%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET580+3 : TPTP v8.1.2. Released v2.2.0. % 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 : Thu Aug 31 15:25:23 EDT 2023 % Result : Theorem 6.70s 1.69s % Output : Proof 9.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.11 % Problem : SET580+3 : TPTP v8.1.2. Released v2.2.0. % 0.00/0.11 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.32 % Computer : n021.cluster.edu % 0.12/0.32 % Model : x86_64 x86_64 % 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.32 % Memory : 8042.1875MB % 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.32 % CPULimit : 300 % 0.12/0.32 % WCLimit : 300 % 0.12/0.32 % DateTime : Sat Aug 26 10:13:26 EDT 2023 % 0.12/0.32 % CPUTime : % 0.16/0.57 ________ _____ % 0.16/0.57 ___ __ \_________(_)________________________________ % 0.16/0.57 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.16/0.57 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.16/0.57 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.16/0.57 % 0.16/0.57 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.16/0.57 (2023-06-19) % 0.16/0.57 % 0.16/0.57 (c) Philipp Rümmer, 2009-2023 % 0.16/0.57 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.16/0.58 Amanda Stjerna. % 0.16/0.58 Free software under BSD-3-Clause. % 0.16/0.58 % 0.16/0.58 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.16/0.58 % 0.16/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.16/0.59 Running up to 7 provers in parallel. % 0.16/0.60 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.16/0.60 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.16/0.60 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.16/0.60 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.16/0.60 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.16/0.60 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.16/0.60 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.70/0.96 Prover 1: Preprocessing ... % 1.96/0.96 Prover 4: Preprocessing ... % 1.96/1.00 Prover 0: Preprocessing ... % 1.96/1.00 Prover 3: Preprocessing ... % 1.96/1.00 Prover 5: Preprocessing ... % 1.96/1.00 Prover 2: Preprocessing ... % 1.96/1.00 Prover 6: Preprocessing ... % 3.95/1.30 Prover 3: Warning: ignoring some quantifiers % 3.95/1.30 Prover 1: Warning: ignoring some quantifiers % 3.95/1.31 Prover 4: Warning: ignoring some quantifiers % 3.95/1.31 Prover 6: Proving ... % 3.95/1.31 Prover 5: Proving ... % 3.95/1.32 Prover 4: Constructing countermodel ... % 3.95/1.32 Prover 1: Constructing countermodel ... % 3.95/1.32 Prover 3: Constructing countermodel ... % 3.95/1.33 Prover 0: Proving ... % 4.48/1.35 Prover 2: Proving ... % 4.73/1.53 Prover 3: gave up % 4.73/1.53 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 4.73/1.55 Prover 1: gave up % 4.73/1.56 Prover 7: Preprocessing ... % 4.73/1.58 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 5.97/1.60 Prover 8: Preprocessing ... % 6.19/1.66 Prover 7: Warning: ignoring some quantifiers % 6.19/1.67 Prover 7: Constructing countermodel ... % 6.70/1.68 Prover 8: Warning: ignoring some quantifiers % 6.70/1.69 Prover 0: proved (1092ms) % 6.70/1.69 % 6.70/1.69 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 6.70/1.69 % 6.70/1.70 Prover 8: Constructing countermodel ... % 6.70/1.70 Prover 2: stopped % 6.70/1.70 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 6.70/1.70 Prover 6: stopped % 6.70/1.71 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 6.70/1.71 Prover 5: stopped % 6.70/1.73 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 6.70/1.73 Prover 10: Preprocessing ... % 6.70/1.73 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 6.70/1.74 Prover 11: Preprocessing ... % 6.70/1.74 Prover 13: Preprocessing ... % 6.70/1.75 Prover 16: Preprocessing ... % 7.40/1.79 Prover 8: gave up % 7.52/1.80 Prover 13: Warning: ignoring some quantifiers % 7.52/1.80 Prover 10: Warning: ignoring some quantifiers % 7.52/1.80 Prover 13: Constructing countermodel ... % 7.52/1.80 Prover 10: Constructing countermodel ... % 7.52/1.80 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 7.74/1.83 Prover 19: Preprocessing ... % 7.74/1.85 Prover 10: gave up % 7.74/1.87 Prover 16: Warning: ignoring some quantifiers % 7.74/1.87 Prover 11: Warning: ignoring some quantifiers % 7.74/1.88 Prover 16: Constructing countermodel ... % 7.74/1.88 Prover 11: Constructing countermodel ... % 8.31/1.92 Prover 13: gave up % 8.31/1.93 Prover 19: Warning: ignoring some quantifiers % 8.31/1.93 Prover 19: Constructing countermodel ... % 8.74/1.99 Prover 19: gave up % 8.74/2.01 Prover 4: Found proof (size 141) % 8.74/2.01 Prover 4: proved (1415ms) % 8.74/2.02 Prover 7: Found proof (size 71) % 8.74/2.02 Prover 7: proved (489ms) % 8.74/2.02 Prover 16: stopped % 8.74/2.02 Prover 11: stopped % 8.74/2.02 % 8.74/2.02 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 