%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET799+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 : n004.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 15:26:29 EDT 2023 % Result : Theorem 8.68s 2.16s % Output : Proof 10.97s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET799+4 : TPTP v8.1.2. Released v3.2.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.33 % Computer : n004.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 15:50:52 EDT 2023 % 0.12/0.33 % CPUTime : % 0.18/0.61 ________ _____ % 0.18/0.61 ___ __ \_________(_)________________________________ % 0.18/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.18/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.18/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.18/0.61 % 0.18/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.18/0.61 (2023-06-19) % 0.18/0.61 % 0.18/0.61 (c) Philipp Rümmer, 2009-2023 % 0.18/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.18/0.61 Amanda Stjerna. % 0.18/0.61 Free software under BSD-3-Clause. % 0.18/0.61 % 0.18/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.18/0.61 % 0.18/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.18/0.63 Running up to 7 provers in parallel. % 0.18/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.18/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.18/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.18/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.18/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.18/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.18/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.64/1.14 Prover 1: Preprocessing ... % 2.64/1.14 Prover 4: Preprocessing ... % 3.20/1.19 Prover 0: Preprocessing ... % 3.20/1.19 Prover 3: Preprocessing ... % 3.20/1.19 Prover 5: Preprocessing ... % 3.20/1.19 Prover 2: Preprocessing ... % 3.20/1.19 Prover 6: Preprocessing ... % 6.32/1.80 Prover 5: Proving ... % 6.93/1.84 Prover 2: Proving ... % 7.49/1.90 Prover 3: Constructing countermodel ... % 7.49/1.93 Prover 6: Proving ... % 7.49/1.95 Prover 1: Constructing countermodel ... % 8.68/2.15 Prover 3: proved (1513ms) % 8.68/2.16 % 8.68/2.16 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 8.68/2.16 % 8.68/2.16 Prover 2: stopped % 8.68/2.16 Prover 5: stopped % 8.68/2.17 Prover 6: stopped % 8.68/2.18 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 8.68/2.18 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 8.68/2.18 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 8.68/2.18 Prover 0: Proving ... % 8.68/2.18 Prover 0: stopped % 8.68/2.18 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 8.68/2.18 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 8.68/2.21 Prover 4: Constructing countermodel ... % 9.32/2.22 Prover 8: Preprocessing ... % 9.32/2.22 Prover 7: Preprocessing ... % 9.32/2.24 Prover 11: Preprocessing ... % 9.32/2.24 Prover 10: Preprocessing ... % 9.32/2.26 Prover 13: Preprocessing ... % 9.32/2.28 Prover 1: Found proof (size 26) % 9.84/2.30 Prover 1: proved (1645ms) % 9.84/2.30 Prover 4: stopped % 9.84/2.30 Prover 10: stopped % 9.84/2.31 Prover 7: stopped % 9.84/2.32 Prover 13: stopped % 9.84/2.34 Prover 11: stopped % 10.48/2.42 Prover 8: Warning: ignoring some quantifiers % 10.48/2.43 Prover 8: Constructing countermodel ... % 10.48/2.44 Prover 8: stopped % 10.48/2.44 % 10.48/2.44 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 10.48/2.44 % 10.48/2.45 % SZS output start Proof for theBenchmark % 10.48/2.45 Assumptions after simplification: % 10.48/2.45 --------------------------------- % 