%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET573+3 : TPTP v8.1.2. Released v2.2.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n021.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 : Thu Aug 31 15:25:20 EDT 2023 % Result : Theorem 3.83s 1.24s % Output : Proof 4.66s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : SET573+3 : TPTP v8.1.2. Released v2.2.0. % 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.16/0.35 % Computer : n021.cluster.edu % 0.16/0.35 % Model : x86_64 x86_64 % 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.35 % Memory : 8042.1875MB % 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.35 % CPULimit : 300 % 0.16/0.35 % WCLimit : 300 % 0.16/0.35 % DateTime : Sat Aug 26 10:59:11 EDT 2023 % 0.16/0.35 % CPUTime : % 0.20/0.63 ________ _____ % 0.20/0.63 ___ __ \_________(_)________________________________ % 0.20/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.63 % 0.20/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.63 (2023-06-19) % 0.20/0.63 % 0.20/0.63 (c) Philipp Rümmer, 2009-2023 % 0.20/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.63 Amanda Stjerna. % 0.20/0.63 Free software under BSD-3-Clause. % 0.20/0.63 % 0.20/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.63 % 0.20/0.63 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.64 Running up to 7 provers in parallel. % 0.20/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.78/0.98 Prover 4: Preprocessing ... % 1.78/0.98 Prover 1: Preprocessing ... % 2.12/1.02 Prover 3: Preprocessing ... % 2.12/1.02 Prover 6: Preprocessing ... % 2.12/1.02 Prover 5: Preprocessing ... % 2.12/1.02 Prover 2: Preprocessing ... % 2.12/1.02 Prover 0: Preprocessing ... % 2.65/1.10 Prover 5: Proving ... % 2.65/1.10 Prover 2: Proving ... % 2.65/1.11 Prover 6: Proving ... % 3.00/1.13 Prover 1: Constructing countermodel ... % 3.00/1.13 Prover 3: Constructing countermodel ... % 3.22/1.16 Prover 0: Proving ... % 3.22/1.16 Prover 4: Constructing countermodel ... % 3.83/1.24 Prover 3: proved (591ms) % 3.83/1.24 % 3.83/1.24 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 3.83/1.24 % 3.83/1.24 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 3.83/1.25 Prover 5: stopped % 3.83/1.25 Prover 6: stopped % 3.83/1.25 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 3.83/1.25 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 3.83/1.25 Prover 2: proved (604ms) % 3.83/1.25 Prover 0: proved (603ms) % 3.83/1.25 % 3.83/1.25 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 3.83/1.25 % 3.83/1.25 % 3.83/1.25 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 3.83/1.25 % 3.83/1.26 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 3.83/1.26 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 3.83/1.26 Prover 7: Preprocessing ... % 3.83/1.27 Prover 10: Preprocessing ... % 3.83/1.27 Prover 8: Preprocessing ... % 4.18/1.28 Prover 7: Warning: ignoring some quantifiers % 4.18/1.28 Prover 11: Preprocessing ... % 4.18/1.28 Prover 13: Preprocessing ... % 4.18/1.28 Prover 7: Constructing countermodel ... % 4.18/1.29 Prover 10: Warning: ignoring some quantifiers % 4.18/1.30 Prover 10: Constructing countermodel ... % 4.18/1.30 Prover 13: Warning: ignoring some quantifiers % 4.18/1.30 Prover 13: Constructing countermodel ... % 4.18/1.31 Prover 4: Found proof (size 19) % 4.18/1.31 Prover 8: Warning: ignoring some quantifiers % 4.18/1.32 Prover 8: Constructing countermodel ... % 4.18/1.32 Prover 1: Found proof (size 18) % 4.18/1.32 Prover 1: proved (676ms) % 4.18/1.32 Prover 4: proved (671ms) % 4.18/1.32 Prover 8: stopped % 4.18/1.32 Prover 13: stopped % 4.18/1.32 Prover 10: stopped % 4.18/1.33 Prover 7: stopped % 4.18/1.34 Prover 11: Constructing countermodel ... % 4.59/1.35 Prover 11: stopped % 4.59/1.35 % 4.59/1.35 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 4.59/1.35 % 4.59/1.35 % SZS output start Proof for theBenchmark % 4.59/1.35 Assumptions after simplification: % 4.59/1.35 --------------------------------- % 4.59/1.35 % 4.59/1.35 (disjoint_defn) % 4.66/1.38 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (disjoint(v0, v1) = % 4.66/1.38 v2) | ~ $i(v1) | ~ $i(v0) | intersect(v0, v1) = 0) & ! [v0: $i] : ! % 4.66/1.38 [v1: $i] : ( ~ (disjoint(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: int] : % 4.66/1.38 ( ~ (v2 = 0) & intersect(v0, v1) = v2)) % 4.66/1.38 % 4.66/1.38 (intersect_defn) % 4.66/1.39 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (intersect(v0, v1) = % 4.66/1.39 v2) | ~ $i(v1) | ~ $i(v0) | ! [v3: $i] : ( ~ (member(v3, v0) = 0) | ~ % 4.66/1.39 $i(v3) | ? [v4: int] : ( ~ (v4 = 0) & member(v3, v1) = v4))) & ! [v0: % 4.66/1.39 $i] : ! [v1: $i] : ( ~ (intersect(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? % 4.66/1.39 [v2: $i] : (member(v2, v1) = 0 & member(v2, v0) = 0 & $i(v2))) % 4.66/1.39 % 4.66/1.39 (prove_th12) % 4.66/1.39 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (disjoint(v1, v2) = 0 & member(v0, % 4.66/1.39 v2) = 0 & member(v0, v1) = 0 & $i(v2) & $i(v1) & $i(v0)) % 4.66/1.39 % 4.66/1.39 (function-axioms) % 4.66/1.39 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 4.66/1.39 [v3: $i] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0)) % 4.66/1.39 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 4.66/1.39 [v3: $i] : (v1 = v0 | ~ (intersect(v3, v2) = v1) | ~ (intersect(v3, v2) = % 4.66/1.39 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 4.66/1.39 $i] : ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) % 4.66/1.39 = v0)) % 4.66/1.39 % 4.66/1.39 Further assumptions not needed in the proof: % 4.66/1.39 -------------------------------------------- % 4.66/1.39 symmetry_of_intersect % 4.66/1.39 % 4.66/1.39 Those formulas are unsatisfiable: % 4.66/1.39 --------------------------------- % 4.66/1.39 % 4.66/1.39 Begin of proof % 4.66/1.39 | % 4.66/1.39 | ALPHA: (intersect_defn) implies: % 4.66/1.40 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (intersect(v0, % 4.66/1.40 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ! [v3: $i] : ( ~ (member(v3, % 4.66/1.40 | v0) = 0) | ~ $i(v3) | ? [v4: int] : ( ~ (v4 = 0) & member(v3, % 4.66/1.40 | v1) = v4))) % 4.66/1.40 | % 4.66/1.40 | ALPHA: (disjoint_defn) implies: % 4.66/1.40 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (disjoint(v0, v1) = 0) | ~ $i(v1) | ~ % 4.66/1.40 | $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & intersect(v0, v1) = v2)) % 4.66/1.40 | % 4.66/1.40 | ALPHA: (function-axioms) implies: % 4.66/1.40 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 4.66/1.40 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) % 4.66/1.40 | = v0)) % 4.66/1.40 | % 4.66/1.40 | DELTA: instantiating (prove_th12) with fresh symbols all_6_0, all_6_1, all_6_2 % 4.66/1.40 | gives: % 4.66/1.40 | (4) disjoint(all_6_1, all_6_0) = 0 & member(all_6_2, all_6_0) = 0 & % 4.66/1.40 | member(all_6_2, all_6_1) = 0 & $i(all_6_0) & $i(all_6_1) & $i(all_6_2) % 4.66/1.40 | % 4.66/1.40 | ALPHA: (4) implies: % 4.66/1.40 | (5) $i(all_6_2) % 4.66/1.40 | (6) $i(all_6_1) % 4.66/1.40 | (7) $i(all_6_0) % 4.66/1.40 | (8) member(all_6_2, all_6_1) = 0 % 4.66/1.40 | (9) member(all_6_2, all_6_0) = 0 % 4.66/1.40 | (10) disjoint(all_6_1, all_6_0) = 0 % 4.66/1.40 | % 4.66/1.40 | GROUND_INST: instantiating (2) with all_6_1, all_6_0, simplifying with (6), % 4.66/1.40 | (7), (10) gives: % 4.66/1.40 | (11) ? [v0: int] : ( ~ (v0 = 0) & intersect(all_6_1, all_6_0) = v0) % 4.66/1.40 | % 4.66/1.40 | DELTA: instantiating (11) with fresh symbol all_13_0 gives: % 4.66/1.41 | (12) ~ (all_13_0 = 0) & intersect(all_6_1, all_6_0) = all_13_0 % 4.66/1.41 | % 4.66/1.41 | ALPHA: (12) implies: % 4.66/1.41 | (13) ~ (all_13_0 = 0) % 4.66/1.41 | (14) intersect(all_6_1, all_6_0) = all_13_0 % 4.66/1.41 | % 4.66/1.41 | GROUND_INST: instantiating (1) with all_6_1, all_6_0, all_13_0, simplifying % 4.66/1.41 | with (6), (7), (14) gives: % 4.66/1.41 | (15) all_13_0 = 0 | ! [v0: $i] : ( ~ (member(v0, all_6_1) = 0) | ~ $i(v0) % 4.66/1.41 | | ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_6_0) = v1)) % 4.66/1.41 | % 4.66/1.41 | BETA: splitting (15) gives: % 4.66/1.41 | % 4.66/1.41 | Case 1: % 4.66/1.41 | | % 4.66/1.41 | | (16) all_13_0 = 0 % 4.66/1.41 | | % 4.66/1.41 | | REDUCE: (13), (16) imply: % 4.66/1.41 | | (17) $false % 4.66/1.41 | | % 4.66/1.41 | | CLOSE: (17) is inconsistent. % 4.66/1.41 | | % 4.66/1.41 | Case 2: % 4.66/1.41 | | % 4.66/1.41 | | (18) ! [v0: $i] : ( ~ (member(v0, all_6_1) = 0) | ~ $i(v0) | ? [v1: % 4.66/1.41 | | int] : ( ~ (v1 = 0) & member(v0, all_6_0) = v1)) % 4.66/1.41 | | % 4.66/1.41 | | GROUND_INST: instantiating (18) with all_6_2, simplifying with (5), (8) % 4.66/1.41 | | gives: % 4.66/1.41 | | (19) ? [v0: int] : ( ~ (v0 = 0) & member(all_6_2, all_6_0) = v0) % 4.66/1.41 | | % 4.66/1.41 | | DELTA: instantiating (19) with fresh symbol all_23_0 gives: % 4.66/1.41 | | (20) ~ (all_23_0 = 0) & member(all_6_2, all_6_0) = all_23_0 % 4.66/1.41 | | % 4.66/1.41 | | ALPHA: (20) implies: % 4.66/1.41 | | (21) ~ (all_23_0 = 0) % 4.66/1.41 | | (22) member(all_6_2, all_6_0) = all_23_0 % 4.66/1.41 | | % 4.66/1.41 | | GROUND_INST: instantiating (3) with 0, all_23_0, all_6_0, all_6_2, % 4.66/1.41 | | simplifying with (9), (22) gives: % 4.66/1.41 | | (23) all_23_0 = 0 % 4.66/1.41 | | % 4.66/1.41 | | REDUCE: (21), (23) imply: % 4.66/1.41 | | (24) $false % 4.66/1.41 | | % 4.66/1.41 | | CLOSE: (24) is inconsistent. % 4.66/1.41 | | % 4.66/1.41 | End of split % 4.66/1.41 | % 4.66/1.41 End of proof % 4.66/1.41 % SZS output end Proof for theBenchmark % 4.66/1.41 % 4.66/1.41 787ms %------------------------------------------------------------------------------