%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWV378+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 : n007.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 22:56:05 EDT 2023 % Result : Theorem 10.63s 2.19s % Output : Proof 13.89s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SWV378+1 : TPTP v8.1.2. Released v3.3.0. % 0.11/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n007.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 08:11:58 EDT 2023 % 0.13/0.34 % CPUTime : % 0.68/0.64 ________ _____ % 0.68/0.64 ___ __ \_________(_)________________________________ % 0.68/0.64 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.68/0.64 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.68/0.64 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.68/0.64 % 0.68/0.64 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.68/0.64 (2023-06-19) % 0.68/0.64 % 0.68/0.64 (c) Philipp Rümmer, 2009-2023 % 0.68/0.64 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.68/0.64 Amanda Stjerna. % 0.68/0.64 Free software under BSD-3-Clause. % 0.68/0.64 % 0.68/0.64 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.68/0.64 % 0.68/0.64 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.68/0.66 Running up to 7 provers in parallel. % 0.68/0.68 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.68/0.68 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.68/0.68 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.68/0.68 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.68/0.68 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.68/0.68 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.68/0.68 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.50/1.18 Prover 4: Preprocessing ... % 3.50/1.18 Prover 1: Preprocessing ... % 3.63/1.22 Prover 2: Preprocessing ... % 3.63/1.22 Prover 6: Preprocessing ... % 3.63/1.22 Prover 3: Preprocessing ... % 3.63/1.22 Prover 0: Preprocessing ... % 3.63/1.22 Prover 5: Preprocessing ... % 7.21/1.75 Prover 3: Warning: ignoring some quantifiers % 7.21/1.76 Prover 1: Warning: ignoring some quantifiers % 7.97/1.80 Prover 3: Constructing countermodel ... % 8.20/1.81 Prover 6: Proving ... % 8.20/1.82 Prover 1: Constructing countermodel ... % 8.36/1.86 Prover 4: Constructing countermodel ... % 8.36/1.86 Prover 5: Proving ... % 8.36/1.87 Prover 0: Proving ... % 9.05/1.99 Prover 2: Proving ... % 10.63/2.19 Prover 0: proved (1518ms) % 10.63/2.19 % 10.63/2.19 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 10.63/2.19 % 10.63/2.19 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 10.63/2.19 Prover 3: stopped % 10.63/2.19 Prover 2: stopped % 10.63/2.20 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 10.63/2.20 Prover 5: stopped % 10.63/2.21 Prover 6: stopped % 11.35/2.22 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 11.35/2.22 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 11.35/2.22 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 11.35/2.23 Prover 8: Preprocessing ... % 11.35/2.24 Prover 7: Preprocessing ... % 11.35/2.25 Prover 10: Preprocessing ... % 11.35/2.27 Prover 13: Preprocessing ... % 11.35/2.28 Prover 11: Preprocessing ... % 12.79/2.41 Prover 7: Warning: ignoring some quantifiers % 12.87/2.42 Prover 1: Found proof (size 105) % 12.87/2.42 Prover 1: proved (1752ms) % 12.87/2.42 Prover 8: Warning: ignoring some quantifiers % 12.87/2.43 Prover 4: stopped % 12.87/2.43 Prover 7: Constructing countermodel ... % 12.87/2.44 Prover 10: Warning: ignoring some quantifiers % 12.87/2.45 Prover 8: Constructing countermodel ... % 12.87/2.45 Prover 7: stopped % 12.87/2.45 Prover 10: Constructing countermodel ... % 12.87/2.46 Prover 13: Warning: ignoring some quantifiers % 12.87/2.46 Prover 8: stopped % 12.87/2.46 Prover 10: stopped % 12.87/2.47 Prover 11: Constructing countermodel ... % 12.87/2.48 Prover 13: Constructing countermodel ... % 12.87/2.49 Prover 11: stopped % 12.87/2.49 Prover 13: stopped % 12.87/2.49 % 12.87/2.49 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 12.87/2.49 % 13.49/2.51 % SZS output start Proof for theBenchmark % 13.49/2.52 Assumptions after simplification: % 13.49/2.52 --------------------------------- % 13.49/2.52 % 13.49/2.52 (ax40) % 13.49/2.54 $i(bad) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (triple(v0, v1, bad) = % 