%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU141+2 : TPTP v8.1.2. Released v3.3.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n031.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 17:42:44 EDT 2023 % Result : Theorem 28.61s 4.64s % Output : Proof 30.62s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.13 % Problem : SEU141+2 : TPTP v8.1.2. Released v3.3.0. % 0.14/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.35 % Computer : n031.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 300 % 0.14/0.35 % DateTime : Wed Aug 23 14:15:20 EDT 2023 % 0.14/0.35 % CPUTime : % 0.21/0.61 ________ _____ % 0.21/0.61 ___ __ \_________(_)________________________________ % 0.21/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.61 % 0.21/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.61 (2023-06-19) % 0.21/0.61 % 0.21/0.61 (c) Philipp Rümmer, 2009-2023 % 0.21/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.61 Amanda Stjerna. % 0.21/0.61 Free software under BSD-3-Clause. % 0.21/0.61 % 0.21/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.61 % 0.21/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.21/0.62 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 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 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 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 % 2.76/1.11 Prover 1: Preprocessing ... % 2.76/1.11 Prover 4: Preprocessing ... % 3.11/1.15 Prover 3: Preprocessing ... % 3.11/1.15 Prover 0: Preprocessing ... % 3.11/1.15 Prover 5: Preprocessing ... % 3.11/1.15 Prover 6: Preprocessing ... % 3.11/1.15 Prover 2: Preprocessing ... % 6.91/1.64 Prover 1: Warning: ignoring some quantifiers % 6.91/1.68 Prover 5: Proving ... % 6.91/1.69 Prover 1: Constructing countermodel ... % 7.97/1.79 Prover 3: Warning: ignoring some quantifiers % 7.97/1.81 Prover 4: Warning: ignoring some quantifiers % 7.97/1.81 Prover 6: Proving ... % 7.97/1.83 Prover 3: Constructing countermodel ... % 8.60/1.88 Prover 4: Constructing countermodel ... % 8.60/1.89 Prover 2: Proving ... % 9.59/2.03 Prover 0: Proving ... % 12.51/2.43 Prover 3: gave up % 12.51/2.43 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 12.51/2.47 Prover 7: Preprocessing ... % 13.85/2.59 Prover 7: Warning: ignoring some quantifiers % 13.85/2.61 Prover 7: Constructing countermodel ... % 18.40/3.19 Prover 1: gave up % 18.40/3.21 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 18.40/3.26 Prover 8: Preprocessing ... % 20.20/3.44 Prover 8: Warning: ignoring some quantifiers % 20.20/3.45 Prover 8: Constructing countermodel ... % 23.81/4.01 Prover 8: gave up % 23.81/4.02 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 24.44/4.06 Prover 9: Preprocessing ... % 26.31/4.28 Prover 9: Warning: ignoring some quantifiers % 26.31/4.29 Prover 9: Constructing countermodel ... % 28.61/4.64 Prover 4: Found proof (size 328) % 28.61/4.64 Prover 4: proved (4006ms) % 28.61/4.64 Prover 9: stopped % 28.61/4.64 Prover 7: stopped % 28.61/4.64 Prover 5: stopped % 28.61/4.64 Prover 6: stopped % 28.61/4.64 Prover 2: stopped % 28.61/4.64 Prover 0: stopped % 28.61/4.64 % 28.61/4.64 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 28.61/4.64 % 29.89/4.76 % SZS output start Proof for theBenchmark % 29.89/4.76 Assumptions after simplification: % 29.89/4.76 --------------------------------- % 29.89/4.76 % 29.89/4.76 (commutativity_k2_xboole_0) % 29.89/4.78 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v1, v0) = v2) | ~ % 29.89/4.78 $i(v1) | ~ $i(v0) | (set_union2(v0, v1) = v2 & $i(v2))) & ! [v0: $i] : ! % 29.89/4.78 [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) % 29.89/4.78 | (set_union2(v1, v0) = v2 & $i(v2))) % 29.89/4.78 % 29.89/4.78 (commutativity_k3_xboole_0) % 29.89/4.79 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_intersection2(v1, v0) = v2) % 29.89/4.79 | ~ $i(v1) | ~ $i(v0) | (set_intersection2(v0, v1) = v2 & $i(v2))) & ! % 29.89/4.79 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_intersection2(v0, v1) = v2) | % 29.89/4.79 ~ $i(v1) | ~ $i(v0) | (set_intersection2(v1, v0) = v2 & $i(v2))) % 29.89/4.79 % 29.89/4.79 (d7_xboole_0) % 29.89/4.79 $i(empty_set) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = empty_set | ~ % 29.89/4.79 (set_intersection2(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( % 29.89/4.79 ~ (v3 = 0) & disjoint(v0, v1) = v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 29.89/4.79 int] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? % 29.89/4.79 [v3: $i] : ( ~ (v3 = empty_set) & set_intersection2(v0, v1) = v3 & $i(v3))) % 29.89/4.79 & ! [v0: $i] : ! [v1: $i] : ( ~ (disjoint(v0, v1) = 0) | ~ $i(v1) | ~ % 29.89/4.79 $i(v0) | set_intersection2(v0, v1) = empty_set) & ! [v0: $i] : ! [v1: $i] % 29.89/4.79 : ( ~ (set_intersection2(v0, v1) = empty_set) | ~ $i(v1) | ~ $i(v0) | % 29.89/4.79 disjoint(v0, v1) = 0) % 29.89/4.79 % 29.89/4.79 (l32_xboole_1) % 29.89/4.79 $i(empty_set) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = empty_set | ~ % 29.89/4.79 (set_difference(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ % 29.89/4.79 (v3 = 0) & subset(v0, v1) = v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 29.89/4.79 int] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: % 29.89/4.79 $i] : ( ~ (v3 = empty_set) & set_difference(v0, v1) = v3 & $i(v3))) & ! % 29.89/4.79 [v0: $i] : ! [v1: $i] : ( ~ (set_difference(v0, v1) = empty_set) | ~ $i(v1) % 29.89/4.79 | ~ $i(v0) | subset(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ( ~ % 29.89/4.79 (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | set_difference(v0, v1) = % 29.89/4.79 empty_set) % 29.89/4.79 % 29.89/4.79 (t12_xboole_1) % 29.89/4.79 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ (set_union2(v0, v1) = % 29.89/4.79 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & subset(v0, v1) % 29.89/4.79 = v3)) & ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) % 29.89/4.79 | ~ $i(v0) | set_union2(v0, v1) = v1) % 29.89/4.79 % 29.89/4.79 (t28_xboole_1) % 29.89/4.79 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (set_intersection2(v0, % 29.89/4.79 v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & % 29.89/4.79 subset(v0, v1) = v3)) & ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v0, v1) = % 29.89/4.79 0) | ~ $i(v1) | ~ $i(v0) | set_intersection2(v0, v1) = v0) % 29.89/4.79 % 29.89/4.79 (t36_xboole_1) % 29.89/4.80 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_difference(v0, v1) = v2) | % 29.89/4.80 ~ $i(v1) | ~ $i(v0) | subset(v2, v0) = 0) % 29.89/4.80 % 29.89/4.80 (t37_xboole_1) % 29.89/4.80 $i(empty_set) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = empty_set | ~ % 29.89/4.80 (set_difference(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ % 29.89/4.80 (v3 = 0) & subset(v0, v1) = v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 29.89/4.80 int] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: % 29.89/4.80 $i] : ( ~ (v3 = empty_set) & set_difference(v0, v1) = v3 & $i(v3))) & ! % 29.89/4.80 [v0: $i] : ! [v1: $i] : ( ~ (set_difference(v0, v1) = empty_set) | ~ $i(v1) % 29.89/4.80 | ~ $i(v0) | subset(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ( ~ % 29.89/4.80 (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | set_difference(v0, v1) = % 29.89/4.80 empty_set) % 29.89/4.80 % 29.89/4.80 (t39_xboole_1) % 29.89/4.80 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_difference(v1, v0) = v2) | % 29.89/4.80 ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (set_union2(v0, v2) = v3 & % 29.89/4.80 set_union2(v0, v1) = v3 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 29.89/4.80 $i] : ( ~ (set_union2(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : % 29.89/4.80 (set_difference(v1, v0) = v3 & set_union2(v0, v3) = v2 & $i(v3) & $i(v2))) % 29.89/4.80 % 29.89/4.80 (t40_xboole_1) % 29.89/4.80 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_difference(v0, v1) = v2) | % 29.89/4.80 ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (set_difference(v3, v1) = v2 & % 29.89/4.80 set_union2(v0, v1) = v3 & $i(v3) & $i(v2))) & ! [v0: $i] : ! [v1: $i] : % 29.89/4.80 ! [v2: $i] : ( ~ (set_union2(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: % 29.89/4.80 $i] : (set_difference(v2, v1) = v3 & set_difference(v0, v1) = v3 & % 29.89/4.80 $i(v3))) % 29.89/4.80 % 29.89/4.80 (t45_xboole_1) % 29.89/4.80 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_difference(v1, v0) = v2) | % 29.89/4.80 ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: $i] : (subset(v0, v1) = v3 & % 29.89/4.80 set_union2(v0, v2) = v4 & $i(v4) & ( ~ (v3 = 0) | v4 = v1))) & ! [v0: $i] % 29.89/4.80 : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] % 29.89/4.80 : (set_difference(v1, v0) = v2 & set_union2(v0, v2) = v1 & $i(v2))) % 29.89/4.80 % 29.89/4.80 (t48_xboole_1) % 29.89/4.80 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_difference(v0, v1) = v2) | % 29.89/4.80 ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (set_difference(v0, v2) = v3 & % 29.89/4.80 set_intersection2(v0, v1) = v3 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! % 29.89/4.80 [v2: $i] : ( ~ (set_intersection2(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? % 29.89/4.80 [v3: $i] : (set_difference(v0, v3) = v2 & set_difference(v0, v1) = v3 & % 29.89/4.80 $i(v3) & $i(v2))) % 29.89/4.80 % 29.89/4.80 (t4_xboole_0) % 29.89/4.80 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 