%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET788+1 : TPTP v8.1.2. Released v3.1.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n001.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 15:26:27 EDT 2023 % Result : Theorem 4.08s 1.23s % Output : Proof 5.24s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : SET788+1 : TPTP v8.1.2. Released v3.1.0. % 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n001.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Sat Aug 26 16:23:16 EDT 2023 % 0.13/0.35 % CPUTime : % 0.21/0.60 ________ _____ % 0.21/0.60 ___ __ \_________(_)________________________________ % 0.21/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.60 % 0.21/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.60 (2023-06-19) % 0.21/0.60 % 0.21/0.60 (c) Philipp Rümmer, 2009-2023 % 0.21/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.60 Amanda Stjerna. % 0.21/0.60 Free software under BSD-3-Clause. % 0.21/0.60 % 0.21/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.60 % 0.21/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.21/0.61 Running up to 7 provers in parallel. % 0.21/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.50/0.91 Prover 4: Preprocessing ... % 1.50/0.91 Prover 1: Preprocessing ... % 2.06/0.95 Prover 3: Preprocessing ... % 2.06/0.95 Prover 5: Preprocessing ... % 2.06/0.95 Prover 0: Preprocessing ... % 2.06/0.95 Prover 2: Preprocessing ... % 2.06/0.95 Prover 6: Preprocessing ... % 2.36/1.02 Prover 5: Proving ... % 2.36/1.02 Prover 2: Proving ... % 2.36/1.04 Prover 6: Proving ... % 2.36/1.04 Prover 1: Constructing countermodel ... % 2.36/1.04 Prover 3: Constructing countermodel ... % 2.82/1.06 Prover 0: Proving ... % 2.82/1.06 Prover 4: Constructing countermodel ... % 4.08/1.23 Prover 3: proved (592ms) % 4.08/1.23 % 4.08/1.23 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 4.08/1.23 % 4.08/1.24 Prover 5: stopped % 4.08/1.24 Prover 2: stopped % 4.08/1.24 Prover 6: stopped % 4.08/1.24 Prover 0: stopped % 4.08/1.25 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 4.08/1.25 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 4.08/1.25 Prover 7: Preprocessing ... % 4.08/1.25 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 4.08/1.25 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 4.08/1.25 Prover 8: Preprocessing ... % 4.08/1.25 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 4.08/1.26 Prover 10: Preprocessing ... % 4.08/1.26 Prover 13: Preprocessing ... % 4.08/1.26 Prover 11: Preprocessing ... % 4.08/1.27 Prover 10: Warning: ignoring some quantifiers % 4.08/1.27 Prover 10: Constructing countermodel ... % 4.08/1.27 Prover 13: Warning: ignoring some quantifiers % 4.08/1.27 Prover 13: Constructing countermodel ... % 4.08/1.27 Prover 7: Warning: ignoring some quantifiers % 