13.49/2.54 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & ok(v2) = v3)) % 13.49/2.54 % 13.49/2.54 (ax41) % 13.49/2.54 $i(bad) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v2 = bad | % 13.49/2.54 ~ (triple(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ok(v3) = % 13.49/2.54 0) % 13.49/2.54 % 13.49/2.54 (ax43) % 13.49/2.55 $i(bad) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] % 13.49/2.55 : ! [v5: $i] : ( ~ (triple(v0, v1, v2) = v4) | ~ (remove_cpq(v4, v3) = v5) | % 13.49/2.55 ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: $i] : % 13.49/2.55 (triple(v0, v1, bad) = v7 & contains_slb(v1, v3) = v6 & $i(v7) & (v7 = v5 | % 13.49/2.55 v6 = 0))) % 13.49/2.55 % 13.49/2.55 (ax44) % 13.49/2.55 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 13.49/2.55 $i] : ! [v6: $i] : ( ~ (remove_pqp(v0, v3) = v4) | ~ (triple(v4, v5, v2) = % 13.49/2.55 v6) | ~ (remove_slb(v1, v3) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | % 13.49/2.55 ~ $i(v0) | ? [v7: any] : ? [v8: $i] : ? [v9: any] : ? [v10: $i] : ? % 13.49/2.55 [v11: $i] : (triple(v0, v1, v2) = v10 & remove_cpq(v10, v3) = v11 & % 13.49/2.55 lookup_slb(v1, v3) = v8 & contains_slb(v1, v3) = v7 & less_than(v8, v3) = % 13.49/2.55 v9 & $i(v11) & $i(v10) & $i(v8) & ( ~ (v9 = 0) | ~ (v7 = 0) | v11 = v6))) % 13.49/2.55 % 13.49/2.55 (ax45) % 13.49/2.55 $i(bad) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] % 13.49/2.55 : ! [v5: $i] : ( ~ (triple(v0, v1, v2) = v4) | ~ (remove_cpq(v4, v3) = v5) | % 13.49/2.55 ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: $i] : % 13.49/2.55 ? [v8: any] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : (remove_pqp(v0, % 13.49/2.55 v3) = v9 & triple(v9, v10, bad) = v11 & lookup_slb(v1, v3) = v7 & % 13.49/2.55 remove_slb(v1, v3) = v10 & contains_slb(v1, v3) = v6 & % 13.49/2.55 strictly_less_than(v3, v7) = v8 & $i(v11) & $i(v10) & $i(v9) & $i(v7) & ( % 13.49/2.55 ~ (v8 = 0) | ~ (v6 = 0) | v11 = v5))) % 13.49/2.55 % 13.49/2.55 (l14_co) % 13.49/2.56 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 13.49/2.56 int] : ? [v6: $i] : ( ~ (v5 = 0) & ok(v6) = 0 & ok(v4) = v5 & triple(v0, % 13.49/2.56 v1, v2) = v4 & remove_cpq(v4, v3) = v6 & $i(v6) & $i(v4) & $i(v3) & $i(v2) % 13.49/2.56 & $i(v1) & $i(v0)) % 13.49/2.56 % 13.49/2.56 (stricly_smaller_definition) % 13.49/2.56 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 13.49/2.56 (strictly_less_than(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : % 13.49/2.56 ? [v4: any] : (less_than(v1, v0) = v4 & less_than(v0, v1) = v3 & ( ~ (v3 = % 13.49/2.56 0) | v4 = 0))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 13.49/2.56 (strictly_less_than(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: int] : ( % 13.49/2.56 ~ (v2 = 0) & less_than(v1, v0) = v2 & less_than(v0, v1) = 0)) % 13.49/2.56 % 13.49/2.56 (totality) % 13.49/2.56 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (less_than(v0, v1) = % 13.49/2.56 v2) | ~ $i(v1) | ~ $i(v0) | less_than(v1, v0) = 0) % 13.49/2.56 % 13.49/2.56 (function-axioms) % 13.49/2.57 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 % 13.49/2.57 | ~ (triple(v4, v3, v2) = v1) | ~ (triple(v4, v3, v2) = v0)) & ! [v0: % 13.49/2.57 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 13.49/2.57 : ! [v4: $i] : (v1 = v0 | ~ (pair_in_list(v4, v3, v2) = v1) | ~ % 13.49/2.57 (pair_in_list(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 13.49/2.57 ! [v3: $i] : (v1 = v0 | ~ (remove_pqp(v3, v2) = v1) | ~ (remove_pqp(v3, v2) % 13.49/2.57 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 % 13.49/2.57 | ~ (insert_pqp(v3, v2) = v1) | ~ (insert_pqp(v3, v2) = v0)) & ! [v0: % 13.49/2.57 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 13.49/2.57 : (v1 = v0 | ~ (contains_cpq(v3, v2) = v1) | ~ (contains_cpq(v3, v2) = v0)) % 13.49/2.57 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 13.49/2.57 (remove_cpq(v3, v2) = v1) | ~ (remove_cpq(v3, v2) = v0)) & ! [v0: $i] : ! % 13.49/2.57 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (insert_cpq(v3, v2) = v1) % 13.49/2.57 | ~ (insert_cpq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 13.49/2.57 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (succ_cpq(v3, % 13.49/2.57 v2) = v1) | ~ (succ_cpq(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 