%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : TIM026_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 : n022.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 07:17:18 PM UTC 2026 % Result : Theorem 11.59s 2.20s % Output : Proof 14.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : TIM026_1 : TPTP v9.3.0. Released v9.3.0. % 0.00/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.17/0.33 % Computer : n022.cluster.edu % 0.17/0.33 % Model : x86_64 x86_64 % 0.17/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.33 % Memory : 8042.1875MB % 0.17/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.33 % CPULimit : 300 % 0.17/0.33 % WCLimit : 300 % 0.17/0.33 % DateTime : Mon May 4 18:23:50 EDT 2026 % 0.17/0.33 % CPUTime : % 0.53/0.60 ________ _____ % 0.53/0.60 ___ __ \_________(_)________________________________ % 0.53/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.53/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.53/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.53/0.60 % 0.53/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.53/0.60 (2023-06-19) % 0.53/0.60 % 0.53/0.60 (c) Philipp Rümmer, 2009-2023 % 0.53/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.53/0.60 Amanda Stjerna. % 0.53/0.60 Free software under BSD-3-Clause. % 0.53/0.60 % 0.53/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.53/0.60 % 0.53/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.53/0.61 Running up to 7 provers in parallel. % 0.53/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.53/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.53/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.53/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.53/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.53/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.53/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.74/1.39 Prover 3: Preprocessing ... % 4.74/1.40 Prover 2: Preprocessing ... % 4.74/1.40 Prover 0: Preprocessing ... % 4.74/1.40 Prover 6: Preprocessing ... % 5.49/1.40 Prover 5: Preprocessing ... % 5.49/1.41 Prover 1: Preprocessing ... % 5.49/1.41 Prover 4: Preprocessing ... % 10.22/2.09 Prover 2: Proving ... % 10.22/2.11 Prover 6: Proving ... % 11.02/2.12 Prover 5: Proving ... % 11.02/2.16 Prover 1: Warning: ignoring some quantifiers % 11.02/2.17 Prover 0: Proving ... % 11.02/2.17 Prover 3: Warning: ignoring some quantifiers % 11.02/2.19 Prover 6: proved (1566ms) % 11.02/2.20 % 11.59/2.20 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 11.59/2.20 % 11.59/2.20 Prover 4: Warning: ignoring some quantifiers % 11.59/2.20 Prover 3: Constructing countermodel ... % 11.59/2.20 Prover 1: Constructing countermodel ... % 11.59/2.20 Prover 5: proved (1573ms) % 11.59/2.20 % 11.59/2.20 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 11.59/2.20 % 11.59/2.20 Prover 0: stopped % 11.59/2.20 Prover 2: stopped % 11.59/2.21 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 11.59/2.21 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 11.59/2.21 Prover 3: stopped % 11.59/2.22 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 11.59/2.22 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 11.59/2.22 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 11.59/2.27 Prover 4: Constructing countermodel ... % 12.33/2.39 Prover 8: Preprocessing ... % 12.33/2.39 Prover 10: Preprocessing ... % 13.12/2.41 Prover 13: Preprocessing ... % 13.12/2.41 Prover 7: Preprocessing ... % 13.12/2.42 Prover 1: Found proof (size 11) % 13.12/2.42 Prover 1: proved (1804ms) % 13.12/2.42 Prover 4: stopped % 13.12/2.44 Prover 11: Preprocessing ... % 13.12/2.47 Prover 10: stopped % 13.12/2.48 Prover 7: stopped % 13.12/2.48 Prover 13: stopped % 13.87/2.51 Prover 11: stopped % 14.38/2.61 Prover 8: Warning: ignoring some quantifiers % 14.38/2.63 Prover 8: Constructing countermodel ... % 