%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWV384+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 : n016.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 22:56:07 EDT 2023 % Result : Theorem 11.58s 2.36s % Output : Proof 14.27s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : SWV384+1 : TPTP v8.1.2. Released v3.3.0. % 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.34 % Computer : n016.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Tue Aug 29 03:49:30 EDT 2023 % 0.12/0.34 % CPUTime : % 0.62/0.61 ________ _____ % 0.62/0.61 ___ __ \_________(_)________________________________ % 0.62/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.62/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.62/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.62/0.61 % 0.62/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.62/0.61 (2023-06-19) % 0.62/0.61 % 0.62/0.61 (c) Philipp Rümmer, 2009-2023 % 0.62/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.62/0.61 Amanda Stjerna. % 0.62/0.61 Free software under BSD-3-Clause. % 0.62/0.61 % 0.62/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.62/0.61 % 0.62/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.62/0.63 Running up to 7 provers in parallel. % 0.68/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.68/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.68/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.68/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.68/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.68/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.68/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 3.73/1.24 Prover 1: Preprocessing ... % 3.73/1.24 Prover 4: Preprocessing ... % 3.78/1.28 Prover 6: Preprocessing ... % 3.78/1.28 Prover 3: Preprocessing ... % 3.78/1.28 Prover 0: Preprocessing ... % 3.78/1.28 Prover 2: Preprocessing ... % 3.78/1.28 Prover 5: Preprocessing ... % 8.14/1.86 Prover 1: Warning: ignoring some quantifiers % 8.14/1.92 Prover 3: Warning: ignoring some quantifiers % 8.87/1.98 Prover 6: Proving ... % 9.28/1.99 Prover 1: Constructing countermodel ... % 9.28/2.00 Prover 3: Constructing countermodel ... % 9.28/2.02 Prover 5: Proving ... % 9.28/2.04 Prover 4: Constructing countermodel ... % 9.77/2.10 Prover 2: Proving ... % 9.77/2.10 Prover 0: Proving ... % 11.58/2.36 Prover 5: proved (1718ms) % 11.58/2.36 % 11.58/2.36 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 11.58/2.36 % 12.05/2.37 Prover 2: stopped % 12.05/2.37 Prover 3: stopped % 12.05/2.37 Prover 6: stopped % 12.05/2.37 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 12.05/2.37 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 12.05/2.37 Prover 0: stopped % 12.05/2.37 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 12.05/2.37 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 12.05/2.38 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 12.30/2.42 Prover 10: Preprocessing ... % 12.53/2.43 Prover 8: Preprocessing ... % 12.53/2.45 Prover 7: Preprocessing ... % 12.53/2.46 Prover 1: Found proof (size 85) % 12.53/2.46 Prover 1: proved (1829ms) % 12.53/2.46 Prover 4: stopped % 12.53/2.47 Prover 13: Preprocessing ... % 12.53/2.47 Prover 11: Preprocessing ... % 12.53/2.50 Prover 10: stopped % 12.53/2.51 Prover 7: stopped % 13.25/2.53 Prover 11: stopped % 13.25/2.54 Prover 13: stopped % 13.59/2.60 Prover 8: Warning: ignoring some quantifiers % 13.59/2.62 Prover 8: Constructing countermodel ... % 13.59/2.63 Prover 8: stopped % 13.59/2.63 % 13.59/2.63 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 13.59/2.63 % 13.59/2.65 % SZS output start Proof for theBenchmark % 13.59/2.65 Assumptions after simplification: % 13.59/2.65 --------------------------------- % 13.59/2.65 % 13.59/2.65 (ax41) % 13.96/2.67 $i(bad) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v2 = bad | % 13.96/2.67 ~ (triple(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ok(v3) = % 13.96/2.67 0) % 13.96/2.67 % 13.96/2.67 (l12_l13) % 13.96/2.68 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (triple(v0, v1, % 13.96/2.68 v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: % 13.96/2.68 any] : ? [v6: $i] : ? [v7: any] : ? [v8: any] : (im_succ_cpq(v3) = v6 & % 13.96/2.68 ok(v6) = v8 & ok(v3) = v5 & check_cpq(v6) = v7 & check_cpq(v3) = v4 & % 13.96/2.68 $i(v6) & ( ~ (v8 = 0) | ~ (v7 = 0) | (v5 = 0 & v4 = 0)))) % 13.96/2.68 % 13.96/2.68 (l20_co) % 13.96/2.68 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: any] : ? [v5: % 13.96/2.68 any] : (ok(v3) = v5 & triple(v0, v1, v2) = v3 & check_cpq(v3) = v4 & $i(v3) % 13.96/2.68 & $i(v2) & $i(v1) & $i(v0) & ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? % 13.96/2.68 [v9: $i] : (ok(v9) = 0 & triple(v6, v7, v8) = v9 & check_cpq(v9) = 0 & % 13.96/2.68 succ_cpq(v3, v9) = 0 & $i(v9) & $i(v8) & $i(v7) & $i(v6)) & ( ~ (v5 = 0) | % 13.96/2.68 ~ (v4 = 0))) % 13.96/2.68 % 13.96/2.68 (l20_induction) % 13.96/2.68 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 13.96/2.68 $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: any] : ? [v9: any] : ? [v10: $i] % 13.96/2.68 : (im_succ_cpq(v7) = v10 & ok(v10) = 0 & ok(v7) = v9 & triple(v3, v4, v5) = v7 % 13.96/2.68 & triple(v0, v1, v2) = v6 & check_cpq(v10) = 0 & check_cpq(v7) = v8 & % 13.96/2.68 succ_cpq(v6, v7) = 0 & $i(v10) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) % 13.96/2.68 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v9 = 0) | ~ (v8 = 0))) | ! [v0: $i] : ! % 13.96/2.68 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (triple(v0, v1, v2) = v3) | ~ % 13.96/2.68 $i(v2) | ~ $i(v1) | ~ $i(v0) | ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : % 13.96/2.68 ! [v7: $i] : ( ~ (triple(v4, v5, v6) = v7) | ~ (succ_cpq(v3, v7) = 0) | ~ % 13.96/2.68 $i(v6) | ~ $i(v5) | ~ $i(v4) | ? [v8: any] : ? [v9: any] : (ok(v7) = % 13.96/2.68 v8 & check_cpq(v7) = v9 & ( ~ (v9 = 0) | ~ (v8 = 0)))) | (ok(v3) = 0 & % 13.96/2.68 check_cpq(v3) = 0)) % 13.96/2.68 % 13.96/2.68 (function-axioms) % 13.96/2.69 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 % 13.96/2.69 | ~ (triple(v4, v3, v2) = v1) | ~ (triple(v4, v3, v2) = v0)) & ! [v0: % 13.96/2.69 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 13.96/2.69 : ! [v4: $i] : (v1 = v0 | ~ (pair_in_list(v4, v3, v2) = v1) | ~ % 13.96/2.69 (pair_in_list(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 13.96/2.69 ! [v3: $i] : (v1 = v0 | ~ (remove_pqp(v3, v2) = v1) | ~ (remove_pqp(v3, v2) % 13.96/2.69 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 % 13.96/2.69 | ~ (insert_pqp(v3, v2) = v1) | ~ (insert_pqp(v3, v2) = v0)) & ! [v0: % 13.96/2.69 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 13.96/2.69 : (v1 = v0 | ~ (contains_cpq(v3, v2) = v1) | ~ (contains_cpq(v3, v2) = v0)) % 13.96/2.69 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 13.96/2.69 (remove_cpq(v3, v2) = v1) | ~ (remove_cpq(v3, v2) = v0)) & ! [v0: $i] : ! % 13.96/2.69 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (insert_cpq(v3, v2) = v1) % 13.96/2.69 | ~ (insert_cpq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 13.96/2.69 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (succ_cpq(v3, % 13.96/2.69 v2) = v1) | ~ (succ_cpq(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 13.96/2.69 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (update_slb(v3, v2) = v1) | ~ % 13.96/2.69 (update_slb(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 13.96/2.69 [v3: $i] : (v1 = v0 | ~ (lookup_slb(v3, v2) = v1) | ~ (lookup_slb(v3, v2) = % 13.96/2.69 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 13.96/2.69 ~ (remove_slb(v3, v2) = v1) | ~ (remove_slb(v3, v2) = v0)) & ! [v0: % 13.96/2.69 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 13.96/2.69 : (v1 = v0 | ~ (contains_slb(v3, v2) = v1) | ~ (contains_slb(v3, v2) = v0)) % 13.96/2.69 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 13.96/2.69 (pair(v3, v2) = v1) | ~ (pair(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 13.96/2.69 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (insert_slb(v3, v2) = v1) | ~ % 13.96/2.69 (insert_slb(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 13.96/2.69 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 13.96/2.69 (strictly_less_than(v3, v2) = v1) | ~ (strictly_less_than(v3, v2) = v0)) & % 13.96/2.69 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 13.96/2.69 $i] : (v1 = v0 | ~ (less_than(v3, v2) = v1) | ~ (less_than(v3, v2) = v0)) % 13.96/2.69 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (im_succ_cpq(v2) = % 13.96/2.69 v1) | ~ (im_succ_cpq(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 13.96/2.69 : (v1 = v0 | ~ (removemin_cpq_res(v2) = v1) | ~ (removemin_cpq_res(v2) = % 13.96/2.69 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 13.96/2.69 (findmin_cpq_res(v2) = v1) | ~ (findmin_cpq_res(v2) = v0)) & ! [v0: $i] : % 13.96/2.69 ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (findmin_pqp_res(v2) = v1) | ~ % 13.96/2.69 (findmin_pqp_res(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 13.96/2.69 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (ok(v2) = v1) | ~ (ok(v2) % 13.96/2.69 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 13.96/2.69 $i] : (v1 = v0 | ~ (check_cpq(v2) = v1) | ~ (check_cpq(v2) = v0)) & ! % 13.96/2.69 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (removemin_cpq_eff(v2) = % 13.96/2.69 v1) | ~ (removemin_cpq_eff(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 13.96/2.69 [v2: $i] : (v1 = v0 | ~ (findmin_cpq_eff(v2) = v1) | ~ (findmin_cpq_eff(v2) % 13.96/2.69 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 13.96/2.69 $i] : (v1 = v0 | ~ (isnonempty_slb(v2) = v1) | ~ (isnonempty_slb(v2) = % 13.96/2.69 v0)) % 13.96/2.69 % 13.96/2.69 Further assumptions not needed in the proof: % 13.96/2.69 -------------------------------------------- % 13.96/2.69 ax18, ax19, ax20, ax21, ax22, ax23, ax24, ax25, ax26, ax27, ax28, ax29, ax30, % 13.96/2.69 ax31, ax32, ax33, ax34, ax35, ax36, ax37, ax38, ax39, ax40, ax42, ax43, ax44, % 13.96/2.69 ax45, ax46, ax47, ax48, ax49, ax50, ax51, ax52, ax53, bottom_smallest, % 13.96/2.69 reflexivity, stricly_smaller_definition, totality, transitivity % 13.96/2.69 % 13.96/2.69 Those formulas are unsatisfiable: % 13.96/2.69 --------------------------------- % 13.96/2.69 % 13.96/2.69 Begin of proof % 13.96/2.69 | % 13.96/2.69 | ALPHA: (ax41) implies: % 13.96/2.69 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v2 = bad | ~ % 13.96/2.69 | (triple(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 13.96/2.69 | ok(v3) = 0) % 13.96/2.69 | % 13.96/2.69 | ALPHA: (function-axioms) implies: % 13.96/2.70 | (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 13.96/2.70 | (v1 = v0 | ~ (check_cpq(v2) = v1) | ~ (check_cpq(v2) = v0)) % 13.96/2.70 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 13.96/2.70 | (v1 = v0 | ~ (ok(v2) = v1) | ~ (ok(v2) = v0)) % 13.96/2.70 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 13.96/2.70 | (im_succ_cpq(v2) = v1) | ~ (im_succ_cpq(v2) = v0)) % 13.96/2.70 | % 13.96/2.70 | DELTA: instantiating (l20_co) with fresh symbols all_47_0, all_47_1, all_47_2, % 13.96/2.70 | all_47_3, all_47_4, all_47_5 gives: % 13.96/2.70 | (5) ok(all_47_2) = all_47_0 & triple(all_47_5, all_47_4, all_47_3) = % 13.96/2.70 | all_47_2 & check_cpq(all_47_2) = all_47_1 & $i(all_47_2) & $i(all_47_3) % 13.96/2.70 | & $i(all_47_4) & $i(all_47_5) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] % 