%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWV366+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 : n022.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 22:56:02 EDT 2023 % Result : Theorem 12.93s 2.46s % Output : Proof 15.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.13 % Problem : SWV366+1 : TPTP v8.1.2. Released v3.3.0. % 0.11/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n022.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Tue Aug 29 05:44:08 EDT 2023 % 0.13/0.35 % CPUTime : % 0.20/0.62 ________ _____ % 0.20/0.62 ___ __ \_________(_)________________________________ % 0.20/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.62 % 0.20/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.62 (2023-06-19) % 0.20/0.62 % 0.20/0.62 (c) Philipp Rümmer, 2009-2023 % 0.20/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.62 Amanda Stjerna. % 0.20/0.62 Free software under BSD-3-Clause. % 0.20/0.62 % 0.20/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.62 % 0.20/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.20/0.63 Running up to 7 provers in parallel. % 0.20/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.20/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 3.96/1.22 Prover 1: Preprocessing ... % 3.96/1.22 Prover 4: Preprocessing ... % 3.96/1.26 Prover 0: Preprocessing ... % 3.96/1.26 Prover 6: Preprocessing ... % 3.96/1.26 Prover 3: Preprocessing ... % 3.96/1.26 Prover 5: Preprocessing ... % 3.96/1.26 Prover 2: Preprocessing ... % 9.21/1.99 Prover 1: Warning: ignoring some quantifiers % 9.99/2.08 Prover 5: Proving ... % 9.99/2.09 Prover 6: Proving ... % 10.43/2.11 Prover 3: Warning: ignoring some quantifiers % 10.43/2.11 Prover 1: Constructing countermodel ... % 10.89/2.17 Prover 3: Constructing countermodel ... % 10.89/2.24 Prover 4: Constructing countermodel ... % 10.89/2.27 Prover 2: Proving ... % 10.89/2.29 Prover 0: Proving ... % 12.93/2.46 Prover 3: proved (1813ms) % 12.93/2.46 % 12.93/2.46 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 12.93/2.46 % 12.93/2.46 Prover 2: stopped % 12.93/2.46 Prover 5: stopped % 12.93/2.47 Prover 0: stopped % 12.93/2.49 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 12.93/2.49 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 12.93/2.49 Prover 6: stopped % 12.93/2.49 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 12.93/2.49 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 12.93/2.50 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 13.46/2.53 Prover 7: Preprocessing ... % 13.46/2.54 Prover 8: Preprocessing ... % 13.91/2.59 Prover 13: Preprocessing ... % 13.91/2.60 Prover 10: Preprocessing ... % 13.91/2.61 Prover 11: Preprocessing ... % 13.91/2.63 Prover 1: Found proof (size 35) % 13.91/2.63 Prover 1: proved (1988ms) % 13.91/2.63 Prover 4: stopped % 13.91/2.65 Prover 10: stopped % 13.91/2.65 Prover 7: stopped % 14.60/2.68 Prover 13: stopped % 14.60/2.68 Prover 11: stopped % 15.04/2.76 Prover 8: Warning: ignoring some quantifiers % 15.04/2.78 Prover 8: Constructing countermodel ... % 15.04/2.79 Prover 8: stopped % 15.04/2.79 % 15.04/2.79 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 15.04/2.79 % 15.04/2.80 % SZS output start Proof for theBenchmark % 15.37/2.81 Assumptions after simplification: % 15.37/2.81 --------------------------------- % 15.37/2.81 % 15.37/2.81 (ax37) % 15.37/2.85 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 15.37/2.85 $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (triple(v0, v6, v2) = v7) | ~ % 15.37/2.85 (pair(v3, v4) = v5) | ~ (insert_slb(v1, v5) = v6) | ~ $i(v4) | ~ $i(v3) | % 15.37/2.85 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v8: any] : ? [v9: any] : ? [v10: % 15.37/2.85 $i] : ? [v11: any] : (triple(v0, v1, v2) = v10 & check_cpq(v10) = v11 & % 15.37/2.85 check_cpq(v7) = v9 & less_than(v4, v3) = v8 & $i(v10) & ( ~ (v8 = 0) | (( % 15.37/2.85 ~ (v11 = 0) | v9 = 0) & ( ~ (v9 = 0) | v11 = 0))))) % 15.37/2.85 % 15.37/2.85 (ax55) % 15.37/2.85 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 15.37/2.85 $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (triple(v0, v6, v2) = v7) | ~ % 15.37/2.85 (pair(v3, v4) = v5) | ~ (insert_slb(v1, v5) = v6) | ~ $i(v4) | ~ $i(v3) | % 15.37/2.85 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v8: $i] : ? [v9: $i] : ? [v10: $i] % 15.37/2.85 : (i(v9) = v10 & i(v7) = v8 & triple(v0, v1, v2) = v9 & insert_pq(v10, v3) = % 15.37/2.85 v8 & $i(v10) & $i(v9) & $i(v8))) % 15.37/2.85 % 15.37/2.85 (l2_co) % 15.37/2.85 ? [v0: $i] : ($i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] % 15.37/2.85 : ! [v5: $i] : ! [v6: $i] : ( ~ (triple(v2, v0, v4) = v6) | ~ (triple(v1, % 15.37/2.85 v0, v3) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ? % 15.37/2.85 [v7: $i] : (i(v6) = v7 & i(v5) = v7 & $i(v7))) & ? [v1: $i] : ? [v2: $i] % 15.37/2.85 : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? % 15.37/2.85 [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ( ~ % 15.37/2.85 (v12 = v10) & i(v11) = v12 & i(v9) = v10 & triple(v2, v8, v4) = v11 & % 15.37/2.85 triple(v1, v8, v3) = v9 & pair(v5, v6) = v7 & insert_slb(v0, v7) = v8 & % 15.37/2.85 $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & % 15.37/2.85 $i(v4) & $i(v3) & $i(v2) & $i(v1))) % 15.37/2.85 % 15.37/2.85 (function-axioms) % 15.37/2.86 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 % 15.37/2.86 | ~ (triple(v4, v3, v2) = v1) | ~ (triple(v4, v3, v2) = v0)) & ! [v0: % 15.37/2.86 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 15.37/2.86 : ! [v4: $i] : (v1 = v0 | ~ (pair_in_list(v4, v3, v2) = v1) | ~ % 15.37/2.86 (pair_in_list(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 15.37/2.86 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 15.37/2.86 (pi_sharp_removemin(v3, v2) = v1) | ~ (pi_sharp_removemin(v3, v2) = v0)) & % 15.37/2.86 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 15.37/2.86 $i] : (v1 = v0 | ~ (pi_sharp_find_min(v3, v2) = v1) | ~ % 15.37/2.86 (pi_sharp_find_min(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 15.37/2.86 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 15.37/2.86 (pi_remove(v3, v2) = v1) | ~ (pi_remove(v3, v2) = v0)) & ! [v0: % 15.37/2.86 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 15.37/2.86 : (v1 = v0 | ~ (pi_sharp_remove(v3, v2) = v1) | ~ (pi_sharp_remove(v3, v2) = % 15.37/2.86 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 15.37/2.86 ~ (remove_pqp(v3, v2) = v1) | ~ (remove_pqp(v3, v2) = v0)) & ! [v0: $i] : % 15.37/2.86 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (insert_pqp(v3, v2) = % 15.37/2.86 v1) | ~ (insert_pqp(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 15.37/2.86 