%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWV376+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 : n027.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 22:56:04 EDT 2023 % Result : Theorem 10.28s 2.37s % Output : Proof 13.63s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : SWV376+1 : TPTP v8.1.2. Released v3.3.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.35 % Computer : n027.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 300 % 0.14/0.35 % DateTime : Tue Aug 29 09:13:53 EDT 2023 % 0.14/0.35 % 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/sandbox/benchmark/theBenchmark.p ... % 0.20/0.64 Running up to 7 provers in parallel. % 0.20/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.35/1.23 Prover 4: Preprocessing ... % 3.35/1.23 Prover 1: Preprocessing ... % 3.35/1.29 Prover 0: Preprocessing ... % 3.35/1.29 Prover 6: Preprocessing ... % 3.35/1.29 Prover 2: Preprocessing ... % 3.35/1.29 Prover 5: Preprocessing ... % 3.35/1.29 Prover 3: Preprocessing ... % 8.89/2.02 Prover 1: Warning: ignoring some quantifiers % 8.89/2.05 Prover 3: Warning: ignoring some quantifiers % 9.59/2.10 Prover 3: Constructing countermodel ... % 9.59/2.11 Prover 1: Constructing countermodel ... % 9.59/2.11 Prover 4: Constructing countermodel ... % 9.59/2.16 Prover 0: Proving ... % 9.59/2.16 Prover 5: Proving ... % 9.59/2.16 Prover 6: Proving ... % 10.28/2.25 Prover 2: Proving ... % 10.28/2.37 Prover 3: proved (1722ms) % 10.28/2.37 % 10.28/2.37 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 10.28/2.37 % 10.28/2.37 Prover 6: stopped % 10.28/2.37 Prover 2: stopped % 10.28/2.39 Prover 0: stopped % 10.28/2.40 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 10.28/2.40 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 10.28/2.40 Prover 5: stopped % 10.28/2.40 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 10.28/2.40 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 10.28/2.40 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 11.76/2.45 Prover 7: Preprocessing ... % 11.76/2.46 Prover 8: Preprocessing ... % 11.76/2.47 Prover 10: Preprocessing ... % 11.76/2.47 Prover 13: Preprocessing ... % 11.76/2.48 Prover 11: Preprocessing ... % 12.42/2.51 Prover 1: Found proof (size 49) % 12.42/2.51 Prover 1: proved (1868ms) % 12.42/2.51 Prover 7: stopped % 12.42/2.52 Prover 4: stopped % 12.42/2.56 Prover 13: stopped % 12.42/2.56 Prover 10: stopped % 12.42/2.57 Prover 11: stopped % 12.98/2.62 Prover 8: Warning: ignoring some quantifiers % 12.98/2.64 Prover 8: Constructing countermodel ... % 12.98/2.65 Prover 8: stopped % 12.98/2.65 % 12.98/2.65 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 12.98/2.65 % 12.98/2.66 % SZS output start Proof for theBenchmark % 12.98/2.67 Assumptions after simplification: % 12.98/2.67 --------------------------------- % 12.98/2.67 % 12.98/2.67 (ax41) % 13.53/2.69 $i(bad) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v2 = bad | % 13.53/2.69 ~ (triple(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ok(v3) = % 13.53/2.69 0) % 13.53/2.69 % 13.53/2.69 (l12_co) % 13.53/2.70 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ( ~ (v4 % 13.53/2.70 = 0) & ok(v3) = v4 & triple(v0, v1, v2) = v3 & $i(v3) & $i(v2) & $i(v1) & % 13.53/2.70 $i(v0) & ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : (ok(v8) = 0 % 13.53/2.70 & triple(v5, v6, v7) = v8 & succ_cpq(v3, v8) = 0 & $i(v8) & $i(v7) & % 13.53/2.70 $i(v6) & $i(v5))) % 13.53/2.70 % 13.53/2.70 (l12_induction) % 13.53/2.70 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 13.53/2.70 $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: int] : ? [v9: $i] : ( ~ (v8 = 0) % 13.53/2.70 & im_succ_cpq(v7) = v9 & ok(v9) = 0 & ok(v7) = v8 & triple(v3, v4, v5) = v7 % 13.53/2.70 & triple(v0, v1, v2) = v6 & succ_cpq(v6, v7) = 0 & $i(v9) & $i(v7) & $i(v6) % 13.53/2.70 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) | ! [v0: $i] : ! % 13.53/2.70 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (triple(v0, v1, v2) = v3) | ~ % 13.53/2.70 $i(v2) | ~ $i(v1) | ~ $i(v0) | ok(v3) = 0 | ! [v4: $i] : ! [v5: $i] : ! % 13.53/2.70 [v6: $i] : ! [v7: $i] : ( ~ (triple(v4, v5, v6) = v7) | ~ (succ_cpq(v3, % 13.53/2.70 v7) = 0) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ? [v8: int] : ( ~ (v8 % 13.53/2.70 = 0) & ok(v7) = v8))) % 13.53/2.70 % 13.53/2.70 (l12_l13) % 13.53/2.70 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (triple(v0, v1, % 13.53/2.70 v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: % 13.53/2.70 $i] : ? [v6: any] : (im_succ_cpq(v3) = v5 & ok(v5) = v6 & ok(v3) = v4 & % 13.53/2.70 $i(v5) & ( ~ (v6 = 0) | v4 = 0))) % 13.53/2.70 % 13.53/2.70 (function-axioms) % 13.62/2.71 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 % 13.62/2.71 | ~ (triple(v4, v3, v2) = v1) | ~ (triple(v4, v3, v2) = v0)) & ! [v0: % 13.62/2.71 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 13.62/2.71 : ! [v4: $i] : (v1 = v0 | ~ (pair_in_list(v4, v3, v2) = v1) | ~ % 13.62/2.71 (pair_in_list(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 13.62/2.71 ! [v3: $i] : (v1 = v0 | ~ (remove_pqp(v3, v2) = v1) | ~ (remove_pqp(v3, v2) % 13.62/2.71 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 % 13.62/2.71 | ~ (insert_pqp(v3, v2) = v1) | ~ (insert_pqp(v3, v2) = v0)) & ! [v0: % 13.62/2.71 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 13.62/2.71 : (v1 = v0 | ~ (contains_cpq(v3, v2) = v1) | ~ (contains_cpq(v3, v2) = v0)) % 13.62/2.71 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 13.62/2.71 (remove_cpq(v3, v2) = v1) | ~ (remove_cpq(v3, v2) = v0)) & ! [v0: $i] : ! % 13.62/2.71 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (insert_cpq(v3, v2) = v1) % 13.62/2.71 | ~ (insert_cpq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 13.62/2.71 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (succ_cpq(v3, % 13.62/2.71 v2) = v1) | ~ (succ_cpq(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 13.62/2.71 