%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWV370+1 : TPTP v8.1.2. Released v3.3.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n031.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 22:56:03 EDT 2023 % Result : Theorem 13.59s 2.66s % Output : Proof 17.48s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.12 % Problem : SWV370+1 : TPTP v8.1.2. Released v3.3.0. % 0.08/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n031.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 : Tue Aug 29 05:16:25 EDT 2023 % 0.13/0.34 % 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 ... % 0.20/0.65 Running up to 7 provers in parallel. % 0.20/0.67 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.67 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.67 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.67 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.67 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.67 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.67 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.69/1.33 Prover 1: Preprocessing ... % 3.69/1.33 Prover 4: Preprocessing ... % 3.69/1.37 Prover 6: Preprocessing ... % 3.69/1.37 Prover 0: Preprocessing ... % 3.69/1.37 Prover 5: Preprocessing ... % 3.69/1.37 Prover 2: Preprocessing ... % 3.69/1.37 Prover 3: Preprocessing ... % 9.46/2.12 Prover 1: Warning: ignoring some quantifiers % 10.51/2.20 Prover 3: Warning: ignoring some quantifiers % 10.51/2.21 Prover 6: Proving ... % 10.84/2.24 Prover 1: Constructing countermodel ... % 10.84/2.24 Prover 3: Constructing countermodel ... % 10.84/2.25 Prover 5: Proving ... % 10.84/2.28 Prover 2: Proving ... % 10.84/2.30 Prover 4: Constructing countermodel ... % 12.39/2.46 Prover 0: Proving ... % 13.59/2.66 Prover 3: proved (1989ms) % 13.59/2.66 % 13.59/2.66 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 13.59/2.66 % 13.59/2.67 Prover 2: stopped % 14.00/2.68 Prover 0: stopped % 14.00/2.68 Prover 6: stopped % 14.00/2.68 Prover 5: stopped % 14.00/2.69 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 14.00/2.69 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 14.00/2.69 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 14.00/2.69 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 14.00/2.69 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 14.56/2.76 Prover 7: Preprocessing ... % 14.69/2.78 Prover 8: Preprocessing ... % 14.69/2.79 Prover 11: Preprocessing ... % 14.69/2.80 Prover 13: Preprocessing ... % 14.69/2.81 Prover 10: Preprocessing ... % 15.74/2.92 Prover 1: Found proof (size 75) % 15.74/2.92 Prover 1: proved (2257ms) % 15.74/2.93 Prover 4: stopped % 15.74/2.94 Prover 13: stopped % 15.74/2.96 Prover 7: Warning: ignoring some quantifiers % 15.74/2.97 Prover 10: Warning: ignoring some quantifiers % 16.16/2.99 Prover 7: Constructing countermodel ... % 16.16/3.00 Prover 10: Constructing countermodel ... % 16.16/3.00 Prover 8: Warning: ignoring some quantifiers % 16.16/3.01 Prover 10: stopped % 16.16/3.02 Prover 8: Constructing countermodel ... % 16.16/3.03 Prover 7: stopped % 16.16/3.03 Prover 8: stopped % 16.69/3.12 Prover 11: Constructing countermodel ... % 16.69/3.14 Prover 11: stopped % 16.69/3.14 % 16.69/3.14 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 16.69/3.14 % 16.69/3.15 % SZS output start Proof for theBenchmark % 16.69/3.16 Assumptions after simplification: % 16.69/3.16 --------------------------------- % 16.69/3.16 % 16.69/3.16 (ax21) % 16.69/3.19 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 16.69/3.19 $i] : ! [v6: int] : (v6 = 0 | ~ (contains_slb(v5, v2) = v6) | ~ (pair(v1, % 16.69/3.19 v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ~ $i(v3) | ~ $i(v2) | ~ % 16.69/3.19 $i(v1) | ~ $i(v0) | ( ~ (v2 = v1) & ? [v7: int] : ( ~ (v7 = 0) & % 16.69/3.19 contains_slb(v0, v2) = v7))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 16.69/3.19 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v2 = v1 | ~ (contains_slb(v5, v2) % 16.69/3.19 = 0) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ~ $i(v3) | % 16.69/3.19 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | contains_slb(v0, v2) = 0) % 16.69/3.19 % 16.69/3.19 (ax37) % 16.69/3.19 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 16.69/3.19 $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (triple(v0, v6, v2) = v7) | ~ % 16.69/3.19 (pair(v3, v4) = v5) | ~ (insert_slb(v1, v5) = v6) | ~ $i(v4) | ~ $i(v3) | % 