%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : TIM028_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 : n028.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 17.21s 3.04s % Output : Proof 22.07s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : TIM028_1 : TPTP v9.3.0. Released v9.3.0. % 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.33 % Computer : n028.cluster.edu % 0.14/0.33 % Model : x86_64 x86_64 % 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.33 % Memory : 8042.1875MB % 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.33 % CPULimit : 300 % 0.14/0.33 % WCLimit : 300 % 0.14/0.33 % DateTime : Mon May 4 18:26:45 EDT 2026 % 0.14/0.34 % CPUTime : % 0.50/0.60 ________ _____ % 0.50/0.60 ___ __ \_________(_)________________________________ % 0.50/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.50/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.50/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.50/0.60 % 0.50/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.50/0.60 (2023-06-19) % 0.50/0.60 % 0.50/0.60 (c) Philipp Rümmer, 2009-2023 % 0.50/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.50/0.60 Amanda Stjerna. % 0.50/0.60 Free software under BSD-3-Clause. % 0.50/0.60 % 0.50/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.50/0.60 % 0.50/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.50/0.61 Running up to 7 provers in parallel. % 0.72/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.72/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.72/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.72/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.72/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.72/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.72/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 5.75/1.50 Prover 6: Preprocessing ... % 5.75/1.52 Prover 3: Preprocessing ... % 5.75/1.54 Prover 2: Preprocessing ... % 5.75/1.55 Prover 0: Preprocessing ... % 5.75/1.56 Prover 5: Preprocessing ... % 5.75/1.56 Prover 1: Preprocessing ... % 5.75/1.57 Prover 4: Preprocessing ... % 10.90/2.26 Prover 5: Proving ... % 10.90/2.27 Prover 2: Proving ... % 10.90/2.27 Prover 1: Warning: ignoring some quantifiers % 10.90/2.28 Prover 4: Warning: ignoring some quantifiers % 10.90/2.28 Prover 3: Warning: ignoring some quantifiers % 11.65/2.30 Prover 6: Proving ... % 11.65/2.30 Prover 3: Constructing countermodel ... % 11.65/2.33 Prover 1: Constructing countermodel ... % 11.65/2.38 Prover 4: Constructing countermodel ... % 11.65/2.39 Prover 0: Proving ... % 17.21/3.04 Prover 3: proved (2414ms) % 17.21/3.04 % 17.21/3.04 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 17.21/3.04 % 17.21/3.05 Prover 2: stopped % 17.21/3.05 Prover 5: stopped % 17.21/3.06 Prover 0: stopped % 17.21/3.06 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 17.21/3.06 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 17.21/3.06 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 17.21/3.07 Prover 6: stopped % 17.21/3.07 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 17.21/3.07 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 18.50/3.22 Prover 7: Preprocessing ... % 18.50/3.23 Prover 8: Preprocessing ... % 18.50/3.24 Prover 10: