%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWV371+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 : n014.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Thu Aug 31 22:56:03 EDT 2023 % Result : Theorem 12.40s 2.39s % Output : Proof 14.40s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWV371+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 : n014.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 02:57:15 EDT 2023 % 0.13/0.35 % CPUTime : % 0.19/0.61 ________ _____ % 0.19/0.61 ___ __ \_________(_)________________________________ % 0.19/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.61 % 0.19/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.61 (2023-06-19) % 0.19/0.61 % 0.19/0.61 (c) Philipp Rümmer, 2009-2023 % 0.19/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.61 Amanda Stjerna. % 0.19/0.61 Free software under BSD-3-Clause. % 0.19/0.61 % 0.19/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.61 % 0.19/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.19/0.62 Running up to 7 provers in parallel. % 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.91/1.23 Prover 1: Preprocessing ... % 3.91/1.23 Prover 4: Preprocessing ... % 4.25/1.26 Prover 6: Preprocessing ... % 4.25/1.26 Prover 5: Preprocessing ... % 4.25/1.26 Prover 2: Preprocessing ... % 4.25/1.26 Prover 3: Preprocessing ... % 4.25/1.28 Prover 0: Preprocessing ... % 9.22/2.04 Prover 1: Warning: ignoring some quantifiers % 9.22/2.12 Prover 1: Constructing countermodel ... % 9.22/2.14 Prover 6: Proving ... % 9.22/2.14 Prover 5: Proving ... % 9.22/2.16 Prover 3: Warning: ignoring some quantifiers % 10.55/2.20 Prover 3: Constructing countermodel ... % 11.27/2.24 Prover 2: Proving ... % 11.27/2.27 Prover 4: Constructing countermodel ... % 11.70/2.29 Prover 0: Proving ... % 12.40/2.39 Prover 3: proved (1757ms) % 12.40/2.39 % 12.40/2.39 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 12.40/2.39 % 12.40/2.39 Prover 0: stopped % 12.40/2.39 Prover 5: stopped % 12.40/2.39 Prover 6: stopped % 12.40/2.39 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 12.40/2.39 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 12.40/2.39 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 12.40/2.39 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 12.40/2.39 Prover 2: stopped % 12.70/2.41 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 12.87/2.47 Prover 7: Preprocessing ... % 12.87/2.49 Prover 8: Preprocessing ... % 12.87/2.50 Prover 10: Preprocessing ... % 12.87/2.50 Prover 11: Preprocessing ... % 12.87/2.51 Prover 13: Preprocessing ... % 12.87/2.52 Prover 1: Found proof (size 35) % 12.87/2.52 Prover 1: proved (1888ms) % 13.50/2.52 Prover 4: stopped % 13.50/2.53 Prover 7: stopped % 13.50/2.54 Prover 10: stopped % 13.50/2.57 Prover 11: stopped % 13.92/2.59 Prover 13: stopped % 13.92/2.65 Prover 8: Warning: ignoring some quantifiers % 14.40/2.68 Prover 8: Constructing countermodel ... % 14.40/2.69 Prover 8: stopped % 14.40/2.69 % 14.40/2.69 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 14.40/2.69 % 14.40/2.69 % SZS output start Proof for theBenchmark % 14.40/2.70 Assumptions after simplification: % 14.40/2.70 --------------------------------- % 14.40/2.70 % 14.40/2.70 (ax58) % 14.40/2.72 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (pi_sharp_find_min(v0, % 14.40/2.72 v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 14.40/2.72 (issmallestelement_pq(v0, v1) = v4 & contains_pq(v0, v1) = v3 & ( ~ (v4 = 0) % 14.40/2.72 | ~ (v3 = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 14.40/2.72 (pi_sharp_find_min(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | % 14.40/2.72 (issmallestelement_pq(v0, v1) = 0 & contains_pq(v0, v1) = 0)) % 14.40/2.72 % 14.40/2.72 (l7_co) % 14.40/2.73 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 14.40/2.73 $i] : ? [v6: $i] : ? [v7: int] : ( ~ (v7 = 0) & phi(v4) = 0 & % 14.40/2.73 pi_sharp_find_min(v5, v6) = v7 & i(v3) = v5 & findmin_cpq_res(v3) = v6 & % 14.40/2.73 triple(v0, v1, v2) = v3 & findmin_cpq_eff(v3) = v4 & $i(v6) & $i(v5) & % 14.40/2.73 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 14.40/2.73 % 14.40/2.73 (l7_l8) % 14.40/2.73 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 14.40/2.73 $i] : ! [v6: int] : (v6 = 0 | ~ (i(v3) = v4) | ~ (findmin_cpq_res(v3) = % 14.40/2.73 v5) | ~ (triple(v0, v1, v2) = v3) | ~ (contains_pq(v4, v5) = v6) | ~ % 14.40/2.73 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v7: $i] : ? [v8: int] : ( ~ (v8 = 0) & % 14.40/2.73 phi(v7) = v8 & findmin_cpq_eff(v3) = v7 & $i(v7))) % 14.40/2.73 % 14.40/2.73 (l7_lX) % 14.40/2.73 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 14.40/2.73 $i] : ! [v6: int] : (v6 = 0 | ~ (i(v3) = v4) | ~ (findmin_cpq_res(v3) = % 14.40/2.73 v5) | ~ (triple(v0, v1, v2) = v3) | ~ (issmallestelement_pq(v4, v5) = % 14.40/2.73 v6) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v7: $i] : ? [v8: int] : ( ~ % 14.40/2.73 (v8 = 0) & phi(v7) = v8 & findmin_cpq_eff(v3) = v7 & $i(v7))) % 14.40/2.73 % 14.40/2.73 (function-axioms) % 14.40/2.74 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 % 14.40/2.74 | ~ (triple(v4, v3, v2) = v1) | ~ (triple(v4, v3, v2) = v0)) & ! [v0: % 14.40/2.74 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 14.40/2.74 : ! [v4: $i] : (v1 = v0 | ~ (pair_in_list(v4, v3, v2) = v1) | ~ % 14.40/2.74 (pair_in_list(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 14.40/2.74 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 14.40/2.74 (pi_sharp_removemin(v3, v2) = v1) | ~ (pi_sharp_removemin(v3, v2) = v0)) & % 14.40/2.74 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 14.40/2.74 $i] : (v1 = v0 | ~ (pi_sharp_find_min(v3, v2) = v1) | ~ % 14.40/2.74 (pi_sharp_find_min(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 14.40/2.74 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 14.40/2.74 (pi_remove(v3, v2) = v1) | ~ (pi_remove(v3, v2) = v0)) & ! [v0: % 14.40/2.74 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 14.40/2.74 : (v1 = v0 | ~ (pi_sharp_remove(v3, v2) = v1) | ~ (pi_sharp_remove(v3, v2) = % 14.40/2.74 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 14.40/2.74 ~ (remove_pqp(v3, v2) = v1) | ~ (remove_pqp(v3, v2) = v0)) & ! [v0: $i] : % 14.40/2.74 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (insert_pqp(v3, v2) = % 14.40/2.74 v1) | ~ (insert_pqp(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 14.40/2.74 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 14.40/2.74 (contains_cpq(v3, v2) = v1) | ~ (contains_cpq(v3, v2) = v0)) & ! [v0: $i] % 14.40/2.74 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (remove_cpq(v3, v2) % 14.40/2.74 = v1) | ~ (remove_cpq(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 14.40/2.74 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (insert_cpq(v3, v2) = v1) | ~ % 14.40/2.74 (insert_cpq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 14.40/2.74 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (succ_cpq(v3, % 14.40/2.74 v2) = v1) | ~ (succ_cpq(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 14.40/2.74 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (update_slb(v3, v2) = v1) | ~ % 14.40/2.74 (update_slb(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 14.40/2.74 [v3: $i] : (v1 = v0 | ~ (lookup_slb(v3, v2) = v1) | ~ (lookup_slb(v3, v2) = % 14.40/2.74 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 14.40/2.74 ~ (remove_slb(v3, v2) = v1) | ~ (remove_slb(v3, v2) = v0)) & ! [v0: % 14.40/2.74 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 14.40/2.74 : (v1 = v0 | ~ (contains_slb(v3, v2) = v1) | ~ (contains_slb(v3, v2) = v0)) % 14.40/2.74 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 14.40/2.74 (pair(v3, v2) = v1) | ~ (pair(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 14.40/2.74 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (insert_slb(v3, v2) = v1) | ~ % 14.40/2.74 (insert_slb(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 14.40/2.74 [v3: $i] : (v1 = v0 | ~ (removemin_pq_res(v3, v2) = v1) | ~ % 14.40/2.74 (removemin_pq_res(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 14.40/2.74 ! [v3: $i] : (v1 = v0 | ~ (removemin_pq_eff(v3, v2) = v1) | ~ % 14.40/2.74 (removemin_pq_eff(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 14.40/2.74 ! [v3: $i] : (v1 = v0 | ~ (findmin_pq_res(v3, v2) = v1) | ~ % 14.40/2.74 (findmin_pq_res(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 14.40/2.74 ! [v3: $i] : (v1 = v0 | ~ (findmin_pq_eff(v3, v2) = v1) | ~ % 14.40/2.74 (findmin_pq_eff(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 14.40/2.74 ! [v3: $i] : (v1 = v0 | ~ (remove_pq(v3, v2) = v1) | ~ (remove_pq(v3, v2) = % 14.40/2.74 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 14.40/2.74 $i] : ! [v3: $i] : (v1 = v0 | ~ (issmallestelement_pq(v3, v2) = v1) | ~ % 14.40/2.74 (issmallestelement_pq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 14.40/2.74 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 14.40/2.74 (contains_pq(v3, v2) = v1) | ~ (contains_pq(v3, v2) = v0)) & ! [v0: $i] : % 14.40/2.74 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (insert_pq(v3, v2) = % 14.40/2.74 v1) | ~ (insert_pq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 14.40/2.74 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 14.40/2.74 (strictly_less_than(v3, v2) = v1) | ~ (strictly_less_than(v3, v2) = v0)) & % 14.40/2.74 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 14.40/2.74 $i] : (v1 = v0 | ~ (less_than(v3, v2) = v1) | ~ (less_than(v3, v2) = v0)) % 14.40/2.74 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 % 14.40/2.74 = v0 | ~ (phi(v2) = v1) | ~ (phi(v2) = v0)) & ! [v0: MultipleValueBool] : % 14.40/2.74 ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (pi_removemin(v2) = % 14.40/2.74 v1) | ~ (pi_removemin(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 14.40/2.74 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (pi_find_min(v2) = v1) | ~ % 14.40/2.74 (pi_find_min(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 % 14.40/2.74 | ~ (i(v2) = v1) | ~ (i(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 14.40/2.74 $i] : (v1 = v0 | ~ (removemin_cpq_res(v2) = v1) | ~ (removemin_cpq_res(v2) % 14.40/2.74 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 