13.96/2.70 | : ? [v3: $i] : (ok(v3) = 0 & triple(v0, v1, v2) = v3 & check_cpq(v3) = % 13.96/2.70 | 0 & succ_cpq(all_47_2, v3) = 0 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) & % 13.96/2.70 | ( ~ (all_47_0 = 0) | ~ (all_47_1 = 0)) % 13.96/2.70 | % 13.96/2.70 | ALPHA: (5) implies: % 13.96/2.70 | (6) $i(all_47_5) % 13.96/2.70 | (7) $i(all_47_4) % 14.12/2.70 | (8) $i(all_47_3) % 14.12/2.70 | (9) check_cpq(all_47_2) = all_47_1 % 14.12/2.70 | (10) triple(all_47_5, all_47_4, all_47_3) = all_47_2 % 14.12/2.70 | (11) ok(all_47_2) = all_47_0 % 14.12/2.70 | (12) ~ (all_47_0 = 0) | ~ (all_47_1 = 0) % 14.12/2.70 | (13) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (ok(v3) = 0 & % 14.12/2.70 | triple(v0, v1, v2) = v3 & check_cpq(v3) = 0 & succ_cpq(all_47_2, v3) % 14.12/2.70 | = 0 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 14.12/2.70 | % 14.12/2.70 | DELTA: instantiating (13) with fresh symbols all_53_0, all_53_1, all_53_2, % 14.12/2.70 | all_53_3 gives: % 14.12/2.70 | (14) ok(all_53_0) = 0 & triple(all_53_3, all_53_2, all_53_1) = all_53_0 & % 14.12/2.70 | check_cpq(all_53_0) = 0 & succ_cpq(all_47_2, all_53_0) = 0 & % 14.12/2.70 | $i(all_53_0) & $i(all_53_1) & $i(all_53_2) & $i(all_53_3) % 14.12/2.70 | % 14.12/2.70 | ALPHA: (14) implies: % 14.12/2.70 | (15) $i(all_53_3) % 14.12/2.70 | (16) $i(all_53_2) % 14.12/2.70 | (17) $i(all_53_1) % 14.12/2.70 | (18) succ_cpq(all_47_2, all_53_0) = 0 % 14.12/2.70 | (19) check_cpq(all_53_0) = 0 % 14.12/2.70 | (20) triple(all_53_3, all_53_2, all_53_1) = all_53_0 % 14.12/2.70 | (21) ok(all_53_0) = 0 % 14.12/2.70 | % 14.12/2.70 | GROUND_INST: instantiating (1) with all_47_5, all_47_4, all_47_3, all_47_2, % 14.12/2.70 | simplifying with (6), (7), (8), (10) gives: % 14.12/2.70 | (22) all_47_3 = bad | ok(all_47_2) = 0 % 14.12/2.70 | % 14.12/2.70 | GROUND_INST: instantiating (l12_l13) with all_47_5, all_47_4, all_47_3, % 14.12/2.70 | all_47_2, simplifying with (6), (7), (8), (10) gives: % 14.12/2.70 | (23) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: any] : ? [v4: % 14.12/2.70 | any] : (im_succ_cpq(all_47_2) = v2 & ok(v2) = v4 & ok(all_47_2) = v1 % 14.12/2.70 | & check_cpq(v2) = v3 & check_cpq(all_47_2) = v0 & $i(v2) & ( ~ (v4 = % 14.12/2.70 | 0) | ~ (v3 = 0) | (v1 = 0 & v0 = 0))) % 14.12/2.70 | % 14.12/2.71 | GROUND_INST: instantiating (l12_l13) with all_53_3, all_53_2, all_53_1, % 14.12/2.71 | all_53_0, simplifying with (15), (16), (17), (20) gives: % 14.12/2.71 | (24) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: any] : ? [v4: % 14.12/2.71 | any] : (im_succ_cpq(all_53_0) = v2 & ok(v2) = v4 & ok(all_53_0) = v1 % 14.12/2.71 | & check_cpq(v2) = v3 & check_cpq(all_53_0) = v0 & $i(v2) & ( ~ (v4 = % 14.12/2.71 | 0) | ~ (v3 = 0) | (v1 = 0 & v0 = 0))) % 14.12/2.71 | % 14.12/2.71 | DELTA: instantiating (24) with fresh symbols all_60_0, all_60_1, all_60_2, % 14.12/2.71 | all_60_3, all_60_4 gives: % 14.12/2.71 | (25) im_succ_cpq(all_53_0) = all_60_2 & ok(all_60_2) = all_60_0 & % 14.12/2.71 | ok(all_53_0) = all_60_3 & check_cpq(all_60_2) = all_60_1 & % 14.12/2.71 | check_cpq(all_53_0) = all_60_4 & $i(all_60_2) & ( ~ (all_60_0 = 0) | % 14.12/2.71 | ~ (all_60_1 = 0) | (all_60_3 = 0 & all_60_4 = 0)) % 14.12/2.71 | % 14.12/2.71 | ALPHA: (25) implies: % 14.12/2.71 | (26) check_cpq(all_53_0) = all_60_4 % 14.12/2.71 | (27) ok(all_53_0) = all_60_3 % 14.12/2.71 | % 14.12/2.71 | DELTA: instantiating (23) with fresh symbols all_62_0, all_62_1, all_62_2, % 14.12/2.71 | all_62_3, all_62_4 gives: % 14.12/2.71 | (28) im_succ_cpq(all_47_2) = all_62_2 & ok(all_62_2) = all_62_0 & % 14.12/2.71 | ok(all_47_2) = all_62_3 & check_cpq(all_62_2) = all_62_1 & % 14.12/2.71 | check_cpq(all_47_2) = all_62_4 & $i(all_62_2) & ( ~ (all_62_0 = 0) | % 14.12/2.71 | ~ (all_62_1 = 0) | (all_62_3 = 0 & all_62_4 = 0)) % 14.12/2.71 | % 