4.08/1.27 Prover 7: Constructing countermodel ... % 4.45/1.28 Prover 8: Warning: ignoring some quantifiers % 4.45/1.28 Prover 8: Constructing countermodel ... % 4.45/1.29 Prover 10: gave up % 4.45/1.29 Prover 13: gave up % 4.45/1.30 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 4.45/1.30 Prover 7: gave up % 4.45/1.30 Prover 16: Preprocessing ... % 4.45/1.31 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 4.45/1.31 Prover 16: Warning: ignoring some quantifiers % 4.45/1.31 Prover 16: Constructing countermodel ... % 4.45/1.32 Prover 19: Preprocessing ... % 4.45/1.33 Prover 4: Found proof (size 68) % 4.45/1.33 Prover 4: proved (704ms) % 4.45/1.33 Prover 1: stopped % 4.45/1.33 Prover 8: stopped % 4.45/1.33 Prover 16: stopped % 4.45/1.34 Prover 11: Constructing countermodel ... % 4.45/1.34 Prover 11: stopped % 4.94/1.36 Prover 19: Warning: ignoring some quantifiers % 4.94/1.36 Prover 19: Constructing countermodel ... % 4.94/1.36 Prover 19: stopped % 4.94/1.36 % 4.94/1.36 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 4.94/1.36 % 4.94/1.37 % SZS output start Proof for theBenchmark % 4.94/1.37 Assumptions after simplification: % 4.94/1.37 --------------------------------- % 4.94/1.37 % 4.94/1.37 (prove_this) % 4.94/1.41 ? [v0: $i] : ? [v1: $i] : ? [v2: any] : ? [v3: any] : (equalish(v1, v0) = % 4.94/1.41 v3 & equalish(v0, v1) = v2 & $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: $i] : % 4.94/1.41 ! [v6: $i] : ! [v7: int] : (v7 = 0 | ~ (equalish(v4, v5) = 0) | ~ % 4.94/1.41 (a_member_of(v6, v5) = v7) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ? [v8: % 4.94/1.41 int] : ( ~ (v8 = 0) & a_member_of(v6, v4) = v8)) & ! [v4: $i] : ! [v5: % 4.94/1.41 $i] : ! [v6: $i] : ! [v7: int] : (v7 = 0 | ~ (equalish(v4, v5) = 0) | % 4.94/1.41 ~ (a_member_of(v6, v4) = v7) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ? [v8: % 4.94/1.41 int] : ( ~ (v8 = 0) & a_member_of(v6, v5) = v8)) & ! [v4: $i] : ! [v5: % 4.94/1.41 $i] : ! [v6: int] : (v6 = 0 | ~ (equalish(v4, v5) = v6) | ~ $i(v5) | ~ % 4.94/1.41 $i(v4) | ? [v7: $i] : ? [v8: any] : ? [v9: any] : (a_member_of(v7, v5) % 4.94/1.41 = v9 & a_member_of(v7, v4) = v8 & $i(v7) & ( ~ (v9 = 0) | ~ (v8 = 0)) & % 4.94/1.41 (v9 = 0 | v8 = 0))) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ % 4.94/1.41 (equalish(v4, v5) = 0) | ~ (a_member_of(v6, v5) = 0) | ~ $i(v6) | ~ % 4.94/1.41 $i(v5) | ~ $i(v4) | a_member_of(v6, v4) = 0) & ! [v4: $i] : ! [v5: $i] % 4.94/1.41 : ! [v6: $i] : ( ~ (equalish(v4, v5) = 0) | ~ (a_member_of(v6, v4) = 0) | % 4.94/1.41 ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | a_member_of(v6, v5) = 0) & ((v3 = 0 & % 4.94/1.41 ~ (v2 = 0)) | (v2 = 0 & ~ (v3 = 0)))) % 4.94/1.41 % 4.94/1.41 (function-axioms) % 4.94/1.41 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 4.94/1.41 [v3: $i] : (v1 = v0 | ~ (equalish(v3, v2) = v1) | ~ (equalish(v3, v2) = v0)) % 4.94/1.41 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 4.94/1.41 [v3: $i] : (v1 = v0 | ~ (a_member_of(v3, v2) = v1) | ~ (a_member_of(v3, v2) % 4.94/1.41 = v0)) % 4.94/1.41 % 4.94/1.41 Those formulas are unsatisfiable: % 4.94/1.41 --------------------------------- % 4.94/1.41 % 4.94/1.41 Begin of proof % 4.94/1.42 | % 4.94/1.42 | ALPHA: (function-axioms) implies: % 4.94/1.42 | (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 4.94/1.42 | ! [v3: $i] : (v1 = v0 | ~ (a_member_of(v3, v2) = v1) | ~ % 4.94/1.42 | (a_member_of(v3, v2) = v0)) % 4.94/1.42 | % 4.94/1.42 | DELTA: instantiating (prove_this) with fresh symbols all_3_0, all_3_1, % 4.94/1.42 | all_3_2, all_3_3 gives: % 4.94/1.43 | (2) equalish(all_3_2, all_3_3) = all_3_0 & equalish(all_3_3, all_3_2) = % 4.94/1.43 | all_3_1 & $i(all_3_2) & $i(all_3_3) & ! [v0: $i] : ! [v1: $i] : ! % 4.94/1.43 | [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (equalish(v0, v1) = 0) | ~ % 4.94/1.43 | (a_member_of(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 4.94/1.43 | [v4: int] : ( ~ (v4 = 0) & a_member_of(v2, v0) = v4)) & ! [v0: $i] : % 4.94/1.43 | ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (equalish(v0, % 4.94/1.43 | v1) = 0) | ~ (a_member_of(v2, v0) = v3) | ~ $i(v2) | ~ $i(v1) % 4.94/1.43 | | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & a_member_of(v2, v1) = % 4.94/1.43 | v4)) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 4.94/1.43 | (equalish(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? % 4.94/1.43 | [v4: any] : ? [v5: any] : (a_member_of(v3, v1) = v5 & % 4.94/1.43 | a_member_of(v3, v0) = v4 & $i(v3) & ( ~ (v5 = 0) | ~ (v4 = 0)) & % 4.94/1.43 | (v5 = 0 | v4 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 4.94/1.43 | (equalish(v0, v1) = 0) | ~ (a_member_of(v2, v1) = 0) | ~ $i(v2) | % 4.94/1.43 | ~ $i(v1) | ~ $i(v0) | a_member_of(v2, v0) = 0) & ! [v0: $i] : ! % 4.94/1.43 | [v1: $i] : ! [v2: $i] : ( ~ (equalish(v0, v1) = 0) | ~ % 4.94/1.43 | (a_member_of(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 4.94/1.43 | a_member_of(v2, v1) = 0) & ((all_3_0 = 0 & ~ (all_3_1 = 0)) | % 4.94/1.43 | (all_3_1 = 0 & ~ (all_3_0 = 0))) % 4.94/1.43 | % 4.94/1.43 | ALPHA: (2) implies: % 4.94/1.43 | (3) $i(all_3_3) % 4.94/1.43 | (4) $i(all_3_2) % 4.94/1.43 | (5) equalish(all_3_3, all_3_2) = all_3_1 % 4.94/1.43 | (6) equalish(all_3_2, all_3_3) = all_3_0 % 4.94/1.43 | (7) (all_3_0 = 0 & ~ (all_3_1 = 0)) | (all_3_1 = 0 & ~ (all_3_0 = 0)) % 4.94/1.43 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equalish(v0, % 4.94/1.43 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: any] : % 4.94/1.43 | ? [v5: any] : (a_member_of(v3, v1) = v5 & a_member_of(v3, v0) = v4 & % 4.94/1.43 | $i(v3) & ( ~ (v5 = 