%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWX000_1 : TPTP v9.1.0. Released v9.1.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n018.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 : Sun Apr 6 10:08:52 AM UTC 2025 % Result : Theorem 11.88s 2.34s % Output : Proof 15.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.01/0.10 % Problem : SWX000_1 : TPTP v9.1.0. Released v9.1.0. % 0.01/0.11 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.11/0.31 % Computer : n018.cluster.edu % 0.11/0.31 % Model : x86_64 x86_64 % 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.31 % Memory : 8042.1875MB % 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.31 % CPULimit : 300 % 0.11/0.31 % WCLimit : 300 % 0.11/0.31 % DateTime : Sun Apr 6 03:10:32 EDT 2025 % 0.16/0.31 % CPUTime : % 0.16/0.55 ________ _____ % 0.16/0.55 ___ __ \_________(_)________________________________ % 0.16/0.55 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.16/0.55 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.16/0.55 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.16/0.55 % 0.16/0.55 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.16/0.55 (2023-06-19) % 0.16/0.55 % 0.16/0.55 (c) Philipp Rümmer, 2009-2023 % 0.16/0.55 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.16/0.55 Amanda Stjerna. % 0.16/0.55 Free software under BSD-3-Clause. % 0.16/0.55 % 0.16/0.55 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.16/0.55 % 0.16/0.55 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.16/0.56 Running up to 7 provers in parallel. % 0.16/0.57 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.16/0.57 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.16/0.57 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.16/0.57 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.16/0.57 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.16/0.57 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.16/0.57 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.69/1.20 Prover 1: Preprocessing ... % 3.69/1.20 Prover 4: Preprocessing ... % 3.69/1.20 Prover 0: Preprocessing ... % 3.89/1.21 Prover 6: Preprocessing ... % 3.89/1.21 Prover 5: Preprocessing ... % 3.89/1.21 Prover 2: Preprocessing ... % 3.89/1.21 Prover 3: Preprocessing ... % 7.42/1.75 Prover 1: Warning: ignoring some quantifiers % 7.42/1.75 Prover 5: Proving ... % 7.42/1.76 Prover 6: Proving ... % 7.42/1.76 Prover 3: Warning: ignoring some quantifiers % 7.42/1.77 Prover 1: Constructing countermodel ... % 7.42/1.78 Prover 3: Constructing countermodel ... % 7.42/1.78 Prover 0: Proving ... % 7.42/1.78 Prover 2: Proving ... % 7.42/1.78 Prover 4: Constructing countermodel ... % 11.88/2.33 Prover 0: proved (1758ms) % 11.88/2.34 % 11.88/2.34 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 11.88/2.34 % 11.88/2.34 Prover 2: stopped % 11.88/2.34 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 11.88/2.34 Prover 5: stopped % 11.88/2.34 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 11.88/2.34 Prover 3: stopped % 11.88/2.35 Prover 6: stopped % 11.88/2.36 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 11.88/2.37 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 11.88/2.37 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 11.88/2.39 Prover 1: gave up % 12.60/2.40 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 12.60/2.46 Prover 7: Preprocessing ... % 12.60/2.47 Prover 10: Preprocessing ... % 12.60/2.49 Prover 11: Preprocessing ... % 13.31/2.50 Prover 8: Preprocessing ... % 13.31/2.52 Prover 13: Preprocessing ... % 13.31/2.53 Prover 16: Preprocessing ... % 13.31/2.57 Prover 7: Warning: ignoring some quantifiers % 13.31/2.58 Prover 7: Constructing countermodel ... % 14.14/2.61 Prover 10: Warning: ignoring some quantifiers % 14.14/2.63 Prover 10: Constructing countermodel ... % 14.14/2.66 Prover 13: Warning: ignoring some quantifiers % 14.14/2.67 Prover 13: Constructing countermodel ... % 14.14/2.67 Prover 16: Warning: ignoring some quantifiers % 14.14/2.68 Prover 16: Constructing countermodel ... % 14.14/2.68 Prover 8: Warning: ignoring some quantifiers % 14.14/2.69 Prover 8: Constructing countermodel ... % 14.86/2.71 Prover 11: Constructing countermodel ... % 14.86/2.72 Prover 4: Found proof (size 142) % 14.86/2.72 Prover 4: proved (2151ms) % 14.86/2.72 Prover 16: stopped % 14.86/2.72 Prover 7: stopped % 14.86/2.72 Prover 11: stopped % 14.86/2.72 Prover 8: stopped % 14.86/2.72 Prover 13: stopped % 14.86/2.72 Prover 10: stopped % 14.86/2.72 % 14.86/2.72 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 14.86/2.72 % 14.86/2.74 % SZS output start Proof for theBenchmark % 14.86/2.74 Assumptions after simplification: % 14.86/2.74 --------------------------------- % 14.86/2.74 % 14.86/2.74 (f__integer__def_ax) % 14.86/2.76 ! [v0: int] : ! [v1: general] : ! [v2: general] : (v2 = v1 | ~ % 14.86/2.76 (f__integer__(v0) = v2) | ~ (f__integer__(v0) = v1)) & ! [v0: int] : ! % 14.86/2.76 [v1: int] : ! [v2: general] : (v1 = v0 | ~ (f__integer__(v1) = v2) | ~ % 14.86/2.76 (f__integer__(v0) = v2)) % 14.86/2.76 % 14.86/2.76 (formula_1_left_0) % 14.86/2.77 ! [v0: general] : ! [v1: general] : ! [v2: int] : ! [v3: int] : ! [v4: % 14.86/2.77 int] : ! [v5: int] : (v2 = 0 | ~ ($lesseq(v5, 1)) | ~ ($lesseq(0, v5)) | % 14.86/2.77 ~ (tp(v0) = v2) | ~ (f__integer__(v5) = v1) | ~ (f__integer__(v4) = v1) | % 14.86/2.77 ~ (f__integer__(v3) = v1) | ~ general(v1) | ~ general(v0) | ? [v6: int] : % 14.86/2.77 ? [v7: general] : ( ~ (v7 = v0) & f__integer__(v6) = v7 & $product(v3, v4) % 14.86/2.77 = v6 & general(v7))) & ! [v0: general] : ! [v1: general] : ! [v2: int] % 14.86/2.77 : ! [v3: int] : ! [v4: int] : ! [v5: int] : (v2 = 0 | ~ ($lesseq(v5, 1)) | % 14.86/2.77 ~ ($lesseq(0, v5)) | ~ (hp(v0) = v2) | ~ (f__integer__(v5) = v1) | ~ % 14.86/2.77 (f__integer__(v4) = v1) | ~ (f__integer__(v3) = v1) | ~ general(v1) | ~ % 14.86/2.77 general(v0) | ? [v6: int] : ? [v7: general] : ( ~ (v7 = v0) & % 14.86/2.77 f__integer__(v6) = v7 & $product(v3, v4) = v6 & general(v7))) % 14.86/2.77 % 14.86/2.77 (formula_2_right_0) % 14.86/2.77 ? [v0: general] : ? [v1: general] : ? [v2: any] : ? [v3: any] : ? [v4: % 14.86/2.77 int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ($lesseq(v7, 1) & % 14.86/2.77 $lesseq(-1, v7) & tp(v0) = v3 & hp(v0) = v2 & f__integer__(v7) = v1 & % 14.86/2.77 f__integer__(v6) = v0 & f__integer__(v5) = v1 & f__integer__(v4) = v1 & % 14.86/2.77 $product(v4, v5) = v6 & general(v1) & general(v0) & ( ~ (v3 = 0) | ~ (v2 = % 14.86/2.77 0))) % 14.86/2.77 % 14.86/2.77 Further assumptions not needed in the proof: % 14.86/2.77 -------------------------------------------- % 14.86/2.77 antisymmetric_ordering_ax, f__symbolic__def_ax, formula_0_transition_axiom_0, % 14.86/2.77 general_universe_ax, maximal_element_ax, minimal_element_ax, % 14.86/2.77 numeral_ordering_ax, numerals_less_than_symbols_ax, p__greater__def_ax, % 14.86/2.77 p__greater_equal__def_ax, p__is_integer__def_ax, p__is_symbolic__def_ax, % 14.86/2.77 p__less__def_ax, strongly_connected_ordering_ax, transitive_ordering_ax % 14.86/2.77 % 14.86/2.77 Those formulas are unsatisfiable: % 14.86/2.77 --------------------------------- % 14.86/2.77 % 14.86/2.77 Begin of proof % 14.86/2.77 | % 14.86/2.77 | ALPHA: (f__integer__def_ax) implies: % 14.86/2.78 | (1) ! [v0: int] : ! [v1: int] : ! [v2: general] : (v1 = v0 | ~ % 14.86/2.78 | (f__integer__(v1) = v2) | ~ (f__integer__(v0) = v2)) % 14.86/2.78 | (2) ! [v0: int] : ! [v1: general] : ! [v2: general] : (v2 = v1 | ~ % 14.86/2.78 | (f__integer__(v0) = v2) | ~ (f__integer__(v0) = v1)) % 14.86/2.78 | % 14.86/2.78 | ALPHA: (formula_1_left_0) implies: % 14.86/2.78 | (3) ! [v0: general] : ! [v1: general] : ! [v2: int] : ! [v3: int] : ! % 14.86/2.78 | [v4: int] : ! [v5: int] : (v2 = 0 | ~ ($lesseq(v5, 1)) | ~ % 14.86/2.78 | ($lesseq(0, v5)) | ~ (hp(v0) = v2) | ~ (f__integer__(v5) = v1) | ~ % 14.86/2.78 | (f__integer__(v4) = v1) | ~ (f__integer__(v3) = v1) | ~ general(v1) % 14.86/2.78 | | ~ general(v0) | ? [v6: int] : ? [v7: general] : ( ~ (v7 = v0) & % 14.86/2.78 | f__integer__(v6) = v7 & $product(v3, v4) = v6 & general(v7))) % 14.86/2.78 | (4) ! [v0: general] : ! [v1: general] : ! [v2: int] : ! [v3: int] : ! % 14.86/2.78 | [v4: int] : ! [v5: int] : (v2 = 0 | ~ ($lesseq(v5, 1)) | ~ % 14.86/2.78 | ($lesseq(0, v5)) | ~ (tp(v0) = v2) | ~ (f__integer__(v5) = v1) | ~ % 14.86/2.78 | (f__integer__(v4) = v1) | ~ (f__integer__(v3) = v1) | ~ general(v1) % 14.86/2.78 | | ~ general(v0) | ? [v6: int] : ? [v7: general] : ( ~ (v7 = v0) & % 14.86/2.78 | f__integer__(v6) = v7 & $product(v3, v4) = v6 & general(v7))) % 14.86/2.78 | % 14.86/2.78 | DELTA: instantiating (formula_2_right_0) with fresh symbols all_25_0, % 14.86/2.78 | all_25_1, all_25_2, all_25_3, all_25_4, all_25_5, all_25_6, all_25_7 % 14.86/2.78 | gives: % 14.86/2.79 | (5) $lesseq(all_25_0, 1) & $lesseq(-1, all_25_0) & tp(all_25_7) = all_25_4 % 14.86/2.79 | & hp(all_25_7) = all_25_5 & f__integer__(all_25_0) = all_25_6 & % 14.86/2.79 | f__integer__(all_25_1) = all_25_7 & f__integer__(all_25_2) = all_25_6 & % 14.86/2.79 | f__integer__(all_25_3) = all_25_6 & $product(all_25_3, all_25_2) = % 14.86/2.79 | all_25_1 & general(all_25_6) & general(all_25_7) & ( ~ (all_25_4 = 0) | % 14.86/2.79 | ~ (all_25_5 = 0)) % 14.86/2.79 | % 14.86/2.79 | ALPHA: (5) implies: % 14.86/2.79 | (6) $lesseq(-1, all_25_0) % 14.86/2.79 | (7) $lesseq(all_25_0, 1) % 14.86/2.79 | (8) general(all_25_7) % 14.86/2.79 | (9) general(all_25_6) % 14.86/2.79 | (10) $product(all_25_3, all_25_2) = all_25_1 % 14.86/2.79 | (11) f__integer__(all_25_3) = all_25_6 % 14.86/2.79 | (12) f__integer__(all_25_2) = all_25_6 % 14.86/2.79 | (13) f__integer__(all_25_1) = all_25_7 % 14.86/2.79 | (14) f__integer__(all_25_0) = all_25_6 % 14.86/2.79 | (15) hp(all_25_7) = all_25_5 % 14.86/2.79 | (16) tp(all_25_7) = all_25_4 % 14.86/2.79 | (17) ~ (all_25_4 = 0) | ~ (all_25_5 = 0) % 14.86/2.79 | % 14.86/2.79 | GROUND_INST: instantiating (1) with all_25_2, all_25_0, all_25_6, simplifying % 14.86/2.79 | with (12), (14) gives: % 14.86/2.79 | (18) all_25_0 = all_25_2 % 14.86/2.79 | % 14.86/2.79 | GROUND_INST: instantiating (1) with all_25_3, all_25_0, all_25_6, simplifying % 14.86/2.79 | with (11), (14) gives: % 14.86/2.79 | (19) all_25_0 = all_25_3 % 14.86/2.79 | % 14.86/2.79 | COMBINE_EQS: (18), (19) imply: % 14.86/2.79 | (20) all_25_2 = all_25_3 % 14.86/2.79 | % 14.86/2.79 | SIMP: (20) implies: % 14.86/2.79 | (21) all_25_2 = all_25_3 % 14.86/2.79 | % 15.36/2.79 | REDUCE: (7), (19) imply: % 15.36/2.79 | (22) $lesseq(all_25_3, 1) % 15.36/2.79 | % 15.36/2.79 | REDUCE: (6), (19) imply: % 15.36/2.79 | (23) $lesseq(-1, all_25_3) % 15.36/2.79 | % 15.36/2.79 | REDUCE: (10), (21) imply: % 15.36/2.79 | (24) $product(all_25_3, all_25_3) = all_25_1 % 15.36/2.79 | % 15.36/2.79 | THEORY_AXIOM GroebnerMultiplication: % 15.36/2.79 | (25) ! [v0: int] : ! [v1: int] : ( ~ ($lesseq(2, $difference($product(2, % 15.36/2.79 | v0), v1))) | ~ ($lesseq(v0, 1)) | ~ ($product(v0, v0) = % 15.36/2.79 | v1)) % 15.36/2.79 | % 15.36/2.80 | GROUND_INST: instantiating (25) with all_25_3, all_25_1, simplifying with (24) % 15.36/2.80 | gives: % 15.36/2.80 | (26) ~ ($lesseq(2, $difference($product(2, all_25_3), all_25_1))) | ~ % 15.36/2.80 | ($lesseq(all_25_3, 1)) % 15.36/2.80 | % 15.36/2.80 | BETA: splitting (26) gives: % 15.36/2.80 | % 15.36/2.80 | Case 1: % 15.36/2.80 | | % 15.36/2.80 | | (27) $lesseq(2, all_25_3) % 15.36/2.80 | | % 15.36/2.80 | | COMBINE_INEQS: (22), (27) imply: % 15.36/2.80 | | (28) $false % 15.36/2.80 | | % 15.36/2.80 | | CLOSE: (28) is inconsistent. % 15.36/2.80 | | % 15.36/2.80 | Case 2: % 15.36/2.80 | | % 15.36/2.80 | | (29) $lesseq(-1, $difference(all_25_1, $product(2, all_25_3))) % 15.36/2.80 | | % 15.36/2.80 | | THEORY_AXIOM GroebnerMultiplication: % 15.36/2.80 | | (30) ! [v0: int] : ! [v1: int] : ( ~ ($lesseq(2, v1)) | ~ ($lesseq(v0, % 15.36/2.80 | | 1)) | ~ ($lesseq(-1, v0)) | ~ ($product(v0, v0) = v1)) % 15.36/2.80 | | % 15.36/2.80 | | GROUND_INST: instantiating (30) with all_25_3, all_25_1, simplifying with % 15.36/2.80 | | (24) gives: % 15.36/2.80 | | (31) ~ ($lesseq(2, all_25_1)) | ~ ($lesseq(all_25_3, 1)) | ~ % 15.36/2.80 | | ($lesseq(-1, all_25_3)) % 15.36/2.80 | | % 15.36/2.80 | | BETA: splitting (31) gives: % 15.36/2.80 | | % 15.36/2.80 | | Case 1: % 15.36/2.80 | | | % 15.36/2.80 | | | (32) $lesseq(2, all_25_3) % 15.36/2.80 | | | % 15.36/2.80 | | | COMBINE_INEQS: (22), (32) imply: % 15.36/2.80 | | | (33) $false % 15.36/2.80 | | | % 15.36/2.80 | | | CLOSE: (33) is inconsistent. % 15.36/2.80 | | | % 15.36/2.80 | | Case 2: % 15.36/2.80 | | | % 15.36/2.80 | | | (34) ~ ($lesseq(2, all_25_1)) | ~ ($lesseq(-1, all_25_3)) % 15.36/2.80 | | | % 15.36/2.80 | | | BETA: splitting (34) gives: % 15.36/2.80 | | | % 15.36/2.80 | | | Case 1: % 15.36/2.80 | | | | % 15.36/2.80 | | | | (35) $lesseq(all_25_3, -2) % 15.36/2.80 | | | | % 15.36/2.80 | | | | COMBINE_INEQS: (23), (35) imply: % 15.36/2.80 | | | | (36) $false % 15.36/2.80 | | | | % 15.36/2.80 | | | | CLOSE: (36) is inconsistent. % 15.36/2.80 | | | | % 15.36/2.80 | | | Case 2: % 15.36/2.80 | | | | % 15.36/2.80 | | | | (37) $lesseq(all_25_1, 1) % 15.36/2.80 | | | | % 15.36/2.80 | | | | THEORY_AXIOM GroebnerMultiplication: % 15.36/2.80 | | | | (38) ! [v0: int] : ! [v1: int] : ( ~ ($lesseq(2, % 15.36/2.80 | | | | $difference($product(-1, v1), $product(2, v0)))) | ~ % 15.36/2.80 | | | | ($lesseq(-1, v0)) | ~ ($product(v0, v0) = v1)) % 15.36/2.80 | | | | % 15.36/2.80 | | | | GROUND_INST: instantiating (38) with all_25_3, all_25_1, simplifying % 15.36/2.80 | | | | with (24) gives: % 15.36/2.80 | | | | (39) ~ ($lesseq(2, $difference($product(-1, all_25_1), $product(2, % 15.36/2.80 | | | | all_25_3)))) | ~ ($lesseq(-1, all_25_3)) % 15.36/2.80 | | | | % 15.36/2.80 | | | | BETA: splitting (39) gives: % 15.36/2.80 | | | | % 15.36/2.80 | | | | Case 1: % 15.36/2.80 | | | | | % 15.36/2.80 | | | | | (40) $lesseq(all_25_3, -2) % 15.36/2.80 | | | | | % 15.36/2.80 | | | | | COMBINE_INEQS: (23), (40) imply: % 15.36/2.80 | | | | | (41) $false % 15.36/2.80 | | | | | % 15.36/2.80 | | | | | CLOSE: (41) is inconsistent. % 15.36/2.80 | | | | | % 15.36/2.80 | | | | Case 2: % 15.36/2.80 | | | | | % 15.36/2.80 | | | | | (42) $lesseq(-1, $sum(all_25_1, $product(2, all_25_3))) % 15.36/2.80 | | | | | % 15.36/2.80 | | | | | GROUND_INST: instantiating (3) with all_25_7, all_25_7, all_25_5, % 15.36/2.80 | | | | | all_25_1, all_25_1, all_25_1, simplifying with (8), (13), % 15.36/2.80 | | | | | (15) gives: % 15.36/2.81 | | | | | (43) all_25_5 = 0 | ~ ($lesseq(all_25_1, 1)) | ~ ($lesseq(0, % 15.36/2.81 | | | | | all_25_1)) | ? [v0: int] : ? [v1: any] : ( ~ (v1 = % 15.36/2.81 | | | | | all_25_7) & f__integer__(v0) = v1 & $product(all_25_1, % 15.36/2.81 | | | | | all_25_1) = v0 & general(v1)) % 15.36/2.81 | | | | | % 15.36/2.81 | | | | | GROUND_INST: instantiating (3) with all_25_7, all_25_6, all_25_5, % 15.36/2.81 | | | | | all_25_3, all_25_3, all_25_3, simplifying with (8), (9), % 15.36/2.81 | | | | | (11), (15) gives: % 15.36/2.81 | | | | | (44) all_25_5 = 0 | ~ ($lesseq(all_25_3, 1)) | ~ ($lesseq(0, % 15.36/2.81 | | | | | all_25_3)) | ? [v0: int] : ? [v1: any] : ( ~ (v1 = % 15.36/2.81 | | | | | all_25_7) & f__integer__(v0) = v1 & $product(all_25_3, % 15.36/2.81 | | | | | all_25_3) = v0 & general(v1)) % 15.36/2.81 | | | | | % 15.36/2.81 | | | | | GROUND_INST: instantiating (4) with all_25_7, all_25_7, all_25_4, % 15.36/2.81 | | | | | all_25_1, all_25_1, all_25_1, simplifying with (8), (13), % 15.36/2.81 | | | | | (16) gives: % 15.36/2.81 | | | | | (45) all_25_4 = 0 | ~ ($lesseq(all_25_1, 1)) | ~ ($lesseq(0, % 15.36/2.81 | | | | | all_25_1)) | ? [v0: int] : ? [v1: any] : ( ~ (v1 = % 15.36/2.81 | | | | | all_25_7) & f__integer__(v0) = v1 & $product(all_25_1, % 15.36/2.81 | | | | | all_25_1) = v0 & general(v1)) % 15.36/2.81 | | | | | % 15.36/2.81 | | | | | GROUND_INST: instantiating (4) with all_25_7, all_25_6, all_25_4, % 15.36/2.81 | | | | | all_25_3, all_25_3, all_25_3, simplifying with (8), (9), % 15.36/2.81 | | | | | (11), (16) gives: % 15.36/2.81 | | | | | (46) all_25_4 = 0 | ~ ($lesseq(all_25_3, 1)) | ~ ($lesseq(0, % 15.36/2.81 | | | | | all_25_3)) | ? [v0: int] : ? [v1: any] : ( ~ (v1 = % 15.36/2.81 | | | | | all_25_7) & f__integer__(v0) = v1 & $product(all_25_3, % 15.36/2.81 | | | | | all_25_3) = v0 & general(v1)) % 15.36/2.81 | | | | | % 15.36/2.81 | | | | | BETA: splitting (17) gives: % 15.36/2.81 | | | | | % 15.36/2.81 | | | | | Case 1: % 15.36/2.81 | | | | | | % 15.36/2.81 | | | | | | (47) ~ (all_25_4 = 0) % 15.36/2.81 | | | | | | % 15.36/2.81 | | | | | | BETA: splitting (46) gives: % 15.36/2.81 | | | | | | % 15.36/2.81 | | | | | | Case 1: % 15.36/2.81 | | | | | | | % 15.36/2.81 | | | | | | | (48) $lesseq(all_25_3, -1) % 15.36/2.81 | | | | | | | % 15.36/2.81 | | | | | | | COMBINE_INEQS: (42), (48) imply: % 15.36/2.81 | | | | | | | (49) $lesseq(1, all_25_1) % 15.36/2.81 | | | | | | | % 15.36/2.81 | | | | | | | ANTI_SYMM: (37), (49) imply: % 15.36/2.81 | | | | | | | (50) all_25_1 = 1 % 15.36/2.81 | | | | | | | % 15.36/2.81 | | | | | | | REDUCE: (13), (50) imply: % 15.36/2.81 | | | | | | | (51) f__integer__(1) = all_25_7 % 15.36/2.81 | | | | | | | % 15.36/2.81 | | | | | | | BETA: splitting (45) gives: % 15.36/2.81 | | | | | | | % 15.36/2.81 | | | | | | | Case 1: % 15.36/2.81 | | | | | | | | % 15.36/2.81 | | | | | | | | (52) $lesseq(all_25_1, -1) % 15.36/2.81 | | | | | | | | % 15.36/2.81 | | | | | | | | REDUCE: (50), (52) imply: % 15.36/2.81 | | | | | | | | (53) $false % 15.36/2.81 | | | | | | | | % 15.36/2.81 | | | | | | | | CLOSE: (53) is inconsistent. % 15.36/2.81 | | | | | | | | % 15.36/2.81 | | | | | | | Case 2: % 15.36/2.81 | | | | | | | | % 15.36/2.81 | | | | | | | | (54) all_25_4 = 0 | ~ ($lesseq(all_25_1, 1)) | ? [v0: int] % 15.36/2.81 | | | | | | | | : ? [v1: any] : ( ~ (v1 = all_25_7) & f__integer__(v0) % 15.36/2.81 | | | | | | | | = v1 & $product(all_25_1, all_25_1) = v0 & % 15.36/2.81 | | | | | | | | general(v1)) % 15.36/2.81 | | | | | | | | % 15.36/2.81 | | | | | | | | BETA: splitting (54) gives: % 15.36/2.81 | | | | | | | | % 15.36/2.82 | | | | | | | | Case 1: % 15.36/2.82 | | | | | | | | | % 15.36/2.82 | | | | | | | | | (55) $lesseq(2, all_25_1) % 15.36/2.82 | | | | | | | | | % 15.36/2.82 | | | | | | | | | REDUCE: (50), (55) imply: % 15.36/2.82 | | | | | | | | | (56) $false % 15.36/2.82 | | | | | | | | | % 15.36/2.82 | | | | | | | | | CLOSE: (56) is inconsistent. % 15.36/2.82 | | | | | | | | | % 15.36/2.82 | | | | | | | | Case 2: % 15.36/2.82 | | | | | | | | | % 15.36/2.82 | | | | | | | | | (57) all_25_4 = 0 | ? [v0: int] : ? [v1: any] : ( ~ (v1 = % 15.36/2.82 | | | | | | | | | all_25_7) & f__integer__(v0) = v1 & % 15.36/2.82 | | | | | | | | | $product(all_25_1, all_25_1) = v0 & general(v1)) % 15.36/2.82 | | | | | | | | | % 15.36/2.82 | | | | | | | | | BETA: splitting (57) gives: % 15.36/2.82 | | | | | | | | | % 15.36/2.82 | | | | | | | | | Case 1: % 15.36/2.82 | | | | | | | | | | % 15.36/2.82 | | | | | | | | | | (58) all_25_4 = 0 % 15.36/2.82 | | | | | | | | | | % 15.36/2.82 | | | | | | | | | | REDUCE: (47), (58) imply: % 15.36/2.82 | | | | | | | | | | (59) $false % 15.36/2.82 | | | | | | | | | | % 15.36/2.82 | | | | | | | | | | CLOSE: (59) is inconsistent. % 15.36/2.82 | | | | | | | | | | % 15.36/2.82 | | | | | | | | | Case 2: % 15.36/2.82 | | | | | | | | | | % 15.36/2.82 | | | | | | | | | | (60) ? [v0: int] : ? [v1: any] : ( ~ (v1 = all_25_7) & % 15.36/2.82 | | | | | | | | | | f__integer__(v0) = v1 & $product(all_25_1, % 15.36/2.82 | | | | | | | | | | all_25_1) = v0 & general(v1)) % 15.36/2.82 | | | | | | | | | | % 15.36/2.82 | | | | | | | | | | DELTA: instantiating (60) with fresh symbols all_92_0, % 15.36/2.82 | | | | | | | | | | all_92_1 gives: % 15.36/2.82 | | | | | | | | | | (61) ~ (all_92_0 = all_25_7) & f__integer__(all_92_1) = % 15.36/2.82 | | | | | | | | | | all_92_0 & $product(all_25_1, all_25_1) = all_92_1 & % 15.36/2.82 | | | | | | | | | | general(all_92_0) % 15.36/2.82 | | | | | | | | | | % 15.36/2.82 | | | | | | | | | | REF_CLOSE: (2), (50), (51), (61) are inconsistent by % 15.36/2.82 | | | | | | | | | | sub-proof #1. % 15.36/2.82 | | | | | | | | | | % 15.36/2.82 | | | | | | | | | End of split % 15.36/2.82 | | | | | | | | | % 15.36/2.82 | | | | | | | | End of split % 15.36/2.82 | | | | | | | | % 15.36/2.82 | | | | | | | End of split % 15.36/2.82 | | | | | | | % 15.36/2.82 | | | | | | Case 2: % 15.36/2.82 | | | | | | | % 15.36/2.82 | | | | | | | (62) $lesseq(0, all_25_3) % 15.36/2.82 | | | | | | | (63) all_25_4 = 0 | ~ ($lesseq(all_25_3, 1)) | ? [v0: int] : % 15.36/2.82 | | | | | | | ? [v1: any] : ( ~ (v1 = all_25_7) & f__integer__(v0) = v1 % 15.36/2.82 | | | | | | | & $product(all_25_3, all_25_3) = v0 & general(v1)) % 15.36/2.82 | | | | | | | % 15.36/2.82 | | | | | | | COMBINE_INEQS: (29), (37) imply: % 15.36/2.82 | | | | | | | (64) $lesseq(all_25_3, 1) % 15.36/2.82 | | | | | | | % 15.36/2.82 | | | | | | | THEORY_AXIOM GroebnerMultiplication: % 15.36/2.82 | | | | | | | (65) ! [v0: int] : ! [v1: int] : ( ~ ($lesseq(1, % 15.36/2.82 | | | | | | | $difference(v1, v0))) | ~ ($lesseq(v0, 1)) | ~ % 15.36/2.82 | | | | | | | ($lesseq(0, v0)) | ~ ($product(v0, v0) = v1)) % 15.36/2.82 | | | | | | | % 15.36/2.82 | | | | | | | GROUND_INST: instantiating (65) with all_25_3, all_25_1, % 15.36/2.82 | | | | | | | simplifying with (24) gives: % 15.36/2.82 | | | | | | | (66) ~ ($lesseq(1, $difference(all_25_1, all_25_3))) | ~ % 15.36/2.82 | | | | | | | ($lesseq(all_25_3, 1)) | ~ ($lesseq(0, all_25_3)) % 15.36/2.82 | | | | | | | % 15.36/2.82 | | | | | | | BETA: splitting (66) gives: % 15.36/2.82 | | | | | | | % 15.36/2.82 | | | | | | | Case 1: % 15.36/2.82 | | | | | | | | % 15.36/2.82 | | | | | | | | (67) $lesseq(all_25_3, -1) % 15.36/2.82 | | | | | | | | % 15.36/2.82 | | | | | | | | COMBINE_INEQS: (62), (67) imply: % 15.36/2.82 | | | | | | | | (68) $false % 15.36/2.82 | | | | | | | | % 15.36/2.82 | | | | | | | | CLOSE: (68) is inconsistent. % 15.36/2.82 | | | | | | | | % 15.36/2.82 | | | | | | | Case 2: % 15.36/2.82 | | | | | | | | % 15.36/2.82 | | | | | | | | (69) ~ ($lesseq(1, $difference(all_25_1, all_25_3))) | ~ % 15.36/2.82 | | | | | | | | ($lesseq(all_25_3, 1)) % 15.36/2.82 | | | | | | | | % 15.36/2.82 | | | | | | | | BETA: splitting (69) gives: % 15.36/2.82 | | | | | | | | % 15.36/2.82 | | | | | | | | Case 1: % 15.36/2.82 | | | | | | | | | % 15.36/2.82 | | | | | | | | | (70) $lesseq(2, all_25_3) % 15.36/2.82 | | | | | | | | | % 15.36/2.82 | | | | | | | | | COMBINE_INEQS: (22), (70) imply: % 15.36/2.82 | | | | | | | | | (71) $false % 15.36/2.82 | | | | | | | | | % 15.36/2.82 | | | | | | | | | CLOSE: (71) is inconsistent. % 15.36/2.82 | | | | | | | | | % 15.36/2.82 | | | | | | | | Case 2: % 15.36/2.82 | | | | | | | | | % 15.36/2.82 | | | | | | | | | (72) $lesseq(all_25_1, all_25_3) % 15.36/2.82 | | | | | | | | | % 15.36/2.82 | | | | | | | | | BETA: splitting (63) gives: % 15.36/2.82 | | | | | | | | | % 15.36/2.82 | | | | | | | | | Case 1: % 15.36/2.82 | | | | | | | | | | % 15.36/2.82 | | | | | | | | | | (73) $lesseq(2, all_25_3) % 15.36/2.82 | | | | | | | | | | % 15.36/2.82 | | | | | | | | | | COMBINE_INEQS: (22), (73) imply: % 15.36/2.82 | | | | | | | | | | (74) $false % 15.36/2.82 | | | | | | | | | | % 15.36/2.82 | | | | | | | | | | CLOSE: (74) is inconsistent. % 15.36/2.82 | | | | | | | | | | % 15.36/2.82 | | | | | | | | | Case 2: % 15.36/2.82 | | | | | | | | | | % 15.36/2.82 | | | | | | | | | | (75) all_25_4 = 0 | ? [v0: int] : ? [v1: any] : ( ~ (v1 % 15.36/2.82 | | | | | | | | | | = all_25_7) & f__integer__(v0) = v1 & % 15.36/2.82 | | | | | | | | | | $product(all_25_3, all_25_3) = v0 & general(v1)) % 15.36/2.82 | | | | | | | | | | % 15.36/2.82 | | | | | | | | | | BETA: splitting (75) gives: % 15.36/2.82 | | | | | | | | | | % 15.36/2.82 | | | | | | | | | | Case 1: % 15.36/2.82 | | | | | | | | | | | % 15.36/2.82 | | | | | | | | | | | (76) all_25_4 = 0 % 15.36/2.82 | | | | | | | | | | | % 15.36/2.82 | | | | | | | | | | | REDUCE: (47), (76) imply: % 15.36/2.83 | | | | | | | | | | | (77) $false % 15.36/2.83 | | | | | | | | | | | % 15.36/2.83 | | | | | | | | | | | CLOSE: (77) is inconsistent. % 15.36/2.83 | | | | | | | | | | | % 15.36/2.83 | | | | | | | | | | Case 2: % 15.36/2.83 | | | | | | | | | | | % 15.36/2.83 | | | | | | | | | | | (78) ? [v0: int] : ? [v1: any] : ( ~ (v1 = all_25_7) % 15.36/2.83 | | | | | | | | | | | & f__integer__(v0) = v1 & $product(all_25_3, % 15.36/2.83 | | | | | | | | | | | all_25_3) = v0 & general(v1)) % 15.36/2.83 | | | | | | | | | | | % 15.36/2.83 | | | | | | | | | | | DELTA: instantiating (78) with fresh symbols all_99_0, % 15.36/2.83 | | | | | | | | | | | all_99_1 gives: % 15.36/2.83 | | | | | | | | | | | (79) ~ (all_99_0 = all_25_7) & f__integer__(all_99_1) % 15.36/2.83 | | | | | | | | | | | = all_99_0 & $product(all_25_3, all_25_3) = % 15.36/2.83 | | | | | | | | | | | all_99_1 & general(all_99_0) % 15.36/2.83 | | | | | | | | | | | % 15.36/2.83 | | | | | | | | | | | ALPHA: (79) implies: % 15.36/2.83 | | | | | | | | | | | (80) ~ (all_99_0 = all_25_7) % 15.36/2.83 | | | | | | | | | | | (81) $product(all_25_3, all_25_3) = all_99_1 % 15.36/2.83 | | | | | | | | | | | (82) f__integer__(all_99_1) = all_99_0 % 15.36/2.83 | | | | | | | | | | | % 15.36/2.83 | | | | | | | | | | | THEORY_AXIOM GroebnerMultiplication: % 15.36/2.83 | | | | | | | | | | | (83) ! [v0: int] : ! [v1: int] : ! [v2: int] : (v2 = % 15.36/2.83 | | | | | | | | | | | v1 | ~ ($product(v0, v0) = v2) | ~ % 15.36/2.83 | | | | | | | | | | | ($product(v0, v0) = v1)) % 15.36/2.83 | | | | | | | | | | | % 15.36/2.83 | | | | | | | | | | | GROUND_INST: instantiating (83) with all_25_3, all_25_1, % 15.36/2.83 | | | | | | | | | | | all_99_1, simplifying with (24), (81) gives: % 15.36/2.83 | | | | | | | | | | | (84) all_99_1 = all_25_1 % 15.36/2.83 | | | | | | | | | | | % 15.36/2.83 | | | | | | | | | | | REDUCE: (82), (84) imply: % 15.36/2.83 | | | | | | | | | | | (85) f__integer__(all_25_1) = all_99_0 % 15.36/2.83 | | | | | | | | | | | % 15.36/2.83 | | | | | | | | | | | GROUND_INST: instantiating (2) with all_25_1, all_25_7, % 15.36/2.83 | | | | | | | | | | | all_99_0, simplifying with (13), (85) gives: % 15.36/2.83 | | | | | | | | | | | (86) all_99_0 = all_25_7 % 15.36/2.83 | | | | | | | | | | | % 15.36/2.83 | | | | | | | | | | | REDUCE: (80), (86) imply: % 15.36/2.83 | | | | | | | | | | | (87) $false % 15.36/2.83 | | | | | | | | | | | % 15.36/2.83 | | | | | | | | | | | CLOSE: (87) is inconsistent. % 15.36/2.83 | | | | | | | | | | | % 15.36/2.83 | | | | | | | | | | End of split % 15.36/2.83 | | | | | | | | | | % 15.36/2.83 | | | | | | | | | End of split % 15.36/2.83 | | | | | | | | | % 15.36/2.83 | | | | | | | | End of split % 15.36/2.83 | | | | | | | | % 15.36/2.83 | | | | | | | End of split % 15.36/2.83 | | | | | | | % 15.36/2.83 | | | | | | End of split % 15.36/2.83 | | | | | | % 15.36/2.83 | | | | | Case 2: % 15.36/2.83 | | | | | | % 15.36/2.83 | | | | | | (88) ~ (all_25_5 = 0) % 15.36/2.83 | | | | | | % 15.36/2.83 | | | | | | BETA: splitting (44) gives: % 15.36/2.83 | | | | | | % 15.36/2.83 | | | | | | Case 1: % 15.36/2.83 | | | | | | | % 15.36/2.83 | | | | | | | (89) $lesseq(all_25_3, -1) % 15.36/2.83 | | | | | | | % 15.36/2.83 | | | | | | | COMBINE_INEQS: (42), (89) imply: % 15.36/2.83 | | | | | | | (90) $lesseq(1, all_25_1) % 15.36/2.83 | | | | | | | % 15.36/2.83 | | | | | | | ANTI_SYMM: (37), (90) imply: % 15.36/2.83 | | | | | | | (91) all_25_1 = 1 % 15.36/2.83 | | | | | | | % 15.36/2.83 | | | | | | | REDUCE: (13), (91) imply: % 15.36/2.83 | | | | | | | (92) f__integer__(1) = all_25_7 % 15.36/2.83 | | | | | | | % 15.36/2.83 | | | | | | | BETA: splitting (43) gives: % 15.36/2.83 | | | | | | | % 15.36/2.83 | | | | | | | Case 1: % 15.36/2.83 | | | | | | | | % 15.36/2.83 | | | | | | | | (93) $lesseq(all_25_1, -1) % 15.36/2.83 | | | | | | | | % 15.36/2.83 | | | | | | | | REDUCE: (91), (93) imply: % 15.36/2.83 | | | | | | | | (94) $false % 15.36/2.83 | | | | | | | | % 15.36/2.83 | | | | | | | | CLOSE: (94) is inconsistent. % 15.36/2.83 | | | | | | | | % 15.36/2.83 | | | | | | | Case 2: % 15.36/2.83 | | | | | | | | % 15.36/2.83 | | | | | | | | (95) all_25_5 = 0 | ~ ($lesseq(all_25_1, 1)) | ? [v0: int] % 15.36/2.83 | | | | | | | | : ? [v1: any] : ( ~ (v1 = all_25_7) & f__integer__(v0) % 15.36/2.83 | | | | | | | | = v1 & $product(all_25_1, all_25_1) = v0 & % 15.36/2.83 | | | | | | | | general(v1)) % 15.36/2.83 | | | | | | | | % 15.36/2.83 | | | | | | | | BETA: splitting (95) gives: % 15.36/2.83 | | | | | | | | % 15.36/2.83 | | | | | | | | Case 1: % 15.36/2.83 | | | | | | | | | % 15.36/2.83 | | | | | | | | | (96) $lesseq(2, all_25_1) % 15.36/2.83 | | | | | | | | | % 15.36/2.83 | | | | | | | | | REDUCE: (91), (96) imply: % 15.36/2.83 | | | | | | | | | (97) $false % 15.36/2.83 | | | | | | | | | % 15.36/2.83 | | | | | | | | | CLOSE: (97) is inconsistent. % 15.36/2.83 | | | | | | | | | % 15.36/2.83 | | | | | | | | Case 2: % 15.36/2.83 | | | | | | | | | % 15.36/2.83 | | | | | | | | | (98) all_25_5 = 0 | ? [v0: int] : ? [v1: any] : ( ~ (v1 = % 15.36/2.83 | | | | | | | | | all_25_7) & f__integer__(v0) = v1 & % 15.36/2.83 | | | | | | | | | $product(all_25_1, all_25_1) = v0 & general(v1)) % 15.36/2.83 | | | | | | | | | % 15.36/2.83 | | | | | | | | | BETA: splitting (98) gives: % 15.36/2.83 | | | | | | | | | % 15.36/2.83 | | | | | | | | | Case 1: % 15.36/2.83 | | | | | | | | | | % 15.36/2.83 | | | | | | | | | | (99) all_25_5 = 0 % 15.36/2.83 | | | | | | | | | | % 15.36/2.83 | | | | | | | | | | REDUCE: (88), (99) imply: % 15.36/2.83 | | | | | | | | | | (100) $false % 15.36/2.83 | | | | | | | | | | % 15.36/2.83 | | | | | | | | | | CLOSE: (100) is inconsistent. % 15.36/2.83 | | | | | | | | | | % 15.36/2.83 | | | | | | | | | Case 2: % 15.36/2.83 | | | | | | | | | | % 15.36/2.84 | | | | | | | | | | (101) ? [v0: int] : ? [v1: any] : ( ~ (v1 = all_25_7) & % 15.36/2.84 | | | | | | | | | | f__integer__(v0) = v1 & $product(all_25_1, % 15.36/2.84 | | | | | | | | | | all_25_1) = v0 & general(v1)) % 15.36/2.84 | | | | | | | | | | % 15.36/2.84 | | | | | | | | | | DELTA: instantiating (101) with fresh symbols all_92_0, % 15.36/2.84 | | | | | | | | | | all_92_1 gives: % 15.36/2.84 | | | | | | | | | | (102) ~ (all_92_0 = all_25_7) & f__integer__(all_92_1) = % 15.36/2.84 | | | | | | | | | | all_92_0 & $product(all_25_1, all_25_1) = all_92_1 % 15.36/2.84 | | | | | | | | | | & general(all_92_0) % 15.36/2.84 | | | | | | | | | | % 15.36/2.84 | | | | | | | | | | REF_CLOSE: (2), (91), (92), (102) are inconsistent by % 15.36/2.84 | | | | | | | | | | sub-proof #1. % 15.36/2.84 | | | | | | | | | | % 15.36/2.84 | | | | | | | | | End of split % 15.36/2.84 | | | | | | | | | % 15.36/2.84 | | | | | | | | End of split % 15.36/2.84 | | | | | | | | % 15.36/2.84 | | | | | | | End of split % 15.36/2.84 | | | | | | | % 15.36/2.84 | | | | | | Case 2: % 15.36/2.84 | | | | | | | % 15.36/2.84 | | | | | | | (103) $lesseq(0, all_25_3) % 15.36/2.84 | | | | | | | (104) all_25_5 = 0 | ~ ($lesseq(all_25_3, 1)) | ? [v0: int] : % 15.36/2.84 | | | | | | | ? [v1: any] : ( ~ (v1 = all_25_7) & f__integer__(v0) = % 15.36/2.84 | | | | | | | v1 & $product(all_25_3, all_25_3) = v0 & general(v1)) % 15.36/2.84 | | | | | | | % 15.36/2.84 | | | | | | | COMBINE_INEQS: (29), (37) imply: % 15.36/2.84 | | | | | | | (105) $lesseq(all_25_3, 1) % 15.36/2.84 | | | | | | | % 15.36/2.84 | | | | | | | THEORY_AXIOM GroebnerMultiplication: % 15.36/2.84 | | | | | | | (106) ! [v0: int] : ! [v1: int] : ( ~ ($lesseq(1, % 15.36/2.84 | | | | | | | $difference(v1, v0))) | ~ ($lesseq(v0, 1)) | ~ % 15.36/2.84 | | | | | | | ($lesseq(0, v0)) | ~ ($product(v0, v0) = v1)) % 15.36/2.84 | | | | | | | % 15.36/2.84 | | | | | | | GROUND_INST: instantiating (106) with all_25_3, all_25_1, % 15.36/2.84 | | | | | | | simplifying with (24) gives: % 15.36/2.84 | | | | | | | (107) ~ ($lesseq(1, $difference(all_25_1, all_25_3))) | ~ % 15.36/2.84 | | | | | | | ($lesseq(all_25_3, 1)) | ~ ($lesseq(0, all_25_3)) % 15.36/2.84 | | | | | | | % 15.36/2.84 | | | | | | | BETA: splitting (107) gives: % 15.36/2.84 | | | | | | | % 15.36/2.84 | | | | | | | Case 1: % 15.36/2.84 | | | | | | | | % 15.36/2.84 | | | | | | | | (108) $lesseq(all_25_3, -1) % 15.36/2.84 | | | | | | | | % 15.36/2.84 | | | | | | | | COMBINE_INEQS: (103), (108) imply: % 15.36/2.84 | | | | | | | | (109) $false % 15.36/2.84 | | | | | | | | % 15.36/2.84 | | | | | | | | CLOSE: (109) is inconsistent. % 15.36/2.84 | | | | | | | | % 15.36/2.84 | | | | | | | Case 2: % 15.36/2.84 | | | | | | | | % 15.36/2.84 | | | | | | | | (110) ~ ($lesseq(1, $difference(all_25_1, all_25_3))) | ~ % 15.36/2.84 | | | | | | | | ($lesseq(all_25_3, 1)) % 15.36/2.84 | | | | | | | | % 15.36/2.84 | | | | | | | | BETA: splitting (110) gives: % 15.36/2.84 | | | | | | | | % 15.36/2.84 | | | | | | | | Case 1: % 15.36/2.84 | | | | | | | | | % 15.36/2.84 | | | | | | | | | (111) $lesseq(2, all_25_3) % 15.36/2.84 | | | | | | | | | % 15.36/2.84 | | | | | | | | | COMBINE_INEQS: (22), (111) imply: % 15.36/2.84 | | | | | | | | | (112) $false % 15.36/2.84 | | | | | | | | | % 15.36/2.84 | | | | | | | | | CLOSE: (112) is inconsistent. % 15.36/2.84 | | | | | | | | | % 15.36/2.84 | | | | | | | | Case 2: % 15.36/2.84 | | | | | | | | | % 15.36/2.84 | | | | | | | | | (113) $lesseq(all_25_1, all_25_3) % 15.36/2.84 | | | | | | | | | % 15.36/2.84 | | | | | | | | | BETA: splitting (104) gives: % 15.36/2.84 | | | | | | | | | % 15.36/2.84 | | | | | | | | | Case 1: % 15.36/2.84 | | | | | | | | | | % 15.36/2.84 | | | | | | | | | | (114) $lesseq(2, all_25_3) % 15.36/2.84 | | | | | | | | | | % 15.36/2.84 | | | | | | | | | | COMBINE_INEQS: (22), (114) imply: % 15.36/2.84 | | | | | | | | | | (115) $false % 15.36/2.84 | | | | | | | | | | % 15.36/2.84 | | | | | | | | | | CLOSE: (115) is inconsistent. % 15.36/2.84 | | | | | | | | | | % 15.36/2.84 | | | | | | | | | Case 2: % 15.36/2.84 | | | | | | | | | | % 15.36/2.84 | | | | | | | | | | (116) all_25_5 = 0 | ? [v0: int] : ? [v1: any] : ( ~ % 15.36/2.84 | | | | | | | | | | (v1 = all_25_7) & f__integer__(v0) = v1 & % 15.36/2.84 | | | | | | | | | | $product(all_25_3, all_25_3) = v0 & general(v1)) % 15.36/2.84 | | | | | | | | | | % 15.36/2.84 | | | | | | | | | | BETA: splitting (116) gives: % 15.36/2.84 | | | | | | | | | | % 15.36/2.84 | | | | | | | | | | Case 1: % 15.36/2.84 | | | | | | | | | | | % 15.36/2.84 | | | | | | | | | | | (117) all_25_5 = 0 % 15.36/2.84 | | | | | | | | | | | % 15.36/2.84 | | | | | | | | | | | REDUCE: (88), (117) imply: % 15.36/2.84 | | | | | | | | | | | (118) $false % 15.36/2.84 | | | | | | | | | | | % 15.36/2.84 | | | | | | | | | | | CLOSE: (118) is inconsistent. % 15.36/2.84 | | | | | | | | | | | % 15.36/2.84 | | | | | | | | | | Case 2: % 15.36/2.84 | | | | | | | | | | | % 15.36/2.84 | | | | | | | | | | | (119) ? [v0: int] : ? [v1: any] : ( ~ (v1 = all_25_7) % 15.36/2.84 | | | | | | | | | | | & f__integer__(v0) = v1 & $product(all_25_3, % 15.36/2.84 | | | | | | | | | | | all_25_3) = v0 & general(v1)) % 15.36/2.84 | | | | | | | | | | | % 15.36/2.84 | | | | | | | | | | | DELTA: instantiating (119) with fresh symbols all_92_0, % 15.36/2.84 | | | | | | | | | | | all_92_1 gives: % 15.36/2.85 | | | | | | | | | | | (120) ~ (all_92_0 = all_25_7) & f__integer__(all_92_1) % 15.36/2.85 | | | | | | | | | | | = all_92_0 & $product(all_25_3, all_25_3) = % 15.36/2.85 | | | | | | | | | | | all_92_1 & general(all_92_0) % 15.36/2.85 | | | | | | | | | | | % 15.36/2.85 | | | | | | | | | | | ALPHA: (120) implies: % 15.36/2.85 | | | | | | | | | | | (121) ~ (all_92_0 = all_25_7) % 15.36/2.85 | | | | | | | | | | | (122) $product(all_25_3, all_25_3) = all_92_1 % 15.36/2.85 | | | | | | | | | | | (123) f__integer__(all_92_1) = all_92_0 % 15.36/2.85 | | | | | | | | | | | % 15.36/2.85 | | | | | | | | | | | THEORY_AXIOM GroebnerMultiplication: % 15.36/2.85 | | | | | | | | | | | (124) ! [v0: int] : ! [v1: int] : ! [v2: int] : (v2 = % 15.36/2.85 | | | | | | | | | | | v1 | ~ ($product(v0, v0) = v2) | ~ % 15.36/2.85 | | | | | | | | | | | ($product(v0, v0) = v1)) % 15.36/2.85 | | | | | | | | | | | % 15.36/2.85 | | | | | | | | | | | GROUND_INST: instantiating (124) with all_25_3, all_25_1, % 15.36/2.85 | | | | | | | | | | | all_92_1, simplifying with (24), (122) gives: % 15.36/2.85 | | | | | | | | | | | (125) all_92_1 = all_25_1 % 15.36/2.85 | | | | | | | | | | | % 15.36/2.85 | | | | | | | | | | | REDUCE: (123), (125) imply: % 15.36/2.85 | | | | | | | | | | | (126) f__integer__(all_25_1) = all_92_0 % 15.36/2.85 | | | | | | | | | | | % 15.36/2.85 | | | | | | | | | | | GROUND_INST: instantiating (2) with all_25_1, all_25_7, % 15.36/2.85 | | | | | | | | | | | all_92_0, simplifying with (13), (126) gives: % 15.36/2.85 | | | | | | | | | | | (127) all_92_0 = all_25_7 % 15.36/2.85 | | | | | | | | | | | % 15.36/2.85 | | | | | | | | | | | REDUCE: (121), (127) imply: % 15.36/2.85 | | | | | | | | | | | (128) $false % 15.36/2.85 | | | | | | | | | | | % 15.36/2.85 | | | | | | | | | | | CLOSE: (128) is inconsistent. % 15.36/2.85 | | | | | | | | | | | % 15.36/2.85 | | | | | | | | | | End of split % 15.36/2.85 | | | | | | | | | | % 15.36/2.85 | | | | | | | | | End of split % 15.36/2.85 | | | | | | | | | % 15.36/2.85 | | | | | | | | End of split % 15.36/2.85 | | | | | | | | % 15.36/2.85 | | | | | | | End of split % 15.36/2.85 | | | | | | | % 15.36/2.85 | | | | | | End of split % 15.36/2.85 | | | | | | % 15.36/2.85 | | | | | End of split % 15.36/2.85 | | | | | % 15.36/2.85 | | | | End of split % 15.36/2.85 | | | | % 15.36/2.85 | | | End of split % 15.36/2.85 | | | % 15.36/2.85 | | End of split % 15.36/2.85 | | % 15.36/2.85 | End of split % 15.36/2.85 | % 15.36/2.85 End of proof % 15.36/2.85 % 15.36/2.85 Sub-proof #1 shows that the following formulas are inconsistent: % 15.36/2.85 ---------------------------------------------------------------- % 15.36/2.85 (1) ~ (all_92_0 = all_25_7) & f__integer__(all_92_1) = all_92_0 & % 15.36/2.85 $product(all_25_1, all_25_1) = all_92_1 & general(all_92_0) % 15.36/2.85 (2) all_25_1 = 1 % 15.36/2.85 (3) ! [v0: int] : ! [v1: general] : ! [v2: general] : (v2 = v1 | ~ % 15.36/2.85 (f__integer__(v0) = v2) | ~ (f__integer__(v0) = v1)) % 15.36/2.85 (4) f__integer__(1) = all_25_7 % 15.36/2.85 % 15.36/2.85 Begin of proof % 15.36/2.85 | % 15.36/2.85 | ALPHA: (1) implies: % 15.36/2.85 | (5) ~ (all_92_0 = all_25_7) % 15.36/2.85 | (6) $product(all_25_1, all_25_1) = all_92_1 % 15.36/2.85 | (7) f__integer__(all_92_1) = all_92_0 % 15.36/2.85 | % 15.36/2.85 | REDUCE: (2), (6) imply: % 15.36/2.85 | (8) $product(1, 1) = all_92_1 % 15.36/2.85 | % 15.36/2.85 | THEORY_AXIOM GroebnerMultiplication: % 15.36/2.85 | (9) ! [v0: int] : (v0 = 1 | ~ ($product(1, 1) = v0)) % 15.36/2.85 | % 15.36/2.85 | GROUND_INST: instantiating (9) with all_92_1, simplifying with (8) gives: % 15.36/2.85 | (10) all_92_1 = 1 % 15.36/2.85 | % 15.36/2.85 | REDUCE: (7), (10) imply: % 15.36/2.85 | (11) f__integer__(1) = all_92_0 % 15.36/2.86 | % 15.36/2.86 | GROUND_INST: instantiating (3) with 1, all_25_7, all_92_0, simplifying with % 15.36/2.86 | (4), (11) gives: % 15.36/2.86 | (12) all_92_0 = all_25_7 % 15.36/2.86 | % 15.36/2.86 | REDUCE: (5), (12) imply: % 15.36/2.86 | (13) $false % 15.36/2.86 | % 15.36/2.86 | CLOSE: (13) is inconsistent. % 15.36/2.86 | % 15.36/2.86 End of proof % 15.36/2.86 % SZS output end Proof for theBenchmark % 15.36/2.86 % 15.36/2.86 2305ms %------------------------------------------------------------------------------