14.12/2.71 | ALPHA: (28) implies: % 14.12/2.71 | (29) check_cpq(all_47_2) = all_62_4 % 14.12/2.71 | (30) ok(all_47_2) = all_62_3 % 14.12/2.71 | % 14.12/2.71 | GROUND_INST: instantiating (2) with all_47_1, all_62_4, all_47_2, simplifying % 14.12/2.71 | with (9), (29) gives: % 14.12/2.71 | (31) all_62_4 = all_47_1 % 14.12/2.71 | % 14.12/2.71 | GROUND_INST: instantiating (2) with 0, all_60_4, all_53_0, simplifying with % 14.12/2.71 | (19), (26) gives: % 14.12/2.71 | (32) all_60_4 = 0 % 14.12/2.71 | % 14.12/2.71 | GROUND_INST: instantiating (3) with all_47_0, all_62_3, all_47_2, simplifying % 14.12/2.71 | with (11), (30) gives: % 14.12/2.71 | (33) all_62_3 = all_47_0 % 14.12/2.71 | % 14.12/2.71 | GROUND_INST: instantiating (3) with 0, all_60_3, all_53_0, simplifying with % 14.12/2.71 | (21), (27) gives: % 14.12/2.71 | (34) all_60_3 = 0 % 14.12/2.71 | % 14.12/2.71 | BETA: splitting (l20_induction) gives: % 14.12/2.71 | % 14.12/2.71 | Case 1: % 14.12/2.71 | | % 14.12/2.71 | | (35) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] % 14.12/2.71 | | : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: any] : ? [v9: % 14.12/2.71 | | any] : ? [v10: $i] : (im_succ_cpq(v7) = v10 & ok(v10) = 0 & % 14.12/2.71 | | ok(v7) = v9 & triple(v3, v4, v5) = v7 & triple(v0, v1, v2) = v6 & % 14.12/2.71 | | check_cpq(v10) = 0 & check_cpq(v7) = v8 & succ_cpq(v6, v7) = 0 & % 14.12/2.71 | | $i(v10) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & % 14.12/2.71 | | $i(v1) & $i(v0) & ( ~ (v9 = 0) | ~ (v8 = 0))) % 14.12/2.71 | | % 14.12/2.71 | | DELTA: instantiating (35) with fresh symbols all_74_0, all_74_1, all_74_2, % 14.12/2.71 | | all_74_3, all_74_4, all_74_5, all_74_6, all_74_7, all_74_8, all_74_9, % 14.12/2.71 | | all_74_10 gives: % 14.12/2.71 | | (36) im_succ_cpq(all_74_3) = all_74_0 & ok(all_74_0) = 0 & ok(all_74_3) = % 14.12/2.71 | | all_74_1 & triple(all_74_7, all_74_6, all_74_5) = all_74_3 & % 14.12/2.71 | | triple(all_74_10, all_74_9, all_74_8) = all_74_4 & % 14.12/2.71 | | check_cpq(all_74_0) = 0 & check_cpq(all_74_3) = all_74_2 & % 14.12/2.71 | | succ_cpq(all_74_4, all_74_3) = 0 & $i(all_74_0) & $i(all_74_3) & % 14.12/2.71 | | $i(all_74_4) & $i(all_74_5) & $i(all_74_6) & $i(all_74_7) & % 14.12/2.71 | | $i(all_74_8) & $i(all_74_9) & $i(all_74_10) & ( ~ (all_74_1 = 0) | % 14.12/2.71 | | ~ (all_74_2 = 0)) % 14.12/2.71 | | % 14.12/2.71 | | ALPHA: (36) implies: % 14.12/2.71 | | (37) $i(all_74_7) % 14.12/2.71 | | (38) $i(all_74_6) % 14.12/2.71 | | (39) $i(all_74_5) % 14.12/2.71 | | (40) check_cpq(all_74_3) = all_74_2 % 14.12/2.71 | | (41) check_cpq(all_74_0) = 0 % 14.12/2.71 | | (42) triple(all_74_7, all_74_6, all_74_5) = all_74_3 % 14.12/2.71 | | (43) ok(all_74_3) = all_74_1 % 14.12/2.71 | | (44) ok(all_74_0) = 0 % 14.12/2.71 | | (45) im_succ_cpq(all_74_3) = all_74_0 % 14.12/2.71 | | (46) ~ (all_74_1 = 0) | ~ (all_74_2 = 0) % 14.12/2.71 | | % 14.12/2.72 | | GROUND_INST: instantiating (l12_l13) with all_74_7, all_74_6, all_74_5, % 14.12/2.72 | | all_74_3, simplifying with (37), (38), (39), (42) gives: % 14.12/2.72 | | (47) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: any] : ? [v4: % 14.12/2.72 | | any] : (im_succ_cpq(all_74_3) = v2 & ok(v2) = v4 & ok(all_74_3) = % 14.12/2.72 | | v1 & check_cpq(v2) = v3 & check_cpq(all_74_3) = v0 & $i(v2) & ( ~ % 14.12/2.72 | | (v4 = 0) | ~ (v3 = 0) | (v1 = 0 & v0 = 0))) % 14.12/2.72 | | % 14.12/2.72 | | DELTA: instantiating (47) with fresh symbols all_81_0, all_81_1, all_81_2, % 14.12/2.72 | | all_81_3, all_81_4 gives: % 14.12/2.72 | | (48) im_succ_cpq(all_74_3) = all_81_2 & ok(all_81_2) = all_81_0 & % 14.12/2.72 | | ok(all_74_3) = all_81_3 & check_cpq(all_81_2) = all_81_1 & % 14.12/2.72 | | check_cpq(all_74_3) = all_81_4 & $i(all_81_2) & ( ~ (all_81_0 = 0) | % 14.12/2.72 | | ~ (all_81_1 = 0) | (all_81_3 = 0 & all_81_4 = 0)) % 