16.69/3.19 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v8: any] : ? [v9: any] : ? [v10: % 16.69/3.19 $i] : ? [v11: any] : (triple(v0, v1, v2) = v10 & check_cpq(v10) = v11 & % 16.69/3.19 check_cpq(v7) = v9 & less_than(v4, v3) = v8 & $i(v10) & ( ~ (v8 = 0) | (( % 16.69/3.19 ~ (v11 = 0) | v9 = 0) & ( ~ (v9 = 0) | v11 = 0))))) % 16.69/3.19 % 16.69/3.19 (ax39) % 16.69/3.19 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 16.69/3.19 int] : (v5 = 0 | ~ (contains_cpq(v4, v3) = v5) | ~ (triple(v0, v1, v2) = % 16.69/3.19 v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ( ~ % 16.69/3.19 (v6 = 0) & contains_slb(v1, v3) = v6)) & ! [v0: $i] : ! [v1: $i] : ! % 16.69/3.19 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (contains_cpq(v4, v3) = 0) | ~ % 16.69/3.19 (triple(v0, v1, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 16.69/3.19 contains_slb(v1, v3) = 0) % 16.69/3.19 % 16.69/3.19 (ax55) % 16.69/3.19 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 16.69/3.19 $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (triple(v0, v6, v2) = v7) | ~ % 16.69/3.19 (pair(v3, v4) = v5) | ~ (insert_slb(v1, v5) = v6) | ~ $i(v4) | ~ $i(v3) | % 16.69/3.19 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v8: $i] : ? [v9: $i] : ? [v10: $i] % 16.69/3.19 : (i(v9) = v10 & i(v7) = v8 & triple(v0, v1, v2) = v9 & insert_pq(v10, v3) = % 16.69/3.19 v8 & $i(v10) & $i(v9) & $i(v8))) % 16.69/3.20 % 16.69/3.20 (ax9) % 16.69/3.20 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 16.69/3.20 | ~ (contains_pq(v3, v2) = v4) | ~ (insert_pq(v0, v1) = v3) | ~ $i(v2) | % 16.69/3.20 ~ $i(v1) | ~ $i(v0) | ( ~ (v2 = v1) & ? [v5: int] : ( ~ (v5 = 0) & % 16.69/3.20 contains_pq(v0, v2) = v5))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 16.69/3.20 ! [v3: $i] : (v2 = v1 | ~ (contains_pq(v3, v2) = 0) | ~ (insert_pq(v0, v1) = % 16.69/3.20 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | contains_pq(v0, v2) = 0) % 16.69/3.20 % 16.69/3.20 (l6_co) % 16.69/3.20 ? [v0: $i] : ($i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] % 16.69/3.20 : ! [v5: $i] : ! [v6: int] : (v6 = 0 | ~ (i(v4) = v5) | ~ (triple(v1, % 16.69/3.20 v0, v2) = v4) | ~ (contains_pq(v5, v3) = v6) | ~ $i(v3) | ~ $i(v2) % 16.69/3.20 | ~ $i(v1) | ? [v7: int] : ( ~ (v7 = 0) & contains_cpq(v4, v3) = v7)) & % 16.69/3.20 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 16.69/3.20 (i(v4) = v5) | ~ (triple(v1, v0, v2) = v4) | ~ (contains_pq(v5, v3) = 0) % 16.69/3.20 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | contains_cpq(v4, v3) = 0) & ? [v1: % 16.69/3.20 $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] % 16.69/3.20 : ? [v7: $i] : ? [v8: $i] : ? [v9: any] : ? [v10: $i] : ? [v11: any] : % 16.69/3.20 (i(v8) = v10 & contains_cpq(v8, v5) = v9 & triple(v1, v7, v2) = v8 & % 16.69/3.20 pair(v3, v4) = v6 & insert_slb(v0, v6) = v7 & contains_pq(v10, v5) = v11 & % 16.69/3.20 $i(v10) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & % 16.69/3.20 $i(v1) & ((v11 = 0 & ~ (v9 = 0)) | (v9 = 0 & ~ (v11 = 0))))) % 16.69/3.20 % 16.69/3.20 (function-axioms) % 16.69/3.21 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 % 16.69/3.21 | ~ (triple(v4, v3, v2) = v1) | ~ (triple(v4, v3, v2) = v0)) & ! [v0: % 16.69/3.21 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 16.69/3.21 : ! [v4: $i] : (v1 = v0 | ~ (pair_in_list(v4, v3, v2) = v1) | ~ % 16.69/3.21 (pair_in_list(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 16.69/3.21 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 16.69/3.21 (pi_sharp_removemin(v3, v2) = v1) | ~ (pi_sharp_removemin(v3, v2) = v0)) & % 16.69/3.21 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 16.69/3.21 $i] : (v1 = v0 | ~ (pi_sharp_find_min(v3, v2) = v1) | ~ % 16.69/3.21 (pi_sharp_find_min(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 16.69/3.21 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 16.69/3.21 (pi_remove(v3, v2) = v1) | ~ (pi_remove(v3, v2) = v0)) & ! [v0: % 16.69/3.21 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 16.69/3.21 : (v1 = v0 | ~ (pi_sharp_remove(v3, v2) = v1) | ~ (pi_sharp_remove(v3, v2) = % 16.69/3.21 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 16.69/3.21 ~ (remove_pqp(v3, v2) = v1) | ~ (remove_pqp(v3, v2) = v0)) & ! [v0: $i] : % 16.69/3.21 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (insert_pqp(v3, v2) = % 16.69/3.21 v1) | ~ (insert_pqp(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 