Preprocessing ... % 18.50/3.26 Prover 13: Preprocessing ... % 18.50/3.26 Prover 11: Preprocessing ... % 20.08/3.42 Prover 7: Warning: ignoring some quantifiers % 20.08/3.44 Prover 7: Constructing countermodel ... % 20.81/3.52 Prover 10: Warning: ignoring some quantifiers % 20.81/3.54 Prover 10: Constructing countermodel ... % 20.81/3.56 Prover 8: Warning: ignoring some quantifiers % 20.81/3.57 Prover 8: Constructing countermodel ... % 20.81/3.57 Prover 13: Warning: ignoring some quantifiers % 20.81/3.59 Prover 13: Constructing countermodel ... % 21.57/3.61 Prover 1: Found proof (size 14) % 21.57/3.61 Prover 1: proved (2989ms) % 21.57/3.61 Prover 13: stopped % 21.57/3.61 Prover 7: stopped % 21.57/3.61 Prover 8: stopped % 21.57/3.61 Prover 4: stopped % 21.57/3.61 Prover 10: stopped % 21.57/3.63 Prover 11: Warning: ignoring some quantifiers % 21.57/3.64 Prover 11: Constructing countermodel ... % 21.57/3.65 Prover 11: stopped % 21.57/3.65 % 21.57/3.65 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 21.57/3.65 % 21.57/3.66 % SZS output start Proof for theBenchmark % 21.57/3.66 Assumptions after simplification: % 21.57/3.66 --------------------------------- % 21.57/3.66 % 21.57/3.66 (lemma_boundary_leap_mar0) % 21.57/3.67 ? [v0: date] : (calc_date(0, 3, 2024, v0) = 0 & ymd(2024, 2, 29) = v0 & % 21.57/3.67 date(v0)) % 21.57/3.67 % 21.57/3.67 (test_zero) % 21.57/3.67 ! [v0: int] : ! [v1: date] : ( ~ (ymd(v0, 2, 29) = v1) | ? [v2: any] : ? % 21.57/3.67 [v3: any] : (calc_date(0, 3, 2024, v1) = v2 & valid_day(29) = v3 & ( ~ (v3 = % 21.57/3.67 0) | ~ (v2 = 0)))) % 21.57/3.67 % 21.57/3.67 (trap_ax) % 21.57/3.68 ! [v0: int] : ! [v1: int] : (v1 = 0 | ~ ($lesseq(v0, 31)) | ~ ($lesseq(1, % 21.57/3.68 v0)) | ~ (valid_day(v0) = v1)) & ! [v0: int] : ( ~ (valid_day(v0) = 0) % 21.57/3.68 | ($lesseq(v0, 31) & $lesseq(1, v0))) % 21.57/3.68 % 21.57/3.68 (function-axioms) % 21.57/3.68 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: time] : ! % 21.57/3.68 [v3: int] : ! [v4: int] : ! [v5: int] : ! [v6: int] : ! [v7: int] : ! % 21.57/3.68 [v8: int] : ! [v9: int] : ! [v10: int] : (v1 = v0 | ~ (calc_datetime(v10, % 21.57/3.68 v9, v8, v7, v6, v5, v4, v3, v2) = v1) | ~ (calc_datetime(v10, v9, v8, % 21.57/3.68 v7, v6, v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 21.57/3.68 MultipleValueBool] : ! [v2: int] : ! [v3: int] : ! [v4: int] : ! [v5: % 21.57/3.68 int] : ! [v6: int] : ! [v7: int] : ! [v8: int] : (v1 = v0 | ~ % 21.57/3.68 (normalize_time(v8, v7, v6, v5, v4, v3, v2) = v1) | ~ (normalize_time(v8, % 21.57/3.68 v7, v6, v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 21.57/3.68 MultipleValueBool] : ! [v2: int] : ! [v3: int] : ! [v4: int] : ! [v5: % 21.57/3.68 int] : ! [v6: int] : ! [v7: int] : (v1 = v0 | ~ (zeller_prep(v7, v6, v5, % 21.57/3.68 v4, v3, v2) = v1) | ~ (zeller_prep(v7, v6, v5, v4, v3, v2) = v0)) & ! % 21.57/3.68 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: date] : ! [v3: % 21.57/3.68 int] : ! [v4: int] : ! [v5: day_name] : ! [v6: int] : (v1 = v0 | ~ % 21.57/3.69 (nth_weekday_date(v6, v5, v4, v3, v2) = v1) | ~ (nth_weekday_date(v6, v5, % 21.57/3.69 v4, v3, v2) = v0)) & ! [v0: time] : ! [v1: time] : ! [v2: int] : ! % 21.57/3.69 [v3: int] : ! [v4: int] : ! [v5: int] : ! [v6: int] : (v1 = v0 | ~ (dt(v6, % 