%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWC448_1 : TPTP v8.3.0. Released v8.3.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n010.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 14 09:00:30 EDT 2024 % Result : Theorem 5.60s 1.53s % Output : Proof 5.60s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : SWC448_1 : TPTP v8.3.0. Released v8.3.0. % 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n010.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 : Mon May 13 14:45:23 EDT 2024 % 0.13/0.34 % CPUTime : % 0.58/0.62 ________ _____ % 0.58/0.62 ___ __ \_________(_)________________________________ % 0.58/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.58/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.58/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.58/0.62 % 0.58/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.58/0.62 (2023-06-19) % 0.58/0.62 % 0.58/0.62 (c) Philipp Rümmer, 2009-2023 % 0.58/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.58/0.62 Amanda Stjerna. % 0.58/0.62 Free software under BSD-3-Clause. % 0.58/0.62 % 0.58/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.58/0.62 % 0.58/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.66/0.63 Running up to 7 provers in parallel. % 0.68/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.68/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.68/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.68/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.68/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.68/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.68/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.40/1.09 Prover 6: Preprocessing ... % 2.40/1.09 Prover 1: Preprocessing ... % 2.40/1.09 Prover 0: Preprocessing ... % 2.40/1.10 Prover 2: Preprocessing ... % 2.40/1.10 Prover 3: Preprocessing ... % 2.40/1.10 Prover 5: Preprocessing ... % 2.40/1.10 Prover 4: Preprocessing ... % 3.45/1.26 Prover 6: Constructing countermodel ... % 3.45/1.27 Prover 4: Constructing countermodel ... % 3.45/1.27 Prover 3: Constructing countermodel ... % 3.45/1.27 Prover 1: Constructing countermodel ... % 3.45/1.27 Prover 0: Proving ... % 3.45/1.30 Prover 2: Proving ... % 3.45/1.30 Prover 5: Proving ... % 4.61/1.40 Prover 1: gave up % 4.61/1.41 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 4.61/1.43 Prover 6: gave up % 4.61/1.43 Prover 7: Preprocessing ... % 4.61/1.43 Prover 3: gave up % 5.16/1.47 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 5.16/1.47 Prover 8: Preprocessing ... % 5.16/1.47 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 5.16/1.47 Prover 7: Constructing countermodel ... % 5.20/1.48 Prover 9: Preprocessing ... % 