%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWW663_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 : n005.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Fri Sep 1 00:51:03 EDT 2023 % Result : Theorem 17.29s 3.16s % Output : Proof 22.60s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.10 % Problem : SWW663_2 : TPTP v8.1.2. Released v6.1.0. % 0.00/0.11 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.10/0.31 % Computer : n005.cluster.edu % 0.10/0.31 % Model : x86_64 x86_64 % 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.31 % Memory : 8042.1875MB % 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64 % 0.10/0.31 % CPULimit : 300 % 0.10/0.31 % WCLimit : 300 % 0.10/0.31 % DateTime : Sun Aug 27 20:21:23 EDT 2023 % 0.10/0.31 % CPUTime : % 0.15/0.53 ________ _____ % 0.15/0.53 ___ __ \_________(_)________________________________ % 0.15/0.53 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.15/0.53 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.15/0.53 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.15/0.53 % 0.15/0.53 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.15/0.53 (2023-06-19) % 0.15/0.53 % 0.15/0.53 (c) Philipp Rümmer, 2009-2023 % 0.15/0.53 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.15/0.53 Amanda Stjerna. % 0.15/0.53 Free software under BSD-3-Clause. % 0.15/0.53 % 0.15/0.53 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.15/0.53 % 0.15/0.53 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.15/0.54 Running up to 7 provers in parallel. % 0.15/0.56 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.15/0.56 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.15/0.56 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.15/0.56 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.15/0.56 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.15/0.56 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.15/0.56 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.11/1.45 Prover 3: Preprocessing ... % 4.11/1.45 Prover 0: Preprocessing ... % 4.11/1.46 Prover 2: Preprocessing ... % 4.11/1.46 Prover 5: Preprocessing ... % 5.09/1.47 Prover 6: Preprocessing ... % 5.09/1.47 Prover 1: Preprocessing ... % 5.09/1.47 Prover 4: Preprocessing ... % 12.72/2.49 Prover 1: Warning: ignoring some quantifiers % 12.94/2.59 Prover 3: Warning: ignoring some quantifiers % 12.94/2.64 Prover 4: Warning: ignoring some quantifiers % 12.94/2.64 Prover 1: Constructing countermodel ... % 12.94/2.65 Prover 3: Constructing countermodel ... % 12.94/2.68 Prover 6: Proving ... % 13.93/2.73 Prover 4: Constructing countermodel ... % 13.93/2.77 Prover 5: Proving ... % 15.05/2.81 Prover 0: Proving ... % 15.72/2.90 Prover 2: Proving ... % 17.29/3.16 Prover 3: proved (2596ms) % 17.29/3.16 % 17.29/3.16 