%------------------------------------------------------------------------------ % 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 : n003.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 11.73s 2.37s % Output : Proof 15.32s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : SWX000_1 : TPTP v9.1.0. Released v9.1.0. % 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n003.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Sun Apr 6 02:57:18 EDT 2025 % 0.13/0.34 % CPUTime : % 0.67/0.64 ________ _____ % 0.67/0.64 ___ __ \_________(_)________________________________ % 0.67/0.64 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.67/0.64 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.67/0.64 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.67/0.64 % 0.67/0.64 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.67/0.64 (2023-06-19) % 0.67/0.64 % 0.67/0.64 (c) Philipp Rümmer, 2009-2023 % 0.67/0.64 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.67/0.64 Amanda Stjerna. % 0.67/0.64 Free software under BSD-3-Clause. % 0.67/0.64 % 0.67/0.64 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.67/0.64 % 0.67/0.64 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.67/0.65 Running up to 7 provers in parallel. % 0.67/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.67/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.67/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.67/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.67/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.67/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.67/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.61/1.31 Prover 3: Preprocessing ... % 3.61/1.31 Prover 4: Preprocessing ... % 3.61/1.31 Prover 0: Preprocessing ... % 3.61/1.31 Prover 5: Preprocessing ... % 3.61/1.31 Prover 2: Preprocessing ... % 3.61/1.31 Prover 6: Preprocessing ... % 3.61/1.31 Prover 1: Preprocessing ... % 8.09/1.88 Prover 1: Warning: ignoring some quantifiers % 8.09/1.88 Prover 5: Proving ... % 8.09/1.90 Prover 1: Constructing countermodel ... % 8.77/1.91 Prover 0: Proving ... % 8.77/1.92 Prover 4: Constructing countermodel ... % 8.77/1.97 Prover 3: Warning: ignoring some quantifiers % 8.77/1.97 Prover 6: Proving ... % 8.77/1.98 Prover 3: Constructing countermodel ... % 10.37/2.17 Prover 2: Proving ... % 11.73/2.37 Prover 0: proved (1710ms) % 11.73/2.37 % 11.73/2.37 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 11.73/2.37 % 11.73/2.37 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 11.73/2.37 Prover 3: stopped % 11.73/2.37 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 11.73/2.38 Prover 5: stopped % 11.73/2.38 Prover 6: stopped % 11.73/2.38 Prover 2: stopped % 12.39/2.39 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 12.39/2.39 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 12.39/2.39 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 13.19/2.49 Prover 10: Preprocessing ... % 13.19/2.49 Prover 7: Preprocessing ... % 13.19/2.49 Prover 1: gave up % 13.26/2.50 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 13.33/2.52 Prover 8: Preprocessing ... % 13.33/2.54 Prover 13: Preprocessing ... % 13.33/2.54 Prover 