14.38/2.64 Prover 8: stopped % 14.38/2.64 % 14.38/2.64 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 14.38/2.64 % 14.38/2.64 % SZS output start Proof for theBenchmark % 14.38/2.65 Assumptions after simplification: % 14.38/2.65 --------------------------------- % 14.38/2.65 % 14.38/2.65 (anchor_1600_jan1) % 14.38/2.66 day_name(saturday) & ? [v0: date] : (ymd(1600, 1, 1) = v0 & weekday(v0, % 14.38/2.66 saturday) = 0 & date(v0)) % 14.38/2.66 % 14.38/2.66 (test_1600) % 14.38/2.66 day_name(saturday) & ? [v0: date] : (ymd(1600, 1, 1) = v0 & date(v0) & ~ % 14.38/2.66 (weekday(v0, saturday) = 0)) % 14.38/2.66 % 14.38/2.66 (function-axioms) % 14.38/2.67 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: time] : ! % 14.38/2.67 [v3: int] : ! [v4: int] : ! [v5: int] : ! [v6: int] : ! [v7: int] : ! % 14.38/2.67 [v8: int] : ! [v9: int] : ! [v10: int] : (v1 = v0 | ~ (calc_datetime(v10, % 14.38/2.67 v9, v8, v7, v6, v5, v4, v3, v2) = v1) | ~ (calc_datetime(v10, v9, v8, % 14.38/2.67 v7, v6, v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 14.38/2.67 MultipleValueBool] : ! [v2: int] : ! [v3: int] : ! [v4: int] : ! [v5: % 14.38/2.67 int] : ! [v6: int] : ! [v7: int] : ! [v8: int] : (v1 = v0 | ~ % 14.38/2.67 (normalize_time(v8, v7, v6, v5, v4, v3, v2) = v1) | ~ (normalize_time(v8, % 14.38/2.67 v7, v6, v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 14.38/2.67 MultipleValueBool] : ! [v2: int] : ! [v3: int] : ! [v4: int] : ! [v5: % 14.38/2.67 int] : ! [v6: int] : ! [v7: int] : (v1 = v0 | ~ (zeller_prep(v7, v6, v5, % 14.38/2.67 v4, v3, v2) = v1) | ~ (zeller_prep(v7, v6, v5, v4, v3, v2) = v0)) & ! % 14.38/2.67 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: date] : ! [v3: % 14.38/2.67 int] : ! [v4: int] : ! [v5: day_name] : ! [v6: int] : (v1 = v0 | ~ % 14.38/2.67 (nth_weekday_date(v6, v5, v4, v3, v2) = v1) | ~ (nth_weekday_date(v6, v5, % 14.38/2.67 v4, v3, v2) = v0)) & ! [v0: time] : ! [v1: time] : ! [v2: int] : ! % 14.38/2.67 [v3: int] : ! [v4: int] : ! [v5: int] : ! [v6: int] : (v1 = v0 | ~ (dt(v6, % 14.38/2.67 v5, v4, v3, v2) = v1) | ~ (dt(v6, v5, v4, v3, v2) = v0)) & ! [v0: % 14.38/2.67 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: date] : ! [v3: % 14.38/2.67 int] : ! [v4: int] : ! [v5: int] : (v1 = v0 | ~ (calc_date(v5, v4, v3, % 14.38/2.67 v2) = v1) | ~ (calc_date(v5, v4, v3, v2) = v0)) & ! [v0: % 14.38/2.67 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: int] : ! [v3: % 14.38/2.67 int] : ! [v4: int] : (v1 = v0 | ~ (calc_nth_offset(v4, v3, v2) = v1) | ~ % 14.38/2.67 (calc_nth_offset(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 14.38/2.67 MultipleValueBool] : ! [v2: int] : ! [v3: int] : ! [v4: int] : (v1 = v0 | % 14.38/2.67 ~ (is_days_in_month(v4, v3, v2) = v1) | ~ (is_days_in_month(v4, v3, v2) = % 14.38/2.67 v0)) & ! [v0: date] : ! [v1: date] : ! [v2: int] : ! [v3: int] : ! % 14.38/2.67 [v4: int] : (v1 = v0 | ~ (ymd(v4, v3, v2) = v1) | ~ (ymd(v4, v3, v2) = v0)) % 14.38/2.67 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: int] : ! % 14.38/2.67 [v3: int] : (v1 = v0 | ~ (is_days_in_year(v3, v2) = v1) | ~ % 14.38/2.67 (is_days_in_year(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 14.38/2.67 MultipleValueBool] : ! [v2: int] : ! [v3: day_name] : (v1 = v0 | ~ % 14.38/2.67 (map_name_to_int(v3, v2) = v1) | ~ (map_name_to_int(v3, v2) = v0)) & ! % 14.38/2.67 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: day_name] : ! % 14.38/2.67 [v3: int] : (v1 = v0 | ~ (map_iso(v3, v2) = v1) | ~ (map_iso(v3, v2) = v0)) % 14.38/2.67 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: day_name] % 14.38/2.67 : ! [v3: date] : (v1 = v0 | ~ (weekday(v3, v2) = v1) | ~ (weekday(v3, v2) = % 14.38/2.67 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 14.38/2.67 int] : (v1 = v0 | ~ (is_leap_year(v2) = v1) | ~ (is_leap_year(v2) = v0)) & % 14.38/2.67 