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 17.29/3.16 % 17.29/3.16 Prover 5: stopped % 17.29/3.16 Prover 6: stopped % 17.29/3.16 Prover 0: stopped % 17.29/3.17 Prover 2: stopped % 17.29/3.17 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 17.29/3.17 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 17.29/3.17 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 17.29/3.17 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 17.29/3.17 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 18.67/3.39 Prover 10: Preprocessing ... % 18.67/3.43 Prover 8: Preprocessing ... % 19.00/3.45 Prover 11: Preprocessing ... % 19.92/3.47 Prover 7: Preprocessing ... % 19.92/3.53 Prover 13: Preprocessing ... % 20.69/3.56 Prover 4: Found proof (size 57) % 20.69/3.56 Prover 4: proved (3002ms) % 20.69/3.56 Prover 1: stopped % 20.69/3.58 Prover 7: stopped % 20.99/3.61 Prover 11: stopped % 21.29/3.66 Prover 10: Warning: ignoring some quantifiers % 21.63/3.71 Prover 13: stopped % 21.63/3.71 Prover 10: Constructing countermodel ... % 21.63/3.73 Prover 10: stopped % 21.63/3.75 Prover 8: Warning: ignoring some quantifiers % 21.94/3.78 Prover 8: Constructing countermodel ... % 21.94/3.79 Prover 8: stopped % 21.94/3.79 % 21.94/3.79 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 21.94/3.79 % 21.94/3.80 % SZS output start Proof for theBenchmark % 21.94/3.81 Assumptions after simplification: % 21.94/3.81 --------------------------------- % 21.94/3.81 % 21.94/3.81 (div_mod_2) % 21.94/3.83 ! [v0: int] : ! [v1: int] : ( ~ ($lesseq(2, $difference(v0, $product(2, % 21.94/3.83 v1)))) | ~ ($lesseq(0, v0)) | ~ (div1(v0, 2) = v1)) & ! [v0: int] % 21.94/3.83 : ! [v1: int] : ( ~ ($lesseq(1, $difference($product(2, v1), v0))) | ~ % 21.94/3.83 ($lesseq(0, v0)) | ~ (div1(v0, 2) = v1)) % 21.94/3.83 % 21.94/3.83 (is_power_of_2_1) % 21.94/3.84 ! [v0: int] : ! [v1: int] : ($product(2, v1) = v0 | ~ ($lesseq(2, v0)) | ~ % 21.94/3.84 (div1(v0, 2) = v1) | ? [v2: int] : ( ~ (v2 = 0) & is_power_of_21(v0) = v2)) % 21.94/3.84 & ! [v0: int] : ( ~ ($lesseq(2, v0)) | ~ (is_power_of_21(v0) = 0) | ? [v1: % 21.94/3.84 int] : ($product(2, v1) = v0 & div1(v0, 2) = v1)) % 21.94/3.84 % 21.94/3.84 (is_power_of_2_def) % 21.94/3.84 ! [v0: int] : ! [v1: int] : ! [v2: int] : (v1 = 0 | ~ ($lesseq(0, v2)) | % 21.94/3.84 ~ (is_power_of_21(v0) = v1) | ~ (power1(2, v2) = v0)) & ! [v0: int] : ( ~ % 21.94/3.84 (is_power_of_21(v0) = 0) | ? [v1: int] : ($lesseq(0, v1) & power1(2, v1) = % 21.94/3.84 v0)) % 21.94/3.84 % 21.94/3.84 (power_0) % 21.94/3.84 ! [v0: int] : ! [v1: int] : (v1 = 1 | ~ (power1(v0, 0) = v1)) % 21.94/3.84 % 21.94/3.84 (power_s_alt) % 21.94/3.84 ! [v0: int] : ! [v1: int] : ! [v2: int] : ( ~ ($lesseq(1, v1)) | ~ % 21.94/3.84 (power1(v0, $sum(v1, -1)) = v2) | ? [v3: int] : (power1(v0, v1) = v3 & % 21.94/3.84 $product(v0, v2) = v3)) & ! [v0: int] : ! [v1: int] : ! [v2: int] : ( ~ % 21.94/3.84 ($lesseq(1, v1)) | ~ (power1(v0, v1) = v2) | ? [v3: int] : (power1(v0, % 21.94/3.84 $sum(v1, -1)) = v3 & $product(v0, v3) = v2)) % 21.94/3.84 % 21.94/3.84 (wP_parameter_compute_sums) % 21.94/3.85 ty(int) & ? [v0: int] : ? [v1: map_int_int] : ? [v2: uni] : ? [v3: int] : % 21.94/3.85 ? [v4: int] : ? [v5: map_int_int] : ? [v6: uni] : ( ~ (v4 = 0) & $lesseq(2, % 21.94/3.85 v0) & is_power_of_21($difference(v0, v3)) = v4 & is_power_of_21(v0) = 0 & % 21.94/3.85 t2tb1(v5) = v6 & t2tb1(v1) = v2 & div1(v0, 2) = v3 & map_int_int(v5) & % 21.94/3.85 map_int_int(v1) & uni(v6) & uni(v2) & ! [v7: int] : ! [v8: uni] : ( ~ % 21.94/3.85 ($lesseq(1, $difference(v0, v7))) | ~ ($lesseq(0, v7)) | ~ (t2tb(v7) = % 21.94/3.85 v8) | ? [v9: uni] : ? [v10: int] : ? [v11: uni] : (tb2t(v11) = v10 & % 21.94/3.85 tb2t(v9) = v10 & get(int, int, v6, v8) = v9 & get(int, int, v2, v8) = % 21.94/3.85 v11 & uni(v11) & uni(v9)))) % 21.94/3.85 % 21.94/3.85 Further assumptions not needed in the proof: % 21.94/3.85 -------------------------------------------- % 21.94/3.85 abs_def, abs_le, abs_pos, array_inversion1, bool_inversion, bridgeL, bridgeL1, % 21.94/3.85 bridgeL2, bridgeR, bridgeR1, bridgeR2, compatOrderMult, const, const_sort1, % 21.94/3.85 div_1, div_bound, div_inf, div_mod, div_mult, div_sign_neg, div_sign_pos, % 21.94/3.85 elts_def1, elts_sort1, get_def, get_sort2, get_sort3, go_left_def, go_right_def, % 21.94/3.85 leaf, length_def1, make_def, make_sort1, match_bool_False, match_bool_True, % 21.94/3.85 match_bool_sort1, mk_array_sort1, mod_1, mod_bound, mod_inf, mod_mult, % 21.94/3.85 mod_sign_neg, mod_sign_pos, node, partial_sum_def, phase1_frame, phase1_frame2, % 21.94/3.85 phase1_inversion, power_1, power_mult, power_mult2, power_s, power_sum, % 21.94/3.85 rounds_toward_zero, select_eq, select_neq, set_def, set_sort2, set_sort3, % 21.94/3.85 sum_def, sum_def_empty, sum_def_non_empty, sum_eq, sum_right_extension, % 21.94/3.85 sum_transitivity, t2tb_sort, t2tb_sort1, t2tb_sort2, true_False, % 21.94/3.85 tuple0_inversion, witness_sort1 % 21.94/3.85 % 21.94/3.85 Those formulas are unsatisfiable: % 21.94/3.85 --------------------------------- % 21.94/3.85 % 21.94/3.85 Begin of proof % 22.41/3.85 | % 22.41/3.85 | ALPHA: (power_s_alt) implies: % 22.41/3.86 | (1) ! [v0: int] : ! [v1: int] : ! [v2: int] : ( ~ ($lesseq(1, v1)) | ~ % 22.41/3.86 | (power1(v0, v1) = v2) | ? [v3: int] : (power1(v0, $sum(v1, -1)) = v3 % 22.41/3.86 | & $product(v0, v3) = v2)) % 22.41/3.86 | % 22.41/3.86 | ALPHA: (div_mod_2) implies: % 22.41/3.86 | (2) ! [v0: int] : ! [v1: int] : ( ~ ($lesseq(1, $difference($product(2, % 22.41/3.86 | v1), v0))) | ~ ($lesseq(0, v0)) | ~ (div1(v0, 2) = v1)) % 22.41/3.86 | (3) ! [v0: int] : ! [v1: int] : ( ~ ($lesseq(2, $difference(v0, % 