29.89/4.80 (set_intersection2(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ~ $i(v3) | ~ % 29.89/4.80 $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & disjoint(v0, v1) = v4)) & % 29.89/4.80 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (disjoint(v0, v1) = % 29.89/4.80 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : % 29.89/4.80 (set_intersection2(v0, v1) = v3 & in(v4, v3) = 0 & $i(v4) & $i(v3))) & ! % 29.89/4.80 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_intersection2(v0, v1) = v2) | % 29.89/4.80 ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: $i] : ? [v5: int] : ($i(v4) & % 29.89/4.80 ((v5 = 0 & in(v4, v2) = 0) | (v3 = 0 & disjoint(v0, v1) = 0)))) & ! [v0: % 29.89/4.80 $i] : ! [v1: $i] : ( ~ (disjoint(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? % 29.89/4.80 [v2: $i] : (set_intersection2(v0, v1) = v2 & $i(v2) & ! [v3: $i] : ( ~ % 29.89/4.80 (in(v3, v2) = 0) | ~ $i(v3)))) % 29.89/4.80 % 29.89/4.80 (t7_xboole_1) % 29.89/4.80 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v0, v1) = v2) | ~ % 29.89/4.80 $i(v1) | ~ $i(v0) | subset(v0, v2) = 0) % 29.89/4.80 % 29.89/4.80 (t83_xboole_1) % 29.89/4.81 ? [v0: $i] : ? [v1: $i] : ? [v2: any] : ? [v3: $i] : (disjoint(v0, v1) = % 29.89/4.81 v2 & set_difference(v0, v1) = v3 & $i(v3) & $i(v1) & $i(v0) & ((v3 = v0 & ~ % 29.89/4.81 (v2 = 0)) | (v2 = 0 & ~ (v3 = v0)))) % 29.89/4.81 % 29.89/4.81 (function-axioms) % 29.89/4.81 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 29.89/4.81 [v3: $i] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0)) % 29.89/4.81 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 29.89/4.81 (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) & ! [v0: % 29.89/4.81 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 29.89/4.81 : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: % 29.89/4.81 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 29.89/4.81 (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) & ! % 29.89/4.81 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 29.89/4.81 (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) & ! [v0: % 29.89/4.81 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 29.89/4.81 : (v1 = v0 | ~ (proper_subset(v3, v2) = v1) | ~ (proper_subset(v3, v2) = % 29.89/4.81 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 29.89/4.81 $i] : ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) % 29.89/4.81 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 % 29.89/4.81 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) % 29.89/4.81 % 29.89/4.81 Further assumptions not needed in the proof: % 29.89/4.81 -------------------------------------------- % 29.89/4.81 antisymmetry_r2_hidden, antisymmetry_r2_xboole_0, d10_xboole_0, d1_xboole_0, % 29.89/4.81 d2_xboole_0, d3_tarski, d3_xboole_0, d4_xboole_0, d8_xboole_0, dt_k1_xboole_0, % 29.89/4.81 dt_k2_xboole_0, dt_k3_xboole_0, dt_k4_xboole_0, fc1_xboole_0, fc2_xboole_0, % 29.89/4.81 fc3_xboole_0, idempotence_k2_xboole_0, idempotence_k3_xboole_0, % 29.89/4.81 irreflexivity_r2_xboole_0, rc1_xboole_0, rc2_xboole_0, reflexivity_r1_tarski, % 29.89/4.81 symmetry_r1_xboole_0, t17_xboole_1, t19_xboole_1, t1_boole, t1_xboole_1, % 29.89/4.81 t26_xboole_1, t2_boole, t2_tarski, t2_xboole_1, t33_xboole_1, t3_boole, % 29.89/4.81 t3_xboole_0, t3_xboole_1, t4_boole, t60_xboole_1, t63_xboole_1, t6_boole, % 29.89/4.81 t7_boole, t8_boole, t8_xboole_1 % 29.89/4.81 % 29.89/4.81 Those formulas are unsatisfiable: % 29.89/4.81 --------------------------------- % 29.89/4.81 % 29.89/4.81 Begin of proof % 29.89/4.81 | % 29.89/4.81 | ALPHA: (commutativity_k2_xboole_0) implies: % 29.89/4.81 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v1, v0) = v2) % 29.89/4.81 | | ~ $i(v1) | ~ $i(v0) | (set_union2(v0, v1) = v2 & $i(v2))) % 29.89/4.81 | % 29.89/4.81 | ALPHA: (commutativity_k3_xboole_0) implies: % 29.89/4.81 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_intersection2(v1, % 29.89/4.81 | v0) = v2) | ~ $i(v1) | ~ $i(v0) | (set_intersection2(v0, v1) = % 29.89/4.81 | v2 & $i(v2))) % 29.89/4.81 | % 29.89/4.81 | ALPHA: (d7_xboole_0) implies: % 29.89/4.81 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (disjoint(v0, % 29.89/4.81 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ( ~ (v3 = % 29.89/4.81 | empty_set) & set_intersection2(v0, v1) = v3 & $i(v3))) % 29.89/4.81 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = empty_set | ~ % 29.89/4.81 | (set_intersection2(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: % 29.89/4.81 | int] : ( ~ (v3 = 0) & disjoint(v0, v1) = v3)) % 29.89/4.81 | % 29.89/4.81 | ALPHA: (t12_xboole_1) implies: % 29.89/4.81 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ % 29.89/4.81 | $i(v0) | set_union2(v0, v1) = v1) % 29.89/4.81 | % 29.89/4.81 | ALPHA: (t28_xboole_1) implies: % 29.89/4.81 | (6) ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ % 29.89/4.81 | $i(v0) | set_intersection2(v0, v1) = v0) % 29.89/4.81 | % 29.89/4.81 | ALPHA: (t37_xboole_1) implies: % 29.89/4.82 | (7) ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ % 29.89/4.82 | $i(v0) | set_difference(v0, v1) = empty_set) % 29.89/4.82 | % 29.89/4.82 | ALPHA: (t39_xboole_1) implies: % 29.89/4.82 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v0, v1) = v2) % 29.89/4.82 | | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (set_difference(v1, v0) = v3 % 29.89/4.82 | & set_union2(v0, v3) = v2 & $i(v3) & $i(v2))) % 29.89/4.82 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_difference(v1, v0) = % 29.89/4.82 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (set_union2(v0, v2) = % 29.89/4.82 | v3 & set_union2(v0, v1) = v3 & $i(v3))) % 29.89/4.82 | % 29.89/4.82 | ALPHA: (t40_xboole_1) implies: % 29.89/4.82 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v0, v1) = % 29.89/4.82 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (set_difference(v2, % 29.89/4.82 | v1) = v3 & set_difference(v0, v1) = v3 & $i(v3))) % 29.89/4.82 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_difference(v0, v1) % 29.89/4.82 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (set_difference(v3, % 29.89/4.82 | v1) = v2 & set_union2(v0, v1) = v3 & $i(v3) & $i(v2))) % 29.89/4.82 | % 29.89/4.82 | ALPHA: (t45_xboole_1) implies: % 29.89/4.82 | (12) ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ % 29.89/4.82 | $i(v0) | ? [v2: $i] : (set_difference(v1, v0) = v2 & set_union2(v0, % 29.89/4.82 | v2) = v1 & $i(v2))) % 29.89/4.82 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_difference(v1, v0) % 29.89/4.82 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: $i] : % 29.89/4.82 | (subset(v0, v1) = v3 & set_union2(v0, v2) = v4 & $i(v4) & ( ~ (v3 = % 29.89/4.82 | 0) | v4 = v1))) % 29.89/4.82 | % 29.89/4.82 | ALPHA: (t48_xboole_1) implies: % 29.89/4.82 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_intersection2(v0, % 29.89/4.82 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : % 29.89/4.82 | (set_difference(v0, v3) = v2 & set_difference(v0, v1) = v3 & $i(v3) % 29.89/4.82 | & $i(v2))) % 29.89/4.82 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_difference(v0, v1) % 29.89/4.82 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (set_difference(v0, % 29.89/4.82 | v2) = v3 & set_intersection2(v0, v1) = v3 & $i(v3))) % 29.89/4.82 | % 29.89/4.82 | ALPHA: (t4_xboole_0) implies: % 29.89/4.82 | (16) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (disjoint(v0, % 29.89/4.82 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : % 29.89/4.82 | (set_intersection2(v0, v1) = v3 & in(v4, v3) = 0 & $i(v4) & $i(v3))) % 29.89/4.82 | % 29.89/4.82 | ALPHA: (function-axioms) implies: % 29.89/4.82 | (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 29.89/4.82 | (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) % 29.89/4.82 | (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 29.89/4.82 | (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = % 29.89/4.82 | v0)) % 29.89/4.82 | (19) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 29.89/4.82 | : ! [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, % 29.89/4.82 | v2) = v0)) % 29.89/4.82 | (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 29.89/4.82 | (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) % 29.89/4.82 | (21) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 29.89/4.82 | : ! [v3: $i] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ % 29.89/4.82 | (disjoint(v3, v2) = v0)) % 29.89/4.82 | % 29.89/4.82 | DELTA: instantiating (t83_xboole_1) with fresh symbols all_57_0, all_57_1, % 29.89/4.82 | all_57_2, all_57_3 gives: % 29.89/4.83 | (22) disjoint(all_57_3, all_57_2) = all_57_1 & set_difference(all_57_3, % 29.89/4.83 | all_57_2) = all_57_0 & $i(all_57_0) & $i(all_57_2) & $i(all_57_3) & % 29.89/4.83 | ((all_57_0 = all_57_3 & ~ (all_57_1 = 0)) | (all_57_1 = 0 & ~ % 29.89/4.83 | (all_57_0 = all_57_3))) % 29.89/4.83 | % 29.89/4.83 | ALPHA: (22) implies: % 29.89/4.83 | (23) $i(all_57_3) % 29.89/4.83 | (24) $i(all_57_2) % 29.89/4.83 | (25) set_difference(all_57_3, all_57_2) = all_57_0 % 29.89/4.83 | (26) disjoint(all_57_3, all_57_2) = all_57_1 % 29.89/4.83 | (27) (all_57_0 = all_57_3 & ~ (all_57_1 = 0)) | (all_57_1 = 0 & ~ % 29.89/4.83 | (all_57_0 = all_57_3)) % 29.89/4.83 | % 29.89/4.83 | GROUND_INST: instantiating (13) with all_57_2, all_57_3, all_57_0, simplifying % 29.89/4.83 | with (23), (24), (25) gives: % 29.89/4.83 | (28) ? [v0: any] : ? [v1: $i] : (subset(all_57_2, all_57_3) = v0 & % 29.89/4.83 | set_union2(all_57_2, all_57_0) = v1 & $i(v1) & ( ~ (v0 = 0) | v1 = % 29.89/4.83 | all_57_3)) % 29.89/4.83 | % 29.89/4.83 | GROUND_INST: instantiating (9) with all_57_2, all_57_3, all_57_0, simplifying % 29.89/4.83 | with (23), (24), (25) gives: % 29.89/4.83 | (29) ? [v0: $i] : (set_union2(all_57_2, all_57_0) = v0 & % 29.89/4.83 | set_union2(all_57_2, all_57_3) = v0 & $i(v0)) % 29.89/4.83 | % 29.89/4.83 | GROUND_INST: instantiating (t36_xboole_1) with all_57_3, all_57_2, all_57_0, % 29.89/4.83 | simplifying with (23), (24), (25) gives: % 29.89/4.83 | (30) subset(all_57_0, all_57_3) = 0 % 29.89/4.83 | % 29.89/4.83 | GROUND_INST: instantiating (11) with all_57_3, all_57_2, all_57_0, simplifying % 29.89/4.83 | with (23), (24), (25) gives: % 29.89/4.83 | (31) ? [v0: $i] : (set_difference(v0, all_57_2) = all_57_0 & % 29.89/4.83 | set_union2(all_57_3, all_57_2) = v0 & $i(v0) & $i(all_57_0)) % 29.89/4.83 | % 29.89/4.83 | GROUND_INST: instantiating (15) with all_57_3, all_57_2, all_57_0, simplifying % 29.89/4.83 | with (23), (24), (25) gives: % 29.89/4.83 | (32) ? [v0: $i] : (set_difference(all_57_3, all_57_0) = v0 & % 29.89/4.83 | set_intersection2(all_57_3, all_57_2) = v0 & $i(v0)) % 29.89/4.83 | % 29.89/4.83 | GROUND_INST: instantiating (16) with all_57_3, all_57_2, all_57_1, simplifying % 29.89/4.83 | with (23), (24), (26) gives: % 29.89/4.83 | (33) all_57_1 = 0 | ? [v0: $i] : ? [v1: $i] : % 29.89/4.83 | (set_intersection2(all_57_3, all_57_2) = v0 & in(v1, v0) = 0 & $i(v1) % 29.89/4.83 | & $i(v0)) % 29.89/4.83 | % 29.89/4.83 | GROUND_INST: instantiating (3) with all_57_3, all_57_2, all_57_1, simplifying % 29.89/4.83 | with (23), (24), (26) gives: % 29.89/4.83 | (34) all_57_1 = 0 | ? [v0: $i] : ( ~ (v0 = empty_set) & % 29.89/4.83 | set_intersection2(all_57_3, all_57_2) = v0 & $i(v0)) % 29.89/4.83 | % 29.89/4.83 | DELTA: instantiating (29) with fresh symbol all_72_0 gives: % 29.89/4.83 | (35) set_union2(all_57_2, all_57_0) = all_72_0 & set_union2(all_57_2, % 29.89/4.83 | all_57_3) = all_72_0 & $i(all_72_0) % 29.89/4.83 | % 29.89/4.83 | ALPHA: (35) implies: % 29.89/4.83 | (36) set_union2(all_57_2, all_57_3) = all_72_0 % 29.89/4.83 | (37) set_union2(all_57_2, all_57_0) = all_72_0 % 29.89/4.83 | % 29.89/4.83 | DELTA: instantiating (32) with fresh symbol all_74_0 gives: % 29.89/4.83 | (38) set_difference(all_57_3, all_57_0) = all_74_0 & % 29.89/4.83 | set_intersection2(all_57_3, all_57_2) = all_74_0 & $i(all_74_0) % 29.89/4.83 | % 29.89/4.83 | ALPHA: (38) implies: % 29.89/4.83 | (39) set_intersection2(all_57_3, all_57_2) = all_74_0 % 29.89/4.83 | (40) set_difference(all_57_3, all_57_0) = all_74_0 % 29.89/4.83 | % 29.89/4.83 | DELTA: instantiating (31) with fresh symbol all_76_0 gives: % 29.89/4.83 | (41) set_difference(all_76_0, all_57_2) = all_57_0 & set_union2(all_57_3, % 29.89/4.83 | all_57_2) = all_76_0 & $i(all_76_0) & $i(all_57_0) % 29.89/4.83 | % 29.89/4.83 | ALPHA: (41) implies: % 29.89/4.83 | (42) $i(all_57_0) % 29.89/4.83 | (43) set_union2(all_57_3, all_57_2) = all_76_0 % 29.89/4.83 | (44) set_difference(all_76_0, all_57_2) = all_57_0 % 29.89/4.83 | % 29.89/4.83 | DELTA: instantiating (28) with fresh symbols all_78_0, all_78_1 gives: % 29.89/4.84 | (45) subset(all_57_2, all_57_3) = all_78_1 & set_union2(all_57_2, all_57_0) % 29.89/4.84 | = all_78_0 & $i(all_78_0) & ( ~ (all_78_1 = 0) | all_78_0 = all_57_3) % 29.89/4.84 | % 29.89/4.84 | ALPHA: (45) implies: % 29.89/4.84 | (46) set_union2(all_57_2, all_57_0) = all_78_0 % 29.89/4.84 | % 29.89/4.84 | GROUND_INST: instantiating (17) with all_72_0, all_78_0, all_57_0, all_57_2, % 29.89/4.84 | simplifying with (37), (46) gives: % 29.89/4.84 | (47) all_78_0 = all_72_0 % 29.89/4.84 | % 29.89/4.84 | GROUND_INST: instantiating (1) with all_57_2, all_57_3, all_76_0, simplifying % 29.89/4.84 | with (23), (24), (43) gives: % 29.89/4.84 | (48) set_union2(all_57_2, all_57_3) = all_76_0 & $i(all_76_0) % 29.89/4.84 | % 29.89/4.84 | ALPHA: (48) implies: % 29.89/4.84 | (49) $i(all_76_0) % 29.89/4.84 | (50) set_union2(all_57_2, all_57_3) = all_76_0 % 29.89/4.84 | % 29.89/4.84 | GROUND_INST: instantiating (t7_xboole_1) with all_57_3, all_57_2, all_76_0, % 29.89/4.84 | simplifying with (23), (24), (43) gives: % 29.89/4.84 | (51) subset(all_57_3, all_76_0) = 0 % 29.89/4.84 | % 29.89/4.84 | GROUND_INST: instantiating (8) with all_57_3, all_57_2, all_76_0, simplifying % 29.89/4.84 | with (23), (24), (43) gives: % 29.89/4.84 | (52) ? [v0: $i] : (set_difference(all_57_2, all_57_3) = v0 & % 29.89/4.84 | set_union2(all_57_3, v0) = all_76_0 & $i(v0) & $i(all_76_0)) % 29.89/4.84 | % 29.89/4.84 | GROUND_INST: instantiating (10) with all_57_2, all_57_3, all_72_0, simplifying % 29.89/4.84 | with (23), (24), (36) gives: % 29.89/4.84 | (53) ? [v0: $i] : (set_difference(all_72_0, all_57_3) = v0 & % 29.89/4.84 | set_difference(all_57_2, all_57_3) = v0 & $i(v0)) % 29.89/4.84 | % 29.89/4.84 | GROUND_INST: instantiating (1) with all_57_0, all_57_2, all_72_0, simplifying % 29.89/4.84 | with (24), (37), (42) gives: % 29.89/4.84 | (54) set_union2(all_57_0, all_57_2) = all_72_0 & $i(all_72_0) % 29.89/4.84 | % 29.89/4.84 | ALPHA: (54) implies: % 29.89/4.84 | (55) set_union2(all_57_0, all_57_2) = all_72_0 % 29.89/4.84 | % 29.89/4.84 | GROUND_INST: instantiating (t7_xboole_1) with all_57_2, all_57_0, all_72_0, % 29.89/4.84 | simplifying with (24), (37), (42) gives: % 29.89/4.84 | (56) subset(all_57_2, all_72_0) = 0 % 29.89/4.84 | % 29.89/4.84 | GROUND_INST: instantiating (10) with all_57_2, all_57_0, all_72_0, simplifying % 29.89/4.84 | with (24), (37), (42) gives: % 29.89/4.84 | (57) ? [v0: $i] : (set_difference(all_72_0, all_57_0) = v0 & % 29.89/4.84 | set_difference(all_57_2, all_57_0) = v0 & $i(v0)) % 29.89/4.84 | % 29.89/4.84 | GROUND_INST: instantiating (8) with all_57_2, all_57_0, all_72_0, simplifying % 29.89/4.84 | with (24), (37), (42) gives: % 29.89/4.84 | (58) ? [v0: $i] : (set_difference(all_57_0, all_57_2) = v0 & % 29.89/4.84 | set_union2(all_57_2, v0) = all_72_0 & $i(v0) & $i(all_72_0)) % 29.89/4.84 | % 29.89/4.84 | GROUND_INST: instantiating (4) with all_57_3, all_57_2, all_74_0, simplifying % 29.89/4.84 | with (23), (24), (39) gives: % 29.89/4.84 | (59) all_74_0 = empty_set | ? [v0: int] : ( ~ (v0 = 0) & % 29.89/4.84 | disjoint(all_57_3, all_57_2) = v0) % 29.89/4.84 | % 29.89/4.84 | GROUND_INST: instantiating (7) with all_57_0, all_57_3, simplifying with (23), % 29.89/4.84 | (30), (42) gives: % 29.89/4.84 | (60) set_difference(all_57_0, all_57_3) = empty_set % 29.89/4.84 | % 29.89/4.84 | GROUND_INST: instantiating (6) with all_57_0, all_57_3, simplifying with (23), % 29.89/4.84 | (30), (42) gives: % 29.89/4.84 | (61) set_intersection2(all_57_0, all_57_3) = all_57_0 % 29.89/4.84 | % 29.89/4.84 | GROUND_INST: instantiating (5) with all_57_0, all_57_3, simplifying with (23), % 29.89/4.84 | (30), (42) gives: % 29.89/4.84 | (62) set_union2(all_57_0, all_57_3) = all_57_3 % 29.89/4.84 | % 29.89/4.84 | GROUND_INST: instantiating (12) with all_57_0, all_57_3, simplifying with % 29.89/4.84 | (23), (30), (42) gives: % 29.89/4.84 | (63) ? [v0: $i] : (set_difference(all_57_3, all_57_0) = v0 & % 29.89/4.84 | set_union2(all_57_0, v0) = all_57_3 & $i(v0)) % 29.89/4.84 | % 30.36/4.84 | GROUND_INST: instantiating (9) with all_57_0, all_57_3, all_74_0, simplifying % 30.36/4.84 | with (23), (40), (42) gives: % 30.36/4.85 | (64) ? [v0: $i] : (set_union2(all_57_0, all_74_0) = v0 & % 30.36/4.85 | set_union2(all_57_0, all_57_3) = v0 & $i(v0)) % 30.36/4.85 | % 30.36/4.85 | GROUND_INST: instantiating (t36_xboole_1) with all_57_3, all_57_0, all_74_0, % 30.36/4.85 | simplifying with (23), (40), (42) gives: % 30.36/4.85 | (65) subset(all_74_0, all_57_3) = 0 % 30.36/4.85 | % 30.36/4.85 | GROUND_INST: instantiating (11) with all_57_3, all_57_0, all_74_0, simplifying % 30.36/4.85 | with (23), (40), (42) gives: % 30.36/4.85 | (66) ? [v0: $i] : (set_difference(v0, all_57_0) = all_74_0 & % 30.36/4.85 | set_union2(all_57_3, all_57_0) = v0 & $i(v0) & $i(all_74_0)) % 30.36/4.85 | % 30.36/4.85 | GROUND_INST: instantiating (15) with all_57_3, all_57_0, all_74_0, simplifying % 30.36/4.85 | with (23), (40), (42) gives: % 30.36/4.85 | (67) ? [v0: $i] : (set_difference(all_57_3, all_74_0) = v0 & % 30.36/4.85 | set_intersection2(all_57_3, all_57_0) = v0 & $i(v0)) % 30.36/4.85 | % 30.36/4.85 | GROUND_INST: instantiating (13) with all_57_2, all_76_0, all_57_0, simplifying % 30.36/4.85 | with (24), (44), (49) gives: % 30.36/4.85 | (68) ? [v0: any] : ? [v1: $i] : (subset(all_57_2, all_76_0) = v0 & % 30.36/4.85 | set_union2(all_57_2, all_57_0) = v1 & $i(v1) & ( ~ (v0 = 0) | v1 = % 30.36/4.85 | all_76_0)) % 30.36/4.85 | % 30.36/4.85 | GROUND_INST: instantiating (9) with all_57_2, all_76_0, all_57_0, simplifying % 30.36/4.85 | with (24), (44), (49) gives: % 30.36/4.85 | (69) ? [v0: $i] : (set_union2(all_57_2, all_76_0) = v0 & % 30.36/4.85 | set_union2(all_57_2, all_57_0) = v0 & $i(v0)) % 30.36/4.85 | % 30.36/4.85 | GROUND_INST: instantiating (11) with all_76_0, all_57_2, all_57_0, simplifying % 30.36/4.85 | with (24), (44), (49) gives: % 30.36/4.85 | (70) ? [v0: $i] : (set_difference(v0, all_57_2) = all_57_0 & % 30.36/4.85 | set_union2(all_76_0, all_57_2) = v0 & $i(v0) & $i(all_57_0)) % 30.36/4.85 | % 30.36/4.85 | GROUND_INST: instantiating (15) with all_76_0, all_57_2, all_57_0, simplifying % 30.36/4.85 | with (24), (44), (49) gives: % 30.36/4.85 | (71) ? [v0: $i] : (set_difference(all_76_0, all_57_0) = v0 & % 30.36/4.85 | set_intersection2(all_76_0, all_57_2) = v0 & $i(v0)) % 30.36/4.85 | % 30.36/4.85 | DELTA: instantiating (57) with fresh symbol all_92_0 gives: % 30.36/4.85 | (72) set_difference(all_72_0, all_57_0) = all_92_0 & % 30.36/4.85 | set_difference(all_57_2, all_57_0) = all_92_0 & $i(all_92_0) % 30.36/4.85 | % 30.36/4.85 | ALPHA: (72) implies: % 30.36/4.85 | (73) set_difference(all_57_2, all_57_0) = all_92_0 % 30.36/4.85 | (74) set_difference(all_72_0, all_57_0) = all_92_0 % 30.36/4.85 | % 30.36/4.85 | DELTA: instantiating (53) with fresh symbol all_94_0 gives: % 30.36/4.85 | (75) set_difference(all_72_0, all_57_3) = all_94_0 & % 30.36/4.85 | set_difference(all_57_2, all_57_3) = all_94_0 & $i(all_94_0) % 30.36/4.85 | % 30.36/4.85 | ALPHA: (75) implies: % 30.36/4.85 | (76) set_difference(all_57_2, all_57_3) = all_94_0 % 30.36/4.85 | (77) set_difference(all_72_0, all_57_3) = all_94_0 % 30.36/4.85 | % 30.36/4.85 | DELTA: instantiating (71) with fresh symbol all_96_0 gives: % 30.36/4.85 | (78) set_difference(all_76_0, all_57_0) = all_96_0 & % 30.36/4.85 | set_intersection2(all_76_0, all_57_2) = all_96_0 & $i(all_96_0) % 30.36/4.85 | % 30.36/4.85 | ALPHA: (78) implies: % 30.36/4.85 | (79) set_intersection2(all_76_0, all_57_2) = all_96_0 % 30.36/4.85 | (80) set_difference(all_76_0, all_57_0) = all_96_0 % 30.36/4.85 | % 30.36/4.85 | DELTA: instantiating (69) with fresh symbol all_98_0 gives: % 30.36/4.85 | (81) set_union2(all_57_2, all_76_0) = all_98_0 & set_union2(all_57_2, % 30.36/4.85 | all_57_0) = all_98_0 & $i(all_98_0) % 30.36/4.85 | % 30.36/4.85 | ALPHA: (81) implies: % 30.36/4.85 | (82) set_union2(all_57_2, all_57_0) = all_98_0 % 30.36/4.85 | (83) set_union2(all_57_2, all_76_0) = all_98_0 % 30.36/4.85 | % 30.36/4.85 | DELTA: instantiating (67) with fresh symbol all_100_0 gives: % 30.36/4.85 | (84) set_difference(all_57_3, all_74_0) = all_100_0 & % 30.36/4.85 | set_intersection2(all_57_3, all_57_0) = all_100_0 & $i(all_100_0) % 30.36/4.85 | % 30.36/4.85 | ALPHA: (84) implies: % 30.36/4.85 | (85) set_intersection2(all_57_3, all_57_0) = all_100_0 % 30.36/4.85 | (86) set_difference(all_57_3, all_74_0) = all_100_0 % 30.36/4.85 | % 30.36/4.85 | DELTA: instantiating (63) with fresh symbol all_102_0 gives: % 30.36/4.85 | (87) set_difference(all_57_3, all_57_0) = all_102_0 & set_union2(all_57_0, % 30.36/4.85 | all_102_0) = all_57_3 & $i(all_102_0) % 30.36/4.85 | % 30.36/4.85 | ALPHA: (87) implies: % 30.36/4.85 | (88) $i(all_102_0) % 30.36/4.85 | (89) set_difference(all_57_3, all_57_0) = all_102_0 % 30.36/4.85 | % 30.36/4.85 | DELTA: instantiating (64) with fresh symbol all_104_0 gives: % 30.36/4.85 | (90) set_union2(all_57_0, all_74_0) = all_104_0 & set_union2(all_57_0, % 30.36/4.85 | all_57_3) = all_104_0 & $i(all_104_0) % 30.36/4.85 | % 30.36/4.85 | ALPHA: (90) implies: % 30.36/4.85 | (91) $i(all_104_0) % 30.36/4.85 | (92) set_union2(all_57_0, all_57_3) = all_104_0 % 30.36/4.85 | (93) set_union2(all_57_0, all_74_0) = all_104_0 % 30.36/4.85 | % 30.36/4.85 | DELTA: instantiating (58) with fresh symbol all_106_0 gives: % 30.36/4.85 | (94) set_difference(all_57_0, all_57_2) = all_106_0 & set_union2(all_57_2, % 30.36/4.85 | all_106_0) = all_72_0 & $i(all_106_0) & $i(all_72_0) % 30.36/4.85 | % 30.36/4.85 | ALPHA: (94) implies: % 30.36/4.85 | (95) $i(all_106_0) % 30.36/4.85 | (96) set_union2(all_57_2, all_106_0) = all_72_0 % 30.36/4.85 | (97) set_difference(all_57_0, all_57_2) = all_106_0 % 30.36/4.85 | % 30.36/4.85 | DELTA: instantiating (52) with fresh symbol all_118_0 gives: % 30.36/4.85 | (98) set_difference(all_57_2, all_57_3) = all_118_0 & set_union2(all_57_3, % 30.36/4.85 | all_118_0) = all_76_0 & $i(all_118_0) & $i(all_76_0) % 30.36/4.85 | % 30.36/4.85 | ALPHA: (98) implies: % 30.36/4.85 | (99) $i(all_118_0) % 30.36/4.85 | (100) set_union2(all_57_3, all_118_0) = all_76_0 % 30.36/4.85 | (101) set_difference(all_57_2, all_57_3) = all_118_0 % 30.36/4.85 | % 30.36/4.85 | DELTA: instantiating (66) with fresh symbol all_120_0 gives: % 30.36/4.85 | (102) set_difference(all_120_0, all_57_0) = all_74_0 & set_union2(all_57_3, % 30.36/4.85 | all_57_0) = all_120_0 & $i(all_120_0) & $i(all_74_0) % 30.36/4.85 | % 30.36/4.85 | ALPHA: (102) implies: % 30.36/4.86 | (103) set_union2(all_57_3, all_57_0) = all_120_0 % 30.36/4.86 | (104) set_difference(all_120_0, all_57_0) = all_74_0 % 30.36/4.86 | % 30.36/4.86 | DELTA: instantiating (70) with fresh symbol all_122_0 gives: % 30.36/4.86 | (105) set_difference(all_122_0, all_57_2) = all_57_0 & set_union2(all_76_0, % 30.36/4.86 | all_57_2) = all_122_0 & $i(all_122_0) & $i(all_57_0) % 30.36/4.86 | % 30.36/4.86 | ALPHA: (105) implies: % 30.36/4.86 | (106) set_union2(all_76_0, all_57_2) = all_122_0 % 30.36/4.86 | (107) set_difference(all_122_0, all_57_2) = all_57_0 % 30.36/4.86 | % 30.36/4.86 | DELTA: instantiating (68) with fresh symbols all_126_0, all_126_1 gives: % 30.36/4.86 | (108) subset(all_57_2, all_76_0) = all_126_1 & set_union2(all_57_2, % 30.36/4.86 | all_57_0) = all_126_0 & $i(all_126_0) & ( ~ (all_126_1 = 0) | % 30.36/4.86 | all_126_0 = all_76_0) % 30.36/4.86 | % 30.36/4.86 | ALPHA: (108) implies: % 30.36/4.86 | (109) set_union2(all_57_2, all_57_0) = all_126_0 % 30.36/4.86 | (110) subset(all_57_2, all_76_0) = all_126_1 % 30.36/4.86 | % 30.36/4.86 | GROUND_INST: instantiating (17) with all_72_0, all_76_0, all_57_3, all_57_2, % 30.36/4.86 | simplifying with (36), (50) gives: % 30.36/4.86 | (111) all_76_0 = all_72_0 % 30.36/4.86 | % 30.36/4.86 | GROUND_INST: instantiating (17) with all_72_0, all_126_0, all_57_0, all_57_2, % 30.36/4.86 | simplifying with (37), (109) gives: % 30.36/4.86 | (112) all_126_0 = all_72_0 % 30.36/4.86 | % 30.36/4.86 | GROUND_INST: instantiating (17) with all_98_0, all_126_0, all_57_0, all_57_2, % 30.36/4.86 | simplifying with (82), (109) gives: % 30.36/4.86 | (113) all_126_0 = all_98_0 % 30.36/4.86 | % 30.36/4.86 | GROUND_INST: instantiating (17) with all_57_3, all_104_0, all_57_3, all_57_0, % 30.36/4.86 | simplifying with (62), (92) gives: % 30.36/4.86 | (114) all_104_0 = all_57_3 % 30.36/4.86 | % 30.36/4.86 | GROUND_INST: instantiating (20) with all_74_0, all_102_0, all_57_0, all_57_3, % 30.36/4.86 | simplifying with (40), (89) gives: % 30.36/4.86 | (115) all_102_0 = all_74_0 % 30.36/4.86 | % 30.36/4.86 | GROUND_INST: instantiating (20) with all_94_0, all_118_0, all_57_3, all_57_2, % 30.36/4.86 | simplifying with (76), (101) gives: % 30.36/4.86 | (116) all_118_0 = all_94_0 % 30.36/4.86 | % 30.36/4.86 | COMBINE_EQS: (112), (113) imply: % 30.36/4.86 | (117) all_98_0 = all_72_0 % 30.36/4.86 | % 30.36/4.86 | REDUCE: (80), (111) imply: % 30.36/4.86 | (118) set_difference(all_72_0, all_57_0) = all_96_0 % 30.36/4.86 | % 30.36/4.86 | REDUCE: (44), (111) imply: % 30.36/4.86 | (119) set_difference(all_72_0, all_57_2) = all_57_0 % 30.36/4.86 | % 30.36/4.86 | REDUCE: (110), (111) imply: % 30.36/4.86 | (120) subset(all_57_2, all_72_0) = all_126_1 % 30.36/4.86 | % 30.36/4.86 | REDUCE: (51), (111) imply: % 30.36/4.86 | (121) subset(all_57_3, all_72_0) = 0 % 30.36/4.86 | % 30.36/4.86 | REDUCE: (79), (111) imply: % 30.36/4.86 | (122) set_intersection2(all_72_0, all_57_2) = all_96_0 % 30.36/4.86 | % 30.36/4.86 | REDUCE: (106), (111) imply: % 30.36/4.86 | (123) set_union2(all_72_0, all_57_2) = all_122_0 % 30.36/4.86 | % 30.36/4.86 | REDUCE: (93), (114) imply: % 30.36/4.86 | (124) set_union2(all_57_0, all_74_0) = all_57_3 % 30.36/4.86 | % 30.36/4.86 | REDUCE: (83), (111), (117) imply: % 30.36/4.86 | (125) set_union2(all_57_2, all_72_0) = all_72_0 % 30.36/4.86 | % 30.36/4.86 | REDUCE: (100), (111), (116) imply: % 30.36/4.86 | (126) set_union2(all_57_3, all_94_0) = all_72_0 % 30.36/4.86 | % 30.36/4.86 | REDUCE: (99), (116) imply: % 30.36/4.86 | (127) $i(all_94_0) % 30.36/4.86 | % 30.36/4.86 | REDUCE: (88), (115) imply: % 30.36/4.86 | (128) $i(all_74_0) % 30.36/4.86 | % 30.36/4.86 | GROUND_INST: instantiating (19) with 0, all_126_1, all_72_0, all_57_2, % 30.36/4.86 | simplifying with (56), (120) gives: % 30.36/4.86 | (129) all_126_1 = 0 % 30.36/4.86 | % 30.36/4.86 | GROUND_INST: instantiating (20) with all_92_0, all_96_0, all_57_0, all_72_0, % 30.36/4.86 | simplifying with (74), (118) gives: % 30.36/4.86 | (130) all_96_0 = all_92_0 % 30.36/4.86 | % 30.36/4.86 | REDUCE: (122), (130) imply: % 30.36/4.86 | (131) set_intersection2(all_72_0, all_57_2) = all_92_0 % 30.36/4.86 | % 30.36/4.86 | GROUND_INST: instantiating (1) with all_57_0, all_57_3, all_120_0, simplifying % 30.36/4.86 | with (23), (42), (103) gives: % 30.36/4.86 | (132) set_union2(all_57_0, all_57_3) = all_120_0 & $i(all_120_0) % 30.36/4.86 | % 30.36/4.86 | ALPHA: (132) implies: % 30.36/4.86 | (133) $i(all_120_0) % 30.36/4.86 | % 30.36/4.86 | GROUND_INST: instantiating (t7_xboole_1) with all_57_3, all_57_0, all_120_0, % 30.36/4.86 | simplifying with (23), (42), (103) gives: % 30.36/4.86 | (134) subset(all_57_3, all_120_0) = 0 % 30.36/4.86 | % 30.36/4.86 | GROUND_INST: instantiating (8) with all_57_3, all_57_0, all_120_0, simplifying % 30.36/4.86 | with (23), (42), (103) gives: % 30.36/4.86 | (135) ? [v0: $i] : (set_difference(all_57_0, all_57_3) = v0 & % 30.36/4.86 | set_union2(all_57_3, v0) = all_120_0 & $i(v0) & $i(all_120_0)) % 30.36/4.86 | % 30.36/4.86 | GROUND_INST: instantiating (1) with all_94_0, all_57_3, all_72_0, simplifying % 30.36/4.86 | with (23), (126), (127) gives: % 30.36/4.86 | (136) set_union2(all_94_0, all_57_3) = all_72_0 & $i(all_72_0) % 30.36/4.86 | % 30.36/4.86 | ALPHA: (136) implies: % 30.36/4.86 | (137) $i(all_72_0) % 30.36/4.86 | % 30.36/4.86 | GROUND_INST: instantiating (8) with all_57_3, all_94_0, all_72_0, simplifying % 30.36/4.86 | with (23), (126), (127) gives: % 30.36/4.86 | (138) ? [v0: $i] : (set_difference(all_94_0, all_57_3) = v0 & % 30.36/4.86 | set_union2(all_57_3, v0) = all_72_0 & $i(v0) & $i(all_72_0)) % 30.36/4.86 | % 30.36/4.86 | GROUND_INST: instantiating (1) with all_72_0, all_57_2, all_72_0, simplifying % 30.36/4.86 | with (24), (125), (137) gives: % 30.36/4.86 | (139) set_union2(all_72_0, all_57_2) = all_72_0 % 30.36/4.86 | % 30.36/4.86 | GROUND_INST: instantiating (1) with all_106_0, all_57_2, all_72_0, simplifying % 30.36/4.86 | with (24), (95), (96) gives: % 30.36/4.86 | (140) set_union2(all_106_0, all_57_2) = all_72_0 & $i(all_72_0) % 30.36/4.86 | % 30.36/4.86 | GROUND_INST: instantiating (10) with all_57_2, all_106_0, all_72_0, % 30.36/4.86 | simplifying with (24), (95), (96) gives: % 30.36/4.86 | (141) ? [v0: $i] : (set_difference(all_72_0, all_106_0) = v0 & % 30.36/4.86 | set_difference(all_57_2, all_106_0) = v0 & $i(v0)) % 30.36/4.86 | % 30.36/4.86 | GROUND_INST: instantiating (1) with all_57_3, all_57_0, all_57_3, simplifying % 30.36/4.86 | with (23), (42), (62) gives: % 30.36/4.86 | (142) set_union2(all_57_3, all_57_0) = all_57_3 % 30.36/4.86 | % 30.36/4.86 | GROUND_INST: instantiating (10) with all_57_0, all_57_3, all_57_3, simplifying % 30.36/4.86 | with (23), (42), (62) gives: % 30.36/4.86 | (143) ? [v0: $i] : (set_difference(all_57_0, all_57_3) = v0 & % 30.36/4.86 | set_difference(all_57_3, all_57_3) = v0 & $i(v0)) % 30.36/4.86 | % 30.36/4.86 | GROUND_INST: instantiating (10) with all_57_0, all_57_2, all_72_0, simplifying % 30.36/4.86 | with (24), (42), (55) gives: % 30.36/4.87 | (144) ? [v0: $i] : (set_difference(all_72_0, all_57_2) = v0 & % 30.36/4.87 | set_difference(all_57_0, all_57_2) = v0 & $i(v0)) % 30.36/4.87 | % 30.36/4.87 | GROUND_INST: instantiating (1) with all_74_0, all_57_0, all_57_3, simplifying % 30.36/4.87 | with (42), (124), (128) gives: % 30.36/4.87 | (145) set_union2(all_74_0, all_57_0) = all_57_3 & $i(all_57_3) % 30.36/4.87 | % 30.36/4.87 | GROUND_INST: instantiating (10) with all_57_0, all_74_0, all_57_3, simplifying % 30.36/4.87 | with (42), (124), (128) gives: % 30.36/4.87 | (146) ? [v0: $i] : (set_difference(all_57_0, all_74_0) = v0 & % 30.36/4.87 | set_difference(all_57_3, all_74_0) = v0 & $i(v0)) % 30.36/4.87 | % 30.36/4.87 | GROUND_INST: instantiating (8) with all_57_0, all_74_0, all_57_3, simplifying % 30.36/4.87 | with (42), (124), (128) gives: % 30.36/4.87 | (147) ? [v0: $i] : (set_difference(all_74_0, all_57_0) = v0 & % 30.36/4.87 | set_union2(all_57_0, v0) = all_57_3 & $i(v0) & $i(all_57_3)) % 30.36/4.87 | % 30.36/4.87 | GROUND_INST: instantiating (1) with all_57_2, all_72_0, all_122_0, simplifying % 30.36/4.87 | with (24), (123), (137) gives: % 30.36/4.87 | (148) set_union2(all_57_2, all_72_0) = all_122_0 & $i(all_122_0) % 30.36/4.87 | % 30.36/4.87 | ALPHA: (148) implies: % 30.36/4.87 | (149) $i(all_122_0) % 30.36/4.87 | % 30.36/4.87 | GROUND_INST: instantiating (2) with all_57_0, all_57_3, all_100_0, simplifying % 30.36/4.87 | with (23), (42), (85) gives: % 30.36/4.87 | (150) set_intersection2(all_57_0, all_57_3) = all_100_0 & $i(all_100_0) % 30.36/4.87 | % 30.36/4.87 | ALPHA: (150) implies: % 30.36/4.87 | (151) set_intersection2(all_57_0, all_57_3) = all_100_0 % 30.36/4.87 | % 30.36/4.87 | GROUND_INST: instantiating (14) with all_57_0, all_57_3, all_57_0, simplifying % 30.36/4.87 | with (23), (42), (61) gives: % 30.36/4.87 | (152) ? [v0: $i] : (set_difference(all_57_0, v0) = all_57_0 & % 30.36/4.87 | set_difference(all_57_0, all_57_3) = v0 & $i(v0)) % 30.36/4.87 | % 30.36/4.87 | GROUND_INST: instantiating (2) with all_57_2, all_72_0, all_92_0, simplifying % 30.36/4.87 | with (24), (131), (137) gives: % 30.36/4.87 | (153) set_intersection2(all_57_2, all_72_0) = all_92_0 & $i(all_92_0) % 30.36/4.87 | % 30.36/4.87 | ALPHA: (153) implies: % 30.36/4.87 | (154) set_intersection2(all_57_2, all_72_0) = all_92_0 % 30.36/4.87 | % 30.36/4.87 | GROUND_INST: instantiating (7) with all_57_3, all_72_0, simplifying with (23), % 30.36/4.87 | (121), (137) gives: % 30.36/4.87 | (155) set_difference(all_57_3, all_72_0) = empty_set % 30.36/4.87 | % 30.36/4.87 | GROUND_INST: instantiating (6) with all_57_2, all_72_0, simplifying with (24), % 30.36/4.87 | (56), (137) gives: % 30.36/4.87 | (156) set_intersection2(all_57_2, all_72_0) = all_57_2 % 30.36/4.87 | % 30.36/4.87 | GROUND_INST: instantiating (5) with all_74_0, all_57_3, simplifying with (23), % 30.36/4.87 | (65), (128) gives: % 30.36/4.87 | (157) set_union2(all_74_0, all_57_3) = all_57_3 % 30.36/4.87 | % 30.36/4.87 | GROUND_INST: instantiating (12) with all_74_0, all_57_3, simplifying with % 30.36/4.87 | (23), (65), (128) gives: % 30.36/4.87 | (158) ? [v0: $i] : (set_difference(all_57_3, all_74_0) = v0 & % 30.36/4.87 | set_union2(all_74_0, v0) = all_57_3 & $i(v0)) % 30.36/4.87 | % 30.36/4.87 | GROUND_INST: instantiating (9) with all_74_0, all_57_3, all_100_0, simplifying % 30.36/4.87 | with (23), (86), (128) gives: % 30.36/4.87 | (159) ? [v0: $i] : (set_union2(all_74_0, all_100_0) = v0 & % 30.36/4.87 | set_union2(all_74_0, all_57_3) = v0 & $i(v0)) % 30.36/4.87 | % 30.36/4.87 | GROUND_INST: instantiating (15) with all_57_3, all_74_0, all_100_0, % 30.36/4.87 | simplifying with (23), (86), (128) gives: % 30.36/4.87 | (160) ? [v0: $i] : (set_difference(all_57_3, all_100_0) = v0 & % 30.36/4.87 | set_intersection2(all_57_3, all_74_0) = v0 & $i(v0)) % 30.36/4.87 | % 30.36/4.87 | GROUND_INST: instantiating (t36_xboole_1) with all_57_2, all_57_0, all_92_0, % 30.36/4.87 | simplifying with (24), (42), (73) gives: % 30.36/4.87 | (161) subset(all_92_0, all_57_2) = 0 % 30.36/4.87 | % 30.36/4.87 | GROUND_INST: instantiating (15) with all_57_2, all_57_0, all_92_0, simplifying % 30.36/4.87 | with (24), (42), (73) gives: % 30.36/4.87 | (162) ? [v0: $i] : (set_difference(all_57_2, all_92_0) = v0 & % 30.36/4.87 | set_intersection2(all_57_2, all_57_0) = v0 & $i(v0)) % 30.36/4.87 | % 30.36/4.87 | GROUND_INST: instantiating (9) with all_57_3, all_57_0, empty_set, simplifying % 30.36/4.87 | with (23), (42), (60) gives: % 30.36/4.87 | (163) ? [v0: $i] : (set_union2(all_57_3, all_57_0) = v0 & % 30.36/4.87 | set_union2(all_57_3, empty_set) = v0 & $i(v0)) % 30.36/4.87 | % 30.36/4.87 | GROUND_INST: instantiating (15) with all_57_0, all_57_3, empty_set, % 30.36/4.87 | simplifying with (23), (42), (60) gives: % 30.36/4.87 | (164) ? [v0: $i] : (set_difference(all_57_0, empty_set) = v0 & % 30.36/4.87 | set_intersection2(all_57_0, all_57_3) = v0 & $i(v0)) % 30.36/4.87 | % 30.36/4.87 | GROUND_INST: instantiating (15) with all_57_0, all_57_2, all_106_0, % 30.36/4.87 | simplifying with (24), (42), (97) gives: % 30.36/4.87 | (165) ? [v0: $i] : (set_difference(all_57_0, all_106_0) = v0 & % 30.36/4.87 | set_intersection2(all_57_0, all_57_2) = v0 & $i(v0)) % 30.36/4.87 | % 30.36/4.87 | GROUND_INST: instantiating (15) with all_72_0, all_57_3, all_94_0, simplifying % 30.36/4.87 | with (23), (77), (137) gives: % 30.36/4.87 | (166) ? [v0: $i] : (set_difference(all_72_0, all_94_0) = v0 & % 30.36/4.87 | set_intersection2(all_72_0, all_57_3) = v0 & $i(v0)) % 30.36/4.87 | % 30.36/4.87 | GROUND_INST: instantiating (15) with all_72_0, all_57_0, all_92_0, simplifying % 30.36/4.87 | with (42), (74), (137) gives: % 30.36/4.87 | (167) ? [v0: $i] : (set_difference(all_72_0, all_92_0) = v0 & % 30.36/4.87 | set_intersection2(all_72_0, all_57_0) = v0 & $i(v0)) % 30.36/4.87 | % 30.36/4.87 | GROUND_INST: instantiating (11) with all_120_0, all_57_0, all_74_0, % 30.36/4.87 | simplifying with (42), (104), (133) gives: % 30.36/4.87 | (168) ? [v0: $i] : (set_difference(v0, all_57_0) = all_74_0 & % 30.36/4.87 | set_union2(all_120_0, all_57_0) = v0 & $i(v0) & $i(all_74_0)) % 30.36/4.87 | % 30.36/4.87 | GROUND_INST: instantiating (15) with all_122_0, all_57_2, all_57_0, % 30.36/4.87 | simplifying with (24), (107), (149) gives: % 30.36/4.87 | (169) ? [v0: $i] : (set_difference(all_122_0, all_57_0) = v0 & % 30.36/4.87 | set_intersection2(all_122_0, all_57_2) = v0 & $i(v0)) % 30.36/4.87 | % 30.36/4.87 | DELTA: instantiating (167) with fresh symbol all_152_0 gives: % 30.36/4.87 | (170) set_difference(all_72_0, all_92_0) = all_152_0 & % 30.36/4.87 | set_intersection2(all_72_0, all_57_0) = all_152_0 & $i(all_152_0) % 30.36/4.87 | % 30.36/4.87 | ALPHA: (170) implies: % 30.36/4.87 | (171) $i(all_152_0) % 30.36/4.87 | (172) set_difference(all_72_0, all_92_0) = all_152_0 % 30.36/4.87 | % 30.36/4.87 | DELTA: instantiating (169) with fresh symbol all_158_0 gives: % 30.36/4.87 | (173) set_difference(all_122_0, all_57_0) = all_158_0 & % 30.36/4.87 | set_intersection2(all_122_0, all_57_2) = all_158_0 & $i(all_158_0) % 30.36/4.87 | % 30.36/4.87 | ALPHA: (173) implies: % 30.36/4.87 | (174) $i(all_158_0) % 30.36/4.87 | (175) set_difference(all_122_0, all_57_0) = all_158_0 % 30.36/4.87 | % 30.36/4.87 | DELTA: instantiating (165) with fresh symbol all_162_0 gives: % 30.36/4.87 | (176) set_difference(all_57_0, all_106_0) = all_162_0 & % 30.36/4.87 | set_intersection2(all_57_0, all_57_2) = all_162_0 & $i(all_162_0) % 30.36/4.87 | % 30.36/4.87 | ALPHA: (176) implies: % 30.36/4.87 | (177) set_intersection2(all_57_0, all_57_2) = all_162_0 % 30.36/4.87 | % 30.36/4.87 | DELTA: instantiating (166) with fresh symbol all_164_0 gives: % 30.36/4.87 | (178) set_difference(all_72_0, all_94_0) = all_164_0 & % 30.36/4.87 | set_intersection2(all_72_0, all_57_3) = all_164_0 & $i(all_164_0) % 30.36/4.87 | % 30.36/4.87 | ALPHA: (178) implies: % 30.36/4.87 | (179) set_intersection2(all_72_0, all_57_3) = all_164_0 % 30.36/4.87 | % 30.36/4.87 | DELTA: instantiating (143) with fresh symbol all_168_0 gives: % 30.36/4.87 | (180) set_difference(all_57_0, all_57_3) = all_168_0 & % 30.36/4.87 | set_difference(all_57_3, all_57_3) = all_168_0 & $i(all_168_0) % 30.36/4.87 | % 30.36/4.87 | ALPHA: (180) implies: % 30.36/4.87 | (181) $i(all_168_0) % 30.36/4.88 | (182) set_difference(all_57_3, all_57_3) = all_168_0 % 30.36/4.88 | (183) set_difference(all_57_0, all_57_3) = all_168_0 % 30.36/4.88 | % 30.36/4.88 | DELTA: instantiating (158) with fresh symbol all_172_0 gives: % 30.36/4.88 | (184) set_difference(all_57_3, all_74_0) = all_172_0 & set_union2(all_74_0, % 30.36/4.88 | all_172_0) = all_57_3 & $i(all_172_0) % 30.36/4.88 | % 30.36/4.88 | ALPHA: (184) implies: % 30.36/4.88 | (185) set_difference(all_57_3, all_74_0) = all_172_0 % 30.36/4.88 | % 30.36/4.88 | DELTA: instantiating (163) with fresh symbol all_174_0 gives: % 30.36/4.88 | (186) set_union2(all_57_3, all_57_0) = all_174_0 & set_union2(all_57_3, % 30.36/4.88 | empty_set) = all_174_0 & $i(all_174_0) % 30.36/4.88 | % 30.36/4.88 | ALPHA: (186) implies: % 30.36/4.88 | (187) set_union2(all_57_3, empty_set) = all_174_0 % 30.36/4.88 | (188) set_union2(all_57_3, all_57_0) = all_174_0 % 30.36/4.88 | % 30.36/4.88 | DELTA: instantiating (162) with fresh symbol all_176_0 gives: % 30.36/4.88 | (189) set_difference(all_57_2, all_92_0) = all_176_0 & % 30.36/4.88 | set_intersection2(all_57_2, all_57_0) = all_176_0 & $i(all_176_0) % 30.36/4.88 | % 30.36/4.88 | ALPHA: (189) implies: % 30.36/4.88 | (190) set_intersection2(all_57_2, all_57_0) = all_176_0 % 30.36/4.88 | (191) set_difference(all_57_2, all_92_0) = all_176_0 % 30.36/4.88 | % 30.36/4.88 | DELTA: instantiating (141) with fresh symbol all_178_0 gives: % 30.36/4.88 | (192) set_difference(all_72_0, all_106_0) = all_178_0 & % 30.36/4.88 | set_difference(all_57_2, all_106_0) = all_178_0 & $i(all_178_0) % 30.36/4.88 | % 30.36/4.88 | ALPHA: (192) implies: % 30.36/4.88 | (193) set_difference(all_72_0, all_106_0) = all_178_0 % 30.36/4.88 | % 30.36/4.88 | DELTA: instantiating (146) with fresh symbol all_182_0 gives: % 30.36/4.88 | (194) set_difference(all_57_0, all_74_0) = all_182_0 & % 30.36/4.88 | set_difference(all_57_3, all_74_0) = all_182_0 & $i(all_182_0) % 30.36/4.88 | % 30.36/4.88 | ALPHA: (194) implies: % 30.36/4.88 | (195) set_difference(all_57_3, all_74_0) = all_182_0 % 30.36/4.88 | (196) set_difference(all_57_0, all_74_0) = all_182_0 % 30.36/4.88 | % 30.36/4.88 | DELTA: instantiating (159) with fresh symbol all_186_0 gives: % 30.36/4.88 | (197) set_union2(all_74_0, all_100_0) = all_186_0 & set_union2(all_74_0, % 30.36/4.88 | all_57_3) = all_186_0 & $i(all_186_0) % 30.36/4.88 | % 30.36/4.88 | ALPHA: (197) implies: % 30.36/4.88 | (198) set_union2(all_74_0, all_57_3) = all_186_0 % 30.36/4.88 | (199) set_union2(all_74_0, all_100_0) = all_186_0 % 30.36/4.88 | % 30.36/4.88 | DELTA: instantiating (164) with fresh symbol all_190_0 gives: % 30.36/4.88 | (200) set_difference(all_57_0, empty_set) = all_190_0 & % 30.36/4.88 | set_intersection2(all_57_0, all_57_3) = all_190_0 & $i(all_190_0) % 30.36/4.88 | % 30.36/4.88 | ALPHA: (200) implies: % 30.36/4.88 | (201) set_intersection2(all_57_0, all_57_3) = all_190_0 % 30.36/4.88 | % 30.36/4.88 | DELTA: instantiating (160) with fresh symbol all_192_0 gives: % 30.36/4.88 | (202) set_difference(all_57_3, all_100_0) = all_192_0 & % 30.36/4.88 | set_intersection2(all_57_3, all_74_0) = all_192_0 & $i(all_192_0) % 30.36/4.88 | % 30.36/4.88 | ALPHA: (202) implies: % 30.36/4.88 | (203) $i(all_192_0) % 30.36/4.88 | (204) set_difference(all_57_3, all_100_0) = all_192_0 % 30.36/4.88 | % 30.36/4.88 | DELTA: instantiating (152) with fresh symbol all_196_0 gives: % 30.36/4.88 | (205) set_difference(all_57_0, all_196_0) = all_57_0 & % 30.36/4.88 | set_difference(all_57_0, all_57_3) = all_196_0 & $i(all_196_0) % 30.36/4.88 | % 30.36/4.88 | ALPHA: (205) implies: % 30.36/4.88 | (206) set_difference(all_57_0, all_57_3) = all_196_0 % 30.36/4.88 | % 30.36/4.88 | DELTA: instantiating (144) with fresh symbol all_198_0 gives: % 30.36/4.88 | (207) set_difference(all_72_0, all_57_2) = all_198_0 & % 30.36/4.88 | set_difference(all_57_0, all_57_2) = all_198_0 & $i(all_198_0) % 30.36/4.88 | % 30.36/4.88 | ALPHA: (207) implies: % 30.36/4.88 | (208) set_difference(all_57_0, all_57_2) = all_198_0 % 30.36/4.88 | (209) set_difference(all_72_0, all_57_2) = all_198_0 % 30.36/4.88 | % 30.36/4.88 | DELTA: instantiating (168) with fresh symbol all_216_0 gives: % 30.36/4.88 | (210) set_difference(all_216_0, all_57_0) = all_74_0 & % 30.36/4.88 | set_union2(all_120_0, all_57_0) = all_216_0 & $i(all_216_0) & % 30.36/4.88 | $i(all_74_0) % 30.36/4.88 | % 30.36/4.88 | ALPHA: (210) implies: % 30.36/4.88 | (211) $i(all_216_0) % 30.36/4.88 | (212) set_union2(all_120_0, all_57_0) = all_216_0 % 30.36/4.88 | % 30.36/4.88 | DELTA: instantiating (138) with fresh symbol all_218_0 gives: % 30.36/4.88 | (213) set_difference(all_94_0, all_57_3) = all_218_0 & set_union2(all_57_3, % 30.36/4.88 | all_218_0) = all_72_0 & $i(all_218_0) & $i(all_72_0) % 30.36/4.88 | % 30.36/4.88 | ALPHA: (213) implies: % 30.36/4.88 | (214) $i(all_218_0) % 30.36/4.88 | (215) set_union2(all_57_3, all_218_0) = all_72_0 % 30.36/4.88 | % 30.36/4.88 | DELTA: instantiating (135) with fresh symbol all_234_0 gives: % 30.36/4.88 | (216) set_difference(all_57_0, all_57_3) = all_234_0 & set_union2(all_57_3, % 30.36/4.88 | all_234_0) = all_120_0 & $i(all_234_0) & $i(all_120_0) % 30.36/4.88 | % 30.36/4.88 | ALPHA: (216) implies: % 30.36/4.88 | (217) set_difference(all_57_0, all_57_3) = all_234_0 % 30.36/4.88 | % 30.36/4.88 | DELTA: instantiating (147) with fresh symbol all_242_0 gives: % 30.36/4.88 | (218) set_difference(all_74_0, all_57_0) = all_242_0 & set_union2(all_57_0, % 30.36/4.88 | all_242_0) = all_57_3 & $i(all_242_0) & $i(all_57_3) % 30.36/4.88 | % 30.36/4.88 | ALPHA: (218) implies: % 30.36/4.88 | (219) $i(all_242_0) % 30.36/4.88 | (220) set_union2(all_57_0, all_242_0) = all_57_3 % 30.36/4.88 | (221) set_difference(all_74_0, all_57_0) = all_242_0 % 30.36/4.88 | % 30.36/4.88 | GROUND_INST: instantiating (17) with all_120_0, all_174_0, all_57_0, all_57_3, % 30.36/4.88 | simplifying with (103), (188) gives: % 30.36/4.88 | (222) all_174_0 = all_120_0 % 30.36/4.88 | % 30.36/4.88 | GROUND_INST: instantiating (17) with all_57_3, all_174_0, all_57_0, all_57_3, % 30.36/4.88 | simplifying with (142), (188) gives: % 30.36/4.88 | (223) all_174_0 = all_57_3 % 30.36/4.88 | % 30.36/4.88 | GROUND_INST: instantiating (17) with all_122_0, all_72_0, all_57_2, all_72_0, % 30.36/4.88 | simplifying with (123), (139) gives: % 30.36/4.88 | (224) all_122_0 = all_72_0 % 30.36/4.88 | % 30.36/4.88 | GROUND_INST: instantiating (17) with all_57_3, all_186_0, all_57_3, all_74_0, % 30.36/4.88 | simplifying with (157), (198) gives: % 30.36/4.88 | (225) all_186_0 = all_57_3 % 30.36/4.88 | % 30.36/4.88 | GROUND_INST: instantiating (18) with all_57_2, all_92_0, all_72_0, all_57_2, % 30.36/4.88 | simplifying with (154), (156) gives: % 30.36/4.88 | (226) all_92_0 = all_57_2 % 30.36/4.88 | % 30.36/4.88 | GROUND_INST: instantiating (18) with all_57_0, all_190_0, all_57_3, all_57_0, % 30.36/4.88 | simplifying with (61), (201) gives: % 30.36/4.88 | (227) all_190_0 = all_57_0 % 30.36/4.88 | % 30.36/4.88 | GROUND_INST: instantiating (18) with all_100_0, all_190_0, all_57_3, all_57_0, % 30.36/4.88 | simplifying with (151), (201) gives: % 30.36/4.88 | (228) all_190_0 = all_100_0 % 30.36/4.88 | % 30.36/4.88 | GROUND_INST: instantiating (20) with all_100_0, all_182_0, all_74_0, all_57_3, % 30.36/4.88 | simplifying with (86), (195) gives: % 30.36/4.88 | (229) all_182_0 = all_100_0 % 30.36/4.88 | % 30.36/4.88 | GROUND_INST: instantiating (20) with all_172_0, all_182_0, all_74_0, all_57_3, % 30.36/4.88 | simplifying with (185), (195) gives: % 30.36/4.88 | (230) all_182_0 = all_172_0 % 30.36/4.88 | % 30.36/4.88 | GROUND_INST: instantiating (20) with all_168_0, all_196_0, all_57_3, all_57_0, % 30.36/4.88 | simplifying with (183), (206) gives: % 30.36/4.88 | (231) all_196_0 = all_168_0 % 30.36/4.88 | % 30.36/4.88 | GROUND_INST: instantiating (20) with empty_set, all_234_0, all_57_3, all_57_0, % 30.36/4.88 | simplifying with (60), (217) gives: % 30.36/4.88 | (232) all_234_0 = empty_set % 30.36/4.88 | % 30.36/4.88 | GROUND_INST: instantiating (20) with all_196_0, all_234_0, all_57_3, all_57_0, % 30.36/4.88 | simplifying with (206), (217) gives: % 30.36/4.88 | (233) all_234_0 = all_196_0 % 30.36/4.88 | % 30.36/4.88 | GROUND_INST: instantiating (20) with all_106_0, all_198_0, all_57_2, all_57_0, % 30.36/4.88 | simplifying with (97), (208) gives: % 30.36/4.88 | (234) all_198_0 = all_106_0 % 30.36/4.88 | % 30.36/4.88 | GROUND_INST: instantiating (20) with all_57_0, all_198_0, all_57_2, all_72_0, % 30.36/4.88 | simplifying with (119), (209) gives: % 30.36/4.88 | (235) all_198_0 = all_57_0 % 30.36/4.88 | % 30.36/4.88 | COMBINE_EQS: (232), (233) imply: % 30.36/4.88 | (236) all_196_0 = empty_set % 30.36/4.88 | % 30.36/4.88 | SIMP: (236) implies: % 30.36/4.88 | (237) all_196_0 = empty_set % 30.36/4.88 | % 30.36/4.88 | COMBINE_EQS: (234), (235) imply: % 30.36/4.88 | (238) all_106_0 = all_57_0 % 30.36/4.88 | % 30.36/4.88 | SIMP: (238) implies: % 30.36/4.88 | (239) all_106_0 = all_57_0 % 30.36/4.88 | % 30.36/4.88 | COMBINE_EQS: (231), (237) imply: % 30.36/4.88 | (240) all_168_0 = empty_set % 30.36/4.88 | % 30.36/4.88 | SIMP: (240) implies: % 30.36/4.88 | (241) all_168_0 = empty_set % 30.36/4.88 | % 30.36/4.88 | COMBINE_EQS: (227), (228) imply: % 30.36/4.88 | (242) all_100_0 = all_57_0 % 30.36/4.88 | % 30.36/4.88 | COMBINE_EQS: (229), (230) imply: % 30.36/4.88 | (243) all_172_0 = all_100_0 % 30.36/4.88 | % 30.36/4.88 | COMBINE_EQS: (222), (223) imply: % 30.36/4.88 | (244) all_120_0 = all_57_3 % 30.36/4.88 | % 30.36/4.88 | COMBINE_EQS: (242), (243) imply: % 30.36/4.88 | (245) all_172_0 = all_57_0 % 30.36/4.88 | % 30.36/4.88 | COMBINE_EQS: (230), (245) imply: % 30.36/4.88 | (246) all_182_0 = all_57_0 % 30.36/4.88 | % 30.36/4.88 | REDUCE: (175), (224) imply: % 30.36/4.88 | (247) set_difference(all_72_0, all_57_0) = all_158_0 % 30.36/4.88 | % 30.36/4.88 | REDUCE: (193), (239) imply: % 30.36/4.88 | (248) set_difference(all_72_0, all_57_0) = all_178_0 % 30.36/4.88 | % 30.36/4.88 | REDUCE: (172), (226) imply: % 30.36/4.88 | (249) set_difference(all_72_0, all_57_2) = all_152_0 % 30.36/4.88 | % 30.36/4.88 | REDUCE: (74), (226) imply: % 30.36/4.88 | (250) set_difference(all_72_0, all_57_0) = all_57_2 % 30.36/4.88 | % 30.36/4.88 | REDUCE: (196), (246) imply: % 30.36/4.88 | (251) set_difference(all_57_0, all_74_0) = all_57_0 % 30.36/4.89 | % 30.36/4.89 | REDUCE: (191), (226) imply: % 30.36/4.89 | (252) set_difference(all_57_2, all_57_2) = all_176_0 % 30.36/4.89 | % 30.36/4.89 | REDUCE: (204), (242) imply: % 30.36/4.89 | (253) set_difference(all_57_3, all_57_0) = all_192_0 % 30.36/4.89 | % 30.36/4.89 | REDUCE: (182), (241) imply: % 30.36/4.89 | (254) set_difference(all_57_3, all_57_3) = empty_set % 30.36/4.89 | % 30.36/4.89 | REDUCE: (161), (226) imply: % 30.36/4.89 | (255) subset(all_57_2, all_57_2) = 0 % 30.36/4.89 | % 30.36/4.89 | REDUCE: (134), (244) imply: % 30.36/4.89 | (256) subset(all_57_3, all_57_3) = 0 % 30.36/4.89 | % 30.36/4.89 | REDUCE: (212), (244) imply: % 30.36/4.89 | (257) set_union2(all_57_3, all_57_0) = all_216_0 % 30.36/4.89 | % 30.36/4.89 | REDUCE: (199), (225), (242) imply: % 30.36/4.89 | (258) set_union2(all_74_0, all_57_0) = all_57_3 % 30.36/4.89 | % 30.36/4.89 | REDUCE: (187), (223) imply: % 30.36/4.89 | (259) set_union2(all_57_3, empty_set) = all_57_3 % 30.36/4.89 | % 30.36/4.89 | REDUCE: (181), (241) imply: % 30.36/4.89 | (260) $i(empty_set) % 30.36/4.89 | % 30.36/4.89 | GROUND_INST: instantiating (17) with all_57_3, all_216_0, all_57_0, all_57_3, % 30.36/4.89 | simplifying with (142), (257) gives: % 30.36/4.89 | (261) all_216_0 = all_57_3 % 30.36/4.89 | % 30.36/4.89 | GROUND_INST: instantiating (20) with all_74_0, all_192_0, all_57_0, all_57_3, % 30.36/4.89 | simplifying with (40), (253) gives: % 30.36/4.89 | (262) all_192_0 = all_74_0 % 30.36/4.89 | % 30.36/4.89 | GROUND_INST: instantiating (20) with all_57_0, all_152_0, all_57_2, all_72_0, % 30.36/4.89 | simplifying with (119), (249) gives: % 30.36/4.89 | (263) all_152_0 = all_57_0 % 30.36/4.89 | % 30.36/4.89 | GROUND_INST: instantiating (20) with all_158_0, all_178_0, all_57_0, all_72_0, % 30.36/4.89 | simplifying with (247), (248) gives: % 30.36/4.89 | (264) all_178_0 = all_158_0 % 30.36/4.89 | % 30.36/4.89 | GROUND_INST: instantiating (20) with all_57_2, all_178_0, all_57_0, all_72_0, % 30.36/4.89 | simplifying with (248), (250) gives: % 30.36/4.89 | (265) all_178_0 = all_57_2 % 30.36/4.89 | % 30.36/4.89 | COMBINE_EQS: (264), (265) imply: % 30.36/4.89 | (266) all_158_0 = all_57_2 % 30.36/4.89 | % 30.36/4.89 | SIMP: (266) implies: % 30.36/4.89 | (267) all_158_0 = all_57_2 % 30.36/4.89 | % 30.36/4.89 | GROUND_INST: instantiating (10) with all_57_3, empty_set, all_57_3, % 30.36/4.89 | simplifying with (23), (259), (260) gives: % 30.36/4.89 | (268) ? [v0: $i] : (set_difference(all_57_3, empty_set) = v0 & $i(v0)) % 30.36/4.89 | % 30.36/4.89 | GROUND_INST: instantiating (1) with all_218_0, all_57_3, all_72_0, simplifying % 30.36/4.89 | with (23), (214), (215) gives: % 30.36/4.89 | (269) set_union2(all_218_0, all_57_3) = all_72_0 & $i(all_72_0) % 30.36/4.89 | % 30.36/4.89 | GROUND_INST: instantiating (1) with all_242_0, all_57_0, all_57_3, simplifying % 30.36/4.89 | with (42), (219), (220) gives: % 30.36/4.89 | (270) set_union2(all_242_0, all_57_0) = all_57_3 & $i(all_57_3) % 30.36/4.89 | % 30.36/4.89 | GROUND_INST: instantiating (10) with all_57_0, all_242_0, all_57_3, % 30.36/4.89 | simplifying with (42), (219), (220) gives: % 30.36/4.89 | (271) ? [v0: $i] : (set_difference(all_57_0, all_242_0) = v0 & % 30.36/4.89 | set_difference(all_57_3, all_242_0) = v0 & $i(v0)) % 30.36/4.89 | % 30.36/4.89 | GROUND_INST: instantiating (10) with all_74_0, all_57_0, all_57_3, simplifying % 30.36/4.89 | with (42), (128), (258) gives: % 30.36/4.89 | (272) ? [v0: $i] : (set_difference(all_74_0, all_57_0) = v0 & % 30.36/4.89 | set_difference(all_57_3, all_57_0) = v0 & $i(v0)) % 30.36/4.89 | % 30.36/4.89 | GROUND_INST: instantiating (2) with all_57_0, all_57_2, all_176_0, simplifying % 30.36/4.89 | with (24), (42), (190) gives: % 30.36/4.89 | (273) set_intersection2(all_57_0, all_57_2) = all_176_0 & $i(all_176_0) % 30.36/4.89 | % 30.36/4.89 | ALPHA: (273) implies: % 30.36/4.89 | (274) set_intersection2(all_57_0, all_57_2) = all_176_0 % 30.36/4.89 | % 30.36/4.89 | GROUND_INST: instantiating (2) with all_57_3, all_72_0, all_164_0, simplifying % 30.36/4.89 | with (23), (137), (179) gives: % 30.36/4.89 | (275) set_intersection2(all_57_3, all_72_0) = all_164_0 & $i(all_164_0) % 30.36/4.89 | % 30.36/4.89 | ALPHA: (275) implies: % 30.36/4.89 | (276) set_intersection2(all_57_3, all_72_0) = all_164_0 % 30.36/4.89 | % 30.36/4.89 | GROUND_INST: instantiating (6) with all_57_3, all_57_3, simplifying with (23), % 30.36/4.89 | (256) gives: % 30.36/4.89 | (277) set_intersection2(all_57_3, all_57_3) = all_57_3 % 30.36/4.89 | % 30.36/4.89 | GROUND_INST: instantiating (7) with all_57_2, all_57_2, simplifying with (24), % 30.36/4.89 | (255) gives: % 30.36/4.89 | (278) set_difference(all_57_2, all_57_2) = empty_set % 30.36/4.89 | % 30.36/4.89 | GROUND_INST: instantiating (12) with all_57_2, all_57_2, simplifying with % 30.36/4.89 | (24), (255) gives: % 30.36/4.89 | (279) ? [v0: $i] : (set_difference(all_57_2, all_57_2) = v0 & % 30.36/4.89 | set_union2(all_57_2, v0) = all_57_2 & $i(v0)) % 30.36/4.89 | % 30.36/4.89 | GROUND_INST: instantiating (15) with all_57_3, all_57_3, empty_set, % 30.36/4.89 | simplifying with (23), (254) gives: % 30.36/4.89 | (280) ? [v0: $i] : (set_difference(all_57_3, empty_set) = v0 & % 30.36/4.89 | set_intersection2(all_57_3, all_57_3) = v0 & $i(v0)) % 30.36/4.89 | % 30.36/4.89 | GROUND_INST: instantiating (15) with all_57_3, all_72_0, empty_set, % 30.36/4.89 | simplifying with (23), (137), (155) gives: % 30.36/4.89 | (281) ? [v0: $i] : (set_difference(all_57_3, empty_set) = v0 & % 30.36/4.89 | set_intersection2(all_57_3, all_72_0) = v0 & $i(v0)) % 30.36/4.89 | % 30.36/4.89 | DELTA: instantiating (268) with fresh symbol all_304_0 gives: % 30.36/4.89 | (282) set_difference(all_57_3, empty_set) = all_304_0 & $i(all_304_0) % 30.36/4.89 | % 30.36/4.89 | ALPHA: (282) implies: % 30.36/4.89 | (283) set_difference(all_57_3, empty_set) = all_304_0 % 30.36/4.89 | % 30.36/4.89 | DELTA: instantiating (279) with fresh symbol all_320_0 gives: % 30.36/4.89 | (284) set_difference(all_57_2, all_57_2) = all_320_0 & set_union2(all_57_2, % 30.36/4.89 | all_320_0) = all_57_2 & $i(all_320_0) % 30.36/4.89 | % 30.36/4.89 | ALPHA: (284) implies: % 30.36/4.89 | (285) set_difference(all_57_2, all_57_2) = all_320_0 % 30.36/4.89 | % 30.36/4.89 | DELTA: instantiating (281) with fresh symbol all_350_0 gives: % 30.36/4.89 | (286) set_difference(all_57_3, empty_set) = all_350_0 & % 30.36/4.89 | set_intersection2(all_57_3, all_72_0) = all_350_0 & $i(all_350_0) % 30.36/4.89 | % 30.36/4.89 | ALPHA: (286) implies: % 30.36/4.89 | (287) set_intersection2(all_57_3, all_72_0) = all_350_0 % 30.36/4.89 | (288) set_difference(all_57_3, empty_set) = all_350_0 % 30.36/4.89 | % 30.36/4.89 | DELTA: instantiating (271) with fresh symbol all_358_0 gives: % 30.36/4.89 | (289) set_difference(all_57_0, all_242_0) = all_358_0 & % 30.36/4.89 | set_difference(all_57_3, all_242_0) = all_358_0 & $i(all_358_0) % 30.36/4.89 | % 30.36/4.89 | ALPHA: (289) implies: % 30.36/4.89 | (290) set_difference(all_57_3, all_242_0) = all_358_0 % 30.36/4.89 | (291) set_difference(all_57_0, all_242_0) = all_358_0 % 30.36/4.89 | % 30.36/4.89 | DELTA: instantiating (280) with fresh symbol all_364_0 gives: % 30.36/4.89 | (292) set_difference(all_57_3, empty_set) = all_364_0 & % 30.36/4.89 | set_intersection2(all_57_3, all_57_3) = all_364_0 & $i(all_364_0) % 30.36/4.89 | % 30.36/4.89 | ALPHA: (292) implies: % 30.36/4.89 | (293) set_intersection2(all_57_3, all_57_3) = all_364_0 % 30.36/4.89 | (294) set_difference(all_57_3, empty_set) = all_364_0 % 30.36/4.89 | % 30.36/4.89 | DELTA: instantiating (272) with fresh symbol all_392_0 gives: % 30.36/4.89 | (295) set_difference(all_74_0, all_57_0) = all_392_0 & % 30.36/4.89 | set_difference(all_57_3, all_57_0) = all_392_0 & $i(all_392_0) % 30.36/4.89 | % 30.36/4.89 | ALPHA: (295) implies: % 30.36/4.89 | (296) set_difference(all_57_3, all_57_0) = all_392_0 % 30.36/4.89 | (297) set_difference(all_74_0, all_57_0) = all_392_0 % 30.36/4.89 | % 30.36/4.89 | GROUND_INST: instantiating (18) with all_57_3, all_364_0, all_57_3, all_57_3, % 30.36/4.89 | simplifying with (277), (293) gives: % 30.36/4.89 | (298) all_364_0 = all_57_3 % 30.36/4.89 | % 30.36/4.89 | GROUND_INST: instantiating (18) with all_164_0, all_350_0, all_72_0, all_57_3, % 30.36/4.89 | simplifying with (276), (287) gives: % 30.36/4.89 | (299) all_350_0 = all_164_0 % 30.36/4.89 | % 30.36/4.89 | GROUND_INST: instantiating (18) with all_162_0, all_176_0, all_57_2, all_57_0, % 30.36/4.89 | simplifying with (177), (274) gives: % 30.36/4.89 | (300) all_176_0 = all_162_0 % 30.36/4.89 | % 30.36/4.89 | GROUND_INST: instantiating (20) with all_350_0, all_364_0, empty_set, % 30.36/4.89 | all_57_3, simplifying with (288), (294) gives: % 30.36/4.89 | (301) all_364_0 = all_350_0 % 30.36/4.89 | % 30.36/4.89 | GROUND_INST: instantiating (20) with all_304_0, all_364_0, empty_set, % 30.36/4.89 | all_57_3, simplifying with (283), (294) gives: % 30.36/4.89 | (302) all_364_0 = all_304_0 % 30.36/4.89 | % 30.36/4.89 | GROUND_INST: instantiating (20) with all_74_0, all_392_0, all_57_0, all_57_3, % 30.36/4.89 | simplifying with (40), (296) gives: % 30.36/4.89 | (303) all_392_0 = all_74_0 % 30.36/4.89 | % 30.36/4.89 | GROUND_INST: instantiating (20) with all_176_0, all_320_0, all_57_2, all_57_2, % 30.36/4.89 | simplifying with (252), (285) gives: % 30.36/4.89 | (304) all_320_0 = all_176_0 % 30.36/4.89 | % 30.36/4.89 | GROUND_INST: instantiating (20) with empty_set, all_320_0, all_57_2, all_57_2, % 30.36/4.89 | simplifying with (278), (285) gives: % 30.36/4.89 | (305) all_320_0 = empty_set % 30.36/4.89 | % 30.36/4.89 | GROUND_INST: instantiating (20) with all_242_0, all_392_0, all_57_0, all_74_0, % 30.36/4.89 | simplifying with (221), (297) gives: % 30.36/4.89 | (306) all_392_0 = all_242_0 % 30.36/4.89 | % 30.36/4.89 | COMBINE_EQS: (303), (306) imply: % 30.36/4.89 | (307) all_242_0 = all_74_0 % 30.36/4.89 | % 30.36/4.89 | SIMP: (307) implies: % 30.36/4.89 | (308) all_242_0 = all_74_0 % 30.36/4.89 | % 30.36/4.89 | COMBINE_EQS: (298), (301) imply: % 30.36/4.89 | (309) all_350_0 = all_57_3 % 30.36/4.89 | % 30.36/4.89 | COMBINE_EQS: (301), (302) imply: % 30.36/4.89 | (310) all_350_0 = all_304_0 % 30.36/4.89 | % 30.36/4.89 | COMBINE_EQS: (299), (310) imply: % 30.36/4.89 | (311) all_304_0 = all_164_0 % 30.36/4.89 | % 30.36/4.89 | COMBINE_EQS: (309), (310) imply: % 30.36/4.89 | (312) all_304_0 = all_57_3 % 30.36/4.89 | % 30.36/4.89 | COMBINE_EQS: (304), (305) imply: % 30.36/4.89 | (313) all_176_0 = empty_set % 30.36/4.89 | % 30.36/4.89 | SIMP: (313) implies: % 30.36/4.89 | (314) all_176_0 = empty_set % 30.36/4.89 | % 30.36/4.89 | COMBINE_EQS: (311), (312) imply: % 30.36/4.89 | (315) all_164_0 = all_57_3 % 30.36/4.89 | % 30.36/4.89 | COMBINE_EQS: (300), (314) imply: % 30.36/4.89 | (316) all_162_0 = empty_set % 30.36/4.89 | % 30.36/4.89 | SIMP: (316) implies: % 30.36/4.89 | (317) all_162_0 = empty_set % 30.36/4.89 | % 30.36/4.89 | REDUCE: (291), (308) imply: % 30.36/4.89 | (318) set_difference(all_57_0, all_74_0) = all_358_0 % 30.36/4.89 | % 30.36/4.89 | REDUCE: (290), (308) imply: % 30.36/4.89 | (319) set_difference(all_57_3, all_74_0) = all_358_0 % 30.36/4.89 | % 30.36/4.89 | REDUCE: (283), (312) imply: % 30.36/4.89 | (320) set_difference(all_57_3, empty_set) = all_57_3 % 30.36/4.89 | % 30.36/4.89 | REDUCE: (177), (317) imply: % 30.36/4.89 | (321) set_intersection2(all_57_0, all_57_2) = empty_set % 30.36/4.89 | % 30.36/4.89 | GROUND_INST: instantiating (20) with all_57_0, all_358_0, all_74_0, all_57_0, % 30.36/4.89 | simplifying with (251), (318) gives: % 30.36/4.89 | (322) all_358_0 = all_57_0 % 30.36/4.89 | % 30.36/4.89 | REDUCE: (319), (322) imply: % 30.36/4.90 | (323) set_difference(all_57_3, all_74_0) = all_57_0 % 30.36/4.90 | % 30.36/4.90 | BETA: splitting (27) gives: % 30.36/4.90 | % 30.36/4.90 | Case 1: % 30.36/4.90 | | % 30.36/4.90 | | (324) all_57_0 = all_57_3 & ~ (all_57_1 = 0) % 30.36/4.90 | | % 30.36/4.90 | | ALPHA: (324) implies: % 30.36/4.90 | | (325) all_57_0 = all_57_3 % 30.36/4.90 | | (326) ~ (all_57_1 = 0) % 30.36/4.90 | | % 30.36/4.90 | | REDUCE: (321), (325) imply: % 30.36/4.90 | | (327) set_intersection2(all_57_3, all_57_2) = empty_set % 30.36/4.90 | | % 30.36/4.90 | | BETA: splitting (34) gives: % 30.36/4.90 | | % 30.36/4.90 | | Case 1: % 30.36/4.90 | | | % 30.36/4.90 | | | (328) all_57_1 = 0 % 30.36/4.90 | | | % 30.36/4.90 | | | REDUCE: (326), (328) imply: % 30.36/4.90 | | | (329) $false % 30.62/4.90 | | | % 30.62/4.90 | | | CLOSE: (329) is inconsistent. % 30.62/4.90 | | | % 30.62/4.90 | | Case 2: % 30.62/4.90 | | | % 30.62/4.90 | | | (330) ? [v0: $i] : ( ~ (v0 = empty_set) & set_intersection2(all_57_3, % 30.62/4.90 | | | all_57_2) = v0 & $i(v0)) % 30.62/4.90 | | | % 30.62/4.90 | | | DELTA: instantiating (330) with fresh symbol all_548_0 gives: % 30.62/4.90 | | | (331) ~ (all_548_0 = empty_set) & set_intersection2(all_57_3, % 30.62/4.90 | | | all_57_2) = all_548_0 & $i(all_548_0) % 30.62/4.90 | | | % 30.62/4.90 | | | ALPHA: (331) implies: % 30.62/4.90 | | | (332) ~ (all_548_0 = empty_set) % 30.62/4.90 | | | (333) set_intersection2(all_57_3, all_57_2) = all_548_0 % 30.62/4.90 | | | % 30.62/4.90 | | | BETA: splitting (33) gives: % 30.62/4.90 | | | % 30.62/4.90 | | | Case 1: % 30.62/4.90 | | | | % 30.62/4.90 | | | | (334) all_57_1 = 0 % 30.62/4.90 | | | | % 30.62/4.90 | | | | REDUCE: (326), (334) imply: % 30.62/4.90 | | | | (335) $false % 30.62/4.90 | | | | % 30.62/4.90 | | | | CLOSE: (335) is inconsistent. % 30.62/4.90 | | | | % 30.62/4.90 | | | Case 2: % 30.62/4.90 | | | | % 30.62/4.90 | | | | (336) ? [v0: $i] : ? [v1: $i] : (set_intersection2(all_57_3, % 30.62/4.90 | | | | all_57_2) = v0 & in(v1, v0) = 0 & $i(v1) & $i(v0)) % 30.62/4.90 | | | | % 30.62/4.90 | | | | DELTA: instantiating (336) with fresh symbols all_557_0, all_557_1 % 30.62/4.90 | | | | gives: % 30.62/4.90 | | | | (337) set_intersection2(all_57_3, all_57_2) = all_557_1 & % 30.62/4.90 | | | | in(all_557_0, all_557_1) = 0 & $i(all_557_0) & $i(all_557_1) % 30.62/4.90 | | | | % 30.62/4.90 | | | | ALPHA: (337) implies: % 30.62/4.90 | | | | (338) set_intersection2(all_57_3, all_57_2) = all_557_1 % 30.62/4.90 | | | | % 30.62/4.90 | | | | GROUND_INST: instantiating (18) with all_548_0, all_557_1, all_57_2, % 30.62/4.90 | | | | all_57_3, simplifying with (333), (338) gives: % 30.62/4.90 | | | | (339) all_557_1 = all_548_0 % 30.62/4.90 | | | | % 30.62/4.90 | | | | GROUND_INST: instantiating (18) with empty_set, all_557_1, all_57_2, % 30.62/4.90 | | | | all_57_3, simplifying with (327), (338) gives: % 30.62/4.90 | | | | (340) all_557_1 = empty_set % 30.62/4.90 | | | | % 30.62/4.90 | | | | COMBINE_EQS: (339), (340) imply: % 30.62/4.90 | | | | (341) all_548_0 = empty_set % 30.62/4.90 | | | | % 30.62/4.90 | | | | SIMP: (341) implies: % 30.62/4.90 | | | | (342) all_548_0 = empty_set % 30.62/4.90 | | | | % 30.62/4.90 | | | | REDUCE: (332), (342) imply: % 30.62/4.90 | | | | (343) $false % 30.62/4.90 | | | | % 30.62/4.90 | | | | CLOSE: (343) is inconsistent. % 30.62/4.90 | | | | % 30.62/4.90 | | | End of split % 30.62/4.90 | | | % 30.62/4.90 | | End of split % 30.62/4.90 | | % 30.62/4.90 | Case 2: % 30.62/4.90 | | % 30.62/4.90 | | (344) all_57_1 = 0 & ~ (all_57_0 = all_57_3) % 30.62/4.90 | | % 30.62/4.90 | | ALPHA: (344) implies: % 30.62/4.90 | | (345) all_57_1 = 0 % 30.62/4.90 | | (346) ~ (all_57_0 = all_57_3) % 30.62/4.90 | | % 30.62/4.90 | | REDUCE: (26), (345) imply: % 30.62/4.90 | | (347) disjoint(all_57_3, all_57_2) = 0 % 30.62/4.90 | | % 30.62/4.90 | | BETA: splitting (59) gives: % 30.62/4.90 | | % 30.62/4.90 | | Case 1: % 30.62/4.90 | | | % 30.62/4.90 | | | (348) all_74_0 = empty_set % 30.62/4.90 | | | % 30.62/4.90 | | | REDUCE: (323), (348) imply: % 30.62/4.90 | | | (349) set_difference(all_57_3, empty_set) = all_57_0 % 30.62/4.90 | | | % 30.62/4.90 | | | GROUND_INST: instantiating (20) with all_57_3, all_57_0, empty_set, % 30.62/4.90 | | | all_57_3, simplifying with (320), (349) gives: % 30.62/4.90 | | | (350) all_57_0 = all_57_3 % 30.62/4.90 | | | % 30.62/4.90 | | | REDUCE: (346), (350) imply: % 30.62/4.90 | | | (351) $false % 30.62/4.90 | | | % 30.62/4.90 | | | CLOSE: (351) is inconsistent. % 30.62/4.90 | | | % 30.62/4.90 | | Case 2: % 30.62/4.90 | | | % 30.62/4.90 | | | (352) ? [v0: int] : ( ~ (v0 = 0) & disjoint(all_57_3, all_57_2) = v0) % 30.62/4.90 | | | % 30.62/4.90 | | | DELTA: instantiating (352) with fresh symbol all_552_0 gives: % 30.62/4.90 | | | (353) ~ (all_552_0 = 0) & disjoint(all_57_3, all_57_2) = all_552_0 % 30.62/4.90 | | | % 30.62/4.90 | | | ALPHA: (353) implies: % 30.62/4.90 | | | (354) ~ (all_552_0 = 0) % 30.62/4.90 | | | (355) disjoint(all_57_3, all_57_2) = all_552_0 % 30.62/4.90 | | | % 30.62/4.90 | | | GROUND_INST: instantiating (21) with 0, all_552_0, all_57_2, all_57_3, % 30.62/4.90 | | | simplifying with (347), (355) gives: % 30.62/4.90 | | | (356) all_552_0 = 0 % 30.62/4.90 | | | % 30.62/4.90 | | | REDUCE: (354), (356) imply: % 30.62/4.90 | | | (357) $false % 30.62/4.90 | | | % 30.62/4.90 | | | CLOSE: (357) is inconsistent. % 30.62/4.90 | | | % 30.62/4.90 | | End of split % 30.62/4.90 | | % 30.62/4.90 | End of split % 30.62/4.90 | % 30.62/4.90 End of proof % 30.62/4.90 % SZS output end Proof for theBenchmark % 30.62/4.90 % 30.62/4.90 4294ms %------------------------------------------------------------------------------