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: int] : (v1 = % 14.38/2.67 v0 | ~ (valid_day(v2) = v1) | ~ (valid_day(v2) = v0)) % 14.38/2.67 % 14.38/2.67 Further assumptions not needed in the proof: % 14.38/2.67 -------------------------------------------- % 14.38/2.67 anchor_1776_jan1, anchor_1969_jan1, anchor_1985_jan1, anchor_2024_apr1, % 14.38/2.67 anchor_2024_feb1, anchor_2024_jan1, anchor_2024_mar1, anchor_2024_may1, % 14.38/2.67 anchor_2025_feb1, anchor_2025_jan1, anchor_2025_mar1, anchor_2025_nov1, % 14.38/2.67 back_decade_peel, back_year_peel_leap, back_year_peel_nonleap, % 14.38/2.67 cache_4yr_2025_to_2028, calc_nth_offset_def_mod7, calc_weekday_zeller, d_24, % 14.38/2.67 d_25, d_26, d_27, d_28, dt_logic, hint_century_back_bridge, % 14.38/2.67 hint_century_multi_bridge, hint_century_threshold_100k, % 14.38/2.67 hint_century_to_decade_bridge, hint_leap_1776_feb, hint_leap_2024_feb, % 14.38/2.67 last_weekday_shortcut, lemma_boundary_dec32, lemma_boundary_jan0_2024, % 14.38/2.67 lemma_boundary_jan0_2025, lemma_boundary_leap_mar0, lemma_boundary_norm_mar0, % 14.38/2.67 m1, m10, m11, m12, m2, m3, m4, m5, m6, m7, m8, m9, map_0, map_1, map_2, map_3, % 14.38/2.67 map_4, map_5, map_6, map_n_0, map_n_1, map_n_2, map_n_3, map_n_4, map_n_5, % 14.38/2.67 map_n_6, map_name_to_int_functional, nth_weekday_logic, rule_back_10year_long, % 14.38/2.67 rule_back_10year_short, rule_back_400yr_cycle, rule_back_century, rule_back_jan, % 14.38/2.67 rule_back_std, rule_base, rule_fwd_10year_long, rule_fwd_400yr_cycle, % 14.38/2.67 rule_fwd_4year, rule_fwd_century, rule_fwd_dec, rule_fwd_safe_4yr_gen, % 14.38/2.67 rule_fwd_std, rule_fwd_year, rule_weekday_month_jump, time_logic, trap_ax, % 14.38/2.67 weekday_400yr_period, weekday_functional, zeller_adj_janfeb, zeller_adj_norm % 14.38/2.67 % 14.38/2.67 Those formulas are unsatisfiable: % 14.38/2.67 --------------------------------- % 14.38/2.67 % 14.38/2.67 Begin of proof % 14.38/2.67 | % 14.38/2.67 | ALPHA: (anchor_1600_jan1) implies: % 14.38/2.67 | (1) ? [v0: date] : (ymd(1600, 1, 1) = v0 & weekday(v0, saturday) = 0 & % 14.38/2.67 | date(v0)) % 14.38/2.67 | % 14.38/2.67 | ALPHA: (test_1600) implies: % 14.38/2.67 | (2) ? [v0: date] : (ymd(1600, 1, 1) = v0 & date(v0) & ~ (weekday(v0, % 14.38/2.67 | saturday) = 0)) % 14.38/2.68 | % 14.38/2.68 | ALPHA: (function-axioms) implies: % 14.38/2.68 | (3) ! [v0: date] : ! [v1: date] : ! [v2: int] : ! [v3: int] : ! [v4: % 14.38/2.68 | int] : (v1 = v0 | ~ (ymd(v4, v3, v2) = v1) | ~ (ymd(v4, v3, v2) = % 14.38/2.68 | v0)) % 14.38/2.68 | % 14.38/2.68 | DELTA: instantiating (1) with fresh symbol all_49_0 gives: % 14.38/2.68 | (4) ymd(1600, 1, 1) = all_49_0 & weekday(all_49_0, saturday) = 0 & % 14.38/2.68 | date(all_49_0) % 14.38/2.68 | % 14.38/2.68 | ALPHA: (4) implies: % 14.38/2.68 | (5) weekday(all_49_0, saturday) = 0 % 14.38/2.68 | (6) ymd(1600, 1, 1) = all_49_0 % 14.38/2.68 | % 14.38/2.68 | DELTA: instantiating (2) with fresh symbol all_75_0 gives: % 14.38/2.68 | (7) ymd(1600, 1, 1) = all_75_0 & date(all_75_0) & ~ (weekday(all_75_0, % 14.38/2.68 | saturday) = 0) % 14.38/2.68 | % 14.38/2.68 | ALPHA: (7) implies: % 14.38/2.68 | (8) ~ (weekday(all_75_0, saturday) = 0) % 14.38/2.68 | (9) ymd(1600, 1, 1) = all_75_0 % 14.38/2.68 | % 14.38/2.68 | GROUND_INST: instantiating (3) with all_49_0, all_75_0, 1, 1, 1600, % 14.38/2.68 | simplifying with (6), (9) gives: % 14.38/2.68 | (10) all_75_0 = all_49_0 % 14.38/2.68 | % 14.38/2.68 | REDUCE: (8), (10) imply: % 14.38/2.68 | (11) ~ (weekday(all_49_0, saturday) = 0) % 14.38/2.68 | % 14.38/2.68 | PRED_UNIFY: (5), (11) imply: % 14.38/2.68 | (12) $false % 14.38/2.68 | % 14.38/2.68 | CLOSE: (12) is inconsistent. % 14.38/2.68 | % 14.38/2.68 End of proof % 14.38/2.68 % SZS output end Proof for theBenchmark % 14.38/2.68 % 14.38/2.68 2084ms %------------------------------------------------------------------------------