%------------------------------------------------------------------------------ % 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 : n007.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 10:08:53 AM UTC 2025 % Result : Theorem 7.49s 1.74s % Output : Proof 9.09s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SWX000_1 : TPTP v9.1.0. Released v9.1.0. % 0.07/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.33 % Computer : n007.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 300 % 0.12/0.33 % DateTime : Sun Apr 6 03:12:22 EDT 2025 % 0.12/0.34 % CPUTime : % 0.66/0.65 ________ _____ % 0.66/0.65 ___ __ \_________(_)________________________________ % 0.66/0.65 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.66/0.65 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.66/0.65 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.66/0.65 % 0.66/0.65 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.66/0.65 (2023-06-19) % 0.66/0.65 % 0.66/0.65 (c) Philipp Rümmer, 2009-2023 % 0.66/0.65 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.66/0.65 Amanda Stjerna. % 0.66/0.65 Free software under BSD-3-Clause. % 0.66/0.65 % 0.66/0.65 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.66/0.66 % 0.66/0.66 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.66/0.67 Running up to 7 provers in parallel. % 0.80/0.68 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.80/0.68 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.80/0.68 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.80/0.68 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.80/0.68 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.80/0.68 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.80/0.68 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.61/1.26 Prover 4: Preprocessing ... % 3.61/1.26 Prover 1: Preprocessing ... % 3.95/1.29 Prover 2: Preprocessing ... % 3.95/1.29 Prover 3: Preprocessing ... % 3.95/1.29 Prover 5: Preprocessing ... % 3.95/1.29 Prover 6: Preprocessing ... % 3.95/1.29 Prover 0: Preprocessing ... % 6.24/1.63 Prover 5: Proving ... % 6.24/1.63 Prover 2: Proving ... % 6.88/1.65 Prover 6: Proving ... % 6.88/1.67 Prover 3: Constructing countermodel ... % 6.88/1.67 Prover 1: Constructing countermodel ... % 7.09/1.69 Prover 0: Proving ... % 7.09/1.69 Prover 4: Constructing countermodel ... % 7.49/1.74 Prover 5: proved (1054ms) % 7.49/1.74 % 7.49/1.74 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 7.49/1.74 % 7.49/1.74 Prover 2: proved (1059ms) % 7.49/1.74 % 7.49/1.74 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 7.49/1.74 % 7.49/1.74 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 7.49/1.74 Prover 3: proved (1061ms) % 7.49/1.74 % 7.49/1.74 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 7.49/1.74 % 7.49/1.74 Prover 0: stopped % 7.49/1.74 Prover 6: stopped % 7.49/1.74 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 7.49/1.75 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 7.49/1.75 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 7.49/1.75 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 8.07/1.82 Prover 1: Found proof (size 12) % 8.07/1.82 Prover 1: proved (1140ms) % 8.07/1.83 Prover 4: Found proof (size 9) % 8.07/1.83 Prover 4: proved (1150ms) % 8.07/1.84 Prover 8: Preprocessing ... % 8.07/1.84 Prover 7: Preprocessing ... % 8.07/1.85 Prover 13: Preprocessing ... % 8.07/1.86 Prover 10: Preprocessing ... % 8.07/1.86 Prover 11: Preprocessing ... % 8.44/1.87 Prover 7: stopped % 8.44/1.87 Prover 10: stopped % 8.44/1.88 Prover 13: stopped % 8.44/1.89 Prover 11: stopped % 8.92/1.94 Prover 8: Warning: ignoring some quantifiers % 8.92/1.96 Prover 8: Constructing countermodel ... % 8.92/1.96 Prover 8: stopped % 8.92/1.96 % 8.92/1.96 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 8.92/1.96 % 8.92/1.96 % SZS output start Proof for theBenchmark % 8.92/1.97 Assumptions after simplification: % 8.92/1.97 --------------------------------- % 8.92/1.97 % 8.92/1.97 (formula_2_right_0) % 9.09/1.99 ! [v0: general] : ! [v1: general] : ! [v2: int] : (v2 = 0 | ~ (hp(v1) = 0) % 9.09/1.99 | ~ (hp(v0) = 0) | ~ (hq(v0, v1) = v2) | ~ general(v1) | ~ general(v0) | % 9.09/1.99 ? [v3: int] : ( ~ (v3 = 0) & tq(v0, v1) = v3)) % 9.09/1.99 % 9.09/1.99 (formula_4_left_0) % 9.09/1.99 ? [v0: general] : ? [v1: general] : ? [v2: int] : ( ~ (v2 = 0) & hp(v1) = 0 % 9.09/1.99 & hp(v0) = 0 & hq(v0, v1) = v2 & tq(v0, v1) = 0 & general(v1) & general(v0)) % 9.09/1.99 % 9.09/1.99 (function-axioms) % 9.09/2.00 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: general] : % 9.09/2.00 ! [v3: general] : (v1 = v0 | ~ (hq(v3, v2) = v1) | ~ (hq(v3, v2) = v0)) & ! % 9.09/2.00 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: general] : ! % 9.09/2.00 [v3: general] : (v1 = v0 | ~ (tq(v3, v2) = v1) | ~ (tq(v3, v2) = v0)) & ! % 9.09/2.00 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: general] : ! % 9.09/2.00 [v3: general] : (v1 = v0 | ~ (p__greater__(v3, v2) = v1) | ~ % 9.09/2.00 (p__greater__(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 9.09/2.00 MultipleValueBool] : ! [v2: general] : ! [v3: general] : (v1 = v0 | ~ % 9.09/2.00 (p__greater_equal__(v3, v2) = v1) | ~ (p__greater_equal__(v3, v2) = v0)) & % 9.09/2.00 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: general] : ! % 9.09/2.00 [v3: general] : (v1 = v0 | ~ (p__less__(v3, v2) = v1) | ~ (p__less__(v3, v2) % 9.09/2.00 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 9.09/2.00 general] : ! [v3: general] : (v1 = v0 | ~ (p__less_equal__(v3, v2) = v1) | % 9.09/2.00 ~ (p__less_equal__(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 9.09/2.00 MultipleValueBool] : ! [v2: general] : (v1 = v0 | ~ (tp(v2) = v1) | ~ % 9.09/2.00 (tp(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 9.09/2.00 ! [v2: general] : (v1 = v0 | ~ (hp(v2) = v1) | ~ (hp(v2) = v0)) & ! [v0: % 9.09/2.00 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: general] : (v1 = % 9.09/2.00 v0 | ~ (p__is_symbolic__(v2) = v1) | ~ (p__is_symbolic__(v2) = v0)) & ! % 9.09/2.00 [v0: general] : ! [v1: general] : ! [v2: symbol] : (v1 = v0 | ~ % 9.09/2.00 (f__symbolic__(v2) = v1) | ~ (f__symbolic__(v2) = v0)) & ! [v0: % 9.09/2.00 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: general] : (v1 = % 9.09/2.00 v0 | ~ (p__is_integer__(v2) = v1) | ~ (p__is_integer__(v2) = v0)) & ! % 9.09/2.00 [v0: general] : ! [v1: general] : ! [v2: int] : (v1 = v0 | ~ % 9.09/2.00 (f__integer__(v2) = v1) | ~ (f__integer__(v2) = v0)) % 9.09/2.00 % 