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (update_slb(v3, v2) = v1) | ~ % 13.62/2.71 (update_slb(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 13.62/2.71 [v3: $i] : (v1 = v0 | ~ (lookup_slb(v3, v2) = v1) | ~ (lookup_slb(v3, v2) = % 13.62/2.71 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 13.62/2.71 ~ (remove_slb(v3, v2) = v1) | ~ (remove_slb(v3, v2) = v0)) & ! [v0: % 13.62/2.71 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 13.62/2.71 : (v1 = v0 | ~ (contains_slb(v3, v2) = v1) | ~ (contains_slb(v3, v2) = v0)) % 13.62/2.71 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 13.62/2.71 (pair(v3, v2) = v1) | ~ (pair(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 13.62/2.71 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (insert_slb(v3, v2) = v1) | ~ % 13.62/2.71 (insert_slb(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 13.62/2.71 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 13.62/2.71 (strictly_less_than(v3, v2) = v1) | ~ (strictly_less_than(v3, v2) = v0)) & % 13.62/2.71 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 13.62/2.71 $i] : (v1 = v0 | ~ (less_than(v3, v2) = v1) | ~ (less_than(v3, v2) = v0)) % 13.62/2.71 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (im_succ_cpq(v2) = % 13.62/2.71 v1) | ~ (im_succ_cpq(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 13.62/2.71 : (v1 = v0 | ~ (removemin_cpq_res(v2) = v1) | ~ (removemin_cpq_res(v2) = % 13.62/2.71 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 13.62/2.71 (findmin_cpq_res(v2) = v1) | ~ (findmin_cpq_res(v2) = v0)) & ! [v0: $i] : % 13.62/2.71 ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (findmin_pqp_res(v2) = v1) | ~ % 13.62/2.71 (findmin_pqp_res(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 13.62/2.71 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (ok(v2) = v1) | ~ (ok(v2) % 13.62/2.71 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 13.62/2.71 $i] : (v1 = v0 | ~ (check_cpq(v2) = v1) | ~ (check_cpq(v2) = v0)) & ! % 13.62/2.71 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (removemin_cpq_eff(v2) = % 13.62/2.71 v1) | ~ (removemin_cpq_eff(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 13.62/2.71 [v2: $i] : (v1 = v0 | ~ (findmin_cpq_eff(v2) = v1) | ~ (findmin_cpq_eff(v2) % 13.62/2.71 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 13.62/2.71 $i] : (v1 = v0 | ~ (isnonempty_slb(v2) = v1) | ~ (isnonempty_slb(v2) = % 13.62/2.71 v0)) % 13.62/2.71 % 13.62/2.71 Further assumptions not needed in the proof: % 13.63/2.71 -------------------------------------------- % 13.63/2.71 ax18, ax19, ax20, ax21, ax22, ax23, ax24, ax25, ax26, ax27, ax28, ax29, ax30, % 13.63/2.71 ax31, ax32, ax33, ax34, ax35, ax36, ax37, ax38, ax39, ax40, ax42, ax43, ax44, % 13.63/2.71 ax45, ax46, ax47, ax48, ax49, ax50, ax51, ax52, ax53, bottom_smallest, % 13.63/2.71 reflexivity, stricly_smaller_definition, totality, transitivity % 13.63/2.71 % 13.63/2.71 Those formulas are unsatisfiable: % 13.63/2.71 --------------------------------- % 13.63/2.71 % 13.63/2.71 Begin of proof % 13.63/2.72 | % 13.63/2.72 | ALPHA: (ax41) implies: % 13.63/2.72 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v2 = bad | ~ % 13.63/2.72 | (triple(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 13.63/2.72 | ok(v3) = 0) % 13.63/2.72 | % 13.63/2.72 | ALPHA: (function-axioms) implies: % 13.63/2.72 | (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 13.63/2.72 | (v1 = v0 | ~ (ok(v2) = v1) | ~ (ok(v2) = v0)) % 13.63/2.72 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 13.63/2.72 | (im_succ_cpq(v2) = v1) | ~ (im_succ_cpq(v2) = v0)) % 13.63/2.72 | % 13.63/2.72 | DELTA: instantiating (l12_co) with fresh symbols all_45_0, all_45_1, all_45_2, % 13.63/2.72 | all_45_3, all_45_4 gives: % 13.63/2.72 | (4) ~ (all_45_0 = 0) & ok(all_45_1) = all_45_0 & triple(all_45_4, % 13.63/2.72 | all_45_3, all_45_2) = all_45_1 & $i(all_45_1) & $i(all_45_2) & % 13.63/2.72 | $i(all_45_3) & $i(all_45_4) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 13.63/2.72 | ? [v3: $i] : (ok(v3) = 0 & triple(v0, v1, v2) = v3 & % 13.63/2.72 | succ_cpq(all_45_1, v3) = 0 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 13.63/2.72 | % 13.63/2.72 | ALPHA: (4) implies: % 13.63/2.72 | (5) ~ (all_45_0 = 0) % 13.63/2.72 | (6) $i(all_45_4) % 13.63/2.72 | (7) $i(all_45_3) % 13.63/2.72 | (8) $i(all_45_2) % 13.63/2.72 | (9) triple(all_45_4, all_45_3, all_45_2) = all_45_1 % 13.63/2.72 | (10) ok(all_45_1) = all_45_0 % 13.63/2.72 | (11) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (ok(v3) = 0 & % 13.63/2.72 | triple(v0, v1, v2) = v3 & succ_cpq(all_45_1, v3) = 0 & $i(v3) & % 13.63/2.72 | $i(v2) & $i(v1) & $i(v0)) % 13.63/2.72 | % 13.63/2.72 | DELTA: instantiating (11) with fresh symbols all_53_0, all_53_1, all_53_2, % 13.63/2.72 | all_53_3 gives: % 13.63/2.72 | (12) ok(all_53_0) = 0 & triple(all_53_3, all_53_2, all_53_1) = all_53_0 & % 13.63/2.72 | succ_cpq(all_45_1, all_53_0) = 0 & $i(all_53_0) & $i(all_53_1) & % 13.63/2.72 | $i(all_53_2) & $i(all_53_3) % 13.63/2.72 | % 13.63/2.72 | ALPHA: (12) implies: % 13.63/2.72 | (13) $i(all_53_3) % 13.63/2.72 | (14) $i(all_53_2) % 13.63/2.72 | (15) $i(all_53_1) % 13.63/2.72 | (16) succ_cpq(all_45_1, all_53_0) = 0 % 13.63/2.72 | (17) triple(all_53_3, all_53_2, all_53_1) = all_53_0 % 13.63/2.72 | (18) ok(all_53_0) = 0 % 13.63/2.72 | % 13.63/2.73 | GROUND_INST: instantiating (1) with all_45_4, all_45_3, all_45_2, all_45_1, % 13.63/2.73 | simplifying with (6), (7), (8), (9) gives: % 13.63/2.73 | (19) all_45_2 = bad | ok(all_45_1) = 0 % 13.63/2.73 | % 13.63/2.73 | GROUND_INST: instantiating (l12_l13) with all_45_4, all_45_3, all_45_2, % 13.63/2.73 | all_45_1, simplifying with (6), (7), (8), (9) gives: % 13.63/2.73 | (20) ? [v0: any] : ? [v1: $i] : ? [v2: any] : (im_succ_cpq(all_45_1) = % 13.63/2.73 | v1 & ok(v1) = v2 & ok(all_45_1) = v0 & $i(v1) & ( ~ (v2 = 0) | v0 = % 13.63/2.73 | 0)) % 13.63/2.73 | % 13.63/2.73 | GROUND_INST: instantiating (l12_l13) with