11: Preprocessing ... % 13.33/2.60 Prover 16: Preprocessing ... % 14.10/2.62 Prover 7: Warning: ignoring some quantifiers % 14.10/2.64 Prover 7: Constructing countermodel ... % 14.10/2.66 Prover 10: Warning: ignoring some quantifiers % 14.10/2.66 Prover 10: Constructing countermodel ... % 14.10/2.68 Prover 13: Warning: ignoring some quantifiers % 14.10/2.69 Prover 13: Constructing countermodel ... % 14.75/2.71 Prover 8: Warning: ignoring some quantifiers % 14.75/2.73 Prover 11: Constructing countermodel ... % 14.75/2.73 Prover 8: Constructing countermodel ... % 14.75/2.74 Prover 4: Found proof (size 63) % 14.75/2.74 Prover 4: proved (2078ms) % 14.75/2.74 Prover 16: Warning: ignoring some quantifiers % 14.75/2.74 Prover 7: stopped % 14.75/2.74 Prover 10: stopped % 14.75/2.74 Prover 13: stopped % 14.75/2.74 Prover 8: stopped % 14.75/2.74 Prover 11: stopped % 14.75/2.74 Prover 16: Constructing countermodel ... % 14.75/2.75 Prover 16: stopped % 14.75/2.75 % 14.75/2.75 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 14.75/2.75 % 14.75/2.76 % SZS output start Proof for theBenchmark % 14.75/2.76 Assumptions after simplification: % 14.75/2.76 --------------------------------- % 14.75/2.76 % 14.75/2.76 (f__integer__def_ax) % 14.75/2.78 ! [v0: int] : ! [v1: general] : ! [v2: general] : (v2 = v1 | ~ % 14.75/2.78 (f__integer__(v0) = v2) | ~ (f__integer__(v0) = v1)) & ! [v0: int] : ! % 14.75/2.78 [v1: int] : ! [v2: general] : (v1 = v0 | ~ (f__integer__(v1) = v2) | ~ % 14.75/2.78 (f__integer__(v0) = v2)) % 14.75/2.78 % 14.75/2.78 (formula_5_unnamed_formula) % 14.75/2.78 ! [v0: int] : ! [v1: int] : ! [v2: general] : ! [v3: general] : ! [v4: % 14.75/2.78 int] : (v4 = 0 | ~ ($lesseq(0, v0)) | ~ (sqrt(v2, v3) = v4) | ~ % 14.75/2.78 (f__integer__(v1) = v3) | ~ (f__integer__(v0) = v2) | ? [v5: int] : ? % 14.75/2.78 [v6: int] : ($product($sum(v0, 1), $sum(v0, 1)) = v6 & $product(v0, v0) = v5 % 14.75/2.78 & ( ~ ($lesseq(1, $difference(v6, v1))) | ~ ($lesseq(v5, v1))))) & ! % 14.75/2.78 [v0: int] : ! [v1: int] : ! [v2: general] : ! [v3: general] : ( ~ % 14.75/2.78 ($lesseq(v0, -1)) | ~ (sqrt(v2, v3) = 0) | ~ (f__integer__(v1) = v3) | ~ % 14.75/2.78 (f__integer__(v0) = v2)) & ! [v0: int] : ! [v1: int] : ! [v2: general] : % 14.75/2.78 ! [v3: general] : ( ~ (sqrt(v2, v3) = 0) | ~ (f__integer__(v1) = v3) | ~ % 14.75/2.78 (f__integer__(v0) = v2) | ? [v4: int] : ? [v5: int] : ($lesseq(1, % 14.75/2.78 $difference(v5, v1)) & $lesseq(v4, v1) & $product($sum(v0, 1), $sum(v0, % 14.75/2.78 1)) = v5 & $product(v0, v0) = v4)) % 14.75/2.78 % 14.75/2.78 (formula_6_unnamed_formula) % 15.32/2.79 ! [v0: int] : ! [v1: int] : ! [v2: general] : ! [v3: general] : ! [v4: % 15.32/2.79 int] : (v4 = 0 | ~ (sqrt(v2, v3) = v4) | ~ (f__integer__($sum(v1, 1)) = % 15.32/2.79 v3) | ~ (f__integer__($sum(v0, 1)) = v2) | ? [v5: general] : ? [v6: % 15.32/2.79 general] : ? [v7: any] : ? [v8: int] : (sqrt(v5, v6) = v7 & % 15.32/2.79 f__integer__(v1) = v6 & f__integer__(v0) = v5 & $product($sum(v0, 1), % 15.32/2.79 $sum(v0, 1)) = v8 & general(v6) & general(v5) & ( ~ (v7 = 0) | ~ % 15.32/2.79 ($lesseq(-1, $difference(v1, v8)))))) & ! [v0: int] : ! [v1: int] : ! % 15.32/2.79 [v2: general] : ! [v3: general] : ( ~ (sqrt(v2, v3) = 0) | ~ % 15.32/2.79 (f__integer__(v1) = v3) | ~ (f__integer__(v0) = v2) | ? [v4: int] : ? % 15.32/2.79 [v5: general] : ? [v6: general] : ? [v7: any] : (sqrt(v5, v6) = v7 & % 15.32/2.79 f__integer__($sum(v1, 1)) = v6 & f__integer__($sum(v0, 1)) = v5 & % 15.32/2.79 $product($sum(v0, 1), $sum(v0, 1)) = v4 & general(v6) & general(v5) & (v7 % 15.32/2.79 = 0 | ~ ($lesseq(-1, $difference(v1, v4)))))) % 15.32/2.79 % 15.32/2.79 (formula_7_inductive_step) % 15.32/2.79 ? [v0: int] : ? [v1: general] : ? [v2: general] : ? [v3: int] : ? [v4: % 15.32/2.79 general] : ($lesseq(0, v0) & sqrt(v4, v1) = 0 & f__integer__(v3) = v4 & % 15.32/2.79 f__integer__($sum(v0, 1)) = v2 & f__integer__(v0) = v1 & general(v4) & % 15.32/2.79 general(v2) & general(v1) & ! [v5: int] : ! [v6: general] : ( ~ % 15.32/2.79 (f__integer__(v5) = v6) | ? [v7: int] : ( ~ (v7 = 0) & sqrt(v6, v2) = % 15.32/2.79 v7))) % 15.32/2.79 % 15.32/2.79 (function-axioms) % 15.32/2.80 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: general] : % 15.32/2.80 ! [v3: general] : (v1 = v0 | ~ (sqrt(v3, v2) = v1) | ~ (sqrt(v3, v2) = v0)) % 15.32/2.80 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: general] : % 15.32/2.80 ! [v3: general] : (v1 = v0 | ~ (p__greater__(v3, v2) = v1) | ~ % 15.32/2.80 (p__greater__(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 15.32/2.80 MultipleValueBool] : ! [v2: general] : ! [v3: general] : (v1 = v0 | ~ % 15.32/2.80 (p__greater_equal__(v3, v2) = v1) | ~ (p__greater_equal__(v3, v2) = v0)) & % 15.32/2.80 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: general] : ! % 15.32/2.80 [v3: general] : (v1 = v0 | ~ (p__less__(v3, v2) = v1) | ~ (p__less__(v3, v2) % 15.32/2.80 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 15.32/2.80 general] : ! [v3: general] : (v1 = v0 | ~ (p__less_equal__(v3, v2) = v1) | % 15.32/2.80 ~ (p__less_equal__(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 15.32/2.80 MultipleValueBool] : ! [v2: general] : (v1 = v0 | ~ (prime(v2) = v1) | ~ % 15.32/2.80 (prime(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] % 15.32/2.80 : ! [v2: general] : (v1 = v0 | ~ (composite_p(v2) = v1) | ~ % 15.32/2.80 (composite_p(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 15.32/2.80 MultipleValueBool] : ! [v2: general] : (v1 = v0 | ~ (sqrtb(v2) = v1) | ~ % 15.32/2.80 (sqrtb(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] % 15.32/2.80 : ! [v2: general] : (v1 = v0 | ~ (composite(v2) = v1) | ~ (composite(v2) = % 15.32/2.80 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 15.32/2.80 general] : (v1 = v0 | ~ (p__is_symbolic__(v2) = v1) | ~ % 15.32/2.80 (p__is_symbolic__(v2) = v0)) & ! [v0: general] : ! [v1: general] : ! [v2: % 15.32/2.80 symbol] : (v1 = v0 | ~ (f__symbolic__(v2) = v1) | ~ (f__symbolic__(v2) = % 15.32/2.80 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 15.32/2.80 general] : (v1 = v0 | ~ (p__is_integer__(v2) = v1) | ~ % 15.32/2.80 (p__is_integer__(v2) = v0)) & ! [v0: general] : ! [v1: general] : ! [v2: % 15.32/2.80 int] : (v1 = v0 | ~ (f__integer__(v2) = v1) | ~ (f__integer__(v2) = v0)) % 15.32/2.80 % 15.32/2.80 Further assumptions not needed in the proof: % 15.32/2.80 -------------------------------------------- % 15.32/2.80 antisymmetric_ordering_ax, f__symbolic__def_ax, formula_0_unnamed_formula, % 15.32/2.80 formula_1_completed_definition_of_composite_1, % 15.32/2.80 formula_2_completed_definition_of_sqrtb_1, % 15.32/2.80 formula_3_completed_definition_of_composite_1, % 15.32/2.80 formula_4_completed_definition_of_prime_1, general_universe_ax, % 15.32/2.80 maximal_element_ax, minimal_element_ax, numeral_ordering_ax, % 15.32/2.80 numerals_less_than_symbols_ax, p__greater__def_ax, p__greater_equal__def_ax, % 15.32/2.80 p__is_integer__def_ax, p__is_symbolic__def_ax, p__less__def_ax, % 15.32/2.80 strongly_connected_ordering_ax, transitive_ordering_ax % 15.32/2.80 % 15.32/2.80 Those formulas are unsatisfiable: % 15.32/2.80 --------------------------------- % 15.32/2.80 % 15.32/2.80 Begin of proof % 15.32/2.80 | % 15.32/2.80 | ALPHA: (f__integer__def_ax) implies: % 15.32/2.80 | (1) ! [v0: int] : ! [v1: general] : ! [v2: general] : (v2 = v1 | ~ % 15.32/2.80 | (f__integer__(v0) = v2) | ~ (f__integer__(v0) = v1)) % 15.32/2.80 | % 15.32/2.80 | ALPHA: (formula_5_unnamed_formula) implies: % 15.32/2.80 | (2) ! [v0: int] : ! [v1: int] : ! [v2: general] : ! [v3: general] : ( ~ % 15.32/2.80 | (sqrt(v2, v3) = 0) | ~ (f__integer__(v1) = v3) | ~ % 15.32/2.80 | (f__integer__(v0) = v2) | ? [v4: int] : ? [v5: int] : ($lesseq(1, % 15.32/2.80 | $difference(v5, v1)) & $lesseq(v4, v1) & $product($sum(v0, 1), % 15.32/2.80 | $sum(v0, 1)) = v5 & $product(v0, v0) = v4)) % 15.32/2.80 | (3) ! [v0: int] : ! [v1: int] : ! [v2: general] : ! [v3: general] : ! % 15.32/2.80 | [v4: int] : (v4 = 0 | ~ ($lesseq(0, v0)) | ~ (sqrt(v2, v3) = v4) | ~ % 15.32/2.80 | (f__integer__(v1) = v3) | ~ (f__integer__(v0) = v2) | ? [v5: int] : % 15.32/2.80 | ? [v6: int] : ($product($sum(v0, 1), $sum(v0, 1)) = v6 & % 15.32/2.80 | $product(v0, v0) = v5 & ( ~ ($lesseq(1, $difference(v6, v1))) | ~ % 15.32/2.80 | ($lesseq(v5, v1))))) % 15.32/2.80 | % 15.32/2.80 | ALPHA: (formula_6_unnamed_formula) implies: % 15.32/2.81 | (4) ! [v0: int] : ! [v1: int] : ! [v2: general] : ! [v3: general] : ( ~ % 15.32/2.81 | (sqrt(v2, v3) = 0) | ~ (f__integer__(v1) = v3) | ~ % 15.32/2.81 | (f__integer__(v0) = v2) | ? [v4: int] : ? [v5: general] : ? [v6: % 15.32/2.81 | general] : ? [v7: any] : (sqrt(v5, v6) = v7 & % 15.32/2.81 | f__integer__($sum(v1, 1)) = v6 & f__integer__($sum(v0, 1)) = v5 & % 15.32/2.81 | $product($sum(v0, 1), $sum(v0, 1)) = v4 & general(v6) & general(v5) % 15.32/2.81 | & (v7 = 0 | ~ ($lesseq(-1, $difference(v1, v4)))))) % 15.32/2.81 | % 15.32/2.81 | ALPHA: (function-axioms) implies: % 15.32/2.81 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 15.32/2.81 | general] : ! [v3: general] : (v1 = v0 | ~ (sqrt(v3, v2) = v1) | ~ % 15.32/2.81 | (sqrt(v3, v2) = v0)) % 15.32/2.81 | % 15.32/2.81 | DELTA: instantiating (formula_7_inductive_step) with fresh symbols all_28_0, % 15.32/2.81 | all_28_1, all_28_2, all_28_3, all_28_4 gives: % 15.32/2.81 | (6) $lesseq(0, all_28_4) & sqrt(all_28_0, all_28_3) = 0 & % 15.32/2.81 | f__integer__(all_28_1) = all_28_0 & f__integer__($sum(all_28_4, 1)) = % 15.32/2.81 | all_28_2 & f__integer__(all_28_4) = all_28_3 & general(all_28_0) & % 15.32/2.81 | general(all_28_2) & general(all_28_3) & ! [v0: int] : ! [v1: general] % 15.32/2.81 | : ( ~ (f__integer__(v0) = v1) | ? [v2: int] : ( ~ (v2 = 0) & sqrt(v1, % 15.32/2.81 | all_28_2) = v2)) % 15.32/2.81 | % 15.32/2.81 | ALPHA: (6) implies: % 15.32/2.81 | (7) f__integer__(all_28_4) = all_28_3 % 15.32/2.81 | (8) f__integer__($sum(all_28_4, 1)) = all_28_2 % 15.32/2.81 | (9) f__integer__(all_28_1) = all_28_0 % 15.32/2.81 | (10) sqrt(all_28_0, all_28_3) = 0 % 15.32/2.81 | (11) ! [v0: int] : ! [v1: general] : ( ~ (f__integer__(v0) = v1) | ? % 15.32/2.81 | [v2: int] : ( ~ (v2 = 0) & sqrt(v1, all_28_2) = v2)) % 15.32/2.81 | % 15.32/2.81 | GROUND_INST: instantiating (11) with all_28_1, all_28_0, simplifying with (9) % 15.32/2.81 | gives: % 15.32/2.81 | (12) ? [v0: int] : ( ~ (v0 = 0) & sqrt(all_28_0, all_28_2) = v0) % 15.32/2.81 | % 15.32/2.81 | GROUND_INST: instantiating (4) with all_28_1, all_28_4, all_28_0, all_28_3, % 15.32/2.81 | simplifying with (7), (9), (10) gives: % 15.32/2.81 | (13) ? [v0: int] : ? [v1: general] : ? [v2: general] : ? [v3: any] : % 15.32/2.81 | (sqrt(v1, v2) = v3 & f__integer__($sum(all_28_1, 1)) = v1 & % 15.32/2.81 | f__integer__($sum(all_28_4, 1)) = v2 & $product($sum(all_28_1, 1), % 15.32/2.81 | $sum(all_28_1, 1)) = v0 & general(v2) & general(v1) & (v3 = 0 | ~ % 15.32/2.81 | ($lesseq(-1, $difference(all_28_4, v0))))) % 15.32/2.81 | % 15.32/2.81 | GROUND_INST: instantiating (2) with all_28_1, all_28_4, all_28_0, all_28_3, % 15.32/2.81 | simplifying with (7), (9), (10) gives: % 15.32/2.81 | (14) ? [v0: int] : ? [v1: int] : ($lesseq(1, $difference(v1, all_28_4)) & % 15.32/2.81 | $lesseq(v0, all_28_4) & $product($sum(all_28_1, 1), $sum(all_28_1, % 15.32/2.81 | 1)) = v1 & $product(all_28_1, all_28_1) = v0) % 15.32/2.81 | % 15.32/2.81 | DELTA: instantiating (12) with fresh symbol all_57_0 gives: % 15.32/2.81 | (15) ~ (all_57_0 = 0) & sqrt(all_28_0, all_28_2) = all_57_0 % 15.32/2.81 | % 15.32/2.81 | ALPHA: (15) implies: % 15.32/2.81 | (16) ~ (all_57_0 = 0) % 15.32/2.81 | (17) sqrt(all_28_0, all_28_2) = all_57_0 % 15.32/2.81 | % 15.32/2.81 | DELTA: instantiating (14) with fresh symbols all_59_0, all_59_1 gives: % 15.32/2.82 | (18) $lesseq(1, $difference(all_59_0, all_28_4)) & $lesseq(all_59_1, % 15.32/2.82 | all_28_4) & $product($sum(all_28_1, 1), $sum(all_28_1, 1)) = % 15.32/2.82 | all_59_0 & $product(all_28_1, all_28_1) = all_59_1 % 15.32/2.82 | % 15.32/2.82 | ALPHA: (18) implies: % 15.32/2.82 | (19) $lesseq(all_59_1, all_28_4) % 15.32/2.82 | (20) $lesseq(1, $difference(all_59_0, all_28_4)) % 15.32/2.82 | (21) $product(all_28_1, all_28_1) = all_59_1 % 15.32/2.82 | (22) $product($sum(all_28_1, 1), $sum(all_28_1, 1)) = all_59_0 % 15.32/2.82 | % 15.32/2.82 | DELTA: instantiating (13) with fresh symbols all_62_0, all_62_1, all_62_2, % 15.32/2.82 | all_62_3 gives: % 15.32/2.82 | (23) sqrt(all_62_2, all_62_1) = all_62_0 & f__integer__($sum(all_28_1, 1)) % 15.32/2.82 | = all_62_2 & f__integer__($sum(all_28_4, 1)) = all_62_1 & % 15.32/2.82 | $product($sum(all_28_1, 1), $sum(all_28_1, 1)) = all_62_3 & % 15.32/2.82 | general(all_62_1) & general(all_62_2) & (all_62_0 = 0 | ~ % 15.32/2.82 | ($lesseq(-1, $difference(all_28_4, all_62_3)))) % 15.32/2.82 | % 15.32/2.82 | ALPHA: (23) implies: % 15.32/2.82 | (24) $product($sum(all_28_1, 1), $sum(all_28_1, 1)) = all_62_3 % 15.32/2.82 | (25) f__integer__($sum(all_28_4, 1)) = all_62_1 % 15.32/2.82 | (26) f__integer__($sum(all_28_1, 1)) = all_62_2 % 15.32/2.82 | (27) sqrt(all_62_2, all_62_1) = all_62_0 % 15.32/2.82 | (28) all_62_0 = 0 | ~ ($lesseq(-1, $difference(all_28_4, all_62_3))) % 15.32/2.82 | % 15.32/2.82 | THEORY_AXIOM GroebnerMultiplication: % 15.32/2.82 | (29) ! [v0: int] : ! [v1: int] : ! [v2: int] : (v2 = v1 | ~ % 15.32/2.82 | ($product($sum(v0, 1), $sum(v0, 1)) = v2) | ~ ($product($sum(v0, % 15.32/2.82 | 1), $sum(v0, 1)) = v1)) % 15.32/2.82 | % 15.32/2.82 | GROUND_INST: instantiating (29) with all_28_1, all_59_0, all_62_3, simplifying % 15.32/2.82 | with (22), (24) gives: % 15.32/2.82 | (30) all_62_3 = all_59_0 % 15.32/2.82 | % 15.32/2.82 | THEORY_AXIOM GroebnerMultiplication: % 15.32/2.82 | (31) ! [v0: int] : ! [v1: int] : ! [v2: int] : % 15.32/2.82 | ($difference($difference(v2, v1), $product(2, v0)) = 1 | ~ % 15.32/2.82 | ($product($sum(v0, 1), $sum(v0, 1)) = v2) | ~ ($product(v0, v0) = % 15.32/2.82 | v1)) % 15.32/2.82 | % 15.32/2.82 | GROUND_INST: instantiating (31) with all_28_1, all_59_1, all_59_0, simplifying % 15.32/2.82 | with (21), (22) gives: % 15.32/2.82 | (32) $difference($difference(all_59_0, all_59_1), $product(2, all_28_1)) = % 15.32/2.82 | 1 % 15.32/2.82 | % 15.32/2.82 | COMBINE_EQS: (30), (32) imply: % 15.32/2.82 | (33) $difference($difference(all_62_3, all_59_1), $product(2, all_28_1)) = % 15.32/2.82 | 1 % 15.32/2.82 | % 15.32/2.82 | REDUCE: (20), (32) imply: % 15.32/2.82 | (34) $lesseq(all_28_4, $sum(all_59_1, $product(2, all_28_1))) % 15.32/2.82 | % 15.32/2.82 | COMBINE_INEQS: (19), (34) imply: % 15.32/2.82 | (35) $lesseq(0, all_28_1) % 15.32/2.82 | % 15.32/2.82 | SIMP: (35) implies: % 15.32/2.82 | (36) $lesseq(0, all_28_1) % 15.32/2.82 | % 15.32/2.82 | REDUCE: (22), (32) imply: % 15.32/2.82 | (37) $product($sum(all_28_1, 1), $sum(all_28_1, 1)) = $sum($sum(all_59_1, % 15.32/2.82 | $product(2, all_28_1)), 1) % 15.32/2.82 | % 15.32/2.82 | GROUND_INST: instantiating (1) with $sum(all_28_4, 1), all_28_2, all_62_1, % 15.32/2.82 | simplifying with (8), (25) gives: % 15.32/2.82 | (38) all_62_1 = all_28_2 % 15.32/2.82 | % 15.32/2.82 | REDUCE: (27), (38) imply: % 15.32/2.82 | (39) sqrt(all_62_2, all_28_2) = all_62_0 % 15.32/2.82 | % 15.32/2.82 | GROUND_INST: instantiating (11) with $sum(all_28_1, 1), all_62_2, simplifying % 15.32/2.82 | with (26) gives: % 15.32/2.82 | (40) ? [v0: int] : ( ~ (v0 = 0) & sqrt(all_62_2, all_28_2) = v0) % 15.32/2.82 | % 15.32/2.82 | GROUND_INST: instantiating (3) with all_28_1, $sum(all_28_4, 1), all_28_0, % 15.32/2.82 | all_28_2, all_57_0, simplifying with (8), (9), (17) gives: % 15.32/2.83 | (41) all_57_0 = 0 | ~ ($lesseq(0, all_28_1)) | ? [v0: int] : ? [v1: int] % 15.32/2.83 | : ($product($sum(all_28_1, 1), $sum(all_28_1, 1)) = v1 & % 15.32/2.83 | $product(all_28_1, all_28_1) = v0 & ( ~ ($lesseq(2, $difference(v1, % 15.32/2.83 | all_28_4))) | ~ ($lesseq(-1, $difference(all_28_4, v0))))) % 15.32/2.83 | % 15.32/2.83 | DELTA: instantiating (40) with fresh symbol all_83_0 gives: % 15.32/2.83 | (42) ~ (all_83_0 = 