14.40/2.74 (findmin_cpq_res(v2) = v1) | ~ (findmin_cpq_res(v2) = v0)) & ! [v0: $i] : % 14.40/2.74 ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (findmin_pqp_res(v2) = v1) | ~ % 14.40/2.74 (findmin_pqp_res(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 14.40/2.74 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (ok(v2) = v1) | ~ (ok(v2) % 14.40/2.74 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 14.40/2.74 $i] : (v1 = v0 | ~ (check_cpq(v2) = v1) | ~ (check_cpq(v2) = v0)) & ! % 14.40/2.74 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (removemin_cpq_eff(v2) = % 14.40/2.74 v1) | ~ (removemin_cpq_eff(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 14.40/2.74 [v2: $i] : (v1 = v0 | ~ (findmin_cpq_eff(v2) = v1) | ~ (findmin_cpq_eff(v2) % 14.40/2.74 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 14.40/2.74 $i] : (v1 = v0 | ~ (isnonempty_slb(v2) = v1) | ~ (isnonempty_slb(v2) = % 14.40/2.74 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 14.40/2.74 $i] : (v1 = v0 | ~ (isnonempty_pq(v2) = v1) | ~ (isnonempty_pq(v2) = v0)) % 14.40/2.74 % 14.40/2.74 Further assumptions not needed in the proof: % 14.40/2.74 -------------------------------------------- % 14.40/2.74 ax10, ax11, ax12, ax13, ax14, ax15, ax16, ax17, ax18, ax19, ax20, ax21, ax22, % 14.40/2.74 ax23, ax24, ax25, ax26, ax27, ax28, ax29, ax30, ax31, ax32, ax33, ax34, ax35, % 14.40/2.74 ax36, ax37, ax38, ax39, ax40, ax41, ax42, ax43, ax44, ax45, ax46, ax47, ax48, % 14.40/2.74 ax49, ax50, ax51, ax52, ax53, ax54, ax55, ax56, ax57, ax59, ax6, ax60, ax61, % 14.40/2.74 ax62, ax7, ax8, ax9, bottom_smallest, reflexivity, stricly_smaller_definition, % 14.40/2.74 totality, transitivity % 14.40/2.74 % 14.40/2.74 Those formulas are unsatisfiable: % 14.40/2.74 --------------------------------- % 14.40/2.74 % 14.40/2.74 Begin of proof % 14.40/2.75 | % 14.40/2.75 | ALPHA: (ax58) implies: % 14.40/2.75 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 14.40/2.75 | (pi_sharp_find_min(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: % 14.40/2.75 | any] : ? [v4: any] : (issmallestelement_pq(v0, v1) = v4 & % 14.40/2.75 | contains_pq(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) % 14.40/2.75 | % 14.40/2.75 | ALPHA: (function-axioms) implies: % 14.40/2.75 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 14.40/2.75 | (findmin_cpq_eff(v2) = v1) | ~ (findmin_cpq_eff(v2) = v0)) % 14.40/2.75 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 14.40/2.75 | (v1 = v0 | ~ (phi(v2) = v1) | ~ (phi(v2) = v0)) % 14.40/2.75 | % 14.40/2.75 | DELTA: instantiating (l7_co) with fresh symbols all_68_0, all_68_1, all_68_2, % 14.40/2.75 | all_68_3, all_68_4, all_68_5, all_68_6, all_68_7 gives: % 14.40/2.75 | (4) ~ (all_68_0 = 0) & phi(all_68_3) = 0 & pi_sharp_find_min(all_68_2, % 14.40/2.75 | all_68_1) = all_68_0 & i(all_68_4) = all_68_2 & % 14.40/2.75 | findmin_cpq_res(all_68_4) = all_68_1 & triple(all_68_7, all_68_6, % 14.40/2.75 | all_68_5) = all_68_4 & findmin_cpq_eff(all_68_4) = all_68_3 & % 14.40/2.75 | $i(all_68_1) & $i(all_68_2) & $i(all_68_3) & $i(all_68_4) & % 14.40/2.75 | $i(all_68_5) & $i(all_68_6) & $i(all_68_7) % 14.40/2.75 | % 14.40/2.75 | ALPHA: (4) implies: % 14.40/2.75 | (5) ~ (all_68_0 = 0) % 14.40/2.75 | (6) $i(all_68_7) % 14.40/2.75 | (7) $i(all_68_6) % 14.40/2.75 | (8) $i(all_68_5) % 14.40/2.75 | (9) $i(all_68_2) % 14.40/2.75 | (10) $i(all_68_1) % 