all_53_3, all_53_2, all_53_1, % 13.63/2.73 | all_53_0, simplifying with (13), (14), (15), (17) gives: % 13.63/2.73 | (21) ? [v0: any] : ? [v1: $i] : ? [v2: any] : (im_succ_cpq(all_53_0) = % 13.63/2.73 | v1 & ok(v1) = v2 & ok(all_53_0) = v0 & $i(v1) & ( ~ (v2 = 0) | v0 = % 13.63/2.73 | 0)) % 13.63/2.73 | % 13.63/2.73 | DELTA: instantiating (21) with fresh symbols all_60_0, all_60_1, all_60_2 % 13.63/2.73 | gives: % 13.63/2.73 | (22) im_succ_cpq(all_53_0) = all_60_1 & ok(all_60_1) = all_60_0 & % 13.63/2.73 | ok(all_53_0) = all_60_2 & $i(all_60_1) & ( ~ (all_60_0 = 0) | all_60_2 % 13.63/2.73 | = 0) % 13.63/2.73 | % 13.63/2.73 | ALPHA: (22) implies: % 13.63/2.73 | (23) ok(all_53_0) = all_60_2 % 13.63/2.73 | % 13.63/2.73 | DELTA: instantiating (20) with fresh symbols all_62_0, all_62_1, all_62_2 % 13.63/2.73 | gives: % 13.63/2.73 | (24) im_succ_cpq(all_45_1) = all_62_1 & ok(all_62_1) = all_62_0 & % 13.63/2.73 | ok(all_45_1) = all_62_2 & $i(all_62_1) & ( ~ (all_62_0 = 0) | all_62_2 % 13.63/2.73 | = 0) % 13.63/2.73 | % 13.63/2.73 | ALPHA: (24) implies: % 13.63/2.73 | (25) ok(all_45_1) = all_62_2 % 13.63/2.73 | % 13.63/2.73 | BETA: splitting (19) gives: % 13.63/2.73 | % 13.63/2.73 | Case 1: % 13.63/2.73 | | % 13.63/2.73 | | (26) ok(all_45_1) = 0 % 13.63/2.73 | | % 13.63/2.73 | | GROUND_INST: instantiating (2) with all_45_0, all_62_2, all_45_1, % 13.63/2.73 | | simplifying with (10), (25) gives: % 13.63/2.73 | | (27) all_62_2 = all_45_0 % 13.63/2.73 | | % 13.63/2.73 | | GROUND_INST: instantiating (2) with 0, all_62_2, all_45_1, simplifying with % 13.63/2.73 | | (25), (26) gives: % 13.63/2.73 | | (28) all_62_2 = 0 % 13.63/2.73 | | % 13.63/2.73 | | COMBINE_EQS: (27), (28) imply: % 13.63/2.73 | | (29) all_45_0 = 0 % 13.63/2.73 | | % 13.63/2.73 | | SIMP: (29) implies: % 13.63/2.73 | | (30) all_45_0 = 0 % 13.63/2.73 | | % 13.63/2.73 | | REDUCE: (5), (30) imply: % 13.63/2.73 | | (31) $false % 13.63/2.73 | | % 13.63/2.73 | | CLOSE: (31) is inconsistent. % 13.63/2.73 | | % 13.63/2.73 | Case 2: % 13.63/2.73 | | % 13.63/2.73 | | (32) all_45_2 = bad % 13.63/2.73 | | (33) ~ (ok(all_45_1) = 0) % 13.63/2.73 | | % 13.63/2.73 | | REDUCE: (9), (32) imply: % 13.63/2.73 | | (34) triple(all_45_4, all_45_3, bad) = all_45_1 % 13.63/2.73 | | % 13.63/2.73 | | REDUCE: (8), (32) imply: % 13.63/2.73 | | (35) $i(bad) % 13.63/2.73 | | % 13.63/2.73 | | GROUND_INST: instantiating (2) with 0, all_60_2, all_53_0, simplifying with % 13.63/2.73 | | (18), (23) gives: % 13.63/2.73 | | (36) all_60_2 = 0 % 13.63/2.73 | | % 13.63/2.73 | | BETA: splitting (l12_induction) gives: % 13.63/2.73 | | % 13.63/2.73 | | Case 1: % 13.63/2.73 | | | % 13.63/2.74 | | | (37) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: % 13.63/2.74 | | | $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: int] : % 13.63/2.74 | | | ? [v9: $i] : ( ~ (v8 = 0) & im_succ_cpq(v7) = v9 & ok(v9) = 0 & % 13.63/2.74 | | | ok(v7) = v8 & triple(v3, v4, v5) = v7 & triple(v0, v1, v2) = v6 % 13.63/2.74 | | | & succ_cpq(v6, v7) = 