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 15.37/2.86 (contains_cpq(v3, v2) = v1) | ~ (contains_cpq(v3, v2) = v0)) & ! [v0: $i] % 15.37/2.86 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (remove_cpq(v3, v2) % 15.37/2.86 = v1) | ~ (remove_cpq(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 15.37/2.86 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (insert_cpq(v3, v2) = v1) | ~ % 15.37/2.86 (insert_cpq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 15.37/2.86 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (succ_cpq(v3, % 15.37/2.86 v2) = v1) | ~ (succ_cpq(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 15.37/2.86 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (update_slb(v3, v2) = v1) | ~ % 15.37/2.86 (update_slb(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 15.37/2.86 [v3: $i] : (v1 = v0 | ~ (lookup_slb(v3, v2) = v1) | ~ (lookup_slb(v3, v2) = % 15.37/2.86 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 15.37/2.86 ~ (remove_slb(v3, v2) = v1) | ~ (remove_slb(v3, v2) = v0)) & ! [v0: % 15.37/2.86 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 15.37/2.86 : (v1 = v0 | ~ (contains_slb(v3, v2) = v1) | ~ (contains_slb(v3, v2) = v0)) % 15.37/2.86 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 15.37/2.86 (pair(v3, v2) = v1) | ~ (pair(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 15.37/2.86 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (insert_slb(v3, v2) = v1) | ~ % 15.37/2.86 (insert_slb(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 15.37/2.86 [v3: $i] : (v1 = v0 | ~ (removemin_pq_res(v3, v2) = v1) | ~ % 15.37/2.86 (removemin_pq_res(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 15.37/2.86 ! [v3: $i] : (v1 = v0 | ~ (removemin_pq_eff(v3, v2) = v1) | ~ % 15.37/2.86 (removemin_pq_eff(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 15.37/2.86 ! [v3: $i] : (v1 = v0 | ~ (findmin_pq_res(v3, v2) = v1) | ~ % 15.37/2.86 (findmin_pq_res(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 15.37/2.86 ! [v3: $i] : (v1 = v0 | ~ (findmin_pq_eff(v3, v2) = v1) | ~ % 15.37/2.86 (findmin_pq_eff(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 15.37/2.86 ! [v3: $i] : (v1 = v0 | ~ (remove_pq(v3, v2) = v1) | ~ (remove_pq(v3, v2) = % 15.37/2.86 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 15.37/2.86 $i] : ! [v3: $i] : (v1 = v0 | ~ (issmallestelement_pq(v3, v2) = v1) | ~ % 15.37/2.86 (issmallestelement_pq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 15.37/2.86 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 15.37/2.86 (contains_pq(v3, v2) = v1) | ~ (contains_pq(v3, v2) = v0)) & ! [v0: $i] : % 15.37/2.86 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (insert_pq(v3, v2) = % 15.37/2.86 v1) | ~ (insert_pq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 15.37/2.86 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 15.37/2.86 (strictly_less_than(v3, v2) = v1) | ~ (strictly_less_than(v3, v2) = v0)) & % 15.37/2.86 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 15.37/2.86 $i] : (v1 = v0 | ~ (less_than(v3, v2) = v1) | ~ (less_than(v3, v2) = v0)) % 15.37/2.86 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 % 15.37/2.86 = v0 | ~ (phi(v2) = v1) | ~ (phi(v2) = v0)) & ! [v0: MultipleValueBool] : % 15.37/2.86 ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (pi_removemin(v2) = % 