14.40/2.75 | (11) findmin_cpq_eff(all_68_4) = all_68_3 % 14.40/2.75 | (12) triple(all_68_7, all_68_6, all_68_5) = all_68_4 % 14.40/2.75 | (13) findmin_cpq_res(all_68_4) = all_68_1 % 14.40/2.75 | (14) i(all_68_4) = all_68_2 % 14.40/2.75 | (15) pi_sharp_find_min(all_68_2, all_68_1) = all_68_0 % 14.40/2.75 | (16) phi(all_68_3) = 0 % 14.40/2.75 | % 14.40/2.75 | GROUND_INST: instantiating (1) with all_68_2, all_68_1, all_68_0, simplifying % 14.40/2.75 | with (9), (10), (15) gives: % 14.40/2.75 | (17) all_68_0 = 0 | ? [v0: any] : ? [v1: any] : % 14.40/2.75 | (issmallestelement_pq(all_68_2, all_68_1) = v1 & contains_pq(all_68_2, % 14.40/2.75 | all_68_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 14.40/2.75 | % 14.40/2.75 | BETA: splitting (17) gives: % 14.40/2.75 | % 14.40/2.75 | Case 1: % 14.40/2.75 | | % 14.40/2.75 | | (18) all_68_0 = 0 % 14.40/2.75 | | % 14.40/2.75 | | REDUCE: (5), (18) imply: % 14.40/2.75 | | (19) $false % 14.40/2.76 | | % 14.40/2.76 | | CLOSE: (19) is inconsistent. % 14.40/2.76 | | % 14.40/2.76 | Case 2: % 14.40/2.76 | | % 14.40/2.76 | | (20) ? [v0: any] : ? [v1: any] : (issmallestelement_pq(all_68_2, % 14.40/2.76 | | all_68_1) = v1 & contains_pq(all_68_2, all_68_1) = v0 & ( ~ (v1 % 14.40/2.76 | | = 0) | ~ (v0 = 0))) % 14.40/2.76 | | % 14.40/2.76 | | DELTA: instantiating (20) with fresh symbols all_87_0, all_87_1 gives: % 14.40/2.76 | | (21) issmallestelement_pq(all_68_2, all_68_1) = all_87_0 & % 14.40/2.76 | | contains_pq(all_68_2, all_68_1) = all_87_1 & ( ~ (all_87_0 = 0) | ~ % 14.40/2.76 | | (all_87_1 = 0)) % 14.40/2.76 | | % 14.40/2.76 | | ALPHA: (21) implies: % 14.40/2.76 | | (22) contains_pq(all_68_2, all_68_1) = all_87_1 % 14.40/2.76 | | (23) issmallestelement_pq(all_68_2, all_68_1) = all_87_0 % 14.40/2.76 | | (24) ~ (all_87_0 = 0) | ~ (all_87_1 = 0) % 14.40/2.76 | | % 14.40/2.76 | | GROUND_INST: instantiating (l7_l8) with all_68_7, all_68_6, all_68_5, % 14.40/2.76 | | all_68_4, all_68_2, all_68_1, all_87_1, simplifying with (6), % 14.40/2.76 | | (7), (8), (12), (13), (14), (22) gives: % 14.40/2.76 | | (25) all_87_1 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & phi(v0) = % 14.40/2.76 | | v1 & findmin_cpq_eff(all_68_4) = v0 & $i(v0)) % 14.40/2.76 | | % 14.40/2.76 | | GROUND_INST: instantiating (l7_lX) with all_68_7, all_68_6, all_68_5, % 14.40/2.76 | | all_68_4, all_68_2, all_68_1, all_87_0, simplifying with (6), % 14.40/2.76 | | (7), (8), (12), (13), (14), (23) gives: % 14.40/2.76 | | (26) all_87_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & phi(v0) = % 14.40/2.76 | | v1 & findmin_cpq_eff(all_68_4) = v0 & $i(v0)) % 14.40/2.76 | | % 14.40/2.76 | | BETA: splitting (26) gives: % 14.40/2.76 | | % 14.40/2.76 | | Case 1: % 14.40/2.76 | | | % 14.40/2.76 | | | (27) all_87_0 = 0 % 14.40/2.76 | | | % 14.40/2.76 | | | BETA: splitting (24) gives: % 14.40/2.76 | | | % 14.40/2.76 | | | Case 1: % 14.40/2.76 | | | | % 14.40/2.76 | | | | (28) ~ (all_87_0 = 0) % 14.40/2.76 | | | | % 14.40/2.76 | | | | REDUCE: (27), (28) imply: % 14.40/2.76 | | | | (29) $false % 14.40/2.76 | | | | % 14.40/2.76 | | | | CLOSE: (29) is inconsistent. % 14.40/2.76 | | | | % 14.40/2.76 | | | Case 2: % 14.40/2.76 | | | | % 14.40/2.76 | | | | (30) ~ (all_87_1 = 0) % 14.40/2.76 | | | | % 14.40/2.76 | | | | BETA: splitting (25) gives: % 14.40/2.76 | | | | % 14.40/2.76 | | | | Case 1: % 14.40/2.76 | | | | | % 14.40/2.76 | | | | | (31) all_87_1 = 0 % 14.40/2.76 | | | | | % 