0) | ~ (v4 = 0)) & (v5 = 0 | v4 = 0))) % 4.94/1.43 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 4.94/1.43 | (equalish(v0, v1) = 0) | ~ (a_member_of(v2, v0) = v3) | ~ $i(v2) | % 4.94/1.43 | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & a_member_of(v2, % 4.94/1.43 | v1) = v4)) % 4.94/1.43 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 4.94/1.43 | (equalish(v0, v1) = 0) | ~ (a_member_of(v2, v1) = v3) | ~ $i(v2) | % 4.94/1.44 | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & % 4.94/1.44 | a_member_of(v2, v0) = v4)) % 4.94/1.44 | % 4.94/1.44 | GROUND_INST: instantiating (8) with all_3_3, all_3_2, all_3_1, simplifying % 4.94/1.44 | with (3), (4), (5) gives: % 4.94/1.44 | (11) all_3_1 = 0 | ? [v0: $i] : ? [v1: any] : ? [v2: any] : % 4.94/1.44 | (a_member_of(v0, all_3_2) = v2 & a_member_of(v0, all_3_3) = v1 & % 4.94/1.44 | $i(v0) & ( ~ (v2 = 0) | ~ (v1 = 0)) & (v2 = 0 | v1 = 0)) % 4.94/1.44 | % 4.94/1.44 | GROUND_INST: instantiating (8) with all_3_2, all_3_3, all_3_0, simplifying % 4.94/1.44 | with (3), (4), (6) gives: % 4.94/1.44 | (12) all_3_0 = 0 | ? [v0: $i] : ? [v1: any] : ? [v2: any] : % 4.94/1.44 | (a_member_of(v0, all_3_2) = v1 & a_member_of(v0, all_3_3) = v2 & % 4.94/1.44 | $i(v0) & ( ~ (v2 = 0) | ~ (v1 = 0)) & (v2 = 0 | v1 = 0)) % 4.94/1.44 | % 4.94/1.44 | BETA: splitting (7) gives: % 4.94/1.44 | % 4.94/1.44 | Case 1: % 4.94/1.44 | | % 4.94/1.44 | | (13) all_3_0 = 0 & ~ (all_3_1 = 0) % 4.94/1.44 | | % 4.94/1.44 | | ALPHA: (13) implies: % 4.94/1.44 | | (14) all_3_0 = 0 % 4.94/1.44 | | (15) ~ (all_3_1 = 0) % 4.94/1.44 | | % 4.94/1.44 | | REDUCE: (6), (14) imply: % 4.94/1.44 | | (16) equalish(all_3_2, all_3_3) = 0 % 4.94/1.44 | | % 4.94/1.44 | | BETA: splitting (11) gives: % 4.94/1.44 | | % 4.94/1.44 | | Case 1: % 4.94/1.44 | | | % 4.94/1.44 | | | (17) all_3_1 = 0 % 4.94/1.44 | | | % 4.94/1.44 | | | REDUCE: (15), (17) imply: % 4.94/1.44 | | | (18) $false % 4.94/1.44 | | | % 4.94/1.44 | | | CLOSE: (18) is inconsistent. % 4.94/1.44 | | | % 4.94/1.44 | | Case 2: % 4.94/1.44 | | | % 4.94/1.44 | | | (19) ? [v0: $i] : ? [v1: any] : ? [v2: any] : (a_member_of(v0, % 4.94/1.44 | | | all_3_2) = v2 & a_member_of(v0, all_3_3) = v1 & $i(v0) & ( ~ % 4.94/1.44 | | | (v2 = 0) | ~ (v1 = 0)) & (v2 = 0 | v1 = 0)) % 4.94/1.44 | | | % 4.94/1.44 | | | DELTA: instantiating (19) with fresh symbols all_17_0, all_17_1, all_17_2 % 4.94/1.44 | | | gives: % 4.94/1.44 | | | (20) a_member_of(all_17_2, all_3_2) = all_17_0 & a_member_of(all_17_2, % 4.94/1.44 | | | all_3_3) = all_17_1 & $i(all_17_2) & ( ~ (all_17_0 = 0) | ~ % 4.94/1.44 | | | (all_17_1 = 0)) & (all_17_0 = 0 | all_17_1 = 0) % 4.94/1.44 | | | % 4.94/1.44 | | | ALPHA: (20) implies: % 4.94/1.44 | | | (21) $i(all_17_2) % 4.94/1.44 | | | (22) a_member_of(all_17_2, all_3_3) = all_17_1 % 4.94/1.44 | | | (23) a_member_of(all_17_2, all_3_2) = all_17_0 % 4.94/1.45 | | | (24) all_17_0 = 0 | all_17_1 = 0 % 4.94/1.45 | | | (25) ~ (all_17_0 = 0) | ~ (all_17_1 = 0) % 4.94/1.45 | | | % 4.94/1.45 | | | GROUND_INST: instantiating (9) with all_3_2, all_3_3, all_17_2, all_17_0, % 4.94/1.45 | | | simplifying with (3), (4), (16), (21), (23) gives: % 4.94/1.45 | | | (26) all_17_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & a_member_of(all_17_2, % 4.94/1.45 | | | all_3_3) = v0) % 4.94/1.45 | | | % 4.94/1.45 | | | GROUND_INST: instantiating (10) with all_3_2, all_3_3, all_17_2, all_17_1, % 4.94/1.45 | | | simplifying with (3), (4), (16), (21), (22) gives: % 4.94/1.45 | | | (27) all_17_1 = 0 | ? [v0: int] : ( ~ (v0 = 0) & a_member_of(all_17_2, % 4.94/1.45 | | | all_3_2) = v0) % 4.94/1.45 | | | % 4.94/1.45 | | | BETA: splitting (24) gives: % 4.94/1.45 | | | % 4.94/1.45 | | | Case 1: % 4.94/1.45 | | | | % 4.94/1.45 | | | | (28) all_17_0 = 0 % 4.94/1.45 | | | | % 4.94/1.45 | | | | REDUCE: (23), (28) imply: % 4.94/1.45 | | | | (29) a_member_of(all_17_2, all_3_2) = 0 % 4.94/1.45 | | | | % 4.94/1.45 | | | | BETA: splitting (25) gives: % 4.94/1.45 | | | | % 4.94/1.45 | | | | Case 1: % 4.94/1.45 | | | | | % 4.94/1.45 | | | | | (30) ~ (all_17_0 = 0) % 4.94/1.45 | | | | | % 4.94/1.45 | | | | | REDUCE: (28), (30) imply: % 4.94/1.45 | | | | | (31) $false % 4.94/1.45 | | | | | % 4.94/1.45 | | | | | CLOSE: (31) is inconsistent. % 4.94/1.45 | | | | | % 4.94/1.45 | | | | Case 2: % 4.94/1.45 | | | | | % 4.94/1.45 | | | | | (32) ~ (all_17_1 = 0) % 4.94/1.45 | | | | | % 4.94/1.45 | | | | | BETA: splitting (27) gives: % 4.94/1.45 | | | | | % 4.94/1.45 | | | | | Case 1: % 4.94/1.45 | | | | | | % 4.94/1.45 | | | | | | (33) all_17_1 = 0 % 4.94/1.45 | | | | | | % 4.94/1.45 | | | | | | REDUCE: (32), (33) imply: % 4.94/1.45 | | | | | | (34) $false % 4.94/1.45 | | | | | | % 4.94/1.45 | | | | | | CLOSE: (34) is inconsistent. % 4.94/1.45 | | | | | | % 4.94/1.45 | | | | | Case 2: % 4.94/1.45 | | | | | | % 4.94/1.45 | | | | | | (35) ? [v0: int] : ( ~ (v0 = 0) & a_member_of(all_17_2, all_3_2) % 4.94/1.45 | | | | | | = v0) % 4.94/1.45 | | | | | | % 4.94/1.45 | | | | | | DELTA: instantiating (35) with fresh symbol all_34_0 gives: % 4.94/1.45 | | | | | | (36) ~ (all_34_0 = 0) & a_member_of(all_17_2, all_3_2) = % 4.94/1.45 | | | | | | all_34_0 % 4.94/1.45 | | | | | | % 4.94/1.45 | | | | | | ALPHA: (36) implies: % 4.94/1.45 | | | | | | (37) ~ (all_34_0 = 0) % 4.94/1.45 | | | | | | (38) a_member_of(all_17_2, all_3_2) = all_34_0 % 4.94/1.45 | | | | | | % 4.94/1.45 | | | | | | GROUND_INST: instantiating (1) with 0, all_34_0, all_3_2, all_17_2, % 4.94/1.45 | | | | | | simplifying with (29), (38) gives: % 4.94/1.45 | | | | | | (39) all_34_0 = 0 % 4.94/1.45 | | | | | | % 4.94/1.45 | | | | | | REDUCE: (37), (39) imply: % 4.94/1.45 | | | | | | (40) $false % 4.94/1.45 | | | | | | % 4.94/1.45 | | | | | | CLOSE: (40) is inconsistent. % 4.94/1.45 | | | | | | % 4.94/1.45 | | | | | End of split % 4.94/1.45 | | | | | % 4.94/1.45 | | | | End of split % 4.94/1.45 | | | | % 4.94/1.45 | | | Case 2: % 4.94/1.45 | | | | % 4.94/1.45 | | | | (41) all_17_1 = 0 % 4.94/1.45 | | | | (42) ~ (all_17_0 = 0) % 4.94/1.45 | | | | % 4.94/1.45 | | | | REDUCE: (22), (41) imply: % 4.94/1.45 | | | | (43) a_member_of(all_17_2, all_3_3) = 0 % 4.94/1.45 | | | | % 4.94/1.45 | | | | BETA: splitting (26) gives: % 4.94/1.45 | | | | % 4.94/1.45 | | | | Case 1: % 4.94/1.45 | | | | | % 4.94/1.45 | | | | | (44) all_17_0 = 0 % 4.94/1.45 | | | | | % 4.94/1.45 | | | | | REDUCE: (42), (44) imply: % 4.94/1.45 | | | | | (45) $false % 4.94/1.45 | | | | | % 4.94/1.45 | | | | | CLOSE: (45) is inconsistent. % 4.94/1.45 | | | | | % 4.94/1.45 | | | | Case 2: % 4.94/1.45 | | | | | % 4.94/1.45 | | | | | (46) ? [v0: int] : ( ~ (v0 = 0) & a_member_of(all_17_2, all_3_3) = % 4.94/1.45 | | | | | v0) % 4.94/1.45 | | | | | % 4.94/1.45 | | | | | DELTA: instantiating (46) with fresh symbol all_30_0 gives: % 4.94/1.45 | | | | | (47) ~ (all_30_0 = 0) & a_member_of(all_17_2, all_3_3) = all_30_0 % 4.94/1.45 | | | | | % 4.94/1.45 | | | | | ALPHA: (47) implies: % 4.94/1.46 | | | | | (48) ~ (all_30_0 = 0) % 4.94/1.46 | | | | | (49) a_member_of(all_17_2, all_3_3) = all_30_0 % 4.94/1.46 | | | | | % 4.94/1.46 | | | | | GROUND_INST: instantiating (1) with 0, all_30_0, all_3_3, all_17_2, % 4.94/1.46 | | | | | simplifying with (43), (49) gives: % 4.94/1.46 | | | | | (50) all_30_0 = 0 % 4.94/1.46 | | | | | % 4.94/1.46 | | | | | REDUCE: (48), (50) imply: % 4.94/1.46 | | | | | (51) $false % 4.94/1.46 | | | | | % 4.94/1.46 | | | | | CLOSE: (51) is inconsistent. % 4.94/1.46 | | | | | % 4.94/1.46 | | | | End of split % 4.94/1.46 | | | | % 4.94/1.46 | | | End of split % 4.94/1.46 | | | % 4.94/1.46 | | End of split % 4.94/1.46 | | % 4.94/1.46 | Case 2: % 4.94/1.46 | | % 4.94/1.46 | | (52) all_3_1 = 0 & ~ (all_3_0 = 0) % 4.94/1.46 | | % 4.94/1.46 | | ALPHA: (52) implies: % 4.94/1.46 | | (53) all_3_1 = 0 % 4.94/1.46 | | (54) ~ (all_3_0 = 0) % 4.94/1.46 | | % 4.94/1.46 | | REDUCE: (5), (53) imply: % 4.94/1.46 | | (55) equalish(all_3_3, all_3_2) = 0 % 4.94/1.46 | | % 4.94/1.46 | | BETA: splitting (12) gives: % 4.94/1.46 | | % 4.94/1.46 | | Case 1: % 4.94/1.46 | | | % 4.94/1.46 | | | (56) all_3_0 = 0 % 4.94/1.46 | | | % 4.94/1.46 | | | REDUCE: (54), (56) imply: % 4.94/1.46 | | | (57) $false % 4.94/1.46 | | | % 4.94/1.46 | | | CLOSE: (57) is inconsistent. % 4.94/1.46 | | | % 4.94/1.46 | | Case 2: % 4.94/1.46 | | | % 4.94/1.46 | | | (58) ? [v0: $i] : ? [v1: any] : ? [v2: any] : (a_member_of(v0, % 4.94/1.46 | | | all_3_2) = v1 & a_member_of(v0, all_3_3) = v2 & $i(v0) & ( ~ % 4.94/1.46 | | | (v2 = 0) | ~ (v1 = 0)) & (v2 = 0 | v1 = 0)) % 4.94/1.46 | | | % 4.94/1.46 | | | DELTA: instantiating (58) with fresh symbols all_17_0, all_17_1, all_17_2 % 4.94/1.46 | | | gives: % 4.94/1.46 | | | (59) a_member_of(all_17_2, all_3_2) = all_17_1 & a_member_of(all_17_2, % 4.94/1.46 | | | all_3_3) = all_17_0 & $i(all_17_2) & ( ~ (all_17_0 = 0) | ~ % 4.94/1.46 | | | (all_17_1 = 0)) & (all_17_0 = 0 | all_17_1 = 0) % 4.94/1.46 | | | % 4.94/1.46 | | | ALPHA: (59) implies: % 4.94/1.46 | | | (60) $i(all_17_2) % 4.94/1.46 | | | (61) a_member_of(all_17_2, all_3_3) = all_17_0 % 4.94/1.46 | | | (62) a_member_of(all_17_2, all_3_2) = all_17_1 % 4.94/1.46 | | | (63) all_17_0 = 0 | all_17_1 = 0 % 4.94/1.46 | | | (64) ~ (all_17_0 = 0) | ~ (all_17_1 = 0) % 4.94/1.46 | | | % 4.94/1.46 | | | GROUND_INST: instantiating (10) with all_3_3, all_3_2, all_17_2, all_17_1, % 4.94/1.46 | | | simplifying with (3), (4), (55), (60), (62) gives: % 4.94/1.46 | | | (65) all_17_1 = 0 | ? [v0: int] : ( ~ (v0 = 0) & a_member_of(all_17_2, % 4.94/1.46 | | | all_3_3) = v0) % 4.94/1.46 | | | % 4.94/1.46 | | | GROUND_INST: instantiating (9) with all_3_3, all_3_2, all_17_2, all_17_0, % 4.94/1.46 | | | simplifying with (3), (4), (55), (60), (61) gives: % 4.94/1.46 | | | (66) all_17_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & a_member_of(all_17_2, % 4.94/1.46 | | | all_3_2) = v0) % 4.94/1.46 | | | % 4.94/1.46 | | | BETA: splitting (63) gives: % 4.94/1.46 | | | % 4.94/1.46 | | | Case 1: % 4.94/1.46 | | | | % 4.94/1.46 | | | | (67) all_17_0 = 0 % 4.94/1.46 | | | | % 4.94/1.46 | | | | REDUCE: (61), (67) imply: % 4.94/1.46 | | | | (68) a_member_of(all_17_2, all_3_3) = 0 % 4.94/1.46 | | | | % 4.94/1.46 | | | | BETA: splitting (64) gives: % 4.94/1.46 | | | | % 4.94/1.46 | | | | Case 1: % 4.94/1.46 | | | | | % 4.94/1.46 | | | | | (69) ~ (all_17_0 = 0) % 4.94/1.46 | | | | | % 4.94/1.46 | | | | | REDUCE: (67), (69) imply: % 4.94/1.46 | | | | | (70) $false % 4.94/1.46 | | | | | % 4.94/1.46 | | | | | CLOSE: (70) is inconsistent. % 4.94/1.46 | | | | | % 4.94/1.46 | | | | Case 2: % 4.94/1.46 | | | | | % 4.94/1.46 | | | | | (71) ~ (all_17_1 = 0) % 4.94/1.46 | | | | | % 4.94/1.46 | | | | | BETA: splitting (65) gives: % 4.94/1.46 | | | | | % 4.94/1.46 | | | | | Case 1: % 4.94/1.46 | | | | | | % 4.94/1.46 | | | | | | (72) all_17_1 = 0 % 4.94/1.46 | | | | | | % 4.94/1.46 | | | | | | REDUCE: (71), (72) imply: % 4.94/1.46 | | | | | | (73) $false % 4.94/1.47 | | | | | | % 4.94/1.47 | | | | | | CLOSE: (73) is inconsistent. % 4.94/1.47 | | | | | | % 4.94/1.47 | | | | | Case 2: % 4.94/1.47 | | | | | | % 4.94/1.47 | | | | | | (74) ? [v0: int] : ( ~ (v0 = 0) & a_member_of(all_17_2, all_3_3) % 4.94/1.47 | | | | | | = v0) % 4.94/1.47 | | | | | | % 4.94/1.47 | | | | | | DELTA: instantiating (74) with