%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWV415+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 : n009.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 22:56:15 EDT 2023 % Result : Theorem 13.16s 2.47s % Output : Proof 15.70s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SWV415+1 : TPTP v8.1.2. Released v3.3.0. % 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.33 % Computer : n009.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 : Tue Aug 29 09:03:05 EDT 2023 % 0.12/0.33 % CPUTime : % 0.48/0.59 ________ _____ % 0.48/0.59 ___ __ \_________(_)________________________________ % 0.48/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.48/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.48/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.48/0.59 % 0.48/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.48/0.59 (2023-06-19) % 0.48/0.59 % 0.48/0.60 (c) Philipp Rümmer, 2009-2023 % 0.48/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.48/0.60 Amanda Stjerna. % 0.48/0.60 Free software under BSD-3-Clause. % 0.48/0.60 % 0.48/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.48/0.60 % 0.48/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.48/0.61 Running up to 7 provers in parallel. % 0.48/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.48/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.48/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.48/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.48/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.48/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.48/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.27/1.15 Prover 1: Preprocessing ... % 3.47/1.16 Prover 4: Preprocessing ... % 3.47/1.20 Prover 3: Preprocessing ... % 3.47/1.20 Prover 0: Preprocessing ... % 3.47/1.20 Prover 6: Preprocessing ... % 3.47/1.20 Prover 5: Preprocessing ... % 3.47/1.20 Prover 2: Preprocessing ... % 9.44/1.98 Prover 1: Warning: ignoring some quantifiers % 9.88/2.05 Prover 3: Warning: ignoring some quantifiers % 10.06/2.07 Prover 5: Proving ... % 10.06/2.09 Prover 1: Constructing countermodel ... % 10.06/2.09 Prover 6: Proving ... % 10.06/2.11 Prover 3: Constructing countermodel ... % 10.06/2.12 Prover 2: Proving ... % 10.59/2.17 Prover 4: Constructing countermodel ... % 10.97/2.24 Prover 0: Proving ... % 13.16/2.47 Prover 5: proved (1851ms) % 13.16/2.47 % 13.16/2.47 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 13.16/2.47 % 13.16/2.48 Prover 0: proved (1855ms) % 13.16/2.48 % 13.16/2.48 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 13.16/2.48 % 13.16/2.48 Prover 2: stopped % 13.16/2.48 Prover 6: stopped % 13.16/2.48 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 13.16/2.48 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 13.16/2.48 Prover 3: stopped % 13.16/2.49 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 13.16/2.49 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 13.16/2.49 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 13.85/2.58 Prover 7: Preprocessing ... % 13.85/2.58 Prover 10: Preprocessing ... % 13.85/2.59 Prover 11: Preprocessing ... % 14.09/2.59 Prover 13: Preprocessing ... % 14.09/2.60 Prover 4: Found proof (size 24) % 14.09/2.60 Prover 8: Preprocessing ... % 14.09/2.61 Prover 4: proved (1985ms) % 14.09/2.62 Prover 1: stopped % 14.43/2.65 Prover 10: stopped % 14.43/2.65 Prover 7: stopped % 14.43/2.69 Prover 11: stopped % 14.43/2.70 Prover 13: stopped % 14.95/2.76 Prover 8: Warning: ignoring some