16.69/3.21 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 16.69/3.21 (contains_cpq(v3, v2) = v1) | ~ (contains_cpq(v3, v2) = v0)) & ! [v0: $i] % 16.69/3.21 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (remove_cpq(v3, v2) % 16.69/3.21 = v1) | ~ (remove_cpq(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 16.69/3.21 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (insert_cpq(v3, v2) = v1) | ~ % 16.69/3.21 (insert_cpq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 16.69/3.21 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (succ_cpq(v3, % 16.69/3.21 v2) = v1) | ~ (succ_cpq(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 16.69/3.21 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (update_slb(v3, v2) = v1) | ~ % 16.69/3.21 (update_slb(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 16.69/3.21 [v3: $i] : (v1 = v0 | ~ (lookup_slb(v3, v2) = v1) | ~ (lookup_slb(v3, v2) = % 16.69/3.21 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 16.69/3.21 ~ (remove_slb(v3, v2) = v1) | ~ (remove_slb(v3, v2) = v0)) & ! [v0: % 16.69/3.21 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 16.69/3.21 : (v1 = v0 | ~ (contains_slb(v3, v2) = v1) | ~ (contains_slb(v3, v2) = v0)) % 16.69/3.21 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 16.69/3.21 (pair(v3, v2) = v1) | ~ (pair(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 16.69/3.21 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (insert_slb(v3, v2) = v1) | ~ % 16.69/3.21 (insert_slb(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 16.69/3.21 [v3: $i] : (v1 = v0 | ~ (removemin_pq_res(v3, v2) = v1) | ~ % 16.69/3.21 (removemin_pq_res(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 16.69/3.21 ! [v3: $i] : (v1 = v0 | ~ (removemin_pq_eff(v3, v2) = v1) | ~ % 16.69/3.21 (removemin_pq_eff(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 16.69/3.21 ! [v3: $i] : (v1 = v0 | ~ (findmin_pq_res(v3, v2) = v1) | ~ % 16.69/3.21 (findmin_pq_res(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 16.69/3.21 ! [v3: $i] : (v1 = v0 | ~ (findmin_pq_eff(v3, v2) = v1) | ~ % 16.69/3.21 (findmin_pq_eff(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 16.69/3.21 ! [v3: $i] : (v1 = v0 | ~ (remove_pq(v3, v2) = v1) | ~ (remove_pq(v3, v2) = % 16.69/3.21 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 16.69/3.21 $i] : ! [v3: $i] : (v1 = v0 | ~ (issmallestelement_pq(v3, v2) = v1) | ~ % 16.69/3.21 (issmallestelement_pq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 16.69/3.21 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 16.69/3.21 (contains_pq(v3, v2) = v1) | ~ (contains_pq(v3, v2) = v0)) & ! [v0: $i] : % 16.69/3.21 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (insert_pq(v3, v2) = % 16.69/3.21 v1) | ~ (insert_pq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 16.69/3.21 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 16.69/3.21 (strictly_less_than(v3, v2) = v1) | ~ (strictly_less_than(v3, v2) = v0)) & % 16.69/3.21 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 16.69/3.21 $i] : (v1 = v0 | ~ (less_than(v3, v2) = v1) | ~ (less_than(v3, v2) = v0)) % 16.69/3.21 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 % 16.69/3.21 = v0 | ~ (phi(v2) = v1) | ~ (phi(v2) = v0)) & ! [v0: MultipleValueBool] : % 16.69/3.21 ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (pi_removemin(v2) = % 16.69/3.21 v1) | ~ (pi_removemin(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 16.69/3.21 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (pi_find_min(v2) = v1) | ~ % 16.69/3.21 (pi_find_min(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 % 16.69/3.21 | ~ (i(v2) = v1) | ~ (i(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 16.69/3.21 $i] : (v1 = v0 | ~ (removemin_cpq_res(v2) = v1) | ~ (removemin_cpq_res(v2) % 16.69/3.21 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 16.69/3.21 (findmin_cpq_res(v2) = v1) | ~ (findmin_cpq_res(v2) = v0)) & ! [v0: $i] : % 16.69/3.21 ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (findmin_pqp_res(v2) = v1) | ~ % 16.69/3.21 (findmin_pqp_res(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 16.69/3.21 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (ok(v2) = v1) | ~ (ok(v2) % 16.69/3.21 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 16.69/3.21 $i] : (v1 = v0 | ~ (check_cpq(v2) = v1) | ~ (check_cpq(v2) = v0)) & ! % 16.69/3.21 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (removemin_cpq_eff(v2) = % 