%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : DAT047_1 : TPTP v8.1.2. Released v5.0.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n021.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 : Wed Aug 30 22:19:00 EDT 2023 % Result : Theorem 7.54s 1.78s % Output : Proof 10.81s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : DAT047_1 : TPTP v8.1.2. Released v5.0.0. % 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.15/0.36 % Computer : n021.cluster.edu % 0.15/0.36 % Model : x86_64 x86_64 % 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.36 % Memory : 8042.1875MB % 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.36 % CPULimit : 300 % 0.15/0.36 % WCLimit : 300 % 0.15/0.36 % DateTime : Thu Aug 24 14:48:10 EDT 2023 % 0.15/0.36 % CPUTime : % 0.22/0.63 ________ _____ % 0.22/0.63 ___ __ \_________(_)________________________________ % 0.22/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.22/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.22/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.22/0.63 % 0.22/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.22/0.63 (2023-06-19) % 0.22/0.63 % 0.22/0.63 (c) Philipp Rümmer, 2009-2023 % 0.22/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.22/0.63 Amanda Stjerna. % 0.22/0.63 Free software under BSD-3-Clause. % 0.22/0.63 % 0.22/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.22/0.63 % 0.22/0.63 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.22/0.64 Running up to 7 provers in parallel. % 0.22/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.22/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.22/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.22/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.22/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.22/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.22/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 2.49/1.08 Prover 1: Preprocessing ... % 2.49/1.09 Prover 4: Preprocessing ... % 2.97/1.12 Prover 2: Preprocessing ... % 2.97/1.12 Prover 0: Preprocessing ... % 2.97/1.12 Prover 5: Preprocessing ... % 2.97/1.12 Prover 3: Preprocessing ... % 2.97/1.12 Prover 6: Preprocessing ... % 4.64/1.40 Prover 5: Proving ... % 4.64/1.42 Prover 1: Constructing countermodel ... % 4.64/1.42 Prover 6: Constructing countermodel ... % 4.64/1.43 Prover 3: Constructing countermodel ... % 4.88/1.46 Prover 4: Constructing countermodel ... % 4.88/1.46 Prover 0: Proving ... % 5.78/1.51 Prover 2: Proving ... % 7.54/1.77 Prover 3: proved (1111ms) % 7.54/1.77 % 7.54/1.78 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 7.54/1.78 % 7.54/1.78 Prover 6: stopped % 7.54/1.78 Prover 2: stopped % 7.54/1.78 Prover 0: stopped % 7.54/1.78 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 7.54/1.78 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 7.54/1.78 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 7.54/1.79 Prover 5: stopped % 7.54/1.80 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 7.95/1.80 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 7.95/1.83 Prover 11: Preprocessing ... % 7.95/1.83 Prover 7: Preprocessing ... % 7.95/1.84 Prover 10: Preprocessing ... % 7.95/1.84 Prover 8: Preprocessing ... % 7.95/1.85 Prover 13: Preprocessing ... % 8.33/1.93 Prover 7: Constructing countermodel ... % 8.33/1.94 Prover 13: Warning: ignoring some quantifiers % 8.33/1.94 Prover 8: Warning: ignoring some quantifiers % 8.33/1.95 Prover 13: Constructing countermodel ... % 9.01/1.96 Prover 8: Constructing countermodel ... % 9.01/1.96 Prover 10: Constructing countermodel ... % 9.01/1.99 Prover 11: Constructing countermodel ... % 9.33/2.11 Prover 1: Found proof (size 169) % 9.33/2.12 Prover 1: proved (1465ms) % 9.33/2.12 Prover 7: stopped % 9.33/2.12 Prover 11: stopped % 9.33/2.12 Prover 13: stopped % 9.33/2.12 Prover 8: stopped % 9.33/2.12 Prover 4: stopped % 9.33/2.12 Prover 10: stopped % 9.33/2.12 % 9.33/2.12 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 9.33/2.12 % 10.26/2.17 % SZS output start Proof for theBenchmark % 10.26/2.17 Assumptions after simplification: % 10.26/2.17 --------------------------------- % 10.26/2.17 % 10.26/2.17 (ax1) % 10.26/2.19 collection(empty) & ! [v0: collection] : ! [v1: int] : ( ~ ($lesseq(v1, -1)) % 10.26/2.19 | ~ (count(v0) = v1) | ~ collection(v0)) & ! [v0: int] : ~ (in(v0, % 10.26/2.19 empty) = 0) % 10.26/2.19 % 10.26/2.19 (ax2) % 10.26/2.20 collection(empty) & ! [v0: int] : ! [v1: collection] : ! [v2: collection] : % 10.26/2.20 ! [v3: int] : (v3 = 0 | ~ (add(v0, v1) = v2) | ~ (in(v0, v2) = v3) | ~ % 10.26/2.20 collection(v1)) & ! [v0: collection] : (v0 = empty | ~ (count(v0) = 0) | % 10.26/2.20 ~ collection(v0)) & ! [v0: int] : (v0 = 0 | ~ (count(empty) = v0)) % 10.26/2.20 % 10.26/2.20 (ax3) % 10.53/2.20 ! [v0: int] : ! [v1: collection] : ! [v2: collection] : ( ~ (remove(v0, v1) % 10.53/2.20 = v2) | ~ (in(v0, v2) = 0) | ~ collection(v1)) & ! [v0: int] : ! [v1: % 