14.40/2.76 | | | | | REDUCE: (30), (31) imply: % 14.40/2.76 | | | | | (32) $false % 14.40/2.76 | | | | | % 14.40/2.76 | | | | | CLOSE: (32) is inconsistent. % 14.40/2.76 | | | | | % 14.40/2.76 | | | | Case 2: % 14.40/2.76 | | | | | % 14.40/2.76 | | | | | (33) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & phi(v0) = v1 & % 14.40/2.76 | | | | | findmin_cpq_eff(all_68_4) = v0 & $i(v0)) % 14.40/2.76 | | | | | % 14.40/2.76 | | | | | DELTA: instantiating (33) with fresh symbols all_108_0, all_108_1 % 14.40/2.76 | | | | | gives: % 14.40/2.76 | | | | | (34) ~ (all_108_0 = 0) & phi(all_108_1) = all_108_0 & % 14.40/2.76 | | | | | findmin_cpq_eff(all_68_4) = all_108_1 & $i(all_108_1) % 14.40/2.76 | | | | | % 14.40/2.76 | | | | | ALPHA: (34) implies: % 14.40/2.76 | | | | | (35) ~ (all_108_0 = 0) % 14.40/2.76 | | | | | (36) findmin_cpq_eff(all_68_4) = all_108_1 % 14.40/2.76 | | | | | (37) phi(all_108_1) = all_108_0 % 14.40/2.76 | | | | | % 14.40/2.76 | | | | | GROUND_INST: instantiating (2) with all_68_3, all_108_1, all_68_4, % 14.40/2.76 | | | | | simplifying with (11), (36) gives: % 14.40/2.76 | | | | | (38) all_108_1 = all_68_3 % 14.40/2.76 | | | | | % 14.40/2.76 | | | | | REDUCE: (37), (38) imply: % 14.40/2.76 | | | | | (39) phi(all_68_3) = all_108_0 % 14.40/2.76 | | | | | % 14.40/2.76 | | | | | GROUND_INST: instantiating (3) with 0, all_108_0, all_68_3, % 14.40/2.76 | | | | | simplifying with (16), (39) gives: % 14.40/2.76 | | | | | (40) all_108_0 = 0 % 14.40/2.76 | | | | | % 14.40/2.76 | | | | | REDUCE: (35), (40) imply: % 14.40/2.76 | | | | | (41) $false % 14.40/2.76 | | | | | % 14.40/2.76 | | | | | CLOSE: (41) is inconsistent. % 14.40/2.76 | | | | | % 14.40/2.76 | | | | End of split % 14.40/2.76 | | | | % 14.40/2.76 | | | End of split % 14.40/2.76 | | | % 14.40/2.76 | | Case 2: % 14.40/2.76 | | | % 14.40/2.77 | | | (42) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & phi(v0) = v1 & % 14.40/2.77 | | | findmin_cpq_eff(all_68_4) = v0 & $i(v0)) % 14.40/2.77 | | | % 14.40/2.77 | | | DELTA: instantiating (42) with fresh symbols all_100_0, all_100_1 gives: % 14.40/2.77 | | | (43) ~ (all_100_0 = 0) & phi(all_100_1) = all_100_0 & % 14.40/2.77 | | | findmin_cpq_eff(all_68_4) = all_100_1 & $i(all_100_1) % 14.40/2.77 | | | % 14.40/2.77 | | | ALPHA: (43) implies: % 14.40/2.77 | | | (44) ~ (all_100_0 = 0) % 14.40/2.77 | | | (45) findmin_cpq_eff(all_68_4) = all_100_1 % 14.40/2.77 | | | (46) phi(all_100_1) = all_100_0 % 14.40/2.77 | | | % 14.40/2.77 | | | GROUND_INST: instantiating (2) with all_68_3, all_100_1, all_68_4, % 14.40/2.77 | | | simplifying with (11), (45) gives: % 14.40/2.77 | | | (47) all_100_1 = all_68_3 % 14.40/2.77 | | | % 14.40/2.77 | | | REDUCE: (46), (47) imply: % 14.40/2.77 | | | (48) phi(all_68_3) = all_100_0 % 14.40/2.77 | | | % 14.40/2.77 | | | GROUND_INST: instantiating (3) with 0, all_100_0, all_68_3, simplifying % 14.40/2.77 | | | with (16), (48) gives: % 14.40/2.77 | | | (49) all_100_0 = 0 % 14.40/2.77 | | | % 14.40/2.77 | | | REDUCE: (44), (49) imply: % 14.40/2.77 | | | (50) $false % 14.40/2.77 | | | % 14.40/2.77 | | | CLOSE: (50) is inconsistent. % 14.40/2.77 | | | % 14.40/2.77 | | End of split % 14.40/2.77 | | % 14.40/2.77 | End of split % 14.40/2.77 | % 14.40/2.77 End of proof % 14.40/2.77 % SZS output end Proof for theBenchmark % 14.40/2.77 % 14.40/2.77 2159ms %------------------------------------------------------------------------------