16.69/3.21 v1) | ~ (removemin_cpq_eff(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 16.69/3.21 [v2: $i] : (v1 = v0 | ~ (findmin_cpq_eff(v2) = v1) | ~ (findmin_cpq_eff(v2) % 16.69/3.21 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 16.69/3.21 $i] : (v1 = v0 | ~ (isnonempty_slb(v2) = v1) | ~ (isnonempty_slb(v2) = % 16.69/3.21 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 16.69/3.21 $i] : (v1 = v0 | ~ (isnonempty_pq(v2) = v1) | ~ (isnonempty_pq(v2) = v0)) % 16.69/3.21 % 16.69/3.21 Further assumptions not needed in the proof: % 16.69/3.21 -------------------------------------------- % 16.69/3.21 ax10, ax11, ax12, ax13, ax14, ax15, ax16, ax17, ax18, ax19, ax20, ax22, ax23, % 16.69/3.21 ax24, ax25, ax26, ax27, ax28, ax29, ax30, ax31, ax32, ax33, ax34, ax35, ax36, % 16.69/3.21 ax38, ax40, ax41, ax42, ax43, ax44, ax45, ax46, ax47, ax48, ax49, ax50, ax51, % 16.69/3.21 ax52, ax53, ax54, ax56, ax57, ax58, ax59, ax6, ax60, ax61, ax62, ax7, ax8, % 16.69/3.21 bottom_smallest, reflexivity, stricly_smaller_definition, totality, transitivity % 16.69/3.21 % 16.69/3.21 Those formulas are unsatisfiable: % 16.69/3.21 --------------------------------- % 16.69/3.21 % 16.69/3.21 Begin of proof % 16.69/3.21 | % 16.69/3.21 | ALPHA: (ax9) implies: % 16.69/3.22 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v2 = v1 | ~ % 16.69/3.22 | (contains_pq(v3, v2) = 0) | ~ (insert_pq(v0, v1) = v3) | ~ $i(v2) | % 16.69/3.22 | ~ $i(v1) | ~ $i(v0) | contains_pq(v0, v2) = 0) % 16.69/3.22 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 16.69/3.22 | (v4 = 0 | ~ (contains_pq(v3, v2) = v4) | ~ (insert_pq(v0, v1) = v3) | % 16.69/3.22 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ( ~ (v2 = v1) & ? [v5: int] : ( % 16.69/3.22 | ~ (v5 = 0) & contains_pq(v0, v2) = v5))) % 16.69/3.22 | % 16.69/3.22 | ALPHA: (ax21) implies: % 16.69/3.22 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 16.69/3.22 | ! [v5: $i] : (v2 = v1 | ~ (contains_slb(v5, v2) = 0) | ~ (pair(v1, % 16.69/3.22 | v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ~ $i(v3) | ~ $i(v2) % 16.69/3.22 | | ~ $i(v1) | ~ $i(v0) | contains_slb(v0, v2) = 0) % 16.69/3.22 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 16.69/3.22 | ! [v5: $i] : ! [v6: int] : (v6 = 0 | ~ (contains_slb(v5, v2) = v6) | % 16.69/3.22 | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ~ $i(v3) | ~ % 16.69/3.22 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ( ~ (v2 = v1) & ? [v7: int] : ( ~ % 16.69/3.22 | (v7 = 0) & contains_slb(v0, v2) = v7))) % 16.69/3.22 | % 16.69/3.22 | ALPHA: (ax39) implies: % 17.00/3.22 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 17.00/3.22 | ~ (contains_cpq(v4, v3) = 0) | ~ (triple(v0, v1, v2) = v4) | ~ % 17.00/3.22 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | contains_slb(v1, v3) = % 17.00/3.22 | 0) % 17.00/3.22 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 17.00/3.22 | ! [v5: int] : (v5 = 0 | ~ (contains_cpq(v4, v3) = v5) | ~ (triple(v0, % 17.00/3.22 | v1, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 17.00/3.22 | ? [v6: int] : ( ~ (v6 = 0) & contains_slb(v1, v3) = v6)) % 17.00/3.22 | % 17.00/3.22 | ALPHA: (function-axioms) implies: % 17.00/3.22 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (i(v2) = v1) | % 17.00/3.22 | ~ (i(v2) = v0)) % 17.00/3.22 | (8) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 17.00/3.22 | ! [v3: $i] : (v1 = v0 | ~ (contains_slb(v3, v2) = v1) | ~ % 17.00/3.22 | (contains_slb(v3, v2) = v0)) % 17.00/3.22 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 17.00/3.22 | (v1 = v0 | ~ (triple(v4, v3, v2) = v1) | ~ (triple(v4, v3, v2) = v0)) % 17.00/3.22 | % 17.00/3.22 | DELTA: instantiating (l6_co) with fresh symbol all_72_0 gives: % 17.00/3.22 | (10) $i(all_72_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 17.00/3.22 | ! [v4: $i] : ! [v5: int] : (v5 = 0 | ~ (i(v3) = v4) | ~ % 17.00/3.22 | (triple(v0, all_72_0, v1) = v3) | ~ (contains_pq(v4, v2) = v5) | ~ % 17.00/3.22 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ( ~ (v6 = 0) & % 17.00/3.22 | contains_cpq(v3, v2) = v6)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 17.00/3.22 | $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (i(v3) = v4) | ~ (triple(v0, % 17.00/3.22 | all_72_0, v1) = v3) | ~ (contains_pq(v4, v2) = 0) | ~ $i(v2) | % 17.00/3.22 | ~ $i(v1) | ~ $i(v0) | contains_cpq(v3, v2) = 0) & ? [v0: $i] : ? % 17.00/3.22 | [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? % 17.00/3.22 | [v6: $i] : ? [v7: $i] : ? [v8: any] : ? [v9: $i] : ? [v10: any] : % 17.00/3.22 | (i(v7) = v9 & contains_cpq(v7, v4) = v8 & triple(v0, v6, v1) = v7 & % 17.00/3.22 | pair(v2, v3) = v5 & insert_slb(all_72_0, v5) = v6 & contains_pq(v9, % 17.00/3.22 | v4) = v10 & $i(v9) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & % 17.00/3.23 | $i(v2) & $i(v1) & $i(v0) & ((v10 = 0 & ~ (v8 = 0)) | (v8 = 0 & ~ % 17.00/3.23 | (v10 = 0)))) % 17.00/3.23 | % 17.00/3.23 | ALPHA: (10) implies: % 17.00/3.23 | (11) $i(all_72_0) % 17.00/3.23 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 17.00/3.23 | ( ~ (i(v3) = v4) | ~ (triple(v0, all_72_0, v1) = v3) | ~ % 17.00/3.23 | (contains_pq(v4, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 17.00/3.23 | contains_cpq(v3, v2) = 0) % 17.00/3.23 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 17.00/3.23 | ! [v5: int] : (v5 = 0 | ~ (i(v3) = v4) | ~ (triple(v0, all_72_0, v1) % 17.00/3.23 | = v3) | ~ (contains_pq(v4, v2) = v5) | ~ $i(v2) | ~ $i(v1) | ~ % 17.00/3.23 | $i(v0) | ? [v6: int] : ( ~ (v6 = 0) & contains_cpq(v3, v2) = v6)) % 17.00/3.23 | (14) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 17.00/3.23 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: any] : ? [v9: $i] : % 17.00/3.23 | ? [v10: any] : (i(v7) = v9 & contains_cpq(v7, v4) = v8 & triple(v0, % 17.00/3.23 | v6, v1) = v7 & pair(v2, v3) = v5 & insert_slb(all_72_0, v5) = v6 & % 17.00/3.23 | contains_pq(v9, v4) = v10 & $i(v9) & $i(v7) & $i(v6) & $i(v5) & % 17.00/3.23 | $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ((v10 = 0 & ~ (v8 = % 17.00/3.23 | 0)) | (v8 = 0 & ~ (v10 = 0)))) % 17.00/3.23 | % 17.00/3.23 | DELTA: instantiating (14) with fresh symbols all_75_0, all_75_1, all_75_2, % 17.00/3.23 | all_75_3, all_75_4, all_75_5, all_75_6, all_75_7, all_75_8, all_75_9, % 17.00/3.23 | all_75_10 gives: % 17.00/3.23 | (15) i(all_75_3) = all_75_1 & contains_cpq(all_75_3, all_75_6) = all_75_2 & % 17.00/3.23 | triple(all_75_10, all_75_4, all_75_9) = all_75_3 & pair(all_75_8, % 17.00/3.23 | all_75_7) = all_75_5 & insert_slb(all_72_0, all_75_5) = all_75_4 & % 17.00/3.23 | contains_pq(all_75_1, all_75_6) = all_75_0 & $i(all_75_1) & % 17.00/3.23 | $i(all_75_3) & $i(all_75_4) & $i(all_75_5) & $i(all_75_6) & % 17.00/3.23 | $i(all_75_7) & $i(all_75_8) & $i(all_75_9) & $i(all_75_10) & % 17.00/3.23 | ((all_75_0 = 0 & ~ (all_75_2 = 0)) | (all_75_2 = 0 & ~ (all_75_0 = % 17.00/3.23 | 0))) % 17.00/3.23 | % 17.00/3.23 | ALPHA: (15) implies: % 17.00/3.23 | (16) $i(all_75_10) % 17.00/3.23 | (17) $i(all_75_9) % 17.00/3.23 | (18) $i(all_75_8) % 17.00/3.23 | (19) $i(all_75_7) % 17.00/3.23 | (20) $i(all_75_6) % 17.00/3.23 | (21) $i(all_75_4) % 17.00/3.23 | (22) contains_pq(all_75_1, all_75_6) = all_75_0 % 17.00/3.23 | (23) insert_slb(all_72_0, all_75_5) = all_75_4 % 17.00/3.23 | (24) pair(all_75_8, all_75_7) = all_75_5 % 17.00/3.23 | (25) triple(all_75_10, all_75_4, all_75_9) = all_75_3 % 17.00/3.23 | (26) contains_cpq(all_75_3, all_75_6) = all_75_2 % 17.00/3.23 | (27) i(all_75_3) = all_75_1 % 17.00/3.23 | (28) (all_75_0 = 0 & ~ (all_75_2 = 0)) | (all_75_2 = 0 & ~ (all_75_0 = % 17.00/3.23 | 0)) % 17.00/3.23 | % 17.00/3.23 | GROUND_INST: instantiating (ax37) with all_75_10, all_72_0, all_75_9, % 17.00/3.23 | all_75_8, all_75_7, all_75_5, all_75_4, all_75_3, simplifying % 17.00/3.23 | with (11), (16), (17), (18), (19), (23), (24), (25) gives: % 17.00/3.23 | (29) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: any] : % 17.00/3.23 | (triple(all_75_10, all_72_0, all_75_9) = v2 & check_cpq(v2) = v3 & % 17.00/3.23 | check_cpq(all_75_3) = v1 & less_than(all_75_7, all_75_8) = v0 & % 17.00/3.23 | $i(v2) & ( ~ (v0 = 0) | (( ~ (v3 = 0) | v1 = 0) & ( ~ (v1 = 0) | v3 % 17.00/3.23 | = 0)))) % 17.00/3.23 | % 17.00/3.23 | GROUND_INST: instantiating (ax55) with all_75_10, all_72_0, all_75_9, % 17.00/3.23 | all_75_8, all_75_7, all_75_5, all_75_4, all_75_3, simplifying % 17.00/3.23 | with (11), (16), (17), (18), (19), (23), (24), (25) gives: % 17.00/3.24 | (30) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (i(v1) = v2 & i(all_75_3) = % 17.00/3.24 | v0 & triple(all_75_10, all_72_0, all_75_9) = v1 & insert_pq(v2, % 17.00/3.24 | all_75_8) = v0 & $i(v2) & $i(v1) & $i(v0)) % 17.00/3.24 | % 17.00/3.24 | GROUND_INST: instantiating (6) with all_75_10, all_75_4, all_75_9, all_75_6, % 17.00/3.24 | all_75_3, all_75_2, simplifying with (16), (17), (20), (21), % 17.00/3.24 | (25), (26) gives: % 17.00/3.24 | (31) all_75_2 = 0 | ? [v0: int] : ( ~ (v0 = 0) & contains_slb(all_75_4, % 17.00/3.24 | all_75_6) = v0) % 17.00/3.24 | % 17.00/3.24 | DELTA: instantiating (30) with fresh symbols all_85_0, all_85_1, all_85_2 % 17.00/3.24 | gives: % 17.00/3.24 | (32) i(all_85_1) = all_85_0 & i(all_75_3) = all_85_2 & triple(all_75_10, % 17.00/3.24 | all_72_0, all_75_9) = all_85_1 & insert_pq(all_85_0, all_75_8) = % 17.00/3.24 | all_85_2 & $i(all_85_0) & $i(all_85_1) & $i(all_85_2) % 17.00/3.24 | % 17.00/3.24 | ALPHA: (32) implies: % 17.00/3.24 | (33) $i(all_85_0) % 17.00/3.24 | (34) insert_pq(all_85_0, all_75_8) = all_85_2 % 17.00/3.24 | (35) triple(all_75_10, all_72_0, all_75_9) = all_85_1 % 17.00/3.24 | (36) i(all_75_3) = all_85_2 % 17.00/3.24 | (37) i(all_85_1) = all_85_0 % 17.00/3.24 | % 17.00/3.24 | DELTA: instantiating (29) with fresh symbols all_87_0, all_87_1, all_87_2, % 17.00/3.24 | all_87_3 gives: % 17.00/3.24 | (38) triple(all_75_10, all_72_0, all_75_9) = all_87_1 & check_cpq(all_87_1) % 17.00/3.24 | = all_87_0 & check_cpq(all_75_3) = all_87_2 & less_than(all_75_7, % 17.00/3.24 | all_75_8) = all_87_3 & $i(all_87_1) & ( ~ (all_87_3 = 0) | (( ~ % 17.00/3.24 | (all_87_0 = 0) | all_87_2 = 0) & ( ~ (all_87_2 = 0) | all_87_0 = % 17.00/3.24 | 0))) % 17.00/3.24 | % 17.00/3.24 | ALPHA: (38) implies: % 17.00/3.24 | (39) triple(all_75_10, all_72_0, all_75_9) = all_87_1 % 17.00/3.24 | % 17.00/3.24 | GROUND_INST: instantiating (9) with all_85_1, all_87_1, all_75_9, all_72_0, % 17.00/3.24 | all_75_10, simplifying with (35), (39) gives: % 17.00/3.24 | (40) all_87_1 = all_85_1 % 17.00/3.24 | % 17.00/3.24 | GROUND_INST: instantiating (7) with all_75_1, all_85_2, all_75_3, simplifying % 17.00/3.24 | with (27), (36) gives: % 17.00/3.24 | (41) all_85_2 = all_75_1 % 17.00/3.24 | % 17.00/3.24 | REDUCE: (34), (41) imply: % 17.00/3.24 | (42) insert_pq(all_85_0, all_75_8) = all_75_1 % 17.00/3.24 | % 17.00/3.24 | GROUND_INST: instantiating (2) with all_85_0, all_75_8, all_75_6, all_75_1, % 17.00/3.24 | all_75_0, simplifying with (18), (20), (22), (33), (42) gives: % 17.00/3.24 | (43) all_75_0 = 0 | ( ~ (all_75_6 = all_75_8) & ? [v0: int] : ( ~ (v0 = 0) % 17.00/3.24 | & contains_pq(all_85_0, all_75_6) = v0)) % 17.00/3.24 | % 17.00/3.24 | BETA: splitting (28) gives: % 17.00/3.24 | % 17.48/3.24 | Case 1: % 17.48/3.24 | | % 17.48/3.24 | | (44) all_75_0 = 0 & ~ (all_75_2 = 0) % 17.48/3.24 | | % 17.48/3.24 | | ALPHA: (44) implies: % 17.48/3.24 | | (45) all_75_0 = 0 % 17.48/3.24 | | (46) ~ (all_75_2 = 0) % 17.48/3.24 | | % 17.48/3.24 | | REDUCE: (22), (45) imply: % 17.48/3.24 | | (47) contains_pq(all_75_1, all_75_6) = 0 % 17.48/3.24 | | % 17.48/3.24 | | BETA: splitting (31) gives: % 17.48/3.24 | | % 17.48/3.24 | | Case 1: % 17.48/3.24 | | | % 17.48/3.24 | | | (48) all_75_2 = 0 % 17.48/3.24 | | | % 17.48/3.24 | | | REDUCE: (46), (48) imply: % 17.48/3.24 | | | (49) $false % 17.48/3.24 | | | % 17.48/3.24 | | | CLOSE: (49) is inconsistent. % 17.48/3.24 | | | % 17.48/3.24 | | Case 2: % 17.48/3.24 | | | % 17.48/3.25 | | | (50) ? [v0: int] : ( ~ (v0 = 0) & contains_slb(all_75_4, all_75_6) = % 17.48/3.25 | | | v0) % 17.48/3.25 | | | % 17.48/3.25 | | | DELTA: instantiating (50) with fresh symbol all_110_0 gives: % 17.48/3.25 | | | (51) ~ (all_110_0 = 0) & contains_slb(all_75_4, all_75_6) = all_110_0 % 17.48/3.25 | | | % 17.48/3.25 | | | ALPHA: (51) implies: % 17.48/3.25 | | | (52) ~ (all_110_0 = 0) % 17.48/3.25 | | | (53) contains_slb(all_75_4, all_75_6) = all_110_0 % 17.48/3.25 | | | % 17.48/3.25 | | | GROUND_INST: instantiating (1) with all_85_0, all_75_8, all_75_6, % 17.48/3.25 | | | all_75_1, simplifying with (18), (20), (33), (42), (47) % 17.48/3.25 | | | gives: % 17.48/3.25 | | | (54) all_75_6 = all_75_8 | contains_pq(all_85_0, all_75_6) = 0 % 17.48/3.25 | | | % 17.48/3.25 | | | GROUND_INST: instantiating (4) with all_72_0, all_75_8, all_75_6, % 17.48/3.25 | | | all_75_7, all_75_5, all_75_4, all_110_0, simplifying with % 17.48/3.25 | | | (11), (18), (19), (20), (23), (24), (53) gives: % 17.48/3.25 | | | (55) all_110_0 = 0 | ( ~ (all_75_6 = all_75_8) & ? [v0: int] : ( ~ (v0 % 17.48/3.25 | | | = 0) & contains_slb(all_72_0, all_75_6) = v0)) % 17.48/3.25 | | | % 17.48/3.25 | | | BETA: splitting (55) gives: % 17.48/3.25 | | | % 17.48/3.25 | | | Case 1: % 17.48/3.25 | | | | % 17.48/3.25 | | | | (56) all_110_0 = 0 % 17.48/3.25 | | | | % 17.48/3.25 | | | | REDUCE: (52), (56) imply: % 17.48/3.25 | | | | (57) $false % 17.48/3.25 | | | | % 17.48/3.25 | | | | CLOSE: (57) is inconsistent. % 17.48/3.25 | | | | % 17.48/3.25 | | | Case 2: % 17.48/3.25 | | | | % 17.48/3.25 | | | | (58) ~ (all_75_6 = all_75_8) & ? [v0: int] : ( ~ (v0 = 0) & % 17.48/3.25 | | | | contains_slb(all_72_0, all_75_6) = v0) % 17.48/3.25 | | | | % 17.48/3.25 | | | | ALPHA: (58) implies: % 17.48/3.25 | | | | (59) ~ (all_75_6 = all_75_8) % 17.48/3.25 | | | | (60) ? [v0: int] : ( ~ (v0 = 0) & contains_slb(all_72_0, all_75_6) = % 17.48/3.25 | | | | v0) % 17.48/3.25 | | | | % 17.48/3.25 | | | | BETA: splitting (54) gives: % 17.48/3.25 | | | | % 17.48/3.25 | | | | Case 1: % 17.48/3.25 | | | | | % 17.48/3.25 | | | | | (61) contains_pq(all_85_0, all_75_6) = 0 % 17.48/3.25 | | | | | % 17.48/3.25 | | | | | GROUND_INST: instantiating (12) with all_75_10, all_75_9, all_75_6, % 17.48/3.25 | | | | | all_85_1, all_85_0, simplifying with (16), (17), (20), % 17.48/3.25 | | | | | (35), (37), (61) gives: % 17.48/3.25 | | | | | (62) contains_cpq(all_85_1, all_75_6) = 0 % 17.48/3.25 | | | | | % 17.48/3.25 | | | | | GROUND_INST: instantiating (5) with all_75_10, all_72_0, all_75_9, % 17.48/3.25 | | | | | all_75_6, all_85_1, simplifying with (11), (16), (17), % 17.48/3.25 | | | | | (20), (35), (62) gives: % 17.48/3.25 | | | | | (63) contains_slb(all_72_0, all_75_6) = 0 % 17.48/3.25 | | | | | % 17.48/3.25 | | | | | DELTA: instantiating (60) with fresh symbol all_139_0 gives: % 17.48/3.25 | | | | | (64) ~ (all_139_0 = 0) & contains_slb(all_72_0, all_75_6) = % 17.48/3.25 | | | | | all_139_0 % 17.48/3.25 | | | | | % 17.48/3.25 | | | | | REF_CLOSE: (8), (63), (64) are inconsistent by sub-proof #1. % 17.48/3.25 | | | | | % 17.48/3.25 | | | | Case 2: % 17.48/3.25 | | | | | % 17.48/3.25 | | | | | (65) all_75_6 = all_75_8 % 17.48/3.25 | | | | | % 17.48/3.25 | | | | | REDUCE: (59), (65) imply: % 17.48/3.25 | | | | | (66) $false % 17.48/3.25 | | | | | % 17.48/3.25 | | | | | CLOSE: (66) is inconsistent. % 17.48/3.25 | | | | | % 17.48/3.25 | | | | End of split % 17.48/3.25 | | | | % 17.48/3.25 | | | End of split % 17.48/3.25 | | | % 17.48/3.25 | | End of split % 17.48/3.25 | | % 17.48/3.25 | Case 2: % 17.48/3.25 | | % 17.48/3.25 | | (67) all_75_2 = 0 & ~ (all_75_0 = 0) % 17.48/3.25 | | % 17.48/3.25 | | ALPHA: (67) implies: % 17.48/3.25 | | (68) all_75_2 = 0 % 17.48/3.25 | | (69) ~ (all_75_0 = 0) % 17.48/3.25 | | % 17.48/3.25 | | REDUCE: (26), (68) imply: % 17.48/3.25 | | (70) contains_cpq(all_75_3, all_75_6) = 0 % 17.48/3.25 | | % 17.48/3.25 | | BETA: splitting (43) gives: % 17.48/3.25 | | % 17.48/3.25 | | Case 1: % 17.48/3.25 | | | % 17.48/3.25 | | | (71) all_75_0 = 0 % 17.48/3.25 | | | % 17.48/3.25 | | | REDUCE: (69), (71) imply: % 17.48/3.25 | | | (72) $false % 17.48/3.25 | | | % 17.48/3.25 | | | CLOSE: (72) is inconsistent. % 17.48/3.25 | | | % 17.48/3.25 | | Case 2: % 17.48/3.25 | | | % 17.48/3.25 | | | (73) ~ (all_75_6 = all_75_8) & ? [v0: int] : ( ~ (v0 = 0) & % 17.48/3.25 | | | contains_pq(all_85_0, all_75_6) = v0) % 17.48/3.25 | | | % 17.48/3.25 | | | ALPHA: (73) implies: % 17.48/3.25 | | | (74) ~ (all_75_6 = all_75_8) % 17.48/3.25 | | | (75) ? [v0: int] : ( ~ (v0 = 0) & contains_pq(all_85_0, all_75_6) = % 17.48/3.25 | | | v0) % 17.48/3.25 | | | % 17.48/3.25 | | | DELTA: instantiating (75) with fresh symbol all_110_0 gives: % 17.48/3.25 | | | (76) ~ (all_110_0 = 0) & contains_pq(all_85_0, all_75_6) = all_110_0 % 17.48/3.25 | | | % 17.48/3.25 | | | ALPHA: (76) implies: % 17.48/3.26 | | | (77) ~ (all_110_0 = 0) % 17.48/3.26 | | | (78) contains_pq(all_85_0, all_75_6) = all_110_0 % 17.48/3.26 | | | % 17.48/3.26 | | | GROUND_INST: instantiating (13) with all_75_10, all_75_9, all_75_6, % 17.48/3.26 | | | all_85_1, all_85_0, all_110_0, simplifying with (16), (17), % 17.48/3.26 | | | (20), (35), (37), (78) gives: % 17.48/3.26 | | | (79) all_110_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & % 17.48/3.26 | | | contains_cpq(all_85_1, all_75_6) = v0) % 17.48/3.26 | | | % 17.48/3.26 | | | GROUND_INST: instantiating (5) with all_75_10, all_75_4, all_75_9, % 17.48/3.26 | | | all_75_6, all_75_3, simplifying with (16), (17), (20), (21), % 17.48/3.26 | | | (25), (70) gives: % 17.48/3.26 | | | (80) contains_slb(all_75_4, all_75_6) = 0 % 17.48/3.26 | | | % 17.48/3.26 | | | BETA: splitting (79) gives: % 17.48/3.26 | | | % 17.48/3.26 | | | Case 1: % 17.48/3.26 | | | | % 17.48/3.26 | | | | (81) all_110_0 = 0 % 17.48/3.26 | | | | % 17.48/3.26 | | | | REDUCE: (77), (81) imply: % 17.48/3.26 | | | | (82) $false % 17.48/3.26 | | | | % 17.48/3.26 | | | | CLOSE: (82) is inconsistent. % 17.48/3.26 | | | | % 17.48/3.26 | | | Case 2: % 17.48/3.26 | | | | % 17.48/3.26 | | | | (83) ? [v0: int] : ( ~ (v0 = 0) & contains_cpq(all_85_1, all_75_6) = % 17.48/3.26 | | | | v0) % 17.48/3.26 | | | | % 17.48/3.26 | | | | DELTA: instantiating (83) with fresh symbol all_122_0 gives: % 17.48/3.26 | | | | (84) ~ (all_122_0 = 0) & contains_cpq(all_85_1, all_75_6) = % 17.48/3.26 | | | | all_122_0 % 17.48/3.26 | | | | % 17.48/3.26 | | | | ALPHA: (84) implies: % 17.48/3.26 | | | | (85) ~ (all_122_0 = 0) % 17.48/3.26 | | | | (86) contains_cpq(all_85_1, all_75_6) = all_122_0 % 17.48/3.26 | | | | % 17.48/3.26 | | | | GROUND_INST: instantiating (3) with all_72_0, all_75_8, all_75_6, % 17.48/3.26 | | | | all_75_7, all_75_5, all_75_4, simplifying with (11), (18), % 17.48/3.26 | | | | (19), (20), (23), (24), (80) gives: % 17.48/3.26 | | | | (87) all_75_6 = all_75_8 | contains_slb(all_72_0, all_75_6) = 0 % 17.48/3.26 | | | | % 17.48/3.26 | | | | GROUND_INST: instantiating (6) with all_75_10, all_72_0, all_75_9, % 17.48/3.26 | | | | all_75_6, all_85_1, all_122_0, simplifying with (11), (16), % 17.48/3.26 | | | | (17), (20), (35), (86) gives: % 17.48/3.26 | | | | (88) all_122_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & % 17.48/3.26 | | | | contains_slb(all_72_0, all_75_6) = v0) % 17.48/3.26 | | | | % 17.48/3.26 | | | | BETA: splitting (87) gives: % 17.48/3.26 | | | | % 17.48/3.26 | | | | Case 1: % 17.48/3.26 | | | | | % 17.48/3.26 | | | | | (89) contains_slb(all_72_0, all_75_6) = 0 % 17.48/3.26 | | | | | % 17.48/3.26 | | | | | BETA: splitting (88) gives: % 17.48/3.26 | | | | | % 17.48/3.26 | | | | | Case 1: % 17.48/3.26 | | | | | | % 17.48/3.26 | | | | | | (90) all_122_0 = 0 % 17.48/3.26 | | | | | | % 17.48/3.26 | | | | | | REDUCE: (85), (90) imply: % 17.48/3.26 | | | | | | (91) $false % 17.48/3.26 | | | | | | % 17.48/3.26 | | | | | | CLOSE: (91) is inconsistent. % 17.48/3.26 | | | | | | % 17.48/3.26 | | | | | Case 2: % 17.48/3.26 | | | | | | % 17.48/3.26 | | | | | | (92) ? [v0: int] : ( ~ (v0 = 0) & contains_slb(all_72_0, % 17.48/3.26 | | | | | | all_75_6) = v0) % 17.48/3.26 | | | | | | % 17.48/3.26 | | | | | | DELTA: instantiating (92) with fresh symbol all_139_0 gives: % 17.48/3.26 | | | | | | (93) ~ (all_139_0 = 0) & contains_slb(all_72_0, all_75_6) = % 17.48/3.26 | | | | | | all_139_0 % 17.48/3.26 | | | | | | % 17.48/3.26 | | | | | | REF_CLOSE: (8), (89), (93) are inconsistent by sub-proof #1. % 17.48/3.26 | | | | | | % 17.48/3.26 | | | | | End of split % 17.48/3.26 | | | | | % 17.48/3.26 | | | | Case 2: % 17.48/3.26 | | | | | % 17.48/3.26 | | | | | (94) all_75_6 = all_75_8 % 17.48/3.26 | | | | | % 17.48/3.26 | | | | | REDUCE: (74), (94) imply: % 17.48/3.26 | | | | | (95) $false % 17.48/3.26 | | | | | % 17.48/3.26 | | | | | CLOSE: (95) is inconsistent. % 17.48/3.26 | | | | | % 17.48/3.26 | | | | End of split % 17.48/3.26 | | | | % 17.48/3.26 | | | End of split % 17.48/3.26 | | | % 17.48/3.26 | | End of split % 17.48/3.26 | | % 17.48/3.26 | End of split % 17.48/3.26 | % 17.48/3.26 End of proof % 17.48/3.26 % 17.48/3.26 Sub-proof #1 shows that the following formulas are inconsistent: % 17.48/3.26 ---------------------------------------------------------------- % 17.48/3.26 (1) ~ (all_139_0 = 0) & contains_slb(all_72_0, all_75_6) = all_139_0 % 17.48/3.26 (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 17.48/3.26 ! [v3: $i] : (v1 = v0 | ~ (contains_slb(v3, v2) = v1) | ~ % 17.48/3.26 (contains_slb(v3, v2) = v0)) % 17.48/3.26 (3) contains_slb(all_72_0, all_75_6) = 0 % 17.48/3.26 % 17.48/3.26 Begin of proof % 17.48/3.26 | % 17.48/3.26 | ALPHA: (1) implies: % 17.48/3.26 | (4) ~ (all_139_0 = 0) % 17.48/3.26 | (5) contains_slb(all_72_0, all_75_6) = all_139_0 % 17.48/3.26 | % 17.48/3.26 | GROUND_INST: instantiating (2) with 0, all_139_0, all_75_6, all_72_0, % 17.48/3.26 | simplifying with (3), (5) gives: % 17.48/3.26 | (6) all_139_0 = 0 % 17.48/3.26 | % 17.48/3.26 | REDUCE: (4), (6) imply: % 17.48/3.26 | (7) $false % 17.48/3.26 | % 17.48/3.26 | CLOSE: (7) is inconsistent. % 17.48/3.26 | % 17.48/3.26 End of proof % 17.48/3.26 % SZS output end Proof for theBenchmark % 17.48/3.26 % 17.48/3.26 2631ms %------------------------------------------------------------------------------