TSTP Solution File: SEU141+2 by Princess---230619
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%------------------------------------------------------------------------------
% 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
%------------------------------------------------------------------------------