%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : TIM013_1 : TPTP v9.3.0. Released v9.3.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n002.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 : Tue May 5 07:17:17 PM UTC 2026 % Result : Theorem 15.68s 2.87s % Output : Proof 20.30s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : TIM013_1 : TPTP v9.3.0. Released v9.3.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.17/0.34 % Computer : n002.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.34 % CPULimit : 300 % 0.17/0.34 % WCLimit : 300 % 0.17/0.34 % DateTime : Mon May 4 18:08:46 EDT 2026 % 0.17/0.34 % CPUTime : % 0.50/0.61 ________ _____ % 0.50/0.61 ___ __ \_________(_)________________________________ % 0.50/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.50/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.50/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.50/0.61 % 0.50/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.50/0.61 (2023-06-19) % 0.50/0.61 % 0.50/0.61 (c) Philipp Rümmer, 2009-2023 % 0.50/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.50/0.61 Amanda Stjerna. % 0.50/0.61 Free software under BSD-3-Clause. % 0.50/0.61 % 0.50/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.50/0.61 % 0.50/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.50/0.62 Running up to 7 provers in parallel. % 0.67/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.67/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.67/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.67/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.67/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.67/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.67/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 5.07/1.43 Prover 0: Preprocessing ... % 5.07/1.43 Prover 1: Preprocessing ... % 5.07/1.44 Prover 3: Preprocessing ... % 5.07/1.44 Prover 2: Preprocessing ... % 5.07/1.44 Prover 4: Preprocessing ... % 5.07/1.44 Prover 6: Preprocessing ... % 5.07/1.44 Prover 5: Preprocessing ... % 10.45/2.13 Prover 2: Proving ... % 10.45/2.13 Prover 5: Proving ... % 10.45/2.15 Prover 6: Proving ... % 10.45/2.15 Prover 4: Warning: ignoring some quantifiers % 10.45/2.19 Prover 1: Warning: ignoring some quantifiers % 10.45/2.19 Prover 3: Warning: ignoring some quantifiers % 11.08/2.22 Prover 3: Constructing countermodel ... % 11.08/2.23 Prover 0: Proving ... % 11.08/2.25 Prover 4: Constructing countermodel ... % 11.08/2.25 Prover 1: Constructing countermodel ... % 15.68/2.87 Prover 3: proved (2238ms) % 15.68/2.87 % 15.68/2.87 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 15.68/2.87 % 15.68/2.87 Prover 5: stopped % 15.68/2.87 Prover 2: stopped % 15.68/2.87 Prover 0: stopped % 15.68/2.88 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 15.68/2.89 Prover 6: stopped % 16.43/2.90 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 16.43/2.90 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 16.43/2.90 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 16.43/2.90 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 18.13/3.13 Prover 8: Preprocessing ... % 18.13/3.14 Prover 11: Preprocessing ... % 18.13/3.15 Prover 7: Preprocessing ... % 18.13/3.16 Prover 10: Preprocessing ... % 18.13/3.18 Prover 13: Preprocessing ... % 19.63/3.32 Prover 1: Found proof (size 14) % 19.63/3.32 Prover 1: proved (2692ms) % 19.63/3.33 Prover 4: stopped % 19.63/3.35 Prover 7: Warning: ignoring some quantifiers % 19.63/3.36 Prover 13: Warning: ignoring some quantifiers % 19.63/3.37 Prover 7: Constructing countermodel ... % 19.63/3.37 Prover 10: Warning: ignoring some quantifiers % 19.63/3.37 Prover 8: Warning: ignoring some quantifiers % 19.63/3.37 Prover 7: stopped % 19.63/3.38 Prover 13: Constructing countermodel ... % 19.63/3.38 Prover 10: Constructing countermodel ... % 19.63/3.38 Prover 13: stopped % 19.63/3.38 Prover 8: Constructing countermodel ... % 19.63/3.39 Prover 10: stopped % 19.63/3.39 Prover 8: stopped % 20.30/3.40 Prover 11: Warning: ignoring some quantifiers % 20.30/3.42 Prover 11: Constructing countermodel ... % 20.30/3.43 Prover 11: stopped % 20.30/3.43 % 20.30/3.43 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 20.30/3.43 % 20.30/3.43 % SZS output start Proof for theBenchmark % 20.30/3.43 Assumptions after simplification: % 20.30/3.43 --------------------------------- % 20.30/3.43 % 20.30/3.44 (lemma_boundary_jan0_2025) % 20.30/3.45 ? [v0: date] : (calc_date(0, 1, 2025, v0) = 0 & ymd(2024, 12, 31) = v0 & % 20.30/3.45 date(v0)) % 20.30/3.45 % 20.30/3.45 (test_year_back) % 20.30/3.45 ! [v0: date] : ( ~ (ymd(2024, 12, 31) = v0) | ? [v1: any] : ? [v2: any] : % 20.30/3.45 (calc_date(0, 1, 2025, v0) = v1 & valid_day(31) = v2 & ( ~ (v2 = 0) | ~ (v1 % 20.30/3.45 = 0)))) % 20.30/3.45 % 20.30/3.45 (trap_ax) % 20.30/3.45 ! [v0: int] : ! [v1: int] : (v1 = 0 | ~ ($lesseq(v0, 31)) | ~ ($lesseq(1, % 20.30/3.45 v0)) | ~ (valid_day(v0) = v1)) & ! [v0: int] : ( ~ (valid_day(v0) = 0) % 20.30/3.45 | ($lesseq(v0, 31) & $lesseq(1, v0))) % 20.30/3.45 % 20.30/3.45 (function-axioms) % 20.30/3.46 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: time] : ! % 20.30/3.46 [v3: int] : ! [v4: int] : ! [v5: int] : ! [v6: int] : ! [v7: int] : ! % 20.30/3.46 [v8: int] : ! [v9: int] : ! [v10: int] : (v1 = v0 | ~ (calc_datetime(v10, % 20.30/3.46 v9, v8, v7, v6, v5, v4, v3, v2) = v1) | ~ (calc_datetime(v10, v9, v8, % 20.30/3.46 v7, v6, v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 20.30/3.46 MultipleValueBool] : ! [v2: int] : ! [v3: int] : ! [v4: int] : ! [v5: % 20.30/3.46 int] : ! [v6: int] : ! [v7: int] : ! [v8: int] : (v1 = v0 | ~ % 20.30/3.46 (normalize_time(v8, v7, v6, v5, v4, v3, v2) = v1) | ~ (normalize_time(v8, % 20.30/3.46 v7, v6, v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 20.30/3.46 MultipleValueBool] : ! [v2: int] : ! [v3: int] : ! [v4: int] : ! [v5: % 20.30/3.46 int] : ! [v6: int] : ! [v7: int] : (v1 = v0 | ~ (zeller_prep(v7, v6, v5, % 20.30/3.46 v4, v3, v2) = v1) | ~ (zeller_prep(v7, v6, v5, v4, v3, v2) = v0)) & ! % 20.30/3.46 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: date] : ! [v3: % 20.30/3.46 int] : ! [v4: int] : ! [v5: day_name] : ! [v6: int] : (v1 = v0 | ~ % 20.30/3.46 (nth_weekday_date(v6, v5, v4, v3, v2) = v1) | ~ (nth_weekday_date(v6, v5, % 20.30/3.46 v4, v3, v2) = v0)) & ! [v0: time] : ! [v1: time] : ! [v2: int] : ! % 20.30/3.46 [v3: int] : ! [v4: int] : ! [v5: int] : ! [v6: int] : (v1 = v0 | ~ (dt(v6, % 20.30/3.46 v5, v4, v3, v2) = v1) | ~ (dt(v6, v5, v4, v3, v2) = v0)) & ! [v0: % 20.30/3.46 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: date] : ! [v3: % 20.30/3.46 int] : ! [v4: int] : ! [v5: int] : (v1 = v0 | ~ (calc_date(v5, v4, v3, % 20.30/3.46 v2) = v1) | ~ (calc_date(v5, v4, v3, v2) = v0)) & ! [v0: % 20.30/3.46 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: int] : ! [v3: % 20.30/3.46 int] : ! [v4: int] : (v1 = v0 | ~ (calc_nth_offset(v4, v3, v2) = v1) | ~ % 20.30/3.46 (calc_nth_offset(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 20.30/3.46 MultipleValueBool] : ! [v2: int] : ! [v3: int] : ! [v4: int] : (v1 = v0 | % 20.30/3.46 ~ (is_days_in_month(v4, v3, v2) = v1) | ~ (is_days_in_month(v4, v3, v2) = % 20.30/3.46 v0)) & ! [v0: date] : ! [v1: date] : ! [v2: int] : ! [v3: int] : ! % 20.30/3.46 [v4: int] : (v1 = v0 | ~ (ymd(v4, v3, v2) = v1) | ~ (ymd(v4, v3, v2) = v0)) % 20.30/3.46 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: int] : ! % 20.30/3.46 [v3: int] : (v1 = v0 | ~ (is_days_in_year(v3, v2) = v1) | ~ % 20.30/3.46 (is_days_in_year(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 20.30/3.46 MultipleValueBool] : ! [v2: int] : ! [v3: day_name] : (v1 = v0 | ~ % 20.30/3.46 (map_name_to_int(v3, v2) = v1) | ~ (map_name_to_int(v3, v2) = v0)) & ! % 20.30/3.46 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: day_name] : ! % 20.30/3.46 [v3: int] : (v1 = v0 | ~ (map_iso(v3, v2) = v1) | ~ (map_iso(v3, v2) = v0)) % 20.30/3.46 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: day_name] % 20.30/3.46 : ! [v3: date] : (v1 = v0 | ~ (weekday(v3, v2) = v1) | ~ (weekday(v3, v2) = % 20.30/3.46 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 20.30/3.46 int] : (v1 = v0 | ~ (is_leap_year(v2) = v1) | ~ (is_leap_year(v2) = v0)) & % 20.30/3.46 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: int] : (v1 = % 20.30/3.46 v0 | ~ (valid_day(v2) = v1) | ~ (valid_day(v2) = v0)) % 20.30/3.46 % 20.30/3.46 Further assumptions not needed in the proof: % 20.30/3.46 -------------------------------------------- % 20.30/3.46 anchor_1600_jan1, anchor_1776_jan1, anchor_1969_jan1, anchor_1985_jan1, % 20.30/3.46 anchor_2024_apr1, anchor_2024_feb1, anchor_2024_jan1, anchor_2024_mar1, % 20.30/3.46 anchor_2024_may1, anchor_2025_feb1, anchor_2025_jan1, anchor_2025_mar1, % 20.30/3.46 anchor_2025_nov1, back_decade_peel, back_year_peel_leap, back_year_peel_nonleap, % 20.30/3.46 cache_4yr_2025_to_2028, calc_nth_offset_def_mod7, calc_weekday_zeller, d_24, % 20.30/3.46 d_25, d_26, d_27, d_28, dt_logic, hint_century_back_bridge, % 20.30/3.46 hint_century_multi_bridge, hint_century_threshold_100k, % 20.30/3.46 hint_century_to_decade_bridge, hint_leap_1776_feb, hint_leap_2024_feb, % 20.30/3.46 last_weekday_shortcut, lemma_boundary_dec32, lemma_boundary_jan0_2024, % 20.30/3.46 lemma_boundary_leap_mar0, lemma_boundary_norm_mar0, m1, m10, m11, m12, m2, m3, % 20.30/3.46 m4, m5, m6, m7, m8, m9, map_0, map_1, map_2, map_3, map_4, map_5, map_6, % 20.30/3.46 map_n_0, map_n_1, map_n_2, map_n_3, map_n_4, map_n_5, map_n_6, % 20.30/3.46 map_name_to_int_functional, nth_weekday_logic, rule_back_10year_long, % 20.30/3.46 rule_back_10year_short, rule_back_400yr_cycle, rule_back_century, rule_back_jan, % 20.30/3.46 