22.41/3.86 | $product(2, v1)))) | ~ ($lesseq(0, v0)) | ~ (div1(v0, 2) = % 22.41/3.86 | v1)) % 22.41/3.86 | % 22.41/3.86 | ALPHA: (is_power_of_2_def) implies: % 22.41/3.86 | (4) ! [v0: int] : ( ~ (is_power_of_21(v0) = 0) | ? [v1: int] : % 22.41/3.86 | ($lesseq(0, v1) & power1(2, v1) = v0)) % 22.41/3.86 | (5) ! [v0: int] : ! [v1: int] : ! [v2: int] : (v1 = 0 | ~ ($lesseq(0, % 22.41/3.86 | v2)) | ~ (is_power_of_21(v0) = v1) | ~ (power1(2, v2) = v0)) % 22.41/3.86 | % 22.41/3.86 | ALPHA: (is_power_of_2_1) implies: % 22.41/3.86 | (6) ! [v0: int] : ( ~ ($lesseq(2, v0)) | ~ (is_power_of_21(v0) = 0) | ? % 22.41/3.86 | [v1: int] : ($product(2, v1) = v0 & div1(v0, 2) = v1)) % 22.41/3.86 | % 22.41/3.86 | ALPHA: (wP_parameter_compute_sums) implies: % 22.41/3.87 | (7) ? [v0: int] : ? [v1: map_int_int] : ? [v2: uni] : ? [v3: int] : ? % 22.41/3.87 | [v4: int] : ? [v5: map_int_int] : ? [v6: uni] : ( ~ (v4 = 0) & % 22.41/3.87 | $lesseq(2, v0) & is_power_of_21($difference(v0, v3)) = v4 & % 22.41/3.87 | is_power_of_21(v0) = 0 & t2tb1(v5) = v6 & t2tb1(v1) = v2 & div1(v0, % 22.41/3.87 | 2) = v3 & map_int_int(v5) & map_int_int(v1) & uni(v6) & uni(v2) & % 22.41/3.87 | ! [v7: int] : ! [v8: uni] : ( ~ ($lesseq(1, $difference(v0, v7))) | % 22.41/3.87 | ~ ($lesseq(0, v7)) | ~ (t2tb(v7) = v8) | ? [v9: uni] : ? [v10: % 22.41/3.87 | int] : ? [v11: uni] : (tb2t(v11) = v10 & tb2t(v9) = v10 & % 22.41/3.87 | get(int, int, v6, v8) = v9 & get(int, int, v2, v8) = v11 & % 22.41/3.87 | uni(v11) & uni(v9)))) % 22.41/3.87 | % 22.41/3.87 | DELTA: instantiating (7) with fresh symbols all_101_0, all_101_1, all_101_2, % 22.41/3.87 | all_101_3, all_101_4, all_101_5, all_101_6 gives: % 22.41/3.87 | (8) ~ (all_101_2 = 0) & $lesseq(2, all_101_6) & % 22.41/3.87 | is_power_of_21($difference(all_101_6, all_101_3)) = all_101_2 & % 22.41/3.87 | is_power_of_21(all_101_6) = 0 & t2tb1(all_101_1) = all_101_0 & % 22.41/3.87 | t2tb1(all_101_5) = all_101_4 & div1(all_101_6, 2) = all_101_3 & % 22.41/3.87 | map_int_int(all_101_1) & map_int_int(all_101_5) & uni(all_101_0) & % 22.41/3.87 | uni(all_101_4) & ! [v0: int] : ! [v1: uni] : ( ~ ($lesseq(1, % 22.41/3.87 | $difference(all_101_6, v0))) | ~ ($lesseq(0, v0)) | ~ (t2tb(v0) % 22.41/3.87 | = v1) | ? [v2: uni] : ? [v3: int] : ? [v4: uni] : (tb2t(v4) = v3 % 22.41/3.87 | & tb2t(v2) = v3 & get(int, int, all_101_0, v1) = v2 & get(int, int, % 22.41/3.87 | all_101_4, v1) = v4 & uni(v4) & uni(v2))) % 22.41/3.87 | % 22.41/3.87 | ALPHA: (8) implies: % 22.41/3.87 | (9) ~ (all_101_2 = 0) % 22.41/3.87 | (10) $lesseq(2, all_101_6) % 22.41/3.87 | (11) div1(all_101_6, 2) = all_101_3 % 22.41/3.87 | (12) is_power_of_21(all_101_6) = 0 % 22.41/3.87 | (13) is_power_of_21($difference(all_101_6, all_101_3)) = all_101_2 % 22.41/3.87 | % 22.41/3.87 | GROUND_INST: instantiating (3) with