9.09/2.00 Further assumptions not needed in the proof: % 9.09/2.00 -------------------------------------------- % 9.09/2.00 antisymmetric_ordering_ax, f__integer__def_ax, f__symbolic__def_ax, % 9.09/2.00 formula_0_transition_axiom_0, formula_1_transition_axiom_1, formula_3_right_1, % 9.09/2.00 general_universe_ax, maximal_element_ax, minimal_element_ax, % 9.09/2.00 numeral_ordering_ax, numerals_less_than_symbols_ax, p__greater__def_ax, % 9.09/2.00 p__greater_equal__def_ax, p__is_integer__def_ax, p__is_symbolic__def_ax, % 9.09/2.00 p__less__def_ax, strongly_connected_ordering_ax, transitive_ordering_ax % 9.09/2.00 % 9.09/2.00 Those formulas are unsatisfiable: % 9.09/2.00 --------------------------------- % 9.09/2.00 % 9.09/2.00 Begin of proof % 9.09/2.00 | % 9.09/2.00 | ALPHA: (function-axioms) implies: % 9.09/2.00 | (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 9.09/2.00 | general] : ! [v3: general] : (v1 = v0 | ~ (tq(v3, v2) = v1) | ~ % 9.09/2.00 | (tq(v3, v2) = v0)) % 9.09/2.00 | % 9.09/2.00 | DELTA: instantiating (formula_4_left_0) with fresh symbols all_27_0, all_27_1, % 9.09/2.00 | all_27_2 gives: % 9.09/2.01 | (2) ~ (all_27_0 = 0) & hp(all_27_1) = 0 & hp(all_27_2) = 0 & hq(all_27_2, % 9.09/2.01 | all_27_1) = all_27_0 & tq(all_27_2, all_27_1) = 0 & general(all_27_1) % 9.09/2.01 | & general(all_27_2) % 9.09/2.01 | % 9.09/2.01 | ALPHA: (2) implies: % 9.09/2.01 | (3) ~ (all_27_0 = 0) % 9.09/2.01 | (4) general(all_27_2) % 9.09/2.01 | (5) general(all_27_1) % 9.09/2.01 | (6) tq(all_27_2, all_27_1) = 0 % 9.09/2.01 | (7) hq(all_27_2, all_27_1) = all_27_0 % 9.09/2.01 | (8) hp(all_27_2) = 0 % 9.09/2.01 | (9) hp(all_27_1) = 0 % 9.09/2.01 | % 9.09/2.01 | GROUND_INST: instantiating (formula_2_right_0) with all_27_2, all_27_1, % 9.09/2.01 | all_27_0, simplifying with (4), (5), (7), (8), (9) gives: % 9.09/2.01 | (10) all_27_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & tq(all_27_2, all_27_1) = % 9.09/2.01 | v0) % 9.09/2.01 | % 9.09/2.01 | BETA: splitting (10) gives: % 9.09/2.01 | % 9.09/2.01 | Case 1: % 9.09/2.01 | | % 9.09/2.01 | | (11) all_27_0 = 0 % 9.09/2.01 | | % 9.09/2.01 | | REDUCE: (3), (11) imply: % 9.09/2.01 | | (12) $false % 9.09/2.01 | | % 9.09/2.01 | | CLOSE: (12) is inconsistent. % 9.09/2.01 | | % 9.09/2.01 | Case 2: % 9.09/2.01 | | % 9.09/2.01 | | (13) ? [v0: int] : ( ~ (v0 = 0) & tq(all_27_2, all_27_1) = v0) % 9.09/2.01 | | % 9.09/2.01 | | DELTA: instantiating (13) with fresh symbol all_36_0 gives: % 9.09/2.01 | | (14) ~ (all_36_0 = 0) & tq(all_27_2, all_27_1) = all_36_0 % 9.09/2.01 | | % 9.09/2.01 | | ALPHA: (14) implies: % 9.09/2.01 | | (15) ~ (all_36_0 = 0) % 9.09/2.01 | | (16) tq(all_27_2, all_27_1) = all_36_0 % 9.09/2.01 | | % 9.09/2.01 | | GROUND_INST: instantiating (1) with 0, all_36_0, all_27_1, all_27_2, % 9.09/2.01 | | simplifying with (6), (16) gives: % 9.09/2.01 | | (17) all_36_0 = 0 % 9.09/2.01 | | % 9.09/2.01 | | REDUCE: (15), (17) imply: % 9.09/2.01 | | (18) $false % 9.09/2.01 | | % 9.09/2.01 | | CLOSE: (18) is inconsistent. % 9.09/2.01 | | % 9.09/2.01 | End of split % 9.09/2.01 | % 9.09/2.01 End of proof % 9.09/2.01 % SZS output end Proof for theBenchmark % 9.09/2.01 % 9.09/2.01 1357ms %------------------------------------------------------------------------------