%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWV394+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 : n013.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 22:56:09 EDT 2023 % Result : Theorem 14.02s 2.62s % Output : Proof 21.09s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWV394+1 : TPTP v8.1.2. Released v3.3.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n013.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 06:47:46 EDT 2023 % 0.13/0.34 % CPUTime : % 0.19/0.60 ________ _____ % 0.19/0.60 ___ __ \_________(_)________________________________ % 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.60 % 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.60 (2023-06-19) % 0.19/0.60 % 0.19/0.60 (c) Philipp Rümmer, 2009-2023 % 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.60 Amanda Stjerna. % 0.19/0.60 Free software under BSD-3-Clause. % 0.19/0.60 % 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.60 % 0.19/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.19/0.61 Running up to 7 provers in parallel. % 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.10/1.20 Prover 1: Preprocessing ... % 3.10/1.20 Prover 4: Preprocessing ... % 3.62/1.25 Prover 0: Preprocessing ... % 3.62/1.25 Prover 2: Preprocessing ... % 3.62/1.25 Prover 3: Preprocessing ... % 3.62/1.25 Prover 6: Preprocessing ... % 3.62/1.25 Prover 5: Preprocessing ... % 8.35/1.84 Prover 1: Warning: ignoring some quantifiers % 8.44/1.87 Prover 3: Warning: ignoring some quantifiers % 8.44/1.89 Prover 6: Proving ... % 8.44/1.91 Prover 5: Proving ... % 8.44/1.91 Prover 3: Constructing countermodel ... % 8.44/1.91 Prover 1: Constructing countermodel ... % 8.44/1.96 Prover 4: Constructing countermodel ... % 8.44/2.00 Prover 2: Proving ... % 9.40/2.01 Prover 0: Proving ... % 13.62/2.60 Prover 0: proved (1983ms) % 14.02/2.62 % 14.02/2.62 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 14.02/2.62 % 14.02/2.62 Prover 2: stopped % 14.02/2.62 Prover 6: stopped % 14.02/2.62 Prover 5: stopped % 14.02/2.63 Prover 3: stopped % 14.02/2.63 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 14.02/2.63 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 14.02/2.63 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 14.02/2.63 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 14.02/2.63 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 14.50/2.68 Prover 8: Preprocessing ... % 14.50/2.70 Prover 7: Preprocessing ... % 14.50/2.70 Prover 13: Preprocessing ... % 14.50/2.71 Prover 11: Preprocessing ... % 14.78/2.71 Prover 10: Preprocessing ... % 15.01/2.81 Prover 8: Warning: ignoring some quantifiers % 15.71/2.83 Prover 8: Constructing countermodel ... % 15.71/2.86 Prover 10: Warning: ignoring some quantifiers % 15.71/2.88 Prover 10: Constructing countermodel ... % 16.18/2.89 Prover 11: Constructing countermodel ... % 16.18/2.91 Prover 7: Warning: ignoring some quantifiers % 16.18/2.93 Prover 7: Constructing countermodel ... % 16.81/2.96 Prover 13: Warning: ignoring some quantifiers % 16.89/2.99 Prover 13: Constructing countermodel ... % 18.00/3.14 Prover 7: gave up % 18.00/3.14 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 18.00/3.22 Prover 16: Preprocessing ... % 18.00/3.23 Prover 10: gave up % 18.00/3.25 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 19.16/3.30 Prover 19: Preprocessing ... % 19.16/3.33 Prover 16: Warning: ignoring some quantifiers % 19.16/3.34 Prover 16: Constructing countermodel ... % 19.97/3.38 Prover 8: gave up % 20.18/3.42 Prover 4: Found proof (size 136) % 20.18/3.42 Prover 4: proved (2799ms) % 20.18/3.42 Prover 16: stopped % 20.18/3.42 Prover 13: stopped % 20.18/3.43 Prover 11: stopped % 20.32/3.43 Prover 1: stopped % 20.32/3.46 Prover 19: Warning: ignoring some quantifiers % 20.32/3.47 Prover 19: Constructing countermodel ... % 20.32/3.48 Prover 19: stopped % 20.32/3.48 % 20.32/3.48 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 20.32/3.48 % 20.32/3.49 % SZS output start Proof for theBenchmark % 20.32/3.50 Assumptions after simplification: % 20.32/3.50 --------------------------------- % 20.32/3.50 % 20.32/3.50 (ax40) % 20.74/3.52 $i(bad) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (triple(v0, v1, bad) = % 20.74/3.52 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & ok(v2) = v3)) % 20.74/3.52 % 20.74/3.52 (ax43) % 20.74/3.52 $i(bad) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] % 20.74/3.52 : ! [v5: $i] : ( ~ (triple(v0, v1, v2) = v4) | ~ (remove_cpq(v4, v3) = v5) | % 20.74/3.52 ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: $i] : % 20.74/3.52 (triple(v0, v1, bad) = v7 & contains_slb(v1, v3) = v6 & $i(v7) & (v7 = v5 | % 20.74/3.52 v6 = 0))) % 20.74/3.52 % 20.74/3.52 (ax44) % 20.74/3.53 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 20.74/3.53 $i] : ! [v6: $i] : ( ~ (remove_pqp(v0, v3) = v4) | ~ (triple(v4, v5, v2) = % 20.74/3.53 v6) | ~ (remove_slb(v1, v3) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | % 20.74/3.53 ~ $i(v0) | ? [v7: any] : ? [v8: $i] : ? [v9: any] : ? [v10: $i] : ? % 20.74/3.53 [v11: $i] : (triple(v0, v1, v2) = v10 & remove_cpq(v10, v3) = v11 & % 20.74/3.53 lookup_slb(v1, v3) = v8 & contains_slb(v1, v3) = v7 & less_than(v8, v3) = % 20.74/3.53 v9 & $i(v11) & $i(v10) & $i(v8) & ( ~ (v9 = 0) | ~ (v7 = 0) | v11 = v6))) % 20.74/3.53 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 20.74/3.53 [v5: $i] : ( ~ (triple(v0, v1, v2) = v4) | ~ (remove_cpq(v4, v3) = v5) | ~ % 20.74/3.53 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: $i] : ? % 20.74/3.53 [v8: any] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : (remove_pqp(v0, v3) % 20.74/3.53 = v9 & triple(v9, v10, v2) = v11 & lookup_slb(v1, v3) = v7 & % 20.74/3.53 remove_slb(v1, v3) = v10 & contains_slb(v1, v3) = v6 & less_than(v7, v3) = % 20.74/3.53 v8 & $i(v11) & $i(v10) & $i(v9) & $i(v7) & ( ~ (v8 = 0) | ~ (v6 = 0) | % 20.74/3.53 v11 = v5))) % 20.74/3.53 % 20.74/3.53 (ax45) % 20.74/3.53 $i(bad) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] % 20.74/3.53 : ! [v5: $i] : ( ~ (triple(v0, v1, v2) = v4) | ~ (remove_cpq(v4, v3) = v5) | % 20.74/3.53 ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: $i] : % 20.74/3.53 ? [v8: any] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : (remove_pqp(v0, % 20.74/3.53 v3) = v9 & triple(v9, v10, bad) = v11 & lookup_slb(v1, v3) = v7 & % 20.74/3.53 remove_slb(v1, v3) = v10 & contains_slb(v1, v3) = v6 & % 20.74/3.53 strictly_less_than(v3, v7) = v8 & $i(v11) & $i(v10) & $i(v9) & $i(v7) & ( % 20.74/3.53 ~ (v8 = 0) | ~ (v6 = 0) | v11 = v5))) % 20.74/3.53 % 20.74/3.53 (l30_co) % 20.74/3.53 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 20.74/3.53 $i] : ? [v6: $i] : ? [v7: int] : ( ~ (v7 = 0) & ok(v5) = 0 & triple(v0, % 20.74/3.53 v1, v2) = v4 & check_cpq(v5) = 0 & remove_cpq(v4, v3) = v5 & % 20.74/3.53 pair_in_list(v1, v3, v6) = 0 & less_than(v6, v3) = v7 & $i(v6) & $i(v5) & % 20.74/3.53 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 20.74/3.53 % 20.74/3.53 (l30_li3132) % 20.74/3.54 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 20.74/3.54 $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: int] : (v8 = 0 | ~ (ok(v6) = 0) | % 20.74/3.54 ~ (triple(v0, v1, v2) = v5) | ~ (remove_cpq(v5, v3) = v6) | ~ % 20.74/3.54 (remove_slb(v1, v3) = v7) | ~ (pair_in_list(v7, v3, v4) = v8) | ~ $i(v4) | % 20.74/3.54 ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v9: any] : ? [v10: any] % 20.74/3.54 : (pair_in_list(v1, v3, v4) = v9 & strictly_less_than(v3, v4) = v10 & ( ~ % 20.74/3.54 (v10 = 0) | ~ (v9 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 20.74/3.54 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (ok(v6) = 0) | ~ % 20.74/3.54 (triple(v0, v1, v2) = v5) | ~ (remove_cpq(v5, v3) = v6) | ~ % 20.74/3.54 (pair_in_list(v1, v3, v4) = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 20.74/3.54 $i(v1) | ~ $i(v0) | ? [v7: any] : ? [v8: $i] : ? [v9: any] : % 20.74/3.54 (remove_slb(v1, v3) = v8 & pair_in_list(v8, v3, v4) = v9 & % 20.74/3.54 strictly_less_than(v3, v4) = v7 & $i(v8) & ( ~ (v7 = 0) | v9 = 0))) & ! % 20.74/3.54 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] % 20.74/3.54 : ! [v6: $i] : ( ~ (ok(v6) = 0) | ~ (triple(v0, v1, v2) = v5) | ~ % 20.74/3.54 (remove_cpq(v5, v3) = v6) | ~ (strictly_less_than(v3, v4) = 0) | ~ $i(v4) % 20.74/3.54 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v7: any] : ? [v8: $i] % 20.74/3.54 : ? [v9: any] : (remove_slb(v1, v3) = v8 & pair_in_list(v8, v3, v4) = v9 & % 20.74/3.54 pair_in_list(v1, v3, v4) = v7 & $i(v8) & ( ~ (v7 = 0) | v9 = 0))) % 20.74/3.54 % 20.74/3.54 (l30_li4142) % 20.74/3.54 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 20.74/3.54 $i] : ! [v6: int] : (v6 = 0 | ~ (triple(v0, v1, v2) = v3) | ~ % 20.74/3.54 (less_than(v5, v4) = v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v2) | ~ $i(v1) | % 20.74/3.54 ~ $i(v0) | ? [v7: int] : (( ~ (v7 = 0) & check_cpq(v3) = v7) | ( ~ (v7 = 0) % 20.74/3.54 & pair_in_list(v1, v4, v5) = v7))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 20.74/3.54 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (triple(v0, v1, v2) = % 20.74/3.54 v3) | ~ (pair_in_list(v1, v4, v5) = 0) | ~ $i(v5) | ~ $i(v4) | ~ % 20.74/3.54 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ((v6 = 0 & less_than(v5, v4) % 20.74/3.54 = 0) | ( ~ (v6 = 0) & check_cpq(v3) = v6))) & ! [v0: $i] : ! [v1: $i] % 20.74/3.54 : ! [v2: $i] : ! [v3: $i] : ( ~ (triple(v0, v1, v2) = v3) | ~ $i(v2) | ~ % 20.74/3.54 $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5: $i] : ? [v6: $i] : ? [v7: int] % 20.74/3.54 : ? [v8: int] : ($i(v6) & $i(v5) & ((v7 = 0 & ~ (v8 = 0) & % 20.74/3.54 pair_in_list(v1, v5, v6) = 0 & less_than(v6, v5) = v8) | (v4 = 0 & % 20.74/3.54 check_cpq(v3) = 0)))) % 20.74/3.54 % 20.74/3.54 (stricly_smaller_definition) % 20.74/3.54 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 20.74/3.54 (strictly_less_than(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : % 20.74/3.54 ? [v4: any] : (less_than(v1, v0) = v4 & less_than(v0, v1) = v3 & ( ~ (v3 = % 20.74/3.54 0) | v4 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | % 20.74/3.54 ~ (less_than(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: % 20.74/3.54 any] : (strictly_less_than(v0, v1) = v4 & less_than(v0, v1) = v3 & ( ~ (v3 % 20.74/3.54 = 0) | v4 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ % 20.74/3.54 (less_than(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: % 20.74/3.54 any] : (strictly_less_than(v0, v1) = v3 & less_than(v0, v1) = v4 & ( ~ (v3 % 20.74/3.54 = 0) | (v4 = 0 & ~ (v2 = 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 20.74/3.54 any] : ( ~ (less_than(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : % 20.74/3.54 ? [v4: any] : (strictly_less_than(v0, v1) = v3 & less_than(v1, v0) = v4 & ( % 20.74/3.54 ~ (v3 = 0) | (v2 = 0 & ~ (v4 = 0))))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 20.74/3.54 (strictly_less_than(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: int] : ( % 20.74/3.54 ~ (v2 = 0) & less_than(v1, v0) = v2 & less_than(v0, v1) = 0)) & ! [v0: % 20.74/3.54 $i] : ! [v1: $i] : ( ~ (less_than(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? % 20.74/3.54 [v2: any] : ? [v3: any] : (strictly_less_than(v0, v1) = v3 & less_than(v1, % 20.74/3.54 v0) = v2 & (v3 = 0 | v2 = 0))) % 20.74/3.54 % 20.74/3.54 (totality) % 20.74/3.55 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (less_than(v1, v0) = % 20.74/3.55 v2) | ~ $i(v1) | ~ $i(v0) | less_than(v0, v1) = 0) & ! [v0: $i] : ! % 20.74/3.55 [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (less_than(v0, v1) = v2) | ~ $i(v1) | % 20.74/3.55 ~ $i(v0) | less_than(v1, v0) = 0) % 20.74/3.55 % 20.74/3.55 (function-axioms) % 20.74/3.55 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 % 20.74/3.55 | ~ (triple(v4, v3, v2) = v1) | ~ (triple(v4, v3, v2) = v0)) & ! [v0: % 20.74/3.55 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 20.74/3.55 : ! [v4: $i] : (v1 = v0 | ~ (pair_in_list(v4, v3, v2) = v1) | ~ % 20.74/3.55 (pair_in_list(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 20.74/3.55 ! [v3: $i] : (v1 = v0 | ~ (remove_pqp(v3, v2) = v1) | ~ (remove_pqp(v3, v2) % 20.74/3.55 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 % 20.74/3.55 | ~ (insert_pqp(v3, v2) = v1) | ~ (insert_pqp(v3, v2) = v0)) & ! [v0: % 20.74/3.55 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 20.74/3.55 : (v1 = v0 | ~ (contains_cpq(v3, v2) = v1) | ~ (contains_cpq(v3, v2) = v0)) % 20.74/3.55 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 20.74/3.55 (remove_cpq(v3, v2) = v1) | ~ (remove_cpq(v3, v2) = v0)) & ! [v0: $i] : ! % 20.74/3.55 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (insert_cpq(v3, v2) = v1) % 20.74/3.55 | ~ (insert_cpq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 20.74/3.55 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (succ_cpq(v3, % 20.74/3.55 v2) = v1) | ~ (succ_cpq(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 20.74/3.55 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (update_slb(v3, v2) = v1) | ~ % 20.74/3.55 (update_slb(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 20.74/3.55 [v3: $i] : (v1 = v0 | ~ (lookup_slb(v3, v2) = v1) | ~ (lookup_slb(v3, v2) = % 20.74/3.55 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 20.74/3.55 ~ (remove_slb(v3, v2) = v1) | ~ (remove_slb(v3, v2) = v0)) & ! [v0: % 20.74/3.55 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 20.74/3.55 : (v1 = v0 | ~ (contains_slb(v3, v2) = v1) | ~ (contains_slb(v3, v2) = v0)) % 20.74/3.55 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 20.74/3.55 (pair(v3, v2) = v1) | ~ (pair(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 20.74/3.55 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (insert_slb(v3, v2) = v1) | ~ % 20.74/3.55 (insert_slb(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 20.74/3.55 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 20.74/3.55 (strictly_less_than(v3, v2) = v1) | ~ (strictly_less_than(v3, v2) = v0)) & % 20.74/3.55 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 20.74/3.55 $i] : (v1 = v0 | ~ (less_than(v3, v2) = v1) | ~ (less_than(v3, v2) = v0)) % 20.74/3.55 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 20.74/3.55 (removemin_cpq_res(v2) = v1) | ~ (removemin_cpq_res(v2) = v0)) & ! [v0: % 20.74/3.55 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (findmin_cpq_res(v2) = v1) | % 20.74/3.55 ~ (findmin_cpq_res(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 20.74/3.55 (v1 = v0 | ~ (findmin_pqp_res(v2) = v1) | ~ (findmin_pqp_res(v2) = v0)) & ! % 20.74/3.55 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 % 20.74/3.55 | ~ (ok(v2) = v1) | ~ (ok(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 20.74/3.55 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (check_cpq(v2) = v1) | % 20.74/3.55 ~ (check_cpq(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 % 20.74/3.55 | ~ (removemin_cpq_eff(v2) = v1) | ~ (removemin_cpq_eff(v2) = v0)) & ! % 20.74/3.55 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (findmin_cpq_eff(v2) = % 20.74/3.55 v1) | ~ (findmin_cpq_eff(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 20.74/3.55 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (isnonempty_slb(v2) = % 20.74/3.55 v1) | ~ (isnonempty_slb(v2) = v0)) % 20.74/3.55 % 20.74/3.55 Further assumptions not needed in the proof: % 20.74/3.55 -------------------------------------------- % 20.74/3.55 ax18, ax19, ax20, ax21, ax22, ax23, ax24, ax25, ax26, ax27, ax28, ax29, ax30, % 20.74/3.55 ax31, ax32, ax33, ax34, ax35, ax36, ax37, ax38, ax39, ax41, ax42, ax46, ax47, % 20.74/3.55 ax48, ax49, ax50, ax51, ax52, ax53, bottom_smallest, reflexivity, transitivity % 20.74/3.55 % 20.74/3.55 Those formulas are unsatisfiable: % 20.74/3.55 --------------------------------- % 20.74/3.55 % 20.74/3.55 Begin of proof % 20.74/3.55 | % 20.74/3.55 | ALPHA: (totality) implies: % 20.74/3.55 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (less_than(v1, % 20.74/3.55 | v0) = v2) | ~ $i(v1) | ~ $i(v0) | less_than(v0, v1) = 0) % 20.74/3.55 | % 20.74/3.55 | ALPHA: (stricly_smaller_definition) implies: % 20.74/3.56 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (less_than(v0, v1) = v2) % 20.74/3.56 | | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 20.74/3.56 | (strictly_less_than(v0, v1) = v3 & less_than(v1, v0) = v4 & ( ~ (v3 = % 20.74/3.56 | 0) | (v2 = 0 & ~ (v4 = 0))))) % 20.74/3.56 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (less_than(v1, v0) = v2) % 20.74/3.56 | | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 20.74/3.56 | (strictly_less_than(v0, v1) = v3 & less_than(v0, v1) = v4 & ( ~ (v3 = % 20.74/3.56 | 0) | (v4 = 0 & ~ (v2 = 0))))) % 20.74/3.56 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (less_than(v1, % 20.74/3.56 | v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 20.74/3.56 | (strictly_less_than(v0, v1) = v4 & less_than(v0, v1) = v3 & ( ~ (v3 = % 20.74/3.56 | 0) | v4 = 0))) % 20.74/3.56 | % 20.74/3.56 | ALPHA: (ax40) implies: % 20.74/3.56 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (triple(v0, v1, bad) = % 20.74/3.56 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & ok(v2) % 20.74/3.56 | = v3)) % 20.74/3.56 | % 20.74/3.56 | ALPHA: (ax43) implies: % 20.74/3.56 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 20.74/3.56 | ! [v5: $i] : ( ~ (triple(v0, v1, v2) = v4) | ~ (remove_cpq(v4, v3) = % 20.74/3.56 | v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] % 20.74/3.56 | : ? [v7: $i] : (triple(v0, v1, bad) = v7 & contains_slb(v1, v3) = v6 % 20.74/3.56 | & $i(v7) & (v7 = v5 | v6 = 0))) % 20.74/3.56 | % 20.74/3.56 | ALPHA: (ax44) implies: % 20.74/3.56 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 20.74/3.56 | ! [v5: $i] : ( ~ (triple(v0, v1, v2) = v4) | ~ (remove_cpq(v4, v3) = % 20.74/3.56 | v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] % 20.74/3.56 | : ? [v7: $i] : ? [v8: any] : ? [v9: $i] : ? [v10: $i] : ? [v11: % 20.74/3.56 | $i] : (remove_pqp(v0, v3) = v9 & triple(v9, v10, v2) = v11 & % 20.74/3.56 | lookup_slb(v1, v3) = v7 & remove_slb(v1, v3) = v10 & % 20.74/3.56 | contains_slb(v1, v3) = v6 & less_than(v7, v3) = v8 & $i(v11) & % 20.74/3.56 | $i(v10) & $i(v9) & $i(v7) & ( ~ (v8 = 0) | ~ (v6 = 0) | v11 = % 20.74/3.56 | v5))) % 20.74/3.56 | % 20.74/3.56 | ALPHA: (ax45) implies: % 20.74/3.56 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 20.74/3.56 | ! [v5: $i] : ( ~ (triple(v0, v1, v2) = v4) | ~ (remove_cpq(v4, v3) = % 20.74/3.56 | v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] % 20.74/3.56 | : ? [v7: $i] : ? [v8: any] : ? [v9: $i] : ? [v10: $i] : ? [v11: % 20.74/3.56 | $i] : (remove_pqp(v0, v3) = v9 & triple(v9, v10, bad) = v11 & % 20.74/3.56 | lookup_slb(v1, v3) = v7 & remove_slb(v1, v3) = v10 & % 20.74/3.56 | contains_slb(v1, v3) = v6 & strictly_less_than(v3, v7) = v8 & % 20.74/3.56 | $i(v11) & $i(v10) & $i(v9) & $i(v7) & ( ~ (v8 = 0) | ~ (v6 = 0) | % 20.74/3.56 | v11 = v5))) % 20.74/3.56 | % 20.74/3.56 | ALPHA: (l30_li4142) implies: % 20.74/3.56 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 20.74/3.56 | ! [v5: $i] : ( ~ (triple(v0, v1, v2) = v3) | ~ (pair_in_list(v1, v4, % 20.74/3.56 | v5) = 0) | ~ $i(v5) | ~ $i(v4) | ~ $i(v2) | ~ $i(v1) | ~ % 20.74/3.56 | $i(v0) | ? [v6: int] : ((v6 = 0 & less_than(v5, v4) = 0) | ( ~ (v6 = % 20.74/3.56 | 0) & check_cpq(v3) = v6))) % 20.74/3.56 | % 20.74/3.56 | ALPHA: (l30_li3132) implies: % 20.74/3.56 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 20.74/3.56 | ! [v5: $i] : ! [v6: $i] : ( ~ (ok(v6) = 0) | ~ (triple(v0, v1, v2) = % 20.74/3.56 | v5) | ~ (remove_cpq(v5, v3) = v6) | ~ (pair_in_list(v1, v3, v4) % 20.74/3.56 | = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 20.74/3.56 | ? [v7: any] : ? [v8: $i] : ? [v9: any] : (remove_slb(v1, v3) = v8 % 20.74/3.56 | & pair_in_list(v8, v3, v4) = v9 & strictly_less_than(v3, v4) = v7 % 20.74/3.56 | & $i(v8) & ( ~ (v7 = 0) | v9 = 0))) % 20.74/3.56 | % 20.74/3.56 | ALPHA: (function-axioms) implies: % 20.74/3.57 | (11) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 20.74/3.57 | : (v1 = v0 | ~ (check_cpq(v2) = v1) | ~ (check_cpq(v2) = v0)) % 20.74/3.57 | (12) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 20.74/3.57 | : (v1 = v0 | ~ (ok(v2) = v1) | ~ (ok(v2) = v0)) % 20.74/3.57 | (13) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 20.74/3.57 | : ! [v3: $i] : (v1 = v0 | ~ (less_than(v3, v2) = v1) | ~ % 20.74/3.57 | (less_than(v3, v2) = v0)) % 20.74/3.57 | (14) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 20.74/3.57 | : ! [v3: $i] : (v1 = v0 | ~ (strictly_less_than(v3, v2) = v1) | ~ % 20.74/3.57 | (strictly_less_than(v3, v2) = v0)) % 20.74/3.57 | (15) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 20.74/3.57 | : ! [v3: $i] : (v1 = v0 | ~ (contains_slb(v3, v2) = v1) | ~ % 20.74/3.57 | (contains_slb(v3, v2) = v0)) % 20.74/3.57 | (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 20.74/3.57 | (remove_slb(v3, v2) = v1) | ~ (remove_slb(v3, v2) = v0)) % 20.74/3.57 | (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 20.74/3.57 | (lookup_slb(v3, v2) = v1) | ~ (lookup_slb(v3, v2) = v0)) % 20.74/3.57 | (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 20.74/3.57 | (remove_pqp(v3, v2) = v1) | ~ (remove_pqp(v3, v2) = v0)) % 20.74/3.57 | % 20.74/3.57 | DELTA: instantiating (l30_co) with fresh symbols all_48_0, all_48_1, all_48_2, % 20.74/3.57 | all_48_3, all_48_4, all_48_5, all_48_6, all_48_7 gives: % 20.74/3.57 | (19) ~ (all_48_0 = 0) & ok(all_48_2) = 0 & triple(all_48_7, all_48_6, % 20.74/3.57 | all_48_5) = all_48_3 & check_cpq(all_48_2) = 0 & % 20.74/3.57 | remove_cpq(all_48_3, all_48_4) = all_48_2 & pair_in_list(all_48_6, % 20.74/3.57 | all_48_4, all_48_1) = 0 & less_than(all_48_1, all_48_4) = all_48_0 & % 20.74/3.57 | $i(all_48_1) & $i(all_48_2) & $i(all_48_3) & $i(all_48_4) & % 20.74/3.57 | $i(all_48_5) & $i(all_48_6) & $i(all_48_7) % 20.74/3.57 | % 20.74/3.57 | ALPHA: (19) implies: % 20.74/3.57 | (20) ~ (all_48_0 = 0) % 20.74/3.57 | (21) $i(all_48_7) % 20.74/3.57 | (22) $i(all_48_6) % 20.74/3.57 | (23) $i(all_48_5) % 20.74/3.57 | (24) $i(all_48_4) % 20.74/3.57 | (25) $i(all_48_1) % 20.74/3.57 | (26) less_than(all_48_1, all_48_4) = all_48_0 % 20.74/3.57 | (27) pair_in_list(all_48_6, all_48_4, all_48_1) = 0 % 20.74/3.57 | (28) remove_cpq(all_48_3, all_48_4) = all_48_2 % 20.74/3.57 | (29) check_cpq(all_48_2) = 0 % 20.74/3.57 | (30) triple(all_48_7, all_48_6, all_48_5) = all_48_3 % 20.74/3.57 | (31) ok(all_48_2) = 0 % 20.74/3.57 | % 20.74/3.57 | GROUND_INST: instantiating (1) with all_48_4, all_48_1, all_48_0, simplifying % 20.74/3.57 | with (24), (25), (26) gives: % 20.74/3.57 | (32) all_48_0 = 0 | less_than(all_48_4, all_48_1) = 0 % 20.74/3.57 | % 20.74/3.57 | GROUND_INST: instantiating (4) with all_48_4, all_48_1, all_48_0, simplifying % 20.74/3.57 | with (24), (25), (26) gives: % 20.74/3.57 | (33) all_48_0 = 0 | ? [v0: any] : ? [v1: any] : % 20.74/3.57 | (strictly_less_than(all_48_4, all_48_1) = v1 & less_than(all_48_4, % 20.74/3.57 | all_48_1) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 20.74/3.57 | % 20.74/3.57 | GROUND_INST: instantiating (3) with all_48_4, all_48_1, all_48_0, simplifying % 20.74/3.57 | with (24), (25), (26) gives: % 20.74/3.57 | (34) ? [v0: any] : ? [v1: any] : (strictly_less_than(all_48_4, all_48_1) % 20.74/3.57 | = v0 & less_than(all_48_4, all_48_1) = v1 & ( ~ (v0 = 0) | (v1 = 0 & % 20.74/3.57 | ~ (all_48_0 = 0)))) % 20.74/3.57 | % 20.74/3.58 | GROUND_INST: instantiating (2) with all_48_1, all_48_4, all_48_0, simplifying % 20.74/3.58 | with (24), (25), (26) gives: % 20.74/3.58 | (35) ? [v0: any] : ? [v1: any] : (strictly_less_than(all_48_1, all_48_4) % 20.74/3.58 | = v0 & less_than(all_48_4, all_48_1) = v1 & ( ~ (v0 = 0) | (all_48_0 % 20.74/3.58 | = 0 & ~ (v1 = 0)))) % 20.74/3.58 | % 20.74/3.58 | GROUND_INST: instantiating (7) with all_48_7, all_48_6, all_48_5, all_48_4, % 20.74/3.58 | all_48_3, all_48_2, simplifying with (21), (22), (23), (24), % 20.74/3.58 | (28), (30) gives: % 20.74/3.58 | (36) ? [v0: any] : ? [v1: $i] : ? [v2: any] : ? [v3: $i] : ? [v4: $i] % 20.74/3.58 | : ? [v5: $i] : (remove_pqp(all_48_7, all_48_4) = v3 & triple(v3, v4, % 20.74/3.58 | all_48_5) = v5 & lookup_slb(all_48_6, all_48_4) = v1 & % 20.74/3.58 | remove_slb(all_48_6, all_48_4) = v4 & contains_slb(all_48_6, % 20.74/3.58 | all_48_4) = v0 & less_than(v1, all_48_4) = v2 & $i(v5) & $i(v4) & % 20.74/3.58 | $i(v3) & $i(v1) & ( ~ (v2 = 0) | ~ (v0 = 0) | v5 = all_48_2)) % 20.74/3.58 | % 20.74/3.58 | GROUND_INST: instantiating (8) with all_48_7, all_48_6, all_48_5, all_48_4, % 20.74/3.58 | all_48_3, all_48_2, simplifying with (21), (22), (23), (24), % 20.74/3.58 | (28), (30) gives: % 20.74/3.58 | (37) ? [v0: any] : ? [v1: $i] : ? [v2: any] : ? [v3: $i] : ? [v4: $i] % 20.74/3.58 | : ? [v5: $i] : (remove_pqp(all_48_7, all_48_4) = v3 & triple(v3, v4, % 20.74/3.58 | bad) = v5 & lookup_slb(all_48_6, all_48_4) = v1 & % 20.74/3.58 | remove_slb(all_48_6, all_48_4) = v4 & contains_slb(all_48_6, % 20.74/3.58 | all_48_4) = v0 & strictly_less_than(all_48_4, v1) = v2 & $i(v5) & % 20.74/3.58 | $i(v4) & $i(v3) & $i(v1) & ( ~ (v2 = 0) | ~ (v0 = 0) | v5 = % 20.74/3.58 | all_48_2)) % 20.74/3.58 | % 20.74/3.58 | GROUND_INST: instantiating (6) with all_48_7, all_48_6, all_48_5, all_48_4, % 20.74/3.58 | all_48_3, all_48_2, simplifying with (21), (22), (23), (24), % 20.74/3.58 | (28), (30) gives: % 20.74/3.58 | (38) ? [v0: any] : ? [v1: $i] : (triple(all_48_7, all_48_6, bad) = v1 & % 20.74/3.58 | contains_slb(all_48_6, all_48_4) = v0 & $i(v1) & (v1 = all_48_2 | v0 % 20.74/3.58 | = 0)) % 20.74/3.58 | % 20.74/3.58 | GROUND_INST: instantiating (10) with all_48_7, all_48_6, all_48_5, all_48_4, % 20.74/3.58 | all_48_1, all_48_3, all_48_2, simplifying with (21), (22), (23), % 20.74/3.58 | (24), (25), (27), (28), (30), (31) gives: % 20.74/3.58 | (39) ? [v0: any] : ? [v1: $i] : ? [v2: any] : (remove_slb(all_48_6, % 20.74/3.58 | all_48_4) = v1 & pair_in_list(v1, all_48_4, all_48_1) = v2 & % 20.74/3.58 | strictly_less_than(all_48_4, all_48_1) = v0 & $i(v1) & ( ~ (v0 = 0) % 20.74/3.58 | | v2 = 0)) % 20.74/3.58 | % 20.74/3.58 | DELTA: instantiating (38) with fresh symbols all_56_0, all_56_1 gives: % 20.74/3.58 | (40) triple(all_48_7, all_48_6, bad) = all_56_0 & contains_slb(all_48_6, % 20.74/3.58 | all_48_4) = all_56_1 & $i(all_56_0) & (all_56_0 = all_48_2 | % 20.74/3.58 | all_56_1 = 0) % 20.74/3.58 | % 20.74/3.58 | ALPHA: (40) implies: % 20.74/3.58 | (41) contains_slb(all_48_6, all_48_4) = all_56_1 % 20.74/3.58 | (42) triple(all_48_7, all_48_6, bad) = all_56_0 % 20.74/3.58 | (43) all_56_0 = all_48_2 | all_56_1 = 0 % 20.74/3.58 | % 20.74/3.58 | DELTA: instantiating (35) with fresh symbols all_58_0, all_58_1 gives: % 20.74/3.58 | (44) strictly_less_than(all_48_1, all_48_4) = all_58_1 & % 20.74/3.58 | less_than(all_48_4, all_48_1) = all_58_0 & ( ~ (all_58_1 = 0) | % 20.74/3.58 | (all_48_0 = 0 & ~ (all_58_0 = 0))) % 20.74/3.58 | % 20.74/3.58 | ALPHA: (44) implies: % 20.74/3.58 | (45) less_than(all_48_4, all_48_1) = all_58_0 % 20.74/3.58 | % 20.74/3.58 | DELTA: instantiating (34) with fresh symbols all_60_0, all_60_1 gives: % 20.74/3.58 | (46) strictly_less_than(all_48_4, all_48_1) = all_60_1 & % 20.74/3.58 | less_than(all_48_4, all_48_1) = all_60_0 & ( ~ (all_60_1 = 0) | % 20.74/3.58 | (all_60_0 = 0 & ~ (all_48_0 = 0))) % 20.74/3.58 | % 20.74/3.58 | ALPHA: (46) implies: % 20.74/3.58 | (47) less_than(all_48_4, all_48_1) = all_60_0 % 20.74/3.58 | (48) strictly_less_than(all_48_4, all_48_1) = all_60_1 % 20.74/3.58 | % 20.74/3.58 | DELTA: instantiating (39) with fresh symbols all_62_0, all_62_1, all_62_2 % 20.74/3.59 | gives: % 21.09/3.59 | (49) remove_slb(all_48_6, all_48_4) = all_62_1 & pair_in_list(all_62_1, % 21.09/3.59 | all_48_4, all_48_1) = all_62_0 & strictly_less_than(all_48_4, % 21.09/3.59 | all_48_1) = all_62_2 & $i(all_62_1) & ( ~ (all_62_2 = 0) | all_62_0 % 21.09/3.59 | = 0) % 21.09/3.59 | % 21.09/3.59 | ALPHA: (49) implies: % 21.09/3.59 | (50) strictly_less_than(all_48_4, all_48_1) = all_62_2 % 21.09/3.59 | (51) pair_in_list(all_62_1, all_48_4, all_48_1) = all_62_0 % 21.09/3.59 | (52) remove_slb(all_48_6, all_48_4) = all_62_1 % 21.09/3.59 | (53) ~ (all_62_2 = 0) | all_62_0 = 0 % 21.09/3.59 | % 21.09/3.59 | DELTA: instantiating (36) with fresh symbols all_66_0, all_66_1, all_66_2, % 21.09/3.59 | all_66_3, all_66_4, all_66_5 gives: % 21.09/3.59 | (54) remove_pqp(all_48_7, all_48_4) = all_66_2 & triple(all_66_2, all_66_1, % 21.09/3.59 | all_48_5) = all_66_0 & lookup_slb(all_48_6, all_48_4) = all_66_4 & % 21.09/3.59 | remove_slb(all_48_6, all_48_4) = all_66_1 & contains_slb(all_48_6, % 21.09/3.59 | all_48_4) = all_66_5 & less_than(all_66_4, all_48_4) = all_66_3 & % 21.09/3.59 | $i(all_66_0) & $i(all_66_1) & $i(all_66_2) & $i(all_66_4) & ( ~ % 21.09/3.59 | (all_66_3 = 0) | ~ (all_66_5 = 0) | all_66_0 = all_48_2) % 21.09/3.59 | % 21.09/3.59 | ALPHA: (54) implies: % 21.09/3.59 | (55) $i(all_66_1) % 21.09/3.59 | (56) less_than(all_66_4, all_48_4) = all_66_3 % 21.09/3.59 | (57) contains_slb(all_48_6, all_48_4) = all_66_5 % 21.09/3.59 | (58) remove_slb(all_48_6, all_48_4) = all_66_1 % 21.09/3.59 | (59) lookup_slb(all_48_6, all_48_4) = all_66_4 % 21.09/3.59 | (60) triple(all_66_2, all_66_1, all_48_5) = all_66_0 % 21.09/3.59 | (61) remove_pqp(all_48_7, all_48_4) = all_66_2 % 21.09/3.59 | (62) ~ (all_66_3 = 0) | ~ (all_66_5 = 0) | all_66_0 = all_48_2 % 21.09/3.59 | % 21.09/3.59 | DELTA: instantiating (37) with fresh symbols all_68_0, all_68_1, all_68_2, % 21.09/3.59 | all_68_3, all_68_4, all_68_5 gives: % 21.09/3.59 | (63) remove_pqp(all_48_7, all_48_4) = all_68_2 & triple(all_68_2, all_68_1, % 21.09/3.59 | bad) = all_68_0 & lookup_slb(all_48_6, all_48_4) = all_68_4 & % 21.09/3.59 | remove_slb(all_48_6, all_48_4) = all_68_1 & contains_slb(all_48_6, % 21.09/3.59 | all_48_4) = all_68_5 & strictly_less_than(all_48_4, all_68_4) = % 21.09/3.59 | all_68_3 & $i(all_68_0) & $i(all_68_1) & $i(all_68_2) & $i(all_68_4) & % 21.09/3.59 | ( ~ (all_68_3 = 0) | ~ (all_68_5 = 0) | all_68_0 = all_48_2) % 21.09/3.59 | % 21.09/3.59 | ALPHA: (63) implies: % 21.09/3.59 | (64) $i(all_68_4) % 21.09/3.59 | (65) $i(all_68_2) % 21.09/3.59 | (66) strictly_less_than(all_48_4, all_68_4) = all_68_3 % 21.09/3.59 | (67) contains_slb(all_48_6, all_48_4) = all_68_5 % 21.09/3.59 | (68) remove_slb(all_48_6, all_48_4) = all_68_1 % 21.09/3.59 | (69) lookup_slb(all_48_6, all_48_4) = all_68_4 % 21.09/3.59 | (70) triple(all_68_2, all_68_1, bad) = all_68_0 % 21.09/3.59 | (71) remove_pqp(all_48_7, all_48_4) = all_68_2 % 21.09/3.59 | (72) ~ (all_68_3 = 0) | ~ (all_68_5 = 0) | all_68_0 = all_48_2 % 21.09/3.59 | % 21.09/3.59 | BETA: splitting (32) gives: % 21.09/3.59 | % 21.09/3.59 | Case 1: % 21.09/3.59 | | % 21.09/3.59 | | (73) less_than(all_48_4, all_48_1) = 0 % 21.09/3.59 | | % 21.09/3.59 | | GROUND_INST: instantiating (13) with all_58_0, all_60_0, all_48_1, all_48_4, % 21.09/3.59 | | simplifying with (45), (47) gives: % 21.09/3.59 | | (74) all_60_0 = all_58_0 % 21.09/3.59 | | % 21.09/3.59 | | GROUND_INST: instantiating (13) with 0, all_60_0, all_48_1, all_48_4, % 21.09/3.59 | | simplifying with (47), (73) gives: % 21.09/3.59 | | (75) all_60_0 = 0 % 21.09/3.59 | | % 21.09/3.59 | | GROUND_INST: instantiating (14) with all_60_1, all_62_2, all_48_1, all_48_4, % 21.09/3.59 | | simplifying with (48), (50) gives: % 21.09/3.59 | | (76) all_62_2 = all_60_1 % 21.09/3.59 | | % 21.09/3.59 | | GROUND_INST: instantiating (15) with