8.74/2.02 % 9.26/2.06 % SZS output start Proof for theBenchmark % 9.26/2.07 Assumptions after simplification: % 9.26/2.07 --------------------------------- % 9.26/2.07 % 9.26/2.07 (commutativity_of_symmetric_difference) % 9.38/2.11 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (symmetric_difference(v1, v0) = % 9.38/2.11 v2) | ~ $i(v1) | ~ $i(v0) | (symmetric_difference(v0, v1) = v2 & % 9.38/2.11 $i(v2))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 9.38/2.11 (symmetric_difference(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 9.38/2.11 (symmetric_difference(v1, v0) = v2 & $i(v2))) % 9.38/2.11 % 9.38/2.11 (difference_defn) % 9.38/2.12 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 9.38/2.12 | ~ (difference(v0, v1) = v3) | ~ (member(v2, v3) = v4) | ~ $i(v2) | ~ % 9.38/2.12 $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (member(v2, v1) = v6 & % 9.38/2.12 member(v2, v0) = v5 & ( ~ (v5 = 0) | v6 = 0))) & ! [v0: $i] : ! [v1: $i] % 9.38/2.12 : ! [v2: $i] : ! [v3: $i] : ( ~ (difference(v0, v1) = v3) | ~ (member(v2, % 9.38/2.12 v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = % 9.38/2.12 0) & member(v2, v1) = v4 & member(v2, v0) = 0)) % 9.38/2.12 % 9.38/2.12 (prove_th23) % 9.38/2.12 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: any] : ? [v5: % 9.38/2.12 any] : ? [v6: any] : (symmetric_difference(v1, v2) = v3 & member(v0, v3) = % 9.38/2.12 v4 & member(v0, v2) = v6 & member(v0, v1) = v5 & $i(v3) & $i(v2) & $i(v1) & % 9.38/2.12 $i(v0) & ((v4 = 0 & ((v6 = 0 & v5 = 0) | ( ~ (v6 = 0) & ~ (v5 = 0)))) | ( ~ % 9.38/2.12 (v4 = 0) & ((v6 = 0 & ~ (v5 = 0)) | (v5 = 0 & ~ (v6 = 0)))))) % 9.38/2.12 % 9.38/2.12 (symmetric_difference_defn) % 9.38/2.13 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (symmetric_difference(v0, v1) = % 9.38/2.13 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : (difference(v1, % 9.38/2.13 v0) = v4 & difference(v0, v1) = v3 & union(v3, v4) = v2 & $i(v4) & % 9.38/2.13 $i(v3) & $i(v2))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 9.38/2.13 (difference(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: % 9.38/2.13 $i] : (symmetric_difference(v0, v1) = v3 & difference(v0, v1) = v4 & % 9.38/2.13 union(v4, v2) = v3 & $i(v4) & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! % 9.38/2.13 [v2: $i] : ( ~ (difference(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] % 9.38/2.13 : ? [v4: $i] : (symmetric_difference(v0, v1) = v3 & difference(v1, v0) = v4 % 9.38/2.13 & union(v2, v4) = v3 & $i(v4) & $i(v3))) % 9.38/2.13 % 9.38/2.13 (union_defn) % 9.38/2.13 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 9.38/2.14 | ~ (union(v0, v1) = v3) | ~ (member(v2, v3) = v4) | ~ $i(v2) | ~ $i(v1) % 9.38/2.14 | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ( ~ (v6 = 0) & ~ (v5 = 0) & % 9.38/2.14 member(v2, v1) = v6 & member(v2, v0) = v5)) & ! [v0: $i] : ! [v1: $i] : % 9.38/2.14 ! [v2: $i] : ! [v3: $i] : ( ~ (union(v0, v1) = v3) | ~ (member(v2, v3) = 0) % 9.38/2.14 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : % 9.38/2.14 (member(v2, v1) = v5 & member(v2, v0) = v4 & (v5 = 0 | v4 = 0))) % 9.38/2.14 % 9.38/2.14 (function-axioms) % 9.38/2.14 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 9.38/2.14 (symmetric_difference(v3, v2) = v1) | ~ (symmetric_difference(v3, v2) = % 9.38/2.14 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 9.38/2.14 ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : % 9.38/2.14 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | % 9.38/2.14 ~ (union(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 9.38/2.14 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (member(v3, % 9.38/2.14 v2) = v1) | ~ (member(v3, v2) = v0)) % 9.38/2.14 % 9.38/2.14 Further assumptions not needed in the proof: % 9.38/2.14 -------------------------------------------- % 9.38/2.14 commutativity_of_union, equal_member_defn % 9.38/2.14 % 9.38/2.14 Those formulas are unsatisfiable: % 9.38/2.14 --------------------------------- % 9.38/2.14 % 9.38/2.14 Begin of proof % 9.38/2.14 | % 9.38/2.14 | ALPHA: (union_defn) implies: % 9.38/2.15 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (union(v0, % 9.38/2.15 | v1) = v3) | ~ (member(v2, v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~ % 9.38/2.15 | $i(v0) | ? [v4: any] : ? [v5: any] : (member(v2, v1) = v5 & % 9.38/2.15 | member(v2, v0) = v4 & (v5 = 0 | v4 = 0))) % 9.38/2.15 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 9.38/2.15 | (v4 = 0 | ~ (union(v0, v1) = v3) | ~ (member(v2, v3) = v4) | ~ % 9.38/2.15 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ( ~ % 9.38/2.15 | (v6 = 0) & ~ (v5 = 0) & member(v2, v1) = v6 & member(v2, v0) = % 9.38/2.15 | v5)) % 9.38/2.15 | % 9.38/2.15 | ALPHA: (difference_defn) implies: % 9.38/2.15 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 9.38/2.15 | (difference(v0, v1) = v3) | ~ (member(v2, v3) = 0) | ~ $i(v2) | ~ % 9.38/2.15 | $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & member(v2, v1) = % 9.38/2.15 | v4 & member(v2, v0) = 0)) % 9.38/2.16 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 9.38/2.16 | (v4 = 0 | ~ (difference(v0, v1) = v3) | ~ (member(v2, v3) = v4) | ~ % 9.38/2.16 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : % 9.38/2.16 | (member(v2, v1) = v6 & member(v2, v0) = v5 & ( ~ (v5 = 0) | v6 = 0))) % 9.38/2.16 | % 9.38/2.16 | ALPHA: (symmetric_difference_defn) implies: % 9.38/2.16 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (difference(v0, v1) = v2) % 9.38/2.16 | | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : % 9.38/2.16 | (symmetric_difference(v0, v1) = v3 & difference(v1, v0) = v4 & % 9.38/2.16 | union(v2, v4) = v3 & $i(v4) & $i(v3))) % 9.38/2.16 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (difference(v1, v0) = v2) % 9.38/2.16 | | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : % 9.38/2.16 | (symmetric_difference(v0, v1) = v3 & difference(v0, v1) = v4 & % 9.38/2.16 | union(v4, v2) = v3 & $i(v4) & $i(v3))) % 9.38/2.16 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (symmetric_difference(v0, % 9.38/2.16 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : % 9.38/2.16 | (difference(v1, v0) = v4 & difference(v0, v1) = v3 & union(v3, v4) = % 9.38/2.16 | v2 & $i(v4) & $i(v3) & $i(v2))) % 9.38/2.16 | % 9.38/2.16 | ALPHA: (commutativity_of_symmetric_difference) implies: % 9.38/2.16 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (symmetric_difference(v1, % 9.38/2.16 | v0) = v2) | ~ $i(v1) | ~ $i(v0) | (symmetric_difference(v0, v1) % 9.38/2.16 | = v2 & $i(v2))) % 9.38/2.16 | % 9.38/2.16 | ALPHA: (function-axioms) implies: % 9.38/2.17 | (9) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 9.38/2.17 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) % 9.38/2.17 | = v0)) % 9.38/2.17 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 9.38/2.17 | (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) % 9.38/2.17 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 9.38/2.17 | (symmetric_difference(v3, v2) = v1) | ~ (symmetric_difference(v3, % 9.38/2.17 | v2) = v0)) % 9.38/2.17 | % 9.38/2.17 | DELTA: instantiating (prove_th23) with fresh symbols all_9_0, all_9_1, % 9.38/2.17 | all_9_2, all_9_3, all_9_4, all_9_5, all_9_6 gives: % 9.38/2.17 | (12) symmetric_difference(all_9_5, all_9_4) = all_9_3 & member(all_9_6, % 9.38/2.17 | all_9_3) = all_9_2 & member(all_9_6, all_9_4) = all_9_0 & % 9.38/2.17 | member(all_9_6, all_9_5) = all_9_1 & $i(all_9_3) & $i(all_9_4) & % 9.38/2.17 | $i(all_9_5) & $i(all_9_6) & ((all_9_2 = 0 & ((all_9_0 = 0 & all_9_1 = % 9.38/2.17 | 0) | ( ~ (all_9_0 = 0) & ~ (all_9_1 = 0)))) | ( ~ (all_9_2 = % 9.38/2.17 | 0) & ((all_9_0 = 0 & ~ (all_9_1 = 0)) | (all_9_1 = 0 & ~ % 9.38/2.17 | (all_9_0 = 0))))) % 9.38/2.17 | % 9.38/2.17 | ALPHA: (12) implies: % 9.38/2.17 | (13) $i(all_9_6) % 9.38/2.17 | (14) $i(all_9_5) % 9.38/2.17 | (15) $i(all_9_4) % 9.38/2.17 | (16) member(all_9_6, all_9_5) = all_9_1 % 9.38/2.17 | (17) member(all_9_6, all_9_4) = all_9_0 % 9.38/2.17 | (18) member(all_9_6, all_9_3) = all_9_2 % 9.38/2.17 | (19) symmetric_difference(all_9_5, all_9_4) = all_9_3 % 9.38/2.17 | (20) (all_9_2 = 0 & ((all_9_0 = 0 & all_9_1 = 0) | ( ~ (all_9_0 = 0) & ~ % 9.38/2.17 | (all_9_1 = 0)))) | ( ~ (all_9_2 = 0) & ((all_9_0 = 0 & ~ % 9.38/2.17 | (all_9_1 = 0)) | (all_9_1 = 0 & ~ (all_9_0 = 0)))) % 9.38/2.17 | % 9.38/2.18 | GROUND_INST: instantiating (8) with all_9_4, all_9_5, all_9_3, simplifying % 9.38/2.18 | with (14), (15), (19) gives: % 9.38/2.18 | (21) symmetric_difference(all_9_4, all_9_5) = all_9_3 & $i(all_9_3) % 9.38/2.18 | % 9.38/2.18 | ALPHA: (21) implies: % 9.38/2.18 | (22) symmetric_difference(all_9_4, all_9_5) = all_9_3 % 9.38/2.18 | % 9.38/2.18 | GROUND_INST: instantiating (7) with all_9_5, all_9_4, all_9_3, simplifying % 9.38/2.18 | with (14), (15), (19) gives: % 9.38/2.18 | (23) ? [v0: $i] : ? [v1: $i] : (difference(all_9_4, all_9_5) = v1 & % 9.38/2.18 | difference(all_9_5, all_9_4) = v0 & union(v0, v1) = all_9_3 & $i(v1) % 9.38/2.18 | & $i(v0) & $i(all_9_3)) % 9.38/2.18 | % 9.38/2.18 | DELTA: instantiating (23) with fresh symbols all_17_0, all_17_1 gives: % 9.38/2.18 | (24) difference(all_9_4, all_9_5) = all_17_0 & difference(all_9_5, all_9_4) % 9.38/2.18 | = all_17_1 & union(all_17_1, all_17_0) = all_9_3 & $i(all_17_0) & % 9.38/2.18 | $i(all_17_1) & $i(all_9_3) % 9.38/2.18 | % 9.38/2.18 | ALPHA: (24) implies: % 9.38/2.18 | (25) $i(all_17_1) % 9.38/2.18 | (26) $i(all_17_0) % 9.38/2.18 | (27) union(all_17_1, all_17_0) = all_9_3 % 9.38/2.18 | (28) difference(all_9_5, all_9_4) = all_17_1 % 9.38/2.18 | (29) difference(all_9_4, all_9_5) = all_17_0 % 9.38/2.18 | % 9.38/2.18 | GROUND_INST: instantiating (2) with