10.53/2.20 collection] : ! [v2: collection] : ( ~ (add(v0, v1) = v2) | ~ % 10.53/2.20 collection(v1) | ? [v3: any] : ? [v4: int] : ? [v5: int] : (count(v2) = % 10.53/2.20 v4 & count(v1) = v5 & in(v0, v1) = v3 & ($difference(v5, v4) = -1 | v3 = % 10.53/2.20 0))) & ! [v0: int] : ! [v1: collection] : ! [v2: collection] : ( ~ % 10.53/2.20 (add(v0, v1) = v2) | ~ collection(v1) | ? [v3: int] : ? [v4: int] : ? % 10.53/2.20 [v5: any] : (count(v2) = v3 & count(v1) = v4 & in(v0, v1) = v5 & ( ~ (v5 = % 10.53/2.20 0) | ~ ($difference(v4, v3) = -1)))) % 10.53/2.20 % 10.53/2.20 (ax4) % 10.53/2.21 ! [v0: int] : ! [v1: collection] : ! [v2: int] : ! [v3: collection] : ! % 10.53/2.21 [v4: int] : (v4 = 0 | ~ (add(v2, v1) = v3) | ~ (in(v0, v3) = v4) | ~ % 10.53/2.21 collection(v1) | ( ~ (v2 = v0) & ? [v5: int] : ( ~ (v5 = 0) & in(v0, v1) = % 10.53/2.21 v5))) & ! [v0: int] : ! [v1: collection] : ! [v2: int] : ! [v3: % 10.53/2.21 collection] : (v2 = v0 | ~ (add(v2, v1) = v3) | ~ (in(v0, v3) = 0) | ~ % 10.53/2.21 collection(v1) | in(v0, v1) = 0) & ! [v0: int] : ! [v1: collection] : ! % 10.53/2.21 [v2: collection] : ( ~ (add(v0, v1) = v2) | ~ collection(v1) | ? [v3: any] : % 10.53/2.21 ? [v4: int] : ? [v5: int] : (count(v2) = v4 & count(v1) = v5 & in(v0, v1) % 10.53/2.21 = v3 & ( ~ (v3 = 0) | v5 = v4))) & ! [v0: int] : ! [v1: collection] : ! % 10.53/2.21 [v2: collection] : ( ~ (add(v0, v1) = v2) | ~ collection(v1) | ? [v3: int] : % 10.53/2.21 ? [v4: int] : ? [v5: any] : (count(v2) = v3 & count(v1) = v4 & in(v0, v1) % 10.53/2.21 = v5 & ( ~ (v4 = v3) | v5 = 0))) % 10.53/2.21 % 10.53/2.21 (ax5) % 10.53/2.22 ! [v0: int] : ! [v1: collection] : ! [v2: int] : ! [v3: collection] : ! % 10.53/2.22 [v4: int] : (v4 = 0 | v2 = v0 | ~ (remove(v2, v1) = v3) | ~ (in(v0, v3) = % 10.53/2.22 v4) | ~ collection(v1) | ? [v5: int] : ( ~ (v5 = 0) & in(v0, v1) = v5)) % 10.53/2.22 & ! [v0: int] : ! [v1: collection] : ! [v2: int] : ! [v3: collection] : ( % 10.53/2.22 ~ (remove(v2, v1) = v3) | ~ (in(v0, v3) = 0) | ~ collection(v1) | ( ~ (v2 % 10.53/2.22 = v0) & in(v0, v1) = 0)) & ! [v0: int] : ! [v1: collection] : ! [v2: % 10.53/2.22 collection] : ( ~ (remove(v0, v1) = v2) | ~ collection(v1) | ? [v3: any] : % 10.53/2.22 ? [v4: int] : ? [v5: int] : (count(v2) = v4 & count(v1) = v5 & in(v0, v1) % 10.53/2.22 = v3 & ( ~ (v3 = 0) | $difference(v5, v4) = 1))) & ! [v0: int] : ! [v1: % 10.53/2.22 collection] : ! [v2: collection] : ( ~ (remove(v0, v1) = v2) | ~ % 10.53/2.22 collection(v1) | ? [v3: int] : ? [v4: int] : ? [v5: any] : (count(v2) = % 10.53/2.22 v3 & count(v1) = v4 & in(v0, v1) = v5 & ( ~ ($difference(v4, v3) = 1) | v5 % 10.53/2.22 = 0))) % 10.53/2.22 % 10.53/2.22 (ax6) % 10.53/2.22 ! [v0: int] : ! [v1: collection] : ! [v2: collection] : ( ~ (remove(v0, v1) % 10.53/2.22 = v2) | ~ collection(v1) | ? [v3: any] : ? [v4: int] : ? [v5: int] : % 10.53/2.22 (count(v2) = v4 & count(v1) = v5 & in(v0, v1) = v3 & (v5 = v4 | v3 = 0))) & % 10.53/2.22 ! [v0: int] : ! [v1: collection] : ! [v2: collection] : ( ~ (remove(v0, v1) % 10.53/2.22 = v2) | ~ collection(v1) | ? [v3: int] : ? [v4: int] : ? [v5: any] : % 10.53/2.22 (count(v2) = v3 & count(v1) = v4 & in(v0, v1) = v5 & ( ~ (v5 = 0) | ~ (v4 = % 10.53/2.22 v3)))) % 10.53/2.22 % 10.53/2.22 (co1) % 10.53/2.22 collection(empty) & ? [v0: collection] : ? [v1: collection] : ? [v2: % 10.53/2.22 collection] : ? [v3: int] : ( ~ (v3 = 1) & remove(3, v0) = v1 & add(5, v1) % 10.53/2.22 = v2 & add(3, empty) = v0 & count(v2) = v3 & collection(v2) & collection(v1) % 10.53/2.22 & collection(v0)) % 10.53/2.22 % 10.53/2.22 (function-axioms) % 10.53/2.23 ! [v0: collection] : ! [v1: collection] : ! [v2: collection] : ! [v3: int] % 10.53/2.23 : (v1 = v0 | ~ (remove(v3, v2) = v1) | ~ (remove(v3, v2) = v0)) & ! [v0: % 10.53/2.23 collection] : ! [v1: collection] : ! [v2: collection] : ! [v3: int] : (v1 % 10.53/2.23 = v0 | ~ (add(v3, v2) = v1) | ~ (add(v3, v2) = v0)) & ! [v0: % 10.53/2.23 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: collection] : ! % 10.53/2.23 [v3: int] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: % 10.53/2.23 int] : ! [v1: int] : ! [v2: collection] : (v1 = v0 | ~ (count(v2) = v1) | % 10.53/2.23 ~ (count(v2) = v0)) % 10.53/2.23 % 10.53/2.23 Further assumptions not needed in the proof: % 10.53/2.23 -------------------------------------------- % 10.53/2.23 ax7 % 10.53/2.23 % 10.53/2.23 Those formulas are unsatisfiable: % 10.53/2.23 --------------------------------- % 10.53/2.23 % 10.53/2.23 Begin of proof % 10.53/2.23 | % 10.53/2.23 | ALPHA: (ax1) implies: % 10.53/2.23 | (1) ! [v0: int] : ~ (in(v0, empty) = 0) % 10.53/2.23 | (2) ! [v0: collection] : ! [v1: int] : ( ~ ($lesseq(v1, -1)) | ~ % 10.53/2.23 | (count(v0) = v1) | ~ collection(v0)) % 10.53/2.23 | % 10.53/2.23 | ALPHA: (ax2) implies: % 10.53/2.23 | (3) ! [v0: int] : (v0 = 0 | ~ (count(empty) = v0)) % 10.53/2.23 | (4) ! [v0: collection] : (v0 = empty | ~ (count(v0) = 0) | ~ % 10.53/2.23 | collection(v0)) % 10.53/2.23 | (5) ! [v0: int] : ! [v1: collection] : ! [v2: collection] : ! [v3: int] % 10.53/2.23 | : (v3 = 0 | ~ (add(v0, v1) = v2) | ~ (in(v0, v2) = v3) | ~ % 10.53/2.23 | collection(v1)) % 10.53/2.23 | % 10.53/2.23 | ALPHA: (ax3) implies: % 10.53/2.23 | (6) ! [v0: int] : ! [v1: collection] : ! [v2: collection] : ( ~ (add(v0, % 10.53/2.23 | v1) = v2) | ~ collection(v1) | ? [v3: int] : ? [v4: int] : ? % 10.53/2.23 | [v5: any] : (count(v2) = v3 & count(v1) = v4 & in(v0, v1) = v5 & ( ~ % 10.53/2.23 | (v5 = 0) | ~ ($difference(v4, v3) = -1)))) % 10.53/2.24 | (7) ! [v0: int] : ! [v1: collection] : ! [v2: collection] : ( ~ (add(v0, % 10.53/2.24 | v1) = v2) | ~ collection(v1) | ? [v3: any] : ? [v4: int] : ? % 10.53/2.24 | [v5: int] : (count(v2) = v4 & count(v1) = v5 & in(v0, v1) = v3 & % 10.53/2.24 | ($difference(v5, v4) = -1 | v3 = 0))) % 10.53/2.24 | % 10.53/2.24 | ALPHA: (ax4) implies: % 10.53/2.24 | (8) ! [v0: int] : ! [v1: collection] : ! [v2: collection] : ( ~ (add(v0, % 10.53/2.24 | v1) = v2) | ~ collection(v1) | ? [v3: int] : ? [v4: int] : ? % 10.53/2.24 | [v5: any] : (count(v2) = v3 & count(v1) = v4 & in(v0, v1) = v5 & ( ~ % 10.53/2.24 | (v4 = v3) | v5 = 0))) % 10.53/2.24 | (9) ! [v0: int] : ! [v1: collection] : ! [v2: collection] : ( ~ (add(v0, % 10.53/2.24 | v1) = v2) | ~ collection(v1) | ? [v3: any] : ? [v4: int] : ? % 10.53/2.24 | [v5: int] : (count(v2) = v4 & count(v1) = v5 & in(v0, v1) = v3 & ( ~ % 10.53/2.24 | (v3 = 0) | v5 = v4))) % 10.53/2.24 | % 10.53/2.24 | ALPHA: (ax5) implies: % 10.53/2.24 | (10) ! [v0: int] : ! [v1: collection] : ! [v2: collection] : ( ~ % 10.53/2.24 | (remove(v0, v1) = v2) | ~ collection(v1) | ? [v3: int] : ? [v4: % 10.53/2.24 | int] : ? [v5: any] : (count(v2) = v3 & count(v1) = v4 & in(v0, % 10.53/2.24 | v1) = v5 & ( ~ ($difference(v4, v3) = 1) | v5 = 0))) % 10.53/2.24 | (11) ! [v0: int] : ! [v1: collection] : ! [v2: collection] : ( ~ % 10.53/2.24 | (remove(v0, v1) = v2) | ~ collection(v1) | ? [v3: any] : ? [v4: % 10.53/2.24 | int] : ? [v5: int] : (count(v2) = v4 & count(v1) = v5 & in(v0, % 10.53/2.24 | v1) = v3 & ( ~ (v3 = 0) | $difference(v5, v4) = 1))) % 10.53/2.24 | % 10.53/2.24 | ALPHA: (ax6) implies: % 10.53/2.24 | (12) ! [v0: int] : ! [v1: collection] : ! [v2: collection] : ( ~ % 10.53/2.24 | (remove(v0, v1) = v2) | ~ collection(v1) | ? [v3: int] : ? [v4: % 10.53/2.24 | int] : ? [v5: any] : (count(v2) = v3 & count(v1) = v4 & in(v0, % 10.53/2.24 | v1) = v5 & ( ~ (v5 = 0) | ~ (v4 = v3)))) % 10.53/2.24 | (13) ! [v0: int] : ! [v1: collection] : ! [v2: collection] : ( ~ % 10.53/2.24 | (remove(v0, v1) = v2) | ~ collection(v1) | ? [v3: any] : ? [v4: % 10.53/2.24 | int] : ? [v5: int] : (count(v2) = v4 & count(v1) = v5 & in(v0, % 10.53/2.24 | v1) = v3 & (v5 = v4 | v3 = 0))) % 10.53/2.24 | % 10.53/2.24 | ALPHA: (co1) implies: % 10.53/2.24 | (14) collection(empty) % 10.53/2.25 | (15) ? [v0: collection] : ? [v1: collection] : ? [v2: collection] : ? % 10.53/2.25 | [v3: int] : ( ~ (v3 = 1) & remove(3, v0) = v1 & add(5, v1) = v2 & % 10.53/2.25 | add(3, empty) = v0 & count(v2) = v3 & collection(v2) & % 10.53/2.25 | collection(v1) & collection(v0)) % 10.53/2.25 | % 10.53/2.25 | ALPHA: (function-axioms) implies: % 10.53/2.25 | (16) ! [v0: int] : ! [v1: int] : ! [v2: collection] : (v1 = v0 | ~ % 10.53/2.25 | (count(v2) = v1) | ~ (count(v2) = v0)) % 10.53/2.25 | (17) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 10.53/2.25 | collection] : ! [v3: int] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ % 10.53/2.25 | (in(v3, v2) = v0)) % 10.53/2.25 | % 10.53/2.25 | DELTA: instantiating (15) with fresh symbols all_13_0, all_13_1, all_13_2, % 10.53/2.25 | all_13_3 gives: % 10.53/2.25 | (18) ~ (all_13_0 = 1) & remove(3, all_13_3) = all_13_2 & add(5, all_13_2) % 10.53/2.25 | = all_13_1 & add(3, empty) = all_13_3 & count(all_13_1) = all_13_0 & % 10.53/2.25 | collection(all_13_1) & collection(all_13_2) & collection(all_13_3) % 10.53/2.25 | % 10.53/2.25 | ALPHA: (18) implies: % 10.53/2.25 | (19) ~ (all_13_0 = 1) % 10.53/2.25 | (20) collection(all_13_3) % 10.53/2.25 | (21) collection(all_13_2) % 10.53/2.25 | (22) count(all_13_1) = all_13_0 % 10.53/2.25 | (23) add(3, empty) = all_13_3 % 10.53/2.25 | (24) add(5, all_13_2) = all_13_1 % 10.53/2.25 | (25) remove(3, all_13_3) = all_13_2 % 10.53/2.25 | % 10.53/2.25 | GROUND_INST: instantiating (9) with 3, empty, all_13_3, simplifying with (14), % 10.53/2.25 | (23) gives: % 10.53/2.25 | (26) ? [v0: any] : ? [v1: int] : ? [v2: int] : (count(all_13_3) = v1 & % 10.53/2.25 | count(empty) = v2 & in(3, empty) = v0 & ( ~ (v0 = 0) | v2 = v1)) % 10.53/2.25 | % 10.53/2.25 | GROUND_INST: instantiating (7) with 3, empty, all_13_3, simplifying with (14), % 10.53/2.25 | (23) gives: % 10.53/2.25 | (27) ? [v0: any] : ? [v1: int] : ? [v2: int] : (count(all_13_3) = v1 & % 10.53/2.25 | count(empty) = v2 & in(3, empty) = v0 & ($difference(v2, v1) = -1 | % 10.53/2.25 | v0 = 0)) % 10.53/2.25 | % 10.53/2.25 | GROUND_INST: instantiating (6) with 