fresh symbol all_34_0 gives: % 4.94/1.47 | | | | | | (75) ~ (all_34_0 = 0) & a_member_of(all_17_2, all_3_3) = % 4.94/1.47 | | | | | | all_34_0 % 4.94/1.47 | | | | | | % 4.94/1.47 | | | | | | ALPHA: (75) implies: % 4.94/1.47 | | | | | | (76) ~ (all_34_0 = 0) % 4.94/1.47 | | | | | | (77) a_member_of(all_17_2, all_3_3) = all_34_0 % 4.94/1.47 | | | | | | % 4.94/1.47 | | | | | | GROUND_INST: instantiating (1) with 0, all_34_0, all_3_3, all_17_2, % 4.94/1.47 | | | | | | simplifying with (68), (77) gives: % 4.94/1.47 | | | | | | (78) all_34_0 = 0 % 4.94/1.47 | | | | | | % 4.94/1.47 | | | | | | REDUCE: (76), (78) imply: % 4.94/1.47 | | | | | | (79) $false % 4.94/1.47 | | | | | | % 4.94/1.47 | | | | | | CLOSE: (79) is inconsistent. % 4.94/1.47 | | | | | | % 4.94/1.47 | | | | | End of split % 4.94/1.47 | | | | | % 4.94/1.47 | | | | End of split % 4.94/1.47 | | | | % 4.94/1.47 | | | Case 2: % 4.94/1.47 | | | | % 4.94/1.47 | | | | (80) all_17_1 = 0 % 4.94/1.47 | | | | (81) ~ (all_17_0 = 0) % 4.94/1.47 | | | | % 4.94/1.47 | | | | REDUCE: (62), (80) imply: % 4.94/1.47 | | | | (82) a_member_of(all_17_2, all_3_2) = 0 % 4.94/1.47 | | | | % 4.94/1.47 | | | | BETA: splitting (66) gives: % 4.94/1.47 | | | | % 4.94/1.47 | | | | Case 1: % 4.94/1.47 | | | | | % 4.94/1.47 | | | | | (83) all_17_0 = 0 % 4.94/1.47 | | | | | % 4.94/1.47 | | | | | REDUCE: (81), (83) imply: % 4.94/1.47 | | | | | (84) $false % 4.94/1.47 | | | | | % 4.94/1.47 | | | | | CLOSE: (84) is inconsistent. % 4.94/1.47 | | | | | % 4.94/1.47 | | | | Case 2: % 4.94/1.47 | | | | | % 4.94/1.47 | | | | | (85) ? [v0: int] : ( ~ (v0 = 0) & a_member_of(all_17_2, all_3_2) = % 4.94/1.47 | | | | | v0) % 4.94/1.47 | | | | | % 4.94/1.47 | | | | | DELTA: instantiating (85) with fresh symbol all_30_0 gives: % 4.94/1.47 | | | | | (86) ~ (all_30_0 = 0) & a_member_of(all_17_2, all_3_2) = all_30_0 % 4.94/1.47 | | | | | % 4.94/1.47 | | | | | ALPHA: (86) implies: % 4.94/1.47 | | | | | (87) ~ (all_30_0 = 0) % 4.94/1.47 | | | | | (88) a_member_of(all_17_2, all_3_2) = all_30_0 % 4.94/1.47 | | | | | % 4.94/1.47 | | | | | GROUND_INST: instantiating (1) with 0, all_30_0, all_3_2, all_17_2, % 4.94/1.47 | | | | | simplifying with (82), (88) gives: % 4.94/1.47 | | | | | (89) all_30_0 = 0 % 4.94/1.47 | | | | | % 4.94/1.47 | | | | | REDUCE: (87), (89) imply: % 4.94/1.47 | | | | | (90) $false % 4.94/1.47 | | | | | % 4.94/1.47 | | | | | CLOSE: (90) is inconsistent. % 4.94/1.47 | | | | | % 4.94/1.47 | | | | End of split % 4.94/1.47 | | | | % 4.94/1.47 | | | End of split % 4.94/1.47 | | | % 4.94/1.47 | | End of split % 4.94/1.47 | | % 4.94/1.47 | End of split % 4.94/1.47 | % 4.94/1.47 End of proof % 5.24/1.47 % SZS output end Proof for theBenchmark % 5.24/1.47 % 5.24/1.47 869ms %------------------------------------------------------------------------------