all_17_1, all_17_0, all_9_6, all_9_3, % 9.38/2.18 | all_9_2, simplifying with (13), (18), (25), (26), (27) gives: % 9.38/2.18 | (30) all_9_2 = 0 | ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = 0) % 9.38/2.18 | & member(all_9_6, all_17_0) = v1 & member(all_9_6, all_17_1) = v0) % 9.38/2.18 | % 9.38/2.19 | GROUND_INST: instantiating (6) with all_9_4, all_9_5, all_17_1, simplifying % 9.38/2.19 | with (14), (15), (28) gives: % 9.38/2.19 | (31) ? [v0: $i] : ? [v1: $i] : (symmetric_difference(all_9_4, all_9_5) = % 9.38/2.19 | v0 & difference(all_9_4, all_9_5) = v1 & union(v1, all_17_1) = v0 & % 9.38/2.19 | $i(v1) & $i(v0)) % 9.38/2.19 | % 9.38/2.19 | GROUND_INST: instantiating (5) with all_9_4, all_9_5, all_17_0, simplifying % 9.38/2.19 | with (14), (15), (29) gives: % 9.38/2.19 | (32) ? [v0: $i] : ? [v1: $i] : (symmetric_difference(all_9_4, all_9_5) = % 9.38/2.19 | v0 & difference(all_9_5, all_9_4) = v1 & union(all_17_0, v1) = v0 & % 9.38/2.19 | $i(v1) & $i(v0)) % 9.38/2.19 | % 9.38/2.19 | GROUND_INST: instantiating (7) with all_9_4, all_9_5, all_9_3, simplifying % 9.38/2.19 | with (14), (15), (22) gives: % 9.38/2.19 | (33) ? [v0: $i] : ? [v1: $i] : (difference(all_9_4, all_9_5) = v0 & % 9.38/2.19 | difference(all_9_5, all_9_4) = v1 & union(v0, v1) = all_9_3 & $i(v1) % 9.38/2.19 | & $i(v0) & $i(all_9_3)) % 9.38/2.19 | % 9.38/2.19 | DELTA: instantiating (32) with fresh symbols all_25_0, all_25_1 gives: % 9.38/2.19 | (34) symmetric_difference(all_9_4, all_9_5) = all_25_1 & % 9.38/2.19 | difference(all_9_5, all_9_4) = all_25_0 & union(all_17_0, all_25_0) = % 9.38/2.19 | all_25_1 & $i(all_25_0) & $i(all_25_1) % 9.38/2.19 | % 9.38/2.19 | ALPHA: (34) implies: % 9.38/2.19 | (35) $i(all_25_0) % 9.38/2.19 | (36) union(all_17_0, all_25_0) = all_25_1 % 9.38/2.19 | (37) difference(all_9_5, all_9_4) = all_25_0 % 9.38/2.19 | (38) symmetric_difference(all_9_4, all_9_5) = all_25_1 % 9.38/2.19 | % 9.38/2.19 | DELTA: instantiating (31) with fresh symbols all_27_0, all_27_1 gives: % 9.38/2.19 | (39) symmetric_difference(all_9_4, all_9_5) = all_27_1 & % 9.38/2.19 | difference(all_9_4, all_9_5) = all_27_0 & union(all_27_0, all_17_1) = % 9.38/2.19 | all_27_1 & $i(all_27_0) & $i(all_27_1) % 9.38/2.19 | % 9.38/2.19 | ALPHA: (39) implies: % 9.38/2.20 | (40) $i(all_27_0) % 9.38/2.20 | (41) difference(all_9_4, all_9_5) = all_27_0 % 9.38/2.20 | (42) symmetric_difference(all_9_4, all_9_5) = all_27_1 % 9.38/2.20 | % 9.38/2.20 | DELTA: instantiating (33) with fresh symbols all_29_0, all_29_1 gives: % 9.38/2.20 | (43) difference(all_9_4, all_9_5) = all_29_1 & difference(all_9_5, all_9_4) % 9.38/2.20 | = all_29_0 & union(all_29_1, all_29_0) = all_9_3 & $i(all_29_0) & % 9.38/2.20 | $i(all_29_1) & $i(all_9_3) % 9.38/2.20 | % 9.38/2.20 | ALPHA: (43) implies: % 9.38/2.20 | (44) difference(all_9_5, all_9_4) = all_29_0 % 9.38/2.20 | (45) difference(all_9_4, all_9_5) = all_29_1 % 9.38/2.20 | % 9.38/2.20 | GROUND_INST: instantiating (10) with all_17_1, all_29_0, all_9_4, all_9_5, % 9.38/2.20 | simplifying with (28), (44) gives: % 9.38/2.20 | (46) all_29_0 = all_17_1 % 9.38/2.20 | % 9.38/2.20 | GROUND_INST: instantiating (10) with all_25_0, all_29_0, all_9_4, all_9_5, % 9.38/2.20 | simplifying with (37), (44) gives: % 9.38/2.20 | (47) all_29_0 = all_25_0 % 9.38/2.20 | % 9.38/2.20 | GROUND_INST: instantiating (10) with all_17_0, all_29_1, all_9_5, all_9_4, % 9.38/2.20 | simplifying with (29), (45) gives: % 9.38/2.20 | (48) all_29_1 = all_17_0 % 9.38/2.20 | % 9.38/2.20 | GROUND_INST: instantiating (10) with all_27_0, all_29_1, all_9_5, all_9_4, % 9.38/2.20 | simplifying with (41), (45) gives: % 9.38/2.20 | (49) all_29_1 = all_27_0 % 9.38/2.20 | % 9.38/2.20 | GROUND_INST: instantiating (11) with all_9_3, all_27_1, all_9_5, all_9_4, % 9.38/2.20 | simplifying with (22), (42) gives: % 9.38/2.20 | (50) all_27_1 = all_9_3 % 9.38/2.20 | % 9.38/2.20 | GROUND_INST: instantiating (11) with all_25_1, all_27_1, all_9_5, all_9_4, % 9.38/2.20 | simplifying with (38), (42) gives: % 9.38/2.20 | (51) all_27_1 = all_25_1 % 9.38/2.20 | % 9.38/2.20 | COMBINE_EQS: (46), (47) imply: % 9.38/2.20 | (52) all_25_0 = all_17_1 % 9.38/2.20 | % 9.38/2.20 | SIMP: (52) implies: % 9.38/2.20 | (53) all_25_0 = all_17_1 % 9.38/2.20 | % 9.38/2.20 | COMBINE_EQS: (48), (49) imply: % 9.38/2.20 | (54) all_27_0 = all_17_0 % 9.38/2.20 | % 9.38/2.20 | SIMP: (54) implies: % 9.38/2.21 | (55) all_27_0 = all_17_0 % 9.38/2.21 | % 9.38/2.21 | COMBINE_EQS: (50), (51) imply: % 9.38/2.21 | (56) all_25_1 = all_9_3 % 9.38/2.21 | % 9.38/2.21 | SIMP: (56) implies: % 9.38/2.21 | (57) all_25_1 = all_9_3 % 9.38/2.21 | % 9.38/2.21 | REDUCE: (36), (53), (57) imply: % 9.38/2.21 | (58) union(all_17_0, all_17_1) = all_9_3 % 9.38/2.21 | % 9.38/2.21 | GROUND_INST: instantiating (2) with all_17_0, all_17_1, all_9_6, all_9_3, % 9.38/2.21 | all_9_2, simplifying with (13), (18), (25), (26), (58) gives: % 9.38/2.21 | (59) all_9_2 = 0 | ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = 0) % 9.38/2.21 | & member(all_9_6, all_17_0) = v0 & member(all_9_6, all_17_1) = v1) % 9.38/2.21 | % 9.38/2.21 | BETA: splitting (20) gives: % 9.38/2.21 | % 9.38/2.21 | Case 1: % 9.38/2.21 | | % 9.38/2.21 | | (60) all_9_2 = 0 & ((all_9_0 = 0 & all_9_1 = 0) | ( ~ (all_9_0 = 0) & ~ % 9.38/2.21 | | (all_9_1 = 0))) % 9.38/2.21 | | % 9.38/2.21 | | ALPHA: (60) implies: % 9.38/2.21 | | (61) all_9_2 = 0 % 9.38/2.21 | | (62) (all_9_0 = 0 & all_9_1 = 0) | ( ~ (all_9_0 = 0) & ~ (all_9_1 = 0)) % 9.38/2.21 | | % 9.38/2.21 | | REDUCE: (18), (61) imply: % 9.38/2.21 | | (63) member(all_9_6, all_9_3) = 0 % 9.38/2.21 | | % 9.38/2.21 | | GROUND_INST: instantiating (1) with all_17_0, all_17_1, all_9_6, all_9_3, % 9.38/2.21 | | simplifying with (13), (25), (26), (58), (63) gives: % 9.38/2.21 | | (64) ? [v0: any] : ? [v1: any] : (member(all_9_6, all_17_0) = v0 & % 9.38/2.22 | | member(all_9_6, all_17_1) = v1 & (v1 = 0 | v0 = 0)) % 9.38/2.22 | | % 9.38/2.22 | | GROUND_INST: instantiating (1) with all_17_1, all_17_0, all_9_6, all_9_3, % 9.38/2.22 | | simplifying with (13), (25), (26), (27), (63) gives: % 9.38/2.22 | | (65) ? [v0: any] : ? [v1: any] : (member(all_9_6, all_17_0) = v1 & % 9.38/2.22 | | member(all_9_6, all_17_1) = v0 & (v1 = 0 | v0 = 0)) % 9.38/2.22 | | % 9.38/2.22 | | DELTA: instantiating (65) with fresh symbols all_54_0, all_54_1 gives: % 9.38/2.22 | | (66) member(all_9_6, all_17_0) = all_54_0 & member(all_9_6, all_17_1) = % 9.38/2.22 | | all_54_1 & (all_54_0 = 0 | all_54_1 = 0) % 9.38/2.22 | | % 9.38/2.22 | | ALPHA: (66) implies: % 9.38/2.22 | | (67) member(all_9_6, all_17_1) = all_54_1 % 9.38/2.22 | | (68) member(all_9_6, all_17_0) = all_54_0 % 9.38/2.22 | | (69) all_54_0 = 0 | all_54_1 = 0 % 9.38/2.22 | | % 9.38/2.22 | | DELTA: instantiating (64) with fresh symbols all_56_0, all_56_1 gives: % 9.38/2.22 | | (70) member(all_9_6, all_17_0) = all_56_1 & member(all_9_6, all_17_1) = % 9.38/2.22 | | all_56_0 & (all_56_0 = 0 | all_56_1 = 0) % 9.38/2.22 | | % 9.38/2.22 | | ALPHA: (70) implies: % 9.38/2.22 | | (71) member(all_9_6, all_17_1) = all_56_0 % 9.38/2.22 | | (72) member(all_9_6, all_17_0) = all_56_1 % 9.38/2.22 | | % 9.38/2.22 | | GROUND_INST: instantiating (9) with all_54_1, all_56_0, all_17_1, all_9_6, % 9.38/2.22 | | simplifying with (67), (71) gives: % 9.38/2.22 | | (73) all_56_0 = all_54_1 % 9.38/2.22 | | % 9.38/2.22 | | GROUND_INST: instantiating (9) with all_54_0, all_56_1, all_17_0, all_9_6, % 9.38/2.22 | | simplifying with (68), (72) gives: % 9.38/2.22 | | (74) all_56_1 = all_54_0 % 9.38/2.22 | | % 9.38/2.22 | | BETA: splitting (62) gives: % 9.38/2.22 | | % 9.38/2.22 | | Case 1: % 9.38/2.22 | | | % 9.38/2.23 | | | (75) all_9_0 = 0 & all_9_1 = 0 % 9.38/2.23 | | | % 9.38/2.23 | | | ALPHA: (75) implies: % 9.38/2.23 | | | (76) all_9_1 = 0 % 9.38/2.23 | | | (77) all_9_0 = 0 % 9.38/2.23 | | | % 9.38/2.23 | | | REDUCE: (17), (77) imply: % 9.38/2.23 | | | (78) member(all_9_6, all_9_4) = 0 % 9.38/2.23 | | | % 9.38/2.23 | | | REDUCE: (16), (76) imply: % 9.38/2.23 | | | (79) member(all_9_6, all_9_5) = 0 % 9.38/2.23 | | | % 9.38/2.23 | | | BETA: splitting (69) gives: % 9.38/2.23 | | | % 9.38/2.23 | | | Case 1: % 9.38/2.23 | | | | % 9.38/2.23 | | | | (80) all_54_0 = 0 % 9.38/2.23 | | | | % 9.38/2.23 | | | | REDUCE: (68), (80) imply: % 9.38/2.23 | | | | (81) member(all_9_6, all_17_0) = 0 % 9.38/2.23 | | | | % 9.38/2.23 | | | | GROUND_INST: instantiating (3) with all_9_4, all_9_5, all_9_6, all_17_0, % 9.38/2.23 | | | | simplifying with (13), (14), (15), (29), (81) gives: % 9.38/2.23 | | | | (82) ? [v0: int] : ( ~ (v0 = 0) & member(all_9_6, all_9_4) = 0 & % 9.38/2.23 | | | | member(all_9_6, all_9_5) = v0) % 9.38/2.23 | | | | % 9.38/2.23 | | | | DELTA: instantiating (82) with fresh symbol all_88_0 gives: % 9.38/2.23 | | | | (83) ~ (all_88_0 = 0) & member(all_9_6, all_9_4) = 0 & % 9.38/2.23 | | | | member(all_9_6, all_9_5) = all_88_0 % 9.38/2.23 | | | | % 9.38/2.23 | | | | ALPHA: (83) implies: % 9.38/2.23 | | | | (84) ~ (all_88_0 = 0) % 9.38/2.23 | | | | (85) member(all_9_6, all_9_5) = all_88_0 % 9.38/2.23 | | | | % 9.38/2.23 | | | | GROUND_INST: instantiating (9) with 0, all_88_0, all_9_5, all_9_6, % 9.38/2.23 | | | | simplifying with (79), (85) gives: % 9.38/2.23 | | | | (86) all_88_0 = 0 % 9.38/2.23 | | | | % 9.38/2.23 | | | | REDUCE: (84), (86) imply: % 9.38/2.23 | | | | (87) $false % 9.38/2.23 | | | | % 9.38/2.23 | | | | CLOSE: (87) is inconsistent. % 9.38/2.23 | | | | % 9.38/2.23 | | | Case 2: % 9.38/2.23 | | | | % 9.38/2.23 | | | | (88) all_54_1 = 0 % 9.38/2.23 | | | | % 9.38/2.23 | | | | REDUCE: (67), (88) imply: % 9.38/2.23 | | | | (89) member(all_9_6, all_17_1) = 0 % 9.38/2.23 | | | | % 9.38/2.24 | | | | GROUND_INST: instantiating (3) with all_9_5, all_9_4, all_9_6, all_17_1, % 