3, empty, all_13_3, simplifying with (14), % 10.53/2.25 | (23) gives: % 10.53/2.25 | (28) ? [v0: int] : ? [v1: int] : ? [v2: any] : (count(all_13_3) = v0 & % 10.53/2.25 | count(empty) = v1 & in(3, empty) = v2 & ( ~ (v2 = 0) | ~ % 10.53/2.25 | ($difference(v1, v0) = -1))) % 10.53/2.25 | % 10.53/2.25 | GROUND_INST: instantiating (8) with 3, empty, all_13_3, simplifying with (14), % 10.53/2.25 | (23) gives: % 10.81/2.26 | (29) ? [v0: int] : ? [v1: int] : ? [v2: any] : (count(all_13_3) = v0 & % 10.81/2.26 | count(empty) = v1 & in(3, empty) = v2 & ( ~ (v1 = v0) | v2 = 0)) % 10.81/2.26 | % 10.81/2.26 | GROUND_INST: instantiating (9) with 5, all_13_2, all_13_1, simplifying with % 10.81/2.26 | (21), (24) gives: % 10.81/2.26 | (30) ? [v0: any] : ? [v1: int] : ? [v2: int] : (count(all_13_1) = v1 & % 10.81/2.26 | count(all_13_2) = v2 & in(5, all_13_2) = v0 & ( ~ (v0 = 0) | v2 = % 10.81/2.26 | v1)) % 10.81/2.26 | % 10.81/2.26 | GROUND_INST: instantiating (7) with 5, all_13_2, all_13_1, simplifying with % 10.81/2.26 | (21), (24) gives: % 10.81/2.26 | (31) ? [v0: any] : ? [v1: int] : ? [v2: int] : (count(all_13_1) = v1 & % 10.81/2.26 | count(all_13_2) = v2 & in(5, all_13_2) = v0 & ($difference(v2, v1) = % 10.81/2.26 | -1 | v0 = 0)) % 10.81/2.26 | % 10.81/2.26 | GROUND_INST: instantiating (6) with 5, all_13_2, all_13_1, simplifying with % 10.81/2.26 | (21), (24) gives: % 10.81/2.26 | (32) ? [v0: int] : ? [v1: int] : ? [v2: any] : (count(all_13_1) = v0 & % 10.81/2.26 | count(all_13_2) = v1 & in(5, all_13_2) = v2 & ( ~ (v2 = 0) | ~ % 10.81/2.26 | ($difference(v1, v0) = -1))) % 10.81/2.26 | % 10.81/2.26 | GROUND_INST: instantiating (8) with 5, all_13_2, all_13_1, simplifying with % 10.81/2.26 | (21), (24) gives: % 10.81/2.26 | (33) ? [v0: int] : ? [v1: int] : ? [v2: any] : (count(all_13_1) = v0 & % 10.81/2.26 | count(all_13_2) = v1 & in(5, all_13_2) = v2 & ( ~ (v1 = v0) | v2 = % 10.81/2.26 | 0)) % 10.81/2.26 | % 10.81/2.26 | GROUND_INST: instantiating (11) with 3, all_13_3, all_13_2, simplifying with % 10.81/2.26 | (20), (25) gives: % 10.81/2.26 | (34) ? [v0: any] : ? [v1: int] : ? [v2: int] : (count(all_13_2) = v1 & % 10.81/2.26 | count(all_13_3) = v2 & in(3, all_13_3) = v0 & ( ~ (v0 = 0) | % 10.81/2.26 | $difference(v2, v1) = 1)) % 10.81/2.26 | % 10.81/2.26 | GROUND_INST: instantiating (13) with 3, all_13_3, all_13_2, simplifying with % 10.81/2.26 | (20), (25) gives: % 10.81/2.26 | (35) ? [v0: any] : ? [v1: int] : ? [v2: int] : (count(all_13_2) = v1 & % 10.81/2.26 | count(all_13_3) = v2 & in(3, all_13_3) = v0 & (v2 = v1 | v0 = 0)) % 10.81/2.26 | % 10.81/2.26 | GROUND_INST: instantiating (12) with 3, all_13_3, all_13_2, simplifying with % 10.81/2.26 | (20), (25) gives: % 10.81/2.26 | (36) ? [v0: int] : ? [v1: int] : ? [v2: any] : (count(all_13_2) = v0 & % 10.81/2.26 | count(all_13_3) = v1 & in(3, all_13_3) = v2 & ( ~ (v2 = 0) | ~ (v1 % 10.81/2.26 | = v0))) % 10.81/2.26 | % 10.81/2.26 | GROUND_INST: instantiating (10) with 3, all_13_3, all_13_2, simplifying with % 10.81/2.26 | (20), (25) gives: % 10.81/2.27 | (37) ? [v0: int] : ? [v1: int] : ? [v2: any] : (count(all_13_2) = v0 & % 10.81/2.27 | count(all_13_3) = v1 & in(3, all_13_3) = v2 & ( ~ ($difference(v1, % 10.81/2.27 | v0) = 1) | v2 = 0)) % 10.81/2.27 | % 10.81/2.27 | DELTA: instantiating (37) with fresh symbols all_22_0, all_22_1, all_22_2 % 10.81/2.27 | gives: % 10.81/2.27 | (38) count(all_13_2) = all_22_2 & count(all_13_3) = all_22_1 & in(3, % 10.81/2.27 | all_13_3) = all_22_0 & ( ~ ($difference(all_22_1, all_22_2) = 1) | % 10.81/2.27 | all_22_0 = 0) % 10.81/2.27 | % 10.81/2.27 | ALPHA: (38) implies: % 10.81/2.27 | (39) in(3, all_13_3) = all_22_0 % 10.81/2.27 | (40) count(all_13_3) = all_22_1 % 10.81/2.27 | (41) count(all_13_2) = all_22_2 % 10.81/2.27 | % 10.81/2.27 | DELTA: instantiating (36) with fresh symbols all_24_0, all_24_1, all_24_2 % 10.81/2.27 | gives: % 10.81/2.27 | (42) count(all_13_2) = all_24_2 & count(all_13_3) = all_24_1 & in(3, % 10.81/2.27 | all_13_3) = all_24_0 & ( ~ (all_24_0 = 0) | ~ (all_24_1 = % 10.81/2.27 | all_24_2)) % 10.81/2.27 | % 10.81/2.27 | ALPHA: (42) implies: % 10.81/2.27 | (43) in(3, all_13_3) = all_24_0 % 10.81/2.27 | (44) count(all_13_3) = all_24_1 % 10.81/2.27 | (45) count(all_13_2) = all_24_2 % 10.81/2.27 | % 10.81/2.27 | DELTA: instantiating (35) with fresh symbols all_26_0, all_26_1, all_26_2 % 10.81/2.27 | gives: % 10.81/2.27 | (46) count(all_13_2) = all_26_1 & count(all_13_3) = all_26_0 & in(3, % 10.81/2.27 | all_13_3) = all_26_2 & (all_26_0 = all_26_1 | all_26_2 = 0) % 10.81/2.27 | % 10.81/2.27 | ALPHA: (46) implies: % 10.81/2.27 | (47) in(3, all_13_3) = all_26_2 % 10.81/2.27 | (48) count(all_13_3) = all_26_0 % 10.81/2.27 | (49) count(all_13_2) = all_26_1 % 10.81/2.27 | % 10.81/2.27 | DELTA: instantiating (34) with fresh symbols all_28_0, all_28_1, all_28_2 % 10.81/2.27 | gives: % 10.81/2.27 | (50) count(all_13_2) = all_28_1 & count(all_13_3) = all_28_0 & in(3, % 10.81/2.27 | all_13_3) = all_28_2 & ( ~ (all_28_2 = 0) | $difference(all_28_0, % 10.81/2.27 | all_28_1) = 1) % 10.81/2.27 | % 10.81/2.27 | ALPHA: (50) implies: % 10.81/2.27 | (51) in(3, all_13_3) = all_28_2 % 10.81/2.27 | (52) count(all_13_3) = all_28_0 % 10.81/2.27 | (53) count(all_13_2) = all_28_1 % 10.81/2.27 | (54) ~ (all_28_2 = 0) | $difference(all_28_0, all_28_1) = 1 % 10.81/2.27 | % 10.81/2.27 | DELTA: instantiating (28) with fresh symbols all_30_0, all_30_1, all_30_2 % 10.81/2.27 | gives: % 10.81/2.27 | (55) count(all_13_3) = all_30_2 & count(empty) = all_30_1 & in(3, empty) = % 10.81/2.27 | all_30_0 & ( ~ (all_30_0 = 0) | ~ ($difference(all_30_1, all_30_2) = % 10.81/2.27 | -1)) % 10.81/2.27 | % 10.81/2.27 | ALPHA: (55) implies: % 10.81/2.27 | (56) in(3, empty) = all_30_0 % 10.81/2.27 | (57) count(all_13_3) = all_30_2 % 10.81/2.27 | % 10.81/2.27 | DELTA: instantiating (32) with fresh symbols all_32_0, all_32_1, all_32_2 % 10.81/2.27 | gives: % 10.81/2.27 | (58) count(all_13_1) = all_32_2 & count(all_13_2) = all_32_1 & in(5, % 10.81/2.27 | all_13_2) = all_32_0 & ( ~ (all_32_0 = 0) | ~ % 10.81/2.27 | ($difference(all_32_1, all_32_2) = -1)) % 10.81/2.27 | % 10.81/2.27 | ALPHA: (58) implies: % 10.81/2.27 | (59) in(5, all_13_2) = all_32_0 % 10.81/2.27 | (60) count(all_13_2) = all_32_1 % 10.81/2.27 | (61) count(all_13_1) = all_32_2 % 10.81/2.27 | % 10.81/2.27 | DELTA: instantiating (30) with fresh symbols all_34_0, all_34_1, all_34_2 % 10.81/2.27 | gives: % 10.81/2.28 | (62) count(all_13_1) = all_34_1 & count(all_13_2) = all_34_0 & in(5, % 10.81/2.28 | all_13_2) = all_34_2 & ( ~ (all_34_2 = 0) | all_34_0 = all_34_1) % 10.81/2.28 | % 10.81/2.28 | ALPHA: (62) implies: % 10.81/2.28 | (63) in(5, all_13_2) = all_34_2 % 10.81/2.28 | (64) count(all_13_2) = all_34_0 % 10.81/2.28 | (65) count(all_13_1) = all_34_1 % 10.81/2.28 | % 10.81/2.28 | DELTA: instantiating (29) with fresh symbols all_36_0, all_36_1, all_36_2 % 10.81/2.28 | gives: % 10.81/2.28 | (66) count(all_13_3) = all_36_2 & count(empty) = all_36_1 & in(3, empty) = % 10.81/2.28 | all_36_0 & ( ~ (all_36_1 = all_36_2) | all_36_0 = 0) % 10.81/2.28 | % 10.81/2.28 | ALPHA: (66) implies: % 10.81/2.28 | (67) count(all_13_3) = all_36_2 % 10.81/2.28 | % 10.81/2.28 | DELTA: instantiating (31) with fresh symbols all_38_0, all_38_1, all_38_2 % 10.81/2.28 | gives: % 10.81/2.28 | (68) count(all_13_1) = all_38_1 & count(all_13_2) = all_38_0 & in(5, % 10.81/2.28 | all_13_2) = all_38_2 & ($difference(all_38_0, all_38_1) = -1 | % 10.81/2.28 | all_38_2 = 0) % 10.81/2.28 | % 10.81/2.28 | ALPHA: (68) implies: % 10.81/2.28 | (69) in(5, all_13_2) = all_38_2 % 10.81/2.28 | (70) count(all_13_2) = all_38_0 % 10.81/2.28 | (71) count(all_13_1) = all_38_1 % 10.81/2.28 | (72) $difference(all_38_0, all_38_1) = -1 | all_38_2 = 0 % 10.81/2.28 | % 10.81/2.28 | DELTA: instantiating (26) with fresh symbols all_40_0, all_40_1, all_40_2 % 10.81/2.28 | gives: % 10.81/2.28 | (73) count(all_13_3) = all_40_1 & count(empty) = all_40_0 & in(3, empty) = % 10.81/2.28 | all_40_2 & ( ~ (all_40_2 = 0) | all_40_0 = all_40_1) % 10.81/2.28 | % 10.81/2.28 | ALPHA: (73) implies: % 10.81/2.28 | (74) in(3, empty) = all_40_2 % 10.81/2.28 | (75) count(empty) = all_40_0 % 10.81/2.28 | (76) count(all_13_3) = all_40_1 % 10.81/2.28 | (77) ~ (all_40_2 = 0) | all_40_0 = all_40_1 % 10.81/2.28 | % 10.81/2.28 | DELTA: instantiating (27) with fresh symbols all_42_0, all_42_1, all_42_2 % 10.81/2.28 | gives: % 10.81/2.28 | (78) count(all_13_3) = all_42_1 & count(empty) = all_42_0 & in(3, empty) = % 10.81/2.28 | all_42_2 & ($difference(all_42_0, all_42_1) = -1 | all_42_2 = 0) % 10.81/2.28 | % 10.81/2.28 | ALPHA: (78) implies: % 10.81/2.28 | (79) in(3, empty) = all_42_2 % 10.81/2.28 | (80) count(empty) = all_42_0 % 10.81/2.28 | (81) count(all_13_3) = all_42_1 % 10.81/2.28 | (82) $difference(all_42_0, all_42_1) = -1 | all_42_2 = 0 % 10.81/2.28 | % 10.81/2.28 | DELTA: instantiating (33) with fresh symbols all_44_0, all_44_1, all_44_2 % 10.81/2.28 | gives: % 10.81/2.28 | (83) count(all_13_1) = all_44_2 & count(all_13_2) = all_44_1 & in(5, % 10.81/2.28 | all_13_2) = all_44_0 & ( ~ (all_44_1 = all_44_2) | all_44_0 = 0) % 10.81/2.28 | % 10.81/2.28 | ALPHA: (83) implies: % 10.81/2.28 | (84) in(5, all_13_2) = all_44_0 % 10.81/2.28 | (85) count(all_13_2) = all_44_1 % 10.81/2.28 | (86) count(all_13_1) = all_44_2 % 10.81/2.28 | % 10.81/2.28 | GROUND_INST: instantiating (17) with all_40_2, all_42_2, empty, 3, simplifying % 10.81/2.28 | with (74), (79) gives: % 10.81/2.29 | (87) all_42_2 = all_40_2 % 10.81/2.29 | % 10.81/2.29 | GROUND_INST: instantiating (17) with all_30_0, all_42_2, empty, 3, simplifying % 10.81/2.29 | with (56), (79) gives: % 10.81/2.29 | (88) all_42_2 = all_30_0 % 10.81/2.29 | % 10.81/2.29 | GROUND_INST: instantiating (17) with all_26_2, all_28_2, all_13_3, 3, % 10.81/2.29 | simplifying with (47), (51) gives: % 10.81/2.29 | (89) all_28_2 = all_26_2 % 10.81/2.29 | % 10.81/2.29 | GROUND_INST: instantiating (17) with all_24_0, all_28_2, all_13_3, 3, % 10.81/2.29 | simplifying with (43), (51) gives: % 10.81/2.29 | (90) all_28_2 = all_24_0 % 10.81/2.29 | % 10.81/2.29 | GROUND_INST: instantiating (17) with all_22_0, all_28_2, all_13_3, 3, % 10.81/2.29 | simplifying with (39), (51) gives: % 10.81/2.29 | (91) all_28_2 = all_22_0 % 10.81/2.29 | % 10.81/2.29 | GROUND_INST: instantiating (17) with all_38_2, all_44_0, all_13_2, 5, % 10.81/2.29 | simplifying with (69), (84) gives: % 10.81/2.29 | (92) all_44_0 = all_38_2 % 10.81/2.29 | % 10.81/2.29 | GROUND_INST: instantiating (17) with all_34_2, all_44_0, all_13_2, 5, % 10.81/2.29 | simplifying with (63), (84) gives: % 10.81/2.29 | (93) all_44_0 = all_34_2 % 10.81/2.29 | % 10.81/2.29 | GROUND_INST: instantiating (17) with all_32_0, all_44_0, all_13_2, 5, % 10.81/2.29 | simplifying with (59), (84) gives: % 10.81/2.29 | (94) all_44_0 = all_32_0 % 10.81/2.29 | % 10.81/2.29 | GROUND_INST: instantiating (16) with all_40_0, all_42_0, empty, simplifying % 10.81/2.29 | with (75), (80) gives: % 10.81/2.29 | (95) all_42_0 = all_40_0 % 10.81/2.29 | % 10.81/2.29 | GROUND_INST: instantiating (3) with all_42_0, simplifying with (80) gives: % 10.81/2.29 | (96) all_42_0 = 0 % 10.81/2.29 | % 10.81/2.29 | GROUND_INST: instantiating (16) with all_28_0, all_36_2, all_13_3, simplifying % 10.81/2.29 | with (52), (67) gives: % 10.81/2.29 | (97) all_36_2 = all_28_0 % 10.81/2.29 | % 10.81/2.29 | GROUND_INST: instantiating (16) with all_26_0, all_40_1, all_13_3, simplifying % 10.81/2.29 | with (48), (76) gives: % 10.81/2.29 | (98) all_40_1 = all_26_0 % 10.81/2.29 | % 10.81/2.29 | GROUND_INST: instantiating (16) with all_22_1, all_40_1, all_13_3, simplifying % 10.81/2.29 | with (40), (76) gives: % 10.81/2.29 | (99) all_40_1 = all_22_1 % 10.81/2.29 | % 10.81/2.29 | GROUND_INST: instantiating (16) with all_36_2, all_42_1, all_13_3, simplifying % 10.81/2.29 | with (67), (81) gives: % 10.81/2.29 | (100) all_42_1 = all_36_2 % 10.81/2.29 | % 10.81/2.29 | GROUND_INST: instantiating (16) with all_30_2, all_42_1, all_13_3, simplifying % 10.81/2.29 | with (57), (81) gives: % 10.81/2.29 | (101) all_42_1 = all_30_2 % 10.81/2.29 | % 10.81/2.29 | GROUND_INST: instantiating (16) with all_26_0, all_42_1, all_13_3, simplifying % 10.81/2.29 | with (48), (81) gives: % 10.81/2.29 | (102) all_42_1 = all_26_0 % 10.81/2.29 | % 10.81/2.29 | GROUND_INST: instantiating (16) with all_24_1, all_42_1, all_13_3, simplifying % 10.81/2.29 | with (44), (81) gives: % 10.81/2.29 | (103) all_42_1 = all_24_1 % 10.81/2.29 | % 10.81/2.29 | GROUND_INST: instantiating (16) with all_28_1, all_32_1, all_13_2, simplifying % 10.81/2.29 | with (53), (60) gives: % 10.81/2.29 | (104) all_32_1 = all_28_1 % 10.81/2.29 | % 10.81/2.29 | GROUND_INST: instantiating (16) with all_24_2, all_32_1, all_13_2, simplifying % 10.81/2.29 | with (45), (60) gives: % 10.81/2.29 | (105) all_32_1 = all_24_2 % 10.81/2.29 | % 10.81/2.29 | GROUND_INST: instantiating (16) with all_34_0, all_38_0, all_13_2, simplifying % 10.81/2.29 | with (64), (70) gives: % 10.81/2.29 | (106) all_38_0 = all_34_0 % 10.81/2.29 | % 10.81/2.29 | GROUND_INST: instantiating (16) with all_32_1, all_38_0, all_13_2, simplifying % 10.81/2.29 | with (60), (70) gives: % 10.81/2.29 | (107) all_38_0 = all_32_1 % 10.81/2.29 | % 10.81/2.29 | GROUND_INST: instantiating (16) with all_22_2, all_38_0, all_13_2, simplifying % 10.81/2.29 | with (41), (70) gives: % 10.81/2.29 | (108) all_38_0 = all_22_2 % 10.81/2.29 | % 10.81/2.29 | GROUND_INST: instantiating (16) with all_32_1, all_44_1, all_13_2, simplifying % 10.81/2.29 | with (60), (85) gives: % 10.81/2.29 | (109) all_44_1 = all_32_1 % 10.81/2.29 | % 10.81/2.29 | GROUND_INST: instantiating (16) with all_26_1, all_44_1, all_13_2, simplifying % 10.81/2.29 | with (49), (85) gives: % 10.81/2.29 | (110) all_44_1 = all_26_1 % 10.81/2.29 | % 10.81/2.30 | GROUND_INST: instantiating (16) with all_13_0, all_34_1, all_13_1, simplifying % 10.81/2.30 | with (22), (65) gives: % 10.81/2.30 | (111) all_34_1 = all_13_0 % 10.81/2.30 | % 10.81/2.30 | GROUND_INST: instantiating (16) with all_34_1, all_38_1, all_13_1, simplifying % 10.81/2.30 | with (65), (71) gives: % 10.81/2.30 | (112) all_38_1 = all_34_1 % 10.81/2.30 | % 10.81/2.30 | GROUND_INST: instantiating (16) with all_38_1, all_44_2, all_13_1, simplifying % 10.81/2.30 | with (71), (86) gives: % 10.81/2.30 | (113) all_44_2 = all_38_1 % 10.81/2.30 | % 10.81/2.30 | GROUND_INST: instantiating (16) with all_32_2, all_44_2, all_13_1, simplifying % 10.81/2.30 | with (61), (86) gives: % 10.81/2.30 | (114) all_44_2 = all_32_2 % 10.81/2.30 | % 10.81/2.30 | COMBINE_EQS: (92), (94) imply: % 10.81/2.30 | (115) all_38_2 = all_32_0 % 10.81/2.30 | % 10.81/2.30 | COMBINE_EQS: (92), (93) imply: % 10.81/2.30 | (116) all_38_2 = all_34_2 % 10.81/2.30 | % 10.81/2.30 | COMBINE_EQS: (109), (110) imply: % 10.81/2.30 | (117) all_32_1 = all_26_1 % 10.81/2.30 | % 10.81/2.30 | SIMP: (117) implies: % 