rule_back_std, rule_base, rule_fwd_10year_long, rule_fwd_400yr_cycle, % 20.30/3.46 rule_fwd_4year, rule_fwd_century, rule_fwd_dec, rule_fwd_safe_4yr_gen, % 20.30/3.46 rule_fwd_std, rule_fwd_year, rule_weekday_month_jump, time_logic, % 20.30/3.46 weekday_400yr_period, weekday_functional, zeller_adj_janfeb, zeller_adj_norm % 20.30/3.46 % 20.30/3.46 Those formulas are unsatisfiable: % 20.30/3.46 --------------------------------- % 20.30/3.46 % 20.30/3.46 Begin of proof % 20.30/3.46 | % 20.30/3.46 | ALPHA: (trap_ax) implies: % 20.30/3.46 | (1) ! [v0: int] : ! [v1: int] : (v1 = 0 | ~ ($lesseq(v0, 31)) | ~ % 20.30/3.46 | ($lesseq(1, v0)) | ~ (valid_day(v0) = v1)) % 20.30/3.46 | % 20.30/3.46 | ALPHA: (function-axioms) implies: % 20.30/3.46 | (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: date] % 20.30/3.46 | : ! [v3: int] : ! [v4: int] : ! [v5: int] : (v1 = v0 | ~ % 20.30/3.46 | (calc_date(v5, v4, v3, v2) = v1) | ~ (calc_date(v5, v4, v3, v2) = % 20.30/3.46 | v0)) % 20.30/3.46 | % 20.30/3.47 | DELTA: instantiating (lemma_boundary_jan0_2025) with fresh symbol all_66_0 % 20.30/3.47 | gives: % 20.30/3.47 | (3) calc_date(0, 1, 2025, all_66_0) = 0 & ymd(2024, 12, 31) = all_66_0 & % 20.30/3.47 | date(all_66_0) % 20.30/3.47 | % 20.30/3.47 | ALPHA: (3) implies: % 20.30/3.47 | (4) ymd(2024, 12, 31) = all_66_0 % 20.30/3.47 | (5) calc_date(0, 1, 2025, all_66_0) = 0 % 20.30/3.47 | % 20.30/3.47 | GROUND_INST: instantiating (test_year_back) with all_66_0, simplifying with % 20.30/3.47 | (4) gives: % 20.30/3.47 | (6) ? [v0: any] : ? [v1: any] : (calc_date(0, 1, 2025, all_66_0) = v0 & % 20.30/3.47 | valid_day(31) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 20.30/3.47 | % 20.30/3.47 | DELTA: instantiating (6) with fresh symbols all_198_0, all_198_1 gives: % 20.30/3.47 | (7) calc_date(0, 1, 2025, all_66_0) = all_198_1 & valid_day(31) = all_198_0 % 20.30/3.47 | & ( ~ (all_198_0 = 0) | ~ (all_198_1 = 0)) % 20.30/3.47 | % 20.30/3.47 | ALPHA: (7) implies: % 20.30/3.47 | (8) valid_day(31) = all_198_0 % 20.30/3.47 | (9) calc_date(0, 1, 2025, all_66_0) = all_198_1 % 20.30/3.47 | (10) ~ (all_198_0 = 0) | ~ (all_198_1 = 0) % 20.30/3.47 | % 20.30/3.47 | GROUND_INST: instantiating (1) with 31, all_198_0, simplifying with (8) gives: % 20.30/3.47 | (11) all_198_0 = 0 % 20.30/3.47 | % 20.30/3.47 | GROUND_INST: instantiating (2) with 0, all_198_1, all_66_0, 2025, 1, 0, % 20.30/3.47 | simplifying with (5), (9) gives: % 20.30/3.47 | (12) all_198_1 = 0 % 20.30/3.47 | % 20.30/3.47 | BETA: splitting (10) gives: % 20.30/3.47 | % 20.30/3.47 | Case 1: % 20.30/3.47 | | % 20.30/3.47 | | (13) ~ (all_198_0 = 0) % 20.30/3.47 | | % 20.30/3.47 | | REDUCE: (11), (13) imply: % 20.30/3.47 | | (14) $false % 20.30/3.47 | | % 20.30/3.47 | | CLOSE: (14) is inconsistent. % 20.30/3.47 | | % 20.30/3.47 | Case 2: % 20.30/3.47 | | % 20.30/3.47 | | (15) ~ (all_198_1 = 0) % 20.30/3.47 | | % 20.30/3.47 | | REDUCE: (12), (15) imply: % 20.30/3.47 | | (16) $false % 20.30/3.47 | | % 20.30/3.47 | | CLOSE: (16) is inconsistent. % 20.30/3.47 | | % 20.30/3.47 | End of split % 20.30/3.47 | % 20.30/3.47 End of proof % 20.30/3.47 % SZS output end Proof for theBenchmark % 20.30/3.47 % 20.30/3.47 2861ms %------------------------------------------------------------------------------