9.38/2.24 | | | | simplifying with (13), (14), (15), (28), (89) gives: % 9.38/2.24 | | | | (90) ? [v0: int] : ( ~ (v0 = 0) & member(all_9_6, all_9_4) = v0 & % 9.38/2.24 | | | | member(all_9_6, all_9_5) = 0) % 9.38/2.24 | | | | % 9.38/2.24 | | | | DELTA: instantiating (90) with fresh symbol all_88_0 gives: % 9.38/2.24 | | | | (91) ~ (all_88_0 = 0) & member(all_9_6, all_9_4) = all_88_0 & % 9.38/2.24 | | | | member(all_9_6, all_9_5) = 0 % 9.38/2.24 | | | | % 9.38/2.24 | | | | ALPHA: (91) implies: % 9.38/2.24 | | | | (92) ~ (all_88_0 = 0) % 9.38/2.24 | | | | (93) member(all_9_6, all_9_4) = all_88_0 % 9.38/2.24 | | | | % 9.38/2.24 | | | | GROUND_INST: instantiating (9) with 0, all_88_0, all_9_4, all_9_6, % 9.38/2.24 | | | | simplifying with (78), (93) gives: % 9.38/2.24 | | | | (94) all_88_0 = 0 % 9.38/2.24 | | | | % 9.38/2.24 | | | | REDUCE: (92), (94) imply: % 9.38/2.24 | | | | (95) $false % 9.38/2.24 | | | | % 9.38/2.24 | | | | CLOSE: (95) is inconsistent. % 9.38/2.24 | | | | % 9.38/2.24 | | | End of split % 9.38/2.24 | | | % 9.38/2.24 | | Case 2: % 9.38/2.24 | | | % 9.38/2.24 | | | (96) ~ (all_9_0 = 0) & ~ (all_9_1 = 0) % 9.38/2.24 | | | % 9.38/2.24 | | | ALPHA: (96) implies: % 9.38/2.24 | | | (97) ~ (all_9_1 = 0) % 9.38/2.24 | | | (98) ~ (all_9_0 = 0) % 9.38/2.24 | | | % 9.38/2.24 | | | BETA: splitting (69) gives: % 9.38/2.24 | | | % 9.38/2.24 | | | Case 1: % 9.38/2.24 | | | | % 9.38/2.24 | | | | (99) all_54_0 = 0 % 9.38/2.24 | | | | % 9.38/2.24 | | | | REDUCE: (68), (99) imply: % 9.38/2.24 | | | | (100) member(all_9_6, all_17_0) = 0 % 9.38/2.24 | | | | % 9.38/2.24 | | | | GROUND_INST: instantiating (3) with all_9_4, all_9_5, all_9_6, all_17_0, % 9.38/2.24 | | | | simplifying with (13), (14), (15), (29), (100) gives: % 9.38/2.24 | | | | (101) ? [v0: int] : ( ~ (v0 = 0) & member(all_9_6, all_9_4) = 0 & % 9.38/2.24 | | | | member(all_9_6, all_9_5) = v0) % 9.38/2.24 | | | | % 9.38/2.24 | | | | DELTA: instantiating (101) with fresh symbol all_88_0 gives: % 9.38/2.24 | | | | (102) ~ (all_88_0 = 0) & member(all_9_6, all_9_4) = 0 & % 9.38/2.24 | | | | member(all_9_6, all_9_5) = all_88_0 % 9.38/2.24 | | | | % 9.38/2.24 | | | | ALPHA: (102) implies: % 9.38/2.24 | | | | (103) member(all_9_6, all_9_4) = 0 % 9.38/2.24 | | | | % 9.38/2.24 | | | | GROUND_INST: instantiating (9) with all_9_0, 0, all_9_4, all_9_6, % 9.38/2.24 | | | | simplifying with (17), (103) gives: % 9.38/2.24 | | | | (104) all_9_0 = 0 % 9.38/2.24 | | | | % 9.38/2.24 | | | | REDUCE: (98), (104) imply: % 9.38/2.24 | | | | (105) $false % 9.38/2.24 | | | | % 9.38/2.24 | | | | CLOSE: (105) is inconsistent. % 9.38/2.24 | | | | % 9.38/2.24 | | | Case 2: % 9.38/2.24 | | | | % 9.38/2.24 | | | | (106) all_54_1 = 0 % 9.38/2.24 | | | | % 9.38/2.24 | | | | REDUCE: (67), (106) imply: % 9.38/2.24 | | | | (107) member(all_9_6, all_17_1) = 0 % 9.38/2.24 | | | | % 9.38/2.25 | | | | GROUND_INST: instantiating (3) with all_9_5, all_9_4, all_9_6, all_17_1, % 9.38/2.25 | | | | simplifying with (13), (14), (15), (28), (107) gives: % 9.38/2.25 | | | | (108) ? [v0: int] : ( ~ (v0 = 0) & member(all_9_6, all_9_4) = v0 & % 9.38/2.25 | | | | member(all_9_6, all_9_5) = 0) % 9.38/2.25 | | | | % 9.38/2.25 | | | | DELTA: instantiating (108) with fresh symbol all_88_0 gives: % 9.38/2.25 | | | | (109) ~ (all_88_0 = 0) & member(all_9_6, all_9_4) = all_88_0 & % 9.38/2.25 | | | | member(all_9_6, all_9_5) = 0 % 9.38/2.25 | | | | % 9.38/2.25 | | | | ALPHA: (109) implies: % 9.38/2.25 | | | | (110) member(all_9_6, all_9_5) = 0 % 9.38/2.25 | | | | % 9.38/2.25 | | | | GROUND_INST: instantiating (9) with all_9_1, 0, all_9_5, all_9_6, % 9.38/2.25 | | | | simplifying with (16), (110) gives: % 9.38/2.25 | | | | (111) all_9_1 = 0 % 9.38/2.25 | | | | % 9.38/2.25 | | | | REDUCE: (97), (111) imply: % 9.38/2.25 | | | | (112) $false % 9.38/2.25 | | | | % 9.38/2.25 | | | | CLOSE: (112) is inconsistent. % 9.38/2.25 | | | | % 9.38/2.25 | | | End of split % 9.38/2.25 | | | % 9.38/2.25 | | End of split % 9.38/2.25 | | % 9.38/2.25 | Case 2: % 9.38/2.25 | | % 9.38/2.25 | | (113) ~ (all_9_2 = 0) & ((all_9_0 = 0 & ~ (all_9_1 = 0)) | (all_9_1 = 0 % 9.38/2.25 | | & ~ (all_9_0 = 0))) % 9.38/2.25 | | % 9.38/2.25 | | ALPHA: (113) implies: % 9.38/2.25 | | (114) ~ (all_9_2 = 0) % 9.38/2.25 | | (115) (all_9_0 = 0 & ~ (all_9_1 = 0)) | (all_9_1 = 0 & ~ (all_9_0 = 0)) % 9.38/2.25 | | % 9.38/2.25 | | BETA: splitting (30) gives: % 9.38/2.25 | | % 9.38/2.25 | | Case 1: % 9.38/2.25 | | | % 9.38/2.25 | | | (116) all_9_2 = 0 % 9.38/2.25 | | | % 9.38/2.25 | | | REDUCE: (114), (116) imply: % 9.38/2.25 | | | (117) $false % 9.38/2.25 | | | % 9.38/2.25 | | | CLOSE: (117) is inconsistent. % 9.38/2.25 | | | % 9.38/2.25 | | Case 2: % 9.38/2.25 | | | % 9.38/2.25 | | | (118) ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = 0) & % 9.38/2.25 | | | member(all_9_6, all_17_0) = v1 & member(all_9_6, all_17_1) = % 