%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWV399+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 : n018.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 22:56:10 EDT 2023 % Result : Theorem 8.46s 1.86s % Output : Proof 10.79s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : SWV399+1 : TPTP v8.1.2. Released v3.3.0. % 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.34 % Computer : n018.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.35 % WCLimit : 300 % 0.14/0.35 % DateTime : Tue Aug 29 08:28:17 EDT 2023 % 0.14/0.35 % CPUTime : % 0.21/0.62 ________ _____ % 0.21/0.62 ___ __ \_________(_)________________________________ % 0.21/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.62 % 0.21/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.62 (2023-06-19) % 0.21/0.62 % 0.21/0.62 (c) Philipp Rümmer, 2009-2023 % 0.21/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.62 Amanda Stjerna. % 0.21/0.62 Free software under BSD-3-Clause. % 0.21/0.62 % 0.21/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.62 % 0.21/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.21/0.63 Running up to 7 provers in parallel. % 0.21/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.82/1.11 Prover 1: Preprocessing ... % 2.82/1.11 Prover 4: Preprocessing ... % 2.82/1.15 Prover 0: Preprocessing ... % 2.82/1.15 Prover 3: Preprocessing ... % 2.82/1.15 Prover 6: Preprocessing ... % 2.82/1.15 Prover 5: Preprocessing ... % 2.82/1.15 Prover 2: Preprocessing ... % 5.02/1.54 Prover 3: Constructing countermodel ... % 5.02/1.54 Prover 1: Constructing countermodel ... % 5.02/1.54 Prover 6: Proving ... % 5.02/1.55 Prover 5: Proving ... % 5.02/1.55 Prover 2: Proving ... % 6.25/1.59 Prover 4: Constructing countermodel ... % 6.51/1.63 Prover 0: Proving ... % 6.71/1.67 Prover 3: gave up % 6.71/1.67 Prover 1: gave up % 6.71/1.67 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 6.71/1.67 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 6.71/1.70 Prover 8: Preprocessing ... % 6.71/1.71 Prover 7: Preprocessing ... % 7.93/1.80 Prover 7: Warning: ignoring some quantifiers % 7.93/1.81 Prover 8: Warning: ignoring some quantifiers % 7.93/1.82 Prover 8: Constructing countermodel ... % 7.93/1.82 Prover 7: Constructing countermodel ... % 8.46/1.86 Prover 0: proved (1221ms) % 8.46/1.86 % 8.46/1.86 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 8.46/1.86 % 8.49/1.87 Prover 2: stopped % 8.49/1.87 Prover 6: stopped % 8.49/1.87 Prover 5: stopped % 8.49/1.88 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 8.49/1.88 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 8.49/1.88 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 8.49/1.88 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 8.76/1.92 Prover 10: Preprocessing ... % 8.76/1.93 Prover 11: Preprocessing ... % 8.76/1.93 Prover 16: Preprocessing ... % 8.76/1.93 Prover 13: Preprocessing ... % 8.97/1.93 Prover 8: gave up % 8.97/1.94 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 8.97/1.96 Prover 19: Preprocessing ... % 8.97/1.98 Prover 10: Warning: ignoring some quantifiers % 8.97/1.99 Prover 10: Constructing countermodel ... % 8.97/2.00 Prover 16: Warning: ignoring some quantifiers % 8.97/2.01 Prover 16: Constructing countermodel ... % 8.97/2.04 Prover 10: gave up % 8.97/2.06 Prover 11: Constructing countermodel ... % 8.97/2.07 Prover 4: Found proof (size 106) % 8.97/2.07 Prover 4: proved (1433ms) % 8.97/2.07 Prover 13: Warning: ignoring some quantifiers % 8.97/2.08 Prover 16: stopped % 8.97/2.08 Prover 7: stopped % 8.97/2.08 Prover 11: stopped % 8.97/2.08 Prover 19: Warning: ignoring some quantifiers % 10.09/2.09 Prover 13: Constructing countermodel ... % 10.09/2.09 Prover 19: Constructing countermodel ... % 10.09/2.10 Prover 13: stopped % 10.09/2.10 Prover 19: stopped % 10.09/2.10 % 10.09/2.10 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 10.09/2.10 % 10.09/2.11 % SZS output start Proof for theBenchmark % 10.09/2.12 Assumptions after simplification: % 10.09/2.12 --------------------------------- % 10.09/2.12 % 10.09/2.12 (l35_co) % 10.09/2.14 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 10.09/2.14 (update_slb(v0, v1) = v2 & pair_in_list(v0, v3, v4) = 0 & % 10.09/2.14 strictly_less_than(v3, v4) = 0 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) % 10.09/2.14 & ! [v5: $i] : ! [v6: $i] : ( ~ (pair_in_list(v2, v5, v6) = 0) | ~ $i(v6) % 10.09/2.14 | ~ $i(v5) | ? [v7: int] : ( ~ (v7 = 0) & strictly_less_than(v5, v6) = % 10.09/2.14 v7)) & ! [v5: $i] : ! [v6: $i] : ( ~ (strictly_less_than(v5, v6) = 0) % 10.09/2.14 | ~ $i(v6) | ~ $i(v5) | ? [v7: int] : ( ~ (v7 = 