all_66_5, all_68_5, all_48_4, all_48_6, % 21.09/3.59 | | simplifying with (57), (67) gives: % 21.09/3.59 | | (77) all_68_5 = all_66_5 % 21.09/3.59 | | % 21.09/3.59 | | GROUND_INST: instantiating (15) with all_56_1, all_68_5, all_48_4, all_48_6, % 21.09/3.59 | | simplifying with (41), (67) gives: % 21.09/3.59 | | (78) all_68_5 = all_56_1 % 21.09/3.59 | | % 21.09/3.59 | | GROUND_INST: instantiating (16) with all_66_1, all_68_1, all_48_4, all_48_6, % 21.09/3.59 | | simplifying with (58), (68) gives: % 21.09/3.59 | | (79) all_68_1 = all_66_1 % 21.09/3.59 | | % 21.09/3.59 | | GROUND_INST: instantiating (16) with all_62_1, all_68_1, all_48_4, all_48_6, % 21.09/3.59 | | simplifying with (52), (68) gives: % 21.09/3.59 | | (80) all_68_1 = all_62_1 % 21.09/3.59 | | % 21.09/3.59 | | GROUND_INST: instantiating (17) with all_66_4, all_68_4, all_48_4, all_48_6, % 21.09/3.59 | | simplifying with (59), (69) gives: % 21.09/3.59 | | (81) all_68_4 = all_66_4 % 21.09/3.59 | | % 21.09/3.59 | | GROUND_INST: instantiating (18) with all_66_2, all_68_2, all_48_4, all_48_7, % 21.09/3.59 | | simplifying with (61), (71) gives: % 21.09/3.59 | | (82) all_68_2 = all_66_2 % 21.09/3.59 | | % 21.09/3.59 | | COMBINE_EQS: (79), (80) imply: % 21.09/3.59 | | (83) all_66_1 = all_62_1 % 21.09/3.59 | | % 21.09/3.59 | | SIMP: (83) implies: % 21.09/3.59 | | (84) all_66_1 = all_62_1 % 21.09/3.59 | | % 21.09/3.59 | | COMBINE_EQS: (77), (78) imply: % 21.09/3.59 | | (85) all_66_5 = all_56_1 % 21.09/3.59 | | % 21.09/3.59 | | SIMP: (85) implies: % 21.09/3.59 | | (86) all_66_5 = all_56_1 % 21.09/3.59 | | % 21.09/3.59 | | COMBINE_EQS: (74), (75) imply: % 21.09/3.59 | | (87) all_58_0 = 0 % 21.09/3.59 | | % 21.09/3.59 | | SIMP: (87) implies: % 21.09/3.59 | | (88) all_58_0 = 0 % 21.09/3.59 | | % 21.09/3.60 | | REDUCE: (70), (80), (82) imply: % 21.09/3.60 | | (89) triple(all_66_2, all_62_1, bad) = all_68_0 % 21.09/3.60 | | % 21.09/3.60 | | REDUCE: (60), (84) imply: % 21.09/3.60 | | (90) triple(all_66_2, all_62_1, all_48_5) = all_66_0 % 21.09/3.60 | | % 21.09/3.60 | | REDUCE: (66), (81) imply: % 21.09/3.60 | | (91) strictly_less_than(all_48_4, all_66_4) = all_68_3 % 21.09/3.60 | | % 21.09/3.60 | | REDUCE: (65), (82) imply: % 21.09/3.60 | | (92) $i(all_66_2) % 21.09/3.60 | | % 21.09/3.60 | | REDUCE: (64), (81) imply: % 21.09/3.60 | | (93) $i(all_66_4) % 21.09/3.60 | | % 21.09/3.60 | | REDUCE: (55), (84) imply: % 21.09/3.60 | | (94) $i(all_62_1) % 21.09/3.60 | | % 21.09/3.60 | | BETA: splitting (33) gives: % 21.09/3.60 | | % 21.09/3.60 | | Case 1: % 21.09/3.60 | | | % 21.09/3.60 | | | (95) all_48_0 = 0 % 21.09/3.60 | | | % 21.09/3.60 | | | REDUCE: (20), (95) imply: % 21.09/3.60 | | | (96) $false % 21.09/3.60 | | | % 21.09/3.60 | | | CLOSE: (96) is inconsistent. % 21.09/3.60 | | | % 21.09/3.60 | | Case 2: % 21.09/3.60 | | | % 21.09/3.60 | | | (97) ? [v0: any] : ? [v1: any] : (strictly_less_than(all_48_4, % 21.09/3.60 | | | all_48_1) = v1 & less_than(all_48_4, all_48_1) = v0 & ( ~ (v0 % 21.09/3.60 | | | = 0) | v1 = 0)) % 21.09/3.60 | | | % 21.09/3.60 | | | DELTA: instantiating (97) with fresh symbols all_102_0, all_102_1 gives: % 21.09/3.60 | | | (98) strictly_less_than(all_48_4, all_48_1) = all_102_0 & % 21.09/3.60 | | | less_than(all_48_4, all_48_1) = all_102_1 & ( ~ (all_102_1 = 0) | % 21.09/3.60 | | | all_102_0 = 0) % 21.09/3.60 | | | % 21.09/3.60 | | | ALPHA: (98) implies: % 21.09/3.60 | | | (99) less_than(all_48_4, all_48_1) = all_102_1 % 21.09/3.60 | | | (100) strictly_less_than(all_48_4, all_48_1) = all_102_0 % 21.09/3.60 | | | (101) ~ (all_102_1 = 0) | all_102_0 = 0 % 21.09/3.60 | | | % 21.09/3.60 | | | GROUND_INST: instantiating (13) with 0, all_102_1, all_48_1, all_48_4, % 21.09/3.60 | | | simplifying with (73), (99) gives: % 21.09/3.60 | | | (102) all_102_1 = 0 % 21.09/3.60 | | | % 21.09/3.60 | | | GROUND_INST: instantiating (14) with all_60_1, all_102_0, all_48_1, % 21.09/3.60 | | | all_48_4, simplifying with (48), (100) gives: % 21.09/3.60 | | | (103) all_102_0 = all_60_1 % 21.09/3.60 | | | % 21.09/3.60 | | | BETA: splitting (101) gives: % 21.09/3.60 | | | % 21.09/3.60 | | | Case 1: % 21.09/3.60 | | | | % 21.09/3.60 | | | | (104) ~ (all_102_1 = 0) % 21.09/3.60 | | | | % 21.09/3.60 | | | | REDUCE: (102), (104) imply: % 21.09/3.60 | | | | (105) $false % 21.09/3.60 | | | | % 21.09/3.60 | | | | CLOSE: (105) is inconsistent. % 21.09/3.60 | | | | % 21.09/3.60 | | | Case 2: % 21.09/3.60 | | | | % 21.09/3.60 | | | | (106) all_102_0 = 0 % 21.09/3.60 | | | | % 21.09/3.60 | | | | COMBINE_EQS: (103), (106) imply: % 21.09/3.60 | | | | (107) all_60_1 = 0 % 21.09/3.60 | | | | % 21.09/3.60 | | | | COMBINE_EQS: (76), (107) imply: % 21.09/3.60 | | | | (108) all_62_2 = 0 % 21.09/3.60 | | | | % 21.09/3.60 | | | | BETA: splitting (53) gives: % 21.09/3.60 | | | | % 21.09/3.60 | | | | Case 1: % 21.09/3.60 | | | | | % 21.09/3.60 | | | | | (109) ~ (all_62_2 = 0) % 21.09/3.60 | | | | | % 21.09/3.60 | | | | | REDUCE: (108), (109) imply: % 21.09/3.60 | | | | | (110) $false % 21.09/3.60 | | | | | % 21.09/3.60 | | | | | CLOSE: (110) is inconsistent. % 21.09/3.60 | | | | | % 21.09/3.60 | | | | Case 2: % 21.09/3.60 | | | | | % 21.09/3.60 | | | | | (111) all_62_0 = 0 % 21.09/3.60 | | | | | % 21.09/3.60 | | | | | REDUCE: (51), (111) imply: % 21.09/3.60 | | | | | (112) pair_in_list(all_62_1, all_48_4, all_48_1) = 0 % 21.09/3.60 | | | | | % 21.09/3.60 | | | | | GROUND_INST: instantiating (1) with all_48_4, all_66_4, all_66_3, % 21.09/3.60 | | | | | simplifying with (24), (56), (93) gives: % 21.09/3.60 | | | | | (113) all_66_3 = 0 | less_than(all_48_4, all_66_4) = 0 % 21.09/3.60 | | | | | % 21.09/3.60 | | | | | GROUND_INST: instantiating (4) with all_48_4, all_66_4, all_66_3, % 21.09/3.60 | | | | | simplifying with (24), (56), (93) gives: % 21.09/3.60 | | | | | (114) all_66_3 = 0 | ? [v0: any] : ? [v1: any] : % 21.09/3.60 | | | | | (strictly_less_than(all_48_4, all_66_4) = v1 & % 21.09/3.60 | | | | | less_than(all_48_4, all_66_4) = v0 & ( ~ (v0 = 0) | v1 = % 21.09/3.60 | | | | | 0)) % 21.09/3.60 | | | | | % 21.09/3.60 | | | | | GROUND_INST: instantiating (5) with all_48_7, all_48_6, all_56_0, % 21.09/3.60 | | | | | simplifying with (21), (22), (42) gives: % 21.09/3.60 | | | | | (115) ? [v0: int] : ( ~ (v0 = 0) & ok(all_56_0) = v0) % 21.09/3.60 | | | | | % 21.09/3.60 | | | | | GROUND_INST: instantiating (5) with all_66_2, all_62_1, all_68_0, % 21.09/3.60 | | | | | simplifying with (89), (92), (94) gives: % 21.09/3.60 | | | | | (116) ? [v0: int] : ( ~ (v0 = 0) & ok(all_68_0) = v0) % 21.09/3.60 | | | | | % 21.09/3.60 | | | | | GROUND_INST: instantiating (9) with all_66_2, all_62_1, all_48_5, % 21.09/3.60 | | | | | all_66_0, all_48_4, all_48_1, simplifying with (23), % 21.09/3.60 | | | | | (24), (25), (90), (92), (94), (112) gives: % 21.09/3.60 | | | | | (117) ? [v0: int] : ((v0 = 0 & less_than(all_48_1, all_48_4) = 0) % 21.09/3.60 | | | | | | ( ~ (v0 = 0) & check_cpq(all_66_0) = v0)) % 21.09/3.60 | | | | | % 21.09/3.60 | | | | | DELTA: instantiating (116) with fresh symbol all_121_0 gives: % 21.09/3.60 | | | | | (118) ~ (all_121_0 = 0) & ok(all_68_0) = all_121_0 % 21.09/3.60 | | | | | % 21.09/3.60 | | | | | ALPHA: (118) implies: % 21.09/3.60 | | | | | (119) ~ (all_121_0 = 0) % 21.09/3.60 | | | | | (120) ok(all_68_0) = all_121_0 % 21.09/3.60 | | | | | % 21.09/3.60 | | | | | DELTA: instantiating (115) with fresh symbol all_123_0 gives: % 21.09/3.60 | | | | | (121) ~ (all_123_0 = 0) & ok(all_56_0) = all_123_0 % 21.09/3.60 | | | | | % 21.09/3.60 | | | | | ALPHA: (121) implies: % 21.09/3.60 | | | | | (122) ~ (all_123_0 = 0) % 21.09/3.60 | | | | | (123) ok(all_56_0) = all_123_0 % 21.09/3.60 | | | | | % 21.09/3.60 | | | | | DELTA: instantiating (117) with fresh symbol all_127_0 gives: % 21.09/3.61 | | | | | (124) (all_127_0 = 0 & less_than(all_48_1, all_48_4) = 0) | ( ~ % 21.09/3.61 | | | | | (all_127_0 = 0) & check_cpq(all_66_0) = all_127_0) % 21.09/3.61 | | | | | % 21.09/3.61 | | | | | BETA: splitting (124) gives: % 21.09/3.61 | | | | | % 21.09/3.61 | | | | | Case 1: % 21.09/3.61 | | | | | | % 21.09/3.61 | | | | | | (125) all_127_0 = 0 & less_than(all_48_1, all_48_4) = 0 % 21.09/3.61 | | | | | | % 21.09/3.61 | | | | | | ALPHA: (125) implies: % 21.09/3.61 | | | | | | (126) less_than(all_48_1, all_48_4) = 0 % 21.09/3.61 | | | | | | % 21.09/3.61 | | | | | | GROUND_INST: instantiating (13) with all_48_0, 0, all_48_4, % 21.09/3.61 | | | | | | all_48_1, simplifying with (26), (126) gives: % 21.09/3.61 | | | | | | (127) all_48_0 = 0 % 21.09/3.61 | | | | | | % 21.09/3.61 | | | | | | REDUCE: (20), (127) imply: % 21.09/3.61 | | | | | | (128) $false % 21.09/3.61 | | | | | | % 21.09/3.61 | | | | | | CLOSE: (128) is inconsistent. % 21.09/3.61 | | | | | | % 21.09/3.61 | | | | | Case 2: % 21.09/3.61 | | | | | | % 21.09/3.61 | | | | | | (129) ~ (all_127_0 = 0) & check_cpq(all_66_0) = all_127_0 % 21.09/3.61 | | | | | | % 21.09/3.61 | | | | | | ALPHA: (129) implies: % 21.09/3.61 | | | | | | (130) ~ (all_127_0 = 0) % 21.09/3.61 | | | | | | (131) check_cpq(all_66_0) = all_127_0 % 21.09/3.61 | | | | | | % 21.09/3.61 | | | | | | BETA: splitting (43) gives: % 21.09/3.61 | | | | | | % 21.09/3.61 | | | | | | Case 1: % 21.09/3.61 | | | | | | | % 21.09/3.61 | | | | | | | (132) all_56_1 = 0 % 21.09/3.61 | | | | | | | % 21.09/3.61 | | | | | | | COMBINE_EQS: (86), (132) imply: % 21.09/3.61 | | | | | | | (133) all_66_5 = 0 % 21.09/3.61 | | | | | | | % 21.09/3.61 | | | | | | | COMBINE_EQS: (78), (132) imply: % 21.09/3.61 | | | | | | | (134) all_68_5 = 0 % 21.09/3.61 | | | | | | | % 21.09/3.61 | | | | | | | BETA: splitting (62) gives: % 21.09/3.61 | | | | | | | % 21.09/3.61 | | | | | | | Case 1: % 21.09/3.61 | | | | | | | | % 21.09/3.61 | | | | | | | | (135) ~ (all_66_3 = 0) % 21.09/3.61 | | | | | | | | % 21.09/3.61 | | | | | | | | BETA: splitting (113) gives: % 21.09/3.61 | | | | | | | | % 21.09/3.61 | | | | | | | | Case 1: % 21.09/3.61 | | | | | | | | | % 21.09/3.61 | | | | | | | | | (136) less_than(all_48_4, all_66_4) = 0 % 21.09/3.61 | | | | | | | | | % 21.09/3.61 | | | | | | | | | BETA: splitting (72) gives: % 21.09/3.61 | | | | | | | | | % 21.09/3.61 | | | | | | | | | Case 1: % 21.09/3.61 | | | | | | | | | | % 21.09/3.61 | | | | | | | | | | (137) ~ (all_68_3 = 0) % 21.09/3.61 | | | | | | | | | | % 21.09/3.61 | | | | | | | | | | BETA: splitting (114) gives: % 21.09/3.61 | | | | | | | | | | % 21.09/3.61 | | | | | | | | | | Case 1: % 21.09/3.61 | | | | | | | | | | | % 21.09/3.61 | | | | | | | | | | | (138) all_66_3 = 0 % 21.09/3.61 | | | | | | | | | | | % 21.09/3.61 | | | | | | | | | | | REDUCE: (135), (138) imply: % 21.09/3.61 | | | | | | | | | | | (139) $false % 21.09/3.61 | | | | | | | | | | | % 21.09/3.61 | | | | | | | | | | | CLOSE: (139) is inconsistent. % 21.09/3.61 | | | | | | | | | | | % 21.09/3.61 | | | | | | | | | | Case 2: % 21.09/3.61 | | | | | | | | | | | % 21.09/3.61 | | | | | | | | | | | (140) ? [v0: any] : ? [v1: any] : % 21.09/3.61 | | | | | | | | | | | (strictly_less_than(all_48_4, all_66_4) = v1 & % 21.09/3.61 | | | | | | | | | | | less_than(all_48_4, all_66_4) = v0 & ( ~ (v0 = % 21.09/3.61 | | | | | | | | | | | 0) | v1 = 0)) % 21.09/3.61 | | | | | | | | | | | % 21.09/3.61 | | | | | | | | | | | DELTA: instantiating (140) with fresh symbols all_403_0, % 21.09/3.61 | | | | | | | | | | | all_403_1 gives: % 21.09/3.61 | | | | | | | | | | | (141) strictly_less_than(all_48_4, all_66_4) = all_403_0 % 21.09/3.61 | | | | | | | | | | | & less_than(all_48_4, all_66_4) = all_403_1 & ( ~ % 21.09/3.61 | | | | | | | | | | | (all_403_1 = 0) | all_403_0 = 0) % 21.09/3.61 | | | | | | | | | | | % 21.09/3.61 | | | | | | | | | | | ALPHA: (141) implies: % 21.09/3.61 | | | | | | | | | | | (142) less_than(all_48_4, all_66_4) = all_403_1 % 21.09/3.61 | | | | | | | | | | | (143) strictly_less_than(all_48_4, all_66_4) = all_403_0 % 21.09/3.61 | | | | | | | | | | | (144) ~ (all_403_1 = 0) | all_403_0 = 0 % 21.09/3.61 | | | | | | | | | | | % 21.09/3.61 | | | | | | | | | | | GROUND_INST: instantiating (13) with 0, all_403_1, all_66_4, % 21.09/3.61 | | | | | | | | | | | all_48_4, simplifying with (136), (142) gives: % 21.09/3.61 | | | | | | | | | | | (145) all_403_1 = 0 % 21.09/3.61 | | | | | | | | | | | % 21.09/3.61 | | | | | | | | | | | GROUND_INST: instantiating (14) with all_68_3, all_403_0, % 21.09/3.61 | | | | | | | | | | | all_66_4, all_48_4, simplifying with (91), (143) % 21.09/3.61 | | | | | | | | | | | gives: % 21.09/3.61 | | | | | | | | | | | (146) all_403_0 = all_68_3 % 21.09/3.61 | | | | | | | | | | | % 21.09/3.61 | | | | | | | | | | | BETA: splitting (144) gives: % 21.09/3.61 | | | | | | | | | | | % 