10.81/2.30 | (118) all_32_1 = all_26_1 % 10.81/2.30 | % 10.81/2.30 | COMBINE_EQS: (113), (114) imply: % 10.81/2.30 | (119) all_38_1 = all_32_2 % 10.81/2.30 | % 10.81/2.30 | SIMP: (119) implies: % 10.81/2.30 | (120) all_38_1 = all_32_2 % 10.81/2.30 | % 10.81/2.30 | COMBINE_EQS: (95), (96) imply: % 10.81/2.30 | (121) all_40_0 = 0 % 10.81/2.30 | % 10.81/2.30 | SIMP: (121) implies: % 10.81/2.30 | (122) all_40_0 = 0 % 10.81/2.30 | % 10.81/2.30 | COMBINE_EQS: (100), (101) imply: % 10.81/2.30 | (123) all_36_2 = all_30_2 % 10.81/2.30 | % 10.81/2.30 | SIMP: (123) implies: % 10.81/2.30 | (124) all_36_2 = all_30_2 % 10.81/2.30 | % 10.81/2.30 | COMBINE_EQS: (101), (102) imply: % 10.81/2.30 | (125) all_30_2 = all_26_0 % 10.81/2.30 | % 10.81/2.30 | COMBINE_EQS: (101), (103) imply: % 10.81/2.30 | (126) all_30_2 = all_24_1 % 10.81/2.30 | % 10.81/2.30 | COMBINE_EQS: (87), (88) imply: % 10.81/2.30 | (127) all_40_2 = all_30_0 % 10.81/2.30 | % 10.81/2.30 | SIMP: (127) implies: % 10.81/2.30 | (128) all_40_2 = all_30_0 % 10.81/2.30 | % 10.81/2.30 | COMBINE_EQS: (98), (99) imply: % 10.81/2.30 | (129) all_26_0 = all_22_1 % 10.81/2.30 | % 10.81/2.30 | SIMP: (129) implies: % 10.81/2.30 | (130) all_26_0 = all_22_1 % 10.81/2.30 | % 10.81/2.30 | COMBINE_EQS: (106), (107) imply: % 10.81/2.30 | (131) all_34_0 = all_32_1 % 10.81/2.30 | % 10.81/2.30 | COMBINE_EQS: (106), (108) imply: % 10.81/2.30 | (132) all_34_0 = all_22_2 % 10.81/2.30 | % 10.81/2.30 | COMBINE_EQS: (112), (120) imply: % 10.81/2.30 | (133) all_34_1 = all_32_2 % 10.81/2.30 | % 10.81/2.30 | SIMP: (133) implies: % 10.81/2.30 | (134) all_34_1 = all_32_2 % 10.81/2.30 | % 10.81/2.30 | COMBINE_EQS: (115), (116) imply: % 10.81/2.30 | (135) all_34_2 = all_32_0 % 10.81/2.30 | % 10.81/2.30 | SIMP: (135) implies: % 10.81/2.30 | (136) all_34_2 = all_32_0 % 10.81/2.30 | % 10.81/2.30 | COMBINE_EQS: (97), (124) imply: % 10.81/2.30 | (137) all_30_2 = all_28_0 % 10.81/2.30 | % 10.81/2.30 | SIMP: (137) implies: % 10.81/2.30 | (138) all_30_2 = all_28_0 % 10.81/2.30 | % 10.81/2.30 | COMBINE_EQS: (131), (132) imply: % 10.81/2.30 | (139) all_32_1 = all_22_2 % 10.81/2.30 | % 10.81/2.30 | SIMP: (139) implies: % 10.81/2.30 | (140) all_32_1 = all_22_2 % 10.81/2.30 | % 10.81/2.30 | COMBINE_EQS: (111), (134) imply: % 10.81/2.30 | (141) all_32_2 = all_13_0 % 10.81/2.30 | % 10.81/2.30 | COMBINE_EQS: (104), (118) imply: % 10.81/2.30 | (142) all_28_1 = all_26_1 % 10.81/2.30 | % 10.81/2.30 | COMBINE_EQS: (104), (140) imply: % 10.81/2.30 | (143) all_28_1 = all_22_2 % 10.81/2.30 | % 10.81/2.30 | COMBINE_EQS: (104), (105) imply: % 10.81/2.30 | (144) all_28_1 = all_24_2 % 10.81/2.30 | % 10.81/2.30 | COMBINE_EQS: (126), (138) imply: % 10.81/2.30 | (145) all_28_0 = all_24_1 % 10.81/2.30 | % 10.81/2.30 | COMBINE_EQS: (125), (138) imply: % 10.81/2.30 | (146) all_28_0 = all_26_0 % 10.81/2.30 | % 10.81/2.30 | COMBINE_EQS: (145), (146) imply: % 10.81/2.30 | (147) all_26_0 = all_24_1 % 10.81/2.30 | % 10.81/2.30 | SIMP: (147) implies: % 10.81/2.30 | (148) all_26_0 = all_24_1 % 10.81/2.30 | % 10.81/2.30 | COMBINE_EQS: (142), (143) imply: % 10.81/2.30 | (149) all_26_1 = all_22_2 % 10.81/2.30 | % 10.81/2.30 | COMBINE_EQS: (142), (144) imply: % 10.81/2.30 | (150) all_26_1 = all_24_2 % 10.81/2.30 | % 10.81/2.30 | COMBINE_EQS: (89), (90) imply: % 10.81/2.30 | (151) all_26_2 = all_24_0 % 10.81/2.30 | % 10.81/2.30 | COMBINE_EQS: (89), (91) imply: % 10.81/2.30 | (152) all_26_2 = all_22_0 % 10.81/2.30 | % 10.81/2.30 | COMBINE_EQS: (130), (148) imply: % 10.81/2.30 | (153) all_24_1 = all_22_1 % 10.81/2.30 | % 10.81/2.30 | SIMP: (153) implies: % 10.81/2.30 | (154) all_24_1 = all_22_1 % 10.81/2.30 | % 10.81/2.30 | COMBINE_EQS: (149), (150) imply: % 10.81/2.30 | (155) all_24_2 = all_22_2 % 10.81/2.30 | % 10.81/2.30 | COMBINE_EQS: (151), (152) imply: % 10.81/2.30 | (156) all_24_0 = all_22_0 % 10.81/2.30 | % 10.81/2.30 | SIMP: (156) implies: % 10.81/2.30 | (157) all_24_0 = all_22_0 % 10.81/2.30 | % 10.81/2.30 | COMBINE_EQS: (145), (154) imply: % 10.81/2.30 | (158) all_28_0 = all_22_1 % 10.81/2.30 | % 10.81/2.30 | COMBINE_EQS: (138), (158) imply: % 10.81/2.30 | (159) all_30_2 = all_22_1 % 10.81/2.30 | % 10.81/2.31 | COMBINE_EQS: (120), (141) imply: % 10.81/2.31 | (160) all_38_1 = all_13_0 % 10.81/2.31 | % 10.81/2.31 | COMBINE_EQS: (101), (159) imply: % 10.81/2.31 | (161) all_42_1 = all_22_1 % 10.81/2.31 | % 10.81/2.31 | GROUND_INST: instantiating (5) with 3, empty, all_13_3, all_22_0, simplifying % 10.81/2.31 | with (14), (23), (39) gives: % 10.81/2.31 | (162) all_22_0 = 0 % 10.81/2.31 | % 10.81/2.31 | GROUND_INST: instantiating (2) with all_13_2, all_22_2, simplifying with (21), % 10.81/2.31 | (41) gives: % 10.81/2.31 | (163) $lesseq(0, all_22_2) % 10.81/2.31 | % 10.81/2.31 | COMBINE_EQS: (91), (162) imply: % 10.81/2.31 | (164) all_28_2 = 0 % 10.81/2.31 | % 10.81/2.31 | BETA: splitting (54) gives: % 10.81/2.31 | % 10.81/2.31 | Case 1: % 10.81/2.31 | | % 10.81/2.31 | | (165) ~ (all_28_2 = 0) % 10.81/2.31 | | % 10.81/2.31 | | REDUCE: (164), (165) imply: % 10.81/2.31 | | (166) $false % 10.81/2.31 | | % 10.81/2.31 | | CLOSE: (166) is inconsistent. % 10.81/2.31 | | % 10.81/2.31 | Case 2: % 10.81/2.31 | | % 10.81/2.31 | | (167) $difference(all_28_0, all_28_1) = 1 % 10.81/2.31 | | % 10.81/2.31 | | COMBINE_EQS: (158), (167) imply: % 10.81/2.31 | | (168) $difference(all_28_1, all_22_1) = -1 % 10.81/2.31 | | % 10.81/2.31 | | COMBINE_EQS: (143), (168) imply: % 10.81/2.31 | | (169) $difference(all_22_1, all_22_2) = 1 % 10.81/2.31 | | % 10.81/2.31 | | SIMP: (169) implies: % 10.81/2.31 | | (170) $difference(all_22_1, all_22_2) = 1 % 10.81/2.31 | | % 10.81/2.31 | | COMBINE_EQS: (99), (170) imply: % 10.81/2.31 | | (171) $difference(all_40_1, all_22_2) = 1 % 10.81/2.31 | | % 10.81/2.31 | | COMBINE_EQS: (161), (170) imply: % 10.81/2.31 | | (172) $difference(all_42_1, all_22_2) = 1 % 10.81/2.31 | | % 10.81/2.31 | | BETA: splitting (77) gives: % 10.81/2.31 | | % 10.81/2.31 | | Case 1: % 10.81/2.31 | | | % 10.81/2.31 | | | (173) ~ (all_40_2 = 0) % 10.81/2.31 | | | % 10.81/2.31 | | | REDUCE: (128), (173) imply: % 10.81/2.31 | | | (174) ~ (all_30_0 = 0) % 10.81/2.31 | | | % 10.81/2.31 | | | BETA: splitting (82) gives: % 10.81/2.31 | | | % 10.81/2.31 | | | Case 1: % 10.81/2.31 | | | | % 10.81/2.31 | | | | (175) all_42_2 = 0 % 10.81/2.31 | | | | % 10.81/2.31 | | | | COMBINE_EQS: (88), (175) imply: % 10.81/2.31 | | | | (176) all_30_0 = 0 % 10.81/2.31 | | | | % 10.81/2.31 | | | | SIMP: (176) implies: % 10.81/2.31 | | | | (177) all_30_0 = 0 % 10.81/2.31 | | | | % 10.81/2.31 | | | | REDUCE: (174), (177) imply: % 10.81/2.31 | | | | (178) $false % 10.81/2.31 | | | | % 10.81/2.31 | | | | CLOSE: (178) is inconsistent. % 10.81/2.31 | | | | % 10.81/2.31 | | | Case 2: % 10.81/2.31 | | | | % 10.81/2.31 | | | | (179) $difference(all_42_0, all_42_1) = -1 % 10.81/2.31 | | | | % 10.81/2.31 | | | | COMBINE_EQS: (96), (179) imply: % 10.81/2.31 | | | | (180) all_42_1 = 1 % 10.81/2.31 | | | | % 10.81/2.31 | | | | SIMP: (180) implies: % 10.81/2.31 | | | | (181) all_42_1 = 1 % 10.81/2.31 | | | | % 10.81/2.31 | | | | COMBINE_EQS: (172), (181) imply: % 10.81/2.31 | | | | (182) all_22_2 = 0 % 10.81/2.31 | | | | % 10.81/2.31 | | | | COMBINE_EQS: (108), (182) imply: % 10.81/2.31 | | | | (183) all_38_0 = 0 % 10.81/2.31 | | | | % 10.81/2.31 | | | | REDUCE: (41), (182) imply: % 10.81/2.31 | | | | (184) count(all_13_2) = 0 % 10.81/2.31 | | | | % 10.81/2.31 | | | | BETA: splitting (72) gives: % 10.81/2.31 | | | | % 10.81/2.31 | | | | Case 1: % 10.81/2.31 | | | | | % 10.81/2.31 | | | | | (185) all_38_2 = 0 % 10.81/2.31 | | | | | % 10.81/2.31 | | | | | COMBINE_EQS: (115), (185) imply: % 10.81/2.31 | | | | | (186) all_32_0 = 0 % 10.81/2.31 | | | | | % 10.81/2.31 | | | | | SIMP: (186) implies: % 10.81/2.31 | | | | | (187) all_32_0 = 0 % 10.81/2.31 | | | | | % 10.81/2.31 | | | | | REDUCE: (59), (187) imply: % 10.81/2.31 | | | | | (188) in(5, all_13_2) = 0 % 10.81/2.31 | | | | | % 10.81/2.31 | | | | | GROUND_INST: instantiating (4) with all_13_2, simplifying with (21), % 10.81/2.31 | | | | | (184) gives: % 10.81/2.31 | | | | | (189) all_13_2 = empty % 10.81/2.31 | | | | | % 10.81/2.31 | | | | | REDUCE: (188), (189) imply: % 10.81/2.31 | | | | | (190) in(5, empty) = 0 % 10.81/2.31 | | | | | % 10.81/2.31 | | | | | GROUND_INST: instantiating (1) with 5, simplifying with (190) gives: % 10.81/2.31 | | | | | (191) $false % 10.81/2.31 | | | | | % 10.81/2.31 | | | | | CLOSE: (191) is inconsistent. % 10.81/2.31 | | | | | % 10.81/2.31 | | | | Case 2: % 10.81/2.31 | | | | | % 10.81/2.31 | | | | | (192) $difference(all_38_0, all_38_1) = -1 % 10.81/2.31 | | | | | % 10.81/2.31 | | | | | COMBINE_EQS: (183), (192) imply: % 10.81/2.31 | | | | | (193) all_38_1 = 1 % 10.81/2.31 | | | | | % 10.81/2.31 | | | | | COMBINE_EQS: (160), (193) imply: % 10.81/2.31 | | | | | (194) all_13_0 = 1 % 10.81/2.31 | | | | | % 10.81/2.31 | | | | | REDUCE: (19), (194) imply: % 10.81/2.31 | | | | | (195) $false % 10.81/2.31 | | | | | % 10.81/2.31 | | | | | CLOSE: (195) is inconsistent. % 10.81/2.31 | | | | | % 10.81/2.31 | | | | End of split % 10.81/2.31 | | | | % 10.81/2.31 | | | End of split % 10.81/2.31 | | | % 10.81/2.31 | | Case 2: % 10.81/2.31 | | | % 10.81/2.32 | | | (196) all_40_0 = all_40_1 % 10.81/2.32 | | | % 10.81/2.32 | | | COMBINE_EQS: (122), (196) imply: % 10.81/2.32 | | | (197) all_40_1 = 0 % 10.81/2.32 | | | % 10.81/2.32 | | | COMBINE_EQS: (171), (197) imply: % 10.81/2.32 | | | (198) all_22_2 = -1 % 10.81/2.32 | | | % 10.81/2.32 | | | REDUCE: (163), (198) imply: % 10.81/2.32 | | | (199) $false % 10.81/2.32 | | | % 10.81/2.32 | | | CLOSE: (199) is inconsistent. % 10.81/2.32 | | | % 10.81/2.32 | | End of split % 10.81/2.32 | | % 10.81/2.32 | End of split % 10.81/2.32 | % 10.81/2.32 End of proof % 10.81/2.32 % SZS output end Proof for theBenchmark % 10.81/2.32 % 10.81/2.32 1686ms %------------------------------------------------------------------------------