%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET793+4 : TPTP v8.1.2. Released v3.2.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n027.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 15:26:28 EDT 2023 % Result : Theorem 7.32s 2.12s % Output : Proof 9.65s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET793+4 : TPTP v8.1.2. Released v3.2.0. % 0.00/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.33 % Computer : n027.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 : Sat Aug 26 10:37:19 EDT 2023 % 0.12/0.34 % CPUTime : % 0.18/0.64 ________ _____ % 0.18/0.64 ___ __ \_________(_)________________________________ % 0.18/0.64 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.18/0.64 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.18/0.64 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.18/0.64 % 0.18/0.64 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.18/0.64 (2023-06-19) % 0.18/0.64 % 0.18/0.64 (c) Philipp Rümmer, 2009-2023 % 0.18/0.64 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.18/0.64 Amanda Stjerna. % 0.18/0.64 Free software under BSD-3-Clause. % 0.18/0.64 % 0.18/0.64 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.18/0.64 % 0.18/0.64 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.18/0.65 Running up to 7 provers in parallel. % 0.18/0.68 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.18/0.68 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.18/0.68 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.18/0.68 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.18/0.68 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.18/0.68 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.18/0.68 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.34/1.16 Prover 1: Preprocessing ... % 2.34/1.17 Prover 4: Preprocessing ... % 2.88/1.23 Prover 2: Preprocessing ... % 2.88/1.23 Prover 6: Preprocessing ... % 2.88/1.23 Prover 0: Preprocessing ... % 2.88/1.23 Prover 3: Preprocessing ... % 2.88/1.24 Prover 5: Preprocessing ... % 5.26/1.74 Prover 2: Proving ... % 5.26/1.74 Prover 5: Proving ... % 5.71/1.87 Prover 6: Proving ... % 6.19/1.92 Prover 3: Constructing countermodel ... % 6.19/1.95 Prover 1: Constructing countermodel ... % 7.32/2.12 Prover 3: proved (1444ms) % 7.32/2.12 % 7.32/2.12 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 7.32/2.12 % 7.32/2.13 Prover 5: stopped % 7.32/2.13 Prover 2: stopped % 7.32/2.13 Prover 6: stopped % 7.32/2.13 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 7.32/2.13 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 7.32/2.13 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 7.32/2.14 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 7.32/2.16 Prover 0: Proving ... % 7.32/2.17 Prover 4: Constructing countermodel ... % 7.32/2.18 Prover 0: stopped % 7.89/2.20 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 7.89/2.21 Prover 7: Preprocessing ... % 7.89/2.22 Prover 10: Preprocessing ... % 7.89/2.24 Prover 8: Preprocessing ... % 7.89/2.25 Prover 11: Preprocessing ... % 7.89/2.26 Prover 13: Preprocessing ... % 8.46/2.31 Prover 1: Found proof (size 50) % 8.46/2.31 Prover 1: proved (1635ms) % 8.46/2.31 Prover 7: Warning: ignoring some quantifiers % 8.46/2.32 Prover 10: Warning: ignoring some quantifiers % 8.46/2.33 Prover 7: Constructing countermodel ... % 8.46/2.34 Prover 10: Constructing countermodel ... % 8.46/2.34 Prover 13: Warning: ignoring some quantifiers % 8.46/2.34 Prover 4: stopped % 8.46/2.34 Prover 7: stopped % 8.46/2.36 Prover 11: stopped % 8.46/2.36 Prover 10: stopped % 8.46/2.37 Prover 13: Constructing countermodel ... % 8.46/2.37 Prover 13: stopped % 8.46/2.42 Prover 8: Warning: ignoring some quantifiers % 8.46/2.43 Prover 8: Constructing countermodel ... % 8.46/2.44 Prover 8: stopped % 8.46/2.44 % 8.46/2.44 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 8.46/2.44 % 8.46/2.45 % SZS output start Proof for theBenchmark % 8.46/2.45 Assumptions after simplification: % 8.46/2.45 --------------------------------- % 8.46/2.45 % 8.46/2.45 (greatest) % 9.37/2.48 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 9.37/2.48 (greatest(v2, v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 9.37/2.48 $i] : ? [v5: int] : ( ~ (v5 = 0) & apply(v0, v4, v2) = v5 & member(v4, % 9.37/2.48 v1) = 0 & $i(v4)) | ? [v4: int] : ( ~ (v4 = 0) & member(v2, v1) = v4)) % 9.37/2.48 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (greatest(v2, v0, v1) = 0) | % 9.37/2.48 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (member(v2, v1) = 0 & ! [v3: $i] : ! % 9.37/2.48 [v4: int] : (v4 = 0 | ~ (apply(v0, v3, v2) = v4) | ~ $i(v3) | ? [v5: % 9.37/2.48 int] : ( ~ (v5 = 0) & member(v3, v1) = v5)))) % 9.37/2.48 % 9.37/2.48 (max) % 9.37/2.49 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (max(v2, % 9.37/2.49 v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ( ~ % 9.37/2.49 (v4 = v2) & apply(v0, v2, v4) = 0 & member(v4, v1) = 0 & $i(v4)) | ? [v4: % 9.37/2.49 int] : ( ~ (v4 = 0) & member(v2, v1) = v4)) & ! [v0: $i] : ! [v1: $i] : % 9.37/2.49 ! [v2: $i] : ( ~ (max(v2, v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 9.37/2.49 (member(v2, v1) = 0 & ! [v3: $i] : (v3 = v2 | ~ (apply(v0, v2, v3) = 0) | % 9.37/2.49 ~ $i(v3) | ? [v4: int] : ( ~ (v4 = 0) & member(v3, v1) = v4)))) % 9.37/2.49 % 9.37/2.49 (thIV5) % 9.37/2.49 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 9.37/2.49 max(v2, v0, v1) = 0 & greatest(v2, v0, v1) = v3 & total_order(v0, v1) = 0 & % 9.37/2.49 $i(v2) & $i(v1) & $i(v0)) % 9.37/2.49 % 9.37/2.49 (total_order) % 9.37/2.50 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (total_order(v0, v1) = % 9.37/2.50 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: int] : % 9.37/2.50 ? [v6: int] : ( ~ (v6 = 0) & ~ (v5 = 0) & apply(v0, v4, v3) = v6 & % 9.37/2.50 apply(v0, v3, v4) = v5 & member(v4, v1) = 0 & member(v3, v1) = 0 & $i(v4) % 9.37/2.50 & $i(v3)) | ? [v3: int] : ( ~ (v3 = 0) & order(v0, v1) = v3)) & ! [v0: % 9.37/2.50 $i] : ! [v1: $i] : ( ~ (total_order(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | % 9.37/2.50 (order(v0, v1) = 0 & ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~ % 9.37/2.50 (apply(v0, v2, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ? [v5: any] : ? % 9.37/2.50 [v6: any] : ? [v7: any] : (apply(v0, v3, v2) = v7 & member(v3, v1) = v6 % 9.37/2.50 & member(v2, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | v7 = 0))))) % 9.37/2.50 % 9.37/2.50 (function-axioms) % 9.52/2.50 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 9.52/2.50 [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (greatest_lower_bound(v5, % 9.52/2.50 v4, v3, v2) = v1) | ~ (greatest_lower_bound(v5, v4, v3, v2) = v0)) & ! % 9.52/2.50 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 9.52/2.50 $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (least_upper_bound(v5, v4, % 9.52/2.50 v3, v2) = v1) | ~ (least_upper_bound(v5, v4, v3, v2) = v0)) & ! [v0: % 9.52/2.50 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 9.52/2.50 : ! [v4: $i] : (v1 = v0 | ~ (min(v4, v3, v2) = v1) | ~ (min(v4, v3, v2) = % 9.52/2.50 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 9.52/2.50 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (max(v4, v3, v2) = v1) | ~ % 9.52/2.50 (max(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 9.52/2.50 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 9.52/2.50 (least(v4, v3, v2) = v1) | ~ (least(v4, v3, v2) = v0)) & ! [v0: % 9.52/2.50 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 9.52/2.50 : ! [v4: $i] : (v1 = v0 | ~ (greatest(v4, v3, v2) = v1) | ~ (greatest(v4, % 9.52/2.50 v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] % 9.52/2.50 : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (lower_bound(v4, v3, % 9.52/2.50 v2) = v1) | ~ (lower_bound(v4, v3, v2) = v0)) & ! [v0: % 9.52/2.50 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 9.52/2.50 : ! [v4: $i] : (v1 = v0 | ~ (upper_bound(v4, v3, v2) = v1) | ~ % 9.52/2.50 (upper_bound(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 9.52/2.50 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 9.52/2.50 (apply(v4, v3, v2) = v1) | ~ (apply(v4, v3, v2) = v0)) & ! [v0: % 9.52/2.50 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 9.52/2.50 : (v1 = v0 | ~ (total_order(v3, v2) = v1) | ~ (total_order(v3, v2) = v0)) & % 9.52/2.50 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 9.52/2.50 $i] : (v1 = v0 | ~ (order(v3, v2) = v1) | ~ (order(v3, v2) = v0)) & ! % 9.52/2.50 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 9.52/2.50 $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) % 9.52/2.50 % 9.52/2.50 Further assumptions not needed in the proof: % 9.52/2.50 -------------------------------------------- % 9.52/2.50 greatest_lower_bound, least, least_upper_bound, lower_bound, min, order, % 9.52/2.50 upper_bound % 9.52/2.50 % 9.52/2.50 Those formulas are unsatisfiable: % 9.52/2.50 --------------------------------- % 9.52/2.50 % 9.52/2.50 Begin of proof % 9.52/2.51 | % 9.52/2.51 | ALPHA: (total_order) implies: % 9.52/2.51 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (total_order(v0, v1) = 0) | ~ $i(v1) | % 9.52/2.51 | ~ $i(v0) | (order(v0, v1) = 0 & ! [v2: $i] : ! [v3: $i] : ! [v4: % 9.52/2.51 | int] : (v4 = 0 | ~ (apply(v0, v2, v3) = v4) | ~ $i(v3) | ~ % 9.52/2.51 | $i(v2) | ? [v5: any] : ? [v6: any] : ? [v7: any] : (apply(v0, % 9.52/2.51 | v3, v2) = v7 & member(v3, v1) = v6 & member(v2, v1) = v5 & ( % 9.52/2.51 | ~ (v6 = 0) | ~ (v5 = 0) | v7 = 0))))) % 9.52/2.51 | % 9.52/2.51 | ALPHA: (greatest) implies: % 9.52/2.51 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 9.52/2.51 | (greatest(v2, v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 9.52/2.51 | [v4: $i] : ? [v5: int] : ( ~ (v5 = 0) & apply(v0, v4, v2) = v5 & % 9.52/2.51 | member(v4, v1) = 0 & $i(v4)) | ? [v4: int] : ( ~ (v4 = 0) & % 9.52/2.51 | member(v2, v1) = v4)) % 9.52/2.51 | % 9.52/2.51 | ALPHA: (max) implies: % 9.52/2.51 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (max(v2, v0, v1) = 0) | % 9.52/2.51 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (member(v2, v1) = 0 & ! [v3: $i] % 9.52/2.51 | : (v3 = v2 | ~ (apply(v0, v2, v3) = 0) | ~ $i(v3) | ? [v4: int] % 9.52/2.51 | : ( ~ (v4 = 0) & member(v3, v1) = v4)))) % 9.52/2.51 | % 9.52/2.51 | ALPHA: (function-axioms) implies: % 9.52/2.51 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 9.52/2.51 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) % 9.52/2.51 | = v0)) % 9.52/2.51 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 9.52/2.51 | ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | ~ % 9.52/2.51 | (apply(v4, v3, v2) = v0)) % 9.52/2.51 | % 9.52/2.52 | DELTA: instantiating (thIV5) with fresh symbols all_13_0, all_13_1, all_13_2, % 9.52/2.52 | all_13_3 gives: % 9.52/2.52 | (6) ~ (all_13_0 = 0) & max(all_13_1, all_13_3, all_13_2) = 0 & % 9.52/2.52 | greatest(all_13_1, all_13_3, all_13_2) = all_13_0 & % 9.52/2.52 | total_order(all_13_3, all_13_2) = 0 & $i(all_13_1) & $i(all_13_2) & % 9.52/2.52 | $i(all_13_3) % 9.52/2.52 | % 9.52/2.52 | ALPHA: (6) implies: % 9.52/2.52 | (7) ~ (all_13_0 = 0) % 9.52/2.52 | (8) $i(all_13_3) % 9.52/2.52 | (9) $i(all_13_2) % 9.52/2.52 | (10) $i(all_13_1) % 9.52/2.52 | (11) total_order(all_13_3, all_13_2) = 0 % 9.52/2.52 | (12) greatest(all_13_1, all_13_3, all_13_2) = all_13_0 % 9.52/2.52 | (13) max(all_13_1, all_13_3, all_13_2) = 0 % 9.52/2.52 | % 9.52/2.52 | GROUND_INST: instantiating (1) with all_13_3, all_13_2, simplifying with (8), % 9.52/2.52 | (9), (11) gives: % 9.52/2.52 | (14) order(all_13_3, all_13_2) = 0 & ! [v0: $i] : ! [v1: $i] : ! [v2: % 9.52/2.52 | int] : (v2 = 0 | ~ (apply(all_13_3, v0, v1) = v2) | ~ $i(v1) | ~ % 9.52/2.52 | $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] : % 9.52/2.52 | (apply(all_13_3, v1, v0) = v5 & member(v1, all_13_2) = v4 & % 9.52/2.52 | member(v0, all_13_2) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0))) % 9.52/2.52 | % 9.52/2.52 | ALPHA: (14) implies: % 9.52/2.52 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 9.52/2.52 | (apply(all_13_3, v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: % 9.52/2.52 | any] : ? [v4: any] : ? [v5: any] : (apply(all_13_3, v1, v0) = v5 % 9.52/2.52 | & member(v1, all_13_2) = v4 & member(v0, all_13_2) = v3 & ( ~ (v4 % 9.52/2.52 | = 0) | ~ (v3 = 0) | v5 = 0))) % 9.52/2.52 | % 9.52/2.52 | GROUND_INST: instantiating (2) with all_13_3, all_13_2, all_13_1, all_13_0, % 9.52/2.52 | simplifying with (8), (9), (10), (12) gives: % 9.52/2.52 | (16) all_13_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 9.52/2.52 | apply(all_13_3, v0, all_13_1) = v1 & member(v0, all_13_2) = 0 & % 9.52/2.52 | $i(v0)) | ? [v0: int] : ( ~ (v0 = 0) & member(all_13_1, all_13_2) = % 9.52/2.52 | v0) % 9.52/2.52 | % 9.52/2.53 | GROUND_INST: instantiating (3) with all_13_3, all_13_2, all_13_1, simplifying % 9.52/2.53 | with (8), (9), (10), (13) gives: % 9.52/2.53 | (17) member(all_13_1, all_13_2) = 0 & ! [v0: any] : (v0 = all_13_1 | ~ % 9.52/2.53 | (apply(all_13_3, all_13_1, v0) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ % 9.52/2.53 | (v1 = 0) & member(v0, all_13_2) = v1)) % 9.52/2.53 | % 9.52/2.53 | ALPHA: (17) implies: % 9.52/2.53 | (18) member(all_13_1, all_13_2) = 0 % 9.65/2.53 | (19) ! [v0: any] : (v0 = all_13_1 | ~ (apply(all_13_3, all_13_1, v0) = 0) % 9.65/2.53 | | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_13_2) = % 9.65/2.53 | v1)) % 9.65/2.53 | % 9.65/2.53 | BETA: splitting (16) gives: % 9.65/2.53 | % 9.65/2.53 | Case 1: % 9.65/2.53 | | % 9.65/2.53 | | (20) all_13_0 = 0 % 9.65/2.53 | | % 9.65/2.53 | | REDUCE: (7), (20) imply: % 9.65/2.53 | | (21) $false % 9.65/2.53 | | % 9.65/2.53 | | CLOSE: (21) is inconsistent. % 9.65/2.53 | | % 9.65/2.53 | Case 2: % 9.65/2.53 | | % 9.65/2.53 | | (22) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & apply(all_13_3, v0, % 9.65/2.53 | | all_13_1) = v1 & member(v0, all_13_2) = 0 & $i(v0)) | ? [v0: % 9.65/2.53 | | int] : ( ~ (v0 = 0) & member(all_13_1, all_13_2) = v0) % 9.65/2.53 | | % 9.65/2.53 | | BETA: splitting (22) gives: % 9.65/2.53 | | % 9.65/2.53 | | Case 1: % 9.65/2.53 | | | % 9.65/2.53 | | | (23) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & apply(all_13_3, v0, % 9.65/2.53 | | | all_13_1) = v1 & member(v0, all_13_2) = 0 & $i(v0)) % 9.65/2.53 | | | % 9.65/2.53 | | | DELTA: instantiating (23) with fresh symbols all_30_0, all_30_1 gives: % 9.65/2.53 | | | (24) ~ (all_30_0 = 0) & apply(all_13_3, all_30_1, all_13_1) = all_30_0 % 9.65/2.53 | | | & member(all_30_1, all_13_2) = 0 & $i(all_30_1) % 9.65/2.53 | | | % 9.65/2.53 | | | ALPHA: (24) implies: % 9.65/2.53 | | | (25) ~ (all_30_0 = 0) % 9.65/2.53 | | | (26) $i(all_30_1) % 9.65/2.53 | | | (27) member(all_30_1, all_13_2) = 0 % 9.65/2.53 | | | (28) apply(all_13_3, all_30_1, all_13_1) = all_30_0 % 9.65/2.53 | | | % 9.65/2.53 | | | GROUND_INST: instantiating (15) with all_30_1, all_13_1, all_30_0, % 9.65/2.53 | | | simplifying with (10), (26), (28) gives: % 9.65/2.54 | | | (29) all_30_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : % 9.65/2.54 | | | (apply(all_13_3, all_13_1, all_30_1) = v2 & member(all_30_1, % 9.65/2.54 | | | all_13_2) = v0 & member(all_13_1, all_13_2) = v1 & ( ~ (v1 = % 9.65/2.54 | | | 0) | ~ (v0 = 0) | v2 = 0)) % 9.65/2.54 | | | % 9.65/2.54 | | | BETA: splitting (29) gives: % 9.65/2.54 | | | % 9.65/2.54 | | | Case 1: % 9.65/2.54 | | | | % 9.65/2.54 | | | | (30) all_30_0 = 0 % 9.65/2.54 | | | | % 9.65/2.54 | | | | REDUCE: (25), (30) imply: % 9.65/2.54 | | | | (31) $false % 9.65/2.54 | | | | % 9.65/2.54 | | | | CLOSE: (31) is inconsistent. % 9.65/2.54 | | | | % 9.65/2.54 | | | Case 2: % 9.65/2.54 | | | | % 9.65/2.54 | | | | (32) ? [v0: any] : ? [v1: any] : ? [v2: any] : (apply(all_13_3, % 9.65/2.54 | | | | all_13_1, all_30_1) = v2 & member(all_30_1, all_13_2) = v0 & % 9.65/2.54 | | | | member(all_13_1, all_13_2) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | % 9.65/2.54 | | | | v2 = 0)) % 9.65/2.54 | | | | % 9.65/2.54 | | | | DELTA: instantiating (32) with fresh symbols all_42_0, all_42_1, % 9.65/2.54 | | | | all_42_2 gives: % 9.65/2.54 | | | | (33) apply(all_13_3, all_13_1, all_30_1) = all_42_0 & % 9.65/2.54 | | | | member(all_30_1, all_13_2) = all_42_2 & member(all_13_1, % 9.65/2.54 | | | | all_13_2) = all_42_1 & ( ~ (all_42_1 = 0) | ~ (all_42_2 = 0) % 9.65/2.54 | | | | | all_42_0 = 0) % 9.65/2.54 | | | | % 9.65/2.54 | | | | ALPHA: (33) implies: % 9.65/2.54 | | | | (34) member(all_13_1, all_13_2) = all_42_1 % 9.65/2.54 | | | | (35) member(all_30_1, all_13_2) = all_42_2 % 9.65/2.54 | | | | (36) apply(all_13_3, all_13_1, all_30_1) = all_42_0 % 9.65/2.54 | | | | (37) ~ (all_42_1 = 0) | ~ (all_42_2 = 0) | all_42_0 = 0 % 9.65/2.54 | | | | % 9.65/2.54 | | | | GROUND_INST: instantiating (4) with 0, all_42_1, all_13_2, all_13_1, % 9.65/2.54 | | | | simplifying with (18), (34) gives: % 9.65/2.54 | | | | (38) all_42_1 = 0 % 9.65/2.54 | | | | % 9.65/2.54 | | | | GROUND_INST: instantiating (4) with 0, all_42_2, all_13_2, all_30_1, % 9.65/2.54 | | | | simplifying with (27), (35) gives: % 9.65/2.54 | | | | (39) all_42_2 = 0 % 9.65/2.54 | | | | % 9.65/2.54 | | | | BETA: splitting (37) gives: % 9.65/2.54 | | | | % 9.65/2.54 | | | | Case 1: % 9.65/2.54 | | | | | % 9.65/2.54 | | | | | (40) ~ (all_42_1 = 0) % 9.65/2.54 | | | | | % 9.65/2.54 | | | | | REDUCE: (38), (40) imply: % 9.65/2.54 | | | | | (41) $false % 9.65/2.54 | | | | | % 9.65/2.54 | | | | | CLOSE: (41) is inconsistent. % 9.65/2.54 | | | | | % 9.65/2.54 | | | | Case 2: % 9.65/2.54 | | | | | % 9.65/2.54 | | | | | (42) ~ (all_42_2 = 0) | all_42_0 = 0 % 9.65/2.54 | | | | | % 9.65/2.54 | | | | | BETA: splitting (42) gives: % 9.65/2.54 | | | | | % 9.65/2.54 | | | | | Case 1: % 9.65/2.54 | | | | | | % 9.65/2.54 | | | | | | (43) ~ (all_42_2 = 0) % 9.65/2.54 | | | | | | % 9.65/2.54 | | | | | | REDUCE: (39), (43) imply: % 9.65/2.54 | | | | | | (44) $false % 9.65/2.54 | | | | | | % 9.65/2.54 | | | | | | CLOSE: (44) is inconsistent. % 9.65/2.54 | | | | | | % 9.65/2.54 | | | | | Case 2: % 9.65/2.54 | | | | | | % 9.65/2.54 | | | | | | (45) all_42_0 = 0 % 9.65/2.54 | | | | | | % 9.65/2.54 | | | | | | REDUCE: (36), (45) imply: % 9.65/2.54 | | | | | | (46) apply(all_13_3, all_13_1, all_30_1) = 0 % 9.65/2.54 | | | | | | % 9.65/2.54 | | | | | | GROUND_INST: instantiating (19) with all_30_1, simplifying with % 9.65/2.54 | | | | | | (26), (46) gives: % 9.65/2.54 | | | | | | (47) all_30_1 = all_13_1 | ? [v0: int] : ( ~ (v0 = 0) & % 9.65/2.54 | | | | | | member(all_30_1, all_13_2) = v0) % 9.65/2.54 | | | | | | % 9.65/2.54 | | | | | | BETA: splitting (47) gives: % 9.65/2.55 | | | | | | % 9.65/2.55 | | | | | | Case 1: % 9.65/2.55 | | | | | | | % 9.65/2.55 | | | | | | | (48) all_30_1 = all_13_1 % 9.65/2.55 | | | | | | | % 9.65/2.55 | | | | | | | REDUCE: (28), (48) imply: % 9.65/2.55 | | | | | | | (49) apply(all_13_3, all_13_1, all_13_1) = all_30_0 % 9.65/2.55 | | | | | | | % 9.65/2.55 | | | | | | | REDUCE: (46), (48) imply: % 9.65/2.55 | | | | | | | (50) apply(all_13_3, all_13_1, all_13_1) = 0 % 9.65/2.55 | | | | | | | % 9.65/2.55 | | | | | | | GROUND_INST: instantiating (5) with 0, all_30_0, all_13_1, % 9.65/2.55 | | | | | | | all_13_1, all_13_3, simplifying with (49), (50) % 9.65/2.55 | | | | | | | gives: % 9.65/2.55 | | | | | | | (51) all_30_0 = 0 % 9.65/2.55 | | | | | | | % 9.65/2.55 | | | | | | | REDUCE: (25), (51) imply: % 9.65/2.55 | | | | | | | (52) $false % 9.65/2.55 | | | | | | | % 9.65/2.55 | | | | | | | CLOSE: (52) is inconsistent. % 9.65/2.55 | | | | | | | % 9.65/2.55 | | | | | | Case 2: % 9.65/2.55 | | | | | | | % 9.65/2.55 | | | | | | | (53) ? [v0: int] : ( ~ (v0 = 0) & member(all_30_1, all_13_2) = % 9.65/2.55 | | | | | | | v0) % 9.65/2.55 | | | | | | | % 9.65/2.55 | | | | | | | DELTA: instantiating (53) with fresh symbol all_63_0 gives: % 9.65/2.55 | | | | | | | (54) ~ (all_63_0 = 0) & member(all_30_1, all_13_2) = all_63_0 % 9.65/2.55 | | | | | | | % 9.65/2.55 | | | | | | | ALPHA: (54) implies: % 9.65/2.55 | | | | | | | (55) ~ (all_63_0 = 0) % 9.65/2.55 | | | | | | | (56) member(all_30_1, all_13_2) = all_63_0 % 9.65/2.55 | | | | | | | % 9.65/2.55 | | | | | | | GROUND_INST: instantiating (4) with 0, all_63_0, all_13_2, % 9.65/2.55 | | | | | | | all_30_1, simplifying with (27), (56) gives: % 9.65/2.55 | | | | | | | (57) all_63_0 = 0 % 9.65/2.55 | | | | | | | % 9.65/2.55 | | | | | | | REDUCE: (55), (57) imply: % 9.65/2.55 | | | | | | | (58) $false % 9.65/2.55 | | | | | | | % 9.65/2.55 | | | | | | | CLOSE: (58) is inconsistent. % 9.65/2.55 | | | | | | | % 9.65/2.55 | | | | | | End of split % 9.65/2.55 | | | | | | % 9.65/2.55 | | | | | End of split % 9.65/2.55 | | | | | % 9.65/2.55 | | | | End of split % 9.65/2.55 | | | | % 9.65/2.55 | | | End of split % 9.65/2.55 | | | % 9.65/2.55 | | Case 2: % 9.65/2.55 | | | % 9.65/2.55 | | | (59) ? [v0: int] : ( ~ (v0 = 0) & member(all_13_1, all_13_2) = v0) % 9.65/2.55 | | | % 9.65/2.55 | | | DELTA: instantiating (59) with fresh symbol all_30_0 gives: % 9.65/2.55 | | | (60) ~ (all_30_0 = 0) & member(all_13_1, all_13_2) = all_30_0 % 9.65/2.55 | | | % 9.65/2.55 | | | ALPHA: (60) implies: % 9.65/2.55 | | | (61) ~ (all_30_0 = 0) % 9.65/2.55 | | | (62) member(all_13_1, all_13_2) = all_30_0 % 9.65/2.55 | | | % 9.65/2.55 | | | GROUND_INST: instantiating (4) with 0, all_30_0, all_13_2, all_13_1, % 9.65/2.55 | | | simplifying with (18), (62) gives: % 9.65/2.55 | | | (63) all_30_0 = 0 % 9.65/2.55 | | | % 9.65/2.55 | | | REDUCE: (61), (63) imply: % 9.65/2.55 | | | (64) $false % 9.65/2.55 | | | % 9.65/2.55 | | | CLOSE: (64) is inconsistent. % 9.65/2.55 | | | % 9.65/2.55 | | End of split % 9.65/2.55 | | % 9.65/2.55 | End of split % 9.65/2.55 | % 9.65/2.55 End of proof % 9.65/2.55 % SZS output end Proof for theBenchmark % 9.65/2.55 % 9.65/2.56 1913ms %------------------------------------------------------------------------------