21.57/3.69 v5, v4, v3, v2) = v1) | ~ (dt(v6, v5, v4, v3, v2) = v0)) & ! [v0: % 21.57/3.69 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: date] : ! [v3: % 21.57/3.69 int] : ! [v4: int] : ! [v5: int] : (v1 = v0 | ~ (calc_date(v5, v4, v3, % 21.57/3.69 v2) = v1) | ~ (calc_date(v5, v4, v3, v2) = v0)) & ! [v0: % 21.57/3.69 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: int] : ! [v3: % 21.57/3.69 int] : ! [v4: int] : (v1 = v0 | ~ (calc_nth_offset(v4, v3, v2) = v1) | ~ % 21.57/3.69 (calc_nth_offset(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 21.57/3.69 MultipleValueBool] : ! [v2: int] : ! [v3: int] : ! [v4: int] : (v1 = v0 | % 21.57/3.69 ~ (is_days_in_month(v4, v3, v2) = v1) | ~ (is_days_in_month(v4, v3, v2) = % 21.57/3.69 v0)) & ! [v0: date] : ! [v1: date] : ! [v2: int] : ! [v3: int] : ! % 21.57/3.69 [v4: int] : (v1 = v0 | ~ (ymd(v4, v3, v2) = v1) | ~ (ymd(v4, v3, v2) = v0)) % 21.57/3.69 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: int] : ! % 21.57/3.69 [v3: int] : (v1 = v0 | ~ (is_days_in_year(v3, v2) = v1) | ~ % 21.57/3.69 (is_days_in_year(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 21.57/3.69 MultipleValueBool] : ! [v2: int] : ! [v3: day_name] : (v1 = v0 | ~ % 21.57/3.69 (map_name_to_int(v3, v2) = v1) | ~ (map_name_to_int(v3, v2) = v0)) & ! % 21.57/3.69 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: day_name] : ! % 21.57/3.69 [v3: int] : (v1 = v0 | ~ (map_iso(v3, v2) = v1) | ~ (map_iso(v3, v2) = v0)) % 21.57/3.69 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: day_name] % 21.57/3.69 : ! [v3: date] : (v1 = v0 | ~ (weekday(v3, v2) = v1) | ~ (weekday(v3, v2) = % 21.57/3.69 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 21.57/3.69 int] : (v1 = v0 | ~ (is_leap_year(v2) = v1) | ~ (is_leap_year(v2) = v0)) & % 21.57/3.69 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: int] : (v1 = % 21.57/3.69 v0 | ~ (valid_day(v2) = v1) | ~ (valid_day(v2) = v0)) % 21.57/3.69 % 21.57/3.69 Further assumptions not needed in the proof: % 21.57/3.69 -------------------------------------------- % 21.57/3.69 anchor_1600_jan1, anchor_1776_jan1, anchor_1969_jan1, anchor_1985_jan1, % 21.57/3.69 anchor_2024_apr1, anchor_2024_feb1, anchor_2024_jan1, anchor_2024_mar1, % 21.57/3.69 anchor_2024_may1, anchor_2025_feb1, anchor_2025_jan1, anchor_2025_mar1, % 21.57/3.69 anchor_2025_nov1, back_decade_peel, back_year_peel_leap, back_year_peel_nonleap, % 21.57/3.69 cache_4yr_2025_to_2028, calc_nth_offset_def_mod7, calc_weekday_zeller, d_24, % 21.57/3.69 d_25, d_26, d_27, d_28, dt_logic, hint_century_back_bridge, % 21.57/3.69 hint_century_multi_bridge, hint_century_threshold_100k, % 21.57/3.69 hint_century_to_decade_bridge, hint_leap_1776_feb, hint_leap_2024_feb, % 21.57/3.69 last_weekday_shortcut, lemma_boundary_dec32, lemma_boundary_jan0_2024, % 21.57/3.69 lemma_boundary_jan0_2025, lemma_boundary_norm_mar0, m1, m10, m11, m12, m2, m3, % 21.57/3.69 m4, m5, m6, m7, m8, m9, map_0, map_1, map_2, map_3, map_4, map_5, map_6, % 21.57/3.69 map_n_0, map_n_1, map_n_2, map_n_3, map_n_4, map_n_5, map_n_6, % 21.57/3.69 map_name_to_int_functional, nth_weekday_logic, rule_back_10year_long, % 21.57/3.69 rule_back_10year_short, rule_back_400yr_cycle, rule_back_century, rule_back_jan, % 21.57/3.69 