%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : GEO080+1 : TPTP v8.1.2. Released v2.4.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n002.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 : Wed Aug 30 23:21:18 EDT 2023 % Result : Theorem 8.43s 1.88s % Output : Proof 12.65s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.11 % Problem : GEO080+1 : TPTP v8.1.2. Released v2.4.0. % 0.10/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.11/0.32 % Computer : n002.cluster.edu % 0.11/0.32 % Model : x86_64 x86_64 % 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.32 % Memory : 8042.1875MB % 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.32 % CPULimit : 300 % 0.11/0.32 % WCLimit : 300 % 0.11/0.32 % DateTime : Tue Aug 29 23:00:50 EDT 2023 % 0.11/0.32 % CPUTime : % 0.16/0.58 ________ _____ % 0.16/0.58 ___ __ \_________(_)________________________________ % 0.16/0.58 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.16/0.58 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.16/0.58 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.16/0.58 % 0.16/0.58 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.16/0.58 (2023-06-19) % 0.16/0.58 % 0.16/0.59 (c) Philipp Rümmer, 2009-2023 % 0.16/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.16/0.59 Amanda Stjerna. % 0.16/0.59 Free software under BSD-3-Clause. % 0.16/0.59 % 0.16/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.16/0.59 % 0.16/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.16/0.60 Running up to 7 provers in parallel. % 0.16/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.16/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.16/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.16/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.16/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.16/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.16/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.33/1.09 Prover 1: Preprocessing ... % 2.33/1.10 Prover 4: Preprocessing ... % 2.98/1.13 Prover 6: Preprocessing ... % 2.98/1.13 Prover 3: Preprocessing ... % 2.98/1.13 Prover 2: Preprocessing ... % 2.98/1.13 Prover 0: Preprocessing ... % 2.98/1.13 Prover 5: Preprocessing ... % 6.98/1.71 Prover 5: Proving ... % 7.23/1.72 Prover 2: Proving ... % 7.35/1.75 Prover 6: Proving ... % 7.35/1.76 Prover 3: Warning: ignoring some quantifiers % 7.35/1.79 Prover 1: Warning: ignoring some quantifiers % 7.35/1.80 Prover 3: Constructing countermodel ... % 7.96/1.82 Prover 1: Constructing countermodel ... % 8.43/1.88 Prover 3: proved (1253ms) % 8.43/1.88 % 8.43/1.88 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 8.43/1.88 % 8.43/1.88 Prover 5: stopped % 8.43/1.89 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 8.43/1.89 Prover 6: stopped % 8.43/1.91 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 8.43/1.91 Prover 2: stopped % 8.43/1.93 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 8.43/1.93 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 8.43/1.96 Prover 7: Preprocessing ... % 8.43/2.00 Prover 10: Preprocessing ... % 8.43/2.01 Prover 8: Preprocessing ... % 8.43/2.01 Prover 1: Found proof (size 14) % 8.43/2.01 Prover 1: proved (1401ms) % 8.43/2.03 Prover 10: stopped % 8.43/2.04 Prover 11: Preprocessing ... % 8.43/2.05 Prover 7: stopped % 10.31/2.14 Prover 11: stopped % 10.31/2.19 Prover 8: Warning: ignoring some quantifiers % 10.96/2.25 Prover 8: Constructing countermodel ... % 10.96/2.26 Prover 8: stopped % 11.38/2.34 Prover 4: Warning: ignoring some quantifiers % 11.72/2.41 Prover 4: Constructing countermodel ... % 11.72/2.43 Prover 4: stopped % 12.41/2.50 Prover 0: Proving ... % 12.41/2.52 Prover 0: stopped % 12.41/2.52 % 12.41/2.52 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 12.41/2.52 % 12.41/2.52 % SZS output start Proof for theBenchmark % 12.41/2.53 Assumptions after simplification: % 12.41/2.53 --------------------------------- % 12.41/2.53 % 12.41/2.53 (part_of_defn) % 12.65/2.56 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (part_of(v1, v0) = v2) % 12.65/2.56 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & % 12.65/2.56 incident_c(v3, v1) = 0 & incident_c(v3, v0) = v4 & $i(v3))) & ! [v0: $i] % 12.65/2.56 : ! [v1: $i] : ( ~ (part_of(v1, v0) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: % 12.65/2.56 $i] : ! [v3: int] : (v3 = 0 | ~ (incident_c(v2, v0) = v3) | ~ $i(v2) | % 12.65/2.56 ? [v4: int] : ( ~ (v4 = 0) & incident_c(v2, v1) = v4))) % 12.65/2.56 % 12.65/2.56 (prove_reflexivity) % 12.65/2.57 ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & part_of(v0, v0) = v1 & $i(v0)) % 12.65/2.57 % 12.65/2.57 (function-axioms) % 12.65/2.57 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 12.65/2.57 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (meet(v4, v3, v2) = v1) | ~ (meet(v4, % 12.65/2.57 v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] % 12.65/2.57 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (inner_point(v3, v2) = v1) | ~ % 12.65/2.57 (inner_point(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 12.65/2.57 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 12.65/2.57 (end_point(v3, v2) = v1) | ~ (end_point(v3, v2) = v0)) & ! [v0: $i] : ! % 12.65/2.57 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sum(v3, v2) = v1) | ~ % 12.65/2.57 (sum(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 12.65/2.57 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (part_of(v3, % 12.65/2.57 v2) = v1) | ~ (part_of(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 12.65/2.58 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 12.65/2.58 (incident_c(v3, v2) = v1) | ~ (incident_c(v3, v2) = v0)) & ! [v0: % 12.65/2.58 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 12.65/2.58 ~ (open(v2) = v1) | ~ (open(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 12.65/2.58 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (closed(v2) = v1) | ~ % 12.65/2.58 (closed(v2) = v0)) % 12.65/2.58 % 12.65/2.58 Further assumptions not needed in the proof: % 12.65/2.58 -------------------------------------------- % 12.65/2.58 c1, c2, c3, c4, c5, c6, c7, c8, c9, closed_defn, end_point_defn, % 12.65/2.58 inner_point_defn, meet_defn, open_defn, sum_defn % 12.65/2.58 % 12.65/2.58 Those formulas are unsatisfiable: % 12.65/2.58 --------------------------------- % 12.65/2.58 % 12.65/2.58 Begin of proof % 12.65/2.58 | % 12.65/2.58 | ALPHA: (part_of_defn) implies: % 12.65/2.58 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (part_of(v1, % 12.65/2.58 | v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : % 12.65/2.58 | ( ~ (v4 = 0) & incident_c(v3, v1) = 0 & incident_c(v3, v0) = v4 & % 12.65/2.58 | $i(v3))) % 12.65/2.58 | % 12.65/2.58 | ALPHA: (function-axioms) implies: % 12.65/2.58 | (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 12.65/2.58 | ! [v3: $i] : (v1 = v0 | ~ (incident_c(v3, v2) = v1) | ~ % 12.65/2.58 | (incident_c(v3, v2) = v0)) % 12.65/2.58 | % 12.65/2.58 | DELTA: instantiating (prove_reflexivity) with fresh symbols all_17_0, all_17_1 % 12.65/2.58 | gives: % 12.65/2.58 | (3) ~ (all_17_0 = 0) & part_of(all_17_1, all_17_1) = all_17_0 & % 12.65/2.58 | $i(all_17_1) % 12.65/2.58 | % 12.65/2.59 | ALPHA: (3) implies: % 12.65/2.59 | (4) ~ (all_17_0 = 0) % 12.65/2.59 | (5) $i(all_17_1) % 12.65/2.59 | (6) part_of(all_17_1, all_17_1) = all_17_0 % 12.65/2.59 | % 12.65/2.59 | GROUND_INST: instantiating (1) with all_17_1, all_17_1, all_17_0, simplifying % 12.65/2.59 | with (5), (6) gives: % 12.65/2.59 | (7) all_17_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 12.65/2.59 | incident_c(v0, all_17_1) = v1 & incident_c(v0, all_17_1) = 0 & % 12.65/2.59 | $i(v0)) % 12.65/2.59 | % 12.65/2.59 | BETA: splitting (7) gives: % 12.65/2.59 | % 12.65/2.59 | Case 1: % 12.65/2.59 | | % 12.65/2.59 | | (8) all_17_0 = 0 % 12.65/2.59 | | % 12.65/2.59 | | REDUCE: (4), (8) imply: % 12.65/2.59 | | (9) $false % 12.65/2.59 | | % 12.65/2.59 | | CLOSE: (9) is inconsistent. % 12.65/2.59 | | % 12.65/2.59 | Case 2: % 12.65/2.59 | | % 12.65/2.59 | | (10) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & incident_c(v0, all_17_1) % 12.65/2.59 | | = v1 & incident_c(v0, all_17_1) = 0 & $i(v0)) % 12.65/2.59 | | % 12.65/2.59 | | DELTA: instantiating (10) with fresh symbols all_36_0, all_36_1 gives: % 12.65/2.60 | | (11) ~ (all_36_0 = 0) & incident_c(all_36_1, all_17_1) = all_36_0 & % 12.65/2.60 | | incident_c(all_36_1, all_17_1) = 0 & $i(all_36_1) % 12.65/2.60 | | % 12.65/2.60 | | ALPHA: (11) implies: % 12.65/2.60 | | (12) ~ (all_36_0 = 0) % 12.65/2.60 | | (13) incident_c(all_36_1, all_17_1) = 0 % 12.65/2.60 | | (14) incident_c(all_36_1, all_17_1) = all_36_0 % 12.65/2.60 | | % 12.65/2.60 | | GROUND_INST: instantiating (2) with 0, all_36_0, all_17_1, all_36_1, % 12.65/2.60 | | simplifying with (13), (14) gives: % 12.65/2.60 | | (15) all_36_0 = 0 % 12.65/2.60 | | % 12.65/2.60 | | REDUCE: (12), (15) imply: % 12.65/2.60 | | (16) $false % 12.65/2.60 | | % 12.65/2.60 | | CLOSE: (16) is inconsistent. % 12.65/2.60 | | % 12.65/2.60 | End of split % 12.65/2.60 | % 12.65/2.60 End of proof % 12.65/2.60 % SZS output end Proof for theBenchmark % 12.65/2.60 % 12.65/2.60 2013ms %------------------------------------------------------------------------------