10.48/2.45 % 10.48/2.45 (least_upper_bound) % 10.48/2.48 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 10.48/2.48 | ~ (least_upper_bound(v0, v1, v2, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 10.48/2.48 $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: int] : ( ~ (v6 = 0) & % 10.48/2.48 upper_bound(v5, v2, v1) = 0 & apply(v2, v0, v5) = v6 & member(v5, v3) = 0 % 10.48/2.48 & $i(v5)) | ? [v5: any] : ? [v6: any] : (upper_bound(v0, v2, v1) = v6 & % 10.48/2.48 member(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v0: $i] : ! % 10.48/2.48 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (least_upper_bound(v0, v1, v2, v3) % 10.48/2.48 = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (upper_bound(v0, % 10.48/2.48 v2, v1) = 0 & member(v0, v1) = 0 & ! [v4: $i] : ( ~ (upper_bound(v4, % 10.48/2.48 v2, v1) = 0) | ~ $i(v4) | ? [v5: any] : ? [v6: any] : (apply(v2, % 10.48/2.48 v0, v4) = v6 & member(v4, v3) = v5 & ( ~ (v5 = 0) | v6 = 0))))) % 10.48/2.48 % 10.48/2.48 (subset) % 10.48/2.48 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) % 10.48/2.48 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & % 10.48/2.48 member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! % 10.48/2.48 [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : ( % 10.48/2.48 ~ (member(v2, v0) = 0) | ~ $i(v2) | member(v2, v1) = 0)) % 10.48/2.48 % 10.48/2.48 (thIV11) % 10.48/2.48 ? [v0: $i] : ? [v1: $i] : (order(v0, v1) = 0 & $i(v1) & $i(v0) & ? [v2: $i] % 10.48/2.48 : ? [v3: $i] : (subset(v3, v1) = 0 & subset(v2, v3) = 0 & subset(v2, v1) = % 10.48/2.48 0 & $i(v3) & $i(v2) & ? [v4: $i] : ? [v5: $i] : ? [v6: int] : ( ~ (v6 = % 10.48/2.48 0) & least_upper_bound(v5, v3, v0, v1) = 0 & least_upper_bound(v4, v2, % 10.48/2.48 v0, v1) = 0 & apply(v0, v4, v5) = v6 & $i(v5) & $i(v4)))) % 10.48/2.48 % 10.48/2.48 (upper_bound) % 10.48/2.48 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 10.48/2.48 (upper_bound(v2, v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 10.48/2.48 $i] : ? [v5: int] : ( ~ (v5 = 0) & apply(v0, v4, v2) = v5 & member(v4, % 10.48/2.48 v1) = 0 & $i(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 10.48/2.48 (upper_bound(v2, v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ! [v3: % 10.48/2.48 $i] : ! [v4: int] : (v4 = 0 | ~ (apply(v0, v3, v2) = v4) | ~ $i(v3) | % 10.48/2.48 ? [v5: int] : ( ~ (v5 = 0) & member(v3, v1) = v5))) % 10.48/2.48 % 10.48/2.48 (function-axioms) % 10.48/2.49 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 10.48/2.49 [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (greatest_lower_bound(v5, % 10.48/2.49 v4, v3, v2) = v1) | ~ (greatest_lower_bound(v5, v4, v3, v2) = v0)) & ! % 10.48/2.49 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 10.48/2.49 $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (least_upper_bound(v5, v4, % 10.48/2.49 v3, v2) = v1) | ~ (least_upper_bound(v5, v4, v3, v2) = v0)) & ! [v0: % 10.48/2.49 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 10.48/2.49 : ! [v4: $i] : (v1 = v0 | ~ (min(v4, v3, v2) = v1) | ~ (min(v4, v3, v2) = % 10.48/2.49 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 10.48/2.49 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (max(v4, v3, v2) = v1) | ~ % 10.48/2.49 (max(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 10.48/2.49 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 10.48/2.49 (least(v4, v3, v2) = v1) | ~ (least(v4, v3, v2) = v0)) & ! [v0: % 10.48/2.49 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 10.48/2.49 : ! [v4: $i] : (v1 = v0 | ~ (greatest(v4, v3, v2) = v1) | ~ (greatest(v4, % 10.48/2.49 v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] % 10.48/2.49 : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (lower_bound(v4, v3, % 10.48/2.49 v2) = v1) | ~ (lower_bound(v4, v3, v2) = v0)) & ! [v0: % 10.48/2.49 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 10.48/2.49 : ! [v4: $i] : (v1 = v0 | ~ (upper_bound(v4, v3, v2) = v1) | ~ % 10.48/2.49 (upper_bound(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 10.48/2.49 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 10.48/2.49 (apply(v4, v3, v2) = v1) | ~ (apply(v4, v3, v2) = v0)) & ! [v0: % 10.48/2.49 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 10.48/2.49 : (v1 = v0 | ~ (total_order(v3, v2) = v1) | ~ (total_order(v3, v2) = v0)) & % 10.48/2.49 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 10.48/2.49 $i] : (v1 = v0 | ~ (order(v3, v2) = v1) | ~ (order(v3, v2) = v0)) & ! % 10.48/2.49 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 10.48/2.49 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: % 10.48/2.49 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 10.48/2.49 (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : ! % 10.48/2.49 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ % 10.48/2.49 (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 10.48/2.49 $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = % 10.48/2.49 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 10.48/2.49 $i] : ! [v3: $i] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ % 10.48/2.49 (equal_set(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 10.48/2.49 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3, % 10.48/2.49 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 10.48/2.49 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 10.48/2.49 (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 10.48/2.49 $i] : ! [v2: $i] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = % 10.48/2.49 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sum(v2) = % 10.48/2.49 v1) | ~ (sum(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 10.48/2.49 v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : ! % 10.48/2.49 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ % 10.48/2.49 (power_set(v2) = v0)) % 10.48/2.49 % 10.48/2.49 Further assumptions not needed in the proof: % 10.48/2.49 -------------------------------------------- % 10.48/2.49 difference, empty_set, equal_set, greatest, greatest_lower_bound, intersection, % 10.48/2.49 least, lower_bound, max, min, order, power_set, product, singleton, sum, % 10.48/2.49 total_order, union, unordered_pair % 10.48/2.49 % 10.48/2.49 Those formulas are unsatisfiable: % 10.48/2.49 --------------------------------- % 10.48/2.49 % 10.48/2.49 Begin of proof % 10.48/2.49 | % 10.48/2.49 | ALPHA: (subset) implies: % 10.48/2.50 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ % 10.48/2.50 | $i(v0) | ! [v2: $i] : ( ~ (member(v2, v0) = 0) | ~ $i(v2) | % 10.48/2.50 | member(v2, v1) = 0)) % 10.48/2.50 | % 10.48/2.50 | ALPHA: (upper_bound) implies: % 10.48/2.50 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (upper_bound(v2, v0, v1) % 10.48/2.50 | = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ! [v3: $i] : ! [v4: % 10.48/2.50 | int] : (v4 = 0 | ~ (apply(v0, v3, v2) = v4) | ~ $i(v3) | ? [v5: % 10.48/2.50 | int] : ( ~ (v5 = 0) & member(v3, v1) = v5))) % 10.48/2.50 | % 10.48/2.50 | ALPHA: (least_upper_bound) implies: % 10.48/2.50 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 10.48/2.50 | (least_upper_bound(v0, v1, v2, v3) = 0) | ~ $i(v3) | ~ $i(v2) | ~ % 10.48/2.50 | $i(v1) | ~ $i(v0) | (upper_bound(v0, v2, v1) = 0 & member(v0, v1) = % 10.48/2.50 | 0 & ! [v4: $i] : ( ~ (upper_bound(v4, v2, v1) = 0) | ~ $i(v4) | % 10.48/2.50 | ? [v5: any] : ? [v6: any] : (apply(v2, v0, v4) = v6 & member(v4, % 10.48/2.50 | v3) = v5 & ( ~ (v5 = 0) | v6 = 0))))) % 10.48/2.50 | % 10.48/2.50 | ALPHA: (function-axioms) implies: % 10.48/2.50 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 10.48/2.50 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) % 10.48/2.50 | = v0)) % 10.48/2.50 | % 10.48/2.50 | DELTA: instantiating (thIV11) with fresh symbols all_25_0, all_25_1 gives: % 10.48/2.50 | (5) order(all_25_1, all_25_0) = 0 & $i(all_25_0) & $i(all_25_1) & ? [v0: % 10.48/2.50 | $i] : ? [v1: $i] : (subset(v1, all_25_0) = 0 & subset(v0, v1) = 0 & % 10.48/2.50 | subset(v0, all_25_0) = 0 & $i(v1) & $i(v0) & ? [v2: $i] : ? [v3: % 10.48/2.50 | $i] : ? [v4: int] : ( ~ (v4 = 0) & least_upper_bound(v3, v1, % 10.48/2.50 | all_25_1, all_25_0) = 0 & least_upper_bound(v2, v0, all_25_1, % 10.48/2.50 | all_25_0) = 0 & apply(all_25_1, v2, v3) = v4 & $i(v3) & $i(v2))) % 10.48/2.50 | % 10.48/2.50 | ALPHA: (5) implies: % 10.48/2.50 | (6) $i(all_25_1) % 10.48/2.50 | (7) $i(all_25_0) % 10.48/2.50 | (8) ? [v0: $i] : ? [v1: $i] : (subset(v1, all_25_0) = 0 & subset(v0, v1) % 10.48/2.50 | = 0 & subset(v0, all_25_0) = 0 & $i(v1) & $i(v0) & ? [v2: $i] : ? % 10.48/2.50 | [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & least_upper_bound(v3, v1, % 10.48/2.50 | all_25_1, all_25_0) = 0 & least_upper_bound(v2, v0, all_25_1, % 10.48/2.50 | all_25_0) = 0 & apply(all_25_1, v2, v3) = v4 & $i(v3) & $i(v2))) % 10.48/2.50 | % 10.48/2.50 | DELTA: instantiating (8) with fresh symbols all_27_0, all_27_1 gives: % 10.48/2.50 | (9) subset(all_27_0, all_25_0) = 0 & subset(all_27_1, all_27_0) = 0 & % 10.48/2.50 | subset(all_27_1, all_25_0) = 0 & $i(all_27_0) & $i(all_27_1) & ? [v0: % 10.48/2.50 | $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & % 10.48/2.50 | least_upper_bound(v1, all_27_0, all_25_1, all_25_0) = 0 & % 10.48/2.50 | least_upper_bound(v0, all_27_1, all_25_1, all_25_0) = 0 & % 10.48/2.50 | apply(all_25_1, v0, v1) = v2 & $i(v1) & $i(v0)) % 10.48/2.50 | % 10.48/2.50 | ALPHA: (9) implies: % 10.48/2.50 | (10) $i(all_27_1) % 10.48/2.50 | (11) $i(all_27_0) % 10.48/2.50 | (12) subset(all_27_1, all_27_0) = 0 % 10.48/2.51 | (13) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & % 10.48/2.51 | least_upper_bound(v1, all_27_0, all_25_1, all_25_0) = 0 & % 10.48/2.51 | least_upper_bound(v0, all_27_1, all_25_1, all_25_0) = 0 & % 10.48/2.51 | apply(all_25_1, v0, v1) = v2 & $i(v1) & $i(v0)) % 10.48/2.51 | % 10.48/2.51 | DELTA: instantiating (13) with fresh symbols all_29_0, all_29_1, all_29_2 % 10.48/2.51 | gives: % 10.48/2.51 | (14) ~ (all_29_0 = 0) & least_upper_bound(all_29_1, all_27_0, all_25_1, % 10.48/2.51 | all_25_0) = 0 & least_upper_bound(all_29_2, all_27_1, all_25_1, % 10.48/2.51 | all_25_0) = 0 & apply(all_25_1, all_29_2, all_29_1) = all_29_0 & % 10.48/2.51 | $i(all_29_1) & $i(all_29_2) % 10.48/2.51 | % 10.48/2.51 | ALPHA: (14) implies: % 10.48/2.51 | (15) ~ (all_29_0 = 0) % 10.48/2.51 | (16) $i(all_29_2) % 10.48/2.51 | (17) $i(all_29_1) % 10.48/2.51 | (18) apply(all_25_1, all_29_2, all_29_1) = all_29_0 % 10.48/2.51 | (19) least_upper_bound(all_29_2, all_27_1, all_25_1, all_25_0) = 0 % 10.48/2.51 | (20) least_upper_bound(all_29_1, all_27_0, all_25_1, all_25_0) = 0 % 10.48/2.51 | % 10.48/2.51 | GROUND_INST: instantiating (1) with all_27_1, all_27_0, simplifying with (10), % 10.48/2.51 | (11), (12) gives: % 