21.09/3.61 | | | | | | | | | | | Case 1: % 21.09/3.61 | | | | | | | | | | | | % 21.09/3.61 | | | | | | | | | | | | (147) ~ (all_403_1 = 0) % 21.09/3.61 | | | | | | | | | | | | % 21.09/3.61 | | | | | | | | | | | | REDUCE: (145), (147) imply: % 21.09/3.61 | | | | | | | | | | | | (148) $false % 21.09/3.61 | | | | | | | | | | | | % 21.09/3.61 | | | | | | | | | | | | CLOSE: (148) is inconsistent. % 21.09/3.61 | | | | | | | | | | | | % 21.09/3.61 | | | | | | | | | | | Case 2: % 21.09/3.61 | | | | | | | | | | | | % 21.09/3.61 | | | | | | | | | | | | (149) all_403_0 = 0 % 21.09/3.61 | | | | | | | | | | | | % 21.09/3.61 | | | | | | | | | | | | COMBINE_EQS: (146), (149) imply: % 21.09/3.61 | | | | | | | | | | | | (150) all_68_3 = 0 % 21.09/3.61 | | | | | | | | | | | | % 21.09/3.61 | | | | | | | | | | | | REDUCE: (137), (150) imply: % 21.09/3.61 | | | | | | | | | | | | (151) $false % 21.09/3.61 | | | | | | | | | | | | % 21.09/3.61 | | | | | | | | | | | | CLOSE: (151) is inconsistent. % 21.09/3.61 | | | | | | | | | | | | % 21.09/3.61 | | | | | | | | | | | End of split % 21.09/3.61 | | | | | | | | | | | % 21.09/3.61 | | | | | | | | | | End of split % 21.09/3.61 | | | | | | | | | | % 21.09/3.61 | | | | | | | | | Case 2: % 21.09/3.61 | | | | | | | | | | % 21.09/3.61 | | | | | | | | | | (152) ~ (all_68_5 = 0) | all_68_0 = all_48_2 % 21.09/3.61 | | | | | | | | | | % 21.09/3.61 | | | | | | | | | | BETA: splitting (152) gives: % 21.09/3.61 | | | | | | | | | | % 21.09/3.61 | | | | | | | | | | Case 1: % 21.09/3.61 | | | | | | | | | | | % 21.09/3.61 | | | | | | | | | | | (153) ~ (all_68_5 = 0) % 21.09/3.61 | | | | | | | | | | | % 21.09/3.61 | | | | | | | | | | | REDUCE: (134), (153) imply: % 21.09/3.61 | | | | | | | | | | | (154) $false % 21.09/3.61 | | | | | | | | | | | % 21.09/3.61 | | | | | | | | | | | CLOSE: (154) is inconsistent. % 21.09/3.61 | | | | | | | | | | | % 21.09/3.61 | | | | | | | | | | Case 2: % 21.09/3.61 | | | | | | | | | | | % 21.09/3.61 | | | | | | | | | | | (155) all_68_0 = all_48_2 % 21.09/3.61 | | | | | | | | | | | % 21.09/3.61 | | | | | | | | | | | REDUCE: (120), (155) imply: % 21.09/3.61 | | | | | | | | | | | (156) ok(all_48_2) = all_121_0 % 21.09/3.61 | | | | | | | | | | | % 21.09/3.61 | | | | | | | | | | | GROUND_INST: instantiating (12) with 0, all_121_0, all_48_2, % 21.09/3.61 | | | | | | | | | | | simplifying with (31), (156) gives: % 21.09/3.61 | | | | | | | | | | | (157) all_121_0 = 0 % 21.09/3.61 | | | | | | | | | | | % 21.09/3.61 | | | | | | | | | | | REDUCE: (119), (157) imply: % 21.09/3.61 | | | | | | | | | | | (158) $false % 21.09/3.61 | | | | | | | | | | | % 21.09/3.61 | | | | | | | | | | | CLOSE: (158) is inconsistent. % 21.09/3.61 | | | | | | | | | | | % 21.09/3.61 | | | | | | | | | | End of split % 21.09/3.61 | | | | | | | | | | % 21.09/3.61 | | | | | | | | | End of split % 21.09/3.61 | | | | | | | | | % 21.09/3.61 | | | | | | | | Case 2: % 21.09/3.61 | | | | | | | | | % 21.09/3.61 | | | | | | | | | (159) all_66_3 = 0 % 21.09/3.61 | | | | | | | | | % 21.09/3.61 | | | | | | | | | REDUCE: (135), (159) imply: % 21.09/3.61 | | | | | | | | | (160) $false % 21.09/3.61 | | | | | | | | | % 21.09/3.61 | | | | | | | | | CLOSE: (160) is inconsistent. % 21.09/3.61 | | | | | | | | | % 21.09/3.61 | | | | | | | | End of split % 21.09/3.61 | | | | | | | | % 21.09/3.61 | | | | | | | Case 2: % 21.09/3.61 | | | | | | | | % 21.09/3.61 | | | | | | | | (161) ~ (all_66_5 = 0) | all_66_0 = all_48_2 % 21.09/3.61 | | | | | | | | % 21.09/3.61 | | | | | | | | BETA: splitting (161) gives: % 21.09/3.61 | | | | | | | | % 21.09/3.61 | | | | | | | | Case 1: % 21.09/3.61 | | | | | | | | | % 21.09/3.61 | | | | | | | | | (162) ~ (all_66_5 = 0) % 21.09/3.61 | | | | | | | | | % 21.09/3.61 | | | | | | | | | REDUCE: (133), (162) imply: % 21.09/3.61 | | | | | | | | | (163) $false % 21.09/3.61 | | | | | | | | | % 21.09/3.61 | | | | | | | | | CLOSE: (163) is inconsistent. % 21.09/3.61 | | | | | | | | | % 21.09/3.61 | | | | | | | | Case 2: % 21.09/3.61 | | | | | | | | | % 21.09/3.61 | | | | | | | | | (164) all_66_0 = all_48_2 % 21.09/3.61 | | | | | | | | | % 21.09/3.61 | | | | | | | | | REDUCE: (131), (164) imply: % 21.09/3.61 | | | | | | | | | (165) check_cpq(all_48_2) = all_127_0 % 21.09/3.61 | | | | | | | | | % 21.09/3.61 | | | | | | | | | GROUND_INST: instantiating (11) with 0, all_127_0, all_48_2, % 21.09/3.61 | | | | | | | | | simplifying with (29), (165) gives: % 21.09/3.61 | | | | | | | | | (166) all_127_0 = 0 % 21.09/3.61 | | | | | | | | | % 21.09/3.61 | | | | | | | | | REDUCE: (130), (166) imply: % 21.09/3.61 | | | | | | | | | (167) $false % 21.09/3.61 | | | | | | | | | % 21.09/3.61 | | | | | | | | | CLOSE: (167) is inconsistent. % 21.09/3.61 | | | | | | | | | % 21.09/3.61 | | | | | | | | End of split % 21.09/3.61 | | | | | | | | % 21.09/3.61 | | | | | | | End of split % 21.09/3.61 | | | | | | | % 21.09/3.61 | | | | | | Case 2: % 21.09/3.61 | | | | | | | % 21.09/3.61 | | | | | | | (168) all_56_0 = all_48_2 % 21.09/3.61 | | | | | | | % 21.09/3.61 | | | | | | | REDUCE: (123), (168) imply: % 21.09/3.61 | | | | | | | (169) ok(all_48_2) = all_123_0 % 21.09/3.61 | | | | | | | % 21.09/3.61 | | | | | | | GROUND_INST: instantiating (12) with 0, all_123_0, all_48_2, % 21.09/3.61 | | | | | | | simplifying with (31), (169) gives: % 21.09/3.61 | | | | | | | (170) all_123_0 = 0 % 21.09/3.61 | | | | | | | % 21.09/3.61 | | | | | | | REDUCE: (122), (170) imply: % 21.09/3.61 | | | | | | | (171) $false % 21.09/3.61 | | | | | | | % 21.09/3.61 | | | | | | | CLOSE: (171) is inconsistent. % 21.09/3.61 | | | | | | | % 21.09/3.61 | | | | | | End of split % 21.09/3.61 | | | | | | % 21.09/3.61 | | | | | End of split % 21.09/3.61 | | | | | % 21.09/3.61 | | | | End of split % 21.09/3.61 | | | | % 21.09/3.61 | | | End of split % 21.09/3.61 | | | % 21.09/3.61 | | End of split % 21.09/3.61 | | % 21.09/3.61 | Case 2: % 21.09/3.61 | | % 21.09/3.61 | | (172) all_48_0 = 0 % 21.09/3.61 | | % 21.09/3.61 | | REDUCE: (20), (172) imply: % 21.09/3.61 | | (173) $false % 21.09/3.61 | | % 21.09/3.61 | | CLOSE: (173) is inconsistent. % 21.09/3.61 | | % 21.09/3.61 | End of split % 21.09/3.61 | % 21.09/3.61 End of proof % 21.09/3.61 % SZS output end Proof for theBenchmark % 21.09/3.61 % 21.09/3.61 3012ms 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