quantifiers % 15.24/2.78 Prover 8: Constructing countermodel ... % 15.24/2.79 Prover 8: stopped % 15.24/2.79 % 15.24/2.79 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 15.24/2.79 % 15.24/2.80 % SZS output start Proof for theBenchmark % 15.24/2.80 Assumptions after simplification: % 15.24/2.80 --------------------------------- % 15.24/2.80 % 15.24/2.80 (ax37) % 15.24/2.83 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 15.24/2.83 $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (triple(v0, v6, v2) = v7) | ~ % 15.24/2.83 (pair(v3, v4) = v5) | ~ (insert_slb(v1, v5) = v6) | ~ $i(v4) | ~ $i(v3) | % 15.24/2.83 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v8: any] : ? [v9: any] : ? [v10: % 15.24/2.83 $i] : ? [v11: any] : (triple(v0, v1, v2) = v10 & check_cpq(v10) = v11 & % 15.24/2.83 check_cpq(v7) = v9 & less_than(v4, v3) = v8 & $i(v10) & ( ~ (v8 = 0) | (( % 15.24/2.83 ~ (v11 = 0) | v9 = 0) & ( ~ (v9 = 0) | v11 = 0))))) % 15.24/2.83 % 15.24/2.83 (ax42) % 15.24/2.83 $i(bottom) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 15.24/2.83 $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (insert_pqp(v0, v3) = % 15.24/2.83 v4) | ~ (triple(v4, v6, v2) = v7) | ~ (pair(v3, bottom) = v5) | ~ % 15.24/2.83 (insert_slb(v1, v5) = v6) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 15.24/2.83 ? [v8: $i] : (triple(v0, v1, v2) = v8 & insert_cpq(v8, v3) = v7 & $i(v8) & % 15.24/2.83 $i(v7))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 15.24/2.83 $i] : ! [v5: $i] : ( ~ (triple(v0, v1, v2) = v4) | ~ (insert_cpq(v4, v3) = % 15.24/2.83 v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: $i] : ? % 15.24/2.83 [v7: $i] : ? [v8: $i] : (insert_pqp(v0, v3) = v6 & triple(v6, v8, v2) = v5 % 15.24/2.83 & pair(v3, bottom) = v7 & insert_slb(v1, v7) = v8 & $i(v8) & $i(v7) & % 15.24/2.83 $i(v6) & $i(v5))) % 15.24/2.83 % 15.24/2.83 (ax50) % 15.24/2.83 $i(create_slb) & $i(bottom) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 15.24/2.83 (triple(v0, create_slb, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 15.24/2.83 findmin_cpq_res(v2) = bottom) % 15.24/2.83 % 15.24/2.83 (ax55) % 15.24/2.83 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 15.24/2.83 $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (triple(v0, v6, v2) = v7) | ~ % 15.24/2.83 (pair(v3, v4) = v5) | ~ (insert_slb(v1, v5) = v6) | ~ $i(v4) | ~ $i(v3) | % 15.24/2.83 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v8: $i] : ? [v9: $i] : ? [v10: $i] % 15.24/2.83 : (i(v9) = v10 & i(v7) = v8 & triple(v0, v1, v2) = v9 & insert_pq(v10, v3) = % 15.24/2.83 v8 & $i(v10) & $i(v9) & $i(v8))) % 15.24/2.83 % 15.24/2.83 (co2) % 15.24/2.83 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 15.24/2.83 $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ( ~ (v8 = v6) & i(v5) = v6 & % 15.24/2.83 i(v4) = v7 & triple(v0, v1, v2) = v4 & insert_cpq(v4, v3) = v5 & % 15.24/2.83 insert_pq(v7, v3) = v8 & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) % 15.24/2.83 & $i(v2) & $i(v1) & $i(v0)) % 15.24/2.83 % 15.24/2.83 (main2_l12) % 15.24/2.84 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 15.24/2.84 $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : (v8 = v6 | ~ (i(v7) = v8) | % 15.24/2.84 ~ (i(v5) = v6) | ~ (triple(v1, v2, v4) = v7) | ~ (triple(v0, v2, v3) = % 15.24/2.84 v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) % 15.24/2.84 % 15.24/2.84 (function-axioms) % 15.24/2.85 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 % 15.24/2.85 | ~ (triple(v4, v3, v2) = v1) | ~ (triple(v4, v3, v2) = v0)) & ! [v0: % 15.24/2.85 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 15.24/2.85 : ! [v4: $i] : (v1 = v0 | ~ (pair_in_list(v4, v3, v2) = v1) | ~ % 15.24/2.85 (pair_in_list(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 15.24/2.85 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 15.24/2.85 (pi_sharp_removemin(v3, v2) = v1) | ~ (pi_sharp_removemin(v3, v2) = v0)) & % 15.24/2.85 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 15.24/2.85 $i] : (v1 = v0 | ~ (pi_sharp_find_min(v3, v2) = v1) | ~ % 15.24/2.85 (pi_sharp_find_min(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 15.24/2.85 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 15.24/2.85 (pi_remove(v3, v2) = v1) | ~ (pi_remove(v3, v2) = v0)) & ! [v0: % 15.24/2.85 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 15.24/2.85 : (v1 = v0 | ~ (pi_sharp_remove(v3, v2) = v1) | ~ (pi_sharp_remove(v3, v2) = % 15.24/2.85 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 15.24/2.85 ~ (remove_pqp(v3, v2) = v1) | ~ (remove_pqp(v3, v2) = v0)) & ! [v0: $i] : % 15.24/2.85 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (insert_pqp(v3, v2) = % 15.24/2.85 v1) | ~ (insert_pqp(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 15.24/2.85 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 15.24/2.85 (contains_cpq(v3, v2) = v1) | ~ (contains_cpq(v3, v2) = v0)) & ! [v0: $i] % 15.24/2.85 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (remove_cpq(v3, v2) % 15.24/2.85 = v1) | ~ (remove_cpq(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 15.24/2.85 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (insert_cpq(v3, v2) = v1) | ~ % 15.24/2.85 (insert_cpq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 15.24/2.85 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (succ_cpq(v3, % 15.24/2.85 v2) = v1) | ~ (succ_cpq(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 15.24/2.85 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (update_slb(v3, v2) = v1) | ~ % 15.24/2.85 (update_slb(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 15.24/2.85 [v3: $i] : (v1 = v0 | ~ (lookup_slb(v3, v2) = v1) | ~ (lookup_slb(v3, v2) = % 15.24/2.85 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 15.24/2.85 ~ (remove_slb(v3, v2) = v1) | ~ (remove_slb(v3, v2) = v0)) & ! [v0: % 15.24/2.85 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 15.24/2.85 : (v1 = v0 | ~ (contains_slb(v3, v2) = v1) | ~ (contains_slb(v3, v2) = v0)) % 15.24/2.85 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 15.24/2.85 (pair(v3, v2) = v1) | ~ (pair(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 15.24/2.85 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (insert_slb(v3, v2) = v1) | ~ % 15.24/2.85 (insert_slb(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 15.24/2.85 [v3: $i] : (v1 = v0 | ~ (removemin_pq_res(v3, v2) = v1) | ~ % 15.24/2.85 (removemin_pq_res(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 15.24/2.85 ! [v3: $i] : (v1 = v0 | ~ (removemin_pq_eff(v3, v2) = v1) | ~ % 15.24/2.85 (removemin_pq_eff(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 15.24/2.85 ! [v3: $i] : (v1 = v0 | ~ (findmin_pq_res(v3, v2) = v1) | ~ % 15.24/2.85 (findmin_pq_res(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 15.24/2.85 ! [v3: $i] : (v1 = v0 | ~ (findmin_pq_eff(v3, v2) = v1) | ~ % 15.24/2.85 (findmin_pq_eff(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 15.24/2.85 ! [v3: $i] : (v1 = v0 | ~ (remove_pq(v3, v2) = v1) | ~ (remove_pq(v3, v2) = % 15.24/2.85 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 15.24/2.85 $i] : ! [v3: $i] : (v1 = v0 | ~ (issmallestelement_pq(v3, v2) = v1) | ~ % 15.24/2.85 (issmallestelement_pq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 15.24/2.85 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 15.24/2.85 (contains_pq(v3, v2) = v1) | ~ (contains_pq(v3, v2) = v0)) & ! [v0: $i] : % 15.24/2.85 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (insert_pq(v3, v2) = % 15.24/2.85 v1) | ~ (insert_pq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 15.24/2.85 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 15.24/2.85 (strictly_less_than(v3, v2) = v1) | ~ (strictly_less_than(v3, v2) = v0)) & % 15.24/2.85 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 15.24/2.85 $i] : (v1 = v0 | ~ (less_than(v3, v2) = v1) | ~ (less_than(v3, v2) = v0)) % 15.24/2.85 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 % 15.24/2.85 = v0 | ~ (phi(v2) = v1) | ~ (phi(v2) = v0)) & ! [v0: MultipleValueBool] : % 15.24/2.85 ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (pi_removemin(v2) = % 15.24/2.85 v1) | ~ (pi_removemin(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 15.24/2.85 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (pi_find_min(v2) = v1) | ~ % 15.24/2.85 (pi_find_min(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 % 15.24/2.85 | ~ (i(v2) = v1) | ~ (i(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 15.24/2.85 $i] : (v1 = v0 | ~ (removemin_cpq_res(v2) = v1) | ~ (removemin_cpq_res(v2) % 15.24/2.85 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 15.24/2.85 (findmin_cpq_res(v2) = v1) | ~ (findmin_cpq_res(v2) = v0)) & ! [v0: $i] : % 15.24/2.85 ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (findmin_pqp_res(v2) = v1) | ~ % 15.24/2.85 (findmin_pqp_res(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 15.24/2.85 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (ok(v2) = v1) | ~ (ok(v2) % 15.24/2.85 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 15.24/2.85 $i] : (v1 = v0 | ~ (check_cpq(v2) = v1) | ~ (check_cpq(v2) = v0)) & ! % 15.24/2.85 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (removemin_cpq_eff(v2) = % 15.24/2.85 v1) | ~ (removemin_cpq_eff(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 15.24/2.85 [v2: $i] : (v1 = v0 | ~ (findmin_cpq_eff(v2) = v1) | ~ (findmin_cpq_eff(v2) % 15.24/2.85 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 15.24/2.85 $i] : (v1 = v0 | ~ (isnonempty_slb(v2) = v1) | ~ (isnonempty_slb(v2) = % 15.24/2.85 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 15.24/2.85 $i] : (v1 = v0 | ~ (isnonempty_pq(v2) = v1) | ~ (isnonempty_pq(v2) = v0)) % 15.24/2.85 % 15.24/2.85 Further assumptions not needed in the proof: % 15.24/2.85 -------------------------------------------- % 15.24/2.85 ax10, ax11, ax12, ax13, ax14, ax15, ax16, ax17, ax18, ax19, ax20, ax21, ax22, % 15.24/2.85 ax23, ax24, ax25, ax26, ax27, ax28, ax29, ax30, ax31, ax32, ax33, ax34, ax35, % 15.24/2.85 ax36, ax38, ax39, ax40, ax41, ax43, ax44, ax45, ax46, ax47, ax48, ax49, ax51, % 15.24/2.85 ax52, ax53, ax54, ax56, ax57, ax58, ax59, ax6, ax60, ax61, ax62, ax7, ax8, ax9, % 15.24/2.85 bottom_smallest, reflexivity, stricly_smaller_definition, totality, transitivity % 15.24/2.85 % 15.24/2.85 Those formulas are unsatisfiable: % 15.24/2.85 --------------------------------- % 15.24/2.85 % 15.24/2.85 Begin of proof % 15.24/2.85 | % 15.24/2.85 | ALPHA: (ax42) implies: % 15.24/2.85 