10.48/2.51 | (21) ! [v0: $i] : ( ~ (member(v0, all_27_1) = 0) | ~ $i(v0) | member(v0, % 10.48/2.51 | all_27_0) = 0) % 10.48/2.51 | % 10.48/2.51 | GROUND_INST: instantiating (3) with all_29_2, all_27_1, all_25_1, all_25_0, % 10.48/2.51 | simplifying with (6), (7), (10), (16), (19) gives: % 10.48/2.51 | (22) upper_bound(all_29_2, all_25_1, all_27_1) = 0 & member(all_29_2, % 10.48/2.51 | all_27_1) = 0 & ! [v0: $i] : ( ~ (upper_bound(v0, all_25_1, % 10.48/2.51 | all_27_1) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: any] : % 10.48/2.51 | (apply(all_25_1, all_29_2, v0) = v2 & member(v0, all_25_0) = v1 & ( % 10.48/2.51 | ~ (v1 = 0) | v2 = 0))) % 10.48/2.51 | % 10.48/2.51 | ALPHA: (22) implies: % 10.48/2.51 | (23) member(all_29_2, all_27_1) = 0 % 10.48/2.51 | % 10.48/2.51 | GROUND_INST: instantiating (3) with all_29_1, all_27_0, all_25_1, all_25_0, % 10.48/2.51 | simplifying with (6), (7), (11), (17), (20) gives: % 10.48/2.51 | (24) upper_bound(all_29_1, all_25_1, all_27_0) = 0 & member(all_29_1, % 10.48/2.51 | all_27_0) = 0 & ! [v0: $i] : ( ~ (upper_bound(v0, all_25_1, % 10.48/2.51 | all_27_0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: any] : % 10.48/2.51 | (apply(all_25_1, all_29_1, v0) = v2 & member(v0, all_25_0) = v1 & ( % 10.48/2.51 | ~ (v1 = 0) | v2 = 0))) % 10.48/2.51 | % 10.48/2.51 | ALPHA: (24) implies: % 10.48/2.51 | (25) upper_bound(all_29_1, all_25_1, all_27_0) = 0 % 10.48/2.51 | % 10.48/2.51 | GROUND_INST: instantiating (21) with all_29_2, simplifying with (16), (23) % 10.48/2.51 | gives: % 10.48/2.51 | (26) member(all_29_2, all_27_0) = 0 % 10.48/2.51 | % 10.48/2.51 | GROUND_INST: instantiating (2) with all_25_1, all_27_0, all_29_1, simplifying % 10.48/2.51 | with (6), (11), (17), (25) gives: % 10.48/2.51 | (27) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (apply(all_25_1, v0, % 10.97/2.51 | all_29_1) = v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & % 10.97/2.51 | member(v0, all_27_0) = v2)) % 10.97/2.51 | % 10.97/2.51 | GROUND_INST: instantiating (27) with all_29_2, all_29_0, simplifying with % 10.97/2.51 | (16), (18) gives: % 10.97/2.51 | (28) all_29_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & member(all_29_2, % 10.97/2.51 | all_27_0) = v0) % 10.97/2.51 | % 10.97/2.51 | BETA: splitting (28) gives: % 10.97/2.51 | % 10.97/2.52 | Case 1: % 10.97/2.52 | | % 10.97/2.52 | | (29) all_29_0 = 0 % 10.97/2.52 | | % 10.97/2.52 | | REDUCE: (15), (29) imply: % 10.97/2.52 | | (30) $false % 10.97/2.52 | | % 10.97/2.52 | | CLOSE: (30) is inconsistent. % 10.97/2.52 | | % 10.97/2.52 | Case 2: % 10.97/2.52 | | % 10.97/2.52 | | (31) ? [v0: int] : ( ~ (v0 = 0) & member(all_29_2, all_27_0) = v0) % 10.97/2.52 | | % 10.97/2.52 | | DELTA: instantiating (31) with fresh symbol all_59_0 gives: % 10.97/2.52 | | (32) ~ (all_59_0 = 0) & member(all_29_2, all_27_0) = all_59_0 % 10.97/2.52 | | % 10.97/2.52 | | ALPHA: (32) implies: % 10.97/2.52 | | (33) ~ (all_59_0 = 0) % 10.97/2.52 | | (34) member(all_29_2, all_27_0) = all_59_0 % 10.97/2.52 | | % 10.97/2.52 | | GROUND_INST: instantiating (4) with 0, all_59_0, all_27_0, all_29_2, % 10.97/2.52 | | simplifying with (26), (34) gives: % 10.97/2.52 | | (35) all_59_0 = 0 % 10.97/2.52 | | % 10.97/2.52 | | REDUCE: (33), (35) imply: % 10.97/2.52 | | (36) $false % 10.97/2.52 | | % 10.97/2.52 | | CLOSE: (36) is inconsistent. % 10.97/2.52 | | % 10.97/2.52 | End of split % 10.97/2.52 | % 10.97/2.52 End of proof % 10.97/2.52 % SZS output end Proof for theBenchmark % 10.97/2.52 % 10.97/2.52 1906ms %------------------------------------------------------------------------------