0 & $i(v9) & $i(v7) & $i(v6) & $i(v5) & % 13.63/2.74 | | | $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 13.63/2.74 | | | % 13.63/2.74 | | | DELTA: instantiating (37) with fresh symbols all_82_0, all_82_1, all_82_2, % 13.63/2.74 | | | all_82_3, all_82_4, all_82_5, all_82_6, all_82_7, all_82_8, % 13.63/2.74 | | | all_82_9 gives: % 13.63/2.74 | | | (38) ~ (all_82_1 = 0) & im_succ_cpq(all_82_2) = all_82_0 & % 13.63/2.74 | | | ok(all_82_0) = 0 & ok(all_82_2) = all_82_1 & triple(all_82_6, % 13.63/2.74 | | | all_82_5, all_82_4) = all_82_2 & triple(all_82_9, all_82_8, % 13.63/2.74 | | | all_82_7) = all_82_3 & succ_cpq(all_82_3, all_82_2) = 0 & % 13.63/2.74 | | | $i(all_82_0) & $i(all_82_2) & $i(all_82_3) & $i(all_82_4) & % 13.63/2.74 | | | $i(all_82_5) & $i(all_82_6) & $i(all_82_7) & $i(all_82_8) & % 13.63/2.74 | | | $i(all_82_9) % 13.63/2.74 | | | % 13.63/2.74 | | | ALPHA: (38) implies: % 13.63/2.74 | | | (39) ~ (all_82_1 = 0) % 13.63/2.74 | | | (40) $i(all_82_6) % 13.63/2.74 | | | (41) $i(all_82_5) % 13.63/2.74 | | | (42) $i(all_82_4) % 13.63/2.74 | | | (43) triple(all_82_6, all_82_5, all_82_4) = all_82_2 % 13.63/2.74 | | | (44) ok(all_82_2) = all_82_1 % 13.63/2.74 | | | (45) ok(all_82_0) = 0 % 13.63/2.74 | | | (46) im_succ_cpq(all_82_2) = all_82_0 % 13.63/2.74 | | | % 13.63/2.74 | | | GROUND_INST: instantiating (l12_l13) with all_82_6, all_82_5, all_82_4, % 13.63/2.74 | | | all_82_2, simplifying with (40), (41), (42), (43) gives: % 13.63/2.74 | | | (47) ? [v0: any] : ? [v1: $i] : ? [v2: any] : (im_succ_cpq(all_82_2) % 13.63/2.74 | | | = v1 & ok(v1) = v2 & ok(all_82_2) = v0 & $i(v1) & ( ~ (v2 = 0) | % 13.63/2.74 | | | v0 = 0)) % 13.63/2.74 | | | % 13.63/2.74 | | | DELTA: instantiating (47) with fresh symbols all_89_0, all_89_1, all_89_2 % 13.63/2.74 | | | gives: % 13.63/2.74 | | | (48) im_succ_cpq(all_82_2) = all_89_1 & ok(all_89_1) = all_89_0 & % 13.63/2.74 | | | ok(all_82_2) = all_89_2 & $i(all_89_1) & ( ~ (all_89_0 = 0) | % 13.63/2.74 | | | all_89_2 = 0) % 13.63/2.74 | | | % 13.63/2.74 | | | ALPHA: (48) implies: % 13.63/2.74 | | | (49) ok(all_82_2) = all_89_2 % 13.63/2.74 | | | (50) ok(all_89_1) = all_89_0 % 13.63/2.74 | | | (51) im_succ_cpq(all_82_2) = all_89_1 % 13.63/2.74 | | | (52) ~ (all_89_0 = 0) | all_89_2 = 0 % 13.63/2.74 | | | % 13.63/2.74 | | | GROUND_INST: instantiating (2) with all_82_1, all_89_2, all_82_2, % 13.63/2.74 | | | simplifying with (44), (49) gives: % 13.63/2.74 | | | (53) all_89_2 = all_82_1 % 13.63/2.74 | | | % 13.63/2.74 | | | GROUND_INST: instantiating (3) with all_82_0, all_89_1, all_82_2, % 13.63/2.74 | | | simplifying with (46), (51) gives: % 13.63/2.74 | | | (54) all_89_1 = all_82_0 % 13.63/2.74 | | | % 13.63/2.74 | | | REDUCE: (50), (54) imply: % 13.63/2.74 | | | (55) ok(all_82_0) = all_89_0 % 13.63/2.74 | | | % 13.63/2.74 | | | BETA: splitting (52) gives: % 13.63/2.74 | | | % 13.63/2.74 | | | Case 1: % 13.63/2.74 | | | | % 13.63/2.74 | | | | (56) ~ (all_89_0 = 0) % 13.63/2.74 | | | | % 