0) & sqrt(all_62_2, all_28_2) = all_83_0 % 15.32/2.83 | % 15.32/2.83 | ALPHA: (42) implies: % 15.32/2.83 | (43) ~ (all_83_0 = 0) % 15.32/2.83 | (44) sqrt(all_62_2, all_28_2) = all_83_0 % 15.32/2.83 | % 15.32/2.83 | BETA: splitting (41) gives: % 15.32/2.83 | % 15.32/2.83 | Case 1: % 15.32/2.83 | | % 15.32/2.83 | | (45) $lesseq(all_28_1, -1) % 15.32/2.83 | | % 15.32/2.83 | | COMBINE_INEQS: (36), (45) imply: % 15.32/2.83 | | (46) $false % 15.32/2.83 | | % 15.32/2.83 | | CLOSE: (46) is inconsistent. % 15.32/2.83 | | % 15.32/2.83 | Case 2: % 15.32/2.83 | | % 15.32/2.83 | | (47) all_57_0 = 0 | ? [v0: int] : ? [v1: int] : % 15.32/2.83 | | ($product($sum(all_28_1, 1), $sum(all_28_1, 1)) = v1 & % 15.32/2.83 | | $product(all_28_1, all_28_1) = v0 & ( ~ ($lesseq(2, % 15.32/2.83 | | $difference(v1, all_28_4))) | ~ ($lesseq(-1, % 15.32/2.83 | | $difference(all_28_4, v0))))) % 15.32/2.83 | | % 15.32/2.83 | | BETA: splitting (47) gives: % 15.32/2.83 | | % 15.32/2.83 | | Case 1: % 15.32/2.83 | | | % 15.32/2.83 | | | (48) all_57_0 = 0 % 15.32/2.83 | | | % 15.32/2.83 | | | REDUCE: (16), (48) imply: % 15.32/2.83 | | | (49) $false % 15.32/2.83 | | | % 15.32/2.83 | | | CLOSE: (49) is inconsistent. % 15.32/2.83 | | | % 15.32/2.83 | | Case 2: % 15.32/2.83 | | | % 15.32/2.83 | | | (50) ? [v0: int] : ? [v1: int] : ($product($sum(all_28_1, 1), % 15.32/2.83 | | | $sum(all_28_1, 1)) = v1 & $product(all_28_1, all_28_1) = v0 & % 15.32/2.83 | | | ( ~ ($lesseq(2, $difference(v1, all_28_4))) | ~ ($lesseq(-1, % 15.32/2.83 | | | $difference(all_28_4, v0))))) % 15.32/2.83 | | | % 15.32/2.83 | | | DELTA: instantiating (50) with fresh symbols all_120_0, all_120_1 gives: % 15.32/2.83 | | | (51) $product($sum(all_28_1, 1), $sum(all_28_1, 1)) = all_120_0 & % 15.32/2.83 | | | $product(all_28_1, all_28_1) = all_120_1 & ( ~ ($lesseq(2, % 15.32/2.83 | | | $difference(all_120_0, all_28_4))) | ~ ($lesseq(-1, % 15.32/2.83 | | | $difference(all_28_4, all_120_1)))) % 15.32/2.83 | | | % 15.32/2.83 | | | ALPHA: (51) implies: % 15.32/2.83 | | | (52) $product(all_28_1, all_28_1) = all_120_1 % 15.32/2.83 | | | (53) $product($sum(all_28_1, 1), $sum(all_28_1, 1)) = all_120_0 % 15.32/2.83 | | | (54) ~ ($lesseq(2, $difference(all_120_0, all_28_4))) | ~ % 15.32/2.83 | | | ($lesseq(-1, $difference(all_28_4, all_120_1))) % 15.32/2.83 | | | % 15.32/2.83 | | | THEORY_AXIOM GroebnerMultiplication: % 15.32/2.83 | | | (55) ! [v0: int] : ! [v1: int] : ! [v2: int] : ! [v3: int] : % 15.32/2.83 | | | ($difference($difference(v3, v2), $product(2, v0)) = 1 | ~ % 15.32/2.83 | | | ($product($sum(v0, 1), $sum(v0, 1)) = v3) | ~ % 15.32/2.83 | | | ($product($sum(v0, 1), $sum(v0, 1)) = $sum($sum(v1, $product(2, % 15.32/2.83 | | | v0)), 1)) | ~ ($product(v0, v0) = v2)) % 15.32/2.83 | | | % 15.32/2.83 | | | GROUND_INST: instantiating (55) with all_28_1, all_59_1, all_120_1, % 15.32/2.83 | | | all_120_0, simplifying with (37), (52), (53) gives: % 15.32/2.83 | | | (56) $difference($difference(all_120_0, all_120_1), $product(2, % 15.32/2.83 | | | all_28_1)) = 1 % 15.32/2.83 | | | % 15.32/2.83 | | | THEORY_AXIOM GroebnerMultiplication: % 15.32/2.83 | | | (57) ! [v0: int] : ! [v1: int] : ! [v2: int] : % 15.32/2.83 | | | ($difference($difference(v2, v1), $product(2, v0)) = 1 | ~ % 15.32/2.83 | | | ($product($sum(v0, 1), $sum(v0, 1)) = v2) | ~ % 15.32/2.83 | | | ($product($sum(v0, 1), $sum(v0, 1)) = $sum($sum(v1, $product(2, % 15.32/2.83 | | | v0)), 1))) % 15.32/2.83 | | | % 15.32/2.83 | | | GROUND_INST: instantiating (57) with all_28_1, all_59_1, all_120_0, % 15.32/2.84 | | | simplifying with (37), (53) gives: % 15.32/2.84 | | | (58) $difference($difference(all_120_0, all_59_1), $product(2, % 15.32/2.84 | | | all_28_1)) = 1 % 15.32/2.84 | | | % 15.32/2.84 | | | COMBINE_EQS: (56), (58) imply: % 15.32/2.84 | | | (59) all_120_1 = all_59_1 % 15.32/2.84 | | | % 15.32/2.84 | | | BETA: splitting (54) gives: % 15.32/2.84 | | | % 15.32/2.84 | | | Case 1: % 15.32/2.84 | | | | % 15.32/2.84 | | | | (60) $lesseq(-1, $difference(all_28_4, all_120_0)) % 15.32/2.84 | | | | % 15.32/2.84 | | | | REDUCE: (58), (60) imply: % 15.32/2.84 | | | | (61) $lesseq(0, $sum($difference($product(-1, all_59_1), $product(2, % 15.32/2.84 | | | | all_28_1)), all_28_4)) % 15.32/2.84 | | | | % 15.32/2.84 | | | | ANTI_SYMM: (34), (61) imply: % 15.32/2.84 | | | | (62) $sum(all_59_1, $product(2, all_28_1)) = all_28_4 % 15.32/2.84 | | | | % 15.32/2.84 | | | | COMBINE_EQS: (33), (62) imply: % 15.32/2.84 | | | | (63) $difference(all_62_3, all_28_4) = 1 % 15.32/2.84 | | | | % 15.32/2.84 | | | | BETA: splitting (28) gives: % 15.32/2.84 | | | | % 15.32/2.84 | | | | Case 1: % 15.32/2.84 | | | | | % 15.32/2.84 | | | | | (64) $lesseq(2, $difference(all_62_3, all_28_4)) % 15.32/2.84 | | | | | % 15.32/2.84 | | | | | REDUCE: (63), (64) imply: % 15.32/2.84 | | | | | (65) $false % 15.32/2.84 | | | | | % 15.32/2.84 | | | | | CLOSE: (65) is inconsistent. % 15.32/2.84 | | | | | % 15.32/2.84 | | | | Case 2: % 15.32/2.84 | | | | | % 15.32/2.84 | | | | | (66) all_62_0 = 0 % 15.32/2.84 | | | | | % 15.32/2.84 | | | | | REDUCE: (39), (66) imply: % 15.32/2.84 | | | | | (67) sqrt(all_62_2, all_28_2) = 0 % 15.32/2.84 | | | | | % 15.32/2.84 | | | | | GROUND_INST: instantiating (5) with 0, all_83_0, all_28_2, all_62_2, % 15.32/2.84 | | | | | simplifying with (44), (67) gives: % 15.32/2.84 | | | | | (68) all_83_0 = 0 % 15.32/2.84 | | | | | % 15.32/2.84 | | | | | REDUCE: (43), (68) imply: % 15.32/2.84 | | | | | (69) $false % 15.32/2.84 | | | | | % 15.32/2.84 | | | | | CLOSE: (69) is inconsistent. % 15.32/2.84 | | | | | % 15.32/2.84 | | | | End of split % 15.32/2.84 | | | | % 15.32/2.84 | | | Case 2: % 15.32/2.84 | | | | % 15.32/2.84 | | | | (70) $lesseq(2, $difference(all_120_1, all_28_4)) % 15.32/2.84 | | | | % 15.32/2.84 | | | | REDUCE: (59), (70) imply: % 15.32/2.84 | | | | (71) $lesseq(2, $difference(all_59_1, all_28_4)) % 15.32/2.84 | | | | % 15.32/2.84 | | | | COMBINE_INEQS: (19), (71) imply: % 15.32/2.84 | | | | (72) $false % 15.32/2.84 | | | | % 15.32/2.84 | | | | CLOSE: (72) is inconsistent. % 15.32/2.84 | | | | % 15.32/2.84 | | | End of split % 15.32/2.84 | | | % 15.32/2.84 | | End of split % 15.32/2.84 | | % 15.32/2.84 | End of split % 15.32/2.84 | % 15.32/2.84 End of proof % 15.32/2.84 % SZS output end Proof for theBenchmark % 15.32/2.84 % 15.32/2.84 2202ms %------------------------------------------------------------------------------