16.39 | | | | | | | | | | | | REDUCE: (143), (157) imply: % 114.27/16.39 | | | | | | | | | | | | (167) div1($difference(-1, $product(15, sc_118_0_3)), 3) % 114.27/16.39 | | | | | | | | | | | | = $difference(-1, $product(5, sc_118_0_3)) % 114.27/16.39 | | | | | | | | | | | | % 114.27/16.39 | | | | | | | | | | | | BETA: splitting (154) gives: % 114.27/16.39 | | | | | | | | | | | | % 114.27/16.39 | | | | | | | | | | | | Case 1: % 114.27/16.39 | | | | | | | | | | | | | % 114.27/16.39 | | | | | | | | | | | | | (168) $lesseq(1, sc_118_0_3) % 114.27/16.39 | | | | | | | | | | | | | % 114.27/16.39 | | | | | | | | | | | | | COMBINE_INEQS: (69), (168) imply: % 114.27/16.39 | | | | | | | | | | | | | (169) $false % 114.27/16.39 | | | | | | | | | | | | | % 114.27/16.39 | | | | | | | | | | | | | CLOSE: (169) is inconsistent. % 114.27/16.39 | | | | | | | | | | | | | % 114.27/16.39 | | | | | | | | | | | | Case 2: % 114.27/16.39 | | | | | | | | | | | | | % 114.27/16.39 | | | | | | | | | | | | | (170) $lesseq(0, all_157_0) % 114.27/16.39 | | | | | | | | | | | | | % 114.27/16.39 | | | | | | | | | | | | | STRENGTHEN: (163), (170) imply: % 114.27/16.39 | | | | | | | | | | | | | (171) $lesseq(1, all_157_0) % 114.27/16.39 | | | | | | | | | | | | | % 114.27/16.39 | | | | | | | | | | | | | BETA: splitting (114) gives: % 114.27/16.39 | | | | | | | | | | | | | % 114.27/16.39 | | | | | | | | | | | | | Case 1: % 114.27/16.39 | | | | | | | | | | | | | | % 114.27/16.39 | | | | | | | | | | | | | | (172) all_169_0 = 0 % 114.27/16.39 | | | | | | | | | | | | | | % 114.27/16.39 | | | | | | | | | | | | | | REDUCE: (162), (172) imply: % 114.27/16.39 | | | | | | | | | | | | | | (173) $false % 114.27/16.39 | | | | | | | | | | | | | | % 114.27/16.39 | | | | | | | | | | | | | | CLOSE: (173) is inconsistent. % 114.27/16.39 | | | | | | | | | | | | | | % 114.27/16.39 | | | | | | | | | | | | | Case 2: % 114.27/16.39 | | | | | | | | | | | | | | % 114.27/16.39 | | | | | | | | | | | | | | (174) all_169_0 = 1 % 114.27/16.39 | | | | | | | | | | | | | | % 114.27/16.39 | | | | | | | | | | | | | | REDUCE: (115), (174) imply: % 114.27/16.39 | | | | | | | | | | | | | | (175) mod1($difference(1, $product(15, sc_118_0_3)), 5) % 114.27/16.39 | | | | | | | | | | | | | | = 1 % 114.27/16.39 | | | | | | | | | | | | | | % 114.27/16.39 | | | | | | | | | | | | | | BETA: splitting (96) gives: % 114.27/16.39 | | | | | | | | | | | | | | % 114.27/16.39 | | | | | | | | | | | | | | Case 1: % 114.27/16.39 | | | | | | | | | | | | | | | % 114.27/16.39 | | | | | | | | | | | | | | | (176) all_157_0 = 0 % 114.27/16.39 | | | | | | | | | | | | | | | % 114.27/16.39 | | | | | | | | | | | | | | | REDUCE: (171), (176) imply: % 114.27/16.39 | | | | | | | | | | | | | | | (177) $false % 114.27/16.39 | | | | | | | | | | | | | | | % 114.27/16.39 | | | | | | | | | | | | | | | CLOSE: (177) is inconsistent. % 114.27/16.39 | | | | | | | | | | | | | | | % 114.27/16.39 | | | | | | | | | | | | | | Case 2: % 114.27/16.39 | | | | | | | | | | | | | | | % 114.27/16.39 | | | | | | | | | | | | | | | (178) all_157_0 = 1 % 114.27/16.40 | | | | | | | | | | | | | | | % 114.27/16.40 | | | | | | | | | | | | | | | REDUCE: (97), (178) imply: % 114.27/16.40 | | | | | | | | | | | | | | | (179) mod1($difference(1, $product(15, sc_118_0_3)), 3) % 114.27/16.40 | | | | | | | | | | | | | | | = 1 % 114.27/16.40 | | | | | | | | | | | | | | | % 114.27/16.40 | | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with $difference(-1, % 114.27/16.40 | | | | | | | | | | | | | | | $product(15, sc_118_0_3)), 15, simplifying with % 114.27/16.40 | | | | | | | | | | | | | | | (77) gives: % 114.27/16.40 | | | | | | | | | | | | | | | (180) ~ ($lesseq(sc_118_0_3, -1)) | ? [v0: int] : % 114.27/16.40 | | | | | | | | | | | | | | | (div1($difference(-1, $product(15, sc_118_0_3)), % 114.27/16.40 | | | | | | | | | | | | | | | 15) = $sum(v0, -1) & div1($product(-15, % 114.27/16.40 | | | | | | | | | | | | | | | sc_118_0_3), 15) = v0) % 114.27/16.40 | | | | | | | | | | | | | | | % 114.27/16.40 | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with $product(-15, sc_118_0_3), % 114.27/16.40 | | | | | | | | | | | | | | | 15, 0, simplifying with (77) gives: % 114.27/16.40 | | | | | | | | | | | | | | | (181) ? [v0: int] : (div1($product(-15, sc_118_0_3), % 114.27/16.40 | | | | | | | | | | | | | | | 15) = v0 & $product(15, v0) = $product(-15, % 114.27/16.40 | | | | | | | | | | | | | | | sc_118_0_3)) % 114.27/16.40 | | | | | | | | | | | | | | | % 114.27/16.40 | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with $product(-15, sc_118_0_3), % 114.27/16.40 | | | | | | | | | | | | | | | 3, 1, simplifying with (179) gives: % 114.27/16.40 | | | | | | | | | | | | | | | (182) ~ ($lesseq(sc_118_0_3, 0) | ? [v0: int] : % 114.27/16.40 | | | | | | | | | | | | | | | (div1($difference(1, $product(15, sc_118_0_3)), % 114.27/16.40 | | | | | | | | | | | | | | | 3) = v0 & div1($product(-15, sc_118_0_3), 3) % 114.27/16.40 | | | | | | | | | | | | | | | = v0) % 114.27/16.40 | | | | | | | | | | | | | | | % 114.27/16.40 | | | | | | | | | | | | | | | GROUND_INST: instantiating (8) with $difference(1, $product(15, % 114.27/16.40 | | | | | | | | | | | | | | | sc_118_0_3)), 5, 1, simplifying with (175) % 114.27/16.40 | | | | | | | | | | | | | | | gives: % 114.27/16.40 | | | | | | | | | | | | | | | (183) ~ ($lesseq(sc_118_0_3, 0) | ? [v0: int] : ( ~ % 114.27/16.40 | | | | | | | | | | | | | | | (v0 = 0) & mod1($difference(2, $product(15, % 114.27/16.40 | | | | | | | | | | | | | | | sc_118_0_3)), 5) = v0) % 114.27/16.40 | | | | | | | | | | | | | | | % 114.27/16.40 | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with $product(-15, sc_118_0_3), % 114.27/16.40 | | | | | | | | | | | | | | | 5, 1, simplifying with (175) gives: % 114.27/16.40 | | | | | | | | | | | | | | | (184) ~ ($lesseq(sc_118_0_3, 0) | ? [v0: int] : % 114.27/16.40 | | | | | | | | | | | | | | | (div1($difference(1, $product(15, sc_118_0_3)), % 114.27/16.40 | | | | | | | | | | | | | | | 5) = v0 & div1($product(-15, sc_118_0_3), 5) % 114.27/16.40 | | | | | | | | | | | | | | | = v0) % 114.27/16.40 | | | | | | | | | | | | | | | % 114.27/16.40 | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with $difference(1, $product(15, % 114.27/16.40 | | | | | | | | | | | | | | | sc_118_0_3)), 5, 1, simplifying with (175) % 114.27/16.40 | | | | | | | | | | | | | | | gives: % 114.27/16.40 | | | | | | | | | | | | | | | (185) ? [v0: int] : (div1($difference(1, $product(15, % 114.27/16.40 | | | | | | | | | | | | | | | sc_118_0_3)), 5) = v0 & $product(5, v0) = % 114.27/16.40 | | | | | | | | | | | | | | | $product(-15, sc_118_0_3)) % 114.27/16.40 | | | | | | | | | | | | | | | % 114.27/16.40 | | | | | | | | | | | | | | | GROUND_INST: instantiating (5) with $difference(1, $product(15, % 114.27/16.40 | | | | | | | | | | | | | | | sc_118_0_3)), 5, 1, simplifying with (175) % 114.27/16.40 | | | | | | | | | | | | | | | gives: % 114.27/16.40 | | | | | | | | | | | | | | | (186) ~ ($lesseq(sc_118_0_3, 0) | ? [v0: int] : % 114.27/16.40 | | | | | | | | | | | | | | | (mod1($difference(2, $product(15, sc_118_0_3)), % 114.27/16.40 | | | | | | | | | | | | | | | 5) = v0 & (v0 = 2 | v0 = 0)) % 114.27/16.40 | | | | | | | | | | | | | | | % 114.27/16.40 | | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with $difference(-2, % 114.27/16.40 | | | | | | | | | | | | | | | $product(15, sc_118_0_3)), 3, 2, simplifying % 114.27/16.40 | | | | | | | | | | | | | | | with (117) gives: % 114.27/16.40 | | | | | | | | | | | | | | | (187) ~ ($lesseq(sc_118_0_3, -1)) | % 114.27/16.40 | | | | | | | | | | | | | | | mod1($difference(-2, $product(15, sc_118_0_3)), 3) % 114.27/16.40 | | | | | | | | | | | | | | | = 1 % 114.27/16.40 | | | | | | | | | | | | | | | % 114.27/16.40 | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with $difference(-2, % 114.27/16.40 | | | | | | | | | | | | | | | $product(15, sc_118_0_3)), 3, 2, simplifying % 114.27/16.40 | | | | | | | | | | | | | | | with (117) gives: % 114.27/16.40 | | | | | | | | | | | | | | | (188) ~ ($lesseq(sc_118_0_3, -1)) | ? [v0: int] : % 114.27/16.40 | | | | | | | | | | | | | | | (div1($difference(-2, $product(15, sc_118_0_3)), % 114.27/16.40 | | | | | | | | | | | | | | | 3) = v0 & div1($difference(-1, $product(15, % 114.27/16.40 | | | | | | | | | | | | | | | sc_118_0_3)), 3) = v0) % 114.27/16.40 | | | | | | | | | | | | | | | % 114.27/16.40 | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with $difference(-2, % 114.27/16.40 | | | | | | | | | | | | | | | $product(15, sc_118_0_3)), 5, 4, simplifying % 114.27/16.40 | | | | | | | | | | | | | | | with (79) gives: % 114.27/16.40 | | | | | | | | | | | | | | | (189) ~ ($lesseq(sc_118_0_3, -1)) | ? [v0: int] : % 114.27/16.40 | | | | | | | | | | | | | | | (div1($difference(-2, $product(15, sc_118_0_3)), % 114.27/16.40 | | | | | | | | | | | | | | | 5) = v0 & div1($difference(-1, $product(15, % 114.27/16.40 | | | | | | | | | | | | | | | sc_118_0_3)), 5) = v0) % 114.27/16.40 | | | | | | | | | | | | | | | % 114.27/16.40 | | | | | | | | | | | | | | | GROUND_INST: instantiating (12) with $product(-15, sc_118_0_3), % 114.27/16.40 | | | | | | | | | | | | | | | $product(-3, sc_118_0_3), simplifying with (72) % 114.27/16.40 | | | | | | | | | | | | | | | gives: % 114.27/16.41 | | | | | | | | | | | | | | | (190) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? % 114.27/16.41 | | | | | | | | | | | | | | | [v3: int] : ? [v4: int] : ? [v5: int] : % 114.27/16.41 | | | | | | | | | | | | | | | ($sum($difference($difference($product(15, v5), % 114.27/16.41 | | | | | | | | | | | | | | | $product(5, v3)), $product(3, v2)), v0) = % 114.27/16.41 | | | | | | | | | | | | | | | 0 & closed_formula_aux1($product(-15, % 114.27/16.41 | | | | | | | | | | | | | | | sc_118_0_3)) = v0 & tr1(v4) = v5 & tr1(v1) = % 114.27/16.41 | | | | | | | | | | | | | | | v2 & tr1($product(-3, sc_118_0_3)) = v3 & % 114.27/16.41 | | | | | | | | | | | | | | | div1($product(-15, sc_118_0_3), 15) = v4 & % 114.27/16.41 | | | | | | | | | | | | | | | div1($product(-15, sc_118_0_3), 3) = v1) % 114.27/16.41 | | | | | | | | | | | | | | | % 114.27/16.41 | | | | | | | | | | | | | | | GROUND_INST: instantiating (rounds_toward_zero) with % 114.27/16.41 | | | | | | | | | | | | | | | $product(-15, sc_118_0_3), 5, $product(-3, % 114.27/16.41 | | | | | | | | | | | | | | | sc_118_0_3), simplifying with (72) gives: % 114.27/16.41 | | | | | | | | | | | | | | | (191) ? [v0: int] : ? [v1: int] : ? [v2: int] : % 114.27/16.41 | | | | | | | | | | | | | | | ($lesseq(v2, v0) & abs1(v1) = v2 & % 114.27/16.41 | | | | | | | | | | | | | | | abs1($product(-15, sc_118_0_3)) = v0 & % 114.27/16.41 | | | | | | | | | | | | | | | $product($product(-3, sc_118_0_3), 5) = v1) % 114.27/16.41 | | | | | | | | | | | | | | | % 114.27/16.41 | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with $difference(-1, % 114.27/16.41 | | | | | | | | | | | | | | | $product(15, sc_118_0_3)), $difference(-1, % 114.27/16.41 | | | | | | | | | | | | | | | $product(5, sc_118_0_3)), simplifying with (167) % 114.27/16.41 | | | | | | | | | | | | | | | gives: % 114.27/16.41 | | | | | | | | | | | | | | | (192) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? % 114.27/16.41 | | | | | | | | | | | | | | | [v3: int] : ? [v4: int] : ? [v5: int] : % 114.27/16.41 | | | | | | | | | | | | | | | ($sum($difference($difference($product(15, v5), % 114.27/16.41 | | | | | | | | | | | | | | | $product(5, v3)), $product(3, v1)), v0) = % 114.27/16.41 | | | | | | | | | | | | | | | 0 & closed_formula_aux1($difference(-1, % 114.27/16.41 | | | | | | | | | | | | | | | $product(15, sc_118_0_3))) = v0 & tr1(v4) = % 114.27/16.41 | | | | | | | | | | | | | | | v5 & tr1(v2) = v3 & tr1($difference(-1, % 114.27/16.41 | | | | | | | | | | | | | | | $product(5, sc_118_0_3))) = v1 & % 114.27/16.41 | | | | | | | | | | | | | | | div1($difference(-1, $product(15, sc_118_0_3)), % 114.27/16.41 | | | | | | | | | | | | | | | 15) = v4 & div1($difference(-1, $product(15, % 114.27/16.41 | | | | | | | | | | | | | | | sc_118_0_3)), 5) = v2) % 114.27/16.41 | | | | | | | | | | | | | | | % 114.27/16.41 | | | | | | | | | | | | | | | GROUND_INST: instantiating (12) with $difference(-1, % 114.27/16.41 | | | | | | | | | | | | | | | $product(15, sc_118_0_3)), $difference(-1, % 114.27/16.41 | | | | | | | | | | | | | | | $product(3, sc_118_0_3)), simplifying with (166) % 114.27/16.41 | | | | | | | | | | | | | | | gives: % 114.27/16.41 | | | | | | | | | | | | | | | (193) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? % 114.27/16.41 | | | | | | | | | | | | | | | [v3: int] : ? [v4: int] : ? [v5: int] : % 114.27/16.41 | | | | | | | | | | | | | | | ($sum($difference($difference($product(15, v5), % 114.27/16.41 | | | | | | | | | | | | | | | $product(5, v3)), $product(3, v2)), v0) = % 114.27/16.41 | | | | | | | | | | | | | | | 0 & closed_formula_aux1($difference(-1, % 114.27/16.41 | | | | | | | | | | | | | | | $product(15, sc_118_0_3))) = v0 & tr1(v4) = % 114.27/16.41 | | | | | | | | | | | | | | | v5 & tr1(v1) = v2 & tr1($difference(-1, % 114.27/16.41 | | | | | | | | | | | | | | | $product(3, sc_118_0_3))) = v3 & % 114.27/16.41 | | | | | | | | | | | | | | | div1($difference(-1, $product(15, sc_118_0_3)), % 114.27/16.41 | | | | | | | | | | | | | | | 15) = v4 & div1($difference(-1, $product(15, % 114.27/16.41 | | | | | | | | | | | | | | | sc_118_0_3)), 3) = v1) % 114.27/16.41 | | | | | | | | | | | | | | | % 114.27/16.41 | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with 0, all_78_0, simplifying % 114.27/16.41 | | | | | | | | | | | | | | | with (47) gives: % 114.27/16.41 | | | | | | | | | | | | | | | (194) ? [v0: int] : ? [v1: int] : ? [v2: int] : ((v2 % 114.27/16.41 | | | | | | | | | | | | | | | = all_78_0 & sum_multiple_3_5_lt1(0) = % 114.27/16.41 | | | | | | | | | | | | | | | all_78_0) | ( ~ (v1 = 0) & ~ (v0 = 0) & % 114.27/16.41 | | | | | | | | | | | | | | | mod1(0, 5) = v1 & mod1(0, 3) = v0)) % 114.27/16.41 | | | | | | | | | | | | | | | % 114.27/16.41 | | | | | | | | | | | | | | | GROUND_INST: instantiating (2) with $product(-15, sc_118_0_3), % 114.27/16.41 | | | | | | | | | | | | | | | $difference(all_76_0, $product(15, sc_118_0_3)), % 114.27/16.41 | | | | | | | | | | | | | | | simplifying with (165) gives: % 114.27/16.41 | | | | | | | | | | | | | | | (195) ~ ($lesseq(sc_118_0_3, 0) | ? [v0: int] : ? % 114.27/16.41 | | | | | | | | | | | | | | | [v1: int] : ? [v2: int] : % 114.27/16.41 | | | | | | | | | | | | | | | (($sum($difference(v2, all_76_0), $product(15, % 114.27/16.41 | | | | | | | | | | | | | | | sc_118_0_3)) = 0 & % 114.27/16.41 | | | | | | | | | | | | | | | sum_multiple_3_5_lt1($product(-15, % 114.27/16.41 | | | | | | | | | | | | | | | sc_118_0_3)) = $difference(all_76_0, % 114.27/16.41 | | | | | | | | | | | | | | | $product(15, sc_118_0_3))) | (v1 = 0 & % 114.27/16.41 | | | | | | | | | | | | | | | mod1($product(-15, sc_118_0_3), 5) = 0) | % 114.27/16.41 | | | | | | | | | | | | | | | (v0 = 0 & mod1($product(-15, sc_118_0_3), 3) = % 114.27/16.41 | | | | | | | | | | | | | | | 0)) % 114.27/16.41 | | | | | | | | | | | | | | | % 114.27/16.41 | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with $product(-15, sc_118_0_3), % 114.27/16.41 | | | | | | | | | | | | | | | all_135_0, simplifying with (87) gives: % 114.27/16.41 | | | | | | | | | | | | | | | (196) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? % 114.27/16.41 | | | | | | | | | | | | | | | [v3: int] : ? [v4: int] : ? [v5: int] : % 114.27/16.41 | | | | | | | | | | | | | | | ($sum($difference($difference($product(15, v5), % 114.27/16.41 | | | | | | | | | | | | | | | $product(5, v3)), $product(3, v1)), % 114.27/16.41 | | | | | | | | | | | | | | | all_135_0) = 0 & tr1(v4) = v5 & tr1(v2) = v3 & % 114.27/16.41 | | | | | | | | | | | | | | | tr1(v0) = v1 & div1($product(-15, sc_118_0_3), % 114.27/16.41 | | | | | | | | | | | | | | | 15) = v4 & div1($product(-15, sc_118_0_3), 5) % 114.27/16.41 | | | | | | | | | | | | | | | = v2 & div1($product(-15, sc_118_0_3), 3) = v0) % 114.27/16.41 | | | | | | | | | | | | | | | % 114.27/16.41 | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with $difference(-1, % 114.27/16.41 | | | | | | | | | | | | | | | $product(15, sc_118_0_3)), all_76_0, simplifying % 114.27/16.41 | | | | | | | | | | | | | | | with (70) gives: % 114.27/16.42 | | | | | | | | | | | | | | | (197) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? % 114.27/16.42 | | | | | | | | | | | | | | | [v3: int] : ? [v4: int] : ? [v5: int] : % 114.27/16.42 | | | | | | | | | | | | | | | ($sum($difference($difference($product(15, v5), % 114.27/16.42 | | | | | | | | | | | | | | | $product(5, v3)), $product(3, v1)), % 114.27/16.42 | | | | | | | | | | | | | | | all_76_0) = 0 & tr1(v4) = v5 & tr1(v2) = v3 & % 114.27/16.42 | | | | | | | | | | | | | | | tr1(v0) = v1 & div1($difference(-1, $product(15, % 114.27/16.42 | | | | | | | | | | | | | | | sc_118_0_3)), 15) = v4 & % 114.27/16.42 | | | | | | | | | | | | | | | div1($difference(-1, $product(15, sc_118_0_3)), % 114.27/16.42 | | | | | | | | | | | | | | | 5) = v2 & div1($difference(-1, $product(15, % 114.27/16.42 | | | | | | | | | | | | | | | sc_118_0_3)), 3) = v0) % 114.27/16.42 | | | | | | | | | | | | | | | % 114.27/16.42 | | | | | | | | | | | | | | | DELTA: instantiating (185) with fresh symbol all_243_0 % 114.27/16.42 | | | | | | | | | | | | | | | gives: % 114.27/16.42 | | | | | | | | | | | | | | | (198) div1($difference(1, $product(15, sc_118_0_3)), 5) % 114.27/16.42 | | | | | | | | | | | | | | | = all_243_0 & $product(5, all_243_0) = % 114.27/16.42 | | | | | | | | | | | | | | | $product(-15, sc_118_0_3) % 114.27/16.42 | | | | | | | | | | | | | | | % 114.27/16.42 | | | | | | | | | | | | | | | ALPHA: (198) implies: % 114.27/16.42 | | | | | | | | | | | | | | | (199) $product(5, all_243_0) = $product(-15, sc_118_0_3) % 114.27/16.42 | | | | | | | | | | | | | | | (200) div1($difference(1, $product(15, sc_118_0_3)), 5) % 114.27/16.42 | | | | | | | | | | | | | | | = all_243_0 % 114.27/16.42 | | | | | | | | | | | | | | | % 114.27/16.42 | | | | | | | | | | | | | | | DELTA: instantiating (181) with fresh symbol all_249_0 % 114.27/16.42 | | | | | | | | | | | | | | | gives: % 114.27/16.42 | | | | | | | | | | | | | | | (201) div1($product(-15, sc_118_0_3), 15) = all_249_0 & % 114.27/16.42 | | | | | | | | | | | | | | | $product(15, all_249_0) = $product(-15, % 114.27/16.42 | | | | | | | | | | | | | | | sc_118_0_3) % 114.27/16.42 | | | | | | | | | | | | | | | % 114.27/16.42 | | | | | | | | | | | | | | | ALPHA: (201) implies: % 114.27/16.42 | | | | | | | | | | | | | | | (202) $product(15, all_249_0) = $product(-15, % 114.27/16.42 | | | | | | | | | | | | | | | sc_118_0_3) % 114.27/16.42 | | | | | | | | | | | | | | | (203) div1($product(-15, sc_118_0_3), 15) = all_249_0 % 114.27/16.42 | | | | | | | | | | | | | | | % 114.27/16.42 | | | | | | | | | | | | | | | DELTA: instantiating (191) with fresh symbols all_263_0, % 114.27/16.42 | | | | | | | | | | | | | | | all_263_1, all_263_2 gives: % 114.27/16.42 | | | | | | | | | | | | | | | (204) $lesseq(all_263_0, all_263_2) & abs1(all_263_1) = % 114.27/16.42 | | | | | | | | | | | | | | | all_263_0 & abs1($product(-15, sc_118_0_3)) = % 114.27/16.42 | | | | | | | | | | | | | | | all_263_2 & $product($product(-3, sc_118_0_3), 5) % 114.27/16.42 | | | | | | | | | | | | | | | = all_263_1 % 114.27/16.42 | | | | | | | | | | | | | | | % 114.27/16.42 | | | | | | | | | | | | | | | ALPHA: (204) implies: % 114.27/16.42 | | | | | | | | | | | | | | | (205) $product($product(-3, sc_118_0_3), 5) = all_263_1 % 114.27/16.42 | | | | | | | | | | | | | | | % 114.27/16.42 | | | | | | | | | | | | | | | DELTA: instantiating (194) with fresh symbols all_273_0, % 114.27/16.42 | | | | | | | | | | | | | | | all_273_1, all_273_2 gives: % 114.27/16.42 | | | | | | | | | | | | | | | (206) (all_273_0 = all_78_0 & sum_multiple_3_5_lt1(0) = % 114.27/16.42 | | | | | | | | | | | | | | | all_78_0) | ( ~ (all_273_1 = 0) & ~ (all_273_2 % 114.27/16.42 | | | | | | | | | | | | | | | = 0) & mod1(0, 5) = all_273_1 & mod1(0, 3) = % 114.27/16.42 | | | | | | | | | | | | | | | all_273_2) % 114.27/16.42 | | | | | | | | | | | | | | | % 114.27/16.42 | | | | | | | | | | | | | | | DELTA: instantiating (192) with fresh symbols all_281_0, % 114.27/16.42 | | | | | | | | | | | | | | | all_281_1, all_281_2, all_281_3, all_281_4, % 114.27/16.42 | | | | | | | | | | | | | | | all_281_5 gives: % 114.27/16.42 | | | | | | | | | | | | | | | (207) $sum($difference($difference($product(15, % 114.27/16.42 | | | | | | | | | | | | | | | all_281_0), $product(5, all_281_2)), % 114.27/16.42 | | | | | | | | | | | | | | | $product(3, all_281_4)), all_281_5) = 0 & % 114.27/16.42 | | | | | | | | | | | | | | | closed_formula_aux1($difference(-1, $product(15, % 114.27/16.42 | | | | | | | | | | | | | | | sc_118_0_3))) = all_281_5 & tr1(all_281_1) = % 114.27/16.42 | | | | | | | | | | | | | | | all_281_0 & tr1(all_281_3) = all_281_2 & % 114.27/16.42 | | | | | | | | | | | | | | | tr1($difference(-1, $product(5, sc_118_0_3))) = % 114.27/16.42 | | | | | | | | | | | | | | | all_281_4 & div1($difference(-1, $product(15, % 114.27/16.42 | | | | | | | | | | | | | | | sc_118_0_3)), 15) = all_281_1 & % 114.27/16.42 | | | | | | | | | | | | | | | div1($difference(-1, $product(15, sc_118_0_3)), 5) % 114.27/16.42 | | | | | | | | | | | | | | | = all_281_3 % 114.27/16.42 | | | | | | | | | | | | | | | % 114.27/16.42 | | | | | | | | | | | | | | | ALPHA: (207) implies: % 114.27/16.42 | | | | | | | | | | | | | | | (208) div1($difference(-1, $product(15, sc_118_0_3)), 5) % 114.27/16.42 | | | | | | | | | | | | | | | = all_281_3 % 114.27/16.42 | | | | | | | | | | | | | | | (209) div1($difference(-1, $product(15, sc_118_0_3)), % 114.27/16.42 | | | | | | | | | | | | | | | 15) = all_281_1 % 114.27/16.42 | | | | | | | | | | | | | | | % 114.27/16.42 | | | | | | | | | | | | | | | DELTA: instantiating (190) with fresh symbols all_283_0, % 114.27/16.42 | | | | | | | | | | | | | | | all_283_1, all_283_2, all_283_3, all_283_4, % 114.27/16.42 | | | | | | | | | | | | | | | all_283_5 gives: % 114.27/16.42 | | | | | | | | | | | | | | | (210) $sum($difference($difference($product(15, % 114.27/16.42 | | | | | | | | | | | | | | | all_283_0), $product(5, all_283_2)), % 114.27/16.42 | | | | | | | | | | | | | | | $product(3, all_283_3)), all_283_5) = 0 & % 114.27/16.42 | | | | | | | | | | | | | | | closed_formula_aux1($product(-15, sc_118_0_3)) = % 114.27/16.42 | | | | | | | | | | | | | | | all_283_5 & tr1(all_283_1) = all_283_0 & % 114.27/16.42 | | | | | | | | | | | | | | | tr1(all_283_4) = all_283_3 & tr1($product(-3, % 114.27/16.42 | | | | | | | | | | | | | | | sc_118_0_3)) = all_283_2 & div1($product(-15, % 114.27/16.42 | | | | | | | | | | | | | | | sc_118_0_3), 15) = all_283_1 & % 114.27/16.42 | | | | | | | | | | | | | | | div1($product(-15, sc_118_0_3), 3) = all_283_4 % 114.27/16.42 | | | | | | | | | | | | | | | % 114.27/16.42 | | | | | | | | | | | | | | | ALPHA: (210) implies: % 114.27/16.42 | | | | | | | | | | | | | | | (211) div1($product(-15, sc_118_0_3), 3) = all_283_4 % 114.27/16.42 | | | | | | | | | | | | | | | (212) div1($product(-15, sc_118_0_3), 15) = all_283_1 % 114.27/16.42 | | | | | | | | | | | | | | | % 114.27/16.42 | | | | | | | | | | | | | | | DELTA: instantiating (193) with fresh symbols all_286_0, % 114.27/16.42 | | | | | | | | | | | | | | | all_286_1, all_286_2, all_286_3, all_286_4, % 114.27/16.42 | | | | | | | | | | | | | | | all_286_5 gives: % 114.27/16.42 | | | | | | | | | | | | | | | (213) $sum($difference($difference($product(15, % 114.27/16.42 | | | | | | | | | | | | | | | all_286_0), $product(5, all_286_2)), % 114.27/16.42 | | | | | | | | | | | | | | | $product(3, all_286_3)), all_286_5) = 0 & % 114.27/16.42 | | | | | | | | | | | | | | | closed_formula_aux1($difference(-1, $product(15, % 114.27/16.42 | | | | | | | | | | | | | | | sc_118_0_3))) = all_286_5 & tr1(all_286_1) = % 114.27/16.42 | | | | | | | | | | | | | | | all_286_0 & tr1(all_286_4) = all_286_3 & % 114.27/16.42 | | | | | | | | | | | | | | | tr1($difference(-1, $product(3, sc_118_0_3))) = % 114.27/16.42 | | | | | | | | | | | | | | | all_286_2 & div1($difference(-1, $product(15, % 114.27/16.42 | | | | | | | | | | | | | | | sc_118_0_3)), 15) = all_286_1 & % 114.27/16.42 | | | | | | | | | | | | | | | div1($difference(-1, $product(15, sc_118_0_3)), 3) % 114.27/16.42 | | | | | | | | | | | | | | | = all_286_4 % 114.27/16.42 | | | | | | | | | | | | | | | % 114.27/16.42 | | | | | | | | | | | | | | | ALPHA: (213) implies: % 114.27/16.42 | | | | | | | | | | | | | | | (214) div1($difference(-1, $product(15, sc_118_0_3)), 3) % 114.27/16.42 | | | | | | | | | | | | | | | = all_286_4 % 114.27/16.42 | | | | | | | | | | | | | | | % 114.27/16.42 | | | | | | | | | | | | | | | DELTA: instantiating (197) with fresh symbols all_288_0, % 114.27/16.42 | | | | | | | | | | | | | | | all_288_1, all_288_2, all_288_3, all_288_4, % 114.27/16.42 | | | | | | | | | | | | | | | all_288_5 gives: % 114.27/16.42 | | | | | | | | | | | | | | | (215) $sum($difference($difference($product(15, % 114.27/16.42 | | | | | | | | | | | | | | | all_288_0), $product(5, all_288_2)), % 114.27/16.42 | | | | | | | | | | | | | | | $product(3, all_288_4)), all_76_0) = 0 & % 114.27/16.42 | | | | | | | | | | | | | | | tr1(all_288_1) = all_288_0 & tr1(all_288_3) = % 114.27/16.42 | | | | | | | | | | | | | | | all_288_2 & tr1(all_288_5) = all_288_4 & % 114.27/16.42 | | | | | | | | | | | | | | | div1($difference(-1, $product(15, sc_118_0_3)), % 114.27/16.42 | | | | | | | | | | | | | | | 15) = all_288_1 & div1($difference(-1, % 114.27/16.42 | | | | | | | | | | | | | | | $product(15, sc_118_0_3)), 5) = all_288_3 & % 114.27/16.42 | | | | | | | | | | | | | | | div1($difference(-1, $product(15, sc_118_0_3)), 3) % 114.27/16.42 | | | | | | | | | | | | | | | = all_288_5 % 114.27/16.42 | | | | | | | | | | | | | | | % 114.27/16.42 | | | | | | | | | | | | | | | ALPHA: (215) implies: % 114.27/16.42 | | | | | | | | | | | | | | | (216) $sum($difference($difference($product(15, % 114.27/16.42 | | | | | | | | | | | | | | | all_288_0), $product(5, all_288_2)), % 114.27/16.42 | | | | | | | | | | | | | | | $product(3, all_288_4)), all_76_0) = 0 % 114.27/16.43 | | | | | | | | | | | | | | | (217) div1($difference(-1, $product(15, sc_118_0_3)), 3) % 114.27/16.43 | | | | | | | | | | | | | | | = all_288_5 % 114.27/16.43 | | | | | | | | | | | | | | | (218) div1($difference(-1, $product(15, sc_118_0_3)), 5) % 114.27/16.43 | | | | | | | | | | | | | | | = all_288_3 % 114.27/16.43 | | | | | | | | | | | | | | | (219) div1($difference(-1, $product(15, sc_118_0_3)), % 114.27/16.43 | | | | | | | | | | | | | | | 15) = all_288_1 % 114.27/16.43 | | | | | | | | | | | | | | | (220) tr1(all_288_5) = all_288_4 % 114.27/16.43 | | | | | | | | | | | | | | | (221) tr1(all_288_3) = all_288_2 % 114.27/16.43 | | | | | | | | | | | | | | | (222) tr1(all_288_1) = all_288_0 % 114.27/16.43 | | | | | | | | | | | | | | | % 114.27/16.43 | | | | | | | | | | | | | | | DELTA: instantiating (196) with fresh symbols all_290_0, % 114.27/16.43 | | | | | | | | | | | | | | | all_290_1, all_290_2, all_290_3, all_290_4, % 114.27/16.43 | | | | | | | | | | | | | | | all_290_5 gives: % 114.27/16.43 | | | | | | | | | | | | | | | (223) $sum($difference($difference($product(15, % 114.27/16.43 | | | | | | | | | | | | | | | all_290_0), $product(5, all_290_2)), % 114.27/16.43 | | | | | | | | | | | | | | | $product(3, all_290_4)), all_135_0) = 0 & % 114.27/16.43 | | | | | | | | | | | | | | | tr1(all_290_1) = all_290_0 & tr1(all_290_3) = % 114.27/16.43 | | | | | | | | | | | | | | | all_290_2 & tr1(all_290_5) = all_290_4 & % 114.27/16.43 | | | | | | | | | | | | | | | div1($product(-15, sc_118_0_3), 15) = all_290_1 & % 114.27/16.43 | | | | | | | | | | | | | | | div1($product(-15, sc_118_0_3), 5) = all_290_3 & % 114.27/16.43 | | | | | | | | | | | | | | | div1($product(-15, sc_118_0_3), 3) = all_290_5 % 114.27/16.43 | | | | | | | | | | | | | | | % 114.27/16.43 | | | | | | | | | | | | | | | ALPHA: (223) implies: % 114.27/16.43 | | | | | | | | | | | | | | | (224) $sum($difference($difference($product(15, % 114.27/16.43 | | | | | | | | | | | | | | | all_290_0), $product(5, all_290_2)), % 114.27/16.43 | | | | | | | | | | | | | | | $product(3, all_290_4)), all_135_0) = 0 % 114.27/16.43 | | | | | | | | | | | | | | | (225) div1($product(-15, sc_118_0_3), 3) = all_290_5 % 114.27/16.43 | | | | | | | | | | | | | | | (226) div1($product(-15, sc_118_0_3), 5) = all_290_3 % 114.27/16.43 | | | | | | | | | | | | | | | (227) div1($product(-15, sc_118_0_3), 15) = all_290_1 % 114.27/16.43 | | | | | | | | | | | | | | | (228) tr1(all_290_5) = all_290_4 % 114.27/16.43 | | | | | | | | | | | | | | | (229) tr1(all_290_3) = all_290_2 % 114.27/16.43 | | | | | | | | | | | | | | | (230) tr1(all_290_1) = all_290_0 % 114.27/16.43 | | | | | | | | | | | | | | | % 114.27/16.43 | | | | | | | | | | | | | | | COL_REDUCE: introducing fresh symbol sc_294_0_3 defined by: % 114.27/16.43 | | | | | | | | | | | | | | | (231) all_290_0 = sc_294_0_3 % 114.27/16.43 | | | | | | | | | | | | | | | % 114.27/16.43 | | | | | | | | | | | | | | | COMBINE_EQS: (224), (231) imply: % 114.27/16.43 | | | | | | | | | | | | | | | (232) $difference($sum($product(5, all_290_2), % 114.27/16.43 | | | | | | | | | | | | | | | $product(3, all_290_4)), all_135_0) = % 114.27/16.43 | | | | | | | | | | | | | | | $product(15, sc_294_0_3) % 114.27/16.43 | | | | | | | | | | | | | | | % 114.27/16.43 | | | | | | | | | | | | | | | SIMP: (232) implies: % 114.27/16.43 | | | | | | | | | | | | | | | (233) $difference($sum($product(5, all_290_2), % 114.27/16.43 | | | | | | | | | | | | | | | $product(3, all_290_4)), all_135_0) = % 114.27/16.43 | | | | | | | | | | | | | | | $product(15, sc_294_0_3) % 114.27/16.43 | | | | | | | | | | | | | | | % 114.27/16.43 | | | | | | | | | | | | | | | COL_REDUCE: introducing fresh symbol sc_294_0_4 defined by: % 114.27/16.43 | | | | | | | | | | | | | | | (234) $difference($sum(all_290_2, all_290_4), % 114.27/16.43 | | | | | | | | | | | | | | | $product(3, sc_294_0_3)) = sc_294_0_4 % 114.27/16.43 | | | | | | | | | | | | | | | % 114.27/16.43 | | | | | | | | | | | | | | | COMBINE_EQS: (233), (234) imply: % 114.27/16.43 | | | | | | | | | | | | | | | (235) $sum($product(2, all_290_4), all_135_0) = % 114.27/16.43 | | | | | | | | | | | | | | | $product(5, sc_294_0_4) % 114.27/16.43 | | | | | | | | | | | | | | | % 114.27/16.43 | | | | | | | | | | | | | | | SIMP: (235) implies: % 114.27/16.43 | | | | | | | | | | | | | | | (236) $sum($product(2, all_290_4), all_135_0) = % 114.27/16.43 | | | | | | | | | | | | | | | $product(5, sc_294_0_4) % 114.27/16.43 | | | | | | | | | | | | | | | % 114.27/16.43 | | | | | | | | | | | | | | | COL_REDUCE: introducing fresh symbol sc_294_0_5 defined by: % 114.27/16.43 | | | | | | | | | | | | | | | (237) $difference(all_290_4, $product(3, sc_294_0_4)) = % 114.27/16.43 | | | | | | | | | | | | | | | sc_294_0_5 % 114.27/16.43 | | | | | | | | | | | | | | | % 114.27/16.43 | | | | | | | | | | | | | | | COMBINE_EQS: (236), (237) imply: % 114.27/16.43 | | | | | | | | | | | | | | | (238) $sum($sum(all_135_0, sc_294_0_4), $product(2, % 114.27/16.43 | | | | | | | | | | | | | | | sc_294_0_5)) = 0 % 114.27/16.43 | | | | | | | | | | | | | | | % 114.27/16.43 | | | | | | | | | | | | | | | COMBINE_EQS: (234), (237) imply: % 114.27/16.43 | | | | | | | | | | | | | | | (239) $sum($sum($difference(all_290_2, $product(3, % 114.27/16.43 | | | | | | | | | | | | | | | sc_294_0_3)), $product(2, sc_294_0_4)), % 114.27/16.43 | | | | | | | | | | | | | | | sc_294_0_5) = 0 % 114.27/16.43 | | | | | | | | | | | | | | | % 114.27/16.43 | | | | | | | | | | | | | | | COL_REDUCE: introducing fresh symbol sc_294_0_6 defined by: % 114.27/16.43 | | | | | | | | | | | | | | | (240) all_288_0 = sc_294_0_6 % 114.27/16.43 | | | | | | | | | | | | | | | % 114.27/16.43 | | | | | | | | | | | | | | | COMBINE_EQS: (216), (240) imply: % 114.27/16.43 | | | | | | | | | | | | | | | (241) $difference($sum($product(5, all_288_2), % 114.27/16.43 | | | | | | | | | | | | | | | $product(3, all_288_4)), all_76_0) = % 114.27/16.43 | | | | | | | | | | | | | | | $product(15, sc_294_0_6) % 114.27/16.43 | | | | | | | | | | | | | | | % 114.27/16.43 | | | | | | | | | | | | | | | SIMP: (241) implies: % 114.27/16.43 | | | | | | | | | | | | | | | (242) $difference($sum($product(5, all_288_2), % 114.27/16.43 | | | | | | | | | | | | | | | $product(3, all_288_4)), all_76_0) = % 114.27/16.43 | | | | | | | | | | | | | | | $product(15, sc_294_0_6) % 114.27/16.43 | | | | | | | | | | | | | | | % 114.27/16.43 | | | | | | | | | | | | | | | COL_REDUCE: introducing fresh symbol sc_294_0_7 defined by: % 114.27/16.43 | | | | | | | | | | | | | | | (243) $difference($sum(all_288_2, all_288_4), % 114.27/16.43 | | | | | | | | | | | | | | | $product(3, sc_294_0_6)) = sc_294_0_7 % 114.27/16.43 | | | | | | | | | | | | | | | % 114.27/16.43 | | | | | | | | | | | | | | | COMBINE_EQS: (242), (243) imply: % 114.27/16.43 | | | | | | | | | | | | | | | (244) $sum($product(2, all_288_4), all_76_0) = % 