14.12/2.72 | | % 14.12/2.72 | | ALPHA: (48) implies: % 14.12/2.72 | | (49) check_cpq(all_74_3) = all_81_4 % 14.12/2.72 | | (50) check_cpq(all_81_2) = all_81_1 % 14.12/2.72 | | (51) ok(all_74_3) = all_81_3 % 14.12/2.72 | | (52) ok(all_81_2) = all_81_0 % 14.12/2.72 | | (53) im_succ_cpq(all_74_3) = all_81_2 % 14.12/2.72 | | (54) ~ (all_81_0 = 0) | ~ (all_81_1 = 0) | (all_81_3 = 0 & all_81_4 = % 14.12/2.72 | | 0) % 14.12/2.72 | | % 14.12/2.72 | | GROUND_INST: instantiating (2) with all_74_2, all_81_4, all_74_3, % 14.12/2.72 | | simplifying with (40), (49) gives: % 14.12/2.72 | | (55) all_81_4 = all_74_2 % 14.12/2.72 | | % 14.12/2.72 | | GROUND_INST: instantiating (3) with all_74_1, all_81_3, all_74_3, % 14.12/2.72 | | simplifying with (43), (51) gives: % 14.12/2.72 | | (56) all_81_3 = all_74_1 % 14.12/2.72 | | % 14.12/2.72 | | GROUND_INST: instantiating (4) with all_74_0, all_81_2, all_74_3, % 14.12/2.72 | | simplifying with (45), (53) gives: % 14.12/2.72 | | (57) all_81_2 = all_74_0 % 14.12/2.72 | | % 14.12/2.72 | | REDUCE: (52), (57) imply: % 14.12/2.72 | | (58) ok(all_74_0) = all_81_0 % 14.12/2.72 | | % 14.12/2.72 | | REDUCE: (50), (57) imply: % 14.12/2.72 | | (59) check_cpq(all_74_0) = all_81_1 % 14.12/2.72 | | % 14.12/2.72 | | GROUND_INST: instantiating (2) with 0, all_81_1, all_74_0, simplifying with % 14.12/2.72 | | (41), (59) gives: % 14.12/2.72 | | (60) all_81_1 = 0 % 14.12/2.72 | | % 14.12/2.72 | | GROUND_INST: instantiating (3) with 0, all_81_0, all_74_0, simplifying with % 14.12/2.72 | | (44), (58) gives: % 14.12/2.72 | | (61) all_81_0 = 0 % 14.12/2.72 | | % 14.12/2.72 | | BETA: splitting (54) gives: % 14.12/2.72 | | % 14.12/2.72 | | Case 1: % 14.12/2.72 | | | % 14.12/2.72 | | | (62) ~ (all_81_0 = 0) % 14.12/2.72 | | | % 14.12/2.72 | | | REDUCE: (61), (62) imply: % 14.12/2.72 | | | (63) $false % 14.12/2.72 | | | % 14.12/2.72 | | | CLOSE: (63) is inconsistent. % 14.12/2.72 | | | % 14.12/2.72 | | Case 2: % 14.12/2.72 | | | % 14.12/2.72 | | | (64) ~ (all_81_1 = 0) | (all_81_3 = 0 & all_81_4 = 0) % 14.12/2.72 | | | % 14.12/2.72 | | | BETA: splitting (64) gives: % 14.12/2.72 | | | % 14.12/2.72 | | | Case 1: % 14.12/2.72 | | | | % 14.12/2.72 | | | | (65) ~ (all_81_1 = 0) % 14.12/2.72 | | | | % 14.12/2.72 | | | | REDUCE: (60), (65) imply: % 14.12/2.72 | | | | (66) $false % 14.12/2.72 | | | | % 14.12/2.72 | | | | CLOSE: (66) is inconsistent. % 14.12/2.72 | | | | % 14.12/2.72 | | | Case 2: % 14.12/2.72 | | | | % 14.12/2.72 | | | | (67) all_81_3 = 0 & all_81_4 = 0 % 14.12/2.72 | | | | % 14.12/2.72 | | | | ALPHA: (67) implies: % 14.12/2.72 | | | | (68) all_81_4 = 0 % 14.12/2.72 | | | | (69) all_81_3 = 0 % 14.12/2.72 | | | | % 14.12/2.72 | | | | COMBINE_EQS: (56), (69) imply: % 14.12/2.72 | | | | (70) all_74_1 = 0 % 14.12/2.72 | | | | % 14.12/2.72 | | | | SIMP: (70) implies: % 14.12/2.72 | | | | (71) all_74_1 = 0 % 14.12/2.72 | | | | % 14.12/2.72 | | | | COMBINE_EQS: (55), (68) imply: % 14.12/2.72 | | | | (72) all_74_2 = 0 % 14.12/2.72 | | | | % 14.12/2.72 | | | | BETA: splitting (46) gives: % 14.12/2.72 | | | | % 14.12/2.72 | | | | Case 1: % 14.12/2.72 | | | | | % 14.12/2.72 | | | | | (73) ~ (all_74_1 = 0) % 14.12/2.72 | | | | | % 14.12/2.72 | | | | | REDUCE: (71), (73) imply: % 14.12/2.72 | | | | | (74) $false % 14.12/2.72 | | | | | % 14.12/2.72 | | | | | CLOSE: (74) is inconsistent. % 14.12/2.72 | | | | | % 14.12/2.72 | | | | Case 2: % 14.12/2.72 | | | | | % 14.12/2.72 | | | | | (75) ~ (all_74_2 = 0) % 14.12/2.72 | | | | | % 14.12/2.73 | | | | | REDUCE: (72), (75) imply: % 14.12/2.73 | | | | | (76) $false % 14.12/2.73 | | | | | % 14.12/2.73 | | | | | CLOSE: (76) is inconsistent. % 14.12/2.73 | | | | | % 14.12/2.73 | | | | End of split % 14.12/2.73 | | | | % 14.12/2.73 | | | End of split % 14.12/2.73 | | | % 14.12/2.73 | | End of split % 14.12/2.73 | | % 