15.37/2.86 v1) | ~ (pi_removemin(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 15.37/2.86 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (pi_find_min(v2) = v1) | ~ % 15.37/2.86 (pi_find_min(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 % 15.37/2.86 | ~ (i(v2) = v1) | ~ (i(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 15.37/2.86 $i] : (v1 = v0 | ~ (removemin_cpq_res(v2) = v1) | ~ (removemin_cpq_res(v2) % 15.37/2.87 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 15.37/2.87 (findmin_cpq_res(v2) = v1) | ~ (findmin_cpq_res(v2) = v0)) & ! [v0: $i] : % 15.37/2.87 ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (findmin_pqp_res(v2) = v1) | ~ % 15.37/2.87 (findmin_pqp_res(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 15.37/2.87 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (ok(v2) = v1) | ~ (ok(v2) % 15.37/2.87 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 15.37/2.87 $i] : (v1 = v0 | ~ (check_cpq(v2) = v1) | ~ (check_cpq(v2) = v0)) & ! % 15.37/2.87 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (removemin_cpq_eff(v2) = % 15.37/2.87 v1) | ~ (removemin_cpq_eff(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 15.37/2.87 [v2: $i] : (v1 = v0 | ~ (findmin_cpq_eff(v2) = v1) | ~ (findmin_cpq_eff(v2) % 15.37/2.87 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 15.37/2.87 $i] : (v1 = v0 | ~ (isnonempty_slb(v2) = v1) | ~ (isnonempty_slb(v2) = % 15.37/2.87 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 15.37/2.87 $i] : (v1 = v0 | ~ (isnonempty_pq(v2) = v1) | ~ (isnonempty_pq(v2) = v0)) % 15.37/2.87 % 15.37/2.87 Further assumptions not needed in the proof: % 15.37/2.87 -------------------------------------------- % 15.37/2.87 ax10, ax11, ax12, ax13, ax14, ax15, ax16, ax17, ax18, ax19, ax20, ax21, ax22, % 15.37/2.87 ax23, ax24, ax25, ax26, ax27, ax28, ax29, ax30, ax31, ax32, ax33, ax34, ax35, % 15.37/2.87 ax36, ax38, ax39, ax40, ax41, ax42, ax43, ax44, ax45, ax46, ax47, ax48, ax49, % 15.37/2.87 ax50, ax51, ax52, ax53, ax54, ax56, ax57, ax58, ax59, ax6, ax60, ax61, ax62, % 15.37/2.87 ax7, ax8, ax9, bottom_smallest, reflexivity, stricly_smaller_definition, % 15.37/2.87 totality, transitivity % 15.37/2.87 % 15.37/2.87 Those formulas are unsatisfiable: % 15.37/2.87 --------------------------------- % 15.37/2.87 % 15.37/2.87 Begin of proof % 15.37/2.87 | % 15.37/2.87 | ALPHA: (function-axioms) implies: % 15.37/2.87 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (i(v2) = v1) | % 15.37/2.87 | ~ (i(v2) = v0)) % 15.37/2.87 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 15.37/2.87 | (insert_pq(v3, v2) = v1) | ~ (insert_pq(v3, v2) = v0)) % 15.37/2.87 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 15.37/2.87 | (v1 = v0 | ~ (triple(v4, v3, v2) = v1) | ~ (triple(v4, v3, v2) = v0)) % 15.37/2.87 | % 15.37/2.87 | DELTA: instantiating (l2_co) with fresh symbol all_72_0 gives: % 15.37/2.87 | (4) $i(all_72_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 15.37/2.87 | ! [v4: $i] : ! [v5: $i] : ( ~ (triple(v1, all_72_0, v3) = v5) | ~ % 15.37/2.87 | (triple(v0, all_72_0, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | % 15.37/2.87 | ~ $i(v0) | ? [v6: $i] : (i(v5) = v6 & i(v4) = v6 & $i(v6))) & ? % 15.37/2.87 | [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? % 15.37/2.87 | [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? % 