5.43/1.51 Prover 4: Found proof (size 34) % 5.43/1.51 Prover 4: proved (874ms) % 5.43/1.52 Prover 7: stopped % 5.43/1.52 Prover 0: stopped % 5.43/1.52 Prover 2: stopped % 5.43/1.52 Prover 5: stopped % 5.43/1.52 Prover 9: Constructing countermodel ... % 5.43/1.52 Prover 8: Warning: ignoring some quantifiers % 5.43/1.53 Prover 9: stopped % 5.60/1.53 Prover 8: Constructing countermodel ... % 5.60/1.53 Prover 8: stopped % 5.60/1.53 % 5.60/1.53 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 5.60/1.53 % 5.60/1.54 % SZS output start Proof for theBenchmark % 5.60/1.54 Assumptions after simplification: % 5.60/1.54 --------------------------------- % 5.60/1.54 % 5.60/1.54 (conjecture_1) % 5.60/1.57 ? [v0: int] : ? [v1: int] : ? [v2: int] : ( ~ (v2 = v1) & $lesseq(0, v0) & % 5.60/1.57 fast(v0) = v2 & small(v0) = v1) % 5.60/1.57 % 5.60/1.57 (formula_1) % 5.60/1.57 ! [v0: int] : ! [v1: int] : ($difference(v1, $product(10, v0)) = 8 | ~ % 5.60/1.57 (f0(v0) = v1)) % 5.60/1.57 % 5.60/1.57 (formula_2) % 5.60/1.57 g0 = 2 % 5.60/1.57 % 5.60/1.57 (formula_3) % 5.60/1.57 ! [v0: int] : ! [v1: int] : (v1 = v0 | ~ (h0(v0) = v1)) % 5.60/1.57 % 5.60/1.57 (formula_4) % 5.60/1.57 ! [v0: int] : ! [v1: int] : ! [v2: int] : (v2 = v1 | ~ ($lesseq(v0, 0) | % 5.60/1.57 ~ (u0(v0, v1) = v2)) & ! [v0: int] : ! [v1: int] : ! [v2: int] : ( ~ % 5.60/1.57 ($lesseq(1, v0)) | ~ (u0($sum(v0, -1), v1) = v2) | ? [v3: int] : (u0(v0, % 5.60/1.57 v1) = v3 & f0(v2) = v3)) & ! [v0: int] : ! [v1: int] : ! [v2: int] % 5.60/1.57 : ( ~ ($lesseq(1, v0)) | ~ (u0(v0, v1) = v2) | ? [v3: int] : (u0($sum(v0, % 5.60/1.57 -1), v1) = v3 & f0(v3) = v2)) % 5.60/1.57 % 5.60/1.57 (formula_5) % 5.60/1.57 ! [v0: int] : ! [v1: int] : ( ~ (v0(v0) = v1) | ? [v2: int] : (u0(g0, v2) = % 5.60/1.57 v1 & h0(v0) = v2)) & ! [v0: int] : ! [v1: int] : ( ~ (h0(v0) = v1) | ? % 5.60/1.57 [v2: int] : (v0(v0) = v2 & u0(g0, v1) = v2)) % 5.60/1.57 % 5.60/1.57 (formula_6) % 5.60/1.58 ! [v0: int] : ! [v1: int] : ( ~ (small(v0) = v1) | v0(v0) = $sum(v1, 1)) & % 5.60/1.58 ! [v0: int] : ! [v1: int] : ( ~ (v0(v0) = v1) | small(v0) = $sum(v1, -1)) % 5.60/1.58 % 5.60/1.58 (formula_7) % 5.60/1.58 ! [v0: int] : ! [v1: int] : ($difference(v1, $product(100, v0)) = 87 | ~ % 5.60/1.58 (fast(v0) = v1)) % 5.60/1.58 % 5.60/1.58 Those formulas are unsatisfiable: % 5.60/1.58 --------------------------------- % 5.60/1.58 % 5.60/1.58 Begin of proof % 5.60/1.58 | % 5.60/1.58 | ALPHA: (formula_4) implies: % 5.60/1.58 | (1) ! [v0: int] : ! [v1: int] : ! [v2: int] : ( ~ ($lesseq(1, v0)) | ~ % 5.60/1.58 | (u0(v0, v1) = v2) | ? [v3: int] : (u0($sum(v0, -1), v1) = v3 & % 5.60/1.58 | f0(v3) = v2)) % 5.60/1.58 | (2) ! [v0: int] : ! [v1: int] : ! [v2: int] : (v2 = v1 | ~ ($lesseq(v0, % 