13.49/2.57 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (update_slb(v3, v2) = v1) | ~ % 13.49/2.57 (update_slb(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 13.49/2.57 [v3: $i] : (v1 = v0 | ~ (lookup_slb(v3, v2) = v1) | ~ (lookup_slb(v3, v2) = % 13.49/2.57 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 13.49/2.57 ~ (remove_slb(v3, v2) = v1) | ~ (remove_slb(v3, v2) = v0)) & ! [v0: % 13.49/2.57 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 13.49/2.57 : (v1 = v0 | ~ (contains_slb(v3, v2) = v1) | ~ (contains_slb(v3, v2) = v0)) % 13.49/2.57 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 13.49/2.57 (pair(v3, v2) = v1) | ~ (pair(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 13.49/2.57 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (insert_slb(v3, v2) = v1) | ~ % 13.49/2.57 (insert_slb(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 13.49/2.57 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 13.49/2.57 (strictly_less_than(v3, v2) = v1) | ~ (strictly_less_than(v3, v2) = v0)) & % 13.49/2.57 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 13.49/2.57 $i] : (v1 = v0 | ~ (less_than(v3, v2) = v1) | ~ (less_than(v3, v2) = v0)) % 13.49/2.57 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 13.49/2.57 (removemin_cpq_res(v2) = v1) | ~ (removemin_cpq_res(v2) = v0)) & ! [v0: % 13.49/2.57 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (findmin_cpq_res(v2) = v1) | % 13.49/2.57 ~ (findmin_cpq_res(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 13.49/2.57 (v1 = v0 | ~ (findmin_pqp_res(v2) = v1) | ~ (findmin_pqp_res(v2) = v0)) & ! % 13.49/2.57 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 % 13.49/2.57 | ~ (ok(v2) = v1) | ~ (ok(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 13.49/2.57 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (check_cpq(v2) = v1) | % 13.49/2.57 ~ (check_cpq(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 % 13.49/2.57 | ~ (removemin_cpq_eff(v2) = v1) | ~ (removemin_cpq_eff(v2) = v0)) & ! % 13.49/2.57 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (findmin_cpq_eff(v2) = % 13.49/2.57 v1) | ~ (findmin_cpq_eff(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 13.49/2.57 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (isnonempty_slb(v2) = % 13.49/2.57 v1) | ~ (isnonempty_slb(v2) = v0)) % 13.49/2.57 % 13.49/2.57 Further assumptions not needed in the proof: % 13.49/2.57 -------------------------------------------- % 13.49/2.57 ax18, ax19, ax20, ax21, ax22, ax23, ax24, ax25, ax26, ax27, ax28, ax29, ax30, % 13.49/2.57 ax31, ax32, ax33, ax34, ax35, ax36, ax37, ax38, ax39, ax42, ax46, ax47, ax48, % 13.49/2.57 ax49, ax50, ax51, ax52, ax53, bottom_smallest, reflexivity, transitivity % 13.49/2.57 % 13.49/2.57 Those formulas are unsatisfiable: % 13.49/2.57 --------------------------------- % 13.49/2.57 % 13.49/2.57 Begin of proof % 13.49/2.57 | % 13.49/2.57 | ALPHA: (stricly_smaller_definition) implies: % 13.49/2.57 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 13.49/2.57 | (strictly_less_than(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: % 13.49/2.57 | any] : ? [v4: any] : (less_than(v1, v0) = v4 & less_than(v0, v1) = % 13.49/2.57 | v3 & ( ~ (v3 = 0) | v4 = 0))) % 13.49/2.57 | % 13.49/2.57 | ALPHA: (ax40) implies: % 13.49/2.57 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (triple(v0, v1, bad) = % 13.49/2.57 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & ok(v2) % 13.49/2.57 | = v3)) % 13.49/2.57 | % 13.49/2.57 | ALPHA: (ax41) implies: % 13.49/2.57 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v2 = bad | ~ % 13.49/2.57 | (triple(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 13.49/2.57 | ok(v3) = 0) % 13.49/2.57 | % 13.49/2.57 | ALPHA: (ax43) implies: % 13.49/2.57 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 13.49/2.57 | ! [v5: $i] : ( ~ (triple(v0, v1, v2) = v4) | ~ (remove_cpq(v4, v3) = % 13.49/2.57 | v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] % 13.49/2.57 | : ? [v7: $i] : (triple(v0, v1, bad) = v7 & contains_slb(v1, v3) = v6 % 13.49/2.57 | & $i(v7) & (v7 = v5 | v6 = 0))) % 13.49/2.57 | % 13.49/2.57 | ALPHA: (ax45) implies: % 13.49/2.57 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 13.49/2.57 | ! [v5: $i] : ( ~ (triple(v0, v1, v2) = v4) | ~ (remove_cpq(v4, v3) = % 13.49/2.57 | v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] % 13.49/2.57 | : ? [v7: $i] : ? [v8: any] : ? [v9: $i] : ? [v10: $i] : ? [v11: % 13.49/2.57 | $i] : (remove_pqp(v0, v3) = v9 & triple(v9, v10, bad) = v11 & % 13.49/2.57 | lookup_slb(v1, v3) = v7 & remove_slb(v1, v3) = v10 & % 13.49/2.57 | contains_slb(v1, v3) = v6 & strictly_less_than(v3, v7) = v8 & % 13.49/2.57 | $i(v11) & $i(v10) & $i(v9) & $i(v7) & ( ~ (v8 = 0) | ~ (v6 = 0) | % 13.49/2.57 | v11 = v5))) % 13.49/2.57 | % 13.49/2.57 | ALPHA: (function-axioms) implies: % 13.49/2.58 | (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 13.49/2.58 | (v1 = v0 | ~ (ok(v2) = v1) | ~ (ok(v2) = v0)) % 13.49/2.58 | (7) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 13.49/2.58 | ! [v3: $i] : (v1 = v0 | ~ (less_than(v3, v2) = v1) | ~ % 13.49/2.58 | (less_than(v3, v2) = v0)) % 13.49/2.58 | (8) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 13.49/2.58 | ! [v3: $i] : (v1 = v0 | ~ (contains_slb(v3, v2) = v1) | ~ % 13.49/2.58 | (contains_slb(v3, v2) = v0)) % 13.49/2.58 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 13.49/2.58 | (lookup_slb(v3, v2) = v1) | ~ (lookup_slb(v3, v2) = v0)) % 13.49/2.58 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 13.49/2.58 | (remove_cpq(v3, v2) = v1) | ~ (remove_cpq(v3, v2) = v0)) % 13.49/2.58 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 13.49/2.58 | (v1 = v0 | ~ (triple(v4, v3, v2) = v1) | ~ (triple(v4, v3, v2) = % 13.49/2.58 | v0)) % 13.49/2.58 | % 13.49/2.58 | DELTA: instantiating (l14_co) with fresh symbols all_44_0, all_44_1, all_44_2, % 13.49/2.58 | all_44_3, all_44_4, all_44_5, all_44_6 gives: % 13.49/2.58 | (12) ~ (all_44_1 = 0) & ok(all_44_0) = 0 & ok(all_44_2) = all_44_1 & % 13.49/2.58 | triple(all_44_6, all_44_5, all_44_4) = all_44_2 & remove_cpq(all_44_2, % 13.49/2.58 | all_44_3) = all_44_0 & $i(all_44_0) & $i(all_44_2) & $i(all_44_3) & % 13.49/2.58 | $i(all_44_4) & $i(all_44_5) & $i(all_44_6) % 13.49/2.58 | % 13.49/2.58 | ALPHA: (12) implies: % 13.49/2.58 | (13) ~ (all_44_1 = 0) % 13.49/2.58 | (14) $i(all_44_6) % 13.49/2.58 | (15) $i(all_44_5) % 13.49/2.58 | (16) $i(all_44_4) % 13.49/2.58 | (17) $i(all_44_3) % 13.49/2.58 | (18) remove_cpq(all_44_2, all_44_3) = all_44_0 % 13.49/2.58 | (19) triple(all_44_6, all_44_5, all_44_4) = all_44_2 % 13.49/2.58 | (20) ok(all_44_2) = all_44_1 % 13.49/2.58 | (21) ok(all_44_0) = 0 % 13.49/2.58 | % 13.49/2.58 | GROUND_INST: instantiating (5) with all_44_6, all_44_5, all_44_4, all_44_3, % 13.49/2.58 | all_44_2, all_44_0, simplifying with (14), (15), (16), (17), % 13.49/2.58 | (18), (19) gives: % 13.49/2.58 | (22) ? [v0: any] : ? [v1: $i] : ? [v2: any] : ? [v3: $i] : ? [v4: $i] % 13.49/2.58 | : ? [v5: $i] : (remove_pqp(all_44_6, all_44_3) = v3 & triple(v3, v4, % 13.49/2.58 | bad) = v5 & lookup_slb(all_44_5, all_44_3) = v1 & % 13.49/2.58 | remove_slb(all_44_5, all_44_3) = v4 & contains_slb(all_44_5, % 13.49/2.58 | all_44_3) = v0 & strictly_less_than(all_44_3, v1) = v2 & $i(v5) & % 13.49/2.58 | $i(v4) & $i(v3) & $i(v1) & ( ~ (v2 = 0) | ~ (v0 = 0) | v5 = % 13.49/2.58 | all_44_0)) % 13.49/2.58 | % 13.49/2.58 | GROUND_INST: instantiating (4) with all_44_6, all_44_5, all_44_4, all_44_3, % 13.49/2.58 | all_44_2, all_44_0, simplifying with (14), (15), (16), (17), % 13.49/2.58 | (18), (19) gives: % 13.49/2.59 | (23) ? [v0: any] : ? [v1: $i] : (triple(all_44_6, all_44_5, bad) = v1 & % 13.49/2.59 | contains_slb(all_44_5, all_44_3) = v0 & $i(v1) & (v1 = all_44_0 | v0 % 13.49/2.59 | = 0)) % 13.49/2.59 | % 13.49/2.59 | GROUND_INST: instantiating (3) with all_44_6, all_44_5, all_44_4, all_44_2, % 13.49/2.59 | simplifying with (14), (15), (16), (19) gives: % 13.49/2.59 | (24) all_44_4 = bad | ok(all_44_2) = 0 % 13.49/2.59 | % 13.49/2.59 | DELTA: instantiating (23) with fresh symbols all_57_0, all_57_1 gives: % 13.49/2.59 | (25) triple(all_44_6, all_44_5, bad) = all_57_0 & contains_slb(all_44_5, % 13.49/2.59 | all_44_3) = all_57_1 & $i(all_57_0) & (all_57_0 = all_44_0 | % 13.49/2.59 | all_57_1 = 0) % 13.49/2.59 | % 13.49/2.59 | ALPHA: (25) implies: % 13.49/2.59 | (26) contains_slb(all_44_5, all_44_3) = all_57_1 % 13.49/2.59 | (27) triple(all_44_6, all_44_5, bad) = all_57_0 % 13.49/2.59 | (28) all_57_0 = all_44_0 | all_57_1 = 0 % 13.49/2.59 | % 13.49/2.59 | DELTA: instantiating (22) with fresh symbols all_59_0, all_59_1, all_59_2, % 13.49/2.59 | all_59_3, all_59_4, all_59_5 gives: % 13.89/2.59 | (29) remove_pqp(all_44_6, all_44_3) = all_59_2 & triple(all_59_2, all_59_1, % 13.89/2.59 | bad) = all_59_0 & lookup_slb(all_44_5, all_44_3) = all_59_4 & % 13.89/2.59 | remove_slb(all_44_5, all_44_3) = all_59_1 & contains_slb(all_44_5, % 13.89/2.59 | all_44_3) = all_59_5 & strictly_less_than(all_44_3, all_59_4) = % 13.89/2.59 | all_59_3 & $i(all_59_0) & $i(all_59_1) & $i(all_59_2) & $i(all_59_4) & % 13.89/2.59 | ( ~ (all_59_3 = 0) | ~ (all_59_5 = 0) | all_59_0 = all_44_0) % 13.89/2.59 | % 13.89/2.59 | ALPHA: (29) implies: % 13.89/2.59 | (30) $i(all_59_4) % 13.89/2.59 | (31) $i(all_59_2) % 13.89/2.59 | (32) $i(all_59_1) % 13.89/2.59 | (33) strictly_less_than(all_44_3, all_59_4) = all_59_3 % 13.89/2.59 | (34) contains_slb(all_44_5, all_44_3) = all_59_5 % 13.89/2.59 | (35) remove_slb(all_44_5, all_44_3) = all_59_1 % 13.89/2.59 | (36) lookup_slb(all_44_5, all_44_3) = all_59_4 % 13.89/2.59 | (37) triple(all_59_2, all_59_1, bad) = all_59_0 % 13.89/2.59 | (38) remove_pqp(all_44_6, all_44_3) = all_59_2 % 13.89/2.59 | (39) ~ (all_59_3 = 0) | ~ (all_59_5 = 0) | all_59_0 = all_44_0 % 13.89/2.59 | % 13.89/2.59 | BETA: splitting (24) gives: % 13.89/2.59 | % 13.89/2.59 | Case 1: % 13.89/2.59 | | % 13.89/2.59 | | (40) ok(all_44_2) = 0 % 13.89/2.59 | | % 13.89/2.59 | | GROUND_INST: instantiating (6) with all_44_1, 0, all_44_2, simplifying with % 13.89/2.59 | | (20), (40) gives: % 13.89/2.59 | | (41) all_44_1 = 0 % 13.89/2.59 | | % 13.89/2.59 | | REDUCE: (13), (41) imply: % 13.89/2.59 | | (42) $false % 13.89/2.59 | | % 13.89/2.59 | | CLOSE: (42) is inconsistent. % 13.89/2.59 | | % 13.89/2.59 | Case 2: % 13.89/2.59 | | % 13.89/2.59 | | (43) all_44_4 = bad % 13.89/2.59 | | (44) ~ (ok(all_44_2) = 0) % 13.89/2.59 | | % 13.89/2.59 | | REDUCE: (19), (43) imply: % 13.89/2.59 | | (45) triple(all_44_6, all_44_5, bad) = all_44_2 % 13.89/2.59 | | % 13.89/2.59 | | REDUCE: (16), (43) imply: % 13.89/2.59 | | (46) $i(bad) % 13.89/2.59 | | % 13.89/2.60 | | GROUND_INST: instantiating (8) with all_57_1, all_59_5, all_44_3, all_44_5, % 13.89/2.60 | | simplifying with (26), (34) gives: % 13.89/2.60 | | (47) all_59_5 = all_57_1 % 13.89/2.60 | | % 13.89/2.60 | | GROUND_INST: instantiating (11) with all_44_2, all_57_0, bad, all_44_5, % 13.89/2.60 | | all_44_6, simplifying with (27), (45) gives: % 13.89/2.60 | | (48) all_57_0 = all_44_2 % 13.89/2.60 | | % 13.89/2.60 | | GROUND_INST: instantiating (1) with all_44_3, all_59_4, all_59_3, % 13.89/2.60 | | simplifying with (17), (30), (33) gives: % 13.89/2.60 | | (49) all_59_3 = 0 | ? [v0: any] : ? [v1: any] : (less_than(all_59_4, % 13.89/2.60 | | all_44_3) = v1 & less_than(all_44_3, all_59_4) = v0 & ( ~ (v0 = % 13.89/2.60 | | 0) | v1 = 0)) % 13.89/2.60 | | % 13.89/2.60 | | GROUND_INST: instantiating (2) with all_59_2, all_59_1, all_59_0, % 13.89/2.60 | | simplifying with (31), (32), (37) gives: % 13.89/2.60 | | (50) ? [v0: int] : ( ~ (v0 = 0) & ok(all_59_0) = v0) % 13.89/2.60 | | % 13.89/2.60 | | GROUND_INST: instantiating (ax44) with all_44_6, all_44_5, bad, all_44_3, % 13.89/2.60 | | all_59_2, all_59_1, all_59_0, simplifying with (14), (15), % 13.89/2.60 | | (17), (35), (37), (38), (46) gives: % 13.89/2.60 | | (51) ? [v0: any] : ? [v1: $i] : ? [v2: any] : ? [v3: $i] : ? [v4: % 13.89/2.60 | | $i] : (triple(all_44_6, all_44_5, bad) = v3 & remove_cpq(v3, % 13.89/2.60 | | all_44_3) = v4 & lookup_slb(all_44_5, all_44_3) = v1 & % 13.89/2.60 | | contains_slb(all_44_5, all_44_3) = v0 & less_than(v1, all_44_3) = % 13.89/2.60 | | v2 & $i(v4) & $i(v3) & $i(v1) & ( ~ (v2 = 0) | ~ (v0 = 0) | v4 = % 13.89/2.60 | | all_59_0)) % 13.89/2.60 | | % 13.89/2.60 | | DELTA: instantiating (50) with fresh symbol all_74_0 gives: % 13.89/2.60 | | (52) ~ (all_74_0 = 0) & ok(all_59_0) = all_74_0 % 13.89/2.60 | | % 13.89/2.60 | | ALPHA: (52) implies: % 13.89/2.60 | | (53) ~ (all_74_0 = 0) % 13.89/2.60 | | (54) ok(all_59_0) = all_74_0 % 13.89/2.60 | | % 13.89/2.60 | | DELTA: instantiating (23) with fresh symbols all_76_0, all_76_1 gives: % 13.89/2.60 | | (55) triple(all_44_6, all_44_5, bad) = all_76_0 & contains_slb(all_44_5, % 13.89/2.60 | | all_44_3) = all_76_1 & $i(all_76_0) & (all_76_0 = all_44_0 | % 