9.38/2.25 | | | v0) % 9.38/2.25 | | | % 9.38/2.25 | | | DELTA: instantiating (118) with fresh symbols all_53_0, all_53_1 gives: % 9.38/2.25 | | | (119) ~ (all_53_0 = 0) & ~ (all_53_1 = 0) & member(all_9_6, all_17_0) % 9.38/2.25 | | | = all_53_0 & member(all_9_6, all_17_1) = all_53_1 % 9.38/2.25 | | | % 9.38/2.25 | | | ALPHA: (119) implies: % 9.38/2.25 | | | (120) member(all_9_6, all_17_1) = all_53_1 % 9.38/2.25 | | | (121) member(all_9_6, all_17_0) = all_53_0 % 9.38/2.25 | | | % 9.38/2.25 | | | BETA: splitting (59) gives: % 9.38/2.25 | | | % 9.38/2.25 | | | Case 1: % 9.38/2.25 | | | | % 9.38/2.25 | | | | (122) all_9_2 = 0 % 9.38/2.25 | | | | % 9.38/2.25 | | | | REDUCE: (114), (122) imply: % 9.38/2.25 | | | | (123) $false % 9.38/2.25 | | | | % 9.38/2.25 | | | | CLOSE: (123) is inconsistent. % 9.38/2.25 | | | | % 9.38/2.25 | | | Case 2: % 9.38/2.25 | | | | % 9.38/2.25 | | | | (124) ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = 0) & % 9.38/2.25 | | | | member(all_9_6, all_17_0) = v0 & member(all_9_6, all_17_1) = % 9.38/2.25 | | | | v1) % 9.38/2.25 | | | | % 9.38/2.25 | | | | DELTA: instantiating (124) with fresh symbols all_58_0, all_58_1 gives: % 9.38/2.25 | | | | (125) ~ (all_58_0 = 0) & ~ (all_58_1 = 0) & member(all_9_6, % 9.38/2.25 | | | | all_17_0) = all_58_1 & member(all_9_6, all_17_1) = all_58_0 % 9.38/2.26 | | | | % 9.38/2.26 | | | | ALPHA: (125) implies: % 9.38/2.26 | | | | (126) ~ (all_58_1 = 0) % 9.38/2.26 | | | | (127) ~ (all_58_0 = 0) % 9.38/2.26 | | | | (128) member(all_9_6, all_17_1) = all_58_0 % 9.38/2.26 | | | | (129) member(all_9_6, all_17_0) = all_58_1 % 9.38/2.26 | | | | % 9.38/2.26 | | | | GROUND_INST: instantiating (9) with all_53_1, all_58_0, all_17_1, % 9.38/2.26 | | | | all_9_6, simplifying with (120), (128) gives: % 9.38/2.26 | | | | (130) all_58_0 = all_53_1 % 9.38/2.26 | | | | % 9.38/2.26 | | | | GROUND_INST: instantiating (9) with all_53_0, all_58_1, all_17_0, % 9.38/2.26 | | | | all_9_6, simplifying with (121), (129) gives: % 9.38/2.26 | | | | (131) all_58_1 = all_53_0 % 9.38/2.26 | | | | % 9.38/2.26 | | | | REDUCE: (127), (130) imply: % 9.38/2.26 | | | | (132) ~ (all_53_1 = 0) % 9.38/2.26 | | | | % 9.38/2.26 | | | | REDUCE: (126), (131) imply: % 9.38/2.26 | | | | (133) ~ (all_53_0 = 0) % 9.38/2.26 | | | | % 9.38/2.26 | | | | GROUND_INST: instantiating (4) with all_9_5, all_9_4, all_9_6, all_17_1, % 9.38/2.26 | | | | all_53_1, simplifying with (13), (14), (15), (28), (120) % 9.38/2.26 | | | | gives: % 9.38/2.26 | | | | (134) all_53_1 = 0 | ? [v0: any] : ? [v1: any] : (member(all_9_6, % 9.38/2.26 | | | | all_9_4) = v1 & member(all_9_6, all_9_5) = v0 & ( ~ (v0 = % 9.38/2.26 | | | | 0) | v1 = 0)) % 9.38/2.26 | | | | % 9.38/2.26 | | | | GROUND_INST: instantiating (4) with all_9_4, all_9_5, all_9_6, all_17_0, % 9.38/2.26 | | | | all_53_0, simplifying with (13), (14), (15), (29), (121) % 9.38/2.26 | | | | gives: % 9.38/2.26 | | | | (135) all_53_0 = 0 | ? [v0: any] : ? [v1: any] : (member(all_9_6, % 9.38/2.26 | | | | all_9_4) = v0 & member(all_9_6, all_9_5) = v1 & ( ~ (v0 = % 9.38/2.26 | | | | 0) | v1 = 0)) % 9.38/2.26 | | | | % 9.38/2.26 | | | | BETA: splitting (115) gives: % 9.38/2.26 | | | | % 9.38/2.26 | | | | Case 1: % 9.38/2.26 | | | | | % 9.38/2.26 | | | | | (136) all_9_0 = 0 & ~ (all_9_1 = 0) % 9.38/2.26 | | | | | % 9.38/2.26 | | | | | ALPHA: (136) implies: % 9.38/2.26 | | | | | (137) all_9_0 = 0 % 9.38/2.26 | | | | | (138) ~ (all_9_1 = 0) % 9.38/2.26 | | | | | % 9.38/2.26 | | | | | REDUCE: (17), (137) imply: % 9.38/2.26 | | | | | (139) member(all_9_6, all_9_4) = 0 % 9.38/2.26 | | | | | % 9.38/2.26 | | | | | BETA: splitting (135) gives: % 9.38/2.26 | | | | | % 9.38/2.26 | | | | | Case 1: % 9.38/2.26 | | | | | | % 9.38/2.26 | | | | | | (140) all_53_0 = 0 % 9.38/2.26 | | | | | | % 9.38/2.26 | | | | | | REDUCE: (133), (140) imply: % 9.38/2.26 | | | | | | (141) $false % 9.38/2.26 | | | | | | % 9.38/2.26 | | | | | | CLOSE: (141) is inconsistent. % 9.38/2.26 | | | | | | % 9.38/2.26 | | | | | Case 2: % 9.38/2.26 | | | | | | % 9.38/2.26 | | | | | | (142) ? [v0: any] : ? [v1: any] : (member(all_9_6, all_9_4) = % 9.38/2.26 | | | | | | v0 & member(all_9_6, all_9_5) = v1 & ( ~ (v0 = 0) | v1 = % 9.38/2.26 | | | | | | 0)) % 9.38/2.26 | | | | | | % 9.38/2.26 | | | | | | DELTA: instantiating (142) with fresh symbols all_82_0, all_82_1 % 9.38/2.26 | | | | | | gives: % 9.38/2.26 | | | | | | (143) member(all_9_6, all_9_4) = all_82_1 & member(all_9_6, % 9.38/2.26 | | | | | | all_9_5) = all_82_0 & ( ~ (all_82_1 = 0) | all_82_0 = 0) % 9.38/2.26 | | | | | | % 9.38/2.26 | | | | | | ALPHA: (143) implies: % 9.38/2.27 | | | | | | (144) member(all_9_6, all_9_5) = all_82_0 % 9.38/2.27 | | | | | | (145) member(all_9_6, all_9_4) = all_82_1 % 9.38/2.27 | | | | | | (146) ~ (all_82_1 = 0) | all_82_0 = 0 % 9.38/2.27 | | | | | | % 9.38/2.27 | | | | | | GROUND_INST: instantiating (9) with all_9_1, all_82_0, all_9_5, % 9.38/2.27 | | | | | | all_9_6, simplifying with (16), (144) gives: % 9.38/2.27 | | | | | | (147) all_82_0 = all_9_1 % 9.38/2.27 | | | | | | % 9.38/2.27 | | | | | | GROUND_INST: instantiating (9) with 0, all_82_1, all_9_4, all_9_6, % 9.38/2.27 | | | | | | simplifying with (139), (145) gives: % 9.38/2.27 | | | | | | (148) all_82_1 = 0 % 9.38/2.27 | | | | | | % 9.38/2.27 | | | | | | BETA: splitting (146) gives: % 9.38/2.27 | | | | | | % 9.38/2.27 | | | | | | Case 1: % 9.38/2.27 | | | | | | | % 9.38/2.27 | | | | | | | (149) ~ (all_82_1 = 0) % 9.38/2.27 | | | | | | | % 9.38/2.27 | | | | | | | REDUCE: (148), (149) imply: % 9.38/2.27 | | | | | | | (150) $false % 9.38/2.27 | | | | | | | % 9.38/2.27 | | | | | | | CLOSE: (150) is inconsistent. % 9.38/2.27 | | | | | | | % 9.38/2.27 | | | | | | Case 2: % 9.38/2.27 | | | | | | | % 9.38/2.27 | | | | | | | (151) all_82_0 = 0 % 9.38/2.27 | | | | | | | % 9.38/2.27 | | | | | | | COMBINE_EQS: (147), (151) imply: % 9.38/2.27 | | | | | | | (152) all_9_1 = 0 % 9.38/2.27 | | | | | | | % 9.38/2.27 | | | | | | | REDUCE: (138), (152) imply: % 9.38/2.27 | | | | | | | (153) $false % 9.38/2.27 | | | | | | | % 9.38/2.27 | | | | | | | CLOSE: (153) is inconsistent. % 9.38/2.27 | | | | | | | % 9.38/2.27 | | | | | | End of split % 9.38/2.27 | | | | | | % 9.38/2.27 | | | | | End of split % 9.38/2.27 | | | | | % 9.38/2.27 | | | | Case 2: % 9.38/2.27 | | | | | % 9.38/2.27 | | | | | (154) all_9_1 = 0 & ~ (all_9_0 = 0) % 9.38/2.27 | | | | | % 9.38/2.27 | | | | | ALPHA: (154) implies: % 9.38/2.27 | | | | | (155) all_9_1 = 0 % 9.38/2.27 | | | | | (156) ~ (all_9_0 = 0) % 9.38/2.27 | | | | | % 9.38/2.27 | | | | | REDUCE: (16), (155) imply: % 9.38/2.27 | | | | | (157) member(all_9_6, all_9_5) = 0 % 9.38/2.27 | | | | | % 9.38/2.27 | | | | | BETA: splitting (134) gives: % 9.38/2.27 | | | | | % 9.38/2.27 | | | | | Case 1: % 9.38/2.27 | | | | | | % 9.38/2.27 | | | | | | (158) all_53_1 = 0 % 9.38/2.27 | | | | | | % 9.38/2.27 | | | | | | REDUCE: (132), (158) imply: % 9.38/2.27 | | | | | | (159) $false % 9.38/2.27 | | | | | | % 9.38/2.27 | | | | | | CLOSE: (159) is inconsistent. % 9.38/2.27 | | | | | | % 9.38/2.27 | | | | | Case 2: % 9.38/2.27 | | | | | | % 9.38/2.27 | | | | | | (160) ? [v0: any] : ? [v1: any] : (member(all_9_6, all_9_4) = % 9.38/2.27 | | | | | | v1 & member(all_9_6, all_9_5) = v0 & ( ~ (v0 = 0) | v1 = % 9.38/2.27 | | | | | | 0)) % 9.38/2.27 | | | | | | % 9.38/2.27 | | | | | | DELTA: instantiating (160) with fresh symbols all_82_0, all_82_1 % 9.38/2.27 | | | | | | gives: % 9.38/2.27 | | | | | | (161) member(all_9_6, all_9_4) = all_82_0 & member(all_9_6, % 9.38/2.27 | | | | | | all_9_5) = all_82_1 & ( ~ (all_82_1 = 0) | all_82_0 = 0) % 9.38/2.27 | | | | | | % 9.38/2.27 | | | | | | ALPHA: (161) implies: % 9.38/2.27 | | | | | | (162) member(all_9_6, all_9_5) = all_82_1 % 9.38/2.27 | | | | | | (163) member(all_9_6, all_9_4) = all_82_0 % 9.38/2.27 | | | | | | (164) ~ (all_82_1 = 0) | all_82_0 = 0 % 9.38/2.27 | | | | | | % 9.38/2.27 | | | | | | GROUND_INST: instantiating (9) with 0, all_82_1, all_9_5, all_9_6, % 9.38/2.27 | | | | | | simplifying with (157), (162) gives: % 9.38/2.27 | | | | | | (165) all_82_1 = 0 % 9.38/2.27 | | | | | | % 9.38/2.27 | | | | | | GROUND_INST: instantiating (9) with all_9_0, all_82_0, all_9_4, % 9.38/2.27 | | | | | | all_9_6, simplifying with (17), (163) gives: % 9.38/2.27 | | | | | | (166) all_82_0 = all_9_0 % 9.38/2.27 | | | | | | % 9.38/2.27 | | | | | | BETA: splitting (164) gives: % 9.38/2.27 | | | | | | % 9.38/2.27 | | | | | | Case 1: % 9.38/2.27 | | | | | | | % 9.38/2.27 | | | | | | | (167) ~ (all_82_1 = 0) % 9.38/2.27 | | | | | | | % 9.38/2.27 | | | | | | | REDUCE: (165), (167) imply: % 9.38/2.27 | | | | | | | (168) $false % 9.38/2.27 | | | | | | | % 9.38/2.27 | | | | | | | CLOSE: (168) is inconsistent. % 9.38/2.27 | | | | | | | % 9.38/2.27 | | | | | | Case 2: % 9.38/2.27 | | | | | | | % 9.38/2.27 | | | | | | | (169) all_82_0 = 0 % 9.38/2.28 | | | | | | | % 9.38/2.28 | | | | | | | COMBINE_EQS: (166), (169) imply: % 9.38/2.28 | | | | | | | (170) all_9_0 = 0 % 9.38/2.28 | | | | | | | % 9.38/2.28 | | | | | | | REDUCE: (156), (170) imply: % 9.38/2.28 | | | | | | | (171) $false % 9.38/2.28 | | | | | | | % 9.38/2.28 | | | | | | | CLOSE: (171) is inconsistent. % 9.38/2.28 | | | | | | | % 9.38/2.28 | | | | | | End of split % 9.38/2.28 | | | | | | % 9.38/2.28 | | | | | End of split % 9.38/2.28 | | | | | % 9.38/2.28 | | | | End of split % 9.38/2.28 | | | | % 9.38/2.28 | | | End of split % 9.38/2.28 | | | % 9.38/2.28 | | End of split % 9.38/2.28 | | % 9.38/2.28 | End of split % 9.38/2.28 | % 9.38/2.28 End of proof % 9.38/2.28 % SZS output end Proof for theBenchmark % 9.38/2.28 % 9.38/2.28 1700ms %------------------------------------------------------------------------------