all_101_6, all_101_3, simplifying with % 22.41/3.88 | (11) gives: % 22.41/3.88 | (14) ~ ($lesseq(2, $difference(all_101_6, $product(2, all_101_3)))) | ~ % 22.41/3.88 | ($lesseq(0, all_101_6)) % 22.41/3.88 | % 22.41/3.88 | GROUND_INST: instantiating (2) with all_101_6, all_101_3, simplifying with % 22.41/3.88 | (11) gives: % 22.41/3.88 | (15) ~ ($lesseq(1, $difference($product(2, all_101_3), all_101_6))) | ~ % 22.41/3.88 | ($lesseq(0, all_101_6)) % 22.41/3.88 | % 22.41/3.88 | GROUND_INST: instantiating (6) with all_101_6, simplifying with (12) gives: % 22.41/3.88 | (16) ~ ($lesseq(2, all_101_6)) | ? [v0: int] : ($product(2, v0) = % 22.41/3.88 | all_101_6 & div1(all_101_6, 2) = v0) % 22.41/3.88 | % 22.41/3.88 | GROUND_INST: instantiating (4) with all_101_6, simplifying with (12) gives: % 22.41/3.88 | (17) ? [v0: int] : ($lesseq(0, v0) & power1(2, v0) = all_101_6) % 22.41/3.88 | % 22.41/3.88 | DELTA: instantiating (17) with fresh symbol all_113_0 gives: % 22.41/3.88 | (18) $lesseq(0, all_113_0) & power1(2, all_113_0) = all_101_6 % 22.41/3.88 | % 22.41/3.88 | ALPHA: (18) implies: % 22.41/3.88 | (19) $lesseq(0, all_113_0) % 22.41/3.88 | (20) power1(2, all_113_0) = all_101_6 % 22.41/3.88 | % 22.41/3.88 | BETA: splitting (15) gives: % 22.41/3.88 | % 22.41/3.88 | Case 1: % 22.41/3.88 | | % 22.41/3.88 | | (21) $lesseq(all_101_6, -1) % 22.41/3.88 | | % 22.41/3.88 | | COMBINE_INEQS: (10), (21) imply: % 22.41/3.88 | | (22) $false % 22.41/3.88 | | % 22.41/3.88 | | CLOSE: (22) is inconsistent. % 22.41/3.88 | | % 22.41/3.88 | Case 2: % 22.41/3.88 | | % 22.41/3.88 | | (23) $lesseq(0, $difference(all_101_6, $product(2, all_101_3))) % 22.41/3.88 | | % 22.41/3.88 | | BETA: splitting (14) gives: % 22.41/3.88 | | % 22.41/3.88 | | Case 1: % 22.41/3.88 | | | % 22.41/3.88 | | | (24) $lesseq(all_101_6, -1) % 22.41/3.88 | | | % 22.41/3.88 | | | COMBINE_INEQS: (10), (24) imply: % 22.41/3.88 | | | (25) $false % 22.41/3.88 | | | % 22.41/3.88 | | | CLOSE: (25) is inconsistent. % 22.41/3.88 | | | % 22.41/3.88 | | Case 2: % 22.41/3.89 | | | % 22.41/3.89 | | | (26) $lesseq(-1, $difference($product(2, all_101_3), all_101_6)) % 22.41/3.89 | | | % 22.41/3.89 | | | COMBINE_INEQS: (10), (26) imply: % 22.41/3.89 | | | (27) $lesseq(1, all_101_3) % 22.41/3.89 | | | % 22.41/3.89 | | | SIMP: (27) implies: % 22.41/3.89 | | | (28) $lesseq(1, all_101_3) % 22.41/3.89 | | | % 22.41/3.89 | | | BETA: splitting (16) gives: % 22.41/3.89 | | | % 22.41/3.89 | | | Case 1: % 22.41/3.89 | | | | % 22.41/3.89 | | | | (29) $lesseq(all_101_6, 1) % 22.41/3.89 | | | | % 22.41/3.89 | | | | COMBINE_INEQS: (10), (29) imply: % 22.41/3.89 | | | | (30) $false % 22.41/3.89 | | | | % 22.41/3.89 | | | | CLOSE: (30) is inconsistent. % 22.41/3.89 | | | | % 22.41/3.89 | | | Case 2: % 22.41/3.89 | | | | % 22.41/3.89 | | | | (31) ? [v0: int] : ($product(2, v0) = all_101_6 & div1(all_101_6, 2) % 22.41/3.89 | | | | = v0) % 22.41/3.89 | | | | % 22.41/3.89 | | | | DELTA: instantiating (31) with fresh symbol all_148_0 gives: % 22.41/3.89 | | | | (32) $product(2, all_148_0) = all_101_6 & div1(all_101_6, 2) = % 22.41/3.89 | | | | all_148_0 % 22.41/3.89 | | | | % 22.41/3.89 | | | | ALPHA: (32) implies: % 22.41/3.89 | | | | (33) $product(2, all_148_0) = all_101_6 % 22.41/3.89 | | | | % 22.41/3.89 | | | | COL_REDUCE: introducing fresh symbol sc_150_0_0 defined by: % 22.41/3.89 | | | | (34) $difference(all_148_0, all_101_6) = sc_150_0_0 % 22.41/3.89 | | | | % 22.41/3.89 | | | | COMBINE_EQS: (33), (34) imply: % 22.41/3.89 | | | | (35) $sum(all_101_6, $product(2, sc_150_0_0)) = 0 % 22.41/3.89 | | | | % 22.41/3.89 | | | | REDUCE: (23), (35) imply: % 22.41/3.89 | | | | (36) $lesseq(sc_150_0_0, $product(-1, all_101_3)) % 22.41/3.89 | | | | % 22.41/3.89 | | | | SIMP: (36) implies: % 22.41/3.89 | | | | (37) $lesseq(sc_150_0_0, $product(-1, all_101_3)) % 22.41/3.89 | | | | % 22.41/3.89 | | | | REDUCE: (26), (35) imply: % 22.41/3.89 | | | | (38) $lesseq(0, $sum(all_101_3, sc_150_0_0)) % 22.41/3.89 | | | | % 22.41/3.89 | | | | SIMP: (38) implies: % 22.41/3.89 | | | | (39) $lesseq(0, $sum(all_101_3, sc_150_0_0)) % 22.60/3.89 | | | | % 22.60/3.89 | | | | ANTI_SYMM: (37), (39) imply: % 22.60/3.89 | | | | (40) $sum(all_101_3, sc_150_0_0) = 0 % 22.60/3.89 | | | | % 22.60/3.89 | | | | REDUCE: (13), (35), (40) imply: % 22.60/3.89 | | | | (41) is_power_of_21($product(-1, sc_150_0_0)) = all_101_2 % 22.60/3.89 | | | | % 22.60/3.89 | | | | REDUCE: (20), (35) imply: % 22.60/3.89 | | | | (42) power1(2, all_113_0) = $product(-2, sc_150_0_0) % 22.60/3.89 | | | | % 22.60/3.90 | | | | GROUND_INST: instantiating (power_0) with 2, $product(-2, sc_150_0_0) % 22.60/3.90 | | | | gives: % 22.60/3.90 | | | | (43) ~ (power1(2, 0) = $product(-2, sc_150_0_0)) % 22.60/3.90 | | | | % 22.60/3.90 | | | | PRED_UNIFY: (42), (43) imply: % 22.60/3.90 | | | | (44) ~ (all_113_0 = 0) % 22.60/3.90 | | | | % 22.60/3.90 | | | | STRENGTHEN: (19), (44) imply: % 22.60/3.90 | | | | (45) $lesseq(1, all_113_0) % 22.60/3.90 | | | | % 22.60/3.90 | | | | GROUND_INST: instantiating (1) with 2, all_113_0, $product(-2, % 22.60/3.90 | | | | sc_150_0_0), simplifying with (42) gives: % 22.60/3.90 | | | | (46) ~ ($lesseq(1, all_113_0)) | ? [v0: int] : (power1(2, % 22.60/3.90 | | | | $sum(all_113_0, -1)) = v0 & $product(2, v0) = $product(-2, % 22.60/3.90 | | | | sc_150_0_0)) % 22.60/3.90 | | | | % 22.60/3.90 | | | | BETA: splitting (46) gives: % 22.60/3.90 | | | | % 22.60/3.90 | | | | Case 1: % 22.60/3.90 | | | | | % 22.60/3.90 | | | | | (47) $lesseq(all_113_0, 0) % 22.60/3.90 | | | | | % 22.60/3.90 | | | | | COMBINE_INEQS: (45), (47) imply: % 22.60/3.90 | | | | | (48) $false % 22.60/3.90 | | | | | % 