%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWV408+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 : n015.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 22:56:13 EDT 2023 % Result : Theorem 11.80s 2.44s % Output : Proof 14.90s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWV408+1 : TPTP v8.1.2. Released v3.3.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n015.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 09:37:41 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 % 3.61/1.21 Prover 1: Preprocessing ... % 3.61/1.21 Prover 4: Preprocessing ... % 3.61/1.27 Prover 3: Preprocessing ... % 3.61/1.27 Prover 6: Preprocessing ... % 3.61/1.27 Prover 0: Preprocessing ... % 3.61/1.27 Prover 5: Preprocessing ... % 3.61/1.27 Prover 2: Preprocessing ... % 8.08/1.85 Prover 1: Warning: ignoring some quantifiers % 8.47/1.89 Prover 3: Warning: ignoring some quantifiers % 8.47/1.94 Prover 1: Constructing countermodel ... % 8.47/1.94 Prover 3: Constructing countermodel ... % 8.47/1.95 Prover 6: Proving ... % 8.96/1.97 Prover 5: Proving ... % 8.96/1.98 Prover 4: Constructing countermodel ... % 8.96/2.00 Prover 0: Proving ... % 8.96/2.10 Prover 2: Proving ... % 11.80/2.44 Prover 2: proved (1773ms) % 11.80/2.44 % 11.80/2.44 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 11.80/2.44 % 11.80/2.44 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 11.80/2.44 Prover 5: stopped % 11.80/2.44 Prover 6: stopped % 11.80/2.44 Prover 0: stopped % 11.80/2.45 Prover 3: stopped % 11.80/2.45 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 11.80/2.45 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 11.80/2.45 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 12.47/2.45 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 12.76/2.49 Prover 7: Preprocessing ... % 12.76/2.51 Prover 11: Preprocessing ... % 12.76/2.52 Prover 8: Preprocessing ... % 12.76/2.52 Prover 10: Preprocessing ... % 12.76/2.53 Prover 13: Preprocessing ... % 13.14/2.64 Prover 4: Found proof (size 73) % 13.14/2.64 Prover 10: Warning: ignoring some quantifiers % 13.14/2.65 Prover 4: proved (1972ms) % 13.14/2.65 Prover 1: stopped % 13.14/2.65 Prover 13: stopped % 13.14/2.67 Prover 10: Constructing countermodel ... % 13.14/2.69 Prover 10: stopped % 13.14/2.69 Prover 8: Warning: ignoring some quantifiers % 13.14/2.70 Prover 7: Warning: ignoring some quantifiers % 13.14/2.71 Prover 7: Constructing countermodel ... % 13.14/2.72 Prover 8: Constructing countermodel ... % 13.14/2.73 Prover 7: stopped % 13.14/2.74 Prover 8: stopped % 13.14/2.74 Prover 11: Constructing countermodel ... % 14.37/2.76 Prover 11: stopped % 14.37/2.76 % 14.37/2.76 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 14.37/2.76 % 14.37/2.77 % SZS output start Proof for theBenchmark % 14.37/2.77 Assumptions after simplification: % 14.37/2.77 --------------------------------- % 14.37/2.77 % 14.37/2.77 (ax20) % 14.37/2.79 $i(create_slb) & ! [v0: $i] : ( ~ (contains_slb(create_slb, v0) = 0) | ~ % 14.37/2.79 $i(v0)) % 14.37/2.79 % 14.37/2.79 (ax47) % 14.37/2.80 $i(bad) & $i(create_slb) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 14.37/2.80 $i] : ! [v4: $i] : (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ~ % 14.37/2.80 (findmin_cpq_eff(v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] % 14.37/2.80 : ? [v6: any] : ? [v7: $i] : ? [v8: $i] : (findmin_pqp_res(v0) = v5 & % 14.37/2.80 triple(v0, v7, bad) = v8 & update_slb(v1, v5) = v7 & contains_slb(v1, v5) % 14.37/2.80 = v6 & $i(v8) & $i(v7) & $i(v5) & (v8 = v4 | v6 = 0))) % 14.37/2.80 % 14.37/2.80 (ax48) % 14.37/2.80 $i(bad) & $i(create_slb) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 14.37/2.80 $i] : ! [v4: $i] : (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ~ % 14.37/2.80 (findmin_cpq_eff(v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] % 14.37/2.80 : ? [v6: any] : ? [v7: $i] : ? [v8: any] : ? [v9: $i] : ? [v10: $i] : % 14.37/2.80 (findmin_pqp_res(v0) = v5 & triple(v0, v9, bad) = v10 & update_slb(v1, v5) = % 14.37/2.80 v9 & lookup_slb(v1, v5) = v7 & contains_slb(v1, v5) = v6 & % 14.37/2.80 strictly_less_than(v5, v7) = v8 & $i(v10) & $i(v9) & $i(v7) & $i(v5) & ( ~ % 14.37/2.80 (v8 = 0) | ~ (v6 = 0) | v10 = v4))) % 14.37/2.80 % 14.37/2.80 (ax49) % 14.37/2.80 $i(create_slb) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! % 14.37/2.80 [v4: $i] : ! [v5: $i] : (v1 = create_slb | ~ (findmin_pqp_res(v0) = v3) | ~ % 14.37/2.80 (triple(v0, v4, v2) = v5) | ~ (update_slb(v1, v3) = v4) | ~ $i(v2) | ~ % 14.37/2.80 $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: $i] : ? [v8: any] : ? [v9: $i] % 14.37/2.80 : ? [v10: $i] : (triple(v0, v1, v2) = v9 & findmin_cpq_eff(v9) = v10 & % 14.37/2.80 lookup_slb(v1, v3) = v7 & contains_slb(v1, v3) = v6 & less_than(v7, v3) = % 14.37/2.80 v8 & $i(v10) & $i(v9) & $i(v7) & ( ~ (v8 = 0) | ~ (v6 = 0) | v10 = v5))) % 14.37/2.80 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = % 14.37/2.80 create_slb | ~ (triple(v0, v1, v2) = v3) | ~ (findmin_cpq_eff(v3) = v4) | % 14.37/2.80 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: any] : ? [v7: $i] % 14.37/2.80 : ? [v8: any] : ? [v9: $i] : ? [v10: $i] : (findmin_pqp_res(v0) = v5 & % 14.37/2.80 triple(v0, v9, v2) = v10 & update_slb(v1, v5) = v9 & lookup_slb(v1, v5) = % 14.37/2.80 v7 & contains_slb(v1, v5) = v6 & less_than(v7, v5) = v8 & $i(v10) & $i(v9) % 14.37/2.80 & $i(v7) & $i(v5) & ( ~ (v8 = 0) | ~ (v6 = 0) | v10 = v4))) % 14.37/2.80 % 14.37/2.80 (ax51) % 14.37/2.81 $i(create_slb) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! % 14.37/2.81 [v4: $i] : (v1 = create_slb | ~ (findmin_cpq_res(v3) = v4) | ~ (triple(v0, % 14.37/2.81 v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (findmin_pqp_res(v0) % 14.37/2.81 = v4 & $i(v4))) % 14.37/2.81 % 14.37/2.81 (ax52) % 14.37/2.81 ! [v0: $i] : ! [v1: $i] : ( ~ (findmin_cpq_res(v0) = v1) | ~ $i(v0) | ? % 14.37/2.81 [v2: $i] : ? [v3: $i] : (removemin_cpq_eff(v0) = v2 & findmin_cpq_eff(v0) = % 14.37/2.81 v3 & remove_cpq(v3, v1) = v2 & $i(v3) & $i(v2))) & ! [v0: $i] : ! [v1: % 14.37/2.81 $i] : ( ~ (removemin_cpq_eff(v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: % 14.37/2.81 $i] : (findmin_cpq_res(v0) = v3 & findmin_cpq_eff(v0) = v2 & % 14.37/2.81 remove_cpq(v2, v3) = v1 & $i(v3) & $i(v2) & $i(v1))) & ! [v0: $i] : ! % 14.37/2.81 [v1: $i] : ( ~ (findmin_cpq_eff(v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: % 14.37/2.81 $i] : (findmin_cpq_res(v0) = v3 & removemin_cpq_eff(v0) = v2 & % 14.37/2.81 remove_cpq(v1, v3) = v2 & $i(v3) & $i(v2))) % 14.37/2.81 % 14.37/2.81 (l44_co) % 14.90/2.81 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 14.90/2.81 $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: int] : ( ~ (v8 = 0) & % 14.90/2.81 findmin_cpq_res(v4) = v5 & findmin_pqp_res(v0) = v6 & triple(v0, v1, v2) = % 14.90/2.81 v4 & update_slb(v1, v6) = v7 & pair_in_list(v7, v3, v6) = v8 & % 14.90/2.81 contains_slb(v1, v3) = 0 & strictly_less_than(v3, v5) = 0 & $i(v7) & $i(v6) % 14.90/2.81 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v9: $i] : ( ~ % 14.90/2.81 (pair_in_list(v7, v3, v9) = 0) | ~ $i(v9) | ? [v10: int] : ( ~ (v10 = 0) % 14.90/2.81 & less_than(v6, v9) = v10)) & ! [v9: $i] : ( ~ (less_than(v6, v9) = 0) % 14.90/2.81 | ~ $i(v9) | ? [v10: int] : ( ~ (v10 = 0) & pair_in_list(v7, v3, v9) = % 14.90/2.81 v10))) % 14.90/2.81 % 14.90/2.81 (l44_l45) % 14.90/2.81 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 14.90/2.81 | ~ (update_slb(v0, v2) = v3) | ~ (pair_in_list(v3, v1, v2) = v4) | ~ % 14.90/2.81 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: $i] : % 14.90/2.81 ? [v8: int] : ? [v9: int] : ($i(v7) & ((v9 = 0 & v8 = 0 & pair_in_list(v3, % 14.90/2.81 v1, v7) = 0 & less_than(v2, v7) = 0) | (contains_slb(v0, v1) = v5 & % 14.90/2.81 strictly_less_than(v1, v2) = v6 & ( ~ (v6 = 0) | ~ (v5 = 0)))))) % 14.90/2.81 % 14.90/2.81 (function-axioms) % 14.90/2.82 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 % 14.90/2.82 | ~ (triple(v4, v3, v2) = v1) | ~ (triple(v4, v3, v2) = v0)) & ! [v0: % 14.90/2.82 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 14.90/2.82 : ! [v4: $i] : (v1 = v0 | ~ (pair_in_list(v4, v3, v2) = v1) | ~ % 14.90/2.82 (pair_in_list(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 14.90/2.82 ! [v3: $i] : (v1 = v0 | ~ (remove_pqp(v3, v2) = v1) | ~ (remove_pqp(v3, v2) % 14.90/2.82 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 % 14.90/2.82 | ~ (insert_pqp(v3, v2) = v1) | ~ (insert_pqp(v3, v2) = v0)) & ! [v0: % 14.90/2.82 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 14.90/2.82 : (v1 = v0 | ~ (contains_cpq(v3, v2) = v1) | ~ (contains_cpq(v3, v2) = v0)) % 14.90/2.82 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 14.90/2.82 (remove_cpq(v3, v2) = v1) | ~ (remove_cpq(v3, v2) = v0)) & ! [v0: $i] : ! % 14.90/2.82 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (insert_cpq(v3, v2) = v1) % 14.90/2.82 | ~ (insert_cpq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 14.90/2.82 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (succ_cpq(v3, % 14.90/2.82 v2) = v1) | ~ (succ_cpq(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 14.90/2.82 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (update_slb(v3, v2) = v1) | ~ % 14.90/2.82 (update_slb(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 14.90/2.82 [v3: $i] : (v1 = v0 | ~ (lookup_slb(v3, v2) = v1) | ~ (lookup_slb(v3, v2) = % 14.90/2.82 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 14.90/2.82 ~ (remove_slb(v3, v2) = v1) | ~ (remove_slb(v3, v2) = v0)) & ! [v0: % 14.90/2.82 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 14.90/2.82 : (v1 = v0 | ~ (contains_slb(v3, v2) = v1) | ~ (contains_slb(v3, v2) = v0)) % 14.90/2.82 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 14.90/2.82 (pair(v3, v2) = v1) | ~ (pair(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 14.90/2.82 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (insert_slb(v3, v2) = v1) | ~ % 14.90/2.82 (insert_slb(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 14.90/2.82 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 14.90/2.82 (strictly_less_than(v3, v2) = v1) | ~ (strictly_less_than(v3, v2) = v0)) & % 14.90/2.82 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 14.90/2.82 $i] : (v1 = v0 | ~ (less_than(v3, v2) = v1) | ~ (less_than(v3, v2) = v0)) % 14.90/2.82 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 14.90/2.82 (removemin_cpq_res(v2) = v1) | ~ (removemin_cpq_res(v2) = v0)) & ! [v0: % 14.90/2.82 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (findmin_cpq_res(v2) = v1) | % 14.90/2.82 ~ (findmin_cpq_res(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 14.90/2.82 (v1 = v0 | ~ (findmin_pqp_res(v2) = v1) | ~ (findmin_pqp_res(v2) = v0)) & ! % 14.90/2.82 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 % 14.90/2.82 | ~ (ok(v2) = v1) | ~ (ok(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 14.90/2.82 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (check_cpq(v2) = v1) | % 14.90/2.82 ~ (check_cpq(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 % 14.90/2.82 | ~ (removemin_cpq_eff(v2) = v1) | ~ (removemin_cpq_eff(v2) = v0)) & ! % 14.90/2.82 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (findmin_cpq_eff(v2) = % 14.90/2.82 v1) | ~ (findmin_cpq_eff(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 14.90/2.82 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (isnonempty_slb(v2) = % 14.90/2.82 v1) | ~ (isnonempty_slb(v2) = v0)) % 14.90/2.82 % 14.90/2.82 Further assumptions not needed in the proof: % 14.90/2.82 -------------------------------------------- % 14.90/2.82 ax18, ax19, ax21, ax22, ax23, ax24, ax25, ax26, ax27, ax28, ax29, ax30, ax31, % 14.90/2.82 ax32, ax33, ax34, ax35, ax36, ax37, ax38, ax39, ax40, ax41, ax42, ax43, ax44, % 14.90/2.82 ax45, ax46, ax50, ax53, bottom_smallest, reflexivity, % 14.90/2.82 stricly_smaller_definition, totality, transitivity % 14.90/2.82 % 14.90/2.82 Those formulas are unsatisfiable: % 14.90/2.82 --------------------------------- % 14.90/2.82 % 14.90/2.82 Begin of proof % 14.90/2.82 | % 14.90/2.82 | ALPHA: (ax20) implies: % 14.90/2.82 | (1) ! [v0: $i] : ( ~ (contains_slb(create_slb, v0) = 0) | ~ $i(v0)) % 14.90/2.82 | % 14.90/2.82 | ALPHA: (ax47) implies: % 14.90/2.82 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 14.90/2.82 | (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ~ % 14.90/2.82 | (findmin_cpq_eff(v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 14.90/2.82 | [v5: $i] : ? [v6: any] : ? [v7: $i] : ? [v8: $i] : % 14.90/2.82 | (findmin_pqp_res(v0) = v5 & triple(v0, v7, bad) = v8 & update_slb(v1, % 14.90/2.82 | v5) = v7 & contains_slb(v1, v5) = v6 & $i(v8) & $i(v7) & $i(v5) & % 14.90/2.82 | (v8 = v4 | v6 = 0))) % 14.90/2.82 | % 14.90/2.82 | ALPHA: (ax48) implies: % 14.90/2.83 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 14.90/2.83 | (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ~ % 14.90/2.83 | (findmin_cpq_eff(v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 14.90/2.83 | [v5: $i] : ? [v6: any] : ? [v7: $i] : ? [v8: any] : ? [v9: $i] : % 14.90/2.83 | ? [v10: $i] : (findmin_pqp_res(v0) = v5 & triple(v0, v9, bad) = v10 & % 14.90/2.83 | update_slb(v1, v5) = v9 & lookup_slb(v1, v5) = v7 & % 14.90/2.83 | contains_slb(v1, v5) = v6 & strictly_less_than(v5, v7) = v8 & % 14.90/2.83 | $i(v10) & $i(v9) & $i(v7) & $i(v5) & ( ~ (v8 = 0) | ~ (v6 = 0) | % 14.90/2.83 | v10 = v4))) % 14.90/2.83 | % 14.90/2.83 | ALPHA: (ax49) implies: % 14.90/2.83 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 14.90/2.83 | (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ~ % 14.90/2.83 | (findmin_cpq_eff(v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 14.90/2.83 | [v5: $i] : ? [v6: any] : ? [v7: $i] : ? [v8: any] : ? [v9: $i] : % 14.90/2.83 | ? [v10: $i] : (findmin_pqp_res(v0) = v5 & triple(v0, v9, v2) = v10 & % 14.90/2.83 | update_slb(v1, v5) = v9 & lookup_slb(v1, v5) = v7 & % 14.90/2.83 | contains_slb(v1, v5) = v6 & less_than(v7, v5) = v8 & $i(v10) & % 14.90/2.83 | $i(v9) & $i(v7) & $i(v5) & ( ~ (v8 = 0) | ~ (v6 = 0) | v10 = v4))) % 14.90/2.83 | % 14.90/2.83 | ALPHA: (ax51) implies: % 14.90/2.83 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 14.90/2.83 | (v1 = create_slb | ~ (findmin_cpq_res(v3) = v4) | ~ (triple(v0, v1, % 14.90/2.83 | v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 14.90/2.83 | (findmin_pqp_res(v0) = v4 & $i(v4))) % 14.90/2.83 | % 14.90/2.83 | ALPHA: (ax52) implies: % 14.90/2.83 | (6) ! [v0: $i] : ! [v1: $i] : ( ~ (findmin_cpq_res(v0) = v1) | ~ $i(v0) % 14.90/2.83 | | ? [v2: $i] : ? [v3: $i] : (removemin_cpq_eff(v0) = v2 & % 14.90/2.83 | findmin_cpq_eff(v0) = v3 & remove_cpq(v3, v1) = v2 & $i(v3) & % 14.90/2.83 | $i(v2))) % 14.90/2.83 | % 14.90/2.83 | ALPHA: (function-axioms) implies: % 14.90/2.83 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 14.90/2.83 | (findmin_pqp_res(v2) = v1) | ~ (findmin_pqp_res(v2) = v0)) % 14.90/2.83 | (8) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 14.90/2.83 | ! [v3: $i] : (v1 = v0 | ~ (less_than(v3, v2) = v1) | ~ % 14.90/2.83 | (less_than(v3, v2) = v0)) % 14.90/2.83 | (9) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 14.90/2.83 | ! [v3: $i] : (v1 = v0 | ~ (strictly_less_than(v3, v2) = v1) | ~ % 14.90/2.83 | (strictly_less_than(v3, v2) = v0)) % 14.90/2.83 | (10) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 14.90/2.83 | : ! [v3: $i] : (v1 = v0 | ~ (contains_slb(v3, v2) = v1) | ~ % 14.90/2.83 | (contains_slb(v3, v2) = v0)) % 14.90/2.83 | % 14.90/2.83 | DELTA: instantiating (l44_co) with fresh symbols all_47_0, all_47_1, all_47_2, % 14.90/2.83 | all_47_3, all_47_4, all_47_5, all_47_6, all_47_7, all_47_8 gives: % 14.90/2.83 | (11) ~ (all_47_0 = 0) & findmin_cpq_res(all_47_4) = all_47_3 & % 14.90/2.83 | findmin_pqp_res(all_47_8) = all_47_2 & triple(all_47_8, all_47_7, % 14.90/2.83 | all_47_6) = all_47_4 & update_slb(all_47_7, all_47_2) = all_47_1 & % 14.90/2.83 | pair_in_list(all_47_1, all_47_5, all_47_2) = all_47_0 & % 14.90/2.83 | contains_slb(all_47_7, all_47_5) = 0 & strictly_less_than(all_47_5, % 14.90/2.83 | all_47_3) = 0 & $i(all_47_1) & $i(all_47_2) & $i(all_47_3) & % 14.90/2.83 | $i(all_47_4) & $i(all_47_5) & $i(all_47_6) & $i(all_47_7) & % 14.90/2.83 | $i(all_47_8) & ! [v0: $i] : ( ~ (pair_in_list(all_47_1, all_47_5, v0) % 14.90/2.83 | = 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & % 14.90/2.83 | less_than(all_47_2, v0) = v1)) & ! [v0: $i] : ( ~ % 14.90/2.83 | (less_than(all_47_2, v0) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = % 14.90/2.83 | 0) & pair_in_list(all_47_1, all_47_5, v0) = v1)) % 14.90/2.83 | % 14.90/2.83 | ALPHA: (11) implies: % 14.90/2.83 | (12) ~ (all_47_0 = 0) % 14.90/2.83 | (13) $i(all_47_8) % 14.90/2.84 | (14) $i(all_47_7) % 14.90/2.84 | (15) $i(all_47_6) % 14.90/2.84 | (16) $i(all_47_5) % 14.90/2.84 | (17) $i(all_47_4) % 14.90/2.84 | (18) $i(all_47_2) % 14.90/2.84 | (19) strictly_less_than(all_47_5, all_47_3) = 0 % 14.90/2.84 | (20) contains_slb(all_47_7, all_47_5) = 0 % 14.90/2.84 | (21) pair_in_list(all_47_1, all_47_5, all_47_2) = all_47_0 % 14.90/2.84 | (22) update_slb(all_47_7, all_47_2) = all_47_1 % 14.90/2.84 | (23) triple(all_47_8, all_47_7, all_47_6) = all_47_4 % 14.90/2.84 | (24) findmin_pqp_res(all_47_8) = all_47_2 % 14.90/2.84 | (25) findmin_cpq_res(all_47_4) = all_47_3 % 14.90/2.84 | (26) ! [v0: $i] : ( ~ (pair_in_list(all_47_1, all_47_5, v0) = 0) | ~ % 14.90/2.84 | $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & less_than(all_47_2, v0) = % 14.90/2.84 | v1)) % 14.90/2.84 | % 14.90/2.84 | GROUND_INST: instantiating (l44_l45) with all_47_7, all_47_5, all_47_2, % 14.90/2.84 | all_47_1, all_47_0, simplifying with (14), (16), (18), (21), (22) % 14.90/2.84 | gives: % 14.90/2.84 | (27) all_47_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: % 14.90/2.84 | int] : ? [v4: int] : ($i(v2) & ((v4 = 0 & v3 = 0 & % 14.90/2.84 | pair_in_list(all_47_1, all_47_5, v2) = 0 & less_than(all_47_2, % 14.90/2.84 | v2) = 0) | (contains_slb(all_47_7, all_47_5) = v0 & % 14.90/2.84 | strictly_less_than(all_47_5, all_47_2) = v1 & ( ~ (v1 = 0) | ~ % 14.90/2.84 | (v0 = 0))))) % 14.90/2.84 | % 14.90/2.84 | GROUND_INST: instantiating (5) with all_47_8, all_47_7, all_47_6, all_47_4, % 14.90/2.84 | all_47_3, simplifying with (13), (14), (15), (23), (25) gives: % 14.90/2.84 | (28) all_47_7 = create_slb | (findmin_pqp_res(all_47_8) = all_47_3 & % 14.90/2.84 | $i(all_47_3)) % 14.90/2.84 | % 14.90/2.84 | GROUND_INST: instantiating (6) with all_47_4, all_47_3, simplifying with (17), % 14.90/2.84 | (25) gives: % 14.90/2.84 | (29) ? [v0: $i] : ? [v1: $i] : (removemin_cpq_eff(all_47_4) = v0 & % 14.90/2.84 | findmin_cpq_eff(all_47_4) = v1 & remove_cpq(v1, all_47_3) = v0 & % 14.90/2.84 | $i(v1) & $i(v0)) % 14.90/2.84 | % 14.90/2.84 | DELTA: instantiating (29) with fresh symbols all_58_0, all_58_1 gives: % 14.90/2.84 | (30) removemin_cpq_eff(all_47_4) = all_58_1 & findmin_cpq_eff(all_47_4) = % 14.90/2.84 | all_58_0 & remove_cpq(all_58_0, all_47_3) = all_58_1 & $i(all_58_0) & % 14.90/2.84 | $i(all_58_1) % 14.90/2.84 | % 14.90/2.84 | ALPHA: (30) implies: % 14.90/2.84 | (31) findmin_cpq_eff(all_47_4) = all_58_0 % 14.90/2.84 | % 14.90/2.84 | BETA: splitting (27) gives: % 14.90/2.84 | % 14.90/2.84 | Case 1: % 14.90/2.84 | | % 14.90/2.84 | | (32) all_47_0 = 0 % 14.90/2.84 | | % 14.90/2.84 | | REDUCE: (12), (32) imply: % 14.90/2.84 | | (33) $false % 14.90/2.84 | | % 14.90/2.84 | | CLOSE: (33) is inconsistent. % 14.90/2.84 | | % 14.90/2.84 | Case 2: % 14.90/2.84 | | % 14.90/2.84 | | (34) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: int] : ? [v4: % 14.90/2.84 | | int] : ($i(v2) & ((v4 = 0 & v3 = 0 & pair_in_list(all_47_1, % 14.90/2.84 | | all_47_5, v2) = 0 & less_than(all_47_2, v2) = 0) | % 14.90/2.84 | | (contains_slb(all_47_7, all_47_5) = v0 & % 14.90/2.84 | | strictly_less_than(all_47_5, all_47_2) = v1 & ( ~ (v1 = 0) | % 14.90/2.84 | | ~ (v0 = 0))))) % 14.90/2.84 | | % 14.90/2.84 | | DELTA: instantiating (34) with fresh symbols all_64_0, all_64_1, all_64_2, % 14.90/2.84 | | all_64_3, all_64_4 gives: % 14.90/2.85 | | (35) $i(all_64_2) & ((all_64_0 = 0 & all_64_1 = 0 & % 14.90/2.85 | | pair_in_list(all_47_1, all_47_5, all_64_2) = 0 & % 14.90/2.85 | | less_than(all_47_2, all_64_2) = 0) | (contains_slb(all_47_7, % 14.90/2.85 | | all_47_5) = all_64_4 & strictly_less_than(all_47_5, all_47_2) % 14.90/2.85 | | = all_64_3 & ( ~ (all_64_3 = 0) | ~ (all_64_4 = 0)))) % 14.90/2.85 | | % 14.90/2.85 | | ALPHA: (35) implies: % 14.90/2.85 | | (36) $i(all_64_2) % 14.90/2.85 | | (37) (all_64_0 = 0 & all_64_1 = 0 & pair_in_list(all_47_1, all_47_5, % 14.90/2.85 | | all_64_2) = 0 & less_than(all_47_2, all_64_2) = 0) | % 14.90/2.85 | | (contains_slb(all_47_7, all_47_5) = all_64_4 & % 14.90/2.85 | | strictly_less_than(all_47_5, all_47_2) = all_64_3 & ( ~ (all_64_3 % 14.90/2.85 | | = 0) | ~ (all_64_4 = 0))) % 14.90/2.85 | | % 14.90/2.85 | | GROUND_INST: instantiating (4) with all_47_8, all_47_7, all_47_6, all_47_4, % 14.90/2.85 | | all_58_0, simplifying with (13), (14), (15), (23), (31) gives: % 14.90/2.85 | | (38) all_47_7 = create_slb | ? [v0: $i] : ? [v1: any] : ? [v2: $i] : % 14.90/2.85 | | ? [v3: any] : ? [v4: $i] : ? [v5: $i] : (findmin_pqp_res(all_47_8) % 14.90/2.85 | | = v0 & triple(all_47_8, v4, all_47_6) = v5 & update_slb(all_47_7, % 14.90/2.85 | | v0) = v4 & lookup_slb(all_47_7, v0) = v2 & % 14.90/2.85 | | contains_slb(all_47_7, v0) = v1 & less_than(v2, v0) = v3 & $i(v5) % 14.90/2.85 | | & $i(v4) & $i(v2) & $i(v0) & ( ~ (v3 = 0) | ~ (v1 = 0) | v5 = % 14.90/2.85 | | all_58_0)) % 14.90/2.85 | | % 14.90/2.85 | | GROUND_INST: instantiating (3) with all_47_8, all_47_7, all_47_6, all_47_4, % 14.90/2.85 | | all_58_0, simplifying with (13), (14), (15), (23), (31) gives: % 14.90/2.85 | | (39) all_47_7 = create_slb | ? [v0: $i] : ? [v1: any] : ? [v2: $i] : % 14.90/2.85 | | ? [v3: any] : ? [v4: $i] : ? [v5: $i] : (findmin_pqp_res(all_47_8) % 14.90/2.85 | | = v0 & triple(all_47_8, v4, bad) = v5 & update_slb(all_47_7, v0) = % 14.90/2.85 | | v4 & lookup_slb(all_47_7, v0) = v2 & contains_slb(all_47_7, v0) = % 14.90/2.85 | | v1 & strictly_less_than(v0, v2) = v3 & $i(v5) & $i(v4) & $i(v2) & % 14.90/2.85 | | $i(v0) & ( ~ (v3 = 0) | ~ (v1 = 0) | v5 = all_58_0)) % 14.90/2.85 | | % 14.90/2.85 | | GROUND_INST: instantiating (2) with all_47_8, all_47_7, all_47_6, all_47_4, % 14.90/2.85 | | all_58_0, simplifying with (13), (14), (15), (23), (31) gives: % 14.90/2.85 | | (40) all_47_7 = create_slb | ? [v0: $i] : ? [v1: any] : ? [v2: $i] : % 14.90/2.85 | | ? [v3: $i] : (findmin_pqp_res(all_47_8) = v0 & triple(all_47_8, v2, % 14.90/2.85 | | bad) = v3 & update_slb(all_47_7, v0) = v2 & % 14.90/2.85 | | contains_slb(all_47_7, v0) = v1 & $i(v3) & $i(v2) & $i(v0) & (v3 = % 14.90/2.85 | | all_58_0 | v1 = 0)) % 14.90/2.85 | | % 14.90/2.85 | | BETA: splitting (28) gives: % 14.90/2.85 | | % 14.90/2.85 | | Case 1: % 14.90/2.85 | | | % 14.90/2.85 | | | (41) all_47_7 = create_slb % 14.90/2.85 | | | % 14.90/2.85 | | | REDUCE: (20), (41) imply: % 14.90/2.85 | | | (42) contains_slb(create_slb, all_47_5) = 0 % 14.90/2.85 | | | % 14.90/2.85 | | | GROUND_INST: instantiating (1) with all_47_5, simplifying with (16), (42) % 14.90/2.85 | | | gives: % 14.90/2.85 | | | (43) $false % 14.90/2.85 | | | % 14.90/2.85 | | | CLOSE: (43) is inconsistent. % 14.90/2.85 | | | % 14.90/2.85 | | Case 2: % 14.90/2.85 | | | % 14.90/2.85 | | | (44) ~ (all_47_7 = create_slb) % 14.90/2.85 | | | (45) findmin_pqp_res(all_47_8) = all_47_3 & $i(all_47_3) % 14.90/2.85 | | | % 14.90/2.85 | | | ALPHA: (45) implies: % 14.90/2.85 | | | (46) findmin_pqp_res(all_47_8) = all_47_3 % 14.90/2.85 | | | % 14.90/2.85 | | | BETA: splitting (40) gives: % 14.90/2.85 | | | % 14.90/2.85 | | | Case 1: % 14.90/2.85 | | | | % 14.90/2.85 | | | | (47) all_47_7 = create_slb % 14.90/2.85 | | | | % 14.90/2.85 | | | | REDUCE: (44), (47) imply: % 14.90/2.86 | | | | (48) $false % 14.90/2.86 | | | | % 14.90/2.86 | | | | CLOSE: (48) is inconsistent. % 14.90/2.86 | | | | % 14.90/2.86 | | | Case 2: % 14.90/2.86 | | | | % 14.90/2.86 | | | | (49) ? [v0: $i] : ? [v1: any] : ? [v2: $i] : ? [v3: $i] : % 14.90/2.86 | | | | (findmin_pqp_res(all_47_8) = v0 & triple(all_47_8, v2, bad) = v3 % 14.90/2.86 | | | | & update_slb(all_47_7, v0) = v2 & contains_slb(all_47_7, v0) = % 14.90/2.86 | | | | v1 & $i(v3) & $i(v2) & $i(v0) & (v3 = all_58_0 | v1 = 0)) % 14.90/2.86 | | | | % 14.90/2.86 | | | | DELTA: instantiating (49) with fresh symbols all_94_0, all_94_1, % 14.90/2.86 | | | | all_94_2, all_94_3 gives: % 14.90/2.86 | | | | (50) findmin_pqp_res(all_47_8) = all_94_3 & triple(all_47_8, % 14.90/2.86 | | | | all_94_1, bad) = all_94_0 & update_slb(all_47_7, all_94_3) = % 14.90/2.86 | | | | all_94_1 & contains_slb(all_47_7, all_94_3) = all_94_2 & % 14.90/2.86 | | | | $i(all_94_0) & $i(all_94_1) & $i(all_94_3) & (all_94_0 = % 14.90/2.86 | | | | all_58_0 | all_94_2 = 0) % 14.90/2.86 | | | | % 14.90/2.86 | | | | ALPHA: (50) implies: % 14.90/2.86 | | | | (51) findmin_pqp_res(all_47_8) = all_94_3 % 14.90/2.86 | | | | % 14.90/2.86 | | | | BETA: splitting (38) gives: % 14.90/2.86 | | | | % 14.90/2.86 | | | | Case 1: % 14.90/2.86 | | | | | % 14.90/2.86 | | | | | (52) all_47_7 = create_slb % 14.90/2.86 | | | | | % 14.90/2.86 | | | | | REDUCE: (44), (52) imply: % 14.90/2.86 | | | | | (53) $false % 14.90/2.86 | | | | | % 14.90/2.86 | | | | | CLOSE: (53) is inconsistent. % 14.90/2.86 | | | | | % 14.90/2.86 | | | | Case 2: % 14.90/2.86 | | | | | % 14.90/2.86 | | | | | (54) ? [v0: $i] : ? [v1: any] : ? [v2: $i] : ? [v3: any] : ? % 14.90/2.86 | | | | | [v4: $i] : ? [v5: $i] : (findmin_pqp_res(all_47_8) = v0 & % 14.90/2.86 | | | | | triple(all_47_8, v4, all_47_6) = v5 & update_slb(all_47_7, % 14.90/2.86 | | | | | v0) = v4 & lookup_slb(all_47_7, v0) = v2 & % 14.90/2.86 | | | | | contains_slb(all_47_7, v0) = v1 & less_than(v2, v0) = v3 & % 14.90/2.86 | | | | | $i(v5) & $i(v4) & $i(v2) & $i(v0) & ( ~ (v3 = 0) | ~ (v1 = % 14.90/2.86 | | | | | 0) | v5 = all_58_0)) % 14.90/2.86 | | | | | % 14.90/2.86 | | | | | DELTA: instantiating (54) with fresh symbols all_99_0, all_99_1, % 14.90/2.86 | | | | | all_99_2, all_99_3, all_99_4, all_99_5 gives: % 14.90/2.86 | | | | | (55) findmin_pqp_res(all_47_8) = all_99_5 & triple(all_47_8, % 14.90/2.86 | | | | | all_99_1, all_47_6) = all_99_0 & update_slb(all_47_7, % 14.90/2.86 | | | | | all_99_5) = all_99_1 & lookup_slb(all_47_7, all_99_5) = % 14.90/2.86 | | | | | all_99_3 & contains_slb(all_47_7, all_99_5) = all_99_4 & % 14.90/2.86 | | | | | less_than(all_99_3, all_99_5) = all_99_2 & $i(all_99_0) & % 14.90/2.86 | | | | | $i(all_99_1) & $i(all_99_3) & $i(all_99_5) & ( ~ (all_99_2 = % 14.90/2.86 | | | | | 0) | ~ (all_99_4 = 0) | all_99_0 = all_58_0) % 14.90/2.86 | | | | | % 14.90/2.86 | | | | | ALPHA: (55) implies: % 14.90/2.86 | | | | | (56) findmin_pqp_res(all_47_8) = all_99_5 % 14.90/2.86 | | | | | % 14.90/2.86 | | | | | BETA: splitting (39) gives: % 14.90/2.86 | | | | | % 14.90/2.86 | | | | | Case 1: % 14.90/2.86 | | | | | | % 14.90/2.86 | | | | | | (57) all_47_7 = create_slb % 14.90/2.86 | | | | | | % 14.90/2.86 | | | | | | REDUCE: (44), (57) imply: % 14.90/2.86 | | | | | | (58) $false % 14.90/2.86 | | | | | | % 14.90/2.86 | | | | | | CLOSE: (58) is inconsistent. % 14.90/2.86 | | | | | | % 14.90/2.86 | | | | | Case 2: % 14.90/2.86 | | | | | | % 14.90/2.86 | | | | | | (59) ? [v0: $i] : ? [v1: any] : ? [v2: $i] : ? [v3: any] : ? % 14.90/2.86 | | | | | | [v4: $i] : ? [v5: $i] : (findmin_pqp_res(all_47_8) = v0 & % 14.90/2.86 | | | | | | triple(all_47_8, v4, bad) = v5 & update_slb(all_47_7, v0) % 14.90/2.86 | | | | | | = v4 & lookup_slb(all_47_7, v0) = v2 & % 14.90/2.86 | | | | | | contains_slb(all_47_7, v0) = v1 & strictly_less_than(v0, % 14.90/2.86 | | | | | | v2) = v3 & $i(v5) & $i(v4) & $i(v2) & $i(v0) & ( ~ (v3 = % 14.90/2.86 | | | | | | 0) | ~ (v1 = 0) | v5 = all_58_0)) % 14.90/2.86 | | | | | | % 14.90/2.86 | | | | | | DELTA: instantiating (59) with fresh symbols all_104_0, all_104_1, % 14.90/2.86 | | | | | | all_104_2, all_104_3, all_104_4, all_104_5 gives: % 14.90/2.86 | | | | | | (60) findmin_pqp_res(all_47_8) = all_104_5 & triple(all_47_8, % 14.90/2.86 | | | | | | all_104_1, bad) = all_104_0 & update_slb(all_47_7, % 14.90/2.86 | | | | | | all_104_5) = all_104_1 & lookup_slb(all_47_7, all_104_5) = % 14.90/2.86 | | | | | | all_104_3 & contains_slb(all_47_7, all_104_5) = all_104_4 & % 14.90/2.86 | | | | | | strictly_less_than(all_104_5, all_104_3) = all_104_2 & % 14.90/2.86 | | | | | | $i(all_104_0) & $i(all_104_1) & $i(all_104_3) & % 14.90/2.86 | | | | | | $i(all_104_5) & ( ~ (all_104_2 = 0) | ~ (all_104_4 = 0) | % 14.90/2.86 | | | | | | all_104_0 = all_58_0) % 14.90/2.86 | | | | | | % 14.90/2.86 | | | | | | ALPHA: (60) implies: % 14.90/2.86 | | | | | | (61) findmin_pqp_res(all_47_8) = all_104_5 % 14.90/2.86 | | | | | | % 14.90/2.86 | | | | | | GROUND_INST: instantiating (7) with all_47_2, all_99_5, all_47_8, % 14.90/2.86 | | | | | | simplifying with (24), (56) gives: % 14.90/2.86 | | | | | | (62) all_99_5 = all_47_2 % 14.90/2.86 | | | | | | % 14.90/2.86 | | | | | | GROUND_INST: instantiating (7) with all_94_3, all_99_5, all_47_8, % 14.90/2.86 | | | | | | simplifying with (51), (56) gives: % 14.90/2.86 | | | | | | (63) all_99_5 = all_94_3 % 14.90/2.86 | | | | | | % 14.90/2.86 | | | | | | GROUND_INST: instantiating (7) with all_94_3, all_104_5, all_47_8, % 14.90/2.86 | | | | | | simplifying with (51), (61) gives: % 14.90/2.86 | | | | | | (64) all_104_5 = all_94_3 % 14.90/2.86 | | | | | | % 14.90/2.86 | | | | | | GROUND_INST: instantiating (7) with all_47_3, all_104_5, all_47_8, % 14.90/2.86 | | | | | | simplifying with (46), (61) gives: % 14.90/2.86 | | | | | | (65) all_104_5 = all_47_3 % 14.90/2.86 | | | | | | % 14.90/2.86 | | | | | | COMBINE_EQS: (64), (65) imply: % 14.90/2.86 | | | | | | (66) all_94_3 = all_47_3 % 14.90/2.87 | | | | | | % 14.90/2.87 | | | | | | SIMP: (66) implies: % 14.90/2.87 | | | | | | (67) all_94_3 = all_47_3 % 14.90/2.87 | | | | | | % 14.90/2.87 | | | | | | COMBINE_EQS: (62), (63) imply: % 14.90/2.87 | | | | | | (68) all_94_3 = all_47_2 % 14.90/2.87 | | | | | | % 14.90/2.87 | | | | | | SIMP: (68) implies: % 14.90/2.87 | | | | | | (69) all_94_3 = all_47_2 % 14.90/2.87 | | | | | | % 14.90/2.87 | | | | | | COMBINE_EQS: (67), (69) imply: % 14.90/2.87 | | | | | | (70) all_47_2 = all_47_3 % 14.90/2.87 | | | | | | % 14.90/2.87 | | | | | | SIMP: (70) implies: % 14.90/2.87 | | | | | | (71) all_47_2 = all_47_3 % 14.90/2.87 | | | | | | % 14.90/2.87 | | | | | | BETA: splitting (37) gives: % 14.90/2.87 | | | | | | % 14.90/2.87 | | | | | | Case 1: % 14.90/2.87 | | | | | | | % 14.90/2.87 | | | | | | | (72) all_64_0 = 0 & all_64_1 = 0 & pair_in_list(all_47_1, % 14.90/2.87 | | | | | | | all_47_5, all_64_2) = 0 & less_than(all_47_2, all_64_2) % 14.90/2.87 | | | | | | | = 0 % 14.90/2.87 | | | | | | | % 14.90/2.87 | | | | | | | ALPHA: (72) implies: % 14.90/2.87 | | | | | | | (73) less_than(all_47_2, all_64_2) = 0 % 14.90/2.87 | | | | | | | (74) pair_in_list(all_47_1, all_47_5, all_64_2) = 0 % 14.90/2.87 | | | | | | | % 14.90/2.87 | | | | | | | REDUCE: (71), (73) imply: % 14.90/2.87 | | | | | | | (75) less_than(all_47_3, all_64_2) = 0 % 14.90/2.87 | | | | | | | % 14.90/2.87 | | | | | | | GROUND_INST: instantiating (26) with all_64_2, simplifying with % 14.90/2.87 | | | | | | | (36), (74) gives: % 14.90/2.87 | | | | | | | (76) ? [v0: int] : ( ~ (v0 = 0) & less_than(all_47_2, % 14.90/2.87 | | | | | | | all_64_2) = v0) % 14.90/2.87 | | | | | | | % 14.90/2.87 | | | | | | | DELTA: instantiating (76) with fresh symbol all_128_0 gives: % 14.90/2.87 | | | | | | | (77) ~ (all_128_0 = 0) & less_than(all_47_2, all_64_2) = % 14.90/2.87 | | | | | | | all_128_0 % 14.90/2.87 | | | | | | | % 14.90/2.87 | | | | | | | ALPHA: (77) implies: % 14.90/2.87 | | | | | | | (78) ~ (all_128_0 = 0) % 14.90/2.87 | | | | | | | (79) less_than(all_47_2, all_64_2) = all_128_0 % 14.90/2.87 | | | | | | | % 14.90/2.87 | | | | | | | REDUCE: (71), (79) imply: % 14.90/2.87 | | | | | | | (80) less_than(all_47_3, all_64_2) = all_128_0 % 14.90/2.87 | | | | | | | % 14.90/2.87 | | | | | | | GROUND_INST: instantiating (8) with 0, all_128_0, all_64_2, % 14.90/2.87 | | | | | | | all_47_3, simplifying with (75), (80) gives: % 14.90/2.87 | | | | | | | (81) all_128_0 = 0 % 14.90/2.87 | | | | | | | % 14.90/2.87 | | | | | | | REDUCE: (78), (81) imply: % 14.90/2.87 | | | | | | | (82) $false % 14.90/2.87 | | | | | | | % 14.90/2.87 | | | | | | | CLOSE: (82) is inconsistent. % 14.90/2.87 | | | | | | | % 14.90/2.87 | | | | | | Case 2: % 14.90/2.87 | | | | | | | % 14.90/2.87 | | | | | | | (83) contains_slb(all_47_7, all_47_5) = all_64_4 & % 14.90/2.87 | | | | | | | strictly_less_than(all_47_5, all_47_2) = all_64_3 & ( ~ % 14.90/2.87 | | | | | | | (all_64_3 = 0) | ~ (all_64_4 = 0)) % 14.90/2.87 | | | | | | | % 14.90/2.87 | | | | | | | ALPHA: (83) implies: % 14.90/2.87 | | | | | | | (84) strictly_less_than(all_47_5, all_47_2) = all_64_3 % 14.90/2.87 | | | | | | | (85) contains_slb(all_47_7, all_47_5) = all_64_4 % 14.90/2.87 | | | | | | | (86) ~ (all_64_3 = 0) | ~ (all_64_4 = 0) % 14.90/2.87 | | | | | | | % 14.90/2.87 | | | | | | | REDUCE: (71), (84) imply: % 14.90/2.87 | | | | | | | (87) strictly_less_than(all_47_5, all_47_3) = all_64_3 % 14.90/2.87 | | | | | | | % 14.90/2.87 | | | | | | | GROUND_INST: instantiating (9) with 0, all_64_3, all_47_3, % 14.90/2.87 | | | | | | | all_47_5, simplifying with (19), (87) gives: % 14.90/2.87 | | | | | | | (88) all_64_3 = 0 % 14.90/2.87 | | | | | | | % 14.90/2.87 | | | | | | | GROUND_INST: instantiating (10) with 0, all_64_4, all_47_5, % 14.90/2.87 | | | | | | | all_47_7, simplifying with (20), (85) gives: % 14.90/2.87 | | | | | | | (89) all_64_4 = 0 % 14.90/2.87 | | | | | | | % 14.90/2.87 | | | | | | | BETA: splitting (86) gives: % 14.90/2.87 | | | | | | | % 14.90/2.87 | | | | | | | Case 1: % 14.90/2.87 | | | | | | | | % 14.90/2.87 | | | | | | | | (90) ~ (all_64_3 = 0) % 14.90/2.87 | | | | | | | | % 14.90/2.87 | | | | | | | | REDUCE: (88), (90) imply: % 14.90/2.87 | | | | | | | | (91) $false % 14.90/2.87 | | | | | | | | % 14.90/2.87 | | | | | | | | CLOSE: (91) is inconsistent. % 14.90/2.87 | | | | | | | | % 14.90/2.87 | | | | | | | Case 2: % 14.90/2.87 | | | | | | | | % 14.90/2.87 | | | | | | | | (92) ~ (all_64_4 = 0) % 14.90/2.87 | | | | | | | | % 14.90/2.87 | | | | | | | | REDUCE: (89), (92) imply: % 14.90/2.87 | | | | | | | | (93) $false % 14.90/2.87 | | | | | | | | % 14.90/2.87 | | | | | | | | CLOSE: (93) is inconsistent. % 14.90/2.87 | | | | | | | | % 14.90/2.87 | | | | | | | End of split % 14.90/2.87 | | | | | | | % 14.90/2.87 | | | | | | End of split % 14.90/2.87 | | | | | | % 14.90/2.87 | | | | | End of split % 14.90/2.87 | | | | | % 14.90/2.87 | | | | End of split % 14.90/2.87 | | | | % 14.90/2.87 | | | End of split % 14.90/2.87 | | | % 14.90/2.87 | | End of split % 14.90/2.87 | | % 14.90/2.87 | End of split % 14.90/2.87 | % 14.90/2.87 End of proof % 14.90/2.87 % SZS output end Proof for theBenchmark % 14.90/2.87 % 14.90/2.87 2241ms %------------------------------------------------------------------------------