13.63/2.74 | | | | GROUND_INST: instantiating (2) with 0, all_89_0, all_82_0, simplifying % 13.63/2.74 | | | | with (45), (55) gives: % 13.63/2.74 | | | | (57) all_89_0 = 0 % 13.63/2.74 | | | | % 13.63/2.74 | | | | REDUCE: (56), (57) imply: % 13.63/2.74 | | | | (58) $false % 13.63/2.74 | | | | % 13.63/2.74 | | | | CLOSE: (58) is inconsistent. % 13.63/2.74 | | | | % 13.63/2.74 | | | Case 2: % 13.63/2.74 | | | | % 13.63/2.74 | | | | (59) all_89_2 = 0 % 13.63/2.74 | | | | % 13.63/2.74 | | | | COMBINE_EQS: (53), (59) imply: % 13.63/2.74 | | | | (60) all_82_1 = 0 % 13.63/2.74 | | | | % 13.63/2.74 | | | | REDUCE: (39), (60) imply: % 13.63/2.75 | | | | (61) $false % 13.63/2.75 | | | | % 13.63/2.75 | | | | CLOSE: (61) is inconsistent. % 13.63/2.75 | | | | % 13.63/2.75 | | | End of split % 13.63/2.75 | | | % 13.63/2.75 | | Case 2: % 13.63/2.75 | | | % 13.63/2.75 | | | (62) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 13.63/2.75 | | | (triple(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 13.63/2.75 | | | ok(v3) = 0 | ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: % 13.63/2.75 | | | $i] : ( ~ (triple(v4, v5, v6) = v7) | ~ (succ_cpq(v3, v7) = % 13.63/2.75 | | | 0) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ? [v8: int] : ( ~ % 13.63/2.75 | | | (v8 = 0) & ok(v7) = v8))) % 13.63/2.75 | | | % 13.63/2.75 | | | GROUND_INST: instantiating (62) with all_45_4, all_45_3, bad, all_45_1, % 13.63/2.75 | | | simplifying with (6), (7), (33), (34), (35) gives: % 13.63/2.75 | | | (63) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 13.63/2.75 | | | (triple(v0, v1, v2) = v3) | ~ (succ_cpq(all_45_1, v3) = 0) | ~ % 13.63/2.75 | | | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & % 13.63/2.75 | | | ok(v3) = v4)) % 13.63/2.75 | | | % 13.63/2.75 | | | GROUND_INST: instantiating (63) with all_53_3, all_53_2, all_53_1, % 13.63/2.75 | | | all_53_0, simplifying with (13), (14), (15), (16), (17) % 13.63/2.75 | | | gives: % 13.63/2.75 | | | (64) ? [v0: int] : ( ~ (v0 = 0) & ok(all_53_0) = v0) % 13.63/2.75 | | | % 13.63/2.75 | | | DELTA: instantiating (64) with fresh symbol all_84_0 gives: % 13.63/2.75 | | | (65) ~ (all_84_0 = 0) & ok(all_53_0) = all_84_0 % 13.63/2.75 | | | % 13.63/2.75 | | | ALPHA: (65) implies: % 13.63/2.75 | | | (66) ~ (all_84_0 = 0) % 13.63/2.75 | | | (67) ok(all_53_0) = all_84_0 % 13.63/2.75 | | | % 13.63/2.75 | | | GROUND_INST: instantiating (2) with 0, all_84_0, all_53_0, simplifying % 13.63/2.75 | | | with (18), (67) gives: % 13.63/2.75 | | | (68) all_84_0 = 0 % 13.63/2.75 | | | % 13.63/2.75 | | | REDUCE: (66), (68) imply: % 13.63/2.75 | | | (69) $false % 13.63/2.75 | | | % 13.63/2.75 | | | CLOSE: (69) is inconsistent. % 13.63/2.75 | | | % 13.63/2.75 | | End of split % 13.63/2.75 | | % 13.63/2.75 | End of split % 13.63/2.75 | % 13.63/2.75 End of proof % 13.63/2.75 % SZS output end Proof for theBenchmark % 13.63/2.75 % 13.63/2.75 2125ms %------------------------------------------------------------------------------