0) & pair_in_list(v2, % 10.09/2.14 v5, v6) = v7))) % 10.09/2.14 % 10.09/2.14 (l35_li3637) % 10.09/2.15 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 10.09/2.15 int] : (v5 = 0 | ~ (update_slb(v0, v3) = v4) | ~ (pair_in_list(v4, v1, v2) % 10.09/2.15 = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? % 10.09/2.15 [v7: any] : (pair_in_list(v0, v1, v2) = v6 & less_than(v3, v2) = v7 & ( ~ % 10.09/2.15 (v7 = 0) | ~ (v6 = 0)))) % 10.09/2.15 % 10.09/2.15 (l35_li3839) % 10.43/2.15 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 10.43/2.15 int] : (v5 = 0 | ~ (update_slb(v0, v3) = v4) | ~ (pair_in_list(v4, v1, v3) % 10.43/2.15 = v5) | ~ (pair_in_list(v0, v1, v2) = 0) | ~ $i(v3) | ~ $i(v2) | ~ % 10.43/2.15 $i(v1) | ~ $i(v0) | ? [v6: int] : ( ~ (v6 = 0) & strictly_less_than(v2, % 10.43/2.15 v3) = v6)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! % 10.43/2.15 [v4: $i] : ! [v5: int] : (v5 = 0 | ~ (update_slb(v0, v3) = v4) | ~ % 10.43/2.15 (pair_in_list(v4, v1, v3) = v5) | ~ (strictly_less_than(v2, v3) = 0) | ~ % 10.43/2.15 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ( ~ (v6 = 0) & % 10.43/2.15 pair_in_list(v0, v1, v2) = v6)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 10.43/2.15 : ! [v3: $i] : ( ~ (pair_in_list(v0, v1, v2) = 0) | ~ % 10.43/2.15 (strictly_less_than(v2, v3) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 10.43/2.15 $i(v0) | ? [v4: $i] : (update_slb(v0, v3) = v4 & pair_in_list(v4, v1, v3) = % 10.43/2.15 0 & $i(v4))) % 10.43/2.15 % 10.43/2.15 (stricly_smaller_definition) % 10.43/2.16 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 10.43/2.16 (strictly_less_than(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : % 10.43/2.16 ? [v4: any] : (less_than(v1, v0) = v4 & less_than(v0, v1) = v3 & ( ~ (v3 = % 10.43/2.16 0) | v4 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | % 10.43/2.16 ~ (less_than(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: % 10.43/2.16 any] : (strictly_less_than(v0, v1) = v4 & less_than(v0, v1) = v3 & ( ~ (v3 % 10.43/2.16 = 0) | v4 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ % 10.43/2.16 (less_than(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: % 10.43/2.16 any] : (strictly_less_than(v0, v1) = v3 & less_than(v0, v1) = v4 & ( ~ (v3 % 10.43/2.16 = 0) | (v4 = 0 & ~ (v2 = 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 10.43/2.16 any] : ( ~ (less_than(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : % 10.43/2.16 ? [v4: any] : (strictly_less_than(v0, v1) = v3 & less_than(v1, v0) = v4 & ( % 10.43/2.16 ~ (v3 = 0) | (v2 = 0 & ~ (v4 = 0))))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 10.43/2.16 (strictly_less_than(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: int] : ( % 10.43/2.16 ~ (v2 = 0) & less_than(v1, v0) = v2 & less_than(v0, v1) = 0)) & ! [v0: % 10.43/2.16 $i] : ! [v1: $i] : ( ~ (less_than(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? % 10.43/2.16 [v2: any] : ? [v3: any] : (strictly_less_than(v0, v1) = v3 & less_than(v1, % 10.43/2.16 v0) = v2 & (v3 = 0 | v2 = 0))) % 10.43/2.16 % 10.43/2.16 (totality) % 10.43/2.16 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (less_than(v1, v0) = % 10.43/2.16 v2) | ~ $i(v1) | ~ $i(v0) | less_than(v0, v1) = 0) & ! [v0: $i] : ! % 10.43/2.16 [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (less_than(v0, v1) = v2) | ~ $i(v1) | % 10.43/2.16 ~ $i(v0) | less_than(v1, v0) = 0) % 10.43/2.16 % 10.43/2.16 (transitivity) % 10.43/2.16 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 10.43/2.16 (less_than(v1, v2) = 0) | ~ (less_than(v0, v2) = v3) | ~ $i(v2) | ~ % 10.43/2.16 $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & less_than(v0, v1) = v4)) % 10.43/2.16 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 10.43/2.16 (less_than(v0, v2) = v3) | ~ (less_than(v0, v1) = 0) | ~ $i(v2) | ~ % 10.43/2.16 $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & less_than(v1, v2) = v4)) % 10.43/2.16 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (less_than(v1, v2) = 0) | ~ % 10.43/2.16 (less_than(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | less_than(v0, % 10.43/2.16 v2) = 0) % 10.43/2.16 % 10.43/2.16 (function-axioms) % 10.43/2.17 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 10.43/2.17 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (pair_in_list(v4, v3, v2) = v1) | ~ % 10.43/2.17 (pair_in_list(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 10.43/2.17 ! [v3: $i] : (v1 = v0 | ~ (update_slb(v3, v2) = v1) | ~ (update_slb(v3, v2) % 10.43/2.17 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 % 10.43/2.17 | ~ (lookup_slb(v3, v2) = v1) | ~ (lookup_slb(v3, v2) = v0)) & ! [v0: $i] % 10.43/2.17 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (remove_slb(v3, v2) % 10.43/2.17 = v1) | ~ (remove_slb(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 10.43/2.17 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 10.43/2.17 (contains_slb(v3, v2) = v1) | ~ (contains_slb(v3, v2) = v0)) & ! [v0: $i] % 10.43/2.17 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (pair(v3, v2) = v1) % 10.43/2.17 | ~ (pair(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 10.43/2.17 [v3: $i] : (v1 = v0 | ~ (insert_slb(v3, v2) = v1) | ~ (insert_slb(v3, v2) = % 10.43/2.17 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 10.43/2.17 $i] : ! [v3: $i] : (v1 = v0 | ~ (strictly_less_than(v3, v2) = v1) | ~ % 10.43/2.17 (strictly_less_than(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 10.43/2.17 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 10.43/2.17 (less_than(v3, v2) = v1) | ~ (less_than(v3, v2) = v0)) & ! [v0: % 10.43/2.17 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 10.43/2.17 ~ (isnonempty_slb(v2) = v1) | ~ (isnonempty_slb(v2) = v0)) % 10.43/2.17 % 10.43/2.17 Further assumptions not needed in the proof: % 10.43/2.17 -------------------------------------------- % 10.43/2.17 ax18, ax19, ax20, ax21, ax22, ax23, ax24, ax25, ax26, ax27, ax28, ax29, ax30, % 10.43/2.17 bottom_smallest, reflexivity % 10.43/2.17 % 10.43/2.17 Those formulas are unsatisfiable: % 10.43/2.17 --------------------------------- % 10.43/2.17 % 10.43/2.17 Begin of proof % 10.43/2.17 | % 10.43/2.17 | ALPHA: (transitivity) implies: % 10.43/2.17 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (less_than(v1, v2) = 0) | % 10.43/2.17 | ~ (less_than(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 10.43/2.17 | less_than(v0, v2) = 0) % 10.43/2.17 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 10.43/2.17 | (less_than(v1, v2) = 0) | ~ (less_than(v0, v2) = v3) | ~ $i(v2) | % 10.43/2.17 | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & less_than(v0, % 10.43/2.17 | v1) = v4)) % 10.43/2.17 | % 10.43/2.17 | ALPHA: (totality) implies: % 10.43/2.17 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (less_than(v1, % 10.43/2.17 | v0) = v2) | ~ $i(v1) | ~ $i(v0) | less_than(v0, v1) = 0) % 10.43/2.17 | % 10.43/2.17 | ALPHA: (stricly_smaller_definition) implies: % 10.43/2.17 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (strictly_less_than(v0, v1) = 0) | ~ % 10.43/2.17 | $i(v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & less_than(v1, v0) % 10.43/2.17 | = v2 & less_than(v0, v1) = 0)) % 10.43/2.17 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (less_than(v0, v1) = v2) % 10.43/2.17 | | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 10.43/2.17 | (strictly_less_than(v0, v1) = v3 & less_than(v1, v0) = v4 & ( ~ (v3 = % 10.43/2.17 | 0) | (v2 = 0 & ~ (v4 = 0))))) % 10.43/2.18 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (less_than(v1, v0) = v2) % 10.43/2.18 | | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 10.43/2.18 | (strictly_less_than(v0, v1) = v3 & less_than(v0, v1) = v4 & ( ~ (v3 = % 10.43/2.18 | 0) | (v4 = 0 & ~ (v2 = 0))))) % 10.43/2.18 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (less_than(v1, % 10.43/2.18 | v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 10.43/2.18 | (strictly_less_than(v0, v1) = v4 & less_than(v0, v1) = v3 & ( ~ (v3 = % 10.43/2.18 | 0) | v4 = 0))) % 10.43/2.18 | % 10.43/2.18 | ALPHA: (l35_li3839) implies: % 10.43/2.18 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 10.43/2.18 | (pair_in_list(v0, v1, v2) = 0) | ~ (strictly_less_than(v2, v3) = 0) % 10.43/2.18 | | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : % 10.43/2.18 | (update_slb(v0, v3) = v4 & pair_in_list(v4, v1, v3) = 0 & $i(v4))) % 10.43/2.18 | % 10.43/2.18 | ALPHA: (function-axioms) implies: % 10.43/2.18 | (9) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 10.43/2.18 | ! [v3: $i] : (v1 = v0 | ~ (less_than(v3, v2) = v1) | ~ % 10.43/2.18 | (less_than(v3, v2) = v0)) % 10.43/2.18 | (10) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 10.43/2.18 | : ! [v3: $i] : (v1 = v0 | ~ (strictly_less_than(v3, v2) = v1) | ~ % 10.43/2.18 | (strictly_less_than(v3, v2) = v0)) % 10.43/2.18 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 10.43/2.18 | (update_slb(v3, v2) = v1) | ~ (update_slb(v3, v2) = v0)) % 10.43/2.18 | (12) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 10.43/2.18 | : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (pair_in_list(v4, v3, v2) % 10.43/2.18 | = v1) | ~ (pair_in_list(v4, v3, v2) = v0)) % 10.43/2.18 | % 10.43/2.18 | DELTA: instantiating (l35_co) with