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 15.24/2.85 | ! [v5: $i] : ( ~ (triple(v0, v1, v2) = v4) | ~ (insert_cpq(v4, v3) = % 15.24/2.85 | v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: $i] : % 15.24/2.85 | ? [v7: $i] : ? [v8: $i] : (insert_pqp(v0, v3) = v6 & triple(v6, v8, % 15.24/2.85 | v2) = v5 & pair(v3, bottom) = v7 & insert_slb(v1, v7) = v8 & % 15.24/2.85 | $i(v8) & $i(v7) & $i(v6) & $i(v5))) % 15.24/2.85 | % 15.24/2.85 | ALPHA: (ax50) implies: % 15.24/2.85 | (2) $i(bottom) % 15.24/2.85 | % 15.24/2.85 | ALPHA: (function-axioms) implies: % 15.24/2.85 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (i(v2) = v1) | % 15.24/2.85 | ~ (i(v2) = v0)) % 15.24/2.85 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 15.24/2.85 | (insert_pq(v3, v2) = v1) | ~ (insert_pq(v3, v2) = v0)) % 15.24/2.85 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 15.24/2.85 | (v1 = v0 | ~ (triple(v4, v3, v2) = v1) | ~ (triple(v4, v3, v2) = v0)) % 15.24/2.85 | % 15.24/2.85 | DELTA: instantiating (co2) with fresh symbols all_69_0, all_69_1, all_69_2, % 15.24/2.85 | all_69_3, all_69_4, all_69_5, all_69_6, all_69_7, all_69_8 gives: % 15.24/2.86 | (6) ~ (all_69_0 = all_69_2) & i(all_69_3) = all_69_2 & i(all_69_4) = % 15.24/2.86 | all_69_1 & triple(all_69_8, all_69_7, all_69_6) = all_69_4 & % 15.24/2.86 | insert_cpq(all_69_4, all_69_5) = all_69_3 & insert_pq(all_69_1, % 15.24/2.86 | all_69_5) = all_69_0 & $i(all_69_0) & $i(all_69_1) & $i(all_69_2) & % 15.24/2.86 | $i(all_69_3) & $i(all_69_4) & $i(all_69_5) & $i(all_69_6) & % 15.24/2.86 | $i(all_69_7) & $i(all_69_8) % 15.24/2.86 | % 15.24/2.86 | ALPHA: (6) implies: % 15.24/2.86 | (7) ~ (all_69_0 = all_69_2) % 15.24/2.86 | (8) $i(all_69_8) % 15.24/2.86 | (9) $i(all_69_7) % 15.24/2.86 | (10) $i(all_69_6) % 15.24/2.86 | (11) $i(all_69_5) % 15.24/2.86 | (12) insert_pq(all_69_1, all_69_5) = all_69_0 % 15.24/2.86 | (13) insert_cpq(all_69_4, all_69_5) = all_69_3 % 15.24/2.86 | (14) triple(all_69_8, all_69_7, all_69_6) = all_69_4 % 15.24/2.86 | (15) i(all_69_4) = all_69_1 % 15.24/2.86 | (16) i(all_69_3) = all_69_2 % 15.24/2.86 | % 15.24/2.86 | GROUND_INST: instantiating (1) with all_69_8, all_69_7, all_69_6, all_69_5, % 15.24/2.86 | all_69_4, all_69_3, simplifying with (8), (9), (10), (11), (13), % 15.24/2.86 | (14) gives: % 15.24/2.86 | (17) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (insert_pqp(all_69_8, % 15.24/2.86 | all_69_5) = v0 & triple(v0, v2, all_69_6) = all_69_3 & % 15.24/2.86 | pair(all_69_5, bottom) = v1 & insert_slb(all_69_7, v1) = v2 & $i(v2) % 15.24/2.86 | & $i(v1) & $i(v0) & $i(all_69_3)) % 15.24/2.86 | % 15.24/2.86 | DELTA: instantiating (17) with fresh symbols all_85_0, all_85_1, all_85_2 % 15.24/2.86 | gives: % 15.24/2.86 | (18) insert_pqp(all_69_8, all_69_5) = all_85_2 & triple(all_85_2, all_85_0, % 15.24/2.86 | all_69_6) = all_69_3 & pair(all_69_5, bottom) = all_85_1 & % 15.24/2.86 | insert_slb(all_69_7, all_85_1) = all_85_0 & $i(all_85_0) & % 15.24/2.86 | $i(all_85_1) & $i(all_85_2) & $i(all_69_3) % 15.24/2.86 | % 15.24/2.86 | ALPHA: (18) implies: % 15.24/2.86 | (19) $i(all_85_2) % 15.24/2.86 | (20) insert_slb(all_69_7, all_85_1) = all_85_0 % 15.24/2.86 | (21) pair(all_69_5, bottom) = all_85_1 % 15.24/2.86 | (22) triple(all_85_2, all_85_0, all_69_6) = all_69_3 % 15.24/2.86 | % 15.24/2.86 | GROUND_INST: instantiating (ax37) with all_85_2, all_69_7, all_69_6, all_69_5, % 15.24/2.86 | bottom, all_85_1, all_85_0, all_69_3, simplifying with (2), (9), % 15.24/2.86 | (10), (11), (19), (20), (21), (22) gives: % 