15.37/2.87 | [v10: $i] : ? [v11: $i] : ( ~ (v11 = v9) & i(v10) = v11 & i(v8) = v9 & % 15.37/2.87 | triple(v1, v7, v3) = v10 & triple(v0, v7, v2) = v8 & pair(v4, v5) = % 15.37/2.87 | v6 & insert_slb(all_72_0, v6) = v7 & $i(v11) & $i(v10) & $i(v9) & % 15.37/2.87 | $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) % 15.37/2.87 | & $i(v0)) % 15.37/2.87 | % 15.37/2.87 | ALPHA: (4) implies: % 15.37/2.87 | (5) $i(all_72_0) % 15.37/2.87 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 15.37/2.87 | ! [v5: $i] : ( ~ (triple(v1, all_72_0, v3) = v5) | ~ (triple(v0, % 15.37/2.87 | all_72_0, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 15.37/2.88 | $i(v0) | ? [v6: $i] : (i(v5) = v6 & i(v4) = v6 & $i(v6))) % 15.37/2.88 | (7) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 15.37/2.88 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? % 15.37/2.88 | [v10: $i] : ? [v11: $i] : ( ~ (v11 = v9) & i(v10) = v11 & i(v8) = v9 & % 15.37/2.88 | triple(v1, v7, v3) = v10 & triple(v0, v7, v2) = v8 & pair(v4, v5) = % 15.37/2.88 | v6 & insert_slb(all_72_0, v6) = v7 & $i(v11) & $i(v10) & $i(v9) & % 15.37/2.88 | $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) % 15.37/2.88 | & $i(v0)) % 15.37/2.88 | % 15.37/2.88 | DELTA: instantiating (7) with fresh symbols all_75_0, all_75_1, all_75_2, % 15.37/2.88 | all_75_3, all_75_4, all_75_5, all_75_6, all_75_7, all_75_8, all_75_9, % 15.37/2.88 | all_75_10, all_75_11 gives: % 15.37/2.88 | (8) ~ (all_75_0 = all_75_2) & i(all_75_1) = all_75_0 & i(all_75_3) = % 15.37/2.88 | all_75_2 & triple(all_75_10, all_75_4, all_75_8) = all_75_1 & % 15.37/2.88 | triple(all_75_11, all_75_4, all_75_9) = all_75_3 & pair(all_75_7, % 15.37/2.88 | all_75_6) = all_75_5 & insert_slb(all_72_0, all_75_5) = all_75_4 & % 15.37/2.88 | $i(all_75_0) & $i(all_75_1) & $i(all_75_2) & $i(all_75_3) & % 15.37/2.88 | $i(all_75_4) & $i(all_75_5) & $i(all_75_6) & $i(all_75_7) & % 15.37/2.88 | $i(all_75_8) & $i(all_75_9) & $i(all_75_10) & $i(all_75_11) % 15.37/2.88 | % 15.37/2.88 | ALPHA: (8) implies: % 15.37/2.88 | (9) ~ (all_75_0 = all_75_2) % 15.37/2.88 | (10) $i(all_75_11) % 15.37/2.88 | (11) $i(all_75_10) % 15.37/2.88 | (12) $i(all_75_9) % 15.37/2.88 | (13) $i(all_75_8) % 15.37/2.88 | (14) $i(all_75_7) % 15.37/2.88 | (15) $i(all_75_6) % 15.37/2.88 | (16) insert_slb(all_72_0, all_75_5) = all_75_4 % 15.37/2.88 | (17) pair(all_75_7, all_75_6) = all_75_5 % 15.37/2.88 | (18) triple(all_75_11, all_75_4, all_75_9) = all_75_3 % 15.37/2.88 | (19) triple(all_75_10, all_75_4, all_75_8) = all_75_1 % 15.37/2.88 | (20) i(all_75_3) = all_75_2 % 15.37/2.88 | (21) i(all_75_1) = all_75_0 % 15.37/2.88 | % 15.37/2.88 | GROUND_INST: instantiating (ax37) with all_75_11, all_72_0, all_75_9, % 15.37/2.88 | all_75_7, all_75_6, all_75_5, all_75_4, all_75_3, simplifying % 15.37/2.88 | with (5), (10), (12), (14), (15), (16), (17), (18) gives: % 15.37/2.88 | (22) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: any] : % 15.37/2.88 | (triple(all_75_11, all_72_0, all_75_9) = v2 & check_cpq(v2) = v3 & % 15.37/2.88 | check_cpq(all_75_3) = v1 & less_than(all_75_6, all_75_7) = v0 & % 15.37/2.88 | $i(v2) & ( ~ (v0 = 0) | (( ~ (v3 = 0) | v1 = 0) & ( ~ (v1 = 0) | v3 % 15.37/2.88 | = 0)))) % 15.37/2.88 | % 15.37/2.88 | GROUND_INST: instantiating (ax55) with all_75_11, all_72_0, all_75_9, % 15.37/2.88 | all_75_7, all_75_6, all_75_5, all_75_4, all_75_3, simplifying % 15.37/2.88 | with (5), (10), (12), (14), (15), (16), (17), (18) gives: % 15.37/2.88 | (23) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (i(v1) = v2 & i(all_75_3) = % 15.37/2.88 | v0 & triple(all_75_11, all_72_0, all_75_9) = v1 & insert_pq(v2, % 15.37/2.88 | all_75_7) = v0 & $i(v2) & $i(v1) & $i(v0)) % 15.37/2.88 | % 15.37/2.88 | GROUND_INST: instantiating (ax37) with all_75_10, all_72_0, all_75_8, % 15.37/2.88 | all_75_7, all_75_6, all_75_5, all_75_4, all_75_1, simplifying % 15.37/2.88 | with (5), (11), (13), (14), (15), (16), (17), (19) gives: % 15.37/2.88 | (24) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: any] : % 15.37/2.88 | (triple(all_75_10, all_72_0, all_75_8) = v2 & check_cpq(v2) = v3 & % 15.37/2.88 | check_cpq(all_75_1) = v1 & less_than(all_75_6, all_75_7) = v0 & % 15.37/2.88 | $i(v2) & ( ~ (v0 = 0) | (( ~ (v3 = 0) | v1 = 0) & ( ~ (v1 = 0) | v3 % 15.37/2.89 | = 0)))) % 15.37/2.89 | % 15.37/2.89 | GROUND_INST: instantiating (ax55) with all_75_10, all_72_0, all_75_8, % 15.37/2.89 | all_75_7, all_75_6, all_75_5, all_75_4, all_75_1, simplifying % 15.37/2.89 | with (5), (11), (13), (14), (15), (16), (17), (19) gives: % 15.37/2.89 | (25) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (i(v1) = v2 & i(all_75_1) = % 15.37/2.89 | v0 & triple(all_75_10, all_72_0, all_75_8) = v1 & insert_pq(v2, % 15.37/2.89 | all_75_7) = v0 & $i(v2) & $i(v1) & $i(v0)) % 15.37/2.89 | % 15.37/2.89 | DELTA: instantiating (23) with fresh symbols all_87_0, all_87_1, all_87_2 % 15.37/2.89 | gives: % 15.37/2.89 | (26) i(all_87_1) = all_87_0 & i(all_75_3) = all_87_2 & triple(all_75_11, % 15.37/2.89 | all_72_0, all_75_9) = all_87_1 & insert_pq(all_87_0, all_75_7) = % 15.37/2.89 | all_87_2 & $i(all_87_0) & $i(all_87_1) & $i(all_87_2) % 15.37/2.89 | % 15.37/2.89 | ALPHA: (26) implies: % 15.37/2.89 | (27) insert_pq(all_87_0, all_75_7) = all_87_2 % 15.37/2.89 | (28) triple(all_75_11, all_72_0, all_75_9) = all_87_1 % 15.37/2.89 | (29) i(all_75_3) = all_87_2 % 15.37/2.89 | (30) i(all_87_1) = all_87_0 % 15.37/2.89 | % 15.37/2.89 | DELTA: instantiating (25) with fresh symbols all_89_0, all_89_1, all_89_2 % 15.37/2.89 | gives: % 15.37/2.89 | (31) i(all_89_1) = all_89_0 & i(all_75_1) = all_89_2 & triple(all_75_10, % 15.37/2.89 | all_72_0, all_75_8) = all_89_1 & insert_pq(all_89_0, all_75_7) = % 15.37/2.89 | all_89_2 & $i(all_89_0) & $i(all_89_1) & $i(all_89_2) % 15.37/2.89 | % 15.37/2.89 | ALPHA: (31) implies: % 15.37/2.89 | (32) insert_pq(all_89_0, all_75_7) = all_89_2 % 15.37/2.89 | (33) triple(all_75_10, all_72_0, all_75_8) = all_89_1 % 15.37/2.89 | (34) i(all_75_1) = all_89_2 % 15.37/2.89 | (35) i(all_89_1) = all_89_0 % 15.37/2.89 | % 15.37/2.89 | DELTA: instantiating (22) with fresh symbols all_91_0, all_91_1, all_91_2, % 15.37/2.89 | all_91_3 gives: % 15.37/2.89 | (36) triple(all_75_11, all_72_0, all_75_9) = all_91_1 & check_cpq(all_91_1) % 15.37/2.89 | = all_91_0 & check_cpq(all_75_3) = all_91_2 & less_than(all_75_6, % 15.37/2.89 | all_75_7) = all_91_3 & $i(all_91_1) & ( ~ (all_91_3 = 0) | (( ~ % 15.37/2.89 | (all_91_0 = 0) | all_91_2 = 0) & ( ~ (all_91_2 = 0) | all_91_0 = % 15.37/2.89 | 0))) % 15.37/2.89 | % 15.37/2.89 | ALPHA: (36) implies: % 15.37/2.89 | (37) triple(all_75_11, all_72_0, all_75_9) = all_91_1 % 15.37/2.89 | % 15.37/2.89 | DELTA: instantiating (24) with fresh symbols all_93_0, all_93_1, all_93_2, % 15.37/2.89 | all_93_3 gives: % 15.37/2.89 | (38) triple(all_75_10, all_72_0, all_75_8) = all_93_1 & check_cpq(all_93_1) % 15.37/2.89 | = all_93_0 & check_cpq(all_75_1) = all_93_2 & less_than(all_75_6, % 15.37/2.89 | all_75_7) = all_93_3 & $i(all_93_1) & ( ~ (all_93_3 = 0) | (( ~ % 15.37/2.89 | (all_93_0 = 0) | all_93_2 = 0) & ( ~ (all_93_2 = 0) | all_93_0 = % 15.37/2.89 | 0))) % 15.37/2.89 | % 15.37/2.89 | ALPHA: (38) implies: % 15.37/2.89 | (39) triple(all_75_10, all_72_0, all_75_8) = all_93_1 % 15.37/2.89 | % 15.37/2.89 | GROUND_INST: instantiating (3) with all_87_1, all_91_1, all_75_9, all_72_0, % 15.37/2.89 | all_75_11, simplifying with (28), (37) gives: % 15.37/2.89 | (40) all_91_1 = all_87_1 % 15.37/2.89 | % 15.37/2.89 | GROUND_INST: instantiating (3) with all_89_1, all_93_1, all_75_8, all_72_0, % 15.37/2.89 | all_75_10, simplifying with (33), (39) gives: % 15.37/2.89 | (41) all_93_1 = all_89_1 % 15.37/2.89 | % 15.37/2.89 | GROUND_INST: instantiating (1) with all_75_2, all_87_2, all_75_3, simplifying % 15.37/2.89 | with (20), (29) gives: % 15.37/2.89 | (42) all_87_2 = all_75_2 % 15.37/2.89 | % 15.37/2.89 | GROUND_INST: instantiating (1) with all_75_0, all_89_2, all_75_1, simplifying % 15.37/2.89 | with (21), (34) gives: % 15.37/2.89 | (43) all_89_2 = all_75_0 % 15.37/2.89 | % 15.37/2.89 | REDUCE: (32), (43) imply: % 15.37/2.89 | (44) insert_pq(all_89_0, all_75_7) = all_75_0 % 15.37/2.89 | % 15.37/2.89 | REDUCE: (27), (42) imply: % 15.37/2.89 | (45) insert_pq(all_87_0, all_75_7) = all_75_2 % 15.37/2.89 | % 15.37/2.89 | GROUND_INST: instantiating (6) with all_75_11, all_75_10, all_75_9, all_75_8, % 15.37/2.89 | all_87_1, all_89_1, simplifying with (10), (11), (12), (13), % 15.37/2.89 | (28), (33) gives: % 15.37/2.89 | (46) ? [v0: $i] : (i(all_89_1) = v0 & i(all_87_1) = v0 & $i(v0)) % 15.37/2.89 | % 15.37/2.89 | DELTA: instantiating (46) with fresh symbol all_105_0 gives: % 15.37/2.90 | (47) i(all_89_1) = all_105_0 & i(all_87_1) = all_105_0 & $i(all_105_0) % 15.37/2.90 | % 15.37/2.90 | ALPHA: (47) implies: % 15.37/2.90 | (48) i(all_87_1) = all_105_0 % 15.37/2.90 | (49) i(all_89_1) = all_105_0 % 15.37/2.90 | % 15.37/2.90 | GROUND_INST: instantiating (1) with all_87_0, all_105_0, all_87_1, simplifying % 15.37/2.90 | with (30), (48) gives: % 15.37/2.90 | (50) all_105_0 = all_87_0 % 15.37/2.90 | % 15.37/2.90 | GROUND_INST: instantiating (1) with all_89_0, all_105_0, all_89_1, simplifying % 15.37/2.90 | with (35), (49) gives: % 15.37/2.90 | (51) all_105_0 = all_89_0 % 15.37/2.90 | % 15.37/2.90 | COMBINE_EQS: (50), (51) imply: % 15.37/2.90 | (52) all_89_0 = all_87_0 % 15.37/2.90 | % 15.37/2.90 | REDUCE: (44), (52) imply: % 15.37/2.90 | (53) insert_pq(all_87_0, all_75_7) = all_75_0 % 15.37/2.90 | % 15.37/2.90 | GROUND_INST: instantiating (2) with all_75_2, all_75_0, all_75_7, all_87_0, % 15.37/2.90 | simplifying with (45), (53) gives: % 15.37/2.90 | (54) all_75_0 = all_75_2 % 15.37/2.90 | % 15.37/2.90 | REDUCE: (9), (54) imply: % 15.37/2.90 | (55) $false % 15.37/2.90 | % 15.37/2.90 | CLOSE: (55) is inconsistent. % 15.37/2.90 | % 15.37/2.90 End of proof % 15.37/2.90 % SZS output end Proof for theBenchmark % 15.37/2.90 % 15.37/2.90 2281ms %------------------------------------------------------------------------------