13.89/2.60 | | all_76_1 = 0) % 13.89/2.60 | | % 13.89/2.60 | | ALPHA: (55) implies: % 13.89/2.60 | | (56) contains_slb(all_44_5, all_44_3) = all_76_1 % 13.89/2.60 | | (57) triple(all_44_6, all_44_5, bad) = all_76_0 % 13.89/2.60 | | % 13.89/2.60 | | DELTA: instantiating (51) with fresh symbols all_78_0, all_78_1, all_78_2, % 13.89/2.60 | | all_78_3, all_78_4 gives: % 13.89/2.60 | | (58) triple(all_44_6, all_44_5, bad) = all_78_1 & remove_cpq(all_78_1, % 13.89/2.60 | | all_44_3) = all_78_0 & lookup_slb(all_44_5, all_44_3) = all_78_3 & % 13.89/2.60 | | contains_slb(all_44_5, all_44_3) = all_78_4 & less_than(all_78_3, % 13.89/2.60 | | all_44_3) = all_78_2 & $i(all_78_0) & $i(all_78_1) & $i(all_78_3) % 13.89/2.60 | | & ( ~ (all_78_2 = 0) | ~ (all_78_4 = 0) | all_78_0 = all_59_0) % 13.89/2.60 | | % 13.89/2.60 | | ALPHA: (58) implies: % 13.89/2.60 | | (59) $i(all_78_3) % 13.89/2.60 | | (60) less_than(all_78_3, all_44_3) = all_78_2 % 13.89/2.60 | | (61) contains_slb(all_44_5, all_44_3) = all_78_4 % 13.89/2.60 | | (62) lookup_slb(all_44_5, all_44_3) = all_78_3 % 13.89/2.60 | | (63) remove_cpq(all_78_1, all_44_3) = all_78_0 % 13.89/2.60 | | (64) triple(all_44_6, all_44_5, bad) = all_78_1 % 13.89/2.60 | | (65) ~ (all_78_2 = 0) | ~ (all_78_4 = 0) | all_78_0 = all_59_0 % 13.89/2.60 | | % 13.89/2.60 | | DELTA: instantiating (22) with fresh symbols all_80_0, all_80_1, all_80_2, % 13.89/2.60 | | all_80_3, all_80_4, all_80_5 gives: % 13.89/2.61 | | (66) remove_pqp(all_44_6, all_44_3) = all_80_2 & triple(all_80_2, % 13.89/2.61 | | all_80_1, bad) = all_80_0 & lookup_slb(all_44_5, all_44_3) = % 13.89/2.61 | | all_80_4 & remove_slb(all_44_5, all_44_3) = all_80_1 & % 13.89/2.61 | | contains_slb(all_44_5, all_44_3) = all_80_5 & % 13.89/2.61 | | strictly_less_than(all_44_3, all_80_4) = all_80_3 & $i(all_80_0) & % 13.89/2.61 | | $i(all_80_1) & $i(all_80_2) & $i(all_80_4) & ( ~ (all_80_3 = 0) | ~ % 13.89/2.61 | | (all_80_5 = 0) | all_80_0 = all_44_0) % 13.89/2.61 | | % 13.89/2.61 | | ALPHA: (66) implies: % 13.89/2.61 | | (67) contains_slb(all_44_5, all_44_3) = all_80_5 % 13.89/2.61 | | (68) lookup_slb(all_44_5, all_44_3) = all_80_4 % 13.89/2.61 | | % 13.89/2.61 | | GROUND_INST: instantiating (8) with all_57_1, all_80_5, all_44_3, all_44_5, % 13.89/2.61 | | simplifying with (26), (67) gives: % 13.89/2.61 | | (69) all_80_5 = all_57_1 % 13.89/2.61 | | % 13.89/2.61 | | GROUND_INST: instantiating (8) with all_78_4, all_80_5, all_44_3, all_44_5, % 13.89/2.61 | | simplifying with (61), (67) gives: % 13.89/2.61 | | (70) all_80_5 = all_78_4 % 13.89/2.61 | | % 13.89/2.61 | | GROUND_INST: instantiating (8) with all_76_1, all_80_5, all_44_3, all_44_5, % 13.89/2.61 | | simplifying with (56), (67) gives: % 13.89/2.61 | | (71) all_80_5 = all_76_1 % 13.89/2.61 | | % 13.89/2.61 | | GROUND_INST: instantiating (9) with all_59_4, all_80_4, all_44_3, all_44_5, % 13.89/2.61 | | simplifying with (36), (68) gives: % 13.89/2.61 | | (72) all_80_4 = all_59_4 % 13.89/2.61 | | % 13.89/2.61 | | GROUND_INST: instantiating (9) with all_78_3, all_80_4, all_44_3, all_44_5, % 13.89/2.61 | | simplifying with (62), (68) gives: % 13.89/2.61 | | (73) all_80_4 = all_78_3 % 13.89/2.61 | | % 13.89/2.61 | | GROUND_INST: instantiating (11) with all_44_2, all_78_1, bad, all_44_5, % 13.89/2.61 | | all_44_6, simplifying with (45), (64) gives: % 13.89/2.61 | | (74) all_78_1 = all_44_2 % 13.89/2.61 | | % 13.89/2.61 | | GROUND_INST: instantiating (11) with all_76_0, all_78_1, bad, all_44_5, % 13.89/2.61 | | all_44_6, simplifying with (57), (64) gives: % 13.89/2.61 | | (75) all_78_1 = all_76_0 % 13.89/2.61 | | % 13.89/2.61 | | COMBINE_EQS: (72), (73) imply: % 13.89/2.61 | | (76) all_78_3 = all_59_4 % 13.89/2.61 | | % 13.89/2.61 | | SIMP: (76) implies: % 13.89/2.61 | | (77) all_78_3 = all_59_4 % 13.89/2.61 | | % 13.89/2.61 | | COMBINE_EQS: (70), (71) imply: % 13.89/2.61 | | (78) all_78_4 = all_76_1 % 13.89/2.61 | | % 13.89/2.61 | | COMBINE_EQS: (69), (70) imply: % 13.89/2.61 | | (79) all_78_4 = all_57_1 % 13.89/2.61 | | % 13.89/2.61 | | COMBINE_EQS: (74), (75) imply: % 13.89/2.61 | | (80) all_76_0 = all_44_2 % 13.89/2.61 | | % 13.89/2.61 | | COMBINE_EQS: (78), (79) imply: % 13.89/2.61 | | (81) all_76_1 = all_57_1 % 13.89/2.61 | | % 13.89/2.61 | | REDUCE: (63), (74) imply: % 13.89/2.61 | | (82) remove_cpq(all_44_2, all_44_3) = all_78_0 % 13.89/2.61 | | % 13.89/2.61 | | REDUCE: (60), (77) imply: % 13.89/2.61 | | (83) less_than(all_59_4, all_44_3) = all_78_2 % 13.89/2.61 | | % 13.89/2.61 | | GROUND_INST: instantiating (10) with all_44_0, all_78_0, all_44_3, all_44_2, % 13.89/2.61 | | simplifying with (18), (82) gives: % 13.89/2.61 | | (84) all_78_0 = all_44_0 % 13.89/2.61 | | % 13.89/2.61 | | BETA: splitting (28) gives: % 13.89/2.61 | | % 13.89/2.61 | | Case 1: % 13.89/2.61 | | | % 13.89/2.61 | | | (85) all_57_1 = 0 % 13.89/2.61 | | | % 13.89/2.61 | | | COMBINE_EQS: (47), (85) imply: % 13.89/2.61 | | | (86) all_59_5 = 0 % 13.89/2.61 | | | % 13.89/2.61 | | | COMBINE_EQS: (79), (85) imply: % 13.89/2.61 | | | (87) all_78_4 = 0 % 13.89/2.61 | | | % 13.89/2.61 | | | BETA: splitting (39) gives: % 13.89/2.61 | | | % 13.89/2.61 | | | Case 1: % 13.89/2.61 | | | | % 13.89/2.61 | | | | (88) ~ (all_59_3 = 0) % 13.89/2.61 | | | | % 13.89/2.61 | | | | BETA: splitting (49) gives: % 13.89/2.61 | | | | % 13.89/2.61 | | | | Case 1: % 13.89/2.61 | | | | | % 13.89/2.61 | | | | | (89) all_59_3 = 0 % 13.89/2.61 | | | | | % 13.89/2.61 | | | | | REDUCE: (88), (89) imply: % 13.89/2.61 | | | | | (90) $false % 13.89/2.61 | | | | | % 13.89/2.61 | | | | | CLOSE: (90) is inconsistent. % 13.89/2.61 | | | | | % 13.89/2.61 | | | | Case 2: % 13.89/2.61 | | | | | % 13.89/2.61 | | | | | (91) ? [v0: any] : ? [v1: any] : (less_than(all_59_4, all_44_3) = % 13.89/2.61 | | | | | v1 & less_than(all_44_3, all_59_4) = v0 & ( ~ (v0 = 0) | v1 % 13.89/2.61 | | | | | = 0)) % 13.89/2.61 | | | | | % 13.89/2.61 | | | | | DELTA: instantiating (91) with fresh symbols all_129_0, all_129_1 % 13.89/2.61 | | | | | gives: % 13.89/2.61 | | | | | (92) less_than(all_59_4, all_44_3) = all_129_0 & % 13.89/2.61 | | | | | less_than(all_44_3, all_59_4) = all_129_1 & ( ~ (all_129_1 = % 13.89/2.61 | | | | | 0) | all_129_0 = 0) % 13.89/2.61 | | | | | % 13.89/2.61 | | | | | ALPHA: (92) implies: % 13.89/2.61 | | | | | (93) less_than(all_44_3, all_59_4) = all_129_1 % 13.89/2.61 | | | | | (94) less_than(all_59_4, all_44_3) = all_129_0 % 13.89/2.61 | | | | | (95) ~ (all_129_1 = 0) | all_129_0 = 0 % 13.89/2.61 | | | | | % 13.89/2.61 | | | | | GROUND_INST: instantiating (7) with all_78_2, all_129_0, all_44_3, % 13.89/2.61 | | | | | all_59_4, simplifying with (83), (94) gives: % 13.89/2.61 | | | | | (96) all_129_0 = all_78_2 % 13.89/2.61 | | | | | % 13.89/2.61 | | | | | GROUND_INST: instantiating (totality) with all_44_3, all_59_4, % 13.89/2.61 | | | | | all_129_1, simplifying with (17), (30), (93) gives: % 13.89/2.61 | | | | | (97) all_129_1 = 0 | less_than(all_59_4, all_44_3) = 0 % 13.89/2.61 | | | | | % 13.89/2.61 | | | | | BETA: splitting (65) gives: % 13.89/2.61 | | | | | % 13.89/2.61 | | | | | Case 1: % 13.89/2.61 | | | | | | % 13.89/2.62 | | | | | | (98) ~ (all_78_2 = 0) % 13.89/2.62 | | | | | | % 13.89/2.62 | | | | | | BETA: splitting (95) gives: % 13.89/2.62 | | | | | | % 13.89/2.62 | | | | | | Case 1: % 13.89/2.62 | | | | | | | % 13.89/2.62 | | | | | | | (99) ~ (all_129_1 = 0) % 13.89/2.62 | | | | | | | % 13.89/2.62 | | | | | | | BETA: splitting (97) gives: % 13.89/2.62 | | | | | | | % 13.89/2.62 | | | | | | | Case 1: % 13.89/2.62 | | | | | | | | % 13.89/2.62 | | | | | | | | (100) less_than(all_59_4, all_44_3) = 0 % 13.89/2.62 | | | | | | | | % 13.89/2.62 | | | | | | | | GROUND_INST: instantiating (7) with all_78_2, 0, all_44_3, % 13.89/2.62 | | | | | | | | all_59_4, simplifying with (83), (100) gives: % 13.89/2.62 | | | | | | | | (101) all_78_2 = 0 % 13.89/2.62 | | | | | | | | % 13.89/2.62 | | | | | | | | REDUCE: (98), (101) imply: % 13.89/2.62 | | | | | | | | (102) $false % 13.89/2.62 | | | | | | | | % 13.89/2.62 | | | | | | | | CLOSE: (102) is inconsistent. % 13.89/2.62 | | | | | | | | % 13.89/2.62 | | | | | | | Case 2: % 13.89/2.62 | | | | | | | | % 13.89/2.62 | | | | | | | | (103) all_129_1 = 0 % 13.89/2.62 | | | | | | | | % 13.89/2.62 | | | | | | | | REDUCE: (99), (103) imply: % 13.89/2.62 | | | | | | | | (104) $false % 13.89/2.62 | | | | | | | | % 13.89/2.62 | | | | | | | | CLOSE: (104) is inconsistent. % 13.89/2.62 | | | | | | | | % 13.89/2.62 | | | | | | | End of split % 13.89/2.62 | | | | | | | % 13.89/2.62 | | | | | | Case 2: % 13.89/2.62 | | | | | | | % 13.89/2.62 | | | | | | | (105) all_129_0 = 0 % 13.89/2.62 | | | | | | | % 13.89/2.62 | | | | | | | COMBINE_EQS: (96), (105) imply: % 13.89/2.62 | | | | | | | (106) all_78_2 = 0 % 13.89/2.62 | | | | | | | % 13.89/2.62 | | | | | | | REDUCE: (98), (106) imply: % 13.89/2.62 | | | | | | | (107) $false % 13.89/2.62 | | | | | | | % 13.89/2.62 | | | | | | | CLOSE: (107) is inconsistent. % 13.89/2.62 | | | | | | | % 13.89/2.62 | | | | | | End of split % 13.89/2.62 | | | | | | % 13.89/2.62 | | | | | Case 2: % 13.89/2.62 | | | | | | % 13.89/2.62 | | | | | | (108) ~ (all_78_4 = 0) | all_78_0 = all_59_0 % 13.89/2.62 | | | | | | % 13.89/2.62 | | | | | | BETA: splitting (108) gives: % 13.89/2.62 | | | | | | % 13.89/2.62 | | | | | | Case 1: % 13.89/2.62 | | | | | | | % 13.89/2.62 | | | | | | | (109) ~ (all_78_4 = 0) % 13.89/2.62 | | | | | | | % 13.89/2.62 | | | | | | | REDUCE: (87), (109) imply: % 13.89/2.62 | | | | | | | (110) $false % 13.89/2.62 | | | | | | | % 13.89/2.62 | | | | | | | CLOSE: (110) is inconsistent. % 13.89/2.62 | | | | | | | % 13.89/2.62 | | | | | | Case 2: % 13.89/2.62 | | | | | | | % 13.89/2.62 | | | | | | | (111) all_78_0 = all_59_0 % 13.89/2.62 | | | | | | | % 13.89/2.62 | | | | | | | COMBINE_EQS: (84), (111) imply: % 13.89/2.62 | | | | | | | (112) all_59_0 = all_44_0 % 13.89/2.62 | | | | | | | % 13.89/2.62 | | | | | | | SIMP: (112) implies: % 13.89/2.62 | | | | | | | (113) all_59_0 = all_44_0 % 13.89/2.62 | | | | | | | % 13.89/2.62 | | | | | | | REDUCE: (54), (113) imply: % 13.89/2.62 | | | | | | | (114) ok(all_44_0) = all_74_0 % 13.89/2.62 | | | | | | | % 13.89/2.62 | | | | | | | GROUND_INST: instantiating (6) with 0, all_74_0, all_44_0, % 13.89/2.62 | | | | | | | simplifying with (21), (114) gives: % 13.89/2.62 | | | | | | | (115) all_74_0 = 0 % 13.89/2.62 | | | | | | | % 13.89/2.62 | | | | | | | REDUCE: (53), (115) imply: % 13.89/2.62 | | | | | | | (116) $false % 13.89/2.62 | | | | | | | % 13.89/2.62 | | | | | | | CLOSE: (116) is inconsistent. % 13.89/2.62 | | | | | | | % 13.89/2.62 | | | | | | End of split % 13.89/2.62 | | | | | | % 13.89/2.62 | | | | | End of split % 13.89/2.62 | | | | | % 13.89/2.62 | | | | End of split % 13.89/2.62 | | | | % 13.89/2.62 | | | Case 2: % 13.89/2.62 | | | | % 13.89/2.62 | | | | (117) ~ (all_59_5 = 0) | all_59_0 = all_44_0 % 13.89/2.62 | | | | % 13.89/2.62 | | | | BETA: splitting (117) gives: % 13.89/2.62 | | | | % 13.89/2.62 | | | | Case 1: % 13.89/2.62 | | | | | % 13.89/2.62 | | | | | (118) ~ (all_59_5 = 0) % 13.89/2.62 | | | | | % 13.89/2.62 | | | | | REDUCE: (86), (118) imply: % 13.89/2.62 | | | | | (119) $false % 13.89/2.62 | | | | | % 13.89/2.62 | | | | | CLOSE: (119) is inconsistent. % 13.89/2.62 | | | | | % 13.89/2.62 | | | | Case 2: % 13.89/2.62 | | | | | % 13.89/2.62 | | | | | (120) all_59_0 = all_44_0 % 13.89/2.62 | | | | | % 13.89/2.62 | | | | | REDUCE: (54), (120) imply: % 13.89/2.62 | | | | | (121) ok(all_44_0) = all_74_0 % 13.89/2.62 | | | | | % 13.89/2.62 | | | | | GROUND_INST: instantiating (6) with 0, all_74_0, all_44_0, simplifying % 13.89/2.62 | | | | | with (21), (121) gives: % 13.89/2.62 | | | | | (122) all_74_0 = 0 % 13.89/2.62 | | | | | % 13.89/2.62 | | | | | REDUCE: (53), (122) imply: % 13.89/2.62 | | | | | (123) $false % 13.89/2.62 | | | | | % 13.89/2.62 | | | | | CLOSE: (123) is inconsistent. % 13.89/2.62 | | | | | % 13.89/2.62 | | | | End of split % 13.89/2.62 | | | | % 13.89/2.62 | | | End of split % 13.89/2.62 | | | % 13.89/2.62 | | Case 2: % 13.89/2.62 | | | % 13.89/2.62 | | | (124) all_57_0 = all_44_0 % 13.89/2.62 | | | % 13.89/2.62 | | | COMBINE_EQS: (48), (124) imply: % 13.89/2.62 | | | (125) all_44_0 = all_44_2 % 13.89/2.62 | | | % 13.89/2.62 | | | SIMP: (125) implies: % 13.89/2.62 | | | (126) all_44_0 = all_44_2 % 13.89/2.62 | | | % 13.89/2.62 | | | REDUCE: (21), (126) imply: % 13.89/2.62 | | | (127) ok(all_44_2) = 0 % 13.89/2.62 | | | % 13.89/2.62 | | | PRED_UNIFY: (44), (127) imply: % 13.89/2.62 | | | (128) $false % 13.89/2.62 | | | % 13.89/2.62 | | | CLOSE: (128) is inconsistent. % 13.89/2.62 | | | % 13.89/2.62 | | End of split % 13.89/2.62 | | % 13.89/2.62 | End of split % 13.89/2.62 | % 13.89/2.62 End of proof % 13.89/2.62 % SZS output end Proof for theBenchmark % 13.89/2.62 % 13.89/2.62 1982ms %------------------------------------------------------------------------------