5.60/1.58 | 0) | ~ (u0(v0, v1) = v2)) % 5.60/1.58 | % 5.60/1.58 | ALPHA: (formula_5) implies: % 5.60/1.58 | (3) ! [v0: int] : ! [v1: int] : ( ~ (v0(v0) = v1) | ? [v2: int] : % 5.60/1.58 | (u0(g0, v2) = v1 & h0(v0) = v2)) % 5.60/1.58 | % 5.60/1.58 | ALPHA: (formula_6) implies: % 5.60/1.58 | (4) ! [v0: int] : ! [v1: int] : ( ~ (small(v0) = v1) | v0(v0) = $sum(v1, % 5.60/1.58 | 1)) % 5.60/1.58 | % 5.60/1.59 | DELTA: instantiating (conjecture_1) with fresh symbols all_10_0, all_10_1, % 5.60/1.59 | all_10_2 gives: % 5.60/1.59 | (5) ~ (all_10_0 = all_10_1) & $lesseq(0, all_10_2) & fast(all_10_2) = % 5.60/1.59 | all_10_0 & small(all_10_2) = all_10_1 % 5.60/1.59 | % 5.60/1.59 | ALPHA: (5) implies: % 5.60/1.59 | (6) ~ (all_10_0 = all_10_1) % 5.60/1.59 | (7) small(all_10_2) = all_10_1 % 5.60/1.59 | (8) fast(all_10_2) = all_10_0 % 5.60/1.59 | % 5.60/1.59 | GROUND_INST: instantiating (formula_7) with all_10_2, all_10_0, simplifying % 5.60/1.59 | with (8) gives: % 5.60/1.59 | (9) $difference(all_10_0, $product(100, all_10_2)) = 87 % 5.60/1.59 | % 5.60/1.59 | REDUCE: (6), (9) imply: % 5.60/1.59 | (10) ~ ($difference(all_10_1, $product(100, all_10_2)) = 87) % 5.60/1.59 | % 5.60/1.59 | SIMP: (10) implies: % 5.60/1.59 | (11) ~ ($difference(all_10_1, $product(100, all_10_2)) = 87) % 5.60/1.59 | % 5.60/1.59 | GROUND_INST: instantiating (4) with all_10_2, all_10_1, simplifying with (7) % 5.60/1.59 | gives: % 5.60/1.59 | (12) v0(all_10_2) = $sum(all_10_1, 1) % 5.60/1.59 | % 5.60/1.59 | GROUND_INST: instantiating (3) with all_10_2, $sum(all_10_1, 1), simplifying % 5.60/1.59 | with (12) gives: % 5.60/1.59 | (13) ? [v0: int] : (u0(g0, v0) = $sum(all_10_1, 1) & h0(all_10_2) = v0) % 5.60/1.59 | % 5.60/1.59 | DELTA: instantiating (13) with fresh symbol all_31_0 gives: % 5.60/1.59 | (14) u0(g0, all_31_0) = $sum(all_10_1, 1) & h0(all_10_2) = all_31_0 % 5.60/1.59 | % 5.60/1.59 | ALPHA: (14) implies: % 5.60/1.59 | (15) h0(all_10_2) = all_31_0 % 5.60/1.59 | (16) u0(g0, all_31_0) = $sum(all_10_1, 1) % 5.60/1.59 | % 5.60/1.59 | REDUCE: (16), (formula_2) imply: % 5.60/1.59 | (17) u0(2, all_31_0) = $sum(all_10_1, 1) % 5.60/1.59 | % 5.60/1.59 | GROUND_INST: instantiating (formula_3) with all_10_2, all_31_0, simplifying % 5.60/1.59 | with (15) gives: % 5.60/1.59 | (18) all_31_0 = all_10_2 % 5.60/1.59 | % 5.60/1.59 | REDUCE: (17), (18) imply: % 5.60/1.59 | (19) u0(2, all_10_2) = $sum(all_10_1, 1) % 5.60/1.59 | % 5.60/1.59 | GROUND_INST: instantiating (1) with 2, all_10_2, $sum(all_10_1, 1), % 5.60/1.59 | simplifying with (19) gives: % 5.60/1.59 | (20) ? [v0: int] : (u0(1, all_10_2) = v0 & f0(v0) = $sum(all_10_1, 1)) % 5.60/1.59 | % 5.60/1.59 | DELTA: instantiating (20) with fresh symbol all_42_0 gives: % 5.60/1.60 | (21) u0(1, all_10_2) = all_42_0 & f0(all_42_0) = $sum(all_10_1, 1) % 5.60/1.60 | % 5.60/1.60 | ALPHA: (21) implies: % 5.60/1.60 | (22) f0(all_42_0) = $sum(all_10_1, 1) % 5.60/1.60 | (23) u0(1, all_10_2) = all_42_0 % 5.60/1.60 | % 5.60/1.60 | GROUND_INST: instantiating (formula_1) with all_42_0, $sum(all_10_1, 1), % 5.60/1.60 | simplifying with (22) gives: % 5.60/1.60 | (24) $difference($product(10, all_42_0), all_10_1) = -7 % 5.60/1.60 | % 5.60/1.60 | COL_REDUCE: introducing fresh symbol sc_50_0_0 defined by: % 5.60/1.60 | (25) $difference(all_42_0, sc_50_0_0) = -1 % 5.60/1.60 | % 5.60/1.60 | COMBINE_EQS: (24), (25) imply: % 5.60/1.60 | (26) $difference(all_10_1, $product(10, sc_50_0_0)) = -3 % 5.60/1.60 | % 5.60/1.60 | SIMP: (26) implies: % 5.60/1.60 | (27) $difference(all_10_1, $product(10, sc_50_0_0)) = -3 % 5.60/1.60 | % 5.60/1.60 | REDUCE: (11), (27) imply: % 5.60/1.60 | (28) ~ ($difference(sc_50_0_0, $product(10, all_10_2)) = 9) % 5.60/1.60 | % 5.60/1.60 | SIMP: (28) implies: % 5.60/1.60 | (29) ~ ($difference(sc_50_0_0, $product(10, all_10_2)) = 9) % 5.60/1.60 | % 5.60/1.60 | REDUCE: (23), (25) imply: % 5.60/1.60 | (30) u0(1, all_10_2) = $sum(sc_50_0_0, -1) % 5.60/1.60 | % 5.60/1.60 | GROUND_INST: instantiating (1) with 1, all_10_2, $sum(sc_50_0_0, -1), % 5.60/1.60 | simplifying with (30) gives: % 5.60/1.60 | (31) ? [v0: int] : (u0(0, all_10_2) = v0 & f0(v0) = $sum(sc_50_0_0, -1)) % 5.60/1.60 | % 5.60/1.60 | DELTA: instantiating (31) with fresh symbol all_57_0 gives: % 5.60/1.60 | (32) u0(0, all_10_2) = all_57_0 & f0(all_57_0) = $sum(sc_50_0_0, -1) % 5.60/1.60 | % 5.60/1.60 | ALPHA: (32) implies: % 5.60/1.60 | (33) f0(all_57_0) = $sum(sc_50_0_0, -1) % 5.60/1.60 | (34) u0(0, all_10_2) = all_57_0 % 5.60/1.60 | % 5.60/1.60 | GROUND_INST: instantiating (formula_1) with all_57_0, $sum(sc_50_0_0, -1), % 5.60/1.60 | simplifying with (33) gives: % 5.60/1.60 | (35) $difference($product(10, all_57_0), sc_50_0_0) = -9 % 5.60/1.60 | % 5.60/1.60 | GROUND_INST: instantiating (2) with 0, all_10_2, all_57_0, simplifying with % 5.60/1.60 | (34) gives: % 5.60/1.60 | (36) all_57_0 = all_10_2 % 5.60/1.60 | % 5.60/1.60 | COMBINE_EQS: (35), (36) imply: % 5.60/1.60 | (37) $difference(sc_50_0_0, $product(10, all_10_2)) = 9 % 5.60/1.60 | % 5.60/1.60 | SIMP: (37) implies: % 5.60/1.60 | (38) $difference(sc_50_0_0, $product(10, all_10_2)) = 9 % 5.60/1.60 | % 5.60/1.60 | REDUCE: (29), (38) imply: % 5.60/1.60 | (39) $false % 5.60/1.60 | % 5.60/1.60 | CLOSE: (39) is inconsistent. % 5.60/1.60 | % 5.60/1.60 End of proof % 5.60/1.60 % SZS output end Proof for theBenchmark % 5.60/1.60 % 5.60/1.60 985ms %------------------------------------------------------------------------------