14.12/2.73 | Case 2: % 14.12/2.73 | | % 14.12/2.73 | | (77) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 14.12/2.73 | | (triple(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ! % 14.12/2.73 | | [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ % 14.12/2.73 | | (triple(v4, v5, v6) = v7) | ~ (succ_cpq(v3, v7) = 0) | ~ % 14.12/2.73 | | $i(v6) | ~ $i(v5) | ~ $i(v4) | ? [v8: any] : ? [v9: any] : % 14.12/2.73 | | (ok(v7) = v8 & check_cpq(v7) = v9 & ( ~ (v9 = 0) | ~ (v8 = % 14.12/2.73 | | 0)))) | (ok(v3) = 0 & check_cpq(v3) = 0)) % 14.12/2.73 | | % 14.12/2.73 | | GROUND_INST: instantiating (77) with all_47_5, all_47_4, all_47_3, all_47_2, % 14.12/2.73 | | simplifying with (6), (7), (8), (10) gives: % 14.12/2.73 | | (78) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 14.12/2.73 | | (triple(v0, v1, v2) = v3) | ~ (succ_cpq(all_47_2, v3) = 0) | ~ % 14.12/2.73 | | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : % 14.12/2.73 | | (ok(v3) = v4 & check_cpq(v3) = v5 & ( ~ (v5 = 0) | ~ (v4 = 0)))) % 14.12/2.73 | | | (ok(all_47_2) = 0 & check_cpq(all_47_2) = 0) % 14.12/2.73 | | % 14.12/2.73 | | BETA: splitting (12) gives: % 14.12/2.73 | | % 14.12/2.73 | | Case 1: % 14.12/2.73 | | | % 14.12/2.73 | | | (79) ~ (all_47_0 = 0) % 14.12/2.73 | | | % 14.12/2.73 | | | BETA: splitting (22) gives: % 14.12/2.73 | | | % 14.12/2.73 | | | Case 1: % 14.12/2.73 | | | | % 14.12/2.73 | | | | (80) ok(all_47_2) = 0 % 14.12/2.73 | | | | % 14.27/2.73 | | | | GROUND_INST: instantiating (3) with all_47_0, 0, all_47_2, simplifying % 14.27/2.73 | | | | with (11), (80) gives: % 14.27/2.73 | | | | (81) all_47_0 = 0 % 14.27/2.73 | | | | % 14.27/2.73 | | | | REDUCE: (79), (81) imply: % 14.27/2.73 | | | | (82) $false % 14.27/2.73 | | | | % 14.27/2.73 | | | | CLOSE: (82) is inconsistent. % 14.27/2.73 | | | | % 14.27/2.73 | | | Case 2: % 14.27/2.73 | | | | % 14.27/2.73 | | | | (83) ~ (ok(all_47_2) = 0) % 14.27/2.73 | | | | % 14.27/2.73 | | | | BETA: splitting (78) gives: % 14.27/2.73 | | | | % 14.27/2.73 | | | | Case 1: % 14.27/2.73 | | | | | % 14.27/2.73 | | | | | (84) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 14.27/2.73 | | | | | (triple(v0, v1, v2) = v3) | ~ (succ_cpq(all_47_2, v3) = 0) % 14.27/2.73 | | | | | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: % 14.27/2.73 | | | | | any] : (ok(v3) = v4 & check_cpq(v3) = v5 & ( ~ (v5 = 0) | % 14.27/2.73 | | | | | ~ (v4 = 0)))) % 14.27/2.73 | | | | | % 14.27/2.73 | | | | | GROUND_INST: instantiating (84) with all_53_3, all_53_2, all_53_1, % 14.27/2.73 | | | | | all_53_0, simplifying with (15), (16), (17), (18), (20) % 14.27/2.73 | | | | | gives: % 14.27/2.73 | | | | | (85) ? [v0: any] : ? [v1: any] : (ok(all_53_0) = v0 & % 14.27/2.73 | | | | | check_cpq(all_53_0) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 14.27/2.73 | | | | | % 14.27/2.73 | | | | | REF_CLOSE: (2), (3), (19), (21), (85) are inconsistent by sub-proof % 14.27/2.73 | | | | | #1. % 14.27/2.73 | | | | | % 14.27/2.73 | | | | Case 2: % 14.27/2.73 | | | | | % 14.27/2.73 | | | | | (86) ok(all_47_2) = 0 & check_cpq(all_47_2) = 0 % 14.27/2.73 | | | | | % 14.27/2.73 | | | | | ALPHA: (86) implies: % 14.27/2.73 | | | | | (87) ok(all_47_2) = 0 % 14.27/2.73 | | | | | % 14.27/2.73 | | | | | PRED_UNIFY: (83), (87) imply: % 14.27/2.73 | | | | | (88) $false % 14.27/2.73 | | | | | % 14.27/2.73 | | | | | CLOSE: (88) is inconsistent. % 14.27/2.73 | | | | | % 14.27/2.73 | | | | End of split % 14.27/2.73 | | | | % 14.27/2.73 | | | End of split % 14.27/2.73 | | | % 14.27/2.73 | | Case 2: % 14.27/2.73 | | | % 14.27/2.74 | | | (89) ~ (all_47_1 = 0) % 14.27/2.74 | | | % 14.27/2.74 | | | BETA: splitting (78) gives: % 14.27/2.74 | | | % 14.27/2.74 | | | Case 1: % 14.27/2.74 | | | | % 14.27/2.74 | | | | (90) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 14.27/2.74 | | | | (triple(v0, v1, v2) = v3) | ~ (succ_cpq(all_47_2, v3) = 0) | % 14.27/2.74 | | | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] % 14.27/2.74 | | | | : (ok(v3) = v4 & check_cpq(v3) = v5 & ( ~ (v5 = 0) | ~ (v4 = % 14.27/2.74 | | | | 0)))) % 14.27/2.74 | | | | % 14.27/2.74 | | | | GROUND_INST: instantiating (90) with all_53_3, all_53_2, all_53_1, % 14.27/2.74 | | | | all_53_0, simplifying with (15), (16), (17), (18), (20) % 14.27/2.74 | | | | gives: % 14.27/2.74 | | | | (91) ? [v0: any] : ? [v1: any] : (ok(all_53_0) = v0 & % 14.27/2.74 | | | | check_cpq(all_53_0) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 14.27/2.74 | | | | % 14.27/2.74 | | | | REF_CLOSE: (2), (3), (19), (21), (91) are inconsistent by sub-proof #1. % 14.27/2.74 | | | | % 14.27/2.74 | | | Case 2: % 14.27/2.74 | | | | % 14.27/2.74 | | | | (92) ok(all_47_2) = 0 & check_cpq(all_47_2) = 0 % 14.27/2.74 | | | | % 14.27/2.74 | | | | ALPHA: (92) implies: % 14.27/2.74 | | | | (93) check_cpq(all_47_2) = 0 % 14.27/2.74 | | | | % 14.27/2.74 | | | | GROUND_INST: instantiating (2) with all_47_1, 0, all_47_2, simplifying % 14.27/2.74 | | | | with (9), (93) gives: % 14.27/2.74 | | | | (94) all_47_1 = 0 % 14.27/2.74 | | | | % 14.27/2.74 | | | | REDUCE: (89), (94) imply: % 14.27/2.74 | | | | (95) $false % 14.27/2.74 | | | | % 14.27/2.74 | | | | CLOSE: (95) is inconsistent. % 14.27/2.74 | | | | % 14.27/2.74 | | | End of split % 14.27/2.74 | | | % 14.27/2.74 | | End of split % 14.27/2.74 | | % 14.27/2.74 | End of split % 14.27/2.74 | % 14.27/2.74 End of proof % 14.27/2.74 % 14.27/2.74 Sub-proof #1 shows that the following formulas are inconsistent: % 14.27/2.74 ---------------------------------------------------------------- % 14.27/2.74 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 14.27/2.74 (v1 = v0 | ~ (ok(v2) = v1) | ~ (ok(v2) = v0)) % 14.27/2.74 (2) ? [v0: any] : ? [v1: any] : (ok(all_53_0) = v0 & check_cpq(all_53_0) = % 14.27/2.74 v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 14.27/2.74 (3) check_cpq(all_53_0) = 0 % 14.27/2.74 (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 14.27/2.74 (v1 = v0 | ~ (check_cpq(v2) = v1) | ~ (check_cpq(v2) = v0)) % 14.27/2.74 (5) ok(all_53_0) = 0 % 14.27/2.74 % 14.27/2.74 Begin of proof % 14.27/2.74 | % 14.27/2.74 | DELTA: instantiating (2) with fresh symbols all_87_0, all_87_1 gives: % 14.27/2.74 | (6) ok(all_53_0) = all_87_1 & check_cpq(all_53_0) = all_87_0 & ( ~ % 14.27/2.74 | (all_87_0 = 0) | ~ (all_87_1 = 0)) % 14.27/2.74 | % 14.27/2.74 | ALPHA: (6) implies: % 14.27/2.74 | (7) check_cpq(all_53_0) = all_87_0 % 14.27/2.74 | (8) ok(all_53_0) = all_87_1 % 14.27/2.74 | (9) ~ (all_87_0 = 0) | ~ (all_87_1 = 0) % 14.27/2.74 | % 14.27/2.74 | GROUND_INST: instantiating (4) with 0, all_87_0, all_53_0, simplifying with % 14.27/2.74 | (3), (7) gives: % 14.27/2.74 | (10) all_87_0 = 0 % 14.27/2.74 | % 14.27/2.74 | GROUND_INST: instantiating (1) with 0, all_87_1, all_53_0, simplifying with % 14.27/2.74 | (5), (8) gives: % 14.27/2.74 | (11) all_87_1 = 0 % 14.27/2.74 | % 14.27/2.74 | BETA: splitting (9) gives: % 14.27/2.74 | % 14.27/2.74 | Case 1: % 14.27/2.74 | | % 14.27/2.74 | | (12) ~ (all_87_0 = 0) % 14.27/2.74 | | % 14.27/2.74 | | REDUCE: (10), (12) imply: % 14.27/2.74 | | (13) $false % 14.27/2.74 | | % 14.27/2.74 | | CLOSE: (13) is inconsistent. % 14.27/2.74 | | % 14.27/2.74 | Case 2: % 14.27/2.74 | | % 14.27/2.74 | | (14) ~ (all_87_1 = 0) % 14.27/2.74 | | % 14.27/2.74 | | REDUCE: (11), (14) imply: % 14.27/2.74 | | (15) $false % 14.27/2.74 | | % 14.27/2.74 | | CLOSE: (15) is inconsistent. % 14.27/2.74 | | % 14.27/2.74 | End of split % 14.27/2.74 | % 14.27/2.74 End of proof % 14.27/2.74 % SZS output end Proof for theBenchmark % 14.27/2.74 % 14.27/2.74 2127ms %------------------------------------------------------------------------------