114.27/16.43 | | | | | | | | | | | | | | | $product(5, sc_294_0_7) % 114.27/16.43 | | | | | | | | | | | | | | | % 114.27/16.43 | | | | | | | | | | | | | | | SIMP: (244) implies: % 114.27/16.43 | | | | | | | | | | | | | | | (245) $sum($product(2, all_288_4), all_76_0) = % 114.27/16.43 | | | | | | | | | | | | | | | $product(5, sc_294_0_7) % 114.27/16.43 | | | | | | | | | | | | | | | % 114.27/16.43 | | | | | | | | | | | | | | | COL_REDUCE: introducing fresh symbol sc_294_0_8 defined by: % 114.27/16.43 | | | | | | | | | | | | | | | (246) $difference(all_288_4, $product(3, sc_294_0_7)) = % 114.27/16.43 | | | | | | | | | | | | | | | sc_294_0_8 % 114.27/16.43 | | | | | | | | | | | | | | | % 115.07/16.43 | | | | | | | | | | | | | | | COMBINE_EQS: (245), (246) imply: % 115.07/16.43 | | | | | | | | | | | | | | | (247) $sum($sum(all_76_0, sc_294_0_7), $product(2, % 115.07/16.43 | | | | | | | | | | | | | | | sc_294_0_8)) = 0 % 115.07/16.43 | | | | | | | | | | | | | | | % 115.07/16.43 | | | | | | | | | | | | | | | COMBINE_EQS: (243), (246) imply: % 115.07/16.43 | | | | | | | | | | | | | | | (248) $sum($sum($difference(all_288_2, $product(3, % 115.07/16.43 | | | | | | | | | | | | | | | sc_294_0_6)), $product(2, sc_294_0_7)), % 115.07/16.43 | | | | | | | | | | | | | | | sc_294_0_8) = 0 % 115.07/16.43 | | | | | | | | | | | | | | | % 115.07/16.43 | | | | | | | | | | | | | | | REDUCE: (164), (238), (247) imply: % 115.07/16.43 | | | | | | | | | | | | | | | (249) ~ ($difference($difference($sum(sc_294_0_4, % 115.07/16.43 | | | | | | | | | | | | | | | $product(2, sc_294_0_5)), sc_294_0_7), % 115.07/16.43 | | | | | | | | | | | | | | | $product(2, sc_294_0_8)) = $product(15, % 115.07/16.43 | | | | | | | | | | | | | | | sc_118_0_3)) % 115.07/16.43 | | | | | | | | | | | | | | | % 115.07/16.43 | | | | | | | | | | | | | | | SIMP: (249) implies: % 115.07/16.43 | | | | | | | | | | | | | | | (250) ~ ($difference($difference($sum(sc_294_0_4, % 115.07/16.43 | | | | | | | | | | | | | | | $product(2, sc_294_0_5)), sc_294_0_7), % 115.07/16.43 | | | | | | | | | | | | | | | $product(2, sc_294_0_8)) = $product(15, % 115.07/16.43 | | | | | | | | | | | | | | | sc_118_0_3)) % 115.07/16.43 | | | | | | | | | | | | | | | % 115.07/16.43 | | | | | | | | | | | | | | | REDUCE: (230), (231) imply: % 115.07/16.43 | | | | | | | | | | | | | | | (251) tr1(all_290_1) = sc_294_0_3 % 115.07/16.43 | | | | | | | | | | | | | | | % 115.07/16.43 | | | | | | | | | | | | | | | REDUCE: (229), (239) imply: % 115.07/16.43 | | | | | | | | | | | | | | | (252) tr1(all_290_3) = % 115.07/16.43 | | | | | | | | | | | | | | | $difference($difference($product(3, sc_294_0_3), % 115.07/16.44 | | | | | | | | | | | | | | | $product(2, sc_294_0_4)), sc_294_0_5) % 115.07/16.44 | | | | | | | | | | | | | | | % 115.07/16.44 | | | | | | | | | | | | | | | REDUCE: (228), (237) imply: % 115.07/16.44 | | | | | | | | | | | | | | | (253) tr1(all_290_5) = $sum($product(3, sc_294_0_4), % 115.07/16.44 | | | | | | | | | | | | | | | sc_294_0_5) % 115.07/16.44 | | | | | | | | | | | | | | | % 115.07/16.44 | | | | | | | | | | | | | | | REDUCE: (222), (240) imply: % 115.07/16.44 | | | | | | | | | | | | | | | (254) tr1(all_288_1) = sc_294_0_6 % 115.07/16.44 | | | | | | | | | | | | | | | % 115.07/16.44 | | | | | | | | | | | | | | | REDUCE: (221), (248) imply: % 115.07/16.44 | | | | | | | | | | | | | | | (255) tr1(all_288_3) = % 115.07/16.44 | | | | | | | | | | | | | | | $difference($difference($product(3, sc_294_0_6), % 115.07/16.44 | | | | | | | | | | | | | | | $product(2, sc_294_0_7)), sc_294_0_8) % 115.07/16.44 | | | | | | | | | | | | | | | % 115.07/16.44 | | | | | | | | | | | | | | | REDUCE: (220), (246) imply: % 115.07/16.44 | | | | | | | | | | | | | | | (256) tr1(all_288_5) = $sum($product(3, sc_294_0_7), % 115.07/16.44 | | | | | | | | | | | | | | | sc_294_0_8) % 115.07/16.44 | | | | | | | | | | | | | | | % 115.07/16.44 | | | | | | | | | | | | | | | THEORY_AXIOM GroebnerMultiplication: % 115.07/16.44 | | | | | | | | | | | | | | | (257) ! [v0: int] : ! [v1: int] : ! [v2: int] : (v2 = % 115.07/16.44 | | | | | | | | | | | | | | | $product(5, v1) | ~ ($product($product(-3, v0), % 115.07/16.44 | | | | | | | | | | | | | | | 5) = v2) | ~ ($product(5, v1) = % 115.07/16.44 | | | | | | | | | | | | | | | $product(-15, v0))) % 115.07/16.44 | | | | | | | | | | | | | | | % 115.07/16.44 | | | | | | | | | | | | | | | GROUND_INST: instantiating (257) with sc_118_0_3, all_243_0, % 115.07/16.44 | | | | | | | | | | | | | | | all_263_1, simplifying with (199), (205) gives: % 115.07/16.44 | | | | | | | | | | | | | | | (258) all_263_1 = $product(5, all_243_0) % 115.07/16.44 | | | | | | | | | | | | | | | % 115.07/16.44 | | | | | | | | | | | | | | | THEORY_AXIOM GroebnerMultiplication: % 115.07/16.44 | | | | | | | | | | | | | | | (259) ! [v0: int] : ! [v1: int] : ! [v2: int] : ! % 115.07/16.44 | | | | | | | | | | | | | | | [v3: int] : (v3 = $product(15, v2) | ~ % 115.07/16.44 | | | | | | | | | | | | | | | ($product($product(-3, v0), 5) = v3) | ~ % 115.07/16.44 | | | | | | | | | | | | | | | ($product(15, v2) = $product(-15, v0)) | ~ % 115.07/16.44 | | | | | | | | | | | | | | | ($product(5, v1) = $product(-15, v0))) % 115.07/16.44 | | | | | | | | | | | | | | | % 115.07/16.44 | | | | | | | | | | | | | | | GROUND_INST: instantiating (259) with sc_118_0_3, all_243_0, % 115.07/16.44 | | | | | | | | | | | | | | | all_249_0, all_263_1, simplifying with (199), % 115.07/16.44 | | | | | | | | | | | | | | | (202), (205) gives: % 115.07/16.44 | | | | | | | | | | | | | | | (260) all_263_1 = $product(15, all_249_0) % 115.07/16.44 | | | | | | | | | | | | | | | % 115.07/16.44 | | | | | | | | | | | | | | | THEORY_AXIOM GroebnerMultiplication: % 115.07/16.44 | | | | | | | | | | | | | | | (261) ! [v0: int] : ! [v1: int] : ! [v2: int] : % 115.07/16.44 | | | | | | | | | | | | | | | ($sum(v2, $product(15, v0)) = 0 | ~ % 115.07/16.44 | | | | | | | | | | | | | | | ($product($product(-3, v0), 5) = v2) | ~ % 115.07/16.44 | | | | | | | | | | | | | | | ($product(5, v1) = $product(-15, v0))) % 115.07/16.44 | | | | | | | | | | | | | | | % 115.07/16.44 | | | | | | | | | | | | | | | GROUND_INST: instantiating (261) with sc_118_0_3, all_243_0, % 115.07/16.44 | | | | | | | | | | | | | | | all_263_1, simplifying with (199), (205) gives: % 115.07/16.44 | | | | | | | | | | | | | | | (262) $sum(all_263_1, $product(15, sc_118_0_3)) = 0 % 115.07/16.44 | | | | | | | | | | | | | | | % 115.07/16.44 | | | | | | | | | | | | | | | COMBINE_EQS: (258), (262) imply: % 115.07/16.44 | | | | | | | | | | | | | | | (263) $sum(all_243_0, $product(3, sc_118_0_3)) = 0 % 115.07/16.44 | | | | | | | | | | | | | | | % 115.07/16.44 | | | | | | | | | | | | | | | SIMP: (263) implies: % 115.07/16.44 | | | | | | | | | | | | | | | (264) $sum(all_243_0, $product(3, sc_118_0_3)) = 0 % 115.07/16.44 | | | | | | | | | | | | | | | % 115.07/16.44 | | | | | | | | | | | | | | | COMBINE_EQS: (258), (260) imply: % 115.07/16.44 | | | | | | | | | | | | | | | (265) $product(3, all_249_0) = all_243_0 % 115.07/16.44 | | | | | | | | | | | | | | | % 115.07/16.44 | | | | | | | | | | | | | | | SIMP: (265) implies: % 115.07/16.44 | | | | | | | | | | | | | | | (266) $product(3, all_249_0) = all_243_0 % 115.07/16.44 | | | | | | | | | | | | | | | % 115.07/16.44 | | | | | | | | | | | | | | | COMBINE_EQS: (264), (266) imply: % 115.07/16.44 | | | | | | | | | | | | | | | (267) $sum(all_249_0, sc_118_0_3) = 0 % 115.07/16.44 | | | | | | | | | | | | | | | % 115.07/16.44 | | | | | | | | | | | | | | | SIMP: (267) implies: % 115.07/16.44 | | | | | | | | | | | | | | | (268) $sum(all_249_0, sc_118_0_3) = 0 % 115.07/16.44 | | | | | | | | | | | | | | | % 115.07/16.44 | | | | | | | | | | | | | | | REDUCE: (200), (264) imply: % 115.07/16.44 | | | | | | | | | | | | | | | (269) div1($difference(1, $product(15, sc_118_0_3)), 5) % 115.07/16.44 | | | | | | | | | | | | | | | = $product(-3, sc_118_0_3) % 115.07/16.44 | | | | | | | | | | | | | | | % 115.07/16.44 | | | | | | | | | | | | | | | REDUCE: (203), (268) imply: % 115.07/16.44 | | | | | | | | | | | | | | | (270) div1($product(-15, sc_118_0_3), 15) = $product(-1, % 115.07/16.44 | | | | | | | | | | | | | | | sc_118_0_3) % 115.07/16.44 | | | | | | | | | | | | | | | % 115.07/16.44 | | | | | | | | | | | | | | | BETA: splitting (180) gives: % 115.07/16.44 | | | | | | | | | | | | | | | % 115.07/16.44 | | | | | | | | | | | | | | | Case 1: % 115.07/16.44 | | | | | | | | | | | | | | | | % 115.07/16.44 | | | | | | | | | | | | | | | | (271) $lesseq(0, sc_118_0_3) % 115.07/16.44 | | | | | | | | | | | | | | | | % 115.07/16.44 | | | | | | | | | | | | | | | | COMBINE_INEQS: (69), (271) imply: % 115.07/16.44 | | | | | | | | | | | | | | | | (272) $false % 115.07/16.44 | | | | | | | | | | | | | | | | % 115.07/16.44 | | | | | | | | | | | | | | | | CLOSE: (272) is inconsistent. % 115.07/16.44 | | | | | | | | | | | | | | | | % 115.07/16.44 | | | | | | | | | | | | | | | Case 2: % 115.07/16.44 | | | | | | | | | | | | | | | | % 115.07/16.44 | | | | | | | | | | | | | | | | (273) ? [v0: int] : (div1($difference(-1, $product(15, % 115.07/16.44 | | | | | | | | | | | | | | | | sc_118_0_3)), 15) = $sum(v0, -1) & % 115.07/16.44 | | | | | | | | | | | | | | | | div1($product(-15, sc_118_0_3), 15) = v0) % 115.07/16.44 | | | | | | | | | | | | | | | | % 115.07/16.44 | | | | | | | | | | | | | | | | DELTA: instantiating (273) with fresh symbol all_315_0 % 115.07/16.44 | | | | | | | | | | | | | | | | gives: % 115.07/16.44 | | | | | | | | | | | | | | | | (274) div1($difference(-1, $product(15, sc_118_0_3)), % 115.07/16.44 | | | | | | | | | | | | | | | | 15) = $sum(all_315_0, -1) & div1($product(-15, % 115.07/16.44 | | | | | | | | | | | | | | | | sc_118_0_3), 15) = all_315_0 % 115.07/16.44 | | | | | | | | | | | | | | | | % 115.07/16.44 | | | | | | | | | | | | | | | | ALPHA: (274) implies: % 115.07/16.44 | | | | | | | | | | | | | | | | (275) div1($product(-15, sc_118_0_3), 15) = all_315_0 % 115.07/16.44 | | | | | | | | | | | | | | | | (276) div1($difference(-1, $product(15, sc_118_0_3)), % 115.07/16.44 | | | | | | | | | | | | | | | | 15) = $sum(all_315_0, -1) % 115.07/16.44 | | | | | | | | | | | | | | | | % 115.07/16.44 | | | | | | | | | | | | | | | | BETA: splitting (184) gives: % 115.07/16.44 | | | | | | | | | | | | | | | | % 115.07/16.44 | | | | | | | | | | | | | | | | Case 1: % 115.07/16.44 | | | | | | | | | | | | | | | | | % 115.07/16.44 | | | | | | | | | | | | | | | | | (277) $lesseq(1, sc_118_0_3) % 115.07/16.44 | | | | | | | | | | | | | | | | | % 115.07/16.44 | | | | | | | | | | | | | | | | | COMBINE_INEQS: (69), (277) imply: % 115.07/16.44 | | | | | | | | | | | | | | | | | (278) $false % 115.07/16.44 | | | | | | | | | | | | | | | | | % 115.07/16.44 | | | | | | | | | | | | | | | | | CLOSE: (278) is inconsistent. % 115.07/16.44 | | | | | | | | | | | | | | | | | % 115.07/16.44 | | | | | | | | | | | | | | | | Case 2: % 115.07/16.44 | | | | | | | | | | | | | | | | | % 115.07/16.44 | | | | | | | | | | | | | | | | | (279) ? [v0: int] : (div1($difference(1, $product(15, % 115.07/16.45 | | | | | | | | | | | | | | | | | sc_118_0_3)), 5) = v0 & div1($product(-15, % 115.07/16.45 | | | | | | | | | | | | | | | | | sc_118_0_3), 5) = v0) % 115.07/16.45 | | | | | | | | | | | | | | | | | % 115.07/16.45 | | | | | | | | | | | | | | | | | DELTA: instantiating (279) with fresh symbol all_328_0 % 115.07/16.45 | | | | | | | | | | | | | | | | | gives: % 115.07/16.45 | | | | | | | | | | | | | | | | | (280) div1($difference(1, $product(15, sc_118_0_3)), 5) % 115.07/16.45 | | | | | | | | | | | | | | | | | = all_328_0 & div1($product(-15, sc_118_0_3), 5) = % 115.07/16.45 | | | | | | | | | | | | | | | | | all_328_0 % 115.07/16.45 | | | | | | | | | | | | | | | | | % 115.07/16.45 | | | | | | | | | | | | | | | | | ALPHA: (280) implies: % 115.07/16.45 | | | | | | | | | | | | | | | | | (281) div1($product(-15, sc_118_0_3), 5) = all_328_0 % 115.07/16.45 | | | | | | | | | | | | | | | | | (282) div1($difference(1, $product(15, sc_118_0_3)), 5) % 115.07/16.45 | | | | | | | | | | | | | | | | | = all_328_0 % 115.07/16.45 | | | | | | | | | | | | | | | | | % 115.07/16.45 | | | | | | | | | | | | | | | | | BETA: splitting (189) gives: % 115.07/16.45 | | | | | | | | | | | | | | | | | % 115.07/16.45 | | | | | | | | | | | | | | | | | Case 1: % 115.07/16.45 | | | | | | | | | | | | | | | | | | % 115.07/16.45 | | | | | | | | | | | | | | | | | | (283) $lesseq(0, sc_118_0_3) % 115.07/16.45 | | | | | | | | | | | | | | | | | | % 115.07/16.45 | | | | | | | | | | | | | | | | | | COMBINE_INEQS: (69), (283) imply: % 115.07/16.45 | | | | | | | | | | | | | | | | | | (284) $false % 115.07/16.45 | | | | | | | | | | | | | | | | | | % 115.07/16.45 | | | | | | | | | | | | | | | | | | CLOSE: (284) is inconsistent. % 115.07/16.45 | | | | | | | | | | | | | | | | | | % 115.07/16.45 | | | | | | | | | | | | | | | | | Case 2: % 115.07/16.45 | | | | | | | | | | | | | | | | | | % 115.07/16.45 | | | | | | | | | | | | | | | | | | (285) ? [v0: int] : (div1($difference(-2, $product(15, % 115.07/16.45 | | | | | | | | | | | | | | | | | | sc_118_0_3)), 5) = v0 & % 115.07/16.45 | | | | | | | | | | | | | | | | | | div1($difference(-1, $product(15, sc_118_0_3)), % 115.07/16.45 | | | | | | | | | | | | | | | | | | 5) = v0) % 115.07/16.45 | | | | | | | | | | | | | | | | | | % 115.07/16.45 | | | | | | | | | | | | | | | | | | DELTA: instantiating (285) with fresh symbol all_350_0 % 115.07/16.45 | | | | | | | | | | | | | | | | | | gives: % 115.07/16.45 | | | | | | | | | | | | | | | | | | (286) div1($difference(-2, $product(15, sc_118_0_3)), 5) % 115.07/16.45 | | | | | | | | | | | | | | | | | | = all_350_0 & div1($difference(-1, $product(15, % 115.07/16.45 | | | | | | | | | | | | | | | | | | sc_118_0_3)), 5) = all_350_0 % 115.07/16.45 | | | | | | | | | | | | | | | | | | % 115.07/16.45 | | | | | | | | | | | | | | | | | | ALPHA: (286) implies: % 115.07/16.45 | | | | | | | | | | | | | | | | | | (287) div1($difference(-1, $product(15, sc_118_0_3)), 5) % 115.07/16.45 | | | | | | | | | | | | | | | | | | = all_350_0 % 115.07/16.45 | | | | | | | | | | | | | | | | | | % 115.07/16.45 | | | | | | | | | | | | | | | | | | BETA: splitting (187) gives: % 115.07/16.45 | | | | | | | | | | | | | | | | | | % 115.07/16.45 | | | | | | | | | | | | | | | | | | Case 1: % 115.07/16.45 | | | | | | | | | | | | | | | | | | | % 115.07/16.45 | | | | | | | | | | | | | | | | | | | (288) mod1($difference(-2, $product(15, sc_118_0_3)), 3) % 115.07/16.45 | | | | | | | | | | | | | | | | | | | = 1 % 115.07/16.45 | | | | | | | | | | | | | | | | | | | % 115.07/16.45 | | | | | | | | | | | | | | | | | | | BETA: splitting (183) gives: % 115.07/16.45 | | | | | | | | | | | | | | | | | | | % 115.07/16.45 | | | | | | | | | | | | | | | | | | | Case 1: % 115.07/16.45 | | | | | | | | | | | | | | | | | | | | % 115.07/16.45 | | | | | | | | | | | | | | | | | | | | (289) $lesseq(1, sc_118_0_3) % 115.07/16.45 | | | | | | | | | | | | | | | | | | | | % 115.07/16.45 | | | | | | | | | | | | | | | | | | | | COMBINE_INEQS: (69), (289) imply: % 115.07/16.45 | | | | | | | | | | | | | | | | | | | | (290) $false % 115.07/16.45 | | | | | | | | | | | | | | | | | | | | % 115.07/16.45 | | | | | | | | | | | | | | | | | | | | CLOSE: (290) is inconsistent. % 115.07/16.45 | | | | | | | | | | | | | | | | | | | | % 115.07/16.45 | | | | | | | | | | | | | | | | | | | Case 2: % 115.07/16.45 | | | | | | | | | | | | | | | | | | | | % 115.07/16.45 | | | | | | | | | | | | | | | | | | | | (291) ? [v0: int] : ( ~ (v0 = 0) & mod1($difference(2, % 115.07/16.45 | | | | | | | | | | | | | | | | | | | | $product(15, sc_118_0_3)), 5) = v0) % 115.07/16.45 | | | | | | | | | | | | | | | | | | | | % 115.07/16.45 | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (291) with fresh symbol all_403_0 % 115.07/16.45 | | | | | | | | | | | | | | | | | | | | gives: % 115.07/16.45 | | | | | | | | | | | | | | | | | | | | (292) ~ (all_403_0 = 0) & mod1($difference(2, % 115.07/16.45 | | | | | | | | | | | | | | | | | | | | $product(15, sc_118_0_3)), 5) = all_403_0 % 115.07/16.45 | | | | | | | | | | | | | | | | | | | | % 115.07/16.45 | | | | | | | | | | | | | | | | | | | | ALPHA: (292) implies: % 115.07/16.45 | | | | | | | | | | | | | | | | | | | | (293) ~ (all_403_0 = 0) % 115.07/16.45 | | | | | | | | | | | | | | | | | | | | (294) mod1($difference(2, $product(15, sc_118_0_3)), 5) % 115.07/16.45 | | | | | | | | | | | | | | | | | | | | = all_403_0 % 115.07/16.45 | | | | | | | | | | | | | | | | | | | | % 115.07/16.45 | | | | | | | | | | | | | | | | | | | | BETA: splitting (182) gives: % 115.07/16.45 | | | | | | | | | | | | | | | | | | | | % 115.07/16.45 | | | | | | | | | | | | | | | | | | | | Case 1: % 115.07/16.45 | | | | | | | | | | | | | | | | | | | | | % 115.07/16.45 | | | | | | | | | | | | | | | | | | | | | (295) $lesseq(1, sc_118_0_3) % 115.07/16.45 | | | | | | | | | | | | | | | | | | | | | % 115.07/16.45 | | | | | | | | | | | | | | | | | | | | | COMBINE_INEQS: (69), (295) imply: % 115.07/16.45 | | | | | | | | | | | | | | | | | | | | | (296) $false % 115.07/16.45 | | | | | | | | | | | | | | | | | | | | | % 115.07/16.45 | | | | | | | | | | | | | | | | | | | | | CLOSE: (296) is inconsistent. % 115.07/16.45 | | | | | | | | | | | | | | | | | | | | | % 115.07/16.45 | | | | | | | | | | | | | | | | | | | | Case 2: % 115.07/16.45 | | | | | | | | | | | | | | | | | | | | | % 115.07/16.45 | | | | | | | | | | | | | | | | | | | | | (297) ? [v0: int] : (div1($difference(1, $product(15, % 115.07/16.45 | | | | | | | | | | | | | | | | | | | | | sc_118_0_3)), 3) = v0 & div1($product(-15, % 115.07/16.45 | | | | | | | | | | | | | | | | | | | | | sc_118_0_3), 3) = v0) % 115.07/16.45 | | | | | | | | | | | | | | | | | | | | | % 115.07/16.45 | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (297) with fresh symbol all_439_0 % 115.07/16.45 | | | | | | | | | | | | | | | | | | | | | gives: % 115.07/16.45 | | | | | | | | | | | | | | | | | | | | | (298) div1($difference(1, $product(15, sc_118_0_3)), 3) % 115.07/16.45 | | | | | | | | | | | | | | | | | | | | | = all_439_0 & div1($product(-15, sc_118_0_3), 3) = % 115.07/16.45 | | | | | | | | | | | | | | | | | | | | | all_439_0 % 115.07/16.45 | | | | | | | | | | | | | | | | | | | | | % 115.07/16.45 | | | | | | | | | | | | | | | | | | | | | ALPHA: (298) implies: % 115.07/16.45 | | | | | | | | | | | | | | | | | | | | | (299) div1($product(-15, sc_118_0_3), 3) = all_439_0 % 115.07/16.45 | | | | | | | | | | | | | | | | | | | | | % 115.07/16.45 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (188) gives: % 115.07/16.45 | | | | | | | | | | | | | | | | | | | | | % 115.07/16.45 | | | | | | | | | | | | | | | | | | | | | Case 1: % 115.07/16.45 | | | | | | | | | | | | | | | | | | | | | | % 115.07/16.45 | | | | | | | | | | | | | | | | | | | | | | (300) $lesseq(0, sc_118_0_3) % 115.07/16.45 | | | | | | | | | | | | | | | | | | | | | | % 115.07/16.45 | | | | | | | | | | | | | | | | | | | | | | COMBINE_INEQS: (69), (300) imply: % 115.07/16.45 | | | | | | | | | | | | | | | | | | | | | | (301) $false % 115.07/16.45 | | | | | | | | | | | | | | | | | | | | | | % 115.07/16.45 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (301) is inconsistent. % 115.07/16.45 | | | | | | | | | | | | | | | | | | | | | | % 115.07/16.45 | | | | | | | | | | | | | | | | | | | | | Case 2: % 115.07/16.45 | | | | | | | | | | | | | | | | | | | | | | % 115.07/16.45 | | | | | | | | | | | | | | | | | | | | | | (302) ? [v0: int] : (div1($difference(-2, $product(15, % 115.07/16.45 | | | | | | | | | | | | | | | | | | | | | | sc_118_0_3)), 3) = v0 & % 115.07/16.45 | | | | | | | | | | | | | | | | | | | | | | div1($difference(-1, $product(15, sc_118_0_3)), % 115.07/16.45 | | | | | | | | | | | | | | | | | | | | | | 3) = v0) % 115.07/16.45 | | | | | | | | | | | | | | | | | | | | | | % 115.07/16.45 | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (302) with fresh symbol all_471_0 % 115.07/16.45 | | | | | | | | | | | | | | | | | | | | | | gives: % 115.07/16.45 | | | | | | | | | | | | | | | | | | | | | | (303) div1($difference(-2, $product(15, sc_118_0_3)), 3) % 115.07/16.45 | | | | | | | | | | | | | | | | | | | | | | = all_471_0 & div1($difference(-1, $product(15, % 115.07/16.45 | | | | | | | | | | | | | | | | | | | | | | sc_118_0_3)), 3) = all_471_0 % 115.07/16.45 | | | | | | | | | | | | | | | | | | | | | | % 115.07/16.45 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (303) implies: % 115.07/16.45 | | | | | | | | | | | | | | | | | | | | | | (304) div1($difference(-1, $product(15, sc_118_0_3)), 3) % 115.07/16.45 | | | | | | | | | | | | | | | | | | | | | | = all_471_0 % 115.07/16.45 | | | | | | | | | | | | | | | | | | | | | | % 115.07/16.45 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (186) gives: % 115.07/16.45 | | | | | | | | | | | | | | | | | | | | | | % 115.07/16.45 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 115.07/16.45 | | | | | | | | | | | | | | | | | | | | | | | % 115.07/16.45 | | | | | | | | | | | | | | | | | | | | | | | (305) $lesseq(1, sc_118_0_3) % 115.07/16.45 | | | | | | | | | | | | | | | | | | | | | | | % 115.07/16.45 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_INEQS: (69), (305) imply: % 115.07/16.45 | | | | | | | | | | | | | | | | | | | | | | | (306) $false % 115.07/16.45 | | | | | | | | | | | | | | | | | | | | | | | % 115.07/16.45 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (306) is inconsistent. % 115.07/16.45 | | | | | | | | | | | | | | | | | | | | | | | % 115.07/16.45 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 115.07/16.45 | | | | | | | | | | | | | | | | | | | | | | | % 115.07/16.45 | | | | | | | | | | | | | | | | | | | | | | | (307) ? [v0: int] : (mod1($difference(2, $product(15, % 115.07/16.45 | | | | | | | | | | | | | | | | | | | | | | | sc_118_0_3)), 5) = v0 & (v0 = 2 | v0 = 0)) % 115.07/16.45 | | | | | | | | | | | | | | | | | | | | | | | % 115.07/16.45 | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (307) with fresh symbol all_511_0 % 115.07/16.45 | | | | | | | | | | | | | | | | | | | | | | | gives: % 115.07/16.45 | | | | | | | | | | | | | | | | | | | | | | | (308) mod1($difference(2, $product(15, sc_118_0_3)), 5) % 115.07/16.45 | | | | | | | | | | | | | | | | | | | | | | | = all_511_0 & (all_511_0 = 2 | all_511_0 = 0) % 115.07/16.45 | | | | | | | | | | | | | | | | | | | | | | | % 115.07/16.45 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (308) implies: % 115.07/16.45 | | | | | | | | | | | | | | | | | | | | | | | (309) mod1($difference(2, $product(15, sc_118_0_3)), 5) % 115.07/16.45 | | | | | | | | | | | | | | | | | | | | | | | = all_511_0 % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | (310) all_511_0 = 2 | all_511_0 = 0 % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives: % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | (311) $lesseq(1, sc_118_0_3) % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_INEQS: (69), (311) imply: % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | (312) $false % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (312) is inconsistent. % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (19) with all_403_0, all_511_0, 5, % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | $difference(2, $product(15, sc_118_0_3)), % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (294), (309) gives: % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | (313) all_511_0 = all_403_0 % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (20) with $product(-5, sc_118_0_3), % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | all_290_5, 3, $product(-15, sc_118_0_3), % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (73), (225) gives: % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | (314) $sum(all_290_5, $product(5, sc_118_0_3)) = 0 % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (20) with all_290_5, all_439_0, 3, % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | $product(-15, sc_118_0_3), simplifying with (225), % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | (299) gives: % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | (315) all_439_0 = all_290_5 % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (20) with all_283_4, all_439_0, 3, % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | $product(-15, sc_118_0_3), simplifying with (211), % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | (299) gives: % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | (316) all_439_0 = all_283_4 % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (20) with all_290_3, all_328_0, 5, % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | $product(-15, sc_118_0_3), simplifying with (226), % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | (281) gives: % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | (317) all_328_0 = all_290_3 % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (20) with all_283_1, all_290_1, 15, % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | $product(-15, sc_118_0_3), simplifying with (212), % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | (227) gives: % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | (318) all_290_1 = all_283_1 % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (20) with $product(-1, sc_118_0_3), % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | all_290_1, 15, $product(-15, sc_118_0_3), % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (227), (270) gives: % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | (319) $sum(all_290_1, sc_118_0_3) = 0 % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (20) with all_283_1, all_315_0, 15, % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | $product(-15, sc_118_0_3), simplifying with (212), % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | (275) gives: % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | (320) all_315_0 = all_283_1 % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (20) with $product(-3, sc_118_0_3), % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | all_328_0, 5, $difference(1, $product(15, % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | sc_118_0_3)), simplifying with (269), (282) % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | gives: % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | (321) $sum(all_328_0, $product(3, sc_118_0_3)) = 0 % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (20) with $difference(-1, % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | $product(5, sc_118_0_3)), all_288_5, 3, % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | $difference(-1, $product(15, sc_118_0_3)), % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (167), (217) gives: % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | (322) $sum(all_288_5, $product(5, sc_118_0_3)) = -1 % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (20) with all_288_5, all_471_0, 3, % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | $difference(-1, $product(15, sc_118_0_3)), % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (217), (304) gives: % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | (323) all_471_0 = all_288_5 % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (20) with all_286_4, all_471_0, 3, % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | $difference(-1, $product(15, sc_118_0_3)), % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (214), (304) gives: % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | (324) all_471_0 = all_286_4 % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (20) with $difference(-1, % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | $product(3, sc_118_0_3)), all_288_3, 5, % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | $difference(-1, $product(15, sc_118_0_3)), % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (166), (218) gives: % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | (325) $sum(all_288_3, $product(3, sc_118_0_3)) = -1 % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (20) with all_288_3, all_350_0, 5, % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | $difference(-1, $product(15, sc_118_0_3)), % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (218), (287) gives: % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | (326) all_350_0 = all_288_3 % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (20) with all_281_3, all_350_0, 5, % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | $difference(-1, $product(15, sc_118_0_3)), % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (208), (287) gives: % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | (327) all_350_0 = all_281_3 % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (20) with all_288_1, $sum(all_315_0, % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | -1), 15, $difference(-1, $product(15, % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | sc_118_0_3)), simplifying with (219), (276) % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | gives: % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | (328) $difference(all_315_0, all_288_1) = 1 % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (20) with all_281_1, $sum(all_315_0, % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | -1), 15, $difference(-1, $product(15, % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | sc_118_0_3)), simplifying with (209), (276) % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | gives: % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | (329) $difference(all_315_0, all_281_1) = 1 % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (323), (324) imply: % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | (330) all_288_5 = all_286_4 % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (330) implies: % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | (331) all_288_5 = all_286_4 % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (315), (316) imply: % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | (332) all_290_5 = all_283_4 % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (332) implies: % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | (333) all_290_5 = all_283_4 % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (326), (327) imply: % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | (334) all_288_3 = all_281_3 % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (334) implies: % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | (335) all_288_3 = all_281_3 % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (317), (321) imply: % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | (336) $sum(all_290_3, $product(3, sc_118_0_3)) = 0 % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (336) implies: % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | (337) $sum(all_290_3, $product(3, sc_118_0_3)) = 0 % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (328), (329) imply: % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | (338) all_288_1 = all_281_1 % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (338) implies: % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | (339) all_288_1 = all_281_1 % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (320), (329) imply: % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | (340) $difference(all_283_1, all_281_1) = 1 % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (340) implies: % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | (341) $difference(all_283_1, all_281_1) = 1 % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (318), (319) imply: % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | (342) $sum(all_283_1, sc_118_0_3) = 0 % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | % 115.07/16.46 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (342) implies: % 115.07/16.47 | | | | | | | | | | | | | | | | | | | | | | | | (343) $sum(all_283_1, sc_118_0_3) = 0 % 115.07/16.47 | | | | | | | | | | | | | | | | | | | | | | | | % 115.07/16.47 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (314), (333) imply: % 115.07/16.47 | | | | | | | | | | | | | | | | | | | | | | | | (344) $sum(all_283_4, $product(5, sc_118_0_3)) = 0 % 115.07/16.47 | | | | | | | | | | | | | | | | | | | | | | | | % 115.07/16.47 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (325), (335) imply: % 115.07/16.47 | | | | | | | | | | | | | | | | | | | | | | | | (345) $sum(all_281_3, $product(3, sc_118_0_3)) = -1 % 115.07/16.47 | | | | | | | | | | | | | | | | | | | | | | | | % 115.07/16.47 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (322), (331) imply: % 115.07/16.47 | | | | | | | | | | | | | | | | | | | | | | | | (346) $sum(all_286_4, $product(5, sc_118_0_3)) = -1 % 115.07/16.47 | | | | | | | | | | | | | | | | | | | | | | | | % 115.07/16.47 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (341), (343) imply: % 115.07/16.47 | | | | | | | | | | | | | | | | | | | | | | | | (347) $sum(all_281_1, sc_118_0_3) = -1 % 115.07/16.47 | | | | | | | | | | | | | | | | | | | | | | | | % 115.07/16.47 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (339), (347) imply: % 115.07/16.47 | | | | | | | | | | | | | | | | | | | | | | | | (348) $sum(all_288_1, sc_118_0_3) = -1 % 115.07/16.47 | | | | | | | | | | | | | | | | | | | | | | | | % 115.07/16.47 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (251), (319) imply: % 115.07/16.47 | | | | | | | | | | | | | | | | | | | | | | | | (349) tr1($product(-1, sc_118_0_3)) = sc_294_0_3 % 115.07/16.47 | | | | | | | | | | | | | | | | | | | | | | | | % 115.07/16.47 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (252), (337) imply: % 115.07/16.47 | | | | | | | | | | | | | | | | | | | | | | | | (350) tr1($product(-3, sc_118_0_3)) = % 115.07/16.47 | | | | | | | | | | | | | | | | | | | | | | | | $difference($difference($product(3, sc_294_0_3), % 115.07/16.47 | | | | | | | | | | | | | | | | | | | | | | | | $product(2, sc_294_0_4)), sc_294_0_5) % 115.07/16.47 | | | | | | | | | | | | | | | | | | | | | | | | % 115.07/16.47 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (253), (314) imply: % 115.07/16.47 | | | | | | | | | | | | | | | | | | | | | | | | (351) tr1($product(-5, sc_118_0_3)) = $sum($product(3, % 115.07/16.47 | | | | | | | | | | | | | | | | | | | | | | | | sc_294_0_4), sc_294_0_5) % 115.07/16.47 | | | | | | | | | | | | | | | | | | | | | | | | % 115.07/16.47 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (254), (348) imply: % 115.24/16.47 | | | | | | | | | | | | | | | | | | | | | | | | (352) tr1($difference(-1, sc_118_0_3)) = sc_294_0_6 % 115.24/16.47 | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.47 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (255), (325) imply: % 115.24/16.47 | | | | | | | | | | | | | | | | | | | | | | | | (353) tr1($difference(-1, $product(3, sc_118_0_3))) = % 115.24/16.47 | | | | | | | | | | | | | | | | | | | | | | | | $difference($difference($product(3, sc_294_0_6), % 115.24/16.47 | | | | | | | | | | | | | | | | | | | | | | | | $product(2, sc_294_0_7)), sc_294_0_8) % 115.24/16.47 | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.47 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (256), (322) imply: % 115.24/16.47 | | | | | | | | | | | | | | | | | | | | | | | | (354) tr1($difference(-1, $product(5, sc_118_0_3))) = % 115.24/16.47 | | | | | | | | | | | | | | | | | | | | | | | | $sum($product(3, sc_294_0_7), sc_294_0_8) % 115.24/16.47 | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.47 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (310) gives: % 115.24/16.47 | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.47 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 115.24/16.47 | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.47 | | | | | | | | | | | | | | | | | | | | | | | | | (355) all_511_0 = 0 % 115.24/16.47 | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.47 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (313), (355) imply: % 115.24/16.47 | | | | | | | | | | | | | | | | | | | | | | | | | (356) all_403_0 = 0 % 115.24/16.47 | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.47 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (293), (356) imply: % 115.24/16.47 | | | | | | | | | | | | | | | | | | | | | | | | | (357) $false % 115.24/16.47 | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.47 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (357) is inconsistent. % 115.24/16.47 | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.47 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 115.24/16.47 | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.47 | | | | | | | | | | | | | | | | | | | | | | | | | (358) all_511_0 = 2 % 115.24/16.47 | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.47 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (313), (358) imply: % 115.24/16.47 | | | | | | | | | | | | | | | | | | | | | | | | | (359) all_403_0 = 2 % 115.24/16.47 | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.47 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (294), (359) imply: % 115.24/16.47 | | | | | | | | | | | | | | | | | | | | | | | | | (360) mod1($difference(2, $product(15, sc_118_0_3)), 5) % 115.24/16.47 | | | | | | | | | | | | | | | | | | | | | | | | | = 2 % 115.24/16.47 | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.47 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 115.24/16.47 | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.47 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 115.24/16.47 | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.47 | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.47 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with $difference(2, $product(15, % 115.24/16.47 | | | | | | | | | | | | | | | | | | | | | | | | | | sc_118_0_3)), 5, 2, simplifying with (360) % 115.24/16.47 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 115.24/16.47 | | | | | | | | | | | | | | | | | | | | | | | | | | (361) ? [v0: int] : (div1($difference(2, $product(15, % 115.24/16.47 | | | | | | | | | | | | | | | | | | | | | | | | | | sc_118_0_3)), 5) = v0 & $product(5, v0) = % 115.24/16.47 | | | | | | | | | | | | | | | | | | | | | | | | | | $product(-15, sc_118_0_3)) % 115.24/16.47 | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.47 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with $difference(-2, % 115.24/16.47 | | | | | | | | | | | | | | | | | | | | | | | | | | $product(15, sc_118_0_3)), 1, simplifying with % 115.24/16.47 | | | | | | | | | | | | | | | | | | | | | | | | | | (288) gives: % 115.24/16.47 | | | | | | | | | | | | | | | | | | | | | | | | | | (362) ~ ($lesseq(sc_118_0_3, -1)) | ? [v0: int] : ? % 115.24/16.47 | | | | | | | | | | | | | | | | | | | | | | | | | | [v1: int] : ? [v2: int] : ((v2 = 0 & % 115.24/16.47 | | | | | | | | | | | | | | | | | | | | | | | | | | p1($difference(-2, $product(15, sc_118_0_3))) % 115.24/16.47 | | | | | | | | | | | | | | | | | | | | | | | | | | = 0) | ( ~ (v1 = 0) & mod1($difference(-2, % 115.24/16.47 | | | | | | | | | | | | | | | | | | | | | | | | | | $product(15, sc_118_0_3)), 5) = v1) | ( ~ % 115.24/16.47 | | | | | | | | | | | | | | | | | | | | | | | | | | (v0 = 0) & p1($difference(-3, $product(15, % 115.24/16.47 | | | | | | | | | | | | | | | | | | | | | | | | | | sc_118_0_3))) = v0)) % 115.24/16.47 | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.47 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (rounds_toward_zero) with % 115.24/16.47 | | | | | | | | | | | | | | | | | | | | | | | | | | $difference(1, $product(15, sc_118_0_3)), 5, % 115.24/16.47 | | | | | | | | | | | | | | | | | | | | | | | | | | $product(-3, sc_118_0_3), simplifying with (269) % 115.24/16.47 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 115.24/16.47 | | | | | | | | | | | | | | | | | | | | | | | | | | (363) ? [v0: int] : ? [v1: int] : ? [v2: int] : % 115.24/16.47 | | | | | | | | | | | | | | | | | | | | | | | | | | ($lesseq(v2, v0) & abs1(v1) = v2 & % 115.24/16.47 | | | | | | | | | | | | | | | | | | | | | | | | | | abs1($difference(1, $product(15, sc_118_0_3))) = % 115.24/16.47 | | | | | | | | | | | | | | | | | | | | | | | | | | v0 & $product($product(-3, sc_118_0_3), 5) = v1) % 115.24/16.47 | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.47 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (tr_repr) with $product(-1, % 115.24/16.47 | | | | | | | | | | | | | | | | | | | | | | | | | | sc_118_0_3), sc_294_0_3, simplifying with (349) % 115.24/16.47 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 115.24/16.47 | | | | | | | | | | | | | | | | | | | | | | | | | | (364) ~ ($lesseq(sc_118_0_3, 0) | $product($product(-1, % 115.24/16.47 | | | | | | | | | | | | | | | | | | | | | | | | | | sc_118_0_3), $difference(1, sc_118_0_3)) = % 115.24/16.47 | | | | | | | | | | | | | | | | | | | | | | | | | | $product(2, sc_294_0_3) % 115.24/16.47 | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.47 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (tr_def) with $product(-1, % 115.24/16.47 | | | | | | | | | | | | | | | | | | | | | | | | | | sc_118_0_3), sc_294_0_3, simplifying with (349) % 115.24/16.47 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 115.24/16.47 | | | | | | | | | | | | | | | | | | | | | | | | | | (365) ? [v0: int] : (div1(v0, 2) = sc_294_0_3 & % 115.24/16.47 | | | | | | | | | | | | | | | | | | | | | | | | | | $product($product(-1, sc_118_0_3), % 115.24/16.47 | | | | | | | | | | | | | | | | | | | | | | | | | | $difference(1, sc_118_0_3)) = v0) % 115.24/16.47 | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.47 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (tr_repr) with $difference(-1, % 115.24/16.47 | | | | | | | | | | | | | | | | | | | | | | | | | | sc_118_0_3), sc_294_0_6, simplifying with (352) % 115.24/16.47 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | (366) ~ ($lesseq(sc_118_0_3, -1)) | % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | $product($difference(-1, sc_118_0_3), $product(-1, % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | sc_118_0_3)) = $product(2, sc_294_0_6) % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (tr_def) with $difference(-1, % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | sc_118_0_3), sc_294_0_6, simplifying with (352) % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | (367) ? [v0: int] : (div1(v0, 2) = sc_294_0_6 & % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | $product($difference(-1, sc_118_0_3), % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | $product(-1, sc_118_0_3)) = v0) % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (tr_repr) with $product(-3, % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | sc_118_0_3), $difference($difference($product(3, % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | sc_294_0_3), $product(2, sc_294_0_4)), % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | sc_294_0_5), simplifying with (350) gives: % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | (368) ~ ($lesseq(sc_118_0_3, 0) | $product($product(-3, % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | sc_118_0_3), $difference(1, $product(3, % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | sc_118_0_3))) = % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | $difference($difference($product(6, sc_294_0_3), % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | $product(4, sc_294_0_4)), $product(2, % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | sc_294_0_5)) % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (tr_repr) with $difference(-1, % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | $product(3, sc_118_0_3)), % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | $difference($difference($product(3, sc_294_0_6), % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | $product(2, sc_294_0_7)), sc_294_0_8), % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (353) gives: % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | (369) ~ ($lesseq(sc_118_0_3, -1)) | % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | $product($difference(-1, $product(3, sc_118_0_3)), % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | $product(-3, sc_118_0_3)) = % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | $difference($difference($product(6, sc_294_0_6), % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | $product(4, sc_294_0_7)), $product(2, % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | sc_294_0_8)) % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (tr_def) with $difference(-1, % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | $product(3, sc_118_0_3)), % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | $difference($difference($product(3, sc_294_0_6), % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | $product(2, sc_294_0_7)), sc_294_0_8), % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (353) gives: % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | (370) ? [v0: int] : (div1(v0, 2) = % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | $difference($difference($product(3, sc_294_0_6), % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | $product(2, sc_294_0_7)), sc_294_0_8) & % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | $product($difference(-1, $product(3, % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | sc_118_0_3)), $product(-3, sc_118_0_3)) = % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | v0) % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (tr_repr) with $product(-5, % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | sc_118_0_3), $sum($product(3, sc_294_0_4), % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | sc_294_0_5), simplifying with (351) gives: % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | (371) ~ ($lesseq(sc_118_0_3, 0) | $product($product(-5, % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | sc_118_0_3), $difference(1, $product(5, % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | sc_118_0_3))) = $sum($product(6, % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | sc_294_0_4), $product(2, sc_294_0_5)) % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (tr_repr) with $difference(-1, % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | $product(5, sc_118_0_3)), $sum($product(3, % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | sc_294_0_7), sc_294_0_8), simplifying with % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | (354) gives: % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | (372) ~ ($lesseq(sc_118_0_3, -1)) | % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | $product($difference(-1, $product(5, sc_118_0_3)), % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | $product(-5, sc_118_0_3)) = $sum($product(6, % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | sc_294_0_7), $product(2, sc_294_0_8)) % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (tr_def) with $difference(-1, % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | $product(5, sc_118_0_3)), $sum($product(3, % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | sc_294_0_7), sc_294_0_8), simplifying with % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | (354) gives: % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | (373) ? [v0: int] : (div1(v0, 2) = $sum($product(3, % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | sc_294_0_7), sc_294_0_8) & % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | $product($difference(-1, $product(5, % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | sc_118_0_3)), $product(-5, sc_118_0_3)) = % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | v0) % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (370) with fresh symbol all_1016_0 % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | (374) div1(all_1016_0, 2) = % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | $difference($difference($product(3, sc_294_0_6), % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | $product(2, sc_294_0_7)), sc_294_0_8) & % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | $product($difference(-1, $product(3, sc_118_0_3)), % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | $product(-3, sc_118_0_3)) = all_1016_0 % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (374) implies: % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | (375) $product($difference(-1, $product(3, sc_118_0_3)), % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | $product(-3, sc_118_0_3)) = all_1016_0 % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (367) with fresh symbol all_1018_0 % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | (376) div1(all_1018_0, 2) = sc_294_0_6 & % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | $product($difference(-1, sc_118_0_3), $product(-1, % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | sc_118_0_3)) = all_1018_0 % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (376) implies: % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | (377) $product($difference(-1, sc_118_0_3), $product(-1, % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | sc_118_0_3)) = all_1018_0 % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (365) with fresh symbol all_1022_0 % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | (378) div1(all_1022_0, 2) = sc_294_0_3 & % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | $product($product(-1, sc_118_0_3), $difference(1, % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | sc_118_0_3)) = all_1022_0 % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (378) implies: % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | (379) $product($product(-1, sc_118_0_3), $difference(1, % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | sc_118_0_3)) = all_1022_0 % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (373) with fresh symbol all_1024_0 % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | (380) div1(all_1024_0, 2) = $sum($product(3, % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | sc_294_0_7), sc_294_0_8) & % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | $product($difference(-1, $product(5, sc_118_0_3)), % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | $product(-5, sc_118_0_3)) = all_1024_0 % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (380) implies: % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | (381) $product($difference(-1, $product(5, sc_118_0_3)), % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | $product(-5, sc_118_0_3)) = all_1024_0 % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (361) with fresh symbol all_1038_0 % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | (382) div1($difference(2, $product(15, sc_118_0_3)), 5) % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | = all_1038_0 & $product(5, all_1038_0) = % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | $product(-15, sc_118_0_3) % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (382) implies: % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | (383) $product(5, all_1038_0) = $product(-15, % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | sc_118_0_3) % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (363) with fresh symbols all_1090_0, % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | all_1090_1, all_1090_2 gives: % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | (384) $lesseq(all_1090_0, all_1090_2) & abs1(all_1090_1) % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | = all_1090_0 & abs1($difference(1, $product(15, % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | sc_118_0_3))) = all_1090_2 & % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | $product($product(-3, sc_118_0_3), 5) = all_1090_1 % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (384) implies: % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | (385) $product($product(-3, sc_118_0_3), 5) = all_1090_1 % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (257) with sc_118_0_3, all_1038_0, % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | all_1090_1, simplifying with (383), (385) gives: % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | (386) all_1090_1 = $product(5, all_1038_0) % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (261) with sc_118_0_3, all_1038_0, % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | all_1090_1, simplifying with (383), (385) gives: % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | (387) $sum(all_1090_1, $product(15, sc_118_0_3)) = 0 % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.48 | | | | | | | | | | | | | | | | | | | | | | | | | | THEORY_AXIOM GroebnerMultiplication: % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | (388) ! [v0: int] : ! [v1: int] : ! [v2: int] : ! % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | [v3: int] : ! [v4: int] : ($difference(v3, % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | $product(10, v2)) = $product(15, v1) | ~ % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | ($product($difference(-1, $product(5, v0)), % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | $product(-5, v0)) = v3) | ~ % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | ($product($difference(-1, v0), $product(-1, v0)) % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | = v1) | ~ ($product($product(-1, v0), % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | $difference(1, v0)) = v2) | ~ ($product(5, % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | v4) = $product(-15, v0))) % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (388) with sc_118_0_3, all_1018_0, % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | all_1022_0, all_1024_0, all_1038_0, simplifying % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | with (377), (379), (381), (383) gives: % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | (389) $difference(all_1024_0, $product(10, all_1022_0)) % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | = $product(15, all_1018_0) % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | THEORY_AXIOM GroebnerMultiplication: % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | (390) ! [v0: int] : ! [v1: int] : ! [v2: int] : ! % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | [v3: int] : ! [v4: int] : ($sum($product(2, v4), % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | $product(45, v2)) = $product(5, v1) | ~ % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | ($product($difference(-1, $product(3, v0)), % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | $product(-3, v0)) = v1) | ~ % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | ($product($product(-3, v0), 5) = v4) | ~ % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | ($product($difference(-1, v0), $product(-1, v0)) % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | = v2) | ~ ($product(5, v3) = $product(-15, % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | v0))) % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (390) with sc_118_0_3, all_1016_0, % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | all_1018_0, all_1038_0, all_1090_1, simplifying % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | with (375), (377), (383), (385) gives: % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | (391) $sum($product(2, all_1090_1), $product(45, % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | all_1018_0)) = $product(5, all_1016_0) % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | THEORY_AXIOM GroebnerMultiplication: % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | (392) ! [v0: int] : ! [v1: int] : ! [v2: int] : ! % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | [v3: int] : ! [v4: int] : % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | ($sum($difference($product(2, v4), $product(15, % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | v2)), $product(15, v1)) = 0 | ~ % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | ($product($product(-3, v0), 5) = v4) | ~ % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | ($product($difference(-1, v0), $product(-1, v0)) % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | = v1) | ~ ($product($product(-1, v0), % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | $difference(1, v0)) = v2) | ~ ($product(5, % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | v3) = $product(-15, v0))) % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (392) with sc_118_0_3, all_1018_0, % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | all_1022_0, all_1038_0, all_1090_1, simplifying % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | with (377), (379), (383), (385) gives: % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | (393) $sum($difference($product(2, all_1090_1), % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | $product(15, all_1022_0)), $product(15, % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | all_1018_0)) = 0 % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (386), (391) imply: % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | (394) $sum($product(2, all_1038_0), $product(9, % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | all_1018_0)) = all_1016_0 % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (394) implies: % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | (395) $sum($product(2, all_1038_0), $product(9, % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | all_1018_0)) = all_1016_0 % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (386), (393) imply: % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | (396) $sum($difference($product(2, all_1038_0), % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | $product(3, all_1022_0)), $product(3, % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | all_1018_0)) = 0 % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (396) implies: % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | (397) $sum($difference($product(2, all_1038_0), % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | $product(3, all_1022_0)), $product(3, % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | all_1018_0)) = 0 % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (386), (387) imply: % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | (398) $sum(all_1038_0, $product(3, sc_118_0_3)) = 0 % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (398) implies: % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | (399) $sum(all_1038_0, $product(3, sc_118_0_3)) = 0 % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (395), (399) imply: % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | (400) $difference($product(9, all_1018_0), all_1016_0) = % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | $product(6, sc_118_0_3) % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (397), (399) imply: % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | (401) $sum($difference(all_1022_0, all_1018_0), % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | $product(2, sc_118_0_3)) = 0 % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (401) implies: % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | (402) $sum($difference(all_1022_0, all_1018_0), % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | $product(2, sc_118_0_3)) = 0 % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (389), (400), (402) imply: % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | (403) $sum($difference($sum(all_1024_0, $product(2, % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | all_1018_0)), $product(3, all_1016_0)), % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | $product(2, sc_118_0_3)) = 0 % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | COL_REDUCE: introducing fresh symbol sc_1170_0_0 defined by: % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | (404) $difference(all_1018_0, sc_118_0_3) = sc_1170_0_0 % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (400), (404) imply: % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | (405) $difference(all_1016_0, $product(3, sc_118_0_3)) = % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | $product(9, sc_1170_0_0) % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (405) implies: % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | (406) $difference(all_1016_0, $product(3, sc_118_0_3)) = % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | $product(9, sc_1170_0_0) % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (403), (404), (406) imply: % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | (407) $difference(all_1024_0, $product(5, sc_118_0_3)) = % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | $product(25, sc_1170_0_0) % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (381), (407) imply: % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | (408) $product($difference(-1, $product(5, sc_118_0_3)), % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | $product(-5, sc_118_0_3)) = $sum($product(5, % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | sc_118_0_3), $product(25, sc_1170_0_0)) % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (371) gives: % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | (409) $product($product(-5, sc_118_0_3), $difference(1, % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | $product(5, sc_118_0_3))) = $sum($product(6, % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | sc_294_0_4), $product(2, sc_294_0_5)) % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (362) gives: % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (410) $lesseq(0, sc_118_0_3) % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_INEQS: (69), (410) imply: % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (411) $false % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (411) is inconsistent. % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 115.24/16.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | THEORY_AXIOM GroebnerMultiplication: % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (412) ! [v0: int] : ! [v1: int] : ! [v2: int] : ! % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | [v3: int] : ($sum($sum($product(6, v3), % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $product(2, v2)), $product(5, v1)) = % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $product(25, v0) | ~ ($product($difference(-1, % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $product(5, v1)), $product(-5, v1)) = % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $sum($product(5, v1), $product(25, v0))) | ~ % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ($product($product(-5, v1), $difference(1, % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $product(5, v1))) = $sum($product(6, v3), % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $product(2, v2)))) % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (412) with sc_1170_0_0, sc_118_0_3, % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sc_294_0_5, sc_294_0_4, simplifying with (408), % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (409) gives: % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (413) $sum($sum($product(6, sc_294_0_4), $product(2, % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sc_294_0_5)), $product(5, sc_118_0_3)) = % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $product(25, sc_1170_0_0) % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COL_REDUCE: introducing fresh symbol sc_1328_0_0 defined by: % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (414) $difference($sum(sc_294_0_4, sc_118_0_3), % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $product(4, sc_1170_0_0)) = sc_1328_0_0 % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (413), (414) imply: % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (415) $sum($difference($difference($product(2, % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sc_294_0_5), sc_118_0_3), sc_1170_0_0), % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $product(6, sc_1328_0_0)) = 0 % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COL_REDUCE: introducing fresh symbol sc_1328_0_1 defined by: % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (416) $sum($difference($difference(sc_294_0_5, % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sc_118_0_3), sc_1170_0_0), $product(3, % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sc_1328_0_0)) = sc_1328_0_1 % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (415), (416) imply: % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (417) $sum($sum(sc_118_0_3, sc_1170_0_0), $product(2, % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sc_1328_0_1)) = 0 % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (416), (417) imply: % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (418) $sum($sum(sc_294_0_5, $product(3, sc_1328_0_0)), % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sc_1328_0_1) = 0 % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (414), (417) imply: % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (419) $difference($difference(sc_294_0_4, $product(5, % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sc_1170_0_0)), sc_1328_0_0) = $product(2, % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sc_1328_0_1) % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (69), (417) imply: % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (420) $lesseq(1, $sum(sc_1170_0_0, $product(2, % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sc_1328_0_1))) % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (250), (417), (418), (419) imply: % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (421) ~ ($sum($difference($sum(sc_294_0_7, $product(2, % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sc_294_0_8)), $product(20, % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sc_1170_0_0)), $product(5, sc_1328_0_0)) = % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $product(30, sc_1328_0_1)) % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (421) implies: % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (422) ~ ($sum($difference($sum(sc_294_0_7, $product(2, % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sc_294_0_8)), $product(20, % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sc_1170_0_0)), $product(5, sc_1328_0_0)) = % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $product(30, sc_1328_0_1)) % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (408), (417) imply: % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (423) $product($sum($sum($product(5, sc_1170_0_0), % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $product(10, sc_1328_0_1)), -1), % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $sum($product(5, sc_1170_0_0), $product(10, % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sc_1328_0_1))) = $difference($product(20, % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sc_1170_0_0), $product(10, sc_1328_0_1)) % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (364) gives: % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (424) $product($product(-1, sc_118_0_3), $difference(1, % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sc_118_0_3)) = $product(2, sc_294_0_3) % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (417), (424) imply: % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (425) $product($sum(sc_1170_0_0, $product(2, % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sc_1328_0_1)), $sum($sum(sc_1170_0_0, % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $product(2, sc_1328_0_1)), 1)) = $product(2, % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sc_294_0_3) % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | THEORY_AXIOM GroebnerMultiplication: % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (426) ! [v0: int] : ! [v1: int] : ! [v2: int] : % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ($difference(v2, v1) = v0 | ~ % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ($product($sum($sum($product(5, v1), % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $product(10, v0)), -1), $sum($product(5, % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | v1), $product(10, v0))) = % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $difference($product(20, v1), $product(10, % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | v0))) | ~ ($product($sum(v1, $product(2, % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | v0)), $sum($sum(v1, $product(2, v0)), % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 1)) = $product(2, v2))) % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (426) with sc_1328_0_1, sc_1170_0_0, % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sc_294_0_3, simplifying with (423), (425) gives: % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (427) $difference(sc_294_0_3, sc_1170_0_0) = sc_1328_0_1 % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (372) gives: % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (428) $product($difference(-1, $product(5, sc_118_0_3)), % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $product(-5, sc_118_0_3)) = $sum($product(6, % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sc_294_0_7), $product(2, sc_294_0_8)) % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (417), (428) imply: % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (429) $product($sum($sum($product(5, sc_1170_0_0), % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $product(10, sc_1328_0_1)), -1), % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $sum($product(5, sc_1170_0_0), $product(10, % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sc_1328_0_1))) = $sum($product(6, % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sc_294_0_7), $product(2, sc_294_0_8)) % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | THEORY_AXIOM GroebnerMultiplication: % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (430) ! [v0: int] : ! [v1: int] : ! [v2: int] : ! % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | [v3: int] : ($sum($difference($sum($product(3, % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | v3), v2), $product(10, v1)), $product(5, % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | v0)) = 0 | ~ % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ($product($sum($sum($product(5, v1), % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $product(10, v0)), -1), $sum($product(5, % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | v1), $product(10, v0))) = % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $sum($product(6, v3), $product(2, v2))) | ~ % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ($product($sum($sum($product(5, v1), % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $product(10, v0)), -1), $sum($product(5, % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | v1), $product(10, v0))) = % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $difference($product(20, v1), $product(10, % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | v0)))) % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (430) with sc_1328_0_1, sc_1170_0_0, % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sc_294_0_8, sc_294_0_7, simplifying with (423), % 115.24/16.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (429) gives: % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (431) $sum($difference($sum($product(3, sc_294_0_7), % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sc_294_0_8), $product(10, sc_1170_0_0)), % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $product(5, sc_1328_0_1)) = 0 % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COL_REDUCE: introducing fresh symbol sc_1460_0_0 defined by: % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (432) $sum($difference(sc_294_0_7, $product(3, % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sc_1170_0_0)), $product(2, sc_1328_0_1)) = % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sc_1460_0_0 % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (431), (432) imply: % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (433) $sum($difference($difference(sc_294_0_8, % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sc_1170_0_0), sc_1328_0_1), $product(3, % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sc_1460_0_0)) = 0 % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (422), (432), (433) imply: % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (434) ~ ($sum($sum($difference($product(3, % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sc_1170_0_0), sc_1328_0_0), $product(6, % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sc_1328_0_1)), sc_1460_0_0) = 0) % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (434) implies: % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (435) ~ ($sum($sum($difference($product(3, % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sc_1170_0_0), sc_1328_0_0), $product(6, % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sc_1328_0_1)), sc_1460_0_0) = 0) % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (369) gives: % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (436) $product($difference(-1, $product(3, sc_118_0_3)), % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $product(-3, sc_118_0_3)) = % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $difference($difference($product(6, sc_294_0_6), % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $product(4, sc_294_0_7)), $product(2, % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sc_294_0_8)) % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (417), (432), (433), (436) imply: % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (437) $product($sum($sum($product(3, sc_1170_0_0), % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $product(6, sc_1328_0_1)), -1), % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $sum($product(3, sc_1170_0_0), $product(6, % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sc_1328_0_1))) = % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $sum($sum($difference($product(6, sc_294_0_6), % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $product(14, sc_1170_0_0)), $product(6, % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sc_1328_0_1)), $product(2, sc_1460_0_0)) % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | THEORY_AXIOM GroebnerMultiplication: % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (438) ! [v0: int] : ! [v1: int] : ! [v2: int] : ! % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | [v3: int] : ($sum($sum($difference($product(3, % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | v3), $product(10, v2)), $product(6, % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | v1)), v0) = 0 | ~ % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ($product($sum($sum($product(5, v2), % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $product(10, v1)), -1), $sum($product(5, % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | v2), $product(10, v1))) = % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $difference($product(20, v2), $product(10, % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | v1))) | ~ ($product($sum($sum($product(3, % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | v2), $product(6, v1)), -1), % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $sum($product(3, v2), $product(6, v1))) = % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $sum($sum($difference($product(6, v3), % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $product(14, v2)), $product(6, v1)), % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $product(2, v0)))) % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (438) with sc_1460_0_0, sc_1328_0_1, % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sc_1170_0_0, sc_294_0_6, simplifying with (423), % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (437) gives: % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (439) $sum($sum($difference($product(3, sc_294_0_6), % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $product(10, sc_1170_0_0)), $product(6, % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sc_1328_0_1)), sc_1460_0_0) = 0 % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COL_REDUCE: introducing fresh symbol sc_1503_0_0 defined by: % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (440) $sum($difference(sc_294_0_6, $product(3, % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sc_1170_0_0)), $product(2, sc_1328_0_1)) = % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sc_1503_0_0 % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (439), (440) imply: % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (441) $difference(sc_1170_0_0, sc_1460_0_0) = % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $product(3, sc_1503_0_0) % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (441) implies: % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (442) $difference(sc_1170_0_0, sc_1460_0_0) = % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $product(3, sc_1503_0_0) % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (417), (442) imply: % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (443) $sum($sum($sum(sc_118_0_3, $product(2, % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sc_1328_0_1)), sc_1460_0_0), $product(3, % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sc_1503_0_0)) = 0 % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (440), (442) imply: % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (444) $difference($sum(sc_294_0_6, $product(2, % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sc_1328_0_1)), $product(3, sc_1460_0_0)) = % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $product(10, sc_1503_0_0) % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (419), (442) imply: % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (445) $difference($difference($difference(sc_294_0_4, % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sc_1328_0_0), $product(2, sc_1328_0_1)), % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $product(5, sc_1460_0_0)) = $product(15, % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sc_1503_0_0) % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (427), (442) imply: % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (446) $difference($difference(sc_294_0_3, sc_1328_0_1), % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sc_1460_0_0) = $product(3, sc_1503_0_0) % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (420), (442) imply: % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (447) $lesseq(1, $sum($sum($product(2, sc_1328_0_1), % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sc_1460_0_0), $product(3, sc_1503_0_0))) % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (435), (442) imply: % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (448) ~ ($difference($difference(sc_1328_0_0, % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $product(6, sc_1328_0_1)), $product(4, % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sc_1460_0_0)) = $product(9, sc_1503_0_0)) % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (448) implies: % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (449) ~ ($difference($difference(sc_1328_0_0, % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $product(6, sc_1328_0_1)), $product(4, % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sc_1460_0_0)) = $product(9, sc_1503_0_0)) % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (423), (442) imply: % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (450) $product($sum($sum($sum($product(10, sc_1328_0_1), % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $product(5, sc_1460_0_0)), $product(15, % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sc_1503_0_0)), -1), $sum($sum($product(10, % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sc_1328_0_1), $product(5, sc_1460_0_0)), % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $product(15, sc_1503_0_0))) = % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $sum($difference($product(20, sc_1460_0_0), % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $product(10, sc_1328_0_1)), $product(60, % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sc_1503_0_0)) % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (366) gives: % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (451) $product($difference(-1, sc_118_0_3), $product(-1, % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sc_118_0_3)) = $product(2, sc_294_0_6) % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (443), (444), (451) imply: % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (452) $product($sum($sum($sum($product(2, sc_1328_0_1), % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sc_1460_0_0), $product(3, sc_1503_0_0)), % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | -1), $sum($sum($product(2, sc_1328_0_1), % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sc_1460_0_0), $product(3, sc_1503_0_0))) = % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $sum($difference($product(6, sc_1460_0_0), % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $product(4, sc_1328_0_1)), $product(20, % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sc_1503_0_0)) % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | THEORY_AXIOM GroebnerMultiplication: % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (453) ! [v0: int] : ! [v1: int] : ! [v2: int] : % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ($difference(v2, $product(3, v1)) = $product(10, % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | v0) | ~ ($product($sum($sum($sum($product(10, % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | v2), $product(5, v1)), $product(15, % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | v0)), -1), $sum($sum($product(10, v2), % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $product(5, v1)), $product(15, v0))) = % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $sum($difference($product(20, v1), % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $product(10, v2)), $product(60, v0))) | ~ % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ($product($sum($sum($sum($product(2, v2), v1), % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $product(3, v0)), -1), % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $sum($sum($product(2, v2), v1), $product(3, % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | v0))) = $sum($difference($product(6, % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | v1), $product(4, v2)), $product(20, % 115.24/16.