15.24/2.86 | (23) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: any] : % 15.24/2.86 | (triple(all_85_2, all_69_7, all_69_6) = v2 & check_cpq(v2) = v3 & % 15.24/2.86 | check_cpq(all_69_3) = v1 & less_than(bottom, all_69_5) = v0 & $i(v2) % 15.24/2.86 | & ( ~ (v0 = 0) | (( ~ (v3 = 0) | v1 = 0) & ( ~ (v1 = 0) | v3 = 0)))) % 15.24/2.86 | % 15.24/2.86 | GROUND_INST: instantiating (ax55) with all_85_2, all_69_7, all_69_6, all_69_5, % 15.24/2.86 | bottom, all_85_1, all_85_0, all_69_3, simplifying with (2), (9), % 15.24/2.86 | (10), (11), (19), (20), (21), (22) gives: % 15.24/2.86 | (24) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (i(v1) = v2 & i(all_69_3) = % 15.24/2.86 | v0 & triple(all_85_2, all_69_7, all_69_6) = v1 & insert_pq(v2, % 15.24/2.86 | all_69_5) = v0 & $i(v2) & $i(v1) & $i(v0)) % 15.24/2.86 | % 15.24/2.86 | DELTA: instantiating (24) with fresh symbols all_95_0, all_95_1, all_95_2 % 15.24/2.86 | gives: % 15.24/2.86 | (25) i(all_95_1) = all_95_0 & i(all_69_3) = all_95_2 & triple(all_85_2, % 15.24/2.86 | all_69_7, all_69_6) = all_95_1 & insert_pq(all_95_0, all_69_5) = % 15.24/2.86 | all_95_2 & $i(all_95_0) & $i(all_95_1) & $i(all_95_2) % 15.24/2.86 | % 15.24/2.86 | ALPHA: (25) implies: % 15.24/2.86 | (26) insert_pq(all_95_0, all_69_5) = all_95_2 % 15.24/2.86 | (27) triple(all_85_2, all_69_7, all_69_6) = all_95_1 % 15.24/2.86 | (28) i(all_69_3) = all_95_2 % 15.24/2.87 | (29) i(all_95_1) = all_95_0 % 15.24/2.87 | % 15.24/2.87 | DELTA: instantiating (23) with fresh symbols all_99_0, all_99_1, all_99_2, % 15.24/2.87 | all_99_3 gives: % 15.24/2.87 | (30) triple(all_85_2, all_69_7, all_69_6) = all_99_1 & check_cpq(all_99_1) % 15.24/2.87 | = all_99_0 & check_cpq(all_69_3) = all_99_2 & less_than(bottom, % 15.24/2.87 | all_69_5) = all_99_3 & $i(all_99_1) & ( ~ (all_99_3 = 0) | (( ~ % 15.24/2.87 | (all_99_0 = 0) | all_99_2 = 0) & ( ~ (all_99_2 = 0) | all_99_0 = % 15.24/2.87 | 0))) % 15.24/2.87 | % 15.24/2.87 | ALPHA: (30) implies: % 15.24/2.87 | (31) triple(all_85_2, all_69_7, all_69_6) = all_99_1 % 15.24/2.87 | % 15.24/2.87 | GROUND_INST: instantiating (5) with all_95_1, all_99_1, all_69_6, all_69_7, % 15.24/2.87 | all_85_2, simplifying with (27), (31) gives: % 15.24/2.87 | (32) all_99_1 = all_95_1 % 15.24/2.87 | % 15.24/2.87 | GROUND_INST: instantiating (3) with all_69_2, all_95_2, all_69_3, simplifying % 15.24/2.87 | with (16), (28) gives: % 15.24/2.87 | (33) all_95_2 = all_69_2 % 15.24/2.87 | % 15.24/2.87 | REDUCE: (26), (33) imply: % 15.24/2.87 | (34) insert_pq(all_95_0, all_69_5) = all_69_2 % 15.24/2.87 | % 15.24/2.87 | GROUND_INST: instantiating (main2_l12) with all_85_2, all_69_8, all_69_7, % 15.24/2.87 | all_69_6, all_69_6, all_95_1, all_95_0, all_69_4, all_69_1, % 15.24/2.87 | simplifying with (8), (9), (10), (14), (15), (19), (27), (29) % 15.24/2.87 | gives: % 15.24/2.87 | (35) all_95_0 = all_69_1 % 15.24/2.87 | % 15.24/2.87 | REDUCE: (34), (35) imply: % 15.24/2.87 | (36) insert_pq(all_69_1, all_69_5) = all_69_2 % 15.24/2.87 | % 15.70/2.87 | GROUND_INST: instantiating (4) with all_69_0, all_69_2, all_69_5, all_69_1, % 15.70/2.87 | simplifying with (12), (36) gives: % 15.70/2.87 | (37) all_69_0 = all_69_2 % 15.70/2.87 | % 15.70/2.87 | REDUCE: (7), (37) imply: % 15.70/2.87 | (38) $false % 15.70/2.87 | % 15.70/2.87 | CLOSE: (38) is inconsistent. % 15.70/2.87 | % 15.70/2.87 End of proof % 15.70/2.87 % SZS output end Proof for theBenchmark % 15.70/2.87 % 15.70/2.87 2274ms %------------------------------------------------------------------------------