22.60/3.90 | | | | | CLOSE: (48) is inconsistent. % 22.60/3.90 | | | | | % 22.60/3.90 | | | | Case 2: % 22.60/3.90 | | | | | % 22.60/3.90 | | | | | (49) ? [v0: int] : (power1(2, $sum(all_113_0, -1)) = v0 & % 22.60/3.90 | | | | | $product(2, v0) = $product(-2, sc_150_0_0)) % 22.60/3.90 | | | | | % 22.60/3.90 | | | | | DELTA: instantiating (49) with fresh symbol all_181_0 gives: % 22.60/3.90 | | | | | (50) power1(2, $sum(all_113_0, -1)) = all_181_0 & $product(2, % 22.60/3.90 | | | | | all_181_0) = $product(-2, sc_150_0_0) % 22.60/3.90 | | | | | % 22.60/3.90 | | | | | ALPHA: (50) implies: % 22.60/3.90 | | | | | (51) $product(2, all_181_0) = $product(-2, sc_150_0_0) % 22.60/3.90 | | | | | (52) power1(2, $sum(all_113_0, -1)) = all_181_0 % 22.60/3.90 | | | | | % 22.60/3.90 | | | | | THEORY_AXIOM GroebnerMultiplication: % 22.60/3.90 | | | | | (53) ! [v0: int] : ! [v1: int] : ($sum(v1, v0) = 0 | ~ % 22.60/3.90 | | | | | ($product(2, v1) = $product(-2, v0))) % 22.60/3.90 | | | | | % 22.60/3.90 | | | | | GROUND_INST: instantiating (53) with sc_150_0_0, all_181_0, % 22.60/3.90 | | | | | simplifying with (51) gives: % 22.60/3.90 | | | | | (54) $sum(all_181_0, sc_150_0_0) = 0 % 22.60/3.90 | | | | | % 22.60/3.90 | | | | | REDUCE: (52), (54) imply: % 22.60/3.90 | | | | | (55) power1(2, $sum(all_113_0, -1)) = $product(-1, sc_150_0_0) % 22.60/3.90 | | | | | % 22.60/3.90 | | | | | GROUND_INST: instantiating (5) with $product(-1, sc_150_0_0), % 22.60/3.90 | | | | | all_101_2, $sum(all_113_0, -1), simplifying with (41), % 22.60/3.90 | | | | | (55) gives: % 22.60/3.90 | | | | | (56) all_101_2 = 0 | ~ ($lesseq(1, all_113_0)) % 22.60/3.90 | | | | | % 22.60/3.90 | | | | | BETA: splitting (56) gives: % 22.60/3.90 | | | | | % 22.60/3.90 | | | | | Case 1: % 22.60/3.90 | | | | | | % 22.60/3.90 | | | | | | (57) $lesseq(all_113_0, 0) % 22.60/3.91 | | | | | | % 22.60/3.91 | | | | | | COMBINE_INEQS: (45), (57) imply: % 22.60/3.91 | | | | | | (58) $false % 22.60/3.91 | | | | | | % 22.60/3.91 | | | | | | CLOSE: (58) is inconsistent. % 22.60/3.91 | | | | | | % 22.60/3.91 | | | | | Case 2: % 22.60/3.91 | | | | | | % 22.60/3.91 | | | | | | (59) all_101_2 = 0 % 22.60/3.91 | | | | | | % 22.60/3.91 | | | | | | REDUCE: (9), (59) imply: % 22.60/3.91 | | | | | | (60) $false % 22.60/3.91 | | | | | | % 22.60/3.91 | | | | | | CLOSE: (60) is inconsistent. % 22.60/3.91 | | | | | | % 22.60/3.91 | | | | | End of split % 22.60/3.91 | | | | | % 22.60/3.91 | | | | End of split % 22.60/3.91 | | | | % 22.60/3.91 | | | End of split % 22.60/3.91 | | | % 22.60/3.91 | | End of split % 22.60/3.91 | | % 22.60/3.91 | End of split % 22.60/3.91 | % 22.60/3.91 End of proof % 22.60/3.91 % SZS output end Proof for theBenchmark % 22.60/3.91 % 22.60/3.91 3378ms %------------------------------------------------------------------------------