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | v0)))) % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (453) with sc_1503_0_0, sc_1460_0_0, % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sc_1328_0_1, simplifying with (450), (452) gives: % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (454) $difference(sc_1328_0_1, $product(3, sc_1460_0_0)) % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = $product(10, sc_1503_0_0) % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (443), (454) imply: % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (455) $sum($sum(sc_118_0_3, $product(7, sc_1460_0_0)), % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $product(23, sc_1503_0_0)) = 0 % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (418), (454) imply: % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (456) $sum($sum($sum(sc_294_0_5, $product(3, % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sc_1328_0_0)), $product(3, sc_1460_0_0)), % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $product(10, sc_1503_0_0)) = 0 % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (445), (454) imply: % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (457) $difference($difference(sc_294_0_4, sc_1328_0_0), % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $product(11, sc_1460_0_0)) = $product(35, % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sc_1503_0_0) % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (446), (454) imply: % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (458) $difference(sc_294_0_3, $product(4, sc_1460_0_0)) % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = $product(13, sc_1503_0_0) % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (447), (454) imply: % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (459) $lesseq(1, $sum($product(7, sc_1460_0_0), % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $product(23, sc_1503_0_0))) % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (449), (454) imply: % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (460) ~ ($difference(sc_1328_0_0, $product(22, % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sc_1460_0_0)) = $product(69, sc_1503_0_0)) % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (450), (454) imply: % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (461) $product($sum($sum($product(35, sc_1460_0_0), % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $product(115, sc_1503_0_0)), -1), % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $sum($product(35, sc_1460_0_0), $product(115, % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sc_1503_0_0))) = $difference($product(-10, % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sc_1460_0_0), $product(40, sc_1503_0_0)) % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (368) gives: % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (462) $product($product(-3, sc_118_0_3), $difference(1, % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $product(3, sc_118_0_3))) = % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $difference($difference($product(6, sc_294_0_3), % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $product(4, sc_294_0_4)), $product(2, % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sc_294_0_5)) % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (455), (456), (457), (458), (462) imply: % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (463) $product($sum($product(21, sc_1460_0_0), % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $product(69, sc_1503_0_0)), % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $sum($sum($product(21, sc_1460_0_0), % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $product(69, sc_1503_0_0)), 1)) = % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $difference($difference($product(2, sc_1328_0_0), % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $product(14, sc_1460_0_0)), $product(42, % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sc_1503_0_0)) % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | THEORY_AXIOM GroebnerMultiplication: % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (464) ! [v0: int] : ! [v1: int] : ! [v2: int] : % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ($difference(v2, $product(22, v1)) = $product(69, % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | v0) | ~ ($product($sum($sum($product(35, v1), % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $product(115, v0)), -1), % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $sum($product(35, v1), $product(115, v0))) = % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $difference($product(-10, v1), $product(40, % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | v0))) | ~ ($product($sum($product(21, % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | v1), $product(69, v0)), % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $sum($sum($product(21, v1), $product(69, % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | v0)), 1)) = % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $difference($difference($product(2, v2), % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $product(14, v1)), $product(42, v0)))) % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (464) with sc_1503_0_0, sc_1460_0_0, % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sc_1328_0_0, simplifying with (461), (463) gives: % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (465) $difference(sc_1328_0_0, $product(22, % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sc_1460_0_0)) = $product(69, sc_1503_0_0) % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (460), (465) imply: % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (466) $false % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (466) is inconsistent. % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (467) $lesseq(1, sc_118_0_3) % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (455), (467) imply: % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (468) $lesseq(1, $difference($product(-7, sc_1460_0_0), % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $product(23, sc_1503_0_0))) % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_INEQS: (459), (468) imply: % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (469) $false % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (469) is inconsistent. % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (470) $lesseq(0, sc_118_0_3) % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (443), (470) imply: % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (471) $lesseq(0, $difference($difference($product(-2, % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sc_1328_0_1), sc_1460_0_0), $product(3, % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sc_1503_0_0))) % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_INEQS: (447), (471) imply: % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (472) $false % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (472) is inconsistent. % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (473) $lesseq(0, sc_118_0_3) % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (417), (473) imply: % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (474) $lesseq(sc_1170_0_0, $product(-2, sc_1328_0_1)) % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_INEQS: (420), (474) imply: % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (475) $false % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (475) is inconsistent. % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (476) $lesseq(0, sc_118_0_3) % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (417), (476) imply: % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (477) $lesseq(sc_1170_0_0, $product(-2, sc_1328_0_1)) % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_INEQS: (420), (477) imply: % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (478) $false % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (478) is inconsistent. % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (479) $lesseq(1, sc_118_0_3) % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (417), (479) imply: % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (480) $lesseq(1, $difference($product(-1, sc_1170_0_0), % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $product(2, sc_1328_0_1))) % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_INEQS: (420), (480) imply: % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (481) $false % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (481) is inconsistent. % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | (482) $lesseq(1, sc_118_0_3) % 115.24/16.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_INEQS: (69), (482) imply: % 115.24/16.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | (483) $false % 115.24/16.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (483) is inconsistent. % 115.24/16.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.53 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 115.24/16.53 | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.53 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 115.24/16.53 | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.53 | | | | | | | | | | | | | | | | | | | | | | | | | | (484) ~ (all_273_1 = 0) & ~ (all_273_2 = 0) & mod1(0, % 115.24/16.53 | | | | | | | | | | | | | | | | | | | | | | | | | | 5) = all_273_1 & mod1(0, 3) = all_273_2 % 115.24/16.53 | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.53 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (484) implies: % 115.24/16.53 | | | | | | | | | | | | | | | | | | | | | | | | | | (485) ~ (all_273_2 = 0) % 115.24/16.53 | | | | | | | | | | | | | | | | | | | | | | | | | | (486) mod1(0, 3) = all_273_2 % 115.24/16.53 | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.53 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (mod_sign_pos) with 0, 3, all_273_2, % 115.24/16.53 | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (486) gives: % 115.24/16.53 | | | | | | | | | | | | | | | | | | | | | | | | | | (487) $lesseq(0, all_273_2) % 115.24/16.53 | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.53 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (mod_sign_neg) with 0, 3, all_273_2, % 115.24/16.53 | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (486) gives: % 115.24/16.53 | | | | | | | | | | | | | | | | | | | | | | | | | | (488) $lesseq(all_273_2, 0) % 115.24/16.53 | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.53 | | | | | | | | | | | | | | | | | | | | | | | | | | ANTI_SYMM: (487), (488) imply: % 115.24/16.53 | | | | | | | | | | | | | | | | | | | | | | | | | | (489) all_273_2 = 0 % 115.24/16.53 | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.53 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (485), (489) imply: % 115.24/16.53 | | | | | | | | | | | | | | | | | | | | | | | | | | (490) $false % 115.24/16.53 | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.53 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (490) is inconsistent. % 115.24/16.53 | | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.53 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 115.24/16.53 | | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.53 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 115.24/16.53 | | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.53 | | | | | | | | | | | | | | | | | | | | | | | End of split % 115.24/16.53 | | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.53 | | | | | | | | | | | | | | | | | | | | | | End of split % 115.24/16.53 | | | | | | | | | | | | | | | | | | | | | | % 115.24/16.53 | | | | | | | | | | | | | | | | | | | | | End of split % 115.24/16.53 | | | | | | | | | | | | | | | | | | | | | % 115.24/16.53 | | | | | | | | | | | | | | | | | | | | End of split % 115.24/16.53 | | | | | | | | | | | | | | | | | | | | % 115.54/16.53 | | | | | | | | | | | | | | | | | | | End of split % 115.54/16.53 | | | | | | | | | | | | | | | | | | | % 115.54/16.53 | | | | | | | | | | | | | | | | | | Case 2: % 115.54/16.53 | | | | | | | | | | | | | | | | | | | % 115.54/16.53 | | | | | | | | | | | | | | | | | | | (491) $lesseq(0, sc_118_0_3) % 115.54/16.53 | | | | | | | | | | | | | | | | | | | % 115.54/16.53 | | | | | | | | | | | | | | | | | | | COMBINE_INEQS: (69), (491) imply: % 115.54/16.53 | | | | | | | | | | | | | | | | | | | (492) $false % 115.54/16.53 | | | | | | | | | | | | | | | | | | | % 115.54/16.53 | | | | | | | | | | | | | | | | | | | CLOSE: (492) is inconsistent. % 115.54/16.53 | | | | | | | | | | | | | | | | | | | % 115.54/16.53 | | | | | | | | | | | | | | | | | | End of split % 115.54/16.53 | | | | | | | | | | | | | | | | | | % 115.54/16.53 | | | | | | | | | | | | | | | | | End of split % 115.54/16.53 | | | | | | | | | | | | | | | | | % 115.54/16.53 | | | | | | | | | | | | | | | | End of split % 115.54/16.53 | | | | | | | | | | | | | | | | % 115.54/16.53 | | | | | | | | | | | | | | | End of split % 115.54/16.53 | | | | | | | | | | | | | | | % 115.54/16.53 | | | | | | | | | | | | | | End of split % 115.54/16.53 | | | | | | | | | | | | | | % 115.54/16.53 | | | | | | | | | | | | | End of split % 115.54/16.53 | | | | | | | | | | | | | % 115.54/16.53 | | | | | | | | | | | | End of split % 115.54/16.53 | | | | | | | | | | | | % 115.54/16.53 | | | | | | | | | | | End of split % 115.54/16.53 | | | | | | | | | | | % 115.54/16.53 | | | | | | | | | | End of split % 115.54/16.53 | | | | | | | | | | % 115.54/16.53 | | | | | | | | | End of split % 115.54/16.53 | | | | | | | | | % 115.54/16.53 | | | | | | | | End of split % 115.54/16.53 | | | | | | | | % 115.54/16.53 | | | | | | | Case 2: % 115.54/16.53 | | | | | | | | % 115.54/16.53 | | | | | | | | (493) $lesseq(all_55_1, 0) % 115.54/16.53 | | | | | | | | % 115.54/16.53 | | | | | | | | REF_CLOSE: (65), (69), (493) are inconsistent by sub-proof #1. % 115.54/16.53 | | | | | | | | % 115.54/16.53 | | | | | | | End of split % 115.54/16.53 | | | | | | | % 115.54/16.53 | | | | | | End of split % 115.54/16.53 | | | | | | % 115.54/16.53 | | | | | End of split % 115.54/16.53 | | | | | % 115.54/16.53 | | | | End of split % 115.54/16.53 | | | | % 115.54/16.53 | | | End of split % 115.54/16.53 | | | % 115.54/16.53 | | Case 2: % 115.54/16.53 | | | % 115.54/16.53 | | | (494) $lesseq(all_55_1, 0) % 115.54/16.53 | | | % 115.54/16.53 | | | REDUCE: (65), (494) imply: % 115.54/16.53 | | | (495) $lesseq(0, sc_118_0_3) % 115.54/16.53 | | | % 115.54/16.53 | | | SIMP: (495) implies: % 115.54/16.53 | | | (496) $lesseq(0, sc_118_0_3) % 115.54/16.53 | | | % 115.54/16.53 | | | COMBINE_INEQS: (69), (496) imply: % 115.54/16.53 | | | (497) $false % 115.54/16.53 | | | % 115.54/16.53 | | | CLOSE: (497) is inconsistent. % 115.54/16.53 | | | % 115.54/16.53 | | End of split % 115.54/16.53 | | % 115.54/16.53 | Case 2: % 115.54/16.53 | | % 115.54/16.54 | | (498) ~ (all_103_1 = 0) & mod1(all_55_1, 3) = all_103_1 % 115.54/16.54 | | % 115.54/16.54 | | ALPHA: (498) implies: % 115.54/16.54 | | (499) ~ (all_103_1 = 0) % 115.54/16.54 | | (500) mod1(all_55_1, 3) = all_103_1 % 115.54/16.54 | | % 115.54/16.54 | | REDUCE: (65), (500) imply: % 115.54/16.54 | | (501) mod1($product(-15, sc_118_0_3), 3) = all_103_1 % 115.54/16.54 | | % 115.54/16.54 | | GROUND_INST: instantiating (19) with 0, all_103_1, 3, $product(-15, % 115.54/16.54 | | sc_118_0_3), simplifying with (74), (501) gives: % 115.54/16.54 | | (502) all_103_1 = 0 % 115.54/16.54 | | % 115.54/16.54 | | REDUCE: (499), (502) imply: % 115.54/16.54 | | (503) $false % 115.54/16.54 | | % 115.54/16.54 | | CLOSE: (503) is inconsistent. % 115.54/16.54 | | % 115.54/16.54 | End of split % 115.54/16.54 | % 115.54/16.54 End of proof % 115.54/16.54 % 115.54/16.54 Sub-proof #1 shows that the following formulas are inconsistent: % 115.54/16.54 ---------------------------------------------------------------- % 115.54/16.54 (1) $lesseq(all_55_1, 0) % 115.54/16.54 (2) $sum(all_55_1, $product(15, sc_118_0_3)) = 0 % 115.54/16.54 (3) $lesseq(sc_118_0_3, -1) % 115.54/16.54 % 115.54/16.54 Begin of proof % 115.54/16.54 | % 115.54/16.54 | REDUCE: (1), (2) imply: % 115.54/16.54 | (4) $lesseq(0, sc_118_0_3) % 115.54/16.54 | % 115.54/16.54 | SIMP: (4) implies: % 115.54/16.54 | (5) $lesseq(0, sc_118_0_3) % 115.54/16.54 | % 115.54/16.54 | COMBINE_INEQS: (3), (5) imply: % 115.54/16.54 | (6) $false % 115.54/16.54 | % 115.54/16.54 | CLOSE: (6) is inconsistent. % 115.54/16.54 | % 115.54/16.54 End of proof % 115.54/16.54 % SZS output end Proof for theBenchmark % 115.54/16.54 % 115.54/16.54 15895ms %------------------------------------------------------------------------------