rule_back_std, rule_base, rule_fwd_10year_long, rule_fwd_400yr_cycle, % 21.57/3.69 rule_fwd_4year, rule_fwd_century, rule_fwd_dec, rule_fwd_safe_4yr_gen, % 21.57/3.69 rule_fwd_std, rule_fwd_year, rule_weekday_month_jump, time_logic, % 21.57/3.69 weekday_400yr_period, weekday_functional, zeller_adj_janfeb, zeller_adj_norm % 21.57/3.69 % 21.57/3.69 Those formulas are unsatisfiable: % 21.57/3.69 --------------------------------- % 21.57/3.69 % 21.57/3.69 Begin of proof % 21.57/3.69 | % 21.57/3.69 | ALPHA: (trap_ax) implies: % 21.57/3.69 | (1) ! [v0: int] : ! [v1: int] : (v1 = 0 | ~ ($lesseq(v0, 31)) | ~ % 21.57/3.69 | ($lesseq(1, v0)) | ~ (valid_day(v0) = v1)) % 21.57/3.69 | % 21.57/3.69 | ALPHA: (function-axioms) implies: % 21.57/3.69 | (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: date] % 21.57/3.69 | : ! [v3: int] : ! [v4: int] : ! [v5: int] : (v1 = v0 | ~ % 21.57/3.69 | (calc_date(v5, v4, v3, v2) = v1) | ~ (calc_date(v5, v4, v3, v2) = % 21.57/3.69 | v0)) % 21.57/3.69 | % 21.57/3.69 | DELTA: instantiating (lemma_boundary_leap_mar0) with fresh symbol all_68_0 % 21.57/3.69 | gives: % 21.57/3.69 | (3) calc_date(0, 3, 2024, all_68_0) = 0 & ymd(2024, 2, 29) = all_68_0 & % 21.57/3.69 | date(all_68_0) % 21.57/3.69 | % 21.57/3.69 | ALPHA: (3) implies: % 21.57/3.69 | (4) ymd(2024, 2, 29) = all_68_0 % 21.57/3.69 | (5) calc_date(0, 3, 2024, all_68_0) = 0 % 21.57/3.69 | % 21.57/3.69 | GROUND_INST: instantiating (test_zero) with 2024, all_68_0, simplifying with % 21.57/3.69 | (4) gives: % 21.57/3.69 | (6) ? [v0: any] : ? [v1: any] : (calc_date(0, 3, 2024, all_68_0) = v0 & % 21.57/3.69 | valid_day(29) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 21.57/3.69 | % 21.57/3.69 | DELTA: instantiating (6) with fresh symbols all_198_0, all_198_1 gives: % 21.57/3.69 | (7) calc_date(0, 3, 2024, all_68_0) = all_198_1 & valid_day(29) = all_198_0 % 21.57/3.69 | & ( ~ (all_198_0 = 0) | ~ (all_198_1 = 0)) % 21.57/3.70 | % 21.57/3.70 | ALPHA: (7) implies: % 21.57/3.70 | (8) valid_day(29) = all_198_0 % 21.57/3.70 | (9) calc_date(0, 3, 2024, all_68_0) = all_198_1 % 21.57/3.70 | (10) ~ (all_198_0 = 0) | ~ (all_198_1 = 0) % 21.57/3.70 | % 21.57/3.70 | GROUND_INST: instantiating (1) with 29, all_198_0, simplifying with (8) gives: % 21.57/3.70 | (11) all_198_0 = 0 % 21.57/3.70 | % 21.57/3.70 | GROUND_INST: instantiating (2) with 0, all_198_1, all_68_0, 2024, 3, 0, % 21.57/3.70 | simplifying with (5), (9) gives: % 21.57/3.70 | (12) all_198_1 = 0 % 21.57/3.70 | % 22.07/3.70 | BETA: splitting (10) gives: % 22.07/3.70 | % 22.07/3.70 | Case 1: % 22.07/3.70 | | % 22.07/3.70 | | (13) ~ (all_198_0 = 0) % 22.07/3.70 | | % 22.07/3.70 | | REDUCE: (11), (13) imply: % 22.07/3.70 | | (14) $false % 22.07/3.70 | | % 22.07/3.70 | | CLOSE: (14) is inconsistent. % 22.07/3.70 | | % 22.07/3.70 | Case 2: % 22.07/3.70 | | % 22.07/3.70 | | (15) ~ (all_198_1 = 0) % 22.07/3.70 | | % 22.07/3.70 | | REDUCE: (12), (15) imply: % 22.07/3.70 | | (16) $false % 22.07/3.70 | | % 22.07/3.70 | | CLOSE: (16) is inconsistent. % 22.07/3.70 | | % 22.07/3.70 | End of split % 22.07/3.70 | % 22.07/3.70 End of proof % 22.07/3.70 % SZS output end Proof for theBenchmark % 22.07/3.70 % 22.07/3.70 3097ms %------------------------------------------------------------------------------