fresh symbols all_25_0, all_25_1, all_25_2, % 10.43/2.18 | all_25_3, all_25_4 gives: % 10.43/2.18 | (13) update_slb(all_25_4, all_25_3) = all_25_2 & pair_in_list(all_25_4, % 10.43/2.18 | all_25_1, all_25_0) = 0 & strictly_less_than(all_25_1, all_25_0) = 0 % 10.43/2.18 | & $i(all_25_0) & $i(all_25_1) & $i(all_25_2) & $i(all_25_3) & % 10.43/2.18 | $i(all_25_4) & ! [v0: $i] : ! [v1: $i] : ( ~ (pair_in_list(all_25_2, % 10.43/2.18 | v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = % 10.43/2.18 | 0) & strictly_less_than(v0, v1) = v2)) & ! [v0: $i] : ! [v1: % 10.43/2.18 | $i] : ( ~ (strictly_less_than(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | % 10.43/2.18 | ? [v2: int] : ( ~ (v2 = 0) & pair_in_list(all_25_2, v0, v1) = v2)) % 10.43/2.18 | % 10.43/2.18 | ALPHA: (13) implies: % 10.43/2.18 | (14) $i(all_25_4) % 10.43/2.18 | (15) $i(all_25_3) % 10.43/2.18 | (16) $i(all_25_1) % 10.43/2.18 | (17) $i(all_25_0) % 10.43/2.18 | (18) strictly_less_than(all_25_1, all_25_0) = 0 % 10.43/2.18 | (19) pair_in_list(all_25_4, all_25_1, all_25_0) = 0 % 10.43/2.18 | (20) update_slb(all_25_4, all_25_3) = all_25_2 % 10.43/2.18 | (21) ! [v0: $i] : ! [v1: $i] : ( ~ (strictly_less_than(v0, v1) = 0) | ~ % 10.43/2.18 | $i(v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & % 10.43/2.18 | pair_in_list(all_25_2, v0, v1) = v2)) % 10.43/2.18 | (22) ! [v0: $i] : ! [v1: $i] : ( ~ (pair_in_list(all_25_2, v0, v1) = 0) | % 10.43/2.18 | ~ $i(v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & % 10.43/2.18 | strictly_less_than(v0, v1) = v2)) % 10.43/2.18 | % 10.43/2.19 | GROUND_INST: instantiating (21) with all_25_1, all_25_0, simplifying with % 10.43/2.19 | (16), (17), (18) gives: % 10.43/2.19 | (23) ? [v0: int] : ( ~ (v0 = 0) & pair_in_list(all_25_2, all_25_1, % 10.43/2.19 | all_25_0) = v0) % 10.43/2.19 | % 10.43/2.19 | GROUND_INST: instantiating (4) with all_25_1, all_25_0, simplifying with (16), % 10.43/2.19 | (17), (18) gives: % 10.43/2.19 | (24) ? [v0: int] : ( ~ (v0 = 0) & less_than(all_25_0, all_25_1) = v0 & % 10.43/2.19 | less_than(all_25_1, all_25_0) = 0) % 10.43/2.19 | % 10.43/2.19 | DELTA: instantiating (23) with fresh symbol all_33_0 gives: % 10.43/2.19 | (25) ~ (all_33_0 = 0) & pair_in_list(all_25_2, all_25_1, all_25_0) = % 10.43/2.19 | all_33_0 % 10.43/2.19 | % 10.43/2.19 | ALPHA: (25) implies: % 10.43/2.19 | (26) ~ (all_33_0 = 0) % 10.43/2.19 | (27) pair_in_list(all_25_2, all_25_1, all_25_0) = all_33_0 % 10.43/2.19 | % 10.43/2.19 | DELTA: instantiating (24) with fresh symbol all_35_0 gives: % 10.43/2.19 | (28) ~ (all_35_0 = 0) & less_than(all_25_0, all_25_1) = all_35_0 & % 10.43/2.19 | less_than(all_25_1, all_25_0) = 0 % 10.43/2.19 | % 10.43/2.19 | ALPHA: (28) implies: % 10.43/2.19 | (29) less_than(all_25_1, all_25_0) = 0 % 10.43/2.19 | (30) less_than(all_25_0, all_25_1) = all_35_0 % 10.43/2.19 | % 10.43/2.19 | GROUND_INST: instantiating (5) with all_25_0, all_25_1, all_35_0, simplifying % 10.43/2.19 | with (16), (17), (30) gives: % 10.43/2.19 | (31) ? [v0: any] : ? [v1: any] : (strictly_less_than(all_25_0, all_25_1) % 10.43/2.19 | = v0 & less_than(all_25_1, all_25_0) = v1 & ( ~ (v0 = 0) | (all_35_0 % 10.43/2.19 | = 0 & ~ (v1 = 0)))) % 10.43/2.19 | % 10.43/2.19 | GROUND_INST: instantiating (l35_li3637) with all_25_4, all_25_1, all_25_0, % 10.43/2.19 | all_25_3, all_25_2, all_33_0, simplifying with (14), (15), (16), % 10.43/2.19 | (17), (20), (27) gives: % 10.43/2.19 | (32) all_33_0 = 0 | ? [v0: any] : ? [v1: any] : (pair_in_list(all_25_4, % 10.43/2.19 | all_25_1, all_25_0) = v0 & less_than(all_25_3, all_25_0) = v1 & ( % 10.43/2.19 | ~ (v1 = 0) | ~ (v0 = 0))) % 10.43/2.19 | % 10.43/2.19 | DELTA: instantiating (31) with fresh symbols all_44_0, all_44_1 gives: % 10.43/2.19 | (33) strictly_less_than(all_25_0, all_25_1) = all_44_1 & % 10.43/2.19 | less_than(all_25_1, all_25_0) = all_44_0 & ( ~ (all_44_1 = 0) | % 10.43/2.19 | (all_35_0 = 0 & ~ (all_44_0 = 0))) % 10.43/2.19 | % 10.43/2.19 | ALPHA: (33) implies: % 10.43/2.19 | (34) less_than(all_25_1, all_25_0) = all_44_0 % 10.43/2.19 | % 10.43/2.19 | BETA: splitting (32) gives: % 10.43/2.19 | % 10.43/2.19 | Case 1: % 10.43/2.19 | | % 10.43/2.19 | | (35) all_33_0 = 0 % 10.43/2.19 | | % 10.43/2.19 | | REDUCE: (26), (35) imply: % 10.43/2.19 | | (36) $false % 10.43/2.19 | | % 10.43/2.19 | | CLOSE: (36) is inconsistent. % 10.43/2.19 | | % 10.43/2.19 | Case 2: % 10.43/2.19 | | % 10.43/2.19 | | (37) ? [v0: any] : ? [v1: any] : (pair_in_list(all_25_4, all_25_1, % 10.43/2.19 | | all_25_0) = v0 & less_than(all_25_3, all_25_0) = v1 & ( ~ (v1 = % 10.43/2.19 | | 0) | ~ (v0 = 0))) % 10.43/2.19 | | % 10.43/2.19 | | DELTA: instantiating (37) with fresh symbols all_54_0, all_54_1 gives: % 10.43/2.19 | | (38) pair_in_list(all_25_4, all_25_1, all_25_0) = all_54_1 & % 10.43/2.19 | | less_than(all_25_3, all_25_0) = all_54_0 & ( ~ (all_54_0 = 0) | ~ % 10.43/2.19 | | (all_54_1 = 0)) % 10.43/2.19 | | % 10.43/2.19 | | ALPHA: (38) implies: % 10.43/2.19 | | (39) less_than(all_25_3, all_25_0) = all_54_0 % 10.43/2.19 | | (40) pair_in_list(all_25_4, all_25_1, all_25_0) = all_54_1 % 10.43/2.19 | | (41) ~ (all_54_0 = 0) | ~ (all_54_1 = 0) % 10.43/2.19 | | % 10.43/2.19 | | GROUND_INST: instantiating (9) with 0, all_44_0, all_25_0, all_25_1, % 10.43/2.19 | | simplifying with (29), (34) gives: % 10.43/2.19 | | (42) all_44_0 = 0 % 10.43/2.19 | | % 10.43/2.20 | | GROUND_INST: instantiating (12) with 0, all_54_1, all_25_0, all_25_1, % 10.43/2.20 | | all_25_4, simplifying with (19), (40) gives: % 10.43/2.20 | | (43) all_54_1 = 0 % 10.43/2.20 | | % 10.43/2.20 | | BETA: splitting (41) gives: % 10.43/2.20 | | % 10.43/2.20 | | Case 1: % 10.43/2.20 | | | % 10.43/2.20 | | | (44) ~ (all_54_0 = 0) % 10.43/2.20 | | | % 10.43/2.20 | | | GROUND_INST: instantiating (2) with all_25_3, all_25_1, all_25_0, % 10.43/2.20 | | | all_54_0, simplifying with (15), (16), (17), (29), (39) % 10.43/2.20 | | | gives: % 10.43/2.20 | | | (45) all_54_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & less_than(all_25_3, % 10.43/2.20 | | | all_25_1) = v0) % 10.43/2.20 | | | % 10.43/2.20 | | | GROUND_INST: instantiating (3) with all_25_0, all_25_3, all_54_0, % 10.43/2.20 | | | simplifying with (15), (17), (39) gives: % 10.43/2.20 | | | (46) all_54_0 = 0 | less_than(all_25_0, all_25_3) = 0 % 10.43/2.20 | | | % 10.43/2.20 | | | GROUND_INST: instantiating (7) with all_25_0, all_25_3, all_54_0, % 10.43/2.20 | | | simplifying with (15), (17), (39) gives: % 10.43/2.20 | | | (47) all_54_0 = 0 | ? [v0: any] : ? [v1: any] : % 10.43/2.20 | | | (strictly_less_than(all_25_0, all_25_3) = v1 & less_than(all_25_0, % 10.43/2.20 | | | all_25_3) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 10.43/2.20 | | | % 10.43/2.20 | | | GROUND_INST: instantiating (6) with all_25_0, all_25_3, all_54_0, % 10.43/2.20 | | | simplifying with (15), (17), (39) gives: % 10.43/2.20 | | | (48) ? [v0: any] : ? [v1: any] : (strictly_less_than(all_25_0, % 10.43/2.20 | | | all_25_3) = v0 & less_than(all_25_0, all_25_3) = v1 & ( ~ (v0 % 10.43/2.20 | | | = 0) | (v1 = 0 & ~ (all_54_0 = 0)))) % 10.43/2.20 | | | % 10.43/2.20 | | | GROUND_INST: instantiating (5) with all_25_3, all_25_0, all_54_0, % 10.43/2.20 | | | simplifying with (15), (17), (39) gives: % 10.43/2.20 | | | (49) ? [v0: any] : ? [v1: any] : (strictly_less_than(all_25_3, % 10.43/2.20 | | | all_25_0) = v0 & less_than(all_25_0, all_25_3) = v1 & ( ~ (v0 % 10.43/2.20 | | | = 0) | (all_54_0 = 0 & ~ (v1 = 0)))) % 10.43/2.20 | | | % 10.43/2.20 | | | DELTA: instantiating (49) with fresh symbols all_69_0, all_69_1 gives: % 10.43/2.20 | | | (50) strictly_less_than(all_25_3, all_25_0) = all_69_1 & % 10.43/2.20 | | | less_than(all_25_0, all_25_3) = all_69_0 & ( ~ (all_69_1 = 0) | % 10.43/2.20 | | | (all_54_0 = 0 & ~ (all_69_0 = 0))) % 10.43/2.20 | | | % 10.43/2.20 | | | ALPHA: (50) implies: % 10.43/2.20 | | | (51) less_than(all_25_0, all_25_3) = all_69_0 % 10.43/2.20 | | | % 10.43/2.20 | | | DELTA: instantiating (48) with fresh symbols all_71_0, all_71_1 gives: % 10.43/2.20 | | | (52) strictly_less_than(all_25_0, all_25_3) = all_71_1 & % 10.43/2.20 | | | less_than(all_25_0, all_25_3) = all_71_0 & ( ~ (all_71_1 = 0) | % 10.43/2.20 | | | (all_71_0 = 0 & ~ (all_54_0 = 0))) % 10.43/2.20 | | | % 10.43/2.20 | | | ALPHA: (52) implies: % 10.43/2.20 | | | (53) less_than(all_25_0, all_25_3) = all_71_0 % 10.43/2.20 | | | (54) strictly_less_than(all_25_0, all_25_3) = all_71_1 % 10.43/2.20 | | | % 10.43/2.20 | | | BETA: splitting (46) gives: % 10.43/2.20 | | | % 10.43/2.20 | | | Case 1: % 10.43/2.20 | | | | % 10.43/2.20 | | | | (55) less_than(all_25_0, all_25_3) = 0 % 10.43/2.20 | | | | % 10.43/2.20 | | | | BETA: splitting (45) gives: % 10.43/2.20 | | | | % 10.43/2.20 | | | | Case 1: % 10.43/2.20 | | | | | % 10.43/2.20 | | | | | (56) all_54_0 = 0 % 10.43/2.20 | | | | | % 10.43/2.20 | | | | | REDUCE: (44), (56) imply: % 10.43/2.20 | | | | | (57) $false % 10.43/2.20 | | | | | % 10.43/2.20 | | | | | CLOSE: (57) is inconsistent. % 10.43/2.20 | | | | | % 10.43/2.20 | | | | Case 2: % 10.43/2.20 | | | | | % 10.43/2.20 | | | | | (58) ? [v0: int] : ( ~ (v0 = 0) & less_than(all_25_3, all_25_1) = % 10.43/2.20 | | | | | v0) % 10.43/2.20 | | | | | % 10.43/2.20 | | | | | DELTA: instantiating (58) with fresh symbol all_84_0 gives: % 10.43/2.20 | | | | | (59) ~ (all_84_0 = 0) & less_than(all_25_3, all_25_1) = all_84_0 % 10.43/2.20 | | | | | % 10.43/2.20 | | | | | ALPHA: (59) implies: % 10.43/2.20 | | | | | (60) ~ (all_84_0 = 0) % 10.43/2.20 | | | | | (61) less_than(all_25_3, all_25_1) = all_84_0 % 10.43/2.20 | | | | | % 10.43/2.20 | | | | | GROUND_INST: instantiating (9) with all_69_0, all_71_0, all_25_3, % 10.43/2.20 | | | | | all_25_0, simplifying with (51), (53) gives: % 10.43/2.20 | | | | | (62) all_71_0 = all_69_0 % 10.43/2.20 | | | | | % 10.43/2.20 | | | | | GROUND_INST: instantiating (9) with 0, all_71_0, all_25_3, all_25_0, % 10.43/2.20 | | | | | simplifying with (53), (55) gives: % 10.43/2.20 | | | | | (63) all_71_0 = 0 % 10.43/2.20 | | | | | % 10.43/2.20 | | | | | COMBINE_EQS: (62), (63) imply: % 10.43/2.20 | | | | | (64) all_69_0 = 0 % 10.43/2.20 | | | | | % 10.43/2.20 | | | | | SIMP: (64) implies: % 10.43/2.21 | | | | | (65) all_69_0 = 0 % 10.43/2.21 | | | | | % 10.43/2.21 | | | | | BETA: splitting (47) gives: % 10.43/2.21 | | | | | % 10.43/2.21 | | | | | Case 1: % 10.43/2.21 | | | | | | % 10.43/2.21 | | | | | | (66) all_54_0 = 0 % 10.43/2.21 | | | | | | % 10.43/2.21 | | | | | | REDUCE: (44), (66) imply: % 10.43/2.21 | | | | | | (67) $false % 10.43/2.21 | | | | | | % 10.43/2.21 | | | | | | CLOSE: (67) is inconsistent. % 10.43/2.21 | | | | | | % 10.43/2.21 | | | | | Case 2: % 10.43/2.21 | | | | | | % 10.43/2.21 | | | | | | (68) ? [v0: any] : ? [v1: any] : (strictly_less_than(all_25_0, % 10.43/2.21 | | | | | | all_25_3) = v1 & less_than(all_25_0, all_25_3) = v0 & ( % 10.43/2.21 | | | | | | ~ (v0 = 0) | v1 = 0)) % 10.43/2.21 | | | | | | % 10.43/2.21 | | | | | | DELTA: instantiating (68) with fresh symbols all_94_0, all_94_1 % 10.43/2.21 | | | | | | gives: % 10.43/2.21 | | | | | | (69) strictly_less_than(all_25_0, all_25_3) = all_94_0 & % 10.43/2.21 | | | | | | less_than(all_25_0, all_25_3) = all_94_1 & ( ~ (all_94_1 = % 10.43/2.21 | | | | | | 0) | all_94_0 = 0) % 10.43/2.21 | | | | | | % 10.43/2.21 | | | | | | ALPHA: (69) implies: % 10.43/2.21 | | | | | | (70) less_than(all_25_0, all_25_3) = all_94_1 % 10.43/2.21 | | | | | | (71) strictly_less_than(all_25_0, all_25_3) = all_94_0 % 10.43/2.21 | | | | | | (72) ~ (all_94_1 = 0) | all_94_0 = 0 % 10.43/2.21 | | | | | | % 10.43/2.21 | | | | | | GROUND_INST: instantiating (9) with 0, all_94_1, all_25_3, all_25_0, % 10.43/2.21 | | | | | | simplifying with (55), (70) gives: % 10.43/2.21 | | | | | | (73) all_94_1 = 0 % 10.43/2.21 | | | | | | % 10.43/2.21 | | | | | | GROUND_INST: instantiating (10) with all_71_1, all_94_0, all_25_3, % 10.43/2.21 | | | | | | all_25_0, simplifying with (54), (71) gives: % 10.43/2.21 | | | | | | (74) all_94_0 = all_71_1 % 10.43/2.21 | | | | | | % 10.43/2.21 | | | | | | BETA: splitting (72) gives: % 10.43/2.21 | | | | | | % 10.43/2.21 | | | | | | Case 1: % 10.43/2.21 | | | | | | | % 10.43/2.21 | | | | | | | (75) ~ (all_94_1 = 0) % 10.43/2.21 | | | | | | | % 10.43/2.21 | | | | | | | REDUCE: (73), (75) imply: % 10.43/2.21 | | | | | | | (76) $false % 10.43/2.21 | | | | | | | % 10.43/2.21 | | | | | | | CLOSE: (76) is inconsistent. % 10.43/2.21 | | | | | | | % 10.43/2.21 | | | | | | Case 2: % 10.43/2.21 | | | | | | | % 10.43/2.21 | | | | | | | (77) all_94_0 = 0 % 10.43/2.21 | | | | | | | % 10.43/2.21 | | | | | | | COMBINE_EQS: (74), (77) imply: % 10.43/2.21 | | | | | | | (78) all_71_1 = 0 % 10.43/2.21 | | | | | | | % 10.43/2.21 | | | | | | | REDUCE: (54), (78) imply: % 10.43/2.21 | | | | | | | (79) strictly_less_than(all_25_0, all_25_3) = 0 % 10.43/2.21 | | | | | | | % 10.43/2.21 | | | | | | | GROUND_INST: instantiating (7) with all_25_1, all_25_3, all_84_0, % 10.43/2.21 | | | | | | | simplifying with (15), (16), (61) gives: % 10.43/2.21 | | | | | | | (80) all_84_0 = 0 | ? [v0: any] : ? [v1: any] : % 10.43/2.21 | | | | | | | (strictly_less_than(all_25_1, all_25_3) = v1 & % 10.43/2.21 | | | | | | | less_than(all_25_1, all_25_3) = v0 & ( ~ (v0 = 0) | v1 = % 10.43/2.21 | | | | | | | 0)) % 10.43/2.21 | | | | | | | % 10.43/2.21 | | | | | | | GROUND_INST: instantiating (6) with all_25_1, all_25_3, all_84_0, % 10.43/2.21 | | | | | | | simplifying with (15), (16), (61) gives: % 10.43/2.21 | | | | | | | (81) ? [v0: any] : ? [v1: any] : % 10.43/2.21 | | | | | | | (strictly_less_than(all_25_1, all_25_3) = v0 & % 10.43/2.21 | | | | | | | less_than(all_25_1, all_25_3) = v1 & ( ~ (v0 = 0) | (v1 % 10.43/2.21 | | | | | | | = 0 & ~ (all_84_0 = 0)))) % 10.43/2.21 | | | | | | | % 10.43/2.21 | | | | | | | GROUND_INST: instantiating (5) with all_25_3, all_25_1, all_84_0, % 10.43/2.21 | | | | | | | simplifying with (15), (16), (61) gives: % 10.43/2.21 | | | | | | | (82) ? [v0: any] : ? [v1: any] : % 10.43/2.21 | | | | | | | (strictly_less_than(all_25_3, all_25_1) = v0 & % 10.43/2.21 | | | | | | | less_than(all_25_1, all_25_3) = v1 & ( ~ (v0 = 0) | % 10.43/2.21 | | | | | | | (all_84_0 = 0 & ~ (v1 = 0)))) % 10.43/2.21 | | | | | | | % 10.43/2.21 | | | | | | | GROUND_INST: instantiating (1) with all_25_1, all_25_0, all_25_3, % 10.43/2.21 | | | | | | | simplifying with (15), (16), (17), (29), (55) gives: % 10.43/2.21 | | | | | | | (83) less_than(all_25_1, all_25_3) = 0 % 10.43/2.21 | | | | | | | % 10.43/2.22 | | | | | | | GROUND_INST: instantiating (8) with all_25_4, all_25_1, all_25_0, % 10.43/2.22 | | | | | | | all_25_3, simplifying with (14), (15), (16), (17), % 10.43/2.22 | | | | | | | (19), (79) gives: % 10.43/2.22 | | | | | | | (84) ? [v0: $i] : (update_slb(all_25_4, all_25_3) = v0 & % 10.43/2.22 | | | | | | | pair_in_list(v0, all_25_1, all_25_3) = 0 & $i(v0)) % 10.43/2.22 | | | | | | | % 10.43/2.22 | | | | | | | DELTA: instantiating (84) with fresh symbol all_112_0 gives: % 10.43/2.22 | | | | | | | (85) update_slb(all_25_4, all_25_3) = all_112_0 & % 10.43/2.22 | | | | | | | pair_in_list(all_112_0, all_25_1, all_25_3) = 0 & % 10.43/2.22 | | | | | | | $i(all_112_0) % 10.43/2.22 | | | | | | | % 10.43/2.22 | | | | | | | ALPHA: (85) implies: % 10.43/2.22 | | | | | | | (86) pair_in_list(all_112_0, all_25_1, all_25_3) = 0 % 10.43/2.22 | | | | | | | (87) update_slb(all_25_4, all_25_3) = all_112_0 % 10.43/2.22 | | | | | | | % 10.43/2.22 | | | | | | | DELTA: instantiating (82) with fresh symbols all_114_0, all_114_1 % 10.43/2.22 | | | | | | | gives: % 10.43/2.22 | | | | | | | (88) strictly_less_than(all_25_3, all_25_1) = all_114_1 & % 10.43/2.22 | | | | | | | less_than(all_25_1, all_25_3) = all_114_0 & ( ~ (all_114_1 % 10.43/2.22 | | | | | | | = 0) | (all_84_0 = 0 & ~ (all_114_0 = 0))) % 10.43/2.22 | | | | | | | % 10.43/2.22 | | | | | | | ALPHA: (88) implies: % 10.43/2.22 | | | | | | | (89) less_than(all_25_1, all_25_3) = all_114_0 % 10.43/2.22 | | | | | | | % 10.43/2.22 | | | | | | | DELTA: instantiating (81) with fresh symbols all_116_0, all_116_1 % 10.43/2.22 | | | | | | | gives: % 10.43/2.22 | | | | | | | (90) strictly_less_than(all_25_1, all_25_3) = all_116_1 & % 10.43/2.22 | | | | | | | less_than(all_25_1, all_25_3) = all_116_0 & ( ~ (all_116_1 % 10.43/2.22 | | | | | | | = 0) | (all_116_0 = 0 & ~ (all_84_0 = 0))) % 10.43/2.22 | | | | | | | % 10.43/2.22 | | | | | | | ALPHA: (90) implies: % 10.43/2.22 | | | | | | | (91) less_than(all_25_1, all_25_3) = all_116_0 % 10.43/2.22 | | | | | | | (92) strictly_less_than(all_25_1, all_25_3) = all_116_1 % 10.43/2.22 | | | | | | | % 10.43/2.22 | | | | | | | GROUND_INST: instantiating (9) with all_114_0, all_116_0, % 10.43/2.22 | | | | | | | all_25_3, all_25_1, simplifying with (89), (91) % 10.43/2.22 | | | | | | | gives: % 10.43/2.22 | | | | | | | (93) all_116_0 = all_114_0 % 10.43/2.22 | | | | | | | % 10.43/2.22 | | | | | | | GROUND_INST: instantiating (9) with 0, all_116_0, all_25_3, % 10.43/2.22 | | | | | | | all_25_1, simplifying with (83), (91) gives: % 10.43/2.22 | | | | | | | (94) all_116_0 = 0 % 10.43/2.22 | | | | | | | % 10.43/2.22 | | | | | | | GROUND_INST: instantiating (11) with all_25_2, all_112_0, % 10.43/2.22 | | | | | | | all_25_3, all_25_4, simplifying with (20), (87) % 10.43/2.22 | | | | | | | gives: % 10.43/2.22 | | | | | | | (95) all_112_0 = all_25_2 % 10.43/2.22 | | | | | | | % 10.43/2.22 | | | | | | | COMBINE_EQS: (93), (94) imply: % 10.43/2.22 | | | | | | | (96) all_114_0 = 0 % 10.43/2.22 | | | | | | | % 10.43/2.22 | | | | | | | SIMP: (96) implies: % 10.43/2.22 | | | | | | | (97) all_114_0 = 0 % 10.43/2.22 | | | | | | | % 10.43/2.22 | | | | | | | REDUCE: (86), (95) imply: % 10.43/2.22 | | | | | | | (98) pair_in_list(all_25_2, all_25_1, all_25_3) = 0 % 10.43/2.22 | | | | | | | % 10.43/2.22 | | | | | | | BETA: splitting (80) gives: % 10.43/2.22 | | | | | | | % 10.43/2.22 | | | | | | | Case 1: % 10.43/2.22 | | | | | | | | % 10.43/2.22 | | | | | | | | (99) all_84_0 = 0 % 10.43/2.22 | | | | | | | | % 10.43/2.22 | | | | | | | | REDUCE: (60), (99) imply: % 10.43/2.22 | | | | | | | | (100) $false % 10.43/2.22 | | | | | | | | % 10.43/2.22 | | | | | | | | CLOSE: (100) is inconsistent. % 10.43/2.22 | | | | | | | | % 10.43/2.22 | | | | | | | Case 2: % 10.43/2.22 | | | | | | | | % 10.79/2.22 | | | | | | | | (101) ? [v0: any] : ? [v1: any] : % 10.79/2.22 | | | | | | | | (strictly_less_than(all_25_1, all_25_3) = v1 & % 10.79/2.22 | | | | | | | | less_than(all_25_1, all_25_3) = v0 & ( ~ (v0 = 0) | % 10.79/2.22 | | | | | | | | v1 = 0)) % 10.79/2.22 | | | | | | | | % 10.79/2.22 | | | | | | | | DELTA: instantiating (101) with fresh symbols all_130_0, % 10.79/2.22 | | | | | | | | all_130_1 gives: % 10.79/2.22 | | | | | | | | (102) strictly_less_than(all_25_1, all_25_3) = all_130_0 & % 10.79/2.22 | | | | | | | | less_than(all_25_1, all_25_3) = all_130_1 & ( ~ % 10.79/2.22 | | | | | | | | (all_130_1 = 0) | all_130_0 = 0) % 10.79/2.22 | | | | | | | | % 10.79/2.22 | | | | | | | | ALPHA: (102) implies: % 10.79/2.22 | | | | | | | | (103) less_than(all_25_1, all_25_3) = all_130_1 % 10.79/2.22 | | | | | | | | (104) strictly_less_than(all_25_1, all_25_3) = all_130_0 % 10.79/2.22 | | | | | | | | (105) ~ (all_130_1 = 0) | all_130_0 = 0 % 10.79/2.22 | | | | | | | | % 10.79/2.22 | | | | | | | | GROUND_INST: instantiating (9) with 0, all_130_1, all_25_3, % 10.79/2.22 | | | | | | | | all_25_1, simplifying with (83), (103) gives: % 10.79/2.22 | | | | | | | | (106) all_130_1 = 0 % 10.79/2.22 | | | | | | | | % 10.79/2.22 | | | | | | | | GROUND_INST: instantiating (10) with all_116_1, all_130_0, % 10.79/2.22 | | | | | | | | all_25_3, all_25_1, simplifying with (92), (104) % 10.79/2.22 | | | | | | | | gives: % 10.79/2.22 | | | | | | | | (107) all_130_0 = all_116_1 % 10.79/2.22 | | | | | | | | % 10.79/2.22 | | | | | | | | BETA: splitting (105) gives: % 10.79/2.22 | | | | | | | | % 10.79/2.22 | | | | | | | | Case 1: % 10.79/2.22 | | | | | | | | | % 10.79/2.22 | | | | | | | | | (108) ~ (all_130_1 = 0) % 10.79/2.22 | | | | | | | | | % 10.79/2.22 | | | | | | | | | REDUCE: (106), (108) imply: % 10.79/2.22 | | | | | | | | | (109) $false % 10.79/2.22 | | | | | | | | | % 10.79/2.22 | | | | | | | | | CLOSE: (109) is inconsistent. % 10.79/2.22 | | | | | | | | | % 10.79/2.22 | | | | | | | | Case 2: % 10.79/2.22 | | | | | | | | | % 10.79/2.22 | | | | | | | | | (110) all_130_0 = 0 % 10.79/2.22 | | | | | | | | | % 10.79/2.22 | | | | | | | | | COMBINE_EQS: (107), (110) imply: % 10.79/2.22 | | | | | | | | | (111) all_116_1 = 0 % 10.79/2.22 | | | | | | | | | % 10.79/2.22 | | | | | | | | | REDUCE: (92), (111) imply: % 10.79/2.22 | | | | | | | | | (112) strictly_less_than(all_25_1, all_25_3) = 0 % 10.79/2.22 | | | | | | | | | % 10.79/2.22 | | | | | | | | | GROUND_INST: instantiating (22) with all_25_1, all_25_3, % 10.79/2.22 | | | | | | | | | simplifying with (15), (16), (98) gives: % 10.79/2.23 | | | | | | | | | (113) ? [v0: int] : ( ~ (v0 = 0) & % 10.79/2.23 | | | | | | | | | strictly_less_than(all_25_1, all_25_3) = v0) % 10.79/2.23 | | | | | | | | | % 10.79/2.23 | | | | | | | | | DELTA: instantiating (113) with fresh symbol all_145_0 gives: % 10.79/2.23 | | | | | | | | | (114) ~ (all_145_0 = 0) & strictly_less_than(all_25_1, % 10.79/2.23 | | | | | | | | | all_25_3) = all_145_0 % 10.79/2.23 | | | | | | | | | % 10.79/2.23 | | | | | | | | | ALPHA: (114) implies: % 10.79/2.23 | | | | | | | | | (115) ~ (all_145_0 = 0) % 10.79/2.23 | | | | | | | | | (116) strictly_less_than(all_25_1, all_25_3) = all_145_0 % 10.79/2.23 | | | | | | | | | % 10.79/2.23 | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_145_0, all_25_3, % 10.79/2.23 | | | | | | | | | all_25_1, simplifying with (112), (116) gives: % 10.79/2.23 | | | | | | | | | (117) all_145_0 = 0 % 10.79/2.23 | | | | | | | | | % 10.79/2.23 | | | | | | | | | REDUCE: (115), (117) imply: % 10.79/2.23 | | | | | | | | | (118) $false % 10.79/2.23 | | | | | | | | | % 10.79/2.23 | | | | | | | | | CLOSE: (118) is inconsistent. % 10.79/2.23 | | | | | | | | | % 10.79/2.23 | | | | | | | | End of split % 10.79/2.23 | | | | | | | | % 10.79/2.23 | | | | | | | End of split % 10.79/2.23 | | | | | | | % 10.79/2.23 | | | | | | End of split % 10.79/2.23 | | | | | | % 10.79/2.23 | | | | | End of split % 10.79/2.23 | | | | | % 10.79/2.23 | | | | End of split % 10.79/2.23 | | | | % 10.79/2.23 | | | Case 2: % 10.79/2.23 | | | | % 10.79/2.23 | | | | (119) all_54_0 = 0 % 10.79/2.23 | | | | % 10.79/2.23 | | | | REDUCE: (44), (119) imply: % 10.79/2.23 | | | | (120) $false % 10.79/2.23 | | | | % 10.79/2.23 | | | | CLOSE: (120) is inconsistent. % 10.79/2.23 | | | | % 10.79/2.23 | | | End of split % 10.79/2.23 | | | % 10.79/2.23 | | Case 2: % 10.79/2.23 | | | % 10.79/2.23 | | | (121) ~ (all_54_1 = 0) % 10.79/2.23 | | | % 10.79/2.23 | | | REDUCE: (43), (121) imply: % 10.79/2.23 | | | (122) $false % 10.79/2.23 | | | % 10.79/2.23 | | | CLOSE: (122) is inconsistent. % 10.79/2.23 | | | % 10.79/2.23 | | End of split % 10.79/2.23 | | % 10.79/2.23 | End of split % 10.79/2.23 | % 10.79/2.23 End of proof % 10.79/2.23 % SZS output end Proof for theBenchmark % 10.79/2.23 % 10.79/2.23 1608ms %------------------------------------------------------------------------------